Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6840,2,Mod(1,6840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6840.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6840 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6840.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: | \(54.6176749826\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1772.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 12x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.32803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6840.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.20191 | 1.21021 | 0.605104 | − | 0.796146i | \(-0.293131\pi\) | ||||
0.605104 | + | 0.796146i | \(0.293131\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.20191 | −1.56844 | −0.784218 | − | 0.620486i | \(-0.786935\pi\) | ||||
−0.784218 | + | 0.620486i | \(0.786935\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.45415 | 1.51271 | 0.756355 | − | 0.654162i | \(-0.226978\pi\) | ||||
0.756355 | + | 0.654162i | \(0.226978\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.65606 | 1.80491 | 0.902457 | − | 0.430780i | \(-0.141762\pi\) | ||||
0.902457 | + | 0.430780i | \(0.141762\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.20191 | 0.594580 | 0.297290 | − | 0.954787i | \(-0.403917\pi\) | ||||
0.297290 | + | 0.954787i | \(0.403917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.20191 | −0.541222 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.8580 | −1.94944 | −0.974719 | − | 0.223432i | \(-0.928274\pi\) | ||||
−0.974719 | + | 0.223432i | \(0.928274\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.85797 | 1.53956 | 0.769778 | − | 0.638311i | \(-0.220367\pi\) | ||||
0.769778 | + | 0.638311i | \(0.220367\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.45415 | −0.526753 | −0.263377 | − | 0.964693i | \(-0.584836\pi\) | ||||
−0.263377 | + | 0.964693i | \(0.584836\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.65606 | −1.26262 | −0.631308 | − | 0.775532i | \(-0.717482\pi\) | ||||
−0.631308 | + | 0.775532i | \(0.717482\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.25224 | 0.464606 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.6561 | 1.46372 | 0.731861 | − | 0.681454i | \(-0.238652\pi\) | ||||
0.731861 | + | 0.681454i | \(0.238652\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.20191 | 0.701426 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.0599 | 1.70025 | 0.850126 | − | 0.526579i | \(-0.176526\pi\) | ||||
0.850126 | + | 0.526579i | \(0.176526\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.74776 | 0.479852 | 0.239926 | − | 0.970791i | \(-0.422877\pi\) | ||||
0.239926 | + | 0.970791i | \(0.422877\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.45415 | −0.676504 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.90830 | −0.819865 | −0.409932 | − | 0.912116i | \(-0.634448\pi\) | ||||
−0.409932 | + | 0.912116i | \(0.634448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.6561 | −1.89813 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.15158 | −0.692107 | −0.346054 | − | 0.938215i | \(-0.612478\pi\) | ||||
−0.346054 | + | 0.938215i | \(0.612478\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.40382 | 0.922439 | 0.461220 | − | 0.887286i | \(-0.347412\pi\) | ||||
0.461220 | + | 0.887286i | \(0.347412\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.8580 | −1.46894 | −0.734471 | − | 0.678640i | \(-0.762570\pi\) | ||||
−0.734471 | + | 0.678640i | \(0.762570\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.4637 | 1.83069 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.142026 | 0.0144205 | 0.00721026 | − | 0.999974i | \(-0.497705\pi\) | ||||
0.00721026 | + | 0.999974i | \(0.497705\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.40382 | −0.438197 | −0.219098 | − | 0.975703i | \(-0.570312\pi\) | ||||
−0.219098 | + | 0.975703i | \(0.570312\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.8076 | −1.26197 | −0.630987 | − | 0.775793i | \(-0.717350\pi\) | ||||
−0.630987 | + | 0.775793i | \(0.717350\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.8076 | 1.23816 | 0.619081 | − | 0.785327i | \(-0.287505\pi\) | ||||
0.619081 | + | 0.785327i | \(0.287505\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.0599 | 1.44248 | 0.721238 | − | 0.692688i | \(-0.243574\pi\) | ||||
0.721238 | + | 0.692688i | \(0.243574\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.05989 | −0.475994 | −0.237997 | − | 0.971266i | \(-0.576491\pi\) | ||||
−0.237997 | + | 0.971266i | \(0.576491\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.65606 | −0.807182 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.8076 | −1.17408 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.0599 | 1.45999 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.49552 | 0.310177 | 0.155089 | − | 0.987901i | \(-0.450434\pi\) | ||||
0.155089 | + | 0.987901i | \(0.450434\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.6057 | 1.36348 | 0.681740 | − | 0.731595i | \(-0.261224\pi\) | ||||
0.681740 | + | 0.731595i | \(0.261224\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.20191 | 0.277641 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.656063 | 0.0560512 | 0.0280256 | − | 0.999607i | \(-0.491078\pi\) | ||||
0.0280256 | + | 0.999607i | \(0.491078\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.40382 | 0.543165 | 0.271583 | − | 0.962415i | \(-0.412453\pi\) | ||||
0.271583 | + | 0.962415i | \(0.412453\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −28.3720 | −2.37259 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.20191 | −0.265904 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.3121 | 1.90980 | 0.954902 | − | 0.296922i | \(-0.0959600\pi\) | ||||
0.954902 | + | 0.296922i | \(0.0959600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.3121 | −1.89711 | −0.948557 | − | 0.316607i | \(-0.897456\pi\) | ||||
−0.948557 | + | 0.316607i | \(0.897456\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | 0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.25224 | 0.498983 | 0.249491 | − | 0.968377i | \(-0.419737\pi\) | ||||
0.249491 | + | 0.968377i | \(0.419737\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 27.7159 | 2.18432 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.85797 | 0.772136 | 0.386068 | − | 0.922470i | \(-0.373833\pi\) | ||||
0.386068 | + | 0.922470i | \(0.373833\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.25224 | 0.483813 | 0.241906 | − | 0.970300i | \(-0.422227\pi\) | ||||
0.241906 | + | 0.970300i | \(0.422227\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.7478 | 1.28829 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.05989 | −0.688810 | −0.344405 | − | 0.938821i | \(-0.611919\pi\) | ||||
−0.344405 | + | 0.938821i | \(0.611919\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.20191 | 0.242042 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.25224 | 0.317827 | 0.158914 | − | 0.987292i | \(-0.449201\pi\) | ||||
0.158914 | + | 0.987292i | \(0.449201\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.5554 | 1.37921 | 0.689606 | − | 0.724184i | \(-0.257784\pi\) | ||||
0.689606 | + | 0.724184i | \(0.257784\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.8580 | 0.871816 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.8076 | 1.52161 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.5140 | 1.62906 | 0.814529 | − | 0.580122i | \(-0.196995\pi\) | ||||
0.814529 | + | 0.580122i | \(0.196995\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.7573 | −1.27820 | −0.639100 | − | 0.769124i | \(-0.720693\pi\) | ||||
−0.639100 | + | 0.769124i | \(0.720693\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.4637 | −1.10174 | −0.550872 | − | 0.834590i | \(-0.685705\pi\) | ||||
−0.550872 | + | 0.834590i | \(0.685705\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.90830 | 0.206164 | 0.103082 | − | 0.994673i | \(-0.467130\pi\) | ||||
0.103082 | + | 0.994673i | \(0.467130\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.2522 | 0.719566 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.85797 | −0.688511 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.20191 | −0.359824 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.49552 | −0.240642 | −0.120321 | − | 0.992735i | \(-0.538392\pi\) | ||||
−0.120321 | + | 0.992735i | \(0.538392\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.45415 | 0.235571 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.40382 | −0.434720 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.8166 | −1.46754 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.504478 | 0.0337823 | 0.0168912 | − | 0.999857i | \(-0.494623\pi\) | ||||
0.0168912 | + | 0.999857i | \(0.494623\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.5644 | −1.29853 | −0.649266 | − | 0.760561i | \(-0.724924\pi\) | ||||
−0.649266 | + | 0.760561i | \(0.724924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.7478 | 1.04064 | 0.520321 | − | 0.853971i | \(-0.325812\pi\) | ||||
0.520321 | + | 0.853971i | \(0.325812\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.1605 | 1.12422 | 0.562112 | − | 0.827061i | \(-0.309989\pi\) | ||||
0.562112 | + | 0.827061i | \(0.309989\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.65606 | 0.564659 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.7064 | 1.14533 | 0.572666 | − | 0.819789i | \(-0.305909\pi\) | ||||
0.572666 | + | 0.819789i | \(0.305909\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.8166 | 1.53416 | 0.767081 | − | 0.641550i | \(-0.221708\pi\) | ||||
0.767081 | + | 0.641550i | \(0.221708\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.25224 | −0.207778 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.45415 | 0.347039 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.10126 | −0.448227 | −0.224114 | − | 0.974563i | \(-0.571949\pi\) | ||||
−0.224114 | + | 0.974563i | \(0.571949\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −45.0281 | −2.83089 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.5644 | −1.34515 | −0.672574 | − | 0.740030i | \(-0.734811\pi\) | ||||
−0.672574 | + | 0.740030i | \(0.734811\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −37.9682 | −2.35923 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.25224 | −0.385530 | −0.192765 | − | 0.981245i | \(-0.561745\pi\) | ||||
−0.192765 | + | 0.981245i | \(0.561745\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.6561 | −0.654597 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.5140 | −1.00688 | −0.503439 | − | 0.864031i | \(-0.667932\pi\) | ||||
−0.503439 | + | 0.864031i | \(0.667932\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.4038 | −1.36094 | −0.680468 | − | 0.732778i | \(-0.738223\pi\) | ||||
−0.680468 | + | 0.732778i | \(0.738223\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.20191 | −0.313687 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.34394 | 0.441254 | 0.220627 | − | 0.975358i | \(-0.429190\pi\) | ||||
0.220627 | + | 0.975358i | \(0.429190\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.85797 | 0.110837 | 0.0554187 | − | 0.998463i | \(-0.482351\pi\) | ||||
0.0554187 | + | 0.998463i | \(0.482351\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.05033 | 0.0624355 | 0.0312177 | − | 0.999513i | \(-0.490061\pi\) | ||||
0.0312177 | + | 0.999513i | \(0.490061\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 31.5644 | 1.86319 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.7478 | 0.919994 | 0.459997 | − | 0.887920i | \(-0.347850\pi\) | ||||
0.459997 | + | 0.887920i | \(0.347850\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.0599 | −0.760376 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 47.2115 | 2.73031 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.0599 | −0.637481 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.74776 | −0.214596 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.5962 | 1.00427 | 0.502133 | − | 0.864790i | \(-0.332549\pi\) | ||||
0.502133 | + | 0.864790i | \(0.332549\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.51404 | −0.369377 | −0.184689 | − | 0.982797i | \(-0.559128\pi\) | ||||
−0.184689 | + | 0.982797i | \(0.559128\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.2115 | 1.65113 | 0.825565 | − | 0.564307i | \(-0.190857\pi\) | ||||
0.825565 | + | 0.564307i | \(0.190857\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.4727 | 1.59918 | 0.799592 | − | 0.600543i | \(-0.205049\pi\) | ||||
0.799592 | + | 0.600543i | \(0.205049\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.6561 | −0.932560 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.00000 | −0.222566 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.45415 | 0.302542 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.7159 | −1.52803 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.9682 | 1.20748 | 0.603740 | − | 0.797181i | \(-0.293676\pi\) | ||||
0.603740 | + | 0.797181i | \(0.293676\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.3535 | 0.618464 | 0.309232 | − | 0.950987i | \(-0.399928\pi\) | ||||
0.309232 | + | 0.950987i | \(0.399928\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.4038 | 0.563399 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | −0.647939 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.2115 | −1.13869 | −0.569346 | − | 0.822098i | \(-0.692803\pi\) | ||||
−0.569346 | + | 0.822098i | \(0.692803\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.3121 | −0.605524 | −0.302762 | − | 0.953066i | \(-0.597909\pi\) | ||||
−0.302762 | + | 0.953066i | \(0.597909\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.4637 | −0.716601 | −0.358300 | − | 0.933606i | \(-0.616644\pi\) | ||||
−0.358300 | + | 0.933606i | \(0.616644\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.90830 | 0.366655 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.88979 | 0.205295 | 0.102648 | − | 0.994718i | \(-0.467269\pi\) | ||||
0.102648 | + | 0.994718i | \(0.467269\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.5140 | 0.862026 | 0.431013 | − | 0.902346i | \(-0.358156\pi\) | ||||
0.431013 | + | 0.902346i | \(0.358156\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 34.1198 | 1.77141 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.45415 | 0.489517 | 0.244759 | − | 0.969584i | \(-0.421291\pi\) | ||||
0.244759 | + | 0.969584i | \(0.421291\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.4637 | 0.899427 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.46371 | 0.280652 | 0.140326 | − | 0.990105i | \(-0.455185\pi\) | ||||
0.140326 | + | 0.990105i | \(0.455185\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.1198 | 1.13027 | 0.565134 | − | 0.824999i | \(-0.308825\pi\) | ||||
0.565134 | + | 0.824999i | \(0.308825\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.6561 | 0.848872 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.0000 | 0.709828 | 0.354914 | − | 0.934899i | \(-0.384510\pi\) | ||||
0.354914 | + | 0.934899i | \(0.384510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −34.6243 | −1.75102 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.15158 | 0.309520 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.1605 | 1.66428 | 0.832140 | − | 0.554566i | \(-0.187116\pi\) | ||||
0.832140 | + | 0.554566i | \(0.187116\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.0694 | 1.85116 | 0.925580 | − | 0.378552i | \(-0.123578\pi\) | ||||
0.925580 | + | 0.378552i | \(0.123578\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.9083 | −0.543381 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 61.6841 | 3.05757 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.5962 | 0.771181 | 0.385591 | − | 0.922670i | \(-0.373998\pi\) | ||||
0.385591 | + | 0.922670i | \(0.373998\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 41.8166 | 2.05766 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.40382 | −0.412527 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.70639 | −0.278775 | −0.139388 | − | 0.990238i | \(-0.544513\pi\) | ||||
−0.139388 | + | 0.990238i | \(0.544513\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.64711 | 0.177749 | 0.0888745 | − | 0.996043i | \(-0.471673\pi\) | ||||
0.0888745 | + | 0.996043i | \(0.471673\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.00000 | −0.194029 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0000 | 0.580721 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −40.5236 | −1.95195 | −0.975976 | − | 0.217876i | \(-0.930087\pi\) | ||||
−0.975976 | + | 0.217876i | \(0.930087\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.14203 | −0.391281 | −0.195640 | − | 0.980676i | \(-0.562679\pi\) | ||||
−0.195640 | + | 0.980676i | \(0.562679\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.65606 | 0.414076 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.1516 | −1.43906 | −0.719528 | − | 0.694463i | \(-0.755642\pi\) | ||||
−0.719528 | + | 0.694463i | \(0.755642\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.6243 | −1.16993 | −0.584967 | − | 0.811057i | \(-0.698892\pi\) | ||||
−0.584967 | + | 0.811057i | \(0.698892\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.8580 | 0.656931 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.545849 | 0.0257602 | 0.0128801 | − | 0.999917i | \(-0.495900\pi\) | ||||
0.0128801 | + | 0.999917i | \(0.495900\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −51.2803 | −2.41470 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.4637 | −0.818711 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.2204 | 1.60076 | 0.800382 | − | 0.599490i | \(-0.204630\pi\) | ||||
0.800382 | + | 0.599490i | \(0.204630\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.687875 | 0.0320375 | 0.0160188 | − | 0.999872i | \(-0.494901\pi\) | ||||
0.0160188 | + | 0.999872i | \(0.494901\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.79809 | −0.222986 | −0.111493 | − | 0.993765i | \(-0.535563\pi\) | ||||
−0.111493 | + | 0.993765i | \(0.535563\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.0090 | −0.509434 | −0.254717 | − | 0.967016i | \(-0.581982\pi\) | ||||
−0.254717 | + | 0.967016i | \(0.581982\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.8076 | 0.591402 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.9682 | 0.826178 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.7981 | 1.22444 | 0.612218 | − | 0.790689i | \(-0.290278\pi\) | ||||
0.612218 | + | 0.790689i | \(0.290278\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −64.6752 | −2.94893 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.142026 | −0.00644905 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.7070 | 0.847695 | 0.423847 | − | 0.905734i | \(-0.360679\pi\) | ||||
0.423847 | + | 0.905734i | \(0.360679\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.1102 | −0.546526 | −0.273263 | − | 0.961939i | \(-0.588103\pi\) | ||||
−0.273263 | + | 0.961939i | \(0.588103\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.8076 | −0.576827 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.1198 | −0.992207 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.59618 | −0.0714547 | −0.0357273 | − | 0.999362i | \(-0.511375\pi\) | ||||
−0.0357273 | + | 0.999362i | \(0.511375\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.55541 | −0.113940 | −0.0569700 | − | 0.998376i | \(-0.518144\pi\) | ||||
−0.0569700 | + | 0.998376i | \(0.518144\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.40382 | 0.195968 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.210868 | −0.00934655 | −0.00467328 | − | 0.999989i | \(-0.501488\pi\) | ||||
−0.00467328 | + | 0.999989i | \(0.501488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.2115 | 0.849865 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.8076 | 0.564372 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.0281 | 1.98033 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.04137 | 0.352299 | 0.176149 | − | 0.984363i | \(-0.443636\pi\) | ||||
0.176149 | + | 0.984363i | \(0.443636\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.39487 | 0.235901 | 0.117951 | − | 0.993019i | \(-0.462368\pi\) | ||||
0.117951 | + | 0.993019i | \(0.462368\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.00000 | 0.348485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 51.9274 | 2.25771 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 53.7669 | 2.32890 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.8076 | −0.553723 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.9179 | −0.728704 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.0599 | −0.645095 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.59618 | 0.410303 | 0.205151 | − | 0.978730i | \(-0.434231\pi\) | ||||
0.205151 | + | 0.978730i | \(0.434231\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.20191 | 0.136406 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.6968 | −0.837594 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.00000 | −0.254228 | −0.127114 | − | 0.991888i | \(-0.540571\pi\) | ||||
−0.127114 | + | 0.991888i | \(0.540571\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.8395 | −0.796824 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.2522 | −1.61214 | −0.806070 | − | 0.591820i | \(-0.798409\pi\) | ||||
−0.806070 | + | 0.591820i | \(0.798409\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.05989 | 0.212871 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.5458 | 0.693638 | 0.346819 | − | 0.937932i | \(-0.387262\pi\) | ||||
0.346819 | + | 0.937932i | \(0.387262\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.7159 | −1.32727 | −0.663636 | − | 0.748056i | \(-0.730987\pi\) | ||||
−0.663636 | + | 0.748056i | \(0.730987\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.65606 | 0.360983 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.7070 | 0.862043 | 0.431022 | − | 0.902342i | \(-0.358153\pi\) | ||||
0.431022 | + | 0.902342i | \(0.358153\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.9083 | 1.11634 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −55.4319 | −2.29575 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.3121 | 0.466901 | 0.233451 | − | 0.972369i | \(-0.424998\pi\) | ||||
0.233451 | + | 0.972369i | \(0.424998\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | −0.0824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.9592 | 1.02495 | 0.512476 | − | 0.858701i | \(-0.328728\pi\) | ||||
0.512476 | + | 0.858701i | \(0.328728\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.8076 | 0.525062 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.4229 | 1.73335 | 0.866677 | − | 0.498869i | \(-0.166251\pi\) | ||||
0.866677 | + | 0.498869i | \(0.166251\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.9083 | 0.689704 | 0.344852 | − | 0.938657i | \(-0.387929\pi\) | ||||
0.344852 | + | 0.938657i | \(0.387929\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.0599 | −0.652927 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.39487 | −0.0566159 | −0.0283080 | − | 0.999599i | \(-0.509012\pi\) | ||||
−0.0283080 | + | 0.999599i | \(0.509012\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −47.2115 | −1.90997 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.8765 | 1.48943 | 0.744714 | − | 0.667384i | \(-0.232586\pi\) | ||||
0.744714 | + | 0.667384i | \(0.232586\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.3032 | −0.656341 | −0.328170 | − | 0.944619i | \(-0.606432\pi\) | ||||
−0.328170 | + | 0.944619i | \(0.606432\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.5236 | −1.46801 | −0.734004 | − | 0.679146i | \(-0.762351\pi\) | ||||
−0.734004 | + | 0.679146i | \(0.762351\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −44.3720 | −1.77773 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 47.4319 | 1.89123 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.6243 | 0.422945 | 0.211472 | − | 0.977384i | \(-0.432174\pi\) | ||||
0.211472 | + | 0.977384i | \(0.432174\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.49552 | −0.138716 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.7382 | 0.702813 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.1611 | −0.717322 | −0.358661 | − | 0.933468i | \(-0.616767\pi\) | ||||
−0.358661 | + | 0.933468i | \(0.616767\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.4542 | 1.08269 | 0.541343 | − | 0.840802i | \(-0.317916\pi\) | ||||
0.541343 | + | 0.840802i | \(0.317916\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.5644 | −0.769155 | −0.384577 | − | 0.923093i | \(-0.625653\pi\) | ||||
−0.384577 | + | 0.923093i | \(0.625653\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −67.9364 | −2.66674 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.1516 | 1.49299 | 0.746493 | − | 0.665393i | \(-0.231736\pi\) | ||||
0.746493 | + | 0.665393i | \(0.231736\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.6057 | −0.609767 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.4727 | 0.485866 | 0.242933 | − | 0.970043i | \(-0.421890\pi\) | ||||
0.242933 | + | 0.970043i | \(0.421890\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.5644 | 0.449802 | 0.224901 | − | 0.974382i | \(-0.427794\pi\) | ||||
0.224901 | + | 0.974382i | \(0.427794\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.20191 | −0.124165 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.7159 | 1.07317 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.4955 | −0.752616 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.46311 | −0.249134 | −0.124567 | − | 0.992211i | \(-0.539754\pi\) | ||||
−0.124567 | + | 0.992211i | \(0.539754\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.9682 | 1.22864 | 0.614319 | − | 0.789058i | \(-0.289431\pi\) | ||||
0.614319 | + | 0.789058i | \(0.289431\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.454754 | 0.0174518 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.68787 | −0.102849 | −0.0514243 | − | 0.998677i | \(-0.516376\pi\) | ||||
−0.0514243 | + | 0.998677i | \(0.516376\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.656063 | −0.0250669 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 58.1198 | 2.21419 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.9083 | −1.02364 | −0.511820 | − | 0.859093i | \(-0.671029\pi\) | ||||
−0.511820 | + | 0.859093i | \(0.671029\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.40382 | −0.242911 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.4319 | −1.49359 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.6243 | −1.23220 | −0.616100 | − | 0.787668i | \(-0.711288\pi\) | ||||
−0.616100 | + | 0.787668i | \(0.711288\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.8580 | −0.447232 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.1007 | −0.530310 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.3631 | −1.10275 | −0.551376 | − | 0.834257i | \(-0.685897\pi\) | ||||
−0.551376 | + | 0.834257i | \(0.685897\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.3121 | −0.648344 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.3720 | 1.06105 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.4134 | −1.05964 | −0.529820 | − | 0.848110i | \(-0.677741\pi\) | ||||
−0.529820 | + | 0.848110i | \(0.677741\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −41.0090 | −1.52725 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.20191 | 0.118916 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −46.1293 | −1.71084 | −0.855421 | − | 0.517933i | \(-0.826702\pi\) | ||||
−0.855421 | + | 0.517933i | \(0.826702\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.8166 | 0.511026 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.6561 | 1.05844 | 0.529218 | − | 0.848486i | \(-0.322485\pi\) | ||||
0.529218 | + | 0.848486i | \(0.322485\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.8076 | −0.766460 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.8166 | −0.949679 | −0.474840 | − | 0.880072i | \(-0.657494\pi\) | ||||
−0.474840 | + | 0.880072i | \(0.657494\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.1198 | 1.39848 | 0.699239 | − | 0.714888i | \(-0.253522\pi\) | ||||
0.699239 | + | 0.714888i | \(0.253522\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.3121 | −0.854090 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 41.0090 | 1.49843 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.31213 | 0.266823 | 0.133412 | − | 0.991061i | \(-0.457407\pi\) | ||||
0.133412 | + | 0.991061i | \(0.457407\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.3121 | 0.848415 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.86753 | −0.140568 | −0.0702839 | − | 0.997527i | \(-0.522391\pi\) | ||||
−0.0702839 | + | 0.997527i | \(0.522391\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.3211 | 0.446639 | 0.223319 | − | 0.974745i | \(-0.428311\pi\) | ||||
0.223319 | + | 0.974745i | \(0.428311\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.2204 | 1.74570 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 71.2306 | 2.57199 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.11977 | −0.292806 | −0.146403 | − | 0.989225i | \(-0.546770\pi\) | ||||
−0.146403 | + | 0.989225i | \(0.546770\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.3439 | 0.623818 | 0.311909 | − | 0.950112i | \(-0.399032\pi\) | ||||
0.311909 | + | 0.950112i | \(0.399032\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00000 | −0.0718421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.85797 | 0.353199 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.9364 | 1.28590 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.25224 | −0.223152 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.2204 | −1.00595 | −0.502975 | − | 0.864301i | \(-0.667761\pi\) | ||||
−0.502975 | + | 0.864301i | \(0.667761\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.2013 | −0.576052 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.4409 | 0.725876 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.56436 | −0.0554126 | −0.0277063 | − | 0.999616i | \(-0.508820\pi\) | ||||
−0.0277063 | + | 0.999616i | \(0.508820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.6243 | 1.22492 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −31.2115 | −1.10143 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.7159 | −0.976859 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.80765 | 0.239344 | 0.119672 | − | 0.992813i | \(-0.461816\pi\) | ||||
0.119672 | + | 0.992813i | \(0.461816\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.5134 | 0.474521 | 0.237260 | − | 0.971446i | \(-0.423751\pi\) | ||||
0.237260 | + | 0.971446i | \(0.423751\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.85797 | −0.345310 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.45415 | −0.120845 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.5326 | 1.10049 | 0.550247 | − | 0.835002i | \(-0.314534\pi\) | ||||
0.550247 | + | 0.835002i | \(0.314534\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.1102 | −1.32844 | −0.664219 | − | 0.747538i | \(-0.731236\pi\) | ||||
−0.664219 | + | 0.747538i | \(0.731236\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.74776 | −0.0607756 | −0.0303878 | − | 0.999538i | \(-0.509674\pi\) | ||||
−0.0303878 | + | 0.999538i | \(0.509674\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.2522 | −0.356075 | −0.178037 | − | 0.984024i | \(-0.556975\pi\) | ||||
−0.178037 | + | 0.984024i | \(0.556975\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.0090 | −0.450734 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.25224 | −0.216368 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.7159 | −0.680670 | −0.340335 | − | 0.940304i | \(-0.610540\pi\) | ||||
−0.340335 | + | 0.940304i | \(0.610540\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.7478 | −0.646475 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.7478 | −0.576140 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 51.4223 | 1.76689 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −102.643 | −3.51857 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.2522 | 0.761902 | 0.380951 | − | 0.924595i | \(-0.375597\pi\) | ||||
0.380951 | + | 0.924595i | \(0.375597\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −53.7848 | −1.83725 | −0.918627 | − | 0.395126i | \(-0.870701\pi\) | ||||
−0.918627 | + | 0.395126i | \(0.870701\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.31213 | 0.181247 | 0.0906237 | − | 0.995885i | \(-0.471114\pi\) | ||||
0.0906237 | + | 0.995885i | \(0.471114\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.31213 | −0.316988 | −0.158494 | − | 0.987360i | \(-0.550664\pi\) | ||||
−0.158494 | + | 0.987360i | \(0.550664\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.05989 | 0.308045 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.0000 | 1.08553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.8166 | 0.739227 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.20191 | −0.108244 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.3625 | 0.822662 | 0.411331 | − | 0.911486i | \(-0.365064\pi\) | ||||
0.411331 | + | 0.911486i | \(0.365064\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 59.0281 | 1.98871 | 0.994353 | − | 0.106122i | \(-0.0338433\pi\) | ||||
0.994353 | + | 0.106122i | \(0.0338433\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.1701 | 1.31818 | 0.659089 | − | 0.752065i | \(-0.270942\pi\) | ||||
0.659089 | + | 0.752065i | \(0.270942\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −55.4319 | −1.86122 | −0.930610 | − | 0.366011i | \(-0.880723\pi\) | ||||
−0.930610 | + | 0.366011i | \(0.880723\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.1924 | 0.375379 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.65606 | −0.289664 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.25224 | −0.142137 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.40382 | −0.213579 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.6243 | −1.42002 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.5554 | −0.616803 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.9083 | 0.627840 | 0.313920 | − | 0.949449i | \(-0.398358\pi\) | ||||
0.313920 | + | 0.949449i | \(0.398358\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.8166 | 0.855342 | 0.427671 | − | 0.903934i | \(-0.359334\pi\) | ||||
0.427671 | + | 0.903934i | \(0.359334\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −43.7159 | −1.44679 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 49.9682 | 1.65009 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.1198 | −1.25746 | −0.628728 | − | 0.777626i | \(-0.716424\pi\) | ||||
−0.628728 | + | 0.777626i | \(0.716424\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −37.6789 | −1.24022 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.8580 | −0.389888 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.5146 | −1.09958 | −0.549790 | − | 0.835303i | \(-0.685292\pi\) | ||||
−0.549790 | + | 0.835303i | \(0.685292\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.25224 | 0.106588 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.8076 | −0.680483 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52.8447 | 1.72636 | 0.863180 | − | 0.504896i | \(-0.168469\pi\) | ||||
0.863180 | + | 0.504896i | \(0.168469\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52.8172 | −1.72179 | −0.860896 | − | 0.508781i | \(-0.830096\pi\) | ||||
−0.860896 | + | 0.508781i | \(0.830096\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 85.3312 | 2.77877 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.0917 | −0.620397 | −0.310198 | − | 0.950672i | \(-0.600395\pi\) | ||||
−0.310198 | + | 0.950672i | \(0.600395\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.7249 | 1.06230 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −46.1707 | −1.49562 | −0.747808 | − | 0.663915i | \(-0.768894\pi\) | ||||
−0.747808 | + | 0.663915i | \(0.768894\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.5140 | −0.728537 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.10065 | 0.0678337 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.7573 | 0.571628 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.5230 | −0.820764 | −0.410382 | − | 0.911914i | \(-0.634605\pi\) | ||||
−0.410382 | + | 0.911914i | \(0.634605\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.9682 | −0.640810 | −0.320405 | − | 0.947281i | \(-0.603819\pi\) | ||||
−0.320405 | + | 0.947281i | \(0.603819\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.5045 | 0.657343 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.34394 | 0.0429964 | 0.0214982 | − | 0.999769i | \(-0.493156\pi\) | ||||
0.0214982 | + | 0.999769i | \(0.493156\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 72.0880 | 2.30394 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52.3720 | 1.67041 | 0.835204 | − | 0.549940i | \(-0.185350\pi\) | ||||
0.835204 | + | 0.549940i | \(0.185350\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.4637 | 0.492715 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −29.8993 | −0.950744 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.28031 | −0.294799 | −0.147399 | − | 0.989077i | \(-0.547090\pi\) | ||||
−0.147399 | + | 0.989077i | \(0.547090\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.90830 | −0.0921994 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.2433 | 0.419419 | 0.209709 | − | 0.977764i | \(-0.432748\pi\) | ||||
0.209709 | + | 0.977764i | \(0.432748\pi\) | |||||||
\(998\) | 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 | 6840.2.a.bh.1.3 | 3 | ||
3.2 | odd | 2 | 2280.2.a.u.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 4560.2.a.bs.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.u.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
4560.2.a.bs.1.1 | 3 | 12.11 | even | 2 | |||
6840.2.a.bh.1.3 | 3 | 1.1 | even | 1 | trivial |