Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.172341 | −0.0995013 | −0.0497506 | − | 0.998762i | \(-0.515843\pi\) | ||||
−0.0497506 | + | 0.998762i | \(0.515843\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.94901 | 1.49259 | 0.746293 | − | 0.665618i | \(-0.231832\pi\) | ||||
0.746293 | + | 0.665618i | \(0.231832\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.97030 | −0.990099 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50533 | 0.755384 | 0.377692 | − | 0.925931i | \(-0.376718\pi\) | ||||
0.377692 | + | 0.925931i | \(0.376718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.08392 | 1.41003 | 0.705013 | − | 0.709195i | \(-0.250941\pi\) | ||||
0.705013 | + | 0.709195i | \(0.250941\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.172341 | 0.0444983 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.79588 | −1.40571 | −0.702853 | − | 0.711335i | \(-0.748091\pi\) | ||||
−0.702853 | + | 0.711335i | \(0.748091\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.40336 | −0.321953 | −0.160976 | − | 0.986958i | \(-0.551464\pi\) | ||||
−0.160976 | + | 0.986958i | \(0.551464\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.680578 | −0.148514 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.18550 | −0.872738 | −0.436369 | − | 0.899768i | \(-0.643736\pi\) | ||||
−0.436369 | + | 0.899768i | \(0.643736\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.02893 | 0.198017 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.24974 | 0.603462 | 0.301731 | − | 0.953393i | \(-0.402436\pi\) | ||||
0.301731 | + | 0.953393i | \(0.402436\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.87221 | −0.515864 | −0.257932 | − | 0.966163i | \(-0.583041\pi\) | ||||
−0.257932 | + | 0.966163i | \(0.583041\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.431771 | −0.0751617 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.94901 | −0.667505 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.92358 | −0.480634 | −0.240317 | − | 0.970695i | \(-0.577251\pi\) | ||||
−0.240317 | + | 0.970695i | \(0.577251\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.876169 | −0.140299 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.1289 | −1.73805 | −0.869023 | − | 0.494771i | \(-0.835252\pi\) | ||||
−0.869023 | + | 0.494771i | \(0.835252\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.07418 | −0.163811 | −0.0819053 | − | 0.996640i | \(-0.526101\pi\) | ||||
−0.0819053 | + | 0.996640i | \(0.526101\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.97030 | 0.442786 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.742520 | 0.108308 | 0.0541539 | − | 0.998533i | \(-0.482754\pi\) | ||||
0.0541539 | + | 0.998533i | \(0.482754\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.59469 | 1.22781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.998869 | 0.139870 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.39320 | −1.01553 | −0.507767 | − | 0.861494i | \(-0.669529\pi\) | ||||
−0.507767 | + | 0.861494i | \(0.669529\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.50533 | −0.337818 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.241857 | 0.0320347 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.2989 | −1.73137 | −0.865685 | − | 0.500589i | \(-0.833117\pi\) | ||||
−0.865685 | + | 0.500589i | \(0.833117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.5530 | −1.73528 | −0.867642 | − | 0.497190i | \(-0.834365\pi\) | ||||
−0.867642 | + | 0.497190i | \(0.834365\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.7297 | −1.47781 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.08392 | −0.630583 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.250028 | −0.0305458 | −0.0152729 | − | 0.999883i | \(-0.504862\pi\) | ||||
−0.0152729 | + | 0.999883i | \(0.504862\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.721335 | 0.0868385 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.16282 | 0.138001 | 0.0690006 | − | 0.997617i | \(-0.478019\pi\) | ||||
0.0690006 | + | 0.997617i | \(0.478019\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.19316 | 1.07598 | 0.537989 | − | 0.842952i | \(-0.319184\pi\) | ||||
0.537989 | + | 0.842952i | \(0.319184\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.172341 | −0.0199003 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.89356 | 1.12748 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.1231 | 1.13894 | 0.569471 | − | 0.822012i | \(-0.307148\pi\) | ||||
0.569471 | + | 0.822012i | \(0.307148\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.73357 | 0.970396 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.6880 | −1.17317 | −0.586583 | − | 0.809889i | \(-0.699527\pi\) | ||||
−0.586583 | + | 0.809889i | \(0.699527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.79588 | 0.628651 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.560065 | −0.0600453 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.6364 | 1.55145 | 0.775726 | − | 0.631069i | \(-0.217384\pi\) | ||||
0.775726 | + | 0.631069i | \(0.217384\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.0765 | 2.10458 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.495000 | 0.0513292 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.40336 | 0.143982 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.29704 | −0.334764 | −0.167382 | − | 0.985892i | \(-0.553531\pi\) | ||||
−0.167382 | + | 0.985892i | \(0.553531\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.44157 | −0.747906 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.66341 | 0.862042 | 0.431021 | − | 0.902342i | \(-0.358153\pi\) | ||||
0.431021 | + | 0.902342i | \(0.358153\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.45638 | 0.734699 | 0.367350 | − | 0.930083i | \(-0.380265\pi\) | ||||
0.367350 | + | 0.930083i | \(0.380265\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.680578 | 0.0664176 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.2815 | −1.47732 | −0.738658 | − | 0.674080i | \(-0.764540\pi\) | ||||
−0.738658 | + | 0.674080i | \(0.764540\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.47754 | −0.428871 | −0.214435 | − | 0.976738i | \(-0.568791\pi\) | ||||
−0.214435 | + | 0.976738i | \(0.568791\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.503854 | 0.0478237 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.16788 | −0.392081 | −0.196041 | − | 0.980596i | \(-0.562808\pi\) | ||||
−0.196041 | + | 0.980596i | \(0.562808\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.18550 | 0.390300 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.1008 | −1.39607 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −22.8880 | −2.09814 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.72334 | −0.429394 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.91797 | 0.172938 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.08740 | −0.540170 | −0.270085 | − | 0.962837i | \(-0.587052\pi\) | ||||
−0.270085 | + | 0.962837i | \(0.587052\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.185125 | 0.0162994 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.0374609 | −0.00327298 | −0.00163649 | − | 0.999999i | \(-0.500521\pi\) | ||||
−0.00163649 | + | 0.999999i | \(0.500521\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.54188 | −0.480542 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.02893 | −0.0885561 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.1557 | −1.38027 | −0.690136 | − | 0.723680i | \(-0.742449\pi\) | ||||
−0.690136 | + | 0.723680i | \(0.742449\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.26258 | −0.446366 | −0.223183 | − | 0.974777i | \(-0.571645\pi\) | ||||
−0.223183 | + | 0.974777i | \(0.571645\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.127967 | −0.0107768 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.7369 | 1.06511 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.24974 | −0.269876 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.48122 | −0.122169 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.0907 | 0.826666 | 0.413333 | − | 0.910580i | \(-0.364365\pi\) | ||||
0.413333 | + | 0.910580i | \(0.364365\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.0956 | −1.14708 | −0.573541 | − | 0.819177i | \(-0.694431\pi\) | ||||
−0.573541 | + | 0.819177i | \(0.694431\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.2155 | 1.39179 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.87221 | 0.230701 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.50373 | −0.359436 | −0.179718 | − | 0.983718i | \(-0.557519\pi\) | ||||
−0.179718 | + | 0.983718i | \(0.557519\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.27415 | 0.101047 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.5286 | −1.30264 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.08183 | −0.163062 | −0.0815308 | − | 0.996671i | \(-0.525981\pi\) | ||||
−0.0815308 | + | 0.996671i | \(0.525981\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.431771 | 0.0336133 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.2807 | −1.10508 | −0.552538 | − | 0.833488i | \(-0.686341\pi\) | ||||
−0.552538 | + | 0.833488i | \(0.686341\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8462 | 0.988172 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.16839 | 0.318765 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.9731 | 1.21441 | 0.607206 | − | 0.794545i | \(-0.292290\pi\) | ||||
0.607206 | + | 0.794545i | \(0.292290\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.94901 | 0.298517 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.29195 | 0.172274 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.8862 | −0.888414 | −0.444207 | − | 0.895924i | \(-0.646515\pi\) | ||||
−0.444207 | + | 0.895924i | \(0.646515\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.4450 | 1.74266 | 0.871328 | − | 0.490701i | \(-0.163259\pi\) | ||||
0.871328 | + | 0.490701i | \(0.163259\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.33574 | 0.172663 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.92358 | 0.214946 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.5206 | −1.06185 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.06325 | 0.295558 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.0712 | 0.801084 | 0.400542 | − | 0.916278i | \(-0.368822\pi\) | ||||
0.400542 | + | 0.916278i | \(0.368822\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.6691 | 0.983923 | 0.491961 | − | 0.870617i | \(-0.336280\pi\) | ||||
0.491961 | + | 0.870617i | \(0.336280\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.876169 | 0.0627438 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.96193 | 0.424770 | 0.212385 | − | 0.977186i | \(-0.431877\pi\) | ||||
0.212385 | + | 0.977186i | \(0.431877\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.2406 | 0.867712 | 0.433856 | − | 0.900982i | \(-0.357153\pi\) | ||||
0.433856 | + | 0.900982i | \(0.357153\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.0430902 | 0.00303935 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.8333 | 0.900719 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1289 | 0.777278 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.4322 | 0.864097 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.51587 | −0.243198 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.8163 | −1.15768 | −0.578841 | − | 0.815441i | \(-0.696495\pi\) | ||||
−0.578841 | + | 0.815441i | \(0.696495\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.200402 | −0.0137313 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.07418 | 0.0732583 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.3424 | −0.769972 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.58436 | −0.107061 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −29.4658 | −1.98208 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.1078 | 0.810798 | 0.405399 | − | 0.914140i | \(-0.367133\pi\) | ||||
0.405399 | + | 0.914140i | \(0.367133\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.97030 | −0.198020 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.55660 | 0.567922 | 0.283961 | − | 0.958836i | \(-0.408351\pi\) | ||||
0.283961 | + | 0.958836i | \(0.408351\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.5042 | 1.28887 | 0.644437 | − | 0.764657i | \(-0.277092\pi\) | ||||
0.644437 | + | 0.764657i | \(0.277092\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.70507 | −0.112185 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.1430 | 1.05756 | 0.528782 | − | 0.848758i | \(-0.322649\pi\) | ||||
0.528782 | + | 0.848758i | \(0.322649\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.742520 | −0.0484367 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.74463 | −0.113326 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.4042 | 1.31984 | 0.659919 | − | 0.751337i | \(-0.270590\pi\) | ||||
0.659919 | + | 0.751337i | \(0.270590\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.6841 | −1.07472 | −0.537358 | − | 0.843354i | \(-0.680578\pi\) | ||||
−0.537358 | + | 0.843354i | \(0.680578\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.59194 | −0.294573 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.59469 | −0.549095 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.13456 | −0.453961 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.84199 | 0.116732 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.38049 | −0.592091 | −0.296046 | − | 0.955174i | \(-0.595668\pi\) | ||||
−0.296046 | + | 0.955174i | \(0.595668\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.4861 | −0.659253 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.998869 | −0.0625516 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.7357 | −0.856807 | −0.428404 | − | 0.903587i | \(-0.640924\pi\) | ||||
−0.428404 | + | 0.903587i | \(0.640924\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.5453 | −0.717387 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.65271 | −0.597488 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0127 | −0.740735 | −0.370368 | − | 0.928885i | \(-0.620768\pi\) | ||||
−0.370368 | + | 0.928885i | \(0.620768\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.39320 | 0.454161 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.52245 | −0.154372 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.4260 | −1.00151 | −0.500755 | − | 0.865589i | \(-0.666944\pi\) | ||||
−0.500755 | + | 0.865589i | \(0.666944\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.82884 | −0.536314 | −0.268157 | − | 0.963375i | \(-0.586415\pi\) | ||||
−0.268157 | + | 0.963375i | \(0.586415\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.46000 | −0.209409 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.50533 | 0.151077 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.90537 | −0.595156 | −0.297578 | − | 0.954698i | \(-0.596179\pi\) | ||||
−0.297578 | + | 0.954698i | \(0.596179\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.53132 | 0.510757 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.53454 | −0.509128 | −0.254564 | − | 0.967056i | \(-0.581932\pi\) | ||||
−0.254564 | + | 0.967056i | \(0.581932\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.4398 | −1.51224 | −0.756120 | − | 0.654433i | \(-0.772907\pi\) | ||||
−0.756120 | + | 0.654433i | \(0.772907\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.241857 | −0.0143263 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −43.9483 | −2.59418 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.5922 | 0.976011 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.568216 | 0.0333094 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.1395 | −1.46867 | −0.734334 | − | 0.678788i | \(-0.762505\pi\) | ||||
−0.734334 | + | 0.678788i | \(0.762505\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.2989 | 0.774292 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.57780 | 0.149579 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.2788 | −1.23058 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.24194 | −0.244501 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.49306 | −0.0857743 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.5530 | 0.776042 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.7002 | 0.667767 | 0.333884 | − | 0.942614i | \(-0.391641\pi\) | ||||
0.333884 | + | 0.942614i | \(0.391641\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.28504 | −0.0731035 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.84370 | 0.217956 | 0.108978 | − | 0.994044i | \(-0.465242\pi\) | ||||
0.108978 | + | 0.994044i | \(0.465242\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.2050 | −1.48119 | −0.740596 | − | 0.671951i | \(-0.765457\pi\) | ||||
−0.740596 | + | 0.671951i | \(0.765457\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.7297 | 0.660896 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.3801 | 1.53782 | 0.768911 | − | 0.639356i | \(-0.220799\pi\) | ||||
0.768911 | + | 0.639356i | \(0.220799\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.14167 | 0.455846 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.63363 | 0.146995 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.13369 | 0.452571 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.08392 | 0.282005 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.771665 | 0.0426732 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.93222 | 0.161659 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.294394 | 0.0161814 | 0.00809068 | − | 0.999967i | \(-0.497425\pi\) | ||||
0.00809068 | + | 0.999967i | \(0.497425\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.68391 | 0.475875 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.250028 | 0.0136605 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.2719 | −0.995333 | −0.497667 | − | 0.867368i | \(-0.665810\pi\) | ||||
−0.497667 | + | 0.867368i | \(0.665810\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.718298 | 0.0390126 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.19582 | −0.389676 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.29746 | 0.340031 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.721335 | −0.0388354 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.2663 | −1.46373 | −0.731866 | − | 0.681449i | \(-0.761350\pi\) | ||||
−0.731866 | + | 0.681449i | \(0.761350\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.2024 | 0.760235 | 0.380117 | − | 0.924938i | \(-0.375884\pi\) | ||||
0.380117 | + | 0.924938i | \(0.375884\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.23099 | 0.279210 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.9886 | −0.691316 | −0.345658 | − | 0.938361i | \(-0.612344\pi\) | ||||
−0.345658 | + | 0.938361i | \(0.612344\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.16282 | −0.0617160 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.94454 | 0.208767 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.7593 | −1.35952 | −0.679762 | − | 0.733432i | \(-0.737917\pi\) | ||||
−0.679762 | + | 0.733432i | \(0.737917\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0306 | −0.896347 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.814026 | 0.0427253 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.19316 | −0.481192 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.93246 | 0.153073 | 0.0765366 | − | 0.997067i | \(-0.475614\pi\) | ||||
0.0765366 | + | 0.997067i | \(0.475614\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 33.0562 | 1.72084 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −29.1958 | −1.51577 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.42751 | −0.177470 | −0.0887350 | − | 0.996055i | \(-0.528282\pi\) | ||||
−0.0887350 | + | 0.996055i | \(0.528282\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.172341 | 0.00889967 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.5214 | 0.850897 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.04806 | −0.464768 | −0.232384 | − | 0.972624i | \(-0.574653\pi\) | ||||
−0.232384 | + | 0.972624i | \(0.574653\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.04911 | 0.0537476 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.7643 | 1.31650 | 0.658248 | − | 0.752801i | \(-0.271298\pi\) | ||||
0.658248 | + | 0.752801i | \(0.271298\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.89356 | −0.504223 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.19063 | 0.162189 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.9374 | 1.41648 | 0.708240 | − | 0.705971i | \(-0.249489\pi\) | ||||
0.708240 | + | 0.705971i | \(0.249489\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.2587 | 1.22681 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.00645607 | 0.000325665 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.1231 | −0.509350 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.9558 | 1.15212 | 0.576060 | − | 0.817407i | \(-0.304589\pi\) | ||||
0.576060 | + | 0.817407i | \(0.304589\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.955095 | 0.0478145 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.6021 | −0.727382 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.73357 | −0.433975 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.32452 | −0.363063 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.4661 | 0.616410 | 0.308205 | − | 0.951320i | \(-0.400272\pi\) | ||||
0.308205 | + | 0.951320i | \(0.400272\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.78429 | 0.137339 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −52.5175 | −2.58422 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.6880 | 0.524656 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.906960 | 0.0444140 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.822135 | −0.0401639 | −0.0200820 | − | 0.999798i | \(-0.506393\pi\) | ||||
−0.0200820 | + | 0.999798i | \(0.506393\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.89826 | 0.189990 | 0.0949948 | − | 0.995478i | \(-0.469717\pi\) | ||||
0.0949948 | + | 0.995478i | \(0.469717\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.20551 | −0.107235 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.79588 | −0.281141 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −53.5209 | −2.59006 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.19509 | −0.105980 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.3758 | −0.499787 | −0.249893 | − | 0.968273i | \(-0.580396\pi\) | ||||
−0.249893 | + | 0.968273i | \(0.580396\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.266162 | 0.0127909 | 0.00639547 | − | 0.999980i | \(-0.497964\pi\) | ||||
0.00639547 | + | 0.999980i | \(0.497964\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.560065 | 0.0268531 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.87376 | 0.280980 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.4599 | 0.833317 | 0.416658 | − | 0.909063i | \(-0.363201\pi\) | ||||
0.416658 | + | 0.909063i | \(0.363201\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −25.5288 | −1.21566 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.30611 | −0.157078 | −0.0785390 | − | 0.996911i | \(-0.525026\pi\) | ||||
−0.0785390 | + | 0.996911i | \(0.525026\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.6364 | −0.693831 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.73905 | −0.0822544 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.4136 | −1.90724 | −0.953619 | − | 0.301018i | \(-0.902674\pi\) | ||||
−0.953619 | + | 0.301018i | \(0.902674\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.8816 | −1.31289 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.42925 | 0.114136 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.0765 | −0.941199 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.7329 | −0.502065 | −0.251033 | − | 0.967979i | \(-0.580770\pi\) | ||||
−0.251033 | + | 0.967979i | \(0.580770\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.96355 | −0.278354 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.208109 | 0.00969258 | 0.00484629 | − | 0.999988i | \(-0.498457\pi\) | ||||
0.00484629 | + | 0.999988i | \(0.498457\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.3676 | −0.760665 | −0.380332 | − | 0.924850i | \(-0.624190\pi\) | ||||
−0.380332 | + | 0.924850i | \(0.624190\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.495000 | −0.0229551 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.3688 | −0.988829 | −0.494415 | − | 0.869226i | \(-0.664618\pi\) | ||||
−0.494415 | + | 0.869226i | \(0.664618\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.987364 | −0.0455922 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.776178 | 0.0357644 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.69117 | −0.123740 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.40336 | −0.0643905 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.9600 | 1.00548 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.5482 | −1.35009 | −0.675047 | − | 0.737775i | \(-0.735877\pi\) | ||||
−0.675047 | + | 0.737775i | \(0.735877\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.8632 | −0.677706 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.84856 | 0.129614 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.29704 | 0.149711 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.3957 | 0.924218 | 0.462109 | − | 0.886823i | \(-0.347093\pi\) | ||||
0.462109 | + | 0.886823i | \(0.347093\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.358786 | 0.0162249 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.0246 | 0.678053 | 0.339026 | − | 0.940777i | \(-0.389902\pi\) | ||||
0.339026 | + | 0.940777i | \(0.389902\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.8351 | −0.848291 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.44157 | 0.334474 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.59198 | 0.205979 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.9864 | 0.715648 | 0.357824 | − | 0.933789i | \(-0.383519\pi\) | ||||
0.357824 | + | 0.933789i | \(0.383519\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.46116 | 0.109957 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.8103 | 0.526594 | 0.263297 | − | 0.964715i | \(-0.415190\pi\) | ||||
0.263297 | + | 0.964715i | \(0.415190\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.66341 | −0.385517 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.21394 | −0.0983244 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −44.2108 | −1.95961 | −0.979805 | − | 0.199954i | \(-0.935921\pi\) | ||||
−0.979805 | + | 0.199954i | \(0.935921\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.3039 | 1.60599 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.44396 | −0.0637522 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.45638 | −0.328568 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.86026 | 0.0818140 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.75282 | −0.120836 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.7082 | −0.644380 | −0.322190 | − | 0.946675i | \(-0.604419\pi\) | ||||
−0.322190 | + | 0.946675i | \(0.604419\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.92390 | −0.302761 | −0.151380 | − | 0.988476i | \(-0.548372\pi\) | ||||
−0.151380 | + | 0.988476i | \(0.548372\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.680578 | −0.0297028 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.6470 | 0.725154 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.48156 | −0.238329 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 39.5017 | 1.71423 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −56.5786 | −2.45069 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.2815 | 0.660676 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.04848 | 0.0883984 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 21.5325 | 0.927471 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.3206 | −1.43256 | −0.716282 | − | 0.697811i | \(-0.754157\pi\) | ||||
−0.716282 | + | 0.697811i | \(0.754157\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.04055 | −0.173397 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.47754 | 0.191797 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.6932 | −0.842021 | −0.421011 | − | 0.907056i | \(-0.638324\pi\) | ||||
−0.421011 | + | 0.907056i | \(0.638324\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 40.2564 | 1.71810 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.56055 | −0.194286 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 39.9764 | 1.69997 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.503854 | −0.0213874 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.1600 | −1.65926 | −0.829632 | − | 0.558310i | \(-0.811450\pi\) | ||||
−0.829632 | + | 0.558310i | \(0.811450\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.46104 | −0.230977 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.50249 | 0.105655 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.2992 | 1.27696 | 0.638480 | − | 0.769638i | \(-0.279564\pi\) | ||||
0.638480 | + | 0.769638i | \(0.279564\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.16788 | 0.175344 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 34.4890 | 1.44840 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.9939 | −1.13164 | −0.565822 | − | 0.824528i | \(-0.691441\pi\) | ||||
−0.565822 | + | 0.824528i | \(0.691441\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.1830 | −1.76530 | −0.882651 | − | 0.470029i | \(-0.844244\pi\) | ||||
−0.882651 | + | 0.470029i | \(0.844244\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.90802 | −0.0797089 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.18550 | −0.174548 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.0524 | −0.543377 | −0.271689 | − | 0.962385i | \(-0.587582\pi\) | ||||
−0.271689 | + | 0.962385i | \(0.587582\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.35575 | −0.0979016 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −42.2072 | −1.75105 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.5224 | −0.767119 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.1008 | 0.624339 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.1703 | 1.41036 | 0.705179 | − | 0.709029i | \(-0.250867\pi\) | ||||
0.705179 | + | 0.709029i | \(0.250867\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.03074 | 0.166084 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.02749 | −0.0422652 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.6877 | −0.521019 | −0.260510 | − | 0.965471i | \(-0.583891\pi\) | ||||
−0.260510 | + | 0.965471i | \(0.583891\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.8880 | 0.938316 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.10956 | −0.0863385 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 43.2204 | 1.76594 | 0.882969 | − | 0.469432i | \(-0.155541\pi\) | ||||
0.882969 | + | 0.469432i | \(0.155541\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.16914 | 0.210854 | 0.105427 | − | 0.994427i | \(-0.466379\pi\) | ||||
0.105427 | + | 0.994427i | \(0.466379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.742658 | 0.0302434 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.72334 | 0.192031 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.0138 | −0.812333 | −0.406167 | − | 0.913799i | \(-0.633135\pi\) | ||||
−0.406167 | + | 0.913799i | \(0.633135\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.21170 | −0.0896227 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.77491 | 0.152717 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.9835 | 1.81687 | 0.908434 | − | 0.418029i | \(-0.137279\pi\) | ||||
0.908434 | + | 0.418029i | \(0.137279\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.91797 | −0.0773402 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.50806 | 0.221746 | 0.110873 | − | 0.993835i | \(-0.464635\pi\) | ||||
0.110873 | + | 0.993835i | \(0.464635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.84120 | −0.114198 | −0.0570988 | − | 0.998369i | \(-0.518185\pi\) | ||||
−0.0570988 | + | 0.998369i | \(0.518185\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.30659 | −0.172817 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 57.7992 | 2.31568 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.605930 | 0.0241985 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.9447 | 0.675630 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.5017 | 1.49292 | 0.746459 | − | 0.665432i | \(-0.231753\pi\) | ||||
0.746459 | + | 0.665432i | \(0.231753\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.89814 | 0.115191 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.08740 | 0.241571 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 43.6947 | 1.73125 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.45392 | −0.136635 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.515023 | 0.0203422 | 0.0101711 | − | 0.999948i | \(-0.496762\pi\) | ||||
0.0101711 | + | 0.999948i | \(0.496762\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.7070 | 1.36871 | 0.684356 | − | 0.729148i | \(-0.260083\pi\) | ||||
0.684356 | + | 0.729148i | \(0.260083\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.185125 | −0.00728930 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.06179 | −0.0810574 | −0.0405287 | − | 0.999178i | \(-0.512904\pi\) | ||||
−0.0405287 | + | 0.999178i | \(0.512904\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.3181 | −1.30785 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.95476 | 0.0766132 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.21345 | −0.164885 | −0.0824426 | − | 0.996596i | \(-0.526272\pi\) | ||||
−0.0824426 | + | 0.996596i | \(0.526272\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.0374609 | 0.00146372 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27.3064 | −1.06533 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.3729 | 1.57271 | 0.786353 | − | 0.617777i | \(-0.211967\pi\) | ||||
0.786353 | + | 0.617777i | \(0.211967\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.51668 | −0.0978876 | −0.0489438 | − | 0.998802i | \(-0.515586\pi\) | ||||
−0.0489438 | + | 0.998802i | \(0.515586\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.07817 | 0.197220 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.54188 | 0.214905 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.6018 | −0.526664 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.08667 | −0.0806755 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.9547 | −1.31081 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.0961 | 0.928836 | 0.464418 | − | 0.885616i | \(-0.346264\pi\) | ||||
0.464418 | + | 0.885616i | \(0.346264\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.02893 | 0.0396035 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.5605 | 1.05923 | 0.529617 | − | 0.848237i | \(-0.322336\pi\) | ||||
0.529617 | + | 0.848237i | \(0.322336\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.0201 | −0.499664 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.47466 | −0.0565089 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.1261 | 1.19101 | 0.595504 | − | 0.803352i | \(-0.296952\pi\) | ||||
0.595504 | + | 0.803352i | \(0.296952\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.1557 | 0.617276 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.36138 | −0.128245 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −37.5864 | −1.43193 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.8852 | −0.414094 | −0.207047 | − | 0.978331i | \(-0.566385\pi\) | ||||
−0.207047 | + | 0.978331i | \(0.566385\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −29.3868 | −1.11631 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.26258 | 0.199621 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 64.5019 | 2.44318 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.78211 | −0.105229 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.7814 | −1.35145 | −0.675723 | − | 0.737156i | \(-0.736168\pi\) | ||||
−0.675723 | + | 0.737156i | \(0.736168\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.10283 | 0.154741 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.127967 | 0.00481951 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 34.2119 | 1.28667 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.6583 | 1.26406 | 0.632031 | − | 0.774943i | \(-0.282221\pi\) | ||||
0.632031 | + | 0.774943i | \(0.282221\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.0687 | −1.12767 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.0216 | 0.450214 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.7369 | −0.476332 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.51649 | −0.131326 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.6906 | 0.398690 | 0.199345 | − | 0.979929i | \(-0.436119\pi\) | ||||
0.199345 | + | 0.979929i | \(0.436119\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.4453 | 1.09660 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.87536 | 0.106936 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.24974 | 0.120692 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.8500 | 1.47795 | 0.738977 | − | 0.673731i | \(-0.235309\pi\) | ||||
0.738977 | + | 0.673731i | \(0.235309\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.4093 | −0.941086 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.22580 | 0.230270 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.7794 | −0.915248 | −0.457624 | − | 0.889146i | \(-0.651299\pi\) | ||||
−0.457624 | + | 0.889146i | \(0.651299\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.48122 | 0.0546356 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.626402 | −0.0230738 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.5981 | −0.941640 | −0.470820 | − | 0.882229i | \(-0.656042\pi\) | ||||
−0.470820 | + | 0.882229i | \(0.656042\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.22958 | 0.0451697 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.9505 | −1.24552 | −0.622762 | − | 0.782411i | \(-0.713989\pi\) | ||||
−0.622762 | + | 0.782411i | \(0.713989\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.0907 | −0.369696 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 31.7467 | 1.16155 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −60.3468 | −2.20502 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.5974 | −0.824589 | −0.412295 | − | 0.911051i | \(-0.635273\pi\) | ||||
−0.412295 | + | 0.911051i | \(0.635273\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.61665 | 0.0589139 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.0956 | 0.512991 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.22886 | −0.190046 | −0.0950231 | − | 0.995475i | \(-0.530292\pi\) | ||||
−0.0950231 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.80718 | 0.0655965 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.7689 | −1.40537 | −0.702686 | − | 0.711500i | \(-0.748016\pi\) | ||||
−0.702686 | + | 0.711500i | \(0.748016\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.6819 | −0.640126 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17.2155 | −0.622427 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −67.6106 | −2.44128 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.509032 | 0.0183562 | 0.00917808 | − | 0.999958i | \(-0.497078\pi\) | ||||
0.00917808 | + | 0.999958i | \(0.497078\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.36722 | 0.0852535 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.6275 | 1.13756 | 0.568781 | − | 0.822489i | \(-0.307415\pi\) | ||||
0.568781 | + | 0.822489i | \(0.307415\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.87221 | −0.103173 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.98972 | 0.0713809 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.6179 | 0.559569 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.91324 | 0.104244 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.34375 | 0.119496 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.50373 | 0.160745 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.1207 | −0.645931 | −0.322966 | − | 0.946411i | \(-0.604680\pi\) | ||||
−0.322966 | + | 0.946411i | \(0.604680\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.07029 | 0.0737041 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.4590 | −0.585215 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −68.9023 | −2.44679 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.27415 | −0.0451896 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.00102 | 0.212567 | 0.106284 | − | 0.994336i | \(-0.466105\pi\) | ||||
0.106284 | + | 0.994336i | \(0.466105\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.30356 | −0.152249 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −43.4744 | −1.53609 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.0319 | 0.812777 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.5286 | 0.582557 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.83087 | 0.0996515 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.3365 | −0.820468 | −0.410234 | − | 0.911980i | \(-0.634553\pi\) | ||||
−0.410234 | + | 0.911980i | \(0.634553\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.0159 | 1.75630 | 0.878149 | − | 0.478388i | \(-0.158779\pi\) | ||||
0.878149 | + | 0.478388i | \(0.158779\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.52157 | 0.0533639 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.08183 | 0.0729234 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.50746 | 0.0527392 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −59.6331 | −2.08375 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.1312 | −1.43549 | −0.717745 | − | 0.696306i | \(-0.754826\pi\) | ||||
−0.717745 | + | 0.696306i | \(0.754826\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.1532 | −1.39965 | −0.699827 | − | 0.714313i | \(-0.746739\pi\) | ||||
−0.699827 | + | 0.714313i | \(0.746739\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.431771 | −0.0150323 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.0711 | 0.697941 | 0.348971 | − | 0.937134i | \(-0.386531\pi\) | ||||
0.348971 | + | 0.937134i | \(0.386531\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.0369 | 0.556985 | 0.278492 | − | 0.960438i | \(-0.410165\pi\) | ||||
0.278492 | + | 0.960438i | \(0.410165\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.70710 | 0.0592188 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −49.8138 | −1.72594 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.2807 | 0.494205 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.95530 | −0.102150 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 50.7575 | 1.75234 | 0.876172 | − | 0.481998i | \(-0.160089\pi\) | ||||
0.876172 | + | 0.481998i | \(0.160089\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.4392 | −0.635833 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.47085 | 0.0506589 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.8462 | −0.441924 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.6525 | −0.640908 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.38433 | 0.150470 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.2367 | 0.419467 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.68631 | 0.331653 | 0.165826 | − | 0.986155i | \(-0.446971\pi\) | ||||
0.165826 | + | 0.986155i | \(0.446971\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.16839 | −0.142556 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.41593 | 0.116686 | 0.0583430 | − | 0.998297i | \(-0.481418\pi\) | ||||
0.0583430 | + | 0.998297i | \(0.481418\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.1090 | −1.57322 | −0.786609 | − | 0.617451i | \(-0.788165\pi\) | ||||
−0.786609 | + | 0.617451i | \(0.788165\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.57410 | 0.258125 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.419035 | 0.0142641 | 0.00713206 | − | 0.999975i | \(-0.497730\pi\) | ||||
0.00713206 | + | 0.999975i | \(0.497730\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.9731 | −0.543101 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.85952 | −0.0971143 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.3618 | 0.860338 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.27112 | −0.0430704 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.79320 | 0.331450 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.94901 | −0.133501 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.8069 | −0.938971 | −0.469486 | − | 0.882940i | \(-0.655561\pi\) | ||||
−0.469486 | + | 0.882940i | \(0.655561\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.33258 | 0.146134 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.0861 | −0.541955 | −0.270978 | − | 0.962586i | \(-0.587347\pi\) | ||||
−0.270978 | + | 0.962586i | \(0.587347\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.1778 | 0.746342 | 0.373171 | − | 0.927763i | \(-0.378270\pi\) | ||||
0.373171 | + | 0.927763i | \(0.378270\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.29195 | −0.0770431 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.5203 | 0.789734 | 0.394867 | − | 0.918738i | \(-0.370791\pi\) | ||||
0.394867 | + | 0.918738i | \(0.370791\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.0392 | −0.806250 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.8804 | 0.733022 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.04202 | −0.0348699 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.8862 | 0.397311 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.66721 | 0.122445 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.33395 | −0.311305 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.8501 | 1.42754 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.731062 | 0.0243282 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.4450 | −0.779340 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.9251 | −0.993646 | −0.496823 | − | 0.867852i | \(-0.665500\pi\) | ||||
−0.496823 | + | 0.867852i | \(0.665500\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −25.7329 | −0.853507 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 56.2978 | 1.86523 | 0.932614 | − | 0.360875i | \(-0.117522\pi\) | ||||
0.932614 | + | 0.360875i | \(0.117522\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.7771 | −0.886191 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.33574 | −0.0772172 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.147934 | −0.00488520 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.1010 | 0.399175 | 0.199588 | − | 0.979880i | \(-0.436040\pi\) | ||||
0.199588 | + | 0.979880i | \(0.436040\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.01643 | −0.0664437 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.91167 | 0.194585 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.92358 | −0.0961267 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.1477 | −0.727425 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.6374 | 0.775518 | 0.387759 | − | 0.921761i | \(-0.373249\pi\) | ||||
0.387759 | + | 0.921761i | \(0.373249\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.0614 | −0.395298 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.662428 | −0.0216869 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.5206 | 0.474873 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.1206 | 0.722648 | 0.361324 | − | 0.932440i | \(-0.382325\pi\) | ||||
0.361324 | + | 0.932440i | \(0.382325\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.51620 | 0.147381 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.4606 | −0.569200 | −0.284600 | − | 0.958646i | \(-0.591861\pi\) | ||||
−0.284600 | + | 0.958646i | \(0.591861\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46.5802 | 1.51686 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.06325 | −0.132178 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.9493 | 1.36317 | 0.681585 | − | 0.731739i | \(-0.261291\pi\) | ||||
0.681585 | + | 0.731739i | \(0.261291\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46.7373 | 1.51716 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.71873 | −0.153015 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.4034 | −0.758112 | −0.379056 | − | 0.925374i | \(-0.623751\pi\) | ||||
−0.379056 | + | 0.925374i | \(0.623751\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.0712 | −0.358256 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.40315 | −0.0453573 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −63.7989 | −2.06017 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.7504 | −0.733884 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 45.3906 | 1.46269 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.6691 | −0.440024 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.4024 | 0.849045 | 0.424523 | − | 0.905417i | \(-0.360442\pi\) | ||||
0.424523 | + | 0.905417i | \(0.360442\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.40177 | −0.0450314 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.3895 | −1.39243 | −0.696217 | − | 0.717831i | \(-0.745135\pi\) | ||||
−0.696217 | + | 0.717831i | \(0.745135\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.7820 | −0.666240 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.876169 | −0.0280599 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49.4544 | −1.58219 | −0.791093 | − | 0.611696i | \(-0.790488\pi\) | ||||
−0.791093 | + | 0.611696i | \(0.790488\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.6689 | 1.17194 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.2996 | 0.424625 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.6175 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.96193 | −0.189963 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.505343 | −0.0160852 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.49598 | 0.142964 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.6310 | −0.655365 | −0.327682 | − | 0.944788i | \(-0.606268\pi\) | ||||
−0.327682 | + | 0.944788i | \(0.606268\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.0507362 | −0.00161007 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.2406 | −0.388053 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.6969 | −0.338775 | −0.169388 | − | 0.985550i | \(-0.554179\pi\) | ||||
−0.169388 | + | 0.985550i | \(0.554179\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.00816 | −0.0951739 |
(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 | 8020.2.a.c.1.13 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.c.1.13 | ✓ | 28 | 1.1 | even | 1 | trivial |