Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 836) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 | ||||||||
\(3\) | 2.41421 | 1.39385 | 0.696923 | − | 0.717146i | \(-0.254552\pi\) | ||||
0.696923 | + | 0.717146i | \(0.254552\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | −0.223607 | − | 0.974679i | \(-0.571783\pi\) | ||||
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | −0.534522 | −0.267261 | − | 0.963624i | \(-0.586119\pi\) | ||||
−0.267261 | + | 0.963624i | \(0.586119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.41421 | −0.392232 | −0.196116 | − | 0.980581i | \(-0.562833\pi\) | ||||
−0.196116 | + | 0.980581i | \(0.562833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.41421 | −0.623347 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.41421 | 0.342997 | 0.171499 | − | 0.985184i | \(-0.445139\pi\) | ||||
0.171499 | + | 0.985184i | \(0.445139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.41421 | −0.745042 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.65685 | −0.971021 | −0.485511 | − | 0.874231i | \(-0.661366\pi\) | ||||
−0.485511 | + | 0.874231i | \(0.661366\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.414214 | −0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.24264 | −1.53062 | −0.765310 | − | 0.643662i | \(-0.777414\pi\) | ||||
−0.765310 | + | 0.643662i | \(0.777414\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.24264 | −0.582395 | −0.291198 | − | 0.956663i | \(-0.594054\pi\) | ||||
−0.291198 | + | 0.956663i | \(0.594054\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.41421 | −0.420261 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.41421 | 0.239046 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.41421 | −1.38329 | −0.691644 | − | 0.722238i | \(-0.743113\pi\) | ||||
−0.691644 | + | 0.722238i | \(0.743113\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.41421 | −0.546712 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.00000 | −0.624695 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000 | 0.914991 | 0.457496 | − | 0.889212i | \(-0.348747\pi\) | ||||
0.457496 | + | 0.889212i | \(0.348747\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.82843 | −0.421637 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.48528 | 0.945976 | 0.472988 | − | 0.881069i | \(-0.343175\pi\) | ||||
0.472988 | + | 0.881069i | \(0.343175\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.41421 | 0.478086 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.17157 | 0.160928 | 0.0804640 | − | 0.996758i | \(-0.474360\pi\) | ||||
0.0804640 | + | 0.996758i | \(0.474360\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.41421 | 0.319770 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.24264 | 0.942912 | 0.471456 | − | 0.881890i | \(-0.343729\pi\) | ||||
0.471456 | + | 0.881890i | \(0.343729\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.41421 | −0.437145 | −0.218573 | − | 0.975821i | \(-0.570140\pi\) | ||||
−0.218573 | + | 0.975821i | \(0.570140\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.00000 | −0.503953 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.41421 | 0.175412 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.72792 | 1.18845 | 0.594227 | − | 0.804297i | \(-0.297458\pi\) | ||||
0.594227 | + | 0.804297i | \(0.297458\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.2426 | −1.35345 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.24264 | −0.147474 | −0.0737372 | − | 0.997278i | \(-0.523493\pi\) | ||||
−0.0737372 | + | 0.997278i | \(0.523493\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.485281 | 0.0567979 | 0.0283989 | − | 0.999597i | \(-0.490959\pi\) | ||||
0.0283989 | + | 0.999597i | \(0.490959\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.65685 | −1.11508 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.41421 | 0.161165 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7279 | 1.20699 | 0.603493 | − | 0.797368i | \(-0.293775\pi\) | ||||
0.603493 | + | 0.797368i | \(0.293775\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.5563 | −1.70753 | −0.853766 | − | 0.520658i | \(-0.825687\pi\) | ||||
−0.853766 | + | 0.520658i | \(0.825687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.41421 | −0.153393 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −19.8995 | −2.13345 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.41421 | 0.255906 | 0.127953 | − | 0.991780i | \(-0.459159\pi\) | ||||
0.127953 | + | 0.991780i | \(0.459159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.82843 | −0.811770 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.58579 | 0.161012 | 0.0805061 | − | 0.996754i | \(-0.474346\pi\) | ||||
0.0805061 | + | 0.996754i | \(0.474346\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.82843 | −0.284268 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.8995 | 1.38305 | 0.691526 | − | 0.722352i | \(-0.256939\pi\) | ||||
0.691526 | + | 0.722352i | \(0.256939\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.41421 | 0.333193 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.31371 | 0.513696 | 0.256848 | − | 0.966452i | \(-0.417316\pi\) | ||||
0.256848 | + | 0.966452i | \(0.417316\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.3137 | −1.92809 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.414214 | −0.0389659 | −0.0194830 | − | 0.999810i | \(-0.506202\pi\) | ||||
−0.0194830 | + | 0.999810i | \(0.506202\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.65685 | 0.434254 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.00000 | −0.369800 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.65685 | −0.870729 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.07107 | −0.627456 | −0.313728 | − | 0.949513i | \(-0.601578\pi\) | ||||
−0.313728 | + | 0.949513i | \(0.601578\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.4853 | 1.27536 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.17157 | −0.277102 | −0.138551 | − | 0.990355i | \(-0.544244\pi\) | ||||
−0.138551 | + | 0.990355i | \(0.544244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.41421 | −0.122628 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.414214 | 0.0356498 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.6569 | −1.25222 | −0.626110 | − | 0.779735i | \(-0.715354\pi\) | ||||
−0.626110 | + | 0.779735i | \(0.715354\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.75736 | 0.318695 | 0.159348 | − | 0.987223i | \(-0.449061\pi\) | ||||
0.159348 | + | 0.987223i | \(0.449061\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.6569 | 1.31854 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.41421 | 0.118262 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.24264 | 0.684514 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.0711 | −0.995605 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.31371 | −0.107623 | −0.0538116 | − | 0.998551i | \(-0.517137\pi\) | ||||
−0.0538116 | + | 0.998551i | \(0.517137\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.4853 | 0.853280 | 0.426640 | − | 0.904422i | \(-0.359697\pi\) | ||||
0.426640 | + | 0.904422i | \(0.359697\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.24264 | 0.260455 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.6569 | −1.01013 | −0.505063 | − | 0.863082i | \(-0.668531\pi\) | ||||
−0.505063 | + | 0.863082i | \(0.668531\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.82843 | 0.224309 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.58579 | 0.519033 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.4853 | −1.76118 | −0.880592 | − | 0.473876i | \(-0.842854\pi\) | ||||
−0.880592 | + | 0.473876i | \(0.842854\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.41421 | 0.187946 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.7574 | −1.21934 | −0.609671 | − | 0.792655i | \(-0.708698\pi\) | ||||
−0.609671 | + | 0.792655i | \(0.708698\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.82843 | 0.216295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.75736 | −0.133610 | −0.0668048 | − | 0.997766i | \(-0.521280\pi\) | ||||
−0.0668048 | + | 0.997766i | \(0.521280\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.65685 | 0.427618 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.4853 | 1.31427 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.58579 | 0.417501 | 0.208751 | − | 0.977969i | \(-0.433060\pi\) | ||||
0.208751 | + | 0.977969i | \(0.433060\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.5858 | −1.00982 | −0.504912 | − | 0.863171i | \(-0.668475\pi\) | ||||
−0.504912 | + | 0.863171i | \(0.668475\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.24264 | −0.609314 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.41421 | 0.618625 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.41421 | −0.103418 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.585786 | 0.0426097 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.0000 | −0.795932 | −0.397966 | − | 0.917400i | \(-0.630284\pi\) | ||||
−0.397966 | + | 0.917400i | \(0.630284\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.1421 | 1.01797 | 0.508987 | − | 0.860774i | \(-0.330020\pi\) | ||||
0.508987 | + | 0.860774i | \(0.330020\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.41421 | 0.244497 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.41421 | −0.670735 | −0.335367 | − | 0.942087i | \(-0.608860\pi\) | ||||
−0.335367 | + | 0.942087i | \(0.608860\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.51472 | −0.107376 | −0.0536878 | − | 0.998558i | \(-0.517098\pi\) | ||||
−0.0536878 | + | 0.998558i | \(0.517098\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.4853 | 1.65652 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.6569 | 0.818151 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | 0.279372 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.1716 | −0.915488 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.75736 | 0.258667 | 0.129334 | − | 0.991601i | \(-0.458716\pi\) | ||||
0.129334 | + | 0.991601i | \(0.458716\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.00000 | −0.205557 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.00000 | −0.409197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.58579 | 0.311303 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.17157 | 0.0791676 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.00000 | −0.134535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.24264 | −0.0832134 | −0.0416067 | − | 0.999134i | \(-0.513248\pi\) | ||||
−0.0416067 | + | 0.999134i | \(0.513248\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.3137 | −0.754247 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.5858 | 0.835348 | 0.417674 | − | 0.908597i | \(-0.362845\pi\) | ||||
0.417674 | + | 0.908597i | \(0.362845\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.656854 | −0.0434062 | −0.0217031 | − | 0.999764i | \(-0.506909\pi\) | ||||
−0.0217031 | + | 0.999764i | \(0.506909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.41421 | 0.224639 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.7279 | 0.964858 | 0.482429 | − | 0.875935i | \(-0.339755\pi\) | ||||
0.482429 | + | 0.875935i | \(0.339755\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.48528 | −0.423053 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.8995 | 1.68235 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.65685 | 0.236542 | 0.118271 | − | 0.992981i | \(-0.462265\pi\) | ||||
0.118271 | + | 0.992981i | \(0.462265\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.3137 | −1.24411 | −0.622053 | − | 0.782975i | \(-0.713701\pi\) | ||||
−0.622053 | + | 0.782975i | \(0.713701\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.6569 | −1.38929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.00000 | 0.319438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.41421 | −0.0899843 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −37.5563 | −2.38004 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.3137 | 0.650996 | 0.325498 | − | 0.945543i | \(-0.394468\pi\) | ||||
0.325498 | + | 0.945543i | \(0.394468\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.65685 | 0.292774 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.41421 | −0.213806 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.51472 | 0.343999 | 0.171999 | − | 0.985097i | \(-0.444977\pi\) | ||||
0.171999 | + | 0.985097i | \(0.444977\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.8995 | 0.739399 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −23.3137 | −1.44308 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.1421 | 0.995367 | 0.497683 | − | 0.867359i | \(-0.334184\pi\) | ||||
0.497683 | + | 0.867359i | \(0.334184\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.17157 | −0.0719691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.82843 | 0.356694 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.6274 | −1.50156 | −0.750780 | − | 0.660552i | \(-0.770322\pi\) | ||||
−0.750780 | + | 0.660552i | \(0.770322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.4853 | 1.24439 | 0.622196 | − | 0.782861i | \(-0.286241\pi\) | ||||
0.622196 | + | 0.782861i | \(0.286241\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.82843 | 0.292230 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.00000 | 0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.1421 | 1.45056 | 0.725280 | − | 0.688454i | \(-0.241710\pi\) | ||||
0.725280 | + | 0.688454i | \(0.241710\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.17157 | −0.549088 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.9706 | 1.13169 | 0.565844 | − | 0.824512i | \(-0.308550\pi\) | ||||
0.565844 | + | 0.824512i | \(0.308550\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.24264 | 0.133311 | 0.0666556 | − | 0.997776i | \(-0.478767\pi\) | ||||
0.0666556 | + | 0.997776i | \(0.478767\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.41421 | −0.143006 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.65685 | 0.333914 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0000 | −0.882353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.82843 | 0.224426 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.5563 | 0.908812 | 0.454406 | − | 0.890795i | \(-0.349852\pi\) | ||||
0.454406 | + | 0.890795i | \(0.349852\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.24264 | −0.421683 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.414214 | 0.0240351 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.58579 | 0.380866 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.48528 | −0.489083 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 33.5563 | 1.92776 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.41421 | 0.195497 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.07107 | 0.175275 | 0.0876375 | − | 0.996152i | \(-0.472068\pi\) | ||||
0.0876375 | + | 0.996152i | \(0.472068\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.3137 | −1.09872 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.3137 | −1.20859 | −0.604295 | − | 0.796761i | \(-0.706545\pi\) | ||||
−0.604295 | + | 0.796761i | \(0.706545\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.6274 | 1.44855 | 0.724274 | − | 0.689513i | \(-0.242175\pi\) | ||||
0.724274 | + | 0.689513i | \(0.242175\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.00000 | 0.225374 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.75736 | 0.154869 | 0.0774344 | − | 0.996997i | \(-0.475327\pi\) | ||||
0.0774344 | + | 0.996997i | \(0.475327\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.24264 | 0.461499 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.8284 | 0.716013 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.41421 | 0.0786889 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.65685 | 0.313786 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −33.7990 | −1.86909 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.17157 | −0.505645 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.10051 | 0.0604892 | 0.0302446 | − | 0.999543i | \(-0.490371\pi\) | ||||
0.0302446 | + | 0.999543i | \(0.490371\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −23.7990 | −1.30418 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.72792 | −0.531493 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.38478 | 0.238854 | 0.119427 | − | 0.992843i | \(-0.461894\pi\) | ||||
0.119427 | + | 0.992843i | \(0.461894\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.00000 | −0.0543125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.24264 | 0.175599 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.2426 | 0.605283 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.4142 | 1.47167 | 0.735836 | − | 0.677160i | \(-0.236789\pi\) | ||||
0.735836 | + | 0.677160i | \(0.236789\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.44365 | −0.237863 | −0.118932 | − | 0.992902i | \(-0.537947\pi\) | ||||
−0.118932 | + | 0.992902i | \(0.537947\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.585786 | 0.0312670 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.68629 | 0.409100 | 0.204550 | − | 0.978856i | \(-0.434427\pi\) | ||||
0.204550 | + | 0.978856i | \(0.434427\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.24264 | 0.0659525 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.82843 | −0.255547 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.14214 | −0.113058 | −0.0565288 | − | 0.998401i | \(-0.518003\pi\) | ||||
−0.0565288 | + | 0.998401i | \(0.518003\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.41421 | 0.126713 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.485281 | −0.0254008 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.14214 | 0.372816 | 0.186408 | − | 0.982472i | \(-0.440315\pi\) | ||||
0.186408 | + | 0.982472i | \(0.440315\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.3137 | −0.588968 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.65685 | −0.0860196 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.3137 | −1.31069 | −0.655347 | − | 0.755328i | \(-0.727478\pi\) | ||||
−0.655347 | + | 0.755328i | \(0.727478\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.7279 | 1.12203 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.6569 | 0.600359 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.4142 | 1.76774 | 0.883870 | − | 0.467733i | \(-0.154929\pi\) | ||||
0.883870 | + | 0.467733i | \(0.154929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.0711 | −0.874577 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.2426 | −0.881058 | −0.440529 | − | 0.897738i | \(-0.645209\pi\) | ||||
−0.440529 | + | 0.897738i | \(0.645209\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.41421 | −0.0720750 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.9706 | 0.862662 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.9706 | 1.62097 | 0.810486 | − | 0.585758i | \(-0.199203\pi\) | ||||
0.810486 | + | 0.585758i | \(0.199203\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.58579 | −0.333058 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.65685 | −0.386237 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.7279 | −0.539780 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.31371 | 0.266687 | 0.133344 | − | 0.991070i | \(-0.457429\pi\) | ||||
0.133344 | + | 0.991070i | \(0.457429\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.41421 | −0.170924 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.2843 | 0.913073 | 0.456536 | − | 0.889705i | \(-0.349090\pi\) | ||||
0.456536 | + | 0.889705i | \(0.349090\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.58579 | 0.228434 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.48528 | 0.471327 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.41421 | 0.417077 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.07107 | 0.448535 | 0.224268 | − | 0.974528i | \(-0.428001\pi\) | ||||
0.224268 | + | 0.974528i | \(0.428001\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −35.3848 | −1.74540 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.2426 | −0.504007 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.5563 | 0.763631 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.07107 | 0.444212 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.1127 | −1.61766 | −0.808831 | − | 0.588042i | \(-0.799899\pi\) | ||||
−0.808831 | + | 0.588042i | \(0.799899\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.1127 | 1.41887 | 0.709433 | − | 0.704773i | \(-0.248951\pi\) | ||||
0.709433 | + | 0.704773i | \(0.248951\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.3431 | 0.891874 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.65685 | −0.274398 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.82843 | 0.233664 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.41421 | 0.164840 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.7990 | 1.82071 | 0.910357 | − | 0.413825i | \(-0.135807\pi\) | ||||
0.910357 | + | 0.413825i | \(0.135807\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.6985 | −1.66750 | −0.833751 | − | 0.552140i | \(-0.813811\pi\) | ||||
−0.833751 | + | 0.552140i | \(0.813811\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.8995 | 0.954108 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.65685 | −0.222768 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.8701 | −1.09153 | −0.545764 | − | 0.837939i | \(-0.683761\pi\) | ||||
−0.545764 | + | 0.837939i | \(0.683761\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.1421 | −0.673435 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.3137 | 0.585042 | 0.292521 | − | 0.956259i | \(-0.405506\pi\) | ||||
0.292521 | + | 0.956259i | \(0.405506\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.41421 | −0.114445 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.17157 | −0.150010 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.8701 | −0.560183 | −0.280091 | − | 0.959973i | \(-0.590365\pi\) | ||||
−0.280091 | + | 0.959973i | \(0.590365\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.3137 | 1.18934 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00000 | −0.0937614 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.384776 | −0.0179991 | −0.00899954 | − | 0.999960i | \(-0.502865\pi\) | ||||
−0.00899954 | + | 0.999960i | \(0.502865\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.585786 | −0.0273422 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.9706 | 0.604099 | 0.302050 | − | 0.953292i | \(-0.402329\pi\) | ||||
0.302050 | + | 0.953292i | \(0.402329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.7990 | −1.15251 | −0.576253 | − | 0.817271i | \(-0.695486\pi\) | ||||
−0.576253 | + | 0.817271i | \(0.695486\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.82843 | 0.363035 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −37.6274 | −1.74119 | −0.870595 | − | 0.492001i | \(-0.836266\pi\) | ||||
−0.870595 | + | 0.492001i | \(0.836266\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.7574 | −0.635256 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −30.5563 | −1.40796 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.00000 | −0.275880 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.31371 | 0.151724 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.7574 | 0.811354 | 0.405677 | − | 0.914016i | \(-0.367036\pi\) | ||||
0.405677 | + | 0.914016i | \(0.367036\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.8995 | 0.542570 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.8995 | 0.723452 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.58579 | −0.0720069 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.8995 | −0.856418 | −0.428209 | − | 0.903680i | \(-0.640855\pi\) | ||||
−0.428209 | + | 0.903680i | \(0.640855\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −54.2843 | −2.45482 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.7279 | 0.845179 | 0.422590 | − | 0.906321i | \(-0.361121\pi\) | ||||
0.422590 | + | 0.906321i | \(0.361121\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.6569 | −0.524998 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.82843 | 0.127128 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.75736 | 0.0788283 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.3431 | 0.552555 | 0.276278 | − | 0.961078i | \(-0.410899\pi\) | ||||
0.276278 | + | 0.961078i | \(0.410899\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −38.0416 | −1.69957 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.48528 | 0.289164 | 0.144582 | − | 0.989493i | \(-0.453816\pi\) | ||||
0.144582 | + | 0.989493i | \(0.453816\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.8995 | −0.618519 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −26.5563 | −1.17941 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.2426 | 1.20751 | 0.603754 | − | 0.797170i | \(-0.293671\pi\) | ||||
0.603754 | + | 0.797170i | \(0.293671\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.686292 | −0.0303597 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.414214 | −0.0182880 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | 0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.48528 | −0.285222 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.24264 | −0.186231 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.92893 | −0.0845081 | −0.0422540 | − | 0.999107i | \(-0.513454\pi\) | ||||
−0.0422540 | + | 0.999107i | \(0.513454\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0000 | 0.699631 | 0.349816 | − | 0.936819i | \(-0.386244\pi\) | ||||
0.349816 | + | 0.936819i | \(0.386244\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.6569 | 0.596034 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.58579 | −0.199760 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.31371 | −0.0571178 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.4853 | 0.888985 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.65685 | 0.245026 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.31371 | −0.229732 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.4853 | 0.581933 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.00000 | 0.215365 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.38478 | −0.188516 | −0.0942581 | − | 0.995548i | \(-0.530048\pi\) | ||||
−0.0942581 | + | 0.995548i | \(0.530048\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −32.7990 | −1.40754 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.0000 | 0.599694 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.6985 | −1.26982 | −0.634908 | − | 0.772588i | \(-0.718962\pi\) | ||||
−0.634908 | + | 0.772588i | \(0.718962\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.65685 | −0.412144 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.24264 | −0.351148 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.1716 | −0.645161 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 20.3137 | 0.862269 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.3137 | −0.564120 | −0.282060 | − | 0.959397i | \(-0.591018\pi\) | ||||
−0.282060 | + | 0.959397i | \(0.591018\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.48528 | −0.358889 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.41421 | −0.144148 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.75736 | 0.326934 | 0.163467 | − | 0.986549i | \(-0.447732\pi\) | ||||
0.163467 | + | 0.986549i | \(0.447732\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.414214 | 0.0174261 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.4142 | 0.563344 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.2426 | −1.18399 | −0.591997 | − | 0.805941i | \(-0.701660\pi\) | ||||
−0.591997 | + | 0.805941i | \(0.701660\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.8995 | −0.665373 | −0.332687 | − | 0.943037i | \(-0.607955\pi\) | ||||
−0.332687 | + | 0.943037i | \(0.607955\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.5563 | −1.10941 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.6274 | 0.776817 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.0000 | −1.12402 | −0.562012 | − | 0.827129i | \(-0.689973\pi\) | ||||
−0.562012 | + | 0.827129i | \(0.689973\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 34.1421 | 1.41890 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.0000 | 0.912714 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.17157 | −0.0485216 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.00000 | 0.165380 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.62742 | 0.190994 | 0.0954970 | − | 0.995430i | \(-0.469556\pi\) | ||||
0.0954970 | + | 0.995430i | \(0.469556\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.24264 | −0.133611 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.7279 | −0.934902 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.0000 | −0.821302 | −0.410651 | − | 0.911793i | \(-0.634698\pi\) | ||||
−0.410651 | + | 0.911793i | \(0.634698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.00000 | 0.0819920 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.65685 | −0.149665 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.3137 | −1.52460 | −0.762298 | − | 0.647226i | \(-0.775929\pi\) | ||||
−0.762298 | + | 0.647226i | \(0.775929\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −47.6985 | −1.94566 | −0.972831 | − | 0.231517i | \(-0.925631\pi\) | ||||
−0.972831 | + | 0.231517i | \(0.925631\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.5147 | 1.12049 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.5858 | 0.510841 | 0.255421 | − | 0.966830i | \(-0.417786\pi\) | ||||
0.255421 | + | 0.966830i | \(0.417786\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 28.1421 | 1.14038 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.17157 | −0.371042 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.3848 | −0.823333 | −0.411667 | − | 0.911334i | \(-0.635053\pi\) | ||||
−0.411667 | + | 0.911334i | \(0.635053\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.65685 | 0.389402 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.4853 | 1.14677 | 0.573387 | − | 0.819285i | \(-0.305629\pi\) | ||||
0.573387 | + | 0.819285i | \(0.305629\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.14214 | 0.206680 | 0.103340 | − | 0.994646i | \(-0.467047\pi\) | ||||
0.103340 | + | 0.994646i | \(0.467047\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.92893 | 0.0774054 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.41421 | −0.136788 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.41421 | −0.0964144 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.8995 | −0.474464 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.3137 | −1.12715 | −0.563575 | − | 0.826065i | \(-0.690575\pi\) | ||||
−0.563575 | + | 0.826065i | \(0.690575\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.07107 | 0.360543 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.07107 | 0.280607 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.07107 | 0.280166 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.51472 | −0.139040 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.04163 | 0.199132 | 0.0995662 | − | 0.995031i | \(-0.468254\pi\) | ||||
0.0995662 | + | 0.995031i | \(0.468254\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.9411 | −1.53569 | −0.767844 | − | 0.640637i | \(-0.778670\pi\) | ||||
−0.767844 | + | 0.640637i | \(0.778670\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.4853 | −0.570357 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.6274 | 0.850261 | 0.425131 | − | 0.905132i | \(-0.360228\pi\) | ||||
0.425131 | + | 0.905132i | \(0.360228\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.24264 | −0.284299 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.0711 | 0.433909 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.1716 | 0.789375 | 0.394687 | − | 0.918815i | \(-0.370853\pi\) | ||||
0.394687 | + | 0.918815i | \(0.370853\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.17157 | 0.123924 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.37258 | 0.0535496 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.5147 | 0.838094 | 0.419047 | − | 0.907964i | \(-0.362364\pi\) | ||||
0.419047 | + | 0.907964i | \(0.362364\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0416 | −0.662843 | −0.331421 | − | 0.943483i | \(-0.607528\pi\) | ||||
−0.331421 | + | 0.943483i | \(0.607528\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.82843 | −0.187521 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.41421 | 0.0548408 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.3848 | 1.48626 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.00000 | −0.115987 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.41421 | 0.131804 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.8284 | 0.494500 | 0.247250 | − | 0.968952i | \(-0.420473\pi\) | ||||
0.247250 | + | 0.968952i | \(0.420473\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.65685 | 0.0637723 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.6274 | 1.56144 | 0.780719 | − | 0.624882i | \(-0.214853\pi\) | ||||
0.780719 | + | 0.624882i | \(0.214853\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.24264 | −0.0860647 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30.3848 | 1.16435 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.8284 | 0.567394 | 0.283697 | − | 0.958914i | \(-0.408439\pi\) | ||||
0.283697 | + | 0.958914i | \(0.408439\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.6569 | 0.560010 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.58579 | −0.0605015 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.65685 | −0.0631211 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.5980 | 1.69659 | 0.848294 | − | 0.529526i | \(-0.177630\pi\) | ||||
0.848294 | + | 0.529526i | \(0.177630\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.00000 | 0.151947 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.75736 | −0.142525 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.65685 | −0.214269 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 35.5563 | 1.34486 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.6274 | 1.23232 | 0.616160 | − | 0.787621i | \(-0.288687\pi\) | ||||
0.616160 | + | 0.787621i | \(0.288687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.41421 | −0.317348 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.6569 | −0.589671 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.6569 | −0.739272 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.68629 | −0.213553 | −0.106777 | − | 0.994283i | \(-0.534053\pi\) | ||||
−0.106777 | + | 0.994283i | \(0.534053\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 30.3431 | 1.13796 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.1005 | 0.565518 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.41421 | −0.0528886 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.82843 | 0.329704 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.6274 | −1.03033 | −0.515164 | − | 0.857091i | \(-0.672269\pi\) | ||||
−0.515164 | + | 0.857091i | \(0.672269\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.3137 | 0.421345 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −46.6274 | −1.73409 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.9706 | 1.22450 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.4853 | −0.722669 | −0.361335 | − | 0.932436i | \(-0.617679\pi\) | ||||
−0.361335 | + | 0.932436i | \(0.617679\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.48528 | 0.313839 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.7574 | 1.09911 | 0.549557 | − | 0.835457i | \(-0.314797\pi\) | ||||
0.549557 | + | 0.835457i | \(0.314797\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.0711 | 0.445248 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.72792 | −0.358333 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.3848 | −1.55915 | −0.779575 | − | 0.626309i | \(-0.784565\pi\) | ||||
−0.779575 | + | 0.626309i | \(0.784565\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.41421 | −0.125424 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.928932 | −0.0340792 | −0.0170396 | − | 0.999855i | \(-0.505424\pi\) | ||||
−0.0170396 | + | 0.999855i | \(0.505424\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.31371 | 0.0481306 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −44.0000 | −1.60988 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.51472 | −0.274582 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.4142 | −0.598963 | −0.299482 | − | 0.954102i | \(-0.596814\pi\) | ||||
−0.299482 | + | 0.954102i | \(0.596814\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.8995 | 0.907388 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.4853 | −0.381598 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.65685 | −0.0602194 | −0.0301097 | − | 0.999547i | \(-0.509586\pi\) | ||||
−0.0301097 | + | 0.999547i | \(0.509586\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.2426 | 0.408082 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.8284 | 0.392530 | 0.196265 | − | 0.980551i | \(-0.437119\pi\) | ||||
0.196265 | + | 0.980551i | \(0.437119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.7990 | 0.716772 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.00000 | −0.144620 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.2426 | −0.369840 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.4558 | −0.485230 | −0.242615 | − | 0.970123i | \(-0.578005\pi\) | ||||
−0.242615 | + | 0.970123i | \(0.578005\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.3137 | 0.479481 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 50.2843 | 1.80860 | 0.904300 | − | 0.426898i | \(-0.140394\pi\) | ||||
0.904300 | + | 0.426898i | \(0.140394\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.9706 | 0.465916 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 28.7279 | 1.03061 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.00000 | −0.143315 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.24264 | 0.0444652 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.41421 | 0.122014 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.6569 | 0.451742 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.9706 | 0.747520 | 0.373760 | − | 0.927525i | \(-0.378068\pi\) | ||||
0.373760 | + | 0.927525i | \(0.378068\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 38.9706 | 1.38739 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.585786 | 0.0208282 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.82843 | 0.171462 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.82843 | −0.100314 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.8995 | 0.669454 | 0.334727 | − | 0.942315i | \(-0.391356\pi\) | ||||
0.334727 | + | 0.942315i | \(0.391356\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.17157 | 0.324467 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.82843 | 0.241271 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.485281 | −0.0171252 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.58579 | −0.232118 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −59.4558 | −2.09294 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.7990 | −1.53989 | −0.769945 | − | 0.638110i | \(-0.779717\pi\) | ||||
−0.769945 | + | 0.638110i | \(0.779717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.2132 | −1.09604 | −0.548022 | − | 0.836464i | \(-0.684619\pi\) | ||||
−0.548022 | + | 0.836464i | \(0.684619\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 49.4558 | 1.73449 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.4853 | 0.787625 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.00000 | 0.209913 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.65685 | 0.197666 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.3848 | 0.641633 | 0.320817 | − | 0.947141i | \(-0.396043\pi\) | ||||
0.320817 | + | 0.947141i | \(0.396043\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.3137 | 0.847523 | 0.423761 | − | 0.905774i | \(-0.360710\pi\) | ||||
0.423761 | + | 0.905774i | \(0.360710\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.65685 | 0.336209 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.0416 | −1.39238 | −0.696192 | − | 0.717856i | \(-0.745124\pi\) | ||||
−0.696192 | + | 0.717856i | \(0.745124\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.3553 | 0.706970 | 0.353485 | − | 0.935440i | \(-0.384997\pi\) | ||||
0.353485 | + | 0.935440i | \(0.384997\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 58.2843 | 2.02186 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.07107 | −0.244998 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.7574 | 0.545306 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.34315 | 0.0464259 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.0711 | −1.38341 | −0.691703 | − | 0.722182i | \(-0.743139\pi\) | ||||
−0.691703 | + | 0.722182i | \(0.743139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.9411 | 1.34280 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 45.7990 | 1.57740 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.0000 | 0.378412 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.41421 | −0.0485930 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.41421 | 0.185815 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.1838 | 1.34320 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.6569 | 1.08391 | 0.541955 | − | 0.840407i | \(-0.317684\pi\) | ||||
0.541955 | + | 0.840407i | \(0.317684\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.82843 | −0.0967302 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −50.6690 | −1.73082 | −0.865411 | − | 0.501063i | \(-0.832943\pi\) | ||||
−0.865411 | + | 0.501063i | \(0.832943\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.6569 | −1.59191 | −0.795956 | − | 0.605355i | \(-0.793031\pi\) | ||||
−0.795956 | + | 0.605355i | \(0.793031\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.6569 | 0.465424 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.3137 | −0.929769 | −0.464885 | − | 0.885371i | \(-0.653904\pi\) | ||||
−0.464885 | + | 0.885371i | \(0.653904\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.75736 | 0.0597520 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −36.2132 | −1.22986 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.7279 | −0.363920 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.7574 | −0.466150 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.48528 | 0.151804 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.7279 | −0.430282 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.1716 | 0.849984 | 0.424992 | − | 0.905197i | \(-0.360277\pi\) | ||||
0.424992 | + | 0.905197i | \(0.360277\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 37.5563 | 1.26674 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.5147 | 0.691158 | 0.345579 | − | 0.938390i | \(-0.387682\pi\) | ||||
0.345579 | + | 0.938390i | \(0.387682\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.4558 | 1.46241 | 0.731203 | − | 0.682160i | \(-0.238959\pi\) | ||||
0.731203 | + | 0.682160i | \(0.238959\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.4853 | −0.587761 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.0000 | −0.738688 | −0.369344 | − | 0.929293i | \(-0.620418\pi\) | ||||
−0.369344 | + | 0.929293i | \(0.620418\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.0000 | 0.335389 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.48528 | 0.317769 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.48528 | 0.217022 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.58579 | −0.186712 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.8995 | 0.530869 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.7279 | 0.891426 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.65685 | 0.0551978 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.4853 | −0.681707 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.5858 | 0.451607 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.4558 | −0.845247 | −0.422624 | − | 0.906305i | \(-0.638891\pi\) | ||||
−0.422624 | + | 0.906305i | \(0.638891\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 39.3137 | 1.30395 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.2010 | 0.404237 | 0.202119 | − | 0.979361i | \(-0.435217\pi\) | ||||
0.202119 | + | 0.979361i | \(0.435217\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.5563 | 0.514840 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.24264 | 0.272493 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.48528 | 0.148117 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.0122 | −1.22092 | −0.610460 | − | 0.792047i | \(-0.709015\pi\) | ||||
−0.610460 | + | 0.792047i | \(0.709015\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.41421 | 0.244307 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.75736 | 0.0578442 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.6569 | 1.10663 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.6274 | −0.743182 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.6274 | −0.479910 | −0.239955 | − | 0.970784i | \(-0.577133\pi\) | ||||
−0.239955 | + | 0.970784i | \(0.577133\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.00000 | −0.163868 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −51.4558 | −1.68459 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.41421 | 0.0462497 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.07107 | 0.165665 | 0.0828323 | − | 0.996564i | \(-0.473603\pi\) | ||||
0.0828323 | + | 0.996564i | \(0.473603\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 61.8701 | 2.01905 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.3553 | −0.565768 | −0.282884 | − | 0.959154i | \(-0.591291\pi\) | ||||
−0.282884 | + | 0.959154i | \(0.591291\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.6274 | 0.606592 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.585786 | −0.0190556 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.3137 | 0.400142 | 0.200071 | − | 0.979781i | \(-0.435883\pi\) | ||||
0.200071 | + | 0.979781i | \(0.435883\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.686292 | −0.0222780 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.65685 | 0.215863 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.61522 | −0.246681 | −0.123341 | − | 0.992364i | \(-0.539361\pi\) | ||||
−0.123341 | + | 0.992364i | \(0.539361\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.0000 | 0.355952 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.8995 | 0.643259 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.7279 | 0.669340 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.4853 | −0.660816 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.0294 | 0.484317 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.1421 | −0.455251 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.3848 | −0.912793 | −0.456396 | − | 0.889777i | \(-0.650860\pi\) | ||||
−0.456396 | + | 0.889777i | \(0.650860\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.41421 | 0.109680 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.5563 | −0.402952 | −0.201476 | − | 0.979493i | \(-0.564574\pi\) | ||||
−0.201476 | + | 0.979493i | \(0.564574\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.31371 | −0.170350 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.6569 | 0.437369 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.78680 | 0.121150 | 0.0605752 | − | 0.998164i | \(-0.480707\pi\) | ||||
0.0605752 | + | 0.998164i | \(0.480707\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.41421 | −0.0771586 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.5980 | −1.26427 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 55.3848 | 1.76650 | 0.883250 | − | 0.468902i | \(-0.155350\pi\) | ||||
0.883250 | + | 0.468902i | \(0.155350\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.41421 | 0.299962 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.1421 | −0.704792 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.9411 | −0.888476 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.3431 | −0.455625 | −0.227813 | − | 0.973705i | \(-0.573157\pi\) | ||||
−0.227813 | + | 0.973705i | \(0.573157\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.65685 | 0.0843127 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.51472 | 0.0480198 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.24264 | 0.261047 | 0.130524 | − | 0.991445i | \(-0.458334\pi\) | ||||
0.130524 | + | 0.991445i | \(0.458334\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.48528 | 0.110269 |
(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 | 3344.2.a.m.1.2 | 2 | ||
4.3 | odd | 2 | 836.2.a.c.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 7524.2.a.h.1.2 | 2 | |||
44.43 | even | 2 | 9196.2.a.h.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
836.2.a.c.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
3344.2.a.m.1.2 | 2 | 1.1 | even | 1 | trivial | ||
7524.2.a.h.1.2 | 2 | 12.11 | even | 2 | |||
9196.2.a.h.1.1 | 2 | 44.43 | even | 2 |