Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(449,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.dc (of order \(6\), degree \(2\), not 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 342) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1889.2 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1889 |
Dual form | 2736.2.dc.a.449.2 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.22474 | + | 0.707107i | 0.547723 | + | 0.316228i | 0.748203 | − | 0.663470i | \(-0.230917\pi\) |
−0.200480 | + | 0.979698i | \(0.564250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.44949 | −0.547856 | −0.273928 | − | 0.961750i | \(-0.588323\pi\) | ||||
−0.273928 | + | 0.961750i | \(0.588323\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.635674i | 0.191663i | 0.995398 | + | 0.0958315i | \(0.0305510\pi\) | ||||
−0.995398 | + | 0.0958315i | \(0.969449\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.17423 | − | 2.98735i | 1.43507 | − | 0.828541i | 0.437573 | − | 0.899183i | \(-0.355838\pi\) |
0.997502 | + | 0.0706424i | \(0.0225049\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.77526 | − | 1.02494i | −0.430563 | − | 0.248585i | 0.269024 | − | 0.963134i | \(-0.413299\pi\) |
−0.699586 | + | 0.714548i | \(0.746632\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | − | 1.73205i | −0.917663 | − | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.89898 | − | 2.82843i | 1.02151 | − | 0.589768i | 0.106967 | − | 0.994263i | \(-0.465886\pi\) |
0.914540 | + | 0.404495i | \(0.132553\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.50000 | − | 2.59808i | −0.300000 | − | 0.519615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.22474 | − | 2.12132i | −0.227429 | − | 0.393919i | 0.729616 | − | 0.683857i | \(-0.239699\pi\) |
−0.957046 | + | 0.289938i | \(0.906365\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.953512i | − | 0.171256i | −0.996327 | − | 0.0856279i | \(-0.972710\pi\) | ||
0.996327 | − | 0.0856279i | \(-0.0272896\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.77526 | − | 1.02494i | −0.300073 | − | 0.173247i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.51059i | 0.412738i | 0.978474 | + | 0.206369i | \(0.0661648\pi\) | ||||
−0.978474 | + | 0.206369i | \(0.933835\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.94949 | − | 3.37662i | 0.297294 | − | 0.514929i | −0.678222 | − | 0.734857i | \(-0.737249\pi\) |
0.975516 | + | 0.219928i | \(0.0705824\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.77526 | + | 1.02494i | −0.258948 | + | 0.149503i | −0.623854 | − | 0.781541i | \(-0.714434\pi\) |
0.364907 | + | 0.931044i | \(0.381101\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.89898 | −0.699854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.44949 | + | 4.24264i | 0.336463 | + | 0.582772i | 0.983765 | − | 0.179463i | \(-0.0574359\pi\) |
−0.647302 | + | 0.762234i | \(0.724103\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.449490 | + | 0.778539i | −0.0606092 | + | 0.104978i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.22474 | − | 12.5136i | 0.940582 | − | 1.62914i | 0.176217 | − | 0.984351i | \(-0.443614\pi\) |
0.764365 | − | 0.644784i | \(-0.223053\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.72474 | + | 2.98735i | 0.220831 | + | 0.382490i | 0.955061 | − | 0.296411i | \(-0.0957898\pi\) |
−0.734230 | + | 0.678901i | \(0.762456\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.44949 | 1.04803 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.84847 | − | 5.10867i | 1.08101 | − | 0.624123i | 0.149843 | − | 0.988710i | \(-0.452123\pi\) |
0.931169 | + | 0.364587i | \(0.118790\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | − | 5.19615i | 0.356034 | − | 0.616670i | −0.631260 | − | 0.775571i | \(-0.717462\pi\) |
0.987294 | + | 0.158901i | \(0.0507952\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.05051 | − | 1.81954i | 0.122953 | − | 0.212961i | −0.797978 | − | 0.602687i | \(-0.794097\pi\) |
0.920931 | + | 0.389726i | \(0.127430\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.921404i | − | 0.105004i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.825765 | − | 0.476756i | −0.0929059 | − | 0.0536392i | 0.452827 | − | 0.891598i | \(-0.350415\pi\) |
−0.545733 | + | 0.837959i | \(0.683749\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.8065i | 1.29593i | 0.761669 | + | 0.647967i | \(0.224380\pi\) | ||||
−0.761669 | + | 0.647967i | \(0.775620\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.44949 | − | 2.51059i | −0.157219 | − | 0.272312i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.12372 | + | 10.6066i | 0.649113 | + | 1.12430i | 0.983335 | + | 0.181803i | \(0.0581933\pi\) |
−0.334221 | + | 0.942495i | \(0.608473\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.50000 | + | 4.33013i | −0.786214 | + | 0.453921i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.67423 | − | 4.94975i | −0.376969 | − | 0.507833i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.3485 | − | 9.43879i | −1.65994 | − | 0.958364i | −0.972742 | − | 0.231890i | \(-0.925509\pi\) |
−0.687193 | − | 0.726474i | \(-0.741158\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.4495 | − | 6.61037i | 1.13927 | − | 0.657756i | 0.193018 | − | 0.981195i | \(-0.438172\pi\) |
0.946249 | + | 0.323439i | \(0.104839\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14.4600i | − | 1.42478i | −0.701782 | − | 0.712392i | \(-0.747612\pi\) | ||
0.701782 | − | 0.712392i | \(-0.252388\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.7980 | 1.52725 | 0.763623 | − | 0.645662i | \(-0.223419\pi\) | ||||
0.763623 | + | 0.645662i | \(0.223419\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.6969 | − | 8.48528i | −1.40771 | − | 0.812743i | −0.412544 | − | 0.910938i | \(-0.635360\pi\) |
−0.995167 | + | 0.0981950i | \(0.968693\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.1464 | 1.61300 | 0.806500 | − | 0.591234i | \(-0.201359\pi\) | ||||
0.806500 | + | 0.591234i | \(0.201359\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | 0.746004 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.57321 | + | 1.48565i | 0.235886 | + | 0.136189i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5959 | 0.963265 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.3137i | − | 1.01193i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.34847 | + | 4.24264i | −0.652071 | + | 0.376473i | −0.789249 | − | 0.614073i | \(-0.789530\pi\) |
0.137178 | + | 0.990546i | \(0.456197\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.7980 | + | 7.38891i | 1.11816 | + | 0.645572i | 0.940931 | − | 0.338598i | \(-0.109953\pi\) |
0.177232 | + | 0.984169i | \(0.443286\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.79796 | + | 2.51059i | 0.502747 | + | 0.217696i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.44949 | − | 3.14626i | 0.465581 | − | 0.268804i | −0.248807 | − | 0.968553i | \(-0.580038\pi\) |
0.714388 | + | 0.699750i | \(0.246705\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.50000 | − | 6.06218i | −0.296866 | − | 0.514187i | 0.678551 | − | 0.734553i | \(-0.262608\pi\) |
−0.975417 | + | 0.220366i | \(0.929275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.89898 | + | 3.28913i | 0.158801 | + | 0.275051i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 3.46410i | − | 0.287678i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.4495 | − | 10.0745i | −1.42952 | − | 0.825333i | −0.432435 | − | 0.901665i | \(-0.642346\pi\) |
−0.997082 | + | 0.0763323i | \(0.975679\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1.55708i | − | 0.126713i | −0.997991 | − | 0.0633566i | \(-0.979819\pi\) | ||
0.997991 | − | 0.0633566i | \(-0.0201806\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.674235 | − | 1.16781i | 0.0541558 | − | 0.0938006i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.17423 | + | 10.6941i | −0.492758 | + | 0.853481i | −0.999965 | − | 0.00834275i | \(-0.997344\pi\) |
0.507208 | + | 0.861824i | \(0.330678\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.10102 | + | 4.09978i | −0.559639 | + | 0.323108i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.69694 | −0.602871 | −0.301435 | − | 0.953487i | \(-0.597466\pi\) | ||||
−0.301435 | + | 0.953487i | \(0.597466\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.22474 | + | 7.31747i | 0.326921 | + | 0.566243i | 0.981899 | − | 0.189404i | \(-0.0606557\pi\) |
−0.654979 | + | 0.755647i | \(0.727322\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.3485 | − | 19.6561i | 0.872959 | − | 1.51201i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.12372 | − | 10.6066i | 0.465578 | − | 0.806405i | −0.533649 | − | 0.845706i | \(-0.679180\pi\) |
0.999227 | + | 0.0393009i | \(0.0125131\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.17423 | + | 3.76588i | 0.164357 | + | 0.284674i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.65153 | + | 2.68556i | −0.345746 | + | 0.199616i | −0.662810 | − | 0.748788i | \(-0.730636\pi\) |
0.317064 | + | 0.948404i | \(0.397303\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.77526 | + | 3.07483i | −0.130519 | + | 0.226066i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.651531 | − | 1.12848i | 0.0476446 | − | 0.0825230i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.2706i | 1.10494i | 0.833532 | + | 0.552472i | \(0.186315\pi\) | ||||
−0.833532 | + | 0.552472i | \(0.813685\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.8485 | + | 8.57277i | 1.06882 | + | 0.617081i | 0.927858 | − | 0.372934i | \(-0.121648\pi\) |
0.140958 | + | 0.990016i | \(0.454982\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.2918i | − | 1.44573i | −0.690989 | − | 0.722865i | \(-0.742825\pi\) | ||
0.690989 | − | 0.722865i | \(-0.257175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.62372 | + | 14.9367i | 0.611320 | + | 1.05884i | 0.991018 | + | 0.133726i | \(0.0426943\pi\) |
−0.379699 | + | 0.925110i | \(0.623972\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.77526 | + | 3.07483i | 0.124598 | + | 0.215811i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.10102 | − | 2.54270i | 0.0761592 | − | 0.175882i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.15153 | − | 1.81954i | −0.216960 | − | 0.125262i | 0.387582 | − | 0.921835i | \(-0.373311\pi\) |
−0.604542 | + | 0.796573i | \(0.706644\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.77526 | − | 2.75699i | 0.325670 | − | 0.188025i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.38211i | 0.0938234i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.2474 | −0.823853 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.17423 | + | 1.25529i | 0.145598 | + | 0.0840608i | 0.571029 | − | 0.820930i | \(-0.306544\pi\) |
−0.425432 | + | 0.904991i | \(0.639878\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.1464 | −1.53628 | −0.768141 | − | 0.640280i | \(-0.778818\pi\) | ||||
−0.768141 | + | 0.640280i | \(0.778818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.2474 | −1.27191 | −0.635954 | − | 0.771727i | \(-0.719393\pi\) | ||||
−0.635954 | + | 0.771727i | \(0.719393\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.2474 | + | 8.80312i | 0.998894 | + | 0.576711i | 0.907921 | − | 0.419142i | \(-0.137669\pi\) |
0.0909728 | + | 0.995853i | \(0.471002\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.89898 | −0.189109 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 22.4846i | − | 1.45440i | −0.686423 | − | 0.727202i | \(-0.740820\pi\) | ||
0.686423 | − | 0.727202i | \(-0.259180\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1515 | − | 7.01569i | 0.782749 | − | 0.451920i | −0.0546547 | − | 0.998505i | \(-0.517406\pi\) |
0.837404 | + | 0.546585i | \(0.184072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.00000 | − | 3.46410i | −0.383326 | − | 0.221313i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.8712 | + | 2.98735i | −1.64614 | + | 0.190080i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.22474 | − | 0.707107i | 0.0773052 | − | 0.0446322i | −0.460849 | − | 0.887478i | \(-0.652455\pi\) |
0.538154 | + | 0.842846i | \(0.319122\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.79796 | + | 3.11416i | 0.113037 | + | 0.195785i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | + | 10.3923i | 0.374270 | + | 0.648254i | 0.990217 | − | 0.139533i | \(-0.0445601\pi\) |
−0.615948 | + | 0.787787i | \(0.711227\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.63907i | − | 0.226121i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.797959 | + | 0.460702i | 0.0492043 | + | 0.0284081i | 0.524400 | − | 0.851472i | \(-0.324290\pi\) |
−0.475196 | + | 0.879880i | \(0.657623\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.92820i | 0.425596i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.2247 | + | 17.7098i | −0.623414 | + | 1.07978i | 0.365432 | + | 0.930838i | \(0.380921\pi\) |
−0.988845 | + | 0.148946i | \(0.952412\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.6969 | − | 27.1879i | 0.953521 | − | 1.65155i | 0.215804 | − | 0.976437i | \(-0.430763\pi\) |
0.737717 | − | 0.675110i | \(-0.235904\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.65153 | − | 0.953512i | 0.0995911 | − | 0.0574989i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.10102 | 0.546827 | 0.273414 | − | 0.961897i | \(-0.411847\pi\) | ||||
0.273414 | + | 0.961897i | \(0.411847\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.5732 | + | 20.0454i | 0.690400 | + | 1.19581i | 0.971707 | + | 0.236190i | \(0.0758988\pi\) |
−0.281307 | + | 0.959618i | \(0.590768\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.44949 | + | 12.9029i | −0.442826 | + | 0.766997i | −0.997898 | − | 0.0648050i | \(-0.979357\pi\) |
0.555072 | + | 0.831802i | \(0.312691\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.39898 | − | 11.0834i | −0.376411 | − | 0.651962i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.6515 | 0.622269 | 0.311135 | − | 0.950366i | \(-0.399291\pi\) | ||||
0.311135 | + | 0.950366i | \(0.399291\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.6969 | − | 10.2173i | 1.03036 | − | 0.594876i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.8990 | − | 29.2699i | 0.977293 | − | 1.69272i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.82577 | + | 4.89437i | −0.162874 | + | 0.282107i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.87832i | 0.279332i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.3485 | + | 7.70674i | 0.761837 | + | 0.439847i | 0.829955 | − | 0.557830i | \(-0.188366\pi\) |
−0.0681177 | + | 0.997677i | \(0.521699\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5.16404i | − | 0.292826i | −0.989224 | − | 0.146413i | \(-0.953227\pi\) | ||
0.989224 | − | 0.146413i | \(-0.0467729\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.3485 | − | 19.6561i | −0.641453 | − | 1.11103i | −0.985108 | − | 0.171934i | \(-0.944998\pi\) |
0.343655 | − | 0.939096i | \(-0.388335\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.67423 | − | 6.36396i | −0.206366 | − | 0.357436i | 0.744201 | − | 0.667955i | \(-0.232830\pi\) |
−0.950567 | + | 0.310520i | \(0.899497\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.34847 | − | 0.778539i | 0.0754998 | − | 0.0435898i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.32577 | + | 7.17461i | 0.296334 | + | 0.399206i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.5227 | − | 8.96204i | −0.861045 | − | 0.497124i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.57321 | − | 1.48565i | 0.141866 | − | 0.0819063i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 18.7026i | − | 1.02799i | −0.857794 | − | 0.513994i | \(-0.828165\pi\) | ||
0.857794 | − | 0.513994i | \(-0.171835\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.4495 | 0.789460 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.80306 | + | 1.04100i | 0.0982190 | + | 0.0567068i | 0.548305 | − | 0.836278i | \(-0.315273\pi\) |
−0.450086 | + | 0.892985i | \(0.648607\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.606123 | 0.0328234 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2474 | 0.931275 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.2247 | − | 16.2956i | −1.51518 | − | 0.874792i | −0.999841 | − | 0.0178073i | \(-0.994331\pi\) |
−0.515342 | − | 0.856984i | \(-0.672335\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.2474 | 1.24441 | 0.622204 | − | 0.782855i | \(-0.286238\pi\) | ||||
0.622204 | + | 0.782855i | \(0.286238\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 3.32124i | − | 0.176772i | −0.996086 | − | 0.0883858i | \(-0.971829\pi\) | ||
0.996086 | − | 0.0883858i | \(-0.0281708\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.34847 | − | 4.24264i | 0.390016 | − | 0.225176i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.79796 | + | 5.65685i | 0.517116 | + | 0.298557i | 0.735754 | − | 0.677249i | \(-0.236828\pi\) |
−0.218638 | + | 0.975806i | \(0.570161\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.57321 | − | 1.48565i | 0.134688 | − | 0.0777623i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.17423 | − | 12.4261i | −0.374492 | − | 0.648639i | 0.615759 | − | 0.787935i | \(-0.288850\pi\) |
−0.990251 | + | 0.139295i | \(0.955516\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.55051 | − | 6.14966i | −0.184333 | − | 0.319275i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.2993i | 0.636835i | 0.947951 | + | 0.318418i | \(0.103151\pi\) | ||||
−0.947951 | + | 0.318418i | \(0.896849\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.6742 | − | 7.31747i | −0.652756 | − | 0.376869i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.0526i | 0.978664i | 0.872098 | + | 0.489332i | \(0.162759\pi\) | ||||
−0.872098 | + | 0.489332i | \(0.837241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.44949 | + | 9.43879i | −0.278456 | + | 0.482300i | −0.971001 | − | 0.239075i | \(-0.923156\pi\) |
0.692545 | + | 0.721374i | \(0.256489\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.651531 | − | 1.12848i | 0.0332051 | − | 0.0575129i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.8990 | + | 13.2207i | −1.16102 | + | 0.670318i | −0.951549 | − | 0.307496i | \(-0.900509\pi\) |
−0.209475 | + | 0.977814i | \(0.567176\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.5959 | −0.586431 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.674235 | − | 1.16781i | −0.0339244 | − | 0.0587588i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.8258 | + | 18.7508i | −0.543330 | + | 0.941074i | 0.455380 | + | 0.890297i | \(0.349503\pi\) |
−0.998710 | + | 0.0507775i | \(0.983830\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.123724 | + | 0.214297i | −0.00617850 | + | 0.0107015i | −0.869098 | − | 0.494640i | \(-0.835300\pi\) |
0.862920 | + | 0.505341i | \(0.168633\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.84847 | − | 4.93369i | −0.141892 | − | 0.245765i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.59592 | −0.0791067 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.0454 | + | 14.4600i | −1.23842 | + | 0.715000i | −0.968770 | − | 0.247960i | \(-0.920240\pi\) |
−0.269645 | + | 0.962960i | \(0.586906\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.4722 | + | 18.1384i | −0.515303 | + | 0.892531i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.34847 | + | 14.4600i | −0.409810 | + | 0.709812i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.74983i | 0.183191i | 0.995796 | + | 0.0915956i | \(0.0291967\pi\) | ||||
−0.995796 | + | 0.0915956i | \(0.970803\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.34847 | + | 0.778539i | 0.0657204 | + | 0.0379437i | 0.532500 | − | 0.846430i | \(-0.321253\pi\) |
−0.466780 | + | 0.884374i | \(0.654586\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.14966i | 0.298303i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.50000 | − | 4.33013i | −0.120983 | − | 0.209550i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.02270 | − | 13.8957i | −0.386440 | − | 0.669334i | 0.605528 | − | 0.795824i | \(-0.292962\pi\) |
−0.991968 | + | 0.126490i | \(0.959629\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.1969 | − | 14.5475i | 1.21089 | − | 0.699106i | 0.247935 | − | 0.968777i | \(-0.420248\pi\) |
0.962953 | + | 0.269670i | \(0.0869148\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.4949 | + | 2.82843i | −1.17175 | + | 0.135302i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.5227 | + | 7.22999i | 0.597676 | + | 0.345068i | 0.768127 | − | 0.640298i | \(-0.221189\pi\) |
−0.170451 | + | 0.985366i | \(0.554522\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.7753 | + | 14.8814i | −1.22462 | + | 0.707034i | −0.965899 | − | 0.258918i | \(-0.916634\pi\) |
−0.258720 | + | 0.965952i | \(0.583301\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.3205i | 0.821071i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.2474 | 0.861150 | 0.430575 | − | 0.902555i | \(-0.358311\pi\) | ||||
0.430575 | + | 0.902555i | \(0.358311\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.2474 | −0.574169 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.6969 | 0.921384 | 0.460692 | − | 0.887560i | \(-0.347601\pi\) | ||||
0.460692 | + | 0.887560i | \(0.347601\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.12372 | − | 5.26758i | −0.424934 | − | 0.245336i | 0.272252 | − | 0.962226i | \(-0.412232\pi\) |
−0.697186 | + | 0.716890i | \(0.745565\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.1464 | −1.86576 | −0.932881 | − | 0.360184i | \(-0.882714\pi\) | ||||
−0.932881 | + | 0.360184i | \(0.882714\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.0703i | 0.975019i | 0.873118 | + | 0.487510i | \(0.162095\pi\) | ||||
−0.873118 | + | 0.487510i | \(0.837905\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.8258 | + | 7.40496i | −0.592239 | + | 0.341929i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.14643 | + | 1.23924i | 0.0986929 | + | 0.0569804i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.50000 | + | 12.9904i | 0.0688247 | + | 0.596040i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.14643 | + | 4.70334i | −0.372220 | + | 0.214901i | −0.674428 | − | 0.738341i | \(-0.735610\pi\) |
0.302208 | + | 0.953242i | \(0.402276\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.50000 | + | 12.9904i | 0.341971 | + | 0.592310i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.3485 | − | 23.1202i | −0.606123 | − | 1.04984i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.6622i | 1.79727i | 0.438702 | + | 0.898633i | \(0.355439\pi\) | ||||
−0.438702 | + | 0.898633i | \(0.644561\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.1464 | + | 15.0956i | 1.17997 | + | 0.681257i | 0.956008 | − | 0.293340i | \(-0.0947669\pi\) |
0.223964 | + | 0.974597i | \(0.428100\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.02118i | 0.226143i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.34847 | + | 7.53177i | −0.195056 | + | 0.337846i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.7474 | + | 37.6677i | −0.973550 | + | 1.68624i | −0.288909 | + | 0.957357i | \(0.593292\pi\) |
−0.684641 | + | 0.728881i | \(0.740041\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.5176 | + | 20.5061i | −1.58365 | + | 0.914322i | −0.589331 | + | 0.807891i | \(0.700609\pi\) |
−0.994320 | + | 0.106430i | \(0.966058\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.6969 | 0.832003 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.67423 | + | 11.5601i | 0.295830 | + | 0.512393i | 0.975178 | − | 0.221424i | \(-0.0710704\pi\) |
−0.679347 | + | 0.733817i | \(0.737737\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.52270 | + | 2.63740i | −0.0673605 | + | 0.116672i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.2247 | − | 17.7098i | 0.450556 | − | 0.780386i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.651531 | − | 1.12848i | −0.0286543 | − | 0.0496307i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.20204 | 0.359338 | 0.179669 | − | 0.983727i | \(-0.442497\pi\) | ||||
0.179669 | + | 0.983727i | \(0.442497\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.5000 | + | 7.79423i | −0.590314 | + | 0.340818i | −0.765222 | − | 0.643767i | \(-0.777371\pi\) |
0.174908 | + | 0.984585i | \(0.444037\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.977296 | + | 1.69273i | −0.0425717 | + | 0.0737363i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.50000 | − | 7.79423i | 0.195652 | − | 0.338880i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.3485 | + | 11.1708i | 0.836507 | + | 0.482958i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 3.11416i | − | 0.134136i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.1742 | − | 26.2825i | −0.652391 | − | 1.12997i | −0.982541 | − | 0.186046i | \(-0.940433\pi\) |
0.330150 | − | 0.943929i | \(-0.392901\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.0000 | − | 20.7846i | −0.514024 | − | 0.890315i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.80306 | − | 1.04100i | 0.0770933 | − | 0.0445099i | −0.460958 | − | 0.887422i | \(-0.652494\pi\) |
0.538051 | + | 0.842912i | \(0.319161\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.22474 | + | 10.6066i | 0.0521759 | + | 0.451856i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.19694 | + | 0.691053i | 0.0508990 | + | 0.0293866i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.5959 | + | 13.0458i | −0.957420 | + | 0.552767i | −0.895378 | − | 0.445307i | \(-0.853095\pi\) |
−0.0620418 | + | 0.998074i | \(0.519761\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 23.2952i | − | 0.985282i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.5959 | −1.07874 | −0.539370 | − | 0.842069i | \(-0.681337\pi\) | ||||
−0.539370 | + | 0.842069i | \(0.681337\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.0000 | + | 12.1244i | 0.883477 | + | 0.510075i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.1010 | −1.30382 | −0.651911 | − | 0.758295i | \(-0.726033\pi\) | ||||
−0.651911 | + | 0.758295i | \(0.726033\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.69694 | 0.154712 | 0.0773560 | − | 0.997004i | \(-0.475352\pi\) | ||||
0.0773560 | + | 0.997004i | \(0.475352\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.6969 | − | 8.48528i | −0.612905 | − | 0.353861i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.79796 | 0.241372 | 0.120686 | − | 0.992691i | \(-0.461491\pi\) | ||||
0.120686 | + | 0.992691i | \(0.461491\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 17.1134i | − | 0.709985i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.69694 | + | 1.55708i | −0.111696 | + | 0.0644876i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.1237 | + | 13.9278i | 0.995693 | + | 0.574863i | 0.906971 | − | 0.421193i | \(-0.138389\pi\) |
0.0887216 | + | 0.996056i | \(0.471722\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.65153 | + | 3.81405i | −0.0680501 | + | 0.157155i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.4722 | − | 7.77817i | 0.553237 | − | 0.319411i | −0.197190 | − | 0.980365i | \(-0.563182\pi\) |
0.750426 | + | 0.660954i | \(0.229848\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.10102 | + | 3.63907i | 0.0861334 | + | 0.149188i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.7980 | + | 32.5590i | 0.768064 | + | 1.33033i | 0.938611 | + | 0.344976i | \(0.112113\pi\) |
−0.170548 | + | 0.985349i | \(0.554554\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.2173i | 0.416774i | 0.978046 | + | 0.208387i | \(0.0668213\pi\) | ||||
−0.978046 | + | 0.208387i | \(0.933179\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.9773 | + | 7.49245i | 0.527602 | + | 0.304611i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.16064i | − | 0.0876979i | −0.999038 | − | 0.0438489i | \(-0.986038\pi\) | ||
0.999038 | − | 0.0438489i | \(-0.0139620\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.12372 | + | 10.6066i | −0.247739 | + | 0.429097i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.44949 | + | 16.3670i | −0.381661 | + | 0.661057i | −0.991300 | − | 0.131623i | \(-0.957981\pi\) |
0.609639 | + | 0.792680i | \(0.291315\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.1010 | − | 16.2241i | 1.13130 | − | 0.653159i | 0.187042 | − | 0.982352i | \(-0.440110\pi\) |
0.944263 | + | 0.329193i | \(0.106777\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.3939 | 1.46279 | 0.731397 | − | 0.681952i | \(-0.238869\pi\) | ||||
0.731397 | + | 0.681952i | \(0.238869\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.87628 | − | 15.3742i | −0.355620 | − | 0.615953i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.500000 | − | 0.866025i | 0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.57321 | − | 4.45694i | 0.102601 | − | 0.177710i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.27526 | + | 12.6011i | 0.289623 | + | 0.501642i | 0.973720 | − | 0.227749i | \(-0.0731366\pi\) |
−0.684096 | + | 0.729392i | \(0.739803\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.0000 | −0.476205 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.3485 | + | 14.6349i | −1.00434 | + | 0.579858i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.0227 | + | 39.8765i | −0.909342 | + | 1.57503i | −0.0943619 | + | 0.995538i | \(0.530081\pi\) |
−0.814980 | + | 0.579489i | \(0.803252\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.2980 | − | 36.8891i | 0.839910 | − | 1.45477i | −0.0500601 | − | 0.998746i | \(-0.515941\pi\) |
0.889970 | − | 0.456020i | \(-0.150725\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.97129i | 0.116814i | 0.998293 | + | 0.0584068i | \(0.0186020\pi\) | ||||
−0.998293 | + | 0.0584068i | \(0.981398\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.95459 | + | 4.59259i | 0.312245 | + | 0.180275i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 38.3908i | − | 1.50235i | −0.660103 | − | 0.751175i | \(-0.729487\pi\) | ||
0.660103 | − | 0.751175i | \(-0.270513\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.4495 | + | 18.0990i | 0.408295 | + | 0.707188i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.69694 | + | 9.86739i | 0.221921 | + | 0.384379i | 0.955391 | − | 0.295343i | \(-0.0954339\pi\) |
−0.733470 | + | 0.679722i | \(0.762101\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.6969 | + | 13.6814i | −0.921704 | + | 0.532146i | −0.884178 | − | 0.467150i | \(-0.845281\pi\) |
−0.0375258 | + | 0.999296i | \(0.511948\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.32577 | + | 7.17461i | 0.206524 | + | 0.278219i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.0000 | − | 6.92820i | −0.464642 | − | 0.268261i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.89898 | + | 1.09638i | −0.0733093 | + | 0.0423251i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 19.0526i | − | 0.734422i | −0.930138 | − | 0.367211i | \(-0.880313\pi\) | ||
0.930138 | − | 0.367211i | \(-0.119687\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.3485 | −1.43542 | −0.717709 | − | 0.696343i | \(-0.754809\pi\) | ||||
−0.717709 | + | 0.696343i | \(0.754809\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 23.6969 | + | 13.6814i | 0.909405 | + | 0.525045i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.0454 | −1.07313 | −0.536564 | − | 0.843860i | \(-0.680278\pi\) | ||||
−0.536564 | + | 0.843860i | \(0.680278\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.89898 | 0.340013 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.3485 | + | 14.6349i | 0.965700 | + | 0.557547i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.696938 | 0.0265128 | 0.0132564 | − | 0.999912i | \(-0.495780\pi\) | ||||
0.0132564 | + | 0.999912i | \(0.495780\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 9.89949i | − | 0.375509i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.4722 | − | 7.77817i | −0.508838 | − | 0.293778i | 0.223518 | − | 0.974700i | \(-0.428246\pi\) |
−0.732356 | + | 0.680922i | \(0.761579\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.34847 | − | 10.0424i | 0.164006 | − | 0.378755i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.5959 | + | 9.58166i | −0.624154 | + | 0.360355i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.17423 | − | 5.49794i | −0.119211 | − | 0.206479i | 0.800244 | − | 0.599674i | \(-0.204703\pi\) |
−0.919455 | + | 0.393195i | \(0.871370\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.69694 | − | 4.67123i | −0.101001 | − | 0.174939i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.37113i | 0.200869i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.1464 | + | 9.89949i | 0.639454 | + | 0.369189i | 0.784404 | − | 0.620250i | \(-0.212969\pi\) |
−0.144950 | + | 0.989439i | \(0.546302\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.9596i | 0.780576i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.67423 | + | 6.36396i | −0.136458 | + | 0.236352i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.82577 | − | 8.35847i | 0.178978 | − | 0.309999i | −0.762553 | − | 0.646926i | \(-0.776054\pi\) |
0.941531 | + | 0.336927i | \(0.109388\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.92168 | + | 3.99624i | −0.256008 | + | 0.147806i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.6969 | −1.13382 | −0.566909 | − | 0.823781i | \(-0.691861\pi\) | ||||
−0.566909 | + | 0.823781i | \(0.691861\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.24745 | + | 5.62475i | 0.119621 | + | 0.207190i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.1969 | − | 40.1783i | 0.853313 | − | 1.47798i | −0.0248879 | − | 0.999690i | \(-0.507923\pi\) |
0.878201 | − | 0.478292i | \(-0.158744\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.6969 | + | 41.0443i | −0.869356 | + | 1.50577i | −0.00670079 | + | 0.999978i | \(0.502133\pi\) |
−0.862656 | + | 0.505792i | \(0.831200\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.2474 | − | 24.6773i | −0.521986 | − | 0.904107i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.8990 | −0.836711 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.2196 | + | 13.9832i | −0.883787 | + | 0.510255i | −0.871905 | − | 0.489675i | \(-0.837116\pi\) |
−0.0118820 | + | 0.999929i | \(0.503782\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.10102 | − | 1.90702i | 0.0400702 | − | 0.0694037i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.1742 | + | 21.0864i | −0.442480 | + | 0.766398i | −0.997873 | − | 0.0651902i | \(-0.979235\pi\) |
0.555393 | + | 0.831588i | \(0.312568\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.8262i | 1.62495i | 0.582996 | + | 0.812475i | \(0.301880\pi\) | ||||
−0.582996 | + | 0.812475i | \(0.698120\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.3031 | + | 12.2993i | 0.771223 | + | 0.445266i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 86.3312i | − | 3.11724i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.29796 | + | 2.24813i | 0.0468056 | + | 0.0810697i | 0.888479 | − | 0.458917i | \(-0.151763\pi\) |
−0.841673 | + | 0.539987i | \(0.818429\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.47219 | − | 7.74607i | −0.160854 | − | 0.278607i | 0.774321 | − | 0.632792i | \(-0.218091\pi\) |
−0.935175 | + | 0.354186i | \(0.884758\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.47730 | + | 1.43027i | −0.0889871 | + | 0.0513767i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.30306 | + | 1.90702i | 0.118193 | + | 0.0682387i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.1237 | + | 8.73169i | −0.539789 | + | 0.311647i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.0737i | 0.858136i | 0.903272 | + | 0.429068i | \(0.141158\pi\) | ||||
−0.903272 | + | 0.429068i | \(0.858842\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.8536 | −0.883691 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.8485 | + | 10.3048i | 0.633818 | + | 0.365935i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38.0908 | −1.34925 | −0.674623 | − | 0.738162i | \(-0.735694\pi\) | ||||
−0.674623 | + | 0.738162i | \(0.735694\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.20204 | 0.148658 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.15663 | + | 0.667783i | 0.0408167 | + | 0.0235655i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.5959 | −0.408702 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.16404i | 0.181558i | 0.995871 | + | 0.0907791i | \(0.0289357\pi\) | ||||
−0.995871 | + | 0.0907791i | \(0.971064\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.6969 | + | 10.2173i | −0.621424 | + | 0.358779i | −0.777423 | − | 0.628978i | \(-0.783474\pi\) |
0.155999 | + | 0.987757i | \(0.450140\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.42679 | − | 5.44256i | −0.330206 | − | 0.190644i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.6464 | + | 10.1298i | −0.477428 | + | 0.354398i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.1691 | − | 19.7276i | 1.19251 | − | 0.688497i | 0.233636 | − | 0.972324i | \(-0.424938\pi\) |
0.958875 | + | 0.283828i | \(0.0916044\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.3485 | + | 30.0484i | 0.604730 | + | 1.04742i | 0.992094 | + | 0.125496i | \(0.0400522\pi\) |
−0.387365 | + | 0.921927i | \(0.626615\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.8207 | − | 41.2586i | −0.828326 | − | 1.43470i | −0.899351 | − | 0.437228i | \(-0.855960\pi\) |
0.0710253 | − | 0.997475i | \(-0.477373\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.9959i | 0.381902i | 0.981600 | + | 0.190951i | \(0.0611572\pi\) | ||||
−0.981600 | + | 0.190951i | \(0.938843\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.69694 | + | 5.02118i | 0.301331 | + | 0.173974i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.9494i | 0.413525i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.02270 | + | 8.69958i | −0.173403 | + | 0.300343i | −0.939607 | − | 0.342254i | \(-0.888810\pi\) |
0.766204 | + | 0.642597i | \(0.222143\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.5000 | − | 19.9186i | 0.396552 | − | 0.686848i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27.7980 | − | 16.0492i | 0.956279 | − | 0.552108i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.3587 | −0.527730 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.10102 | + | 12.2993i | 0.243420 | + | 0.421616i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.8258 | − | 25.6790i | 0.507625 | − | 0.879231i | −0.492337 | − | 0.870405i | \(-0.663857\pi\) |
0.999961 | − | 0.00882655i | \(-0.00280961\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.42679 | + | 5.93537i | −0.117057 | + | 0.202748i | −0.918600 | − | 0.395188i | \(-0.870679\pi\) |
0.801543 | + | 0.597937i | \(0.204013\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.94949 | + | 3.37662i | 0.0665157 | + | 0.115209i | 0.897365 | − | 0.441288i | \(-0.145478\pi\) |
−0.830850 | + | 0.556497i | \(0.812145\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.3485 | 1.27136 | 0.635678 | − | 0.771954i | \(-0.280720\pi\) | ||||
0.635678 | + | 0.771954i | \(0.280720\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.0000 | − | 8.66025i | 0.510015 | − | 0.294457i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.303062 | − | 0.524918i | 0.0102807 | − | 0.0178066i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.5227 | − | 52.8669i | 1.03422 | − | 1.79133i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.3991i | 0.554391i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.5227 | + | 14.1582i | 0.828073 | + | 0.478088i | 0.853192 | − | 0.521596i | \(-0.174663\pi\) |
−0.0251195 | + | 0.999684i | \(0.507997\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.04989i | 0.0690625i | 0.999404 | + | 0.0345312i | \(0.0109938\pi\) | ||||
−0.999404 | + | 0.0345312i | \(0.989006\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.94949 | − | 5.10867i | −0.0992582 | − | 0.171920i | 0.812120 | − | 0.583491i | \(-0.198314\pi\) |
−0.911378 | + | 0.411571i | \(0.864980\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.3258 | − | 19.6168i | −0.380282 | − | 0.658668i | 0.610820 | − | 0.791769i | \(-0.290840\pi\) |
−0.991102 | + | 0.133101i | \(0.957506\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.6515 | − | 6.14966i | 0.357241 | − | 0.206253i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.87628 | − | 1.02494i | 0.297033 | − | 0.0342984i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.6969 | − | 8.48528i | −0.491264 | − | 0.283632i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.02270 | + | 1.16781i | −0.0674610 | + | 0.0389486i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 10.0424i | − | 0.334560i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.59592 | −0.252497 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.6969 | − | 20.6096i | −1.18530 | − | 0.684332i | −0.228063 | − | 0.973646i | \(-0.573239\pi\) |
−0.957234 | + | 0.289315i | \(0.906573\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.50510 | −0.248383 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.5505 | − | 10.7101i | −0.612592 | − | 0.353680i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.04541 | −0.298380 | −0.149190 | − | 0.988809i | \(-0.547667\pi\) | ||||
−0.149190 | + | 0.988809i | \(0.547667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 35.8481i | − | 1.17996i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.52270 | − | 3.76588i | 0.214465 | − | 0.123822i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.5732 | + | 20.5382i | 1.16712 | + | 0.673837i | 0.953000 | − | 0.302971i | \(-0.0979785\pi\) |
0.214119 | + | 0.976807i | \(0.431312\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.5959 | + | 8.48528i | 0.642230 | + | 0.278094i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.59592 | − | 0.921404i | 0.0521921 | − | 0.0301331i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.19694 | − | 14.1975i | −0.267782 | − | 0.463813i | 0.700507 | − | 0.713646i | \(-0.252957\pi\) |
−0.968289 | + | 0.249833i | \(0.919624\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.4495 | − | 35.4196i | −0.666634 | − | 1.15464i | −0.978839 | − | 0.204630i | \(-0.934401\pi\) |
0.312205 | − | 0.950015i | \(-0.398932\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.4949 | + | 19.3383i | 1.08844 | + | 0.628410i | 0.933160 | − | 0.359461i | \(-0.117039\pi\) |
0.155278 | + | 0.987871i | \(0.450373\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 12.5529i | − | 0.407486i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.550510 | − | 0.953512i | 0.0178328 | − | 0.0308873i | −0.856971 | − | 0.515364i | \(-0.827657\pi\) |
0.874804 | + | 0.484477i | \(0.160990\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.7980 | + | 18.7026i | −0.349414 | + | 0.605202i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.89898 | + | 4.56048i | −0.255071 | + | 0.147266i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.0908 | 0.970671 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.1237 | + | 20.9989i | 0.390276 | + | 0.675979i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.17423 | − | 10.6941i | 0.198550 | − | 0.343899i | −0.749508 | − | 0.661995i | \(-0.769710\pi\) |
0.948058 | + | 0.318096i | \(0.103043\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.8207 | − | 25.6701i | 0.475618 | − | 0.823794i | −0.523992 | − | 0.851723i | \(-0.675558\pi\) |
0.999610 | + | 0.0279290i | \(0.00889124\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.07321 | + | 8.78706i | 0.162640 | + | 0.281700i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.247449 | 0.00791659 | 0.00395829 | − | 0.999992i | \(-0.498740\pi\) | ||||
0.00395829 | + | 0.999992i | \(0.498740\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.74235 | + | 3.89270i | −0.215486 | + | 0.124411i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.24745 | + | 16.0171i | −0.294948 | + | 0.510865i | −0.974973 | − | 0.222324i | \(-0.928636\pi\) |
0.680025 | + | 0.733189i | \(0.261969\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.3485 | − | 24.8523i | 0.457180 | − | 0.791859i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 22.0560i | − | 0.701339i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.8712 | − | 30.5252i | −1.67951 | − | 0.969664i | −0.961974 | − | 0.273141i | \(-0.911937\pi\) |
−0.717534 | − | 0.696523i | \(-0.754729\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.3916i | 0.773265i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.5227 | + | 35.5464i | 0.649961 | + | 1.12576i | 0.983132 | + | 0.182898i | \(0.0585479\pi\) |
−0.333171 | + | 0.942866i | \(0.608119\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2736.2.dc.a.1889.2 | 4 | ||
3.2 | odd | 2 | 2736.2.dc.b.1889.1 | 4 | |||
4.3 | odd | 2 | 342.2.s.b.179.2 | yes | 4 | ||
12.11 | even | 2 | 342.2.s.a.179.1 | yes | 4 | ||
19.12 | odd | 6 | 2736.2.dc.b.449.1 | 4 | |||
57.50 | even | 6 | inner | 2736.2.dc.a.449.2 | 4 | ||
76.31 | even | 6 | 342.2.s.a.107.1 | ✓ | 4 | ||
228.107 | odd | 6 | 342.2.s.b.107.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
342.2.s.a.107.1 | ✓ | 4 | 76.31 | even | 6 | ||
342.2.s.a.179.1 | yes | 4 | 12.11 | even | 2 | ||
342.2.s.b.107.2 | yes | 4 | 228.107 | odd | 6 | ||
342.2.s.b.179.2 | yes | 4 | 4.3 | odd | 2 | ||
2736.2.dc.a.449.2 | 4 | 57.50 | even | 6 | inner | ||
2736.2.dc.a.1889.2 | 4 | 1.1 | even | 1 | trivial | ||
2736.2.dc.b.449.1 | 4 | 19.12 | odd | 6 | |||
2736.2.dc.b.1889.1 | 4 | 3.2 | odd | 2 |