Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(0\) |
Dimension: | \(49\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.604236 | −0.348856 | −0.174428 | − | 0.984670i | \(-0.555808\pi\) | ||||
−0.174428 | + | 0.984670i | \(0.555808\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.43680 | −0.642558 | −0.321279 | − | 0.946985i | \(-0.604113\pi\) | ||||
−0.321279 | + | 0.946985i | \(0.604113\pi\) | |||||||
\(6\) | 0.604236 | 0.246678 | ||||||||
\(7\) | 3.64541 | 1.37783 | 0.688917 | − | 0.724840i | \(-0.258086\pi\) | ||||
0.688917 | + | 0.724840i | \(0.258086\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.63490 | −0.878300 | ||||||||
\(10\) | 1.43680 | 0.454357 | ||||||||
\(11\) | 1.25520 | 0.378457 | 0.189228 | − | 0.981933i | \(-0.439401\pi\) | ||||
0.189228 | + | 0.981933i | \(0.439401\pi\) | |||||||
\(12\) | −0.604236 | −0.174428 | ||||||||
\(13\) | 5.16126 | 1.43148 | 0.715738 | − | 0.698369i | \(-0.246090\pi\) | ||||
0.715738 | + | 0.698369i | \(0.246090\pi\) | |||||||
\(14\) | −3.64541 | −0.974276 | ||||||||
\(15\) | 0.868169 | 0.224160 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.80826 | −1.40871 | −0.704355 | − | 0.709848i | \(-0.748764\pi\) | ||||
−0.704355 | + | 0.709848i | \(0.748764\pi\) | |||||||
\(18\) | 2.63490 | 0.621052 | ||||||||
\(19\) | 6.69723 | 1.53645 | 0.768225 | − | 0.640179i | \(-0.221140\pi\) | ||||
0.768225 | + | 0.640179i | \(0.221140\pi\) | |||||||
\(20\) | −1.43680 | −0.321279 | ||||||||
\(21\) | −2.20269 | −0.480666 | ||||||||
\(22\) | −1.25520 | −0.267609 | ||||||||
\(23\) | 5.93367 | 1.23725 | 0.618627 | − | 0.785684i | \(-0.287689\pi\) | ||||
0.618627 | + | 0.785684i | \(0.287689\pi\) | |||||||
\(24\) | 0.604236 | 0.123339 | ||||||||
\(25\) | −2.93559 | −0.587119 | ||||||||
\(26\) | −5.16126 | −1.01221 | ||||||||
\(27\) | 3.40481 | 0.655256 | ||||||||
\(28\) | 3.64541 | 0.688917 | ||||||||
\(29\) | 8.42225 | 1.56397 | 0.781986 | − | 0.623296i | \(-0.214207\pi\) | ||||
0.781986 | + | 0.623296i | \(0.214207\pi\) | |||||||
\(30\) | −0.868169 | −0.158505 | ||||||||
\(31\) | −2.36368 | −0.424529 | −0.212264 | − | 0.977212i | \(-0.568084\pi\) | ||||
−0.212264 | + | 0.977212i | \(0.568084\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.758437 | −0.132027 | ||||||||
\(34\) | 5.80826 | 0.996108 | ||||||||
\(35\) | −5.23774 | −0.885339 | ||||||||
\(36\) | −2.63490 | −0.439150 | ||||||||
\(37\) | 7.09569 | 1.16652 | 0.583262 | − | 0.812284i | \(-0.301776\pi\) | ||||
0.583262 | + | 0.812284i | \(0.301776\pi\) | |||||||
\(38\) | −6.69723 | −1.08643 | ||||||||
\(39\) | −3.11862 | −0.499379 | ||||||||
\(40\) | 1.43680 | 0.227179 | ||||||||
\(41\) | −10.5916 | −1.65413 | −0.827064 | − | 0.562108i | \(-0.809990\pi\) | ||||
−0.827064 | + | 0.562108i | \(0.809990\pi\) | |||||||
\(42\) | 2.20269 | 0.339882 | ||||||||
\(43\) | −6.98296 | −1.06489 | −0.532445 | − | 0.846464i | \(-0.678727\pi\) | ||||
−0.532445 | + | 0.846464i | \(0.678727\pi\) | |||||||
\(44\) | 1.25520 | 0.189228 | ||||||||
\(45\) | 3.78583 | 0.564359 | ||||||||
\(46\) | −5.93367 | −0.874871 | ||||||||
\(47\) | −13.2976 | −1.93965 | −0.969827 | − | 0.243794i | \(-0.921608\pi\) | ||||
−0.969827 | + | 0.243794i | \(0.921608\pi\) | |||||||
\(48\) | −0.604236 | −0.0872140 | ||||||||
\(49\) | 6.28900 | 0.898429 | ||||||||
\(50\) | 2.93559 | 0.415156 | ||||||||
\(51\) | 3.50956 | 0.491437 | ||||||||
\(52\) | 5.16126 | 0.715738 | ||||||||
\(53\) | 13.3065 | 1.82779 | 0.913896 | − | 0.405949i | \(-0.133059\pi\) | ||||
0.913896 | + | 0.405949i | \(0.133059\pi\) | |||||||
\(54\) | −3.40481 | −0.463336 | ||||||||
\(55\) | −1.80348 | −0.243181 | ||||||||
\(56\) | −3.64541 | −0.487138 | ||||||||
\(57\) | −4.04671 | −0.536000 | ||||||||
\(58\) | −8.42225 | −1.10590 | ||||||||
\(59\) | 5.92430 | 0.771278 | 0.385639 | − | 0.922650i | \(-0.373981\pi\) | ||||
0.385639 | + | 0.922650i | \(0.373981\pi\) | |||||||
\(60\) | 0.868169 | 0.112080 | ||||||||
\(61\) | 4.34325 | 0.556097 | 0.278048 | − | 0.960567i | \(-0.410312\pi\) | ||||
0.278048 | + | 0.960567i | \(0.410312\pi\) | |||||||
\(62\) | 2.36368 | 0.300187 | ||||||||
\(63\) | −9.60528 | −1.21015 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.41572 | −0.919807 | ||||||||
\(66\) | 0.758437 | 0.0933572 | ||||||||
\(67\) | 3.74536 | 0.457569 | 0.228785 | − | 0.973477i | \(-0.426525\pi\) | ||||
0.228785 | + | 0.973477i | \(0.426525\pi\) | |||||||
\(68\) | −5.80826 | −0.704355 | ||||||||
\(69\) | −3.58534 | −0.431624 | ||||||||
\(70\) | 5.23774 | 0.626029 | ||||||||
\(71\) | −10.3568 | −1.22912 | −0.614561 | − | 0.788869i | \(-0.710667\pi\) | ||||
−0.614561 | + | 0.788869i | \(0.710667\pi\) | |||||||
\(72\) | 2.63490 | 0.310526 | ||||||||
\(73\) | 12.4391 | 1.45589 | 0.727943 | − | 0.685638i | \(-0.240477\pi\) | ||||
0.727943 | + | 0.685638i | \(0.240477\pi\) | |||||||
\(74\) | −7.09569 | −0.824858 | ||||||||
\(75\) | 1.77379 | 0.204820 | ||||||||
\(76\) | 6.69723 | 0.768225 | ||||||||
\(77\) | 4.57572 | 0.521451 | ||||||||
\(78\) | 3.11862 | 0.353114 | ||||||||
\(79\) | −0.511714 | −0.0575723 | −0.0287862 | − | 0.999586i | \(-0.509164\pi\) | ||||
−0.0287862 | + | 0.999586i | \(0.509164\pi\) | |||||||
\(80\) | −1.43680 | −0.160640 | ||||||||
\(81\) | 5.84739 | 0.649710 | ||||||||
\(82\) | 10.5916 | 1.16964 | ||||||||
\(83\) | −5.36832 | −0.589250 | −0.294625 | − | 0.955613i | \(-0.595195\pi\) | ||||
−0.294625 | + | 0.955613i | \(0.595195\pi\) | |||||||
\(84\) | −2.20269 | −0.240333 | ||||||||
\(85\) | 8.34533 | 0.905178 | ||||||||
\(86\) | 6.98296 | 0.752991 | ||||||||
\(87\) | −5.08903 | −0.545601 | ||||||||
\(88\) | −1.25520 | −0.133805 | ||||||||
\(89\) | 10.3756 | 1.09981 | 0.549907 | − | 0.835226i | \(-0.314663\pi\) | ||||
0.549907 | + | 0.835226i | \(0.314663\pi\) | |||||||
\(90\) | −3.78583 | −0.399062 | ||||||||
\(91\) | 18.8149 | 1.97234 | ||||||||
\(92\) | 5.93367 | 0.618627 | ||||||||
\(93\) | 1.42822 | 0.148099 | ||||||||
\(94\) | 13.2976 | 1.37154 | ||||||||
\(95\) | −9.62261 | −0.987259 | ||||||||
\(96\) | 0.604236 | 0.0616696 | ||||||||
\(97\) | −12.2990 | −1.24877 | −0.624386 | − | 0.781116i | \(-0.714651\pi\) | ||||
−0.624386 | + | 0.781116i | \(0.714651\pi\) | |||||||
\(98\) | −6.28900 | −0.635285 | ||||||||
\(99\) | −3.30732 | −0.332399 | ||||||||
\(100\) | −2.93559 | −0.293559 | ||||||||
\(101\) | −6.36043 | −0.632887 | −0.316443 | − | 0.948611i | \(-0.602489\pi\) | ||||
−0.316443 | + | 0.948611i | \(0.602489\pi\) | |||||||
\(102\) | −3.50956 | −0.347498 | ||||||||
\(103\) | 9.09708 | 0.896362 | 0.448181 | − | 0.893943i | \(-0.352072\pi\) | ||||
0.448181 | + | 0.893943i | \(0.352072\pi\) | |||||||
\(104\) | −5.16126 | −0.506103 | ||||||||
\(105\) | 3.16483 | 0.308856 | ||||||||
\(106\) | −13.3065 | −1.29244 | ||||||||
\(107\) | −3.27920 | −0.317012 | −0.158506 | − | 0.987358i | \(-0.550668\pi\) | ||||
−0.158506 | + | 0.987358i | \(0.550668\pi\) | |||||||
\(108\) | 3.40481 | 0.327628 | ||||||||
\(109\) | −15.3607 | −1.47129 | −0.735646 | − | 0.677366i | \(-0.763121\pi\) | ||||
−0.735646 | + | 0.677366i | \(0.763121\pi\) | |||||||
\(110\) | 1.80348 | 0.171955 | ||||||||
\(111\) | −4.28747 | −0.406949 | ||||||||
\(112\) | 3.64541 | 0.344459 | ||||||||
\(113\) | 6.23554 | 0.586591 | 0.293295 | − | 0.956022i | \(-0.405248\pi\) | ||||
0.293295 | + | 0.956022i | \(0.405248\pi\) | |||||||
\(114\) | 4.04671 | 0.379009 | ||||||||
\(115\) | −8.52552 | −0.795008 | ||||||||
\(116\) | 8.42225 | 0.781986 | ||||||||
\(117\) | −13.5994 | −1.25727 | ||||||||
\(118\) | −5.92430 | −0.545376 | ||||||||
\(119\) | −21.1735 | −1.94097 | ||||||||
\(120\) | −0.868169 | −0.0792526 | ||||||||
\(121\) | −9.42447 | −0.856770 | ||||||||
\(122\) | −4.34325 | −0.393220 | ||||||||
\(123\) | 6.39982 | 0.577052 | ||||||||
\(124\) | −2.36368 | −0.212264 | ||||||||
\(125\) | 11.4019 | 1.01982 | ||||||||
\(126\) | 9.60528 | 0.855706 | ||||||||
\(127\) | −10.1210 | −0.898092 | −0.449046 | − | 0.893509i | \(-0.648236\pi\) | ||||
−0.449046 | + | 0.893509i | \(0.648236\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.21935 | 0.371493 | ||||||||
\(130\) | 7.41572 | 0.650402 | ||||||||
\(131\) | 15.4757 | 1.35211 | 0.676057 | − | 0.736849i | \(-0.263687\pi\) | ||||
0.676057 | + | 0.736849i | \(0.263687\pi\) | |||||||
\(132\) | −0.758437 | −0.0660135 | ||||||||
\(133\) | 24.4142 | 2.11698 | ||||||||
\(134\) | −3.74536 | −0.323550 | ||||||||
\(135\) | −4.89204 | −0.421040 | ||||||||
\(136\) | 5.80826 | 0.498054 | ||||||||
\(137\) | 6.90624 | 0.590040 | 0.295020 | − | 0.955491i | \(-0.404674\pi\) | ||||
0.295020 | + | 0.955491i | \(0.404674\pi\) | |||||||
\(138\) | 3.58534 | 0.305204 | ||||||||
\(139\) | 13.8548 | 1.17515 | 0.587573 | − | 0.809171i | \(-0.300083\pi\) | ||||
0.587573 | + | 0.809171i | \(0.300083\pi\) | |||||||
\(140\) | −5.23774 | −0.442670 | ||||||||
\(141\) | 8.03489 | 0.676660 | ||||||||
\(142\) | 10.3568 | 0.869121 | ||||||||
\(143\) | 6.47842 | 0.541752 | ||||||||
\(144\) | −2.63490 | −0.219575 | ||||||||
\(145\) | −12.1011 | −1.00494 | ||||||||
\(146\) | −12.4391 | −1.02947 | ||||||||
\(147\) | −3.80004 | −0.313422 | ||||||||
\(148\) | 7.09569 | 0.583262 | ||||||||
\(149\) | −6.32983 | −0.518560 | −0.259280 | − | 0.965802i | \(-0.583485\pi\) | ||||
−0.259280 | + | 0.965802i | \(0.583485\pi\) | |||||||
\(150\) | −1.77379 | −0.144830 | ||||||||
\(151\) | −8.72970 | −0.710413 | −0.355207 | − | 0.934788i | \(-0.615589\pi\) | ||||
−0.355207 | + | 0.934788i | \(0.615589\pi\) | |||||||
\(152\) | −6.69723 | −0.543217 | ||||||||
\(153\) | 15.3042 | 1.23727 | ||||||||
\(154\) | −4.57572 | −0.368722 | ||||||||
\(155\) | 3.39614 | 0.272785 | ||||||||
\(156\) | −3.11862 | −0.249690 | ||||||||
\(157\) | 20.8602 | 1.66483 | 0.832413 | − | 0.554156i | \(-0.186959\pi\) | ||||
0.832413 | + | 0.554156i | \(0.186959\pi\) | |||||||
\(158\) | 0.511714 | 0.0407098 | ||||||||
\(159\) | −8.04028 | −0.637636 | ||||||||
\(160\) | 1.43680 | 0.113589 | ||||||||
\(161\) | 21.6306 | 1.70473 | ||||||||
\(162\) | −5.84739 | −0.459414 | ||||||||
\(163\) | −13.1918 | −1.03326 | −0.516629 | − | 0.856209i | \(-0.672813\pi\) | ||||
−0.516629 | + | 0.856209i | \(0.672813\pi\) | |||||||
\(164\) | −10.5916 | −0.827064 | ||||||||
\(165\) | 1.08973 | 0.0848350 | ||||||||
\(166\) | 5.36832 | 0.416663 | ||||||||
\(167\) | −5.01703 | −0.388229 | −0.194115 | − | 0.980979i | \(-0.562183\pi\) | ||||
−0.194115 | + | 0.980979i | \(0.562183\pi\) | |||||||
\(168\) | 2.20269 | 0.169941 | ||||||||
\(169\) | 13.6386 | 1.04913 | ||||||||
\(170\) | −8.34533 | −0.640058 | ||||||||
\(171\) | −17.6465 | −1.34946 | ||||||||
\(172\) | −6.98296 | −0.532445 | ||||||||
\(173\) | −15.6351 | −1.18872 | −0.594358 | − | 0.804201i | \(-0.702594\pi\) | ||||
−0.594358 | + | 0.804201i | \(0.702594\pi\) | |||||||
\(174\) | 5.08903 | 0.385798 | ||||||||
\(175\) | −10.7014 | −0.808953 | ||||||||
\(176\) | 1.25520 | 0.0946142 | ||||||||
\(177\) | −3.57967 | −0.269065 | ||||||||
\(178\) | −10.3756 | −0.777686 | ||||||||
\(179\) | 7.24607 | 0.541597 | 0.270798 | − | 0.962636i | \(-0.412712\pi\) | ||||
0.270798 | + | 0.962636i | \(0.412712\pi\) | |||||||
\(180\) | 3.78583 | 0.282179 | ||||||||
\(181\) | 10.1106 | 0.751515 | 0.375757 | − | 0.926718i | \(-0.377383\pi\) | ||||
0.375757 | + | 0.926718i | \(0.377383\pi\) | |||||||
\(182\) | −18.8149 | −1.39465 | ||||||||
\(183\) | −2.62435 | −0.193998 | ||||||||
\(184\) | −5.93367 | −0.437436 | ||||||||
\(185\) | −10.1951 | −0.749560 | ||||||||
\(186\) | −1.42822 | −0.104722 | ||||||||
\(187\) | −7.29052 | −0.533136 | ||||||||
\(188\) | −13.2976 | −0.969827 | ||||||||
\(189\) | 12.4119 | 0.902834 | ||||||||
\(190\) | 9.62261 | 0.698098 | ||||||||
\(191\) | −21.2628 | −1.53852 | −0.769261 | − | 0.638935i | \(-0.779375\pi\) | ||||
−0.769261 | + | 0.638935i | \(0.779375\pi\) | |||||||
\(192\) | −0.604236 | −0.0436070 | ||||||||
\(193\) | 23.2946 | 1.67678 | 0.838390 | − | 0.545071i | \(-0.183497\pi\) | ||||
0.838390 | + | 0.545071i | \(0.183497\pi\) | |||||||
\(194\) | 12.2990 | 0.883015 | ||||||||
\(195\) | 4.48085 | 0.320880 | ||||||||
\(196\) | 6.28900 | 0.449214 | ||||||||
\(197\) | −6.08827 | −0.433771 | −0.216886 | − | 0.976197i | \(-0.569590\pi\) | ||||
−0.216886 | + | 0.976197i | \(0.569590\pi\) | |||||||
\(198\) | 3.30732 | 0.235041 | ||||||||
\(199\) | 21.0792 | 1.49426 | 0.747132 | − | 0.664675i | \(-0.231430\pi\) | ||||
0.747132 | + | 0.664675i | \(0.231430\pi\) | |||||||
\(200\) | 2.93559 | 0.207578 | ||||||||
\(201\) | −2.26308 | −0.159626 | ||||||||
\(202\) | 6.36043 | 0.447518 | ||||||||
\(203\) | 30.7025 | 2.15490 | ||||||||
\(204\) | 3.50956 | 0.245718 | ||||||||
\(205\) | 15.2180 | 1.06287 | ||||||||
\(206\) | −9.09708 | −0.633824 | ||||||||
\(207\) | −15.6346 | −1.08668 | ||||||||
\(208\) | 5.16126 | 0.357869 | ||||||||
\(209\) | 8.40637 | 0.581480 | ||||||||
\(210\) | −3.16483 | −0.218394 | ||||||||
\(211\) | 14.9328 | 1.02801 | 0.514007 | − | 0.857786i | \(-0.328161\pi\) | ||||
0.514007 | + | 0.857786i | \(0.328161\pi\) | |||||||
\(212\) | 13.3065 | 0.913896 | ||||||||
\(213\) | 6.25793 | 0.428787 | ||||||||
\(214\) | 3.27920 | 0.224162 | ||||||||
\(215\) | 10.0331 | 0.684254 | ||||||||
\(216\) | −3.40481 | −0.231668 | ||||||||
\(217\) | −8.61657 | −0.584931 | ||||||||
\(218\) | 15.3607 | 1.04036 | ||||||||
\(219\) | −7.51615 | −0.507894 | ||||||||
\(220\) | −1.80348 | −0.121590 | ||||||||
\(221\) | −29.9779 | −2.01653 | ||||||||
\(222\) | 4.28747 | 0.287756 | ||||||||
\(223\) | −0.170298 | −0.0114040 | −0.00570199 | − | 0.999984i | \(-0.501815\pi\) | ||||
−0.00570199 | + | 0.999984i | \(0.501815\pi\) | |||||||
\(224\) | −3.64541 | −0.243569 | ||||||||
\(225\) | 7.73499 | 0.515666 | ||||||||
\(226\) | −6.23554 | −0.414782 | ||||||||
\(227\) | 15.9952 | 1.06164 | 0.530819 | − | 0.847485i | \(-0.321884\pi\) | ||||
0.530819 | + | 0.847485i | \(0.321884\pi\) | |||||||
\(228\) | −4.04671 | −0.268000 | ||||||||
\(229\) | 17.4374 | 1.15230 | 0.576149 | − | 0.817345i | \(-0.304555\pi\) | ||||
0.576149 | + | 0.817345i | \(0.304555\pi\) | |||||||
\(230\) | 8.52552 | 0.562156 | ||||||||
\(231\) | −2.76481 | −0.181911 | ||||||||
\(232\) | −8.42225 | −0.552948 | ||||||||
\(233\) | 15.6646 | 1.02622 | 0.513110 | − | 0.858323i | \(-0.328493\pi\) | ||||
0.513110 | + | 0.858323i | \(0.328493\pi\) | |||||||
\(234\) | 13.5994 | 0.889021 | ||||||||
\(235\) | 19.1060 | 1.24634 | ||||||||
\(236\) | 5.92430 | 0.385639 | ||||||||
\(237\) | 0.309196 | 0.0200844 | ||||||||
\(238\) | 21.1735 | 1.37247 | ||||||||
\(239\) | 14.5533 | 0.941374 | 0.470687 | − | 0.882300i | \(-0.344006\pi\) | ||||
0.470687 | + | 0.882300i | \(0.344006\pi\) | |||||||
\(240\) | 0.868169 | 0.0560401 | ||||||||
\(241\) | −23.9038 | −1.53978 | −0.769889 | − | 0.638178i | \(-0.779688\pi\) | ||||
−0.769889 | + | 0.638178i | \(0.779688\pi\) | |||||||
\(242\) | 9.42447 | 0.605828 | ||||||||
\(243\) | −13.7476 | −0.881911 | ||||||||
\(244\) | 4.34325 | 0.278048 | ||||||||
\(245\) | −9.03606 | −0.577293 | ||||||||
\(246\) | −6.39982 | −0.408037 | ||||||||
\(247\) | 34.5662 | 2.19939 | ||||||||
\(248\) | 2.36368 | 0.150094 | ||||||||
\(249\) | 3.24373 | 0.205563 | ||||||||
\(250\) | −11.4019 | −0.721119 | ||||||||
\(251\) | 1.63167 | 0.102990 | 0.0514949 | − | 0.998673i | \(-0.483601\pi\) | ||||
0.0514949 | + | 0.998673i | \(0.483601\pi\) | |||||||
\(252\) | −9.60528 | −0.605076 | ||||||||
\(253\) | 7.44794 | 0.468248 | ||||||||
\(254\) | 10.1210 | 0.635047 | ||||||||
\(255\) | −5.04255 | −0.315777 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.3390 | 1.20633 | 0.603167 | − | 0.797615i | \(-0.293905\pi\) | ||||
0.603167 | + | 0.797615i | \(0.293905\pi\) | |||||||
\(258\) | −4.21935 | −0.262686 | ||||||||
\(259\) | 25.8667 | 1.60728 | ||||||||
\(260\) | −7.41572 | −0.459904 | ||||||||
\(261\) | −22.1918 | −1.37364 | ||||||||
\(262\) | −15.4757 | −0.956089 | ||||||||
\(263\) | 0.734054 | 0.0452637 | 0.0226319 | − | 0.999744i | \(-0.492795\pi\) | ||||
0.0226319 | + | 0.999744i | \(0.492795\pi\) | |||||||
\(264\) | 0.758437 | 0.0466786 | ||||||||
\(265\) | −19.1189 | −1.17446 | ||||||||
\(266\) | −24.4142 | −1.49693 | ||||||||
\(267\) | −6.26933 | −0.383677 | ||||||||
\(268\) | 3.74536 | 0.228785 | ||||||||
\(269\) | −25.4233 | −1.55009 | −0.775043 | − | 0.631908i | \(-0.782272\pi\) | ||||
−0.775043 | + | 0.631908i | \(0.782272\pi\) | |||||||
\(270\) | 4.89204 | 0.297720 | ||||||||
\(271\) | 11.6790 | 0.709448 | 0.354724 | − | 0.934971i | \(-0.384575\pi\) | ||||
0.354724 | + | 0.934971i | \(0.384575\pi\) | |||||||
\(272\) | −5.80826 | −0.352177 | ||||||||
\(273\) | −11.3686 | −0.688062 | ||||||||
\(274\) | −6.90624 | −0.417221 | ||||||||
\(275\) | −3.68476 | −0.222199 | ||||||||
\(276\) | −3.58534 | −0.215812 | ||||||||
\(277\) | 18.4363 | 1.10773 | 0.553865 | − | 0.832606i | \(-0.313152\pi\) | ||||
0.553865 | + | 0.832606i | \(0.313152\pi\) | |||||||
\(278\) | −13.8548 | −0.830954 | ||||||||
\(279\) | 6.22805 | 0.372864 | ||||||||
\(280\) | 5.23774 | 0.313015 | ||||||||
\(281\) | 3.55935 | 0.212333 | 0.106166 | − | 0.994348i | \(-0.466142\pi\) | ||||
0.106166 | + | 0.994348i | \(0.466142\pi\) | |||||||
\(282\) | −8.03489 | −0.478471 | ||||||||
\(283\) | −18.2571 | −1.08527 | −0.542635 | − | 0.839969i | \(-0.682573\pi\) | ||||
−0.542635 | + | 0.839969i | \(0.682573\pi\) | |||||||
\(284\) | −10.3568 | −0.614561 | ||||||||
\(285\) | 5.81433 | 0.344411 | ||||||||
\(286\) | −6.47842 | −0.383077 | ||||||||
\(287\) | −38.6106 | −2.27911 | ||||||||
\(288\) | 2.63490 | 0.155263 | ||||||||
\(289\) | 16.7359 | 0.984462 | ||||||||
\(290\) | 12.1011 | 0.710602 | ||||||||
\(291\) | 7.43148 | 0.435641 | ||||||||
\(292\) | 12.4391 | 0.727943 | ||||||||
\(293\) | 12.8218 | 0.749058 | 0.374529 | − | 0.927215i | \(-0.377804\pi\) | ||||
0.374529 | + | 0.927215i | \(0.377804\pi\) | |||||||
\(294\) | 3.80004 | 0.221623 | ||||||||
\(295\) | −8.51205 | −0.495591 | ||||||||
\(296\) | −7.09569 | −0.412429 | ||||||||
\(297\) | 4.27372 | 0.247986 | ||||||||
\(298\) | 6.32983 | 0.366677 | ||||||||
\(299\) | 30.6252 | 1.77110 | ||||||||
\(300\) | 1.77379 | 0.102410 | ||||||||
\(301\) | −25.4557 | −1.46724 | ||||||||
\(302\) | 8.72970 | 0.502338 | ||||||||
\(303\) | 3.84320 | 0.220786 | ||||||||
\(304\) | 6.69723 | 0.384113 | ||||||||
\(305\) | −6.24040 | −0.357325 | ||||||||
\(306\) | −15.3042 | −0.874881 | ||||||||
\(307\) | 28.7357 | 1.64004 | 0.820018 | − | 0.572338i | \(-0.193963\pi\) | ||||
0.820018 | + | 0.572338i | \(0.193963\pi\) | |||||||
\(308\) | 4.57572 | 0.260726 | ||||||||
\(309\) | −5.49679 | −0.312701 | ||||||||
\(310\) | −3.39614 | −0.192888 | ||||||||
\(311\) | 16.3801 | 0.928828 | 0.464414 | − | 0.885618i | \(-0.346265\pi\) | ||||
0.464414 | + | 0.885618i | \(0.346265\pi\) | |||||||
\(312\) | 3.11862 | 0.176557 | ||||||||
\(313\) | 17.9921 | 1.01698 | 0.508488 | − | 0.861069i | \(-0.330205\pi\) | ||||
0.508488 | + | 0.861069i | \(0.330205\pi\) | |||||||
\(314\) | −20.8602 | −1.17721 | ||||||||
\(315\) | 13.8009 | 0.777593 | ||||||||
\(316\) | −0.511714 | −0.0287862 | ||||||||
\(317\) | −12.5951 | −0.707409 | −0.353705 | − | 0.935357i | \(-0.615078\pi\) | ||||
−0.353705 | + | 0.935357i | \(0.615078\pi\) | |||||||
\(318\) | 8.04028 | 0.450877 | ||||||||
\(319\) | 10.5716 | 0.591896 | ||||||||
\(320\) | −1.43680 | −0.0803198 | ||||||||
\(321\) | 1.98141 | 0.110592 | ||||||||
\(322\) | −21.6306 | −1.20543 | ||||||||
\(323\) | −38.8993 | −2.16441 | ||||||||
\(324\) | 5.84739 | 0.324855 | ||||||||
\(325\) | −15.1514 | −0.840447 | ||||||||
\(326\) | 13.1918 | 0.730624 | ||||||||
\(327\) | 9.28152 | 0.513269 | ||||||||
\(328\) | 10.5916 | 0.584822 | ||||||||
\(329\) | −48.4752 | −2.67252 | ||||||||
\(330\) | −1.08973 | −0.0599874 | ||||||||
\(331\) | 29.9652 | 1.64704 | 0.823518 | − | 0.567290i | \(-0.192008\pi\) | ||||
0.823518 | + | 0.567290i | \(0.192008\pi\) | |||||||
\(332\) | −5.36832 | −0.294625 | ||||||||
\(333\) | −18.6964 | −1.02456 | ||||||||
\(334\) | 5.01703 | 0.274519 | ||||||||
\(335\) | −5.38135 | −0.294015 | ||||||||
\(336\) | −2.20269 | −0.120166 | ||||||||
\(337\) | −8.61063 | −0.469051 | −0.234526 | − | 0.972110i | \(-0.575354\pi\) | ||||
−0.234526 | + | 0.972110i | \(0.575354\pi\) | |||||||
\(338\) | −13.6386 | −0.741844 | ||||||||
\(339\) | −3.76774 | −0.204636 | ||||||||
\(340\) | 8.34533 | 0.452589 | ||||||||
\(341\) | −2.96689 | −0.160666 | ||||||||
\(342\) | 17.6465 | 0.954215 | ||||||||
\(343\) | −2.59188 | −0.139948 | ||||||||
\(344\) | 6.98296 | 0.376496 | ||||||||
\(345\) | 5.15142 | 0.277343 | ||||||||
\(346\) | 15.6351 | 0.840548 | ||||||||
\(347\) | 16.3894 | 0.879827 | 0.439913 | − | 0.898040i | \(-0.355009\pi\) | ||||
0.439913 | + | 0.898040i | \(0.355009\pi\) | |||||||
\(348\) | −5.08903 | −0.272800 | ||||||||
\(349\) | −22.7834 | −1.21957 | −0.609784 | − | 0.792568i | \(-0.708744\pi\) | ||||
−0.609784 | + | 0.792568i | \(0.708744\pi\) | |||||||
\(350\) | 10.7014 | 0.572016 | ||||||||
\(351\) | 17.5731 | 0.937984 | ||||||||
\(352\) | −1.25520 | −0.0669024 | ||||||||
\(353\) | 13.7280 | 0.730668 | 0.365334 | − | 0.930877i | \(-0.380955\pi\) | ||||
0.365334 | + | 0.930877i | \(0.380955\pi\) | |||||||
\(354\) | 3.57967 | 0.190258 | ||||||||
\(355\) | 14.8806 | 0.789783 | ||||||||
\(356\) | 10.3756 | 0.549907 | ||||||||
\(357\) | 12.7938 | 0.677119 | ||||||||
\(358\) | −7.24607 | −0.382967 | ||||||||
\(359\) | −1.25394 | −0.0661802 | −0.0330901 | − | 0.999452i | \(-0.510535\pi\) | ||||
−0.0330901 | + | 0.999452i | \(0.510535\pi\) | |||||||
\(360\) | −3.78583 | −0.199531 | ||||||||
\(361\) | 25.8529 | 1.36068 | ||||||||
\(362\) | −10.1106 | −0.531401 | ||||||||
\(363\) | 5.69461 | 0.298889 | ||||||||
\(364\) | 18.8149 | 0.986169 | ||||||||
\(365\) | −17.8725 | −0.935491 | ||||||||
\(366\) | 2.62435 | 0.137177 | ||||||||
\(367\) | 37.2407 | 1.94395 | 0.971974 | − | 0.235089i | \(-0.0755381\pi\) | ||||
0.971974 | + | 0.235089i | \(0.0755381\pi\) | |||||||
\(368\) | 5.93367 | 0.309314 | ||||||||
\(369\) | 27.9077 | 1.45282 | ||||||||
\(370\) | 10.1951 | 0.530019 | ||||||||
\(371\) | 48.5077 | 2.51839 | ||||||||
\(372\) | 1.42822 | 0.0740497 | ||||||||
\(373\) | −29.4837 | −1.52661 | −0.763303 | − | 0.646041i | \(-0.776424\pi\) | ||||
−0.763303 | + | 0.646041i | \(0.776424\pi\) | |||||||
\(374\) | 7.29052 | 0.376984 | ||||||||
\(375\) | −6.88944 | −0.355769 | ||||||||
\(376\) | 13.2976 | 0.685771 | ||||||||
\(377\) | 43.4694 | 2.23879 | ||||||||
\(378\) | −12.4119 | −0.638400 | ||||||||
\(379\) | −18.9379 | −0.972774 | −0.486387 | − | 0.873744i | \(-0.661685\pi\) | ||||
−0.486387 | + | 0.873744i | \(0.661685\pi\) | |||||||
\(380\) | −9.62261 | −0.493630 | ||||||||
\(381\) | 6.11547 | 0.313305 | ||||||||
\(382\) | 21.2628 | 1.08790 | ||||||||
\(383\) | −16.9575 | −0.866487 | −0.433244 | − | 0.901277i | \(-0.642631\pi\) | ||||
−0.433244 | + | 0.901277i | \(0.642631\pi\) | |||||||
\(384\) | 0.604236 | 0.0308348 | ||||||||
\(385\) | −6.57441 | −0.335063 | ||||||||
\(386\) | −23.2946 | −1.18566 | ||||||||
\(387\) | 18.3994 | 0.935293 | ||||||||
\(388\) | −12.2990 | −0.624386 | ||||||||
\(389\) | 4.38067 | 0.222109 | 0.111054 | − | 0.993814i | \(-0.464577\pi\) | ||||
0.111054 | + | 0.993814i | \(0.464577\pi\) | |||||||
\(390\) | −4.48085 | −0.226897 | ||||||||
\(391\) | −34.4643 | −1.74293 | ||||||||
\(392\) | −6.28900 | −0.317643 | ||||||||
\(393\) | −9.35095 | −0.471693 | ||||||||
\(394\) | 6.08827 | 0.306723 | ||||||||
\(395\) | 0.735233 | 0.0369936 | ||||||||
\(396\) | −3.30732 | −0.166199 | ||||||||
\(397\) | 8.28590 | 0.415858 | 0.207929 | − | 0.978144i | \(-0.433328\pi\) | ||||
0.207929 | + | 0.978144i | \(0.433328\pi\) | |||||||
\(398\) | −21.0792 | −1.05660 | ||||||||
\(399\) | −14.7519 | −0.738519 | ||||||||
\(400\) | −2.93559 | −0.146780 | ||||||||
\(401\) | 16.7756 | 0.837731 | 0.418866 | − | 0.908048i | \(-0.362428\pi\) | ||||
0.418866 | + | 0.908048i | \(0.362428\pi\) | |||||||
\(402\) | 2.26308 | 0.112872 | ||||||||
\(403\) | −12.1996 | −0.607703 | ||||||||
\(404\) | −6.36043 | −0.316443 | ||||||||
\(405\) | −8.40155 | −0.417476 | ||||||||
\(406\) | −30.7025 | −1.52374 | ||||||||
\(407\) | 8.90651 | 0.441479 | ||||||||
\(408\) | −3.50956 | −0.173749 | ||||||||
\(409\) | −27.2041 | −1.34516 | −0.672578 | − | 0.740027i | \(-0.734813\pi\) | ||||
−0.672578 | + | 0.740027i | \(0.734813\pi\) | |||||||
\(410\) | −15.2180 | −0.751565 | ||||||||
\(411\) | −4.17300 | −0.205839 | ||||||||
\(412\) | 9.09708 | 0.448181 | ||||||||
\(413\) | 21.5965 | 1.06269 | ||||||||
\(414\) | 15.6346 | 0.768399 | ||||||||
\(415\) | 7.71323 | 0.378627 | ||||||||
\(416\) | −5.16126 | −0.253052 | ||||||||
\(417\) | −8.37156 | −0.409957 | ||||||||
\(418\) | −8.40637 | −0.411169 | ||||||||
\(419\) | 25.3846 | 1.24012 | 0.620059 | − | 0.784555i | \(-0.287108\pi\) | ||||
0.620059 | + | 0.784555i | \(0.287108\pi\) | |||||||
\(420\) | 3.16483 | 0.154428 | ||||||||
\(421\) | 34.7267 | 1.69248 | 0.846238 | − | 0.532805i | \(-0.178862\pi\) | ||||
0.846238 | + | 0.532805i | \(0.178862\pi\) | |||||||
\(422\) | −14.9328 | −0.726915 | ||||||||
\(423\) | 35.0378 | 1.70360 | ||||||||
\(424\) | −13.3065 | −0.646222 | ||||||||
\(425\) | 17.0507 | 0.827080 | ||||||||
\(426\) | −6.25793 | −0.303198 | ||||||||
\(427\) | 15.8329 | 0.766209 | ||||||||
\(428\) | −3.27920 | −0.158506 | ||||||||
\(429\) | −3.91449 | −0.188994 | ||||||||
\(430\) | −10.0331 | −0.483841 | ||||||||
\(431\) | 20.0671 | 0.966597 | 0.483299 | − | 0.875456i | \(-0.339439\pi\) | ||||
0.483299 | + | 0.875456i | \(0.339439\pi\) | |||||||
\(432\) | 3.40481 | 0.163814 | ||||||||
\(433\) | 7.70027 | 0.370051 | 0.185026 | − | 0.982734i | \(-0.440763\pi\) | ||||
0.185026 | + | 0.982734i | \(0.440763\pi\) | |||||||
\(434\) | 8.61657 | 0.413609 | ||||||||
\(435\) | 7.31193 | 0.350580 | ||||||||
\(436\) | −15.3607 | −0.735646 | ||||||||
\(437\) | 39.7391 | 1.90098 | ||||||||
\(438\) | 7.51615 | 0.359135 | ||||||||
\(439\) | 6.62499 | 0.316193 | 0.158097 | − | 0.987424i | \(-0.449464\pi\) | ||||
0.158097 | + | 0.987424i | \(0.449464\pi\) | |||||||
\(440\) | 1.80348 | 0.0859774 | ||||||||
\(441\) | −16.5709 | −0.789090 | ||||||||
\(442\) | 29.9779 | 1.42591 | ||||||||
\(443\) | 12.7949 | 0.607905 | 0.303953 | − | 0.952687i | \(-0.401694\pi\) | ||||
0.303953 | + | 0.952687i | \(0.401694\pi\) | |||||||
\(444\) | −4.28747 | −0.203475 | ||||||||
\(445\) | −14.9078 | −0.706695 | ||||||||
\(446\) | 0.170298 | 0.00806383 | ||||||||
\(447\) | 3.82471 | 0.180903 | ||||||||
\(448\) | 3.64541 | 0.172229 | ||||||||
\(449\) | 3.90612 | 0.184341 | 0.0921706 | − | 0.995743i | \(-0.470619\pi\) | ||||
0.0921706 | + | 0.995743i | \(0.470619\pi\) | |||||||
\(450\) | −7.73499 | −0.364631 | ||||||||
\(451\) | −13.2946 | −0.626016 | ||||||||
\(452\) | 6.23554 | 0.293295 | ||||||||
\(453\) | 5.27480 | 0.247832 | ||||||||
\(454\) | −15.9952 | −0.750691 | ||||||||
\(455\) | −27.0333 | −1.26734 | ||||||||
\(456\) | 4.04671 | 0.189505 | ||||||||
\(457\) | −11.3275 | −0.529879 | −0.264940 | − | 0.964265i | \(-0.585352\pi\) | ||||
−0.264940 | + | 0.964265i | \(0.585352\pi\) | |||||||
\(458\) | −17.4374 | −0.814797 | ||||||||
\(459\) | −19.7760 | −0.923065 | ||||||||
\(460\) | −8.52552 | −0.397504 | ||||||||
\(461\) | 17.1518 | 0.798838 | 0.399419 | − | 0.916769i | \(-0.369212\pi\) | ||||
0.399419 | + | 0.916769i | \(0.369212\pi\) | |||||||
\(462\) | 2.76481 | 0.128631 | ||||||||
\(463\) | −36.7951 | −1.71001 | −0.855007 | − | 0.518616i | \(-0.826447\pi\) | ||||
−0.855007 | + | 0.518616i | \(0.826447\pi\) | |||||||
\(464\) | 8.42225 | 0.390993 | ||||||||
\(465\) | −2.05207 | −0.0951625 | ||||||||
\(466\) | −15.6646 | −0.725648 | ||||||||
\(467\) | 30.8429 | 1.42724 | 0.713620 | − | 0.700533i | \(-0.247054\pi\) | ||||
0.713620 | + | 0.700533i | \(0.247054\pi\) | |||||||
\(468\) | −13.5994 | −0.628633 | ||||||||
\(469\) | 13.6534 | 0.630455 | ||||||||
\(470\) | −19.1060 | −0.881296 | ||||||||
\(471\) | −12.6045 | −0.580784 | ||||||||
\(472\) | −5.92430 | −0.272688 | ||||||||
\(473\) | −8.76500 | −0.403015 | ||||||||
\(474\) | −0.309196 | −0.0142018 | ||||||||
\(475\) | −19.6604 | −0.902079 | ||||||||
\(476\) | −21.1735 | −0.970484 | ||||||||
\(477\) | −35.0613 | −1.60535 | ||||||||
\(478\) | −14.5533 | −0.665652 | ||||||||
\(479\) | 24.7595 | 1.13129 | 0.565644 | − | 0.824649i | \(-0.308627\pi\) | ||||
0.565644 | + | 0.824649i | \(0.308627\pi\) | |||||||
\(480\) | −0.868169 | −0.0396263 | ||||||||
\(481\) | 36.6227 | 1.66985 | ||||||||
\(482\) | 23.9038 | 1.08879 | ||||||||
\(483\) | −13.0700 | −0.594706 | ||||||||
\(484\) | −9.42447 | −0.428385 | ||||||||
\(485\) | 17.6712 | 0.802408 | ||||||||
\(486\) | 13.7476 | 0.623605 | ||||||||
\(487\) | 32.5380 | 1.47444 | 0.737218 | − | 0.675654i | \(-0.236139\pi\) | ||||
0.737218 | + | 0.675654i | \(0.236139\pi\) | |||||||
\(488\) | −4.34325 | −0.196610 | ||||||||
\(489\) | 7.97094 | 0.360458 | ||||||||
\(490\) | 9.03606 | 0.408208 | ||||||||
\(491\) | −14.6230 | −0.659929 | −0.329964 | − | 0.943993i | \(-0.607037\pi\) | ||||
−0.329964 | + | 0.943993i | \(0.607037\pi\) | |||||||
\(492\) | 6.39982 | 0.288526 | ||||||||
\(493\) | −48.9186 | −2.20318 | ||||||||
\(494\) | −34.5662 | −1.55521 | ||||||||
\(495\) | 4.75198 | 0.213585 | ||||||||
\(496\) | −2.36368 | −0.106132 | ||||||||
\(497\) | −37.7546 | −1.69353 | ||||||||
\(498\) | −3.24373 | −0.145355 | ||||||||
\(499\) | −5.96238 | −0.266913 | −0.133456 | − | 0.991055i | \(-0.542608\pi\) | ||||
−0.133456 | + | 0.991055i | \(0.542608\pi\) | |||||||
\(500\) | 11.4019 | 0.509908 | ||||||||
\(501\) | 3.03147 | 0.135436 | ||||||||
\(502\) | −1.63167 | −0.0728248 | ||||||||
\(503\) | −3.41382 | −0.152215 | −0.0761073 | − | 0.997100i | \(-0.524249\pi\) | ||||
−0.0761073 | + | 0.997100i | \(0.524249\pi\) | |||||||
\(504\) | 9.60528 | 0.427853 | ||||||||
\(505\) | 9.13869 | 0.406667 | ||||||||
\(506\) | −7.44794 | −0.331101 | ||||||||
\(507\) | −8.24096 | −0.365994 | ||||||||
\(508\) | −10.1210 | −0.449046 | ||||||||
\(509\) | −13.1028 | −0.580772 | −0.290386 | − | 0.956910i | \(-0.593784\pi\) | ||||
−0.290386 | + | 0.956910i | \(0.593784\pi\) | |||||||
\(510\) | 5.04255 | 0.223288 | ||||||||
\(511\) | 45.3456 | 2.00597 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 22.8028 | 1.00677 | ||||||||
\(514\) | −19.3390 | −0.853006 | ||||||||
\(515\) | −13.0707 | −0.575965 | ||||||||
\(516\) | 4.21935 | 0.185747 | ||||||||
\(517\) | −16.6911 | −0.734076 | ||||||||
\(518\) | −25.8667 | −1.13652 | ||||||||
\(519\) | 9.44730 | 0.414690 | ||||||||
\(520\) | 7.41572 | 0.325201 | ||||||||
\(521\) | −33.6475 | −1.47412 | −0.737061 | − | 0.675826i | \(-0.763787\pi\) | ||||
−0.737061 | + | 0.675826i | \(0.763787\pi\) | |||||||
\(522\) | 22.1918 | 0.971307 | ||||||||
\(523\) | −5.33535 | −0.233298 | −0.116649 | − | 0.993173i | \(-0.537215\pi\) | ||||
−0.116649 | + | 0.993173i | \(0.537215\pi\) | |||||||
\(524\) | 15.4757 | 0.676057 | ||||||||
\(525\) | 6.46620 | 0.282208 | ||||||||
\(526\) | −0.734054 | −0.0320063 | ||||||||
\(527\) | 13.7288 | 0.598038 | ||||||||
\(528\) | −0.758437 | −0.0330067 | ||||||||
\(529\) | 12.2084 | 0.530800 | ||||||||
\(530\) | 19.1189 | 0.830470 | ||||||||
\(531\) | −15.6099 | −0.677413 | ||||||||
\(532\) | 24.4142 | 1.05849 | ||||||||
\(533\) | −54.6659 | −2.36784 | ||||||||
\(534\) | 6.26933 | 0.271301 | ||||||||
\(535\) | 4.71157 | 0.203699 | ||||||||
\(536\) | −3.74536 | −0.161775 | ||||||||
\(537\) | −4.37834 | −0.188939 | ||||||||
\(538\) | 25.4233 | 1.09608 | ||||||||
\(539\) | 7.89395 | 0.340017 | ||||||||
\(540\) | −4.89204 | −0.210520 | ||||||||
\(541\) | 23.5305 | 1.01165 | 0.505827 | − | 0.862635i | \(-0.331187\pi\) | ||||
0.505827 | + | 0.862635i | \(0.331187\pi\) | |||||||
\(542\) | −11.6790 | −0.501656 | ||||||||
\(543\) | −6.10919 | −0.262170 | ||||||||
\(544\) | 5.80826 | 0.249027 | ||||||||
\(545\) | 22.0704 | 0.945391 | ||||||||
\(546\) | 11.3686 | 0.486533 | ||||||||
\(547\) | −18.4401 | −0.788442 | −0.394221 | − | 0.919016i | \(-0.628986\pi\) | ||||
−0.394221 | + | 0.919016i | \(0.628986\pi\) | |||||||
\(548\) | 6.90624 | 0.295020 | ||||||||
\(549\) | −11.4440 | −0.488419 | ||||||||
\(550\) | 3.68476 | 0.157119 | ||||||||
\(551\) | 56.4058 | 2.40297 | ||||||||
\(552\) | 3.58534 | 0.152602 | ||||||||
\(553\) | −1.86541 | −0.0793251 | ||||||||
\(554\) | −18.4363 | −0.783284 | ||||||||
\(555\) | 6.16026 | 0.261489 | ||||||||
\(556\) | 13.8548 | 0.587573 | ||||||||
\(557\) | 13.6225 | 0.577203 | 0.288602 | − | 0.957449i | \(-0.406810\pi\) | ||||
0.288602 | + | 0.957449i | \(0.406810\pi\) | |||||||
\(558\) | −6.22805 | −0.263654 | ||||||||
\(559\) | −36.0409 | −1.52437 | ||||||||
\(560\) | −5.23774 | −0.221335 | ||||||||
\(561\) | 4.40520 | 0.185988 | ||||||||
\(562\) | −3.55935 | −0.150142 | ||||||||
\(563\) | 32.5236 | 1.37071 | 0.685353 | − | 0.728211i | \(-0.259648\pi\) | ||||
0.685353 | + | 0.728211i | \(0.259648\pi\) | |||||||
\(564\) | 8.03489 | 0.338330 | ||||||||
\(565\) | −8.95925 | −0.376919 | ||||||||
\(566\) | 18.2571 | 0.767402 | ||||||||
\(567\) | 21.3161 | 0.895193 | ||||||||
\(568\) | 10.3568 | 0.434560 | ||||||||
\(569\) | −36.9267 | −1.54805 | −0.774024 | − | 0.633156i | \(-0.781759\pi\) | ||||
−0.774024 | + | 0.633156i | \(0.781759\pi\) | |||||||
\(570\) | −5.81433 | −0.243536 | ||||||||
\(571\) | 9.27192 | 0.388018 | 0.194009 | − | 0.981000i | \(-0.437851\pi\) | ||||
0.194009 | + | 0.981000i | \(0.437851\pi\) | |||||||
\(572\) | 6.47842 | 0.270876 | ||||||||
\(573\) | 12.8478 | 0.536722 | ||||||||
\(574\) | 38.6106 | 1.61158 | ||||||||
\(575\) | −17.4188 | −0.726416 | ||||||||
\(576\) | −2.63490 | −0.109787 | ||||||||
\(577\) | −9.24587 | −0.384911 | −0.192455 | − | 0.981306i | \(-0.561645\pi\) | ||||
−0.192455 | + | 0.981306i | \(0.561645\pi\) | |||||||
\(578\) | −16.7359 | −0.696120 | ||||||||
\(579\) | −14.0754 | −0.584955 | ||||||||
\(580\) | −12.1011 | −0.502472 | ||||||||
\(581\) | −19.5697 | −0.811889 | ||||||||
\(582\) | −7.43148 | −0.308045 | ||||||||
\(583\) | 16.7023 | 0.691740 | ||||||||
\(584\) | −12.4391 | −0.514733 | ||||||||
\(585\) | 19.5397 | 0.807866 | ||||||||
\(586\) | −12.8218 | −0.529664 | ||||||||
\(587\) | −4.81423 | −0.198705 | −0.0993523 | − | 0.995052i | \(-0.531677\pi\) | ||||
−0.0993523 | + | 0.995052i | \(0.531677\pi\) | |||||||
\(588\) | −3.80004 | −0.156711 | ||||||||
\(589\) | −15.8301 | −0.652268 | ||||||||
\(590\) | 8.51205 | 0.350436 | ||||||||
\(591\) | 3.67875 | 0.151324 | ||||||||
\(592\) | 7.09569 | 0.291631 | ||||||||
\(593\) | −21.1738 | −0.869503 | −0.434752 | − | 0.900550i | \(-0.643164\pi\) | ||||
−0.434752 | + | 0.900550i | \(0.643164\pi\) | |||||||
\(594\) | −4.27372 | −0.175353 | ||||||||
\(595\) | 30.4221 | 1.24719 | ||||||||
\(596\) | −6.32983 | −0.259280 | ||||||||
\(597\) | −12.7368 | −0.521283 | ||||||||
\(598\) | −30.6252 | −1.25236 | ||||||||
\(599\) | 21.8533 | 0.892902 | 0.446451 | − | 0.894808i | \(-0.352688\pi\) | ||||
0.446451 | + | 0.894808i | \(0.352688\pi\) | |||||||
\(600\) | −1.77379 | −0.0724148 | ||||||||
\(601\) | −13.4413 | −0.548280 | −0.274140 | − | 0.961690i | \(-0.588393\pi\) | ||||
−0.274140 | + | 0.961690i | \(0.588393\pi\) | |||||||
\(602\) | 25.4557 | 1.03750 | ||||||||
\(603\) | −9.86866 | −0.401883 | ||||||||
\(604\) | −8.72970 | −0.355207 | ||||||||
\(605\) | 13.5411 | 0.550525 | ||||||||
\(606\) | −3.84320 | −0.156119 | ||||||||
\(607\) | −24.7732 | −1.00551 | −0.502756 | − | 0.864428i | \(-0.667681\pi\) | ||||
−0.502756 | + | 0.864428i | \(0.667681\pi\) | |||||||
\(608\) | −6.69723 | −0.271609 | ||||||||
\(609\) | −18.5516 | −0.751748 | ||||||||
\(610\) | 6.24040 | 0.252667 | ||||||||
\(611\) | −68.6324 | −2.77657 | ||||||||
\(612\) | 15.3042 | 0.618634 | ||||||||
\(613\) | 13.4739 | 0.544204 | 0.272102 | − | 0.962268i | \(-0.412281\pi\) | ||||
0.272102 | + | 0.962268i | \(0.412281\pi\) | |||||||
\(614\) | −28.7357 | −1.15968 | ||||||||
\(615\) | −9.19528 | −0.370790 | ||||||||
\(616\) | −4.57572 | −0.184361 | ||||||||
\(617\) | −27.9390 | −1.12478 | −0.562391 | − | 0.826872i | \(-0.690118\pi\) | ||||
−0.562391 | + | 0.826872i | \(0.690118\pi\) | |||||||
\(618\) | 5.49679 | 0.221113 | ||||||||
\(619\) | 26.5867 | 1.06861 | 0.534304 | − | 0.845292i | \(-0.320574\pi\) | ||||
0.534304 | + | 0.845292i | \(0.320574\pi\) | |||||||
\(620\) | 3.39614 | 0.136392 | ||||||||
\(621\) | 20.2030 | 0.810719 | ||||||||
\(622\) | −16.3801 | −0.656780 | ||||||||
\(623\) | 37.8234 | 1.51536 | ||||||||
\(624\) | −3.11862 | −0.124845 | ||||||||
\(625\) | −1.70432 | −0.0681728 | ||||||||
\(626\) | −17.9921 | −0.719111 | ||||||||
\(627\) | −5.07943 | −0.202853 | ||||||||
\(628\) | 20.8602 | 0.832413 | ||||||||
\(629\) | −41.2136 | −1.64329 | ||||||||
\(630\) | −13.8009 | −0.549841 | ||||||||
\(631\) | −17.6145 | −0.701223 | −0.350612 | − | 0.936521i | \(-0.614026\pi\) | ||||
−0.350612 | + | 0.936521i | \(0.614026\pi\) | |||||||
\(632\) | 0.511714 | 0.0203549 | ||||||||
\(633\) | −9.02291 | −0.358629 | ||||||||
\(634\) | 12.5951 | 0.500214 | ||||||||
\(635\) | 14.5419 | 0.577077 | ||||||||
\(636\) | −8.04028 | −0.318818 | ||||||||
\(637\) | 32.4592 | 1.28608 | ||||||||
\(638\) | −10.5716 | −0.418534 | ||||||||
\(639\) | 27.2890 | 1.07954 | ||||||||
\(640\) | 1.43680 | 0.0567947 | ||||||||
\(641\) | 40.1910 | 1.58745 | 0.793724 | − | 0.608278i | \(-0.208139\pi\) | ||||
0.793724 | + | 0.608278i | \(0.208139\pi\) | |||||||
\(642\) | −1.98141 | −0.0782001 | ||||||||
\(643\) | −47.6277 | −1.87825 | −0.939126 | − | 0.343574i | \(-0.888363\pi\) | ||||
−0.939126 | + | 0.343574i | \(0.888363\pi\) | |||||||
\(644\) | 21.6306 | 0.852366 | ||||||||
\(645\) | −6.06239 | −0.238706 | ||||||||
\(646\) | 38.8993 | 1.53047 | ||||||||
\(647\) | −10.8067 | −0.424854 | −0.212427 | − | 0.977177i | \(-0.568137\pi\) | ||||
−0.212427 | + | 0.977177i | \(0.568137\pi\) | |||||||
\(648\) | −5.84739 | −0.229707 | ||||||||
\(649\) | 7.43617 | 0.291895 | ||||||||
\(650\) | 15.1514 | 0.594286 | ||||||||
\(651\) | 5.20644 | 0.204057 | ||||||||
\(652\) | −13.1918 | −0.516629 | ||||||||
\(653\) | 26.5205 | 1.03783 | 0.518914 | − | 0.854826i | \(-0.326336\pi\) | ||||
0.518914 | + | 0.854826i | \(0.326336\pi\) | |||||||
\(654\) | −9.28152 | −0.362936 | ||||||||
\(655\) | −22.2355 | −0.868812 | ||||||||
\(656\) | −10.5916 | −0.413532 | ||||||||
\(657\) | −32.7757 | −1.27870 | ||||||||
\(658\) | 48.4752 | 1.88976 | ||||||||
\(659\) | 21.3336 | 0.831038 | 0.415519 | − | 0.909584i | \(-0.363600\pi\) | ||||
0.415519 | + | 0.909584i | \(0.363600\pi\) | |||||||
\(660\) | 1.08973 | 0.0424175 | ||||||||
\(661\) | −25.6443 | −0.997447 | −0.498724 | − | 0.866761i | \(-0.666198\pi\) | ||||
−0.498724 | + | 0.866761i | \(0.666198\pi\) | |||||||
\(662\) | −29.9652 | −1.16463 | ||||||||
\(663\) | 18.1138 | 0.703480 | ||||||||
\(664\) | 5.36832 | 0.208331 | ||||||||
\(665\) | −35.0784 | −1.36028 | ||||||||
\(666\) | 18.6964 | 0.724472 | ||||||||
\(667\) | 49.9748 | 1.93503 | ||||||||
\(668\) | −5.01703 | −0.194115 | ||||||||
\(669\) | 0.102900 | 0.00397834 | ||||||||
\(670\) | 5.38135 | 0.207900 | ||||||||
\(671\) | 5.45165 | 0.210459 | ||||||||
\(672\) | 2.20269 | 0.0849705 | ||||||||
\(673\) | −29.2008 | −1.12561 | −0.562805 | − | 0.826590i | \(-0.690278\pi\) | ||||
−0.562805 | + | 0.826590i | \(0.690278\pi\) | |||||||
\(674\) | 8.61063 | 0.331669 | ||||||||
\(675\) | −9.99514 | −0.384713 | ||||||||
\(676\) | 13.6386 | 0.524563 | ||||||||
\(677\) | 5.13469 | 0.197342 | 0.0986711 | − | 0.995120i | \(-0.468541\pi\) | ||||
0.0986711 | + | 0.995120i | \(0.468541\pi\) | |||||||
\(678\) | 3.76774 | 0.144699 | ||||||||
\(679\) | −44.8348 | −1.72060 | ||||||||
\(680\) | −8.34533 | −0.320029 | ||||||||
\(681\) | −9.66487 | −0.370359 | ||||||||
\(682\) | 2.96689 | 0.113608 | ||||||||
\(683\) | −36.5170 | −1.39728 | −0.698642 | − | 0.715472i | \(-0.746212\pi\) | ||||
−0.698642 | + | 0.715472i | \(0.746212\pi\) | |||||||
\(684\) | −17.6465 | −0.674732 | ||||||||
\(685\) | −9.92291 | −0.379135 | ||||||||
\(686\) | 2.59188 | 0.0989583 | ||||||||
\(687\) | −10.5363 | −0.401986 | ||||||||
\(688\) | −6.98296 | −0.266223 | ||||||||
\(689\) | 68.6785 | 2.61644 | ||||||||
\(690\) | −5.15142 | −0.196111 | ||||||||
\(691\) | −45.0275 | −1.71293 | −0.856463 | − | 0.516208i | \(-0.827343\pi\) | ||||
−0.856463 | + | 0.516208i | \(0.827343\pi\) | |||||||
\(692\) | −15.6351 | −0.594358 | ||||||||
\(693\) | −12.0565 | −0.457990 | ||||||||
\(694\) | −16.3894 | −0.622132 | ||||||||
\(695\) | −19.9066 | −0.755100 | ||||||||
\(696\) | 5.08903 | 0.192899 | ||||||||
\(697\) | 61.5186 | 2.33018 | ||||||||
\(698\) | 22.7834 | 0.862365 | ||||||||
\(699\) | −9.46511 | −0.358003 | ||||||||
\(700\) | −10.7014 | −0.404476 | ||||||||
\(701\) | 2.23727 | 0.0845006 | 0.0422503 | − | 0.999107i | \(-0.486547\pi\) | ||||
0.0422503 | + | 0.999107i | \(0.486547\pi\) | |||||||
\(702\) | −17.5731 | −0.663255 | ||||||||
\(703\) | 47.5215 | 1.79231 | ||||||||
\(704\) | 1.25520 | 0.0473071 | ||||||||
\(705\) | −11.5446 | −0.434793 | ||||||||
\(706\) | −13.7280 | −0.516660 | ||||||||
\(707\) | −23.1864 | −0.872013 | ||||||||
\(708\) | −3.57967 | −0.134532 | ||||||||
\(709\) | 20.3051 | 0.762575 | 0.381287 | − | 0.924457i | \(-0.375481\pi\) | ||||
0.381287 | + | 0.924457i | \(0.375481\pi\) | |||||||
\(710\) | −14.8806 | −0.558461 | ||||||||
\(711\) | 1.34831 | 0.0505657 | ||||||||
\(712\) | −10.3756 | −0.388843 | ||||||||
\(713\) | −14.0253 | −0.525251 | ||||||||
\(714\) | −12.7938 | −0.478795 | ||||||||
\(715\) | −9.30821 | −0.348107 | ||||||||
\(716\) | 7.24607 | 0.270798 | ||||||||
\(717\) | −8.79363 | −0.328404 | ||||||||
\(718\) | 1.25394 | 0.0467964 | ||||||||
\(719\) | −37.7728 | −1.40869 | −0.704343 | − | 0.709860i | \(-0.748758\pi\) | ||||
−0.704343 | + | 0.709860i | \(0.748758\pi\) | |||||||
\(720\) | 3.78583 | 0.141090 | ||||||||
\(721\) | 33.1626 | 1.23504 | ||||||||
\(722\) | −25.8529 | −0.962147 | ||||||||
\(723\) | 14.4435 | 0.537160 | ||||||||
\(724\) | 10.1106 | 0.375757 | ||||||||
\(725\) | −24.7243 | −0.918237 | ||||||||
\(726\) | −5.69461 | −0.211347 | ||||||||
\(727\) | −7.60722 | −0.282136 | −0.141068 | − | 0.990000i | \(-0.545054\pi\) | ||||
−0.141068 | + | 0.990000i | \(0.545054\pi\) | |||||||
\(728\) | −18.8149 | −0.697327 | ||||||||
\(729\) | −9.23534 | −0.342050 | ||||||||
\(730\) | 17.8725 | 0.661492 | ||||||||
\(731\) | 40.5588 | 1.50012 | ||||||||
\(732\) | −2.62435 | −0.0969988 | ||||||||
\(733\) | −23.1004 | −0.853232 | −0.426616 | − | 0.904433i | \(-0.640294\pi\) | ||||
−0.426616 | + | 0.904433i | \(0.640294\pi\) | |||||||
\(734\) | −37.2407 | −1.37458 | ||||||||
\(735\) | 5.45992 | 0.201392 | ||||||||
\(736\) | −5.93367 | −0.218718 | ||||||||
\(737\) | 4.70118 | 0.173170 | ||||||||
\(738\) | −27.9077 | −1.02730 | ||||||||
\(739\) | −14.6479 | −0.538831 | −0.269416 | − | 0.963024i | \(-0.586831\pi\) | ||||
−0.269416 | + | 0.963024i | \(0.586831\pi\) | |||||||
\(740\) | −10.1951 | −0.374780 | ||||||||
\(741\) | −20.8861 | −0.767271 | ||||||||
\(742\) | −48.5077 | −1.78077 | ||||||||
\(743\) | −36.8091 | −1.35039 | −0.675197 | − | 0.737637i | \(-0.735941\pi\) | ||||
−0.675197 | + | 0.737637i | \(0.735941\pi\) | |||||||
\(744\) | −1.42822 | −0.0523611 | ||||||||
\(745\) | 9.09472 | 0.333205 | ||||||||
\(746\) | 29.4837 | 1.07947 | ||||||||
\(747\) | 14.1450 | 0.517538 | ||||||||
\(748\) | −7.29052 | −0.266568 | ||||||||
\(749\) | −11.9540 | −0.436791 | ||||||||
\(750\) | 6.88944 | 0.251567 | ||||||||
\(751\) | −22.6642 | −0.827030 | −0.413515 | − | 0.910497i | \(-0.635699\pi\) | ||||
−0.413515 | + | 0.910497i | \(0.635699\pi\) | |||||||
\(752\) | −13.2976 | −0.484914 | ||||||||
\(753\) | −0.985912 | −0.0359286 | ||||||||
\(754\) | −43.4694 | −1.58306 | ||||||||
\(755\) | 12.5429 | 0.456482 | ||||||||
\(756\) | 12.4119 | 0.451417 | ||||||||
\(757\) | 23.5313 | 0.855259 | 0.427629 | − | 0.903954i | \(-0.359349\pi\) | ||||
0.427629 | + | 0.903954i | \(0.359349\pi\) | |||||||
\(758\) | 18.9379 | 0.687855 | ||||||||
\(759\) | −4.50031 | −0.163351 | ||||||||
\(760\) | 9.62261 | 0.349049 | ||||||||
\(761\) | 45.9150 | 1.66442 | 0.832208 | − | 0.554464i | \(-0.187077\pi\) | ||||
0.832208 | + | 0.554464i | \(0.187077\pi\) | |||||||
\(762\) | −6.11547 | −0.221540 | ||||||||
\(763\) | −55.9962 | −2.02720 | ||||||||
\(764\) | −21.2628 | −0.769261 | ||||||||
\(765\) | −21.9891 | −0.795017 | ||||||||
\(766\) | 16.9575 | 0.612699 | ||||||||
\(767\) | 30.5768 | 1.10407 | ||||||||
\(768\) | −0.604236 | −0.0218035 | ||||||||
\(769\) | 44.5169 | 1.60532 | 0.802660 | − | 0.596437i | \(-0.203417\pi\) | ||||
0.802660 | + | 0.596437i | \(0.203417\pi\) | |||||||
\(770\) | 6.57441 | 0.236925 | ||||||||
\(771\) | −11.6853 | −0.420837 | ||||||||
\(772\) | 23.2946 | 0.838390 | ||||||||
\(773\) | 0.840719 | 0.0302386 | 0.0151193 | − | 0.999886i | \(-0.495187\pi\) | ||||
0.0151193 | + | 0.999886i | \(0.495187\pi\) | |||||||
\(774\) | −18.3994 | −0.661352 | ||||||||
\(775\) | 6.93880 | 0.249249 | ||||||||
\(776\) | 12.2990 | 0.441507 | ||||||||
\(777\) | −15.6296 | −0.560709 | ||||||||
\(778\) | −4.38067 | −0.157054 | ||||||||
\(779\) | −70.9343 | −2.54149 | ||||||||
\(780\) | 4.48085 | 0.160440 | ||||||||
\(781\) | −12.9998 | −0.465170 | ||||||||
\(782\) | 34.4643 | 1.23244 | ||||||||
\(783\) | 28.6761 | 1.02480 | ||||||||
\(784\) | 6.28900 | 0.224607 | ||||||||
\(785\) | −29.9720 | −1.06975 | ||||||||
\(786\) | 9.35095 | 0.333537 | ||||||||
\(787\) | −49.6311 | −1.76916 | −0.884578 | − | 0.466392i | \(-0.845554\pi\) | ||||
−0.884578 | + | 0.466392i | \(0.845554\pi\) | |||||||
\(788\) | −6.08827 | −0.216886 | ||||||||
\(789\) | −0.443542 | −0.0157905 | ||||||||
\(790\) | −0.735233 | −0.0261584 | ||||||||
\(791\) | 22.7311 | 0.808225 | ||||||||
\(792\) | 3.30732 | 0.117521 | ||||||||
\(793\) | 22.4167 | 0.796039 | ||||||||
\(794\) | −8.28590 | −0.294056 | ||||||||
\(795\) | 11.5523 | 0.409718 | ||||||||
\(796\) | 21.0792 | 0.747132 | ||||||||
\(797\) | −1.52550 | −0.0540362 | −0.0270181 | − | 0.999635i | \(-0.508601\pi\) | ||||
−0.0270181 | + | 0.999635i | \(0.508601\pi\) | |||||||
\(798\) | 14.7519 | 0.522212 | ||||||||
\(799\) | 77.2359 | 2.73241 | ||||||||
\(800\) | 2.93559 | 0.103789 | ||||||||
\(801\) | −27.3387 | −0.965967 | ||||||||
\(802\) | −16.7756 | −0.592365 | ||||||||
\(803\) | 15.6135 | 0.550990 | ||||||||
\(804\) | −2.26308 | −0.0798128 | ||||||||
\(805\) | −31.0790 | −1.09539 | ||||||||
\(806\) | 12.1996 | 0.429711 | ||||||||
\(807\) | 15.3617 | 0.540757 | ||||||||
\(808\) | 6.36043 | 0.223759 | ||||||||
\(809\) | 37.6212 | 1.32269 | 0.661346 | − | 0.750081i | \(-0.269985\pi\) | ||||
0.661346 | + | 0.750081i | \(0.269985\pi\) | |||||||
\(810\) | 8.40155 | 0.295200 | ||||||||
\(811\) | 32.2386 | 1.13205 | 0.566025 | − | 0.824388i | \(-0.308481\pi\) | ||||
0.566025 | + | 0.824388i | \(0.308481\pi\) | |||||||
\(812\) | 30.7025 | 1.07745 | ||||||||
\(813\) | −7.05687 | −0.247495 | ||||||||
\(814\) | −8.90651 | −0.312173 | ||||||||
\(815\) | 18.9540 | 0.663929 | ||||||||
\(816\) | 3.50956 | 0.122859 | ||||||||
\(817\) | −46.7665 | −1.63615 | ||||||||
\(818\) | 27.2041 | 0.951168 | ||||||||
\(819\) | −49.5754 | −1.73230 | ||||||||
\(820\) | 15.2180 | 0.531437 | ||||||||
\(821\) | −0.740478 | −0.0258429 | −0.0129214 | − | 0.999917i | \(-0.504113\pi\) | ||||
−0.0129214 | + | 0.999917i | \(0.504113\pi\) | |||||||
\(822\) | 4.17300 | 0.145550 | ||||||||
\(823\) | −28.0508 | −0.977790 | −0.488895 | − | 0.872343i | \(-0.662600\pi\) | ||||
−0.488895 | + | 0.872343i | \(0.662600\pi\) | |||||||
\(824\) | −9.09708 | −0.316912 | ||||||||
\(825\) | 2.22646 | 0.0775155 | ||||||||
\(826\) | −21.5965 | −0.751438 | ||||||||
\(827\) | 9.27975 | 0.322688 | 0.161344 | − | 0.986898i | \(-0.448417\pi\) | ||||
0.161344 | + | 0.986898i | \(0.448417\pi\) | |||||||
\(828\) | −15.6346 | −0.543340 | ||||||||
\(829\) | 18.4664 | 0.641364 | 0.320682 | − | 0.947187i | \(-0.396088\pi\) | ||||
0.320682 | + | 0.947187i | \(0.396088\pi\) | |||||||
\(830\) | −7.71323 | −0.267730 | ||||||||
\(831\) | −11.1399 | −0.386438 | ||||||||
\(832\) | 5.16126 | 0.178935 | ||||||||
\(833\) | −36.5281 | −1.26563 | ||||||||
\(834\) | 8.37156 | 0.289883 | ||||||||
\(835\) | 7.20848 | 0.249460 | ||||||||
\(836\) | 8.40637 | 0.290740 | ||||||||
\(837\) | −8.04787 | −0.278175 | ||||||||
\(838\) | −25.3846 | −0.876897 | ||||||||
\(839\) | 26.1233 | 0.901876 | 0.450938 | − | 0.892555i | \(-0.351090\pi\) | ||||
0.450938 | + | 0.892555i | \(0.351090\pi\) | |||||||
\(840\) | −3.16483 | −0.109197 | ||||||||
\(841\) | 41.9342 | 1.44601 | ||||||||
\(842\) | −34.7267 | −1.19676 | ||||||||
\(843\) | −2.15069 | −0.0740736 | ||||||||
\(844\) | 14.9328 | 0.514007 | ||||||||
\(845\) | −19.5960 | −0.674124 | ||||||||
\(846\) | −35.0378 | −1.20463 | ||||||||
\(847\) | −34.3561 | −1.18049 | ||||||||
\(848\) | 13.3065 | 0.456948 | ||||||||
\(849\) | 11.0316 | 0.378603 | ||||||||
\(850\) | −17.0507 | −0.584834 | ||||||||
\(851\) | 42.1035 | 1.44329 | ||||||||
\(852\) | 6.25793 | 0.214393 | ||||||||
\(853\) | 17.0664 | 0.584342 | 0.292171 | − | 0.956366i | \(-0.405622\pi\) | ||||
0.292171 | + | 0.956366i | \(0.405622\pi\) | |||||||
\(854\) | −15.8329 | −0.541792 | ||||||||
\(855\) | 25.3546 | 0.867109 | ||||||||
\(856\) | 3.27920 | 0.112081 | ||||||||
\(857\) | −50.0097 | −1.70830 | −0.854150 | − | 0.520027i | \(-0.825922\pi\) | ||||
−0.854150 | + | 0.520027i | \(0.825922\pi\) | |||||||
\(858\) | 3.91449 | 0.133639 | ||||||||
\(859\) | −28.0648 | −0.957560 | −0.478780 | − | 0.877935i | \(-0.658921\pi\) | ||||
−0.478780 | + | 0.877935i | \(0.658921\pi\) | |||||||
\(860\) | 10.0331 | 0.342127 | ||||||||
\(861\) | 23.3299 | 0.795082 | ||||||||
\(862\) | −20.0671 | −0.683487 | ||||||||
\(863\) | −25.3345 | −0.862397 | −0.431198 | − | 0.902257i | \(-0.641909\pi\) | ||||
−0.431198 | + | 0.902257i | \(0.641909\pi\) | |||||||
\(864\) | −3.40481 | −0.115834 | ||||||||
\(865\) | 22.4646 | 0.763819 | ||||||||
\(866\) | −7.70027 | −0.261666 | ||||||||
\(867\) | −10.1124 | −0.343435 | ||||||||
\(868\) | −8.61657 | −0.292465 | ||||||||
\(869\) | −0.642303 | −0.0217886 | ||||||||
\(870\) | −7.31193 | −0.247898 | ||||||||
\(871\) | 19.3308 | 0.654999 | ||||||||
\(872\) | 15.3607 | 0.520181 | ||||||||
\(873\) | 32.4065 | 1.09680 | ||||||||
\(874\) | −39.7391 | −1.34420 | ||||||||
\(875\) | 41.5646 | 1.40514 | ||||||||
\(876\) | −7.51615 | −0.253947 | ||||||||
\(877\) | 45.4841 | 1.53589 | 0.767945 | − | 0.640516i | \(-0.221279\pi\) | ||||
0.767945 | + | 0.640516i | \(0.221279\pi\) | |||||||
\(878\) | −6.62499 | −0.223583 | ||||||||
\(879\) | −7.74740 | −0.261313 | ||||||||
\(880\) | −1.80348 | −0.0607952 | ||||||||
\(881\) | 24.9893 | 0.841912 | 0.420956 | − | 0.907081i | \(-0.361695\pi\) | ||||
0.420956 | + | 0.907081i | \(0.361695\pi\) | |||||||
\(882\) | 16.5709 | 0.557971 | ||||||||
\(883\) | −41.2111 | −1.38686 | −0.693432 | − | 0.720522i | \(-0.743902\pi\) | ||||
−0.693432 | + | 0.720522i | \(0.743902\pi\) | |||||||
\(884\) | −29.9779 | −1.00827 | ||||||||
\(885\) | 5.14329 | 0.172890 | ||||||||
\(886\) | −12.7949 | −0.429854 | ||||||||
\(887\) | 8.50083 | 0.285430 | 0.142715 | − | 0.989764i | \(-0.454417\pi\) | ||||
0.142715 | + | 0.989764i | \(0.454417\pi\) | |||||||
\(888\) | 4.28747 | 0.143878 | ||||||||
\(889\) | −36.8951 | −1.23742 | ||||||||
\(890\) | 14.9078 | 0.499709 | ||||||||
\(891\) | 7.33964 | 0.245887 | ||||||||
\(892\) | −0.170298 | −0.00570199 | ||||||||
\(893\) | −89.0571 | −2.98018 | ||||||||
\(894\) | −3.82471 | −0.127917 | ||||||||
\(895\) | −10.4112 | −0.348007 | ||||||||
\(896\) | −3.64541 | −0.121785 | ||||||||
\(897\) | −18.5049 | −0.617859 | ||||||||
\(898\) | −3.90612 | −0.130349 | ||||||||
\(899\) | −19.9075 | −0.663951 | ||||||||
\(900\) | 7.73499 | 0.257833 | ||||||||
\(901\) | −77.2877 | −2.57483 | ||||||||
\(902\) | 13.2946 | 0.442660 | ||||||||
\(903\) | 15.3813 | 0.511857 | ||||||||
\(904\) | −6.23554 | −0.207391 | ||||||||
\(905\) | −14.5269 | −0.482892 | ||||||||
\(906\) | −5.27480 | −0.175244 | ||||||||
\(907\) | 7.58359 | 0.251809 | 0.125904 | − | 0.992042i | \(-0.459817\pi\) | ||||
0.125904 | + | 0.992042i | \(0.459817\pi\) | |||||||
\(908\) | 15.9952 | 0.530819 | ||||||||
\(909\) | 16.7591 | 0.555864 | ||||||||
\(910\) | 27.0333 | 0.896147 | ||||||||
\(911\) | 12.0184 | 0.398187 | 0.199094 | − | 0.979980i | \(-0.436200\pi\) | ||||
0.199094 | + | 0.979980i | \(0.436200\pi\) | |||||||
\(912\) | −4.04671 | −0.134000 | ||||||||
\(913\) | −6.73832 | −0.223006 | ||||||||
\(914\) | 11.3275 | 0.374681 | ||||||||
\(915\) | 3.77068 | 0.124655 | ||||||||
\(916\) | 17.4374 | 0.576149 | ||||||||
\(917\) | 56.4151 | 1.86299 | ||||||||
\(918\) | 19.7760 | 0.652706 | ||||||||
\(919\) | −36.7776 | −1.21318 | −0.606591 | − | 0.795014i | \(-0.707463\pi\) | ||||
−0.606591 | + | 0.795014i | \(0.707463\pi\) | |||||||
\(920\) | 8.52552 | 0.281078 | ||||||||
\(921\) | −17.3632 | −0.572136 | ||||||||
\(922\) | −17.1518 | −0.564864 | ||||||||
\(923\) | −53.4540 | −1.75946 | ||||||||
\(924\) | −2.76481 | −0.0909557 | ||||||||
\(925\) | −20.8301 | −0.684889 | ||||||||
\(926\) | 36.7951 | 1.20916 | ||||||||
\(927\) | −23.9699 | −0.787274 | ||||||||
\(928\) | −8.42225 | −0.276474 | ||||||||
\(929\) | −17.2955 | −0.567448 | −0.283724 | − | 0.958906i | \(-0.591570\pi\) | ||||
−0.283724 | + | 0.958906i | \(0.591570\pi\) | |||||||
\(930\) | 2.05207 | 0.0672901 | ||||||||
\(931\) | 42.1189 | 1.38039 | ||||||||
\(932\) | 15.6646 | 0.513110 | ||||||||
\(933\) | −9.89742 | −0.324027 | ||||||||
\(934\) | −30.8429 | −1.00921 | ||||||||
\(935\) | 10.4751 | 0.342571 | ||||||||
\(936\) | 13.5994 | 0.444510 | ||||||||
\(937\) | −2.89678 | −0.0946336 | −0.0473168 | − | 0.998880i | \(-0.515067\pi\) | ||||
−0.0473168 | + | 0.998880i | \(0.515067\pi\) | |||||||
\(938\) | −13.6534 | −0.445799 | ||||||||
\(939\) | −10.8715 | −0.354778 | ||||||||
\(940\) | 19.1060 | 0.623170 | ||||||||
\(941\) | −11.1406 | −0.363172 | −0.181586 | − | 0.983375i | \(-0.558123\pi\) | ||||
−0.181586 | + | 0.983375i | \(0.558123\pi\) | |||||||
\(942\) | 12.6045 | 0.410677 | ||||||||
\(943\) | −62.8469 | −2.04658 | ||||||||
\(944\) | 5.92430 | 0.192819 | ||||||||
\(945\) | −17.8335 | −0.580124 | ||||||||
\(946\) | 8.76500 | 0.284975 | ||||||||
\(947\) | −30.1415 | −0.979468 | −0.489734 | − | 0.871872i | \(-0.662906\pi\) | ||||
−0.489734 | + | 0.871872i | \(0.662906\pi\) | |||||||
\(948\) | 0.309196 | 0.0100422 | ||||||||
\(949\) | 64.2014 | 2.08407 | ||||||||
\(950\) | 19.6604 | 0.637866 | ||||||||
\(951\) | 7.61040 | 0.246784 | ||||||||
\(952\) | 21.1735 | 0.686236 | ||||||||
\(953\) | −47.6824 | −1.54458 | −0.772292 | − | 0.635268i | \(-0.780890\pi\) | ||||
−0.772292 | + | 0.635268i | \(0.780890\pi\) | |||||||
\(954\) | 35.0613 | 1.13515 | ||||||||
\(955\) | 30.5505 | 0.988590 | ||||||||
\(956\) | 14.5533 | 0.470687 | ||||||||
\(957\) | −6.38774 | −0.206486 | ||||||||
\(958\) | −24.7595 | −0.799942 | ||||||||
\(959\) | 25.1760 | 0.812977 | ||||||||
\(960\) | 0.868169 | 0.0280200 | ||||||||
\(961\) | −25.4130 | −0.819775 | ||||||||
\(962\) | −36.6227 | −1.18076 | ||||||||
\(963\) | 8.64036 | 0.278432 | ||||||||
\(964\) | −23.9038 | −0.769889 | ||||||||
\(965\) | −33.4697 | −1.07743 | ||||||||
\(966\) | 13.0700 | 0.420521 | ||||||||
\(967\) | 7.62412 | 0.245175 | 0.122588 | − | 0.992458i | \(-0.460881\pi\) | ||||
0.122588 | + | 0.992458i | \(0.460881\pi\) | |||||||
\(968\) | 9.42447 | 0.302914 | ||||||||
\(969\) | 23.5043 | 0.755068 | ||||||||
\(970\) | −17.6712 | −0.567388 | ||||||||
\(971\) | −1.00004 | −0.0320927 | −0.0160464 | − | 0.999871i | \(-0.505108\pi\) | ||||
−0.0160464 | + | 0.999871i | \(0.505108\pi\) | |||||||
\(972\) | −13.7476 | −0.440955 | ||||||||
\(973\) | 50.5063 | 1.61916 | ||||||||
\(974\) | −32.5380 | −1.04258 | ||||||||
\(975\) | 9.15501 | 0.293195 | ||||||||
\(976\) | 4.34325 | 0.139024 | ||||||||
\(977\) | −3.08999 | −0.0988574 | −0.0494287 | − | 0.998778i | \(-0.515740\pi\) | ||||
−0.0494287 | + | 0.998778i | \(0.515740\pi\) | |||||||
\(978\) | −7.97094 | −0.254883 | ||||||||
\(979\) | 13.0235 | 0.416233 | ||||||||
\(980\) | −9.03606 | −0.288646 | ||||||||
\(981\) | 40.4740 | 1.29224 | ||||||||
\(982\) | 14.6230 | 0.466640 | ||||||||
\(983\) | 24.2772 | 0.774321 | 0.387161 | − | 0.922012i | \(-0.373456\pi\) | ||||
0.387161 | + | 0.922012i | \(0.373456\pi\) | |||||||
\(984\) | −6.39982 | −0.204019 | ||||||||
\(985\) | 8.74765 | 0.278723 | ||||||||
\(986\) | 48.9186 | 1.55789 | ||||||||
\(987\) | 29.2905 | 0.932325 | ||||||||
\(988\) | 34.5662 | 1.09970 | ||||||||
\(989\) | −41.4345 | −1.31754 | ||||||||
\(990\) | −4.75198 | −0.151028 | ||||||||
\(991\) | −44.3775 | −1.40970 | −0.704850 | − | 0.709357i | \(-0.748985\pi\) | ||||
−0.704850 | + | 0.709357i | \(0.748985\pi\) | |||||||
\(992\) | 2.36368 | 0.0750468 | ||||||||
\(993\) | −18.1060 | −0.574578 | ||||||||
\(994\) | 37.7546 | 1.19750 | ||||||||
\(995\) | −30.2867 | −0.960152 | ||||||||
\(996\) | 3.24373 | 0.102782 | ||||||||
\(997\) | −3.52797 | −0.111732 | −0.0558660 | − | 0.998438i | \(-0.517792\pi\) | ||||
−0.0558660 | + | 0.998438i | \(0.517792\pi\) | |||||||
\(998\) | 5.96238 | 0.188736 | ||||||||
\(999\) | 24.1595 | 0.764372 |
(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 | 4034.2.a.c.1.18 | ✓ | 49 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.c.1.18 | ✓ | 49 | 1.1 | even | 1 | trivial |