Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7168.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 7 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.25928\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.25928 | 0.890446 | 0.445223 | − | 0.895420i | \(-0.353124\pi\) | ||||
0.445223 | + | 0.895420i | \(0.353124\pi\) | |||||||
\(3\) | 1.78089 | 1.02820 | 0.514099 | − | 0.857731i | \(-0.328126\pi\) | ||||
0.514099 | + | 0.857731i | \(0.328126\pi\) | |||||||
\(4\) | −0.414214 | −0.207107 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.24264 | 0.915554 | ||||||||
\(7\) | −0.828427 | −0.313116 | −0.156558 | − | 0.987669i | \(-0.550040\pi\) | ||||
−0.156558 | + | 0.987669i | \(0.550040\pi\) | |||||||
\(8\) | −3.04017 | −1.07486 | ||||||||
\(9\) | 0.171573 | 0.0571910 | ||||||||
\(10\) | 1.25928 | 0.398219 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | −0.737669 | −0.212947 | ||||||||
\(13\) | 4.29945 | 1.19245 | 0.596227 | − | 0.802816i | \(-0.296666\pi\) | ||||
0.596227 | + | 0.802816i | \(0.296666\pi\) | |||||||
\(14\) | −1.04322 | −0.278813 | ||||||||
\(15\) | 1.78089 | 0.459824 | ||||||||
\(16\) | −3.00000 | −0.750000 | ||||||||
\(17\) | 7.65685 | 1.85706 | 0.928530 | − | 0.371257i | \(-0.121073\pi\) | ||||
0.928530 | + | 0.371257i | \(0.121073\pi\) | |||||||
\(18\) | 0.216058 | 0.0509254 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.414214 | −0.0926210 | ||||||||
\(21\) | −1.47534 | −0.321945 | ||||||||
\(22\) | 2.51856 | 0.536959 | ||||||||
\(23\) | −0.828427 | −0.172739 | −0.0863695 | − | 0.996263i | \(-0.527527\pi\) | ||||
−0.0863695 | + | 0.996263i | \(0.527527\pi\) | |||||||
\(24\) | −5.41421 | −1.10517 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.41421 | 1.06181 | ||||||||
\(27\) | −5.03712 | −0.969394 | ||||||||
\(28\) | 0.343146 | 0.0648485 | ||||||||
\(29\) | 8.59890 | 1.59678 | 0.798388 | − | 0.602143i | \(-0.205686\pi\) | ||||
0.798388 | + | 0.602143i | \(0.205686\pi\) | |||||||
\(30\) | 2.24264 | 0.409448 | ||||||||
\(31\) | 3.56178 | 0.639715 | 0.319857 | − | 0.947466i | \(-0.396365\pi\) | ||||
0.319857 | + | 0.947466i | \(0.396365\pi\) | |||||||
\(32\) | 2.30250 | 0.407029 | ||||||||
\(33\) | 3.56178 | 0.620027 | ||||||||
\(34\) | 9.64212 | 1.65361 | ||||||||
\(35\) | −0.828427 | −0.140030 | ||||||||
\(36\) | −0.0710678 | −0.0118446 | ||||||||
\(37\) | 0.737669 | 0.121272 | 0.0606360 | − | 0.998160i | \(-0.480687\pi\) | ||||
0.0606360 | + | 0.998160i | \(0.480687\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.65685 | 1.22608 | ||||||||
\(40\) | −3.04017 | −0.480693 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | −1.85786 | −0.286675 | ||||||||
\(43\) | −4.82843 | −0.736328 | −0.368164 | − | 0.929761i | \(-0.620014\pi\) | ||||
−0.368164 | + | 0.929761i | \(0.620014\pi\) | |||||||
\(44\) | −0.828427 | −0.124890 | ||||||||
\(45\) | 0.171573 | 0.0255766 | ||||||||
\(46\) | −1.04322 | −0.153815 | ||||||||
\(47\) | 10.4853 | 1.52944 | 0.764718 | − | 0.644365i | \(-0.222878\pi\) | ||||
0.764718 | + | 0.644365i | \(0.222878\pi\) | |||||||
\(48\) | −5.34267 | −0.771148 | ||||||||
\(49\) | −6.31371 | −0.901958 | ||||||||
\(50\) | 1.25928 | 0.178089 | ||||||||
\(51\) | 13.6360 | 1.90943 | ||||||||
\(52\) | −1.78089 | −0.246965 | ||||||||
\(53\) | −7.86123 | −1.07982 | −0.539912 | − | 0.841722i | \(-0.681542\pi\) | ||||
−0.539912 | + | 0.841722i | \(0.681542\pi\) | |||||||
\(54\) | −6.34315 | −0.863193 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 2.51856 | 0.336557 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.8284 | 1.42184 | ||||||||
\(59\) | −7.12356 | −0.927409 | −0.463705 | − | 0.885990i | \(-0.653480\pi\) | ||||
−0.463705 | + | 0.885990i | \(0.653480\pi\) | |||||||
\(60\) | −0.737669 | −0.0952327 | ||||||||
\(61\) | −2.82843 | −0.362143 | −0.181071 | − | 0.983470i | \(-0.557957\pi\) | ||||
−0.181071 | + | 0.983470i | \(0.557957\pi\) | |||||||
\(62\) | 4.48528 | 0.569631 | ||||||||
\(63\) | −0.142136 | −0.0179074 | ||||||||
\(64\) | 8.89949 | 1.11244 | ||||||||
\(65\) | 4.29945 | 0.533281 | ||||||||
\(66\) | 4.48528 | 0.552100 | ||||||||
\(67\) | 6.81801 | 0.832953 | 0.416476 | − | 0.909147i | \(-0.363265\pi\) | ||||
0.416476 | + | 0.909147i | \(0.363265\pi\) | |||||||
\(68\) | −3.17157 | −0.384610 | ||||||||
\(69\) | −1.47534 | −0.177610 | ||||||||
\(70\) | −1.04322 | −0.124689 | ||||||||
\(71\) | 13.6360 | 1.61830 | 0.809149 | − | 0.587603i | \(-0.199928\pi\) | ||||
0.809149 | + | 0.587603i | \(0.199928\pi\) | |||||||
\(72\) | −0.521611 | −0.0614724 | ||||||||
\(73\) | −11.6569 | −1.36433 | −0.682166 | − | 0.731198i | \(-0.738962\pi\) | ||||
−0.682166 | + | 0.731198i | \(0.738962\pi\) | |||||||
\(74\) | 0.928932 | 0.107986 | ||||||||
\(75\) | 1.78089 | 0.205640 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.65685 | −0.188816 | ||||||||
\(78\) | 9.64212 | 1.09176 | ||||||||
\(79\) | 7.12356 | 0.801464 | 0.400732 | − | 0.916195i | \(-0.368756\pi\) | ||||
0.400732 | + | 0.916195i | \(0.368756\pi\) | |||||||
\(80\) | −3.00000 | −0.335410 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.82843 | 0.969046 | 0.484523 | − | 0.874779i | \(-0.338993\pi\) | ||||
0.484523 | + | 0.874779i | \(0.338993\pi\) | |||||||
\(84\) | 0.611105 | 0.0666770 | ||||||||
\(85\) | 7.65685 | 0.830502 | ||||||||
\(86\) | −6.08034 | −0.655660 | ||||||||
\(87\) | 15.3137 | 1.64180 | ||||||||
\(88\) | −6.08034 | −0.648167 | ||||||||
\(89\) | −15.7225 | −1.66658 | −0.833289 | − | 0.552838i | \(-0.813545\pi\) | ||||
−0.833289 | + | 0.552838i | \(0.813545\pi\) | |||||||
\(90\) | 0.216058 | 0.0227745 | ||||||||
\(91\) | −3.56178 | −0.373376 | ||||||||
\(92\) | 0.343146 | 0.0357754 | ||||||||
\(93\) | 6.34315 | 0.657754 | ||||||||
\(94\) | 13.2039 | 1.36188 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.10051 | 0.418506 | ||||||||
\(97\) | 4.29945 | 0.436543 | 0.218272 | − | 0.975888i | \(-0.429958\pi\) | ||||
0.218272 | + | 0.975888i | \(0.429958\pi\) | |||||||
\(98\) | −7.95073 | −0.803145 | ||||||||
\(99\) | 0.343146 | 0.0344874 | ||||||||
\(100\) | −0.414214 | −0.0414214 | ||||||||
\(101\) | 0.485281 | 0.0482873 | 0.0241437 | − | 0.999708i | \(-0.492314\pi\) | ||||
0.0241437 | + | 0.999708i | \(0.492314\pi\) | |||||||
\(102\) | 17.1716 | 1.70024 | ||||||||
\(103\) | −5.34267 | −0.526429 | −0.263215 | − | 0.964737i | \(-0.584783\pi\) | ||||
−0.263215 | + | 0.964737i | \(0.584783\pi\) | |||||||
\(104\) | −13.0711 | −1.28172 | ||||||||
\(105\) | −1.47534 | −0.143978 | ||||||||
\(106\) | −9.89949 | −0.961524 | ||||||||
\(107\) | −13.9416 | −1.34778 | −0.673891 | − | 0.738830i | \(-0.735378\pi\) | ||||
−0.673891 | + | 0.738830i | \(0.735378\pi\) | |||||||
\(108\) | 2.08644 | 0.200768 | ||||||||
\(109\) | −18.6731 | −1.78856 | −0.894281 | − | 0.447505i | \(-0.852313\pi\) | ||||
−0.894281 | + | 0.447505i | \(0.852313\pi\) | |||||||
\(110\) | 2.51856 | 0.240135 | ||||||||
\(111\) | 1.31371 | 0.124692 | ||||||||
\(112\) | 2.48528 | 0.234837 | ||||||||
\(113\) | −9.33657 | −0.878311 | −0.439155 | − | 0.898411i | \(-0.644722\pi\) | ||||
−0.439155 | + | 0.898411i | \(0.644722\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.828427 | −0.0772512 | ||||||||
\(116\) | −3.56178 | −0.330703 | ||||||||
\(117\) | 0.737669 | 0.0681975 | ||||||||
\(118\) | −8.97056 | −0.825807 | ||||||||
\(119\) | −6.34315 | −0.581475 | ||||||||
\(120\) | −5.41421 | −0.494248 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −3.56178 | −0.322469 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.47534 | −0.132489 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.178989 | −0.0159456 | ||||||||
\(127\) | −17.5034 | −1.55317 | −0.776586 | − | 0.630011i | \(-0.783050\pi\) | ||||
−0.776586 | + | 0.630011i | \(0.783050\pi\) | |||||||
\(128\) | 6.60195 | 0.583536 | ||||||||
\(129\) | −8.59890 | −0.757091 | ||||||||
\(130\) | 5.41421 | 0.474858 | ||||||||
\(131\) | 15.3137 | 1.33796 | 0.668982 | − | 0.743278i | \(-0.266730\pi\) | ||||
0.668982 | + | 0.743278i | \(0.266730\pi\) | |||||||
\(132\) | −1.47534 | −0.128412 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.58579 | 0.741699 | ||||||||
\(135\) | −5.03712 | −0.433526 | ||||||||
\(136\) | −23.2781 | −1.99608 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | −1.85786 | −0.158152 | ||||||||
\(139\) | 19.6569 | 1.66727 | 0.833636 | − | 0.552314i | \(-0.186255\pi\) | ||||
0.833636 | + | 0.552314i | \(0.186255\pi\) | |||||||
\(140\) | 0.343146 | 0.0290011 | ||||||||
\(141\) | 18.6731 | 1.57256 | ||||||||
\(142\) | 17.1716 | 1.44101 | ||||||||
\(143\) | 8.59890 | 0.719076 | ||||||||
\(144\) | −0.514719 | −0.0428932 | ||||||||
\(145\) | 8.59890 | 0.714100 | ||||||||
\(146\) | −14.6792 | −1.21486 | ||||||||
\(147\) | −11.2440 | −0.927392 | ||||||||
\(148\) | −0.305553 | −0.0251163 | ||||||||
\(149\) | −14.8284 | −1.21479 | −0.607396 | − | 0.794399i | \(-0.707786\pi\) | ||||
−0.607396 | + | 0.794399i | \(0.707786\pi\) | |||||||
\(150\) | 2.24264 | 0.183111 | ||||||||
\(151\) | −10.6853 | −0.869561 | −0.434781 | − | 0.900536i | \(-0.643174\pi\) | ||||
−0.434781 | + | 0.900536i | \(0.643174\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.31371 | 0.106207 | ||||||||
\(154\) | −2.08644 | −0.168130 | ||||||||
\(155\) | 3.56178 | 0.286089 | ||||||||
\(156\) | −3.17157 | −0.253929 | ||||||||
\(157\) | 18.0000 | 1.43656 | 0.718278 | − | 0.695756i | \(-0.244931\pi\) | ||||
0.718278 | + | 0.695756i | \(0.244931\pi\) | |||||||
\(158\) | 8.97056 | 0.713660 | ||||||||
\(159\) | −14.0000 | −1.11027 | ||||||||
\(160\) | 2.30250 | 0.182029 | ||||||||
\(161\) | 0.686292 | 0.0540873 | ||||||||
\(162\) | −11.9446 | −0.938458 | ||||||||
\(163\) | 7.17157 | 0.561721 | 0.280860 | − | 0.959749i | \(-0.409380\pi\) | ||||
0.280860 | + | 0.959749i | \(0.409380\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.56178 | 0.277284 | ||||||||
\(166\) | 11.1175 | 0.862882 | ||||||||
\(167\) | −16.8923 | −1.30716 | −0.653581 | − | 0.756857i | \(-0.726734\pi\) | ||||
−0.653581 | + | 0.756857i | \(0.726734\pi\) | |||||||
\(168\) | 4.48528 | 0.346047 | ||||||||
\(169\) | 5.48528 | 0.421945 | ||||||||
\(170\) | 9.64212 | 0.739517 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | 2.82411 | 0.214713 | 0.107357 | − | 0.994221i | \(-0.465761\pi\) | ||||
0.107357 | + | 0.994221i | \(0.465761\pi\) | |||||||
\(174\) | 19.2842 | 1.46194 | ||||||||
\(175\) | −0.828427 | −0.0626232 | ||||||||
\(176\) | −6.00000 | −0.452267 | ||||||||
\(177\) | −12.6863 | −0.953560 | ||||||||
\(178\) | −19.7990 | −1.48400 | ||||||||
\(179\) | 17.1978 | 1.28542 | 0.642712 | − | 0.766108i | \(-0.277809\pi\) | ||||
0.642712 | + | 0.766108i | \(0.277809\pi\) | |||||||
\(180\) | −0.0710678 | −0.00529708 | ||||||||
\(181\) | −10.0742 | −0.748812 | −0.374406 | − | 0.927265i | \(-0.622153\pi\) | ||||
−0.374406 | + | 0.927265i | \(0.622153\pi\) | |||||||
\(182\) | −4.48528 | −0.332471 | ||||||||
\(183\) | −5.03712 | −0.372355 | ||||||||
\(184\) | 2.51856 | 0.185671 | ||||||||
\(185\) | 0.737669 | 0.0542345 | ||||||||
\(186\) | 7.98780 | 0.585694 | ||||||||
\(187\) | 15.3137 | 1.11985 | ||||||||
\(188\) | −4.34315 | −0.316756 | ||||||||
\(189\) | 4.17289 | 0.303533 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.34315 | −0.169544 | −0.0847720 | − | 0.996400i | \(-0.527016\pi\) | ||||
−0.0847720 | + | 0.996400i | \(0.527016\pi\) | |||||||
\(192\) | 15.8490 | 1.14381 | ||||||||
\(193\) | −20.0219 | −1.44121 | −0.720605 | − | 0.693346i | \(-0.756136\pi\) | ||||
−0.720605 | + | 0.693346i | \(0.756136\pi\) | |||||||
\(194\) | 5.41421 | 0.388718 | ||||||||
\(195\) | 7.65685 | 0.548319 | ||||||||
\(196\) | 2.61522 | 0.186802 | ||||||||
\(197\) | 9.31371 | 0.663574 | 0.331787 | − | 0.943354i | \(-0.392348\pi\) | ||||
0.331787 | + | 0.943354i | \(0.392348\pi\) | |||||||
\(198\) | 0.432117 | 0.0307092 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | −3.04017 | −0.214973 | ||||||||
\(201\) | 12.1421 | 0.856440 | ||||||||
\(202\) | 0.611105 | 0.0429972 | ||||||||
\(203\) | −7.12356 | −0.499976 | ||||||||
\(204\) | −5.64823 | −0.395455 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.72792 | −0.468757 | ||||||||
\(207\) | −0.142136 | −0.00987911 | ||||||||
\(208\) | −12.8984 | −0.894340 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.85786 | −0.128205 | ||||||||
\(211\) | −13.6360 | −0.938743 | −0.469371 | − | 0.883001i | \(-0.655519\pi\) | ||||
−0.469371 | + | 0.883001i | \(0.655519\pi\) | |||||||
\(212\) | 3.25623 | 0.223639 | ||||||||
\(213\) | 24.2843 | 1.66393 | ||||||||
\(214\) | −17.5563 | −1.20013 | ||||||||
\(215\) | −4.82843 | −0.329296 | ||||||||
\(216\) | 15.3137 | 1.04197 | ||||||||
\(217\) | −2.95068 | −0.200305 | ||||||||
\(218\) | −23.5147 | −1.59262 | ||||||||
\(219\) | −20.7596 | −1.40280 | ||||||||
\(220\) | −0.828427 | −0.0558525 | ||||||||
\(221\) | 32.9203 | 2.21446 | ||||||||
\(222\) | 1.65433 | 0.111031 | ||||||||
\(223\) | 0.305553 | 0.0204613 | 0.0102307 | − | 0.999948i | \(-0.496743\pi\) | ||||
0.0102307 | + | 0.999948i | \(0.496743\pi\) | |||||||
\(224\) | −1.90746 | −0.127447 | ||||||||
\(225\) | 0.171573 | 0.0114382 | ||||||||
\(226\) | −11.7574 | −0.782088 | ||||||||
\(227\) | −16.8923 | −1.12118 | −0.560589 | − | 0.828094i | \(-0.689425\pi\) | ||||
−0.560589 | + | 0.828094i | \(0.689425\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.48528 | −0.296396 | −0.148198 | − | 0.988958i | \(-0.547347\pi\) | ||||
−0.148198 | + | 0.988958i | \(0.547347\pi\) | |||||||
\(230\) | −1.04322 | −0.0687880 | ||||||||
\(231\) | −2.95068 | −0.194140 | ||||||||
\(232\) | −26.1421 | −1.71632 | ||||||||
\(233\) | −9.31371 | −0.610161 | −0.305081 | − | 0.952327i | \(-0.598683\pi\) | ||||
−0.305081 | + | 0.952327i | \(0.598683\pi\) | |||||||
\(234\) | 0.928932 | 0.0607262 | ||||||||
\(235\) | 10.4853 | 0.683984 | ||||||||
\(236\) | 2.95068 | 0.192073 | ||||||||
\(237\) | 12.6863 | 0.824063 | ||||||||
\(238\) | −7.98780 | −0.517772 | ||||||||
\(239\) | 9.65685 | 0.624650 | 0.312325 | − | 0.949975i | \(-0.398892\pi\) | ||||
0.312325 | + | 0.949975i | \(0.398892\pi\) | |||||||
\(240\) | −5.34267 | −0.344868 | ||||||||
\(241\) | 24.3214 | 1.56668 | 0.783339 | − | 0.621595i | \(-0.213515\pi\) | ||||
0.783339 | + | 0.621595i | \(0.213515\pi\) | |||||||
\(242\) | −8.81496 | −0.566647 | ||||||||
\(243\) | −1.78089 | −0.114244 | ||||||||
\(244\) | 1.17157 | 0.0750023 | ||||||||
\(245\) | −6.31371 | −0.403368 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10.8284 | −0.687606 | ||||||||
\(249\) | 15.7225 | 0.996371 | ||||||||
\(250\) | 1.25928 | 0.0796439 | ||||||||
\(251\) | 20.9706 | 1.32365 | 0.661825 | − | 0.749658i | \(-0.269782\pi\) | ||||
0.661825 | + | 0.749658i | \(0.269782\pi\) | |||||||
\(252\) | 0.0588745 | 0.00370875 | ||||||||
\(253\) | −1.65685 | −0.104166 | ||||||||
\(254\) | −22.0416 | −1.38301 | ||||||||
\(255\) | 13.6360 | 0.853921 | ||||||||
\(256\) | −9.48528 | −0.592830 | ||||||||
\(257\) | 20.0219 | 1.24893 | 0.624466 | − | 0.781052i | \(-0.285316\pi\) | ||||
0.624466 | + | 0.781052i | \(0.285316\pi\) | |||||||
\(258\) | −10.8284 | −0.674148 | ||||||||
\(259\) | −0.611105 | −0.0379722 | ||||||||
\(260\) | −1.78089 | −0.110446 | ||||||||
\(261\) | 1.47534 | 0.0913212 | ||||||||
\(262\) | 19.2842 | 1.19138 | ||||||||
\(263\) | −16.1421 | −0.995367 | −0.497683 | − | 0.867359i | \(-0.665816\pi\) | ||||
−0.497683 | + | 0.867359i | \(0.665816\pi\) | |||||||
\(264\) | −10.8284 | −0.666444 | ||||||||
\(265\) | −7.86123 | −0.482912 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −28.0000 | −1.71357 | ||||||||
\(268\) | −2.82411 | −0.172510 | ||||||||
\(269\) | 8.59890 | 0.524284 | 0.262142 | − | 0.965029i | \(-0.415571\pi\) | ||||
0.262142 | + | 0.965029i | \(0.415571\pi\) | |||||||
\(270\) | −6.34315 | −0.386032 | ||||||||
\(271\) | 30.9706 | 1.88133 | 0.940664 | − | 0.339340i | \(-0.110204\pi\) | ||||
0.940664 | + | 0.339340i | \(0.110204\pi\) | |||||||
\(272\) | −22.9706 | −1.39279 | ||||||||
\(273\) | −6.34315 | −0.383905 | ||||||||
\(274\) | −2.51856 | −0.152152 | ||||||||
\(275\) | 2.00000 | 0.120605 | ||||||||
\(276\) | 0.611105 | 0.0367842 | ||||||||
\(277\) | −17.3137 | −1.04028 | −0.520140 | − | 0.854081i | \(-0.674120\pi\) | ||||
−0.520140 | + | 0.854081i | \(0.674120\pi\) | |||||||
\(278\) | 24.7535 | 1.48462 | ||||||||
\(279\) | 0.611105 | 0.0365859 | ||||||||
\(280\) | 2.51856 | 0.150513 | ||||||||
\(281\) | 14.2471 | 0.849912 | 0.424956 | − | 0.905214i | \(-0.360289\pi\) | ||||
0.424956 | + | 0.905214i | \(0.360289\pi\) | |||||||
\(282\) | 23.5147 | 1.40028 | ||||||||
\(283\) | −9.79899 | −0.582489 | −0.291245 | − | 0.956649i | \(-0.594069\pi\) | ||||
−0.291245 | + | 0.956649i | \(0.594069\pi\) | |||||||
\(284\) | −5.64823 | −0.335161 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.8284 | 0.640298 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.395047 | 0.0232784 | ||||||||
\(289\) | 41.6274 | 2.44867 | ||||||||
\(290\) | 10.8284 | 0.635867 | ||||||||
\(291\) | 7.65685 | 0.448853 | ||||||||
\(292\) | 4.82843 | 0.282562 | ||||||||
\(293\) | −17.9355 | −1.04780 | −0.523901 | − | 0.851779i | \(-0.675524\pi\) | ||||
−0.523901 | + | 0.851779i | \(0.675524\pi\) | |||||||
\(294\) | −14.1594 | −0.825792 | ||||||||
\(295\) | −7.12356 | −0.414750 | ||||||||
\(296\) | −2.24264 | −0.130351 | ||||||||
\(297\) | −10.0742 | −0.584567 | ||||||||
\(298\) | −18.6731 | −1.08171 | ||||||||
\(299\) | −3.56178 | −0.205983 | ||||||||
\(300\) | −0.737669 | −0.0425894 | ||||||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | −13.4558 | −0.774297 | ||||||||
\(303\) | 0.864233 | 0.0496489 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.82843 | −0.161955 | ||||||||
\(306\) | 1.65433 | 0.0945716 | ||||||||
\(307\) | 3.25623 | 0.185843 | 0.0929214 | − | 0.995673i | \(-0.470379\pi\) | ||||
0.0929214 | + | 0.995673i | \(0.470379\pi\) | |||||||
\(308\) | 0.686292 | 0.0391051 | ||||||||
\(309\) | −9.51472 | −0.541273 | ||||||||
\(310\) | 4.48528 | 0.254747 | ||||||||
\(311\) | −20.3431 | −1.15355 | −0.576777 | − | 0.816902i | \(-0.695690\pi\) | ||||
−0.576777 | + | 0.816902i | \(0.695690\pi\) | |||||||
\(312\) | −23.2781 | −1.31787 | ||||||||
\(313\) | 24.6274 | 1.39202 | 0.696012 | − | 0.718030i | \(-0.254956\pi\) | ||||
0.696012 | + | 0.718030i | \(0.254956\pi\) | |||||||
\(314\) | 22.6670 | 1.27918 | ||||||||
\(315\) | −0.142136 | −0.00800844 | ||||||||
\(316\) | −2.95068 | −0.165989 | ||||||||
\(317\) | −5.77479 | −0.324345 | −0.162172 | − | 0.986762i | \(-0.551850\pi\) | ||||
−0.162172 | + | 0.986762i | \(0.551850\pi\) | |||||||
\(318\) | −17.6299 | −0.988637 | ||||||||
\(319\) | 17.1978 | 0.962892 | ||||||||
\(320\) | 8.89949 | 0.497497 | ||||||||
\(321\) | −24.8284 | −1.38579 | ||||||||
\(322\) | 0.864233 | 0.0481618 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 3.92893 | 0.218274 | ||||||||
\(325\) | 4.29945 | 0.238491 | ||||||||
\(326\) | 9.03102 | 0.500182 | ||||||||
\(327\) | −33.2548 | −1.83900 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.68629 | −0.478891 | ||||||||
\(330\) | 4.48528 | 0.246907 | ||||||||
\(331\) | −17.8089 | −0.978866 | −0.489433 | − | 0.872041i | \(-0.662796\pi\) | ||||
−0.489433 | + | 0.872041i | \(0.662796\pi\) | |||||||
\(332\) | −3.65685 | −0.200696 | ||||||||
\(333\) | 0.126564 | 0.00693567 | ||||||||
\(334\) | −21.2721 | −1.16396 | ||||||||
\(335\) | 6.81801 | 0.372508 | ||||||||
\(336\) | 4.42602 | 0.241459 | ||||||||
\(337\) | −13.5095 | −0.735907 | −0.367954 | − | 0.929844i | \(-0.619941\pi\) | ||||
−0.367954 | + | 0.929844i | \(0.619941\pi\) | |||||||
\(338\) | 6.90751 | 0.375719 | ||||||||
\(339\) | −16.6274 | −0.903077 | ||||||||
\(340\) | −3.17157 | −0.172003 | ||||||||
\(341\) | 7.12356 | 0.385763 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.0294 | 0.595534 | ||||||||
\(344\) | 14.6792 | 0.791452 | ||||||||
\(345\) | −1.47534 | −0.0794296 | ||||||||
\(346\) | 3.55635 | 0.191191 | ||||||||
\(347\) | 19.1716 | 1.02918 | 0.514592 | − | 0.857435i | \(-0.327943\pi\) | ||||
0.514592 | + | 0.857435i | \(0.327943\pi\) | |||||||
\(348\) | −6.34315 | −0.340028 | ||||||||
\(349\) | −29.3137 | −1.56913 | −0.784563 | − | 0.620049i | \(-0.787113\pi\) | ||||
−0.784563 | + | 0.620049i | \(0.787113\pi\) | |||||||
\(350\) | −1.04322 | −0.0557626 | ||||||||
\(351\) | −21.6569 | −1.15596 | ||||||||
\(352\) | 4.60500 | 0.245448 | ||||||||
\(353\) | 7.65685 | 0.407533 | 0.203767 | − | 0.979019i | \(-0.434682\pi\) | ||||
0.203767 | + | 0.979019i | \(0.434682\pi\) | |||||||
\(354\) | −15.9756 | −0.849093 | ||||||||
\(355\) | 13.6360 | 0.723725 | ||||||||
\(356\) | 6.51246 | 0.345160 | ||||||||
\(357\) | −11.2965 | −0.597872 | ||||||||
\(358\) | 21.6569 | 1.14460 | ||||||||
\(359\) | −2.68629 | −0.141777 | −0.0708885 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708885 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(360\) | −0.521611 | −0.0274913 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −12.6863 | −0.666777 | ||||||||
\(363\) | −12.4662 | −0.654308 | ||||||||
\(364\) | 1.47534 | 0.0773287 | ||||||||
\(365\) | −11.6569 | −0.610148 | ||||||||
\(366\) | −6.34315 | −0.331562 | ||||||||
\(367\) | 3.17157 | 0.165555 | 0.0827774 | − | 0.996568i | \(-0.473621\pi\) | ||||
0.0827774 | + | 0.996568i | \(0.473621\pi\) | |||||||
\(368\) | 2.48528 | 0.129554 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.928932 | 0.0482929 | ||||||||
\(371\) | 6.51246 | 0.338110 | ||||||||
\(372\) | −2.62742 | −0.136225 | ||||||||
\(373\) | −10.8119 | −0.559819 | −0.279910 | − | 0.960026i | \(-0.590305\pi\) | ||||
−0.279910 | + | 0.960026i | \(0.590305\pi\) | |||||||
\(374\) | 19.2842 | 0.997165 | ||||||||
\(375\) | 1.78089 | 0.0919648 | ||||||||
\(376\) | −31.8771 | −1.64393 | ||||||||
\(377\) | 36.9706 | 1.90408 | ||||||||
\(378\) | 5.25483 | 0.270279 | ||||||||
\(379\) | −17.1978 | −0.883392 | −0.441696 | − | 0.897165i | \(-0.645623\pi\) | ||||
−0.441696 | + | 0.897165i | \(0.645623\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −31.1716 | −1.59697 | ||||||||
\(382\) | −2.95068 | −0.150970 | ||||||||
\(383\) | 32.6147 | 1.66653 | 0.833267 | − | 0.552871i | \(-0.186468\pi\) | ||||
0.833267 | + | 0.552871i | \(0.186468\pi\) | |||||||
\(384\) | 11.7574 | 0.599990 | ||||||||
\(385\) | −1.65685 | −0.0844411 | ||||||||
\(386\) | −25.2132 | −1.28332 | ||||||||
\(387\) | −0.828427 | −0.0421113 | ||||||||
\(388\) | −1.78089 | −0.0904110 | ||||||||
\(389\) | −20.6274 | −1.04585 | −0.522926 | − | 0.852378i | \(-0.675160\pi\) | ||||
−0.522926 | + | 0.852378i | \(0.675160\pi\) | |||||||
\(390\) | 9.64212 | 0.488248 | ||||||||
\(391\) | −6.34315 | −0.320787 | ||||||||
\(392\) | 19.1948 | 0.969482 | ||||||||
\(393\) | 27.2720 | 1.37569 | ||||||||
\(394\) | 11.7286 | 0.590877 | ||||||||
\(395\) | 7.12356 | 0.358425 | ||||||||
\(396\) | −0.142136 | −0.00714258 | ||||||||
\(397\) | −14.0000 | −0.702640 | −0.351320 | − | 0.936255i | \(-0.614267\pi\) | ||||
−0.351320 | + | 0.936255i | \(0.614267\pi\) | |||||||
\(398\) | −5.03712 | −0.252488 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | −0.150000 | ||||||||
\(401\) | −10.0742 | −0.503084 | −0.251542 | − | 0.967846i | \(-0.580938\pi\) | ||||
−0.251542 | + | 0.967846i | \(0.580938\pi\) | |||||||
\(402\) | 15.2904 | 0.762613 | ||||||||
\(403\) | 15.3137 | 0.762830 | ||||||||
\(404\) | −0.201010 | −0.0100006 | ||||||||
\(405\) | −9.48528 | −0.471327 | ||||||||
\(406\) | −8.97056 | −0.445202 | ||||||||
\(407\) | 1.47534 | 0.0731298 | ||||||||
\(408\) | −41.4558 | −2.05237 | ||||||||
\(409\) | 12.7718 | 0.631524 | 0.315762 | − | 0.948838i | \(-0.397740\pi\) | ||||
0.315762 | + | 0.948838i | \(0.397740\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.56178 | −0.175690 | ||||||||
\(412\) | 2.21301 | 0.109027 | ||||||||
\(413\) | 5.90135 | 0.290387 | ||||||||
\(414\) | −0.178989 | −0.00879681 | ||||||||
\(415\) | 8.82843 | 0.433370 | ||||||||
\(416\) | 9.89949 | 0.485363 | ||||||||
\(417\) | 35.0067 | 1.71429 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.9706 | −1.21989 | −0.609946 | − | 0.792443i | \(-0.708809\pi\) | ||||
−0.609946 | + | 0.792443i | \(0.708809\pi\) | |||||||
\(420\) | 0.611105 | 0.0298189 | ||||||||
\(421\) | −10.0742 | −0.490988 | −0.245494 | − | 0.969398i | \(-0.578950\pi\) | ||||
−0.245494 | + | 0.969398i | \(0.578950\pi\) | |||||||
\(422\) | −17.1716 | −0.835899 | ||||||||
\(423\) | 1.79899 | 0.0874699 | ||||||||
\(424\) | 23.8995 | 1.16066 | ||||||||
\(425\) | 7.65685 | 0.371412 | ||||||||
\(426\) | 30.5807 | 1.48164 | ||||||||
\(427\) | 2.34315 | 0.113393 | ||||||||
\(428\) | 5.77479 | 0.279135 | ||||||||
\(429\) | 15.3137 | 0.739353 | ||||||||
\(430\) | −6.08034 | −0.293220 | ||||||||
\(431\) | 3.56178 | 0.171565 | 0.0857825 | − | 0.996314i | \(-0.472661\pi\) | ||||
0.0857825 | + | 0.996314i | \(0.472661\pi\) | |||||||
\(432\) | 15.1114 | 0.727046 | ||||||||
\(433\) | 4.91056 | 0.235986 | 0.117993 | − | 0.993014i | \(-0.462354\pi\) | ||||
0.117993 | + | 0.993014i | \(0.462354\pi\) | |||||||
\(434\) | −3.71573 | −0.178361 | ||||||||
\(435\) | 15.3137 | 0.734236 | ||||||||
\(436\) | 7.73467 | 0.370423 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −26.1421 | −1.24912 | ||||||||
\(439\) | 2.95068 | 0.140828 | 0.0704141 | − | 0.997518i | \(-0.477568\pi\) | ||||
0.0704141 | + | 0.997518i | \(0.477568\pi\) | |||||||
\(440\) | −6.08034 | −0.289869 | ||||||||
\(441\) | −1.08326 | −0.0515839 | ||||||||
\(442\) | 41.4558 | 1.97185 | ||||||||
\(443\) | 20.1421 | 0.956982 | 0.478491 | − | 0.878093i | \(-0.341184\pi\) | ||||
0.478491 | + | 0.878093i | \(0.341184\pi\) | |||||||
\(444\) | −0.544156 | −0.0258245 | ||||||||
\(445\) | −15.7225 | −0.745316 | ||||||||
\(446\) | 0.384776 | 0.0182197 | ||||||||
\(447\) | −26.4078 | −1.24905 | ||||||||
\(448\) | −7.37258 | −0.348322 | ||||||||
\(449\) | −8.59890 | −0.405807 | −0.202904 | − | 0.979199i | \(-0.565038\pi\) | ||||
−0.202904 | + | 0.979199i | \(0.565038\pi\) | |||||||
\(450\) | 0.216058 | 0.0101851 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 3.86733 | 0.181904 | ||||||||
\(453\) | −19.0294 | −0.894081 | ||||||||
\(454\) | −21.2721 | −0.998348 | ||||||||
\(455\) | −3.56178 | −0.166979 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.31371 | 0.248565 | 0.124282 | − | 0.992247i | \(-0.460337\pi\) | ||||
0.124282 | + | 0.992247i | \(0.460337\pi\) | |||||||
\(458\) | −5.64823 | −0.263924 | ||||||||
\(459\) | −38.5685 | −1.80022 | ||||||||
\(460\) | 0.343146 | 0.0159993 | ||||||||
\(461\) | −10.6863 | −0.497710 | −0.248855 | − | 0.968541i | \(-0.580054\pi\) | ||||
−0.248855 | + | 0.968541i | \(0.580054\pi\) | |||||||
\(462\) | −3.71573 | −0.172871 | ||||||||
\(463\) | −32.8284 | −1.52567 | −0.762833 | − | 0.646595i | \(-0.776192\pi\) | ||||
−0.762833 | + | 0.646595i | \(0.776192\pi\) | |||||||
\(464\) | −25.7967 | −1.19758 | ||||||||
\(465\) | 6.34315 | 0.294156 | ||||||||
\(466\) | −11.7286 | −0.543315 | ||||||||
\(467\) | 38.4853 | 1.78089 | 0.890443 | − | 0.455094i | \(-0.150394\pi\) | ||||
0.890443 | + | 0.455094i | \(0.150394\pi\) | |||||||
\(468\) | −0.305553 | −0.0141242 | ||||||||
\(469\) | −5.64823 | −0.260811 | ||||||||
\(470\) | 13.2039 | 0.609051 | ||||||||
\(471\) | 32.0560 | 1.47706 | ||||||||
\(472\) | 21.6569 | 0.996838 | ||||||||
\(473\) | −9.65685 | −0.444023 | ||||||||
\(474\) | 15.9756 | 0.733783 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.62742 | 0.120427 | ||||||||
\(477\) | −1.34877 | −0.0617561 | ||||||||
\(478\) | 12.1607 | 0.556217 | ||||||||
\(479\) | 10.0000 | 0.456912 | 0.228456 | − | 0.973554i | \(-0.426632\pi\) | ||||
0.228456 | + | 0.973554i | \(0.426632\pi\) | |||||||
\(480\) | 4.10051 | 0.187162 | ||||||||
\(481\) | 3.17157 | 0.144611 | ||||||||
\(482\) | 30.6274 | 1.39504 | ||||||||
\(483\) | 1.22221 | 0.0556125 | ||||||||
\(484\) | 2.89949 | 0.131795 | ||||||||
\(485\) | 4.29945 | 0.195228 | ||||||||
\(486\) | −2.24264 | −0.101728 | ||||||||
\(487\) | −29.6640 | −1.34421 | −0.672103 | − | 0.740458i | \(-0.734609\pi\) | ||||
−0.672103 | + | 0.740458i | \(0.734609\pi\) | |||||||
\(488\) | 8.59890 | 0.389254 | ||||||||
\(489\) | 12.7718 | 0.577560 | ||||||||
\(490\) | −7.95073 | −0.359177 | ||||||||
\(491\) | 32.2843 | 1.45697 | 0.728484 | − | 0.685062i | \(-0.240225\pi\) | ||||
0.728484 | + | 0.685062i | \(0.240225\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 65.8405 | 2.96531 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.343146 | 0.0154233 | ||||||||
\(496\) | −10.6853 | −0.479786 | ||||||||
\(497\) | −11.2965 | −0.506715 | ||||||||
\(498\) | 19.7990 | 0.887214 | ||||||||
\(499\) | 1.02944 | 0.0460839 | 0.0230420 | − | 0.999734i | \(-0.492665\pi\) | ||||
0.0230420 | + | 0.999734i | \(0.492665\pi\) | |||||||
\(500\) | −0.414214 | −0.0185242 | ||||||||
\(501\) | −30.0833 | −1.34402 | ||||||||
\(502\) | 26.4078 | 1.17864 | ||||||||
\(503\) | 2.48528 | 0.110813 | 0.0554066 | − | 0.998464i | \(-0.482354\pi\) | ||||
0.0554066 | + | 0.998464i | \(0.482354\pi\) | |||||||
\(504\) | 0.432117 | 0.0192480 | ||||||||
\(505\) | 0.485281 | 0.0215947 | ||||||||
\(506\) | −2.08644 | −0.0927537 | ||||||||
\(507\) | 9.76869 | 0.433843 | ||||||||
\(508\) | 7.25013 | 0.321672 | ||||||||
\(509\) | −32.9203 | −1.45917 | −0.729583 | − | 0.683893i | \(-0.760286\pi\) | ||||
−0.729583 | + | 0.683893i | \(0.760286\pi\) | |||||||
\(510\) | 17.1716 | 0.760370 | ||||||||
\(511\) | 9.65685 | 0.427194 | ||||||||
\(512\) | −25.1485 | −1.11142 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 25.2132 | 1.11211 | ||||||||
\(515\) | −5.34267 | −0.235426 | ||||||||
\(516\) | 3.56178 | 0.156799 | ||||||||
\(517\) | 20.9706 | 0.922284 | ||||||||
\(518\) | −0.769553 | −0.0338122 | ||||||||
\(519\) | 5.02944 | 0.220768 | ||||||||
\(520\) | −13.0711 | −0.573204 | ||||||||
\(521\) | −17.1978 | −0.753450 | −0.376725 | − | 0.926325i | \(-0.622950\pi\) | ||||
−0.376725 | + | 0.926325i | \(0.622950\pi\) | |||||||
\(522\) | 1.85786 | 0.0813165 | ||||||||
\(523\) | 15.4169 | 0.674135 | 0.337067 | − | 0.941481i | \(-0.390565\pi\) | ||||
0.337067 | + | 0.941481i | \(0.390565\pi\) | |||||||
\(524\) | −6.34315 | −0.277102 | ||||||||
\(525\) | −1.47534 | −0.0643890 | ||||||||
\(526\) | −20.3275 | −0.886320 | ||||||||
\(527\) | 27.2720 | 1.18799 | ||||||||
\(528\) | −10.6853 | −0.465020 | ||||||||
\(529\) | −22.3137 | −0.970161 | ||||||||
\(530\) | −9.89949 | −0.430007 | ||||||||
\(531\) | −1.22221 | −0.0530394 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −35.2598 | −1.52584 | ||||||||
\(535\) | −13.9416 | −0.602747 | ||||||||
\(536\) | −20.7279 | −0.895310 | ||||||||
\(537\) | 30.6274 | 1.32167 | ||||||||
\(538\) | 10.8284 | 0.466847 | ||||||||
\(539\) | −12.6274 | −0.543901 | ||||||||
\(540\) | 2.08644 | 0.0897862 | ||||||||
\(541\) | 22.1421 | 0.951965 | 0.475982 | − | 0.879455i | \(-0.342093\pi\) | ||||
0.475982 | + | 0.879455i | \(0.342093\pi\) | |||||||
\(542\) | 39.0006 | 1.67522 | ||||||||
\(543\) | −17.9411 | −0.769927 | ||||||||
\(544\) | 17.6299 | 0.755877 | ||||||||
\(545\) | −18.6731 | −0.799870 | ||||||||
\(546\) | −7.98780 | −0.341846 | ||||||||
\(547\) | 11.8551 | 0.506889 | 0.253444 | − | 0.967350i | \(-0.418437\pi\) | ||||
0.253444 | + | 0.967350i | \(0.418437\pi\) | |||||||
\(548\) | 0.828427 | 0.0353887 | ||||||||
\(549\) | −0.485281 | −0.0207113 | ||||||||
\(550\) | 2.51856 | 0.107392 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 4.48528 | 0.190906 | ||||||||
\(553\) | −5.90135 | −0.250951 | ||||||||
\(554\) | −21.8028 | −0.926313 | ||||||||
\(555\) | 1.31371 | 0.0557638 | ||||||||
\(556\) | −8.14214 | −0.345303 | ||||||||
\(557\) | −28.6274 | −1.21298 | −0.606491 | − | 0.795090i | \(-0.707424\pi\) | ||||
−0.606491 | + | 0.795090i | \(0.707424\pi\) | |||||||
\(558\) | 0.769553 | 0.0325778 | ||||||||
\(559\) | −20.7596 | −0.878037 | ||||||||
\(560\) | 2.48528 | 0.105022 | ||||||||
\(561\) | 27.2720 | 1.15143 | ||||||||
\(562\) | 17.9411 | 0.756801 | ||||||||
\(563\) | −26.1023 | −1.10008 | −0.550040 | − | 0.835139i | \(-0.685387\pi\) | ||||
−0.550040 | + | 0.835139i | \(0.685387\pi\) | |||||||
\(564\) | −7.73467 | −0.325688 | ||||||||
\(565\) | −9.33657 | −0.392793 | ||||||||
\(566\) | −12.3397 | −0.518675 | ||||||||
\(567\) | 7.85786 | 0.329999 | ||||||||
\(568\) | −41.4558 | −1.73945 | ||||||||
\(569\) | −15.7225 | −0.659120 | −0.329560 | − | 0.944135i | \(-0.606900\pi\) | ||||
−0.329560 | + | 0.944135i | \(0.606900\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.3137 | 0.557161 | 0.278581 | − | 0.960413i | \(-0.410136\pi\) | ||||
0.278581 | + | 0.960413i | \(0.410136\pi\) | |||||||
\(572\) | −3.56178 | −0.148926 | ||||||||
\(573\) | −4.17289 | −0.174325 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.828427 | −0.0345478 | ||||||||
\(576\) | 1.52691 | 0.0636213 | ||||||||
\(577\) | 10.0000 | 0.416305 | 0.208153 | − | 0.978096i | \(-0.433255\pi\) | ||||
0.208153 | + | 0.978096i | \(0.433255\pi\) | |||||||
\(578\) | 52.4206 | 2.18041 | ||||||||
\(579\) | −35.6569 | −1.48185 | ||||||||
\(580\) | −3.56178 | −0.147895 | ||||||||
\(581\) | −7.31371 | −0.303424 | ||||||||
\(582\) | 9.64212 | 0.399679 | ||||||||
\(583\) | −15.7225 | −0.651158 | ||||||||
\(584\) | 35.4388 | 1.46647 | ||||||||
\(585\) | 0.737669 | 0.0304989 | ||||||||
\(586\) | −22.5858 | −0.933010 | ||||||||
\(587\) | 18.4853 | 0.762969 | 0.381485 | − | 0.924375i | \(-0.375413\pi\) | ||||
0.381485 | + | 0.924375i | \(0.375413\pi\) | |||||||
\(588\) | 4.65743 | 0.192069 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −8.97056 | −0.369312 | ||||||||
\(591\) | 16.5867 | 0.682286 | ||||||||
\(592\) | −2.21301 | −0.0909541 | ||||||||
\(593\) | −9.31371 | −0.382468 | −0.191234 | − | 0.981544i | \(-0.561249\pi\) | ||||
−0.191234 | + | 0.981544i | \(0.561249\pi\) | |||||||
\(594\) | −12.6863 | −0.520525 | ||||||||
\(595\) | −6.34315 | −0.260044 | ||||||||
\(596\) | 6.14214 | 0.251592 | ||||||||
\(597\) | −7.12356 | −0.291548 | ||||||||
\(598\) | −4.48528 | −0.183417 | ||||||||
\(599\) | −34.3956 | −1.40537 | −0.702683 | − | 0.711503i | \(-0.748015\pi\) | ||||
−0.702683 | + | 0.711503i | \(0.748015\pi\) | |||||||
\(600\) | −5.41421 | −0.221034 | ||||||||
\(601\) | −17.1978 | −0.701513 | −0.350757 | − | 0.936467i | \(-0.614076\pi\) | ||||
−0.350757 | + | 0.936467i | \(0.614076\pi\) | |||||||
\(602\) | 5.03712 | 0.205298 | ||||||||
\(603\) | 1.16979 | 0.0476374 | ||||||||
\(604\) | 4.42602 | 0.180092 | ||||||||
\(605\) | −7.00000 | −0.284590 | ||||||||
\(606\) | 1.08831 | 0.0442096 | ||||||||
\(607\) | 33.2258 | 1.34859 | 0.674297 | − | 0.738460i | \(-0.264447\pi\) | ||||
0.674297 | + | 0.738460i | \(0.264447\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.6863 | −0.514074 | ||||||||
\(610\) | −3.56178 | −0.144212 | ||||||||
\(611\) | 45.0810 | 1.82378 | ||||||||
\(612\) | −0.544156 | −0.0219962 | ||||||||
\(613\) | −14.2843 | −0.576936 | −0.288468 | − | 0.957489i | \(-0.593146\pi\) | ||||
−0.288468 | + | 0.957489i | \(0.593146\pi\) | |||||||
\(614\) | 4.10051 | 0.165483 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.03712 | 0.202951 | ||||||||
\(617\) | 30.2843 | 1.21920 | 0.609599 | − | 0.792710i | \(-0.291330\pi\) | ||||
0.609599 | + | 0.792710i | \(0.291330\pi\) | |||||||
\(618\) | −11.9817 | −0.481975 | ||||||||
\(619\) | −18.9706 | −0.762491 | −0.381246 | − | 0.924474i | \(-0.624505\pi\) | ||||
−0.381246 | + | 0.924474i | \(0.624505\pi\) | |||||||
\(620\) | −1.47534 | −0.0592510 | ||||||||
\(621\) | 4.17289 | 0.167452 | ||||||||
\(622\) | −25.6177 | −1.02718 | ||||||||
\(623\) | 13.0249 | 0.521832 | ||||||||
\(624\) | −22.9706 | −0.919558 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 31.0128 | 1.23952 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.45584 | −0.297521 | ||||||||
\(629\) | 5.64823 | 0.225210 | ||||||||
\(630\) | −0.178989 | −0.00713108 | ||||||||
\(631\) | 18.2843 | 0.727885 | 0.363943 | − | 0.931421i | \(-0.381430\pi\) | ||||
0.363943 | + | 0.931421i | \(0.381430\pi\) | |||||||
\(632\) | −21.6569 | −0.861463 | ||||||||
\(633\) | −24.2843 | −0.965213 | ||||||||
\(634\) | −7.27208 | −0.288811 | ||||||||
\(635\) | −17.5034 | −0.694600 | ||||||||
\(636\) | 5.79899 | 0.229945 | ||||||||
\(637\) | −27.1455 | −1.07554 | ||||||||
\(638\) | 21.6569 | 0.857403 | ||||||||
\(639\) | 2.33957 | 0.0925520 | ||||||||
\(640\) | 6.60195 | 0.260965 | ||||||||
\(641\) | −21.3707 | −0.844092 | −0.422046 | − | 0.906575i | \(-0.638688\pi\) | ||||
−0.422046 | + | 0.906575i | \(0.638688\pi\) | |||||||
\(642\) | −31.2659 | −1.23397 | ||||||||
\(643\) | 9.51472 | 0.375224 | 0.187612 | − | 0.982243i | \(-0.439925\pi\) | ||||
0.187612 | + | 0.982243i | \(0.439925\pi\) | |||||||
\(644\) | −0.284271 | −0.0112019 | ||||||||
\(645\) | −8.59890 | −0.338581 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.1716 | −1.06822 | −0.534112 | − | 0.845413i | \(-0.679354\pi\) | ||||
−0.534112 | + | 0.845413i | \(0.679354\pi\) | |||||||
\(648\) | 28.8369 | 1.13282 | ||||||||
\(649\) | −14.2471 | −0.559249 | ||||||||
\(650\) | 5.41421 | 0.212363 | ||||||||
\(651\) | −5.25483 | −0.205953 | ||||||||
\(652\) | −2.97056 | −0.116336 | ||||||||
\(653\) | 27.6569 | 1.08230 | 0.541148 | − | 0.840927i | \(-0.317990\pi\) | ||||
0.541148 | + | 0.840927i | \(0.317990\pi\) | |||||||
\(654\) | −41.8772 | −1.63753 | ||||||||
\(655\) | 15.3137 | 0.598356 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.00000 | −0.0780274 | ||||||||
\(658\) | −10.9385 | −0.426426 | ||||||||
\(659\) | −20.1485 | −0.784873 | −0.392437 | − | 0.919779i | \(-0.628368\pi\) | ||||
−0.392437 | + | 0.919779i | \(0.628368\pi\) | |||||||
\(660\) | −1.47534 | −0.0574275 | ||||||||
\(661\) | 2.95068 | 0.114768 | 0.0573840 | − | 0.998352i | \(-0.481724\pi\) | ||||
0.0573840 | + | 0.998352i | \(0.481724\pi\) | |||||||
\(662\) | −22.4264 | −0.871627 | ||||||||
\(663\) | 58.6274 | 2.27690 | ||||||||
\(664\) | −26.8399 | −1.04159 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.159380 | 0.00617583 | ||||||||
\(667\) | −7.12356 | −0.275826 | ||||||||
\(668\) | 6.99700 | 0.270722 | ||||||||
\(669\) | 0.544156 | 0.0210383 | ||||||||
\(670\) | 8.58579 | 0.331698 | ||||||||
\(671\) | −5.65685 | −0.218380 | ||||||||
\(672\) | −3.39697 | −0.131041 | ||||||||
\(673\) | 50.8557 | 1.96034 | 0.980172 | − | 0.198146i | \(-0.0634921\pi\) | ||||
0.980172 | + | 0.198146i | \(0.0634921\pi\) | |||||||
\(674\) | −17.0122 | −0.655285 | ||||||||
\(675\) | −5.03712 | −0.193879 | ||||||||
\(676\) | −2.27208 | −0.0873876 | ||||||||
\(677\) | 2.21301 | 0.0850528 | 0.0425264 | − | 0.999095i | \(-0.486459\pi\) | ||||
0.0425264 | + | 0.999095i | \(0.486459\pi\) | |||||||
\(678\) | −20.9386 | −0.804141 | ||||||||
\(679\) | −3.56178 | −0.136689 | ||||||||
\(680\) | −23.2781 | −0.892676 | ||||||||
\(681\) | −30.0833 | −1.15279 | ||||||||
\(682\) | 8.97056 | 0.343501 | ||||||||
\(683\) | −11.8551 | −0.453624 | −0.226812 | − | 0.973939i | \(-0.572830\pi\) | ||||
−0.226812 | + | 0.973939i | \(0.572830\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.00000 | −0.0764161 | ||||||||
\(686\) | 13.8892 | 0.530290 | ||||||||
\(687\) | −7.98780 | −0.304753 | ||||||||
\(688\) | 14.4853 | 0.552246 | ||||||||
\(689\) | −33.7990 | −1.28764 | ||||||||
\(690\) | −1.85786 | −0.0707277 | ||||||||
\(691\) | 16.6274 | 0.632537 | 0.316268 | − | 0.948670i | \(-0.397570\pi\) | ||||
0.316268 | + | 0.948670i | \(0.397570\pi\) | |||||||
\(692\) | −1.16979 | −0.0444686 | ||||||||
\(693\) | −0.284271 | −0.0107986 | ||||||||
\(694\) | 24.1424 | 0.916432 | ||||||||
\(695\) | 19.6569 | 0.745627 | ||||||||
\(696\) | −46.5563 | −1.76471 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −36.9142 | −1.39722 | ||||||||
\(699\) | −16.5867 | −0.627367 | ||||||||
\(700\) | 0.343146 | 0.0129697 | ||||||||
\(701\) | −24.4853 | −0.924796 | −0.462398 | − | 0.886672i | \(-0.653011\pi\) | ||||
−0.462398 | + | 0.886672i | \(0.653011\pi\) | |||||||
\(702\) | −27.2720 | −1.02932 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 17.7990 | 0.670825 | ||||||||
\(705\) | 18.6731 | 0.703271 | ||||||||
\(706\) | 9.64212 | 0.362886 | ||||||||
\(707\) | −0.402020 | −0.0151195 | ||||||||
\(708\) | 5.25483 | 0.197489 | ||||||||
\(709\) | −5.31371 | −0.199561 | −0.0997803 | − | 0.995009i | \(-0.531814\pi\) | ||||
−0.0997803 | + | 0.995009i | \(0.531814\pi\) | |||||||
\(710\) | 17.1716 | 0.644438 | ||||||||
\(711\) | 1.22221 | 0.0458365 | ||||||||
\(712\) | 47.7990 | 1.79134 | ||||||||
\(713\) | −2.95068 | −0.110504 | ||||||||
\(714\) | −14.2254 | −0.532372 | ||||||||
\(715\) | 8.59890 | 0.321581 | ||||||||
\(716\) | −7.12356 | −0.266220 | ||||||||
\(717\) | 17.1978 | 0.642264 | ||||||||
\(718\) | −3.38279 | −0.126245 | ||||||||
\(719\) | 31.9411 | 1.19120 | 0.595601 | − | 0.803280i | \(-0.296914\pi\) | ||||
0.595601 | + | 0.803280i | \(0.296914\pi\) | |||||||
\(720\) | −0.514719 | −0.0191824 | ||||||||
\(721\) | 4.42602 | 0.164833 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 43.3137 | 1.61085 | ||||||||
\(724\) | 4.17289 | 0.155084 | ||||||||
\(725\) | 8.59890 | 0.319355 | ||||||||
\(726\) | −15.6985 | −0.582625 | ||||||||
\(727\) | 6.48528 | 0.240526 | 0.120263 | − | 0.992742i | \(-0.461626\pi\) | ||||
0.120263 | + | 0.992742i | \(0.461626\pi\) | |||||||
\(728\) | 10.8284 | 0.401328 | ||||||||
\(729\) | 25.2843 | 0.936454 | ||||||||
\(730\) | −14.6792 | −0.543303 | ||||||||
\(731\) | −36.9706 | −1.36741 | ||||||||
\(732\) | 2.08644 | 0.0771172 | ||||||||
\(733\) | −35.6569 | −1.31702 | −0.658508 | − | 0.752574i | \(-0.728812\pi\) | ||||
−0.658508 | + | 0.752574i | \(0.728812\pi\) | |||||||
\(734\) | 3.99390 | 0.147417 | ||||||||
\(735\) | −11.2440 | −0.414742 | ||||||||
\(736\) | −1.90746 | −0.0703097 | ||||||||
\(737\) | 13.6360 | 0.502289 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.37258 | 0.0504913 | 0.0252456 | − | 0.999681i | \(-0.491963\pi\) | ||||
0.0252456 | + | 0.999681i | \(0.491963\pi\) | |||||||
\(740\) | −0.305553 | −0.0112323 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.20101 | 0.301069 | ||||||||
\(743\) | 6.81801 | 0.250129 | 0.125064 | − | 0.992149i | \(-0.460086\pi\) | ||||
0.125064 | + | 0.992149i | \(0.460086\pi\) | |||||||
\(744\) | −19.2842 | −0.706995 | ||||||||
\(745\) | −14.8284 | −0.543272 | ||||||||
\(746\) | −13.6152 | −0.498489 | ||||||||
\(747\) | 1.51472 | 0.0554207 | ||||||||
\(748\) | −6.34315 | −0.231928 | ||||||||
\(749\) | 11.5496 | 0.422012 | ||||||||
\(750\) | 2.24264 | 0.0818897 | ||||||||
\(751\) | −6.51246 | −0.237643 | −0.118822 | − | 0.992916i | \(-0.537912\pi\) | ||||
−0.118822 | + | 0.992916i | \(0.537912\pi\) | |||||||
\(752\) | −31.4558 | −1.14708 | ||||||||
\(753\) | 37.3463 | 1.36097 | ||||||||
\(754\) | 46.5563 | 1.69548 | ||||||||
\(755\) | −10.6853 | −0.388880 | ||||||||
\(756\) | −1.72847 | −0.0628637 | ||||||||
\(757\) | −6.68629 | −0.243017 | −0.121509 | − | 0.992590i | \(-0.538773\pi\) | ||||
−0.121509 | + | 0.992590i | \(0.538773\pi\) | |||||||
\(758\) | −21.6569 | −0.786612 | ||||||||
\(759\) | −2.95068 | −0.107103 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.17157 | −0.332469 | −0.166235 | − | 0.986086i | \(-0.553161\pi\) | ||||
−0.166235 | + | 0.986086i | \(0.553161\pi\) | |||||||
\(762\) | −39.2537 | −1.42201 | ||||||||
\(763\) | 15.4693 | 0.560028 | ||||||||
\(764\) | 0.970563 | 0.0351137 | ||||||||
\(765\) | 1.31371 | 0.0474972 | ||||||||
\(766\) | 41.0711 | 1.48396 | ||||||||
\(767\) | −30.6274 | −1.10589 | ||||||||
\(768\) | −16.8923 | −0.609547 | ||||||||
\(769\) | 14.1421 | 0.509978 | 0.254989 | − | 0.966944i | \(-0.417928\pi\) | ||||
0.254989 | + | 0.966944i | \(0.417928\pi\) | |||||||
\(770\) | −2.08644 | −0.0751902 | ||||||||
\(771\) | 35.6569 | 1.28415 | ||||||||
\(772\) | 8.29335 | 0.298484 | ||||||||
\(773\) | 18.5466 | 0.667074 | 0.333537 | − | 0.942737i | \(-0.391758\pi\) | ||||
0.333537 | + | 0.942737i | \(0.391758\pi\) | |||||||
\(774\) | −1.04322 | −0.0374978 | ||||||||
\(775\) | 3.56178 | 0.127943 | ||||||||
\(776\) | −13.0711 | −0.469224 | ||||||||
\(777\) | −1.08831 | −0.0390430 | ||||||||
\(778\) | −25.9757 | −0.931274 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −3.17157 | −0.113561 | ||||||||
\(781\) | 27.2720 | 0.975871 | ||||||||
\(782\) | −7.98780 | −0.285643 | ||||||||
\(783\) | −43.3137 | −1.54791 | ||||||||
\(784\) | 18.9411 | 0.676469 | ||||||||
\(785\) | 18.0000 | 0.642448 | ||||||||
\(786\) | 34.3431 | 1.22498 | ||||||||
\(787\) | 46.2507 | 1.64866 | 0.824330 | − | 0.566109i | \(-0.191552\pi\) | ||||
0.824330 | + | 0.566109i | \(0.191552\pi\) | |||||||
\(788\) | −3.85786 | −0.137431 | ||||||||
\(789\) | −28.7474 | −1.02343 | ||||||||
\(790\) | 8.97056 | 0.319158 | ||||||||
\(791\) | 7.73467 | 0.275013 | ||||||||
\(792\) | −1.04322 | −0.0370693 | ||||||||
\(793\) | −12.1607 | −0.431839 | ||||||||
\(794\) | −17.6299 | −0.625663 | ||||||||
\(795\) | −14.0000 | −0.496529 | ||||||||
\(796\) | 1.65685 | 0.0587256 | ||||||||
\(797\) | −0.737669 | −0.0261296 | −0.0130648 | − | 0.999915i | \(-0.504159\pi\) | ||||
−0.0130648 | + | 0.999915i | \(0.504159\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 80.2843 | 2.84025 | ||||||||
\(800\) | 2.30250 | 0.0814057 | ||||||||
\(801\) | −2.69755 | −0.0953132 | ||||||||
\(802\) | −12.6863 | −0.447969 | ||||||||
\(803\) | −23.3137 | −0.822723 | ||||||||
\(804\) | −5.02944 | −0.177375 | ||||||||
\(805\) | 0.686292 | 0.0241886 | ||||||||
\(806\) | 19.2842 | 0.679259 | ||||||||
\(807\) | 15.3137 | 0.539068 | ||||||||
\(808\) | −1.47534 | −0.0519022 | ||||||||
\(809\) | −13.3137 | −0.468085 | −0.234043 | − | 0.972226i | \(-0.575196\pi\) | ||||
−0.234043 | + | 0.972226i | \(0.575196\pi\) | |||||||
\(810\) | −11.9446 | −0.419691 | ||||||||
\(811\) | −33.7845 | −1.18633 | −0.593167 | − | 0.805079i | \(-0.702123\pi\) | ||||
−0.593167 | + | 0.805079i | \(0.702123\pi\) | |||||||
\(812\) | 2.95068 | 0.103548 | ||||||||
\(813\) | 55.1552 | 1.93438 | ||||||||
\(814\) | 1.85786 | 0.0651181 | ||||||||
\(815\) | 7.17157 | 0.251209 | ||||||||
\(816\) | −40.9081 | −1.43207 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 16.0833 | 0.562338 | ||||||||
\(819\) | −0.611105 | −0.0213537 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.68629 | 0.0937522 | 0.0468761 | − | 0.998901i | \(-0.485073\pi\) | ||||
0.0468761 | + | 0.998901i | \(0.485073\pi\) | |||||||
\(822\) | −4.48528 | −0.156442 | ||||||||
\(823\) | 42.0833 | 1.46693 | 0.733465 | − | 0.679727i | \(-0.237902\pi\) | ||||
0.733465 | + | 0.679727i | \(0.237902\pi\) | |||||||
\(824\) | 16.2426 | 0.565839 | ||||||||
\(825\) | 3.56178 | 0.124005 | ||||||||
\(826\) | 7.43146 | 0.258573 | ||||||||
\(827\) | −18.9787 | −0.659954 | −0.329977 | − | 0.943989i | \(-0.607041\pi\) | ||||
−0.329977 | + | 0.943989i | \(0.607041\pi\) | |||||||
\(828\) | 0.0588745 | 0.00204603 | ||||||||
\(829\) | 42.9945 | 1.49326 | 0.746631 | − | 0.665239i | \(-0.231670\pi\) | ||||
0.746631 | + | 0.665239i | \(0.231670\pi\) | |||||||
\(830\) | 11.1175 | 0.385893 | ||||||||
\(831\) | −30.8338 | −1.06961 | ||||||||
\(832\) | 38.2629 | 1.32653 | ||||||||
\(833\) | −48.3431 | −1.67499 | ||||||||
\(834\) | 44.0833 | 1.52648 | ||||||||
\(835\) | −16.8923 | −0.584581 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.9411 | −0.620136 | ||||||||
\(838\) | −31.4449 | −1.08625 | ||||||||
\(839\) | −31.4449 | −1.08560 | −0.542800 | − | 0.839862i | \(-0.682636\pi\) | ||||
−0.542800 | + | 0.839862i | \(0.682636\pi\) | |||||||
\(840\) | 4.48528 | 0.154757 | ||||||||
\(841\) | 44.9411 | 1.54969 | ||||||||
\(842\) | −12.6863 | −0.437198 | ||||||||
\(843\) | 25.3726 | 0.873878 | ||||||||
\(844\) | 5.64823 | 0.194420 | ||||||||
\(845\) | 5.48528 | 0.188699 | ||||||||
\(846\) | 2.26543 | 0.0778872 | ||||||||
\(847\) | 5.79899 | 0.199256 | ||||||||
\(848\) | 23.5837 | 0.809868 | ||||||||
\(849\) | −17.4509 | −0.598914 | ||||||||
\(850\) | 9.64212 | 0.330722 | ||||||||
\(851\) | −0.611105 | −0.0209484 | ||||||||
\(852\) | −10.0589 | −0.344611 | ||||||||
\(853\) | 36.3431 | 1.24437 | 0.622183 | − | 0.782872i | \(-0.286246\pi\) | ||||
0.622183 | + | 0.782872i | \(0.286246\pi\) | |||||||
\(854\) | 2.95068 | 0.100970 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 42.3848 | 1.44868 | ||||||||
\(857\) | 17.0712 | 0.583142 | 0.291571 | − | 0.956549i | \(-0.405822\pi\) | ||||
0.291571 | + | 0.956549i | \(0.405822\pi\) | |||||||
\(858\) | 19.2842 | 0.658353 | ||||||||
\(859\) | −44.2843 | −1.51096 | −0.755480 | − | 0.655172i | \(-0.772596\pi\) | ||||
−0.755480 | + | 0.655172i | \(0.772596\pi\) | |||||||
\(860\) | 2.00000 | 0.0681994 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.48528 | 0.152769 | ||||||||
\(863\) | −24.6269 | −0.838310 | −0.419155 | − | 0.907915i | \(-0.637674\pi\) | ||||
−0.419155 | + | 0.907915i | \(0.637674\pi\) | |||||||
\(864\) | −11.5980 | −0.394571 | ||||||||
\(865\) | 2.82411 | 0.0960227 | ||||||||
\(866\) | 6.18377 | 0.210133 | ||||||||
\(867\) | 74.1339 | 2.51772 | ||||||||
\(868\) | 1.22221 | 0.0414845 | ||||||||
\(869\) | 14.2471 | 0.483301 | ||||||||
\(870\) | 19.2842 | 0.653797 | ||||||||
\(871\) | 29.3137 | 0.993257 | ||||||||
\(872\) | 56.7696 | 1.92246 | ||||||||
\(873\) | 0.737669 | 0.0249663 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.828427 | −0.0280059 | ||||||||
\(876\) | 8.59890 | 0.290530 | ||||||||
\(877\) | −10.8119 | −0.365092 | −0.182546 | − | 0.983197i | \(-0.558434\pi\) | ||||
−0.182546 | + | 0.983197i | \(0.558434\pi\) | |||||||
\(878\) | 3.71573 | 0.125400 | ||||||||
\(879\) | −31.9411 | −1.07735 | ||||||||
\(880\) | −6.00000 | −0.202260 | ||||||||
\(881\) | 4.48528 | 0.151113 | 0.0755565 | − | 0.997142i | \(-0.475927\pi\) | ||||
0.0755565 | + | 0.997142i | \(0.475927\pi\) | |||||||
\(882\) | −1.36413 | −0.0459326 | ||||||||
\(883\) | 3.85786 | 0.129827 | 0.0649137 | − | 0.997891i | \(-0.479323\pi\) | ||||
0.0649137 | + | 0.997891i | \(0.479323\pi\) | |||||||
\(884\) | −13.6360 | −0.458629 | ||||||||
\(885\) | −12.6863 | −0.426445 | ||||||||
\(886\) | 25.3646 | 0.852140 | ||||||||
\(887\) | 1.16979 | 0.0392776 | 0.0196388 | − | 0.999807i | \(-0.493748\pi\) | ||||
0.0196388 | + | 0.999807i | \(0.493748\pi\) | |||||||
\(888\) | −3.99390 | −0.134026 | ||||||||
\(889\) | 14.5003 | 0.486323 | ||||||||
\(890\) | −19.7990 | −0.663664 | ||||||||
\(891\) | −18.9706 | −0.635538 | ||||||||
\(892\) | −0.126564 | −0.00423768 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −33.2548 | −1.11221 | ||||||||
\(895\) | 17.1978 | 0.574859 | ||||||||
\(896\) | −5.46924 | −0.182714 | ||||||||
\(897\) | −6.34315 | −0.211791 | ||||||||
\(898\) | −10.8284 | −0.361349 | ||||||||
\(899\) | 30.6274 | 1.02148 | ||||||||
\(900\) | −0.0710678 | −0.00236893 | ||||||||
\(901\) | −60.1923 | −2.00530 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.12356 | 0.237057 | ||||||||
\(904\) | 28.3848 | 0.944064 | ||||||||
\(905\) | −10.0742 | −0.334879 | ||||||||
\(906\) | −23.9634 | −0.796130 | ||||||||
\(907\) | 30.5283 | 1.01367 | 0.506837 | − | 0.862042i | \(-0.330814\pi\) | ||||
0.506837 | + | 0.862042i | \(0.330814\pi\) | |||||||
\(908\) | 6.99700 | 0.232204 | ||||||||
\(909\) | 0.0832611 | 0.00276160 | ||||||||
\(910\) | −4.48528 | −0.148686 | ||||||||
\(911\) | −26.6609 | −0.883316 | −0.441658 | − | 0.897183i | \(-0.645610\pi\) | ||||
−0.441658 | + | 0.897183i | \(0.645610\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.6569 | 0.584357 | ||||||||
\(914\) | 6.69145 | 0.221333 | ||||||||
\(915\) | −5.03712 | −0.166522 | ||||||||
\(916\) | 1.85786 | 0.0613856 | ||||||||
\(917\) | −12.6863 | −0.418938 | ||||||||
\(918\) | −48.5685 | −1.60300 | ||||||||
\(919\) | 0.284271 | 0.00937724 | 0.00468862 | − | 0.999989i | \(-0.498508\pi\) | ||||
0.00468862 | + | 0.999989i | \(0.498508\pi\) | |||||||
\(920\) | 2.51856 | 0.0830345 | ||||||||
\(921\) | 5.79899 | 0.191083 | ||||||||
\(922\) | −13.4570 | −0.443184 | ||||||||
\(923\) | 58.6274 | 1.92974 | ||||||||
\(924\) | 1.22221 | 0.0402078 | ||||||||
\(925\) | 0.737669 | 0.0242544 | ||||||||
\(926\) | −41.3402 | −1.35852 | ||||||||
\(927\) | −0.916658 | −0.0301070 | ||||||||
\(928\) | 19.7990 | 0.649934 | ||||||||
\(929\) | −6.00000 | −0.196854 | −0.0984268 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984268 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(930\) | 7.98780 | 0.261930 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.85786 | 0.126369 | ||||||||
\(933\) | −36.2289 | −1.18608 | ||||||||
\(934\) | 48.4638 | 1.58578 | ||||||||
\(935\) | 15.3137 | 0.500812 | ||||||||
\(936\) | −2.24264 | −0.0733030 | ||||||||
\(937\) | 10.9706 | 0.358393 | 0.179196 | − | 0.983813i | \(-0.442650\pi\) | ||||
0.179196 | + | 0.983813i | \(0.442650\pi\) | |||||||
\(938\) | −7.11270 | −0.232238 | ||||||||
\(939\) | 43.8587 | 1.43128 | ||||||||
\(940\) | −4.34315 | −0.141658 | ||||||||
\(941\) | 2.95068 | 0.0961893 | 0.0480947 | − | 0.998843i | \(-0.484685\pi\) | ||||
0.0480947 | + | 0.998843i | \(0.484685\pi\) | |||||||
\(942\) | 40.3675 | 1.31525 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 21.3707 | 0.695557 | ||||||||
\(945\) | 4.17289 | 0.135744 | ||||||||
\(946\) | −12.1607 | −0.395378 | ||||||||
\(947\) | −4.14214 | −0.134601 | −0.0673007 | − | 0.997733i | \(-0.521439\pi\) | ||||
−0.0673007 | + | 0.997733i | \(0.521439\pi\) | |||||||
\(948\) | −5.25483 | −0.170669 | ||||||||
\(949\) | −50.1181 | −1.62690 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.2843 | −0.333490 | ||||||||
\(952\) | 19.2842 | 0.625006 | ||||||||
\(953\) | −1.34877 | −0.0436911 | −0.0218455 | − | 0.999761i | \(-0.506954\pi\) | ||||
−0.0218455 | + | 0.999761i | \(0.506954\pi\) | |||||||
\(954\) | −1.69848 | −0.0549905 | ||||||||
\(955\) | −2.34315 | −0.0758224 | ||||||||
\(956\) | −4.00000 | −0.129369 | ||||||||
\(957\) | 30.6274 | 0.990044 | ||||||||
\(958\) | 12.5928 | 0.406855 | ||||||||
\(959\) | 1.65685 | 0.0535026 | ||||||||
\(960\) | 15.8490 | 0.511525 | ||||||||
\(961\) | −18.3137 | −0.590765 | ||||||||
\(962\) | 3.99390 | 0.128768 | ||||||||
\(963\) | −2.39200 | −0.0770810 | ||||||||
\(964\) | −10.0742 | −0.324469 | ||||||||
\(965\) | −20.0219 | −0.644528 | ||||||||
\(966\) | 1.53911 | 0.0495199 | ||||||||
\(967\) | 21.5147 | 0.691867 | 0.345933 | − | 0.938259i | \(-0.387562\pi\) | ||||
0.345933 | + | 0.938259i | \(0.387562\pi\) | |||||||
\(968\) | 21.2812 | 0.684004 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.41421 | 0.173840 | ||||||||
\(971\) | 7.73467 | 0.248217 | 0.124109 | − | 0.992269i | \(-0.460393\pi\) | ||||
0.124109 | + | 0.992269i | \(0.460393\pi\) | |||||||
\(972\) | 0.737669 | 0.0236608 | ||||||||
\(973\) | −16.2843 | −0.522050 | ||||||||
\(974\) | −37.3553 | −1.19694 | ||||||||
\(975\) | 7.65685 | 0.245216 | ||||||||
\(976\) | 8.48528 | 0.271607 | ||||||||
\(977\) | 47.9051 | 1.53262 | 0.766309 | − | 0.642472i | \(-0.222091\pi\) | ||||
0.766309 | + | 0.642472i | \(0.222091\pi\) | |||||||
\(978\) | 16.0833 | 0.514286 | ||||||||
\(979\) | −31.4449 | −1.00498 | ||||||||
\(980\) | 2.61522 | 0.0835403 | ||||||||
\(981\) | −3.20380 | −0.102290 | ||||||||
\(982\) | 40.6549 | 1.29735 | ||||||||
\(983\) | 33.8369 | 1.07923 | 0.539615 | − | 0.841912i | \(-0.318570\pi\) | ||||
0.539615 | + | 0.841912i | \(0.318570\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.31371 | 0.296759 | ||||||||
\(986\) | 82.9117 | 2.64045 | ||||||||
\(987\) | −15.4693 | −0.492394 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.00000 | 0.127193 | ||||||||
\(990\) | 0.432117 | 0.0137336 | ||||||||
\(991\) | 27.8832 | 0.885737 | 0.442869 | − | 0.896586i | \(-0.353961\pi\) | ||||
0.442869 | + | 0.896586i | \(0.353961\pi\) | |||||||
\(992\) | 8.20101 | 0.260382 | ||||||||
\(993\) | −31.7157 | −1.00647 | ||||||||
\(994\) | −14.2254 | −0.451202 | ||||||||
\(995\) | −4.00000 | −0.126809 | ||||||||
\(996\) | −6.51246 | −0.206355 | ||||||||
\(997\) | −7.65685 | −0.242495 | −0.121248 | − | 0.992622i | \(-0.538689\pi\) | ||||
−0.121248 | + | 0.992622i | \(0.538689\pi\) | |||||||
\(998\) | 1.29635 | 0.0410352 | ||||||||
\(999\) | −3.71573 | −0.117560 |
(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 | 1805.2.a.m.1.3 | yes | 4 | |
5.4 | even | 2 | 9025.2.a.bn.1.2 | 4 | |||
19.18 | odd | 2 | inner | 1805.2.a.m.1.2 | ✓ | 4 | |
95.94 | odd | 2 | 9025.2.a.bn.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.a.m.1.2 | ✓ | 4 | 19.18 | odd | 2 | inner | |
1805.2.a.m.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
9025.2.a.bn.1.2 | 4 | 5.4 | even | 2 | |||
9025.2.a.bn.1.3 | 4 | 95.94 | odd | 2 |