Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2842,2,Mod(1,2842)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2842, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2842.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2842 = 2 \cdot 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2842.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: | \(22.6934842544\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.369849.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + 3x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 406) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.299252\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2842.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.04241 | 1.17919 | 0.589594 | − | 0.807700i | \(-0.299288\pi\) | ||||
0.589594 | + | 0.807700i | \(0.299288\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.868034 | −0.388196 | −0.194098 | − | 0.980982i | \(-0.562178\pi\) | ||||
−0.194098 | + | 0.980982i | \(0.562178\pi\) | |||||||
\(6\) | −2.04241 | −0.833812 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.17146 | 0.390486 | ||||||||
\(10\) | 0.868034 | 0.274496 | ||||||||
\(11\) | −4.52582 | −1.36459 | −0.682293 | − | 0.731079i | \(-0.739017\pi\) | ||||
−0.682293 | + | 0.731079i | \(0.739017\pi\) | |||||||
\(12\) | 2.04241 | 0.589594 | ||||||||
\(13\) | 4.81113 | 1.33437 | 0.667183 | − | 0.744894i | \(-0.267500\pi\) | ||||
0.667183 | + | 0.744894i | \(0.267500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.77288 | −0.457757 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.259761 | −0.0630012 | −0.0315006 | − | 0.999504i | \(-0.510029\pi\) | ||||
−0.0315006 | + | 0.999504i | \(0.510029\pi\) | |||||||
\(18\) | −1.17146 | −0.276115 | ||||||||
\(19\) | 1.04241 | 0.239146 | 0.119573 | − | 0.992825i | \(-0.461847\pi\) | ||||
0.119573 | + | 0.992825i | \(0.461847\pi\) | |||||||
\(20\) | −0.868034 | −0.194098 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.52582 | 0.964907 | ||||||||
\(23\) | −7.24235 | −1.51013 | −0.755067 | − | 0.655648i | \(-0.772396\pi\) | ||||
−0.755067 | + | 0.655648i | \(0.772396\pi\) | |||||||
\(24\) | −2.04241 | −0.416906 | ||||||||
\(25\) | −4.24652 | −0.849304 | ||||||||
\(26\) | −4.81113 | −0.943540 | ||||||||
\(27\) | −3.73464 | −0.718732 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 1.77288 | 0.323683 | ||||||||
\(31\) | −2.40963 | −0.432783 | −0.216391 | − | 0.976307i | \(-0.569429\pi\) | ||||
−0.216391 | + | 0.976307i | \(0.569429\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −9.24359 | −1.60910 | ||||||||
\(34\) | 0.259761 | 0.0445486 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.17146 | 0.195243 | ||||||||
\(37\) | −7.46202 | −1.22675 | −0.613375 | − | 0.789792i | \(-0.710188\pi\) | ||||
−0.613375 | + | 0.789792i | \(0.710188\pi\) | |||||||
\(38\) | −1.04241 | −0.169102 | ||||||||
\(39\) | 9.82632 | 1.57347 | ||||||||
\(40\) | 0.868034 | 0.137248 | ||||||||
\(41\) | 5.52999 | 0.863639 | 0.431820 | − | 0.901960i | \(-0.357872\pi\) | ||||
0.431820 | + | 0.901960i | \(0.357872\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.24794 | 0.952802 | 0.476401 | − | 0.879228i | \(-0.341941\pi\) | ||||
0.476401 | + | 0.879228i | \(0.341941\pi\) | |||||||
\(44\) | −4.52582 | −0.682293 | ||||||||
\(45\) | −1.01686 | −0.151585 | ||||||||
\(46\) | 7.24235 | 1.06783 | ||||||||
\(47\) | −12.0092 | −1.75172 | −0.875862 | − | 0.482561i | \(-0.839707\pi\) | ||||
−0.875862 | + | 0.482561i | \(0.839707\pi\) | |||||||
\(48\) | 2.04241 | 0.294797 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.24652 | 0.600548 | ||||||||
\(51\) | −0.530539 | −0.0742903 | ||||||||
\(52\) | 4.81113 | 0.667183 | ||||||||
\(53\) | 5.23942 | 0.719690 | 0.359845 | − | 0.933012i | \(-0.382830\pi\) | ||||
0.359845 | + | 0.933012i | \(0.382830\pi\) | |||||||
\(54\) | 3.73464 | 0.508220 | ||||||||
\(55\) | 3.92856 | 0.529727 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.12904 | 0.281999 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | −10.8814 | −1.41664 | −0.708320 | − | 0.705891i | \(-0.750547\pi\) | ||||
−0.708320 | + | 0.705891i | \(0.750547\pi\) | |||||||
\(60\) | −1.77288 | −0.228878 | ||||||||
\(61\) | 14.4456 | 1.84958 | 0.924788 | − | 0.380483i | \(-0.124242\pi\) | ||||
0.924788 | + | 0.380483i | \(0.124242\pi\) | |||||||
\(62\) | 2.40963 | 0.306023 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.17622 | −0.517996 | ||||||||
\(66\) | 9.24359 | 1.13781 | ||||||||
\(67\) | 6.20553 | 0.758126 | 0.379063 | − | 0.925371i | \(-0.376246\pi\) | ||||
0.379063 | + | 0.925371i | \(0.376246\pi\) | |||||||
\(68\) | −0.259761 | −0.0315006 | ||||||||
\(69\) | −14.7919 | −1.78073 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.47016 | −1.12390 | −0.561951 | − | 0.827171i | \(-0.689949\pi\) | ||||
−0.561951 | + | 0.827171i | \(0.689949\pi\) | |||||||
\(72\) | −1.17146 | −0.138058 | ||||||||
\(73\) | −10.6617 | −1.24786 | −0.623931 | − | 0.781479i | \(-0.714466\pi\) | ||||
−0.623931 | + | 0.781479i | \(0.714466\pi\) | |||||||
\(74\) | 7.46202 | 0.867443 | ||||||||
\(75\) | −8.67315 | −1.00149 | ||||||||
\(76\) | 1.04241 | 0.119573 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −9.82632 | −1.11261 | ||||||||
\(79\) | −13.8798 | −1.56160 | −0.780799 | − | 0.624782i | \(-0.785188\pi\) | ||||
−0.780799 | + | 0.624782i | \(0.785188\pi\) | |||||||
\(80\) | −0.868034 | −0.0970491 | ||||||||
\(81\) | −11.1421 | −1.23801 | ||||||||
\(82\) | −5.52999 | −0.610685 | ||||||||
\(83\) | −6.90833 | −0.758287 | −0.379144 | − | 0.925338i | \(-0.623781\pi\) | ||||
−0.379144 | + | 0.925338i | \(0.623781\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.225481 | 0.0244569 | ||||||||
\(86\) | −6.24794 | −0.673733 | ||||||||
\(87\) | 2.04241 | 0.218970 | ||||||||
\(88\) | 4.52582 | 0.482454 | ||||||||
\(89\) | −1.73757 | −0.184182 | −0.0920908 | − | 0.995751i | \(-0.529355\pi\) | ||||
−0.0920908 | + | 0.995751i | \(0.529355\pi\) | |||||||
\(90\) | 1.01686 | 0.107187 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.24235 | −0.755067 | ||||||||
\(93\) | −4.92147 | −0.510332 | ||||||||
\(94\) | 12.0092 | 1.23866 | ||||||||
\(95\) | −0.904851 | −0.0928358 | ||||||||
\(96\) | −2.04241 | −0.208453 | ||||||||
\(97\) | 5.00070 | 0.507744 | 0.253872 | − | 0.967238i | \(-0.418296\pi\) | ||||
0.253872 | + | 0.967238i | \(0.418296\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.30180 | −0.532851 | ||||||||
\(100\) | −4.24652 | −0.424652 | ||||||||
\(101\) | 9.18777 | 0.914217 | 0.457109 | − | 0.889411i | \(-0.348885\pi\) | ||||
0.457109 | + | 0.889411i | \(0.348885\pi\) | |||||||
\(102\) | 0.530539 | 0.0525312 | ||||||||
\(103\) | −1.83455 | −0.180764 | −0.0903820 | − | 0.995907i | \(-0.528809\pi\) | ||||
−0.0903820 | + | 0.995907i | \(0.528809\pi\) | |||||||
\(104\) | −4.81113 | −0.471770 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.23942 | −0.508898 | ||||||||
\(107\) | 8.27836 | 0.800300 | 0.400150 | − | 0.916450i | \(-0.368958\pi\) | ||||
0.400150 | + | 0.916450i | \(0.368958\pi\) | |||||||
\(108\) | −3.73464 | −0.359366 | ||||||||
\(109\) | −2.21154 | −0.211827 | −0.105914 | − | 0.994375i | \(-0.533777\pi\) | ||||
−0.105914 | + | 0.994375i | \(0.533777\pi\) | |||||||
\(110\) | −3.92856 | −0.374574 | ||||||||
\(111\) | −15.2405 | −1.44657 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.22861 | 0.115578 | 0.0577891 | − | 0.998329i | \(-0.481595\pi\) | ||||
0.0577891 | + | 0.998329i | \(0.481595\pi\) | |||||||
\(114\) | −2.12904 | −0.199403 | ||||||||
\(115\) | 6.28660 | 0.586228 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | 5.63603 | 0.521051 | ||||||||
\(118\) | 10.8814 | 1.00172 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.77288 | 0.161841 | ||||||||
\(121\) | 9.48302 | 0.862092 | ||||||||
\(122\) | −14.4456 | −1.30785 | ||||||||
\(123\) | 11.2945 | 1.01839 | ||||||||
\(124\) | −2.40963 | −0.216391 | ||||||||
\(125\) | 8.02629 | 0.717893 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.7966 | −1.49046 | −0.745230 | − | 0.666807i | \(-0.767660\pi\) | ||||
−0.745230 | + | 0.666807i | \(0.767660\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 12.7609 | 1.12353 | ||||||||
\(130\) | 4.17622 | 0.366279 | ||||||||
\(131\) | −5.41544 | −0.473149 | −0.236574 | − | 0.971613i | \(-0.576025\pi\) | ||||
−0.236574 | + | 0.971613i | \(0.576025\pi\) | |||||||
\(132\) | −9.24359 | −0.804552 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.20553 | −0.536076 | ||||||||
\(135\) | 3.24180 | 0.279009 | ||||||||
\(136\) | 0.259761 | 0.0222743 | ||||||||
\(137\) | −13.2042 | −1.12811 | −0.564055 | − | 0.825738i | \(-0.690759\pi\) | ||||
−0.564055 | + | 0.825738i | \(0.690759\pi\) | |||||||
\(138\) | 14.7919 | 1.25917 | ||||||||
\(139\) | −13.8810 | −1.17737 | −0.588687 | − | 0.808361i | \(-0.700355\pi\) | ||||
−0.588687 | + | 0.808361i | \(0.700355\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.5278 | −2.06561 | ||||||||
\(142\) | 9.47016 | 0.794718 | ||||||||
\(143\) | −21.7743 | −1.82086 | ||||||||
\(144\) | 1.17146 | 0.0976215 | ||||||||
\(145\) | −0.868034 | −0.0720863 | ||||||||
\(146\) | 10.6617 | 0.882372 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.46202 | −0.613375 | ||||||||
\(149\) | 0.148831 | 0.0121927 | 0.00609635 | − | 0.999981i | \(-0.498059\pi\) | ||||
0.00609635 | + | 0.999981i | \(0.498059\pi\) | |||||||
\(150\) | 8.67315 | 0.708160 | ||||||||
\(151\) | 11.4143 | 0.928886 | 0.464443 | − | 0.885603i | \(-0.346255\pi\) | ||||
0.464443 | + | 0.885603i | \(0.346255\pi\) | |||||||
\(152\) | −1.04241 | −0.0845510 | ||||||||
\(153\) | −0.304299 | −0.0246011 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.09164 | 0.168005 | ||||||||
\(156\) | 9.82632 | 0.786735 | ||||||||
\(157\) | 10.0814 | 0.804580 | 0.402290 | − | 0.915512i | \(-0.368214\pi\) | ||||
0.402290 | + | 0.915512i | \(0.368214\pi\) | |||||||
\(158\) | 13.8798 | 1.10422 | ||||||||
\(159\) | 10.7011 | 0.848650 | ||||||||
\(160\) | 0.868034 | 0.0686241 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 11.1421 | 0.875403 | ||||||||
\(163\) | 3.25834 | 0.255213 | 0.127606 | − | 0.991825i | \(-0.459271\pi\) | ||||
0.127606 | + | 0.991825i | \(0.459271\pi\) | |||||||
\(164\) | 5.52999 | 0.431820 | ||||||||
\(165\) | 8.02375 | 0.624648 | ||||||||
\(166\) | 6.90833 | 0.536190 | ||||||||
\(167\) | −13.2848 | −1.02801 | −0.514003 | − | 0.857789i | \(-0.671838\pi\) | ||||
−0.514003 | + | 0.857789i | \(0.671838\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.1469 | 0.780534 | ||||||||
\(170\) | −0.225481 | −0.0172936 | ||||||||
\(171\) | 1.22114 | 0.0933832 | ||||||||
\(172\) | 6.24794 | 0.476401 | ||||||||
\(173\) | −13.3968 | −1.01854 | −0.509269 | − | 0.860607i | \(-0.670084\pi\) | ||||
−0.509269 | + | 0.860607i | \(0.670084\pi\) | |||||||
\(174\) | −2.04241 | −0.154835 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.52582 | −0.341146 | ||||||||
\(177\) | −22.2244 | −1.67049 | ||||||||
\(178\) | 1.73757 | 0.130236 | ||||||||
\(179\) | −6.33944 | −0.473832 | −0.236916 | − | 0.971530i | \(-0.576137\pi\) | ||||
−0.236916 | + | 0.971530i | \(0.576137\pi\) | |||||||
\(180\) | −1.01686 | −0.0757926 | ||||||||
\(181\) | −20.7120 | −1.53951 | −0.769754 | − | 0.638341i | \(-0.779621\pi\) | ||||
−0.769754 | + | 0.638341i | \(0.779621\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 29.5040 | 2.18100 | ||||||||
\(184\) | 7.24235 | 0.533913 | ||||||||
\(185\) | 6.47729 | 0.476220 | ||||||||
\(186\) | 4.92147 | 0.360859 | ||||||||
\(187\) | 1.17563 | 0.0859705 | ||||||||
\(188\) | −12.0092 | −0.875862 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.904851 | 0.0656448 | ||||||||
\(191\) | 13.2608 | 0.959517 | 0.479758 | − | 0.877401i | \(-0.340724\pi\) | ||||
0.479758 | + | 0.877401i | \(0.340724\pi\) | |||||||
\(192\) | 2.04241 | 0.147399 | ||||||||
\(193\) | 1.55926 | 0.112238 | 0.0561191 | − | 0.998424i | \(-0.482127\pi\) | ||||
0.0561191 | + | 0.998424i | \(0.482127\pi\) | |||||||
\(194\) | −5.00070 | −0.359029 | ||||||||
\(195\) | −8.52957 | −0.610815 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.2602 | 1.58597 | 0.792986 | − | 0.609239i | \(-0.208525\pi\) | ||||
0.792986 | + | 0.609239i | \(0.208525\pi\) | |||||||
\(198\) | 5.30180 | 0.376783 | ||||||||
\(199\) | −5.13225 | −0.363816 | −0.181908 | − | 0.983316i | \(-0.558227\pi\) | ||||
−0.181908 | + | 0.983316i | \(0.558227\pi\) | |||||||
\(200\) | 4.24652 | 0.300274 | ||||||||
\(201\) | 12.6743 | 0.893973 | ||||||||
\(202\) | −9.18777 | −0.646449 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.530539 | −0.0371452 | ||||||||
\(205\) | −4.80022 | −0.335262 | ||||||||
\(206\) | 1.83455 | 0.127819 | ||||||||
\(207\) | −8.48410 | −0.589686 | ||||||||
\(208\) | 4.81113 | 0.333592 | ||||||||
\(209\) | −4.71778 | −0.326335 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.7400 | 1.70317 | 0.851586 | − | 0.524214i | \(-0.175641\pi\) | ||||
0.851586 | + | 0.524214i | \(0.175641\pi\) | |||||||
\(212\) | 5.23942 | 0.359845 | ||||||||
\(213\) | −19.3420 | −1.32529 | ||||||||
\(214\) | −8.27836 | −0.565897 | ||||||||
\(215\) | −5.42342 | −0.369875 | ||||||||
\(216\) | 3.73464 | 0.254110 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.21154 | 0.149784 | ||||||||
\(219\) | −21.7757 | −1.47147 | ||||||||
\(220\) | 3.92856 | 0.264864 | ||||||||
\(221\) | −1.24974 | −0.0840667 | ||||||||
\(222\) | 15.2405 | 1.02288 | ||||||||
\(223\) | 8.31616 | 0.556891 | 0.278446 | − | 0.960452i | \(-0.410181\pi\) | ||||
0.278446 | + | 0.960452i | \(0.410181\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.97461 | −0.331641 | ||||||||
\(226\) | −1.22861 | −0.0817261 | ||||||||
\(227\) | −1.88729 | −0.125264 | −0.0626319 | − | 0.998037i | \(-0.519949\pi\) | ||||
−0.0626319 | + | 0.998037i | \(0.519949\pi\) | |||||||
\(228\) | 2.12904 | 0.140999 | ||||||||
\(229\) | 1.27985 | 0.0845748 | 0.0422874 | − | 0.999105i | \(-0.486535\pi\) | ||||
0.0422874 | + | 0.999105i | \(0.486535\pi\) | |||||||
\(230\) | −6.28660 | −0.414526 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | 25.2784 | 1.65604 | 0.828022 | − | 0.560696i | \(-0.189466\pi\) | ||||
0.828022 | + | 0.560696i | \(0.189466\pi\) | |||||||
\(234\) | −5.63603 | −0.368439 | ||||||||
\(235\) | 10.4244 | 0.680013 | ||||||||
\(236\) | −10.8814 | −0.708320 | ||||||||
\(237\) | −28.3483 | −1.84142 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.9113 | −1.67606 | −0.838031 | − | 0.545622i | \(-0.816293\pi\) | ||||
−0.838031 | + | 0.545622i | \(0.816293\pi\) | |||||||
\(240\) | −1.77288 | −0.114439 | ||||||||
\(241\) | −4.46734 | −0.287767 | −0.143883 | − | 0.989595i | \(-0.545959\pi\) | ||||
−0.143883 | + | 0.989595i | \(0.545959\pi\) | |||||||
\(242\) | −9.48302 | −0.609591 | ||||||||
\(243\) | −11.5528 | −0.741111 | ||||||||
\(244\) | 14.4456 | 0.924788 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.2945 | −0.720113 | ||||||||
\(247\) | 5.01519 | 0.319109 | ||||||||
\(248\) | 2.40963 | 0.153012 | ||||||||
\(249\) | −14.1097 | −0.894164 | ||||||||
\(250\) | −8.02629 | −0.507627 | ||||||||
\(251\) | 3.34504 | 0.211137 | 0.105568 | − | 0.994412i | \(-0.466334\pi\) | ||||
0.105568 | + | 0.994412i | \(0.466334\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.7775 | 2.06071 | ||||||||
\(254\) | 16.7966 | 1.05391 | ||||||||
\(255\) | 0.460526 | 0.0288392 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.8611 | −1.36366 | −0.681829 | − | 0.731512i | \(-0.738815\pi\) | ||||
−0.681829 | + | 0.731512i | \(0.738815\pi\) | |||||||
\(258\) | −12.7609 | −0.794458 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.17622 | −0.258998 | ||||||||
\(261\) | 1.17146 | 0.0725114 | ||||||||
\(262\) | 5.41544 | 0.334567 | ||||||||
\(263\) | 22.4538 | 1.38456 | 0.692280 | − | 0.721629i | \(-0.256606\pi\) | ||||
0.692280 | + | 0.721629i | \(0.256606\pi\) | |||||||
\(264\) | 9.24359 | 0.568904 | ||||||||
\(265\) | −4.54799 | −0.279381 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.54883 | −0.217185 | ||||||||
\(268\) | 6.20553 | 0.379063 | ||||||||
\(269\) | −14.9206 | −0.909726 | −0.454863 | − | 0.890561i | \(-0.650312\pi\) | ||||
−0.454863 | + | 0.890561i | \(0.650312\pi\) | |||||||
\(270\) | −3.24180 | −0.197289 | ||||||||
\(271\) | 14.5421 | 0.883369 | 0.441684 | − | 0.897170i | \(-0.354381\pi\) | ||||
0.441684 | + | 0.897170i | \(0.354381\pi\) | |||||||
\(272\) | −0.259761 | −0.0157503 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.2042 | 0.797694 | ||||||||
\(275\) | 19.2190 | 1.15895 | ||||||||
\(276\) | −14.7919 | −0.890366 | ||||||||
\(277\) | 8.12828 | 0.488381 | 0.244191 | − | 0.969727i | \(-0.421478\pi\) | ||||
0.244191 | + | 0.969727i | \(0.421478\pi\) | |||||||
\(278\) | 13.8810 | 0.832529 | ||||||||
\(279\) | −2.82278 | −0.168995 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.24131 | 0.431980 | 0.215990 | − | 0.976396i | \(-0.430702\pi\) | ||||
0.215990 | + | 0.976396i | \(0.430702\pi\) | |||||||
\(282\) | 24.5278 | 1.46061 | ||||||||
\(283\) | −3.71191 | −0.220650 | −0.110325 | − | 0.993896i | \(-0.535189\pi\) | ||||
−0.110325 | + | 0.993896i | \(0.535189\pi\) | |||||||
\(284\) | −9.47016 | −0.561951 | ||||||||
\(285\) | −1.84808 | −0.109471 | ||||||||
\(286\) | 21.7743 | 1.28754 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.17146 | −0.0690288 | ||||||||
\(289\) | −16.9325 | −0.996031 | ||||||||
\(290\) | 0.868034 | 0.0509727 | ||||||||
\(291\) | 10.2135 | 0.598726 | ||||||||
\(292\) | −10.6617 | −0.623931 | ||||||||
\(293\) | 22.7486 | 1.32899 | 0.664494 | − | 0.747294i | \(-0.268647\pi\) | ||||
0.664494 | + | 0.747294i | \(0.268647\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.44544 | 0.549935 | ||||||||
\(296\) | 7.46202 | 0.433721 | ||||||||
\(297\) | 16.9023 | 0.980771 | ||||||||
\(298\) | −0.148831 | −0.00862154 | ||||||||
\(299\) | −34.8438 | −2.01507 | ||||||||
\(300\) | −8.67315 | −0.500745 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −11.4143 | −0.656821 | ||||||||
\(303\) | 18.7652 | 1.07803 | ||||||||
\(304\) | 1.04241 | 0.0597866 | ||||||||
\(305\) | −12.5393 | −0.717999 | ||||||||
\(306\) | 0.304299 | 0.0173956 | ||||||||
\(307\) | 4.92960 | 0.281347 | 0.140674 | − | 0.990056i | \(-0.455073\pi\) | ||||
0.140674 | + | 0.990056i | \(0.455073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.74692 | −0.213155 | ||||||||
\(310\) | −2.09164 | −0.118797 | ||||||||
\(311\) | 9.61384 | 0.545151 | 0.272575 | − | 0.962134i | \(-0.412125\pi\) | ||||
0.272575 | + | 0.962134i | \(0.412125\pi\) | |||||||
\(312\) | −9.82632 | −0.556306 | ||||||||
\(313\) | −31.8007 | −1.79748 | −0.898742 | − | 0.438477i | \(-0.855518\pi\) | ||||
−0.898742 | + | 0.438477i | \(0.855518\pi\) | |||||||
\(314\) | −10.0814 | −0.568924 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.8798 | −0.780799 | ||||||||
\(317\) | −9.64071 | −0.541476 | −0.270738 | − | 0.962653i | \(-0.587268\pi\) | ||||
−0.270738 | + | 0.962653i | \(0.587268\pi\) | |||||||
\(318\) | −10.7011 | −0.600086 | ||||||||
\(319\) | −4.52582 | −0.253397 | ||||||||
\(320\) | −0.868034 | −0.0485246 | ||||||||
\(321\) | 16.9078 | 0.943704 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.270778 | −0.0150665 | ||||||||
\(324\) | −11.1421 | −0.619003 | ||||||||
\(325\) | −20.4305 | −1.13328 | ||||||||
\(326\) | −3.25834 | −0.180463 | ||||||||
\(327\) | −4.51688 | −0.249784 | ||||||||
\(328\) | −5.52999 | −0.305343 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −8.02375 | −0.441693 | ||||||||
\(331\) | −3.55713 | −0.195517 | −0.0977587 | − | 0.995210i | \(-0.531167\pi\) | ||||
−0.0977587 | + | 0.995210i | \(0.531167\pi\) | |||||||
\(332\) | −6.90833 | −0.379144 | ||||||||
\(333\) | −8.74144 | −0.479028 | ||||||||
\(334\) | 13.2848 | 0.726910 | ||||||||
\(335\) | −5.38661 | −0.294302 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.9327 | −1.63054 | −0.815269 | − | 0.579082i | \(-0.803411\pi\) | ||||
−0.815269 | + | 0.579082i | \(0.803411\pi\) | |||||||
\(338\) | −10.1469 | −0.551921 | ||||||||
\(339\) | 2.50934 | 0.136289 | ||||||||
\(340\) | 0.225481 | 0.0122284 | ||||||||
\(341\) | 10.9055 | 0.590569 | ||||||||
\(342\) | −1.22114 | −0.0660319 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.24794 | −0.336867 | ||||||||
\(345\) | 12.8398 | 0.691274 | ||||||||
\(346\) | 13.3968 | 0.720215 | ||||||||
\(347\) | 22.7359 | 1.22053 | 0.610264 | − | 0.792198i | \(-0.291063\pi\) | ||||
0.610264 | + | 0.792198i | \(0.291063\pi\) | |||||||
\(348\) | 2.04241 | 0.109485 | ||||||||
\(349\) | −4.50926 | −0.241375 | −0.120688 | − | 0.992691i | \(-0.538510\pi\) | ||||
−0.120688 | + | 0.992691i | \(0.538510\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.9678 | −0.959052 | ||||||||
\(352\) | 4.52582 | 0.241227 | ||||||||
\(353\) | 5.88890 | 0.313435 | 0.156717 | − | 0.987644i | \(-0.449909\pi\) | ||||
0.156717 | + | 0.987644i | \(0.449909\pi\) | |||||||
\(354\) | 22.2244 | 1.18121 | ||||||||
\(355\) | 8.22042 | 0.436294 | ||||||||
\(356\) | −1.73757 | −0.0920908 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.33944 | 0.335050 | ||||||||
\(359\) | −18.8561 | −0.995188 | −0.497594 | − | 0.867410i | \(-0.665783\pi\) | ||||
−0.497594 | + | 0.867410i | \(0.665783\pi\) | |||||||
\(360\) | 1.01686 | 0.0535935 | ||||||||
\(361\) | −17.9134 | −0.942809 | ||||||||
\(362\) | 20.7120 | 1.08860 | ||||||||
\(363\) | 19.3683 | 1.01657 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.25475 | 0.484416 | ||||||||
\(366\) | −29.5040 | −1.54220 | ||||||||
\(367\) | 34.3704 | 1.79412 | 0.897060 | − | 0.441909i | \(-0.145699\pi\) | ||||
0.897060 | + | 0.441909i | \(0.145699\pi\) | |||||||
\(368\) | −7.24235 | −0.377533 | ||||||||
\(369\) | 6.47815 | 0.337239 | ||||||||
\(370\) | −6.47729 | −0.336738 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.92147 | −0.255166 | ||||||||
\(373\) | 8.60633 | 0.445619 | 0.222809 | − | 0.974862i | \(-0.428477\pi\) | ||||
0.222809 | + | 0.974862i | \(0.428477\pi\) | |||||||
\(374\) | −1.17563 | −0.0607903 | ||||||||
\(375\) | 16.3930 | 0.846531 | ||||||||
\(376\) | 12.0092 | 0.619328 | ||||||||
\(377\) | 4.81113 | 0.247786 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.16987 | −0.162825 | −0.0814126 | − | 0.996680i | \(-0.525943\pi\) | ||||
−0.0814126 | + | 0.996680i | \(0.525943\pi\) | |||||||
\(380\) | −0.904851 | −0.0464179 | ||||||||
\(381\) | −34.3057 | −1.75753 | ||||||||
\(382\) | −13.2608 | −0.678481 | ||||||||
\(383\) | 1.48444 | 0.0758514 | 0.0379257 | − | 0.999281i | \(-0.487925\pi\) | ||||
0.0379257 | + | 0.999281i | \(0.487925\pi\) | |||||||
\(384\) | −2.04241 | −0.104227 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.55926 | −0.0793644 | ||||||||
\(387\) | 7.31920 | 0.372056 | ||||||||
\(388\) | 5.00070 | 0.253872 | ||||||||
\(389\) | 4.47816 | 0.227052 | 0.113526 | − | 0.993535i | \(-0.463785\pi\) | ||||
0.113526 | + | 0.993535i | \(0.463785\pi\) | |||||||
\(390\) | 8.52957 | 0.431912 | ||||||||
\(391\) | 1.88128 | 0.0951403 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.0606 | −0.557932 | ||||||||
\(394\) | −22.2602 | −1.12145 | ||||||||
\(395\) | 12.0481 | 0.606207 | ||||||||
\(396\) | −5.30180 | −0.266426 | ||||||||
\(397\) | −11.8046 | −0.592458 | −0.296229 | − | 0.955117i | \(-0.595729\pi\) | ||||
−0.296229 | + | 0.955117i | \(0.595729\pi\) | |||||||
\(398\) | 5.13225 | 0.257256 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.24652 | −0.212326 | ||||||||
\(401\) | −19.0594 | −0.951782 | −0.475891 | − | 0.879504i | \(-0.657874\pi\) | ||||
−0.475891 | + | 0.879504i | \(0.657874\pi\) | |||||||
\(402\) | −12.6743 | −0.632135 | ||||||||
\(403\) | −11.5930 | −0.577491 | ||||||||
\(404\) | 9.18777 | 0.457109 | ||||||||
\(405\) | 9.67168 | 0.480590 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.7718 | 1.67400 | ||||||||
\(408\) | 0.530539 | 0.0262656 | ||||||||
\(409\) | −20.5188 | −1.01459 | −0.507294 | − | 0.861773i | \(-0.669354\pi\) | ||||
−0.507294 | + | 0.861773i | \(0.669354\pi\) | |||||||
\(410\) | 4.80022 | 0.237066 | ||||||||
\(411\) | −26.9684 | −1.33025 | ||||||||
\(412\) | −1.83455 | −0.0903820 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8.48410 | 0.416971 | ||||||||
\(415\) | 5.99666 | 0.294364 | ||||||||
\(416\) | −4.81113 | −0.235885 | ||||||||
\(417\) | −28.3508 | −1.38835 | ||||||||
\(418\) | 4.71778 | 0.230754 | ||||||||
\(419\) | −13.1307 | −0.641475 | −0.320737 | − | 0.947168i | \(-0.603931\pi\) | ||||
−0.320737 | + | 0.947168i | \(0.603931\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.0216 | −0.878321 | −0.439160 | − | 0.898409i | \(-0.644724\pi\) | ||||
−0.439160 | + | 0.898409i | \(0.644724\pi\) | |||||||
\(422\) | −24.7400 | −1.20432 | ||||||||
\(423\) | −14.0683 | −0.684024 | ||||||||
\(424\) | −5.23942 | −0.254449 | ||||||||
\(425\) | 1.10308 | 0.0535072 | ||||||||
\(426\) | 19.3420 | 0.937123 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.27836 | 0.400150 | ||||||||
\(429\) | −44.4721 | −2.14713 | ||||||||
\(430\) | 5.42342 | 0.261541 | ||||||||
\(431\) | 28.0392 | 1.35060 | 0.675300 | − | 0.737543i | \(-0.264014\pi\) | ||||
0.675300 | + | 0.737543i | \(0.264014\pi\) | |||||||
\(432\) | −3.73464 | −0.179683 | ||||||||
\(433\) | 16.0875 | 0.773118 | 0.386559 | − | 0.922265i | \(-0.373664\pi\) | ||||
0.386559 | + | 0.922265i | \(0.373664\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.77288 | −0.0850033 | ||||||||
\(436\) | −2.21154 | −0.105914 | ||||||||
\(437\) | −7.54953 | −0.361143 | ||||||||
\(438\) | 21.7757 | 1.04048 | ||||||||
\(439\) | 28.4144 | 1.35615 | 0.678074 | − | 0.734994i | \(-0.262815\pi\) | ||||
0.678074 | + | 0.734994i | \(0.262815\pi\) | |||||||
\(440\) | −3.92856 | −0.187287 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.24974 | 0.0594442 | ||||||||
\(443\) | 29.2378 | 1.38913 | 0.694565 | − | 0.719430i | \(-0.255597\pi\) | ||||
0.694565 | + | 0.719430i | \(0.255597\pi\) | |||||||
\(444\) | −15.2405 | −0.723284 | ||||||||
\(445\) | 1.50827 | 0.0714986 | ||||||||
\(446\) | −8.31616 | −0.393781 | ||||||||
\(447\) | 0.303974 | 0.0143775 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.3895 | 0.631890 | 0.315945 | − | 0.948778i | \(-0.397679\pi\) | ||||
0.315945 | + | 0.948778i | \(0.397679\pi\) | |||||||
\(450\) | 4.97461 | 0.234506 | ||||||||
\(451\) | −25.0277 | −1.17851 | ||||||||
\(452\) | 1.22861 | 0.0577891 | ||||||||
\(453\) | 23.3128 | 1.09533 | ||||||||
\(454\) | 1.88729 | 0.0885748 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.12904 | −0.0997016 | ||||||||
\(457\) | 17.7237 | 0.829081 | 0.414541 | − | 0.910031i | \(-0.363942\pi\) | ||||
0.414541 | + | 0.910031i | \(0.363942\pi\) | |||||||
\(458\) | −1.27985 | −0.0598034 | ||||||||
\(459\) | 0.970113 | 0.0452810 | ||||||||
\(460\) | 6.28660 | 0.293114 | ||||||||
\(461\) | 40.2149 | 1.87299 | 0.936497 | − | 0.350675i | \(-0.114048\pi\) | ||||
0.936497 | + | 0.350675i | \(0.114048\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.6300 | −1.56292 | −0.781460 | − | 0.623955i | \(-0.785525\pi\) | ||||
−0.781460 | + | 0.623955i | \(0.785525\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | 4.27200 | 0.198109 | ||||||||
\(466\) | −25.2784 | −1.17100 | ||||||||
\(467\) | −17.1603 | −0.794084 | −0.397042 | − | 0.917800i | \(-0.629963\pi\) | ||||
−0.397042 | + | 0.917800i | \(0.629963\pi\) | |||||||
\(468\) | 5.63603 | 0.260526 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −10.4244 | −0.480842 | ||||||||
\(471\) | 20.5903 | 0.948751 | ||||||||
\(472\) | 10.8814 | 0.500858 | ||||||||
\(473\) | −28.2770 | −1.30018 | ||||||||
\(474\) | 28.3483 | 1.30208 | ||||||||
\(475\) | −4.42663 | −0.203108 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.13776 | 0.281029 | ||||||||
\(478\) | 25.9113 | 1.18515 | ||||||||
\(479\) | −43.1048 | −1.96951 | −0.984755 | − | 0.173948i | \(-0.944348\pi\) | ||||
−0.984755 | + | 0.173948i | \(0.944348\pi\) | |||||||
\(480\) | 1.77288 | 0.0809207 | ||||||||
\(481\) | −35.9007 | −1.63693 | ||||||||
\(482\) | 4.46734 | 0.203482 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.48302 | 0.431046 | ||||||||
\(485\) | −4.34077 | −0.197104 | ||||||||
\(486\) | 11.5528 | 0.524045 | ||||||||
\(487\) | −30.7365 | −1.39280 | −0.696401 | − | 0.717653i | \(-0.745216\pi\) | ||||
−0.696401 | + | 0.717653i | \(0.745216\pi\) | |||||||
\(488\) | −14.4456 | −0.653924 | ||||||||
\(489\) | 6.65487 | 0.300944 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.2771 | 0.554058 | 0.277029 | − | 0.960861i | \(-0.410650\pi\) | ||||
0.277029 | + | 0.960861i | \(0.410650\pi\) | |||||||
\(492\) | 11.2945 | 0.509197 | ||||||||
\(493\) | −0.259761 | −0.0116990 | ||||||||
\(494\) | −5.01519 | −0.225644 | ||||||||
\(495\) | 4.60214 | 0.206851 | ||||||||
\(496\) | −2.40963 | −0.108196 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 14.1097 | 0.632269 | ||||||||
\(499\) | 1.36698 | 0.0611943 | 0.0305972 | − | 0.999532i | \(-0.490259\pi\) | ||||
0.0305972 | + | 0.999532i | \(0.490259\pi\) | |||||||
\(500\) | 8.02629 | 0.358947 | ||||||||
\(501\) | −27.1330 | −1.21221 | ||||||||
\(502\) | −3.34504 | −0.149296 | ||||||||
\(503\) | −23.5002 | −1.04782 | −0.523912 | − | 0.851773i | \(-0.675528\pi\) | ||||
−0.523912 | + | 0.851773i | \(0.675528\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.97530 | −0.354896 | ||||||||
\(506\) | −32.7775 | −1.45714 | ||||||||
\(507\) | 20.7243 | 0.920397 | ||||||||
\(508\) | −16.7966 | −0.745230 | ||||||||
\(509\) | −13.3589 | −0.592124 | −0.296062 | − | 0.955169i | \(-0.595673\pi\) | ||||
−0.296062 | + | 0.955169i | \(0.595673\pi\) | |||||||
\(510\) | −0.460526 | −0.0203924 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −3.89305 | −0.171882 | ||||||||
\(514\) | 21.8611 | 0.964251 | ||||||||
\(515\) | 1.59245 | 0.0701719 | ||||||||
\(516\) | 12.7609 | 0.561767 | ||||||||
\(517\) | 54.3515 | 2.39038 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −27.3618 | −1.20105 | ||||||||
\(520\) | 4.17622 | 0.183139 | ||||||||
\(521\) | 22.8211 | 0.999810 | 0.499905 | − | 0.866080i | \(-0.333368\pi\) | ||||
0.499905 | + | 0.866080i | \(0.333368\pi\) | |||||||
\(522\) | −1.17146 | −0.0512733 | ||||||||
\(523\) | 23.1709 | 1.01319 | 0.506597 | − | 0.862183i | \(-0.330903\pi\) | ||||
0.506597 | + | 0.862183i | \(0.330903\pi\) | |||||||
\(524\) | −5.41544 | −0.236574 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.4538 | −0.979031 | ||||||||
\(527\) | 0.625928 | 0.0272658 | ||||||||
\(528\) | −9.24359 | −0.402276 | ||||||||
\(529\) | 29.4516 | 1.28050 | ||||||||
\(530\) | 4.54799 | 0.197552 | ||||||||
\(531\) | −12.7471 | −0.553178 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.6055 | 1.15241 | ||||||||
\(534\) | 3.54883 | 0.153573 | ||||||||
\(535\) | −7.18590 | −0.310673 | ||||||||
\(536\) | −6.20553 | −0.268038 | ||||||||
\(537\) | −12.9478 | −0.558737 | ||||||||
\(538\) | 14.9206 | 0.643273 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.24180 | 0.139505 | ||||||||
\(541\) | 31.9244 | 1.37254 | 0.686269 | − | 0.727348i | \(-0.259247\pi\) | ||||
0.686269 | + | 0.727348i | \(0.259247\pi\) | |||||||
\(542\) | −14.5421 | −0.624636 | ||||||||
\(543\) | −42.3024 | −1.81537 | ||||||||
\(544\) | 0.259761 | 0.0111371 | ||||||||
\(545\) | 1.91969 | 0.0822305 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.1123 | 1.62956 | 0.814781 | − | 0.579768i | \(-0.196857\pi\) | ||||
0.814781 | + | 0.579768i | \(0.196857\pi\) | |||||||
\(548\) | −13.2042 | −0.564055 | ||||||||
\(549\) | 16.9225 | 0.722233 | ||||||||
\(550\) | −19.2190 | −0.819499 | ||||||||
\(551\) | 1.04241 | 0.0444084 | ||||||||
\(552\) | 14.7919 | 0.629584 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8.12828 | −0.345338 | ||||||||
\(555\) | 13.2293 | 0.561553 | ||||||||
\(556\) | −13.8810 | −0.588687 | ||||||||
\(557\) | −0.0241543 | −0.00102345 | −0.000511725 | − | 1.00000i | \(-0.500163\pi\) | ||||
−0.000511725 | 1.00000i | \(0.500163\pi\) | ||||||||
\(558\) | 2.82278 | 0.119498 | ||||||||
\(559\) | 30.0596 | 1.27139 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.40112 | 0.101375 | ||||||||
\(562\) | −7.24131 | −0.305456 | ||||||||
\(563\) | −14.5356 | −0.612604 | −0.306302 | − | 0.951934i | \(-0.599092\pi\) | ||||
−0.306302 | + | 0.951934i | \(0.599092\pi\) | |||||||
\(564\) | −24.5278 | −1.03281 | ||||||||
\(565\) | −1.06648 | −0.0448671 | ||||||||
\(566\) | 3.71191 | 0.156023 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.47016 | 0.397359 | ||||||||
\(569\) | 14.1911 | 0.594922 | 0.297461 | − | 0.954734i | \(-0.403860\pi\) | ||||
0.297461 | + | 0.954734i | \(0.403860\pi\) | |||||||
\(570\) | 1.84808 | 0.0774076 | ||||||||
\(571\) | −23.7143 | −0.992415 | −0.496207 | − | 0.868204i | \(-0.665274\pi\) | ||||
−0.496207 | + | 0.868204i | \(0.665274\pi\) | |||||||
\(572\) | −21.7743 | −0.910428 | ||||||||
\(573\) | 27.0840 | 1.13145 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.7547 | 1.28256 | ||||||||
\(576\) | 1.17146 | 0.0488107 | ||||||||
\(577\) | −14.1396 | −0.588640 | −0.294320 | − | 0.955707i | \(-0.595093\pi\) | ||||
−0.294320 | + | 0.955707i | \(0.595093\pi\) | |||||||
\(578\) | 16.9325 | 0.704300 | ||||||||
\(579\) | 3.18466 | 0.132350 | ||||||||
\(580\) | −0.868034 | −0.0360431 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −10.2135 | −0.423363 | ||||||||
\(583\) | −23.7127 | −0.982078 | ||||||||
\(584\) | 10.6617 | 0.441186 | ||||||||
\(585\) | −4.89226 | −0.202270 | ||||||||
\(586\) | −22.7486 | −0.939736 | ||||||||
\(587\) | 11.6325 | 0.480124 | 0.240062 | − | 0.970758i | \(-0.422832\pi\) | ||||
0.240062 | + | 0.970758i | \(0.422832\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.51183 | −0.103498 | ||||||||
\(590\) | −9.44544 | −0.388863 | ||||||||
\(591\) | 45.4645 | 1.87016 | ||||||||
\(592\) | −7.46202 | −0.306687 | ||||||||
\(593\) | 13.0595 | 0.536288 | 0.268144 | − | 0.963379i | \(-0.413590\pi\) | ||||
0.268144 | + | 0.963379i | \(0.413590\pi\) | |||||||
\(594\) | −16.9023 | −0.693510 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.148831 | 0.00609635 | ||||||||
\(597\) | −10.4822 | −0.429007 | ||||||||
\(598\) | 34.8438 | 1.42487 | ||||||||
\(599\) | 45.5493 | 1.86109 | 0.930546 | − | 0.366174i | \(-0.119333\pi\) | ||||
0.930546 | + | 0.366174i | \(0.119333\pi\) | |||||||
\(600\) | 8.67315 | 0.354080 | ||||||||
\(601\) | 32.3140 | 1.31812 | 0.659058 | − | 0.752092i | \(-0.270955\pi\) | ||||
0.659058 | + | 0.752092i | \(0.270955\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.26951 | 0.296037 | ||||||||
\(604\) | 11.4143 | 0.464443 | ||||||||
\(605\) | −8.23158 | −0.334661 | ||||||||
\(606\) | −18.7652 | −0.762286 | ||||||||
\(607\) | −4.77660 | −0.193876 | −0.0969381 | − | 0.995290i | \(-0.530905\pi\) | ||||
−0.0969381 | + | 0.995290i | \(0.530905\pi\) | |||||||
\(608\) | −1.04241 | −0.0422755 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.5393 | 0.507702 | ||||||||
\(611\) | −57.7779 | −2.33744 | ||||||||
\(612\) | −0.304299 | −0.0123005 | ||||||||
\(613\) | −2.02485 | −0.0817830 | −0.0408915 | − | 0.999164i | \(-0.513020\pi\) | ||||
−0.0408915 | + | 0.999164i | \(0.513020\pi\) | |||||||
\(614\) | −4.92960 | −0.198943 | ||||||||
\(615\) | −9.80403 | −0.395337 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.2876 | 0.776491 | 0.388246 | − | 0.921556i | \(-0.373081\pi\) | ||||
0.388246 | + | 0.921556i | \(0.373081\pi\) | |||||||
\(618\) | 3.74692 | 0.150723 | ||||||||
\(619\) | −8.99043 | −0.361356 | −0.180678 | − | 0.983542i | \(-0.557829\pi\) | ||||
−0.180678 | + | 0.983542i | \(0.557829\pi\) | |||||||
\(620\) | 2.09164 | 0.0840023 | ||||||||
\(621\) | 27.0476 | 1.08538 | ||||||||
\(622\) | −9.61384 | −0.385480 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 9.82632 | 0.393367 | ||||||||
\(625\) | 14.2655 | 0.570620 | ||||||||
\(626\) | 31.8007 | 1.27101 | ||||||||
\(627\) | −9.63566 | −0.384811 | ||||||||
\(628\) | 10.0814 | 0.402290 | ||||||||
\(629\) | 1.93834 | 0.0772867 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.4821 | 1.41252 | 0.706259 | − | 0.707953i | \(-0.250381\pi\) | ||||
0.706259 | + | 0.707953i | \(0.250381\pi\) | |||||||
\(632\) | 13.8798 | 0.552108 | ||||||||
\(633\) | 50.5294 | 2.00836 | ||||||||
\(634\) | 9.64071 | 0.382881 | ||||||||
\(635\) | 14.5800 | 0.578591 | ||||||||
\(636\) | 10.7011 | 0.424325 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.52582 | 0.179179 | ||||||||
\(639\) | −11.0939 | −0.438867 | ||||||||
\(640\) | 0.868034 | 0.0343120 | ||||||||
\(641\) | −31.7682 | −1.25477 | −0.627384 | − | 0.778710i | \(-0.715874\pi\) | ||||
−0.627384 | + | 0.778710i | \(0.715874\pi\) | |||||||
\(642\) | −16.9078 | −0.667300 | ||||||||
\(643\) | −44.8753 | −1.76971 | −0.884855 | − | 0.465866i | \(-0.845743\pi\) | ||||
−0.884855 | + | 0.465866i | \(0.845743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.0769 | −0.436152 | ||||||||
\(646\) | 0.270778 | 0.0106536 | ||||||||
\(647\) | 36.1562 | 1.42145 | 0.710724 | − | 0.703471i | \(-0.248368\pi\) | ||||
0.710724 | + | 0.703471i | \(0.248368\pi\) | |||||||
\(648\) | 11.1421 | 0.437701 | ||||||||
\(649\) | 49.2473 | 1.93313 | ||||||||
\(650\) | 20.4305 | 0.801352 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.25834 | 0.127606 | ||||||||
\(653\) | −30.9296 | −1.21037 | −0.605185 | − | 0.796085i | \(-0.706901\pi\) | ||||
−0.605185 | + | 0.796085i | \(0.706901\pi\) | |||||||
\(654\) | 4.51688 | 0.176624 | ||||||||
\(655\) | 4.70078 | 0.183675 | ||||||||
\(656\) | 5.52999 | 0.215910 | ||||||||
\(657\) | −12.4898 | −0.487273 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.2313 | −1.64510 | −0.822550 | − | 0.568693i | \(-0.807449\pi\) | ||||
−0.822550 | + | 0.568693i | \(0.807449\pi\) | |||||||
\(660\) | 8.02375 | 0.312324 | ||||||||
\(661\) | 20.5109 | 0.797780 | 0.398890 | − | 0.916999i | \(-0.369395\pi\) | ||||
0.398890 | + | 0.916999i | \(0.369395\pi\) | |||||||
\(662\) | 3.55713 | 0.138252 | ||||||||
\(663\) | −2.55249 | −0.0991305 | ||||||||
\(664\) | 6.90833 | 0.268095 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.74144 | 0.338724 | ||||||||
\(667\) | −7.24235 | −0.280425 | ||||||||
\(668\) | −13.2848 | −0.514003 | ||||||||
\(669\) | 16.9850 | 0.656680 | ||||||||
\(670\) | 5.38661 | 0.208103 | ||||||||
\(671\) | −65.3784 | −2.52390 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.41486 | −0.0930861 | −0.0465431 | − | 0.998916i | \(-0.514820\pi\) | ||||
−0.0465431 | + | 0.998916i | \(0.514820\pi\) | |||||||
\(674\) | 29.9327 | 1.15297 | ||||||||
\(675\) | 15.8592 | 0.610422 | ||||||||
\(676\) | 10.1469 | 0.390267 | ||||||||
\(677\) | −26.0598 | −1.00156 | −0.500780 | − | 0.865575i | \(-0.666953\pi\) | ||||
−0.500780 | + | 0.865575i | \(0.666953\pi\) | |||||||
\(678\) | −2.50934 | −0.0963705 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.225481 | −0.00864680 | ||||||||
\(681\) | −3.85463 | −0.147710 | ||||||||
\(682\) | −10.9055 | −0.417595 | ||||||||
\(683\) | −30.3162 | −1.16002 | −0.580008 | − | 0.814611i | \(-0.696950\pi\) | ||||
−0.580008 | + | 0.814611i | \(0.696950\pi\) | |||||||
\(684\) | 1.22114 | 0.0466916 | ||||||||
\(685\) | 11.4617 | 0.437928 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.61398 | 0.0997297 | ||||||||
\(688\) | 6.24794 | 0.238201 | ||||||||
\(689\) | 25.2075 | 0.960330 | ||||||||
\(690\) | −12.8398 | −0.488804 | ||||||||
\(691\) | 28.0275 | 1.06622 | 0.533108 | − | 0.846047i | \(-0.321024\pi\) | ||||
0.533108 | + | 0.846047i | \(0.321024\pi\) | |||||||
\(692\) | −13.3968 | −0.509269 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.7359 | −0.863043 | ||||||||
\(695\) | 12.0492 | 0.457053 | ||||||||
\(696\) | −2.04241 | −0.0774175 | ||||||||
\(697\) | −1.43647 | −0.0544103 | ||||||||
\(698\) | 4.50926 | 0.170678 | ||||||||
\(699\) | 51.6290 | 1.95279 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.56961 | 0.361439 | 0.180720 | − | 0.983535i | \(-0.442157\pi\) | ||||
0.180720 | + | 0.983535i | \(0.442157\pi\) | |||||||
\(702\) | 17.9678 | 0.678152 | ||||||||
\(703\) | −7.77852 | −0.293373 | ||||||||
\(704\) | −4.52582 | −0.170573 | ||||||||
\(705\) | 21.2910 | 0.801864 | ||||||||
\(706\) | −5.88890 | −0.221632 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −22.2244 | −0.835243 | ||||||||
\(709\) | 35.2632 | 1.32434 | 0.662169 | − | 0.749355i | \(-0.269636\pi\) | ||||
0.662169 | + | 0.749355i | \(0.269636\pi\) | |||||||
\(710\) | −8.22042 | −0.308507 | ||||||||
\(711\) | −16.2596 | −0.609782 | ||||||||
\(712\) | 1.73757 | 0.0651180 | ||||||||
\(713\) | 17.4514 | 0.653559 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.9008 | 0.706850 | ||||||||
\(716\) | −6.33944 | −0.236916 | ||||||||
\(717\) | −52.9216 | −1.97639 | ||||||||
\(718\) | 18.8561 | 0.703704 | ||||||||
\(719\) | −3.29912 | −0.123036 | −0.0615181 | − | 0.998106i | \(-0.519594\pi\) | ||||
−0.0615181 | + | 0.998106i | \(0.519594\pi\) | |||||||
\(720\) | −1.01686 | −0.0378963 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 17.9134 | 0.666667 | ||||||||
\(723\) | −9.12416 | −0.339331 | ||||||||
\(724\) | −20.7120 | −0.769754 | ||||||||
\(725\) | −4.24652 | −0.157712 | ||||||||
\(726\) | −19.3683 | −0.718823 | ||||||||
\(727\) | 18.2413 | 0.676532 | 0.338266 | − | 0.941051i | \(-0.390160\pi\) | ||||
0.338266 | + | 0.941051i | \(0.390160\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.83061 | 0.364097 | ||||||||
\(730\) | −9.25475 | −0.342534 | ||||||||
\(731\) | −1.62297 | −0.0600277 | ||||||||
\(732\) | 29.5040 | 1.09050 | ||||||||
\(733\) | 44.8721 | 1.65739 | 0.828694 | − | 0.559703i | \(-0.189085\pi\) | ||||
0.828694 | + | 0.559703i | \(0.189085\pi\) | |||||||
\(734\) | −34.3704 | −1.26863 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.24235 | 0.266956 | ||||||||
\(737\) | −28.0851 | −1.03453 | ||||||||
\(738\) | −6.47815 | −0.238464 | ||||||||
\(739\) | 0.811066 | 0.0298355 | 0.0149178 | − | 0.999889i | \(-0.495251\pi\) | ||||
0.0149178 | + | 0.999889i | \(0.495251\pi\) | |||||||
\(740\) | 6.47729 | 0.238110 | ||||||||
\(741\) | 10.2431 | 0.376290 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.9370 | 1.09828 | 0.549142 | − | 0.835729i | \(-0.314955\pi\) | ||||
0.549142 | + | 0.835729i | \(0.314955\pi\) | |||||||
\(744\) | 4.92147 | 0.180430 | ||||||||
\(745\) | −0.129190 | −0.00473316 | ||||||||
\(746\) | −8.60633 | −0.315100 | ||||||||
\(747\) | −8.09281 | −0.296100 | ||||||||
\(748\) | 1.17563 | 0.0429853 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −16.3930 | −0.598588 | ||||||||
\(751\) | 13.5353 | 0.493910 | 0.246955 | − | 0.969027i | \(-0.420570\pi\) | ||||
0.246955 | + | 0.969027i | \(0.420570\pi\) | |||||||
\(752\) | −12.0092 | −0.437931 | ||||||||
\(753\) | 6.83196 | 0.248970 | ||||||||
\(754\) | −4.81113 | −0.175211 | ||||||||
\(755\) | −9.90803 | −0.360590 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.4918 | −1.18094 | −0.590468 | − | 0.807061i | \(-0.701057\pi\) | ||||
−0.590468 | + | 0.807061i | \(0.701057\pi\) | |||||||
\(758\) | 3.16987 | 0.115135 | ||||||||
\(759\) | 66.9453 | 2.42996 | ||||||||
\(760\) | 0.904851 | 0.0328224 | ||||||||
\(761\) | −10.7653 | −0.390243 | −0.195121 | − | 0.980779i | \(-0.562510\pi\) | ||||
−0.195121 | + | 0.980779i | \(0.562510\pi\) | |||||||
\(762\) | 34.3057 | 1.24276 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 13.2608 | 0.479758 | ||||||||
\(765\) | 0.264141 | 0.00955005 | ||||||||
\(766\) | −1.48444 | −0.0536351 | ||||||||
\(767\) | −52.3519 | −1.89032 | ||||||||
\(768\) | 2.04241 | 0.0736993 | ||||||||
\(769\) | 53.4576 | 1.92773 | 0.963866 | − | 0.266389i | \(-0.0858304\pi\) | ||||
0.963866 | + | 0.266389i | \(0.0858304\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44.6494 | −1.60801 | ||||||||
\(772\) | 1.55926 | 0.0561191 | ||||||||
\(773\) | −21.5547 | −0.775269 | −0.387635 | − | 0.921813i | \(-0.626708\pi\) | ||||
−0.387635 | + | 0.921813i | \(0.626708\pi\) | |||||||
\(774\) | −7.31920 | −0.263083 | ||||||||
\(775\) | 10.2325 | 0.367564 | ||||||||
\(776\) | −5.00070 | −0.179515 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.47816 | −0.160550 | ||||||||
\(779\) | 5.76454 | 0.206536 | ||||||||
\(780\) | −8.52957 | −0.305408 | ||||||||
\(781\) | 42.8602 | 1.53366 | ||||||||
\(782\) | −1.88128 | −0.0672743 | ||||||||
\(783\) | −3.73464 | −0.133465 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.75096 | −0.312335 | ||||||||
\(786\) | 11.0606 | 0.394517 | ||||||||
\(787\) | −12.7403 | −0.454141 | −0.227071 | − | 0.973878i | \(-0.572915\pi\) | ||||
−0.227071 | + | 0.973878i | \(0.572915\pi\) | |||||||
\(788\) | 22.2602 | 0.792986 | ||||||||
\(789\) | 45.8599 | 1.63266 | ||||||||
\(790\) | −12.0481 | −0.428653 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.30180 | 0.188391 | ||||||||
\(793\) | 69.4999 | 2.46801 | ||||||||
\(794\) | 11.8046 | 0.418931 | ||||||||
\(795\) | −9.28889 | −0.329443 | ||||||||
\(796\) | −5.13225 | −0.181908 | ||||||||
\(797\) | −14.5075 | −0.513884 | −0.256942 | − | 0.966427i | \(-0.582715\pi\) | ||||
−0.256942 | + | 0.966427i | \(0.582715\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.11952 | 0.110361 | ||||||||
\(800\) | 4.24652 | 0.150137 | ||||||||
\(801\) | −2.03548 | −0.0719203 | ||||||||
\(802\) | 19.0594 | 0.673012 | ||||||||
\(803\) | 48.2531 | 1.70282 | ||||||||
\(804\) | 12.6743 | 0.446987 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.5930 | 0.408348 | ||||||||
\(807\) | −30.4741 | −1.07274 | ||||||||
\(808\) | −9.18777 | −0.323225 | ||||||||
\(809\) | 18.1617 | 0.638532 | 0.319266 | − | 0.947665i | \(-0.396564\pi\) | ||||
0.319266 | + | 0.947665i | \(0.396564\pi\) | |||||||
\(810\) | −9.67168 | −0.339828 | ||||||||
\(811\) | −4.45962 | −0.156598 | −0.0782992 | − | 0.996930i | \(-0.524949\pi\) | ||||
−0.0782992 | + | 0.996930i | \(0.524949\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.7010 | 1.04166 | ||||||||
\(814\) | −33.7718 | −1.18370 | ||||||||
\(815\) | −2.82834 | −0.0990726 | ||||||||
\(816\) | −0.530539 | −0.0185726 | ||||||||
\(817\) | 6.51295 | 0.227859 | ||||||||
\(818\) | 20.5188 | 0.717422 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.80022 | −0.167631 | ||||||||
\(821\) | −19.6618 | −0.686202 | −0.343101 | − | 0.939298i | \(-0.611477\pi\) | ||||
−0.343101 | + | 0.939298i | \(0.611477\pi\) | |||||||
\(822\) | 26.9684 | 0.940631 | ||||||||
\(823\) | 34.0102 | 1.18552 | 0.592760 | − | 0.805379i | \(-0.298038\pi\) | ||||
0.592760 | + | 0.805379i | \(0.298038\pi\) | |||||||
\(824\) | 1.83455 | 0.0639097 | ||||||||
\(825\) | 39.2531 | 1.36662 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.94008 | −0.345650 | −0.172825 | − | 0.984953i | \(-0.555290\pi\) | ||||
−0.172825 | + | 0.984953i | \(0.555290\pi\) | |||||||
\(828\) | −8.48410 | −0.294843 | ||||||||
\(829\) | −0.831125 | −0.0288662 | −0.0144331 | − | 0.999896i | \(-0.504594\pi\) | ||||
−0.0144331 | + | 0.999896i | \(0.504594\pi\) | |||||||
\(830\) | −5.99666 | −0.208147 | ||||||||
\(831\) | 16.6013 | 0.575894 | ||||||||
\(832\) | 4.81113 | 0.166796 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 28.3508 | 0.981709 | ||||||||
\(835\) | 11.5316 | 0.399068 | ||||||||
\(836\) | −4.71778 | −0.163168 | ||||||||
\(837\) | 8.99911 | 0.311055 | ||||||||
\(838\) | 13.1307 | 0.453591 | ||||||||
\(839\) | 20.4554 | 0.706199 | 0.353100 | − | 0.935586i | \(-0.385128\pi\) | ||||
0.353100 | + | 0.935586i | \(0.385128\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 18.0216 | 0.621066 | ||||||||
\(843\) | 14.7897 | 0.509386 | ||||||||
\(844\) | 24.7400 | 0.851586 | ||||||||
\(845\) | −8.80789 | −0.303001 | ||||||||
\(846\) | 14.0683 | 0.483678 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.23942 | 0.179922 | ||||||||
\(849\) | −7.58126 | −0.260188 | ||||||||
\(850\) | −1.10308 | −0.0378353 | ||||||||
\(851\) | 54.0426 | 1.85255 | ||||||||
\(852\) | −19.3420 | −0.662646 | ||||||||
\(853\) | 12.6286 | 0.432394 | 0.216197 | − | 0.976350i | \(-0.430635\pi\) | ||||
0.216197 | + | 0.976350i | \(0.430635\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.05999 | −0.0362510 | ||||||||
\(856\) | −8.27836 | −0.282949 | ||||||||
\(857\) | −35.0864 | −1.19853 | −0.599265 | − | 0.800551i | \(-0.704540\pi\) | ||||
−0.599265 | + | 0.800551i | \(0.704540\pi\) | |||||||
\(858\) | 44.4721 | 1.51825 | ||||||||
\(859\) | 18.8935 | 0.644637 | 0.322318 | − | 0.946631i | \(-0.395538\pi\) | ||||
0.322318 | + | 0.946631i | \(0.395538\pi\) | |||||||
\(860\) | −5.42342 | −0.184937 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28.0392 | −0.955018 | ||||||||
\(863\) | 42.0411 | 1.43110 | 0.715548 | − | 0.698564i | \(-0.246177\pi\) | ||||
0.715548 | + | 0.698564i | \(0.246177\pi\) | |||||||
\(864\) | 3.73464 | 0.127055 | ||||||||
\(865\) | 11.6289 | 0.395393 | ||||||||
\(866\) | −16.0875 | −0.546677 | ||||||||
\(867\) | −34.5832 | −1.17451 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 62.8174 | 2.13093 | ||||||||
\(870\) | 1.77288 | 0.0601064 | ||||||||
\(871\) | 29.8556 | 1.01162 | ||||||||
\(872\) | 2.21154 | 0.0748922 | ||||||||
\(873\) | 5.85810 | 0.198267 | ||||||||
\(874\) | 7.54953 | 0.255367 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −21.7757 | −0.735733 | ||||||||
\(877\) | 52.8075 | 1.78318 | 0.891592 | − | 0.452840i | \(-0.149589\pi\) | ||||
0.891592 | + | 0.452840i | \(0.149589\pi\) | |||||||
\(878\) | −28.4144 | −0.958941 | ||||||||
\(879\) | 46.4621 | 1.56713 | ||||||||
\(880\) | 3.92856 | 0.132432 | ||||||||
\(881\) | −27.6107 | −0.930229 | −0.465114 | − | 0.885251i | \(-0.653987\pi\) | ||||
−0.465114 | + | 0.885251i | \(0.653987\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.24316 | 0.176446 | 0.0882232 | − | 0.996101i | \(-0.471881\pi\) | ||||
0.0882232 | + | 0.996101i | \(0.471881\pi\) | |||||||
\(884\) | −1.24974 | −0.0420334 | ||||||||
\(885\) | 19.2915 | 0.648477 | ||||||||
\(886\) | −29.2378 | −0.982264 | ||||||||
\(887\) | −26.5924 | −0.892887 | −0.446444 | − | 0.894812i | \(-0.647310\pi\) | ||||
−0.446444 | + | 0.894812i | \(0.647310\pi\) | |||||||
\(888\) | 15.2405 | 0.511439 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.50827 | −0.0505572 | ||||||||
\(891\) | 50.4269 | 1.68937 | ||||||||
\(892\) | 8.31616 | 0.278446 | ||||||||
\(893\) | −12.5186 | −0.418918 | ||||||||
\(894\) | −0.303974 | −0.0101664 | ||||||||
\(895\) | 5.50285 | 0.183940 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −71.1656 | −2.37615 | ||||||||
\(898\) | −13.3895 | −0.446813 | ||||||||
\(899\) | −2.40963 | −0.0803657 | ||||||||
\(900\) | −4.97461 | −0.165820 | ||||||||
\(901\) | −1.36100 | −0.0453414 | ||||||||
\(902\) | 25.0277 | 0.833332 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.22861 | −0.0408631 | ||||||||
\(905\) | 17.9787 | 0.597631 | ||||||||
\(906\) | −23.3128 | −0.774516 | ||||||||
\(907\) | 39.9778 | 1.32744 | 0.663721 | − | 0.747980i | \(-0.268976\pi\) | ||||
0.663721 | + | 0.747980i | \(0.268976\pi\) | |||||||
\(908\) | −1.88729 | −0.0626319 | ||||||||
\(909\) | 10.7631 | 0.356989 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.5464 | 1.47589 | 0.737944 | − | 0.674862i | \(-0.235797\pi\) | ||||
0.737944 | + | 0.674862i | \(0.235797\pi\) | |||||||
\(912\) | 2.12904 | 0.0704997 | ||||||||
\(913\) | 31.2658 | 1.03475 | ||||||||
\(914\) | −17.7237 | −0.586249 | ||||||||
\(915\) | −25.6105 | −0.846656 | ||||||||
\(916\) | 1.27985 | 0.0422874 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.970113 | −0.0320185 | ||||||||
\(919\) | −52.9806 | −1.74767 | −0.873835 | − | 0.486223i | \(-0.838374\pi\) | ||||
−0.873835 | + | 0.486223i | \(0.838374\pi\) | |||||||
\(920\) | −6.28660 | −0.207263 | ||||||||
\(921\) | 10.0683 | 0.331761 | ||||||||
\(922\) | −40.2149 | −1.32441 | ||||||||
\(923\) | −45.5621 | −1.49970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 31.6876 | 1.04188 | ||||||||
\(926\) | 33.6300 | 1.10515 | ||||||||
\(927\) | −2.14910 | −0.0705858 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | 44.6379 | 1.46452 | 0.732261 | − | 0.681024i | \(-0.238465\pi\) | ||||
0.732261 | + | 0.681024i | \(0.238465\pi\) | |||||||
\(930\) | −4.27200 | −0.140084 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 25.2784 | 0.828022 | ||||||||
\(933\) | 19.6354 | 0.642836 | ||||||||
\(934\) | 17.1603 | 0.561502 | ||||||||
\(935\) | −1.02049 | −0.0333735 | ||||||||
\(936\) | −5.63603 | −0.184219 | ||||||||
\(937\) | −39.7696 | −1.29921 | −0.649607 | − | 0.760270i | \(-0.725067\pi\) | ||||
−0.649607 | + | 0.760270i | \(0.725067\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −64.9503 | −2.11957 | ||||||||
\(940\) | 10.4244 | 0.340007 | ||||||||
\(941\) | −7.66901 | −0.250002 | −0.125001 | − | 0.992157i | \(-0.539893\pi\) | ||||
−0.125001 | + | 0.992157i | \(0.539893\pi\) | |||||||
\(942\) | −20.5903 | −0.670868 | ||||||||
\(943\) | −40.0501 | −1.30421 | ||||||||
\(944\) | −10.8814 | −0.354160 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 28.2770 | 0.919366 | ||||||||
\(947\) | −39.8309 | −1.29433 | −0.647165 | − | 0.762350i | \(-0.724046\pi\) | ||||
−0.647165 | + | 0.762350i | \(0.724046\pi\) | |||||||
\(948\) | −28.3483 | −0.920710 | ||||||||
\(949\) | −51.2950 | −1.66511 | ||||||||
\(950\) | 4.42663 | 0.143619 | ||||||||
\(951\) | −19.6903 | −0.638503 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.43327 | −0.176001 | −0.0880004 | − | 0.996120i | \(-0.528048\pi\) | ||||
−0.0880004 | + | 0.996120i | \(0.528048\pi\) | |||||||
\(954\) | −6.13776 | −0.198717 | ||||||||
\(955\) | −11.5108 | −0.372481 | ||||||||
\(956\) | −25.9113 | −0.838031 | ||||||||
\(957\) | −9.24359 | −0.298803 | ||||||||
\(958\) | 43.1048 | 1.39265 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.77288 | −0.0572196 | ||||||||
\(961\) | −25.1937 | −0.812699 | ||||||||
\(962\) | 35.9007 | 1.15749 | ||||||||
\(963\) | 9.69775 | 0.312506 | ||||||||
\(964\) | −4.46734 | −0.143883 | ||||||||
\(965\) | −1.35349 | −0.0435705 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.8343 | −1.37746 | −0.688729 | − | 0.725019i | \(-0.741831\pi\) | ||||
−0.688729 | + | 0.725019i | \(0.741831\pi\) | |||||||
\(968\) | −9.48302 | −0.304796 | ||||||||
\(969\) | −0.553042 | −0.0177663 | ||||||||
\(970\) | 4.34077 | 0.139374 | ||||||||
\(971\) | −22.8379 | −0.732903 | −0.366452 | − | 0.930437i | \(-0.619427\pi\) | ||||
−0.366452 | + | 0.930437i | \(0.619427\pi\) | |||||||
\(972\) | −11.5528 | −0.370556 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 30.7365 | 0.984860 | ||||||||
\(975\) | −41.7276 | −1.33635 | ||||||||
\(976\) | 14.4456 | 0.462394 | ||||||||
\(977\) | −21.1921 | −0.677996 | −0.338998 | − | 0.940787i | \(-0.610088\pi\) | ||||
−0.338998 | + | 0.940787i | \(0.610088\pi\) | |||||||
\(978\) | −6.65487 | −0.212799 | ||||||||
\(979\) | 7.86390 | 0.251331 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.59073 | −0.0827155 | ||||||||
\(982\) | −12.2771 | −0.391778 | ||||||||
\(983\) | 29.4370 | 0.938895 | 0.469447 | − | 0.882960i | \(-0.344453\pi\) | ||||
0.469447 | + | 0.882960i | \(0.344453\pi\) | |||||||
\(984\) | −11.2945 | −0.360056 | ||||||||
\(985\) | −19.3226 | −0.615669 | ||||||||
\(986\) | 0.259761 | 0.00827247 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.01519 | 0.159554 | ||||||||
\(989\) | −45.2498 | −1.43886 | ||||||||
\(990\) | −4.60214 | −0.146266 | ||||||||
\(991\) | −21.8055 | −0.692674 | −0.346337 | − | 0.938110i | \(-0.612575\pi\) | ||||
−0.346337 | + | 0.938110i | \(0.612575\pi\) | |||||||
\(992\) | 2.40963 | 0.0765059 | ||||||||
\(993\) | −7.26513 | −0.230552 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.45497 | 0.141232 | ||||||||
\(996\) | −14.1097 | −0.447082 | ||||||||
\(997\) | 4.80466 | 0.152165 | 0.0760825 | − | 0.997102i | \(-0.475759\pi\) | ||||
0.0760825 | + | 0.997102i | \(0.475759\pi\) | |||||||
\(998\) | −1.36698 | −0.0432709 | ||||||||
\(999\) | 27.8680 | 0.881704 |
(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 | 2842.2.a.s.1.5 | 5 | ||
7.3 | odd | 6 | 406.2.e.c.233.5 | ✓ | 10 | ||
7.5 | odd | 6 | 406.2.e.c.291.5 | yes | 10 | ||
7.6 | odd | 2 | 2842.2.a.v.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
406.2.e.c.233.5 | ✓ | 10 | 7.3 | odd | 6 | ||
406.2.e.c.291.5 | yes | 10 | 7.5 | odd | 6 | ||
2842.2.a.s.1.5 | 5 | 1.1 | even | 1 | trivial | ||
2842.2.a.v.1.1 | 5 | 7.6 | odd | 2 |