Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(1,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, 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("735.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.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: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4352.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.27133\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 735.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.68554 | −1.19186 | −0.595930 | − | 0.803037i | \(-0.703216\pi\) | ||||
−0.595930 | + | 0.803037i | \(0.703216\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.841058 | 0.420529 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.68554 | −0.688120 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.95345 | 0.690648 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.68554 | 0.533016 | ||||||||
\(11\) | 1.77522 | 0.535250 | 0.267625 | − | 0.963523i | \(-0.413761\pi\) | ||||
0.267625 | + | 0.963523i | \(0.413761\pi\) | |||||||
\(12\) | 0.841058 | 0.242793 | ||||||||
\(13\) | −3.05320 | −0.846807 | −0.423403 | − | 0.905941i | \(-0.639165\pi\) | ||||
−0.423403 | + | 0.905941i | \(0.639165\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −4.97474 | −1.24368 | ||||||||
\(17\) | 7.59587 | 1.84227 | 0.921134 | − | 0.389246i | \(-0.127264\pi\) | ||||
0.921134 | + | 0.389246i | \(0.127264\pi\) | |||||||
\(18\) | −1.68554 | −0.397287 | ||||||||
\(19\) | −3.12845 | −0.717715 | −0.358858 | − | 0.933392i | \(-0.616834\pi\) | ||||
−0.358858 | + | 0.933392i | \(0.616834\pi\) | |||||||
\(20\) | −0.841058 | −0.188066 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.99222 | −0.637943 | ||||||||
\(23\) | −4.18165 | −0.871935 | −0.435967 | − | 0.899962i | \(-0.643594\pi\) | ||||
−0.435967 | + | 0.899962i | \(0.643594\pi\) | |||||||
\(24\) | 1.95345 | 0.398746 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.14631 | 1.00927 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.08532 | 1.31571 | 0.657856 | − | 0.753144i | \(-0.271464\pi\) | ||||
0.657856 | + | 0.753144i | \(0.271464\pi\) | |||||||
\(30\) | 1.68554 | 0.307737 | ||||||||
\(31\) | −0.871553 | −0.156536 | −0.0782678 | − | 0.996932i | \(-0.524939\pi\) | ||||
−0.0782678 | + | 0.996932i | \(0.524939\pi\) | |||||||
\(32\) | 4.47824 | 0.791649 | ||||||||
\(33\) | 1.77522 | 0.309027 | ||||||||
\(34\) | −12.8032 | −2.19572 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.841058 | 0.140176 | ||||||||
\(37\) | 9.91375 | 1.62981 | 0.814905 | − | 0.579594i | \(-0.196789\pi\) | ||||
0.814905 | + | 0.579594i | \(0.196789\pi\) | |||||||
\(38\) | 5.27314 | 0.855415 | ||||||||
\(39\) | −3.05320 | −0.488904 | ||||||||
\(40\) | −1.95345 | −0.308867 | ||||||||
\(41\) | 2.76744 | 0.432201 | 0.216101 | − | 0.976371i | \(-0.430666\pi\) | ||||
0.216101 | + | 0.976371i | \(0.430666\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.317883 | 0.0484767 | 0.0242384 | − | 0.999706i | \(-0.492284\pi\) | ||||
0.0242384 | + | 0.999706i | \(0.492284\pi\) | |||||||
\(44\) | 1.49307 | 0.225088 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 7.04836 | 1.03922 | ||||||||
\(47\) | 10.4853 | 1.52944 | 0.764718 | − | 0.644365i | \(-0.222878\pi\) | ||||
0.764718 | + | 0.644365i | \(0.222878\pi\) | |||||||
\(48\) | −4.97474 | −0.718042 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.68554 | −0.238372 | ||||||||
\(51\) | 7.59587 | 1.06363 | ||||||||
\(52\) | −2.56792 | −0.356107 | ||||||||
\(53\) | 3.63899 | 0.499854 | 0.249927 | − | 0.968265i | \(-0.419593\pi\) | ||||
0.249927 | + | 0.968265i | \(0.419593\pi\) | |||||||
\(54\) | −1.68554 | −0.229373 | ||||||||
\(55\) | −1.77522 | −0.239371 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.12845 | −0.414373 | ||||||||
\(58\) | −11.9426 | −1.56814 | ||||||||
\(59\) | −9.57060 | −1.24599 | −0.622993 | − | 0.782227i | \(-0.714084\pi\) | ||||
−0.622993 | + | 0.782227i | \(0.714084\pi\) | |||||||
\(60\) | −0.841058 | −0.108580 | ||||||||
\(61\) | −6.58579 | −0.843224 | −0.421612 | − | 0.906776i | \(-0.638535\pi\) | ||||
−0.421612 | + | 0.906776i | \(0.638535\pi\) | |||||||
\(62\) | 1.46904 | 0.186568 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.40120 | 0.300150 | ||||||||
\(65\) | 3.05320 | 0.378703 | ||||||||
\(66\) | −2.99222 | −0.368316 | ||||||||
\(67\) | 14.0202 | 1.71283 | 0.856417 | − | 0.516284i | \(-0.172685\pi\) | ||||
0.856417 | + | 0.516284i | \(0.172685\pi\) | |||||||
\(68\) | 6.38857 | 0.774727 | ||||||||
\(69\) | −4.18165 | −0.503412 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.13853 | 0.728509 | 0.364255 | − | 0.931299i | \(-0.381324\pi\) | ||||
0.364255 | + | 0.931299i | \(0.381324\pi\) | |||||||
\(72\) | 1.95345 | 0.230216 | ||||||||
\(73\) | −7.68897 | −0.899926 | −0.449963 | − | 0.893047i | \(-0.648563\pi\) | ||||
−0.449963 | + | 0.893047i | \(0.648563\pi\) | |||||||
\(74\) | −16.7101 | −1.94250 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −2.63121 | −0.301820 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.14631 | 0.582705 | ||||||||
\(79\) | 14.0811 | 1.58425 | 0.792126 | − | 0.610357i | \(-0.208974\pi\) | ||||
0.792126 | + | 0.610357i | \(0.208974\pi\) | |||||||
\(80\) | 4.97474 | 0.556193 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.66464 | −0.515123 | ||||||||
\(83\) | 12.8284 | 1.40810 | 0.704051 | − | 0.710149i | \(-0.251372\pi\) | ||||
0.704051 | + | 0.710149i | \(0.251372\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.59587 | −0.823887 | ||||||||
\(86\) | −0.535806 | −0.0577775 | ||||||||
\(87\) | 7.08532 | 0.759626 | ||||||||
\(88\) | 3.46780 | 0.369669 | ||||||||
\(89\) | −4.82843 | −0.511812 | −0.255906 | − | 0.966702i | \(-0.582374\pi\) | ||||
−0.255906 | + | 0.966702i | \(0.582374\pi\) | |||||||
\(90\) | 1.68554 | 0.177672 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.51701 | −0.366674 | ||||||||
\(93\) | −0.871553 | −0.0903758 | ||||||||
\(94\) | −17.6734 | −1.82287 | ||||||||
\(95\) | 3.12845 | 0.320972 | ||||||||
\(96\) | 4.47824 | 0.457059 | ||||||||
\(97\) | 16.6238 | 1.68789 | 0.843946 | − | 0.536428i | \(-0.180227\pi\) | ||||
0.843946 | + | 0.536428i | \(0.180227\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.77522 | 0.178417 | ||||||||
\(100\) | 0.841058 | 0.0841058 | ||||||||
\(101\) | −12.4243 | −1.23626 | −0.618132 | − | 0.786075i | \(-0.712110\pi\) | ||||
−0.618132 | + | 0.786075i | \(0.712110\pi\) | |||||||
\(102\) | −12.8032 | −1.26770 | ||||||||
\(103\) | −3.91375 | −0.385633 | −0.192817 | − | 0.981235i | \(-0.561762\pi\) | ||||
−0.192817 | + | 0.981235i | \(0.561762\pi\) | |||||||
\(104\) | −5.96427 | −0.584845 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.13368 | −0.595756 | ||||||||
\(107\) | 3.73210 | 0.360795 | 0.180398 | − | 0.983594i | \(-0.442262\pi\) | ||||
0.180398 | + | 0.983594i | \(0.442262\pi\) | |||||||
\(108\) | 0.841058 | 0.0809309 | ||||||||
\(109\) | 7.65685 | 0.733394 | 0.366697 | − | 0.930341i | \(-0.380489\pi\) | ||||
0.366697 | + | 0.930341i | \(0.380489\pi\) | |||||||
\(110\) | 2.99222 | 0.285297 | ||||||||
\(111\) | 9.91375 | 0.940971 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.4023 | 1.82521 | 0.912605 | − | 0.408842i | \(-0.134067\pi\) | ||||
0.912605 | + | 0.408842i | \(0.134067\pi\) | |||||||
\(114\) | 5.27314 | 0.493874 | ||||||||
\(115\) | 4.18165 | 0.389941 | ||||||||
\(116\) | 5.95917 | 0.553295 | ||||||||
\(117\) | −3.05320 | −0.282269 | ||||||||
\(118\) | 16.1317 | 1.48504 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.95345 | −0.178325 | ||||||||
\(121\) | −7.84858 | −0.713508 | ||||||||
\(122\) | 11.1006 | 1.00500 | ||||||||
\(123\) | 2.76744 | 0.249531 | ||||||||
\(124\) | −0.733027 | −0.0658277 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.1463 | −1.34402 | −0.672009 | − | 0.740543i | \(-0.734568\pi\) | ||||
−0.672009 | + | 0.740543i | \(0.734568\pi\) | |||||||
\(128\) | −13.0038 | −1.14939 | ||||||||
\(129\) | 0.317883 | 0.0279881 | ||||||||
\(130\) | −5.14631 | −0.451361 | ||||||||
\(131\) | 13.5252 | 1.18170 | 0.590850 | − | 0.806781i | \(-0.298792\pi\) | ||||
0.590850 | + | 0.806781i | \(0.298792\pi\) | |||||||
\(132\) | 1.49307 | 0.129955 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −23.6316 | −2.04146 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 14.8381 | 1.27236 | ||||||||
\(137\) | 2.73988 | 0.234084 | 0.117042 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117042 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(138\) | 7.04836 | 0.599996 | ||||||||
\(139\) | −6.67889 | −0.566496 | −0.283248 | − | 0.959047i | \(-0.591412\pi\) | ||||
−0.283248 | + | 0.959047i | \(0.591412\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.4853 | 0.883020 | ||||||||
\(142\) | −10.3468 | −0.868280 | ||||||||
\(143\) | −5.42012 | −0.453253 | ||||||||
\(144\) | −4.97474 | −0.414561 | ||||||||
\(145\) | −7.08532 | −0.588404 | ||||||||
\(146\) | 12.9601 | 1.07259 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.33804 | 0.685383 | ||||||||
\(149\) | 1.36423 | 0.111762 | 0.0558812 | − | 0.998437i | \(-0.482203\pi\) | ||||
0.0558812 | + | 0.998437i | \(0.482203\pi\) | |||||||
\(150\) | −1.68554 | −0.137624 | ||||||||
\(151\) | −23.8022 | −1.93700 | −0.968499 | − | 0.249017i | \(-0.919893\pi\) | ||||
−0.968499 | + | 0.249017i | \(0.919893\pi\) | |||||||
\(152\) | −6.11126 | −0.495688 | ||||||||
\(153\) | 7.59587 | 0.614089 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.871553 | 0.0700048 | ||||||||
\(156\) | −2.56792 | −0.205598 | ||||||||
\(157\) | −12.7101 | −1.01437 | −0.507187 | − | 0.861836i | \(-0.669314\pi\) | ||||
−0.507187 | + | 0.861836i | \(0.669314\pi\) | |||||||
\(158\) | −23.7344 | −1.88821 | ||||||||
\(159\) | 3.63899 | 0.288591 | ||||||||
\(160\) | −4.47824 | −0.354036 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.68554 | −0.132429 | ||||||||
\(163\) | −9.70227 | −0.759941 | −0.379970 | − | 0.924999i | \(-0.624066\pi\) | ||||
−0.379970 | + | 0.924999i | \(0.624066\pi\) | |||||||
\(164\) | 2.32758 | 0.181753 | ||||||||
\(165\) | −1.77522 | −0.138201 | ||||||||
\(166\) | −21.6229 | −1.67826 | ||||||||
\(167\) | −12.8486 | −0.994253 | −0.497127 | − | 0.867678i | \(-0.665612\pi\) | ||||
−0.497127 | + | 0.867678i | \(0.665612\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.67794 | −0.282919 | ||||||||
\(170\) | 12.8032 | 0.981958 | ||||||||
\(171\) | −3.12845 | −0.239238 | ||||||||
\(172\) | 0.267358 | 0.0203859 | ||||||||
\(173\) | −15.9949 | −1.21607 | −0.608035 | − | 0.793910i | \(-0.708042\pi\) | ||||
−0.608035 | + | 0.793910i | \(0.708042\pi\) | |||||||
\(174\) | −11.9426 | −0.905368 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.83127 | −0.665682 | ||||||||
\(177\) | −9.57060 | −0.719371 | ||||||||
\(178\) | 8.13853 | 0.610008 | ||||||||
\(179\) | −24.8807 | −1.85967 | −0.929835 | − | 0.367976i | \(-0.880051\pi\) | ||||
−0.929835 | + | 0.367976i | \(0.880051\pi\) | |||||||
\(180\) | −0.841058 | −0.0626888 | ||||||||
\(181\) | −3.18583 | −0.236801 | −0.118400 | − | 0.992966i | \(-0.537777\pi\) | ||||
−0.118400 | + | 0.992966i | \(0.537777\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.58579 | −0.486835 | ||||||||
\(184\) | −8.16864 | −0.602200 | ||||||||
\(185\) | −9.91375 | −0.728873 | ||||||||
\(186\) | 1.46904 | 0.107715 | ||||||||
\(187\) | 13.4844 | 0.986073 | ||||||||
\(188\) | 8.81873 | 0.643172 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.27314 | −0.382553 | ||||||||
\(191\) | −2.34676 | −0.169805 | −0.0849026 | − | 0.996389i | \(-0.527058\pi\) | ||||
−0.0849026 | + | 0.996389i | \(0.527058\pi\) | |||||||
\(192\) | 2.40120 | 0.173291 | ||||||||
\(193\) | 23.1307 | 1.66499 | 0.832494 | − | 0.554035i | \(-0.186912\pi\) | ||||
0.832494 | + | 0.554035i | \(0.186912\pi\) | |||||||
\(194\) | −28.0202 | −2.01173 | ||||||||
\(195\) | 3.05320 | 0.218645 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.03895 | −0.216516 | −0.108258 | − | 0.994123i | \(-0.534527\pi\) | ||||
−0.108258 | + | 0.994123i | \(0.534527\pi\) | |||||||
\(198\) | −2.99222 | −0.212648 | ||||||||
\(199\) | −4.42200 | −0.313467 | −0.156734 | − | 0.987641i | \(-0.550096\pi\) | ||||
−0.156734 | + | 0.987641i | \(0.550096\pi\) | |||||||
\(200\) | 1.95345 | 0.138130 | ||||||||
\(201\) | 14.0202 | 0.988906 | ||||||||
\(202\) | 20.9417 | 1.47345 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.38857 | 0.447289 | ||||||||
\(205\) | −2.76744 | −0.193286 | ||||||||
\(206\) | 6.59680 | 0.459621 | ||||||||
\(207\) | −4.18165 | −0.290645 | ||||||||
\(208\) | 15.1889 | 1.05316 | ||||||||
\(209\) | −5.55369 | −0.384157 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.57153 | 0.314717 | 0.157359 | − | 0.987542i | \(-0.449702\pi\) | ||||
0.157359 | + | 0.987542i | \(0.449702\pi\) | |||||||
\(212\) | 3.06060 | 0.210203 | ||||||||
\(213\) | 6.13853 | 0.420605 | ||||||||
\(214\) | −6.29061 | −0.430017 | ||||||||
\(215\) | −0.317883 | −0.0216795 | ||||||||
\(216\) | 1.95345 | 0.132915 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −12.9060 | −0.874102 | ||||||||
\(219\) | −7.68897 | −0.519573 | ||||||||
\(220\) | −1.49307 | −0.100662 | ||||||||
\(221\) | −23.1917 | −1.56004 | ||||||||
\(222\) | −16.7101 | −1.12151 | ||||||||
\(223\) | −4.53581 | −0.303740 | −0.151870 | − | 0.988400i | \(-0.548530\pi\) | ||||
−0.151870 | + | 0.988400i | \(0.548530\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −32.7034 | −2.17539 | ||||||||
\(227\) | 8.44955 | 0.560817 | 0.280408 | − | 0.959881i | \(-0.409530\pi\) | ||||
0.280408 | + | 0.959881i | \(0.409530\pi\) | |||||||
\(228\) | −2.63121 | −0.174256 | ||||||||
\(229\) | −19.0711 | −1.26025 | −0.630126 | − | 0.776493i | \(-0.716997\pi\) | ||||
−0.630126 | + | 0.776493i | \(0.716997\pi\) | |||||||
\(230\) | −7.04836 | −0.464755 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.8408 | 0.908693 | ||||||||
\(233\) | 9.08303 | 0.595049 | 0.297524 | − | 0.954714i | \(-0.403839\pi\) | ||||
0.297524 | + | 0.954714i | \(0.403839\pi\) | |||||||
\(234\) | 5.14631 | 0.336425 | ||||||||
\(235\) | −10.4853 | −0.683984 | ||||||||
\(236\) | −8.04944 | −0.523974 | ||||||||
\(237\) | 14.0811 | 0.914669 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.1532 | −1.10955 | −0.554773 | − | 0.832002i | \(-0.687195\pi\) | ||||
−0.554773 | + | 0.832002i | \(0.687195\pi\) | |||||||
\(240\) | 4.97474 | 0.321118 | ||||||||
\(241\) | 19.9839 | 1.28728 | 0.643638 | − | 0.765330i | \(-0.277424\pi\) | ||||
0.643638 | + | 0.765330i | \(0.277424\pi\) | |||||||
\(242\) | 13.2291 | 0.850401 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.53903 | −0.354600 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.66464 | −0.297406 | ||||||||
\(247\) | 9.55179 | 0.607766 | ||||||||
\(248\) | −1.70253 | −0.108111 | ||||||||
\(249\) | 12.8284 | 0.812969 | ||||||||
\(250\) | 1.68554 | 0.106603 | ||||||||
\(251\) | −4.93484 | −0.311484 | −0.155742 | − | 0.987798i | \(-0.549777\pi\) | ||||
−0.155742 | + | 0.987798i | \(0.549777\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.42336 | −0.466703 | ||||||||
\(254\) | 25.5298 | 1.60188 | ||||||||
\(255\) | −7.59587 | −0.475672 | ||||||||
\(256\) | 17.1161 | 1.06976 | ||||||||
\(257\) | −1.55045 | −0.0967141 | −0.0483571 | − | 0.998830i | \(-0.515399\pi\) | ||||
−0.0483571 | + | 0.998830i | \(0.515399\pi\) | |||||||
\(258\) | −0.535806 | −0.0333578 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.56792 | 0.159256 | ||||||||
\(261\) | 7.08532 | 0.438570 | ||||||||
\(262\) | −22.7973 | −1.40842 | ||||||||
\(263\) | 13.1165 | 0.808797 | 0.404399 | − | 0.914583i | \(-0.367481\pi\) | ||||
0.404399 | + | 0.914583i | \(0.367481\pi\) | |||||||
\(264\) | 3.46780 | 0.213429 | ||||||||
\(265\) | −3.63899 | −0.223541 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.82843 | −0.295495 | ||||||||
\(268\) | 11.7918 | 0.720297 | ||||||||
\(269\) | 4.69676 | 0.286366 | 0.143183 | − | 0.989696i | \(-0.454266\pi\) | ||||
0.143183 | + | 0.989696i | \(0.454266\pi\) | |||||||
\(270\) | 1.68554 | 0.102579 | ||||||||
\(271\) | 17.6339 | 1.07118 | 0.535591 | − | 0.844477i | \(-0.320089\pi\) | ||||
0.535591 | + | 0.844477i | \(0.320089\pi\) | |||||||
\(272\) | −37.7874 | −2.29120 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.61819 | −0.278995 | ||||||||
\(275\) | 1.77522 | 0.107050 | ||||||||
\(276\) | −3.51701 | −0.211699 | ||||||||
\(277\) | −15.8528 | −0.952500 | −0.476250 | − | 0.879310i | \(-0.658004\pi\) | ||||
−0.476250 | + | 0.879310i | \(0.658004\pi\) | |||||||
\(278\) | 11.2576 | 0.675184 | ||||||||
\(279\) | −0.871553 | −0.0521785 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.6779 | 0.994923 | 0.497461 | − | 0.867486i | \(-0.334266\pi\) | ||||
0.497461 | + | 0.867486i | \(0.334266\pi\) | |||||||
\(282\) | −17.6734 | −1.05244 | ||||||||
\(283\) | −12.8129 | −0.761645 | −0.380823 | − | 0.924648i | \(-0.624359\pi\) | ||||
−0.380823 | + | 0.924648i | \(0.624359\pi\) | |||||||
\(284\) | 5.16286 | 0.306359 | ||||||||
\(285\) | 3.12845 | 0.185313 | ||||||||
\(286\) | 9.13585 | 0.540214 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.47824 | 0.263883 | ||||||||
\(289\) | 40.6972 | 2.39395 | ||||||||
\(290\) | 11.9426 | 0.701295 | ||||||||
\(291\) | 16.6238 | 0.974505 | ||||||||
\(292\) | −6.46687 | −0.378445 | ||||||||
\(293\) | 6.57153 | 0.383913 | 0.191957 | − | 0.981403i | \(-0.438517\pi\) | ||||
0.191957 | + | 0.981403i | \(0.438517\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.57060 | 0.557222 | ||||||||
\(296\) | 19.3660 | 1.12562 | ||||||||
\(297\) | 1.77522 | 0.103009 | ||||||||
\(298\) | −2.29948 | −0.133205 | ||||||||
\(299\) | 12.7674 | 0.738360 | ||||||||
\(300\) | 0.841058 | 0.0485585 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 40.1197 | 2.30863 | ||||||||
\(303\) | −12.4243 | −0.713757 | ||||||||
\(304\) | 15.5632 | 0.892611 | ||||||||
\(305\) | 6.58579 | 0.377101 | ||||||||
\(306\) | −12.8032 | −0.731908 | ||||||||
\(307\) | −15.3137 | −0.874000 | −0.437000 | − | 0.899462i | \(-0.643959\pi\) | ||||
−0.437000 | + | 0.899462i | \(0.643959\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.91375 | −0.222645 | ||||||||
\(310\) | −1.46904 | −0.0834359 | ||||||||
\(311\) | −15.7464 | −0.892894 | −0.446447 | − | 0.894810i | \(-0.647311\pi\) | ||||
−0.446447 | + | 0.894810i | \(0.647311\pi\) | |||||||
\(312\) | −5.96427 | −0.337660 | ||||||||
\(313\) | 20.0165 | 1.13140 | 0.565701 | − | 0.824610i | \(-0.308606\pi\) | ||||
0.565701 | + | 0.824610i | \(0.308606\pi\) | |||||||
\(314\) | 21.4234 | 1.20899 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.8431 | 0.666225 | ||||||||
\(317\) | −22.8664 | −1.28431 | −0.642154 | − | 0.766576i | \(-0.721959\pi\) | ||||
−0.642154 | + | 0.766576i | \(0.721959\pi\) | |||||||
\(318\) | −6.13368 | −0.343960 | ||||||||
\(319\) | 12.5780 | 0.704234 | ||||||||
\(320\) | −2.40120 | −0.134231 | ||||||||
\(321\) | 3.73210 | 0.208305 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.7633 | −1.32222 | ||||||||
\(324\) | 0.841058 | 0.0467255 | ||||||||
\(325\) | −3.05320 | −0.169361 | ||||||||
\(326\) | 16.3536 | 0.905743 | ||||||||
\(327\) | 7.65685 | 0.423425 | ||||||||
\(328\) | 5.40604 | 0.298499 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.99222 | 0.164716 | ||||||||
\(331\) | −12.3990 | −0.681512 | −0.340756 | − | 0.940152i | \(-0.610683\pi\) | ||||
−0.340756 | + | 0.940152i | \(0.610683\pi\) | |||||||
\(332\) | 10.7895 | 0.592148 | ||||||||
\(333\) | 9.91375 | 0.543270 | ||||||||
\(334\) | 21.6569 | 1.18501 | ||||||||
\(335\) | −14.0202 | −0.766003 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.625303 | 0.0340624 | 0.0170312 | − | 0.999855i | \(-0.494579\pi\) | ||||
0.0170312 | + | 0.999855i | \(0.494579\pi\) | |||||||
\(338\) | 6.19933 | 0.337199 | ||||||||
\(339\) | 19.4023 | 1.05379 | ||||||||
\(340\) | −6.38857 | −0.346469 | ||||||||
\(341\) | −1.54720 | −0.0837856 | ||||||||
\(342\) | 5.27314 | 0.285138 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.620968 | 0.0334804 | ||||||||
\(345\) | 4.18165 | 0.225133 | ||||||||
\(346\) | 26.9601 | 1.44938 | ||||||||
\(347\) | −1.71653 | −0.0921481 | −0.0460740 | − | 0.998938i | \(-0.514671\pi\) | ||||
−0.0460740 | + | 0.998938i | \(0.514671\pi\) | |||||||
\(348\) | 5.95917 | 0.319445 | ||||||||
\(349\) | 15.0491 | 0.805557 | 0.402779 | − | 0.915297i | \(-0.368044\pi\) | ||||
0.402779 | + | 0.915297i | \(0.368044\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.05320 | −0.162968 | ||||||||
\(352\) | 7.94988 | 0.423730 | ||||||||
\(353\) | −22.4633 | −1.19560 | −0.597799 | − | 0.801646i | \(-0.703958\pi\) | ||||
−0.597799 | + | 0.801646i | \(0.703958\pi\) | |||||||
\(354\) | 16.1317 | 0.857389 | ||||||||
\(355\) | −6.13853 | −0.325799 | ||||||||
\(356\) | −4.06099 | −0.215232 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 41.9375 | 2.21647 | ||||||||
\(359\) | 3.43208 | 0.181138 | 0.0905690 | − | 0.995890i | \(-0.471131\pi\) | ||||
0.0905690 | + | 0.995890i | \(0.471131\pi\) | |||||||
\(360\) | −1.95345 | −0.102956 | ||||||||
\(361\) | −9.21282 | −0.484885 | ||||||||
\(362\) | 5.36985 | 0.282233 | ||||||||
\(363\) | −7.84858 | −0.411944 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.68897 | 0.402459 | ||||||||
\(366\) | 11.1006 | 0.580239 | ||||||||
\(367\) | −24.1908 | −1.26275 | −0.631375 | − | 0.775478i | \(-0.717509\pi\) | ||||
−0.631375 | + | 0.775478i | \(0.717509\pi\) | |||||||
\(368\) | 20.8026 | 1.08441 | ||||||||
\(369\) | 2.76744 | 0.144067 | ||||||||
\(370\) | 16.7101 | 0.868715 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.733027 | −0.0380057 | ||||||||
\(373\) | −0.856934 | −0.0443704 | −0.0221852 | − | 0.999754i | \(-0.507062\pi\) | ||||
−0.0221852 | + | 0.999754i | \(0.507062\pi\) | |||||||
\(374\) | −22.7285 | −1.17526 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 20.4824 | 1.05630 | ||||||||
\(377\) | −21.6329 | −1.11415 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.63159 | 0.289275 | 0.144638 | − | 0.989485i | \(-0.453798\pi\) | ||||
0.144638 | + | 0.989485i | \(0.453798\pi\) | |||||||
\(380\) | 2.63121 | 0.134978 | ||||||||
\(381\) | −15.1463 | −0.775969 | ||||||||
\(382\) | 3.95556 | 0.202384 | ||||||||
\(383\) | 5.39996 | 0.275925 | 0.137963 | − | 0.990437i | \(-0.455945\pi\) | ||||
0.137963 | + | 0.990437i | \(0.455945\pi\) | |||||||
\(384\) | −13.0038 | −0.663598 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −38.9879 | −1.98443 | ||||||||
\(387\) | 0.317883 | 0.0161589 | ||||||||
\(388\) | 13.9816 | 0.709808 | ||||||||
\(389\) | 14.2485 | 0.722430 | 0.361215 | − | 0.932483i | \(-0.382362\pi\) | ||||
0.361215 | + | 0.932483i | \(0.382362\pi\) | |||||||
\(390\) | −5.14631 | −0.260594 | ||||||||
\(391\) | −31.7633 | −1.60634 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.5252 | 0.682255 | ||||||||
\(394\) | 5.12229 | 0.258057 | ||||||||
\(395\) | −14.0811 | −0.708499 | ||||||||
\(396\) | 1.49307 | 0.0750294 | ||||||||
\(397\) | 11.6532 | 0.584860 | 0.292430 | − | 0.956287i | \(-0.405536\pi\) | ||||
0.292430 | + | 0.956287i | \(0.405536\pi\) | |||||||
\(398\) | 7.45347 | 0.373609 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.97474 | −0.248737 | ||||||||
\(401\) | −2.65778 | −0.132723 | −0.0663617 | − | 0.997796i | \(-0.521139\pi\) | ||||
−0.0663617 | + | 0.997796i | \(0.521139\pi\) | |||||||
\(402\) | −23.6316 | −1.17864 | ||||||||
\(403\) | 2.66103 | 0.132555 | ||||||||
\(404\) | −10.4496 | −0.519885 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.5991 | 0.872356 | ||||||||
\(408\) | 14.8381 | 0.734596 | ||||||||
\(409\) | 26.9206 | 1.33114 | 0.665569 | − | 0.746337i | \(-0.268189\pi\) | ||||
0.665569 | + | 0.746337i | \(0.268189\pi\) | |||||||
\(410\) | 4.66464 | 0.230370 | ||||||||
\(411\) | 2.73988 | 0.135148 | ||||||||
\(412\) | −3.29169 | −0.162170 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.04836 | 0.346408 | ||||||||
\(415\) | −12.8284 | −0.629723 | ||||||||
\(416\) | −13.6730 | −0.670374 | ||||||||
\(417\) | −6.67889 | −0.327067 | ||||||||
\(418\) | 9.36099 | 0.457861 | ||||||||
\(419\) | 15.1917 | 0.742165 | 0.371082 | − | 0.928600i | \(-0.378987\pi\) | ||||
0.371082 | + | 0.928600i | \(0.378987\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.757744 | −0.0369302 | −0.0184651 | − | 0.999830i | \(-0.505878\pi\) | ||||
−0.0184651 | + | 0.999830i | \(0.505878\pi\) | |||||||
\(422\) | −7.70552 | −0.375099 | ||||||||
\(423\) | 10.4853 | 0.509812 | ||||||||
\(424\) | 7.10858 | 0.345223 | ||||||||
\(425\) | 7.59587 | 0.368454 | ||||||||
\(426\) | −10.3468 | −0.501302 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.13891 | 0.151725 | ||||||||
\(429\) | −5.42012 | −0.261686 | ||||||||
\(430\) | 0.535806 | 0.0258389 | ||||||||
\(431\) | 23.1091 | 1.11313 | 0.556563 | − | 0.830806i | \(-0.312120\pi\) | ||||
0.556563 | + | 0.830806i | \(0.312120\pi\) | |||||||
\(432\) | −4.97474 | −0.239347 | ||||||||
\(433\) | −15.4522 | −0.742587 | −0.371294 | − | 0.928516i | \(-0.621086\pi\) | ||||
−0.371294 | + | 0.928516i | \(0.621086\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.08532 | −0.339715 | ||||||||
\(436\) | 6.43986 | 0.308413 | ||||||||
\(437\) | 13.0821 | 0.625801 | ||||||||
\(438\) | 12.9601 | 0.619257 | ||||||||
\(439\) | 28.5843 | 1.36425 | 0.682127 | − | 0.731234i | \(-0.261055\pi\) | ||||
0.682127 | + | 0.731234i | \(0.261055\pi\) | |||||||
\(440\) | −3.46780 | −0.165321 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 39.0907 | 1.85935 | ||||||||
\(443\) | −22.1110 | −1.05052 | −0.525262 | − | 0.850941i | \(-0.676033\pi\) | ||||
−0.525262 | + | 0.850941i | \(0.676033\pi\) | |||||||
\(444\) | 8.33804 | 0.395706 | ||||||||
\(445\) | 4.82843 | 0.228889 | ||||||||
\(446\) | 7.64530 | 0.362015 | ||||||||
\(447\) | 1.36423 | 0.0645260 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.4393 | −1.24775 | −0.623875 | − | 0.781524i | \(-0.714443\pi\) | ||||
−0.623875 | + | 0.781524i | \(0.714443\pi\) | |||||||
\(450\) | −1.68554 | −0.0794573 | ||||||||
\(451\) | 4.91282 | 0.231336 | ||||||||
\(452\) | 16.3184 | 0.767554 | ||||||||
\(453\) | −23.8022 | −1.11833 | ||||||||
\(454\) | −14.2421 | −0.668415 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.11126 | −0.286186 | ||||||||
\(457\) | 35.0063 | 1.63753 | 0.818763 | − | 0.574132i | \(-0.194660\pi\) | ||||
0.818763 | + | 0.574132i | \(0.194660\pi\) | |||||||
\(458\) | 32.1451 | 1.50204 | ||||||||
\(459\) | 7.59587 | 0.354545 | ||||||||
\(460\) | 3.51701 | 0.163982 | ||||||||
\(461\) | 8.77790 | 0.408828 | 0.204414 | − | 0.978885i | \(-0.434471\pi\) | ||||
0.204414 | + | 0.978885i | \(0.434471\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −42.1655 | −1.95960 | −0.979799 | − | 0.199983i | \(-0.935911\pi\) | ||||
−0.979799 | + | 0.199983i | \(0.935911\pi\) | |||||||
\(464\) | −35.2476 | −1.63633 | ||||||||
\(465\) | 0.871553 | 0.0404173 | ||||||||
\(466\) | −15.3098 | −0.709215 | ||||||||
\(467\) | 11.1275 | 0.514919 | 0.257460 | − | 0.966289i | \(-0.417115\pi\) | ||||
0.257460 | + | 0.966289i | \(0.417115\pi\) | |||||||
\(468\) | −2.56792 | −0.118702 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 17.6734 | 0.815213 | ||||||||
\(471\) | −12.7101 | −0.585649 | ||||||||
\(472\) | −18.6957 | −0.860538 | ||||||||
\(473\) | 0.564314 | 0.0259472 | ||||||||
\(474\) | −23.7344 | −1.09016 | ||||||||
\(475\) | −3.12845 | −0.143543 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.63899 | 0.166618 | ||||||||
\(478\) | 28.9124 | 1.32242 | ||||||||
\(479\) | 24.5949 | 1.12377 | 0.561886 | − | 0.827215i | \(-0.310076\pi\) | ||||
0.561886 | + | 0.827215i | \(0.310076\pi\) | |||||||
\(480\) | −4.47824 | −0.204403 | ||||||||
\(481\) | −30.2687 | −1.38013 | ||||||||
\(482\) | −33.6837 | −1.53425 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.60112 | −0.300051 | ||||||||
\(485\) | −16.6238 | −0.754848 | ||||||||
\(486\) | −1.68554 | −0.0764578 | ||||||||
\(487\) | −33.1665 | −1.50292 | −0.751458 | − | 0.659781i | \(-0.770649\pi\) | ||||
−0.751458 | + | 0.659781i | \(0.770649\pi\) | |||||||
\(488\) | −12.8650 | −0.582371 | ||||||||
\(489\) | −9.70227 | −0.438752 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.8513 | 1.16665 | 0.583326 | − | 0.812238i | \(-0.301751\pi\) | ||||
0.583326 | + | 0.812238i | \(0.301751\pi\) | |||||||
\(492\) | 2.32758 | 0.104935 | ||||||||
\(493\) | 53.8191 | 2.42389 | ||||||||
\(494\) | −16.1000 | −0.724371 | ||||||||
\(495\) | −1.77522 | −0.0797903 | ||||||||
\(496\) | 4.33575 | 0.194681 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −21.6229 | −0.968944 | ||||||||
\(499\) | 0.610504 | 0.0273299 | 0.0136650 | − | 0.999907i | \(-0.495650\pi\) | ||||
0.0136650 | + | 0.999907i | \(0.495650\pi\) | |||||||
\(500\) | −0.841058 | −0.0376133 | ||||||||
\(501\) | −12.8486 | −0.574032 | ||||||||
\(502\) | 8.31788 | 0.371245 | ||||||||
\(503\) | 9.49080 | 0.423174 | 0.211587 | − | 0.977359i | \(-0.432137\pi\) | ||||
0.211587 | + | 0.977359i | \(0.432137\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.4243 | 0.552874 | ||||||||
\(506\) | 12.5124 | 0.556244 | ||||||||
\(507\) | −3.67794 | −0.163343 | ||||||||
\(508\) | −12.7389 | −0.565199 | ||||||||
\(509\) | −21.6673 | −0.960387 | −0.480193 | − | 0.877163i | \(-0.659434\pi\) | ||||
−0.480193 | + | 0.877163i | \(0.659434\pi\) | |||||||
\(510\) | 12.8032 | 0.566934 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2.84232 | −0.125614 | ||||||||
\(513\) | −3.12845 | −0.138124 | ||||||||
\(514\) | 2.61334 | 0.115270 | ||||||||
\(515\) | 3.91375 | 0.172460 | ||||||||
\(516\) | 0.267358 | 0.0117698 | ||||||||
\(517\) | 18.6137 | 0.818630 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.9949 | −0.702098 | ||||||||
\(520\) | 5.96427 | 0.261551 | ||||||||
\(521\) | 34.3939 | 1.50683 | 0.753413 | − | 0.657548i | \(-0.228406\pi\) | ||||
0.753413 | + | 0.657548i | \(0.228406\pi\) | |||||||
\(522\) | −11.9426 | −0.522714 | ||||||||
\(523\) | −22.7779 | −0.996008 | −0.498004 | − | 0.867175i | \(-0.665934\pi\) | ||||
−0.498004 | + | 0.867175i | \(0.665934\pi\) | |||||||
\(524\) | 11.3755 | 0.496940 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.1084 | −0.963973 | ||||||||
\(527\) | −6.62020 | −0.288380 | ||||||||
\(528\) | −8.83127 | −0.384332 | ||||||||
\(529\) | −5.51379 | −0.239730 | ||||||||
\(530\) | 6.13368 | 0.266430 | ||||||||
\(531\) | −9.57060 | −0.415329 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.44955 | −0.365991 | ||||||||
\(534\) | 8.13853 | 0.352188 | ||||||||
\(535\) | −3.73210 | −0.161353 | ||||||||
\(536\) | 27.3876 | 1.18297 | ||||||||
\(537\) | −24.8807 | −1.07368 | ||||||||
\(538\) | −7.91659 | −0.341308 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.841058 | −0.0361934 | ||||||||
\(541\) | 27.4045 | 1.17821 | 0.589107 | − | 0.808055i | \(-0.299480\pi\) | ||||
0.589107 | + | 0.808055i | \(0.299480\pi\) | |||||||
\(542\) | −29.7227 | −1.27670 | ||||||||
\(543\) | −3.18583 | −0.136717 | ||||||||
\(544\) | 34.0161 | 1.45843 | ||||||||
\(545\) | −7.65685 | −0.327984 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.1421 | −0.775702 | −0.387851 | − | 0.921722i | \(-0.626782\pi\) | ||||
−0.387851 | + | 0.921722i | \(0.626782\pi\) | |||||||
\(548\) | 2.30440 | 0.0984391 | ||||||||
\(549\) | −6.58579 | −0.281075 | ||||||||
\(550\) | −2.99222 | −0.127589 | ||||||||
\(551\) | −22.1661 | −0.944306 | ||||||||
\(552\) | −8.16864 | −0.347680 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 26.7205 | 1.13525 | ||||||||
\(555\) | −9.91375 | −0.420815 | ||||||||
\(556\) | −5.61734 | −0.238228 | ||||||||
\(557\) | 22.0582 | 0.934635 | 0.467318 | − | 0.884090i | \(-0.345220\pi\) | ||||
0.467318 | + | 0.884090i | \(0.345220\pi\) | |||||||
\(558\) | 1.46904 | 0.0621894 | ||||||||
\(559\) | −0.970563 | −0.0410504 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.4844 | 0.569310 | ||||||||
\(562\) | −28.1114 | −1.18581 | ||||||||
\(563\) | −10.1577 | −0.428096 | −0.214048 | − | 0.976823i | \(-0.568665\pi\) | ||||
−0.214048 | + | 0.976823i | \(0.568665\pi\) | |||||||
\(564\) | 8.81873 | 0.371336 | ||||||||
\(565\) | −19.4023 | −0.816259 | ||||||||
\(566\) | 21.5966 | 0.907774 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.9913 | 0.503143 | ||||||||
\(569\) | −42.5256 | −1.78277 | −0.891383 | − | 0.453251i | \(-0.850264\pi\) | ||||
−0.891383 | + | 0.453251i | \(0.850264\pi\) | |||||||
\(570\) | −5.27314 | −0.220867 | ||||||||
\(571\) | −22.7688 | −0.952844 | −0.476422 | − | 0.879217i | \(-0.658067\pi\) | ||||
−0.476422 | + | 0.879217i | \(0.658067\pi\) | |||||||
\(572\) | −4.55864 | −0.190606 | ||||||||
\(573\) | −2.34676 | −0.0980371 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.18165 | −0.174387 | ||||||||
\(576\) | 2.40120 | 0.100050 | ||||||||
\(577\) | 40.4467 | 1.68382 | 0.841909 | − | 0.539619i | \(-0.181432\pi\) | ||||
0.841909 | + | 0.539619i | \(0.181432\pi\) | |||||||
\(578\) | −68.5969 | −2.85325 | ||||||||
\(579\) | 23.1307 | 0.961281 | ||||||||
\(580\) | −5.95917 | −0.247441 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −28.0202 | −1.16147 | ||||||||
\(583\) | 6.46002 | 0.267547 | ||||||||
\(584\) | −15.0200 | −0.621532 | ||||||||
\(585\) | 3.05320 | 0.126234 | ||||||||
\(586\) | −11.0766 | −0.457570 | ||||||||
\(587\) | 21.7918 | 0.899443 | 0.449721 | − | 0.893169i | \(-0.351523\pi\) | ||||
0.449721 | + | 0.893169i | \(0.351523\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.72661 | 0.112348 | ||||||||
\(590\) | −16.1317 | −0.664130 | ||||||||
\(591\) | −3.03895 | −0.125006 | ||||||||
\(592\) | −49.3183 | −2.02697 | ||||||||
\(593\) | −2.09084 | −0.0858605 | −0.0429303 | − | 0.999078i | \(-0.513669\pi\) | ||||
−0.0429303 | + | 0.999078i | \(0.513669\pi\) | |||||||
\(594\) | −2.99222 | −0.122772 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.14740 | 0.0469993 | ||||||||
\(597\) | −4.42200 | −0.180980 | ||||||||
\(598\) | −21.5201 | −0.880021 | ||||||||
\(599\) | −21.7247 | −0.887647 | −0.443824 | − | 0.896114i | \(-0.646378\pi\) | ||||
−0.443824 | + | 0.896114i | \(0.646378\pi\) | |||||||
\(600\) | 1.95345 | 0.0797491 | ||||||||
\(601\) | −15.6711 | −0.639238 | −0.319619 | − | 0.947546i | \(-0.603555\pi\) | ||||
−0.319619 | + | 0.947546i | \(0.603555\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.0202 | 0.570945 | ||||||||
\(604\) | −20.0191 | −0.814564 | ||||||||
\(605\) | 7.84858 | 0.319090 | ||||||||
\(606\) | 20.9417 | 0.850698 | ||||||||
\(607\) | −15.3688 | −0.623801 | −0.311901 | − | 0.950115i | \(-0.600966\pi\) | ||||
−0.311901 | + | 0.950115i | \(0.600966\pi\) | |||||||
\(608\) | −14.0100 | −0.568179 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.1006 | −0.449451 | ||||||||
\(611\) | −32.0137 | −1.29514 | ||||||||
\(612\) | 6.38857 | 0.258242 | ||||||||
\(613\) | −24.9958 | −1.00957 | −0.504786 | − | 0.863245i | \(-0.668429\pi\) | ||||
−0.504786 | + | 0.863245i | \(0.668429\pi\) | |||||||
\(614\) | 25.8119 | 1.04168 | ||||||||
\(615\) | −2.76744 | −0.111594 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.9738 | 0.965148 | 0.482574 | − | 0.875855i | \(-0.339702\pi\) | ||||
0.482574 | + | 0.875855i | \(0.339702\pi\) | |||||||
\(618\) | 6.59680 | 0.265362 | ||||||||
\(619\) | 7.31466 | 0.294001 | 0.147000 | − | 0.989136i | \(-0.453038\pi\) | ||||
0.147000 | + | 0.989136i | \(0.453038\pi\) | |||||||
\(620\) | 0.733027 | 0.0294391 | ||||||||
\(621\) | −4.18165 | −0.167804 | ||||||||
\(622\) | 26.5412 | 1.06420 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 15.1889 | 0.608042 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −33.7388 | −1.34847 | ||||||||
\(627\) | −5.55369 | −0.221793 | ||||||||
\(628\) | −10.6899 | −0.426573 | ||||||||
\(629\) | 75.3035 | 3.00255 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.18204 | 0.0470561 | 0.0235281 | − | 0.999723i | \(-0.492510\pi\) | ||||
0.0235281 | + | 0.999723i | \(0.492510\pi\) | |||||||
\(632\) | 27.5068 | 1.09416 | ||||||||
\(633\) | 4.57153 | 0.181702 | ||||||||
\(634\) | 38.5424 | 1.53071 | ||||||||
\(635\) | 15.1463 | 0.601063 | ||||||||
\(636\) | 3.06060 | 0.121361 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −21.2008 | −0.839348 | ||||||||
\(639\) | 6.13853 | 0.242836 | ||||||||
\(640\) | 13.0038 | 0.514021 | ||||||||
\(641\) | −40.6917 | −1.60722 | −0.803612 | − | 0.595154i | \(-0.797091\pi\) | ||||
−0.803612 | + | 0.595154i | \(0.797091\pi\) | |||||||
\(642\) | −6.29061 | −0.248271 | ||||||||
\(643\) | −20.2771 | −0.799649 | −0.399824 | − | 0.916592i | \(-0.630929\pi\) | ||||
−0.399824 | + | 0.916592i | \(0.630929\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.317883 | −0.0125166 | ||||||||
\(646\) | 40.0540 | 1.57590 | ||||||||
\(647\) | 39.8990 | 1.56859 | 0.784295 | − | 0.620388i | \(-0.213025\pi\) | ||||
0.784295 | + | 0.620388i | \(0.213025\pi\) | |||||||
\(648\) | 1.95345 | 0.0767386 | ||||||||
\(649\) | −16.9900 | −0.666914 | ||||||||
\(650\) | 5.14631 | 0.201855 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.16018 | −0.319577 | ||||||||
\(653\) | 7.10318 | 0.277969 | 0.138985 | − | 0.990295i | \(-0.455616\pi\) | ||||
0.138985 | + | 0.990295i | \(0.455616\pi\) | |||||||
\(654\) | −12.9060 | −0.504663 | ||||||||
\(655\) | −13.5252 | −0.528473 | ||||||||
\(656\) | −13.7673 | −0.537522 | ||||||||
\(657\) | −7.68897 | −0.299975 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.8404 | −0.811826 | −0.405913 | − | 0.913912i | \(-0.633046\pi\) | ||||
−0.405913 | + | 0.913912i | \(0.633046\pi\) | |||||||
\(660\) | −1.49307 | −0.0581175 | ||||||||
\(661\) | −41.5545 | −1.61628 | −0.808141 | − | 0.588989i | \(-0.799526\pi\) | ||||
−0.808141 | + | 0.588989i | \(0.799526\pi\) | |||||||
\(662\) | 20.8991 | 0.812267 | ||||||||
\(663\) | −23.1917 | −0.900692 | ||||||||
\(664\) | 25.0597 | 0.972503 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.7101 | −0.647502 | ||||||||
\(667\) | −29.6283 | −1.14721 | ||||||||
\(668\) | −10.8064 | −0.418113 | ||||||||
\(669\) | −4.53581 | −0.175364 | ||||||||
\(670\) | 23.6316 | 0.912968 | ||||||||
\(671\) | −11.6912 | −0.451335 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.34943 | −0.206206 | −0.103103 | − | 0.994671i | \(-0.532877\pi\) | ||||
−0.103103 | + | 0.994671i | \(0.532877\pi\) | |||||||
\(674\) | −1.05397 | −0.0405976 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −3.09336 | −0.118976 | ||||||||
\(677\) | −2.83488 | −0.108953 | −0.0544766 | − | 0.998515i | \(-0.517349\pi\) | ||||
−0.0544766 | + | 0.998515i | \(0.517349\pi\) | |||||||
\(678\) | −32.7034 | −1.25596 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −14.8381 | −0.569016 | ||||||||
\(681\) | 8.44955 | 0.323788 | ||||||||
\(682\) | 2.60787 | 0.0998607 | ||||||||
\(683\) | 23.1724 | 0.886666 | 0.443333 | − | 0.896357i | \(-0.353796\pi\) | ||||
0.443333 | + | 0.896357i | \(0.353796\pi\) | |||||||
\(684\) | −2.63121 | −0.100607 | ||||||||
\(685\) | −2.73988 | −0.104685 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.0711 | −0.727607 | ||||||||
\(688\) | −1.58139 | −0.0602898 | ||||||||
\(689\) | −11.1106 | −0.423280 | ||||||||
\(690\) | −7.04836 | −0.268326 | ||||||||
\(691\) | 38.9678 | 1.48240 | 0.741202 | − | 0.671283i | \(-0.234256\pi\) | ||||
0.741202 | + | 0.671283i | \(0.234256\pi\) | |||||||
\(692\) | −13.4526 | −0.511393 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.89328 | 0.109828 | ||||||||
\(695\) | 6.67889 | 0.253345 | ||||||||
\(696\) | 13.8408 | 0.524634 | ||||||||
\(697\) | 21.0211 | 0.796230 | ||||||||
\(698\) | −25.3658 | −0.960111 | ||||||||
\(699\) | 9.08303 | 0.343552 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.2421 | 0.764533 | 0.382267 | − | 0.924052i | \(-0.375144\pi\) | ||||
0.382267 | + | 0.924052i | \(0.375144\pi\) | |||||||
\(702\) | 5.14631 | 0.194235 | ||||||||
\(703\) | −31.0146 | −1.16974 | ||||||||
\(704\) | 4.26266 | 0.160655 | ||||||||
\(705\) | −10.4853 | −0.394899 | ||||||||
\(706\) | 37.8628 | 1.42499 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −8.04944 | −0.302516 | ||||||||
\(709\) | −32.2128 | −1.20978 | −0.604889 | − | 0.796310i | \(-0.706782\pi\) | ||||
−0.604889 | + | 0.796310i | \(0.706782\pi\) | |||||||
\(710\) | 10.3468 | 0.388307 | ||||||||
\(711\) | 14.0811 | 0.528084 | ||||||||
\(712\) | −9.43208 | −0.353482 | ||||||||
\(713\) | 3.64453 | 0.136489 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.42012 | 0.202701 | ||||||||
\(716\) | −20.9261 | −0.782046 | ||||||||
\(717\) | −17.1532 | −0.640597 | ||||||||
\(718\) | −5.78492 | −0.215891 | ||||||||
\(719\) | 8.45867 | 0.315455 | 0.157728 | − | 0.987483i | \(-0.449583\pi\) | ||||
0.157728 | + | 0.987483i | \(0.449583\pi\) | |||||||
\(720\) | 4.97474 | 0.185398 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 15.5286 | 0.577915 | ||||||||
\(723\) | 19.9839 | 0.743209 | ||||||||
\(724\) | −2.67947 | −0.0995816 | ||||||||
\(725\) | 7.08532 | 0.263142 | ||||||||
\(726\) | 13.2291 | 0.490979 | ||||||||
\(727\) | 11.6550 | 0.432260 | 0.216130 | − | 0.976365i | \(-0.430657\pi\) | ||||
0.216130 | + | 0.976365i | \(0.430657\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −12.9601 | −0.479675 | ||||||||
\(731\) | 2.41460 | 0.0893072 | ||||||||
\(732\) | −5.53903 | −0.204728 | ||||||||
\(733\) | −13.0182 | −0.480840 | −0.240420 | − | 0.970669i | \(-0.577285\pi\) | ||||
−0.240420 | + | 0.970669i | \(0.577285\pi\) | |||||||
\(734\) | 40.7747 | 1.50502 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.7265 | −0.690266 | ||||||||
\(737\) | 24.8889 | 0.916794 | ||||||||
\(738\) | −4.66464 | −0.171708 | ||||||||
\(739\) | −24.3413 | −0.895409 | −0.447704 | − | 0.894182i | \(-0.647758\pi\) | ||||
−0.447704 | + | 0.894182i | \(0.647758\pi\) | |||||||
\(740\) | −8.33804 | −0.306512 | ||||||||
\(741\) | 9.55179 | 0.350894 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.1174 | −0.444545 | −0.222272 | − | 0.974985i | \(-0.571347\pi\) | ||||
−0.222272 | + | 0.974985i | \(0.571347\pi\) | |||||||
\(744\) | −1.70253 | −0.0624179 | ||||||||
\(745\) | −1.36423 | −0.0499816 | ||||||||
\(746\) | 1.44440 | 0.0528833 | ||||||||
\(747\) | 12.8284 | 0.469368 | ||||||||
\(748\) | 11.3411 | 0.414673 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.68554 | 0.0615474 | ||||||||
\(751\) | 11.3779 | 0.415187 | 0.207594 | − | 0.978215i | \(-0.433437\pi\) | ||||
0.207594 | + | 0.978215i | \(0.433437\pi\) | |||||||
\(752\) | −52.1615 | −1.90214 | ||||||||
\(753\) | −4.93484 | −0.179835 | ||||||||
\(754\) | 36.4633 | 1.32791 | ||||||||
\(755\) | 23.8022 | 0.866252 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.5664 | −1.11096 | −0.555478 | − | 0.831531i | \(-0.687465\pi\) | ||||
−0.555478 | + | 0.831531i | \(0.687465\pi\) | |||||||
\(758\) | −9.49230 | −0.344776 | ||||||||
\(759\) | −7.42336 | −0.269451 | ||||||||
\(760\) | 6.11126 | 0.221679 | ||||||||
\(761\) | −10.3128 | −0.373838 | −0.186919 | − | 0.982375i | \(-0.559850\pi\) | ||||
−0.186919 | + | 0.982375i | \(0.559850\pi\) | |||||||
\(762\) | 25.5298 | 0.924846 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.97376 | −0.0714081 | ||||||||
\(765\) | −7.59587 | −0.274629 | ||||||||
\(766\) | −9.10187 | −0.328864 | ||||||||
\(767\) | 29.2210 | 1.05511 | ||||||||
\(768\) | 17.1161 | 0.617624 | ||||||||
\(769\) | −4.12788 | −0.148855 | −0.0744276 | − | 0.997226i | \(-0.523713\pi\) | ||||
−0.0744276 | + | 0.997226i | \(0.523713\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.55045 | −0.0558379 | ||||||||
\(772\) | 19.4543 | 0.700176 | ||||||||
\(773\) | 13.1041 | 0.471323 | 0.235661 | − | 0.971835i | \(-0.424274\pi\) | ||||
0.235661 | + | 0.971835i | \(0.424274\pi\) | |||||||
\(774\) | −0.535806 | −0.0192592 | ||||||||
\(775\) | −0.871553 | −0.0313071 | ||||||||
\(776\) | 32.4737 | 1.16574 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.0165 | −0.861035 | ||||||||
\(779\) | −8.65778 | −0.310197 | ||||||||
\(780\) | 2.56792 | 0.0919464 | ||||||||
\(781\) | 10.8972 | 0.389934 | ||||||||
\(782\) | 53.5384 | 1.91453 | ||||||||
\(783\) | 7.08532 | 0.253209 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.7101 | 0.453641 | ||||||||
\(786\) | −22.7973 | −0.813152 | ||||||||
\(787\) | −8.39444 | −0.299230 | −0.149615 | − | 0.988744i | \(-0.547803\pi\) | ||||
−0.149615 | + | 0.988744i | \(0.547803\pi\) | |||||||
\(788\) | −2.55594 | −0.0910514 | ||||||||
\(789\) | 13.1165 | 0.466959 | ||||||||
\(790\) | 23.7344 | 0.844432 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.46780 | 0.123223 | ||||||||
\(793\) | 20.1078 | 0.714047 | ||||||||
\(794\) | −19.6421 | −0.697070 | ||||||||
\(795\) | −3.63899 | −0.129062 | ||||||||
\(796\) | −3.71916 | −0.131822 | ||||||||
\(797\) | 16.8032 | 0.595199 | 0.297599 | − | 0.954691i | \(-0.403814\pi\) | ||||
0.297599 | + | 0.954691i | \(0.403814\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 79.6448 | 2.81763 | ||||||||
\(800\) | 4.47824 | 0.158330 | ||||||||
\(801\) | −4.82843 | −0.170604 | ||||||||
\(802\) | 4.47981 | 0.158188 | ||||||||
\(803\) | −13.6496 | −0.481685 | ||||||||
\(804\) | 11.7918 | 0.415864 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.48528 | −0.157987 | ||||||||
\(807\) | 4.69676 | 0.165334 | ||||||||
\(808\) | −24.2702 | −0.853823 | ||||||||
\(809\) | 19.6926 | 0.692354 | 0.346177 | − | 0.938169i | \(-0.387480\pi\) | ||||
0.346177 | + | 0.938169i | \(0.387480\pi\) | |||||||
\(810\) | 1.68554 | 0.0592240 | ||||||||
\(811\) | −17.3568 | −0.609481 | −0.304740 | − | 0.952435i | \(-0.598570\pi\) | ||||
−0.304740 | + | 0.952435i | \(0.598570\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.6339 | 0.618447 | ||||||||
\(814\) | −29.6641 | −1.03973 | ||||||||
\(815\) | 9.70227 | 0.339856 | ||||||||
\(816\) | −37.7874 | −1.32282 | ||||||||
\(817\) | −0.994481 | −0.0347925 | ||||||||
\(818\) | −45.3758 | −1.58653 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.32758 | −0.0812825 | ||||||||
\(821\) | 35.9696 | 1.25535 | 0.627674 | − | 0.778476i | \(-0.284007\pi\) | ||||
0.627674 | + | 0.778476i | \(0.284007\pi\) | |||||||
\(822\) | −4.61819 | −0.161078 | ||||||||
\(823\) | −31.1463 | −1.08569 | −0.542846 | − | 0.839832i | \(-0.682653\pi\) | ||||
−0.542846 | + | 0.839832i | \(0.682653\pi\) | |||||||
\(824\) | −7.64530 | −0.266337 | ||||||||
\(825\) | 1.77522 | 0.0618053 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −52.2577 | −1.81718 | −0.908589 | − | 0.417691i | \(-0.862839\pi\) | ||||
−0.908589 | + | 0.417691i | \(0.862839\pi\) | |||||||
\(828\) | −3.51701 | −0.122225 | ||||||||
\(829\) | −4.55083 | −0.158057 | −0.0790284 | − | 0.996872i | \(-0.525182\pi\) | ||||
−0.0790284 | + | 0.996872i | \(0.525182\pi\) | |||||||
\(830\) | 21.6229 | 0.750541 | ||||||||
\(831\) | −15.8528 | −0.549926 | ||||||||
\(832\) | −7.33135 | −0.254169 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 11.2576 | 0.389818 | ||||||||
\(835\) | 12.8486 | 0.444644 | ||||||||
\(836\) | −4.67098 | −0.161549 | ||||||||
\(837\) | −0.871553 | −0.0301253 | ||||||||
\(838\) | −25.6063 | −0.884556 | ||||||||
\(839\) | −43.3994 | −1.49832 | −0.749158 | − | 0.662392i | \(-0.769541\pi\) | ||||
−0.749158 | + | 0.662392i | \(0.769541\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.2018 | 0.731096 | ||||||||
\(842\) | 1.27721 | 0.0440156 | ||||||||
\(843\) | 16.6779 | 0.574419 | ||||||||
\(844\) | 3.84493 | 0.132348 | ||||||||
\(845\) | 3.67794 | 0.126525 | ||||||||
\(846\) | −17.6734 | −0.607624 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −18.1030 | −0.621660 | ||||||||
\(849\) | −12.8129 | −0.439736 | ||||||||
\(850\) | −12.8032 | −0.439145 | ||||||||
\(851\) | −41.4558 | −1.42109 | ||||||||
\(852\) | 5.16286 | 0.176877 | ||||||||
\(853\) | 11.9238 | 0.408263 | 0.204132 | − | 0.978943i | \(-0.434563\pi\) | ||||
0.204132 | + | 0.978943i | \(0.434563\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.12845 | 0.106991 | ||||||||
\(856\) | 7.29045 | 0.249183 | ||||||||
\(857\) | 34.5003 | 1.17851 | 0.589254 | − | 0.807947i | \(-0.299422\pi\) | ||||
0.589254 | + | 0.807947i | \(0.299422\pi\) | |||||||
\(858\) | 9.13585 | 0.311893 | ||||||||
\(859\) | −48.5311 | −1.65586 | −0.827930 | − | 0.560831i | \(-0.810482\pi\) | ||||
−0.827930 | + | 0.560831i | \(0.810482\pi\) | |||||||
\(860\) | −0.267358 | −0.00911685 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −38.9514 | −1.32669 | ||||||||
\(863\) | 37.2431 | 1.26777 | 0.633884 | − | 0.773428i | \(-0.281460\pi\) | ||||
0.633884 | + | 0.773428i | \(0.281460\pi\) | |||||||
\(864\) | 4.47824 | 0.152353 | ||||||||
\(865\) | 15.9949 | 0.543843 | ||||||||
\(866\) | 26.0454 | 0.885059 | ||||||||
\(867\) | 40.6972 | 1.38215 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.9972 | 0.847971 | ||||||||
\(870\) | 11.9426 | 0.404893 | ||||||||
\(871\) | −42.8064 | −1.45044 | ||||||||
\(872\) | 14.9573 | 0.506517 | ||||||||
\(873\) | 16.6238 | 0.562631 | ||||||||
\(874\) | −22.0504 | −0.745866 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.46687 | −0.218495 | ||||||||
\(877\) | 22.4399 | 0.757740 | 0.378870 | − | 0.925450i | \(-0.376313\pi\) | ||||
0.378870 | + | 0.925450i | \(0.376313\pi\) | |||||||
\(878\) | −48.1801 | −1.62600 | ||||||||
\(879\) | 6.57153 | 0.221652 | ||||||||
\(880\) | 8.83127 | 0.297702 | ||||||||
\(881\) | −15.4844 | −0.521681 | −0.260841 | − | 0.965382i | \(-0.584000\pi\) | ||||
−0.260841 | + | 0.965382i | \(0.584000\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.19173 | 0.242021 | 0.121011 | − | 0.992651i | \(-0.461387\pi\) | ||||
0.121011 | + | 0.992651i | \(0.461387\pi\) | |||||||
\(884\) | −19.5056 | −0.656044 | ||||||||
\(885\) | 9.57060 | 0.321712 | ||||||||
\(886\) | 37.2690 | 1.25208 | ||||||||
\(887\) | −26.8201 | −0.900530 | −0.450265 | − | 0.892895i | \(-0.648670\pi\) | ||||
−0.450265 | + | 0.892895i | \(0.648670\pi\) | |||||||
\(888\) | 19.3660 | 0.649880 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8.13853 | −0.272804 | ||||||||
\(891\) | 1.77522 | 0.0594722 | ||||||||
\(892\) | −3.81488 | −0.127732 | ||||||||
\(893\) | −32.8026 | −1.09770 | ||||||||
\(894\) | −2.29948 | −0.0769060 | ||||||||
\(895\) | 24.8807 | 0.831670 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.7674 | 0.426292 | ||||||||
\(898\) | 44.5647 | 1.48714 | ||||||||
\(899\) | −6.17523 | −0.205956 | ||||||||
\(900\) | 0.841058 | 0.0280353 | ||||||||
\(901\) | 27.6413 | 0.920865 | ||||||||
\(902\) | −8.28077 | −0.275720 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 37.9013 | 1.26058 | ||||||||
\(905\) | 3.18583 | 0.105900 | ||||||||
\(906\) | 40.1197 | 1.33289 | ||||||||
\(907\) | 22.5054 | 0.747281 | 0.373640 | − | 0.927574i | \(-0.378109\pi\) | ||||
0.373640 | + | 0.927574i | \(0.378109\pi\) | |||||||
\(908\) | 7.10657 | 0.235840 | ||||||||
\(909\) | −12.4243 | −0.412088 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.8798 | −1.38754 | −0.693769 | − | 0.720197i | \(-0.744051\pi\) | ||||
−0.693769 | + | 0.720197i | \(0.744051\pi\) | |||||||
\(912\) | 15.5632 | 0.515349 | ||||||||
\(913\) | 22.7733 | 0.753687 | ||||||||
\(914\) | −59.0046 | −1.95170 | ||||||||
\(915\) | 6.58579 | 0.217719 | ||||||||
\(916\) | −16.0399 | −0.529973 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −12.8032 | −0.422567 | ||||||||
\(919\) | −13.8119 | −0.455613 | −0.227807 | − | 0.973706i | \(-0.573155\pi\) | ||||
−0.227807 | + | 0.973706i | \(0.573155\pi\) | |||||||
\(920\) | 8.16864 | 0.269312 | ||||||||
\(921\) | −15.3137 | −0.504604 | ||||||||
\(922\) | −14.7955 | −0.487265 | ||||||||
\(923\) | −18.7422 | −0.616906 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.91375 | 0.325962 | ||||||||
\(926\) | 71.0719 | 2.33557 | ||||||||
\(927\) | −3.91375 | −0.128544 | ||||||||
\(928\) | 31.7298 | 1.04158 | ||||||||
\(929\) | −1.12291 | −0.0368414 | −0.0184207 | − | 0.999830i | \(-0.505864\pi\) | ||||
−0.0184207 | + | 0.999830i | \(0.505864\pi\) | |||||||
\(930\) | −1.46904 | −0.0481717 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.63936 | 0.250235 | ||||||||
\(933\) | −15.7464 | −0.515512 | ||||||||
\(934\) | −18.7559 | −0.613711 | ||||||||
\(935\) | −13.4844 | −0.440985 | ||||||||
\(936\) | −5.96427 | −0.194948 | ||||||||
\(937\) | −1.43208 | −0.0467839 | −0.0233920 | − | 0.999726i | \(-0.507447\pi\) | ||||
−0.0233920 | + | 0.999726i | \(0.507447\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.0165 | 0.653215 | ||||||||
\(940\) | −8.81873 | −0.287635 | ||||||||
\(941\) | 19.6972 | 0.642109 | 0.321055 | − | 0.947061i | \(-0.395963\pi\) | ||||
0.321055 | + | 0.947061i | \(0.395963\pi\) | |||||||
\(942\) | 21.4234 | 0.698011 | ||||||||
\(943\) | −11.5725 | −0.376851 | ||||||||
\(944\) | 47.6112 | 1.54961 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.951175 | −0.0309254 | ||||||||
\(947\) | 25.1807 | 0.818264 | 0.409132 | − | 0.912475i | \(-0.365832\pi\) | ||||
0.409132 | + | 0.912475i | \(0.365832\pi\) | |||||||
\(948\) | 11.8431 | 0.384645 | ||||||||
\(949\) | 23.4760 | 0.762063 | ||||||||
\(950\) | 5.27314 | 0.171083 | ||||||||
\(951\) | −22.8664 | −0.741495 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.0884 | 1.52534 | 0.762671 | − | 0.646786i | \(-0.223887\pi\) | ||||
0.762671 | + | 0.646786i | \(0.223887\pi\) | |||||||
\(954\) | −6.13368 | −0.198585 | ||||||||
\(955\) | 2.34676 | 0.0759392 | ||||||||
\(956\) | −14.4268 | −0.466596 | ||||||||
\(957\) | 12.5780 | 0.406590 | ||||||||
\(958\) | −41.4558 | −1.33938 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.40120 | −0.0774983 | ||||||||
\(961\) | −30.2404 | −0.975497 | ||||||||
\(962\) | 51.0192 | 1.64493 | ||||||||
\(963\) | 3.73210 | 0.120265 | ||||||||
\(964\) | 16.8076 | 0.541337 | ||||||||
\(965\) | −23.1307 | −0.744605 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.32113 | −0.0746425 | −0.0373212 | − | 0.999303i | \(-0.511882\pi\) | ||||
−0.0373212 | + | 0.999303i | \(0.511882\pi\) | |||||||
\(968\) | −15.3318 | −0.492783 | ||||||||
\(969\) | −23.7633 | −0.763386 | ||||||||
\(970\) | 28.0202 | 0.899673 | ||||||||
\(971\) | −12.5592 | −0.403044 | −0.201522 | − | 0.979484i | \(-0.564589\pi\) | ||||
−0.201522 | + | 0.979484i | \(0.564589\pi\) | |||||||
\(972\) | 0.841058 | 0.0269770 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 55.9035 | 1.79126 | ||||||||
\(975\) | −3.05320 | −0.0977808 | ||||||||
\(976\) | 32.7626 | 1.04870 | ||||||||
\(977\) | −9.66637 | −0.309255 | −0.154627 | − | 0.987973i | \(-0.549418\pi\) | ||||
−0.154627 | + | 0.987973i | \(0.549418\pi\) | |||||||
\(978\) | 16.3536 | 0.522931 | ||||||||
\(979\) | −8.57153 | −0.273947 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.65685 | 0.244465 | ||||||||
\(982\) | −43.5734 | −1.39048 | ||||||||
\(983\) | −46.0559 | −1.46895 | −0.734477 | − | 0.678633i | \(-0.762573\pi\) | ||||
−0.734477 | + | 0.678633i | \(0.762573\pi\) | |||||||
\(984\) | 5.40604 | 0.172338 | ||||||||
\(985\) | 3.03895 | 0.0968290 | ||||||||
\(986\) | −90.7145 | −2.88894 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.03361 | 0.255583 | ||||||||
\(989\) | −1.32928 | −0.0422686 | ||||||||
\(990\) | 2.99222 | 0.0950989 | ||||||||
\(991\) | 27.8138 | 0.883534 | 0.441767 | − | 0.897130i | \(-0.354352\pi\) | ||||
0.441767 | + | 0.897130i | \(0.354352\pi\) | |||||||
\(992\) | −3.90303 | −0.123921 | ||||||||
\(993\) | −12.3990 | −0.393471 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.42200 | 0.140187 | ||||||||
\(996\) | 10.7895 | 0.341877 | ||||||||
\(997\) | 46.5505 | 1.47427 | 0.737134 | − | 0.675746i | \(-0.236178\pi\) | ||||
0.737134 | + | 0.675746i | \(0.236178\pi\) | |||||||
\(998\) | −1.02903 | −0.0325734 | ||||||||
\(999\) | 9.91375 | 0.313657 |
(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 | 735.2.a.o.1.1 | yes | 4 | |
3.2 | odd | 2 | 2205.2.a.bg.1.4 | 4 | |||
5.4 | even | 2 | 3675.2.a.bk.1.4 | 4 | |||
7.2 | even | 3 | 735.2.i.m.361.4 | 8 | |||
7.3 | odd | 6 | 735.2.i.n.226.4 | 8 | |||
7.4 | even | 3 | 735.2.i.m.226.4 | 8 | |||
7.5 | odd | 6 | 735.2.i.n.361.4 | 8 | |||
7.6 | odd | 2 | 735.2.a.n.1.1 | ✓ | 4 | ||
21.20 | even | 2 | 2205.2.a.bf.1.4 | 4 | |||
35.34 | odd | 2 | 3675.2.a.bl.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
735.2.a.n.1.1 | ✓ | 4 | 7.6 | odd | 2 | ||
735.2.a.o.1.1 | yes | 4 | 1.1 | even | 1 | trivial | |
735.2.i.m.226.4 | 8 | 7.4 | even | 3 | |||
735.2.i.m.361.4 | 8 | 7.2 | even | 3 | |||
735.2.i.n.226.4 | 8 | 7.3 | odd | 6 | |||
735.2.i.n.361.4 | 8 | 7.5 | odd | 6 | |||
2205.2.a.bf.1.4 | 4 | 21.20 | even | 2 | |||
2205.2.a.bg.1.4 | 4 | 3.2 | odd | 2 | |||
3675.2.a.bk.1.4 | 4 | 5.4 | even | 2 | |||
3675.2.a.bl.1.4 | 4 | 35.34 | odd | 2 |