Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,3,Mod(73,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.73");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.v (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.80928951697\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{41})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 21x^{2} + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 217.2 | ||
Root | \(2.70156i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.217 |
Dual form | 360.3.v.c.73.2 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 4.70156 | + | 1.70156i | 0.940312 | + | 0.340312i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.70156 | + | 6.70156i | 0.957366 | + | 0.957366i | 0.999128 | − | 0.0417616i | \(-0.0132970\pi\) |
−0.0417616 | + | 0.999128i | \(0.513297\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.40312 | 0.127557 | 0.0637784 | − | 0.997964i | \(-0.479685\pi\) | ||||
0.0637784 | + | 0.997964i | \(0.479685\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −14.4031 | + | 14.4031i | −1.10793 | + | 1.10793i | −0.114511 | + | 0.993422i | \(0.536530\pi\) |
−0.993422 | + | 0.114511i | \(0.963470\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.40312 | + | 2.40312i | 0.141360 | + | 0.141360i | 0.774246 | − | 0.632885i | \(-0.218130\pi\) |
−0.632885 | + | 0.774246i | \(0.718130\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 22.8062i | − | 1.20033i | −0.799877 | − | 0.600164i | \(-0.795102\pi\) | ||
0.799877 | − | 0.600164i | \(-0.204898\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.104686 | − | 0.104686i | 0.00455158 | − | 0.00455158i | −0.704827 | − | 0.709379i | \(-0.748976\pi\) |
0.709379 | + | 0.704827i | \(0.248976\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.2094 | + | 16.0000i | 0.768375 | + | 0.640000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 45.6125i | 1.57284i | 0.617689 | + | 0.786422i | \(0.288069\pi\) | ||||
−0.617689 | + | 0.786422i | \(0.711931\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.59688 | −0.0837702 | −0.0418851 | − | 0.999122i | \(-0.513336\pi\) | ||||
−0.0418851 | + | 0.999122i | \(0.513336\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 20.1047 | + | 42.9109i | 0.574420 | + | 1.22603i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.6125 | + | 10.6125i | 0.286824 | + | 0.286824i | 0.835823 | − | 0.548999i | \(-0.184991\pi\) |
−0.548999 | + | 0.835823i | \(0.684991\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 44.6281 | 1.08849 | 0.544245 | − | 0.838926i | \(-0.316816\pi\) | ||||
0.544245 | + | 0.838926i | \(0.316816\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 26.7016 | − | 26.7016i | 0.620967 | − | 0.620967i | −0.324812 | − | 0.945779i | \(-0.605301\pi\) |
0.945779 | + | 0.324812i | \(0.105301\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4922 | + | 10.4922i | 0.223238 | + | 0.223238i | 0.809861 | − | 0.586622i | \(-0.199543\pi\) |
−0.586622 | + | 0.809861i | \(0.699543\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 40.8219i | 0.833099i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00000 | − | 3.00000i | 0.0566038 | − | 0.0566038i | −0.678238 | − | 0.734842i | \(-0.737256\pi\) |
0.734842 | + | 0.678238i | \(0.237256\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.59688 | + | 2.38750i | 0.119943 | + | 0.0434091i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 41.1938i | − | 0.698199i | −0.937086 | − | 0.349100i | \(-0.886487\pi\) | ||
0.937086 | − | 0.349100i | \(-0.113513\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −57.4031 | −0.941035 | −0.470517 | − | 0.882391i | \(-0.655933\pi\) | ||||
−0.470517 | + | 0.882391i | \(0.655933\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −92.2250 | + | 43.2094i | −1.41885 | + | 0.664760i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 34.7016 | + | 34.7016i | 0.517934 | + | 0.517934i | 0.916946 | − | 0.399012i | \(-0.130647\pi\) |
−0.399012 | + | 0.916946i | \(0.630647\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −45.4031 | −0.639481 | −0.319740 | − | 0.947505i | \(-0.603596\pi\) | ||||
−0.319740 | + | 0.947505i | \(0.603596\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3875 | − | 11.3875i | 0.155993 | − | 0.155993i | −0.624795 | − | 0.780789i | \(-0.714818\pi\) |
0.780789 | + | 0.624795i | \(0.214818\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.40312 | + | 9.40312i | 0.122118 | + | 0.122118i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 86.4500i | − | 1.09430i | −0.837033 | − | 0.547152i | \(-0.815712\pi\) | ||
0.837033 | − | 0.547152i | \(-0.184288\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 81.7172 | − | 81.7172i | 0.984544 | − | 0.984544i | −0.0153380 | − | 0.999882i | \(-0.504882\pi\) |
0.999882 | + | 0.0153380i | \(0.00488242\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.20937 | + | 15.3875i | 0.0848161 | + | 0.181029i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 91.2250i | − | 1.02500i | −0.858687 | − | 0.512500i | \(-0.828719\pi\) | ||
0.858687 | − | 0.512500i | \(-0.171281\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −193.047 | −2.12139 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 38.8062 | − | 107.225i | 0.408487 | − | 1.12868i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 49.0000 | + | 49.0000i | 0.505155 | + | 0.505155i | 0.913035 | − | 0.407881i | \(-0.133732\pi\) |
−0.407881 | + | 0.913035i | \(0.633732\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −60.0312 | −0.594369 | −0.297184 | − | 0.954820i | \(-0.596048\pi\) | ||||
−0.297184 | + | 0.954820i | \(0.596048\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 61.5078 | − | 61.5078i | 0.597163 | − | 0.597163i | −0.342393 | − | 0.939557i | \(-0.611238\pi\) |
0.939557 | + | 0.342393i | \(0.111238\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −67.5391 | − | 67.5391i | −0.631206 | − | 0.631206i | 0.317164 | − | 0.948371i | \(-0.397269\pi\) |
−0.948371 | + | 0.317164i | \(0.897269\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.0469i | 0.174742i | 0.996176 | + | 0.0873709i | \(0.0278465\pi\) | ||||
−0.996176 | + | 0.0873709i | \(0.972153\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.82187 | + | 8.82187i | −0.0780696 | + | 0.0780696i | −0.745063 | − | 0.666994i | \(-0.767581\pi\) |
0.666994 | + | 0.745063i | \(0.267581\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.670320 | − | 0.314059i | 0.00582887 | − | 0.00273095i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 32.2094i | 0.270667i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −119.031 | −0.983729 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 63.0891 | + | 107.911i | 0.504713 | + | 0.863287i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.7016 | + | 14.7016i | 0.115760 | + | 0.115760i | 0.762614 | − | 0.646854i | \(-0.223916\pi\) |
−0.646854 | + | 0.762614i | \(0.723916\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −237.884 | −1.81591 | −0.907956 | − | 0.419066i | \(-0.862357\pi\) | ||||
−0.907956 | + | 0.419066i | \(0.862357\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 152.837 | − | 152.837i | 1.14915 | − | 1.14915i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −86.6125 | − | 86.6125i | −0.632208 | − | 0.632208i | 0.316413 | − | 0.948621i | \(-0.397521\pi\) |
−0.948621 | + | 0.316413i | \(0.897521\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 246.806i | − | 1.77558i | −0.460244 | − | 0.887792i | \(-0.652238\pi\) | ||
0.460244 | − | 0.887792i | \(-0.347762\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.2094 | + | 20.2094i | −0.141324 | + | 0.141324i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −77.6125 | + | 214.450i | −0.535259 | + | 1.47897i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 121.853i | − | 0.817806i | −0.912578 | − | 0.408903i | \(-0.865911\pi\) | ||
0.912578 | − | 0.408903i | \(-0.134089\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 245.528 | 1.62601 | 0.813007 | − | 0.582254i | \(-0.197829\pi\) | ||||
0.813007 | + | 0.582254i | \(0.197829\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.2094 | − | 4.41875i | −0.0787701 | − | 0.0285080i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −146.466 | − | 146.466i | −0.932902 | − | 0.932902i | 0.0649843 | − | 0.997886i | \(-0.479300\pi\) |
−0.997886 | + | 0.0649843i | \(0.979300\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.40312 | 0.00871506 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −174.973 | + | 174.973i | −1.07346 | + | 1.07346i | −0.0763776 | + | 0.997079i | \(0.524335\pi\) |
−0.997079 | + | 0.0763776i | \(0.975665\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 203.330 | + | 203.330i | 1.21754 | + | 1.21754i | 0.968490 | + | 0.249053i | \(0.0801194\pi\) |
0.249053 | + | 0.968490i | \(0.419881\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 245.900i | − | 1.45503i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 168.612 | − | 168.612i | 0.974639 | − | 0.974639i | −0.0250476 | − | 0.999686i | \(-0.507974\pi\) |
0.999686 | + | 0.0250476i | \(0.00797372\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.5078 | + | 235.958i | 0.122902 | + | 1.34833i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 27.5813i | − | 0.154085i | −0.997028 | − | 0.0770426i | \(-0.975452\pi\) | ||
0.997028 | − | 0.0770426i | \(-0.0245477\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −88.3875 | −0.488329 | −0.244164 | − | 0.969734i | \(-0.578514\pi\) | ||||
−0.244164 | + | 0.969734i | \(0.578514\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 31.8375 | + | 67.9531i | 0.172095 | + | 0.367314i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.37188 | + | 3.37188i | 0.0180315 | + | 0.0180315i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 79.4969 | 0.416214 | 0.208107 | − | 0.978106i | \(-0.433270\pi\) | ||||
0.208107 | + | 0.978106i | \(0.433270\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 104.822 | − | 104.822i | 0.543118 | − | 0.543118i | −0.381323 | − | 0.924442i | \(-0.624532\pi\) |
0.924442 | + | 0.381323i | \(0.124532\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −68.1625 | − | 68.1625i | −0.346003 | − | 0.346003i | 0.512616 | − | 0.858618i | \(-0.328677\pi\) |
−0.858618 | + | 0.512616i | \(0.828677\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 250.512i | 1.25886i | 0.777059 | + | 0.629428i | \(0.216711\pi\) | ||||
−0.777059 | + | 0.629428i | \(0.783289\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −305.675 | + | 305.675i | −1.50579 | + | 1.50579i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 209.822 | + | 75.9375i | 1.02352 | + | 0.370427i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 32.0000i | − | 0.153110i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −332.628 | −1.57644 | −0.788218 | − | 0.615396i | \(-0.788996\pi\) | ||||
−0.788218 | + | 0.615396i | \(0.788996\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 170.973 | − | 80.1047i | 0.795225 | − | 0.372580i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.4031 | − | 17.4031i | −0.0801987 | − | 0.0801987i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −69.2250 | −0.313235 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 187.602 | − | 187.602i | 0.841263 | − | 0.841263i | −0.147761 | − | 0.989023i | \(-0.547207\pi\) |
0.989023 | + | 0.147761i | \(0.0472065\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 152.167 | + | 152.167i | 0.670340 | + | 0.670340i | 0.957794 | − | 0.287454i | \(-0.0928090\pi\) |
−0.287454 | + | 0.957794i | \(0.592809\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 196.062i | 0.856168i | 0.903739 | + | 0.428084i | \(0.140811\pi\) | ||||
−0.903739 | + | 0.428084i | \(0.859189\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 60.7906 | − | 60.7906i | 0.260904 | − | 0.260904i | −0.564517 | − | 0.825421i | \(-0.690938\pi\) |
0.825421 | + | 0.564517i | \(0.190938\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 31.4766 | + | 67.1828i | 0.133943 | + | 0.285884i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 178.388i | − | 0.746391i | −0.927753 | − | 0.373196i | \(-0.878262\pi\) | ||
0.927753 | − | 0.373196i | \(-0.121738\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 89.8219 | 0.372705 | 0.186352 | − | 0.982483i | \(-0.440333\pi\) | ||||
0.186352 | + | 0.982483i | \(0.440333\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −69.4609 | + | 191.927i | −0.283514 | + | 0.783374i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 328.481 | + | 328.481i | 1.32988 | + | 1.32988i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.46561 | 0.0217753 | 0.0108877 | − | 0.999941i | \(-0.496534\pi\) | ||||
0.0108877 | + | 0.999941i | \(0.496534\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.146888 | − | 0.146888i | 0.000580585 | − | 0.000580585i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 340.078 | + | 340.078i | 1.32326 | + | 1.32326i | 0.911120 | + | 0.412141i | \(0.135219\pi\) |
0.412141 | + | 0.911120i | \(0.364781\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 142.241i | 0.549192i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 29.3609 | − | 29.3609i | 0.111638 | − | 0.111638i | −0.649081 | − | 0.760719i | \(-0.724846\pi\) |
0.760719 | + | 0.649081i | \(0.224846\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.2094 | − | 9.00000i | 0.0724882 | − | 0.0339623i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 403.047i | 1.49832i | 0.662392 | + | 0.749158i | \(0.269542\pi\) | ||||
−0.662392 | + | 0.749158i | \(0.730458\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −308.984 | −1.14016 | −0.570082 | − | 0.821588i | \(-0.693089\pi\) | ||||
−0.570082 | + | 0.821588i | \(0.693089\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 26.9531 | + | 22.4500i | 0.0980114 | + | 0.0816363i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.59688 | + | 9.59688i | 0.0346458 | + | 0.0346458i | 0.724217 | − | 0.689572i | \(-0.242201\pi\) |
−0.689572 | + | 0.724217i | \(0.742201\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 268.628 | 0.955972 | 0.477986 | − | 0.878367i | \(-0.341367\pi\) | ||||
0.477986 | + | 0.878367i | \(0.341367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −116.942 | + | 116.942i | −0.413223 | + | 0.413223i | −0.882860 | − | 0.469637i | \(-0.844385\pi\) |
0.469637 | + | 0.882860i | \(0.344385\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 299.078 | + | 299.078i | 1.04208 | + | 1.04208i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 277.450i | − | 0.960035i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 133.691 | − | 133.691i | 0.456282 | − | 0.456282i | −0.441151 | − | 0.897433i | \(-0.645430\pi\) |
0.897433 | + | 0.441151i | \(0.145430\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 70.0937 | − | 193.675i | 0.237606 | − | 0.656525i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.01562i | 0.0100857i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 357.884 | 1.18898 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −269.884 | − | 97.6750i | −0.884867 | − | 0.320246i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −109.298 | − | 109.298i | −0.356021 | − | 0.356021i | 0.506323 | − | 0.862344i | \(-0.331004\pi\) |
−0.862344 | + | 0.506323i | \(0.831004\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −428.691 | −1.37843 | −0.689213 | − | 0.724559i | \(-0.742044\pi\) | ||||
−0.689213 | + | 0.724559i | \(0.742044\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 299.334 | − | 299.334i | 0.956340 | − | 0.956340i | −0.0427462 | − | 0.999086i | \(-0.513611\pi\) |
0.999086 | + | 0.0427462i | \(0.0136107\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −412.109 | − | 412.109i | −1.30003 | − | 1.30003i | −0.928369 | − | 0.371661i | \(-0.878788\pi\) |
−0.371661 | − | 0.928369i | \(-0.621212\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 64.0000i | 0.200627i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 54.8062 | − | 54.8062i | 0.169679 | − | 0.169679i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −507.125 | + | 46.2250i | −1.56038 | + | 0.142231i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 140.628i | 0.427441i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.9219 | 0.0390390 | 0.0195195 | − | 0.999809i | \(-0.493786\pi\) | ||||
0.0195195 | + | 0.999809i | \(0.493786\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 104.105 | + | 222.198i | 0.310760 | + | 0.663279i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −61.3250 | − | 61.3250i | −0.181973 | − | 0.181973i | 0.610242 | − | 0.792215i | \(-0.291072\pi\) |
−0.792215 | + | 0.610242i | \(0.791072\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.64374 | −0.0106855 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 54.8062 | − | 54.8062i | 0.159785 | − | 0.159785i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −179.183 | − | 179.183i | −0.516377 | − | 0.516377i | 0.400096 | − | 0.916473i | \(-0.368977\pi\) |
−0.916473 | + | 0.400096i | \(0.868977\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 240.962i | − | 0.690437i | −0.938522 | − | 0.345218i | \(-0.887805\pi\) | ||
0.938522 | − | 0.345218i | \(-0.112195\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −141.900 | + | 141.900i | −0.401983 | + | 0.401983i | −0.878931 | − | 0.476948i | \(-0.841743\pi\) |
0.476948 | + | 0.878931i | \(0.341743\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −213.466 | − | 77.2562i | −0.601312 | − | 0.217623i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 238.325i | 0.663858i | 0.943304 | + | 0.331929i | \(0.107699\pi\) | ||||
−0.943304 | + | 0.331929i | \(0.892301\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −159.125 | −0.440789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 72.9156 | − | 34.1625i | 0.199769 | − | 0.0935959i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 259.477 | + | 259.477i | 0.707021 | + | 0.707021i | 0.965908 | − | 0.258887i | \(-0.0833557\pi\) |
−0.258887 | + | 0.965908i | \(0.583356\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 40.2094 | 0.108381 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −310.350 | + | 310.350i | −0.832037 | + | 0.832037i | −0.987795 | − | 0.155758i | \(-0.950218\pi\) |
0.155758 | + | 0.987795i | \(0.450218\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −656.962 | − | 656.962i | −1.74261 | − | 1.74261i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 90.1562i | 0.237879i | 0.992901 | + | 0.118940i | \(0.0379495\pi\) | ||||
−0.992901 | + | 0.118940i | \(0.962051\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 209.298 | − | 209.298i | 0.546471 | − | 0.546471i | −0.378947 | − | 0.925418i | \(-0.623714\pi\) |
0.925418 | + | 0.378947i | \(0.123714\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 28.2094 | + | 60.2094i | 0.0732711 | + | 0.156388i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 193.372i | − | 0.497100i | −0.968619 | − | 0.248550i | \(-0.920046\pi\) | ||
0.968619 | − | 0.248550i | \(-0.0799540\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.503149 | 0.00128683 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 147.100 | − | 406.450i | 0.372405 | − | 1.02899i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 80.2250 | + | 80.2250i | 0.202078 | + | 0.202078i | 0.800890 | − | 0.598812i | \(-0.204360\pi\) |
−0.598812 | + | 0.800890i | \(0.704360\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 727.800 | 1.81496 | 0.907481 | − | 0.420093i | \(-0.138002\pi\) | ||||
0.907481 | + | 0.420093i | \(0.138002\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 37.4031 | − | 37.4031i | 0.0928117 | − | 0.0928117i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.8907 | + | 14.8907i | 0.0365864 | + | 0.0365864i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 355.403i | 0.868956i | 0.900682 | + | 0.434478i | \(0.143067\pi\) | ||||
−0.900682 | + | 0.434478i | \(0.856933\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 276.062 | − | 276.062i | 0.668432 | − | 0.668432i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 523.245 | − | 245.152i | 1.26083 | − | 0.590727i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 767.644i | − | 1.83209i | −0.401081 | − | 0.916043i | \(-0.631365\pi\) | ||
0.401081 | − | 0.916043i | \(-0.368635\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 446.722 | 1.06110 | 0.530549 | − | 0.847655i | \(-0.321986\pi\) | ||||
0.530549 | + | 0.847655i | \(0.321986\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.71252 | + | 84.6125i | 0.0181471 | + | 0.199088i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −384.691 | − | 384.691i | −0.900915 | − | 0.900915i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −303.791 | −0.704851 | −0.352425 | − | 0.935840i | \(-0.614643\pi\) | ||||
−0.352425 | + | 0.935840i | \(0.614643\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −610.350 | + | 610.350i | −1.40958 | + | 1.40958i | −0.647625 | + | 0.761959i | \(0.724238\pi\) |
−0.761959 | + | 0.647625i | \(0.775762\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.38750 | − | 2.38750i | −0.00546339 | − | 0.00546339i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 737.925i | − | 1.68092i | −0.541872 | − | 0.840461i | \(-0.682284\pi\) | ||
0.541872 | − | 0.840461i | \(-0.317716\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −481.508 | + | 481.508i | −1.08693 | + | 1.08693i | −0.0910817 | + | 0.995843i | \(0.529032\pi\) |
−0.995843 | + | 0.0910817i | \(0.970968\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 155.225 | − | 428.900i | 0.348820 | − | 0.963820i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 568.428i | 1.26599i | 0.774157 | + | 0.632993i | \(0.218174\pi\) | ||||
−0.774157 | + | 0.632993i | \(0.781826\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 62.6188 | 0.138844 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −907.622 | − | 328.481i | −1.99477 | − | 0.721937i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −108.791 | − | 108.791i | −0.238054 | − | 0.238054i | 0.577990 | − | 0.816044i | \(-0.303837\pi\) |
−0.816044 | + | 0.577990i | \(0.803837\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −348.281 | −0.755491 | −0.377745 | − | 0.925910i | \(-0.623301\pi\) | ||||
−0.377745 | + | 0.925910i | \(0.623301\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −307.330 | + | 307.330i | −0.663779 | + | 0.663779i | −0.956269 | − | 0.292490i | \(-0.905516\pi\) |
0.292490 | + | 0.956269i | \(0.405516\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −50.3453 | − | 50.3453i | −0.107806 | − | 0.107806i | 0.651146 | − | 0.758952i | \(-0.274288\pi\) |
−0.758952 | + | 0.651146i | \(0.774288\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 465.109i | 0.991704i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 37.4656 | − | 37.4656i | 0.0792085 | − | 0.0792085i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 364.900 | − | 438.094i | 0.768210 | − | 0.922303i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 445.862i | − | 0.930819i | −0.885095 | − | 0.465410i | \(-0.845907\pi\) | ||
0.885095 | − | 0.465410i | \(-0.154093\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −305.706 | −0.635564 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 147.000 | + | 313.753i | 0.303093 | + | 0.646914i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −322.136 | − | 322.136i | −0.661470 | − | 0.661470i | 0.294256 | − | 0.955727i | \(-0.404928\pi\) |
−0.955727 | + | 0.294256i | \(0.904928\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 362.953 | 0.739212 | 0.369606 | − | 0.929189i | \(-0.379493\pi\) | ||||
0.369606 | + | 0.929189i | \(0.379493\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −109.612 | + | 109.612i | −0.222338 | + | 0.222338i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −304.272 | − | 304.272i | −0.612217 | − | 0.612217i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 555.831i | − | 1.11389i | −0.830549 | − | 0.556945i | \(-0.811973\pi\) | ||
0.830549 | − | 0.556945i | \(-0.188027\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 173.717 | − | 173.717i | 0.345362 | − | 0.345362i | −0.513017 | − | 0.858379i | \(-0.671472\pi\) |
0.858379 | + | 0.513017i | \(0.171472\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −282.241 | − | 102.147i | −0.558892 | − | 0.202271i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 213.737i | − | 0.419916i | −0.977710 | − | 0.209958i | \(-0.932667\pi\) | ||
0.977710 | − | 0.209958i | \(-0.0673328\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 152.628 | 0.298685 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 393.842 | − | 184.523i | 0.764742 | − | 0.358298i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.7218 | + | 14.7218i | 0.0284755 | + | 0.0284755i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −312.094 | −0.599028 | −0.299514 | − | 0.954092i | \(-0.596825\pi\) | ||||
−0.299514 | + | 0.954092i | \(0.596825\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −197.655 | + | 197.655i | −0.377925 | + | 0.377925i | −0.870353 | − | 0.492428i | \(-0.836109\pi\) |
0.492428 | + | 0.870353i | \(0.336109\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.24062 | − | 6.24062i | −0.0118418 | − | 0.0118418i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 528.978i | 0.999959i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −642.784 | + | 642.784i | −1.20597 | + | 1.20597i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −202.617 | − | 432.461i | −0.378724 | − | 0.808338i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 57.2782i | 0.106267i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 172.031 | 0.317988 | 0.158994 | − | 0.987280i | \(-0.449175\pi\) | ||||
0.158994 | + | 0.987280i | \(0.449175\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −32.4094 | + | 89.5500i | −0.0594668 | + | 0.164312i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −60.9422 | − | 60.9422i | −0.111412 | − | 0.111412i | 0.649203 | − | 0.760615i | \(-0.275102\pi\) |
−0.760615 | + | 0.649203i | \(0.775102\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1040.25 | 1.88793 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 579.350 | − | 579.350i | 1.04765 | − | 1.04765i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 441.575 | + | 441.575i | 0.792774 | + | 0.792774i | 0.981944 | − | 0.189171i | \(-0.0605799\pi\) |
−0.189171 | + | 0.981944i | \(0.560580\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 769.172i | 1.37598i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −502.764 | + | 502.764i | −0.893009 | + | 0.893009i | −0.994805 | − | 0.101796i | \(-0.967541\pi\) |
0.101796 | + | 0.994805i | \(0.467541\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −56.4875 | + | 26.4656i | −0.0999779 | + | 0.0468418i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 518.753i | 0.911693i | 0.890059 | + | 0.455846i | \(0.150663\pi\) | ||||
−0.890059 | + | 0.455846i | \(0.849337\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1034.07 | 1.81098 | 0.905492 | − | 0.424363i | \(-0.139502\pi\) | ||||
0.905492 | + | 0.424363i | \(0.139502\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.68594 | − | 0.335978i | 0.00641033 | − | 0.000584309i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 220.172 | + | 220.172i | 0.381580 | + | 0.381580i | 0.871671 | − | 0.490091i | \(-0.163036\pi\) |
−0.490091 | + | 0.871671i | \(0.663036\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1095.27 | 1.88514 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.20937 | − | 4.20937i | 0.00722019 | − | 0.00722019i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 547.517 | + | 547.517i | 0.932738 | + | 0.932738i | 0.997876 | − | 0.0651384i | \(-0.0207489\pi\) |
−0.0651384 | + | 0.997876i | \(0.520749\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 59.2250i | 0.100552i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 165.450 | − | 165.450i | 0.279005 | − | 0.279005i | −0.553707 | − | 0.832712i | \(-0.686787\pi\) |
0.832712 | + | 0.553707i | \(0.186787\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −54.8062 | + | 151.434i | −0.0921113 | + | 0.254512i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 997.987i | 1.66609i | 0.553206 | + | 0.833045i | \(0.313404\pi\) | ||||
−0.553206 | + | 0.833045i | \(0.686596\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 691.372 | 1.15037 | 0.575185 | − | 0.818024i | \(-0.304930\pi\) | ||||
0.575185 | + | 0.818024i | \(0.304930\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −559.633 | − | 202.539i | −0.925013 | − | 0.334775i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 115.833 | + | 115.833i | 0.190828 | + | 0.190828i | 0.796054 | − | 0.605226i | \(-0.206917\pi\) |
−0.605226 | + | 0.796054i | \(0.706917\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −302.241 | −0.494665 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −72.7906 | + | 72.7906i | −0.118745 | + | 0.118745i | −0.763982 | − | 0.645237i | \(-0.776758\pi\) |
0.645237 | + | 0.763982i | \(0.276758\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.5344 | − | 17.5344i | −0.0284188 | − | 0.0284188i | 0.692755 | − | 0.721173i | \(-0.256397\pi\) |
−0.721173 | + | 0.692755i | \(0.756397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1026.99i | 1.65912i | 0.558419 | + | 0.829559i | \(0.311408\pi\) | ||||
−0.558419 | + | 0.829559i | \(0.688592\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 611.350 | − | 611.350i | 0.981300 | − | 0.981300i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 113.000 | + | 614.700i | 0.180800 | + | 0.983520i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 51.0063i | 0.0810911i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 246.241 | 0.390239 | 0.195119 | − | 0.980780i | \(-0.437491\pi\) | ||||
0.195119 | + | 0.980780i | \(0.437491\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 44.1047 | + | 94.1359i | 0.0694562 | + | 0.148246i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −587.962 | − | 587.962i | −0.923018 | − | 0.923018i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −825.822 | −1.28833 | −0.644167 | − | 0.764885i | \(-0.722796\pi\) | ||||
−0.644167 | + | 0.764885i | \(0.722796\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.2453 | − | 15.2453i | 0.0237096 | − | 0.0237096i | −0.695153 | − | 0.718862i | \(-0.744663\pi\) |
0.718862 | + | 0.695153i | \(0.244663\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −359.414 | − | 359.414i | −0.555509 | − | 0.555509i | 0.372517 | − | 0.928025i | \(-0.378495\pi\) |
−0.928025 | + | 0.372517i | \(0.878495\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 57.8000i | − | 0.0890600i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 247.187 | − | 247.187i | 0.378541 | − | 0.378541i | −0.492034 | − | 0.870576i | \(-0.663747\pi\) |
0.870576 | + | 0.492034i | \(0.163747\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1118.43 | − | 404.775i | −1.70752 | − | 0.617977i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 400.606i | 0.607900i | 0.952688 | + | 0.303950i | \(0.0983056\pi\) | ||||
−0.952688 | + | 0.303950i | \(0.901694\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 121.947 | 0.184488 | 0.0922442 | − | 0.995736i | \(-0.470596\pi\) | ||||
0.0922442 | + | 0.995736i | \(0.470596\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 978.637 | − | 458.512i | 1.47164 | − | 0.689492i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.77501 | + | 4.77501i | 0.00715893 | + | 0.00715893i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −80.5437 | −0.120035 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −645.450 | + | 645.450i | −0.959064 | + | 0.959064i | −0.999194 | − | 0.0401306i | \(-0.987223\pi\) |
0.0401306 | + | 0.999194i | \(0.487223\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 684.087 | + | 684.087i | 1.01047 | + | 1.01047i | 0.999945 | + | 0.0105243i | \(0.00335004\pi\) |
0.0105243 | + | 0.999945i | \(0.496650\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 656.753i | 0.967236i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −164.252 | + | 164.252i | −0.240485 | + | 0.240485i | −0.817051 | − | 0.576565i | \(-0.804393\pi\) |
0.576565 | + | 0.817051i | \(0.304393\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −259.837 | − | 554.591i | −0.379325 | − | 0.809621i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 86.4187i | 0.125426i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −241.403 | −0.349353 | −0.174677 | − | 0.984626i | \(-0.555888\pi\) | ||||
−0.174677 | + | 0.984626i | \(0.555888\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 419.956 | − | 1160.37i | 0.604253 | − | 1.66960i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 107.247 | + | 107.247i | 0.153869 | + | 0.153869i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −353.822 | −0.504739 | −0.252369 | − | 0.967631i | \(-0.581210\pi\) | ||||
−0.252369 | + | 0.967631i | \(0.581210\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 242.031 | − | 242.031i | 0.344283 | − | 0.344283i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −402.303 | − | 402.303i | −0.569028 | − | 0.569028i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 362.762i | 0.511654i | 0.966723 | + | 0.255827i | \(0.0823477\pi\) | ||||
−0.966723 | + | 0.255827i | \(0.917652\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.271857 | + | 0.271857i | −0.000381287 | + | 0.000381287i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −129.403 | + | 60.6281i | −0.180983 | + | 0.0847946i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1191.41i | 1.65704i | 0.559959 | + | 0.828520i | \(0.310817\pi\) | ||||
−0.559959 | + | 0.828520i | \(0.689183\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 824.397 | 1.14341 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −729.800 | + | 876.187i | −1.00662 | + | 1.20853i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 304.502 | + | 304.502i | 0.418847 | + | 0.418847i | 0.884806 | − | 0.465959i | \(-0.154291\pi\) |
−0.465959 | + | 0.884806i | \(0.654291\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 128.334 | 0.175560 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −117.263 | + | 117.263i | −0.159976 | + | 0.159976i | −0.782556 | − | 0.622580i | \(-0.786085\pi\) |
0.622580 | + | 0.782556i | \(0.286085\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 48.6906 | + | 48.6906i | 0.0660659 | + | 0.0660659i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 692.669i | − | 0.937305i | −0.883383 | − | 0.468653i | \(-0.844740\pi\) | ||
0.883383 | − | 0.468653i | \(-0.155260\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −826.301 | + | 826.301i | −1.11212 | + | 1.11212i | −0.119251 | + | 0.992864i | \(0.538049\pi\) |
−0.992864 | + | 0.119251i | \(0.961951\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 207.341 | − | 572.900i | 0.278310 | − | 0.768993i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 905.234i | − | 1.20859i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 61.4031 | 0.0817618 | 0.0408809 | − | 0.999164i | \(-0.486984\pi\) | ||||
0.0408809 | + | 0.999164i | \(0.486984\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1154.37 | + | 417.781i | 1.52896 | + | 0.553353i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 366.372 | + | 366.372i | 0.483979 | + | 0.483979i | 0.906400 | − | 0.422421i | \(-0.138820\pi\) |
−0.422421 | + | 0.906400i | \(0.638820\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 895.675 | 1.17697 | 0.588486 | − | 0.808508i | \(-0.299724\pi\) | ||||
0.588486 | + | 0.808508i | \(0.299724\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −127.644 | + | 127.644i | −0.167292 | + | 0.167292i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 593.319 | + | 593.319i | 0.773558 | + | 0.773558i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 241.675i | − | 0.314272i | −0.987577 | − | 0.157136i | \(-0.949774\pi\) | ||
0.987577 | − | 0.157136i | \(-0.0502261\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −359.459 | + | 359.459i | −0.465019 | + | 0.465019i | −0.900296 | − | 0.435278i | \(-0.856650\pi\) |
0.435278 | + | 0.900296i | \(0.356650\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −49.8844 | − | 41.5500i | −0.0643669 | − | 0.0536129i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1017.80i | − | 1.30655i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −63.7062 | −0.0815701 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −439.397 | − | 937.837i | −0.559741 | − | 1.19470i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 171.789 | + | 171.789i | 0.218283 | + | 0.218283i | 0.807775 | − | 0.589491i | \(-0.200672\pi\) |
−0.589491 | + | 0.807775i | \(0.700672\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −118.241 | −0.149482 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 826.784 | − | 826.784i | 1.04260 | − | 1.04260i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 547.891 | + | 547.891i | 0.687441 | + | 0.687441i | 0.961666 | − | 0.274224i | \(-0.0884211\pi\) |
−0.274224 | + | 0.961666i | \(0.588421\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 50.4281i | 0.0631140i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.9781 | − | 15.9781i | 0.0198980 | − | 0.0198980i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.59688 | + | 2.38750i | 0.00819488 | + | 0.00296584i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 225.925i | − | 0.279264i | −0.990203 | − | 0.139632i | \(-0.955408\pi\) | ||
0.990203 | − | 0.139632i | \(-0.0445920\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1083.03 | 1.33543 | 0.667715 | − | 0.744417i | \(-0.267272\pi\) | ||||
0.667715 | + | 0.744417i | \(0.267272\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1120.38 | + | 524.920i | −1.37470 | + | 0.644074i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −608.962 | − | 608.962i | −0.745364 | − | 0.745364i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −125.297 | −0.152615 | −0.0763074 | − | 0.997084i | \(-0.524313\pi\) | ||||
−0.0763074 | + | 0.997084i | \(0.524313\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −408.480 | + | 408.480i | −0.496330 | + | 0.496330i | −0.910293 | − | 0.413963i | \(-0.864144\pi\) |
0.413963 | + | 0.910293i | \(0.364144\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −705.508 | − | 705.508i | −0.853093 | − | 0.853093i | 0.137420 | − | 0.990513i | \(-0.456119\pi\) |
−0.990513 | + | 0.137420i | \(0.956119\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1040.20i | − | 1.25476i | −0.778713 | − | 0.627380i | \(-0.784127\pi\) | ||
0.778713 | − | 0.627380i | \(-0.215873\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −98.1000 | + | 98.1000i | −0.117767 | + | 0.117767i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 609.989 | + | 1301.95i | 0.730526 | + | 1.55922i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 154.512i | − | 0.184163i | −0.995751 | − | 0.0920813i | \(-0.970648\pi\) | ||
0.995751 | − | 0.0920813i | \(-0.0293520\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1239.50 | −1.47384 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 418.414 | − | 1156.11i | 0.495165 | − | 1.36818i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −797.695 | − | 797.695i | −0.941789 | − | 0.941789i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.22197 | 0.00261101 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −572.141 | + | 572.141i | −0.670739 | + | 0.670739i | −0.957886 | − | 0.287147i | \(-0.907293\pi\) |
0.287147 | + | 0.957886i | \(0.407293\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 81.2625 | + | 81.2625i | 0.0948221 | + | 0.0948221i | 0.752927 | − | 0.658105i | \(-0.228642\pi\) |
−0.658105 | + | 0.752927i | \(0.728642\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 214.094i | 0.249236i | 0.992205 | + | 0.124618i | \(0.0397705\pi\) | ||||
−0.992205 | + | 0.124618i | \(0.960229\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 72.8172 | − | 72.8172i | 0.0843768 | − | 0.0843768i | −0.663659 | − | 0.748036i | \(-0.730997\pi\) |
0.748036 | + | 0.663659i | \(0.230997\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1079.65 | − | 505.837i | 1.24815 | − | 0.584783i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 121.300i | − | 0.139586i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −999.622 | −1.14767 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −300.377 | + | 1145.97i | −0.343287 | + | 1.30968i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −922.841 | − | 922.841i | −1.05227 | − | 1.05227i | −0.998556 | − | 0.0537133i | \(-0.982894\pi\) |
−0.0537133 | − | 0.998556i | \(-0.517106\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −364.922 | −0.414213 | −0.207107 | − | 0.978318i | \(-0.566405\pi\) | ||||
−0.207107 | + | 0.978318i | \(0.566405\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −274.786 | + | 274.786i | −0.311196 | + | 0.311196i | −0.845373 | − | 0.534177i | \(-0.820622\pi\) |
0.534177 | + | 0.845373i | \(0.320622\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −609.464 | − | 609.464i | −0.687107 | − | 0.687107i | 0.274484 | − | 0.961592i | \(-0.411493\pi\) |
−0.961592 | + | 0.274484i | \(0.911493\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 197.047i | 0.221650i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 239.287 | − | 239.287i | 0.267959 | − | 0.267959i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 46.9312 | − | 129.675i | 0.0524371 | − | 0.144888i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 118.450i | − | 0.131757i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.4187 | 0.0160030 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −415.559 | − | 150.397i | −0.459182 | − | 0.166184i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 112.439 | + | 112.439i | 0.123968 | + | 0.123968i | 0.766369 | − | 0.642401i | \(-0.222062\pi\) |
−0.642401 | + | 0.766369i | \(0.722062\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1469.90 | −1.61350 | −0.806752 | − | 0.590890i | \(-0.798777\pi\) | ||||
−0.806752 | + | 0.590890i | \(0.798777\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 114.659 | − | 114.659i | 0.125585 | − | 0.125585i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1594.20 | − | 1594.20i | −1.73849 | − | 1.73849i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 503.662i | − | 0.548055i | −0.961722 | − | 0.274027i | \(-0.911644\pi\) | ||
0.961722 | − | 0.274027i | \(-0.0883559\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 653.947 | − | 653.947i | 0.708501 | − | 0.708501i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.0595 | + | 373.659i | 0.0368210 | + | 0.403956i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1016.43i | − | 1.09411i | −0.837097 | − | 0.547055i | \(-0.815749\pi\) | ||
0.837097 | − | 0.547055i | \(-0.184251\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 930.994 | 0.999993 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.1156 | + | 21.5906i | 0.0108189 | + | 0.0230915i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −678.841 | − | 678.841i | −0.724483 | − | 0.724483i | 0.245032 | − | 0.969515i | \(-0.421202\pi\) |
−0.969515 | + | 0.245032i | \(0.921202\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 603.987 | 0.641857 | 0.320928 | − | 0.947103i | \(-0.396005\pi\) | ||||
0.320928 | + | 0.947103i | \(0.396005\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.67196 | − | 4.67196i | 0.00495435 | − | 0.00495435i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.02658 | − | 1.02658i | −0.00108403 | − | 0.00108403i | 0.706565 | − | 0.707649i | \(-0.250244\pi\) |
−0.707649 | + | 0.706565i | \(0.750244\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 328.031i | 0.345660i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −531.459 | + | 531.459i | −0.557670 | + | 0.557670i | −0.928643 | − | 0.370974i | \(-0.879024\pi\) |
0.370974 | + | 0.928643i | \(0.379024\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 373.759 | + | 135.269i | 0.391371 | + | 0.141643i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1160.88i | − | 1.21051i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −954.256 | −0.992983 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 671.187 | − | 314.466i | 0.695531 | − | 0.325871i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −303.392 | − | 303.392i | −0.313746 | − | 0.313746i | 0.532613 | − | 0.846359i | \(-0.321210\pi\) |
−0.846359 | + | 0.532613i | \(0.821210\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1156.04 | 1.19057 | 0.595284 | − | 0.803516i | \(-0.297040\pi\) | ||||
0.595284 | + | 0.803516i | \(0.297040\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1653.99 | − | 1653.99i | 1.69988 | − | 1.69988i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 287.000 | + | 287.000i | 0.293756 | + | 0.293756i | 0.838562 | − | 0.544806i | \(-0.183397\pi\) |
−0.544806 | + | 0.838562i | \(0.683397\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 128.000i | − | 0.130746i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 868.523 | − | 868.523i | 0.883544 | − | 0.883544i | −0.110349 | − | 0.993893i | \(-0.535197\pi\) |
0.993893 | + | 0.110349i | \(0.0351969\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −204.488 | − | 436.453i | −0.207602 | − | 0.443100i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 5.59058i | − | 0.00565276i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1263.28 | −1.27476 | −0.637379 | − | 0.770551i | \(-0.719981\pi\) | ||||
−0.637379 | + | 0.770551i | \(0.719981\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −426.263 | + | 1177.80i | −0.428405 | + | 1.18372i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 992.547 | + | 992.547i | 0.995533 | + | 0.995533i | 0.999990 | − | 0.00445673i | \(-0.00141863\pi\) |
−0.00445673 | + | 0.999990i | \(0.501419\pi\) | |||||||
\(998\) | 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 | 360.3.v.c.217.2 | 4 | ||
3.2 | odd | 2 | 40.3.l.b.17.2 | ✓ | 4 | ||
4.3 | odd | 2 | 720.3.bh.l.577.2 | 4 | |||
5.2 | odd | 4 | 1800.3.v.k.793.1 | 4 | |||
5.3 | odd | 4 | inner | 360.3.v.c.73.2 | 4 | ||
5.4 | even | 2 | 1800.3.v.k.1657.1 | 4 | |||
12.11 | even | 2 | 80.3.p.d.17.1 | 4 | |||
15.2 | even | 4 | 200.3.l.e.193.1 | 4 | |||
15.8 | even | 4 | 40.3.l.b.33.2 | yes | 4 | ||
15.14 | odd | 2 | 200.3.l.e.57.1 | 4 | |||
20.3 | even | 4 | 720.3.bh.l.433.2 | 4 | |||
24.5 | odd | 2 | 320.3.p.l.257.1 | 4 | |||
24.11 | even | 2 | 320.3.p.i.257.2 | 4 | |||
60.23 | odd | 4 | 80.3.p.d.33.1 | 4 | |||
60.47 | odd | 4 | 400.3.p.i.193.2 | 4 | |||
60.59 | even | 2 | 400.3.p.i.257.2 | 4 | |||
120.53 | even | 4 | 320.3.p.l.193.1 | 4 | |||
120.83 | odd | 4 | 320.3.p.i.193.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.3.l.b.17.2 | ✓ | 4 | 3.2 | odd | 2 | ||
40.3.l.b.33.2 | yes | 4 | 15.8 | even | 4 | ||
80.3.p.d.17.1 | 4 | 12.11 | even | 2 | |||
80.3.p.d.33.1 | 4 | 60.23 | odd | 4 | |||
200.3.l.e.57.1 | 4 | 15.14 | odd | 2 | |||
200.3.l.e.193.1 | 4 | 15.2 | even | 4 | |||
320.3.p.i.193.2 | 4 | 120.83 | odd | 4 | |||
320.3.p.i.257.2 | 4 | 24.11 | even | 2 | |||
320.3.p.l.193.1 | 4 | 120.53 | even | 4 | |||
320.3.p.l.257.1 | 4 | 24.5 | odd | 2 | |||
360.3.v.c.73.2 | 4 | 5.3 | odd | 4 | inner | ||
360.3.v.c.217.2 | 4 | 1.1 | even | 1 | trivial | ||
400.3.p.i.193.2 | 4 | 60.47 | odd | 4 | |||
400.3.p.i.257.2 | 4 | 60.59 | even | 2 | |||
720.3.bh.l.433.2 | 4 | 20.3 | even | 4 | |||
720.3.bh.l.577.2 | 4 | 4.3 | odd | 2 | |||
1800.3.v.k.793.1 | 4 | 5.2 | odd | 4 | |||
1800.3.v.k.1657.1 | 4 | 5.4 | even | 2 |