Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1260,2,Mod(361,1260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1260, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1260.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1260.s (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.0611506547\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 541.2 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1260.541 |
Dual form | 1260.2.s.e.361.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(757\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.62132 | + | 2.09077i | 0.612801 | + | 0.790237i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.12132 | − | 3.67423i | −0.639602 | − | 1.10782i | −0.985520 | − | 0.169559i | \(-0.945766\pi\) |
0.345918 | − | 0.938265i | \(-0.387568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.24264 | 0.899347 | 0.449673 | − | 0.893193i | \(-0.351540\pi\) | ||||
0.449673 | + | 0.893193i | \(0.351540\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.12132 | + | 3.67423i | 0.514496 | + | 0.891133i | 0.999859 | + | 0.0168199i | \(0.00535420\pi\) |
−0.485363 | + | 0.874313i | \(0.661312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.50000 | − | 6.06218i | 0.802955 | − | 1.39076i | −0.114708 | − | 0.993399i | \(-0.536593\pi\) |
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.12132 | + | 3.67423i | −0.442326 | + | 0.766131i | −0.997862 | − | 0.0653618i | \(-0.979180\pi\) |
0.555536 | + | 0.831493i | \(0.312513\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.75736 | 0.326333 | 0.163167 | − | 0.986599i | \(-0.447829\pi\) | ||||
0.163167 | + | 0.986599i | \(0.447829\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.74264 | + | 8.21449i | 0.851803 | + | 1.47537i | 0.879579 | + | 0.475753i | \(0.157824\pi\) |
−0.0277757 | + | 0.999614i | \(0.508842\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.62132 | + | 0.358719i | −0.443084 | + | 0.0606347i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.62132 | + | 2.80821i | −0.266543 | + | 0.461667i | −0.967967 | − | 0.251078i | \(-0.919215\pi\) |
0.701423 | + | 0.712745i | \(0.252548\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.24264 | 0.662589 | 0.331295 | − | 0.943527i | \(-0.392515\pi\) | ||||
0.331295 | + | 0.943527i | \(0.392515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.24264 | 0.494498 | 0.247249 | − | 0.968952i | \(-0.420473\pi\) | ||||
0.247249 | + | 0.968952i | \(0.420473\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | + | 5.19615i | −0.437595 | + | 0.757937i | −0.997503 | − | 0.0706177i | \(-0.977503\pi\) |
0.559908 | + | 0.828554i | \(0.310836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.74264 | + | 6.77962i | −0.248949 | + | 0.968517i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.24264 | + | 7.34847i | 0.582772 | + | 1.00939i | 0.995149 | + | 0.0983769i | \(0.0313651\pi\) |
−0.412378 | + | 0.911013i | \(0.635302\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.24264 | 0.572078 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.12132 | − | 8.87039i | −0.666739 | − | 1.15483i | −0.978811 | − | 0.204767i | \(-0.934356\pi\) |
0.312072 | − | 0.950059i | \(-0.398977\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.24264 | + | 3.88437i | −0.287141 | + | 0.497342i | −0.973126 | − | 0.230273i | \(-0.926038\pi\) |
0.685985 | + | 0.727615i | \(0.259371\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.62132 | + | 2.80821i | −0.201100 | + | 0.348315i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.62132 | + | 4.54026i | 0.320245 | + | 0.554681i | 0.980539 | − | 0.196327i | \(-0.0629013\pi\) |
−0.660293 | + | 0.751008i | \(0.729568\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7279 | 1.51053 | 0.755263 | − | 0.655422i | \(-0.227509\pi\) | ||||
0.755263 | + | 0.655422i | \(0.227509\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.62132 | − | 8.00436i | −0.540885 | − | 0.936840i | −0.998854 | − | 0.0478714i | \(-0.984756\pi\) |
0.457969 | − | 0.888968i | \(-0.348577\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.24264 | − | 10.3923i | 0.483494 | − | 1.18431i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.50000 | + | 9.52628i | −0.618798 | + | 1.07179i | 0.370907 | + | 0.928670i | \(0.379047\pi\) |
−0.989705 | + | 0.143120i | \(0.954286\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.2426 | 1.12428 | 0.562138 | − | 0.827043i | \(-0.309979\pi\) | ||||
0.562138 | + | 0.827043i | \(0.309979\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.24264 | −0.460179 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.12132 | + | 8.87039i | −0.542859 | + | 0.940259i | 0.455879 | + | 0.890042i | \(0.349325\pi\) |
−0.998738 | + | 0.0502176i | \(0.984009\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.25736 | + | 6.77962i | 0.551121 | + | 0.710697i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.50000 | + | 6.06218i | 0.359092 | + | 0.621966i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.485281 | −0.0492729 | −0.0246364 | − | 0.999696i | \(-0.507843\pi\) | ||||
−0.0246364 | + | 0.999696i | \(0.507843\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.87868 | − | 6.71807i | −0.385943 | − | 0.668473i | 0.605956 | − | 0.795498i | \(-0.292791\pi\) |
−0.991900 | + | 0.127025i | \(0.959457\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.62132 | − | 14.9326i | 0.849484 | − | 1.47135i | −0.0321856 | − | 0.999482i | \(-0.510247\pi\) |
0.881670 | − | 0.471867i | \(-0.156420\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.36396 | − | 11.0227i | 0.615227 | − | 1.06561i | −0.375117 | − | 0.926977i | \(-0.622398\pi\) |
0.990345 | − | 0.138628i | \(-0.0442691\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.74264 | + | 8.21449i | 0.454263 | + | 0.786806i | 0.998645 | − | 0.0520310i | \(-0.0165695\pi\) |
−0.544383 | + | 0.838837i | \(0.683236\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.12132 | − | 3.67423i | −0.197814 | − | 0.342624i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.24264 | + | 10.3923i | −0.388922 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.50000 | + | 6.06218i | −0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.75736 | −0.244676 | −0.122338 | − | 0.992488i | \(-0.539039\pi\) | ||||
−0.122338 | + | 0.992488i | \(0.539039\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.24264 | − | 12.5446i | 0.632792 | − | 1.09603i | −0.354186 | − | 0.935175i | \(-0.615242\pi\) |
0.986978 | − | 0.160854i | \(-0.0514247\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.3492 | − | 2.51104i | 1.59108 | − | 0.217734i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.12132 | + | 3.67423i | 0.181237 | + | 0.313911i | 0.942302 | − | 0.334764i | \(-0.108657\pi\) |
−0.761065 | + | 0.648675i | \(0.775323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.4853 | −1.31344 | −0.656722 | − | 0.754133i | \(-0.728058\pi\) | ||||
−0.656722 | + | 0.754133i | \(0.728058\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.87868 | − | 11.9142i | −0.575224 | − | 0.996317i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.878680 | + | 1.52192i | −0.0729704 | + | 0.126388i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | + | 10.3923i | −0.491539 | + | 0.851371i | −0.999953 | − | 0.00974235i | \(-0.996899\pi\) |
0.508413 | + | 0.861113i | \(0.330232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.2426 | − | 19.4728i | −0.914913 | − | 1.58468i | −0.807028 | − | 0.590513i | \(-0.798926\pi\) |
−0.107885 | − | 0.994163i | \(-0.534408\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.48528 | −0.761876 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.24264 | + | 5.61642i | 0.258791 | + | 0.448239i | 0.965918 | − | 0.258847i | \(-0.0833426\pi\) |
−0.707127 | + | 0.707086i | \(0.750009\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.1213 | + | 1.52192i | −0.876483 | + | 0.119944i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | + | 6.92820i | −0.313304 | + | 0.542659i | −0.979076 | − | 0.203497i | \(-0.934769\pi\) |
0.665771 | + | 0.746156i | \(0.268103\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.7279 | −1.44921 | −0.724605 | − | 0.689164i | \(-0.757978\pi\) | ||||
−0.724605 | + | 0.689164i | \(0.757978\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.48528 | −0.191175 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.2426 | + | 17.7408i | −0.778734 | + | 1.34881i | 0.153938 | + | 0.988080i | \(0.450804\pi\) |
−0.932672 | + | 0.360726i | \(0.882529\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | − | 2.44949i | 0.0755929 | − | 0.185164i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.00000 | − | 5.19615i | −0.224231 | − | 0.388379i | 0.731858 | − | 0.681457i | \(-0.238654\pi\) |
−0.956088 | + | 0.293079i | \(0.905320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.0000 | −0.966282 | −0.483141 | − | 0.875542i | \(-0.660504\pi\) | ||||
−0.483141 | + | 0.875542i | \(0.660504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.62132 | − | 2.80821i | −0.119202 | − | 0.206464i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.00000 | − | 15.5885i | 0.658145 | − | 1.13994i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | − | 5.19615i | 0.217072 | − | 0.375980i | −0.736839 | − | 0.676068i | \(-0.763683\pi\) |
0.953912 | + | 0.300088i | \(0.0970159\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.37868 | − | 5.85204i | −0.243203 | − | 0.421239i | 0.718422 | − | 0.695607i | \(-0.244865\pi\) |
−0.961625 | + | 0.274368i | \(0.911531\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.2426 | 1.15724 | 0.578620 | − | 0.815597i | \(-0.303591\pi\) | ||||
0.578620 | + | 0.815597i | \(0.303591\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.24264 | − | 9.08052i | −0.371641 | − | 0.643701i | 0.618177 | − | 0.786039i | \(-0.287871\pi\) |
−0.989818 | + | 0.142338i | \(0.954538\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.84924 | + | 3.67423i | 0.199978 | + | 0.257881i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.12132 | + | 3.67423i | −0.148159 | + | 0.256620i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −29.6985 | −2.05429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.4853 | 1.54795 | 0.773975 | − | 0.633216i | \(-0.218265\pi\) | ||||
0.773975 | + | 0.633216i | \(0.218265\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.62132 | + | 2.80821i | −0.110573 | + | 0.191518i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.48528 | + | 23.2341i | −0.643903 | + | 1.57723i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.87868 | + | 11.9142i | 0.462710 | + | 0.801437i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.51472 | −0.503223 | −0.251611 | − | 0.967828i | \(-0.580960\pi\) | ||||
−0.251611 | + | 0.967828i | \(0.580960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.60660 | − | 13.1750i | −0.504868 | − | 0.874457i | −0.999984 | − | 0.00563010i | \(-0.998208\pi\) |
0.495116 | − | 0.868827i | \(-0.335125\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.50000 | − | 6.06218i | 0.231287 | − | 0.400600i | −0.726900 | − | 0.686743i | \(-0.759040\pi\) |
0.958187 | + | 0.286143i | \(0.0923732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.24264 | − | 12.5446i | 0.474481 | − | 0.821825i | −0.525092 | − | 0.851046i | \(-0.675969\pi\) |
0.999573 | + | 0.0292201i | \(0.00930237\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00000 | − | 5.19615i | −0.195698 | − | 0.338960i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.9706 | −0.709627 | −0.354813 | − | 0.934937i | \(-0.615456\pi\) | ||||
−0.354813 | + | 0.934937i | \(0.615456\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | + | 3.46410i | 0.128831 | + | 0.223142i | 0.923224 | − | 0.384262i | \(-0.125544\pi\) |
−0.794393 | + | 0.607404i | \(0.792211\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.00000 | − | 4.89898i | −0.319438 | − | 0.312984i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.3492 | − | 19.6575i | 0.722135 | − | 1.25077i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7279 | 1.18210 | 0.591048 | − | 0.806636i | \(-0.298714\pi\) | ||||
0.591048 | + | 0.806636i | \(0.298714\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.12132 | − | 8.87039i | 0.319459 | − | 0.553320i | −0.660916 | − | 0.750460i | \(-0.729832\pi\) |
0.980375 | + | 0.197140i | \(0.0631654\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.50000 | + | 1.16320i | −0.528164 | + | 0.0722776i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.24264 | − | 7.34847i | −0.261612 | − | 0.453126i | 0.705058 | − | 0.709150i | \(-0.250921\pi\) |
−0.966671 | + | 0.256023i | \(0.917588\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.48528 | −0.521247 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.24264 | − | 2.15232i | −0.0757651 | − | 0.131229i | 0.825654 | − | 0.564177i | \(-0.190807\pi\) |
−0.901419 | + | 0.432948i | \(0.857473\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.7279 | − | 20.3134i | 0.712421 | − | 1.23395i | −0.251525 | − | 0.967851i | \(-0.580932\pi\) |
0.963946 | − | 0.266098i | \(-0.0857344\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.12132 | + | 3.67423i | −0.127920 | + | 0.221565i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.86396 | − | 15.3528i | −0.532584 | − | 0.922462i | −0.999276 | − | 0.0380425i | \(-0.987888\pi\) |
0.466692 | − | 0.884420i | \(-0.345446\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.9706 | −1.72824 | −0.864119 | − | 0.503287i | \(-0.832124\pi\) | ||||
−0.864119 | + | 0.503287i | \(0.832124\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.8640 | − | 20.5490i | −0.705239 | − | 1.22151i | −0.966605 | − | 0.256270i | \(-0.917506\pi\) |
0.261366 | − | 0.965240i | \(-0.415827\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.87868 | + | 8.87039i | 0.406036 | + | 0.523602i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.500000 | + | 0.866025i | −0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.97056 | 0.290383 | 0.145192 | − | 0.989404i | \(-0.453620\pi\) | ||||
0.145192 | + | 0.989404i | \(0.453620\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.2426 | 0.596350 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.87868 | + | 11.9142i | −0.397804 | + | 0.689017i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.25736 | + | 6.77962i | 0.303029 | + | 0.390771i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.24264 | − | 3.88437i | −0.128413 | − | 0.222418i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.24264 | 0.185067 | 0.0925336 | − | 0.995710i | \(-0.470503\pi\) | ||||
0.0925336 | + | 0.995710i | \(0.470503\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.6066 | + | 18.3712i | 0.601445 | + | 1.04173i | 0.992602 | + | 0.121410i | \(0.0387415\pi\) |
−0.391157 | + | 0.920324i | \(0.627925\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.8640 | + | 20.5490i | −0.670591 | + | 1.16150i | 0.307146 | + | 0.951662i | \(0.400626\pi\) |
−0.977737 | + | 0.209835i | \(0.932707\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.3640 | + | 21.4150i | −0.694429 | + | 1.20279i | 0.275943 | + | 0.961174i | \(0.411010\pi\) |
−0.970373 | + | 0.241613i | \(0.922324\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.72792 | − | 6.45695i | −0.208724 | − | 0.361520i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.6985 | 1.65247 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.62132 | − | 2.80821i | −0.0899347 | − | 0.155771i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.7279 | + | 2.15232i | −0.867108 | + | 0.118661i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.50000 | + | 14.7224i | −0.467202 | + | 0.809218i | −0.999298 | − | 0.0374662i | \(-0.988071\pi\) |
0.532096 | + | 0.846684i | \(0.321405\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.24264 | −0.286436 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.7279 | −0.747808 | −0.373904 | − | 0.927467i | \(-0.621981\pi\) | ||||
−0.373904 | + | 0.927467i | \(0.621981\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.1213 | − | 34.8511i | 1.08963 | − | 1.88730i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.0000 | − | 20.7846i | −0.644194 | − | 1.11578i | −0.984487 | − | 0.175457i | \(-0.943860\pi\) |
0.340293 | − | 0.940319i | \(-0.389474\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.0000 | −0.535288 | −0.267644 | − | 0.963518i | \(-0.586245\pi\) | ||||
−0.267644 | + | 0.963518i | \(0.586245\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.12132 | − | 8.87039i | −0.272580 | − | 0.472123i | 0.696941 | − | 0.717128i | \(-0.254544\pi\) |
−0.969522 | + | 0.245005i | \(0.921210\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.36396 | + | 11.0227i | −0.337764 | + | 0.585024i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.878680 | − | 1.52192i | 0.0463749 | − | 0.0803237i | −0.841906 | − | 0.539624i | \(-0.818566\pi\) |
0.888281 | + | 0.459300i | \(0.151900\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | − | 25.9808i | −0.789474 | − | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.24264 | 0.483782 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.8640 | − | 30.9413i | −0.932491 | − | 1.61512i | −0.779048 | − | 0.626965i | \(-0.784297\pi\) |
−0.153443 | − | 0.988157i | \(-0.549036\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.48528 | + | 20.7846i | −0.440534 | + | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.86396 | + | 15.3528i | −0.458959 | + | 0.794939i | −0.998906 | − | 0.0467591i | \(-0.985111\pi\) |
0.539948 | + | 0.841699i | \(0.318444\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.69848 | 0.293487 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.4558 | −1.05075 | −0.525373 | − | 0.850872i | \(-0.676074\pi\) | ||||
−0.525373 | + | 0.850872i | \(0.676074\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.7279 | − | 22.0454i | 0.650366 | − | 1.12647i | −0.332668 | − | 0.943044i | \(-0.607949\pi\) |
0.983034 | − | 0.183424i | \(-0.0587180\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.87868 | + | 8.87039i | 0.350570 | + | 0.452077i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.6066 | − | 18.3712i | −0.537776 | − | 0.931455i | −0.999023 | − | 0.0441839i | \(-0.985931\pi\) |
0.461247 | − | 0.887272i | \(-0.347402\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | −0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.50000 | − | 9.52628i | −0.276735 | − | 0.479319i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.37868 | − | 7.58410i | 0.219760 | − | 0.380635i | −0.734975 | − | 0.678094i | \(-0.762806\pi\) |
0.954734 | + | 0.297460i | \(0.0961394\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.75736 | + | 3.04384i | −0.0877583 | + | 0.152002i | −0.906563 | − | 0.422070i | \(-0.861304\pi\) |
0.818805 | + | 0.574072i | \(0.194637\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.3787 | + | 26.6367i | 0.766067 | + | 1.32687i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.7574 | 0.681927 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.50000 | − | 14.7224i | −0.420298 | − | 0.727977i | 0.575670 | − | 0.817682i | \(-0.304741\pi\) |
−0.995968 | + | 0.0897044i | \(0.971408\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.2426 | − | 25.0892i | 0.504007 | − | 1.23456i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.12132 | + | 8.87039i | −0.251396 | + | 0.435430i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.4853 | 0.707652 | 0.353826 | − | 0.935311i | \(-0.384880\pi\) | ||||
0.353826 | + | 0.935311i | \(0.384880\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.4853 | 1.53450 | 0.767249 | − | 0.641349i | \(-0.221625\pi\) | ||||
0.767249 | + | 0.641349i | \(0.221625\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.12132 | − | 3.67423i | 0.102899 | − | 0.178227i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.7574 | + | 1.60896i | −0.568978 | + | 0.0778629i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.72792 | + | 16.8493i | 0.468578 | + | 0.811600i | 0.999355 | − | 0.0359112i | \(-0.0114333\pi\) |
−0.530777 | + | 0.847511i | \(0.678100\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.2426 | 1.59754 | 0.798770 | − | 0.601637i | \(-0.205485\pi\) | ||||
0.798770 | + | 0.601637i | \(0.205485\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.8492 | + | 25.7196i | 0.710336 | + | 1.23034i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.00000 | − | 8.66025i | 0.238637 | − | 0.413331i | −0.721686 | − | 0.692220i | \(-0.756633\pi\) |
0.960323 | + | 0.278889i | \(0.0899661\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.2426 | − | 17.7408i | 0.486643 | − | 0.842890i | −0.513240 | − | 0.858245i | \(-0.671555\pi\) |
0.999882 | + | 0.0153558i | \(0.00488809\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.12132 | − | 8.87039i | −0.242774 | − | 0.420497i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | − | 15.5885i | −0.423793 | − | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.50000 | + | 1.16320i | −0.398486 | + | 0.0545316i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.1066 | + | 27.8975i | −0.753435 | + | 1.30499i | 0.192714 | + | 0.981255i | \(0.438271\pi\) |
−0.946149 | + | 0.323733i | \(0.895062\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.7279 | −0.872246 | −0.436123 | − | 0.899887i | \(-0.643649\pi\) | ||||
−0.436123 | + | 0.899887i | \(0.643649\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.2721 | 0.477384 | 0.238692 | − | 0.971095i | \(-0.423281\pi\) | ||||
0.238692 | + | 0.971095i | \(0.423281\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.48528 | + | 9.50079i | −0.253829 | + | 0.439644i | −0.964577 | − | 0.263803i | \(-0.915023\pi\) |
0.710748 | + | 0.703447i | \(0.248357\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.24264 | + | 12.8418i | −0.242083 | + | 0.592979i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.87868 | − | 11.9142i | −0.316282 | − | 0.547817i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.00000 | −0.321182 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.00000 | + | 10.3923i | 0.274147 | + | 0.474837i | 0.969920 | − | 0.243426i | \(-0.0782712\pi\) |
−0.695773 | + | 0.718262i | \(0.744938\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.25736 | + | 9.10601i | −0.239715 | + | 0.415198i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.242641 | − | 0.420266i | 0.0110177 | − | 0.0190833i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.8640 | + | 32.6733i | 0.854808 | + | 1.48057i | 0.876823 | + | 0.480813i | \(0.159658\pi\) |
−0.0220157 | + | 0.999758i | \(0.507008\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.5147 | −0.700169 | −0.350085 | − | 0.936718i | \(-0.613847\pi\) | ||||
−0.350085 | + | 0.936718i | \(0.613847\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.72792 | + | 6.45695i | 0.167897 | + | 0.290806i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.6360 | + | 26.6112i | 0.925653 | + | 1.19367i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.74264 | + | 16.8747i | −0.436140 | + | 0.755417i | −0.997388 | − | 0.0722305i | \(-0.976988\pi\) |
0.561247 | + | 0.827648i | \(0.310322\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.4853 | 1.18092 | 0.590460 | − | 0.807067i | \(-0.298946\pi\) | ||||
0.590460 | + | 0.807067i | \(0.298946\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.75736 | 0.345198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.72792 | + | 16.8493i | −0.431183 | + | 0.746830i | −0.996975 | − | 0.0777173i | \(-0.975237\pi\) |
0.565793 | + | 0.824547i | \(0.308570\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.24264 | − | 22.6398i | 0.408870 | − | 1.00152i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.62132 | + | 14.9326i | 0.379901 | + | 0.658007i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.4558 | 1.11955 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.72792 | − | 11.6531i | −0.294756 | − | 0.510532i | 0.680172 | − | 0.733052i | \(-0.261905\pi\) |
−0.974928 | + | 0.222520i | \(0.928572\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.62132 | − | 4.54026i | 0.114622 | − | 0.198532i | −0.803006 | − | 0.595970i | \(-0.796768\pi\) |
0.917629 | + | 0.397439i | \(0.130101\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.1213 | + | 34.8511i | −0.876498 | + | 1.51814i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.50000 | + | 4.33013i | 0.108696 | + | 0.188266i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.7574 | 0.595897 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.36396 | + | 11.0227i | 0.275138 | + | 0.476553i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.6066 | − | 7.97887i | 1.23217 | − | 0.343674i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.4706 | − | 35.4561i | 0.880098 | − | 1.52437i | 0.0288675 | − | 0.999583i | \(-0.490810\pi\) |
0.851231 | − | 0.524792i | \(-0.175857\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.48528 | −0.406305 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.4558 | 1.43047 | 0.715234 | − | 0.698885i | \(-0.246320\pi\) | ||||
0.715234 | + | 0.698885i | \(0.246320\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.15076 | − | 10.6534i | 0.262031 | − | 0.453851i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.8345 | + | 3.94591i | −1.22617 | + | 0.167797i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.0000 | − | 25.9808i | −0.635570 | − | 1.10084i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) |
0.350824 | − | 0.936442i | \(-0.385902\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.5147 | 0.444725 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.00000 | − | 5.19615i | −0.126435 | − | 0.218992i | 0.795858 | − | 0.605483i | \(-0.207020\pi\) |
−0.922293 | + | 0.386492i | \(0.873687\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.00000 | + | 15.5885i | −0.378633 | + | 0.655811i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.8492 | + | 36.1119i | −0.874046 | + | 1.51389i | −0.0162699 | + | 0.999868i | \(0.505179\pi\) |
−0.857776 | + | 0.514024i | \(0.828154\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.4706 | + | 25.0637i | 0.605574 | + | 1.04889i | 0.991960 | + | 0.126548i | \(0.0403898\pi\) |
−0.386386 | + | 0.922337i | \(0.626277\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.24264 | 0.176930 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.37868 | − | 11.0482i | −0.265548 | − | 0.459942i | 0.702159 | − | 0.712020i | \(-0.252220\pi\) |
−0.967707 | + | 0.252078i | \(0.918886\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.6066 | + | 21.4150i | 0.688958 | + | 0.888444i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0000 | − | 31.1769i | 0.745484 | − | 1.29122i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −45.2132 | −1.86615 | −0.933074 | − | 0.359684i | \(-0.882885\pi\) | ||||
−0.933074 | + | 0.359684i | \(0.882885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 66.3970 | 2.73584 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.60660 | − | 2.78272i | 0.0659752 | − | 0.114272i | −0.831151 | − | 0.556047i | \(-0.812318\pi\) |
0.897126 | + | 0.441774i | \(0.145651\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.87868 | − | 8.87039i | −0.281998 | − | 0.363650i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.2426 | − | 28.1331i | −0.663656 | − | 1.14949i | −0.979648 | − | 0.200724i | \(-0.935670\pi\) |
0.315991 | − | 0.948762i | \(-0.397663\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.48528 | −0.142168 | −0.0710838 | − | 0.997470i | \(-0.522646\pi\) | ||||
−0.0710838 | + | 0.997470i | \(0.522646\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.50000 | − | 6.06218i | −0.142295 | − | 0.246463i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.6213 | − | 25.3249i | 0.593461 | − | 1.02790i | −0.400301 | − | 0.916384i | \(-0.631094\pi\) |
0.993762 | − | 0.111521i | \(-0.0355722\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.72792 | + | 16.8493i | −0.393550 | + | 0.681648i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.72792 | + | 4.72490i | 0.110180 | + | 0.190837i | 0.915843 | − | 0.401537i | \(-0.131524\pi\) |
−0.805663 | + | 0.592374i | \(0.798191\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.4853 | 1.06626 | 0.533129 | − | 0.846034i | \(-0.321016\pi\) | ||||
0.533129 | + | 0.846034i | \(0.321016\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.98528 | + | 10.3668i | 0.240569 | + | 0.416677i | 0.960876 | − | 0.276977i | \(-0.0893327\pi\) |
−0.720308 | + | 0.693655i | \(0.755999\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −26.8492 | + | 3.67423i | −1.07569 | + | 0.147205i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.7574 | −0.548542 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.37868 | − | 2.38794i | 0.0547112 | − | 0.0947626i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.65076 | + | 21.9839i | −0.223891 | + | 0.871032i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.1213 | + | 29.6550i | 0.676251 | + | 1.17130i | 0.976101 | + | 0.217316i | \(0.0697301\pi\) |
−0.299850 | + | 0.953986i | \(0.596937\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.7279 | −0.777993 | −0.388997 | − | 0.921239i | \(-0.627178\pi\) | ||||
−0.388997 | + | 0.921239i | \(0.627178\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.12132 | + | 8.87039i | 0.201340 | + | 0.348731i | 0.948960 | − | 0.315395i | \(-0.102137\pi\) |
−0.747621 | + | 0.664126i | \(0.768804\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.7279 | + | 37.6339i | −0.852896 | + | 1.47726i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.12132 | − | 8.87039i | 0.200413 | − | 0.347125i | −0.748249 | − | 0.663418i | \(-0.769105\pi\) |
0.948661 | + | 0.316293i | \(0.102438\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.24264 | + | 12.5446i | 0.282993 | + | 0.490159i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.9706 | −1.59599 | −0.797993 | − | 0.602666i | \(-0.794105\pi\) | ||||
−0.797993 | + | 0.602666i | \(0.794105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.01472 | + | 1.75754i | 0.0394680 | + | 0.0683605i | 0.885085 | − | 0.465430i | \(-0.154100\pi\) |
−0.845617 | + | 0.533791i | \(0.820767\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.00000 | + | 17.1464i | −0.271448 | + | 0.664910i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.72792 | + | 6.45695i | −0.144346 | + | 0.250014i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.0294 | 0.734623 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.7279 | 1.14593 | 0.572964 | − | 0.819581i | \(-0.305794\pi\) | ||||
0.572964 | + | 0.819581i | \(0.305794\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.36396 | − | 11.0227i | 0.244587 | − | 0.423637i | −0.717428 | − | 0.696632i | \(-0.754681\pi\) |
0.962015 | + | 0.272995i | \(0.0880143\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.786797 | − | 1.01461i | −0.0301945 | − | 0.0389372i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.6066 | + | 28.7635i | 0.635434 | + | 1.10060i | 0.986423 | + | 0.164224i | \(0.0525121\pi\) |
−0.350989 | + | 0.936380i | \(0.614155\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.24264 | −0.162103 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.7574 | + | 23.8284i | 0.524114 | + | 0.907791i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.4706 | + | 23.3317i | −0.512444 | + | 0.887580i | 0.487452 | + | 0.873150i | \(0.337927\pi\) |
−0.999896 | + | 0.0144296i | \(0.995407\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.74264 | − | 13.4106i | 0.293695 | − | 0.508695i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | + | 15.5885i | 0.340899 | + | 0.590455i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.78680 | −0.331873 | −0.165936 | − | 0.986136i | \(-0.553065\pi\) | ||||
−0.165936 | + | 0.986136i | \(0.553065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.3492 | + | 19.6575i | 0.428045 | + | 0.741395i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.75736 | − | 19.0016i | 0.291746 | − | 0.714628i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.2426 | − | 31.5972i | 0.685117 | − | 1.18666i | −0.288283 | − | 0.957545i | \(-0.593085\pi\) |
0.973400 | − | 0.229112i | \(-0.0735822\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −40.2426 | −1.50710 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.7574 | 0.514496 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.2426 | − | 22.9369i | 0.493867 | − | 0.855403i | −0.506108 | − | 0.862470i | \(-0.668916\pi\) |
0.999975 | + | 0.00706717i | \(0.00224957\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45.1985 | − | 6.18527i | 1.68328 | − | 0.230352i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.878680 | − | 1.52192i | −0.0326333 | − | 0.0565226i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.757359 | 0.0280889 | 0.0140445 | − | 0.999901i | \(-0.495529\pi\) | ||||
0.0140445 | + | 0.999901i | \(0.495529\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.87868 | + | 11.9142i | 0.254417 | + | 0.440663i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.893398 | + | 1.54741i | −0.0329984 | + | 0.0571549i | −0.882053 | − | 0.471150i | \(-0.843839\pi\) |
0.849055 | + | 0.528305i | \(0.177172\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.1213 | − | 19.2627i | 0.409659 | − | 0.709550i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.74264 | + | 13.4106i | 0.284818 | + | 0.493319i | 0.972565 | − | 0.232632i | \(-0.0747336\pi\) |
−0.687747 | + | 0.725950i | \(0.741400\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.2132 | −0.558118 | −0.279059 | − | 0.960274i | \(-0.590023\pi\) | ||||
−0.279059 | + | 0.960274i | \(0.590023\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.00000 | − | 10.3923i | −0.219823 | − | 0.380745i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.3640 | − | 4.56575i | 1.21909 | − | 0.166829i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.4706 | + | 38.9202i | −0.819962 | + | 1.42022i | 0.0857467 | + | 0.996317i | \(0.472672\pi\) |
−0.905709 | + | 0.423900i | \(0.860661\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.4853 | 0.818323 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.02944 | 0.328180 | 0.164090 | − | 0.986445i | \(-0.447531\pi\) | ||||
0.164090 | + | 0.986445i | \(0.447531\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.1213 | − | 40.0473i | 0.838147 | − | 1.45171i | −0.0532948 | − | 0.998579i | \(-0.516972\pi\) |
0.891442 | − | 0.453135i | \(-0.149694\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.48528 | + | 23.2341i | −0.343390 | + | 0.841131i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.6066 | − | 28.7635i | −0.599630 | − | 1.03859i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.00000 | 0.180305 | 0.0901523 | − | 0.995928i | \(-0.471265\pi\) | ||||
0.0901523 | + | 0.995928i | \(0.471265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.84924 | + | 10.1312i | 0.210383 | + | 0.364393i | 0.951834 | − | 0.306613i | \(-0.0991957\pi\) |
−0.741452 | + | 0.671006i | \(0.765862\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.74264 | − | 8.21449i | 0.170361 | − | 0.295073i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.8492 | − | 25.7196i | 0.532029 | − | 0.921502i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.0000 | − | 46.7654i | −0.966136 | − | 1.67340i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.48528 | −0.231470 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.2426 | − | 24.6690i | −0.507695 | − | 0.879354i | −0.999960 | − | 0.00890869i | \(-0.997164\pi\) |
0.492265 | − | 0.870445i | \(-0.336169\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.1838 | + | 37.6339i | 1.03766 | + | 1.33811i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.27208 | + | 12.5956i | −0.258239 | + | 0.447283i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.7574 | 1.12490 | 0.562452 | − | 0.826830i | \(-0.309858\pi\) | ||||
0.562452 | + | 0.826830i | \(0.309858\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.4558 | −0.900563 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.6066 | + | 33.9596i | −0.691902 | + | 1.19841i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.24264 | − | 10.3923i | 0.149533 | − | 0.366281i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.9706 | + | 24.1977i | 0.491179 | + | 0.850747i | 0.999948 | − | 0.0101560i | \(-0.00323282\pi\) |
−0.508770 | + | 0.860903i | \(0.669899\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.9411 | 0.419310 | 0.209655 | − | 0.977775i | \(-0.432766\pi\) | ||||
0.209655 | + | 0.977775i | \(0.432766\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.00000 | − | 6.92820i | −0.140114 | − | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.3492 | − | 19.6575i | 0.397060 | − | 0.687728i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.84924 | − | 4.93503i | 0.0994392 | − | 0.172234i | −0.812013 | − | 0.583639i | \(-0.801628\pi\) |
0.911453 | + | 0.411405i | \(0.134962\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.4853 | + | 33.7495i | 0.679214 | + | 1.17643i | 0.975218 | + | 0.221247i | \(0.0710126\pi\) |
−0.296004 | + | 0.955187i | \(0.595654\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43.4558 | −1.51111 | −0.755554 | − | 0.655087i | \(-0.772632\pi\) | ||||
−0.755554 | + | 0.655087i | \(0.772632\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.50000 | − | 9.52628i | −0.191023 | − | 0.330861i | 0.754567 | − | 0.656223i | \(-0.227847\pi\) |
−0.945589 | + | 0.325362i | \(0.894514\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.6066 | + | 7.97887i | −0.991160 | + | 0.276451i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.36396 | − | 16.2189i | 0.324053 | − | 0.561277i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.7574 | −0.889243 | −0.444621 | − | 0.895719i | \(-0.646662\pi\) | ||||
−0.444621 | + | 0.895719i | \(0.646662\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.9117 | −0.893506 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.24264 | − | 2.15232i | 0.0427481 | − | 0.0740419i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.3492 | + | 2.51104i | −0.630487 | + | 0.0862802i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.87868 | − | 11.9142i | −0.235798 | − | 0.408414i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.7279 | −0.880907 | −0.440454 | − | 0.897775i | \(-0.645182\pi\) | ||||
−0.440454 | + | 0.897775i | \(0.645182\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.12132 | + | 3.67423i | 0.0724629 | + | 0.125509i | 0.899980 | − | 0.435931i | \(-0.143581\pi\) |
−0.827517 | + | 0.561440i | \(0.810247\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0000 | − | 19.0526i | 0.375315 | − | 0.650065i | −0.615059 | − | 0.788481i | \(-0.710868\pi\) |
0.990374 | + | 0.138416i | \(0.0442012\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.7574 | + | 18.6323i | −0.366185 | + | 0.634251i | −0.988966 | − | 0.148146i | \(-0.952670\pi\) |
0.622781 | + | 0.782396i | \(0.286003\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.2426 | − | 17.7408i | −0.348260 | − | 0.603204i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46.6690 | 1.58314 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.50000 | + | 14.7224i | 0.288012 | + | 0.498851i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.62132 | + | 2.09077i | 0.0548106 | + | 0.0706809i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.00000 | − | 8.66025i | 0.168838 | − | 0.292436i | −0.769174 | − | 0.639040i | \(-0.779332\pi\) |
0.938012 | + | 0.346604i | \(0.112665\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.9706 | −1.38033 | −0.690167 | − | 0.723650i | \(-0.742463\pi\) | ||||
−0.690167 | + | 0.723650i | \(0.742463\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.72792 | 0.192760 | 0.0963800 | − | 0.995345i | \(-0.469274\pi\) | ||||
0.0963800 | + | 0.995345i | \(0.469274\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.60660 | − | 13.1750i | 0.255405 | − | 0.442374i | −0.709601 | − | 0.704604i | \(-0.751125\pi\) |
0.965005 | + | 0.262230i | \(0.0844580\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.47056 | − | 5.76500i | −0.149938 | − | 0.193352i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.0000 | + | 36.3731i | 0.702738 | + | 1.21718i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.00000 | 0.200558 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.33452 | + | 14.4358i | 0.277972 | + | 0.481462i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.0000 | + | 31.1769i | −0.599667 | + | 1.03865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.50000 | − | 11.2583i | 0.216067 | − | 0.374240i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.1360 | + | 26.2164i | 0.502584 | + | 0.870501i | 0.999996 | + | 0.00298623i | \(0.000950549\pi\) |
−0.497412 | + | 0.867515i | \(0.665716\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.2132 | −1.69677 | −0.848385 | − | 0.529380i | \(-0.822424\pi\) | ||||
−0.848385 | + | 0.529380i | \(0.822424\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.7279 | − | 37.6339i | −0.719089 | − | 1.24550i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 37.9706 | − | 5.19615i | 1.25390 | − | 0.171592i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.9853 | + | 29.4194i | −0.560293 | + | 0.970455i | 0.437178 | + | 0.899375i | \(0.355978\pi\) |
−0.997471 | + | 0.0710804i | \(0.977355\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.2721 | 1.35849 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.24264 | 0.106617 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.3640 | − | 31.8073i | 0.602502 | − | 1.04356i | −0.389939 | − | 0.920841i | \(-0.627504\pi\) |
0.992441 | − | 0.122723i | \(-0.0391628\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.0000 | + | 34.2929i | 1.14708 | + | 1.12390i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.00000 | + | 15.5885i | 0.294331 | + | 0.509797i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.6985 | −0.610853 | −0.305426 | − | 0.952216i | \(-0.598799\pi\) | ||||
−0.305426 | + | 0.952216i | \(0.598799\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.8492 | − | 41.3081i | −0.777463 | − | 1.34661i | −0.933400 | − | 0.358838i | \(-0.883173\pi\) |
0.155937 | − | 0.987767i | \(-0.450160\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.00000 | + | 15.5885i | −0.293080 | + | 0.507630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.60660 | + | 2.78272i | −0.0522075 | + | 0.0904261i | −0.890948 | − | 0.454105i | \(-0.849959\pi\) |
0.838741 | + | 0.544531i | \(0.183292\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.9853 | − | 25.9553i | −0.486443 | − | 0.842544i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.5147 | 0.891289 | 0.445645 | − | 0.895210i | \(-0.352975\pi\) | ||||
0.445645 | + | 0.895210i | \(0.352975\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.00000 | + | 5.19615i | 0.0970777 | + | 0.168144i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.24264 | + | 10.3923i | −0.137002 | + | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4853 | + | 51.0700i | −0.951138 | + | 1.64742i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.75736 | 0.217527 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.2426 | −1.13333 | −0.566663 | − | 0.823949i | \(-0.691766\pi\) | ||||
−0.566663 | + | 0.823949i | \(0.691766\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.4853 | − | 45.8739i | 0.849953 | − | 1.47216i | −0.0312961 | − | 0.999510i | \(-0.509963\pi\) |
0.881249 | − | 0.472652i | \(-0.156703\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.1066 | − | 32.3762i | −0.804881 | − | 1.03793i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.39340 | − | 7.60959i | −0.140557 | − | 0.243452i | 0.787149 | − | 0.616762i | \(-0.211556\pi\) |
−0.927707 | + | 0.373310i | \(0.878223\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43.4558 | 1.38885 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.8492 | − | 36.1119i | −0.664988 | − | 1.15179i | −0.979289 | − | 0.202469i | \(-0.935103\pi\) |
0.314301 | − | 0.949323i | \(-0.398230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.12132 | + | 14.0665i | −0.258767 | + | 0.448197i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.87868 | + | 11.9142i | −0.218729 | + | 0.378850i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.47056 | − | 12.9394i | −0.237310 | − | 0.411033i | 0.722631 | − | 0.691234i | \(-0.242932\pi\) |
−0.959942 | + | 0.280200i | \(0.909599\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.4853 | 0.332406 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.8640 | + | 22.2810i | 0.407406 | + | 0.705647i | 0.994598 | − | 0.103800i | \(-0.0331002\pi\) |
−0.587192 | + | 0.809447i | \(0.699767\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1260.2.s.e.541.2 | 4 | ||
3.2 | odd | 2 | 420.2.q.d.121.2 | ✓ | 4 | ||
7.2 | even | 3 | 8820.2.a.bk.1.2 | 2 | |||
7.4 | even | 3 | inner | 1260.2.s.e.361.2 | 4 | ||
7.5 | odd | 6 | 8820.2.a.bf.1.2 | 2 | |||
12.11 | even | 2 | 1680.2.bg.t.961.1 | 4 | |||
15.2 | even | 4 | 2100.2.bc.f.1549.1 | 8 | |||
15.8 | even | 4 | 2100.2.bc.f.1549.4 | 8 | |||
15.14 | odd | 2 | 2100.2.q.k.1801.1 | 4 | |||
21.2 | odd | 6 | 2940.2.a.r.1.1 | 2 | |||
21.5 | even | 6 | 2940.2.a.p.1.1 | 2 | |||
21.11 | odd | 6 | 420.2.q.d.361.2 | yes | 4 | ||
21.17 | even | 6 | 2940.2.q.q.361.2 | 4 | |||
21.20 | even | 2 | 2940.2.q.q.961.2 | 4 | |||
84.11 | even | 6 | 1680.2.bg.t.1201.1 | 4 | |||
105.32 | even | 12 | 2100.2.bc.f.949.4 | 8 | |||
105.53 | even | 12 | 2100.2.bc.f.949.1 | 8 | |||
105.74 | odd | 6 | 2100.2.q.k.1201.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.q.d.121.2 | ✓ | 4 | 3.2 | odd | 2 | ||
420.2.q.d.361.2 | yes | 4 | 21.11 | odd | 6 | ||
1260.2.s.e.361.2 | 4 | 7.4 | even | 3 | inner | ||
1260.2.s.e.541.2 | 4 | 1.1 | even | 1 | trivial | ||
1680.2.bg.t.961.1 | 4 | 12.11 | even | 2 | |||
1680.2.bg.t.1201.1 | 4 | 84.11 | even | 6 | |||
2100.2.q.k.1201.1 | 4 | 105.74 | odd | 6 | |||
2100.2.q.k.1801.1 | 4 | 15.14 | odd | 2 | |||
2100.2.bc.f.949.1 | 8 | 105.53 | even | 12 | |||
2100.2.bc.f.949.4 | 8 | 105.32 | even | 12 | |||
2100.2.bc.f.1549.1 | 8 | 15.2 | even | 4 | |||
2100.2.bc.f.1549.4 | 8 | 15.8 | even | 4 | |||
2940.2.a.p.1.1 | 2 | 21.5 | even | 6 | |||
2940.2.a.r.1.1 | 2 | 21.2 | odd | 6 | |||
2940.2.q.q.361.2 | 4 | 21.17 | even | 6 | |||
2940.2.q.q.961.2 | 4 | 21.20 | even | 2 | |||
8820.2.a.bf.1.2 | 2 | 7.5 | odd | 6 | |||
8820.2.a.bk.1.2 | 2 | 7.2 | even | 3 |