Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.23 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.206596 | −0.146086 | −0.0730428 | − | 0.997329i | \(-0.523271\pi\) | ||||
−0.0730428 | + | 0.997329i | \(0.523271\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.95732 | −0.978659 | ||||||||
\(5\) | −2.96369 | −1.32540 | −0.662701 | − | 0.748884i | \(-0.730590\pi\) | ||||
−0.662701 | + | 0.748884i | \(0.730590\pi\) | |||||||
\(6\) | 0.206596 | 0.0843425 | ||||||||
\(7\) | −3.29821 | −1.24661 | −0.623303 | − | 0.781981i | \(-0.714210\pi\) | ||||
−0.623303 | + | 0.781981i | \(0.714210\pi\) | |||||||
\(8\) | 0.817567 | 0.289054 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.612286 | 0.193622 | ||||||||
\(11\) | −2.02436 | −0.610367 | −0.305184 | − | 0.952294i | \(-0.598718\pi\) | ||||
−0.305184 | + | 0.952294i | \(0.598718\pi\) | |||||||
\(12\) | 1.95732 | 0.565029 | ||||||||
\(13\) | −4.52233 | −1.25427 | −0.627134 | − | 0.778911i | \(-0.715772\pi\) | ||||
−0.627134 | + | 0.778911i | \(0.715772\pi\) | |||||||
\(14\) | 0.681397 | 0.182111 | ||||||||
\(15\) | 2.96369 | 0.765221 | ||||||||
\(16\) | 3.74573 | 0.936432 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.206596 | −0.0486952 | ||||||||
\(19\) | 2.84222 | 0.652050 | 0.326025 | − | 0.945361i | \(-0.394291\pi\) | ||||
0.326025 | + | 0.945361i | \(0.394291\pi\) | |||||||
\(20\) | 5.80088 | 1.29712 | ||||||||
\(21\) | 3.29821 | 0.719728 | ||||||||
\(22\) | 0.418225 | 0.0891658 | ||||||||
\(23\) | −6.15139 | −1.28265 | −0.641327 | − | 0.767268i | \(-0.721616\pi\) | ||||
−0.641327 | + | 0.767268i | \(0.721616\pi\) | |||||||
\(24\) | −0.817567 | −0.166885 | ||||||||
\(25\) | 3.78344 | 0.756688 | ||||||||
\(26\) | 0.934296 | 0.183230 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 6.45564 | 1.22000 | ||||||||
\(29\) | 3.35506 | 0.623018 | 0.311509 | − | 0.950243i | \(-0.399166\pi\) | ||||
0.311509 | + | 0.950243i | \(0.399166\pi\) | |||||||
\(30\) | −0.612286 | −0.111788 | ||||||||
\(31\) | −3.97663 | −0.714224 | −0.357112 | − | 0.934062i | \(-0.616238\pi\) | ||||
−0.357112 | + | 0.934062i | \(0.616238\pi\) | |||||||
\(32\) | −2.40899 | −0.425853 | ||||||||
\(33\) | 2.02436 | 0.352396 | ||||||||
\(34\) | 0.206596 | 0.0354310 | ||||||||
\(35\) | 9.77486 | 1.65225 | ||||||||
\(36\) | −1.95732 | −0.326220 | ||||||||
\(37\) | −6.02124 | −0.989886 | −0.494943 | − | 0.868926i | \(-0.664811\pi\) | ||||
−0.494943 | + | 0.868926i | \(0.664811\pi\) | |||||||
\(38\) | −0.587192 | −0.0952551 | ||||||||
\(39\) | 4.52233 | 0.724152 | ||||||||
\(40\) | −2.42301 | −0.383112 | ||||||||
\(41\) | −5.50704 | −0.860055 | −0.430028 | − | 0.902816i | \(-0.641496\pi\) | ||||
−0.430028 | + | 0.902816i | \(0.641496\pi\) | |||||||
\(42\) | −0.681397 | −0.105142 | ||||||||
\(43\) | −0.805249 | −0.122799 | −0.0613996 | − | 0.998113i | \(-0.519556\pi\) | ||||
−0.0613996 | + | 0.998113i | \(0.519556\pi\) | |||||||
\(44\) | 3.96231 | 0.597341 | ||||||||
\(45\) | −2.96369 | −0.441800 | ||||||||
\(46\) | 1.27085 | 0.187377 | ||||||||
\(47\) | 2.71134 | 0.395489 | 0.197745 | − | 0.980254i | \(-0.436638\pi\) | ||||
0.197745 | + | 0.980254i | \(0.436638\pi\) | |||||||
\(48\) | −3.74573 | −0.540650 | ||||||||
\(49\) | 3.87818 | 0.554026 | ||||||||
\(50\) | −0.781645 | −0.110541 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 8.85163 | 1.22750 | ||||||||
\(53\) | 7.81249 | 1.07313 | 0.536564 | − | 0.843860i | \(-0.319722\pi\) | ||||
0.536564 | + | 0.843860i | \(0.319722\pi\) | |||||||
\(54\) | 0.206596 | 0.0281142 | ||||||||
\(55\) | 5.99957 | 0.808981 | ||||||||
\(56\) | −2.69651 | −0.360336 | ||||||||
\(57\) | −2.84222 | −0.376461 | ||||||||
\(58\) | −0.693142 | −0.0910140 | ||||||||
\(59\) | 0.000491989 0 | 6.40516e−5 0 | 3.20258e−5 | − | 1.00000i | \(-0.499990\pi\) | ||||
3.20258e−5 | 1.00000i | \(0.499990\pi\) | ||||||||
\(60\) | −5.80088 | −0.748890 | ||||||||
\(61\) | 10.2945 | 1.31808 | 0.659040 | − | 0.752108i | \(-0.270963\pi\) | ||||
0.659040 | + | 0.752108i | \(0.270963\pi\) | |||||||
\(62\) | 0.821556 | 0.104338 | ||||||||
\(63\) | −3.29821 | −0.415535 | ||||||||
\(64\) | −6.99377 | −0.874222 | ||||||||
\(65\) | 13.4028 | 1.66241 | ||||||||
\(66\) | −0.418225 | −0.0514799 | ||||||||
\(67\) | 6.98424 | 0.853261 | 0.426630 | − | 0.904426i | \(-0.359701\pi\) | ||||
0.426630 | + | 0.904426i | \(0.359701\pi\) | |||||||
\(68\) | 1.95732 | 0.237360 | ||||||||
\(69\) | 6.15139 | 0.740540 | ||||||||
\(70\) | −2.01945 | −0.241370 | ||||||||
\(71\) | 12.7098 | 1.50838 | 0.754189 | − | 0.656657i | \(-0.228030\pi\) | ||||
0.754189 | + | 0.656657i | \(0.228030\pi\) | |||||||
\(72\) | 0.817567 | 0.0963512 | ||||||||
\(73\) | −0.595084 | −0.0696493 | −0.0348246 | − | 0.999393i | \(-0.511087\pi\) | ||||
−0.0348246 | + | 0.999393i | \(0.511087\pi\) | |||||||
\(74\) | 1.24397 | 0.144608 | ||||||||
\(75\) | −3.78344 | −0.436874 | ||||||||
\(76\) | −5.56313 | −0.638134 | ||||||||
\(77\) | 6.67676 | 0.760887 | ||||||||
\(78\) | −0.934296 | −0.105788 | ||||||||
\(79\) | 10.0119 | 1.12643 | 0.563216 | − | 0.826310i | \(-0.309564\pi\) | ||||
0.563216 | + | 0.826310i | \(0.309564\pi\) | |||||||
\(80\) | −11.1012 | −1.24115 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.13773 | 0.125642 | ||||||||
\(83\) | −10.2303 | −1.12293 | −0.561463 | − | 0.827502i | \(-0.689761\pi\) | ||||
−0.561463 | + | 0.827502i | \(0.689761\pi\) | |||||||
\(84\) | −6.45564 | −0.704368 | ||||||||
\(85\) | 2.96369 | 0.321457 | ||||||||
\(86\) | 0.166361 | 0.0179392 | ||||||||
\(87\) | −3.35506 | −0.359700 | ||||||||
\(88\) | −1.65505 | −0.176429 | ||||||||
\(89\) | 6.31716 | 0.669618 | 0.334809 | − | 0.942286i | \(-0.391328\pi\) | ||||
0.334809 | + | 0.942286i | \(0.391328\pi\) | |||||||
\(90\) | 0.612286 | 0.0645407 | ||||||||
\(91\) | 14.9156 | 1.56358 | ||||||||
\(92\) | 12.0402 | 1.25528 | ||||||||
\(93\) | 3.97663 | 0.412357 | ||||||||
\(94\) | −0.560152 | −0.0577752 | ||||||||
\(95\) | −8.42345 | −0.864228 | ||||||||
\(96\) | 2.40899 | 0.245866 | ||||||||
\(97\) | 6.62727 | 0.672898 | 0.336449 | − | 0.941702i | \(-0.390774\pi\) | ||||
0.336449 | + | 0.941702i | \(0.390774\pi\) | |||||||
\(98\) | −0.801217 | −0.0809352 | ||||||||
\(99\) | −2.02436 | −0.203456 | ||||||||
\(100\) | −7.40540 | −0.740540 | ||||||||
\(101\) | 4.37106 | 0.434937 | 0.217468 | − | 0.976067i | \(-0.430220\pi\) | ||||
0.217468 | + | 0.976067i | \(0.430220\pi\) | |||||||
\(102\) | −0.206596 | −0.0204561 | ||||||||
\(103\) | 10.8198 | 1.06610 | 0.533052 | − | 0.846082i | \(-0.321045\pi\) | ||||
0.533052 | + | 0.846082i | \(0.321045\pi\) | |||||||
\(104\) | −3.69731 | −0.362551 | ||||||||
\(105\) | −9.77486 | −0.953929 | ||||||||
\(106\) | −1.61403 | −0.156769 | ||||||||
\(107\) | 13.2838 | 1.28419 | 0.642097 | − | 0.766624i | \(-0.278065\pi\) | ||||
0.642097 | + | 0.766624i | \(0.278065\pi\) | |||||||
\(108\) | 1.95732 | 0.188343 | ||||||||
\(109\) | 7.51938 | 0.720226 | 0.360113 | − | 0.932909i | \(-0.382738\pi\) | ||||
0.360113 | + | 0.932909i | \(0.382738\pi\) | |||||||
\(110\) | −1.23949 | −0.118181 | ||||||||
\(111\) | 6.02124 | 0.571511 | ||||||||
\(112\) | −12.3542 | −1.16736 | ||||||||
\(113\) | 6.82917 | 0.642434 | 0.321217 | − | 0.947006i | \(-0.395908\pi\) | ||||
0.321217 | + | 0.947006i | \(0.395908\pi\) | |||||||
\(114\) | 0.587192 | 0.0549955 | ||||||||
\(115\) | 18.2308 | 1.70003 | ||||||||
\(116\) | −6.56691 | −0.609722 | ||||||||
\(117\) | −4.52233 | −0.418089 | ||||||||
\(118\) | −0.000101643 0 | −9.35701e−6 0 | ||||||||
\(119\) | 3.29821 | 0.302346 | ||||||||
\(120\) | 2.42301 | 0.221190 | ||||||||
\(121\) | −6.90197 | −0.627452 | ||||||||
\(122\) | −2.12681 | −0.192552 | ||||||||
\(123\) | 5.50704 | 0.496553 | ||||||||
\(124\) | 7.78353 | 0.698981 | ||||||||
\(125\) | 3.60550 | 0.322485 | ||||||||
\(126\) | 0.681397 | 0.0607037 | ||||||||
\(127\) | −1.72390 | −0.152971 | −0.0764857 | − | 0.997071i | \(-0.524370\pi\) | ||||
−0.0764857 | + | 0.997071i | \(0.524370\pi\) | |||||||
\(128\) | 6.26286 | 0.553564 | ||||||||
\(129\) | 0.805249 | 0.0708982 | ||||||||
\(130\) | −2.76896 | −0.242854 | ||||||||
\(131\) | 12.7234 | 1.11165 | 0.555825 | − | 0.831300i | \(-0.312403\pi\) | ||||
0.555825 | + | 0.831300i | \(0.312403\pi\) | |||||||
\(132\) | −3.96231 | −0.344875 | ||||||||
\(133\) | −9.37423 | −0.812849 | ||||||||
\(134\) | −1.44292 | −0.124649 | ||||||||
\(135\) | 2.96369 | 0.255074 | ||||||||
\(136\) | −0.817567 | −0.0701058 | ||||||||
\(137\) | −6.52930 | −0.557836 | −0.278918 | − | 0.960315i | \(-0.589976\pi\) | ||||
−0.278918 | + | 0.960315i | \(0.589976\pi\) | |||||||
\(138\) | −1.27085 | −0.108182 | ||||||||
\(139\) | −16.1046 | −1.36597 | −0.682986 | − | 0.730431i | \(-0.739319\pi\) | ||||
−0.682986 | + | 0.730431i | \(0.739319\pi\) | |||||||
\(140\) | −19.1325 | −1.61699 | ||||||||
\(141\) | −2.71134 | −0.228336 | ||||||||
\(142\) | −2.62580 | −0.220352 | ||||||||
\(143\) | 9.15482 | 0.765564 | ||||||||
\(144\) | 3.74573 | 0.312144 | ||||||||
\(145\) | −9.94333 | −0.825749 | ||||||||
\(146\) | 0.122942 | 0.0101748 | ||||||||
\(147\) | −3.87818 | −0.319867 | ||||||||
\(148\) | 11.7855 | 0.968761 | ||||||||
\(149\) | −11.1683 | −0.914945 | −0.457472 | − | 0.889224i | \(-0.651245\pi\) | ||||
−0.457472 | + | 0.889224i | \(0.651245\pi\) | |||||||
\(150\) | 0.781645 | 0.0638210 | ||||||||
\(151\) | 8.50804 | 0.692375 | 0.346187 | − | 0.938165i | \(-0.387476\pi\) | ||||
0.346187 | + | 0.938165i | \(0.387476\pi\) | |||||||
\(152\) | 2.32370 | 0.188477 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −1.37939 | −0.111155 | ||||||||
\(155\) | 11.7855 | 0.946633 | ||||||||
\(156\) | −8.85163 | −0.708698 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | −2.06843 | −0.164555 | ||||||||
\(159\) | −7.81249 | −0.619571 | ||||||||
\(160\) | 7.13948 | 0.564426 | ||||||||
\(161\) | 20.2886 | 1.59896 | ||||||||
\(162\) | −0.206596 | −0.0162317 | ||||||||
\(163\) | −21.7533 | −1.70385 | −0.851925 | − | 0.523664i | \(-0.824565\pi\) | ||||
−0.851925 | + | 0.523664i | \(0.824565\pi\) | |||||||
\(164\) | 10.7790 | 0.841701 | ||||||||
\(165\) | −5.99957 | −0.467066 | ||||||||
\(166\) | 2.11355 | 0.164043 | ||||||||
\(167\) | −2.07171 | −0.160314 | −0.0801569 | − | 0.996782i | \(-0.525542\pi\) | ||||
−0.0801569 | + | 0.996782i | \(0.525542\pi\) | |||||||
\(168\) | 2.69651 | 0.208040 | ||||||||
\(169\) | 7.45145 | 0.573189 | ||||||||
\(170\) | −0.612286 | −0.0469602 | ||||||||
\(171\) | 2.84222 | 0.217350 | ||||||||
\(172\) | 1.57613 | 0.120179 | ||||||||
\(173\) | −6.97136 | −0.530023 | −0.265011 | − | 0.964245i | \(-0.585376\pi\) | ||||
−0.265011 | + | 0.964245i | \(0.585376\pi\) | |||||||
\(174\) | 0.693142 | 0.0525469 | ||||||||
\(175\) | −12.4786 | −0.943292 | ||||||||
\(176\) | −7.58270 | −0.571568 | ||||||||
\(177\) | −0.000491989 0 | −3.69802e−5 0 | ||||||||
\(178\) | −1.30510 | −0.0978215 | ||||||||
\(179\) | −15.8036 | −1.18122 | −0.590609 | − | 0.806958i | \(-0.701113\pi\) | ||||
−0.590609 | + | 0.806958i | \(0.701113\pi\) | |||||||
\(180\) | 5.80088 | 0.432372 | ||||||||
\(181\) | 15.5742 | 1.15762 | 0.578812 | − | 0.815461i | \(-0.303517\pi\) | ||||
0.578812 | + | 0.815461i | \(0.303517\pi\) | |||||||
\(182\) | −3.08150 | −0.228416 | ||||||||
\(183\) | −10.2945 | −0.760994 | ||||||||
\(184\) | −5.02917 | −0.370755 | ||||||||
\(185\) | 17.8451 | 1.31200 | ||||||||
\(186\) | −0.821556 | −0.0602394 | ||||||||
\(187\) | 2.02436 | 0.148036 | ||||||||
\(188\) | −5.30695 | −0.387049 | ||||||||
\(189\) | 3.29821 | 0.239909 | ||||||||
\(190\) | 1.74025 | 0.126251 | ||||||||
\(191\) | −9.33763 | −0.675647 | −0.337824 | − | 0.941209i | \(-0.609691\pi\) | ||||
−0.337824 | + | 0.941209i | \(0.609691\pi\) | |||||||
\(192\) | 6.99377 | 0.504732 | ||||||||
\(193\) | −12.2457 | −0.881468 | −0.440734 | − | 0.897638i | \(-0.645282\pi\) | ||||
−0.440734 | + | 0.897638i | \(0.645282\pi\) | |||||||
\(194\) | −1.36917 | −0.0983006 | ||||||||
\(195\) | −13.4028 | −0.959792 | ||||||||
\(196\) | −7.59083 | −0.542202 | ||||||||
\(197\) | −20.2355 | −1.44172 | −0.720861 | − | 0.693080i | \(-0.756253\pi\) | ||||
−0.720861 | + | 0.693080i | \(0.756253\pi\) | |||||||
\(198\) | 0.418225 | 0.0297219 | ||||||||
\(199\) | 0.253590 | 0.0179765 | 0.00898825 | − | 0.999960i | \(-0.497139\pi\) | ||||
0.00898825 | + | 0.999960i | \(0.497139\pi\) | |||||||
\(200\) | 3.09322 | 0.218723 | ||||||||
\(201\) | −6.98424 | −0.492630 | ||||||||
\(202\) | −0.903045 | −0.0635380 | ||||||||
\(203\) | −11.0657 | −0.776658 | ||||||||
\(204\) | −1.95732 | −0.137040 | ||||||||
\(205\) | 16.3211 | 1.13992 | ||||||||
\(206\) | −2.23532 | −0.155742 | ||||||||
\(207\) | −6.15139 | −0.427551 | ||||||||
\(208\) | −16.9394 | −1.17454 | ||||||||
\(209\) | −5.75367 | −0.397990 | ||||||||
\(210\) | 2.01945 | 0.139355 | ||||||||
\(211\) | −22.3520 | −1.53877 | −0.769386 | − | 0.638784i | \(-0.779438\pi\) | ||||
−0.769386 | + | 0.638784i | \(0.779438\pi\) | |||||||
\(212\) | −15.2915 | −1.05023 | ||||||||
\(213\) | −12.7098 | −0.870863 | ||||||||
\(214\) | −2.74438 | −0.187602 | ||||||||
\(215\) | 2.38651 | 0.162758 | ||||||||
\(216\) | −0.817567 | −0.0556284 | ||||||||
\(217\) | 13.1157 | 0.890355 | ||||||||
\(218\) | −1.55347 | −0.105215 | ||||||||
\(219\) | 0.595084 | 0.0402120 | ||||||||
\(220\) | −11.7431 | −0.791717 | ||||||||
\(221\) | 4.52233 | 0.304205 | ||||||||
\(222\) | −1.24397 | −0.0834895 | ||||||||
\(223\) | 9.37799 | 0.627996 | 0.313998 | − | 0.949424i | \(-0.398331\pi\) | ||||
0.313998 | + | 0.949424i | \(0.398331\pi\) | |||||||
\(224\) | 7.94534 | 0.530870 | ||||||||
\(225\) | 3.78344 | 0.252229 | ||||||||
\(226\) | −1.41088 | −0.0938503 | ||||||||
\(227\) | −16.6181 | −1.10298 | −0.551490 | − | 0.834181i | \(-0.685941\pi\) | ||||
−0.551490 | + | 0.834181i | \(0.685941\pi\) | |||||||
\(228\) | 5.56313 | 0.368427 | ||||||||
\(229\) | 8.54414 | 0.564612 | 0.282306 | − | 0.959324i | \(-0.408901\pi\) | ||||
0.282306 | + | 0.959324i | \(0.408901\pi\) | |||||||
\(230\) | −3.76641 | −0.248350 | ||||||||
\(231\) | −6.67676 | −0.439298 | ||||||||
\(232\) | 2.74298 | 0.180086 | ||||||||
\(233\) | −10.6121 | −0.695224 | −0.347612 | − | 0.937638i | \(-0.613007\pi\) | ||||
−0.347612 | + | 0.937638i | \(0.613007\pi\) | |||||||
\(234\) | 0.934296 | 0.0610768 | ||||||||
\(235\) | −8.03555 | −0.524182 | ||||||||
\(236\) | −0.000962980 0 | −6.26846e−5 0 | ||||||||
\(237\) | −10.0119 | −0.650346 | ||||||||
\(238\) | −0.681397 | −0.0441684 | ||||||||
\(239\) | 10.1801 | 0.658494 | 0.329247 | − | 0.944244i | \(-0.393205\pi\) | ||||
0.329247 | + | 0.944244i | \(0.393205\pi\) | |||||||
\(240\) | 11.1012 | 0.716578 | ||||||||
\(241\) | −6.02177 | −0.387896 | −0.193948 | − | 0.981012i | \(-0.562129\pi\) | ||||
−0.193948 | + | 0.981012i | \(0.562129\pi\) | |||||||
\(242\) | 1.42592 | 0.0916617 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −20.1497 | −1.28995 | ||||||||
\(245\) | −11.4937 | −0.734306 | ||||||||
\(246\) | −1.13773 | −0.0725392 | ||||||||
\(247\) | −12.8534 | −0.817845 | ||||||||
\(248\) | −3.25116 | −0.206449 | ||||||||
\(249\) | 10.2303 | 0.648322 | ||||||||
\(250\) | −0.744882 | −0.0471105 | ||||||||
\(251\) | 9.91638 | 0.625916 | 0.312958 | − | 0.949767i | \(-0.398680\pi\) | ||||
0.312958 | + | 0.949767i | \(0.398680\pi\) | |||||||
\(252\) | 6.45564 | 0.406667 | ||||||||
\(253\) | 12.4526 | 0.782890 | ||||||||
\(254\) | 0.356151 | 0.0223469 | ||||||||
\(255\) | −2.96369 | −0.185593 | ||||||||
\(256\) | 12.6937 | 0.793354 | ||||||||
\(257\) | −14.5981 | −0.910604 | −0.455302 | − | 0.890337i | \(-0.650469\pi\) | ||||
−0.455302 | + | 0.890337i | \(0.650469\pi\) | |||||||
\(258\) | −0.166361 | −0.0103572 | ||||||||
\(259\) | 19.8593 | 1.23400 | ||||||||
\(260\) | −26.2335 | −1.62693 | ||||||||
\(261\) | 3.35506 | 0.207673 | ||||||||
\(262\) | −2.62861 | −0.162396 | ||||||||
\(263\) | 9.62897 | 0.593748 | 0.296874 | − | 0.954917i | \(-0.404056\pi\) | ||||
0.296874 | + | 0.954917i | \(0.404056\pi\) | |||||||
\(264\) | 1.65505 | 0.101861 | ||||||||
\(265\) | −23.1538 | −1.42233 | ||||||||
\(266\) | 1.93668 | 0.118746 | ||||||||
\(267\) | −6.31716 | −0.386604 | ||||||||
\(268\) | −13.6704 | −0.835051 | ||||||||
\(269\) | −24.2163 | −1.47650 | −0.738248 | − | 0.674529i | \(-0.764347\pi\) | ||||
−0.738248 | + | 0.674529i | \(0.764347\pi\) | |||||||
\(270\) | −0.612286 | −0.0372626 | ||||||||
\(271\) | 0.936971 | 0.0569169 | 0.0284585 | − | 0.999595i | \(-0.490940\pi\) | ||||
0.0284585 | + | 0.999595i | \(0.490940\pi\) | |||||||
\(272\) | −3.74573 | −0.227118 | ||||||||
\(273\) | −14.9156 | −0.902732 | ||||||||
\(274\) | 1.34893 | 0.0814917 | ||||||||
\(275\) | −7.65904 | −0.461858 | ||||||||
\(276\) | −12.0402 | −0.724736 | ||||||||
\(277\) | −14.1399 | −0.849582 | −0.424791 | − | 0.905291i | \(-0.639652\pi\) | ||||
−0.424791 | + | 0.905291i | \(0.639652\pi\) | |||||||
\(278\) | 3.32714 | 0.199549 | ||||||||
\(279\) | −3.97663 | −0.238075 | ||||||||
\(280\) | 7.99160 | 0.477589 | ||||||||
\(281\) | 32.3428 | 1.92941 | 0.964704 | − | 0.263338i | \(-0.0848236\pi\) | ||||
0.964704 | + | 0.263338i | \(0.0848236\pi\) | |||||||
\(282\) | 0.560152 | 0.0333565 | ||||||||
\(283\) | 24.0543 | 1.42988 | 0.714940 | − | 0.699186i | \(-0.246454\pi\) | ||||
0.714940 | + | 0.699186i | \(0.246454\pi\) | |||||||
\(284\) | −24.8772 | −1.47619 | ||||||||
\(285\) | 8.42345 | 0.498962 | ||||||||
\(286\) | −1.89135 | −0.111838 | ||||||||
\(287\) | 18.1634 | 1.07215 | ||||||||
\(288\) | −2.40899 | −0.141951 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 2.05425 | 0.120630 | ||||||||
\(291\) | −6.62727 | −0.388498 | ||||||||
\(292\) | 1.16477 | 0.0681629 | ||||||||
\(293\) | 27.9330 | 1.63186 | 0.815932 | − | 0.578148i | \(-0.196224\pi\) | ||||
0.815932 | + | 0.578148i | \(0.196224\pi\) | |||||||
\(294\) | 0.801217 | 0.0467279 | ||||||||
\(295\) | −0.00145810 | −8.48940e−5 0 | ||||||||
\(296\) | −4.92277 | −0.286130 | ||||||||
\(297\) | 2.02436 | 0.117465 | ||||||||
\(298\) | 2.30733 | 0.133660 | ||||||||
\(299\) | 27.8186 | 1.60879 | ||||||||
\(300\) | 7.40540 | 0.427551 | ||||||||
\(301\) | 2.65588 | 0.153082 | ||||||||
\(302\) | −1.75773 | −0.101146 | ||||||||
\(303\) | −4.37106 | −0.251111 | ||||||||
\(304\) | 10.6462 | 0.610601 | ||||||||
\(305\) | −30.5098 | −1.74698 | ||||||||
\(306\) | 0.206596 | 0.0118103 | ||||||||
\(307\) | 28.8610 | 1.64718 | 0.823592 | − | 0.567182i | \(-0.191966\pi\) | ||||
0.823592 | + | 0.567182i | \(0.191966\pi\) | |||||||
\(308\) | −13.0685 | −0.744649 | ||||||||
\(309\) | −10.8198 | −0.615515 | ||||||||
\(310\) | −2.43484 | −0.138289 | ||||||||
\(311\) | −14.5043 | −0.822465 | −0.411232 | − | 0.911531i | \(-0.634902\pi\) | ||||
−0.411232 | + | 0.911531i | \(0.634902\pi\) | |||||||
\(312\) | 3.69731 | 0.209319 | ||||||||
\(313\) | −4.22057 | −0.238561 | −0.119280 | − | 0.992861i | \(-0.538059\pi\) | ||||
−0.119280 | + | 0.992861i | \(0.538059\pi\) | |||||||
\(314\) | 0.206596 | 0.0116589 | ||||||||
\(315\) | 9.77486 | 0.550751 | ||||||||
\(316\) | −19.5966 | −1.10239 | ||||||||
\(317\) | 5.40649 | 0.303659 | 0.151829 | − | 0.988407i | \(-0.451484\pi\) | ||||
0.151829 | + | 0.988407i | \(0.451484\pi\) | |||||||
\(318\) | 1.61403 | 0.0905104 | ||||||||
\(319\) | −6.79184 | −0.380270 | ||||||||
\(320\) | 20.7274 | 1.15869 | ||||||||
\(321\) | −13.2838 | −0.741429 | ||||||||
\(322\) | −4.19154 | −0.233585 | ||||||||
\(323\) | −2.84222 | −0.158145 | ||||||||
\(324\) | −1.95732 | −0.108740 | ||||||||
\(325\) | −17.1100 | −0.949090 | ||||||||
\(326\) | 4.49415 | 0.248908 | ||||||||
\(327\) | −7.51938 | −0.415822 | ||||||||
\(328\) | −4.50237 | −0.248602 | ||||||||
\(329\) | −8.94255 | −0.493019 | ||||||||
\(330\) | 1.23949 | 0.0682315 | ||||||||
\(331\) | 23.6438 | 1.29958 | 0.649789 | − | 0.760114i | \(-0.274857\pi\) | ||||
0.649789 | + | 0.760114i | \(0.274857\pi\) | |||||||
\(332\) | 20.0240 | 1.09896 | ||||||||
\(333\) | −6.02124 | −0.329962 | ||||||||
\(334\) | 0.428008 | 0.0234195 | ||||||||
\(335\) | −20.6991 | −1.13091 | ||||||||
\(336\) | 12.3542 | 0.673977 | ||||||||
\(337\) | −14.6867 | −0.800035 | −0.400017 | − | 0.916508i | \(-0.630996\pi\) | ||||
−0.400017 | + | 0.916508i | \(0.630996\pi\) | |||||||
\(338\) | −1.53944 | −0.0837346 | ||||||||
\(339\) | −6.82917 | −0.370909 | ||||||||
\(340\) | −5.80088 | −0.314597 | ||||||||
\(341\) | 8.05012 | 0.435939 | ||||||||
\(342\) | −0.587192 | −0.0317517 | ||||||||
\(343\) | 10.2964 | 0.555954 | ||||||||
\(344\) | −0.658345 | −0.0354956 | ||||||||
\(345\) | −18.2308 | −0.981513 | ||||||||
\(346\) | 1.44026 | 0.0774286 | ||||||||
\(347\) | −0.0908107 | −0.00487497 | −0.00243749 | − | 0.999997i | \(-0.500776\pi\) | ||||
−0.00243749 | + | 0.999997i | \(0.500776\pi\) | |||||||
\(348\) | 6.56691 | 0.352023 | ||||||||
\(349\) | −28.7455 | −1.53871 | −0.769356 | − | 0.638820i | \(-0.779423\pi\) | ||||
−0.769356 | + | 0.638820i | \(0.779423\pi\) | |||||||
\(350\) | 2.57803 | 0.137801 | ||||||||
\(351\) | 4.52233 | 0.241384 | ||||||||
\(352\) | 4.87665 | 0.259927 | ||||||||
\(353\) | −3.49073 | −0.185793 | −0.0928963 | − | 0.995676i | \(-0.529613\pi\) | ||||
−0.0928963 | + | 0.995676i | \(0.529613\pi\) | |||||||
\(354\) | 0.000101643 0 | 5.40227e−6 0 | ||||||||
\(355\) | −37.6680 | −1.99921 | ||||||||
\(356\) | −12.3647 | −0.655327 | ||||||||
\(357\) | −3.29821 | −0.174560 | ||||||||
\(358\) | 3.26497 | 0.172559 | ||||||||
\(359\) | −1.58297 | −0.0835462 | −0.0417731 | − | 0.999127i | \(-0.513301\pi\) | ||||
−0.0417731 | + | 0.999127i | \(0.513301\pi\) | |||||||
\(360\) | −2.42301 | −0.127704 | ||||||||
\(361\) | −10.9218 | −0.574831 | ||||||||
\(362\) | −3.21758 | −0.169112 | ||||||||
\(363\) | 6.90197 | 0.362260 | ||||||||
\(364\) | −29.1945 | −1.53021 | ||||||||
\(365\) | 1.76364 | 0.0923133 | ||||||||
\(366\) | 2.12681 | 0.111170 | ||||||||
\(367\) | 7.06116 | 0.368590 | 0.184295 | − | 0.982871i | \(-0.441000\pi\) | ||||
0.184295 | + | 0.982871i | \(0.441000\pi\) | |||||||
\(368\) | −23.0414 | −1.20112 | ||||||||
\(369\) | −5.50704 | −0.286685 | ||||||||
\(370\) | −3.68672 | −0.191664 | ||||||||
\(371\) | −25.7672 | −1.33777 | ||||||||
\(372\) | −7.78353 | −0.403557 | ||||||||
\(373\) | −1.51149 | −0.0782621 | −0.0391310 | − | 0.999234i | \(-0.512459\pi\) | ||||
−0.0391310 | + | 0.999234i | \(0.512459\pi\) | |||||||
\(374\) | −0.418225 | −0.0216259 | ||||||||
\(375\) | −3.60550 | −0.186187 | ||||||||
\(376\) | 2.21670 | 0.114317 | ||||||||
\(377\) | −15.1727 | −0.781432 | ||||||||
\(378\) | −0.681397 | −0.0350473 | ||||||||
\(379\) | −32.5267 | −1.67079 | −0.835393 | − | 0.549654i | \(-0.814760\pi\) | ||||
−0.835393 | + | 0.549654i | \(0.814760\pi\) | |||||||
\(380\) | 16.4874 | 0.845784 | ||||||||
\(381\) | 1.72390 | 0.0883180 | ||||||||
\(382\) | 1.92912 | 0.0987023 | ||||||||
\(383\) | 12.0659 | 0.616541 | 0.308271 | − | 0.951299i | \(-0.400250\pi\) | ||||
0.308271 | + | 0.951299i | \(0.400250\pi\) | |||||||
\(384\) | −6.26286 | −0.319600 | ||||||||
\(385\) | −19.7878 | −1.00848 | ||||||||
\(386\) | 2.52992 | 0.128770 | ||||||||
\(387\) | −0.805249 | −0.0409331 | ||||||||
\(388\) | −12.9717 | −0.658537 | ||||||||
\(389\) | 39.1118 | 1.98304 | 0.991522 | − | 0.129937i | \(-0.0414774\pi\) | ||||
0.991522 | + | 0.129937i | \(0.0414774\pi\) | |||||||
\(390\) | 2.76896 | 0.140212 | ||||||||
\(391\) | 6.15139 | 0.311089 | ||||||||
\(392\) | 3.17067 | 0.160143 | ||||||||
\(393\) | −12.7234 | −0.641811 | ||||||||
\(394\) | 4.18058 | 0.210615 | ||||||||
\(395\) | −29.6723 | −1.49297 | ||||||||
\(396\) | 3.96231 | 0.199114 | ||||||||
\(397\) | 15.7417 | 0.790051 | 0.395026 | − | 0.918670i | \(-0.370736\pi\) | ||||
0.395026 | + | 0.918670i | \(0.370736\pi\) | |||||||
\(398\) | −0.0523907 | −0.00262611 | ||||||||
\(399\) | 9.37423 | 0.469299 | ||||||||
\(400\) | 14.1718 | 0.708588 | ||||||||
\(401\) | 4.06914 | 0.203203 | 0.101602 | − | 0.994825i | \(-0.467603\pi\) | ||||
0.101602 | + | 0.994825i | \(0.467603\pi\) | |||||||
\(402\) | 1.44292 | 0.0719662 | ||||||||
\(403\) | 17.9836 | 0.895828 | ||||||||
\(404\) | −8.55556 | −0.425655 | ||||||||
\(405\) | −2.96369 | −0.147267 | ||||||||
\(406\) | 2.28613 | 0.113459 | ||||||||
\(407\) | 12.1892 | 0.604194 | ||||||||
\(408\) | 0.817567 | 0.0404756 | ||||||||
\(409\) | 32.9540 | 1.62947 | 0.814735 | − | 0.579834i | \(-0.196882\pi\) | ||||
0.814735 | + | 0.579834i | \(0.196882\pi\) | |||||||
\(410\) | −3.37189 | −0.166526 | ||||||||
\(411\) | 6.52930 | 0.322067 | ||||||||
\(412\) | −21.1777 | −1.04335 | ||||||||
\(413\) | −0.00162268 | −7.98471e−5 0 | ||||||||
\(414\) | 1.27085 | 0.0624591 | ||||||||
\(415\) | 30.3196 | 1.48833 | ||||||||
\(416\) | 10.8942 | 0.534134 | ||||||||
\(417\) | 16.1046 | 0.788644 | ||||||||
\(418\) | 1.18869 | 0.0581406 | ||||||||
\(419\) | 0.836509 | 0.0408662 | 0.0204331 | − | 0.999791i | \(-0.493495\pi\) | ||||
0.0204331 | + | 0.999791i | \(0.493495\pi\) | |||||||
\(420\) | 19.1325 | 0.933571 | ||||||||
\(421\) | −26.6633 | −1.29949 | −0.649745 | − | 0.760152i | \(-0.725125\pi\) | ||||
−0.649745 | + | 0.760152i | \(0.725125\pi\) | |||||||
\(422\) | 4.61783 | 0.224792 | ||||||||
\(423\) | 2.71134 | 0.131830 | ||||||||
\(424\) | 6.38723 | 0.310192 | ||||||||
\(425\) | −3.78344 | −0.183524 | ||||||||
\(426\) | 2.62580 | 0.127221 | ||||||||
\(427\) | −33.9535 | −1.64313 | ||||||||
\(428\) | −26.0006 | −1.25679 | ||||||||
\(429\) | −9.15482 | −0.441999 | ||||||||
\(430\) | −0.493043 | −0.0237766 | ||||||||
\(431\) | 15.4797 | 0.745633 | 0.372817 | − | 0.927905i | \(-0.378392\pi\) | ||||
0.372817 | + | 0.927905i | \(0.378392\pi\) | |||||||
\(432\) | −3.74573 | −0.180217 | ||||||||
\(433\) | −15.4925 | −0.744520 | −0.372260 | − | 0.928129i | \(-0.621417\pi\) | ||||
−0.372260 | + | 0.928129i | \(0.621417\pi\) | |||||||
\(434\) | −2.70966 | −0.130068 | ||||||||
\(435\) | 9.94333 | 0.476746 | ||||||||
\(436\) | −14.7178 | −0.704855 | ||||||||
\(437\) | −17.4836 | −0.836354 | ||||||||
\(438\) | −0.122942 | −0.00587440 | ||||||||
\(439\) | −27.3681 | −1.30621 | −0.653104 | − | 0.757268i | \(-0.726533\pi\) | ||||
−0.653104 | + | 0.757268i | \(0.726533\pi\) | |||||||
\(440\) | 4.90505 | 0.233839 | ||||||||
\(441\) | 3.87818 | 0.184675 | ||||||||
\(442\) | −0.934296 | −0.0444399 | ||||||||
\(443\) | −16.7822 | −0.797344 | −0.398672 | − | 0.917093i | \(-0.630529\pi\) | ||||
−0.398672 | + | 0.917093i | \(0.630529\pi\) | |||||||
\(444\) | −11.7855 | −0.559314 | ||||||||
\(445\) | −18.7221 | −0.887512 | ||||||||
\(446\) | −1.93746 | −0.0917412 | ||||||||
\(447\) | 11.1683 | 0.528243 | ||||||||
\(448\) | 23.0669 | 1.08981 | ||||||||
\(449\) | 18.4042 | 0.868549 | 0.434275 | − | 0.900781i | \(-0.357005\pi\) | ||||
0.434275 | + | 0.900781i | \(0.357005\pi\) | |||||||
\(450\) | −0.781645 | −0.0368471 | ||||||||
\(451\) | 11.1482 | 0.524949 | ||||||||
\(452\) | −13.3669 | −0.628724 | ||||||||
\(453\) | −8.50804 | −0.399743 | ||||||||
\(454\) | 3.43323 | 0.161130 | ||||||||
\(455\) | −44.2051 | −2.07237 | ||||||||
\(456\) | −2.32370 | −0.108817 | ||||||||
\(457\) | −1.54464 | −0.0722551 | −0.0361275 | − | 0.999347i | \(-0.511502\pi\) | ||||
−0.0361275 | + | 0.999347i | \(0.511502\pi\) | |||||||
\(458\) | −1.76519 | −0.0824817 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −35.6835 | −1.66375 | ||||||||
\(461\) | 30.9109 | 1.43967 | 0.719833 | − | 0.694148i | \(-0.244219\pi\) | ||||
0.719833 | + | 0.694148i | \(0.244219\pi\) | |||||||
\(462\) | 1.37939 | 0.0641752 | ||||||||
\(463\) | −24.7695 | −1.15113 | −0.575567 | − | 0.817754i | \(-0.695219\pi\) | ||||
−0.575567 | + | 0.817754i | \(0.695219\pi\) | |||||||
\(464\) | 12.5671 | 0.583414 | ||||||||
\(465\) | −11.7855 | −0.546539 | ||||||||
\(466\) | 2.19243 | 0.101562 | ||||||||
\(467\) | 18.4197 | 0.852361 | 0.426181 | − | 0.904638i | \(-0.359859\pi\) | ||||
0.426181 | + | 0.904638i | \(0.359859\pi\) | |||||||
\(468\) | 8.85163 | 0.409167 | ||||||||
\(469\) | −23.0355 | −1.06368 | ||||||||
\(470\) | 1.66011 | 0.0765754 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 0.000402234 0 | 1.85143e−5 0 | ||||||||
\(473\) | 1.63011 | 0.0749526 | ||||||||
\(474\) | 2.06843 | 0.0950062 | ||||||||
\(475\) | 10.7534 | 0.493399 | ||||||||
\(476\) | −6.45564 | −0.295894 | ||||||||
\(477\) | 7.81249 | 0.357709 | ||||||||
\(478\) | −2.10316 | −0.0961965 | ||||||||
\(479\) | 37.0653 | 1.69355 | 0.846777 | − | 0.531947i | \(-0.178540\pi\) | ||||
0.846777 | + | 0.531947i | \(0.178540\pi\) | |||||||
\(480\) | −7.13948 | −0.325871 | ||||||||
\(481\) | 27.2300 | 1.24158 | ||||||||
\(482\) | 1.24407 | 0.0566661 | ||||||||
\(483\) | −20.2886 | −0.923162 | ||||||||
\(484\) | 13.5094 | 0.614061 | ||||||||
\(485\) | −19.6412 | −0.891860 | ||||||||
\(486\) | 0.206596 | 0.00937139 | ||||||||
\(487\) | −21.9334 | −0.993895 | −0.496948 | − | 0.867780i | \(-0.665546\pi\) | ||||
−0.496948 | + | 0.867780i | \(0.665546\pi\) | |||||||
\(488\) | 8.41647 | 0.380996 | ||||||||
\(489\) | 21.7533 | 0.983718 | ||||||||
\(490\) | 2.37456 | 0.107272 | ||||||||
\(491\) | 4.66692 | 0.210615 | 0.105308 | − | 0.994440i | \(-0.466417\pi\) | ||||
0.105308 | + | 0.994440i | \(0.466417\pi\) | |||||||
\(492\) | −10.7790 | −0.485956 | ||||||||
\(493\) | −3.35506 | −0.151104 | ||||||||
\(494\) | 2.65547 | 0.119475 | ||||||||
\(495\) | 5.99957 | 0.269660 | ||||||||
\(496\) | −14.8954 | −0.668822 | ||||||||
\(497\) | −41.9197 | −1.88035 | ||||||||
\(498\) | −2.11355 | −0.0947105 | ||||||||
\(499\) | −0.286947 | −0.0128455 | −0.00642275 | − | 0.999979i | \(-0.502044\pi\) | ||||
−0.00642275 | + | 0.999979i | \(0.502044\pi\) | |||||||
\(500\) | −7.05710 | −0.315603 | ||||||||
\(501\) | 2.07171 | 0.0925572 | ||||||||
\(502\) | −2.04869 | −0.0914373 | ||||||||
\(503\) | 12.3518 | 0.550741 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(504\) | −2.69651 | −0.120112 | ||||||||
\(505\) | −12.9545 | −0.576466 | ||||||||
\(506\) | −2.57266 | −0.114369 | ||||||||
\(507\) | −7.45145 | −0.330931 | ||||||||
\(508\) | 3.37422 | 0.149707 | ||||||||
\(509\) | 7.66157 | 0.339593 | 0.169796 | − | 0.985479i | \(-0.445689\pi\) | ||||
0.169796 | + | 0.985479i | \(0.445689\pi\) | |||||||
\(510\) | 0.612286 | 0.0271125 | ||||||||
\(511\) | 1.96271 | 0.0868252 | ||||||||
\(512\) | −15.1482 | −0.669461 | ||||||||
\(513\) | −2.84222 | −0.125487 | ||||||||
\(514\) | 3.01591 | 0.133026 | ||||||||
\(515\) | −32.0664 | −1.41302 | ||||||||
\(516\) | −1.57613 | −0.0693852 | ||||||||
\(517\) | −5.48872 | −0.241393 | ||||||||
\(518\) | −4.10286 | −0.180269 | ||||||||
\(519\) | 6.97136 | 0.306009 | ||||||||
\(520\) | 10.9577 | 0.480525 | ||||||||
\(521\) | −5.42090 | −0.237494 | −0.118747 | − | 0.992925i | \(-0.537888\pi\) | ||||
−0.118747 | + | 0.992925i | \(0.537888\pi\) | |||||||
\(522\) | −0.693142 | −0.0303380 | ||||||||
\(523\) | 12.6758 | 0.554274 | 0.277137 | − | 0.960830i | \(-0.410614\pi\) | ||||
0.277137 | + | 0.960830i | \(0.410614\pi\) | |||||||
\(524\) | −24.9038 | −1.08793 | ||||||||
\(525\) | 12.4786 | 0.544610 | ||||||||
\(526\) | −1.98931 | −0.0867380 | ||||||||
\(527\) | 3.97663 | 0.173225 | ||||||||
\(528\) | 7.58270 | 0.329995 | ||||||||
\(529\) | 14.8396 | 0.645200 | ||||||||
\(530\) | 4.78348 | 0.207781 | ||||||||
\(531\) | 0.000491989 0 | 2.13505e−5 0 | ||||||||
\(532\) | 18.3484 | 0.795502 | ||||||||
\(533\) | 24.9046 | 1.07874 | ||||||||
\(534\) | 1.30510 | 0.0564773 | ||||||||
\(535\) | −39.3690 | −1.70207 | ||||||||
\(536\) | 5.71008 | 0.246638 | ||||||||
\(537\) | 15.8036 | 0.681977 | ||||||||
\(538\) | 5.00300 | 0.215695 | ||||||||
\(539\) | −7.85083 | −0.338159 | ||||||||
\(540\) | −5.80088 | −0.249630 | ||||||||
\(541\) | 13.3446 | 0.573730 | 0.286865 | − | 0.957971i | \(-0.407387\pi\) | ||||
0.286865 | + | 0.957971i | \(0.407387\pi\) | |||||||
\(542\) | −0.193575 | −0.00831474 | ||||||||
\(543\) | −15.5742 | −0.668354 | ||||||||
\(544\) | 2.40899 | 0.103284 | ||||||||
\(545\) | −22.2851 | −0.954588 | ||||||||
\(546\) | 3.08150 | 0.131876 | ||||||||
\(547\) | −37.6872 | −1.61139 | −0.805693 | − | 0.592333i | \(-0.798207\pi\) | ||||
−0.805693 | + | 0.592333i | \(0.798207\pi\) | |||||||
\(548\) | 12.7799 | 0.545931 | ||||||||
\(549\) | 10.2945 | 0.439360 | ||||||||
\(550\) | 1.58233 | 0.0674708 | ||||||||
\(551\) | 9.53580 | 0.406239 | ||||||||
\(552\) | 5.02917 | 0.214056 | ||||||||
\(553\) | −33.0215 | −1.40422 | ||||||||
\(554\) | 2.92124 | 0.124112 | ||||||||
\(555\) | −17.8451 | −0.757481 | ||||||||
\(556\) | 31.5218 | 1.33682 | ||||||||
\(557\) | −35.6177 | −1.50917 | −0.754586 | − | 0.656201i | \(-0.772162\pi\) | ||||
−0.754586 | + | 0.656201i | \(0.772162\pi\) | |||||||
\(558\) | 0.821556 | 0.0347792 | ||||||||
\(559\) | 3.64160 | 0.154023 | ||||||||
\(560\) | 36.6140 | 1.54722 | ||||||||
\(561\) | −2.02436 | −0.0854685 | ||||||||
\(562\) | −6.68189 | −0.281859 | ||||||||
\(563\) | 8.61111 | 0.362915 | 0.181457 | − | 0.983399i | \(-0.441919\pi\) | ||||
0.181457 | + | 0.983399i | \(0.441919\pi\) | |||||||
\(564\) | 5.30695 | 0.223463 | ||||||||
\(565\) | −20.2395 | −0.851483 | ||||||||
\(566\) | −4.96953 | −0.208885 | ||||||||
\(567\) | −3.29821 | −0.138512 | ||||||||
\(568\) | 10.3911 | 0.436002 | ||||||||
\(569\) | 39.4240 | 1.65274 | 0.826370 | − | 0.563127i | \(-0.190402\pi\) | ||||
0.826370 | + | 0.563127i | \(0.190402\pi\) | |||||||
\(570\) | −1.74025 | −0.0728912 | ||||||||
\(571\) | −33.0428 | −1.38280 | −0.691399 | − | 0.722473i | \(-0.743005\pi\) | ||||
−0.691399 | + | 0.722473i | \(0.743005\pi\) | |||||||
\(572\) | −17.9189 | −0.749226 | ||||||||
\(573\) | 9.33763 | 0.390085 | ||||||||
\(574\) | −3.75248 | −0.156626 | ||||||||
\(575\) | −23.2734 | −0.970569 | ||||||||
\(576\) | −6.99377 | −0.291407 | ||||||||
\(577\) | 22.7303 | 0.946275 | 0.473137 | − | 0.880989i | \(-0.343121\pi\) | ||||
0.473137 | + | 0.880989i | \(0.343121\pi\) | |||||||
\(578\) | −0.206596 | −0.00859327 | ||||||||
\(579\) | 12.2457 | 0.508916 | ||||||||
\(580\) | 19.4623 | 0.808127 | ||||||||
\(581\) | 33.7418 | 1.39985 | ||||||||
\(582\) | 1.36917 | 0.0567539 | ||||||||
\(583\) | −15.8153 | −0.655002 | ||||||||
\(584\) | −0.486521 | −0.0201324 | ||||||||
\(585\) | 13.4028 | 0.554136 | ||||||||
\(586\) | −5.77085 | −0.238392 | ||||||||
\(587\) | −13.8143 | −0.570179 | −0.285089 | − | 0.958501i | \(-0.592023\pi\) | ||||
−0.285089 | + | 0.958501i | \(0.592023\pi\) | |||||||
\(588\) | 7.59083 | 0.313041 | ||||||||
\(589\) | −11.3024 | −0.465709 | ||||||||
\(590\) | 0.000301238 0 | 1.24018e−5 0 | ||||||||
\(591\) | 20.2355 | 0.832378 | ||||||||
\(592\) | −22.5539 | −0.926961 | ||||||||
\(593\) | 28.1086 | 1.15428 | 0.577141 | − | 0.816644i | \(-0.304168\pi\) | ||||
0.577141 | + | 0.816644i | \(0.304168\pi\) | |||||||
\(594\) | −0.418225 | −0.0171600 | ||||||||
\(595\) | −9.77486 | −0.400730 | ||||||||
\(596\) | 21.8600 | 0.895419 | ||||||||
\(597\) | −0.253590 | −0.0103787 | ||||||||
\(598\) | −5.74722 | −0.235021 | ||||||||
\(599\) | 16.7476 | 0.684288 | 0.342144 | − | 0.939648i | \(-0.388847\pi\) | ||||
0.342144 | + | 0.939648i | \(0.388847\pi\) | |||||||
\(600\) | −3.09322 | −0.126280 | ||||||||
\(601\) | −36.3144 | −1.48130 | −0.740649 | − | 0.671893i | \(-0.765482\pi\) | ||||
−0.740649 | + | 0.671893i | \(0.765482\pi\) | |||||||
\(602\) | −0.548694 | −0.0223631 | ||||||||
\(603\) | 6.98424 | 0.284420 | ||||||||
\(604\) | −16.6529 | −0.677599 | ||||||||
\(605\) | 20.4553 | 0.831626 | ||||||||
\(606\) | 0.903045 | 0.0366837 | ||||||||
\(607\) | 10.1764 | 0.413047 | 0.206523 | − | 0.978442i | \(-0.433785\pi\) | ||||
0.206523 | + | 0.978442i | \(0.433785\pi\) | |||||||
\(608\) | −6.84687 | −0.277677 | ||||||||
\(609\) | 11.0657 | 0.448404 | ||||||||
\(610\) | 6.30320 | 0.255209 | ||||||||
\(611\) | −12.2616 | −0.496049 | ||||||||
\(612\) | 1.95732 | 0.0791199 | ||||||||
\(613\) | −34.9243 | −1.41058 | −0.705290 | − | 0.708919i | \(-0.749183\pi\) | ||||
−0.705290 | + | 0.708919i | \(0.749183\pi\) | |||||||
\(614\) | −5.96257 | −0.240630 | ||||||||
\(615\) | −16.3211 | −0.658132 | ||||||||
\(616\) | 5.45870 | 0.219937 | ||||||||
\(617\) | −14.6332 | −0.589112 | −0.294556 | − | 0.955634i | \(-0.595172\pi\) | ||||
−0.294556 | + | 0.955634i | \(0.595172\pi\) | |||||||
\(618\) | 2.23532 | 0.0899179 | ||||||||
\(619\) | 26.5532 | 1.06726 | 0.533631 | − | 0.845717i | \(-0.320827\pi\) | ||||
0.533631 | + | 0.845717i | \(0.320827\pi\) | |||||||
\(620\) | −23.0679 | −0.926431 | ||||||||
\(621\) | 6.15139 | 0.246847 | ||||||||
\(622\) | 2.99654 | 0.120150 | ||||||||
\(623\) | −20.8353 | −0.834749 | ||||||||
\(624\) | 16.9394 | 0.678120 | ||||||||
\(625\) | −29.6028 | −1.18411 | ||||||||
\(626\) | 0.871953 | 0.0348503 | ||||||||
\(627\) | 5.75367 | 0.229780 | ||||||||
\(628\) | 1.95732 | 0.0781055 | ||||||||
\(629\) | 6.02124 | 0.240083 | ||||||||
\(630\) | −2.01945 | −0.0804568 | ||||||||
\(631\) | 4.91139 | 0.195519 | 0.0977596 | − | 0.995210i | \(-0.468832\pi\) | ||||
0.0977596 | + | 0.995210i | \(0.468832\pi\) | |||||||
\(632\) | 8.18544 | 0.325599 | ||||||||
\(633\) | 22.3520 | 0.888411 | ||||||||
\(634\) | −1.11696 | −0.0443602 | ||||||||
\(635\) | 5.10910 | 0.202748 | ||||||||
\(636\) | 15.2915 | 0.606349 | ||||||||
\(637\) | −17.5384 | −0.694897 | ||||||||
\(638\) | 1.40317 | 0.0555519 | ||||||||
\(639\) | 12.7098 | 0.502793 | ||||||||
\(640\) | −18.5612 | −0.733694 | ||||||||
\(641\) | −10.3957 | −0.410604 | −0.205302 | − | 0.978699i | \(-0.565818\pi\) | ||||
−0.205302 | + | 0.978699i | \(0.565818\pi\) | |||||||
\(642\) | 2.74438 | 0.108312 | ||||||||
\(643\) | −28.3287 | −1.11718 | −0.558588 | − | 0.829445i | \(-0.688657\pi\) | ||||
−0.558588 | + | 0.829445i | \(0.688657\pi\) | |||||||
\(644\) | −39.7112 | −1.56484 | ||||||||
\(645\) | −2.38651 | −0.0939686 | ||||||||
\(646\) | 0.587192 | 0.0231027 | ||||||||
\(647\) | 3.79379 | 0.149149 | 0.0745745 | − | 0.997215i | \(-0.476240\pi\) | ||||
0.0745745 | + | 0.997215i | \(0.476240\pi\) | |||||||
\(648\) | 0.817567 | 0.0321171 | ||||||||
\(649\) | −0.000995963 0 | −3.90950e−5 0 | ||||||||
\(650\) | 3.53485 | 0.138648 | ||||||||
\(651\) | −13.1157 | −0.514047 | ||||||||
\(652\) | 42.5781 | 1.66749 | ||||||||
\(653\) | −1.93435 | −0.0756971 | −0.0378486 | − | 0.999283i | \(-0.512050\pi\) | ||||
−0.0378486 | + | 0.999283i | \(0.512050\pi\) | |||||||
\(654\) | 1.55347 | 0.0607457 | ||||||||
\(655\) | −37.7082 | −1.47338 | ||||||||
\(656\) | −20.6279 | −0.805384 | ||||||||
\(657\) | −0.595084 | −0.0232164 | ||||||||
\(658\) | 1.84750 | 0.0720229 | ||||||||
\(659\) | 41.5604 | 1.61896 | 0.809481 | − | 0.587146i | \(-0.199748\pi\) | ||||
0.809481 | + | 0.587146i | \(0.199748\pi\) | |||||||
\(660\) | 11.7431 | 0.457098 | ||||||||
\(661\) | 7.16370 | 0.278635 | 0.139318 | − | 0.990248i | \(-0.455509\pi\) | ||||
0.139318 | + | 0.990248i | \(0.455509\pi\) | |||||||
\(662\) | −4.88471 | −0.189850 | ||||||||
\(663\) | −4.52233 | −0.175633 | ||||||||
\(664\) | −8.36399 | −0.324586 | ||||||||
\(665\) | 27.7823 | 1.07735 | ||||||||
\(666\) | 1.24397 | 0.0482027 | ||||||||
\(667\) | −20.6383 | −0.799116 | ||||||||
\(668\) | 4.05500 | 0.156893 | ||||||||
\(669\) | −9.37799 | −0.362574 | ||||||||
\(670\) | 4.27636 | 0.165210 | ||||||||
\(671\) | −20.8398 | −0.804513 | ||||||||
\(672\) | −7.94534 | −0.306498 | ||||||||
\(673\) | −47.6487 | −1.83672 | −0.918362 | − | 0.395742i | \(-0.870487\pi\) | ||||
−0.918362 | + | 0.395742i | \(0.870487\pi\) | |||||||
\(674\) | 3.03421 | 0.116874 | ||||||||
\(675\) | −3.78344 | −0.145625 | ||||||||
\(676\) | −14.5849 | −0.560956 | ||||||||
\(677\) | 11.6955 | 0.449495 | 0.224747 | − | 0.974417i | \(-0.427844\pi\) | ||||
0.224747 | + | 0.974417i | \(0.427844\pi\) | |||||||
\(678\) | 1.41088 | 0.0541845 | ||||||||
\(679\) | −21.8581 | −0.838838 | ||||||||
\(680\) | 2.42301 | 0.0929183 | ||||||||
\(681\) | 16.6181 | 0.636806 | ||||||||
\(682\) | −1.66312 | −0.0636843 | ||||||||
\(683\) | 43.8188 | 1.67668 | 0.838340 | − | 0.545148i | \(-0.183526\pi\) | ||||
0.838340 | + | 0.545148i | \(0.183526\pi\) | |||||||
\(684\) | −5.56313 | −0.212711 | ||||||||
\(685\) | 19.3508 | 0.739356 | ||||||||
\(686\) | −2.12720 | −0.0812169 | ||||||||
\(687\) | −8.54414 | −0.325979 | ||||||||
\(688\) | −3.01624 | −0.114993 | ||||||||
\(689\) | −35.3307 | −1.34599 | ||||||||
\(690\) | 3.76641 | 0.143385 | ||||||||
\(691\) | 20.9087 | 0.795404 | 0.397702 | − | 0.917515i | \(-0.369808\pi\) | ||||
0.397702 | + | 0.917515i | \(0.369808\pi\) | |||||||
\(692\) | 13.6452 | 0.518711 | ||||||||
\(693\) | 6.67676 | 0.253629 | ||||||||
\(694\) | 0.0187611 | 0.000712163 0 | ||||||||
\(695\) | 47.7289 | 1.81046 | ||||||||
\(696\) | −2.74298 | −0.103972 | ||||||||
\(697\) | 5.50704 | 0.208594 | ||||||||
\(698\) | 5.93871 | 0.224784 | ||||||||
\(699\) | 10.6121 | 0.401388 | ||||||||
\(700\) | 24.4246 | 0.923161 | ||||||||
\(701\) | −14.9812 | −0.565831 | −0.282915 | − | 0.959145i | \(-0.591302\pi\) | ||||
−0.282915 | + | 0.959145i | \(0.591302\pi\) | |||||||
\(702\) | −0.934296 | −0.0352627 | ||||||||
\(703\) | −17.1137 | −0.645455 | ||||||||
\(704\) | 14.1579 | 0.533596 | ||||||||
\(705\) | 8.03555 | 0.302636 | ||||||||
\(706\) | 0.721171 | 0.0271416 | ||||||||
\(707\) | −14.4167 | −0.542195 | ||||||||
\(708\) | 0.000962980 0 | 3.61910e−5 0 | ||||||||
\(709\) | 39.0216 | 1.46549 | 0.732743 | − | 0.680505i | \(-0.238240\pi\) | ||||
0.732743 | + | 0.680505i | \(0.238240\pi\) | |||||||
\(710\) | 7.78206 | 0.292055 | ||||||||
\(711\) | 10.0119 | 0.375477 | ||||||||
\(712\) | 5.16470 | 0.193555 | ||||||||
\(713\) | 24.4618 | 0.916101 | ||||||||
\(714\) | 0.681397 | 0.0255007 | ||||||||
\(715\) | −27.1320 | −1.01468 | ||||||||
\(716\) | 30.9327 | 1.15601 | ||||||||
\(717\) | −10.1801 | −0.380182 | ||||||||
\(718\) | 0.327036 | 0.0122049 | ||||||||
\(719\) | 0.467610 | 0.0174389 | 0.00871945 | − | 0.999962i | \(-0.497224\pi\) | ||||
0.00871945 | + | 0.999962i | \(0.497224\pi\) | |||||||
\(720\) | −11.1012 | −0.413716 | ||||||||
\(721\) | −35.6859 | −1.32901 | ||||||||
\(722\) | 2.25640 | 0.0839745 | ||||||||
\(723\) | 6.02177 | 0.223952 | ||||||||
\(724\) | −30.4837 | −1.13292 | ||||||||
\(725\) | 12.6937 | 0.471431 | ||||||||
\(726\) | −1.42592 | −0.0529209 | ||||||||
\(727\) | −17.1421 | −0.635767 | −0.317883 | − | 0.948130i | \(-0.602972\pi\) | ||||
−0.317883 | + | 0.948130i | \(0.602972\pi\) | |||||||
\(728\) | 12.1945 | 0.451958 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.364362 | −0.0134856 | ||||||||
\(731\) | 0.805249 | 0.0297832 | ||||||||
\(732\) | 20.1497 | 0.744753 | ||||||||
\(733\) | −10.4110 | −0.384537 | −0.192269 | − | 0.981342i | \(-0.561584\pi\) | ||||
−0.192269 | + | 0.981342i | \(0.561584\pi\) | |||||||
\(734\) | −1.45881 | −0.0538456 | ||||||||
\(735\) | 11.4937 | 0.423952 | ||||||||
\(736\) | 14.8186 | 0.546222 | ||||||||
\(737\) | −14.1386 | −0.520802 | ||||||||
\(738\) | 1.13773 | 0.0418806 | ||||||||
\(739\) | 5.63361 | 0.207236 | 0.103618 | − | 0.994617i | \(-0.466958\pi\) | ||||
0.103618 | + | 0.994617i | \(0.466958\pi\) | |||||||
\(740\) | −34.9285 | −1.28400 | ||||||||
\(741\) | 12.8534 | 0.472183 | ||||||||
\(742\) | 5.32341 | 0.195429 | ||||||||
\(743\) | −28.7343 | −1.05416 | −0.527079 | − | 0.849816i | \(-0.676713\pi\) | ||||
−0.527079 | + | 0.849816i | \(0.676713\pi\) | |||||||
\(744\) | 3.25116 | 0.119193 | ||||||||
\(745\) | 33.0994 | 1.21267 | ||||||||
\(746\) | 0.312268 | 0.0114330 | ||||||||
\(747\) | −10.2303 | −0.374309 | ||||||||
\(748\) | −3.96231 | −0.144877 | ||||||||
\(749\) | −43.8127 | −1.60088 | ||||||||
\(750\) | 0.744882 | 0.0271992 | ||||||||
\(751\) | −15.8107 | −0.576941 | −0.288470 | − | 0.957489i | \(-0.593147\pi\) | ||||
−0.288470 | + | 0.957489i | \(0.593147\pi\) | |||||||
\(752\) | 10.1559 | 0.370349 | ||||||||
\(753\) | −9.91638 | −0.361373 | ||||||||
\(754\) | 3.13461 | 0.114156 | ||||||||
\(755\) | −25.2152 | −0.917674 | ||||||||
\(756\) | −6.45564 | −0.234789 | ||||||||
\(757\) | 26.1004 | 0.948637 | 0.474318 | − | 0.880353i | \(-0.342695\pi\) | ||||
0.474318 | + | 0.880353i | \(0.342695\pi\) | |||||||
\(758\) | 6.71990 | 0.244078 | ||||||||
\(759\) | −12.4526 | −0.452001 | ||||||||
\(760\) | −6.88673 | −0.249808 | ||||||||
\(761\) | −17.0426 | −0.617794 | −0.308897 | − | 0.951096i | \(-0.599960\pi\) | ||||
−0.308897 | + | 0.951096i | \(0.599960\pi\) | |||||||
\(762\) | −0.356151 | −0.0129020 | ||||||||
\(763\) | −24.8005 | −0.897837 | ||||||||
\(764\) | 18.2767 | 0.661228 | ||||||||
\(765\) | 2.96369 | 0.107152 | ||||||||
\(766\) | −2.49278 | −0.0900678 | ||||||||
\(767\) | −0.00222494 | −8.03378e−5 0 | ||||||||
\(768\) | −12.6937 | −0.458043 | ||||||||
\(769\) | 41.2812 | 1.48864 | 0.744320 | − | 0.667823i | \(-0.232774\pi\) | ||||
0.744320 | + | 0.667823i | \(0.232774\pi\) | |||||||
\(770\) | 4.08809 | 0.147324 | ||||||||
\(771\) | 14.5981 | 0.525738 | ||||||||
\(772\) | 23.9688 | 0.862656 | ||||||||
\(773\) | −10.1049 | −0.363447 | −0.181723 | − | 0.983350i | \(-0.558168\pi\) | ||||
−0.181723 | + | 0.983350i | \(0.558168\pi\) | |||||||
\(774\) | 0.166361 | 0.00597973 | ||||||||
\(775\) | −15.0453 | −0.540445 | ||||||||
\(776\) | 5.41824 | 0.194503 | ||||||||
\(777\) | −19.8593 | −0.712449 | ||||||||
\(778\) | −8.08034 | −0.289694 | ||||||||
\(779\) | −15.6522 | −0.560799 | ||||||||
\(780\) | 26.2335 | 0.939309 | ||||||||
\(781\) | −25.7292 | −0.920665 | ||||||||
\(782\) | −1.27085 | −0.0454456 | ||||||||
\(783\) | −3.35506 | −0.119900 | ||||||||
\(784\) | 14.5266 | 0.518808 | ||||||||
\(785\) | 2.96369 | 0.105779 | ||||||||
\(786\) | 2.62861 | 0.0937593 | ||||||||
\(787\) | 38.9370 | 1.38795 | 0.693977 | − | 0.719997i | \(-0.255857\pi\) | ||||
0.693977 | + | 0.719997i | \(0.255857\pi\) | |||||||
\(788\) | 39.6074 | 1.41095 | ||||||||
\(789\) | −9.62897 | −0.342800 | ||||||||
\(790\) | 6.13018 | 0.218102 | ||||||||
\(791\) | −22.5240 | −0.800862 | ||||||||
\(792\) | −1.65505 | −0.0588096 | ||||||||
\(793\) | −46.5552 | −1.65323 | ||||||||
\(794\) | −3.25217 | −0.115415 | ||||||||
\(795\) | 23.1538 | 0.821180 | ||||||||
\(796\) | −0.496356 | −0.0175929 | ||||||||
\(797\) | −5.96014 | −0.211119 | −0.105559 | − | 0.994413i | \(-0.533663\pi\) | ||||
−0.105559 | + | 0.994413i | \(0.533663\pi\) | |||||||
\(798\) | −1.93668 | −0.0685577 | ||||||||
\(799\) | −2.71134 | −0.0959202 | ||||||||
\(800\) | −9.11426 | −0.322238 | ||||||||
\(801\) | 6.31716 | 0.223206 | ||||||||
\(802\) | −0.840668 | −0.0296850 | ||||||||
\(803\) | 1.20466 | 0.0425116 | ||||||||
\(804\) | 13.6704 | 0.482117 | ||||||||
\(805\) | −60.1290 | −2.11927 | ||||||||
\(806\) | −3.71535 | −0.130868 | ||||||||
\(807\) | 24.2163 | 0.852456 | ||||||||
\(808\) | 3.57364 | 0.125720 | ||||||||
\(809\) | 45.2004 | 1.58916 | 0.794581 | − | 0.607159i | \(-0.207691\pi\) | ||||
0.794581 | + | 0.607159i | \(0.207691\pi\) | |||||||
\(810\) | 0.612286 | 0.0215136 | ||||||||
\(811\) | −18.7209 | −0.657380 | −0.328690 | − | 0.944438i | \(-0.606607\pi\) | ||||
−0.328690 | + | 0.944438i | \(0.606607\pi\) | |||||||
\(812\) | 21.6590 | 0.760083 | ||||||||
\(813\) | −0.936971 | −0.0328610 | ||||||||
\(814\) | −2.51823 | −0.0882640 | ||||||||
\(815\) | 64.4700 | 2.25828 | ||||||||
\(816\) | 3.74573 | 0.131127 | ||||||||
\(817\) | −2.28869 | −0.0800712 | ||||||||
\(818\) | −6.80817 | −0.238042 | ||||||||
\(819\) | 14.9156 | 0.521193 | ||||||||
\(820\) | −31.9457 | −1.11559 | ||||||||
\(821\) | −7.15064 | −0.249559 | −0.124780 | − | 0.992184i | \(-0.539822\pi\) | ||||
−0.124780 | + | 0.992184i | \(0.539822\pi\) | |||||||
\(822\) | −1.34893 | −0.0470493 | ||||||||
\(823\) | 13.0128 | 0.453598 | 0.226799 | − | 0.973942i | \(-0.427174\pi\) | ||||
0.226799 | + | 0.973942i | \(0.427174\pi\) | |||||||
\(824\) | 8.84589 | 0.308161 | ||||||||
\(825\) | 7.65904 | 0.266654 | ||||||||
\(826\) | 0.000335240 0 | 1.16645e−5 0 | ||||||||
\(827\) | 40.2504 | 1.39964 | 0.699821 | − | 0.714318i | \(-0.253263\pi\) | ||||
0.699821 | + | 0.714318i | \(0.253263\pi\) | |||||||
\(828\) | 12.0402 | 0.418427 | ||||||||
\(829\) | 22.0878 | 0.767142 | 0.383571 | − | 0.923511i | \(-0.374694\pi\) | ||||
0.383571 | + | 0.923511i | \(0.374694\pi\) | |||||||
\(830\) | −6.26390 | −0.217423 | ||||||||
\(831\) | 14.1399 | 0.490506 | ||||||||
\(832\) | 31.6281 | 1.09651 | ||||||||
\(833\) | −3.87818 | −0.134371 | ||||||||
\(834\) | −3.32714 | −0.115210 | ||||||||
\(835\) | 6.13990 | 0.212480 | ||||||||
\(836\) | 11.2618 | 0.389496 | ||||||||
\(837\) | 3.97663 | 0.137452 | ||||||||
\(838\) | −0.172820 | −0.00596995 | ||||||||
\(839\) | 24.3018 | 0.838990 | 0.419495 | − | 0.907758i | \(-0.362207\pi\) | ||||
0.419495 | + | 0.907758i | \(0.362207\pi\) | |||||||
\(840\) | −7.99160 | −0.275736 | ||||||||
\(841\) | −17.7436 | −0.611848 | ||||||||
\(842\) | 5.50854 | 0.189837 | ||||||||
\(843\) | −32.3428 | −1.11394 | ||||||||
\(844\) | 43.7499 | 1.50593 | ||||||||
\(845\) | −22.0838 | −0.759705 | ||||||||
\(846\) | −0.560152 | −0.0192584 | ||||||||
\(847\) | 22.7641 | 0.782185 | ||||||||
\(848\) | 29.2635 | 1.00491 | ||||||||
\(849\) | −24.0543 | −0.825541 | ||||||||
\(850\) | 0.781645 | 0.0268102 | ||||||||
\(851\) | 37.0390 | 1.26968 | ||||||||
\(852\) | 24.8772 | 0.852278 | ||||||||
\(853\) | −1.23958 | −0.0424423 | −0.0212211 | − | 0.999775i | \(-0.506755\pi\) | ||||
−0.0212211 | + | 0.999775i | \(0.506755\pi\) | |||||||
\(854\) | 7.01467 | 0.240037 | ||||||||
\(855\) | −8.42345 | −0.288076 | ||||||||
\(856\) | 10.8604 | 0.371201 | ||||||||
\(857\) | −33.5881 | −1.14735 | −0.573674 | − | 0.819083i | \(-0.694483\pi\) | ||||
−0.573674 | + | 0.819083i | \(0.694483\pi\) | |||||||
\(858\) | 1.89135 | 0.0645696 | ||||||||
\(859\) | −41.5601 | −1.41801 | −0.709006 | − | 0.705203i | \(-0.750856\pi\) | ||||
−0.709006 | + | 0.705203i | \(0.750856\pi\) | |||||||
\(860\) | −4.67115 | −0.159285 | ||||||||
\(861\) | −18.1634 | −0.619006 | ||||||||
\(862\) | −3.19806 | −0.108926 | ||||||||
\(863\) | −8.15597 | −0.277633 | −0.138816 | − | 0.990318i | \(-0.544330\pi\) | ||||
−0.138816 | + | 0.990318i | \(0.544330\pi\) | |||||||
\(864\) | 2.40899 | 0.0819554 | ||||||||
\(865\) | 20.6609 | 0.702493 | ||||||||
\(866\) | 3.20068 | 0.108764 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −25.6717 | −0.871354 | ||||||||
\(869\) | −20.2678 | −0.687537 | ||||||||
\(870\) | −2.05425 | −0.0696458 | ||||||||
\(871\) | −31.5850 | −1.07022 | ||||||||
\(872\) | 6.14759 | 0.208184 | ||||||||
\(873\) | 6.62727 | 0.224299 | ||||||||
\(874\) | 3.61204 | 0.122179 | ||||||||
\(875\) | −11.8917 | −0.402012 | ||||||||
\(876\) | −1.16477 | −0.0393539 | ||||||||
\(877\) | −14.7098 | −0.496716 | −0.248358 | − | 0.968668i | \(-0.579891\pi\) | ||||
−0.248358 | + | 0.968668i | \(0.579891\pi\) | |||||||
\(878\) | 5.65414 | 0.190818 | ||||||||
\(879\) | −27.9330 | −0.942157 | ||||||||
\(880\) | 22.4728 | 0.757556 | ||||||||
\(881\) | −35.4621 | −1.19475 | −0.597374 | − | 0.801963i | \(-0.703789\pi\) | ||||
−0.597374 | + | 0.801963i | \(0.703789\pi\) | |||||||
\(882\) | −0.801217 | −0.0269784 | ||||||||
\(883\) | 24.9029 | 0.838050 | 0.419025 | − | 0.907975i | \(-0.362372\pi\) | ||||
0.419025 | + | 0.907975i | \(0.362372\pi\) | |||||||
\(884\) | −8.85163 | −0.297713 | ||||||||
\(885\) | 0.00145810 | 4.90136e−5 0 | ||||||||
\(886\) | 3.46713 | 0.116481 | ||||||||
\(887\) | 17.0693 | 0.573132 | 0.286566 | − | 0.958061i | \(-0.407486\pi\) | ||||
0.286566 | + | 0.958061i | \(0.407486\pi\) | |||||||
\(888\) | 4.92277 | 0.165197 | ||||||||
\(889\) | 5.68578 | 0.190695 | ||||||||
\(890\) | 3.86791 | 0.129653 | ||||||||
\(891\) | −2.02436 | −0.0678186 | ||||||||
\(892\) | −18.3557 | −0.614594 | ||||||||
\(893\) | 7.70621 | 0.257879 | ||||||||
\(894\) | −2.30733 | −0.0771687 | ||||||||
\(895\) | 46.8370 | 1.56559 | ||||||||
\(896\) | −20.6562 | −0.690076 | ||||||||
\(897\) | −27.8186 | −0.928836 | ||||||||
\(898\) | −3.80224 | −0.126882 | ||||||||
\(899\) | −13.3418 | −0.444974 | ||||||||
\(900\) | −7.40540 | −0.246847 | ||||||||
\(901\) | −7.81249 | −0.260272 | ||||||||
\(902\) | −2.30318 | −0.0766875 | ||||||||
\(903\) | −2.65588 | −0.0883821 | ||||||||
\(904\) | 5.58330 | 0.185698 | ||||||||
\(905\) | −46.1571 | −1.53432 | ||||||||
\(906\) | 1.75773 | 0.0583966 | ||||||||
\(907\) | −1.80384 | −0.0598956 | −0.0299478 | − | 0.999551i | \(-0.509534\pi\) | ||||
−0.0299478 | + | 0.999551i | \(0.509534\pi\) | |||||||
\(908\) | 32.5269 | 1.07944 | ||||||||
\(909\) | 4.37106 | 0.144979 | ||||||||
\(910\) | 9.13261 | 0.302743 | ||||||||
\(911\) | 17.2375 | 0.571104 | 0.285552 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285552 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(912\) | −10.6462 | −0.352530 | ||||||||
\(913\) | 20.7099 | 0.685398 | ||||||||
\(914\) | 0.319116 | 0.0105554 | ||||||||
\(915\) | 30.5098 | 1.00862 | ||||||||
\(916\) | −16.7236 | −0.552563 | ||||||||
\(917\) | −41.9644 | −1.38579 | ||||||||
\(918\) | −0.206596 | −0.00681869 | ||||||||
\(919\) | 29.7998 | 0.983006 | 0.491503 | − | 0.870876i | \(-0.336448\pi\) | ||||
0.491503 | + | 0.870876i | \(0.336448\pi\) | |||||||
\(920\) | 14.9049 | 0.491400 | ||||||||
\(921\) | −28.8610 | −0.951003 | ||||||||
\(922\) | −6.38608 | −0.210314 | ||||||||
\(923\) | −57.4780 | −1.89191 | ||||||||
\(924\) | 13.0685 | 0.429923 | ||||||||
\(925\) | −22.7810 | −0.749035 | ||||||||
\(926\) | 5.11728 | 0.168164 | ||||||||
\(927\) | 10.8198 | 0.355368 | ||||||||
\(928\) | −8.08228 | −0.265314 | ||||||||
\(929\) | 36.6222 | 1.20153 | 0.600767 | − | 0.799424i | \(-0.294862\pi\) | ||||
0.600767 | + | 0.799424i | \(0.294862\pi\) | |||||||
\(930\) | 2.43484 | 0.0798414 | ||||||||
\(931\) | 11.0226 | 0.361252 | ||||||||
\(932\) | 20.7713 | 0.680387 | ||||||||
\(933\) | 14.5043 | 0.474850 | ||||||||
\(934\) | −3.80544 | −0.124518 | ||||||||
\(935\) | −5.99957 | −0.196207 | ||||||||
\(936\) | −3.69731 | −0.120850 | ||||||||
\(937\) | 26.2106 | 0.856262 | 0.428131 | − | 0.903717i | \(-0.359172\pi\) | ||||
0.428131 | + | 0.903717i | \(0.359172\pi\) | |||||||
\(938\) | 4.75904 | 0.155388 | ||||||||
\(939\) | 4.22057 | 0.137733 | ||||||||
\(940\) | 15.7281 | 0.512995 | ||||||||
\(941\) | 31.3776 | 1.02288 | 0.511440 | − | 0.859319i | \(-0.329112\pi\) | ||||
0.511440 | + | 0.859319i | \(0.329112\pi\) | |||||||
\(942\) | −0.206596 | −0.00673127 | ||||||||
\(943\) | 33.8760 | 1.10315 | ||||||||
\(944\) | 0.00184286 | 5.99800e−5 0 | ||||||||
\(945\) | −9.77486 | −0.317976 | ||||||||
\(946\) | −0.336775 | −0.0109495 | ||||||||
\(947\) | 31.8858 | 1.03615 | 0.518075 | − | 0.855335i | \(-0.326649\pi\) | ||||
0.518075 | + | 0.855335i | \(0.326649\pi\) | |||||||
\(948\) | 19.5966 | 0.636467 | ||||||||
\(949\) | 2.69116 | 0.0873589 | ||||||||
\(950\) | −2.22161 | −0.0720784 | ||||||||
\(951\) | −5.40649 | −0.175318 | ||||||||
\(952\) | 2.69651 | 0.0873943 | ||||||||
\(953\) | −32.6370 | −1.05722 | −0.528608 | − | 0.848866i | \(-0.677286\pi\) | ||||
−0.528608 | + | 0.848866i | \(0.677286\pi\) | |||||||
\(954\) | −1.61403 | −0.0522562 | ||||||||
\(955\) | 27.6738 | 0.895504 | ||||||||
\(956\) | −19.9256 | −0.644441 | ||||||||
\(957\) | 6.79184 | 0.219549 | ||||||||
\(958\) | −7.65754 | −0.247404 | ||||||||
\(959\) | 21.5350 | 0.695401 | ||||||||
\(960\) | −20.7274 | −0.668972 | ||||||||
\(961\) | −15.1864 | −0.489885 | ||||||||
\(962\) | −5.62562 | −0.181377 | ||||||||
\(963\) | 13.2838 | 0.428064 | ||||||||
\(964\) | 11.7865 | 0.379618 | ||||||||
\(965\) | 36.2926 | 1.16830 | ||||||||
\(966\) | 4.19154 | 0.134861 | ||||||||
\(967\) | −0.913185 | −0.0293661 | −0.0146830 | − | 0.999892i | \(-0.504674\pi\) | ||||
−0.0146830 | + | 0.999892i | \(0.504674\pi\) | |||||||
\(968\) | −5.64282 | −0.181367 | ||||||||
\(969\) | 2.84222 | 0.0913052 | ||||||||
\(970\) | 4.05779 | 0.130288 | ||||||||
\(971\) | −21.3000 | −0.683550 | −0.341775 | − | 0.939782i | \(-0.611028\pi\) | ||||
−0.341775 | + | 0.939782i | \(0.611028\pi\) | |||||||
\(972\) | 1.95732 | 0.0627810 | ||||||||
\(973\) | 53.1162 | 1.70283 | ||||||||
\(974\) | 4.53135 | 0.145194 | ||||||||
\(975\) | 17.1100 | 0.547958 | ||||||||
\(976\) | 38.5605 | 1.23429 | ||||||||
\(977\) | 16.5788 | 0.530404 | 0.265202 | − | 0.964193i | \(-0.414561\pi\) | ||||
0.265202 | + | 0.964193i | \(0.414561\pi\) | |||||||
\(978\) | −4.49415 | −0.143707 | ||||||||
\(979\) | −12.7882 | −0.408713 | ||||||||
\(980\) | 22.4968 | 0.718635 | ||||||||
\(981\) | 7.51938 | 0.240075 | ||||||||
\(982\) | −0.964168 | −0.0307678 | ||||||||
\(983\) | 34.5744 | 1.10275 | 0.551376 | − | 0.834257i | \(-0.314103\pi\) | ||||
0.551376 | + | 0.834257i | \(0.314103\pi\) | |||||||
\(984\) | 4.50237 | 0.143530 | ||||||||
\(985\) | 59.9718 | 1.91086 | ||||||||
\(986\) | 0.693142 | 0.0220741 | ||||||||
\(987\) | 8.94255 | 0.284645 | ||||||||
\(988\) | 25.1583 | 0.800392 | ||||||||
\(989\) | 4.95340 | 0.157509 | ||||||||
\(990\) | −1.23949 | −0.0393935 | ||||||||
\(991\) | 13.4427 | 0.427020 | 0.213510 | − | 0.976941i | \(-0.431510\pi\) | ||||
0.213510 | + | 0.976941i | \(0.431510\pi\) | |||||||
\(992\) | 9.57965 | 0.304154 | ||||||||
\(993\) | −23.6438 | −0.750312 | ||||||||
\(994\) | 8.66044 | 0.274693 | ||||||||
\(995\) | −0.751561 | −0.0238261 | ||||||||
\(996\) | −20.0240 | −0.634486 | ||||||||
\(997\) | 30.8122 | 0.975831 | 0.487915 | − | 0.872891i | \(-0.337757\pi\) | ||||
0.487915 | + | 0.872891i | \(0.337757\pi\) | |||||||
\(998\) | 0.0592821 | 0.00187654 | ||||||||
\(999\) | 6.02124 | 0.190504 |
(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 | 8007.2.a.f.1.23 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.23 | ✓ | 48 | 1.1 | even | 1 | trivial |