Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(1,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4560.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.a (trivial) |
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: | yes |
Analytic conductor: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.64575 | −0.622036 | −0.311018 | − | 0.950404i | \(-0.600670\pi\) | ||||
−0.311018 | + | 0.950404i | \(0.600670\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.354249 | 0.106810 | 0.0534050 | − | 0.998573i | \(-0.482993\pi\) | ||||
0.0534050 | + | 0.998573i | \(0.482993\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.64575 | 1.01115 | 0.505575 | − | 0.862783i | \(-0.331280\pi\) | ||||
0.505575 | + | 0.862783i | \(0.331280\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.64575 | −0.359132 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | −0.417029 | −0.208514 | − | 0.978019i | \(-0.566863\pi\) | ||||
−0.208514 | + | 0.978019i | \(0.566863\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.64575 | 1.79117 | 0.895586 | − | 0.444889i | \(-0.146757\pi\) | ||||
0.895586 | + | 0.444889i | \(0.146757\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.354249 | 0.0616668 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.64575 | −0.278183 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.93725 | −1.14048 | −0.570239 | − | 0.821479i | \(-0.693149\pi\) | ||||
−0.570239 | + | 0.821479i | \(0.693149\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.64575 | 0.583787 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.64575 | 0.257023 | 0.128512 | − | 0.991708i | \(-0.458980\pi\) | ||||
0.128512 | + | 0.991708i | \(0.458980\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.93725 | 0.752924 | 0.376462 | − | 0.926432i | \(-0.377141\pi\) | ||||
0.376462 | + | 0.926432i | \(0.377141\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.29150 | −0.613072 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.00000 | 0.549442 | 0.274721 | − | 0.961524i | \(-0.411414\pi\) | ||||
0.274721 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.354249 | 0.0477669 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.29150 | −0.428517 | −0.214259 | − | 0.976777i | \(-0.568734\pi\) | ||||
−0.214259 | + | 0.976777i | \(0.568734\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.2915 | 1.44573 | 0.722864 | − | 0.690990i | \(-0.242825\pi\) | ||||
0.722864 | + | 0.690990i | \(0.242825\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.64575 | −0.207345 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.64575 | 0.452200 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.29150 | 0.390629 | 0.195315 | − | 0.980741i | \(-0.437427\pi\) | ||||
0.195315 | + | 0.980741i | \(0.437427\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.583005 | −0.0664396 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.8745 | 1.74245 | 0.871227 | − | 0.490881i | \(-0.163325\pi\) | ||||
0.871227 | + | 0.490881i | \(0.163325\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.64575 | 1.03413 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.2288 | −1.29625 | −0.648123 | − | 0.761536i | \(-0.724446\pi\) | ||||
−0.648123 | + | 0.761536i | \(0.724446\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | −0.628971 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.00000 | 0.207390 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.2288 | 1.85085 | 0.925425 | − | 0.378931i | \(-0.123708\pi\) | ||||
0.925425 | + | 0.378931i | \(0.123708\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.354249 | 0.0356033 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.8745 | 1.57957 | 0.789786 | − | 0.613382i | \(-0.210191\pi\) | ||||
0.789786 | + | 0.613382i | \(0.210191\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.5830 | −1.43691 | −0.718453 | − | 0.695575i | \(-0.755150\pi\) | ||||
−0.718453 | + | 0.695575i | \(0.755150\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.64575 | −0.160609 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.5830 | −1.40979 | −0.704896 | − | 0.709311i | \(-0.749006\pi\) | ||||
−0.704896 | + | 0.709311i | \(0.749006\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.29150 | 0.506834 | 0.253417 | − | 0.967357i | \(-0.418446\pi\) | ||||
0.253417 | + | 0.967357i | \(0.418446\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.93725 | −0.658455 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.8745 | 1.68149 | 0.840746 | − | 0.541430i | \(-0.182117\pi\) | ||||
0.840746 | + | 0.541430i | \(0.182117\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.00000 | −0.186501 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.64575 | 0.337050 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8745 | −0.988592 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.64575 | 0.148392 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.58301 | 0.229205 | 0.114602 | − | 0.993411i | \(-0.463441\pi\) | ||||
0.114602 | + | 0.993411i | \(0.463441\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.93725 | 0.434701 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.64575 | −0.668012 | −0.334006 | − | 0.942571i | \(-0.608401\pi\) | ||||
−0.334006 | + | 0.942571i | \(0.608401\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.64575 | −0.142705 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.583005 | −0.0498095 | −0.0249047 | − | 0.999690i | \(-0.507928\pi\) | ||||
−0.0249047 | + | 0.999690i | \(0.507928\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.8745 | 1.51610 | 0.758048 | − | 0.652199i | \(-0.226153\pi\) | ||||
0.758048 | + | 0.652199i | \(0.226153\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.29150 | 0.108001 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.64575 | 0.801036 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.29150 | −0.353957 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.00000 | −0.488273 | −0.244137 | − | 0.969741i | \(-0.578505\pi\) | ||||
−0.244137 | + | 0.969741i | \(0.578505\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | 0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.8745 | 1.26692 | 0.633462 | − | 0.773774i | \(-0.281633\pi\) | ||||
0.633462 | + | 0.773774i | \(0.281633\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.00000 | 0.317221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.29150 | 0.259407 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.64575 | −0.755514 | −0.377757 | − | 0.925905i | \(-0.623304\pi\) | ||||
−0.377757 | + | 0.925905i | \(0.623304\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.354249 | 0.0275782 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.29150 | 0.0999395 | 0.0499697 | − | 0.998751i | \(-0.484088\pi\) | ||||
0.0499697 | + | 0.998751i | \(0.484088\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.291503 | 0.0224233 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.70850 | 0.662095 | 0.331047 | − | 0.943614i | \(-0.392598\pi\) | ||||
0.331047 | + | 0.943614i | \(0.392598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.64575 | −0.124407 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.29150 | −0.247404 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.29150 | 0.544992 | 0.272496 | − | 0.962157i | \(-0.412151\pi\) | ||||
0.272496 | + | 0.962157i | \(0.412151\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.29150 | −0.393314 | −0.196657 | − | 0.980472i | \(-0.563009\pi\) | ||||
−0.196657 | + | 0.980472i | \(0.563009\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.2915 | 0.834692 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.93725 | −0.510037 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.64575 | −0.119711 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.9373 | −0.791392 | −0.395696 | − | 0.918382i | \(-0.629497\pi\) | ||||
−0.395696 | + | 0.918382i | \(0.629497\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.93725 | 0.211428 | 0.105714 | − | 0.994397i | \(-0.466287\pi\) | ||||
0.105714 | + | 0.994397i | \(0.466287\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.64575 | 0.261078 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.0000 | 1.70993 | 0.854965 | − | 0.518686i | \(-0.173579\pi\) | ||||
0.854965 | + | 0.518686i | \(0.173579\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.2915 | 1.65109 | 0.825545 | − | 0.564336i | \(-0.190868\pi\) | ||||
0.825545 | + | 0.564336i | \(0.190868\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | −0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.8745 | −1.11417 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.64575 | 0.114944 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.00000 | −0.139010 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.354249 | 0.0245039 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.5830 | 0.728564 | 0.364282 | − | 0.931289i | \(-0.381314\pi\) | ||||
0.364282 | + | 0.931289i | \(0.381314\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.29150 | 0.225530 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.93725 | 0.336718 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.29150 | −0.223442 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.00000 | −0.135147 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.41699 | 0.0948890 | 0.0474445 | − | 0.998874i | \(-0.484892\pi\) | ||||
0.0474445 | + | 0.998874i | \(0.484892\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.2915 | −1.67866 | −0.839328 | − | 0.543625i | \(-0.817051\pi\) | ||||
−0.839328 | + | 0.543625i | \(0.817051\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.29150 | 0.481836 | 0.240918 | − | 0.970545i | \(-0.422552\pi\) | ||||
0.240918 | + | 0.970545i | \(0.422552\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.583005 | −0.0383589 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.0000 | 1.44127 | 0.720634 | − | 0.693316i | \(-0.243851\pi\) | ||||
0.720634 | + | 0.693316i | \(0.243851\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.00000 | 0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.0627 | 0.844959 | 0.422479 | − | 0.906373i | \(-0.361160\pi\) | ||||
0.422479 | + | 0.906373i | \(0.361160\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.58301 | −0.295217 | −0.147609 | − | 0.989046i | \(-0.547158\pi\) | ||||
−0.147609 | + | 0.989046i | \(0.547158\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.29150 | −0.274174 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.64575 | 0.231974 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.8745 | 1.00601 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.22876 | 0.393156 | 0.196578 | − | 0.980488i | \(-0.437017\pi\) | ||||
0.196578 | + | 0.980488i | \(0.437017\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.708497 | −0.0445428 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.87451 | −0.615955 | −0.307977 | − | 0.951394i | \(-0.599652\pi\) | ||||
−0.307977 | + | 0.951394i | \(0.599652\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.4170 | 0.709418 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.64575 | 0.597057 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.29150 | 0.0796375 | 0.0398187 | − | 0.999207i | \(-0.487322\pi\) | ||||
0.0398187 | + | 0.999207i | \(0.487322\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.00000 | 0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.2288 | −0.748388 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.93725 | 0.301030 | 0.150515 | − | 0.988608i | \(-0.451907\pi\) | ||||
0.150515 | + | 0.988608i | \(0.451907\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.7085 | −0.771986 | −0.385993 | − | 0.922502i | \(-0.626141\pi\) | ||||
−0.385993 | + | 0.922502i | \(0.626141\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.00000 | −0.363137 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.354249 | 0.0213620 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.5830 | −1.47705 | −0.738525 | − | 0.674226i | \(-0.764477\pi\) | ||||
−0.738525 | + | 0.674226i | \(0.764477\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.00000 | 0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.93725 | −0.294532 | −0.147266 | − | 0.989097i | \(-0.547047\pi\) | ||||
−0.147266 | + | 0.989097i | \(0.547047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.77124 | 0.224177 | 0.112089 | − | 0.993698i | \(-0.464246\pi\) | ||||
0.112089 | + | 0.993698i | \(0.464246\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00000 | 0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.70850 | −0.159878 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.2288 | 1.06859 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.8745 | −1.04424 | −0.522120 | − | 0.852872i | \(-0.674859\pi\) | ||||
−0.522120 | + | 0.852872i | \(0.674859\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.29150 | −0.191639 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.354249 | 0.0205556 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.29150 | −0.421678 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.12549 | −0.468346 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.8745 | 0.911967 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.2915 | 0.646550 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.7085 | −0.725312 | −0.362656 | − | 0.931923i | \(-0.618130\pi\) | ||||
−0.362656 | + | 0.931923i | \(0.618130\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.5830 | −0.829598 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.35425 | 0.246907 | 0.123453 | − | 0.992350i | \(-0.460603\pi\) | ||||
0.123453 | + | 0.992350i | \(0.460603\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.7085 | −1.05747 | −0.528733 | − | 0.848788i | \(-0.677333\pi\) | ||||
−0.528733 | + | 0.848788i | \(0.677333\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.64575 | −0.0927276 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.5830 | 1.26839 | 0.634194 | − | 0.773174i | \(-0.281332\pi\) | ||||
0.634194 | + | 0.773174i | \(0.281332\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.41699 | 0.191315 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.5830 | −0.813944 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.64575 | 0.202230 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.29150 | 0.292621 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.87451 | 0.544399 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.5830 | −0.911484 | −0.455742 | − | 0.890112i | \(-0.650626\pi\) | ||||
−0.455742 | + | 0.890112i | \(0.650626\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.93725 | −0.380159 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.2288 | −1.21088 | −0.605439 | − | 0.795892i | \(-0.707002\pi\) | ||||
−0.605439 | + | 0.795892i | \(0.707002\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.8745 | 0.970810 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.708497 | 0.0383673 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5830 | 1.00339 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.00000 | −0.107676 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.29150 | −0.498794 | −0.249397 | − | 0.968401i | \(-0.580232\pi\) | ||||
−0.249397 | + | 0.968401i | \(0.580232\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.1660 | −1.45416 | −0.727082 | − | 0.686551i | \(-0.759124\pi\) | ||||
−0.727082 | + | 0.686551i | \(0.759124\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.64575 | 0.194596 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −35.1660 | −1.87170 | −0.935849 | − | 0.352401i | \(-0.885365\pi\) | ||||
−0.935849 | + | 0.352401i | \(0.885365\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.29150 | 0.174695 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.2288 | 0.539853 | 0.269927 | − | 0.962881i | \(-0.413001\pi\) | ||||
0.269927 | + | 0.962881i | \(0.413001\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.8745 | −0.570764 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.00000 | −0.104685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.228757 | −0.0119410 | −0.00597050 | − | 0.999982i | \(-0.501900\pi\) | ||||
−0.00597050 | + | 0.999982i | \(0.501900\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.64575 | 0.0856744 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.58301 | −0.341773 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.35425 | −0.432567 | −0.216283 | − | 0.976331i | \(-0.569393\pi\) | ||||
−0.216283 | + | 0.976331i | \(0.569393\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 35.1660 | 1.81114 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.0000 | −0.513665 | −0.256833 | − | 0.966456i | \(-0.582679\pi\) | ||||
−0.256833 | + | 0.966456i | \(0.582679\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.58301 | 0.132331 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.41699 | 0.276796 | 0.138398 | − | 0.990377i | \(-0.455805\pi\) | ||||
0.138398 | + | 0.990377i | \(0.455805\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.583005 | −0.0297127 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.93725 | 0.250975 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.64575 | −0.385677 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.0000 | −0.702640 | −0.351320 | − | 0.936255i | \(-0.614267\pi\) | ||||
−0.351320 | + | 0.936255i | \(0.614267\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.64575 | −0.0823906 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.35425 | 0.317316 | 0.158658 | − | 0.987334i | \(-0.449283\pi\) | ||||
0.158658 | + | 0.987334i | \(0.449283\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.29150 | 0.363216 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.45751 | −0.121814 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.70850 | −0.331714 | −0.165857 | − | 0.986150i | \(-0.553039\pi\) | ||||
−0.165857 | + | 0.986150i | \(0.553039\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.583005 | −0.0287575 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.41699 | 0.266553 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.8745 | 0.779249 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.8745 | 0.875318 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.9373 | 1.90221 | 0.951105 | − | 0.308869i | \(-0.0999504\pi\) | ||||
0.951105 | + | 0.308869i | \(0.0999504\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.583005 | −0.0284139 | −0.0142070 | − | 0.999899i | \(-0.504522\pi\) | ||||
−0.0142070 | + | 0.999899i | \(0.504522\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.00000 | −0.291730 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.5830 | −0.899295 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.29150 | 0.0623543 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 32.4575 | 1.56342 | 0.781712 | − | 0.623640i | \(-0.214347\pi\) | ||||
0.781712 | + | 0.623640i | \(0.214347\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.2288 | −1.26047 | −0.630237 | − | 0.776403i | \(-0.717042\pi\) | ||||
−0.630237 | + | 0.776403i | \(0.717042\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.64575 | 0.462478 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.00000 | −0.0956730 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.16601 | −0.246560 | −0.123280 | − | 0.992372i | \(-0.539341\pi\) | ||||
−0.123280 | + | 0.992372i | \(0.539341\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.29150 | −0.204357 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.58301 | −0.407791 | −0.203895 | − | 0.978993i | \(-0.565360\pi\) | ||||
−0.203895 | + | 0.978993i | \(0.565360\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.2288 | −0.579699 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.35425 | −0.111104 | −0.0555519 | − | 0.998456i | \(-0.517692\pi\) | ||||
−0.0555519 | + | 0.998456i | \(0.517692\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.583005 | 0.0274526 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.00000 | −0.281905 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.00000 | −0.281284 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.29150 | 0.434638 | 0.217319 | − | 0.976101i | \(-0.430269\pi\) | ||||
0.217319 | + | 0.976101i | \(0.430269\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.00000 | −0.279448 | −0.139724 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139724 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.77124 | 0.361160 | 0.180580 | − | 0.983560i | \(-0.442202\pi\) | ||||
0.180580 | + | 0.983560i | \(0.442202\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.00000 | 0.0927478 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.583005 | 0.0269783 | 0.0134891 | − | 0.999909i | \(-0.495706\pi\) | ||||
0.0134891 | + | 0.999909i | \(0.495706\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.58301 | 0.303975 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.8745 | 0.731459 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.74902 | 0.0804198 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.00000 | 0.183147 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.5203 | 0.617756 | 0.308878 | − | 0.951102i | \(-0.400046\pi\) | ||||
0.308878 | + | 0.951102i | \(0.400046\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.2915 | −1.15319 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.29150 | 0.149769 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.2288 | 0.827725 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.29150 | −0.149152 | −0.0745761 | − | 0.997215i | \(-0.523760\pi\) | ||||
−0.0745761 | + | 0.997215i | \(0.523760\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.64575 | −0.436196 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.8118 | 1.48077 | 0.740387 | − | 0.672181i | \(-0.234642\pi\) | ||||
0.740387 | + | 0.672181i | \(0.234642\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.354249 | 0.0159223 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.41699 | −0.242985 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.2915 | −0.863606 | −0.431803 | − | 0.901968i | \(-0.642122\pi\) | ||||
−0.431803 | + | 0.901968i | \(0.642122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.29150 | 0.0577001 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.29150 | 0.0575853 | 0.0287926 | − | 0.999585i | \(-0.490834\pi\) | ||||
0.0287926 | + | 0.999585i | \(0.490834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.8745 | 0.706406 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.291503 | 0.0129461 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 34.3542 | 1.52273 | 0.761363 | − | 0.648326i | \(-0.224531\pi\) | ||||
0.761363 | + | 0.648326i | \(0.224531\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.29150 | 0.145608 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.5830 | −0.642604 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.12549 | −0.0934790 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.70850 | 0.382261 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.8118 | 1.17464 | 0.587322 | − | 0.809353i | \(-0.300182\pi\) | ||||
0.587322 | + | 0.809353i | \(0.300182\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.12549 | −0.267849 | −0.133925 | − | 0.990992i | \(-0.542758\pi\) | ||||
−0.133925 | + | 0.990992i | \(0.542758\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.64575 | −0.0718265 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.29150 | −0.142839 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.00000 | 0.259889 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.5830 | −0.630478 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.29150 | 0.314652 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.52026 | −0.0654822 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.0000 | −1.11783 | −0.558914 | − | 0.829226i | \(-0.688782\pi\) | ||||
−0.558914 | + | 0.829226i | \(0.688782\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.29150 | −0.227080 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.29150 | 0.226663 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.4575 | 1.72984 | 0.864919 | − | 0.501911i | \(-0.167370\pi\) | ||||
0.864919 | + | 0.501911i | \(0.167370\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.2915 | 0.481910 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.64575 | 0.410923 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.1660 | −0.559876 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.93725 | −0.294470 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.0000 | −0.423714 | −0.211857 | − | 0.977301i | \(-0.567951\pi\) | ||||
−0.211857 | + | 0.977301i | \(0.567951\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.0000 | 0.761319 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.87451 | 0.163291 | 0.0816455 | − | 0.996661i | \(-0.473982\pi\) | ||||
0.0816455 | + | 0.996661i | \(0.473982\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.8745 | 0.751986 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.64575 | −0.0691151 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.479741 | 0.0201118 | 0.0100559 | − | 0.999949i | \(-0.496799\pi\) | ||||
0.0100559 | + | 0.999949i | \(0.496799\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.8745 | −0.580630 | −0.290315 | − | 0.956931i | \(-0.593760\pi\) | ||||
−0.290315 | + | 0.956931i | \(0.593760\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.9373 | −0.456910 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.00000 | −0.0834058 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.8745 | 1.16043 | 0.580215 | − | 0.814463i | \(-0.302968\pi\) | ||||
0.580215 | + | 0.814463i | \(0.302968\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.93725 | 0.122068 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.1255 | −1.08387 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.41699 | 0.0586859 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.64575 | 0.150733 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.5830 | −1.50994 | −0.754971 | − | 0.655758i | \(-0.772349\pi\) | ||||
−0.754971 | + | 0.655758i | \(0.772349\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.00000 | 0.0824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.0000 | 0.987228 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.4170 | −0.633100 | −0.316550 | − | 0.948576i | \(-0.602525\pi\) | ||||
−0.316550 | + | 0.948576i | \(0.602525\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.2915 | 0.953258 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.41699 | 0.221332 | 0.110666 | − | 0.993858i | \(-0.464702\pi\) | ||||
0.110666 | + | 0.993858i | \(0.464702\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.8745 | −0.647535 | −0.323767 | − | 0.946137i | \(-0.604950\pi\) | ||||
−0.323767 | + | 0.946137i | \(0.604950\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.8745 | −0.442112 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.4575 | 0.505635 | 0.252817 | − | 0.967514i | \(-0.418643\pi\) | ||||
0.252817 | + | 0.967514i | \(0.418643\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.8745 | −0.643268 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.8745 | −0.884948 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.4575 | −0.583933 | −0.291967 | − | 0.956428i | \(-0.594310\pi\) | ||||
−0.291967 | + | 0.956428i | \(0.594310\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.64575 | 0.0663631 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.8745 | 1.52231 | 0.761153 | − | 0.648573i | \(-0.224634\pi\) | ||||
0.761153 | + | 0.648573i | \(0.224634\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | −0.0802572 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.1255 | 0.806311 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.354249 | 0.0141473 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.1660 | −1.47956 | −0.739778 | − | 0.672851i | \(-0.765069\pi\) | ||||
−0.739778 | + | 0.672851i | \(0.765069\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.5830 | 0.420637 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.58301 | 0.102503 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.6458 | −0.619907 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.29150 | 0.130210 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.2288 | −0.798988 | −0.399494 | − | 0.916736i | \(-0.630814\pi\) | ||||
−0.399494 | + | 0.916736i | \(0.630814\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −44.9373 | −1.77215 | −0.886076 | − | 0.463540i | \(-0.846579\pi\) | ||||
−0.886076 | + | 0.463540i | \(0.846579\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.93725 | 0.194404 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.2915 | 0.994312 | 0.497156 | − | 0.867661i | \(-0.334378\pi\) | ||||
0.497156 | + | 0.867661i | \(0.334378\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.16601 | −0.0457699 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.29150 | −0.129004 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.00000 | −0.156532 | −0.0782660 | − | 0.996933i | \(-0.524938\pi\) | ||||
−0.0782660 | + | 0.996933i | \(0.524938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.64575 | −0.298744 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.00000 | −0.0780274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.1660 | −0.512875 | −0.256437 | − | 0.966561i | \(-0.582549\pi\) | ||||
−0.256437 | + | 0.966561i | \(0.582549\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.29150 | −0.205816 | −0.102908 | − | 0.994691i | \(-0.532815\pi\) | ||||
−0.102908 | + | 0.994691i | \(0.532815\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.64575 | −0.0638195 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.2915 | −0.746970 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.41699 | 0.0547842 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.00000 | 0.154418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.52026 | 0.366979 | 0.183490 | − | 0.983022i | \(-0.441261\pi\) | ||||
0.183490 | + | 0.983022i | \(0.441261\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.00000 | −0.153732 | −0.0768662 | − | 0.997041i | \(-0.524491\pi\) | ||||
−0.0768662 | + | 0.997041i | \(0.524491\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.0000 | −1.15129 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.2915 | −0.969172 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.00000 | −0.306111 | −0.153056 | − | 0.988218i | \(-0.548911\pi\) | ||||
−0.153056 | + | 0.988218i | \(0.548911\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.583005 | −0.0222755 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.29150 | 0.278188 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.5830 | 0.555568 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.2915 | −1.19038 | −0.595192 | − | 0.803583i | \(-0.702924\pi\) | ||||
−0.595192 | + | 0.803583i | \(0.702924\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.583005 | −0.0221465 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.8745 | 0.678019 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.0000 | 0.832116 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.0000 | −0.377695 | −0.188847 | − | 0.982006i | \(-0.560475\pi\) | ||||
−0.188847 | + | 0.982006i | \(0.560475\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.93725 | −0.261643 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.00000 | −0.225973 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −26.1255 | −0.982550 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.4575 | −1.21897 | −0.609484 | − | 0.792799i | \(-0.708623\pi\) | ||||
−0.609484 | + | 0.792799i | \(0.708623\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000 | 0.300023 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.00000 | −0.149801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.29150 | 0.0482995 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.0627 | 0.487837 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.64575 | 0.285138 | 0.142569 | − | 0.989785i | \(-0.454464\pi\) | ||||
0.142569 | + | 0.989785i | \(0.454464\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.0000 | 0.893807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.58301 | −0.170444 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.64575 | 0.358234 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.9778 | 1.48269 | 0.741347 | − | 0.671122i | \(-0.234187\pi\) | ||||
0.741347 | + | 0.671122i | \(0.234187\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.5830 | −1.20348 | −0.601740 | − | 0.798692i | \(-0.705526\pi\) | ||||
−0.601740 | + | 0.798692i | \(0.705526\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.29150 | −0.158294 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.41699 | −0.0521957 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.5830 | 0.389302 | 0.194651 | − | 0.980873i | \(-0.437643\pi\) | ||||
0.194651 | + | 0.980873i | \(0.437643\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.64575 | 0.133930 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.7490 | 1.16476 | 0.582379 | − | 0.812917i | \(-0.302122\pi\) | ||||
0.582379 | + | 0.812917i | \(0.302122\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | 0.219823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.8745 | 0.580818 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.0000 | 0.876941 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.3320 | −1.32577 | −0.662887 | − | 0.748719i | \(-0.730669\pi\) | ||||
−0.662887 | + | 0.748719i | \(0.730669\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.22876 | 0.226989 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.00000 | −0.218362 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.8745 | −0.722351 | −0.361176 | − | 0.932498i | \(-0.617625\pi\) | ||||
−0.361176 | + | 0.932498i | \(0.617625\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.708497 | −0.0257168 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.1660 | −0.404768 | −0.202384 | − | 0.979306i | \(-0.564869\pi\) | ||||
−0.202384 | + | 0.979306i | \(0.564869\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.70850 | −0.315269 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0000 | −0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.7490 | 0.784290 | 0.392145 | − | 0.919904i | \(-0.371733\pi\) | ||||
0.392145 | + | 0.919904i | \(0.371733\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.87451 | −0.355622 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.00000 | 0.0718421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.4170 | 0.409582 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.64575 | 0.0589652 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.16601 | 0.0417231 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.64575 | 0.344711 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.8745 | 0.566585 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.2915 | −0.402499 | −0.201249 | − | 0.979540i | \(-0.564500\pi\) | ||||
−0.201249 | + | 0.979540i | \(0.564500\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.29150 | 0.0459787 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.4170 | −1.04595 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.1660 | 1.46185 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.00000 | 0.141865 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.2915 | 1.39178 | 0.695888 | − | 0.718150i | \(-0.255011\pi\) | ||||
0.695888 | + | 0.718150i | \(0.255011\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.2288 | −0.432082 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.708497 | −0.0250023 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.29150 | 0.116010 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.93725 | 0.173800 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.58301 | −0.301762 | −0.150881 | − | 0.988552i | \(-0.548211\pi\) | ||||
−0.150881 | + | 0.988552i | \(0.548211\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.41699 | −0.190216 | −0.0951082 | − | 0.995467i | \(-0.530320\pi\) | ||||
−0.0951082 | + | 0.995467i | \(0.530320\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.7085 | −0.445706 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.64575 | −0.337876 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.93725 | 0.172733 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.00000 | −0.209657 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.7085 | 0.513330 | 0.256665 | − | 0.966500i | \(-0.417376\pi\) | ||||
0.256665 | + | 0.966500i | \(0.417376\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.2693 | 1.50827 | 0.754136 | − | 0.656718i | \(-0.228056\pi\) | ||||
0.754136 | + | 0.656718i | \(0.228056\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.354249 | 0.0123334 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.7085 | −0.789652 | −0.394826 | − | 0.918756i | \(-0.629195\pi\) | ||||
−0.394826 | + | 0.918756i | \(0.629195\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.8745 | −0.968122 | −0.484061 | − | 0.875034i | \(-0.660839\pi\) | ||||
−0.484061 | + | 0.875034i | \(0.660839\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.5830 | −0.852775 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.29150 | 0.0446943 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.00000 | 0.0691301 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.7085 | 0.991127 | 0.495564 | − | 0.868572i | \(-0.334962\pi\) | ||||
0.495564 | + | 0.868572i | \(0.334962\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 64.0405 | 2.20829 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.93725 | −0.170048 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.291503 | 0.0100280 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.8967 | 0.614939 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.77124 | 0.129429 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.8745 | 0.475612 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.2915 | −1.55075 | −0.775376 | − | 0.631500i | \(-0.782440\pi\) | ||||
−0.775376 | + | 0.631500i | \(0.782440\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.7490 | −0.811251 | −0.405625 | − | 0.914039i | \(-0.632946\pi\) | ||||
−0.405625 | + | 0.914039i | \(0.632946\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.83399 | −0.0966945 | −0.0483472 | − | 0.998831i | \(-0.515395\pi\) | ||||
−0.0483472 | + | 0.998831i | \(0.515395\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.70850 | −0.0923053 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.16601 | −0.0396915 | −0.0198457 | − | 0.999803i | \(-0.506318\pi\) | ||||
−0.0198457 | + | 0.999803i | \(0.506318\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.70850 | 0.296098 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.0000 | −0.577350 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.83399 | 0.0961365 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.5830 | −0.494126 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.2288 | 0.616950 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.64575 | −0.0556365 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.8118 | −0.567693 | −0.283846 | − | 0.958870i | \(-0.591611\pi\) | ||||
−0.283846 | + | 0.958870i | \(0.591611\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.8745 | −0.602892 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.7085 | −1.30412 | −0.652061 | − | 0.758166i | \(-0.726095\pi\) | ||||
−0.652061 | + | 0.758166i | \(0.726095\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.6458 | −0.863048 | −0.431524 | − | 0.902101i | \(-0.642024\pi\) | ||||
−0.431524 | + | 0.902101i | \(0.642024\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.29150 | −0.110643 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.7490 | −1.46895 | −0.734474 | − | 0.678637i | \(-0.762571\pi\) | ||||
−0.734474 | + | 0.678637i | \(0.762571\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.25098 | −0.142573 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.354249 | 0.0118678 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.00000 | −0.200782 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.29150 | 0.243728 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.29150 | −0.243456 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.2915 | 0.643408 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.12549 | −0.270399 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.29150 | −0.175895 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −53.8745 | −1.78887 | −0.894437 | − | 0.447194i | \(-0.852423\pi\) | ||||
−0.894437 | + | 0.447194i | \(0.852423\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.8745 | 0.526524 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.7490 | −0.786840 | −0.393420 | − | 0.919359i | \(-0.628708\pi\) | ||||
−0.393420 | + | 0.919359i | \(0.628708\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.62352 | 0.186111 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.2915 | 0.373286 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.5830 | 0.415527 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.5830 | −0.612997 | −0.306498 | − | 0.951871i | \(-0.599157\pi\) | ||||
−0.306498 | + | 0.951871i | \(0.599157\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.7085 | −0.418759 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0000 | 0.394985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.93725 | −0.228096 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.5830 | −0.478969 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.8745 | −0.520826 | −0.260413 | − | 0.965497i | \(-0.583859\pi\) | ||||
−0.260413 | + | 0.965497i | \(0.583859\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.29150 | −0.140648 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.35425 | 0.142552 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.2915 | 0.564889 | 0.282444 | − | 0.959284i | \(-0.408855\pi\) | ||||
0.282444 | + | 0.959284i | \(0.408855\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.7085 | −0.610529 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.2288 | −0.529042 | −0.264521 | − | 0.964380i | \(-0.585214\pi\) | ||||
−0.264521 | + | 0.964380i | \(0.585214\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.29150 | −0.107186 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.64575 | −0.0535363 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.7085 | −0.867910 | −0.433955 | − | 0.900935i | \(-0.642882\pi\) | ||||
−0.433955 | + | 0.900935i | \(0.642882\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.29150 | −0.236692 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.5830 | 0.732304 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.7085 | −0.929959 | −0.464980 | − | 0.885321i | \(-0.653938\pi\) | ||||
−0.464980 | + | 0.885321i | \(0.653938\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.9373 | −0.353921 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.41699 | 0.110456 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.959482 | 0.0309833 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.5830 | −0.469931 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.93725 | 0.0945535 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51.5203 | −1.65678 | −0.828390 | − | 0.560152i | \(-0.810743\pi\) | ||||
−0.828390 | + | 0.560152i | \(0.810743\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.7490 | 0.377044 | 0.188522 | − | 0.982069i | \(-0.439630\pi\) | ||||
0.188522 | + | 0.982069i | \(0.439630\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.4170 | −0.943066 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.64575 | 0.116757 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50.3320 | −1.61026 | −0.805132 | − | 0.593096i | \(-0.797906\pi\) | ||||
−0.805132 | + | 0.593096i | \(0.797906\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.33202 | −0.138452 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.29150 | 0.168945 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.2915 | −1.06183 | −0.530917 | − | 0.847424i | \(-0.678152\pi\) | ||||
−0.530917 | + | 0.847424i | \(0.678152\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.0000 | 0.764704 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.87451 | 0.314309 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.87451 | −0.313991 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.74902 | 0.119091 | 0.0595457 | − | 0.998226i | \(-0.481035\pi\) | ||||
0.0595457 | + | 0.998226i | \(0.481035\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.5830 | −0.526246 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.2915 | 0.738390 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.2915 | −1.68776 | −0.843879 | − | 0.536533i | \(-0.819734\pi\) | ||||
−0.843879 | + | 0.536533i | \(0.819734\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.93725 | −0.219485 |
(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 | 4560.2.a.bp.1.1 | 2 | ||
4.3 | odd | 2 | 2280.2.a.n.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 6840.2.a.w.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.n.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
4560.2.a.bp.1.1 | 2 | 1.1 | even | 1 | trivial | ||
6840.2.a.w.1.2 | 2 | 12.11 | even | 2 |