Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.13366265625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 12x^{6} + 10x^{5} + 41x^{4} - 20x^{3} - 48x^{2} + 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1875) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.31354\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.31354 | −0.928815 | −0.464408 | − | 0.885622i | \(-0.653733\pi\) | ||||
−0.464408 | + | 0.885622i | \(0.653733\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.274605 | −0.137303 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.19091 | 1.58401 | 0.792007 | − | 0.610512i | \(-0.209036\pi\) | ||||
0.792007 | + | 0.610512i | \(0.209036\pi\) | |||||||
\(8\) | 2.98779 | 1.05634 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.167760 | 0.0505816 | 0.0252908 | − | 0.999680i | \(-0.491949\pi\) | ||||
0.0252908 | + | 0.999680i | \(0.491949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.39519 | −0.941658 | −0.470829 | − | 0.882225i | \(-0.656045\pi\) | ||||
−0.470829 | + | 0.882225i | \(0.656045\pi\) | |||||||
\(14\) | −5.50493 | −1.47126 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.37538 | −0.843845 | ||||||||
\(17\) | −4.57476 | −1.10954 | −0.554771 | − | 0.832003i | \(-0.687194\pi\) | ||||
−0.554771 | + | 0.832003i | \(0.687194\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.78258 | 0.867784 | 0.433892 | − | 0.900965i | \(-0.357140\pi\) | ||||
0.433892 | + | 0.900965i | \(0.357140\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.220360 | −0.0469810 | ||||||||
\(23\) | −8.31374 | −1.73353 | −0.866767 | − | 0.498713i | \(-0.833806\pi\) | ||||
−0.866767 | + | 0.498713i | \(0.833806\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.45973 | 0.874626 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.15084 | −0.217489 | ||||||||
\(29\) | −2.74553 | −0.509833 | −0.254916 | − | 0.966963i | \(-0.582048\pi\) | ||||
−0.254916 | + | 0.966963i | \(0.582048\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.71771 | −1.38614 | −0.693070 | − | 0.720870i | \(-0.743742\pi\) | ||||
−0.693070 | + | 0.720870i | \(0.743742\pi\) | |||||||
\(32\) | −1.54187 | −0.272567 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00914 | 1.03056 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.07700 | 0.341457 | 0.170728 | − | 0.985318i | \(-0.445388\pi\) | ||||
0.170728 | + | 0.985318i | \(0.445388\pi\) | |||||||
\(38\) | −4.96858 | −0.806011 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.28043 | 0.199969 | 0.0999845 | − | 0.994989i | \(-0.468121\pi\) | ||||
0.0999845 | + | 0.994989i | \(0.468121\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.6226 | 1.77243 | 0.886217 | − | 0.463270i | \(-0.153324\pi\) | ||||
0.886217 | + | 0.463270i | \(0.153324\pi\) | |||||||
\(44\) | −0.0460679 | −0.00694499 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.9204 | 1.61013 | ||||||||
\(47\) | 9.99490 | 1.45791 | 0.728953 | − | 0.684564i | \(-0.240007\pi\) | ||||
0.728953 | + | 0.684564i | \(0.240007\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.5637 | 1.50910 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.932338 | 0.129292 | ||||||||
\(53\) | 1.07165 | 0.147203 | 0.0736015 | − | 0.997288i | \(-0.476551\pi\) | ||||
0.0736015 | + | 0.997288i | \(0.476551\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.5216 | 1.67326 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.60638 | 0.473540 | ||||||||
\(59\) | 4.95536 | 0.645133 | 0.322566 | − | 0.946547i | \(-0.395454\pi\) | ||||
0.322566 | + | 0.946547i | \(0.395454\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.36706 | 0.303071 | 0.151536 | − | 0.988452i | \(-0.451578\pi\) | ||||
0.151536 | + | 0.988452i | \(0.451578\pi\) | |||||||
\(62\) | 10.1375 | 1.28747 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.77608 | 1.09701 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.2369 | 1.49497 | 0.747486 | − | 0.664277i | \(-0.231261\pi\) | ||||
0.747486 | + | 0.664277i | \(0.231261\pi\) | |||||||
\(68\) | 1.25625 | 0.152343 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.1746 | −1.68222 | −0.841109 | − | 0.540866i | \(-0.818097\pi\) | ||||
−0.841109 | + | 0.540866i | \(0.818097\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.67832 | −1.01572 | −0.507860 | − | 0.861439i | \(-0.669563\pi\) | ||||
−0.507860 | + | 0.861439i | \(0.669563\pi\) | |||||||
\(74\) | −2.72823 | −0.317150 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.03872 | −0.119149 | ||||||||
\(77\) | 0.703068 | 0.0801220 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.64466 | −0.297547 | −0.148774 | − | 0.988871i | \(-0.547533\pi\) | ||||
−0.148774 | + | 0.988871i | \(0.547533\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.68189 | −0.185734 | ||||||||
\(83\) | 14.3131 | 1.57106 | 0.785532 | − | 0.618821i | \(-0.212389\pi\) | ||||
0.785532 | + | 0.618821i | \(0.212389\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −15.2668 | −1.64626 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.501233 | 0.0534316 | ||||||||
\(89\) | 4.06867 | 0.431278 | 0.215639 | − | 0.976473i | \(-0.430817\pi\) | ||||
0.215639 | + | 0.976473i | \(0.430817\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.2289 | −1.49160 | ||||||||
\(92\) | 2.28300 | 0.238019 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −13.1287 | −1.35412 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.78196 | −0.282466 | −0.141233 | − | 0.989976i | \(-0.545107\pi\) | ||||
−0.141233 | + | 0.989976i | \(0.545107\pi\) | |||||||
\(98\) | −13.8759 | −1.40167 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.7004 | 1.06473 | 0.532366 | − | 0.846514i | \(-0.321303\pi\) | ||||
0.532366 | + | 0.846514i | \(0.321303\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.61627 | −0.356322 | −0.178161 | − | 0.984001i | \(-0.557015\pi\) | ||||
−0.178161 | + | 0.984001i | \(0.557015\pi\) | |||||||
\(104\) | −10.1441 | −0.994714 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.40766 | −0.136724 | ||||||||
\(107\) | −0.522034 | −0.0504669 | −0.0252335 | − | 0.999682i | \(-0.508033\pi\) | ||||
−0.0252335 | + | 0.999682i | \(0.508033\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.5033 | 1.10181 | 0.550907 | − | 0.834566i | \(-0.314282\pi\) | ||||
0.550907 | + | 0.834566i | \(0.314282\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −14.1459 | −1.33666 | ||||||||
\(113\) | 20.1421 | 1.89481 | 0.947404 | − | 0.320041i | \(-0.103697\pi\) | ||||
0.947404 | + | 0.320041i | \(0.103697\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.753938 | 0.0700014 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.50908 | −0.599209 | ||||||||
\(119\) | −19.1724 | −1.75753 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9719 | −0.997441 | ||||||||
\(122\) | −3.10924 | −0.281497 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.11932 | 0.190321 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.3345 | 1.44945 | 0.724726 | − | 0.689037i | \(-0.241966\pi\) | ||||
0.724726 | + | 0.689037i | \(0.241966\pi\) | |||||||
\(128\) | −8.44401 | −0.746352 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.9147 | −1.65259 | −0.826294 | − | 0.563239i | \(-0.809555\pi\) | ||||
−0.826294 | + | 0.563239i | \(0.809555\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.8524 | 1.37458 | ||||||||
\(134\) | −16.0737 | −1.38855 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −13.6684 | −1.17206 | ||||||||
\(137\) | 13.5975 | 1.16171 | 0.580856 | − | 0.814006i | \(-0.302718\pi\) | ||||
0.580856 | + | 0.814006i | \(0.302718\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.36103 | −0.285079 | −0.142540 | − | 0.989789i | \(-0.545527\pi\) | ||||
−0.142540 | + | 0.989789i | \(0.545527\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 18.6190 | 1.56247 | ||||||||
\(143\) | −0.569579 | −0.0476306 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.3993 | 0.943417 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.570355 | −0.0468829 | ||||||||
\(149\) | 6.33430 | 0.518926 | 0.259463 | − | 0.965753i | \(-0.416454\pi\) | ||||
0.259463 | + | 0.965753i | \(0.416454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.375265 | 0.0305386 | 0.0152693 | − | 0.999883i | \(-0.495139\pi\) | ||||
0.0152693 | + | 0.999883i | \(0.495139\pi\) | |||||||
\(152\) | 11.3016 | 0.916678 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.923510 | −0.0744185 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.5002 | 0.838004 | 0.419002 | − | 0.907985i | \(-0.362380\pi\) | ||||
0.419002 | + | 0.907985i | \(0.362380\pi\) | |||||||
\(158\) | 3.47387 | 0.276366 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −34.8421 | −2.74594 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.8457 | −1.08448 | −0.542241 | − | 0.840223i | \(-0.682424\pi\) | ||||
−0.542241 | + | 0.840223i | \(0.682424\pi\) | |||||||
\(164\) | −0.351612 | −0.0274563 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.8008 | −1.45923 | ||||||||
\(167\) | 1.08114 | 0.0836611 | 0.0418306 | − | 0.999125i | \(-0.486681\pi\) | ||||
0.0418306 | + | 0.999125i | \(0.486681\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.47265 | −0.113281 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.19163 | −0.243360 | ||||||||
\(173\) | 18.2635 | 1.38854 | 0.694272 | − | 0.719712i | \(-0.255726\pi\) | ||||
0.694272 | + | 0.719712i | \(0.255726\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.566255 | −0.0426831 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.34437 | −0.400578 | ||||||||
\(179\) | 6.93140 | 0.518077 | 0.259039 | − | 0.965867i | \(-0.416594\pi\) | ||||
0.259039 | + | 0.965867i | \(0.416594\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.1858 | 0.980091 | 0.490045 | − | 0.871697i | \(-0.336980\pi\) | ||||
0.490045 | + | 0.871697i | \(0.336980\pi\) | |||||||
\(182\) | 18.6903 | 1.38542 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −24.8397 | −1.83121 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.767463 | −0.0561224 | ||||||||
\(188\) | −2.74465 | −0.200174 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.3938 | −1.69272 | −0.846358 | − | 0.532614i | \(-0.821210\pi\) | ||||
−0.846358 | + | 0.532614i | \(0.821210\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.06435 | −0.652466 | −0.326233 | − | 0.945289i | \(-0.605779\pi\) | ||||
−0.326233 | + | 0.945289i | \(0.605779\pi\) | |||||||
\(194\) | 3.65423 | 0.262358 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.90084 | −0.207203 | ||||||||
\(197\) | 13.2823 | 0.946327 | 0.473163 | − | 0.880975i | \(-0.343112\pi\) | ||||
0.473163 | + | 0.880975i | \(0.343112\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.9985 | 1.70121 | 0.850606 | − | 0.525804i | \(-0.176235\pi\) | ||||
0.850606 | + | 0.525804i | \(0.176235\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.0555 | −0.988938 | ||||||||
\(203\) | −11.5063 | −0.807582 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.75013 | 0.330957 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 11.4601 | 0.794613 | ||||||||
\(209\) | 0.634567 | 0.0438939 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.75260 | −0.533711 | −0.266855 | − | 0.963737i | \(-0.585985\pi\) | ||||
−0.266855 | + | 0.963737i | \(0.585985\pi\) | |||||||
\(212\) | −0.294282 | −0.0202114 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.685714 | 0.0468744 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −32.3442 | −2.19567 | ||||||||
\(218\) | −15.1101 | −1.02338 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.5322 | 1.04481 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.1577 | −1.48379 | −0.741895 | − | 0.670517i | \(-0.766073\pi\) | ||||
−0.741895 | + | 0.670517i | \(0.766073\pi\) | |||||||
\(224\) | −6.46185 | −0.431751 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −26.4575 | −1.75993 | ||||||||
\(227\) | 11.9286 | 0.791729 | 0.395864 | − | 0.918309i | \(-0.370445\pi\) | ||||
0.395864 | + | 0.918309i | \(0.370445\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.73897 | −0.511406 | −0.255703 | − | 0.966755i | \(-0.582307\pi\) | ||||
−0.255703 | + | 0.966755i | \(0.582307\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.20308 | −0.538559 | ||||||||
\(233\) | 2.85168 | 0.186820 | 0.0934099 | − | 0.995628i | \(-0.470223\pi\) | ||||
0.0934099 | + | 0.995628i | \(0.470223\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.36077 | −0.0885784 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 25.1837 | 1.63242 | ||||||||
\(239\) | 19.9126 | 1.28804 | 0.644020 | − | 0.765009i | \(-0.277265\pi\) | ||||
0.644020 | + | 0.765009i | \(0.277265\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.61379 | 0.426032 | 0.213016 | − | 0.977049i | \(-0.431671\pi\) | ||||
0.213016 | + | 0.977049i | \(0.431671\pi\) | |||||||
\(242\) | 14.4120 | 0.926439 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.650008 | −0.0416125 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.8426 | −0.817155 | ||||||||
\(248\) | −23.0589 | −1.46424 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0644 | 0.761501 | 0.380750 | − | 0.924678i | \(-0.375666\pi\) | ||||
0.380750 | + | 0.924678i | \(0.375666\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.39472 | −0.0876850 | ||||||||
\(254\) | −21.4561 | −1.34627 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.46059 | −0.403787 | ||||||||
\(257\) | 12.7951 | 0.798136 | 0.399068 | − | 0.916921i | \(-0.369334\pi\) | ||||
0.399068 | + | 0.916921i | \(0.369334\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.70451 | 0.540872 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 24.8453 | 1.53495 | ||||||||
\(263\) | 10.5225 | 0.648843 | 0.324422 | − | 0.945913i | \(-0.394830\pi\) | ||||
0.324422 | + | 0.945913i | \(0.394830\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −20.8229 | −1.27673 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.36031 | −0.205264 | ||||||||
\(269\) | −6.80128 | −0.414681 | −0.207341 | − | 0.978269i | \(-0.566481\pi\) | ||||
−0.207341 | + | 0.978269i | \(0.566481\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.66981 | 0.344416 | 0.172208 | − | 0.985061i | \(-0.444910\pi\) | ||||
0.172208 | + | 0.985061i | \(0.444910\pi\) | |||||||
\(272\) | 15.4415 | 0.936281 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.8609 | −1.07902 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.874982 | 0.0525726 | 0.0262863 | − | 0.999654i | \(-0.491632\pi\) | ||||
0.0262863 | + | 0.999654i | \(0.491632\pi\) | |||||||
\(278\) | 4.41486 | 0.264786 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.85806 | 0.289808 | 0.144904 | − | 0.989446i | \(-0.453713\pi\) | ||||
0.144904 | + | 0.989446i | \(0.453713\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.4230 | 0.679024 | 0.339512 | − | 0.940602i | \(-0.389738\pi\) | ||||
0.339512 | + | 0.940602i | \(0.389738\pi\) | |||||||
\(284\) | 3.89242 | 0.230973 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.748167 | 0.0442400 | ||||||||
\(287\) | 5.36615 | 0.316754 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.92839 | 0.231082 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.38311 | 0.139461 | ||||||||
\(293\) | −0.0808664 | −0.00472427 | −0.00236213 | − | 0.999997i | \(-0.500752\pi\) | ||||
−0.00236213 | + | 0.999997i | \(0.500752\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.20564 | 0.360696 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.32038 | −0.481987 | ||||||||
\(299\) | 28.2268 | 1.63240 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 48.7093 | 2.80756 | ||||||||
\(302\) | −0.492927 | −0.0283647 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.7677 | −0.732275 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.77807 | −0.443918 | −0.221959 | − | 0.975056i | \(-0.571245\pi\) | ||||
−0.221959 | + | 0.975056i | \(0.571245\pi\) | |||||||
\(308\) | −0.193066 | −0.0110010 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.6181 | 0.772213 | 0.386106 | − | 0.922454i | \(-0.373820\pi\) | ||||
0.386106 | + | 0.922454i | \(0.373820\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.85037 | 0.274159 | 0.137079 | − | 0.990560i | \(-0.456228\pi\) | ||||
0.137079 | + | 0.990560i | \(0.456228\pi\) | |||||||
\(314\) | −13.7924 | −0.778351 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.726237 | 0.0408540 | ||||||||
\(317\) | 22.3020 | 1.25260 | 0.626302 | − | 0.779580i | \(-0.284568\pi\) | ||||
0.626302 | + | 0.779580i | \(0.284568\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.460592 | −0.0257882 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 45.7666 | 2.55047 | ||||||||
\(323\) | −17.3044 | −0.962842 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 18.1870 | 1.00728 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.82565 | 0.211236 | ||||||||
\(329\) | 41.8877 | 2.30934 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.144235 | 0.00792788 | 0.00396394 | − | 0.999992i | \(-0.498738\pi\) | ||||
0.00396394 | + | 0.999992i | \(0.498738\pi\) | |||||||
\(332\) | −3.93045 | −0.215711 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.42012 | −0.0777057 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.1832 | 0.554717 | 0.277358 | − | 0.960767i | \(-0.410541\pi\) | ||||
0.277358 | + | 0.960767i | \(0.410541\pi\) | |||||||
\(338\) | 1.93439 | 0.105217 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.29472 | −0.0701133 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.9351 | 0.806418 | ||||||||
\(344\) | 34.7260 | 1.87230 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −23.9898 | −1.28970 | ||||||||
\(347\) | −10.5782 | −0.567870 | −0.283935 | − | 0.958844i | \(-0.591640\pi\) | ||||
−0.283935 | + | 0.958844i | \(0.591640\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.1511 | −1.56042 | −0.780210 | − | 0.625517i | \(-0.784888\pi\) | ||||
−0.780210 | + | 0.625517i | \(0.784888\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.258665 | −0.0137869 | ||||||||
\(353\) | −3.81907 | −0.203268 | −0.101634 | − | 0.994822i | \(-0.532407\pi\) | ||||
−0.101634 | + | 0.994822i | \(0.532407\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.11728 | −0.0592156 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.10469 | −0.481198 | ||||||||
\(359\) | 10.9849 | 0.579759 | 0.289879 | − | 0.957063i | \(-0.406385\pi\) | ||||
0.289879 | + | 0.957063i | \(0.406385\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.69207 | −0.246951 | ||||||||
\(362\) | −17.3201 | −0.910323 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.90734 | 0.204800 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.07169 | 0.212541 | 0.106270 | − | 0.994337i | \(-0.466109\pi\) | ||||
0.106270 | + | 0.994337i | \(0.466109\pi\) | |||||||
\(368\) | 28.0620 | 1.46283 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.49120 | 0.233171 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.92973 | 0.0999175 | 0.0499588 | − | 0.998751i | \(-0.484091\pi\) | ||||
0.0499588 | + | 0.998751i | \(0.484091\pi\) | |||||||
\(374\) | 1.00810 | 0.0521274 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 29.8627 | 1.54005 | ||||||||
\(377\) | 9.32162 | 0.480088 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.6050 | 0.750210 | 0.375105 | − | 0.926982i | \(-0.377607\pi\) | ||||
0.375105 | + | 0.926982i | \(0.377607\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 30.7288 | 1.57222 | ||||||||
\(383\) | 31.5290 | 1.61106 | 0.805530 | − | 0.592556i | \(-0.201881\pi\) | ||||
0.805530 | + | 0.592556i | \(0.201881\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.9064 | 0.606021 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.763942 | 0.0387833 | ||||||||
\(389\) | −14.6046 | −0.740485 | −0.370242 | − | 0.928935i | \(-0.620725\pi\) | ||||
−0.370242 | + | 0.928935i | \(0.620725\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 38.0333 | 1.92343 | ||||||||
\(392\) | 31.5621 | 1.59413 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.4469 | −0.878962 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.2793 | 0.766845 | 0.383422 | − | 0.923573i | \(-0.374745\pi\) | ||||
0.383422 | + | 0.923573i | \(0.374745\pi\) | |||||||
\(398\) | −31.5231 | −1.58011 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.7148 | 0.784760 | 0.392380 | − | 0.919803i | \(-0.371652\pi\) | ||||
0.392380 | + | 0.919803i | \(0.371652\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.2031 | 1.30527 | ||||||||
\(404\) | −2.93839 | −0.146190 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.1140 | 0.750094 | ||||||||
\(407\) | 0.348438 | 0.0172714 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.4187 | 0.614064 | 0.307032 | − | 0.951699i | \(-0.400664\pi\) | ||||
0.307032 | + | 0.951699i | \(0.400664\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.993047 | 0.0489239 | ||||||||
\(413\) | 20.7674 | 1.02190 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.23496 | 0.256665 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.833531 | −0.0407693 | ||||||||
\(419\) | 9.08687 | 0.443923 | 0.221961 | − | 0.975055i | \(-0.428754\pi\) | ||||
0.221961 | + | 0.975055i | \(0.428754\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.15620 | 0.251298 | 0.125649 | − | 0.992075i | \(-0.459899\pi\) | ||||
0.125649 | + | 0.992075i | \(0.459899\pi\) | |||||||
\(422\) | 10.1834 | 0.495719 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.20188 | 0.155497 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.92014 | 0.480069 | ||||||||
\(428\) | 0.143353 | 0.00692924 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.66953 | −0.176755 | −0.0883776 | − | 0.996087i | \(-0.528168\pi\) | ||||
−0.0883776 | + | 0.996087i | \(0.528168\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.7340 | −0.852242 | −0.426121 | − | 0.904666i | \(-0.640120\pi\) | ||||
−0.426121 | + | 0.904666i | \(0.640120\pi\) | |||||||
\(434\) | 42.4855 | 2.03937 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.15886 | −0.151282 | ||||||||
\(437\) | −31.4474 | −1.50433 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.1823 | −1.24961 | −0.624806 | − | 0.780780i | \(-0.714822\pi\) | ||||
−0.624806 | + | 0.780780i | \(0.714822\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −20.4022 | −0.970433 | ||||||||
\(443\) | −19.2199 | −0.913166 | −0.456583 | − | 0.889681i | \(-0.650927\pi\) | ||||
−0.456583 | + | 0.889681i | \(0.650927\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 29.1051 | 1.37817 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 36.7797 | 1.73768 | ||||||||
\(449\) | −33.6407 | −1.58760 | −0.793802 | − | 0.608177i | \(-0.791901\pi\) | ||||
−0.793802 | + | 0.608177i | \(0.791901\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.214805 | 0.0101148 | ||||||||
\(452\) | −5.53112 | −0.260162 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.6687 | −0.735369 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.0255 | −1.12387 | −0.561933 | − | 0.827183i | \(-0.689942\pi\) | ||||
−0.561933 | + | 0.827183i | \(0.689942\pi\) | |||||||
\(458\) | 10.1655 | 0.475001 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.4282 | 0.671990 | 0.335995 | − | 0.941864i | \(-0.390927\pi\) | ||||
0.335995 | + | 0.941864i | \(0.390927\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.95599 | −0.137377 | −0.0686883 | − | 0.997638i | \(-0.521881\pi\) | ||||
−0.0686883 | + | 0.997638i | \(0.521881\pi\) | |||||||
\(464\) | 9.26722 | 0.430220 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.74581 | −0.173521 | ||||||||
\(467\) | −37.1933 | −1.72110 | −0.860551 | − | 0.509364i | \(-0.829881\pi\) | ||||
−0.860551 | + | 0.509364i | \(0.829881\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 51.2836 | 2.36806 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14.8056 | 0.681482 | ||||||||
\(473\) | 1.94982 | 0.0896526 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.26483 | 0.241313 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −26.1561 | −1.19635 | ||||||||
\(479\) | 8.65394 | 0.395409 | 0.197704 | − | 0.980262i | \(-0.436651\pi\) | ||||
0.197704 | + | 0.980262i | \(0.436651\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.05182 | −0.321535 | ||||||||
\(482\) | −8.68750 | −0.395705 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.01293 | 0.136951 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.4645 | 1.74299 | 0.871496 | − | 0.490402i | \(-0.163150\pi\) | ||||
0.871496 | + | 0.490402i | \(0.163150\pi\) | |||||||
\(488\) | 7.07229 | 0.320148 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.0853 | −1.35773 | −0.678865 | − | 0.734263i | \(-0.737528\pi\) | ||||
−0.678865 | + | 0.734263i | \(0.737528\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.5601 | 0.565680 | ||||||||
\(494\) | 16.8693 | 0.758986 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 26.0502 | 1.16969 | ||||||||
\(497\) | −59.4045 | −2.66466 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.6343 | −0.878951 | −0.439476 | − | 0.898254i | \(-0.644836\pi\) | ||||
−0.439476 | + | 0.898254i | \(0.644836\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.8472 | −0.707293 | ||||||||
\(503\) | 30.4802 | 1.35904 | 0.679522 | − | 0.733655i | \(-0.262187\pi\) | ||||
0.679522 | + | 0.733655i | \(0.262187\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.83202 | 0.0814431 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.48554 | −0.199014 | ||||||||
\(509\) | −11.4371 | −0.506942 | −0.253471 | − | 0.967343i | \(-0.581572\pi\) | ||||
−0.253471 | + | 0.967343i | \(0.581572\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.3700 | −1.60892 | ||||||||
\(512\) | 25.3743 | 1.12140 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −16.8069 | −0.741321 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.67675 | 0.0737433 | ||||||||
\(518\) | −11.4337 | −0.502370 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.6733 | −0.730471 | −0.365236 | − | 0.930915i | \(-0.619012\pi\) | ||||
−0.365236 | + | 0.930915i | \(0.619012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.54272 | 0.111185 | 0.0555926 | − | 0.998454i | \(-0.482295\pi\) | ||||
0.0555926 | + | 0.998454i | \(0.482295\pi\) | |||||||
\(524\) | 5.19409 | 0.226905 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.8217 | −0.602656 | ||||||||
\(527\) | 35.3066 | 1.53798 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 46.1182 | 2.00514 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.35316 | −0.188734 | ||||||||
\(533\) | −4.34730 | −0.188302 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 36.5612 | 1.57921 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.93377 | 0.385162 | ||||||||
\(539\) | 1.77217 | 0.0763327 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.3649 | 1.13352 | 0.566758 | − | 0.823884i | \(-0.308197\pi\) | ||||
0.566758 | + | 0.823884i | \(0.308197\pi\) | |||||||
\(542\) | −7.44753 | −0.319899 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.05370 | 0.302425 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.8319 | −0.634165 | −0.317082 | − | 0.948398i | \(-0.602703\pi\) | ||||
−0.317082 | + | 0.948398i | \(0.602703\pi\) | |||||||
\(548\) | −3.73394 | −0.159506 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.3852 | −0.442425 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.0835 | −0.471319 | ||||||||
\(554\) | −1.14933 | −0.0488302 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.922957 | 0.0391421 | ||||||||
\(557\) | 18.7407 | 0.794069 | 0.397034 | − | 0.917804i | \(-0.370039\pi\) | ||||
0.397034 | + | 0.917804i | \(0.370039\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −39.4611 | −1.66903 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.38127 | −0.269178 | ||||||||
\(563\) | −32.1447 | −1.35474 | −0.677368 | − | 0.735644i | \(-0.736879\pi\) | ||||
−0.677368 | + | 0.735644i | \(0.736879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15.0045 | −0.630688 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −42.3508 | −1.77700 | ||||||||
\(569\) | 2.14141 | 0.0897725 | 0.0448862 | − | 0.998992i | \(-0.485707\pi\) | ||||
0.0448862 | + | 0.998992i | \(0.485707\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.8476 | 0.495805 | 0.247902 | − | 0.968785i | \(-0.420259\pi\) | ||||
0.247902 | + | 0.968785i | \(0.420259\pi\) | |||||||
\(572\) | 0.156409 | 0.00653981 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.04866 | −0.294205 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.6985 | 0.653539 | 0.326769 | − | 0.945104i | \(-0.394040\pi\) | ||||
0.326769 | + | 0.945104i | \(0.394040\pi\) | |||||||
\(578\) | −5.16011 | −0.214632 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 59.9847 | 2.48859 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.179781 | 0.00744577 | ||||||||
\(584\) | −25.9290 | −1.07295 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.106221 | 0.00438797 | ||||||||
\(587\) | −2.32845 | −0.0961055 | −0.0480527 | − | 0.998845i | \(-0.515302\pi\) | ||||
−0.0480527 | + | 0.998845i | \(0.515302\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.1929 | −1.20287 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.01067 | −0.288137 | ||||||||
\(593\) | −34.0275 | −1.39734 | −0.698672 | − | 0.715442i | \(-0.746225\pi\) | ||||
−0.698672 | + | 0.715442i | \(0.746225\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.73943 | −0.0712499 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −37.0771 | −1.51619 | ||||||||
\(599\) | 2.93932 | 0.120097 | 0.0600486 | − | 0.998195i | \(-0.480874\pi\) | ||||
0.0600486 | + | 0.998195i | \(0.480874\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.17826 | 0.211225 | 0.105613 | − | 0.994407i | \(-0.466320\pi\) | ||||
0.105613 | + | 0.994407i | \(0.466320\pi\) | |||||||
\(602\) | −63.9818 | −2.60770 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.103050 | −0.00419303 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.45215 | 0.0589409 | 0.0294705 | − | 0.999566i | \(-0.490618\pi\) | ||||
0.0294705 | + | 0.999566i | \(0.490618\pi\) | |||||||
\(608\) | −5.83227 | −0.236530 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −33.9346 | −1.37285 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.1889 | 1.66361 | 0.831803 | − | 0.555072i | \(-0.187309\pi\) | ||||
0.831803 | + | 0.555072i | \(0.187309\pi\) | |||||||
\(614\) | 10.2168 | 0.412318 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.10062 | 0.0846364 | ||||||||
\(617\) | 33.9582 | 1.36711 | 0.683553 | − | 0.729901i | \(-0.260434\pi\) | ||||
0.683553 | + | 0.729901i | \(0.260434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.1879 | −1.25355 | −0.626774 | − | 0.779201i | \(-0.715625\pi\) | ||||
−0.626774 | + | 0.779201i | \(0.715625\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.8880 | −0.717243 | ||||||||
\(623\) | 17.0514 | 0.683151 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.37117 | −0.254643 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.88340 | −0.115060 | ||||||||
\(629\) | −9.50177 | −0.378860 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.9274 | 0.872917 | 0.436459 | − | 0.899724i | \(-0.356233\pi\) | ||||
0.436459 | + | 0.899724i | \(0.356233\pi\) | |||||||
\(632\) | −7.90168 | −0.314312 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −29.2946 | −1.16344 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −35.8658 | −1.42105 | ||||||||
\(638\) | 0.605007 | 0.0239524 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.2185 | 0.759083 | 0.379542 | − | 0.925175i | \(-0.376082\pi\) | ||||
0.379542 | + | 0.925175i | \(0.376082\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.6611 | −0.538739 | −0.269370 | − | 0.963037i | \(-0.586815\pi\) | ||||
−0.269370 | + | 0.963037i | \(0.586815\pi\) | |||||||
\(644\) | 9.56782 | 0.377025 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 22.7301 | 0.894302 | ||||||||
\(647\) | 30.7060 | 1.20718 | 0.603588 | − | 0.797296i | \(-0.293737\pi\) | ||||
0.603588 | + | 0.797296i | \(0.293737\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.831313 | 0.0326319 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.80211 | 0.148902 | ||||||||
\(653\) | 5.75846 | 0.225346 | 0.112673 | − | 0.993632i | \(-0.464059\pi\) | ||||
0.112673 | + | 0.993632i | \(0.464059\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.32193 | −0.168743 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −55.0212 | −2.14495 | ||||||||
\(659\) | −15.9750 | −0.622298 | −0.311149 | − | 0.950361i | \(-0.600714\pi\) | ||||
−0.311149 | + | 0.950361i | \(0.600714\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.1613 | 1.21203 | 0.606017 | − | 0.795451i | \(-0.292766\pi\) | ||||
0.606017 | + | 0.795451i | \(0.292766\pi\) | |||||||
\(662\) | −0.189459 | −0.00736354 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 42.7645 | 1.65958 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.8256 | 0.883812 | ||||||||
\(668\) | −0.296887 | −0.0114869 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.397099 | 0.0153298 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.1758 | 0.739174 | 0.369587 | − | 0.929196i | \(-0.379499\pi\) | ||||
0.369587 | + | 0.929196i | \(0.379499\pi\) | |||||||
\(674\) | −13.3761 | −0.515229 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.404398 | 0.0155538 | ||||||||
\(677\) | 25.2153 | 0.969105 | 0.484552 | − | 0.874762i | \(-0.338983\pi\) | ||||
0.484552 | + | 0.874762i | \(0.338983\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.6590 | −0.447429 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.70068 | 0.0651223 | ||||||||
\(683\) | −28.1160 | −1.07583 | −0.537914 | − | 0.843000i | \(-0.680788\pi\) | ||||
−0.537914 | + | 0.843000i | \(0.680788\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −19.6179 | −0.749013 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −39.2308 | −1.49566 | ||||||||
\(689\) | −3.63847 | −0.138615 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.8688 | 0.451511 | 0.225756 | − | 0.974184i | \(-0.427515\pi\) | ||||
0.225756 | + | 0.974184i | \(0.427515\pi\) | |||||||
\(692\) | −5.01524 | −0.190651 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.8950 | 0.527446 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.85764 | −0.221874 | ||||||||
\(698\) | 38.2912 | 1.44934 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.1748 | −0.988608 | −0.494304 | − | 0.869289i | \(-0.664577\pi\) | ||||
−0.494304 | + | 0.869289i | \(0.664577\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.85642 | 0.296311 | ||||||||
\(704\) | 1.47228 | 0.0554886 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.01651 | 0.188799 | ||||||||
\(707\) | 44.8444 | 1.68655 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.8934 | 0.747111 | 0.373556 | − | 0.927608i | \(-0.378138\pi\) | ||||
0.373556 | + | 0.927608i | \(0.378138\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.1563 | 0.455578 | ||||||||
\(713\) | 64.1630 | 2.40292 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.90340 | −0.0711333 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.4291 | −0.538489 | ||||||||
\(719\) | −53.3070 | −1.98802 | −0.994008 | − | 0.109309i | \(-0.965136\pi\) | ||||
−0.994008 | + | 0.109309i | \(0.965136\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.1555 | −0.564419 | ||||||||
\(722\) | 6.16324 | 0.229372 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.62088 | −0.134569 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.0186 | 0.779537 | 0.389768 | − | 0.920913i | \(-0.372555\pi\) | ||||
0.389768 | + | 0.920913i | \(0.372555\pi\) | |||||||
\(728\) | −42.5131 | −1.57564 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −53.1707 | −1.96659 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.4993 | −0.904901 | −0.452451 | − | 0.891789i | \(-0.649450\pi\) | ||||
−0.452451 | + | 0.891789i | \(0.649450\pi\) | |||||||
\(734\) | −5.34834 | −0.197411 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.8187 | 0.472505 | ||||||||
\(737\) | 2.05286 | 0.0756182 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.3415 | −0.417203 | −0.208601 | − | 0.978001i | \(-0.566891\pi\) | ||||
−0.208601 | + | 0.978001i | \(0.566891\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.89938 | −0.216573 | ||||||||
\(743\) | 20.0546 | 0.735732 | 0.367866 | − | 0.929879i | \(-0.380088\pi\) | ||||
0.367866 | + | 0.929879i | \(0.380088\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.53478 | −0.0928049 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.210749 | 0.00770576 | ||||||||
\(749\) | −2.18779 | −0.0799403 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.7620 | −0.392711 | −0.196355 | − | 0.980533i | \(-0.562911\pi\) | ||||
−0.196355 | + | 0.980533i | \(0.562911\pi\) | |||||||
\(752\) | −33.7366 | −1.23025 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.2443 | −0.445913 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.8528 | 1.33944 | 0.669718 | − | 0.742615i | \(-0.266415\pi\) | ||||
0.669718 | + | 0.742615i | \(0.266415\pi\) | |||||||
\(758\) | −19.1843 | −0.696806 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.5973 | 0.565403 | 0.282701 | − | 0.959208i | \(-0.408769\pi\) | ||||
0.282701 | + | 0.959208i | \(0.408769\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 48.2092 | 1.74529 | ||||||||
\(764\) | 6.42406 | 0.232414 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −41.4148 | −1.49638 | ||||||||
\(767\) | −16.8244 | −0.607494 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.4385 | −0.376423 | −0.188212 | − | 0.982128i | \(-0.560269\pi\) | ||||
−0.188212 | + | 0.982128i | \(0.560269\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.48912 | 0.0895853 | ||||||||
\(773\) | 29.1248 | 1.04755 | 0.523773 | − | 0.851858i | \(-0.324524\pi\) | ||||
0.523773 | + | 0.851858i | \(0.324524\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.31193 | −0.298381 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19.1838 | 0.687773 | ||||||||
\(779\) | 4.84332 | 0.173530 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.37794 | −0.0850894 | ||||||||
\(782\) | −49.9584 | −1.78651 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −35.6565 | −1.27345 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.9945 | −1.81776 | −0.908879 | − | 0.417060i | \(-0.863060\pi\) | ||||
−0.908879 | + | 0.417060i | \(0.863060\pi\) | |||||||
\(788\) | −3.64740 | −0.129933 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 84.4135 | 3.00140 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.03664 | −0.285389 | ||||||||
\(794\) | −20.0700 | −0.712257 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.59013 | −0.233581 | ||||||||
\(797\) | −36.6176 | −1.29706 | −0.648532 | − | 0.761188i | \(-0.724617\pi\) | ||||
−0.648532 | + | 0.761188i | \(0.724617\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −45.7242 | −1.61761 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.6421 | −0.728897 | ||||||||
\(803\) | −1.45588 | −0.0513768 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −34.4189 | −1.21235 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 31.9706 | 1.12472 | ||||||||
\(809\) | −34.4639 | −1.21168 | −0.605842 | − | 0.795585i | \(-0.707164\pi\) | ||||
−0.605842 | + | 0.795585i | \(0.707164\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.3834 | 1.24248 | 0.621240 | − | 0.783620i | \(-0.286629\pi\) | ||||
0.621240 | + | 0.783620i | \(0.286629\pi\) | |||||||
\(812\) | 3.15968 | 0.110883 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.457689 | −0.0160420 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 43.9635 | 1.53809 | ||||||||
\(818\) | −16.3125 | −0.570352 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.15613 | 0.0752493 | 0.0376246 | − | 0.999292i | \(-0.488021\pi\) | ||||
0.0376246 | + | 0.999292i | \(0.488021\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.5492 | 1.20431 | 0.602154 | − | 0.798380i | \(-0.294309\pi\) | ||||
0.602154 | + | 0.798380i | \(0.294309\pi\) | |||||||
\(824\) | −10.8047 | −0.376398 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.2789 | −0.949155 | ||||||||
\(827\) | 21.2543 | 0.739083 | 0.369542 | − | 0.929214i | \(-0.379515\pi\) | ||||
0.369542 | + | 0.929214i | \(0.379515\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.8519 | 1.00207 | 0.501035 | − | 0.865427i | \(-0.332953\pi\) | ||||
0.501035 | + | 0.865427i | \(0.332953\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −29.7965 | −1.03301 | ||||||||
\(833\) | −48.3263 | −1.67441 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.174255 | −0.00602675 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.9360 | −0.412322 | ||||||||
\(839\) | −0.443198 | −0.0153009 | −0.00765045 | − | 0.999971i | \(-0.502435\pi\) | ||||
−0.00765045 | + | 0.999971i | \(0.502435\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.4620 | −0.740071 | ||||||||
\(842\) | −6.77289 | −0.233409 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.12890 | 0.0732799 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −45.9820 | −1.57996 | ||||||||
\(848\) | −3.61724 | −0.124217 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.2676 | −0.591927 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.0351 | 0.994142 | 0.497071 | − | 0.867710i | \(-0.334409\pi\) | ||||
0.497071 | + | 0.867710i | \(0.334409\pi\) | |||||||
\(854\) | −13.0305 | −0.445895 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.55973 | −0.0533104 | ||||||||
\(857\) | −44.1483 | −1.50808 | −0.754039 | − | 0.656830i | \(-0.771897\pi\) | ||||
−0.754039 | + | 0.656830i | \(0.771897\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.1393 | 1.74485 | 0.872426 | − | 0.488747i | \(-0.162546\pi\) | ||||
0.872426 | + | 0.488747i | \(0.162546\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.82009 | 0.164173 | ||||||||
\(863\) | 2.01515 | 0.0685967 | 0.0342983 | − | 0.999412i | \(-0.489080\pi\) | ||||
0.0342983 | + | 0.999412i | \(0.489080\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 23.2944 | 0.791575 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.88188 | 0.301471 | ||||||||
\(869\) | −0.443669 | −0.0150504 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.5466 | −1.40775 | ||||||||
\(872\) | 34.3694 | 1.16390 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 41.3075 | 1.39725 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.02192 | −0.169578 | −0.0847891 | − | 0.996399i | \(-0.527022\pi\) | ||||
−0.0847891 | + | 0.996399i | \(0.527022\pi\) | |||||||
\(878\) | 34.3916 | 1.16066 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.2541 | 1.42358 | 0.711789 | − | 0.702393i | \(-0.247885\pi\) | ||||
0.711789 | + | 0.702393i | \(0.247885\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 56.8687 | 1.91379 | 0.956893 | − | 0.290442i | \(-0.0938024\pi\) | ||||
0.956893 | + | 0.290442i | \(0.0938024\pi\) | |||||||
\(884\) | −4.26522 | −0.143455 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.2462 | 0.848162 | ||||||||
\(887\) | 17.1287 | 0.575127 | 0.287563 | − | 0.957762i | \(-0.407155\pi\) | ||||
0.287563 | + | 0.957762i | \(0.407155\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 68.4563 | 2.29595 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.08462 | 0.203728 | ||||||||
\(893\) | 37.8065 | 1.26515 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −35.3880 | −1.18223 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 44.1885 | 1.47459 | ||||||||
\(899\) | 21.1892 | 0.706700 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.90255 | −0.163328 | ||||||||
\(902\) | −0.282155 | −0.00939474 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 60.1803 | 2.00157 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −57.9111 | −1.92291 | −0.961454 | − | 0.274967i | \(-0.911333\pi\) | ||||
−0.961454 | + | 0.274967i | \(0.911333\pi\) | |||||||
\(908\) | −3.27565 | −0.108706 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.89167 | −0.261463 | −0.130731 | − | 0.991418i | \(-0.541733\pi\) | ||||
−0.130731 | + | 0.991418i | \(0.541733\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.40117 | 0.0794670 | ||||||||
\(914\) | 31.5585 | 1.04386 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.12516 | 0.0702173 | ||||||||
\(917\) | −79.2699 | −2.61772 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.66345 | −0.120846 | −0.0604230 | − | 0.998173i | \(-0.519245\pi\) | ||||
−0.0604230 | + | 0.998173i | \(0.519245\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.9521 | −0.624155 | ||||||||
\(923\) | 48.1256 | 1.58407 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.88282 | 0.127597 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.23327 | 0.138964 | ||||||||
\(929\) | 49.7787 | 1.63319 | 0.816594 | − | 0.577213i | \(-0.195860\pi\) | ||||
0.816594 | + | 0.577213i | \(0.195860\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 39.9580 | 1.30957 | ||||||||
\(932\) | −0.783087 | −0.0256509 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 48.8550 | 1.59859 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.69363 | −0.316677 | −0.158338 | − | 0.987385i | \(-0.550614\pi\) | ||||
−0.158338 | + | 0.987385i | \(0.550614\pi\) | |||||||
\(938\) | −67.3632 | −2.19949 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.4206 | −0.893886 | −0.446943 | − | 0.894562i | \(-0.647487\pi\) | ||||
−0.446943 | + | 0.894562i | \(0.647487\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.6451 | −0.346653 | ||||||||
\(944\) | −16.7262 | −0.544392 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.56117 | −0.0832707 | ||||||||
\(947\) | 12.7622 | 0.414716 | 0.207358 | − | 0.978265i | \(-0.433514\pi\) | ||||
0.207358 | + | 0.978265i | \(0.433514\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.4646 | 0.956461 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −57.2830 | −1.85655 | ||||||||
\(953\) | −22.3816 | −0.725012 | −0.362506 | − | 0.931981i | \(-0.618079\pi\) | ||||
−0.362506 | + | 0.931981i | \(0.618079\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.46811 | −0.176851 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.3673 | −0.367262 | ||||||||
\(959\) | 56.9858 | 1.84017 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.5630 | 0.921386 | ||||||||
\(962\) | 9.26287 | 0.298647 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.81618 | −0.0584953 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.4419 | −1.33268 | −0.666342 | − | 0.745647i | \(-0.732141\pi\) | ||||
−0.666342 | + | 0.745647i | \(0.732141\pi\) | |||||||
\(968\) | −32.7816 | −1.05364 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.7475 | −1.30765 | −0.653824 | − | 0.756646i | \(-0.726836\pi\) | ||||
−0.653824 | + | 0.756646i | \(0.726836\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.0858 | −0.451569 | ||||||||
\(974\) | −50.5248 | −1.61892 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.98974 | −0.255745 | ||||||||
\(977\) | 21.8246 | 0.698231 | 0.349116 | − | 0.937080i | \(-0.386482\pi\) | ||||
0.349116 | + | 0.937080i | \(0.386482\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.682562 | 0.0218148 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 39.5183 | 1.26108 | ||||||||
\(983\) | 15.8023 | 0.504016 | 0.252008 | − | 0.967725i | \(-0.418909\pi\) | ||||
0.252008 | + | 0.967725i | \(0.418909\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −16.4983 | −0.525412 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.52665 | 0.112198 | ||||||||
\(989\) | −96.6275 | −3.07257 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.78545 | 0.247313 | 0.123657 | − | 0.992325i | \(-0.460538\pi\) | ||||
0.123657 | + | 0.992325i | \(0.460538\pi\) | |||||||
\(992\) | 11.8997 | 0.377817 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 78.0303 | 2.47497 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.9919 | 0.664820 | 0.332410 | − | 0.943135i | \(-0.392138\pi\) | ||||
0.332410 | + | 0.943135i | \(0.392138\pi\) | |||||||
\(998\) | 25.7905 | 0.816383 | ||||||||
\(999\) | 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 | 5625.2.a.u.1.3 | 8 | ||
3.2 | odd | 2 | 1875.2.a.o.1.6 | yes | 8 | ||
5.4 | even | 2 | 5625.2.a.bc.1.6 | 8 | |||
15.2 | even | 4 | 1875.2.b.g.1249.12 | 16 | |||
15.8 | even | 4 | 1875.2.b.g.1249.5 | 16 | |||
15.14 | odd | 2 | 1875.2.a.n.1.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.n.1.3 | ✓ | 8 | 15.14 | odd | 2 | ||
1875.2.a.o.1.6 | yes | 8 | 3.2 | odd | 2 | ||
1875.2.b.g.1249.5 | 16 | 15.8 | even | 4 | |||
1875.2.b.g.1249.12 | 16 | 15.2 | even | 4 | |||
5625.2.a.u.1.3 | 8 | 1.1 | even | 1 | trivial | ||
5625.2.a.bc.1.6 | 8 | 5.4 | even | 2 |