Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7605,2,Mod(1,7605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7605, 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("7605.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7605.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: | \(60.7262307372\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.3352656.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 6x^{3} + 10x^{2} + 6x - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 585) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.626791\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7605.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.626791 | 0.443208 | 0.221604 | − | 0.975137i | \(-0.428871\pi\) | ||||
0.221604 | + | 0.975137i | \(0.428871\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.60713 | −0.803566 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.43127 | −1.67486 | −0.837431 | − | 0.546543i | \(-0.815943\pi\) | ||||
−0.837431 | + | 0.546543i | \(0.815943\pi\) | |||||||
\(8\) | −2.26092 | −0.799356 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.626791 | 0.198209 | ||||||||
\(11\) | 6.05806 | 1.82657 | 0.913287 | − | 0.407317i | \(-0.133536\pi\) | ||||
0.913287 | + | 0.407317i | \(0.133536\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.77748 | −0.742313 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.79714 | 0.449285 | ||||||||
\(17\) | 5.84106 | 1.41666 | 0.708332 | − | 0.705879i | \(-0.249448\pi\) | ||||
0.708332 | + | 0.705879i | \(0.249448\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.60713 | 0.827533 | 0.413766 | − | 0.910383i | \(-0.364213\pi\) | ||||
0.413766 | + | 0.910383i | \(0.364213\pi\) | |||||||
\(20\) | −1.60713 | −0.359366 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.79714 | 0.809553 | ||||||||
\(23\) | −2.26092 | −0.471434 | −0.235717 | − | 0.971822i | \(-0.575744\pi\) | ||||
−0.235717 | + | 0.971822i | \(0.575744\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.12164 | 1.34586 | ||||||||
\(29\) | −8.08506 | −1.50136 | −0.750679 | − | 0.660668i | \(-0.770273\pi\) | ||||
−0.750679 | + | 0.660668i | \(0.770273\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.45826 | −1.15994 | −0.579969 | − | 0.814638i | \(-0.696935\pi\) | ||||
−0.579969 | + | 0.814638i | \(0.696935\pi\) | |||||||
\(32\) | 5.64827 | 0.998483 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.66112 | 0.627878 | ||||||||
\(35\) | −4.43127 | −0.749021 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.79714 | 0.295448 | 0.147724 | − | 0.989029i | \(-0.452805\pi\) | ||||
0.147724 | + | 0.989029i | \(0.452805\pi\) | |||||||
\(38\) | 2.26092 | 0.366770 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.26092 | −0.357483 | ||||||||
\(41\) | −7.99175 | −1.24810 | −0.624051 | − | 0.781384i | \(-0.714514\pi\) | ||||
−0.624051 | + | 0.781384i | \(0.714514\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.48751 | 0.989336 | 0.494668 | − | 0.869082i | \(-0.335290\pi\) | ||||
0.494668 | + | 0.869082i | \(0.335290\pi\) | |||||||
\(44\) | −9.73610 | −1.46777 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.41713 | −0.208944 | ||||||||
\(47\) | −3.22841 | −0.470912 | −0.235456 | − | 0.971885i | \(-0.575658\pi\) | ||||
−0.235456 | + | 0.971885i | \(0.575658\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.6361 | 1.80516 | ||||||||
\(50\) | 0.626791 | 0.0886417 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.0768 | −1.38416 | −0.692078 | − | 0.721823i | \(-0.743304\pi\) | ||||
−0.692078 | + | 0.721823i | \(0.743304\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.05806 | 0.816869 | ||||||||
\(56\) | 10.0187 | 1.33881 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.06764 | −0.665414 | ||||||||
\(59\) | 3.12921 | 0.407388 | 0.203694 | − | 0.979035i | \(-0.434705\pi\) | ||||
0.203694 | + | 0.979035i | \(0.434705\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.45826 | −0.314748 | −0.157374 | − | 0.987539i | \(-0.550303\pi\) | ||||
−0.157374 | + | 0.987539i | \(0.550303\pi\) | |||||||
\(62\) | −4.04798 | −0.514095 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.0539916 | −0.00674895 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.33864 | 0.530049 | 0.265025 | − | 0.964242i | \(-0.414620\pi\) | ||||
0.265025 | + | 0.964242i | \(0.414620\pi\) | |||||||
\(68\) | −9.38735 | −1.13838 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.77748 | −0.331972 | ||||||||
\(71\) | 8.49484 | 1.00815 | 0.504076 | − | 0.863659i | \(-0.331833\pi\) | ||||
0.504076 | + | 0.863659i | \(0.331833\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.819388 | 0.0959021 | 0.0479511 | − | 0.998850i | \(-0.484731\pi\) | ||||
0.0479511 | + | 0.998850i | \(0.484731\pi\) | |||||||
\(74\) | 1.12643 | 0.130945 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.79714 | −0.664978 | ||||||||
\(77\) | −26.8449 | −3.05926 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.42187 | −0.947535 | −0.473767 | − | 0.880650i | \(-0.657106\pi\) | ||||
−0.473767 | + | 0.880650i | \(0.657106\pi\) | |||||||
\(80\) | 1.79714 | 0.200926 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.00916 | −0.553169 | ||||||||
\(83\) | 2.35423 | 0.258410 | 0.129205 | − | 0.991618i | \(-0.458757\pi\) | ||||
0.129205 | + | 0.991618i | \(0.458757\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.84106 | 0.633552 | ||||||||
\(86\) | 4.06631 | 0.438482 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −13.6968 | −1.46008 | ||||||||
\(89\) | 0.773413 | 0.0819816 | 0.0409908 | − | 0.999160i | \(-0.486949\pi\) | ||||
0.0409908 | + | 0.999160i | \(0.486949\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.63360 | 0.378829 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.02354 | −0.208712 | ||||||||
\(95\) | 3.60713 | 0.370084 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.32104 | 0.641804 | 0.320902 | − | 0.947112i | \(-0.396014\pi\) | ||||
0.320902 | + | 0.947112i | \(0.396014\pi\) | |||||||
\(98\) | 7.92022 | 0.800063 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.60713 | −0.160713 | ||||||||
\(101\) | 8.91695 | 0.887270 | 0.443635 | − | 0.896208i | \(-0.353689\pi\) | ||||
0.443635 | + | 0.896208i | \(0.353689\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.112968 | 0.0111311 | 0.00556556 | − | 0.999985i | \(-0.498228\pi\) | ||||
0.00556556 | + | 0.999985i | \(0.498228\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.31605 | −0.613469 | ||||||||
\(107\) | 7.75025 | 0.749245 | 0.374622 | − | 0.927177i | \(-0.377772\pi\) | ||||
0.374622 | + | 0.927177i | \(0.377772\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.4744 | 1.09905 | 0.549525 | − | 0.835477i | \(-0.314809\pi\) | ||||
0.549525 | + | 0.835477i | \(0.314809\pi\) | |||||||
\(110\) | 3.79714 | 0.362043 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.96361 | −0.752490 | ||||||||
\(113\) | −6.24739 | −0.587705 | −0.293852 | − | 0.955851i | \(-0.594937\pi\) | ||||
−0.293852 | + | 0.955851i | \(0.594937\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.26092 | −0.210832 | ||||||||
\(116\) | 12.9938 | 1.20644 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.96136 | 0.180558 | ||||||||
\(119\) | −25.8833 | −2.37272 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.7001 | 2.33637 | ||||||||
\(122\) | −1.54082 | −0.139499 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.3793 | 0.932087 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.2034 | 0.994143 | 0.497071 | − | 0.867710i | \(-0.334409\pi\) | ||||
0.497071 | + | 0.867710i | \(0.334409\pi\) | |||||||
\(128\) | −11.3304 | −1.00147 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.494893 | 0.0432390 | 0.0216195 | − | 0.999766i | \(-0.493118\pi\) | ||||
0.0216195 | + | 0.999766i | \(0.493118\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.9842 | −1.38600 | ||||||||
\(134\) | 2.71942 | 0.234922 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −13.2062 | −1.13242 | ||||||||
\(137\) | 23.1498 | 1.97782 | 0.988909 | − | 0.148521i | \(-0.0474512\pi\) | ||||
0.988909 | + | 0.148521i | \(0.0474512\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.9574 | −1.01421 | −0.507107 | − | 0.861883i | \(-0.669285\pi\) | ||||
−0.507107 | + | 0.861883i | \(0.669285\pi\) | |||||||
\(140\) | 7.12164 | 0.601888 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.32450 | 0.446822 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.08506 | −0.671427 | ||||||||
\(146\) | 0.513585 | 0.0425046 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.88824 | −0.237412 | ||||||||
\(149\) | −21.2179 | −1.73823 | −0.869117 | − | 0.494606i | \(-0.835312\pi\) | ||||
−0.869117 | + | 0.494606i | \(0.835312\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.4623 | −1.58382 | −0.791909 | − | 0.610639i | \(-0.790913\pi\) | ||||
−0.791909 | + | 0.610639i | \(0.790913\pi\) | |||||||
\(152\) | −8.15544 | −0.661493 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −16.8261 | −1.35589 | ||||||||
\(155\) | −6.45826 | −0.518740 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.6547 | 1.64842 | 0.824212 | − | 0.566282i | \(-0.191618\pi\) | ||||
0.824212 | + | 0.566282i | \(0.191618\pi\) | |||||||
\(158\) | −5.27876 | −0.419955 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.64827 | 0.446535 | ||||||||
\(161\) | 10.0187 | 0.789587 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.85980 | 0.380649 | 0.190324 | − | 0.981721i | \(-0.439046\pi\) | ||||
0.190324 | + | 0.981721i | \(0.439046\pi\) | |||||||
\(164\) | 12.8438 | 1.00293 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.47561 | 0.114530 | ||||||||
\(167\) | 2.57995 | 0.199642 | 0.0998212 | − | 0.995005i | \(-0.468173\pi\) | ||||
0.0998212 | + | 0.995005i | \(0.468173\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3.66112 | 0.280795 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.4263 | −0.794997 | ||||||||
\(173\) | 10.2468 | 0.779048 | 0.389524 | − | 0.921016i | \(-0.372640\pi\) | ||||
0.389524 | + | 0.921016i | \(0.372640\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.43127 | −0.334972 | ||||||||
\(176\) | 10.8872 | 0.820652 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.484769 | 0.0363349 | ||||||||
\(179\) | 10.6028 | 0.792492 | 0.396246 | − | 0.918144i | \(-0.370313\pi\) | ||||
0.396246 | + | 0.918144i | \(0.370313\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.8618 | 1.25333 | 0.626664 | − | 0.779289i | \(-0.284420\pi\) | ||||
0.626664 | + | 0.779289i | \(0.284420\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.11176 | 0.376844 | ||||||||
\(185\) | 1.79714 | 0.132128 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 35.3855 | 2.58764 | ||||||||
\(188\) | 5.18848 | 0.378409 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.26092 | 0.164024 | ||||||||
\(191\) | 10.9910 | 0.795279 | 0.397640 | − | 0.917542i | \(-0.369829\pi\) | ||||
0.397640 | + | 0.917542i | \(0.369829\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.65173 | 0.478802 | 0.239401 | − | 0.970921i | \(-0.423049\pi\) | ||||
0.239401 | + | 0.970921i | \(0.423049\pi\) | |||||||
\(194\) | 3.96197 | 0.284453 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −20.3079 | −1.45057 | ||||||||
\(197\) | 23.9860 | 1.70893 | 0.854466 | − | 0.519508i | \(-0.173885\pi\) | ||||
0.854466 | + | 0.519508i | \(0.173885\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.9103 | −1.48229 | −0.741147 | − | 0.671343i | \(-0.765718\pi\) | ||||
−0.741147 | + | 0.671343i | \(0.765718\pi\) | |||||||
\(200\) | −2.26092 | −0.159871 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.58907 | 0.393246 | ||||||||
\(203\) | 35.8270 | 2.51457 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.99175 | −0.558168 | ||||||||
\(206\) | 0.0708076 | 0.00493340 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.8522 | 1.51155 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.1308 | 0.903961 | 0.451981 | − | 0.892028i | \(-0.350718\pi\) | ||||
0.451981 | + | 0.892028i | \(0.350718\pi\) | |||||||
\(212\) | 16.1948 | 1.11226 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.85779 | 0.332072 | ||||||||
\(215\) | 6.48751 | 0.442444 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.6183 | 1.94274 | ||||||||
\(218\) | 7.19207 | 0.487108 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.73610 | −0.656408 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.2007 | 1.41970 | 0.709851 | − | 0.704351i | \(-0.248762\pi\) | ||||
0.709851 | + | 0.704351i | \(0.248762\pi\) | |||||||
\(224\) | −25.0290 | −1.67232 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.91581 | −0.260476 | ||||||||
\(227\) | 9.23944 | 0.613243 | 0.306622 | − | 0.951832i | \(-0.400801\pi\) | ||||
0.306622 | + | 0.951832i | \(0.400801\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.16502 | −0.209150 | −0.104575 | − | 0.994517i | \(-0.533348\pi\) | ||||
−0.104575 | + | 0.994517i | \(0.533348\pi\) | |||||||
\(230\) | −1.41713 | −0.0934425 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.2797 | 1.20012 | ||||||||
\(233\) | −2.83723 | −0.185873 | −0.0929364 | − | 0.995672i | \(-0.529625\pi\) | ||||
−0.0929364 | + | 0.995672i | \(0.529625\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.22841 | −0.210598 | ||||||||
\(236\) | −5.02905 | −0.327364 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −16.2234 | −1.05161 | ||||||||
\(239\) | 0.634366 | 0.0410337 | 0.0205169 | − | 0.999790i | \(-0.493469\pi\) | ||||
0.0205169 | + | 0.999790i | \(0.493469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.898466 | 0.0578753 | 0.0289376 | − | 0.999581i | \(-0.490788\pi\) | ||||
0.0289376 | + | 0.999581i | \(0.490788\pi\) | |||||||
\(242\) | 16.1086 | 1.03550 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.95076 | 0.252921 | ||||||||
\(245\) | 12.6361 | 0.807293 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 14.6016 | 0.927204 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.626791 | 0.0396418 | ||||||||
\(251\) | −14.4568 | −0.912503 | −0.456252 | − | 0.889851i | \(-0.650808\pi\) | ||||
−0.456252 | + | 0.889851i | \(0.650808\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.6968 | −0.861110 | ||||||||
\(254\) | 7.02221 | 0.440613 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.99380 | −0.437113 | ||||||||
\(257\) | 0.418504 | 0.0261056 | 0.0130528 | − | 0.999915i | \(-0.495845\pi\) | ||||
0.0130528 | + | 0.999915i | \(0.495845\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.96361 | −0.494835 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.310195 | 0.0191639 | ||||||||
\(263\) | −2.49052 | −0.153572 | −0.0767861 | − | 0.997048i | \(-0.524466\pi\) | ||||
−0.0767861 | + | 0.997048i | \(0.524466\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.0768 | −0.619013 | ||||||||
\(266\) | −10.0187 | −0.614288 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.97277 | −0.425930 | ||||||||
\(269\) | −1.76858 | −0.107832 | −0.0539160 | − | 0.998545i | \(-0.517170\pi\) | ||||
−0.0539160 | + | 0.998545i | \(0.517170\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.4035 | 1.23943 | 0.619714 | − | 0.784828i | \(-0.287249\pi\) | ||||
0.619714 | + | 0.784828i | \(0.287249\pi\) | |||||||
\(272\) | 10.4972 | 0.636486 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.5101 | 0.876586 | ||||||||
\(275\) | 6.05806 | 0.365315 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.84494 | −0.291104 | −0.145552 | − | 0.989351i | \(-0.546496\pi\) | ||||
−0.145552 | + | 0.989351i | \(0.546496\pi\) | |||||||
\(278\) | −7.49480 | −0.449508 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.0187 | 0.598734 | ||||||||
\(281\) | 5.20237 | 0.310347 | 0.155174 | − | 0.987887i | \(-0.450406\pi\) | ||||
0.155174 | + | 0.987887i | \(0.450406\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.0203 | 0.595647 | 0.297824 | − | 0.954621i | \(-0.403739\pi\) | ||||
0.297824 | + | 0.954621i | \(0.403739\pi\) | |||||||
\(284\) | −13.6523 | −0.810117 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35.4136 | 2.09040 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.1179 | 1.00694 | ||||||||
\(290\) | −5.06764 | −0.297582 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.31687 | −0.0770637 | ||||||||
\(293\) | 7.50698 | 0.438562 | 0.219281 | − | 0.975662i | \(-0.429629\pi\) | ||||
0.219281 | + | 0.975662i | \(0.429629\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.12921 | 0.182190 | ||||||||
\(296\) | −4.06319 | −0.236168 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.2992 | −0.770400 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.7479 | −1.65700 | ||||||||
\(302\) | −12.1988 | −0.701962 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.48252 | 0.371798 | ||||||||
\(305\) | −2.45826 | −0.140760 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.4404 | 0.652940 | 0.326470 | − | 0.945208i | \(-0.394141\pi\) | ||||
0.326470 | + | 0.945208i | \(0.394141\pi\) | |||||||
\(308\) | 43.1433 | 2.45832 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.04798 | −0.229910 | ||||||||
\(311\) | −24.2351 | −1.37424 | −0.687122 | − | 0.726542i | \(-0.741126\pi\) | ||||
−0.687122 | + | 0.726542i | \(0.741126\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.8796 | −1.06714 | −0.533570 | − | 0.845756i | \(-0.679150\pi\) | ||||
−0.533570 | + | 0.845756i | \(0.679150\pi\) | |||||||
\(314\) | 12.9462 | 0.730595 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.5351 | 0.761407 | ||||||||
\(317\) | 22.3459 | 1.25507 | 0.627534 | − | 0.778589i | \(-0.284064\pi\) | ||||
0.627534 | + | 0.778589i | \(0.284064\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −48.9797 | −2.74234 | ||||||||
\(320\) | −0.0539916 | −0.00301822 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.27966 | 0.349952 | ||||||||
\(323\) | 21.0695 | 1.17234 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.04608 | 0.168707 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 18.0687 | 0.997677 | ||||||||
\(329\) | 14.3059 | 0.788712 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.6887 | 1.24708 | 0.623541 | − | 0.781790i | \(-0.285693\pi\) | ||||
0.623541 | + | 0.781790i | \(0.285693\pi\) | |||||||
\(332\) | −3.78356 | −0.207650 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.61709 | 0.0884832 | ||||||||
\(335\) | 4.33864 | 0.237045 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.166960 | −0.00909489 | −0.00454745 | − | 0.999990i | \(-0.501448\pi\) | ||||
−0.00454745 | + | 0.999990i | \(0.501448\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.38735 | −0.509101 | ||||||||
\(341\) | −39.1245 | −2.11871 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −24.9752 | −1.34854 | ||||||||
\(344\) | −14.6677 | −0.790831 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.42259 | 0.345281 | ||||||||
\(347\) | −14.6343 | −0.785611 | −0.392806 | − | 0.919622i | \(-0.628495\pi\) | ||||
−0.392806 | + | 0.919622i | \(0.628495\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.22712 | −0.119215 | −0.0596074 | − | 0.998222i | \(-0.518985\pi\) | ||||
−0.0596074 | + | 0.998222i | \(0.518985\pi\) | |||||||
\(350\) | −2.77748 | −0.148463 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 34.2176 | 1.82380 | ||||||||
\(353\) | 5.93939 | 0.316122 | 0.158061 | − | 0.987429i | \(-0.449476\pi\) | ||||
0.158061 | + | 0.987429i | \(0.449476\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.49484 | 0.450859 | ||||||||
\(356\) | −1.24298 | −0.0658777 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.64576 | 0.351239 | ||||||||
\(359\) | 10.9234 | 0.576516 | 0.288258 | − | 0.957553i | \(-0.406924\pi\) | ||||
0.288258 | + | 0.957553i | \(0.406924\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.98860 | −0.315189 | ||||||||
\(362\) | 10.5688 | 0.555486 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.819388 | 0.0428887 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.64448 | 0.451238 | 0.225619 | − | 0.974216i | \(-0.427560\pi\) | ||||
0.225619 | + | 0.974216i | \(0.427560\pi\) | |||||||
\(368\) | −4.06319 | −0.211808 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.12643 | 0.0585604 | ||||||||
\(371\) | 44.6530 | 2.31827 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.3052 | 0.947808 | 0.473904 | − | 0.880577i | \(-0.342844\pi\) | ||||
0.473904 | + | 0.880577i | \(0.342844\pi\) | |||||||
\(374\) | 22.1793 | 1.14686 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.29917 | 0.376426 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.0062 | 1.54131 | 0.770657 | − | 0.637250i | \(-0.219928\pi\) | ||||
0.770657 | + | 0.637250i | \(0.219928\pi\) | |||||||
\(380\) | −5.79714 | −0.297387 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.88905 | 0.352474 | ||||||||
\(383\) | 14.5360 | 0.742754 | 0.371377 | − | 0.928482i | \(-0.378886\pi\) | ||||
0.371377 | + | 0.928482i | \(0.378886\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.8449 | −1.36814 | ||||||||
\(386\) | 4.16925 | 0.212209 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.1587 | −0.515732 | ||||||||
\(389\) | −24.5259 | −1.24351 | −0.621756 | − | 0.783211i | \(-0.713581\pi\) | ||||
−0.621756 | + | 0.783211i | \(0.713581\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.2062 | −0.667864 | ||||||||
\(392\) | −28.5693 | −1.44297 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.0342 | 0.757413 | ||||||||
\(395\) | −8.42187 | −0.423750 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.44090 | 0.473825 | 0.236913 | − | 0.971531i | \(-0.423864\pi\) | ||||
0.236913 | + | 0.971531i | \(0.423864\pi\) | |||||||
\(398\) | −13.1064 | −0.656965 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.79714 | 0.0898570 | ||||||||
\(401\) | 0.488375 | 0.0243883 | 0.0121941 | − | 0.999926i | \(-0.496118\pi\) | ||||
0.0121941 | + | 0.999926i | \(0.496118\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.3307 | −0.712980 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.4561 | 1.11448 | ||||||||
\(407\) | 10.8872 | 0.539658 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.7203 | −1.02455 | −0.512277 | − | 0.858820i | \(-0.671198\pi\) | ||||
−0.512277 | + | 0.858820i | \(0.671198\pi\) | |||||||
\(410\) | −5.00916 | −0.247385 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.181555 | −0.00894458 | ||||||||
\(413\) | −13.8664 | −0.682319 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.35423 | 0.115565 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13.6968 | 0.669932 | ||||||||
\(419\) | −4.54748 | −0.222159 | −0.111079 | − | 0.993812i | \(-0.535431\pi\) | ||||
−0.111079 | + | 0.993812i | \(0.535431\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.0991 | −1.51568 | −0.757840 | − | 0.652441i | \(-0.773745\pi\) | ||||
−0.757840 | + | 0.652441i | \(0.773745\pi\) | |||||||
\(422\) | 8.23027 | 0.400643 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 22.7828 | 1.10643 | ||||||||
\(425\) | 5.84106 | 0.283333 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.8932 | 0.527160 | ||||||||
\(428\) | −12.4557 | −0.602068 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.06631 | 0.196095 | ||||||||
\(431\) | 34.2162 | 1.64813 | 0.824067 | − | 0.566492i | \(-0.191700\pi\) | ||||
0.824067 | + | 0.566492i | \(0.191700\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.56326 | −0.267353 | −0.133676 | − | 0.991025i | \(-0.542678\pi\) | ||||
−0.133676 | + | 0.991025i | \(0.542678\pi\) | |||||||
\(434\) | 17.9377 | 0.861037 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.4409 | −0.883159 | ||||||||
\(437\) | −8.15544 | −0.390127 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.81949 | −0.134567 | −0.0672834 | − | 0.997734i | \(-0.521433\pi\) | ||||
−0.0672834 | + | 0.997734i | \(0.521433\pi\) | |||||||
\(440\) | −13.6968 | −0.652969 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.0635 | 0.715686 | 0.357843 | − | 0.933782i | \(-0.383512\pi\) | ||||
0.357843 | + | 0.933782i | \(0.383512\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.773413 | 0.0366633 | ||||||||
\(446\) | 13.2884 | 0.629224 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.239251 | 0.0113036 | ||||||||
\(449\) | 3.84456 | 0.181436 | 0.0907181 | − | 0.995877i | \(-0.471084\pi\) | ||||
0.0907181 | + | 0.995877i | \(0.471084\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −48.4145 | −2.27975 | ||||||||
\(452\) | 10.0404 | 0.472260 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.79120 | 0.271795 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.4280 | −1.42336 | −0.711682 | − | 0.702502i | \(-0.752066\pi\) | ||||
−0.711682 | + | 0.702502i | \(0.752066\pi\) | |||||||
\(458\) | −1.98381 | −0.0926973 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.63360 | 0.169417 | ||||||||
\(461\) | 30.7921 | 1.43413 | 0.717066 | − | 0.697006i | \(-0.245485\pi\) | ||||
0.717066 | + | 0.697006i | \(0.245485\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.9034 | 0.599674 | 0.299837 | − | 0.953991i | \(-0.403068\pi\) | ||||
0.299837 | + | 0.953991i | \(0.403068\pi\) | |||||||
\(464\) | −14.5300 | −0.674537 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.77835 | −0.0823804 | ||||||||
\(467\) | −10.2346 | −0.473601 | −0.236800 | − | 0.971558i | \(-0.576099\pi\) | ||||
−0.236800 | + | 0.971558i | \(0.576099\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.2257 | −0.887759 | ||||||||
\(470\) | −2.02354 | −0.0933389 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.07489 | −0.325648 | ||||||||
\(473\) | 39.3017 | 1.80709 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.60713 | 0.165507 | ||||||||
\(476\) | 41.5979 | 1.90664 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.397615 | 0.0181865 | ||||||||
\(479\) | 35.0043 | 1.59939 | 0.799693 | − | 0.600408i | \(-0.204995\pi\) | ||||
0.799693 | + | 0.600408i | \(0.204995\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.563151 | 0.0256508 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −41.3034 | −1.87743 | ||||||||
\(485\) | 6.32104 | 0.287024 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.53185 | 0.0694147 | 0.0347074 | − | 0.999398i | \(-0.488950\pi\) | ||||
0.0347074 | + | 0.999398i | \(0.488950\pi\) | |||||||
\(488\) | 5.55794 | 0.251596 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.92022 | 0.357799 | ||||||||
\(491\) | 25.0248 | 1.12935 | 0.564676 | − | 0.825313i | \(-0.309001\pi\) | ||||
0.564676 | + | 0.825313i | \(0.309001\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −47.2253 | −2.12692 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.6064 | −0.521143 | ||||||||
\(497\) | −37.6429 | −1.68852 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.7838 | −1.24377 | −0.621887 | − | 0.783107i | \(-0.713634\pi\) | ||||
−0.621887 | + | 0.783107i | \(0.713634\pi\) | |||||||
\(500\) | −1.60713 | −0.0718732 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.06138 | −0.404429 | ||||||||
\(503\) | −43.0139 | −1.91789 | −0.958947 | − | 0.283587i | \(-0.908476\pi\) | ||||
−0.958947 | + | 0.283587i | \(0.908476\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.91695 | 0.396799 | ||||||||
\(506\) | −8.58503 | −0.381651 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.0054 | −0.798860 | ||||||||
\(509\) | 1.13704 | 0.0503983 | 0.0251992 | − | 0.999682i | \(-0.491978\pi\) | ||||
0.0251992 | + | 0.999682i | \(0.491978\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.63093 | −0.160623 | ||||||||
\(512\) | 18.2771 | 0.807742 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.262315 | 0.0115702 | ||||||||
\(515\) | 0.112968 | 0.00497798 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.5579 | −0.860155 | ||||||||
\(518\) | −4.99152 | −0.219315 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.7311 | −1.34635 | −0.673177 | − | 0.739481i | \(-0.735071\pi\) | ||||
−0.673177 | + | 0.739481i | \(0.735071\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.2654 | −0.754962 | −0.377481 | − | 0.926017i | \(-0.623210\pi\) | ||||
−0.377481 | + | 0.926017i | \(0.623210\pi\) | |||||||
\(524\) | −0.795358 | −0.0347454 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.56104 | −0.0680645 | ||||||||
\(527\) | −37.7231 | −1.64324 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.8882 | −0.777750 | ||||||||
\(530\) | −6.31605 | −0.274352 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 25.6887 | 1.11375 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.75025 | 0.335072 | ||||||||
\(536\) | −9.80931 | −0.423698 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.10853 | −0.0477921 | ||||||||
\(539\) | 76.5505 | 3.29726 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.8625 | 0.767970 | 0.383985 | − | 0.923339i | \(-0.374551\pi\) | ||||
0.383985 | + | 0.923339i | \(0.374551\pi\) | |||||||
\(542\) | 12.7888 | 0.549325 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 32.9919 | 1.41451 | ||||||||
\(545\) | 11.4744 | 0.491510 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.97952 | −0.212909 | −0.106455 | − | 0.994318i | \(-0.533950\pi\) | ||||
−0.106455 | + | 0.994318i | \(0.533950\pi\) | |||||||
\(548\) | −37.2048 | −1.58931 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.79714 | 0.161911 | ||||||||
\(551\) | −29.1639 | −1.24242 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 37.3196 | 1.58699 | ||||||||
\(554\) | −3.03676 | −0.129020 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.2171 | 0.814989 | ||||||||
\(557\) | −36.9312 | −1.56482 | −0.782412 | − | 0.622761i | \(-0.786011\pi\) | ||||
−0.782412 | + | 0.622761i | \(0.786011\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −7.96361 | −0.336524 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.26080 | 0.137549 | ||||||||
\(563\) | 9.36568 | 0.394716 | 0.197358 | − | 0.980331i | \(-0.436764\pi\) | ||||
0.197358 | + | 0.980331i | \(0.436764\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.24739 | −0.262830 | ||||||||
\(566\) | 6.28066 | 0.263996 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19.2062 | −0.805873 | ||||||||
\(569\) | 0.436833 | 0.0183130 | 0.00915650 | − | 0.999958i | \(-0.497085\pi\) | ||||
0.00915650 | + | 0.999958i | \(0.497085\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.69561 | −0.196505 | −0.0982525 | − | 0.995162i | \(-0.531325\pi\) | ||||
−0.0982525 | + | 0.995162i | \(0.531325\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 22.1969 | 0.926482 | ||||||||
\(575\) | −2.26092 | −0.0942869 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.2121 | 1.25775 | 0.628873 | − | 0.777508i | \(-0.283517\pi\) | ||||
0.628873 | + | 0.777508i | \(0.283517\pi\) | |||||||
\(578\) | 10.7294 | 0.446283 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.9938 | 0.539536 | ||||||||
\(581\) | −10.4322 | −0.432801 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −61.0459 | −2.52826 | ||||||||
\(584\) | −1.85257 | −0.0766599 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.70531 | 0.194375 | ||||||||
\(587\) | −43.7538 | −1.80591 | −0.902956 | − | 0.429733i | \(-0.858608\pi\) | ||||
−0.902956 | + | 0.429733i | \(0.858608\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.2958 | −0.959887 | ||||||||
\(590\) | 1.96136 | 0.0807480 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.22971 | 0.132740 | ||||||||
\(593\) | −5.94151 | −0.243989 | −0.121994 | − | 0.992531i | \(-0.538929\pi\) | ||||
−0.121994 | + | 0.992531i | \(0.538929\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.8833 | −1.06111 | ||||||||
\(596\) | 34.0999 | 1.39679 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.0505 | 1.51384 | 0.756922 | − | 0.653506i | \(-0.226702\pi\) | ||||
0.756922 | + | 0.653506i | \(0.226702\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.2822 | −1.52077 | −0.760387 | − | 0.649470i | \(-0.774991\pi\) | ||||
−0.760387 | + | 0.649470i | \(0.774991\pi\) | |||||||
\(602\) | −18.0189 | −0.734397 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 31.2785 | 1.27270 | ||||||||
\(605\) | 25.7001 | 1.04486 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.4929 | 0.994135 | 0.497068 | − | 0.867712i | \(-0.334410\pi\) | ||||
0.497068 | + | 0.867712i | \(0.334410\pi\) | |||||||
\(608\) | 20.3741 | 0.826277 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.54082 | −0.0623859 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.47202 | −0.382571 | −0.191286 | − | 0.981534i | \(-0.561266\pi\) | ||||
−0.191286 | + | 0.981534i | \(0.561266\pi\) | |||||||
\(614\) | 7.17076 | 0.289388 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 60.6941 | 2.44544 | ||||||||
\(617\) | 1.19807 | 0.0482326 | 0.0241163 | − | 0.999709i | \(-0.492323\pi\) | ||||
0.0241163 | + | 0.999709i | \(0.492323\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.2559 | 0.773959 | 0.386979 | − | 0.922088i | \(-0.373518\pi\) | ||||
0.386979 | + | 0.922088i | \(0.373518\pi\) | |||||||
\(620\) | 10.3793 | 0.416842 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.1903 | −0.609077 | ||||||||
\(623\) | −3.42720 | −0.137308 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −11.8336 | −0.472966 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −33.1948 | −1.32462 | ||||||||
\(629\) | 10.4972 | 0.418551 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.25990 | −0.249203 | −0.124601 | − | 0.992207i | \(-0.539765\pi\) | ||||
−0.124601 | + | 0.992207i | \(0.539765\pi\) | |||||||
\(632\) | 19.0412 | 0.757417 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.0062 | 0.556257 | ||||||||
\(635\) | 11.2034 | 0.444594 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −30.7001 | −1.21543 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.3304 | −0.447873 | ||||||||
\(641\) | −8.84417 | −0.349324 | −0.174662 | − | 0.984628i | \(-0.555883\pi\) | ||||
−0.174662 | + | 0.984628i | \(0.555883\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.1012 | 1.26595 | 0.632973 | − | 0.774174i | \(-0.281834\pi\) | ||||
0.632973 | + | 0.774174i | \(0.281834\pi\) | |||||||
\(644\) | −16.1014 | −0.634486 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.2062 | 0.519589 | ||||||||
\(647\) | 14.7567 | 0.580145 | 0.290072 | − | 0.957005i | \(-0.406321\pi\) | ||||
0.290072 | + | 0.957005i | \(0.406321\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.9569 | 0.744125 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.81034 | −0.305877 | ||||||||
\(653\) | −26.6491 | −1.04286 | −0.521430 | − | 0.853294i | \(-0.674601\pi\) | ||||
−0.521430 | + | 0.853294i | \(0.674601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.494893 | 0.0193371 | ||||||||
\(656\) | −14.3623 | −0.560753 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.96684 | 0.349564 | ||||||||
\(659\) | −2.44953 | −0.0954202 | −0.0477101 | − | 0.998861i | \(-0.515192\pi\) | ||||
−0.0477101 | + | 0.998861i | \(0.515192\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.4711 | −0.640652 | −0.320326 | − | 0.947307i | \(-0.603792\pi\) | ||||
−0.320326 | + | 0.947307i | \(0.603792\pi\) | |||||||
\(662\) | 14.2211 | 0.552718 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.32272 | −0.206562 | ||||||||
\(665\) | −15.9842 | −0.619840 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.2797 | 0.707791 | ||||||||
\(668\) | −4.14632 | −0.160426 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.71942 | 0.105060 | ||||||||
\(671\) | −14.8923 | −0.574911 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.38749 | −0.0534838 | −0.0267419 | − | 0.999642i | \(-0.508513\pi\) | ||||
−0.0267419 | + | 0.999642i | \(0.508513\pi\) | |||||||
\(674\) | −0.104649 | −0.00403093 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.0636 | −0.886407 | −0.443203 | − | 0.896421i | \(-0.646158\pi\) | ||||
−0.443203 | + | 0.896421i | \(0.646158\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.0102 | −1.07493 | ||||||||
\(680\) | −13.2062 | −0.506433 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −24.5229 | −0.939032 | ||||||||
\(683\) | 21.0160 | 0.804155 | 0.402078 | − | 0.915606i | \(-0.368288\pi\) | ||||
0.402078 | + | 0.915606i | \(0.368288\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.1498 | 0.884507 | ||||||||
\(686\) | −15.6543 | −0.597683 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.6590 | 0.444494 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.0578 | 0.915200 | 0.457600 | − | 0.889158i | \(-0.348709\pi\) | ||||
0.457600 | + | 0.889158i | \(0.348709\pi\) | |||||||
\(692\) | −16.4679 | −0.626017 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.17266 | −0.348190 | ||||||||
\(695\) | −11.9574 | −0.453571 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −46.6802 | −1.76814 | ||||||||
\(698\) | −1.39594 | −0.0528370 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.12164 | 0.269173 | ||||||||
\(701\) | −20.0188 | −0.756099 | −0.378050 | − | 0.925785i | \(-0.623405\pi\) | ||||
−0.378050 | + | 0.925785i | \(0.623405\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.48252 | 0.244493 | ||||||||
\(704\) | −0.327085 | −0.0123275 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.72276 | 0.140108 | ||||||||
\(707\) | −39.5134 | −1.48605 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0592 | −0.640672 | −0.320336 | − | 0.947304i | \(-0.603796\pi\) | ||||
−0.320336 | + | 0.947304i | \(0.603796\pi\) | |||||||
\(710\) | 5.32450 | 0.199825 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.74862 | −0.0655325 | ||||||||
\(713\) | 14.6016 | 0.546835 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.0401 | −0.636820 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.84671 | 0.255517 | ||||||||
\(719\) | 42.1119 | 1.57051 | 0.785254 | − | 0.619174i | \(-0.212532\pi\) | ||||
0.785254 | + | 0.619174i | \(0.212532\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.500593 | −0.0186431 | ||||||||
\(722\) | −3.75360 | −0.139695 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −27.0992 | −1.00713 | ||||||||
\(725\) | −8.08506 | −0.300271 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.62167 | 0.134320 | 0.0671601 | − | 0.997742i | \(-0.478606\pi\) | ||||
0.0671601 | + | 0.997742i | \(0.478606\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.513585 | 0.0190086 | ||||||||
\(731\) | 37.8939 | 1.40156 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.2438 | 0.378362 | 0.189181 | − | 0.981942i | \(-0.439417\pi\) | ||||
0.189181 | + | 0.981942i | \(0.439417\pi\) | |||||||
\(734\) | 5.41829 | 0.199993 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.7703 | −0.470719 | ||||||||
\(737\) | 26.2837 | 0.968174 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.26945 | −0.340982 | −0.170491 | − | 0.985359i | \(-0.554535\pi\) | ||||
−0.170491 | + | 0.985359i | \(0.554535\pi\) | |||||||
\(740\) | −2.88824 | −0.106174 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 27.9881 | 1.02748 | ||||||||
\(743\) | 44.7671 | 1.64234 | 0.821172 | − | 0.570680i | \(-0.193320\pi\) | ||||
0.821172 | + | 0.570680i | \(0.193320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.2179 | −0.777362 | ||||||||
\(746\) | 11.4735 | 0.420076 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −56.8691 | −2.07934 | ||||||||
\(749\) | −34.3434 | −1.25488 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.3403 | 0.559776 | 0.279888 | − | 0.960033i | \(-0.409703\pi\) | ||||
0.279888 | + | 0.960033i | \(0.409703\pi\) | |||||||
\(752\) | −5.80190 | −0.211574 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.4623 | −0.708305 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.00296 | 0.218181 | 0.109091 | − | 0.994032i | \(-0.465206\pi\) | ||||
0.109091 | + | 0.994032i | \(0.465206\pi\) | |||||||
\(758\) | 18.8076 | 0.683123 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.15544 | −0.295829 | ||||||||
\(761\) | −20.9651 | −0.759984 | −0.379992 | − | 0.924990i | \(-0.624073\pi\) | ||||
−0.379992 | + | 0.924990i | \(0.624073\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −50.8462 | −1.84076 | ||||||||
\(764\) | −17.6640 | −0.639060 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.11103 | 0.329195 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.8152 | 1.58002 | 0.790008 | − | 0.613096i | \(-0.210076\pi\) | ||||
0.790008 | + | 0.613096i | \(0.210076\pi\) | |||||||
\(770\) | −16.8261 | −0.606372 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.6902 | −0.384749 | ||||||||
\(773\) | −3.37220 | −0.121290 | −0.0606449 | − | 0.998159i | \(-0.519316\pi\) | ||||
−0.0606449 | + | 0.998159i | \(0.519316\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.45826 | −0.231988 | ||||||||
\(776\) | −14.2914 | −0.513030 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.3726 | −0.551135 | ||||||||
\(779\) | −28.8273 | −1.03284 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 51.4623 | 1.84146 | ||||||||
\(782\) | −8.27751 | −0.296003 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 22.7089 | 0.811032 | ||||||||
\(785\) | 20.6547 | 0.737198 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.7844 | 1.27558 | 0.637789 | − | 0.770211i | \(-0.279849\pi\) | ||||
0.637789 | + | 0.770211i | \(0.279849\pi\) | |||||||
\(788\) | −38.5487 | −1.37324 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.27876 | −0.187810 | ||||||||
\(791\) | 27.6838 | 0.984324 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 5.91748 | 0.210003 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 33.6057 | 1.19112 | ||||||||
\(797\) | 28.3251 | 1.00333 | 0.501663 | − | 0.865063i | \(-0.332722\pi\) | ||||
0.501663 | + | 0.865063i | \(0.332722\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.8573 | −0.667124 | ||||||||
\(800\) | 5.64827 | 0.199697 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.306109 | 0.0108091 | ||||||||
\(803\) | 4.96390 | 0.175172 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.0187 | 0.353114 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20.1605 | −0.709245 | ||||||||
\(809\) | 29.1396 | 1.02450 | 0.512248 | − | 0.858838i | \(-0.328813\pi\) | ||||
0.512248 | + | 0.858838i | \(0.328813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.3733 | 0.574946 | 0.287473 | − | 0.957789i | \(-0.407185\pi\) | ||||
0.287473 | + | 0.957789i | \(0.407185\pi\) | |||||||
\(812\) | −57.5788 | −2.02062 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.82399 | 0.239181 | ||||||||
\(815\) | 4.85980 | 0.170231 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.4013 | 0.818708 | ||||||||
\(818\) | −12.9873 | −0.454091 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.8438 | 0.448525 | ||||||||
\(821\) | 35.1612 | 1.22713 | 0.613566 | − | 0.789643i | \(-0.289734\pi\) | ||||
0.613566 | + | 0.789643i | \(0.289734\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.6847 | 0.686164 | 0.343082 | − | 0.939305i | \(-0.388529\pi\) | ||||
0.343082 | + | 0.939305i | \(0.388529\pi\) | |||||||
\(824\) | −0.255413 | −0.00889772 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.69132 | −0.302410 | ||||||||
\(827\) | 11.6881 | 0.406436 | 0.203218 | − | 0.979134i | \(-0.434860\pi\) | ||||
0.203218 | + | 0.979134i | \(0.434860\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.5203 | −1.58099 | −0.790493 | − | 0.612472i | \(-0.790175\pi\) | ||||
−0.790493 | + | 0.612472i | \(0.790175\pi\) | |||||||
\(830\) | 1.47561 | 0.0512192 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 73.8084 | 2.55731 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.57995 | 0.0892828 | ||||||||
\(836\) | −35.1194 | −1.21463 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.85032 | −0.0984626 | ||||||||
\(839\) | 29.0477 | 1.00284 | 0.501420 | − | 0.865204i | \(-0.332811\pi\) | ||||
0.501420 | + | 0.865204i | \(0.332811\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.3681 | 1.25407 | ||||||||
\(842\) | −19.4927 | −0.671762 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21.1029 | −0.726393 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −113.884 | −3.91310 | ||||||||
\(848\) | −18.1094 | −0.621880 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.66112 | 0.125576 | ||||||||
\(851\) | −4.06319 | −0.139284 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.3320 | 1.65486 | 0.827429 | − | 0.561571i | \(-0.189803\pi\) | ||||
0.827429 | + | 0.561571i | \(0.189803\pi\) | |||||||
\(854\) | 6.82778 | 0.233642 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.5227 | −0.598913 | ||||||||
\(857\) | 41.2151 | 1.40788 | 0.703940 | − | 0.710260i | \(-0.251422\pi\) | ||||
0.703940 | + | 0.710260i | \(0.251422\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.5448 | −1.79280 | −0.896402 | − | 0.443242i | \(-0.853828\pi\) | ||||
−0.896402 | + | 0.443242i | \(0.853828\pi\) | |||||||
\(860\) | −10.4263 | −0.355533 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.4464 | 0.730467 | ||||||||
\(863\) | −22.9888 | −0.782549 | −0.391275 | − | 0.920274i | \(-0.627966\pi\) | ||||
−0.391275 | + | 0.920274i | \(0.627966\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.2468 | 0.348401 | ||||||||
\(866\) | −3.48700 | −0.118493 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −45.9934 | −1.56112 | ||||||||
\(869\) | −51.0202 | −1.73074 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −25.9427 | −0.878532 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.11176 | −0.172908 | ||||||||
\(875\) | −4.43127 | −0.149804 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.2984 | 1.76599 | 0.882995 | − | 0.469381i | \(-0.155523\pi\) | ||||
0.882995 | + | 0.469381i | \(0.155523\pi\) | |||||||
\(878\) | −1.76723 | −0.0596412 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.8872 | 0.367007 | ||||||||
\(881\) | 33.6966 | 1.13527 | 0.567634 | − | 0.823281i | \(-0.307859\pi\) | ||||
0.567634 | + | 0.823281i | \(0.307859\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.4392 | −0.687835 | −0.343917 | − | 0.939000i | \(-0.611754\pi\) | ||||
−0.343917 | + | 0.939000i | \(0.611754\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.44165 | 0.317198 | ||||||||
\(887\) | 20.2005 | 0.678268 | 0.339134 | − | 0.940738i | \(-0.389866\pi\) | ||||
0.339134 | + | 0.940738i | \(0.389866\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −49.6454 | −1.66505 | ||||||||
\(890\) | 0.484769 | 0.0162495 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −34.0723 | −1.14083 | ||||||||
\(893\) | −11.6453 | −0.389695 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.6028 | 0.354413 | ||||||||
\(896\) | 50.2080 | 1.67733 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.40974 | 0.0804140 | ||||||||
\(899\) | 52.2154 | 1.74148 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −58.8592 | −1.96088 | ||||||||
\(902\) | −30.3458 | −1.01040 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.1248 | 0.469785 | ||||||||
\(905\) | 16.8618 | 0.560505 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.8029 | −1.38804 | −0.694022 | − | 0.719954i | \(-0.744163\pi\) | ||||
−0.694022 | + | 0.719954i | \(0.744163\pi\) | |||||||
\(908\) | −14.8490 | −0.492782 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.42332 | 0.113420 | 0.0567098 | − | 0.998391i | \(-0.481939\pi\) | ||||
0.0567098 | + | 0.998391i | \(0.481939\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.2621 | 0.472005 | ||||||||
\(914\) | −19.0720 | −0.630847 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.08661 | 0.168066 | ||||||||
\(917\) | −2.19300 | −0.0724193 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.05207 | 0.232626 | 0.116313 | − | 0.993213i | \(-0.462892\pi\) | ||||
0.116313 | + | 0.993213i | \(0.462892\pi\) | |||||||
\(920\) | 5.11176 | 0.168530 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 19.3002 | 0.635619 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.79714 | 0.0590896 | ||||||||
\(926\) | 8.08776 | 0.265780 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −45.6666 | −1.49908 | ||||||||
\(929\) | −10.0420 | −0.329467 | −0.164733 | − | 0.986338i | \(-0.552676\pi\) | ||||
−0.164733 | + | 0.986338i | \(0.552676\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.5802 | 1.49383 | ||||||||
\(932\) | 4.55980 | 0.149361 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.41496 | −0.209904 | ||||||||
\(935\) | 35.3855 | 1.15723 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.84613 | 0.190985 | 0.0954924 | − | 0.995430i | \(-0.469557\pi\) | ||||
0.0954924 | + | 0.995430i | \(0.469557\pi\) | |||||||
\(938\) | −12.0505 | −0.393462 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.18848 | 0.169230 | ||||||||
\(941\) | −46.1640 | −1.50490 | −0.752452 | − | 0.658647i | \(-0.771129\pi\) | ||||
−0.752452 | + | 0.658647i | \(0.771129\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.0687 | 0.588398 | ||||||||
\(944\) | 5.62363 | 0.183033 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.6340 | 0.800919 | ||||||||
\(947\) | −14.4830 | −0.470635 | −0.235318 | − | 0.971919i | \(-0.575613\pi\) | ||||
−0.235318 | + | 0.971919i | \(0.575613\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.26092 | 0.0733539 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 58.5200 | 1.89665 | ||||||||
\(953\) | 38.4423 | 1.24527 | 0.622635 | − | 0.782513i | \(-0.286062\pi\) | ||||
0.622635 | + | 0.782513i | \(0.286062\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.9910 | 0.355660 | ||||||||
\(956\) | −1.01951 | −0.0329733 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.9404 | 0.708862 | ||||||||
\(959\) | −102.583 | −3.31257 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.7092 | 0.345457 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.44395 | −0.0465066 | ||||||||
\(965\) | 6.65173 | 0.214127 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.2627 | −1.42339 | −0.711696 | − | 0.702487i | \(-0.752073\pi\) | ||||
−0.711696 | + | 0.702487i | \(0.752073\pi\) | |||||||
\(968\) | −58.1058 | −1.86759 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.96197 | 0.127211 | ||||||||
\(971\) | 44.4059 | 1.42505 | 0.712527 | − | 0.701644i | \(-0.247550\pi\) | ||||
0.712527 | + | 0.701644i | \(0.247550\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 52.9865 | 1.69867 | ||||||||
\(974\) | 0.960150 | 0.0307652 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.41784 | −0.141412 | ||||||||
\(977\) | −3.38438 | −0.108276 | −0.0541379 | − | 0.998533i | \(-0.517241\pi\) | ||||
−0.0541379 | + | 0.998533i | \(0.517241\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.68538 | 0.149745 | ||||||||
\(980\) | −20.3079 | −0.648714 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.6853 | 0.500538 | ||||||||
\(983\) | 39.6424 | 1.26440 | 0.632198 | − | 0.774807i | \(-0.282153\pi\) | ||||
0.632198 | + | 0.774807i | \(0.282153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.9860 | 0.764257 | ||||||||
\(986\) | −29.6004 | −0.942669 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.6677 | −0.466407 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.3443 | −1.44041 | −0.720205 | − | 0.693761i | \(-0.755952\pi\) | ||||
−0.720205 | + | 0.693761i | \(0.755952\pi\) | |||||||
\(992\) | −36.4780 | −1.15818 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −23.5943 | −0.748365 | ||||||||
\(995\) | −20.9103 | −0.662902 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.9968 | 1.71010 | 0.855048 | − | 0.518549i | \(-0.173528\pi\) | ||||
0.855048 | + | 0.518549i | \(0.173528\pi\) | |||||||
\(998\) | −17.4147 | −0.551251 | ||||||||
\(999\) | 0 | 0 |
(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 | 7605.2.a.cn.1.3 | 5 | ||
3.2 | odd | 2 | 7605.2.a.cl.1.3 | 5 | |||
13.4 | even | 6 | 585.2.j.i.406.3 | yes | 10 | ||
13.10 | even | 6 | 585.2.j.i.451.3 | yes | 10 | ||
13.12 | even | 2 | 7605.2.a.cm.1.3 | 5 | |||
39.17 | odd | 6 | 585.2.j.h.406.3 | ✓ | 10 | ||
39.23 | odd | 6 | 585.2.j.h.451.3 | yes | 10 | ||
39.38 | odd | 2 | 7605.2.a.co.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.j.h.406.3 | ✓ | 10 | 39.17 | odd | 6 | ||
585.2.j.h.451.3 | yes | 10 | 39.23 | odd | 6 | ||
585.2.j.i.406.3 | yes | 10 | 13.4 | even | 6 | ||
585.2.j.i.451.3 | yes | 10 | 13.10 | even | 6 | ||
7605.2.a.cl.1.3 | 5 | 3.2 | odd | 2 | |||
7605.2.a.cm.1.3 | 5 | 13.12 | even | 2 | |||
7605.2.a.cn.1.3 | 5 | 1.1 | even | 1 | trivial | ||
7605.2.a.co.1.3 | 5 | 39.38 | odd | 2 |