Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6014,2,Mod(1,6014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6014, 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("6014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6014 = 2 \cdot 31 \cdot 97 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6014.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: | \(48.0220317756\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 6014.1 |
$q$-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 | ||||||||
\(3\) | −1.52309 | −0.879358 | −0.439679 | − | 0.898155i | \(-0.644908\pi\) | ||||
−0.439679 | + | 0.898155i | \(0.644908\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.0721797 | −0.0322798 | −0.0161399 | − | 0.999870i | \(-0.505138\pi\) | ||||
−0.0161399 | + | 0.999870i | \(0.505138\pi\) | |||||||
\(6\) | 1.52309 | 0.621800 | ||||||||
\(7\) | 3.89998 | 1.47405 | 0.737027 | − | 0.675863i | \(-0.236229\pi\) | ||||
0.737027 | + | 0.675863i | \(0.236229\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.680188 | −0.226729 | ||||||||
\(10\) | 0.0721797 | 0.0228252 | ||||||||
\(11\) | 1.26492 | 0.381389 | 0.190695 | − | 0.981649i | \(-0.438926\pi\) | ||||
0.190695 | + | 0.981649i | \(0.438926\pi\) | |||||||
\(12\) | −1.52309 | −0.439679 | ||||||||
\(13\) | 3.78887 | 1.05084 | 0.525422 | − | 0.850842i | \(-0.323908\pi\) | ||||
0.525422 | + | 0.850842i | \(0.323908\pi\) | |||||||
\(14\) | −3.89998 | −1.04231 | ||||||||
\(15\) | 0.109936 | 0.0283855 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.52558 | −1.82522 | −0.912611 | − | 0.408830i | \(-0.865937\pi\) | ||||
−0.912611 | + | 0.408830i | \(0.865937\pi\) | |||||||
\(18\) | 0.680188 | 0.160322 | ||||||||
\(19\) | 2.59237 | 0.594730 | 0.297365 | − | 0.954764i | \(-0.403892\pi\) | ||||
0.297365 | + | 0.954764i | \(0.403892\pi\) | |||||||
\(20\) | −0.0721797 | −0.0161399 | ||||||||
\(21\) | −5.94003 | −1.29622 | ||||||||
\(22\) | −1.26492 | −0.269683 | ||||||||
\(23\) | 1.46163 | 0.304770 | 0.152385 | − | 0.988321i | \(-0.451305\pi\) | ||||
0.152385 | + | 0.988321i | \(0.451305\pi\) | |||||||
\(24\) | 1.52309 | 0.310900 | ||||||||
\(25\) | −4.99479 | −0.998958 | ||||||||
\(26\) | −3.78887 | −0.743059 | ||||||||
\(27\) | 5.60527 | 1.07873 | ||||||||
\(28\) | 3.89998 | 0.737027 | ||||||||
\(29\) | 5.05456 | 0.938609 | 0.469305 | − | 0.883036i | \(-0.344505\pi\) | ||||
0.469305 | + | 0.883036i | \(0.344505\pi\) | |||||||
\(30\) | −0.109936 | −0.0200716 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.92660 | −0.335378 | ||||||||
\(34\) | 7.52558 | 1.29063 | ||||||||
\(35\) | −0.281500 | −0.0475821 | ||||||||
\(36\) | −0.680188 | −0.113365 | ||||||||
\(37\) | −3.19836 | −0.525808 | −0.262904 | − | 0.964822i | \(-0.584680\pi\) | ||||
−0.262904 | + | 0.964822i | \(0.584680\pi\) | |||||||
\(38\) | −2.59237 | −0.420538 | ||||||||
\(39\) | −5.77080 | −0.924068 | ||||||||
\(40\) | 0.0721797 | 0.0114126 | ||||||||
\(41\) | 6.54873 | 1.02274 | 0.511370 | − | 0.859361i | \(-0.329138\pi\) | ||||
0.511370 | + | 0.859361i | \(0.329138\pi\) | |||||||
\(42\) | 5.94003 | 0.916567 | ||||||||
\(43\) | 4.82172 | 0.735305 | 0.367653 | − | 0.929963i | \(-0.380162\pi\) | ||||
0.367653 | + | 0.929963i | \(0.380162\pi\) | |||||||
\(44\) | 1.26492 | 0.190695 | ||||||||
\(45\) | 0.0490958 | 0.00731877 | ||||||||
\(46\) | −1.46163 | −0.215505 | ||||||||
\(47\) | −7.18513 | −1.04806 | −0.524030 | − | 0.851700i | \(-0.675572\pi\) | ||||
−0.524030 | + | 0.851700i | \(0.675572\pi\) | |||||||
\(48\) | −1.52309 | −0.219840 | ||||||||
\(49\) | 8.20984 | 1.17283 | ||||||||
\(50\) | 4.99479 | 0.706370 | ||||||||
\(51\) | 11.4622 | 1.60502 | ||||||||
\(52\) | 3.78887 | 0.525422 | ||||||||
\(53\) | −6.50668 | −0.893761 | −0.446880 | − | 0.894594i | \(-0.647465\pi\) | ||||
−0.446880 | + | 0.894594i | \(0.647465\pi\) | |||||||
\(54\) | −5.60527 | −0.762780 | ||||||||
\(55\) | −0.0913019 | −0.0123111 | ||||||||
\(56\) | −3.89998 | −0.521157 | ||||||||
\(57\) | −3.94842 | −0.522981 | ||||||||
\(58\) | −5.05456 | −0.663697 | ||||||||
\(59\) | 7.31482 | 0.952309 | 0.476154 | − | 0.879362i | \(-0.342030\pi\) | ||||
0.476154 | + | 0.879362i | \(0.342030\pi\) | |||||||
\(60\) | 0.109936 | 0.0141927 | ||||||||
\(61\) | 4.13851 | 0.529882 | 0.264941 | − | 0.964265i | \(-0.414648\pi\) | ||||
0.264941 | + | 0.964265i | \(0.414648\pi\) | |||||||
\(62\) | 1.00000 | 0.127000 | ||||||||
\(63\) | −2.65272 | −0.334211 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.273480 | −0.0339210 | ||||||||
\(66\) | 1.92660 | 0.237148 | ||||||||
\(67\) | 9.24848 | 1.12988 | 0.564941 | − | 0.825132i | \(-0.308899\pi\) | ||||
0.564941 | + | 0.825132i | \(0.308899\pi\) | |||||||
\(68\) | −7.52558 | −0.912611 | ||||||||
\(69\) | −2.22619 | −0.268002 | ||||||||
\(70\) | 0.281500 | 0.0336456 | ||||||||
\(71\) | −0.0717312 | −0.00851293 | −0.00425646 | − | 0.999991i | \(-0.501355\pi\) | ||||
−0.00425646 | + | 0.999991i | \(0.501355\pi\) | |||||||
\(72\) | 0.680188 | 0.0801610 | ||||||||
\(73\) | −6.45943 | −0.756019 | −0.378009 | − | 0.925802i | \(-0.623391\pi\) | ||||
−0.378009 | + | 0.925802i | \(0.623391\pi\) | |||||||
\(74\) | 3.19836 | 0.371802 | ||||||||
\(75\) | 7.60753 | 0.878442 | ||||||||
\(76\) | 2.59237 | 0.297365 | ||||||||
\(77\) | 4.93318 | 0.562188 | ||||||||
\(78\) | 5.77080 | 0.653415 | ||||||||
\(79\) | 12.4804 | 1.40415 | 0.702075 | − | 0.712103i | \(-0.252257\pi\) | ||||
0.702075 | + | 0.712103i | \(0.252257\pi\) | |||||||
\(80\) | −0.0721797 | −0.00806994 | ||||||||
\(81\) | −6.49678 | −0.721864 | ||||||||
\(82\) | −6.54873 | −0.723186 | ||||||||
\(83\) | 0.0614961 | 0.00675007 | 0.00337504 | − | 0.999994i | \(-0.498926\pi\) | ||||
0.00337504 | + | 0.999994i | \(0.498926\pi\) | |||||||
\(84\) | −5.94003 | −0.648110 | ||||||||
\(85\) | 0.543194 | 0.0589177 | ||||||||
\(86\) | −4.82172 | −0.519939 | ||||||||
\(87\) | −7.69857 | −0.825373 | ||||||||
\(88\) | −1.26492 | −0.134841 | ||||||||
\(89\) | 5.60595 | 0.594230 | 0.297115 | − | 0.954842i | \(-0.403976\pi\) | ||||
0.297115 | + | 0.954842i | \(0.403976\pi\) | |||||||
\(90\) | −0.0490958 | −0.00517515 | ||||||||
\(91\) | 14.7765 | 1.54900 | ||||||||
\(92\) | 1.46163 | 0.152385 | ||||||||
\(93\) | 1.52309 | 0.157937 | ||||||||
\(94\) | 7.18513 | 0.741090 | ||||||||
\(95\) | −0.187117 | −0.0191978 | ||||||||
\(96\) | 1.52309 | 0.155450 | ||||||||
\(97\) | 1.00000 | 0.101535 | ||||||||
\(98\) | −8.20984 | −0.829319 | ||||||||
\(99\) | −0.860387 | −0.0864721 | ||||||||
\(100\) | −4.99479 | −0.499479 | ||||||||
\(101\) | −11.6500 | −1.15922 | −0.579610 | − | 0.814894i | \(-0.696795\pi\) | ||||
−0.579610 | + | 0.814894i | \(0.696795\pi\) | |||||||
\(102\) | −11.4622 | −1.13492 | ||||||||
\(103\) | 11.3568 | 1.11902 | 0.559510 | − | 0.828824i | \(-0.310989\pi\) | ||||
0.559510 | + | 0.828824i | \(0.310989\pi\) | |||||||
\(104\) | −3.78887 | −0.371529 | ||||||||
\(105\) | 0.428750 | 0.0418417 | ||||||||
\(106\) | 6.50668 | 0.631984 | ||||||||
\(107\) | 17.5759 | 1.69913 | 0.849563 | − | 0.527487i | \(-0.176866\pi\) | ||||
0.849563 | + | 0.527487i | \(0.176866\pi\) | |||||||
\(108\) | 5.60527 | 0.539367 | ||||||||
\(109\) | 8.70260 | 0.833557 | 0.416779 | − | 0.909008i | \(-0.363159\pi\) | ||||
0.416779 | + | 0.909008i | \(0.363159\pi\) | |||||||
\(110\) | 0.0913019 | 0.00870530 | ||||||||
\(111\) | 4.87141 | 0.462373 | ||||||||
\(112\) | 3.89998 | 0.368513 | ||||||||
\(113\) | −2.35657 | −0.221687 | −0.110844 | − | 0.993838i | \(-0.535355\pi\) | ||||
−0.110844 | + | 0.993838i | \(0.535355\pi\) | |||||||
\(114\) | 3.94842 | 0.369803 | ||||||||
\(115\) | −0.105500 | −0.00983792 | ||||||||
\(116\) | 5.05456 | 0.469305 | ||||||||
\(117\) | −2.57715 | −0.238257 | ||||||||
\(118\) | −7.31482 | −0.673384 | ||||||||
\(119\) | −29.3496 | −2.69047 | ||||||||
\(120\) | −0.109936 | −0.0100358 | ||||||||
\(121\) | −9.39997 | −0.854542 | ||||||||
\(122\) | −4.13851 | −0.374683 | ||||||||
\(123\) | −9.97432 | −0.899355 | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | 0.721421 | 0.0645259 | ||||||||
\(126\) | 2.65272 | 0.236323 | ||||||||
\(127\) | −8.40371 | −0.745709 | −0.372855 | − | 0.927890i | \(-0.621621\pi\) | ||||
−0.372855 | + | 0.927890i | \(0.621621\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.34392 | −0.646596 | ||||||||
\(130\) | 0.273480 | 0.0239858 | ||||||||
\(131\) | −4.72359 | −0.412702 | −0.206351 | − | 0.978478i | \(-0.566159\pi\) | ||||
−0.206351 | + | 0.978478i | \(0.566159\pi\) | |||||||
\(132\) | −1.92660 | −0.167689 | ||||||||
\(133\) | 10.1102 | 0.876665 | ||||||||
\(134\) | −9.24848 | −0.798947 | ||||||||
\(135\) | −0.404587 | −0.0348213 | ||||||||
\(136\) | 7.52558 | 0.645313 | ||||||||
\(137\) | 7.39319 | 0.631643 | 0.315821 | − | 0.948819i | \(-0.397720\pi\) | ||||
0.315821 | + | 0.948819i | \(0.397720\pi\) | |||||||
\(138\) | 2.22619 | 0.189506 | ||||||||
\(139\) | 4.04853 | 0.343392 | 0.171696 | − | 0.985150i | \(-0.445075\pi\) | ||||
0.171696 | + | 0.985150i | \(0.445075\pi\) | |||||||
\(140\) | −0.281500 | −0.0237911 | ||||||||
\(141\) | 10.9436 | 0.921620 | ||||||||
\(142\) | 0.0717312 | 0.00601955 | ||||||||
\(143\) | 4.79264 | 0.400780 | ||||||||
\(144\) | −0.680188 | −0.0566824 | ||||||||
\(145\) | −0.364837 | −0.0302981 | ||||||||
\(146\) | 6.45943 | 0.534586 | ||||||||
\(147\) | −12.5043 | −1.03134 | ||||||||
\(148\) | −3.19836 | −0.262904 | ||||||||
\(149\) | −20.2864 | −1.66193 | −0.830963 | − | 0.556327i | \(-0.812210\pi\) | ||||
−0.830963 | + | 0.556327i | \(0.812210\pi\) | |||||||
\(150\) | −7.60753 | −0.621152 | ||||||||
\(151\) | −12.6915 | −1.03282 | −0.516411 | − | 0.856341i | \(-0.672732\pi\) | ||||
−0.516411 | + | 0.856341i | \(0.672732\pi\) | |||||||
\(152\) | −2.59237 | −0.210269 | ||||||||
\(153\) | 5.11881 | 0.413831 | ||||||||
\(154\) | −4.93318 | −0.397527 | ||||||||
\(155\) | 0.0721797 | 0.00579762 | ||||||||
\(156\) | −5.77080 | −0.462034 | ||||||||
\(157\) | −10.4383 | −0.833067 | −0.416533 | − | 0.909120i | \(-0.636755\pi\) | ||||
−0.416533 | + | 0.909120i | \(0.636755\pi\) | |||||||
\(158\) | −12.4804 | −0.992884 | ||||||||
\(159\) | 9.91027 | 0.785936 | ||||||||
\(160\) | 0.0721797 | 0.00570631 | ||||||||
\(161\) | 5.70032 | 0.449248 | ||||||||
\(162\) | 6.49678 | 0.510435 | ||||||||
\(163\) | 3.32897 | 0.260745 | 0.130373 | − | 0.991465i | \(-0.458383\pi\) | ||||
0.130373 | + | 0.991465i | \(0.458383\pi\) | |||||||
\(164\) | 6.54873 | 0.511370 | ||||||||
\(165\) | 0.139061 | 0.0108259 | ||||||||
\(166\) | −0.0614961 | −0.00477302 | ||||||||
\(167\) | −6.53936 | −0.506031 | −0.253015 | − | 0.967462i | \(-0.581422\pi\) | ||||
−0.253015 | + | 0.967462i | \(0.581422\pi\) | |||||||
\(168\) | 5.94003 | 0.458283 | ||||||||
\(169\) | 1.35554 | 0.104272 | ||||||||
\(170\) | −0.543194 | −0.0416611 | ||||||||
\(171\) | −1.76330 | −0.134843 | ||||||||
\(172\) | 4.82172 | 0.367653 | ||||||||
\(173\) | 8.69790 | 0.661289 | 0.330645 | − | 0.943755i | \(-0.392734\pi\) | ||||
0.330645 | + | 0.943755i | \(0.392734\pi\) | |||||||
\(174\) | 7.69857 | 0.583627 | ||||||||
\(175\) | −19.4796 | −1.47252 | ||||||||
\(176\) | 1.26492 | 0.0953473 | ||||||||
\(177\) | −11.1412 | −0.837420 | ||||||||
\(178\) | −5.60595 | −0.420184 | ||||||||
\(179\) | 2.43635 | 0.182101 | 0.0910506 | − | 0.995846i | \(-0.470977\pi\) | ||||
0.0910506 | + | 0.995846i | \(0.470977\pi\) | |||||||
\(180\) | 0.0490958 | 0.00365939 | ||||||||
\(181\) | 6.44436 | 0.479006 | 0.239503 | − | 0.970896i | \(-0.423016\pi\) | ||||
0.239503 | + | 0.970896i | \(0.423016\pi\) | |||||||
\(182\) | −14.7765 | −1.09531 | ||||||||
\(183\) | −6.30333 | −0.465956 | ||||||||
\(184\) | −1.46163 | −0.107753 | ||||||||
\(185\) | 0.230857 | 0.0169730 | ||||||||
\(186\) | −1.52309 | −0.111679 | ||||||||
\(187\) | −9.51929 | −0.696119 | ||||||||
\(188\) | −7.18513 | −0.524030 | ||||||||
\(189\) | 21.8604 | 1.59011 | ||||||||
\(190\) | 0.187117 | 0.0135749 | ||||||||
\(191\) | −1.00262 | −0.0725472 | −0.0362736 | − | 0.999342i | \(-0.511549\pi\) | ||||
−0.0362736 | + | 0.999342i | \(0.511549\pi\) | |||||||
\(192\) | −1.52309 | −0.109920 | ||||||||
\(193\) | 5.49049 | 0.395214 | 0.197607 | − | 0.980281i | \(-0.436683\pi\) | ||||
0.197607 | + | 0.980281i | \(0.436683\pi\) | |||||||
\(194\) | −1.00000 | −0.0717958 | ||||||||
\(195\) | 0.416535 | 0.0298287 | ||||||||
\(196\) | 8.20984 | 0.586417 | ||||||||
\(197\) | 3.29099 | 0.234473 | 0.117237 | − | 0.993104i | \(-0.462596\pi\) | ||||
0.117237 | + | 0.993104i | \(0.462596\pi\) | |||||||
\(198\) | 0.860387 | 0.0611450 | ||||||||
\(199\) | −20.0998 | −1.42484 | −0.712419 | − | 0.701754i | \(-0.752401\pi\) | ||||
−0.712419 | + | 0.701754i | \(0.752401\pi\) | |||||||
\(200\) | 4.99479 | 0.353185 | ||||||||
\(201\) | −14.0863 | −0.993570 | ||||||||
\(202\) | 11.6500 | 0.819693 | ||||||||
\(203\) | 19.7127 | 1.38356 | ||||||||
\(204\) | 11.4622 | 0.802512 | ||||||||
\(205\) | −0.472686 | −0.0330138 | ||||||||
\(206\) | −11.3568 | −0.791266 | ||||||||
\(207\) | −0.994182 | −0.0691004 | ||||||||
\(208\) | 3.78887 | 0.262711 | ||||||||
\(209\) | 3.27915 | 0.226824 | ||||||||
\(210\) | −0.428750 | −0.0295866 | ||||||||
\(211\) | 12.2752 | 0.845059 | 0.422529 | − | 0.906349i | \(-0.361142\pi\) | ||||
0.422529 | + | 0.906349i | \(0.361142\pi\) | |||||||
\(212\) | −6.50668 | −0.446880 | ||||||||
\(213\) | 0.109253 | 0.00748591 | ||||||||
\(214\) | −17.5759 | −1.20146 | ||||||||
\(215\) | −0.348030 | −0.0237355 | ||||||||
\(216\) | −5.60527 | −0.381390 | ||||||||
\(217\) | −3.89998 | −0.264748 | ||||||||
\(218\) | −8.70260 | −0.589414 | ||||||||
\(219\) | 9.83831 | 0.664811 | ||||||||
\(220\) | −0.0913019 | −0.00615557 | ||||||||
\(221\) | −28.5135 | −1.91802 | ||||||||
\(222\) | −4.87141 | −0.326947 | ||||||||
\(223\) | 19.9653 | 1.33697 | 0.668487 | − | 0.743724i | \(-0.266942\pi\) | ||||
0.668487 | + | 0.743724i | \(0.266942\pi\) | |||||||
\(224\) | −3.89998 | −0.260578 | ||||||||
\(225\) | 3.39740 | 0.226493 | ||||||||
\(226\) | 2.35657 | 0.156757 | ||||||||
\(227\) | −9.62939 | −0.639125 | −0.319563 | − | 0.947565i | \(-0.603536\pi\) | ||||
−0.319563 | + | 0.947565i | \(0.603536\pi\) | |||||||
\(228\) | −3.94842 | −0.261490 | ||||||||
\(229\) | 12.8718 | 0.850590 | 0.425295 | − | 0.905055i | \(-0.360170\pi\) | ||||
0.425295 | + | 0.905055i | \(0.360170\pi\) | |||||||
\(230\) | 0.105500 | 0.00695646 | ||||||||
\(231\) | −7.51369 | −0.494364 | ||||||||
\(232\) | −5.05456 | −0.331848 | ||||||||
\(233\) | −16.1117 | −1.05551 | −0.527755 | − | 0.849396i | \(-0.676966\pi\) | ||||
−0.527755 | + | 0.849396i | \(0.676966\pi\) | |||||||
\(234\) | 2.57715 | 0.168473 | ||||||||
\(235\) | 0.518621 | 0.0338311 | ||||||||
\(236\) | 7.31482 | 0.476154 | ||||||||
\(237\) | −19.0087 | −1.23475 | ||||||||
\(238\) | 29.3496 | 1.90245 | ||||||||
\(239\) | −7.28439 | −0.471188 | −0.235594 | − | 0.971852i | \(-0.575704\pi\) | ||||
−0.235594 | + | 0.971852i | \(0.575704\pi\) | |||||||
\(240\) | 0.109936 | 0.00709637 | ||||||||
\(241\) | 15.8406 | 1.02038 | 0.510191 | − | 0.860061i | \(-0.329575\pi\) | ||||
0.510191 | + | 0.860061i | \(0.329575\pi\) | |||||||
\(242\) | 9.39997 | 0.604253 | ||||||||
\(243\) | −6.92061 | −0.443957 | ||||||||
\(244\) | 4.13851 | 0.264941 | ||||||||
\(245\) | −0.592584 | −0.0378588 | ||||||||
\(246\) | 9.97432 | 0.635940 | ||||||||
\(247\) | 9.82215 | 0.624969 | ||||||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | −0.0936643 | −0.00593573 | ||||||||
\(250\) | −0.721421 | −0.0456267 | ||||||||
\(251\) | 23.3857 | 1.47609 | 0.738047 | − | 0.674749i | \(-0.235748\pi\) | ||||
0.738047 | + | 0.674749i | \(0.235748\pi\) | |||||||
\(252\) | −2.65272 | −0.167106 | ||||||||
\(253\) | 1.84885 | 0.116236 | ||||||||
\(254\) | 8.40371 | 0.527296 | ||||||||
\(255\) | −0.827336 | −0.0518098 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.2262 | −0.762652 | −0.381326 | − | 0.924441i | \(-0.624532\pi\) | ||||
−0.381326 | + | 0.924441i | \(0.624532\pi\) | |||||||
\(258\) | 7.34392 | 0.457213 | ||||||||
\(259\) | −12.4736 | −0.775069 | ||||||||
\(260\) | −0.273480 | −0.0169605 | ||||||||
\(261\) | −3.43806 | −0.212810 | ||||||||
\(262\) | 4.72359 | 0.291824 | ||||||||
\(263\) | 17.1286 | 1.05619 | 0.528097 | − | 0.849184i | \(-0.322906\pi\) | ||||
0.528097 | + | 0.849184i | \(0.322906\pi\) | |||||||
\(264\) | 1.92660 | 0.118574 | ||||||||
\(265\) | 0.469650 | 0.0288504 | ||||||||
\(266\) | −10.1102 | −0.619895 | ||||||||
\(267\) | −8.53839 | −0.522541 | ||||||||
\(268\) | 9.24848 | 0.564941 | ||||||||
\(269\) | −5.93482 | −0.361852 | −0.180926 | − | 0.983497i | \(-0.557910\pi\) | ||||
−0.180926 | + | 0.983497i | \(0.557910\pi\) | |||||||
\(270\) | 0.404587 | 0.0246224 | ||||||||
\(271\) | 29.9704 | 1.82057 | 0.910286 | − | 0.413980i | \(-0.135862\pi\) | ||||
0.910286 | + | 0.413980i | \(0.135862\pi\) | |||||||
\(272\) | −7.52558 | −0.456305 | ||||||||
\(273\) | −22.5060 | −1.36213 | ||||||||
\(274\) | −7.39319 | −0.446639 | ||||||||
\(275\) | −6.31803 | −0.380992 | ||||||||
\(276\) | −2.22619 | −0.134001 | ||||||||
\(277\) | −3.95743 | −0.237779 | −0.118889 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118889 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(278\) | −4.04853 | −0.242814 | ||||||||
\(279\) | 0.680188 | 0.0407218 | ||||||||
\(280\) | 0.281500 | 0.0168228 | ||||||||
\(281\) | −16.3944 | −0.978010 | −0.489005 | − | 0.872281i | \(-0.662640\pi\) | ||||
−0.489005 | + | 0.872281i | \(0.662640\pi\) | |||||||
\(282\) | −10.9436 | −0.651683 | ||||||||
\(283\) | −12.3852 | −0.736225 | −0.368113 | − | 0.929781i | \(-0.619996\pi\) | ||||
−0.368113 | + | 0.929781i | \(0.619996\pi\) | |||||||
\(284\) | −0.0717312 | −0.00425646 | ||||||||
\(285\) | 0.284996 | 0.0168817 | ||||||||
\(286\) | −4.79264 | −0.283394 | ||||||||
\(287\) | 25.5399 | 1.50757 | ||||||||
\(288\) | 0.680188 | 0.0400805 | ||||||||
\(289\) | 39.6344 | 2.33143 | ||||||||
\(290\) | 0.364837 | 0.0214240 | ||||||||
\(291\) | −1.52309 | −0.0892853 | ||||||||
\(292\) | −6.45943 | −0.378009 | ||||||||
\(293\) | −8.57860 | −0.501167 | −0.250584 | − | 0.968095i | \(-0.580623\pi\) | ||||
−0.250584 | + | 0.968095i | \(0.580623\pi\) | |||||||
\(294\) | 12.5043 | 0.729268 | ||||||||
\(295\) | −0.527982 | −0.0307403 | ||||||||
\(296\) | 3.19836 | 0.185901 | ||||||||
\(297\) | 7.09024 | 0.411417 | ||||||||
\(298\) | 20.2864 | 1.17516 | ||||||||
\(299\) | 5.53792 | 0.320266 | ||||||||
\(300\) | 7.60753 | 0.439221 | ||||||||
\(301\) | 18.8046 | 1.08388 | ||||||||
\(302\) | 12.6915 | 0.730316 | ||||||||
\(303\) | 17.7441 | 1.01937 | ||||||||
\(304\) | 2.59237 | 0.148683 | ||||||||
\(305\) | −0.298716 | −0.0171045 | ||||||||
\(306\) | −5.11881 | −0.292623 | ||||||||
\(307\) | 27.5872 | 1.57449 | 0.787243 | − | 0.616643i | \(-0.211508\pi\) | ||||
0.787243 | + | 0.616643i | \(0.211508\pi\) | |||||||
\(308\) | 4.93318 | 0.281094 | ||||||||
\(309\) | −17.2975 | −0.984019 | ||||||||
\(310\) | −0.0721797 | −0.00409953 | ||||||||
\(311\) | −20.4691 | −1.16069 | −0.580347 | − | 0.814369i | \(-0.697083\pi\) | ||||
−0.580347 | + | 0.814369i | \(0.697083\pi\) | |||||||
\(312\) | 5.77080 | 0.326707 | ||||||||
\(313\) | 13.7204 | 0.775522 | 0.387761 | − | 0.921760i | \(-0.373249\pi\) | ||||
0.387761 | + | 0.921760i | \(0.373249\pi\) | |||||||
\(314\) | 10.4383 | 0.589067 | ||||||||
\(315\) | 0.191473 | 0.0107883 | ||||||||
\(316\) | 12.4804 | 0.702075 | ||||||||
\(317\) | 23.4019 | 1.31438 | 0.657191 | − | 0.753724i | \(-0.271744\pi\) | ||||
0.657191 | + | 0.753724i | \(0.271744\pi\) | |||||||
\(318\) | −9.91027 | −0.555740 | ||||||||
\(319\) | 6.39364 | 0.357975 | ||||||||
\(320\) | −0.0721797 | −0.00403497 | ||||||||
\(321\) | −26.7697 | −1.49414 | ||||||||
\(322\) | −5.70032 | −0.317666 | ||||||||
\(323\) | −19.5091 | −1.08551 | ||||||||
\(324\) | −6.49678 | −0.360932 | ||||||||
\(325\) | −18.9246 | −1.04975 | ||||||||
\(326\) | −3.32897 | −0.184375 | ||||||||
\(327\) | −13.2549 | −0.732995 | ||||||||
\(328\) | −6.54873 | −0.361593 | ||||||||
\(329\) | −28.0219 | −1.54490 | ||||||||
\(330\) | −0.139061 | −0.00765507 | ||||||||
\(331\) | 13.8521 | 0.761383 | 0.380691 | − | 0.924702i | \(-0.375686\pi\) | ||||
0.380691 | + | 0.924702i | \(0.375686\pi\) | |||||||
\(332\) | 0.0614961 | 0.00337504 | ||||||||
\(333\) | 2.17549 | 0.119216 | ||||||||
\(334\) | 6.53936 | 0.357818 | ||||||||
\(335\) | −0.667553 | −0.0364723 | ||||||||
\(336\) | −5.94003 | −0.324055 | ||||||||
\(337\) | 29.5301 | 1.60861 | 0.804304 | − | 0.594218i | \(-0.202539\pi\) | ||||
0.804304 | + | 0.594218i | \(0.202539\pi\) | |||||||
\(338\) | −1.35554 | −0.0737317 | ||||||||
\(339\) | 3.58927 | 0.194942 | ||||||||
\(340\) | 0.543194 | 0.0294589 | ||||||||
\(341\) | −1.26492 | −0.0684995 | ||||||||
\(342\) | 1.76330 | 0.0953483 | ||||||||
\(343\) | 4.71835 | 0.254767 | ||||||||
\(344\) | −4.82172 | −0.259970 | ||||||||
\(345\) | 0.160686 | 0.00865105 | ||||||||
\(346\) | −8.69790 | −0.467602 | ||||||||
\(347\) | −7.62554 | −0.409360 | −0.204680 | − | 0.978829i | \(-0.565615\pi\) | ||||
−0.204680 | + | 0.978829i | \(0.565615\pi\) | |||||||
\(348\) | −7.69857 | −0.412687 | ||||||||
\(349\) | 33.1412 | 1.77401 | 0.887004 | − | 0.461761i | \(-0.152782\pi\) | ||||
0.887004 | + | 0.461761i | \(0.152782\pi\) | |||||||
\(350\) | 19.4796 | 1.04123 | ||||||||
\(351\) | 21.2376 | 1.13358 | ||||||||
\(352\) | −1.26492 | −0.0674207 | ||||||||
\(353\) | −4.72300 | −0.251380 | −0.125690 | − | 0.992070i | \(-0.540114\pi\) | ||||
−0.125690 | + | 0.992070i | \(0.540114\pi\) | |||||||
\(354\) | 11.1412 | 0.592146 | ||||||||
\(355\) | 0.00517754 | 0.000274795 0 | ||||||||
\(356\) | 5.60595 | 0.297115 | ||||||||
\(357\) | 44.7022 | 2.36589 | ||||||||
\(358\) | −2.43635 | −0.128765 | ||||||||
\(359\) | 30.3409 | 1.60133 | 0.800667 | − | 0.599110i | \(-0.204479\pi\) | ||||
0.800667 | + | 0.599110i | \(0.204479\pi\) | |||||||
\(360\) | −0.0490958 | −0.00258758 | ||||||||
\(361\) | −12.2796 | −0.646296 | ||||||||
\(362\) | −6.44436 | −0.338708 | ||||||||
\(363\) | 14.3170 | 0.751449 | ||||||||
\(364\) | 14.7765 | 0.774500 | ||||||||
\(365\) | 0.466240 | 0.0244041 | ||||||||
\(366\) | 6.30333 | 0.329480 | ||||||||
\(367\) | −12.5646 | −0.655869 | −0.327934 | − | 0.944701i | \(-0.606352\pi\) | ||||
−0.327934 | + | 0.944701i | \(0.606352\pi\) | |||||||
\(368\) | 1.46163 | 0.0761926 | ||||||||
\(369\) | −4.45437 | −0.231885 | ||||||||
\(370\) | −0.230857 | −0.0120017 | ||||||||
\(371\) | −25.3759 | −1.31745 | ||||||||
\(372\) | 1.52309 | 0.0789687 | ||||||||
\(373\) | −16.2479 | −0.841284 | −0.420642 | − | 0.907227i | \(-0.638195\pi\) | ||||
−0.420642 | + | 0.907227i | \(0.638195\pi\) | |||||||
\(374\) | 9.51929 | 0.492231 | ||||||||
\(375\) | −1.09879 | −0.0567414 | ||||||||
\(376\) | 7.18513 | 0.370545 | ||||||||
\(377\) | 19.1511 | 0.986331 | ||||||||
\(378\) | −21.8604 | −1.12438 | ||||||||
\(379\) | 2.07245 | 0.106455 | 0.0532273 | − | 0.998582i | \(-0.483049\pi\) | ||||
0.0532273 | + | 0.998582i | \(0.483049\pi\) | |||||||
\(380\) | −0.187117 | −0.00959888 | ||||||||
\(381\) | 12.7996 | 0.655745 | ||||||||
\(382\) | 1.00262 | 0.0512987 | ||||||||
\(383\) | −15.6530 | −0.799833 | −0.399917 | − | 0.916551i | \(-0.630961\pi\) | ||||
−0.399917 | + | 0.916551i | \(0.630961\pi\) | |||||||
\(384\) | 1.52309 | 0.0777250 | ||||||||
\(385\) | −0.356076 | −0.0181473 | ||||||||
\(386\) | −5.49049 | −0.279459 | ||||||||
\(387\) | −3.27968 | −0.166715 | ||||||||
\(388\) | 1.00000 | 0.0507673 | ||||||||
\(389\) | 0.655386 | 0.0332294 | 0.0166147 | − | 0.999862i | \(-0.494711\pi\) | ||||
0.0166147 | + | 0.999862i | \(0.494711\pi\) | |||||||
\(390\) | −0.416535 | −0.0210921 | ||||||||
\(391\) | −10.9996 | −0.556273 | ||||||||
\(392\) | −8.20984 | −0.414660 | ||||||||
\(393\) | 7.19447 | 0.362913 | ||||||||
\(394\) | −3.29099 | −0.165797 | ||||||||
\(395\) | −0.900829 | −0.0453256 | ||||||||
\(396\) | −0.860387 | −0.0432361 | ||||||||
\(397\) | 18.2764 | 0.917264 | 0.458632 | − | 0.888626i | \(-0.348340\pi\) | ||||
0.458632 | + | 0.888626i | \(0.348340\pi\) | |||||||
\(398\) | 20.0998 | 1.00751 | ||||||||
\(399\) | −15.3988 | −0.770902 | ||||||||
\(400\) | −4.99479 | −0.249740 | ||||||||
\(401\) | 13.3275 | 0.665545 | 0.332772 | − | 0.943007i | \(-0.392016\pi\) | ||||
0.332772 | + | 0.943007i | \(0.392016\pi\) | |||||||
\(402\) | 14.0863 | 0.702560 | ||||||||
\(403\) | −3.78887 | −0.188737 | ||||||||
\(404\) | −11.6500 | −0.579610 | ||||||||
\(405\) | 0.468936 | 0.0233016 | ||||||||
\(406\) | −19.7127 | −0.978325 | ||||||||
\(407\) | −4.04569 | −0.200537 | ||||||||
\(408\) | −11.4622 | −0.567461 | ||||||||
\(409\) | 35.4803 | 1.75439 | 0.877194 | − | 0.480137i | \(-0.159413\pi\) | ||||
0.877194 | + | 0.480137i | \(0.159413\pi\) | |||||||
\(410\) | 0.472686 | 0.0233443 | ||||||||
\(411\) | −11.2605 | −0.555440 | ||||||||
\(412\) | 11.3568 | 0.559510 | ||||||||
\(413\) | 28.5277 | 1.40375 | ||||||||
\(414\) | 0.994182 | 0.0488614 | ||||||||
\(415\) | −0.00443877 | −0.000217891 0 | ||||||||
\(416\) | −3.78887 | −0.185765 | ||||||||
\(417\) | −6.16628 | −0.301964 | ||||||||
\(418\) | −3.27915 | −0.160389 | ||||||||
\(419\) | 29.6289 | 1.44747 | 0.723733 | − | 0.690080i | \(-0.242425\pi\) | ||||
0.723733 | + | 0.690080i | \(0.242425\pi\) | |||||||
\(420\) | 0.428750 | 0.0209209 | ||||||||
\(421\) | −15.7535 | −0.767778 | −0.383889 | − | 0.923379i | \(-0.625415\pi\) | ||||
−0.383889 | + | 0.923379i | \(0.625415\pi\) | |||||||
\(422\) | −12.2752 | −0.597547 | ||||||||
\(423\) | 4.88725 | 0.237626 | ||||||||
\(424\) | 6.50668 | 0.315992 | ||||||||
\(425\) | 37.5887 | 1.82332 | ||||||||
\(426\) | −0.109253 | −0.00529334 | ||||||||
\(427\) | 16.1401 | 0.781074 | ||||||||
\(428\) | 17.5759 | 0.849563 | ||||||||
\(429\) | −7.29963 | −0.352429 | ||||||||
\(430\) | 0.348030 | 0.0167835 | ||||||||
\(431\) | 10.2828 | 0.495307 | 0.247653 | − | 0.968849i | \(-0.420341\pi\) | ||||
0.247653 | + | 0.968849i | \(0.420341\pi\) | |||||||
\(432\) | 5.60527 | 0.269684 | ||||||||
\(433\) | −3.49173 | −0.167802 | −0.0839009 | − | 0.996474i | \(-0.526738\pi\) | ||||
−0.0839009 | + | 0.996474i | \(0.526738\pi\) | |||||||
\(434\) | 3.89998 | 0.187205 | ||||||||
\(435\) | 0.555681 | 0.0266429 | ||||||||
\(436\) | 8.70260 | 0.416779 | ||||||||
\(437\) | 3.78908 | 0.181256 | ||||||||
\(438\) | −9.83831 | −0.470092 | ||||||||
\(439\) | 1.97908 | 0.0944563 | 0.0472281 | − | 0.998884i | \(-0.484961\pi\) | ||||
0.0472281 | + | 0.998884i | \(0.484961\pi\) | |||||||
\(440\) | 0.0913019 | 0.00435265 | ||||||||
\(441\) | −5.58424 | −0.265916 | ||||||||
\(442\) | 28.5135 | 1.35625 | ||||||||
\(443\) | −14.2391 | −0.676520 | −0.338260 | − | 0.941053i | \(-0.609838\pi\) | ||||
−0.338260 | + | 0.941053i | \(0.609838\pi\) | |||||||
\(444\) | 4.87141 | 0.231187 | ||||||||
\(445\) | −0.404636 | −0.0191816 | ||||||||
\(446\) | −19.9653 | −0.945383 | ||||||||
\(447\) | 30.8981 | 1.46143 | ||||||||
\(448\) | 3.89998 | 0.184257 | ||||||||
\(449\) | −16.6508 | −0.785800 | −0.392900 | − | 0.919581i | \(-0.628528\pi\) | ||||
−0.392900 | + | 0.919581i | \(0.628528\pi\) | |||||||
\(450\) | −3.39740 | −0.160155 | ||||||||
\(451\) | 8.28365 | 0.390062 | ||||||||
\(452\) | −2.35657 | −0.110844 | ||||||||
\(453\) | 19.3304 | 0.908221 | ||||||||
\(454\) | 9.62939 | 0.451930 | ||||||||
\(455\) | −1.06657 | −0.0500014 | ||||||||
\(456\) | 3.94842 | 0.184902 | ||||||||
\(457\) | 32.8349 | 1.53595 | 0.767975 | − | 0.640480i | \(-0.221265\pi\) | ||||
0.767975 | + | 0.640480i | \(0.221265\pi\) | |||||||
\(458\) | −12.8718 | −0.601458 | ||||||||
\(459\) | −42.1829 | −1.96893 | ||||||||
\(460\) | −0.105500 | −0.00491896 | ||||||||
\(461\) | −6.69769 | −0.311942 | −0.155971 | − | 0.987762i | \(-0.549851\pi\) | ||||
−0.155971 | + | 0.987762i | \(0.549851\pi\) | |||||||
\(462\) | 7.51369 | 0.349568 | ||||||||
\(463\) | −27.6004 | −1.28270 | −0.641350 | − | 0.767248i | \(-0.721625\pi\) | ||||
−0.641350 | + | 0.767248i | \(0.721625\pi\) | |||||||
\(464\) | 5.05456 | 0.234652 | ||||||||
\(465\) | −0.109936 | −0.00509818 | ||||||||
\(466\) | 16.1117 | 0.746359 | ||||||||
\(467\) | −17.6138 | −0.815071 | −0.407535 | − | 0.913189i | \(-0.633612\pi\) | ||||
−0.407535 | + | 0.913189i | \(0.633612\pi\) | |||||||
\(468\) | −2.57715 | −0.119129 | ||||||||
\(469\) | 36.0689 | 1.66551 | ||||||||
\(470\) | −0.518621 | −0.0239222 | ||||||||
\(471\) | 15.8985 | 0.732564 | ||||||||
\(472\) | −7.31482 | −0.336692 | ||||||||
\(473\) | 6.09911 | 0.280437 | ||||||||
\(474\) | 19.0087 | 0.873100 | ||||||||
\(475\) | −12.9483 | −0.594111 | ||||||||
\(476\) | −29.3496 | −1.34524 | ||||||||
\(477\) | 4.42577 | 0.202642 | ||||||||
\(478\) | 7.28439 | 0.333180 | ||||||||
\(479\) | 35.7829 | 1.63496 | 0.817482 | − | 0.575954i | \(-0.195369\pi\) | ||||
0.817482 | + | 0.575954i | \(0.195369\pi\) | |||||||
\(480\) | −0.109936 | −0.00501789 | ||||||||
\(481\) | −12.1182 | −0.552542 | ||||||||
\(482\) | −15.8406 | −0.721520 | ||||||||
\(483\) | −8.68211 | −0.395050 | ||||||||
\(484\) | −9.39997 | −0.427271 | ||||||||
\(485\) | −0.0721797 | −0.00327751 | ||||||||
\(486\) | 6.92061 | 0.313925 | ||||||||
\(487\) | −4.91312 | −0.222635 | −0.111317 | − | 0.993785i | \(-0.535507\pi\) | ||||
−0.111317 | + | 0.993785i | \(0.535507\pi\) | |||||||
\(488\) | −4.13851 | −0.187341 | ||||||||
\(489\) | −5.07033 | −0.229288 | ||||||||
\(490\) | 0.592584 | 0.0267702 | ||||||||
\(491\) | 1.21826 | 0.0549795 | 0.0274897 | − | 0.999622i | \(-0.491249\pi\) | ||||
0.0274897 | + | 0.999622i | \(0.491249\pi\) | |||||||
\(492\) | −9.97432 | −0.449677 | ||||||||
\(493\) | −38.0385 | −1.71317 | ||||||||
\(494\) | −9.82215 | −0.441920 | ||||||||
\(495\) | 0.0621025 | 0.00279130 | ||||||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | −0.279750 | −0.0125485 | ||||||||
\(498\) | 0.0936643 | 0.00419720 | ||||||||
\(499\) | −40.6275 | −1.81874 | −0.909369 | − | 0.415991i | \(-0.863435\pi\) | ||||
−0.909369 | + | 0.415991i | \(0.863435\pi\) | |||||||
\(500\) | 0.721421 | 0.0322629 | ||||||||
\(501\) | 9.96005 | 0.444982 | ||||||||
\(502\) | −23.3857 | −1.04376 | ||||||||
\(503\) | −0.804360 | −0.0358646 | −0.0179323 | − | 0.999839i | \(-0.505708\pi\) | ||||
−0.0179323 | + | 0.999839i | \(0.505708\pi\) | |||||||
\(504\) | 2.65272 | 0.118162 | ||||||||
\(505\) | 0.840896 | 0.0374194 | ||||||||
\(506\) | −1.84885 | −0.0821913 | ||||||||
\(507\) | −2.06462 | −0.0916928 | ||||||||
\(508\) | −8.40371 | −0.372855 | ||||||||
\(509\) | 20.4784 | 0.907691 | 0.453845 | − | 0.891080i | \(-0.350052\pi\) | ||||
0.453845 | + | 0.891080i | \(0.350052\pi\) | |||||||
\(510\) | 0.827336 | 0.0366350 | ||||||||
\(511\) | −25.1916 | −1.11441 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 14.5309 | 0.641556 | ||||||||
\(514\) | 12.2262 | 0.539276 | ||||||||
\(515\) | −0.819732 | −0.0361217 | ||||||||
\(516\) | −7.34392 | −0.323298 | ||||||||
\(517\) | −9.08865 | −0.399718 | ||||||||
\(518\) | 12.4736 | 0.548057 | ||||||||
\(519\) | −13.2477 | −0.581510 | ||||||||
\(520\) | 0.273480 | 0.0119929 | ||||||||
\(521\) | −7.42604 | −0.325341 | −0.162670 | − | 0.986680i | \(-0.552011\pi\) | ||||
−0.162670 | + | 0.986680i | \(0.552011\pi\) | |||||||
\(522\) | 3.43806 | 0.150480 | ||||||||
\(523\) | −5.87234 | −0.256779 | −0.128390 | − | 0.991724i | \(-0.540981\pi\) | ||||
−0.128390 | + | 0.991724i | \(0.540981\pi\) | |||||||
\(524\) | −4.72359 | −0.206351 | ||||||||
\(525\) | 29.6692 | 1.29487 | ||||||||
\(526\) | −17.1286 | −0.746842 | ||||||||
\(527\) | 7.52558 | 0.327819 | ||||||||
\(528\) | −1.92660 | −0.0838444 | ||||||||
\(529\) | −20.8636 | −0.907115 | ||||||||
\(530\) | −0.469650 | −0.0204003 | ||||||||
\(531\) | −4.97546 | −0.215916 | ||||||||
\(532\) | 10.1102 | 0.438332 | ||||||||
\(533\) | 24.8123 | 1.07474 | ||||||||
\(534\) | 8.53839 | 0.369492 | ||||||||
\(535\) | −1.26862 | −0.0548474 | ||||||||
\(536\) | −9.24848 | −0.399473 | ||||||||
\(537\) | −3.71078 | −0.160132 | ||||||||
\(538\) | 5.93482 | 0.255868 | ||||||||
\(539\) | 10.3848 | 0.447306 | ||||||||
\(540\) | −0.404587 | −0.0174106 | ||||||||
\(541\) | 41.0196 | 1.76357 | 0.881784 | − | 0.471653i | \(-0.156342\pi\) | ||||
0.881784 | + | 0.471653i | \(0.156342\pi\) | |||||||
\(542\) | −29.9704 | −1.28734 | ||||||||
\(543\) | −9.81536 | −0.421217 | ||||||||
\(544\) | 7.52558 | 0.322657 | ||||||||
\(545\) | −0.628151 | −0.0269070 | ||||||||
\(546\) | 22.5060 | 0.963168 | ||||||||
\(547\) | 7.59911 | 0.324914 | 0.162457 | − | 0.986716i | \(-0.448058\pi\) | ||||
0.162457 | + | 0.986716i | \(0.448058\pi\) | |||||||
\(548\) | 7.39319 | 0.315821 | ||||||||
\(549\) | −2.81497 | −0.120140 | ||||||||
\(550\) | 6.31803 | 0.269402 | ||||||||
\(551\) | 13.1033 | 0.558219 | ||||||||
\(552\) | 2.22619 | 0.0947531 | ||||||||
\(553\) | 48.6731 | 2.06979 | ||||||||
\(554\) | 3.95743 | 0.168135 | ||||||||
\(555\) | −0.351617 | −0.0149253 | ||||||||
\(556\) | 4.04853 | 0.171696 | ||||||||
\(557\) | 10.0402 | 0.425416 | 0.212708 | − | 0.977116i | \(-0.431772\pi\) | ||||
0.212708 | + | 0.977116i | \(0.431772\pi\) | |||||||
\(558\) | −0.680188 | −0.0287947 | ||||||||
\(559\) | 18.2689 | 0.772691 | ||||||||
\(560\) | −0.281500 | −0.0118955 | ||||||||
\(561\) | 14.4988 | 0.612138 | ||||||||
\(562\) | 16.3944 | 0.691557 | ||||||||
\(563\) | 36.4540 | 1.53635 | 0.768176 | − | 0.640238i | \(-0.221164\pi\) | ||||
0.768176 | + | 0.640238i | \(0.221164\pi\) | |||||||
\(564\) | 10.9436 | 0.460810 | ||||||||
\(565\) | 0.170096 | 0.00715601 | ||||||||
\(566\) | 12.3852 | 0.520590 | ||||||||
\(567\) | −25.3373 | −1.06407 | ||||||||
\(568\) | 0.0717312 | 0.00300977 | ||||||||
\(569\) | 1.42838 | 0.0598808 | 0.0299404 | − | 0.999552i | \(-0.490468\pi\) | ||||
0.0299404 | + | 0.999552i | \(0.490468\pi\) | |||||||
\(570\) | −0.284996 | −0.0119372 | ||||||||
\(571\) | 45.0446 | 1.88506 | 0.942528 | − | 0.334126i | \(-0.108441\pi\) | ||||
0.942528 | + | 0.334126i | \(0.108441\pi\) | |||||||
\(572\) | 4.79264 | 0.200390 | ||||||||
\(573\) | 1.52709 | 0.0637950 | ||||||||
\(574\) | −25.5399 | −1.06602 | ||||||||
\(575\) | −7.30052 | −0.304453 | ||||||||
\(576\) | −0.680188 | −0.0283412 | ||||||||
\(577\) | 9.06730 | 0.377477 | 0.188738 | − | 0.982027i | \(-0.439560\pi\) | ||||
0.188738 | + | 0.982027i | \(0.439560\pi\) | |||||||
\(578\) | −39.6344 | −1.64857 | ||||||||
\(579\) | −8.36252 | −0.347535 | ||||||||
\(580\) | −0.364837 | −0.0151490 | ||||||||
\(581\) | 0.239834 | 0.00994997 | ||||||||
\(582\) | 1.52309 | 0.0631342 | ||||||||
\(583\) | −8.23045 | −0.340871 | ||||||||
\(584\) | 6.45943 | 0.267293 | ||||||||
\(585\) | 0.186018 | 0.00769089 | ||||||||
\(586\) | 8.57860 | 0.354379 | ||||||||
\(587\) | 11.9782 | 0.494391 | 0.247196 | − | 0.968966i | \(-0.420491\pi\) | ||||
0.247196 | + | 0.968966i | \(0.420491\pi\) | |||||||
\(588\) | −12.5043 | −0.515671 | ||||||||
\(589\) | −2.59237 | −0.106817 | ||||||||
\(590\) | 0.527982 | 0.0217367 | ||||||||
\(591\) | −5.01248 | −0.206186 | ||||||||
\(592\) | −3.19836 | −0.131452 | ||||||||
\(593\) | 29.6574 | 1.21789 | 0.608943 | − | 0.793214i | \(-0.291594\pi\) | ||||
0.608943 | + | 0.793214i | \(0.291594\pi\) | |||||||
\(594\) | −7.09024 | −0.290916 | ||||||||
\(595\) | 2.11845 | 0.0868479 | ||||||||
\(596\) | −20.2864 | −0.830963 | ||||||||
\(597\) | 30.6139 | 1.25294 | ||||||||
\(598\) | −5.53792 | −0.226462 | ||||||||
\(599\) | 16.8699 | 0.689284 | 0.344642 | − | 0.938734i | \(-0.388000\pi\) | ||||
0.344642 | + | 0.938734i | \(0.388000\pi\) | |||||||
\(600\) | −7.60753 | −0.310576 | ||||||||
\(601\) | 18.1570 | 0.740638 | 0.370319 | − | 0.928905i | \(-0.379248\pi\) | ||||
0.370319 | + | 0.928905i | \(0.379248\pi\) | |||||||
\(602\) | −18.8046 | −0.766418 | ||||||||
\(603\) | −6.29071 | −0.256177 | ||||||||
\(604\) | −12.6915 | −0.516411 | ||||||||
\(605\) | 0.678487 | 0.0275844 | ||||||||
\(606\) | −17.7441 | −0.720804 | ||||||||
\(607\) | −5.14842 | −0.208968 | −0.104484 | − | 0.994527i | \(-0.533319\pi\) | ||||
−0.104484 | + | 0.994527i | \(0.533319\pi\) | |||||||
\(608\) | −2.59237 | −0.105134 | ||||||||
\(609\) | −30.0243 | −1.21664 | ||||||||
\(610\) | 0.298716 | 0.0120947 | ||||||||
\(611\) | −27.2235 | −1.10135 | ||||||||
\(612\) | 5.11881 | 0.206916 | ||||||||
\(613\) | 16.8775 | 0.681676 | 0.340838 | − | 0.940122i | \(-0.389289\pi\) | ||||
0.340838 | + | 0.940122i | \(0.389289\pi\) | |||||||
\(614\) | −27.5872 | −1.11333 | ||||||||
\(615\) | 0.719944 | 0.0290310 | ||||||||
\(616\) | −4.93318 | −0.198763 | ||||||||
\(617\) | 45.9380 | 1.84939 | 0.924696 | − | 0.380705i | \(-0.124319\pi\) | ||||
0.924696 | + | 0.380705i | \(0.124319\pi\) | |||||||
\(618\) | 17.2975 | 0.695807 | ||||||||
\(619\) | −2.57732 | −0.103591 | −0.0517957 | − | 0.998658i | \(-0.516494\pi\) | ||||
−0.0517957 | + | 0.998658i | \(0.516494\pi\) | |||||||
\(620\) | 0.0721797 | 0.00289881 | ||||||||
\(621\) | 8.19282 | 0.328766 | ||||||||
\(622\) | 20.4691 | 0.820735 | ||||||||
\(623\) | 21.8631 | 0.875927 | ||||||||
\(624\) | −5.77080 | −0.231017 | ||||||||
\(625\) | 24.9219 | 0.996875 | ||||||||
\(626\) | −13.7204 | −0.548377 | ||||||||
\(627\) | −4.99445 | −0.199459 | ||||||||
\(628\) | −10.4383 | −0.416533 | ||||||||
\(629\) | 24.0695 | 0.959716 | ||||||||
\(630\) | −0.191473 | −0.00762846 | ||||||||
\(631\) | 23.4076 | 0.931843 | 0.465922 | − | 0.884826i | \(-0.345723\pi\) | ||||
0.465922 | + | 0.884826i | \(0.345723\pi\) | |||||||
\(632\) | −12.4804 | −0.496442 | ||||||||
\(633\) | −18.6962 | −0.743109 | ||||||||
\(634\) | −23.4019 | −0.929408 | ||||||||
\(635\) | 0.606578 | 0.0240713 | ||||||||
\(636\) | 9.91027 | 0.392968 | ||||||||
\(637\) | 31.1060 | 1.23247 | ||||||||
\(638\) | −6.39364 | −0.253127 | ||||||||
\(639\) | 0.0487907 | 0.00193013 | ||||||||
\(640\) | 0.0721797 | 0.00285316 | ||||||||
\(641\) | 13.1966 | 0.521235 | 0.260618 | − | 0.965442i | \(-0.416074\pi\) | ||||
0.260618 | + | 0.965442i | \(0.416074\pi\) | |||||||
\(642\) | 26.7697 | 1.05652 | ||||||||
\(643\) | 39.6538 | 1.56379 | 0.781897 | − | 0.623408i | \(-0.214252\pi\) | ||||
0.781897 | + | 0.623408i | \(0.214252\pi\) | |||||||
\(644\) | 5.70032 | 0.224624 | ||||||||
\(645\) | 0.530083 | 0.0208720 | ||||||||
\(646\) | 19.5091 | 0.767575 | ||||||||
\(647\) | 5.80527 | 0.228229 | 0.114114 | − | 0.993468i | \(-0.463597\pi\) | ||||
0.114114 | + | 0.993468i | \(0.463597\pi\) | |||||||
\(648\) | 6.49678 | 0.255218 | ||||||||
\(649\) | 9.25270 | 0.363200 | ||||||||
\(650\) | 18.9246 | 0.742284 | ||||||||
\(651\) | 5.94003 | 0.232808 | ||||||||
\(652\) | 3.32897 | 0.130373 | ||||||||
\(653\) | −2.88821 | −0.113024 | −0.0565122 | − | 0.998402i | \(-0.517998\pi\) | ||||
−0.0565122 | + | 0.998402i | \(0.517998\pi\) | |||||||
\(654\) | 13.2549 | 0.518306 | ||||||||
\(655\) | 0.340948 | 0.0133219 | ||||||||
\(656\) | 6.54873 | 0.255685 | ||||||||
\(657\) | 4.39363 | 0.171412 | ||||||||
\(658\) | 28.0219 | 1.09241 | ||||||||
\(659\) | −0.478385 | −0.0186352 | −0.00931761 | − | 0.999957i | \(-0.502966\pi\) | ||||
−0.00931761 | + | 0.999957i | \(0.502966\pi\) | |||||||
\(660\) | 0.139061 | 0.00541295 | ||||||||
\(661\) | −12.5627 | −0.488632 | −0.244316 | − | 0.969696i | \(-0.578563\pi\) | ||||
−0.244316 | + | 0.969696i | \(0.578563\pi\) | |||||||
\(662\) | −13.8521 | −0.538379 | ||||||||
\(663\) | 43.4286 | 1.68663 | ||||||||
\(664\) | −0.0614961 | −0.00238651 | ||||||||
\(665\) | −0.729751 | −0.0282985 | ||||||||
\(666\) | −2.17549 | −0.0842985 | ||||||||
\(667\) | 7.38789 | 0.286060 | ||||||||
\(668\) | −6.53936 | −0.253015 | ||||||||
\(669\) | −30.4090 | −1.17568 | ||||||||
\(670\) | 0.667553 | 0.0257898 | ||||||||
\(671\) | 5.23490 | 0.202091 | ||||||||
\(672\) | 5.94003 | 0.229142 | ||||||||
\(673\) | −8.32713 | −0.320987 | −0.160494 | − | 0.987037i | \(-0.551309\pi\) | ||||
−0.160494 | + | 0.987037i | \(0.551309\pi\) | |||||||
\(674\) | −29.5301 | −1.13746 | ||||||||
\(675\) | −27.9971 | −1.07761 | ||||||||
\(676\) | 1.35554 | 0.0521362 | ||||||||
\(677\) | 46.0135 | 1.76844 | 0.884221 | − | 0.467068i | \(-0.154690\pi\) | ||||
0.884221 | + | 0.467068i | \(0.154690\pi\) | |||||||
\(678\) | −3.58927 | −0.137845 | ||||||||
\(679\) | 3.89998 | 0.149667 | ||||||||
\(680\) | −0.543194 | −0.0208306 | ||||||||
\(681\) | 14.6665 | 0.562020 | ||||||||
\(682\) | 1.26492 | 0.0484365 | ||||||||
\(683\) | −13.1792 | −0.504287 | −0.252143 | − | 0.967690i | \(-0.581135\pi\) | ||||
−0.252143 | + | 0.967690i | \(0.581135\pi\) | |||||||
\(684\) | −1.76330 | −0.0674215 | ||||||||
\(685\) | −0.533639 | −0.0203893 | ||||||||
\(686\) | −4.71835 | −0.180148 | ||||||||
\(687\) | −19.6049 | −0.747973 | ||||||||
\(688\) | 4.82172 | 0.183826 | ||||||||
\(689\) | −24.6530 | −0.939203 | ||||||||
\(690\) | −0.160686 | −0.00611722 | ||||||||
\(691\) | −46.2645 | −1.75998 | −0.879991 | − | 0.474990i | \(-0.842452\pi\) | ||||
−0.879991 | + | 0.474990i | \(0.842452\pi\) | |||||||
\(692\) | 8.69790 | 0.330645 | ||||||||
\(693\) | −3.35549 | −0.127465 | ||||||||
\(694\) | 7.62554 | 0.289461 | ||||||||
\(695\) | −0.292222 | −0.0110846 | ||||||||
\(696\) | 7.69857 | 0.291814 | ||||||||
\(697\) | −49.2830 | −1.86673 | ||||||||
\(698\) | −33.1412 | −1.25441 | ||||||||
\(699\) | 24.5396 | 0.928172 | ||||||||
\(700\) | −19.4796 | −0.736259 | ||||||||
\(701\) | 31.8234 | 1.20195 | 0.600976 | − | 0.799267i | \(-0.294779\pi\) | ||||
0.600976 | + | 0.799267i | \(0.294779\pi\) | |||||||
\(702\) | −21.2376 | −0.801563 | ||||||||
\(703\) | −8.29134 | −0.312714 | ||||||||
\(704\) | 1.26492 | 0.0476736 | ||||||||
\(705\) | −0.789908 | −0.0297497 | ||||||||
\(706\) | 4.72300 | 0.177753 | ||||||||
\(707\) | −45.4349 | −1.70875 | ||||||||
\(708\) | −11.1412 | −0.418710 | ||||||||
\(709\) | 28.0995 | 1.05530 | 0.527649 | − | 0.849462i | \(-0.323073\pi\) | ||||
0.527649 | + | 0.849462i | \(0.323073\pi\) | |||||||
\(710\) | −0.00517754 | −0.000194310 0 | ||||||||
\(711\) | −8.48899 | −0.318362 | ||||||||
\(712\) | −5.60595 | −0.210092 | ||||||||
\(713\) | −1.46163 | −0.0547384 | ||||||||
\(714\) | −44.7022 | −1.67294 | ||||||||
\(715\) | −0.345931 | −0.0129371 | ||||||||
\(716\) | 2.43635 | 0.0910506 | ||||||||
\(717\) | 11.0948 | 0.414343 | ||||||||
\(718\) | −30.3409 | −1.13231 | ||||||||
\(719\) | −14.9996 | −0.559392 | −0.279696 | − | 0.960089i | \(-0.590234\pi\) | ||||
−0.279696 | + | 0.960089i | \(0.590234\pi\) | |||||||
\(720\) | 0.0490958 | 0.00182969 | ||||||||
\(721\) | 44.2913 | 1.64950 | ||||||||
\(722\) | 12.2796 | 0.457000 | ||||||||
\(723\) | −24.1267 | −0.897282 | ||||||||
\(724\) | 6.44436 | 0.239503 | ||||||||
\(725\) | −25.2465 | −0.937631 | ||||||||
\(726\) | −14.3170 | −0.531354 | ||||||||
\(727\) | −9.74867 | −0.361558 | −0.180779 | − | 0.983524i | \(-0.557862\pi\) | ||||
−0.180779 | + | 0.983524i | \(0.557862\pi\) | |||||||
\(728\) | −14.7765 | −0.547654 | ||||||||
\(729\) | 30.0311 | 1.11226 | ||||||||
\(730\) | −0.466240 | −0.0172563 | ||||||||
\(731\) | −36.2862 | −1.34209 | ||||||||
\(732\) | −6.30333 | −0.232978 | ||||||||
\(733\) | −42.3700 | −1.56497 | −0.782486 | − | 0.622668i | \(-0.786049\pi\) | ||||
−0.782486 | + | 0.622668i | \(0.786049\pi\) | |||||||
\(734\) | 12.5646 | 0.463769 | ||||||||
\(735\) | 0.902561 | 0.0332915 | ||||||||
\(736\) | −1.46163 | −0.0538763 | ||||||||
\(737\) | 11.6986 | 0.430924 | ||||||||
\(738\) | 4.45437 | 0.163968 | ||||||||
\(739\) | −48.5373 | −1.78547 | −0.892737 | − | 0.450578i | \(-0.851218\pi\) | ||||
−0.892737 | + | 0.450578i | \(0.851218\pi\) | |||||||
\(740\) | 0.230857 | 0.00848648 | ||||||||
\(741\) | −14.9601 | −0.549571 | ||||||||
\(742\) | 25.3759 | 0.931579 | ||||||||
\(743\) | −24.2013 | −0.887860 | −0.443930 | − | 0.896061i | \(-0.646416\pi\) | ||||
−0.443930 | + | 0.896061i | \(0.646416\pi\) | |||||||
\(744\) | −1.52309 | −0.0558393 | ||||||||
\(745\) | 1.46427 | 0.0536466 | ||||||||
\(746\) | 16.2479 | 0.594878 | ||||||||
\(747\) | −0.0418289 | −0.00153044 | ||||||||
\(748\) | −9.51929 | −0.348060 | ||||||||
\(749\) | 68.5456 | 2.50460 | ||||||||
\(750\) | 1.09879 | 0.0401222 | ||||||||
\(751\) | 43.2325 | 1.57757 | 0.788787 | − | 0.614666i | \(-0.210709\pi\) | ||||
0.788787 | + | 0.614666i | \(0.210709\pi\) | |||||||
\(752\) | −7.18513 | −0.262015 | ||||||||
\(753\) | −35.6186 | −1.29801 | ||||||||
\(754\) | −19.1511 | −0.697442 | ||||||||
\(755\) | 0.916072 | 0.0333393 | ||||||||
\(756\) | 21.8604 | 0.795056 | ||||||||
\(757\) | 44.9322 | 1.63309 | 0.816544 | − | 0.577283i | \(-0.195887\pi\) | ||||
0.816544 | + | 0.577283i | \(0.195887\pi\) | |||||||
\(758\) | −2.07245 | −0.0752748 | ||||||||
\(759\) | −2.81597 | −0.102213 | ||||||||
\(760\) | 0.187117 | 0.00678743 | ||||||||
\(761\) | −42.8925 | −1.55485 | −0.777425 | − | 0.628976i | \(-0.783475\pi\) | ||||
−0.777425 | + | 0.628976i | \(0.783475\pi\) | |||||||
\(762\) | −12.7996 | −0.463682 | ||||||||
\(763\) | 33.9399 | 1.22871 | ||||||||
\(764\) | −1.00262 | −0.0362736 | ||||||||
\(765\) | −0.369475 | −0.0133584 | ||||||||
\(766\) | 15.6530 | 0.565568 | ||||||||
\(767\) | 27.7149 | 1.00073 | ||||||||
\(768\) | −1.52309 | −0.0549599 | ||||||||
\(769\) | −24.1125 | −0.869521 | −0.434760 | − | 0.900546i | \(-0.643167\pi\) | ||||
−0.434760 | + | 0.900546i | \(0.643167\pi\) | |||||||
\(770\) | 0.356076 | 0.0128321 | ||||||||
\(771\) | 18.6217 | 0.670644 | ||||||||
\(772\) | 5.49049 | 0.197607 | ||||||||
\(773\) | 51.7220 | 1.86031 | 0.930155 | − | 0.367166i | \(-0.119672\pi\) | ||||
0.930155 | + | 0.367166i | \(0.119672\pi\) | |||||||
\(774\) | 3.27968 | 0.117886 | ||||||||
\(775\) | 4.99479 | 0.179418 | ||||||||
\(776\) | −1.00000 | −0.0358979 | ||||||||
\(777\) | 18.9984 | 0.681563 | ||||||||
\(778\) | −0.655386 | −0.0234967 | ||||||||
\(779\) | 16.9767 | 0.608255 | ||||||||
\(780\) | 0.416535 | 0.0149143 | ||||||||
\(781\) | −0.0907346 | −0.00324674 | ||||||||
\(782\) | 10.9996 | 0.393345 | ||||||||
\(783\) | 28.3322 | 1.01251 | ||||||||
\(784\) | 8.20984 | 0.293209 | ||||||||
\(785\) | 0.753433 | 0.0268912 | ||||||||
\(786\) | −7.19447 | −0.256618 | ||||||||
\(787\) | −27.9081 | −0.994815 | −0.497408 | − | 0.867517i | \(-0.665715\pi\) | ||||
−0.497408 | + | 0.867517i | \(0.665715\pi\) | |||||||
\(788\) | 3.29099 | 0.117237 | ||||||||
\(789\) | −26.0884 | −0.928773 | ||||||||
\(790\) | 0.900829 | 0.0320501 | ||||||||
\(791\) | −9.19057 | −0.326779 | ||||||||
\(792\) | 0.860387 | 0.0305725 | ||||||||
\(793\) | 15.6803 | 0.556823 | ||||||||
\(794\) | −18.2764 | −0.648604 | ||||||||
\(795\) | −0.715321 | −0.0253698 | ||||||||
\(796\) | −20.0998 | −0.712419 | ||||||||
\(797\) | −26.9757 | −0.955529 | −0.477765 | − | 0.878488i | \(-0.658553\pi\) | ||||
−0.477765 | + | 0.878488i | \(0.658553\pi\) | |||||||
\(798\) | 15.3988 | 0.545110 | ||||||||
\(799\) | 54.0723 | 1.91294 | ||||||||
\(800\) | 4.99479 | 0.176592 | ||||||||
\(801\) | −3.81311 | −0.134729 | ||||||||
\(802\) | −13.3275 | −0.470611 | ||||||||
\(803\) | −8.17069 | −0.288337 | ||||||||
\(804\) | −14.0863 | −0.496785 | ||||||||
\(805\) | −0.411448 | −0.0145016 | ||||||||
\(806\) | 3.78887 | 0.133457 | ||||||||
\(807\) | 9.03928 | 0.318198 | ||||||||
\(808\) | 11.6500 | 0.409846 | ||||||||
\(809\) | 14.0554 | 0.494162 | 0.247081 | − | 0.968995i | \(-0.420529\pi\) | ||||
0.247081 | + | 0.968995i | \(0.420529\pi\) | |||||||
\(810\) | −0.468936 | −0.0164767 | ||||||||
\(811\) | −26.7527 | −0.939416 | −0.469708 | − | 0.882822i | \(-0.655641\pi\) | ||||
−0.469708 | + | 0.882822i | \(0.655641\pi\) | |||||||
\(812\) | 19.7127 | 0.691780 | ||||||||
\(813\) | −45.6477 | −1.60093 | ||||||||
\(814\) | 4.04569 | 0.141801 | ||||||||
\(815\) | −0.240284 | −0.00841679 | ||||||||
\(816\) | 11.4622 | 0.401256 | ||||||||
\(817\) | 12.4997 | 0.437308 | ||||||||
\(818\) | −35.4803 | −1.24054 | ||||||||
\(819\) | −10.0508 | −0.351204 | ||||||||
\(820\) | −0.472686 | −0.0165069 | ||||||||
\(821\) | 8.98723 | 0.313656 | 0.156828 | − | 0.987626i | \(-0.449873\pi\) | ||||
0.156828 | + | 0.987626i | \(0.449873\pi\) | |||||||
\(822\) | 11.2605 | 0.392755 | ||||||||
\(823\) | 5.86772 | 0.204536 | 0.102268 | − | 0.994757i | \(-0.467390\pi\) | ||||
0.102268 | + | 0.994757i | \(0.467390\pi\) | |||||||
\(824\) | −11.3568 | −0.395633 | ||||||||
\(825\) | 9.62295 | 0.335028 | ||||||||
\(826\) | −28.5277 | −0.992604 | ||||||||
\(827\) | 1.30007 | 0.0452080 | 0.0226040 | − | 0.999744i | \(-0.492804\pi\) | ||||
0.0226040 | + | 0.999744i | \(0.492804\pi\) | |||||||
\(828\) | −0.994182 | −0.0345502 | ||||||||
\(829\) | −45.0904 | −1.56605 | −0.783026 | − | 0.621989i | \(-0.786325\pi\) | ||||
−0.783026 | + | 0.621989i | \(0.786325\pi\) | |||||||
\(830\) | 0.00443877 | 0.000154072 0 | ||||||||
\(831\) | 6.02753 | 0.209093 | ||||||||
\(832\) | 3.78887 | 0.131355 | ||||||||
\(833\) | −61.7838 | −2.14068 | ||||||||
\(834\) | 6.16628 | 0.213521 | ||||||||
\(835\) | 0.472009 | 0.0163345 | ||||||||
\(836\) | 3.27915 | 0.113412 | ||||||||
\(837\) | −5.60527 | −0.193746 | ||||||||
\(838\) | −29.6289 | −1.02351 | ||||||||
\(839\) | 1.74493 | 0.0602417 | 0.0301208 | − | 0.999546i | \(-0.490411\pi\) | ||||
0.0301208 | + | 0.999546i | \(0.490411\pi\) | |||||||
\(840\) | −0.428750 | −0.0147933 | ||||||||
\(841\) | −3.45137 | −0.119013 | ||||||||
\(842\) | 15.7535 | 0.542901 | ||||||||
\(843\) | 24.9702 | 0.860021 | ||||||||
\(844\) | 12.2752 | 0.422529 | ||||||||
\(845\) | −0.0978426 | −0.00336589 | ||||||||
\(846\) | −4.88725 | −0.168027 | ||||||||
\(847\) | −36.6597 | −1.25964 | ||||||||
\(848\) | −6.50668 | −0.223440 | ||||||||
\(849\) | 18.8638 | 0.647405 | ||||||||
\(850\) | −37.5887 | −1.28928 | ||||||||
\(851\) | −4.67482 | −0.160251 | ||||||||
\(852\) | 0.109253 | 0.00374296 | ||||||||
\(853\) | 6.32932 | 0.216712 | 0.108356 | − | 0.994112i | \(-0.465441\pi\) | ||||
0.108356 | + | 0.994112i | \(0.465441\pi\) | |||||||
\(854\) | −16.1401 | −0.552303 | ||||||||
\(855\) | 0.127275 | 0.00435270 | ||||||||
\(856\) | −17.5759 | −0.600732 | ||||||||
\(857\) | −7.72730 | −0.263959 | −0.131980 | − | 0.991252i | \(-0.542133\pi\) | ||||
−0.131980 | + | 0.991252i | \(0.542133\pi\) | |||||||
\(858\) | 7.29963 | 0.249205 | ||||||||
\(859\) | −45.6097 | −1.55618 | −0.778091 | − | 0.628151i | \(-0.783812\pi\) | ||||
−0.778091 | + | 0.628151i | \(0.783812\pi\) | |||||||
\(860\) | −0.348030 | −0.0118677 | ||||||||
\(861\) | −38.8997 | −1.32570 | ||||||||
\(862\) | −10.2828 | −0.350235 | ||||||||
\(863\) | −56.3762 | −1.91907 | −0.959533 | − | 0.281595i | \(-0.909137\pi\) | ||||
−0.959533 | + | 0.281595i | \(0.909137\pi\) | |||||||
\(864\) | −5.60527 | −0.190695 | ||||||||
\(865\) | −0.627812 | −0.0213463 | ||||||||
\(866\) | 3.49173 | 0.118654 | ||||||||
\(867\) | −60.3668 | −2.05016 | ||||||||
\(868\) | −3.89998 | −0.132374 | ||||||||
\(869\) | 15.7867 | 0.535527 | ||||||||
\(870\) | −0.555681 | −0.0188393 | ||||||||
\(871\) | 35.0413 | 1.18733 | ||||||||
\(872\) | −8.70260 | −0.294707 | ||||||||
\(873\) | −0.680188 | −0.0230209 | ||||||||
\(874\) | −3.78908 | −0.128168 | ||||||||
\(875\) | 2.81353 | 0.0951146 | ||||||||
\(876\) | 9.83831 | 0.332406 | ||||||||
\(877\) | 9.34976 | 0.315719 | 0.157860 | − | 0.987462i | \(-0.449541\pi\) | ||||
0.157860 | + | 0.987462i | \(0.449541\pi\) | |||||||
\(878\) | −1.97908 | −0.0667907 | ||||||||
\(879\) | 13.0660 | 0.440705 | ||||||||
\(880\) | −0.0913019 | −0.00307779 | ||||||||
\(881\) | 1.16486 | 0.0392450 | 0.0196225 | − | 0.999807i | \(-0.493754\pi\) | ||||
0.0196225 | + | 0.999807i | \(0.493754\pi\) | |||||||
\(882\) | 5.58424 | 0.188031 | ||||||||
\(883\) | −28.2285 | −0.949964 | −0.474982 | − | 0.879996i | \(-0.657545\pi\) | ||||
−0.474982 | + | 0.879996i | \(0.657545\pi\) | |||||||
\(884\) | −28.5135 | −0.959011 | ||||||||
\(885\) | 0.804166 | 0.0270317 | ||||||||
\(886\) | 14.2391 | 0.478372 | ||||||||
\(887\) | 31.5848 | 1.06051 | 0.530256 | − | 0.847837i | \(-0.322096\pi\) | ||||
0.530256 | + | 0.847837i | \(0.322096\pi\) | |||||||
\(888\) | −4.87141 | −0.163474 | ||||||||
\(889\) | −32.7743 | −1.09922 | ||||||||
\(890\) | 0.404636 | 0.0135634 | ||||||||
\(891\) | −8.21793 | −0.275311 | ||||||||
\(892\) | 19.9653 | 0.668487 | ||||||||
\(893\) | −18.6265 | −0.623313 | ||||||||
\(894\) | −30.8981 | −1.03339 | ||||||||
\(895\) | −0.175855 | −0.00587818 | ||||||||
\(896\) | −3.89998 | −0.130289 | ||||||||
\(897\) | −8.43476 | −0.281629 | ||||||||
\(898\) | 16.6508 | 0.555644 | ||||||||
\(899\) | −5.05456 | −0.168579 | ||||||||
\(900\) | 3.39740 | 0.113247 | ||||||||
\(901\) | 48.9665 | 1.63131 | ||||||||
\(902\) | −8.28365 | −0.275815 | ||||||||
\(903\) | −28.6412 | −0.953118 | ||||||||
\(904\) | 2.35657 | 0.0783783 | ||||||||
\(905\) | −0.465152 | −0.0154622 | ||||||||
\(906\) | −19.3304 | −0.642209 | ||||||||
\(907\) | 38.3482 | 1.27333 | 0.636666 | − | 0.771140i | \(-0.280313\pi\) | ||||
0.636666 | + | 0.771140i | \(0.280313\pi\) | |||||||
\(908\) | −9.62939 | −0.319563 | ||||||||
\(909\) | 7.92421 | 0.262830 | ||||||||
\(910\) | 1.06657 | 0.0353563 | ||||||||
\(911\) | 12.2582 | 0.406132 | 0.203066 | − | 0.979165i | \(-0.434909\pi\) | ||||
0.203066 | + | 0.979165i | \(0.434909\pi\) | |||||||
\(912\) | −3.94842 | −0.130745 | ||||||||
\(913\) | 0.0777879 | 0.00257440 | ||||||||
\(914\) | −32.8349 | −1.08608 | ||||||||
\(915\) | 0.454973 | 0.0150409 | ||||||||
\(916\) | 12.8718 | 0.425295 | ||||||||
\(917\) | −18.4219 | −0.608345 | ||||||||
\(918\) | 42.1829 | 1.39224 | ||||||||
\(919\) | −31.2508 | −1.03087 | −0.515434 | − | 0.856929i | \(-0.672369\pi\) | ||||
−0.515434 | + | 0.856929i | \(0.672369\pi\) | |||||||
\(920\) | 0.105500 | 0.00347823 | ||||||||
\(921\) | −42.0179 | −1.38454 | ||||||||
\(922\) | 6.69769 | 0.220577 | ||||||||
\(923\) | −0.271780 | −0.00894576 | ||||||||
\(924\) | −7.51369 | −0.247182 | ||||||||
\(925\) | 15.9752 | 0.525260 | ||||||||
\(926\) | 27.6004 | 0.907006 | ||||||||
\(927\) | −7.72477 | −0.253715 | ||||||||
\(928\) | −5.05456 | −0.165924 | ||||||||
\(929\) | 41.9899 | 1.37764 | 0.688822 | − | 0.724931i | \(-0.258128\pi\) | ||||
0.688822 | + | 0.724931i | \(0.258128\pi\) | |||||||
\(930\) | 0.109936 | 0.00360496 | ||||||||
\(931\) | 21.2829 | 0.697520 | ||||||||
\(932\) | −16.1117 | −0.527755 | ||||||||
\(933\) | 31.1763 | 1.02067 | ||||||||
\(934\) | 17.6138 | 0.576342 | ||||||||
\(935\) | 0.687100 | 0.0224706 | ||||||||
\(936\) | 2.57715 | 0.0842367 | ||||||||
\(937\) | −38.5166 | −1.25828 | −0.629141 | − | 0.777291i | \(-0.716593\pi\) | ||||
−0.629141 | + | 0.777291i | \(0.716593\pi\) | |||||||
\(938\) | −36.0689 | −1.17769 | ||||||||
\(939\) | −20.8974 | −0.681961 | ||||||||
\(940\) | 0.518621 | 0.0169156 | ||||||||
\(941\) | 40.9593 | 1.33524 | 0.667618 | − | 0.744504i | \(-0.267314\pi\) | ||||
0.667618 | + | 0.744504i | \(0.267314\pi\) | |||||||
\(942\) | −15.8985 | −0.518001 | ||||||||
\(943\) | 9.57181 | 0.311701 | ||||||||
\(944\) | 7.31482 | 0.238077 | ||||||||
\(945\) | −1.57788 | −0.0513285 | ||||||||
\(946\) | −6.09911 | −0.198299 | ||||||||
\(947\) | −25.3440 | −0.823570 | −0.411785 | − | 0.911281i | \(-0.635095\pi\) | ||||
−0.411785 | + | 0.911281i | \(0.635095\pi\) | |||||||
\(948\) | −19.0087 | −0.617375 | ||||||||
\(949\) | −24.4739 | −0.794458 | ||||||||
\(950\) | 12.9483 | 0.420100 | ||||||||
\(951\) | −35.6433 | −1.15581 | ||||||||
\(952\) | 29.3496 | 0.951226 | ||||||||
\(953\) | 45.2715 | 1.46649 | 0.733244 | − | 0.679965i | \(-0.238005\pi\) | ||||
0.733244 | + | 0.679965i | \(0.238005\pi\) | |||||||
\(954\) | −4.42577 | −0.143289 | ||||||||
\(955\) | 0.0723691 | 0.00234181 | ||||||||
\(956\) | −7.28439 | −0.235594 | ||||||||
\(957\) | −9.73811 | −0.314788 | ||||||||
\(958\) | −35.7829 | −1.15609 | ||||||||
\(959\) | 28.8333 | 0.931075 | ||||||||
\(960\) | 0.109936 | 0.00354818 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 12.1182 | 0.390706 | ||||||||
\(963\) | −11.9549 | −0.385242 | ||||||||
\(964\) | 15.8406 | 0.510191 | ||||||||
\(965\) | −0.396302 | −0.0127574 | ||||||||
\(966\) | 8.68211 | 0.279342 | ||||||||
\(967\) | −53.6869 | −1.72645 | −0.863227 | − | 0.504816i | \(-0.831560\pi\) | ||||
−0.863227 | + | 0.504816i | \(0.831560\pi\) | |||||||
\(968\) | 9.39997 | 0.302126 | ||||||||
\(969\) | 29.7141 | 0.954556 | ||||||||
\(970\) | 0.0721797 | 0.00231755 | ||||||||
\(971\) | −16.5124 | −0.529907 | −0.264954 | − | 0.964261i | \(-0.585357\pi\) | ||||
−0.264954 | + | 0.964261i | \(0.585357\pi\) | |||||||
\(972\) | −6.92061 | −0.221979 | ||||||||
\(973\) | 15.7892 | 0.506178 | ||||||||
\(974\) | 4.91312 | 0.157426 | ||||||||
\(975\) | 28.8239 | 0.923105 | ||||||||
\(976\) | 4.13851 | 0.132470 | ||||||||
\(977\) | −21.2877 | −0.681055 | −0.340528 | − | 0.940235i | \(-0.610606\pi\) | ||||
−0.340528 | + | 0.940235i | \(0.610606\pi\) | |||||||
\(978\) | 5.07033 | 0.162131 | ||||||||
\(979\) | 7.09111 | 0.226633 | ||||||||
\(980\) | −0.592584 | −0.0189294 | ||||||||
\(981\) | −5.91940 | −0.188992 | ||||||||
\(982\) | −1.21826 | −0.0388764 | ||||||||
\(983\) | 27.4940 | 0.876923 | 0.438461 | − | 0.898750i | \(-0.355524\pi\) | ||||
0.438461 | + | 0.898750i | \(0.355524\pi\) | |||||||
\(984\) | 9.97432 | 0.317970 | ||||||||
\(985\) | −0.237543 | −0.00756873 | ||||||||
\(986\) | 38.0385 | 1.21139 | ||||||||
\(987\) | 42.6799 | 1.35852 | ||||||||
\(988\) | 9.82215 | 0.312484 | ||||||||
\(989\) | 7.04756 | 0.224099 | ||||||||
\(990\) | −0.0621025 | −0.00197375 | ||||||||
\(991\) | 48.3298 | 1.53525 | 0.767623 | − | 0.640901i | \(-0.221439\pi\) | ||||
0.767623 | + | 0.640901i | \(0.221439\pi\) | |||||||
\(992\) | 1.00000 | 0.0317500 | ||||||||
\(993\) | −21.0981 | −0.669528 | ||||||||
\(994\) | 0.279750 | 0.00887314 | ||||||||
\(995\) | 1.45080 | 0.0459935 | ||||||||
\(996\) | −0.0936643 | −0.00296787 | ||||||||
\(997\) | −8.32851 | −0.263766 | −0.131883 | − | 0.991265i | \(-0.542102\pi\) | ||||
−0.131883 | + | 0.991265i | \(0.542102\pi\) | |||||||
\(998\) | 40.6275 | 1.28604 | ||||||||
\(999\) | −17.9277 | −0.567207 |
(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 | 6014.2.a.j.1.10 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6014.2.a.j.1.10 | ✓ | 32 | 1.1 | even | 1 | trivial |