Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1617,2,Mod(1,1617)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1617, 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("1617.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1617 = 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1617.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: | \(12.9118100068\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 3x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.22833\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1617.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.22833 | −1.57567 | −0.787833 | − | 0.615889i | \(-0.788797\pi\) | ||||
−0.787833 | + | 0.615889i | \(0.788797\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.96545 | 1.48272 | ||||||||
\(5\) | 4.15133 | 1.85653 | 0.928266 | − | 0.371917i | \(-0.121299\pi\) | ||||
0.928266 | + | 0.371917i | \(0.121299\pi\) | |||||||
\(6\) | 2.22833 | 0.909711 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.15133 | −0.760611 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −9.25053 | −2.92527 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −2.96545 | −0.856051 | ||||||||
\(13\) | −2.93089 | −0.812884 | −0.406442 | − | 0.913677i | \(-0.633231\pi\) | ||||
−0.406442 | + | 0.913677i | \(0.633231\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.15133 | −1.07187 | ||||||||
\(16\) | −1.13702 | −0.284255 | ||||||||
\(17\) | 1.36535 | 0.331145 | 0.165573 | − | 0.986198i | \(-0.447053\pi\) | ||||
0.165573 | + | 0.986198i | \(0.447053\pi\) | |||||||
\(18\) | −2.22833 | −0.525222 | ||||||||
\(19\) | 4.10247 | 0.941170 | 0.470585 | − | 0.882355i | \(-0.344043\pi\) | ||||
0.470585 | + | 0.882355i | \(0.344043\pi\) | |||||||
\(20\) | 12.3106 | 2.75272 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.22833 | −0.475081 | ||||||||
\(23\) | 2.93732 | 0.612473 | 0.306236 | − | 0.951956i | \(-0.400930\pi\) | ||||
0.306236 | + | 0.951956i | \(0.400930\pi\) | |||||||
\(24\) | 2.15133 | 0.439139 | ||||||||
\(25\) | 12.2336 | 2.44671 | ||||||||
\(26\) | 6.53099 | 1.28083 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.97976 | −1.66750 | −0.833750 | − | 0.552143i | \(-0.813810\pi\) | ||||
−0.833750 | + | 0.552143i | \(0.813810\pi\) | |||||||
\(30\) | 9.25053 | 1.68891 | ||||||||
\(31\) | 4.10889 | 0.737978 | 0.368989 | − | 0.929434i | \(-0.379704\pi\) | ||||
0.368989 | + | 0.929434i | \(0.379704\pi\) | |||||||
\(32\) | 6.83632 | 1.20850 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −3.04244 | −0.521775 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.96545 | 0.494241 | ||||||||
\(37\) | 10.2160 | 1.67950 | 0.839748 | − | 0.542976i | \(-0.182703\pi\) | ||||
0.839748 | + | 0.542976i | \(0.182703\pi\) | |||||||
\(38\) | −9.14164 | −1.48297 | ||||||||
\(39\) | 2.93089 | 0.469319 | ||||||||
\(40\) | −8.93089 | −1.41210 | ||||||||
\(41\) | −6.60157 | −1.03099 | −0.515496 | − | 0.856892i | \(-0.672392\pi\) | ||||
−0.515496 | + | 0.856892i | \(0.672392\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.8644 | 1.65681 | 0.828406 | − | 0.560128i | \(-0.189248\pi\) | ||||
0.828406 | + | 0.560128i | \(0.189248\pi\) | |||||||
\(44\) | 2.96545 | 0.447058 | ||||||||
\(45\) | 4.15133 | 0.618844 | ||||||||
\(46\) | −6.54530 | −0.965053 | ||||||||
\(47\) | 6.22044 | 0.907344 | 0.453672 | − | 0.891169i | \(-0.350114\pi\) | ||||
0.453672 | + | 0.891169i | \(0.350114\pi\) | |||||||
\(48\) | 1.13702 | 0.164115 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −27.2604 | −3.85520 | ||||||||
\(51\) | −1.36535 | −0.191187 | ||||||||
\(52\) | −8.69141 | −1.20528 | ||||||||
\(53\) | −6.71954 | −0.923000 | −0.461500 | − | 0.887140i | \(-0.652688\pi\) | ||||
−0.461500 | + | 0.887140i | \(0.652688\pi\) | |||||||
\(54\) | 2.22833 | 0.303237 | ||||||||
\(55\) | 4.15133 | 0.559765 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.10247 | −0.543385 | ||||||||
\(58\) | 20.0099 | 2.62742 | ||||||||
\(59\) | −0.797142 | −0.103779 | −0.0518895 | − | 0.998653i | \(-0.516524\pi\) | ||||
−0.0518895 | + | 0.998653i | \(0.516524\pi\) | |||||||
\(60\) | −12.3106 | −1.58929 | ||||||||
\(61\) | −7.77690 | −0.995730 | −0.497865 | − | 0.867255i | \(-0.665883\pi\) | ||||
−0.497865 | + | 0.867255i | \(0.665883\pi\) | |||||||
\(62\) | −9.15595 | −1.16281 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.9595 | −1.61994 | ||||||||
\(65\) | −12.1671 | −1.50914 | ||||||||
\(66\) | 2.22833 | 0.274288 | ||||||||
\(67\) | −11.7751 | −1.43856 | −0.719279 | − | 0.694722i | \(-0.755528\pi\) | ||||
−0.719279 | + | 0.694722i | \(0.755528\pi\) | |||||||
\(68\) | 4.04887 | 0.490997 | ||||||||
\(69\) | −2.93732 | −0.353611 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.68825 | −0.675071 | −0.337536 | − | 0.941313i | \(-0.609593\pi\) | ||||
−0.337536 | + | 0.941313i | \(0.609593\pi\) | |||||||
\(72\) | −2.15133 | −0.253537 | ||||||||
\(73\) | 13.5702 | 1.58827 | 0.794134 | − | 0.607743i | \(-0.207925\pi\) | ||||
0.794134 | + | 0.607743i | \(0.207925\pi\) | |||||||
\(74\) | −22.7645 | −2.64633 | ||||||||
\(75\) | −12.2336 | −1.41261 | ||||||||
\(76\) | 12.1656 | 1.39550 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.53099 | −0.739489 | ||||||||
\(79\) | −4.38755 | −0.493638 | −0.246819 | − | 0.969062i | \(-0.579385\pi\) | ||||
−0.246819 | + | 0.969062i | \(0.579385\pi\) | |||||||
\(80\) | −4.72015 | −0.527728 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 14.7105 | 1.62450 | ||||||||
\(83\) | 6.01116 | 0.659810 | 0.329905 | − | 0.944014i | \(-0.392983\pi\) | ||||
0.329905 | + | 0.944014i | \(0.392983\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.66801 | 0.614782 | ||||||||
\(86\) | −24.2096 | −2.61058 | ||||||||
\(87\) | 8.97976 | 0.962731 | ||||||||
\(88\) | −2.15133 | −0.229333 | ||||||||
\(89\) | 1.32024 | 0.139946 | 0.0699728 | − | 0.997549i | \(-0.477709\pi\) | ||||
0.0699728 | + | 0.997549i | \(0.477709\pi\) | |||||||
\(90\) | −9.25053 | −0.975091 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.71045 | 0.908128 | ||||||||
\(93\) | −4.10889 | −0.426072 | ||||||||
\(94\) | −13.8612 | −1.42967 | ||||||||
\(95\) | 17.0307 | 1.74731 | ||||||||
\(96\) | −6.83632 | −0.697729 | ||||||||
\(97\) | 2.57463 | 0.261414 | 0.130707 | − | 0.991421i | \(-0.458275\pi\) | ||||
0.130707 | + | 0.991421i | \(0.458275\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 36.2780 | 3.62780 | ||||||||
\(101\) | −8.79910 | −0.875543 | −0.437772 | − | 0.899086i | \(-0.644232\pi\) | ||||
−0.437772 | + | 0.899086i | \(0.644232\pi\) | |||||||
\(102\) | 3.04244 | 0.301247 | ||||||||
\(103\) | 17.5840 | 1.73260 | 0.866301 | − | 0.499523i | \(-0.166491\pi\) | ||||
0.866301 | + | 0.499523i | \(0.166491\pi\) | |||||||
\(104\) | 6.30532 | 0.618288 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.9733 | 1.45434 | ||||||||
\(107\) | 4.97976 | 0.481411 | 0.240706 | − | 0.970598i | \(-0.422621\pi\) | ||||
0.240706 | + | 0.970598i | \(0.422621\pi\) | |||||||
\(108\) | −2.96545 | −0.285350 | ||||||||
\(109\) | −11.3249 | −1.08473 | −0.542363 | − | 0.840144i | \(-0.682470\pi\) | ||||
−0.542363 | + | 0.840144i | \(0.682470\pi\) | |||||||
\(110\) | −9.25053 | −0.882003 | ||||||||
\(111\) | −10.2160 | −0.969658 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.25842 | 0.588743 | 0.294371 | − | 0.955691i | \(-0.404890\pi\) | ||||
0.294371 | + | 0.955691i | \(0.404890\pi\) | |||||||
\(114\) | 9.14164 | 0.856193 | ||||||||
\(115\) | 12.1938 | 1.13708 | ||||||||
\(116\) | −26.6290 | −2.47244 | ||||||||
\(117\) | −2.93089 | −0.270961 | ||||||||
\(118\) | 1.77629 | 0.163521 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.93089 | 0.815275 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 17.3295 | 1.56894 | ||||||||
\(123\) | 6.60157 | 0.595243 | ||||||||
\(124\) | 12.1847 | 1.09422 | ||||||||
\(125\) | 30.0289 | 2.68587 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.04706 | −0.625326 | −0.312663 | − | 0.949864i | \(-0.601221\pi\) | ||||
−0.312663 | + | 0.949864i | \(0.601221\pi\) | |||||||
\(128\) | 15.2054 | 1.34398 | ||||||||
\(129\) | −10.8644 | −0.956561 | ||||||||
\(130\) | 27.1123 | 2.37791 | ||||||||
\(131\) | 10.6993 | 0.934802 | 0.467401 | − | 0.884045i | \(-0.345190\pi\) | ||||
0.467401 | + | 0.884045i | \(0.345190\pi\) | |||||||
\(132\) | −2.96545 | −0.258109 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 26.2388 | 2.26669 | ||||||||
\(135\) | −4.15133 | −0.357290 | ||||||||
\(136\) | −2.93732 | −0.251873 | ||||||||
\(137\) | −13.7306 | −1.17308 | −0.586541 | − | 0.809919i | \(-0.699511\pi\) | ||||
−0.586541 | + | 0.809919i | \(0.699511\pi\) | |||||||
\(138\) | 6.54530 | 0.557173 | ||||||||
\(139\) | 4.63927 | 0.393498 | 0.196749 | − | 0.980454i | \(-0.436962\pi\) | ||||
0.196749 | + | 0.980454i | \(0.436962\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.22044 | −0.523855 | ||||||||
\(142\) | 12.6753 | 1.06369 | ||||||||
\(143\) | −2.93089 | −0.245094 | ||||||||
\(144\) | −1.13702 | −0.0947516 | ||||||||
\(145\) | −37.2780 | −3.09577 | ||||||||
\(146\) | −30.2388 | −2.50258 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 30.2949 | 2.49023 | ||||||||
\(149\) | 2.32110 | 0.190152 | 0.0950761 | − | 0.995470i | \(-0.469691\pi\) | ||||
0.0950761 | + | 0.995470i | \(0.469691\pi\) | |||||||
\(150\) | 27.2604 | 2.22580 | ||||||||
\(151\) | 18.2435 | 1.48463 | 0.742317 | − | 0.670048i | \(-0.233727\pi\) | ||||
0.742317 | + | 0.670048i | \(0.233727\pi\) | |||||||
\(152\) | −8.82577 | −0.715864 | ||||||||
\(153\) | 1.36535 | 0.110382 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.0574 | 1.37008 | ||||||||
\(156\) | 8.69141 | 0.695870 | ||||||||
\(157\) | 24.1293 | 1.92573 | 0.962863 | − | 0.269989i | \(-0.0870200\pi\) | ||||
0.962863 | + | 0.269989i | \(0.0870200\pi\) | |||||||
\(158\) | 9.77690 | 0.777808 | ||||||||
\(159\) | 6.71954 | 0.532894 | ||||||||
\(160\) | 28.3798 | 2.24362 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.22833 | −0.175074 | ||||||||
\(163\) | −23.1240 | −1.81121 | −0.905605 | − | 0.424123i | \(-0.860582\pi\) | ||||
−0.905605 | + | 0.424123i | \(0.860582\pi\) | |||||||
\(164\) | −19.5766 | −1.52867 | ||||||||
\(165\) | −4.15133 | −0.323181 | ||||||||
\(166\) | −13.3948 | −1.03964 | ||||||||
\(167\) | 11.2453 | 0.870188 | 0.435094 | − | 0.900385i | \(-0.356715\pi\) | ||||
0.435094 | + | 0.900385i | \(0.356715\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.40986 | −0.339220 | ||||||||
\(170\) | −12.6302 | −0.968691 | ||||||||
\(171\) | 4.10247 | 0.313723 | ||||||||
\(172\) | 32.2179 | 2.45659 | ||||||||
\(173\) | −6.61065 | −0.502598 | −0.251299 | − | 0.967909i | \(-0.580858\pi\) | ||||
−0.251299 | + | 0.967909i | \(0.580858\pi\) | |||||||
\(174\) | −20.0099 | −1.51694 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.13702 | −0.0857061 | ||||||||
\(177\) | 0.797142 | 0.0599168 | ||||||||
\(178\) | −2.94194 | −0.220508 | ||||||||
\(179\) | 8.05725 | 0.602227 | 0.301114 | − | 0.953588i | \(-0.402642\pi\) | ||||
0.301114 | + | 0.953588i | \(0.402642\pi\) | |||||||
\(180\) | 12.3106 | 0.917574 | ||||||||
\(181\) | 7.48794 | 0.556574 | 0.278287 | − | 0.960498i | \(-0.410233\pi\) | ||||
0.278287 | + | 0.960498i | \(0.410233\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.77690 | 0.574885 | ||||||||
\(184\) | −6.31914 | −0.465853 | ||||||||
\(185\) | 42.4099 | 3.11804 | ||||||||
\(186\) | 9.15595 | 0.671347 | ||||||||
\(187\) | 1.36535 | 0.0998441 | ||||||||
\(188\) | 18.4464 | 1.34534 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −37.9500 | −2.75318 | ||||||||
\(191\) | 13.0184 | 0.941981 | 0.470991 | − | 0.882138i | \(-0.343897\pi\) | ||||
0.470991 | + | 0.882138i | \(0.343897\pi\) | |||||||
\(192\) | 12.9595 | 0.935273 | ||||||||
\(193\) | −9.32487 | −0.671219 | −0.335609 | − | 0.942001i | \(-0.608942\pi\) | ||||
−0.335609 | + | 0.942001i | \(0.608942\pi\) | |||||||
\(194\) | −5.73712 | −0.411901 | ||||||||
\(195\) | 12.1671 | 0.871305 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.6101 | −1.25466 | −0.627332 | − | 0.778752i | \(-0.715853\pi\) | ||||
−0.627332 | + | 0.778752i | \(0.715853\pi\) | |||||||
\(198\) | −2.22833 | −0.158360 | ||||||||
\(199\) | 13.8129 | 0.979172 | 0.489586 | − | 0.871955i | \(-0.337148\pi\) | ||||
0.489586 | + | 0.871955i | \(0.337148\pi\) | |||||||
\(200\) | −26.3184 | −1.86099 | ||||||||
\(201\) | 11.7751 | 0.830551 | ||||||||
\(202\) | 19.6073 | 1.37956 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.04887 | −0.283477 | ||||||||
\(205\) | −27.4053 | −1.91407 | ||||||||
\(206\) | −39.1829 | −2.73000 | ||||||||
\(207\) | 2.93732 | 0.204158 | ||||||||
\(208\) | 3.33248 | 0.231066 | ||||||||
\(209\) | 4.10247 | 0.283774 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0572 | 0.692370 | 0.346185 | − | 0.938166i | \(-0.387477\pi\) | ||||
0.346185 | + | 0.938166i | \(0.387477\pi\) | |||||||
\(212\) | −19.9264 | −1.36855 | ||||||||
\(213\) | 5.68825 | 0.389753 | ||||||||
\(214\) | −11.0965 | −0.758544 | ||||||||
\(215\) | 45.1019 | 3.07593 | ||||||||
\(216\) | 2.15133 | 0.146380 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 25.2355 | 1.70916 | ||||||||
\(219\) | −13.5702 | −0.916987 | ||||||||
\(220\) | 12.3106 | 0.829977 | ||||||||
\(221\) | −4.00169 | −0.269183 | ||||||||
\(222\) | 22.7645 | 1.52786 | ||||||||
\(223\) | 16.0924 | 1.07763 | 0.538814 | − | 0.842425i | \(-0.318873\pi\) | ||||
0.538814 | + | 0.842425i | \(0.318873\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.2336 | 0.815570 | ||||||||
\(226\) | −13.9458 | −0.927662 | ||||||||
\(227\) | −28.7384 | −1.90743 | −0.953717 | − | 0.300707i | \(-0.902777\pi\) | ||||
−0.953717 | + | 0.300707i | \(0.902777\pi\) | |||||||
\(228\) | −12.1656 | −0.805689 | ||||||||
\(229\) | 16.0960 | 1.06366 | 0.531828 | − | 0.846852i | \(-0.321505\pi\) | ||||
0.531828 | + | 0.846852i | \(0.321505\pi\) | |||||||
\(230\) | −27.1717 | −1.79165 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.3184 | 1.26832 | ||||||||
\(233\) | −11.5029 | −0.753578 | −0.376789 | − | 0.926299i | \(-0.622972\pi\) | ||||
−0.376789 | + | 0.926299i | \(0.622972\pi\) | |||||||
\(234\) | 6.53099 | 0.426944 | ||||||||
\(235\) | 25.8231 | 1.68451 | ||||||||
\(236\) | −2.36388 | −0.153876 | ||||||||
\(237\) | 4.38755 | 0.285002 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.00207 | 0.0648188 | 0.0324094 | − | 0.999475i | \(-0.489682\pi\) | ||||
0.0324094 | + | 0.999475i | \(0.489682\pi\) | |||||||
\(240\) | 4.72015 | 0.304684 | ||||||||
\(241\) | −2.84601 | −0.183327 | −0.0916637 | − | 0.995790i | \(-0.529218\pi\) | ||||
−0.0916637 | + | 0.995790i | \(0.529218\pi\) | |||||||
\(242\) | −2.22833 | −0.143242 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −23.0620 | −1.47639 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −14.7105 | −0.937904 | ||||||||
\(247\) | −12.0239 | −0.765062 | ||||||||
\(248\) | −8.83958 | −0.561314 | ||||||||
\(249\) | −6.01116 | −0.380942 | ||||||||
\(250\) | −66.9142 | −4.23203 | ||||||||
\(251\) | −15.0021 | −0.946923 | −0.473461 | − | 0.880815i | \(-0.656996\pi\) | ||||
−0.473461 | + | 0.880815i | \(0.656996\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.93732 | 0.184667 | ||||||||
\(254\) | 15.7032 | 0.985305 | ||||||||
\(255\) | −5.66801 | −0.354945 | ||||||||
\(256\) | −7.96365 | −0.497728 | ||||||||
\(257\) | 25.3193 | 1.57937 | 0.789687 | − | 0.613510i | \(-0.210243\pi\) | ||||
0.789687 | + | 0.613510i | \(0.210243\pi\) | |||||||
\(258\) | 24.2096 | 1.50722 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −36.0809 | −2.23764 | ||||||||
\(261\) | −8.97976 | −0.555833 | ||||||||
\(262\) | −23.8415 | −1.47294 | ||||||||
\(263\) | −19.9569 | −1.23059 | −0.615296 | − | 0.788296i | \(-0.710964\pi\) | ||||
−0.615296 | + | 0.788296i | \(0.710964\pi\) | |||||||
\(264\) | 2.15133 | 0.132405 | ||||||||
\(265\) | −27.8950 | −1.71358 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.32024 | −0.0807976 | ||||||||
\(268\) | −34.9184 | −2.13298 | ||||||||
\(269\) | −6.87283 | −0.419044 | −0.209522 | − | 0.977804i | \(-0.567191\pi\) | ||||
−0.209522 | + | 0.977804i | \(0.567191\pi\) | |||||||
\(270\) | 9.25053 | 0.562969 | ||||||||
\(271\) | 1.85606 | 0.112748 | 0.0563739 | − | 0.998410i | \(-0.482046\pi\) | ||||
0.0563739 | + | 0.998410i | \(0.482046\pi\) | |||||||
\(272\) | −1.55243 | −0.0941297 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 30.5962 | 1.84839 | ||||||||
\(275\) | 12.2336 | 0.737711 | ||||||||
\(276\) | −8.71045 | −0.524308 | ||||||||
\(277\) | 27.4458 | 1.64906 | 0.824528 | − | 0.565821i | \(-0.191441\pi\) | ||||
0.824528 | + | 0.565821i | \(0.191441\pi\) | |||||||
\(278\) | −10.3378 | −0.620022 | ||||||||
\(279\) | 4.10889 | 0.245993 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.6172 | 1.58785 | 0.793925 | − | 0.608015i | \(-0.208034\pi\) | ||||
0.793925 | + | 0.608015i | \(0.208034\pi\) | |||||||
\(282\) | 13.8612 | 0.825421 | ||||||||
\(283\) | −15.3524 | −0.912605 | −0.456302 | − | 0.889825i | \(-0.650826\pi\) | ||||
−0.456302 | + | 0.889825i | \(0.650826\pi\) | |||||||
\(284\) | −16.8682 | −1.00094 | ||||||||
\(285\) | −17.0307 | −1.00881 | ||||||||
\(286\) | 6.53099 | 0.386186 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.83632 | 0.402834 | ||||||||
\(289\) | −15.1358 | −0.890343 | ||||||||
\(290\) | 83.0675 | 4.87789 | ||||||||
\(291\) | −2.57463 | −0.150927 | ||||||||
\(292\) | 40.2416 | 2.35496 | ||||||||
\(293\) | 6.69021 | 0.390846 | 0.195423 | − | 0.980719i | \(-0.437392\pi\) | ||||
0.195423 | + | 0.980719i | \(0.437392\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.30920 | −0.192669 | ||||||||
\(296\) | −21.9780 | −1.27744 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −5.17218 | −0.299616 | ||||||||
\(299\) | −8.60896 | −0.497869 | ||||||||
\(300\) | −36.2780 | −2.09451 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −40.6525 | −2.33929 | ||||||||
\(303\) | 8.79910 | 0.505495 | ||||||||
\(304\) | −4.66458 | −0.267532 | ||||||||
\(305\) | −32.2845 | −1.84860 | ||||||||
\(306\) | −3.04244 | −0.173925 | ||||||||
\(307\) | 4.99820 | 0.285262 | 0.142631 | − | 0.989776i | \(-0.454444\pi\) | ||||
0.142631 | + | 0.989776i | \(0.454444\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.5840 | −1.00032 | ||||||||
\(310\) | −38.0094 | −2.15879 | ||||||||
\(311\) | −13.2851 | −0.753328 | −0.376664 | − | 0.926350i | \(-0.622929\pi\) | ||||
−0.376664 | + | 0.926350i | \(0.622929\pi\) | |||||||
\(312\) | −6.30532 | −0.356969 | ||||||||
\(313\) | −26.7511 | −1.51206 | −0.756031 | − | 0.654536i | \(-0.772864\pi\) | ||||
−0.756031 | + | 0.654536i | \(0.772864\pi\) | |||||||
\(314\) | −53.7680 | −3.03430 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.0110 | −0.731928 | ||||||||
\(317\) | −11.8100 | −0.663315 | −0.331657 | − | 0.943400i | \(-0.607608\pi\) | ||||
−0.331657 | + | 0.943400i | \(0.607608\pi\) | |||||||
\(318\) | −14.9733 | −0.839663 | ||||||||
\(319\) | −8.97976 | −0.502770 | ||||||||
\(320\) | −53.7993 | −3.00747 | ||||||||
\(321\) | −4.97976 | −0.277943 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.60129 | 0.311664 | ||||||||
\(324\) | 2.96545 | 0.164747 | ||||||||
\(325\) | −35.8553 | −1.98889 | ||||||||
\(326\) | 51.5278 | 2.85386 | ||||||||
\(327\) | 11.3249 | 0.626267 | ||||||||
\(328\) | 14.2022 | 0.784183 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 9.25053 | 0.509225 | ||||||||
\(331\) | 24.2493 | 1.33286 | 0.666432 | − | 0.745566i | \(-0.267821\pi\) | ||||
0.666432 | + | 0.745566i | \(0.267821\pi\) | |||||||
\(332\) | 17.8258 | 0.978316 | ||||||||
\(333\) | 10.2160 | 0.559832 | ||||||||
\(334\) | −25.0582 | −1.37112 | ||||||||
\(335\) | −48.8823 | −2.67073 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.57781 | −0.194895 | −0.0974477 | − | 0.995241i | \(-0.531068\pi\) | ||||
−0.0974477 | + | 0.995241i | \(0.531068\pi\) | |||||||
\(338\) | 9.82663 | 0.534498 | ||||||||
\(339\) | −6.25842 | −0.339911 | ||||||||
\(340\) | 16.8082 | 0.911552 | ||||||||
\(341\) | 4.10889 | 0.222509 | ||||||||
\(342\) | −9.14164 | −0.494323 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −23.3730 | −1.26019 | ||||||||
\(345\) | −12.1938 | −0.656491 | ||||||||
\(346\) | 14.7307 | 0.791927 | ||||||||
\(347\) | 27.5601 | 1.47950 | 0.739752 | − | 0.672879i | \(-0.234943\pi\) | ||||
0.739752 | + | 0.672879i | \(0.234943\pi\) | |||||||
\(348\) | 26.6290 | 1.42746 | ||||||||
\(349\) | 9.76978 | 0.522964 | 0.261482 | − | 0.965208i | \(-0.415789\pi\) | ||||
0.261482 | + | 0.965208i | \(0.415789\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.93089 | 0.156440 | ||||||||
\(352\) | 6.83632 | 0.364377 | ||||||||
\(353\) | −5.73155 | −0.305060 | −0.152530 | − | 0.988299i | \(-0.548742\pi\) | ||||
−0.152530 | + | 0.988299i | \(0.548742\pi\) | |||||||
\(354\) | −1.77629 | −0.0944089 | ||||||||
\(355\) | −23.6138 | −1.25329 | ||||||||
\(356\) | 3.91511 | 0.207501 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −17.9542 | −0.948909 | ||||||||
\(359\) | 2.23888 | 0.118163 | 0.0590817 | − | 0.998253i | \(-0.481183\pi\) | ||||
0.0590817 | + | 0.998253i | \(0.481183\pi\) | |||||||
\(360\) | −8.93089 | −0.470699 | ||||||||
\(361\) | −2.16977 | −0.114198 | ||||||||
\(362\) | −16.6856 | −0.876975 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 56.3343 | 2.94867 | ||||||||
\(366\) | −17.3295 | −0.905827 | ||||||||
\(367\) | 20.5129 | 1.07077 | 0.535383 | − | 0.844610i | \(-0.320167\pi\) | ||||
0.535383 | + | 0.844610i | \(0.320167\pi\) | |||||||
\(368\) | −3.33979 | −0.174098 | ||||||||
\(369\) | −6.60157 | −0.343664 | ||||||||
\(370\) | −94.5032 | −4.91299 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −12.1847 | −0.631747 | ||||||||
\(373\) | 23.4031 | 1.21176 | 0.605882 | − | 0.795554i | \(-0.292820\pi\) | ||||
0.605882 | + | 0.795554i | \(0.292820\pi\) | |||||||
\(374\) | −3.04244 | −0.157321 | ||||||||
\(375\) | −30.0289 | −1.55069 | ||||||||
\(376\) | −13.3822 | −0.690136 | ||||||||
\(377\) | 26.3187 | 1.35548 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.34413 | 0.274510 | 0.137255 | − | 0.990536i | \(-0.456172\pi\) | ||||
0.137255 | + | 0.990536i | \(0.456172\pi\) | |||||||
\(380\) | 50.5036 | 2.59078 | ||||||||
\(381\) | 7.04706 | 0.361032 | ||||||||
\(382\) | −29.0094 | −1.48425 | ||||||||
\(383\) | 31.5344 | 1.61133 | 0.805667 | − | 0.592369i | \(-0.201807\pi\) | ||||
0.805667 | + | 0.592369i | \(0.201807\pi\) | |||||||
\(384\) | −15.2054 | −0.775949 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.7789 | 1.05762 | ||||||||
\(387\) | 10.8644 | 0.552271 | ||||||||
\(388\) | 7.63492 | 0.387605 | ||||||||
\(389\) | −18.7309 | −0.949692 | −0.474846 | − | 0.880069i | \(-0.657496\pi\) | ||||
−0.474846 | + | 0.880069i | \(0.657496\pi\) | |||||||
\(390\) | −27.1123 | −1.37289 | ||||||||
\(391\) | 4.01046 | 0.202818 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.6993 | −0.539708 | ||||||||
\(394\) | 39.2410 | 1.97693 | ||||||||
\(395\) | −18.2142 | −0.916455 | ||||||||
\(396\) | 2.96545 | 0.149019 | ||||||||
\(397\) | 26.4506 | 1.32752 | 0.663760 | − | 0.747946i | \(-0.268960\pi\) | ||||
0.663760 | + | 0.747946i | \(0.268960\pi\) | |||||||
\(398\) | −30.7797 | −1.54285 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.9098 | −0.695490 | ||||||||
\(401\) | −0.603254 | −0.0301251 | −0.0150625 | − | 0.999887i | \(-0.504795\pi\) | ||||
−0.0150625 | + | 0.999887i | \(0.504795\pi\) | |||||||
\(402\) | −26.2388 | −1.30867 | ||||||||
\(403\) | −12.0427 | −0.599890 | ||||||||
\(404\) | −26.0933 | −1.29819 | ||||||||
\(405\) | 4.15133 | 0.206281 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.2160 | 0.506387 | ||||||||
\(408\) | 2.93732 | 0.145419 | ||||||||
\(409\) | 5.29261 | 0.261703 | 0.130851 | − | 0.991402i | \(-0.458229\pi\) | ||||
0.130851 | + | 0.991402i | \(0.458229\pi\) | |||||||
\(410\) | 61.0680 | 3.01593 | ||||||||
\(411\) | 13.7306 | 0.677280 | ||||||||
\(412\) | 52.1444 | 2.56897 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.54530 | −0.321684 | ||||||||
\(415\) | 24.9543 | 1.22496 | ||||||||
\(416\) | −20.0365 | −0.982371 | ||||||||
\(417\) | −4.63927 | −0.227186 | ||||||||
\(418\) | −9.14164 | −0.447132 | ||||||||
\(419\) | 0.251997 | 0.0123108 | 0.00615542 | − | 0.999981i | \(-0.498041\pi\) | ||||
0.00615542 | + | 0.999981i | \(0.498041\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.5812 | −1.39296 | −0.696482 | − | 0.717575i | \(-0.745252\pi\) | ||||
−0.696482 | + | 0.717575i | \(0.745252\pi\) | |||||||
\(422\) | −22.4109 | −1.09094 | ||||||||
\(423\) | 6.22044 | 0.302448 | ||||||||
\(424\) | 14.4560 | 0.702043 | ||||||||
\(425\) | 16.7031 | 0.810217 | ||||||||
\(426\) | −12.6753 | −0.614120 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14.7672 | 0.713800 | ||||||||
\(429\) | 2.93089 | 0.141505 | ||||||||
\(430\) | −100.502 | −4.84663 | ||||||||
\(431\) | −25.3748 | −1.22226 | −0.611131 | − | 0.791529i | \(-0.709285\pi\) | ||||
−0.611131 | + | 0.791529i | \(0.709285\pi\) | |||||||
\(432\) | 1.13702 | 0.0547049 | ||||||||
\(433\) | −27.9009 | −1.34083 | −0.670415 | − | 0.741986i | \(-0.733884\pi\) | ||||
−0.670415 | + | 0.741986i | \(0.733884\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 37.2780 | 1.78734 | ||||||||
\(436\) | −33.5833 | −1.60835 | ||||||||
\(437\) | 12.0502 | 0.576441 | ||||||||
\(438\) | 30.2388 | 1.44487 | ||||||||
\(439\) | 9.84542 | 0.469896 | 0.234948 | − | 0.972008i | \(-0.424508\pi\) | ||||
0.234948 | + | 0.972008i | \(0.424508\pi\) | |||||||
\(440\) | −8.93089 | −0.425764 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.91708 | 0.424142 | ||||||||
\(443\) | −5.45568 | −0.259207 | −0.129604 | − | 0.991566i | \(-0.541371\pi\) | ||||
−0.129604 | + | 0.991566i | \(0.541371\pi\) | |||||||
\(444\) | −30.2949 | −1.43773 | ||||||||
\(445\) | 5.48077 | 0.259814 | ||||||||
\(446\) | −35.8592 | −1.69798 | ||||||||
\(447\) | −2.32110 | −0.109784 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.1735 | −1.04643 | −0.523217 | − | 0.852200i | \(-0.675268\pi\) | ||||
−0.523217 | + | 0.852200i | \(0.675268\pi\) | |||||||
\(450\) | −27.2604 | −1.28507 | ||||||||
\(451\) | −6.60157 | −0.310856 | ||||||||
\(452\) | 18.5590 | 0.872942 | ||||||||
\(453\) | −18.2435 | −0.857154 | ||||||||
\(454\) | 64.0385 | 3.00548 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.82577 | 0.413304 | ||||||||
\(457\) | 10.9245 | 0.511025 | 0.255513 | − | 0.966806i | \(-0.417756\pi\) | ||||
0.255513 | + | 0.966806i | \(0.417756\pi\) | |||||||
\(458\) | −35.8673 | −1.67597 | ||||||||
\(459\) | −1.36535 | −0.0637290 | ||||||||
\(460\) | 36.1600 | 1.68597 | ||||||||
\(461\) | −24.0300 | −1.11919 | −0.559594 | − | 0.828767i | \(-0.689043\pi\) | ||||
−0.559594 | + | 0.828767i | \(0.689043\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.5192 | 0.721240 | 0.360620 | − | 0.932713i | \(-0.382565\pi\) | ||||
0.360620 | + | 0.932713i | \(0.382565\pi\) | |||||||
\(464\) | 10.2102 | 0.473995 | ||||||||
\(465\) | −17.0574 | −0.791016 | ||||||||
\(466\) | 25.6322 | 1.18739 | ||||||||
\(467\) | 4.27670 | 0.197902 | 0.0989510 | − | 0.995092i | \(-0.468451\pi\) | ||||
0.0989510 | + | 0.995092i | \(0.468451\pi\) | |||||||
\(468\) | −8.69141 | −0.401760 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −57.5424 | −2.65423 | ||||||||
\(471\) | −24.1293 | −1.11182 | ||||||||
\(472\) | 1.71492 | 0.0789354 | ||||||||
\(473\) | 10.8644 | 0.499548 | ||||||||
\(474\) | −9.77690 | −0.449068 | ||||||||
\(475\) | 50.1878 | 2.30277 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.71954 | −0.307667 | ||||||||
\(478\) | −2.23295 | −0.102133 | ||||||||
\(479\) | 21.5428 | 0.984316 | 0.492158 | − | 0.870506i | \(-0.336208\pi\) | ||||
0.492158 | + | 0.870506i | \(0.336208\pi\) | |||||||
\(480\) | −28.3798 | −1.29536 | ||||||||
\(481\) | −29.9419 | −1.36523 | ||||||||
\(482\) | 6.34184 | 0.288863 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.96545 | 0.134793 | ||||||||
\(485\) | 10.6881 | 0.485323 | ||||||||
\(486\) | 2.22833 | 0.101079 | ||||||||
\(487\) | 4.21246 | 0.190885 | 0.0954423 | − | 0.995435i | \(-0.469573\pi\) | ||||
0.0954423 | + | 0.995435i | \(0.469573\pi\) | |||||||
\(488\) | 16.7307 | 0.757363 | ||||||||
\(489\) | 23.1240 | 1.04570 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.33575 | −0.331058 | −0.165529 | − | 0.986205i | \(-0.552933\pi\) | ||||
−0.165529 | + | 0.986205i | \(0.552933\pi\) | |||||||
\(492\) | 19.5766 | 0.882581 | ||||||||
\(493\) | −12.2605 | −0.552185 | ||||||||
\(494\) | 26.7932 | 1.20548 | ||||||||
\(495\) | 4.15133 | 0.186588 | ||||||||
\(496\) | −4.67189 | −0.209774 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13.3948 | 0.600237 | ||||||||
\(499\) | 10.2067 | 0.456916 | 0.228458 | − | 0.973554i | \(-0.426632\pi\) | ||||
0.228458 | + | 0.973554i | \(0.426632\pi\) | |||||||
\(500\) | 89.0491 | 3.98240 | ||||||||
\(501\) | −11.2453 | −0.502403 | ||||||||
\(502\) | 33.4295 | 1.49203 | ||||||||
\(503\) | −0.843347 | −0.0376030 | −0.0188015 | − | 0.999823i | \(-0.505985\pi\) | ||||
−0.0188015 | + | 0.999823i | \(0.505985\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.5280 | −1.62547 | ||||||||
\(506\) | −6.54530 | −0.290974 | ||||||||
\(507\) | 4.40986 | 0.195849 | ||||||||
\(508\) | −20.8977 | −0.927185 | ||||||||
\(509\) | −37.9401 | −1.68167 | −0.840833 | − | 0.541294i | \(-0.817935\pi\) | ||||
−0.840833 | + | 0.541294i | \(0.817935\pi\) | |||||||
\(510\) | 12.6302 | 0.559274 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −12.6652 | −0.559730 | ||||||||
\(513\) | −4.10247 | −0.181128 | ||||||||
\(514\) | −56.4197 | −2.48857 | ||||||||
\(515\) | 72.9970 | 3.21663 | ||||||||
\(516\) | −32.2179 | −1.41832 | ||||||||
\(517\) | 6.22044 | 0.273575 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.61065 | 0.290175 | ||||||||
\(520\) | 26.1755 | 1.14787 | ||||||||
\(521\) | −2.65140 | −0.116160 | −0.0580800 | − | 0.998312i | \(-0.518498\pi\) | ||||
−0.0580800 | + | 0.998312i | \(0.518498\pi\) | |||||||
\(522\) | 20.0099 | 0.875807 | ||||||||
\(523\) | −11.1984 | −0.489672 | −0.244836 | − | 0.969565i | \(-0.578734\pi\) | ||||
−0.244836 | + | 0.969565i | \(0.578734\pi\) | |||||||
\(524\) | 31.7282 | 1.38605 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 44.4704 | 1.93900 | ||||||||
\(527\) | 5.61006 | 0.244378 | ||||||||
\(528\) | 1.13702 | 0.0494824 | ||||||||
\(529\) | −14.3722 | −0.624877 | ||||||||
\(530\) | 62.1593 | 2.70003 | ||||||||
\(531\) | −0.797142 | −0.0345930 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.3485 | 0.838076 | ||||||||
\(534\) | 2.94194 | 0.127310 | ||||||||
\(535\) | 20.6726 | 0.893756 | ||||||||
\(536\) | 25.3321 | 1.09418 | ||||||||
\(537\) | −8.05725 | −0.347696 | ||||||||
\(538\) | 15.3149 | 0.660273 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −12.3106 | −0.529762 | ||||||||
\(541\) | −7.34389 | −0.315739 | −0.157869 | − | 0.987460i | \(-0.550462\pi\) | ||||
−0.157869 | + | 0.987460i | \(0.550462\pi\) | |||||||
\(542\) | −4.13592 | −0.177653 | ||||||||
\(543\) | −7.48794 | −0.321338 | ||||||||
\(544\) | 9.33395 | 0.400190 | ||||||||
\(545\) | −47.0133 | −2.01383 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.85901 | −0.336027 | −0.168014 | − | 0.985785i | \(-0.553735\pi\) | ||||
−0.168014 | + | 0.985785i | \(0.553735\pi\) | |||||||
\(548\) | −40.7173 | −1.73936 | ||||||||
\(549\) | −7.77690 | −0.331910 | ||||||||
\(550\) | −27.2604 | −1.16239 | ||||||||
\(551\) | −36.8392 | −1.56940 | ||||||||
\(552\) | 6.31914 | 0.268961 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −61.1582 | −2.59836 | ||||||||
\(555\) | −42.4099 | −1.80020 | ||||||||
\(556\) | 13.7575 | 0.583449 | ||||||||
\(557\) | 23.2643 | 0.985738 | 0.492869 | − | 0.870103i | \(-0.335948\pi\) | ||||
0.492869 | + | 0.870103i | \(0.335948\pi\) | |||||||
\(558\) | −9.15595 | −0.387602 | ||||||||
\(559\) | −31.8425 | −1.34680 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.36535 | −0.0576450 | ||||||||
\(562\) | −59.3119 | −2.50192 | ||||||||
\(563\) | 28.7199 | 1.21040 | 0.605200 | − | 0.796073i | \(-0.293093\pi\) | ||||
0.605200 | + | 0.796073i | \(0.293093\pi\) | |||||||
\(564\) | −18.4464 | −0.776733 | ||||||||
\(565\) | 25.9808 | 1.09302 | ||||||||
\(566\) | 34.2102 | 1.43796 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.2373 | 0.513467 | ||||||||
\(569\) | 20.8646 | 0.874689 | 0.437344 | − | 0.899294i | \(-0.355919\pi\) | ||||
0.437344 | + | 0.899294i | \(0.355919\pi\) | |||||||
\(570\) | 37.9500 | 1.58955 | ||||||||
\(571\) | 7.29832 | 0.305425 | 0.152712 | − | 0.988271i | \(-0.451199\pi\) | ||||
0.152712 | + | 0.988271i | \(0.451199\pi\) | |||||||
\(572\) | −8.69141 | −0.363406 | ||||||||
\(573\) | −13.0184 | −0.543853 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 35.9338 | 1.49854 | ||||||||
\(576\) | −12.9595 | −0.539980 | ||||||||
\(577\) | −27.1280 | −1.12935 | −0.564677 | − | 0.825312i | \(-0.690999\pi\) | ||||
−0.564677 | + | 0.825312i | \(0.690999\pi\) | |||||||
\(578\) | 33.7276 | 1.40288 | ||||||||
\(579\) | 9.32487 | 0.387528 | ||||||||
\(580\) | −110.546 | −4.59016 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.73712 | 0.237811 | ||||||||
\(583\) | −6.71954 | −0.278295 | ||||||||
\(584\) | −29.1939 | −1.20805 | ||||||||
\(585\) | −12.1671 | −0.503048 | ||||||||
\(586\) | −14.9080 | −0.615843 | ||||||||
\(587\) | −11.4493 | −0.472562 | −0.236281 | − | 0.971685i | \(-0.575929\pi\) | ||||
−0.236281 | + | 0.971685i | \(0.575929\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.8566 | 0.694563 | ||||||||
\(590\) | 7.37398 | 0.303582 | ||||||||
\(591\) | 17.6101 | 0.724381 | ||||||||
\(592\) | −11.6158 | −0.477405 | ||||||||
\(593\) | −13.0829 | −0.537251 | −0.268626 | − | 0.963245i | \(-0.586569\pi\) | ||||
−0.268626 | + | 0.963245i | \(0.586569\pi\) | |||||||
\(594\) | 2.22833 | 0.0914294 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.88311 | 0.281943 | ||||||||
\(597\) | −13.8129 | −0.565325 | ||||||||
\(598\) | 19.1836 | 0.784475 | ||||||||
\(599\) | −11.8121 | −0.482628 | −0.241314 | − | 0.970447i | \(-0.577578\pi\) | ||||
−0.241314 | + | 0.970447i | \(0.577578\pi\) | |||||||
\(600\) | 26.3184 | 1.07445 | ||||||||
\(601\) | 10.3074 | 0.420448 | 0.210224 | − | 0.977653i | \(-0.432581\pi\) | ||||
0.210224 | + | 0.977653i | \(0.432581\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.7751 | −0.479519 | ||||||||
\(604\) | 54.1001 | 2.20130 | ||||||||
\(605\) | 4.15133 | 0.168776 | ||||||||
\(606\) | −19.6073 | −0.796492 | ||||||||
\(607\) | −39.4839 | −1.60260 | −0.801301 | − | 0.598262i | \(-0.795858\pi\) | ||||
−0.801301 | + | 0.598262i | \(0.795858\pi\) | |||||||
\(608\) | 28.0458 | 1.13741 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 71.9405 | 2.91278 | ||||||||
\(611\) | −18.2314 | −0.737565 | ||||||||
\(612\) | 4.04887 | 0.163666 | ||||||||
\(613\) | −38.5827 | −1.55834 | −0.779170 | − | 0.626812i | \(-0.784359\pi\) | ||||
−0.779170 | + | 0.626812i | \(0.784359\pi\) | |||||||
\(614\) | −11.1376 | −0.449478 | ||||||||
\(615\) | 27.4053 | 1.10509 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.06789 | −0.244284 | −0.122142 | − | 0.992513i | \(-0.538976\pi\) | ||||
−0.122142 | + | 0.992513i | \(0.538976\pi\) | |||||||
\(618\) | 39.1829 | 1.57617 | ||||||||
\(619\) | 19.3039 | 0.775890 | 0.387945 | − | 0.921682i | \(-0.373185\pi\) | ||||
0.387945 | + | 0.921682i | \(0.373185\pi\) | |||||||
\(620\) | 50.5827 | 2.03145 | ||||||||
\(621\) | −2.93732 | −0.117870 | ||||||||
\(622\) | 29.6035 | 1.18699 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.33248 | −0.133406 | ||||||||
\(625\) | 63.4921 | 2.53969 | ||||||||
\(626\) | 59.6102 | 2.38250 | ||||||||
\(627\) | −4.10247 | −0.163837 | ||||||||
\(628\) | 71.5541 | 2.85532 | ||||||||
\(629\) | 13.9484 | 0.556158 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.4894 | 0.656434 | 0.328217 | − | 0.944602i | \(-0.393552\pi\) | ||||
0.328217 | + | 0.944602i | \(0.393552\pi\) | |||||||
\(632\) | 9.43908 | 0.375466 | ||||||||
\(633\) | −10.0572 | −0.399740 | ||||||||
\(634\) | 26.3165 | 1.04516 | ||||||||
\(635\) | −29.2547 | −1.16094 | ||||||||
\(636\) | 19.9264 | 0.790134 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 20.0099 | 0.792198 | ||||||||
\(639\) | −5.68825 | −0.225024 | ||||||||
\(640\) | 63.1228 | 2.49515 | ||||||||
\(641\) | 1.31734 | 0.0520318 | 0.0260159 | − | 0.999662i | \(-0.491718\pi\) | ||||
0.0260159 | + | 0.999662i | \(0.491718\pi\) | |||||||
\(642\) | 11.0965 | 0.437945 | ||||||||
\(643\) | −31.5586 | −1.24455 | −0.622275 | − | 0.782799i | \(-0.713791\pi\) | ||||
−0.622275 | + | 0.782799i | \(0.713791\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −45.1019 | −1.77589 | ||||||||
\(646\) | −12.4815 | −0.491079 | ||||||||
\(647\) | 30.7334 | 1.20825 | 0.604126 | − | 0.796888i | \(-0.293522\pi\) | ||||
0.604126 | + | 0.796888i | \(0.293522\pi\) | |||||||
\(648\) | −2.15133 | −0.0845123 | ||||||||
\(649\) | −0.797142 | −0.0312905 | ||||||||
\(650\) | 79.8973 | 3.13383 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −68.5729 | −2.68552 | ||||||||
\(653\) | 36.9929 | 1.44764 | 0.723822 | − | 0.689987i | \(-0.242384\pi\) | ||||
0.723822 | + | 0.689987i | \(0.242384\pi\) | |||||||
\(654\) | −25.2355 | −0.986787 | ||||||||
\(655\) | 44.4163 | 1.73549 | ||||||||
\(656\) | 7.50611 | 0.293064 | ||||||||
\(657\) | 13.5702 | 0.529423 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.6348 | −0.842773 | −0.421386 | − | 0.906881i | \(-0.638456\pi\) | ||||
−0.421386 | + | 0.906881i | \(0.638456\pi\) | |||||||
\(660\) | −12.3106 | −0.479188 | ||||||||
\(661\) | 1.97068 | 0.0766504 | 0.0383252 | − | 0.999265i | \(-0.487798\pi\) | ||||
0.0383252 | + | 0.999265i | \(0.487798\pi\) | |||||||
\(662\) | −54.0355 | −2.10015 | ||||||||
\(663\) | 4.00169 | 0.155413 | ||||||||
\(664\) | −12.9320 | −0.501859 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −22.7645 | −0.882108 | ||||||||
\(667\) | −26.3764 | −1.02130 | ||||||||
\(668\) | 33.3473 | 1.29025 | ||||||||
\(669\) | −16.0924 | −0.622169 | ||||||||
\(670\) | 108.926 | 4.20818 | ||||||||
\(671\) | −7.77690 | −0.300224 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.24081 | 0.0478297 | 0.0239148 | − | 0.999714i | \(-0.492387\pi\) | ||||
0.0239148 | + | 0.999714i | \(0.492387\pi\) | |||||||
\(674\) | 7.97252 | 0.307090 | ||||||||
\(675\) | −12.2336 | −0.470870 | ||||||||
\(676\) | −13.0772 | −0.502970 | ||||||||
\(677\) | 8.82859 | 0.339310 | 0.169655 | − | 0.985504i | \(-0.445735\pi\) | ||||
0.169655 | + | 0.985504i | \(0.445735\pi\) | |||||||
\(678\) | 13.9458 | 0.535586 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −12.1938 | −0.467610 | ||||||||
\(681\) | 28.7384 | 1.10126 | ||||||||
\(682\) | −9.15595 | −0.350600 | ||||||||
\(683\) | 0.0255618 | 0.000978097 0 | 0.000489048 | − | 1.00000i | \(-0.499844\pi\) | ||||
0.000489048 | 1.00000i | \(0.499844\pi\) | ||||||||
\(684\) | 12.1656 | 0.465165 | ||||||||
\(685\) | −57.0002 | −2.17787 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.0960 | −0.614102 | ||||||||
\(688\) | −12.3531 | −0.470957 | ||||||||
\(689\) | 19.6942 | 0.750291 | ||||||||
\(690\) | 27.1717 | 1.03441 | ||||||||
\(691\) | −28.4635 | −1.08280 | −0.541402 | − | 0.840764i | \(-0.682106\pi\) | ||||
−0.541402 | + | 0.840764i | \(0.682106\pi\) | |||||||
\(692\) | −19.6035 | −0.745214 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −61.4130 | −2.33120 | ||||||||
\(695\) | 19.2592 | 0.730542 | ||||||||
\(696\) | −19.3184 | −0.732264 | ||||||||
\(697\) | −9.01343 | −0.341408 | ||||||||
\(698\) | −21.7703 | −0.824017 | ||||||||
\(699\) | 11.5029 | 0.435078 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.6422 | 1.08180 | 0.540901 | − | 0.841087i | \(-0.318084\pi\) | ||||
0.540901 | + | 0.841087i | \(0.318084\pi\) | |||||||
\(702\) | −6.53099 | −0.246496 | ||||||||
\(703\) | 41.9107 | 1.58069 | ||||||||
\(704\) | −12.9595 | −0.488430 | ||||||||
\(705\) | −25.8231 | −0.972554 | ||||||||
\(706\) | 12.7718 | 0.480672 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.36388 | 0.0888401 | ||||||||
\(709\) | 1.20078 | 0.0450964 | 0.0225482 | − | 0.999746i | \(-0.492822\pi\) | ||||
0.0225482 | + | 0.999746i | \(0.492822\pi\) | |||||||
\(710\) | 52.6194 | 1.97477 | ||||||||
\(711\) | −4.38755 | −0.164546 | ||||||||
\(712\) | −2.84028 | −0.106444 | ||||||||
\(713\) | 12.0691 | 0.451992 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.1671 | −0.455024 | ||||||||
\(716\) | 23.8933 | 0.892936 | ||||||||
\(717\) | −1.00207 | −0.0374231 | ||||||||
\(718\) | −4.98896 | −0.186186 | ||||||||
\(719\) | 4.07177 | 0.151851 | 0.0759256 | − | 0.997113i | \(-0.475809\pi\) | ||||
0.0759256 | + | 0.997113i | \(0.475809\pi\) | |||||||
\(720\) | −4.72015 | −0.175909 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.83496 | 0.179939 | ||||||||
\(723\) | 2.84601 | 0.105844 | ||||||||
\(724\) | 22.2051 | 0.825246 | ||||||||
\(725\) | −109.854 | −4.07989 | ||||||||
\(726\) | 2.22833 | 0.0827010 | ||||||||
\(727\) | −26.4800 | −0.982088 | −0.491044 | − | 0.871135i | \(-0.663385\pi\) | ||||
−0.491044 | + | 0.871135i | \(0.663385\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −125.531 | −4.64612 | ||||||||
\(731\) | 14.8337 | 0.548646 | ||||||||
\(732\) | 23.0620 | 0.852395 | ||||||||
\(733\) | −6.65113 | −0.245665 | −0.122833 | − | 0.992427i | \(-0.539198\pi\) | ||||
−0.122833 | + | 0.992427i | \(0.539198\pi\) | |||||||
\(734\) | −45.7095 | −1.68717 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.0804 | 0.740174 | ||||||||
\(737\) | −11.7751 | −0.433741 | ||||||||
\(738\) | 14.7105 | 0.541499 | ||||||||
\(739\) | −45.9618 | −1.69073 | −0.845365 | − | 0.534189i | \(-0.820617\pi\) | ||||
−0.845365 | + | 0.534189i | \(0.820617\pi\) | |||||||
\(740\) | 125.764 | 4.62319 | ||||||||
\(741\) | 12.0239 | 0.441709 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.1782 | −0.776951 | −0.388476 | − | 0.921459i | \(-0.626998\pi\) | ||||
−0.388476 | + | 0.921459i | \(0.626998\pi\) | |||||||
\(744\) | 8.83958 | 0.324075 | ||||||||
\(745\) | 9.63567 | 0.353024 | ||||||||
\(746\) | −52.1497 | −1.90934 | ||||||||
\(747\) | 6.01116 | 0.219937 | ||||||||
\(748\) | 4.04887 | 0.148041 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 66.9142 | 2.44336 | ||||||||
\(751\) | −12.1534 | −0.443484 | −0.221742 | − | 0.975105i | \(-0.571174\pi\) | ||||
−0.221742 | + | 0.975105i | \(0.571174\pi\) | |||||||
\(752\) | −7.07276 | −0.257917 | ||||||||
\(753\) | 15.0021 | 0.546706 | ||||||||
\(754\) | −58.6467 | −2.13579 | ||||||||
\(755\) | 75.7348 | 2.75627 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.19862 | 0.334330 | 0.167165 | − | 0.985929i | \(-0.446539\pi\) | ||||
0.167165 | + | 0.985929i | \(0.446539\pi\) | |||||||
\(758\) | −11.9085 | −0.432536 | ||||||||
\(759\) | −2.93732 | −0.106618 | ||||||||
\(760\) | −36.6387 | −1.32902 | ||||||||
\(761\) | 5.49123 | 0.199057 | 0.0995285 | − | 0.995035i | \(-0.468267\pi\) | ||||
0.0995285 | + | 0.995035i | \(0.468267\pi\) | |||||||
\(762\) | −15.7032 | −0.568866 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 38.6055 | 1.39670 | ||||||||
\(765\) | 5.66801 | 0.204927 | ||||||||
\(766\) | −70.2690 | −2.53892 | ||||||||
\(767\) | 2.33634 | 0.0843602 | ||||||||
\(768\) | 7.96365 | 0.287363 | ||||||||
\(769\) | 2.72497 | 0.0982650 | 0.0491325 | − | 0.998792i | \(-0.484354\pi\) | ||||
0.0491325 | + | 0.998792i | \(0.484354\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.3193 | −0.911852 | ||||||||
\(772\) | −27.6524 | −0.995231 | ||||||||
\(773\) | −35.7910 | −1.28731 | −0.643657 | − | 0.765314i | \(-0.722583\pi\) | ||||
−0.643657 | + | 0.765314i | \(0.722583\pi\) | |||||||
\(774\) | −24.2096 | −0.870194 | ||||||||
\(775\) | 50.2663 | 1.80562 | ||||||||
\(776\) | −5.53888 | −0.198834 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 41.7385 | 1.49640 | ||||||||
\(779\) | −27.0827 | −0.970338 | ||||||||
\(780\) | 36.0809 | 1.29190 | ||||||||
\(781\) | −5.68825 | −0.203542 | ||||||||
\(782\) | −8.93662 | −0.319573 | ||||||||
\(783\) | 8.97976 | 0.320910 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 100.169 | 3.57517 | ||||||||
\(786\) | 23.8415 | 0.850400 | ||||||||
\(787\) | −12.5410 | −0.447037 | −0.223518 | − | 0.974700i | \(-0.571754\pi\) | ||||
−0.223518 | + | 0.974700i | \(0.571754\pi\) | |||||||
\(788\) | −52.2217 | −1.86032 | ||||||||
\(789\) | 19.9569 | 0.710483 | ||||||||
\(790\) | 40.5872 | 1.44403 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.15133 | −0.0764443 | ||||||||
\(793\) | 22.7933 | 0.809413 | ||||||||
\(794\) | −58.9407 | −2.09173 | ||||||||
\(795\) | 27.8950 | 0.989335 | ||||||||
\(796\) | 40.9615 | 1.45184 | ||||||||
\(797\) | 22.4031 | 0.793557 | 0.396778 | − | 0.917914i | \(-0.370128\pi\) | ||||
0.396778 | + | 0.917914i | \(0.370128\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.49306 | 0.300463 | ||||||||
\(800\) | 83.6325 | 2.95685 | ||||||||
\(801\) | 1.32024 | 0.0466485 | ||||||||
\(802\) | 1.34425 | 0.0474670 | ||||||||
\(803\) | 13.5702 | 0.478881 | ||||||||
\(804\) | 34.9184 | 1.23148 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.8351 | 0.945227 | ||||||||
\(807\) | 6.87283 | 0.241935 | ||||||||
\(808\) | 18.9298 | 0.665948 | ||||||||
\(809\) | −11.0528 | −0.388595 | −0.194298 | − | 0.980943i | \(-0.562243\pi\) | ||||
−0.194298 | + | 0.980943i | \(0.562243\pi\) | |||||||
\(810\) | −9.25053 | −0.325030 | ||||||||
\(811\) | 44.6572 | 1.56813 | 0.784063 | − | 0.620682i | \(-0.213144\pi\) | ||||
0.784063 | + | 0.620682i | \(0.213144\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.85606 | −0.0650950 | ||||||||
\(814\) | −22.7645 | −0.797897 | ||||||||
\(815\) | −95.9953 | −3.36257 | ||||||||
\(816\) | 1.55243 | 0.0543458 | ||||||||
\(817\) | 44.5710 | 1.55934 | ||||||||
\(818\) | −11.7937 | −0.412356 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −81.2689 | −2.83803 | ||||||||
\(821\) | −4.67317 | −0.163095 | −0.0815474 | − | 0.996669i | \(-0.525986\pi\) | ||||
−0.0815474 | + | 0.996669i | \(0.525986\pi\) | |||||||
\(822\) | −30.5962 | −1.06717 | ||||||||
\(823\) | −45.7856 | −1.59598 | −0.797992 | − | 0.602668i | \(-0.794104\pi\) | ||||
−0.797992 | + | 0.602668i | \(0.794104\pi\) | |||||||
\(824\) | −37.8290 | −1.31784 | ||||||||
\(825\) | −12.2336 | −0.425918 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −54.7414 | −1.90355 | −0.951773 | − | 0.306803i | \(-0.900741\pi\) | ||||
−0.951773 | + | 0.306803i | \(0.900741\pi\) | |||||||
\(828\) | 8.71045 | 0.302709 | ||||||||
\(829\) | 2.42271 | 0.0841442 | 0.0420721 | − | 0.999115i | \(-0.486604\pi\) | ||||
0.0420721 | + | 0.999115i | \(0.486604\pi\) | |||||||
\(830\) | −55.6064 | −1.93013 | ||||||||
\(831\) | −27.4458 | −0.952083 | ||||||||
\(832\) | 37.9830 | 1.31682 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.3378 | 0.357970 | ||||||||
\(835\) | 46.6830 | 1.61553 | ||||||||
\(836\) | 12.1656 | 0.420758 | ||||||||
\(837\) | −4.10889 | −0.142024 | ||||||||
\(838\) | −0.561531 | −0.0193978 | ||||||||
\(839\) | −47.6581 | −1.64534 | −0.822670 | − | 0.568519i | \(-0.807517\pi\) | ||||
−0.822670 | + | 0.568519i | \(0.807517\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 51.6361 | 1.78055 | ||||||||
\(842\) | 63.6883 | 2.19484 | ||||||||
\(843\) | −26.6172 | −0.916746 | ||||||||
\(844\) | 29.8242 | 1.02659 | ||||||||
\(845\) | −18.3068 | −0.629773 | ||||||||
\(846\) | −13.8612 | −0.476557 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.64025 | 0.262367 | ||||||||
\(849\) | 15.3524 | 0.526893 | ||||||||
\(850\) | −37.2199 | −1.27663 | ||||||||
\(851\) | 30.0076 | 1.02865 | ||||||||
\(852\) | 16.8682 | 0.577895 | ||||||||
\(853\) | −33.7510 | −1.15561 | −0.577806 | − | 0.816174i | \(-0.696091\pi\) | ||||
−0.577806 | + | 0.816174i | \(0.696091\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17.0307 | 0.582438 | ||||||||
\(856\) | −10.7131 | −0.366167 | ||||||||
\(857\) | 14.5889 | 0.498347 | 0.249173 | − | 0.968459i | \(-0.419841\pi\) | ||||
0.249173 | + | 0.968459i | \(0.419841\pi\) | |||||||
\(858\) | −6.53099 | −0.222964 | ||||||||
\(859\) | −19.2582 | −0.657081 | −0.328540 | − | 0.944490i | \(-0.606557\pi\) | ||||
−0.328540 | + | 0.944490i | \(0.606557\pi\) | |||||||
\(860\) | 133.747 | 4.56075 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 56.5435 | 1.92588 | ||||||||
\(863\) | −19.2935 | −0.656757 | −0.328379 | − | 0.944546i | \(-0.606502\pi\) | ||||
−0.328379 | + | 0.944546i | \(0.606502\pi\) | |||||||
\(864\) | −6.83632 | −0.232576 | ||||||||
\(865\) | −27.4430 | −0.933090 | ||||||||
\(866\) | 62.1723 | 2.11270 | ||||||||
\(867\) | 15.1358 | 0.514040 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.38755 | −0.148837 | ||||||||
\(870\) | −83.0675 | −2.81625 | ||||||||
\(871\) | 34.5116 | 1.16938 | ||||||||
\(872\) | 24.3635 | 0.825054 | ||||||||
\(873\) | 2.57463 | 0.0871380 | ||||||||
\(874\) | −26.8519 | −0.908279 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −40.2416 | −1.35964 | ||||||||
\(877\) | 13.3358 | 0.450318 | 0.225159 | − | 0.974322i | \(-0.427710\pi\) | ||||
0.225159 | + | 0.974322i | \(0.427710\pi\) | |||||||
\(878\) | −21.9388 | −0.740400 | ||||||||
\(879\) | −6.69021 | −0.225655 | ||||||||
\(880\) | −4.72015 | −0.159116 | ||||||||
\(881\) | −29.9312 | −1.00841 | −0.504203 | − | 0.863585i | \(-0.668214\pi\) | ||||
−0.504203 | + | 0.863585i | \(0.668214\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.0855 | −0.406709 | −0.203354 | − | 0.979105i | \(-0.565184\pi\) | ||||
−0.203354 | + | 0.979105i | \(0.565184\pi\) | |||||||
\(884\) | −11.8668 | −0.399123 | ||||||||
\(885\) | 3.30920 | 0.111238 | ||||||||
\(886\) | 12.1571 | 0.408424 | ||||||||
\(887\) | −13.5112 | −0.453663 | −0.226832 | − | 0.973934i | \(-0.572837\pi\) | ||||
−0.226832 | + | 0.973934i | \(0.572837\pi\) | |||||||
\(888\) | 21.9780 | 0.737532 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.2130 | −0.409379 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 47.7212 | 1.59782 | ||||||||
\(893\) | 25.5191 | 0.853965 | ||||||||
\(894\) | 5.17218 | 0.172984 | ||||||||
\(895\) | 33.4483 | 1.11805 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.60896 | 0.287445 | ||||||||
\(898\) | 49.4099 | 1.64883 | ||||||||
\(899\) | −36.8968 | −1.23058 | ||||||||
\(900\) | 36.2780 | 1.20927 | ||||||||
\(901\) | −9.17451 | −0.305647 | ||||||||
\(902\) | 14.7105 | 0.489805 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.4639 | −0.447804 | ||||||||
\(905\) | 31.0849 | 1.03330 | ||||||||
\(906\) | 40.6525 | 1.35059 | ||||||||
\(907\) | 55.3387 | 1.83749 | 0.918746 | − | 0.394849i | \(-0.129203\pi\) | ||||
0.918746 | + | 0.394849i | \(0.129203\pi\) | |||||||
\(908\) | −85.2221 | −2.82820 | ||||||||
\(909\) | −8.79910 | −0.291848 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.5802 | −1.84145 | −0.920727 | − | 0.390207i | \(-0.872403\pi\) | ||||
−0.920727 | + | 0.390207i | \(0.872403\pi\) | |||||||
\(912\) | 4.66458 | 0.154460 | ||||||||
\(913\) | 6.01116 | 0.198940 | ||||||||
\(914\) | −24.3433 | −0.805205 | ||||||||
\(915\) | 32.2845 | 1.06729 | ||||||||
\(916\) | 47.7320 | 1.57711 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.04244 | 0.100416 | ||||||||
\(919\) | 6.73991 | 0.222329 | 0.111165 | − | 0.993802i | \(-0.464542\pi\) | ||||
0.111165 | + | 0.993802i | \(0.464542\pi\) | |||||||
\(920\) | −26.2329 | −0.864872 | ||||||||
\(921\) | −4.99820 | −0.164696 | ||||||||
\(922\) | 53.5467 | 1.76347 | ||||||||
\(923\) | 16.6717 | 0.548754 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 124.978 | 4.10924 | ||||||||
\(926\) | −34.5819 | −1.13643 | ||||||||
\(927\) | 17.5840 | 0.577534 | ||||||||
\(928\) | −61.3885 | −2.01518 | ||||||||
\(929\) | −20.7649 | −0.681275 | −0.340637 | − | 0.940195i | \(-0.610643\pi\) | ||||
−0.340637 | + | 0.940195i | \(0.610643\pi\) | |||||||
\(930\) | 38.0094 | 1.24638 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −34.1111 | −1.11735 | ||||||||
\(933\) | 13.2851 | 0.434934 | ||||||||
\(934\) | −9.52989 | −0.311828 | ||||||||
\(935\) | 5.66801 | 0.185364 | ||||||||
\(936\) | 6.30532 | 0.206096 | ||||||||
\(937\) | 50.2053 | 1.64013 | 0.820067 | − | 0.572267i | \(-0.193936\pi\) | ||||
0.820067 | + | 0.572267i | \(0.193936\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.7511 | 0.872989 | ||||||||
\(940\) | 76.5770 | 2.49767 | ||||||||
\(941\) | 16.0665 | 0.523753 | 0.261876 | − | 0.965101i | \(-0.415659\pi\) | ||||
0.261876 | + | 0.965101i | \(0.415659\pi\) | |||||||
\(942\) | 53.7680 | 1.75186 | ||||||||
\(943\) | −19.3909 | −0.631454 | ||||||||
\(944\) | 0.906366 | 0.0294997 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.2096 | −0.787120 | ||||||||
\(947\) | −47.7275 | −1.55094 | −0.775468 | − | 0.631387i | \(-0.782486\pi\) | ||||
−0.775468 | + | 0.631387i | \(0.782486\pi\) | |||||||
\(948\) | 13.0110 | 0.422579 | ||||||||
\(949\) | −39.7727 | −1.29108 | ||||||||
\(950\) | −111.835 | −3.62840 | ||||||||
\(951\) | 11.8100 | 0.382965 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.32944 | 0.302210 | 0.151105 | − | 0.988518i | \(-0.451717\pi\) | ||||
0.151105 | + | 0.988518i | \(0.451717\pi\) | |||||||
\(954\) | 14.9733 | 0.484780 | ||||||||
\(955\) | 54.0439 | 1.74882 | ||||||||
\(956\) | 2.97160 | 0.0961083 | ||||||||
\(957\) | 8.97976 | 0.290274 | ||||||||
\(958\) | −48.0044 | −1.55095 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 53.7993 | 1.73636 | ||||||||
\(961\) | −14.1170 | −0.455388 | ||||||||
\(962\) | 66.7205 | 2.15115 | ||||||||
\(963\) | 4.97976 | 0.160470 | ||||||||
\(964\) | −8.43968 | −0.271824 | ||||||||
\(965\) | −38.7106 | −1.24614 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.9165 | −1.02637 | −0.513183 | − | 0.858279i | \(-0.671534\pi\) | ||||
−0.513183 | + | 0.858279i | \(0.671534\pi\) | |||||||
\(968\) | −2.15133 | −0.0691464 | ||||||||
\(969\) | −5.60129 | −0.179939 | ||||||||
\(970\) | −23.8167 | −0.764708 | ||||||||
\(971\) | 24.8052 | 0.796037 | 0.398019 | − | 0.917377i | \(-0.369698\pi\) | ||||
0.398019 | + | 0.917377i | \(0.369698\pi\) | |||||||
\(972\) | −2.96545 | −0.0951167 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9.38674 | −0.300770 | ||||||||
\(975\) | 35.8553 | 1.14829 | ||||||||
\(976\) | 8.84249 | 0.283041 | ||||||||
\(977\) | −2.76926 | −0.0885966 | −0.0442983 | − | 0.999018i | \(-0.514105\pi\) | ||||
−0.0442983 | + | 0.999018i | \(0.514105\pi\) | |||||||
\(978\) | −51.5278 | −1.64768 | ||||||||
\(979\) | 1.32024 | 0.0421952 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.3249 | −0.361575 | ||||||||
\(982\) | 16.3465 | 0.521637 | ||||||||
\(983\) | −11.9348 | −0.380661 | −0.190331 | − | 0.981720i | \(-0.560956\pi\) | ||||
−0.190331 | + | 0.981720i | \(0.560956\pi\) | |||||||
\(984\) | −14.2022 | −0.452748 | ||||||||
\(985\) | −73.1052 | −2.32933 | ||||||||
\(986\) | 27.3204 | 0.870059 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −35.6562 | −1.13438 | ||||||||
\(989\) | 31.9123 | 1.01475 | ||||||||
\(990\) | −9.25053 | −0.294001 | ||||||||
\(991\) | −10.4194 | −0.330982 | −0.165491 | − | 0.986211i | \(-0.552921\pi\) | ||||
−0.165491 | + | 0.986211i | \(0.552921\pi\) | |||||||
\(992\) | 28.0897 | 0.891848 | ||||||||
\(993\) | −24.2493 | −0.769529 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 57.3420 | 1.81786 | ||||||||
\(996\) | −17.8258 | −0.564831 | ||||||||
\(997\) | −0.00770883 | −0.000244141 0 | −0.000122070 | − | 1.00000i | \(-0.500039\pi\) | ||||
−0.000122070 | 1.00000i | \(0.500039\pi\) | ||||||||
\(998\) | −22.7440 | −0.719947 | ||||||||
\(999\) | −10.2160 | −0.323219 |
(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 | 1617.2.a.u.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 4851.2.a.bx.1.4 | 4 | |||
7.6 | odd | 2 | 1617.2.a.v.1.1 | yes | 4 | ||
21.20 | even | 2 | 4851.2.a.by.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1617.2.a.u.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1617.2.a.v.1.1 | yes | 4 | 7.6 | odd | 2 | ||
4851.2.a.bx.1.4 | 4 | 3.2 | odd | 2 | |||
4851.2.a.by.1.4 | 4 | 21.20 | even | 2 |