Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 19 x^{12} + 36 x^{11} + 134 x^{10} - 237 x^{9} - 438 x^{8} + 716 x^{7} + 662 x^{6} - 1007 x^{5} - 384 x^{4} + 579 x^{3} + 44 x^{2} - 112 x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.55282\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.55282 | −1.80512 | −0.902559 | − | 0.430566i | \(-0.858314\pi\) | ||||
−0.902559 | + | 0.430566i | \(0.858314\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.51690 | 2.25845 | ||||||||
\(5\) | −1.95019 | −0.872151 | −0.436075 | − | 0.899910i | \(-0.643632\pi\) | ||||
−0.436075 | + | 0.899910i | \(0.643632\pi\) | |||||||
\(6\) | −2.55282 | −1.04219 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −6.42520 | −2.27165 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.97848 | 1.57433 | ||||||||
\(11\) | 5.66056 | 1.70672 | 0.853362 | − | 0.521320i | \(-0.174560\pi\) | ||||
0.853362 | + | 0.521320i | \(0.174560\pi\) | |||||||
\(12\) | 4.51690 | 1.30392 | ||||||||
\(13\) | −4.68475 | −1.29932 | −0.649658 | − | 0.760227i | \(-0.725088\pi\) | ||||
−0.649658 | + | 0.760227i | \(0.725088\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.95019 | −0.503536 | ||||||||
\(16\) | 7.36860 | 1.84215 | ||||||||
\(17\) | −4.34161 | −1.05300 | −0.526498 | − | 0.850177i | \(-0.676495\pi\) | ||||
−0.526498 | + | 0.850177i | \(0.676495\pi\) | |||||||
\(18\) | −2.55282 | −0.601706 | ||||||||
\(19\) | 5.53739 | 1.27037 | 0.635183 | − | 0.772362i | \(-0.280925\pi\) | ||||
0.635183 | + | 0.772362i | \(0.280925\pi\) | |||||||
\(20\) | −8.80881 | −1.96971 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −14.4504 | −3.08084 | ||||||||
\(23\) | −3.74585 | −0.781064 | −0.390532 | − | 0.920589i | \(-0.627709\pi\) | ||||
−0.390532 | + | 0.920589i | \(0.627709\pi\) | |||||||
\(24\) | −6.42520 | −1.31154 | ||||||||
\(25\) | −1.19677 | −0.239353 | ||||||||
\(26\) | 11.9593 | 2.34542 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.177428 | −0.0329475 | −0.0164737 | − | 0.999864i | \(-0.505244\pi\) | ||||
−0.0164737 | + | 0.999864i | \(0.505244\pi\) | |||||||
\(30\) | 4.97848 | 0.908943 | ||||||||
\(31\) | −0.750655 | −0.134822 | −0.0674108 | − | 0.997725i | \(-0.521474\pi\) | ||||
−0.0674108 | + | 0.997725i | \(0.521474\pi\) | |||||||
\(32\) | −5.96031 | −1.05364 | ||||||||
\(33\) | 5.66056 | 0.985377 | ||||||||
\(34\) | 11.0834 | 1.90078 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.51690 | 0.752817 | ||||||||
\(37\) | 8.28667 | 1.36232 | 0.681160 | − | 0.732134i | \(-0.261476\pi\) | ||||
0.681160 | + | 0.732134i | \(0.261476\pi\) | |||||||
\(38\) | −14.1360 | −2.29316 | ||||||||
\(39\) | −4.68475 | −0.750160 | ||||||||
\(40\) | 12.5304 | 1.98122 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.12975 | 0.934779 | 0.467389 | − | 0.884052i | \(-0.345195\pi\) | ||||
0.467389 | + | 0.884052i | \(0.345195\pi\) | |||||||
\(44\) | 25.5682 | 3.85455 | ||||||||
\(45\) | −1.95019 | −0.290717 | ||||||||
\(46\) | 9.56250 | 1.40991 | ||||||||
\(47\) | −0.738793 | −0.107764 | −0.0538820 | − | 0.998547i | \(-0.517159\pi\) | ||||
−0.0538820 | + | 0.998547i | \(0.517159\pi\) | |||||||
\(48\) | 7.36860 | 1.06357 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.05513 | 0.432061 | ||||||||
\(51\) | −4.34161 | −0.607947 | ||||||||
\(52\) | −21.1605 | −2.93444 | ||||||||
\(53\) | −13.5974 | −1.86775 | −0.933876 | − | 0.357598i | \(-0.883596\pi\) | ||||
−0.933876 | + | 0.357598i | \(0.883596\pi\) | |||||||
\(54\) | −2.55282 | −0.347395 | ||||||||
\(55\) | −11.0392 | −1.48852 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.53739 | 0.733446 | ||||||||
\(58\) | 0.452941 | 0.0594741 | ||||||||
\(59\) | 4.83812 | 0.629870 | 0.314935 | − | 0.949113i | \(-0.398017\pi\) | ||||
0.314935 | + | 0.949113i | \(0.398017\pi\) | |||||||
\(60\) | −8.80881 | −1.13721 | ||||||||
\(61\) | −10.3042 | −1.31932 | −0.659662 | − | 0.751562i | \(-0.729301\pi\) | ||||
−0.659662 | + | 0.751562i | \(0.729301\pi\) | |||||||
\(62\) | 1.91629 | 0.243369 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.478424 | 0.0598030 | ||||||||
\(65\) | 9.13614 | 1.13320 | ||||||||
\(66\) | −14.4504 | −1.77872 | ||||||||
\(67\) | 13.7621 | 1.68131 | 0.840655 | − | 0.541571i | \(-0.182170\pi\) | ||||
0.840655 | + | 0.541571i | \(0.182170\pi\) | |||||||
\(68\) | −19.6106 | −2.37814 | ||||||||
\(69\) | −3.74585 | −0.450948 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.8518 | −1.88126 | −0.940629 | − | 0.339436i | \(-0.889764\pi\) | ||||
−0.940629 | + | 0.339436i | \(0.889764\pi\) | |||||||
\(72\) | −6.42520 | −0.757217 | ||||||||
\(73\) | 9.26794 | 1.08473 | 0.542365 | − | 0.840143i | \(-0.317529\pi\) | ||||
0.542365 | + | 0.840143i | \(0.317529\pi\) | |||||||
\(74\) | −21.1544 | −2.45915 | ||||||||
\(75\) | −1.19677 | −0.138191 | ||||||||
\(76\) | 25.0119 | 2.86906 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 11.9593 | 1.35413 | ||||||||
\(79\) | 8.55260 | 0.962242 | 0.481121 | − | 0.876654i | \(-0.340230\pi\) | ||||
0.481121 | + | 0.876654i | \(0.340230\pi\) | |||||||
\(80\) | −14.3701 | −1.60663 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.55282 | 0.281912 | ||||||||
\(83\) | −10.1927 | −1.11880 | −0.559400 | − | 0.828898i | \(-0.688968\pi\) | ||||
−0.559400 | + | 0.828898i | \(0.688968\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.46696 | 0.918371 | ||||||||
\(86\) | −15.6482 | −1.68739 | ||||||||
\(87\) | −0.177428 | −0.0190222 | ||||||||
\(88\) | −36.3702 | −3.87708 | ||||||||
\(89\) | −6.24247 | −0.661700 | −0.330850 | − | 0.943683i | \(-0.607335\pi\) | ||||
−0.330850 | + | 0.943683i | \(0.607335\pi\) | |||||||
\(90\) | 4.97848 | 0.524778 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −16.9197 | −1.76400 | ||||||||
\(93\) | −0.750655 | −0.0778393 | ||||||||
\(94\) | 1.88601 | 0.194527 | ||||||||
\(95\) | −10.7990 | −1.10795 | ||||||||
\(96\) | −5.96031 | −0.608322 | ||||||||
\(97\) | −11.0576 | −1.12273 | −0.561364 | − | 0.827569i | \(-0.689723\pi\) | ||||
−0.561364 | + | 0.827569i | \(0.689723\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.66056 | 0.568908 | ||||||||
\(100\) | −5.40567 | −0.540567 | ||||||||
\(101\) | −5.94360 | −0.591410 | −0.295705 | − | 0.955279i | \(-0.595555\pi\) | ||||
−0.295705 | + | 0.955279i | \(0.595555\pi\) | |||||||
\(102\) | 11.0834 | 1.09742 | ||||||||
\(103\) | −9.42784 | −0.928952 | −0.464476 | − | 0.885586i | \(-0.653757\pi\) | ||||
−0.464476 | + | 0.885586i | \(0.653757\pi\) | |||||||
\(104\) | 30.1004 | 2.95159 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 34.7118 | 3.37151 | ||||||||
\(107\) | −4.90421 | −0.474108 | −0.237054 | − | 0.971496i | \(-0.576182\pi\) | ||||
−0.237054 | + | 0.971496i | \(0.576182\pi\) | |||||||
\(108\) | 4.51690 | 0.434639 | ||||||||
\(109\) | 7.10598 | 0.680629 | 0.340315 | − | 0.940312i | \(-0.389466\pi\) | ||||
0.340315 | + | 0.940312i | \(0.389466\pi\) | |||||||
\(110\) | 28.1810 | 2.68695 | ||||||||
\(111\) | 8.28667 | 0.786536 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.5531 | 1.55719 | 0.778594 | − | 0.627528i | \(-0.215933\pi\) | ||||
0.778594 | + | 0.627528i | \(0.215933\pi\) | |||||||
\(114\) | −14.1360 | −1.32396 | ||||||||
\(115\) | 7.30512 | 0.681206 | ||||||||
\(116\) | −0.801423 | −0.0744102 | ||||||||
\(117\) | −4.68475 | −0.433105 | ||||||||
\(118\) | −12.3509 | −1.13699 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 12.5304 | 1.14386 | ||||||||
\(121\) | 21.0419 | 1.91290 | ||||||||
\(122\) | 26.3049 | 2.38154 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −3.39064 | −0.304488 | ||||||||
\(125\) | 12.0849 | 1.08090 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.96925 | −0.440950 | −0.220475 | − | 0.975393i | \(-0.570761\pi\) | ||||
−0.220475 | + | 0.975393i | \(0.570761\pi\) | |||||||
\(128\) | 10.6993 | 0.945693 | ||||||||
\(129\) | 6.12975 | 0.539695 | ||||||||
\(130\) | −23.3229 | −2.04556 | ||||||||
\(131\) | 15.3014 | 1.33689 | 0.668446 | − | 0.743761i | \(-0.266960\pi\) | ||||
0.668446 | + | 0.743761i | \(0.266960\pi\) | |||||||
\(132\) | 25.5682 | 2.22543 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −35.1322 | −3.03496 | ||||||||
\(135\) | −1.95019 | −0.167845 | ||||||||
\(136\) | 27.8957 | 2.39204 | ||||||||
\(137\) | −11.3447 | −0.969242 | −0.484621 | − | 0.874724i | \(-0.661042\pi\) | ||||
−0.484621 | + | 0.874724i | \(0.661042\pi\) | |||||||
\(138\) | 9.56250 | 0.814014 | ||||||||
\(139\) | 0.201634 | 0.0171024 | 0.00855119 | − | 0.999963i | \(-0.497278\pi\) | ||||
0.00855119 | + | 0.999963i | \(0.497278\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.738793 | −0.0622176 | ||||||||
\(142\) | 40.4667 | 3.39589 | ||||||||
\(143\) | −26.5183 | −2.21757 | ||||||||
\(144\) | 7.36860 | 0.614050 | ||||||||
\(145\) | 0.346017 | 0.0287352 | ||||||||
\(146\) | −23.6594 | −1.95807 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 37.4301 | 3.07673 | ||||||||
\(149\) | −2.73172 | −0.223791 | −0.111896 | − | 0.993720i | \(-0.535692\pi\) | ||||
−0.111896 | + | 0.993720i | \(0.535692\pi\) | |||||||
\(150\) | 3.05513 | 0.249450 | ||||||||
\(151\) | −9.57461 | −0.779171 | −0.389585 | − | 0.920990i | \(-0.627382\pi\) | ||||
−0.389585 | + | 0.920990i | \(0.627382\pi\) | |||||||
\(152\) | −35.5789 | −2.88583 | ||||||||
\(153\) | −4.34161 | −0.350999 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.46392 | 0.117585 | ||||||||
\(156\) | −21.1605 | −1.69420 | ||||||||
\(157\) | −9.56163 | −0.763101 | −0.381551 | − | 0.924348i | \(-0.624610\pi\) | ||||
−0.381551 | + | 0.924348i | \(0.624610\pi\) | |||||||
\(158\) | −21.8333 | −1.73696 | ||||||||
\(159\) | −13.5974 | −1.07835 | ||||||||
\(160\) | 11.6237 | 0.918936 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.55282 | −0.200569 | ||||||||
\(163\) | 3.62324 | 0.283794 | 0.141897 | − | 0.989881i | \(-0.454680\pi\) | ||||
0.141897 | + | 0.989881i | \(0.454680\pi\) | |||||||
\(164\) | −4.51690 | −0.352711 | ||||||||
\(165\) | −11.0392 | −0.859397 | ||||||||
\(166\) | 26.0203 | 2.01956 | ||||||||
\(167\) | −7.01612 | −0.542923 | −0.271462 | − | 0.962449i | \(-0.587507\pi\) | ||||
−0.271462 | + | 0.962449i | \(0.587507\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.94686 | 0.688220 | ||||||||
\(170\) | −21.6146 | −1.65777 | ||||||||
\(171\) | 5.53739 | 0.423455 | ||||||||
\(172\) | 27.6875 | 2.11115 | ||||||||
\(173\) | −14.3292 | −1.08943 | −0.544713 | − | 0.838622i | \(-0.683361\pi\) | ||||
−0.544713 | + | 0.838622i | \(0.683361\pi\) | |||||||
\(174\) | 0.452941 | 0.0343374 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 41.7104 | 3.14404 | ||||||||
\(177\) | 4.83812 | 0.363656 | ||||||||
\(178\) | 15.9359 | 1.19445 | ||||||||
\(179\) | 5.16712 | 0.386208 | 0.193104 | − | 0.981178i | \(-0.438144\pi\) | ||||
0.193104 | + | 0.981178i | \(0.438144\pi\) | |||||||
\(180\) | −8.80881 | −0.656570 | ||||||||
\(181\) | −12.3174 | −0.915547 | −0.457774 | − | 0.889069i | \(-0.651353\pi\) | ||||
−0.457774 | + | 0.889069i | \(0.651353\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.3042 | −0.761712 | ||||||||
\(184\) | 24.0679 | 1.77431 | ||||||||
\(185\) | −16.1606 | −1.18815 | ||||||||
\(186\) | 1.91629 | 0.140509 | ||||||||
\(187\) | −24.5760 | −1.79717 | ||||||||
\(188\) | −3.33705 | −0.243380 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 27.5678 | 1.99998 | ||||||||
\(191\) | 12.5939 | 0.911263 | 0.455632 | − | 0.890168i | \(-0.349413\pi\) | ||||
0.455632 | + | 0.890168i | \(0.349413\pi\) | |||||||
\(192\) | 0.478424 | 0.0345273 | ||||||||
\(193\) | 10.3925 | 0.748068 | 0.374034 | − | 0.927415i | \(-0.377974\pi\) | ||||
0.374034 | + | 0.927415i | \(0.377974\pi\) | |||||||
\(194\) | 28.2281 | 2.02666 | ||||||||
\(195\) | 9.13614 | 0.654252 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.06825 | −0.147357 | −0.0736785 | − | 0.997282i | \(-0.523474\pi\) | ||||
−0.0736785 | + | 0.997282i | \(0.523474\pi\) | |||||||
\(198\) | −14.4504 | −1.02695 | ||||||||
\(199\) | 1.70462 | 0.120837 | 0.0604187 | − | 0.998173i | \(-0.480756\pi\) | ||||
0.0604187 | + | 0.998173i | \(0.480756\pi\) | |||||||
\(200\) | 7.68946 | 0.543727 | ||||||||
\(201\) | 13.7621 | 0.970705 | ||||||||
\(202\) | 15.1729 | 1.06756 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −19.6106 | −1.37302 | ||||||||
\(205\) | 1.95019 | 0.136207 | ||||||||
\(206\) | 24.0676 | 1.67687 | ||||||||
\(207\) | −3.74585 | −0.260355 | ||||||||
\(208\) | −34.5200 | −2.39353 | ||||||||
\(209\) | 31.3447 | 2.16816 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.6714 | −0.941176 | −0.470588 | − | 0.882353i | \(-0.655958\pi\) | ||||
−0.470588 | + | 0.882353i | \(0.655958\pi\) | |||||||
\(212\) | −61.4183 | −4.21822 | ||||||||
\(213\) | −15.8518 | −1.08615 | ||||||||
\(214\) | 12.5196 | 0.855821 | ||||||||
\(215\) | −11.9542 | −0.815268 | ||||||||
\(216\) | −6.42520 | −0.437180 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −18.1403 | −1.22862 | ||||||||
\(219\) | 9.26794 | 0.626270 | ||||||||
\(220\) | −49.8628 | −3.36175 | ||||||||
\(221\) | 20.3394 | 1.36817 | ||||||||
\(222\) | −21.1544 | −1.41979 | ||||||||
\(223\) | −16.0359 | −1.07384 | −0.536921 | − | 0.843633i | \(-0.680413\pi\) | ||||
−0.536921 | + | 0.843633i | \(0.680413\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.19677 | −0.0797844 | ||||||||
\(226\) | −42.2572 | −2.81091 | ||||||||
\(227\) | 4.13224 | 0.274266 | 0.137133 | − | 0.990553i | \(-0.456211\pi\) | ||||
0.137133 | + | 0.990553i | \(0.456211\pi\) | |||||||
\(228\) | 25.0119 | 1.65645 | ||||||||
\(229\) | 21.4431 | 1.41700 | 0.708499 | − | 0.705711i | \(-0.249372\pi\) | ||||
0.708499 | + | 0.705711i | \(0.249372\pi\) | |||||||
\(230\) | −18.6487 | −1.22966 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.14001 | 0.0748452 | ||||||||
\(233\) | −24.1939 | −1.58500 | −0.792498 | − | 0.609874i | \(-0.791220\pi\) | ||||
−0.792498 | + | 0.609874i | \(0.791220\pi\) | |||||||
\(234\) | 11.9593 | 0.781806 | ||||||||
\(235\) | 1.44078 | 0.0939864 | ||||||||
\(236\) | 21.8533 | 1.42253 | ||||||||
\(237\) | 8.55260 | 0.555551 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.87757 | −0.638927 | −0.319463 | − | 0.947599i | \(-0.603503\pi\) | ||||
−0.319463 | + | 0.947599i | \(0.603503\pi\) | |||||||
\(240\) | −14.3701 | −0.927589 | ||||||||
\(241\) | −12.3991 | −0.798694 | −0.399347 | − | 0.916800i | \(-0.630763\pi\) | ||||
−0.399347 | + | 0.916800i | \(0.630763\pi\) | |||||||
\(242\) | −53.7163 | −3.45302 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −46.5433 | −2.97963 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.55282 | 0.162762 | ||||||||
\(247\) | −25.9413 | −1.65060 | ||||||||
\(248\) | 4.82311 | 0.306268 | ||||||||
\(249\) | −10.1927 | −0.645939 | ||||||||
\(250\) | −30.8505 | −1.95116 | ||||||||
\(251\) | 16.8450 | 1.06324 | 0.531622 | − | 0.846981i | \(-0.321583\pi\) | ||||
0.531622 | + | 0.846981i | \(0.321583\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.2036 | −1.33306 | ||||||||
\(254\) | 12.6856 | 0.795966 | ||||||||
\(255\) | 8.46696 | 0.530222 | ||||||||
\(256\) | −28.2702 | −1.76689 | ||||||||
\(257\) | −19.3000 | −1.20390 | −0.601950 | − | 0.798533i | \(-0.705610\pi\) | ||||
−0.601950 | + | 0.798533i | \(0.705610\pi\) | |||||||
\(258\) | −15.6482 | −0.974213 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 41.2670 | 2.55927 | ||||||||
\(261\) | −0.177428 | −0.0109825 | ||||||||
\(262\) | −39.0618 | −2.41325 | ||||||||
\(263\) | −15.4752 | −0.954242 | −0.477121 | − | 0.878838i | \(-0.658320\pi\) | ||||
−0.477121 | + | 0.878838i | \(0.658320\pi\) | |||||||
\(264\) | −36.3702 | −2.23843 | ||||||||
\(265\) | 26.5176 | 1.62896 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.24247 | −0.382033 | ||||||||
\(268\) | 62.1621 | 3.79716 | ||||||||
\(269\) | 26.1638 | 1.59524 | 0.797618 | − | 0.603163i | \(-0.206093\pi\) | ||||
0.797618 | + | 0.603163i | \(0.206093\pi\) | |||||||
\(270\) | 4.97848 | 0.302981 | ||||||||
\(271\) | −2.15147 | −0.130692 | −0.0653461 | − | 0.997863i | \(-0.520815\pi\) | ||||
−0.0653461 | + | 0.997863i | \(0.520815\pi\) | |||||||
\(272\) | −31.9916 | −1.93977 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 28.9610 | 1.74960 | ||||||||
\(275\) | −6.77437 | −0.408510 | ||||||||
\(276\) | −16.9197 | −1.01844 | ||||||||
\(277\) | −13.6100 | −0.817744 | −0.408872 | − | 0.912592i | \(-0.634078\pi\) | ||||
−0.408872 | + | 0.912592i | \(0.634078\pi\) | |||||||
\(278\) | −0.514736 | −0.0308718 | ||||||||
\(279\) | −0.750655 | −0.0449406 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.40118 | 0.501172 | 0.250586 | − | 0.968094i | \(-0.419377\pi\) | ||||
0.250586 | + | 0.968094i | \(0.419377\pi\) | |||||||
\(282\) | 1.88601 | 0.112310 | ||||||||
\(283\) | 26.5602 | 1.57884 | 0.789421 | − | 0.613853i | \(-0.210381\pi\) | ||||
0.789421 | + | 0.613853i | \(0.210381\pi\) | |||||||
\(284\) | −71.6009 | −4.24873 | ||||||||
\(285\) | −10.7990 | −0.639675 | ||||||||
\(286\) | 67.6965 | 4.00298 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.96031 | −0.351215 | ||||||||
\(289\) | 1.84959 | 0.108800 | ||||||||
\(290\) | −0.883320 | −0.0518703 | ||||||||
\(291\) | −11.0576 | −0.648208 | ||||||||
\(292\) | 41.8624 | 2.44981 | ||||||||
\(293\) | −15.7692 | −0.921249 | −0.460624 | − | 0.887595i | \(-0.652374\pi\) | ||||
−0.460624 | + | 0.887595i | \(0.652374\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.43525 | −0.549342 | ||||||||
\(296\) | −53.2435 | −3.09472 | ||||||||
\(297\) | 5.66056 | 0.328459 | ||||||||
\(298\) | 6.97360 | 0.403970 | ||||||||
\(299\) | 17.5484 | 1.01485 | ||||||||
\(300\) | −5.40567 | −0.312097 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 24.4423 | 1.40650 | ||||||||
\(303\) | −5.94360 | −0.341451 | ||||||||
\(304\) | 40.8028 | 2.34020 | ||||||||
\(305\) | 20.0952 | 1.15065 | ||||||||
\(306\) | 11.0834 | 0.633594 | ||||||||
\(307\) | −16.4452 | −0.938577 | −0.469288 | − | 0.883045i | \(-0.655490\pi\) | ||||
−0.469288 | + | 0.883045i | \(0.655490\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.42784 | −0.536331 | ||||||||
\(310\) | −3.73713 | −0.212254 | ||||||||
\(311\) | −27.3350 | −1.55003 | −0.775013 | − | 0.631945i | \(-0.782257\pi\) | ||||
−0.775013 | + | 0.631945i | \(0.782257\pi\) | |||||||
\(312\) | 30.1004 | 1.70410 | ||||||||
\(313\) | 13.6155 | 0.769591 | 0.384795 | − | 0.923002i | \(-0.374272\pi\) | ||||
0.384795 | + | 0.923002i | \(0.374272\pi\) | |||||||
\(314\) | 24.4091 | 1.37749 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 38.6312 | 2.17318 | ||||||||
\(317\) | 19.2420 | 1.08074 | 0.540370 | − | 0.841427i | \(-0.318284\pi\) | ||||
0.540370 | + | 0.841427i | \(0.318284\pi\) | |||||||
\(318\) | 34.7118 | 1.94654 | ||||||||
\(319\) | −1.00434 | −0.0562322 | ||||||||
\(320\) | −0.933016 | −0.0521572 | ||||||||
\(321\) | −4.90421 | −0.273727 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.0412 | −1.33769 | ||||||||
\(324\) | 4.51690 | 0.250939 | ||||||||
\(325\) | 5.60655 | 0.310995 | ||||||||
\(326\) | −9.24948 | −0.512282 | ||||||||
\(327\) | 7.10598 | 0.392961 | ||||||||
\(328\) | 6.42520 | 0.354772 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 28.1810 | 1.55131 | ||||||||
\(331\) | −24.5569 | −1.34977 | −0.674884 | − | 0.737924i | \(-0.735806\pi\) | ||||
−0.674884 | + | 0.737924i | \(0.735806\pi\) | |||||||
\(332\) | −46.0396 | −2.52675 | ||||||||
\(333\) | 8.28667 | 0.454107 | ||||||||
\(334\) | 17.9109 | 0.980041 | ||||||||
\(335\) | −26.8387 | −1.46636 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.52040 | 0.137295 | 0.0686474 | − | 0.997641i | \(-0.478132\pi\) | ||||
0.0686474 | + | 0.997641i | \(0.478132\pi\) | |||||||
\(338\) | −22.8397 | −1.24232 | ||||||||
\(339\) | 16.5531 | 0.899043 | ||||||||
\(340\) | 38.2444 | 2.07410 | ||||||||
\(341\) | −4.24913 | −0.230103 | ||||||||
\(342\) | −14.1360 | −0.764386 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −39.3849 | −2.12349 | ||||||||
\(345\) | 7.30512 | 0.393294 | ||||||||
\(346\) | 36.5798 | 1.96654 | ||||||||
\(347\) | −4.19148 | −0.225010 | −0.112505 | − | 0.993651i | \(-0.535888\pi\) | ||||
−0.112505 | + | 0.993651i | \(0.535888\pi\) | |||||||
\(348\) | −0.801423 | −0.0429608 | ||||||||
\(349\) | 24.1274 | 1.29151 | 0.645756 | − | 0.763544i | \(-0.276542\pi\) | ||||
0.645756 | + | 0.763544i | \(0.276542\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.68475 | −0.250053 | ||||||||
\(352\) | −33.7387 | −1.79828 | ||||||||
\(353\) | 10.5251 | 0.560196 | 0.280098 | − | 0.959971i | \(-0.409633\pi\) | ||||
0.280098 | + | 0.959971i | \(0.409633\pi\) | |||||||
\(354\) | −12.3509 | −0.656441 | ||||||||
\(355\) | 30.9139 | 1.64074 | ||||||||
\(356\) | −28.1966 | −1.49442 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.1907 | −0.697152 | ||||||||
\(359\) | 2.78928 | 0.147213 | 0.0736064 | − | 0.997287i | \(-0.476549\pi\) | ||||
0.0736064 | + | 0.997287i | \(0.476549\pi\) | |||||||
\(360\) | 12.5304 | 0.660408 | ||||||||
\(361\) | 11.6627 | 0.613828 | ||||||||
\(362\) | 31.4442 | 1.65267 | ||||||||
\(363\) | 21.0419 | 1.10442 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.0742 | −0.946049 | ||||||||
\(366\) | 26.3049 | 1.37498 | ||||||||
\(367\) | 1.55422 | 0.0811298 | 0.0405649 | − | 0.999177i | \(-0.487084\pi\) | ||||
0.0405649 | + | 0.999177i | \(0.487084\pi\) | |||||||
\(368\) | −27.6017 | −1.43884 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | 41.2551 | 2.14475 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.39064 | −0.175796 | ||||||||
\(373\) | 18.7337 | 0.969992 | 0.484996 | − | 0.874516i | \(-0.338821\pi\) | ||||
0.484996 | + | 0.874516i | \(0.338821\pi\) | |||||||
\(374\) | 62.7380 | 3.24411 | ||||||||
\(375\) | 12.0849 | 0.624059 | ||||||||
\(376\) | 4.74689 | 0.244802 | ||||||||
\(377\) | 0.831203 | 0.0428091 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.75137 | −0.398161 | −0.199081 | − | 0.979983i | \(-0.563796\pi\) | ||||
−0.199081 | + | 0.979983i | \(0.563796\pi\) | |||||||
\(380\) | −48.7778 | −2.50225 | ||||||||
\(381\) | −4.96925 | −0.254582 | ||||||||
\(382\) | −32.1500 | −1.64494 | ||||||||
\(383\) | 6.64806 | 0.339700 | 0.169850 | − | 0.985470i | \(-0.445672\pi\) | ||||
0.169850 | + | 0.985470i | \(0.445672\pi\) | |||||||
\(384\) | 10.6993 | 0.545996 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.5302 | −1.35035 | ||||||||
\(387\) | 6.12975 | 0.311593 | ||||||||
\(388\) | −49.9461 | −2.53563 | ||||||||
\(389\) | 17.4068 | 0.882561 | 0.441280 | − | 0.897369i | \(-0.354524\pi\) | ||||
0.441280 | + | 0.897369i | \(0.354524\pi\) | |||||||
\(390\) | −23.3229 | −1.18100 | ||||||||
\(391\) | 16.2630 | 0.822457 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.3014 | 0.771855 | ||||||||
\(394\) | 5.27988 | 0.265997 | ||||||||
\(395\) | −16.6792 | −0.839220 | ||||||||
\(396\) | 25.5682 | 1.28485 | ||||||||
\(397\) | −13.3867 | −0.671860 | −0.335930 | − | 0.941887i | \(-0.609050\pi\) | ||||
−0.335930 | + | 0.941887i | \(0.609050\pi\) | |||||||
\(398\) | −4.35160 | −0.218126 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.81849 | −0.440924 | ||||||||
\(401\) | 36.5410 | 1.82477 | 0.912385 | − | 0.409334i | \(-0.134239\pi\) | ||||
0.912385 | + | 0.409334i | \(0.134239\pi\) | |||||||
\(402\) | −35.1322 | −1.75224 | ||||||||
\(403\) | 3.51663 | 0.175176 | ||||||||
\(404\) | −26.8466 | −1.33567 | ||||||||
\(405\) | −1.95019 | −0.0969056 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 46.9072 | 2.32510 | ||||||||
\(408\) | 27.8957 | 1.38104 | ||||||||
\(409\) | −2.65442 | −0.131252 | −0.0656262 | − | 0.997844i | \(-0.520904\pi\) | ||||
−0.0656262 | + | 0.997844i | \(0.520904\pi\) | |||||||
\(410\) | −4.97848 | −0.245870 | ||||||||
\(411\) | −11.3447 | −0.559592 | ||||||||
\(412\) | −42.5846 | −2.09799 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 9.56250 | 0.469971 | ||||||||
\(415\) | 19.8778 | 0.975761 | ||||||||
\(416\) | 27.9226 | 1.36902 | ||||||||
\(417\) | 0.201634 | 0.00987407 | ||||||||
\(418\) | −80.0176 | −3.91379 | ||||||||
\(419\) | −0.446259 | −0.0218012 | −0.0109006 | − | 0.999941i | \(-0.503470\pi\) | ||||
−0.0109006 | + | 0.999941i | \(0.503470\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.6932 | −0.521154 | −0.260577 | − | 0.965453i | \(-0.583913\pi\) | ||||
−0.260577 | + | 0.965453i | \(0.583913\pi\) | |||||||
\(422\) | 34.9006 | 1.69893 | ||||||||
\(423\) | −0.738793 | −0.0359213 | ||||||||
\(424\) | 87.3663 | 4.24288 | ||||||||
\(425\) | 5.19589 | 0.252038 | ||||||||
\(426\) | 40.4667 | 1.96062 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −22.1519 | −1.07075 | ||||||||
\(429\) | −26.5183 | −1.28032 | ||||||||
\(430\) | 30.5169 | 1.47165 | ||||||||
\(431\) | −21.0322 | −1.01308 | −0.506542 | − | 0.862215i | \(-0.669077\pi\) | ||||
−0.506542 | + | 0.862215i | \(0.669077\pi\) | |||||||
\(432\) | 7.36860 | 0.354522 | ||||||||
\(433\) | −29.5953 | −1.42226 | −0.711131 | − | 0.703060i | \(-0.751817\pi\) | ||||
−0.711131 | + | 0.703060i | \(0.751817\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.346017 | 0.0165902 | ||||||||
\(436\) | 32.0970 | 1.53717 | ||||||||
\(437\) | −20.7423 | −0.992237 | ||||||||
\(438\) | −23.6594 | −1.13049 | ||||||||
\(439\) | −28.4888 | −1.35970 | −0.679849 | − | 0.733352i | \(-0.737955\pi\) | ||||
−0.679849 | + | 0.733352i | \(0.737955\pi\) | |||||||
\(440\) | 70.9288 | 3.38140 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −51.9228 | −2.46971 | ||||||||
\(443\) | −25.4898 | −1.21106 | −0.605528 | − | 0.795824i | \(-0.707038\pi\) | ||||
−0.605528 | + | 0.795824i | \(0.707038\pi\) | |||||||
\(444\) | 37.4301 | 1.77635 | ||||||||
\(445\) | 12.1740 | 0.577102 | ||||||||
\(446\) | 40.9367 | 1.93841 | ||||||||
\(447\) | −2.73172 | −0.129206 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.8396 | −1.73857 | −0.869284 | − | 0.494313i | \(-0.835420\pi\) | ||||
−0.869284 | + | 0.494313i | \(0.835420\pi\) | |||||||
\(450\) | 3.05513 | 0.144020 | ||||||||
\(451\) | −5.66056 | −0.266545 | ||||||||
\(452\) | 74.7689 | 3.51683 | ||||||||
\(453\) | −9.57461 | −0.449855 | ||||||||
\(454\) | −10.5489 | −0.495083 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −35.5789 | −1.66613 | ||||||||
\(457\) | −1.99720 | −0.0934253 | −0.0467126 | − | 0.998908i | \(-0.514875\pi\) | ||||
−0.0467126 | + | 0.998908i | \(0.514875\pi\) | |||||||
\(458\) | −54.7404 | −2.55785 | ||||||||
\(459\) | −4.34161 | −0.202649 | ||||||||
\(460\) | 32.9965 | 1.53847 | ||||||||
\(461\) | 13.9093 | 0.647819 | 0.323909 | − | 0.946088i | \(-0.395003\pi\) | ||||
0.323909 | + | 0.946088i | \(0.395003\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.9009 | −1.71493 | −0.857464 | − | 0.514544i | \(-0.827961\pi\) | ||||
−0.857464 | + | 0.514544i | \(0.827961\pi\) | |||||||
\(464\) | −1.30739 | −0.0606941 | ||||||||
\(465\) | 1.46392 | 0.0678876 | ||||||||
\(466\) | 61.7628 | 2.86111 | ||||||||
\(467\) | 17.4145 | 0.805847 | 0.402924 | − | 0.915234i | \(-0.367994\pi\) | ||||
0.402924 | + | 0.915234i | \(0.367994\pi\) | |||||||
\(468\) | −21.1605 | −0.978146 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.67807 | −0.169657 | ||||||||
\(471\) | −9.56163 | −0.440577 | ||||||||
\(472\) | −31.0859 | −1.43085 | ||||||||
\(473\) | 34.6978 | 1.59541 | ||||||||
\(474\) | −21.8333 | −1.00283 | ||||||||
\(475\) | −6.62697 | −0.304066 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.5974 | −0.622584 | ||||||||
\(478\) | 25.2157 | 1.15334 | ||||||||
\(479\) | 13.7314 | 0.627403 | 0.313702 | − | 0.949522i | \(-0.398431\pi\) | ||||
0.313702 | + | 0.949522i | \(0.398431\pi\) | |||||||
\(480\) | 11.6237 | 0.530548 | ||||||||
\(481\) | −38.8210 | −1.77008 | ||||||||
\(482\) | 31.6526 | 1.44174 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 95.0444 | 4.32020 | ||||||||
\(485\) | 21.5644 | 0.979189 | ||||||||
\(486\) | −2.55282 | −0.115798 | ||||||||
\(487\) | −6.36380 | −0.288371 | −0.144186 | − | 0.989551i | \(-0.546056\pi\) | ||||
−0.144186 | + | 0.989551i | \(0.546056\pi\) | |||||||
\(488\) | 66.2069 | 2.99704 | ||||||||
\(489\) | 3.62324 | 0.163849 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.00639387 | −0.000288551 0 | −0.000144276 | − | 1.00000i | \(-0.500046\pi\) | ||||
−0.000144276 | 1.00000i | \(0.500046\pi\) | ||||||||
\(492\) | −4.51690 | −0.203638 | ||||||||
\(493\) | 0.770321 | 0.0346935 | ||||||||
\(494\) | 66.2235 | 2.97954 | ||||||||
\(495\) | −11.0392 | −0.496173 | ||||||||
\(496\) | −5.53128 | −0.248362 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 26.0203 | 1.16600 | ||||||||
\(499\) | −38.1651 | −1.70850 | −0.854252 | − | 0.519859i | \(-0.825984\pi\) | ||||
−0.854252 | + | 0.519859i | \(0.825984\pi\) | |||||||
\(500\) | 54.5861 | 2.44117 | ||||||||
\(501\) | −7.01612 | −0.313457 | ||||||||
\(502\) | −43.0022 | −1.91928 | ||||||||
\(503\) | −2.51350 | −0.112071 | −0.0560356 | − | 0.998429i | \(-0.517846\pi\) | ||||
−0.0560356 | + | 0.998429i | \(0.517846\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.5911 | 0.515799 | ||||||||
\(506\) | 54.1291 | 2.40633 | ||||||||
\(507\) | 8.94686 | 0.397344 | ||||||||
\(508\) | −22.4456 | −0.995863 | ||||||||
\(509\) | 12.5359 | 0.555643 | 0.277821 | − | 0.960633i | \(-0.410388\pi\) | ||||
0.277821 | + | 0.960633i | \(0.410388\pi\) | |||||||
\(510\) | −21.6146 | −0.957113 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 50.7703 | 2.24375 | ||||||||
\(513\) | 5.53739 | 0.244482 | ||||||||
\(514\) | 49.2695 | 2.17318 | ||||||||
\(515\) | 18.3861 | 0.810186 | ||||||||
\(516\) | 27.6875 | 1.21887 | ||||||||
\(517\) | −4.18198 | −0.183923 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.3292 | −0.628981 | ||||||||
\(520\) | −58.7015 | −2.57423 | ||||||||
\(521\) | −30.4047 | −1.33206 | −0.666028 | − | 0.745927i | \(-0.732007\pi\) | ||||
−0.666028 | + | 0.745927i | \(0.732007\pi\) | |||||||
\(522\) | 0.452941 | 0.0198247 | ||||||||
\(523\) | −33.7300 | −1.47491 | −0.737454 | − | 0.675397i | \(-0.763972\pi\) | ||||
−0.737454 | + | 0.675397i | \(0.763972\pi\) | |||||||
\(524\) | 69.1150 | 3.01930 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 39.5054 | 1.72252 | ||||||||
\(527\) | 3.25905 | 0.141967 | ||||||||
\(528\) | 41.7104 | 1.81521 | ||||||||
\(529\) | −8.96858 | −0.389938 | ||||||||
\(530\) | −67.6946 | −2.94047 | ||||||||
\(531\) | 4.83812 | 0.209957 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.68475 | 0.202919 | ||||||||
\(534\) | 15.9359 | 0.689614 | ||||||||
\(535\) | 9.56414 | 0.413494 | ||||||||
\(536\) | −88.4244 | −3.81935 | ||||||||
\(537\) | 5.16712 | 0.222978 | ||||||||
\(538\) | −66.7916 | −2.87959 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −8.80881 | −0.379071 | ||||||||
\(541\) | 15.4447 | 0.664020 | 0.332010 | − | 0.943276i | \(-0.392273\pi\) | ||||
0.332010 | + | 0.943276i | \(0.392273\pi\) | |||||||
\(542\) | 5.49231 | 0.235915 | ||||||||
\(543\) | −12.3174 | −0.528592 | ||||||||
\(544\) | 25.8774 | 1.10948 | ||||||||
\(545\) | −13.8580 | −0.593611 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.4856 | 1.21795 | 0.608977 | − | 0.793188i | \(-0.291580\pi\) | ||||
0.608977 | + | 0.793188i | \(0.291580\pi\) | |||||||
\(548\) | −51.2428 | −2.18898 | ||||||||
\(549\) | −10.3042 | −0.439775 | ||||||||
\(550\) | 17.2938 | 0.737408 | ||||||||
\(551\) | −0.982486 | −0.0418553 | ||||||||
\(552\) | 24.0679 | 1.02440 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 34.7439 | 1.47612 | ||||||||
\(555\) | −16.1606 | −0.685978 | ||||||||
\(556\) | 0.910762 | 0.0386249 | ||||||||
\(557\) | 20.6469 | 0.874838 | 0.437419 | − | 0.899258i | \(-0.355893\pi\) | ||||
0.437419 | + | 0.899258i | \(0.355893\pi\) | |||||||
\(558\) | 1.91629 | 0.0811230 | ||||||||
\(559\) | −28.7164 | −1.21457 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.5760 | −1.03760 | ||||||||
\(562\) | −21.4467 | −0.904675 | ||||||||
\(563\) | −8.58979 | −0.362017 | −0.181008 | − | 0.983482i | \(-0.557936\pi\) | ||||
−0.181008 | + | 0.983482i | \(0.557936\pi\) | |||||||
\(564\) | −3.33705 | −0.140515 | ||||||||
\(565\) | −32.2817 | −1.35810 | ||||||||
\(566\) | −67.8035 | −2.84999 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 101.851 | 4.27356 | ||||||||
\(569\) | 26.9090 | 1.12809 | 0.564043 | − | 0.825746i | \(-0.309245\pi\) | ||||
0.564043 | + | 0.825746i | \(0.309245\pi\) | |||||||
\(570\) | 27.5678 | 1.15469 | ||||||||
\(571\) | 9.87805 | 0.413384 | 0.206692 | − | 0.978406i | \(-0.433730\pi\) | ||||
0.206692 | + | 0.978406i | \(0.433730\pi\) | |||||||
\(572\) | −119.781 | −5.00827 | ||||||||
\(573\) | 12.5939 | 0.526118 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.48291 | 0.186950 | ||||||||
\(576\) | 0.478424 | 0.0199343 | ||||||||
\(577\) | −28.6511 | −1.19276 | −0.596380 | − | 0.802702i | \(-0.703395\pi\) | ||||
−0.596380 | + | 0.802702i | \(0.703395\pi\) | |||||||
\(578\) | −4.72168 | −0.196396 | ||||||||
\(579\) | 10.3925 | 0.431897 | ||||||||
\(580\) | 1.56293 | 0.0648969 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 28.2281 | 1.17009 | ||||||||
\(583\) | −76.9691 | −3.18773 | ||||||||
\(584\) | −59.5484 | −2.46413 | ||||||||
\(585\) | 9.13614 | 0.377733 | ||||||||
\(586\) | 40.2561 | 1.66296 | ||||||||
\(587\) | −45.8713 | −1.89331 | −0.946656 | − | 0.322246i | \(-0.895562\pi\) | ||||
−0.946656 | + | 0.322246i | \(0.895562\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.15667 | −0.171273 | ||||||||
\(590\) | 24.0865 | 0.991626 | ||||||||
\(591\) | −2.06825 | −0.0850766 | ||||||||
\(592\) | 61.0611 | 2.50960 | ||||||||
\(593\) | −20.0783 | −0.824516 | −0.412258 | − | 0.911067i | \(-0.635260\pi\) | ||||
−0.412258 | + | 0.911067i | \(0.635260\pi\) | |||||||
\(594\) | −14.4504 | −0.592907 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.3389 | −0.505422 | ||||||||
\(597\) | 1.70462 | 0.0697655 | ||||||||
\(598\) | −44.7979 | −1.83192 | ||||||||
\(599\) | −5.35572 | −0.218829 | −0.109414 | − | 0.993996i | \(-0.534898\pi\) | ||||
−0.109414 | + | 0.993996i | \(0.534898\pi\) | |||||||
\(600\) | 7.68946 | 0.313921 | ||||||||
\(601\) | −2.39952 | −0.0978785 | −0.0489393 | − | 0.998802i | \(-0.515584\pi\) | ||||
−0.0489393 | + | 0.998802i | \(0.515584\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.7621 | 0.560437 | ||||||||
\(604\) | −43.2476 | −1.75972 | ||||||||
\(605\) | −41.0357 | −1.66834 | ||||||||
\(606\) | 15.1729 | 0.616359 | ||||||||
\(607\) | −4.62908 | −0.187889 | −0.0939443 | − | 0.995577i | \(-0.529948\pi\) | ||||
−0.0939443 | + | 0.995577i | \(0.529948\pi\) | |||||||
\(608\) | −33.0046 | −1.33851 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −51.2995 | −2.07706 | ||||||||
\(611\) | 3.46106 | 0.140019 | ||||||||
\(612\) | −19.6106 | −0.792713 | ||||||||
\(613\) | 36.3740 | 1.46913 | 0.734567 | − | 0.678536i | \(-0.237385\pi\) | ||||
0.734567 | + | 0.678536i | \(0.237385\pi\) | |||||||
\(614\) | 41.9817 | 1.69424 | ||||||||
\(615\) | 1.95019 | 0.0786392 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.3982 | −1.02249 | −0.511247 | − | 0.859434i | \(-0.670816\pi\) | ||||
−0.511247 | + | 0.859434i | \(0.670816\pi\) | |||||||
\(618\) | 24.0676 | 0.968140 | ||||||||
\(619\) | −46.4558 | −1.86722 | −0.933609 | − | 0.358294i | \(-0.883359\pi\) | ||||
−0.933609 | + | 0.358294i | \(0.883359\pi\) | |||||||
\(620\) | 6.61238 | 0.265560 | ||||||||
\(621\) | −3.74585 | −0.150316 | ||||||||
\(622\) | 69.7814 | 2.79798 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −34.5200 | −1.38191 | ||||||||
\(625\) | −17.5839 | −0.703357 | ||||||||
\(626\) | −34.7578 | −1.38920 | ||||||||
\(627\) | 31.3447 | 1.25179 | ||||||||
\(628\) | −43.1889 | −1.72343 | ||||||||
\(629\) | −35.9775 | −1.43452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.1736 | 1.51967 | 0.759834 | − | 0.650118i | \(-0.225280\pi\) | ||||
0.759834 | + | 0.650118i | \(0.225280\pi\) | |||||||
\(632\) | −54.9522 | −2.18588 | ||||||||
\(633\) | −13.6714 | −0.543388 | ||||||||
\(634\) | −49.1215 | −1.95086 | ||||||||
\(635\) | 9.69098 | 0.384575 | ||||||||
\(636\) | −61.4183 | −2.43539 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.56390 | 0.101506 | ||||||||
\(639\) | −15.8518 | −0.627086 | ||||||||
\(640\) | −20.8656 | −0.824787 | ||||||||
\(641\) | −23.1486 | −0.914314 | −0.457157 | − | 0.889386i | \(-0.651132\pi\) | ||||
−0.457157 | + | 0.889386i | \(0.651132\pi\) | |||||||
\(642\) | 12.5196 | 0.494109 | ||||||||
\(643\) | −11.2230 | −0.442591 | −0.221296 | − | 0.975207i | \(-0.571029\pi\) | ||||
−0.221296 | + | 0.975207i | \(0.571029\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.9542 | −0.470695 | ||||||||
\(646\) | 61.3729 | 2.41469 | ||||||||
\(647\) | 12.6618 | 0.497787 | 0.248894 | − | 0.968531i | \(-0.419933\pi\) | ||||
0.248894 | + | 0.968531i | \(0.419933\pi\) | |||||||
\(648\) | −6.42520 | −0.252406 | ||||||||
\(649\) | 27.3865 | 1.07501 | ||||||||
\(650\) | −14.3125 | −0.561383 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.3658 | 0.640935 | ||||||||
\(653\) | 24.5628 | 0.961218 | 0.480609 | − | 0.876935i | \(-0.340416\pi\) | ||||
0.480609 | + | 0.876935i | \(0.340416\pi\) | |||||||
\(654\) | −18.1403 | −0.709342 | ||||||||
\(655\) | −29.8407 | −1.16597 | ||||||||
\(656\) | −7.36860 | −0.287695 | ||||||||
\(657\) | 9.26794 | 0.361577 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.2897 | −0.985147 | −0.492573 | − | 0.870271i | \(-0.663944\pi\) | ||||
−0.492573 | + | 0.870271i | \(0.663944\pi\) | |||||||
\(660\) | −49.8628 | −1.94091 | ||||||||
\(661\) | −14.9100 | −0.579932 | −0.289966 | − | 0.957037i | \(-0.593644\pi\) | ||||
−0.289966 | + | 0.957037i | \(0.593644\pi\) | |||||||
\(662\) | 62.6893 | 2.43649 | ||||||||
\(663\) | 20.3394 | 0.789915 | ||||||||
\(664\) | 65.4904 | 2.54152 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −21.1544 | −0.819716 | ||||||||
\(667\) | 0.664618 | 0.0257341 | ||||||||
\(668\) | −31.6911 | −1.22617 | ||||||||
\(669\) | −16.0359 | −0.619983 | ||||||||
\(670\) | 68.5145 | 2.64694 | ||||||||
\(671\) | −58.3278 | −2.25172 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.1061 | −1.00632 | −0.503158 | − | 0.864195i | \(-0.667829\pi\) | ||||
−0.503158 | + | 0.864195i | \(0.667829\pi\) | |||||||
\(674\) | −6.43413 | −0.247833 | ||||||||
\(675\) | −1.19677 | −0.0460635 | ||||||||
\(676\) | 40.4121 | 1.55431 | ||||||||
\(677\) | 29.9611 | 1.15150 | 0.575750 | − | 0.817626i | \(-0.304710\pi\) | ||||
0.575750 | + | 0.817626i | \(0.304710\pi\) | |||||||
\(678\) | −42.2572 | −1.62288 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −54.4019 | −2.08622 | ||||||||
\(681\) | 4.13224 | 0.158348 | ||||||||
\(682\) | 10.8473 | 0.415364 | ||||||||
\(683\) | 22.2547 | 0.851551 | 0.425776 | − | 0.904829i | \(-0.360001\pi\) | ||||
0.425776 | + | 0.904829i | \(0.360001\pi\) | |||||||
\(684\) | 25.0119 | 0.956352 | ||||||||
\(685\) | 22.1243 | 0.845325 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.4431 | 0.818105 | ||||||||
\(688\) | 45.1677 | 1.72200 | ||||||||
\(689\) | 63.7005 | 2.42680 | ||||||||
\(690\) | −18.6487 | −0.709943 | ||||||||
\(691\) | −25.3537 | −0.964500 | −0.482250 | − | 0.876034i | \(-0.660180\pi\) | ||||
−0.482250 | + | 0.876034i | \(0.660180\pi\) | |||||||
\(692\) | −64.7234 | −2.46042 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.7001 | 0.406170 | ||||||||
\(695\) | −0.393225 | −0.0149159 | ||||||||
\(696\) | 1.14001 | 0.0432119 | ||||||||
\(697\) | 4.34161 | 0.164450 | ||||||||
\(698\) | −61.5931 | −2.33133 | ||||||||
\(699\) | −24.1939 | −0.915098 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.2025 | 1.36735 | 0.683675 | − | 0.729787i | \(-0.260381\pi\) | ||||
0.683675 | + | 0.729787i | \(0.260381\pi\) | |||||||
\(702\) | 11.9593 | 0.451376 | ||||||||
\(703\) | 45.8866 | 1.73064 | ||||||||
\(704\) | 2.70815 | 0.102067 | ||||||||
\(705\) | 1.44078 | 0.0542631 | ||||||||
\(706\) | −26.8688 | −1.01122 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 21.8533 | 0.821298 | ||||||||
\(709\) | −45.5410 | −1.71033 | −0.855165 | − | 0.518356i | \(-0.826544\pi\) | ||||
−0.855165 | + | 0.518356i | \(0.826544\pi\) | |||||||
\(710\) | −78.9178 | −2.96173 | ||||||||
\(711\) | 8.55260 | 0.320747 | ||||||||
\(712\) | 40.1091 | 1.50315 | ||||||||
\(713\) | 2.81185 | 0.105304 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 51.7157 | 1.93406 | ||||||||
\(716\) | 23.3394 | 0.872233 | ||||||||
\(717\) | −9.87757 | −0.368884 | ||||||||
\(718\) | −7.12054 | −0.265736 | ||||||||
\(719\) | −42.9208 | −1.60067 | −0.800337 | − | 0.599550i | \(-0.795346\pi\) | ||||
−0.800337 | + | 0.599550i | \(0.795346\pi\) | |||||||
\(720\) | −14.3701 | −0.535544 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −29.7729 | −1.10803 | ||||||||
\(723\) | −12.3991 | −0.461126 | ||||||||
\(724\) | −55.6366 | −2.06772 | ||||||||
\(725\) | 0.212339 | 0.00788608 | ||||||||
\(726\) | −53.7163 | −1.99360 | ||||||||
\(727\) | −39.9954 | −1.48335 | −0.741673 | − | 0.670762i | \(-0.765967\pi\) | ||||
−0.741673 | + | 0.670762i | \(0.765967\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 46.1403 | 1.70773 | ||||||||
\(731\) | −26.6130 | −0.984318 | ||||||||
\(732\) | −46.5433 | −1.72029 | ||||||||
\(733\) | −9.46168 | −0.349475 | −0.174737 | − | 0.984615i | \(-0.555908\pi\) | ||||
−0.174737 | + | 0.984615i | \(0.555908\pi\) | |||||||
\(734\) | −3.96766 | −0.146449 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.3265 | 0.822964 | ||||||||
\(737\) | 77.9013 | 2.86953 | ||||||||
\(738\) | 2.55282 | 0.0939707 | ||||||||
\(739\) | 15.2622 | 0.561429 | 0.280714 | − | 0.959791i | \(-0.409429\pi\) | ||||
0.280714 | + | 0.959791i | \(0.409429\pi\) | |||||||
\(740\) | −72.9957 | −2.68338 | ||||||||
\(741\) | −25.9413 | −0.952977 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.0213 | −1.39487 | −0.697433 | − | 0.716650i | \(-0.745674\pi\) | ||||
−0.697433 | + | 0.716650i | \(0.745674\pi\) | |||||||
\(744\) | 4.82311 | 0.176824 | ||||||||
\(745\) | 5.32737 | 0.195180 | ||||||||
\(746\) | −47.8237 | −1.75095 | ||||||||
\(747\) | −10.1927 | −0.372933 | ||||||||
\(748\) | −111.007 | −4.05882 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −30.8505 | −1.12650 | ||||||||
\(751\) | −12.7453 | −0.465082 | −0.232541 | − | 0.972587i | \(-0.574704\pi\) | ||||
−0.232541 | + | 0.972587i | \(0.574704\pi\) | |||||||
\(752\) | −5.44386 | −0.198517 | ||||||||
\(753\) | 16.8450 | 0.613865 | ||||||||
\(754\) | −2.12191 | −0.0772755 | ||||||||
\(755\) | 18.6723 | 0.679554 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.3160 | −1.35627 | −0.678137 | − | 0.734936i | \(-0.737212\pi\) | ||||
−0.678137 | + | 0.734936i | \(0.737212\pi\) | |||||||
\(758\) | 19.7879 | 0.718728 | ||||||||
\(759\) | −21.2036 | −0.769643 | ||||||||
\(760\) | 69.3855 | 2.51688 | ||||||||
\(761\) | 25.7820 | 0.934596 | 0.467298 | − | 0.884100i | \(-0.345227\pi\) | ||||
0.467298 | + | 0.884100i | \(0.345227\pi\) | |||||||
\(762\) | 12.6856 | 0.459551 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 56.8854 | 2.05804 | ||||||||
\(765\) | 8.46696 | 0.306124 | ||||||||
\(766\) | −16.9713 | −0.613199 | ||||||||
\(767\) | −22.6654 | −0.818400 | ||||||||
\(768\) | −28.2702 | −1.02011 | ||||||||
\(769\) | −49.9035 | −1.79957 | −0.899783 | − | 0.436337i | \(-0.856275\pi\) | ||||
−0.899783 | + | 0.436337i | \(0.856275\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.3000 | −0.695072 | ||||||||
\(772\) | 46.9418 | 1.68947 | ||||||||
\(773\) | 20.0169 | 0.719957 | 0.359978 | − | 0.932961i | \(-0.382784\pi\) | ||||
0.359978 | + | 0.932961i | \(0.382784\pi\) | |||||||
\(774\) | −15.6482 | −0.562462 | ||||||||
\(775\) | 0.898359 | 0.0322700 | ||||||||
\(776\) | 71.0473 | 2.55045 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −44.4365 | −1.59313 | ||||||||
\(779\) | −5.53739 | −0.198398 | ||||||||
\(780\) | 41.2670 | 1.47760 | ||||||||
\(781\) | −89.7299 | −3.21079 | ||||||||
\(782\) | −41.5167 | −1.48463 | ||||||||
\(783\) | −0.177428 | −0.00634074 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.6470 | 0.665539 | ||||||||
\(786\) | −39.0618 | −1.39329 | ||||||||
\(787\) | 0.551603 | 0.0196625 | 0.00983127 | − | 0.999952i | \(-0.496871\pi\) | ||||
0.00983127 | + | 0.999952i | \(0.496871\pi\) | |||||||
\(788\) | −9.34210 | −0.332798 | ||||||||
\(789\) | −15.4752 | −0.550932 | ||||||||
\(790\) | 42.5790 | 1.51489 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −36.3702 | −1.29236 | ||||||||
\(793\) | 48.2728 | 1.71422 | ||||||||
\(794\) | 34.1739 | 1.21279 | ||||||||
\(795\) | 26.5176 | 0.940481 | ||||||||
\(796\) | 7.69961 | 0.272905 | ||||||||
\(797\) | 10.0903 | 0.357416 | 0.178708 | − | 0.983902i | \(-0.442808\pi\) | ||||
0.178708 | + | 0.983902i | \(0.442808\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.20755 | 0.113475 | ||||||||
\(800\) | 7.13310 | 0.252193 | ||||||||
\(801\) | −6.24247 | −0.220567 | ||||||||
\(802\) | −93.2826 | −3.29392 | ||||||||
\(803\) | 52.4617 | 1.85133 | ||||||||
\(804\) | 62.1621 | 2.19229 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.97733 | −0.316213 | ||||||||
\(807\) | 26.1638 | 0.921010 | ||||||||
\(808\) | 38.1888 | 1.34348 | ||||||||
\(809\) | −26.6690 | −0.937632 | −0.468816 | − | 0.883296i | \(-0.655319\pi\) | ||||
−0.468816 | + | 0.883296i | \(0.655319\pi\) | |||||||
\(810\) | 4.97848 | 0.174926 | ||||||||
\(811\) | 9.19171 | 0.322764 | 0.161382 | − | 0.986892i | \(-0.448405\pi\) | ||||
0.161382 | + | 0.986892i | \(0.448405\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.15147 | −0.0754552 | ||||||||
\(814\) | −119.746 | −4.19709 | ||||||||
\(815\) | −7.06600 | −0.247511 | ||||||||
\(816\) | −31.9916 | −1.11993 | ||||||||
\(817\) | 33.9429 | 1.18751 | ||||||||
\(818\) | 6.77625 | 0.236926 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.80881 | 0.307617 | ||||||||
\(821\) | −26.5679 | −0.927225 | −0.463613 | − | 0.886038i | \(-0.653447\pi\) | ||||
−0.463613 | + | 0.886038i | \(0.653447\pi\) | |||||||
\(822\) | 28.9610 | 1.01013 | ||||||||
\(823\) | 16.3412 | 0.569618 | 0.284809 | − | 0.958584i | \(-0.408070\pi\) | ||||
0.284809 | + | 0.958584i | \(0.408070\pi\) | |||||||
\(824\) | 60.5757 | 2.11026 | ||||||||
\(825\) | −6.77437 | −0.235853 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.2489 | −0.912763 | −0.456382 | − | 0.889784i | \(-0.650855\pi\) | ||||
−0.456382 | + | 0.889784i | \(0.650855\pi\) | |||||||
\(828\) | −16.9197 | −0.587999 | ||||||||
\(829\) | −29.3109 | −1.01801 | −0.509004 | − | 0.860764i | \(-0.669986\pi\) | ||||
−0.509004 | + | 0.860764i | \(0.669986\pi\) | |||||||
\(830\) | −50.7444 | −1.76136 | ||||||||
\(831\) | −13.6100 | −0.472125 | ||||||||
\(832\) | −2.24129 | −0.0777029 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.514736 | −0.0178239 | ||||||||
\(835\) | 13.6827 | 0.473511 | ||||||||
\(836\) | 141.581 | 4.89669 | ||||||||
\(837\) | −0.750655 | −0.0259464 | ||||||||
\(838\) | 1.13922 | 0.0393537 | ||||||||
\(839\) | −19.9983 | −0.690418 | −0.345209 | − | 0.938526i | \(-0.612192\pi\) | ||||
−0.345209 | + | 0.938526i | \(0.612192\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9685 | −0.998914 | ||||||||
\(842\) | 27.2978 | 0.940745 | ||||||||
\(843\) | 8.40118 | 0.289352 | ||||||||
\(844\) | −61.7522 | −2.12560 | ||||||||
\(845\) | −17.4481 | −0.600231 | ||||||||
\(846\) | 1.88601 | 0.0648422 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −100.194 | −3.44068 | ||||||||
\(849\) | 26.5602 | 0.911544 | ||||||||
\(850\) | −13.2642 | −0.454958 | ||||||||
\(851\) | −31.0407 | −1.06406 | ||||||||
\(852\) | −71.6009 | −2.45301 | ||||||||
\(853\) | 38.0278 | 1.30205 | 0.651024 | − | 0.759057i | \(-0.274340\pi\) | ||||
0.651024 | + | 0.759057i | \(0.274340\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.7990 | −0.369317 | ||||||||
\(856\) | 31.5106 | 1.07701 | ||||||||
\(857\) | −44.7944 | −1.53015 | −0.765074 | − | 0.643943i | \(-0.777297\pi\) | ||||
−0.765074 | + | 0.643943i | \(0.777297\pi\) | |||||||
\(858\) | 67.6965 | 2.31112 | ||||||||
\(859\) | 48.2166 | 1.64513 | 0.822564 | − | 0.568672i | \(-0.192543\pi\) | ||||
0.822564 | + | 0.568672i | \(0.192543\pi\) | |||||||
\(860\) | −53.9958 | −1.84124 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 53.6914 | 1.82874 | ||||||||
\(863\) | −34.7794 | −1.18391 | −0.591953 | − | 0.805973i | \(-0.701643\pi\) | ||||
−0.591953 | + | 0.805973i | \(0.701643\pi\) | |||||||
\(864\) | −5.96031 | −0.202774 | ||||||||
\(865\) | 27.9446 | 0.950144 | ||||||||
\(866\) | 75.5516 | 2.56735 | ||||||||
\(867\) | 1.84959 | 0.0628155 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 48.4125 | 1.64228 | ||||||||
\(870\) | −0.883320 | −0.0299474 | ||||||||
\(871\) | −64.4720 | −2.18455 | ||||||||
\(872\) | −45.6573 | −1.54615 | ||||||||
\(873\) | −11.0576 | −0.374243 | ||||||||
\(874\) | 52.9513 | 1.79111 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 41.8624 | 1.41440 | ||||||||
\(877\) | 35.4222 | 1.19612 | 0.598062 | − | 0.801450i | \(-0.295938\pi\) | ||||
0.598062 | + | 0.801450i | \(0.295938\pi\) | |||||||
\(878\) | 72.7269 | 2.45441 | ||||||||
\(879\) | −15.7692 | −0.531883 | ||||||||
\(880\) | −81.3431 | −2.74207 | ||||||||
\(881\) | −42.7231 | −1.43938 | −0.719689 | − | 0.694297i | \(-0.755715\pi\) | ||||
−0.719689 | + | 0.694297i | \(0.755715\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.6770 | 0.965057 | 0.482528 | − | 0.875880i | \(-0.339719\pi\) | ||||
0.482528 | + | 0.875880i | \(0.339719\pi\) | |||||||
\(884\) | 91.8709 | 3.08995 | ||||||||
\(885\) | −9.43525 | −0.317163 | ||||||||
\(886\) | 65.0709 | 2.18610 | ||||||||
\(887\) | −32.6181 | −1.09521 | −0.547604 | − | 0.836738i | \(-0.684460\pi\) | ||||
−0.547604 | + | 0.836738i | \(0.684460\pi\) | |||||||
\(888\) | −53.2435 | −1.78674 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −31.0780 | −1.04174 | ||||||||
\(891\) | 5.66056 | 0.189636 | ||||||||
\(892\) | −72.4325 | −2.42522 | ||||||||
\(893\) | −4.09099 | −0.136900 | ||||||||
\(894\) | 6.97360 | 0.233232 | ||||||||
\(895\) | −10.0769 | −0.336832 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.5484 | 0.585923 | ||||||||
\(898\) | 94.0450 | 3.13832 | ||||||||
\(899\) | 0.133187 | 0.00444203 | ||||||||
\(900\) | −5.40567 | −0.180189 | ||||||||
\(901\) | 59.0348 | 1.96673 | ||||||||
\(902\) | 14.4504 | 0.481146 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −106.357 | −3.53739 | ||||||||
\(905\) | 24.0213 | 0.798495 | ||||||||
\(906\) | 24.4423 | 0.812040 | ||||||||
\(907\) | 19.3298 | 0.641836 | 0.320918 | − | 0.947107i | \(-0.396009\pi\) | ||||
0.320918 | + | 0.947107i | \(0.396009\pi\) | |||||||
\(908\) | 18.6649 | 0.619417 | ||||||||
\(909\) | −5.94360 | −0.197137 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.54007 | −0.216682 | −0.108341 | − | 0.994114i | \(-0.534554\pi\) | ||||
−0.108341 | + | 0.994114i | \(0.534554\pi\) | |||||||
\(912\) | 40.8028 | 1.35112 | ||||||||
\(913\) | −57.6966 | −1.90948 | ||||||||
\(914\) | 5.09851 | 0.168644 | ||||||||
\(915\) | 20.0952 | 0.664328 | ||||||||
\(916\) | 96.8563 | 3.20022 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 11.0834 | 0.365805 | ||||||||
\(919\) | 6.00261 | 0.198008 | 0.0990039 | − | 0.995087i | \(-0.468434\pi\) | ||||
0.0990039 | + | 0.995087i | \(0.468434\pi\) | |||||||
\(920\) | −46.9369 | −1.54746 | ||||||||
\(921\) | −16.4452 | −0.541888 | ||||||||
\(922\) | −35.5079 | −1.16939 | ||||||||
\(923\) | 74.2615 | 2.44435 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.91721 | −0.326076 | ||||||||
\(926\) | 94.2013 | 3.09565 | ||||||||
\(927\) | −9.42784 | −0.309651 | ||||||||
\(928\) | 1.05752 | 0.0347149 | ||||||||
\(929\) | −1.82438 | −0.0598559 | −0.0299279 | − | 0.999552i | \(-0.509528\pi\) | ||||
−0.0299279 | + | 0.999552i | \(0.509528\pi\) | |||||||
\(930\) | −3.73713 | −0.122545 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −109.282 | −3.57964 | ||||||||
\(933\) | −27.3350 | −0.894908 | ||||||||
\(934\) | −44.4561 | −1.45465 | ||||||||
\(935\) | 47.9277 | 1.56740 | ||||||||
\(936\) | 30.1004 | 0.983864 | ||||||||
\(937\) | −9.00232 | −0.294093 | −0.147047 | − | 0.989130i | \(-0.546977\pi\) | ||||
−0.147047 | + | 0.989130i | \(0.546977\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.6155 | 0.444323 | ||||||||
\(940\) | 6.50788 | 0.212264 | ||||||||
\(941\) | 32.6025 | 1.06281 | 0.531405 | − | 0.847118i | \(-0.321664\pi\) | ||||
0.531405 | + | 0.847118i | \(0.321664\pi\) | |||||||
\(942\) | 24.4091 | 0.795293 | ||||||||
\(943\) | 3.74585 | 0.121982 | ||||||||
\(944\) | 35.6502 | 1.16031 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −88.5774 | −2.87990 | ||||||||
\(947\) | −50.3619 | −1.63654 | −0.818271 | − | 0.574833i | \(-0.805067\pi\) | ||||
−0.818271 | + | 0.574833i | \(0.805067\pi\) | |||||||
\(948\) | 38.6312 | 1.25468 | ||||||||
\(949\) | −43.4180 | −1.40941 | ||||||||
\(950\) | 16.9175 | 0.548875 | ||||||||
\(951\) | 19.2420 | 0.623966 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.18696 | 0.135629 | 0.0678145 | − | 0.997698i | \(-0.478397\pi\) | ||||
0.0678145 | + | 0.997698i | \(0.478397\pi\) | |||||||
\(954\) | 34.7118 | 1.12384 | ||||||||
\(955\) | −24.5605 | −0.794759 | ||||||||
\(956\) | −44.6160 | −1.44298 | ||||||||
\(957\) | −1.00434 | −0.0324657 | ||||||||
\(958\) | −35.0538 | −1.13254 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.933016 | −0.0301130 | ||||||||
\(961\) | −30.4365 | −0.981823 | ||||||||
\(962\) | 99.1030 | 3.19521 | ||||||||
\(963\) | −4.90421 | −0.158036 | ||||||||
\(964\) | −56.0053 | −1.80381 | ||||||||
\(965\) | −20.2673 | −0.652428 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.6993 | 0.826433 | 0.413216 | − | 0.910633i | \(-0.364405\pi\) | ||||
0.413216 | + | 0.910633i | \(0.364405\pi\) | |||||||
\(968\) | −135.199 | −4.34545 | ||||||||
\(969\) | −24.0412 | −0.772315 | ||||||||
\(970\) | −55.0501 | −1.76755 | ||||||||
\(971\) | 22.0085 | 0.706287 | 0.353143 | − | 0.935569i | \(-0.385113\pi\) | ||||
0.353143 | + | 0.935569i | \(0.385113\pi\) | |||||||
\(972\) | 4.51690 | 0.144880 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 16.2457 | 0.520544 | ||||||||
\(975\) | 5.60655 | 0.179553 | ||||||||
\(976\) | −75.9278 | −2.43039 | ||||||||
\(977\) | −23.2219 | −0.742935 | −0.371467 | − | 0.928446i | \(-0.621145\pi\) | ||||
−0.371467 | + | 0.928446i | \(0.621145\pi\) | |||||||
\(978\) | −9.24948 | −0.295766 | ||||||||
\(979\) | −35.3359 | −1.12934 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.10598 | 0.226876 | ||||||||
\(982\) | 0.0163224 | 0.000520869 0 | ||||||||
\(983\) | −24.3469 | −0.776545 | −0.388273 | − | 0.921545i | \(-0.626928\pi\) | ||||
−0.388273 | + | 0.921545i | \(0.626928\pi\) | |||||||
\(984\) | 6.42520 | 0.204828 | ||||||||
\(985\) | 4.03348 | 0.128517 | ||||||||
\(986\) | −1.96649 | −0.0626259 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −117.174 | −3.72781 | ||||||||
\(989\) | −22.9612 | −0.730122 | ||||||||
\(990\) | 28.1810 | 0.895651 | ||||||||
\(991\) | −6.13977 | −0.195036 | −0.0975181 | − | 0.995234i | \(-0.531090\pi\) | ||||
−0.0975181 | + | 0.995234i | \(0.531090\pi\) | |||||||
\(992\) | 4.47414 | 0.142054 | ||||||||
\(993\) | −24.5569 | −0.779289 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.32433 | −0.105388 | ||||||||
\(996\) | −46.0396 | −1.45882 | ||||||||
\(997\) | −43.0435 | −1.36320 | −0.681601 | − | 0.731724i | \(-0.738716\pi\) | ||||
−0.681601 | + | 0.731724i | \(0.738716\pi\) | |||||||
\(998\) | 97.4287 | 3.08405 | ||||||||
\(999\) | 8.28667 | 0.262179 |
(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 | 6027.2.a.bk.1.2 | 14 | ||
7.3 | odd | 6 | 861.2.i.g.247.13 | ✓ | 28 | ||
7.5 | odd | 6 | 861.2.i.g.739.13 | yes | 28 | ||
7.6 | odd | 2 | 6027.2.a.bj.1.2 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.g.247.13 | ✓ | 28 | 7.3 | odd | 6 | ||
861.2.i.g.739.13 | yes | 28 | 7.5 | odd | 6 | ||
6027.2.a.bj.1.2 | 14 | 7.6 | odd | 2 | |||
6027.2.a.bk.1.2 | 14 | 1.1 | even | 1 | trivial |