Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3332,2,Mod(1,3332)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3332, 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("3332.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3332.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: | \(26.6061539535\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 3 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 476) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3332.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.30278 | 1.90686 | 0.953429 | − | 0.301617i | \(-0.0975264\pi\) | ||||
0.953429 | + | 0.301617i | \(0.0975264\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.302776 | −0.135405 | −0.0677027 | − | 0.997706i | \(-0.521567\pi\) | ||||
−0.0677027 | + | 0.997706i | \(0.521567\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.90833 | 2.63611 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.60555 | −0.785603 | −0.392802 | − | 0.919623i | \(-0.628494\pi\) | ||||
−0.392802 | + | 0.919623i | \(0.628494\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.605551 | −0.167950 | −0.0839749 | − | 0.996468i | \(-0.526762\pi\) | ||||
−0.0839749 | + | 0.996468i | \(0.526762\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.60555 | 0.960324 | 0.480162 | − | 0.877180i | \(-0.340578\pi\) | ||||
0.480162 | + | 0.877180i | \(0.340578\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.90833 | −0.981665 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.2111 | 3.11983 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.39445 | −0.258943 | −0.129471 | − | 0.991583i | \(-0.541328\pi\) | ||||
−0.129471 | + | 0.991583i | \(0.541328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.3028 | 1.85043 | 0.925217 | − | 0.379439i | \(-0.123883\pi\) | ||||
0.925217 | + | 0.379439i | \(0.123883\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.60555 | −1.49803 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.21110 | −1.18550 | −0.592749 | − | 0.805387i | \(-0.701957\pi\) | ||||
−0.592749 | + | 0.805387i | \(0.701957\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.51388 | 1.32964 | 0.664822 | − | 0.747002i | \(-0.268507\pi\) | ||||
0.664822 | + | 0.747002i | \(0.268507\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.697224 | −0.106326 | −0.0531629 | − | 0.998586i | \(-0.516930\pi\) | ||||
−0.0531629 | + | 0.998586i | \(0.516930\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.39445 | −0.356943 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.0000 | −1.45865 | −0.729325 | − | 0.684167i | \(-0.760166\pi\) | ||||
−0.729325 | + | 0.684167i | \(0.760166\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.30278 | 0.462481 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.30278 | 0.591032 | 0.295516 | − | 0.955338i | \(-0.404508\pi\) | ||||
0.295516 | + | 0.955338i | \(0.404508\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.788897 | 0.106375 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 19.8167 | 2.62478 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.21110 | 1.19918 | 0.599592 | − | 0.800306i | \(-0.295330\pi\) | ||||
0.599592 | + | 0.800306i | \(0.295330\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.697224 | 0.0892704 | 0.0446352 | − | 0.999003i | \(-0.485787\pi\) | ||||
0.0446352 | + | 0.999003i | \(0.485787\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.183346 | 0.0227413 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.30278 | 0.770007 | 0.385003 | − | 0.922915i | \(-0.374200\pi\) | ||||
0.385003 | + | 0.922915i | \(0.374200\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.2111 | 1.83120 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.51388 | −0.528309 | −0.264155 | − | 0.964480i | \(-0.585093\pi\) | ||||
−0.264155 | + | 0.964480i | \(0.585093\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −16.2111 | −1.87190 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.00000 | −0.675053 | −0.337526 | − | 0.941316i | \(-0.609590\pi\) | ||||
−0.337526 | + | 0.941316i | \(0.609590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.8167 | 3.31296 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.21110 | 0.571993 | 0.285996 | − | 0.958231i | \(-0.407675\pi\) | ||||
0.285996 | + | 0.958231i | \(0.407675\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.302776 | −0.0328406 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.60555 | −0.493767 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 34.0278 | 3.52851 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.81665 | −0.186385 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.9083 | 1.31064 | 0.655321 | − | 0.755350i | \(-0.272533\pi\) | ||||
0.655321 | + | 0.755350i | \(0.272533\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −20.6056 | −2.07094 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.4222 | −1.63407 | −0.817035 | − | 0.576588i | \(-0.804384\pi\) | ||||
−0.817035 | + | 0.576588i | \(0.804384\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.21110 | 0.119333 | 0.0596667 | − | 0.998218i | \(-0.480996\pi\) | ||||
0.0596667 | + | 0.998218i | \(0.480996\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.6056 | −1.60532 | −0.802660 | − | 0.596437i | \(-0.796582\pi\) | ||||
−0.802660 | + | 0.596437i | \(0.796582\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −23.8167 | −2.26058 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.78890 | 0.450502 | 0.225251 | − | 0.974301i | \(-0.427680\pi\) | ||||
0.225251 | + | 0.974301i | \(0.427680\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.39445 | −0.130033 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.78890 | −0.442734 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.21110 | −0.382828 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 28.1194 | 2.53544 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.1194 | 1.78531 | 0.892655 | − | 0.450740i | \(-0.148840\pi\) | ||||
0.892655 | + | 0.450740i | \(0.148840\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.30278 | −0.202748 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.4222 | −1.60956 | −0.804778 | − | 0.593576i | \(-0.797716\pi\) | ||||
−0.804778 | + | 0.593576i | \(0.797716\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.90833 | −0.422442 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.9083 | −1.18827 | −0.594134 | − | 0.804366i | \(-0.702505\pi\) | ||||
−0.594134 | + | 0.804366i | \(0.702505\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.5139 | 1.65515 | 0.827573 | − | 0.561358i | \(-0.189721\pi\) | ||||
0.827573 | + | 0.561358i | \(0.189721\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −33.0278 | −2.78144 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.57779 | 0.131942 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.422205 | 0.0350622 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.90833 | −0.484029 | −0.242015 | − | 0.970273i | \(-0.577808\pi\) | ||||
−0.242015 | + | 0.970273i | \(0.577808\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1194 | −0.904886 | −0.452443 | − | 0.891793i | \(-0.649447\pi\) | ||||
−0.452443 | + | 0.891793i | \(0.649447\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.90833 | 0.639350 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.11943 | −0.250559 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.8167 | 1.74116 | 0.870579 | − | 0.492028i | \(-0.163744\pi\) | ||||
0.870579 | + | 0.492028i | \(0.163744\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.2111 | 1.12701 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.183346 | −0.0143608 | −0.00718039 | − | 0.999974i | \(-0.502286\pi\) | ||||
−0.00718039 | + | 0.999974i | \(0.502286\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.60555 | 0.202842 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.1194 | −1.78904 | −0.894518 | − | 0.447033i | \(-0.852481\pi\) | ||||
−0.894518 | + | 0.447033i | \(0.852481\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6333 | −0.971793 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 47.4500 | 3.62859 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.90833 | 0.449202 | 0.224601 | − | 0.974451i | \(-0.427892\pi\) | ||||
0.224601 | + | 0.974451i | \(0.427892\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 30.4222 | 2.28667 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.9083 | 1.63751 | 0.818753 | − | 0.574146i | \(-0.194666\pi\) | ||||
0.818753 | + | 0.574146i | \(0.194666\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.6333 | −1.60799 | −0.803996 | − | 0.594635i | \(-0.797296\pi\) | ||||
−0.803996 | + | 0.594635i | \(0.797296\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.30278 | 0.170226 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.18335 | 0.160523 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.60555 | −0.190537 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.72498 | 0.631317 | 0.315659 | − | 0.948873i | \(-0.397775\pi\) | ||||
0.315659 | + | 0.948873i | \(0.397775\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.6056 | −0.907367 | −0.453684 | − | 0.891163i | \(-0.649890\pi\) | ||||
−0.453684 | + | 0.891163i | \(0.649890\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.605551 | 0.0433644 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.0278 | 0.928189 | 0.464095 | − | 0.885786i | \(-0.346380\pi\) | ||||
0.464095 | + | 0.885786i | \(0.346380\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.51388 | 0.319980 | 0.159990 | − | 0.987119i | \(-0.448854\pi\) | ||||
0.159990 | + | 0.987119i | \(0.448854\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.8167 | 1.46829 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.57779 | −0.180041 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 36.4222 | 2.53152 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.6333 | −1.08138 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.02776 | 0.621496 | 0.310748 | − | 0.950492i | \(-0.399420\pi\) | ||||
0.310748 | + | 0.950492i | \(0.399420\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.60555 | −0.452605 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.211103 | 0.0143971 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.9083 | −1.00741 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.605551 | −0.0407338 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.6333 | −1.44867 | −0.724337 | − | 0.689446i | \(-0.757854\pi\) | ||||
−0.724337 | + | 0.689446i | \(0.757854\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −38.8167 | −2.58778 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.9083 | −0.724011 | −0.362006 | − | 0.932176i | \(-0.617908\pi\) | ||||
−0.362006 | + | 0.932176i | \(0.617908\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.8167 | −1.04519 | −0.522597 | − | 0.852580i | \(-0.675037\pi\) | ||||
−0.522597 | + | 0.852580i | \(0.675037\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.21110 | −0.0793420 | −0.0396710 | − | 0.999213i | \(-0.512631\pi\) | ||||
−0.0396710 | + | 0.999213i | \(0.512631\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.02776 | 0.197509 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.8167 | −1.28723 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.69722 | −0.562577 | −0.281288 | − | 0.959623i | \(-0.590762\pi\) | ||||
−0.281288 | + | 0.959623i | \(0.590762\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.09167 | −0.199152 | −0.0995761 | − | 0.995030i | \(-0.531749\pi\) | ||||
−0.0995761 | + | 0.995030i | \(0.531749\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 49.8444 | 3.19752 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.63331 | −0.231182 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.2111 | 1.09071 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.2111 | −1.46507 | −0.732536 | − | 0.680728i | \(-0.761663\pi\) | ||||
−0.732536 | + | 0.680728i | \(0.761663\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0000 | −0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.00000 | −0.0626224 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.81665 | −0.487589 | −0.243795 | − | 0.969827i | \(-0.578392\pi\) | ||||
−0.243795 | + | 0.969827i | \(0.578392\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.0278 | −0.682601 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.42221 | −0.396010 | −0.198005 | − | 0.980201i | \(-0.563446\pi\) | ||||
−0.198005 | + | 0.980201i | \(0.563446\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.30278 | −0.0800289 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.60555 | 0.404253 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1833 | 0.618594 | 0.309297 | − | 0.950965i | \(-0.399906\pi\) | ||||
0.309297 | + | 0.950965i | \(0.399906\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.7889 | 0.771200 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.0278 | −0.662594 | −0.331297 | − | 0.943527i | \(-0.607486\pi\) | ||||
−0.331297 | + | 0.943527i | \(0.607486\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 81.4777 | 4.87794 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.3028 | −1.21116 | −0.605581 | − | 0.795784i | \(-0.707059\pi\) | ||||
−0.605581 | + | 0.795784i | \(0.707059\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.3028 | −0.612436 | −0.306218 | − | 0.951961i | \(-0.599064\pi\) | ||||
−0.306218 | + | 0.951961i | \(0.599064\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.00000 | −0.355409 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 42.6333 | 2.49921 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.8167 | 1.15770 | 0.578851 | − | 0.815434i | \(-0.303501\pi\) | ||||
0.578851 | + | 0.815434i | \(0.303501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.78890 | −0.162376 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −42.2389 | −2.45095 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.78890 | −0.161286 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −54.2389 | −3.11594 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.211103 | −0.0120877 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.0000 | 1.48390 | 0.741949 | − | 0.670456i | \(-0.233902\pi\) | ||||
0.741949 | + | 0.670456i | \(0.233902\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | 0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.7250 | −0.948387 | −0.474193 | − | 0.880421i | \(-0.657260\pi\) | ||||
−0.474193 | + | 0.880421i | \(0.657260\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.7250 | −1.51059 | −0.755293 | − | 0.655388i | \(-0.772505\pi\) | ||||
−0.755293 | + | 0.655388i | \(0.772505\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.39445 | −0.302982 | −0.151491 | − | 0.988459i | \(-0.548408\pi\) | ||||
−0.151491 | + | 0.988459i | \(0.548408\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.63331 | 0.203426 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −54.8444 | −3.06112 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.00000 | 0.333849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.97224 | 0.164870 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.60555 | −0.365288 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.7250 | −1.79873 | −0.899364 | − | 0.437201i | \(-0.855970\pi\) | ||||
−0.899364 | + | 0.437201i | \(0.855970\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −57.0278 | −3.12510 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.90833 | −0.104263 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.2111 | 1.37334 | 0.686668 | − | 0.726971i | \(-0.259073\pi\) | ||||
0.686668 | + | 0.726971i | \(0.259073\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.8167 | 0.859043 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.8444 | −1.45371 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.60555 | −0.247955 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.00000 | 0.322097 | 0.161048 | − | 0.986947i | \(-0.448512\pi\) | ||||
0.161048 | + | 0.986947i | \(0.448512\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.78890 | −0.256344 | −0.128172 | − | 0.991752i | \(-0.540911\pi\) | ||||
−0.128172 | + | 0.991752i | \(0.540911\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.81665 | −0.523974 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.60555 | 0.138680 | 0.0693398 | − | 0.997593i | \(-0.477911\pi\) | ||||
0.0693398 | + | 0.997593i | \(0.477911\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.605551 | 0.0321393 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35.5139 | −1.87435 | −0.937175 | − | 0.348859i | \(-0.886569\pi\) | ||||
−0.937175 | + | 0.348859i | \(0.886569\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.9083 | −0.729998 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.36669 | 0.0715359 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.72498 | 0.298842 | 0.149421 | − | 0.988774i | \(-0.452259\pi\) | ||||
0.149421 | + | 0.988774i | \(0.452259\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 67.3305 | 3.50509 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.69722 | 0.450325 | 0.225163 | − | 0.974321i | \(-0.427709\pi\) | ||||
0.225163 | + | 0.974321i | \(0.427709\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.90833 | 0.511664 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.844410 | 0.0434893 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.2389 | 1.14233 | 0.571167 | − | 0.820834i | \(-0.306491\pi\) | ||||
0.571167 | + | 0.820834i | \(0.306491\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 66.4500 | 3.40433 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.0278 | −1.68764 | −0.843820 | − | 0.536627i | \(-0.819698\pi\) | ||||
−0.843820 | + | 0.536627i | \(0.819698\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.51388 | −0.280286 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.9083 | −1.26290 | −0.631451 | − | 0.775416i | \(-0.717540\pi\) | ||||
−0.631451 | + | 0.775416i | \(0.717540\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.60555 | 0.232913 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −60.8444 | −3.06919 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.81665 | 0.0914058 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.9083 | 0.848605 | 0.424302 | − | 0.905521i | \(-0.360519\pi\) | ||||
0.424302 | + | 0.905521i | \(0.360519\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.0000 | 1.19850 | 0.599251 | − | 0.800561i | \(-0.295465\pi\) | ||||
0.599251 | + | 0.800561i | \(0.295465\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.23886 | −0.310780 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.02776 | −0.448593 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.7889 | 0.931331 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.0278 | −1.63312 | −0.816559 | − | 0.577262i | \(-0.804121\pi\) | ||||
−0.816559 | + | 0.577262i | \(0.804121\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −45.9361 | −2.26586 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.57779 | −0.0774509 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 64.4500 | 3.15613 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.30278 | −0.112498 | −0.0562490 | − | 0.998417i | \(-0.517914\pi\) | ||||
−0.0562490 | + | 0.998417i | \(0.517914\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.90833 | 0.482902 | 0.241451 | − | 0.970413i | \(-0.422377\pi\) | ||||
0.241451 | + | 0.970413i | \(0.422377\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −79.0833 | −3.84516 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.90833 | −0.238089 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.21110 | 0.251594 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.8444 | −1.87107 | −0.935535 | − | 0.353235i | \(-0.885082\pi\) | ||||
−0.935535 | + | 0.353235i | \(0.885082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.6333 | 1.52020 | 0.760100 | − | 0.649806i | \(-0.225150\pi\) | ||||
0.760100 | + | 0.649806i | \(0.225150\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.39445 | 0.0668587 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.6333 | 1.32188 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.30278 | −0.157633 | −0.0788164 | − | 0.996889i | \(-0.525114\pi\) | ||||
−0.0788164 | + | 0.996889i | \(0.525114\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.4222 | 0.875265 | 0.437633 | − | 0.899154i | \(-0.355817\pi\) | ||||
0.437633 | + | 0.899154i | \(0.355817\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.605551 | −0.0287059 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.5139 | −0.922975 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.2389 | 0.860745 | 0.430372 | − | 0.902651i | \(-0.358382\pi\) | ||||
0.430372 | + | 0.902651i | \(0.358382\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.1833 | −1.04457 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −36.7250 | −1.72549 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.9083 | 0.790938 | 0.395469 | − | 0.918479i | \(-0.370582\pi\) | ||||
0.395469 | + | 0.918479i | \(0.370582\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.2111 | 0.756669 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.21110 | 0.242705 | 0.121353 | − | 0.992609i | \(-0.461277\pi\) | ||||
0.121353 | + | 0.992609i | \(0.461277\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.5416 | −0.815229 | −0.407614 | − | 0.913154i | \(-0.633639\pi\) | ||||
−0.407614 | + | 0.913154i | \(0.633639\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.3028 | −0.477780 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.78890 | −0.129055 | −0.0645274 | − | 0.997916i | \(-0.520554\pi\) | ||||
−0.0645274 | + | 0.997916i | \(0.520554\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 72.0555 | 3.32014 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.81665 | 0.0835298 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −29.4500 | −1.35126 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 34.0278 | 1.55802 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.6972 | 0.945680 | 0.472840 | − | 0.881148i | \(-0.343229\pi\) | ||||
0.472840 | + | 0.881148i | \(0.343229\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.36669 | 0.199104 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.90833 | −0.177468 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.6333 | −1.34281 | −0.671407 | − | 0.741089i | \(-0.734310\pi\) | ||||
−0.671407 | + | 0.741089i | \(0.734310\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.605551 | −0.0273840 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.3028 | 1.54806 | 0.774031 | − | 0.633147i | \(-0.218237\pi\) | ||||
0.774031 | + | 0.633147i | \(0.218237\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.39445 | −0.0628028 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.23886 | 0.280416 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.00000 | −0.268597 | −0.134298 | − | 0.990941i | \(-0.542878\pi\) | ||||
−0.134298 | + | 0.990941i | \(0.542878\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −76.3583 | −3.41144 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.1194 | −1.61049 | −0.805243 | − | 0.592945i | \(-0.797965\pi\) | ||||
−0.805243 | + | 0.592945i | \(0.797965\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.97224 | 0.221262 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −41.7250 | −1.85307 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.6056 | −0.470083 | −0.235041 | − | 0.971985i | \(-0.575523\pi\) | ||||
−0.235041 | + | 0.971985i | \(0.575523\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 97.2666 | 4.29443 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.366692 | −0.0161584 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.0555 | 1.14592 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.5139 | 0.856564 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.3305 | 1.41643 | 0.708213 | − | 0.705999i | \(-0.249502\pi\) | ||||
0.708213 | + | 0.705999i | \(0.249502\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.0278 | 0.832026 | 0.416013 | − | 0.909359i | \(-0.363427\pi\) | ||||
0.416013 | + | 0.909359i | \(0.363427\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.3028 | 0.448796 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.78890 | −0.0777781 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 72.8444 | 3.16118 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.15559 | −0.223313 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.02776 | 0.217369 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 72.3583 | 3.12249 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.8167 | −0.765998 | −0.382999 | − | 0.923749i | \(-0.625109\pi\) | ||||
−0.382999 | + | 0.923749i | \(0.625109\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −71.4500 | −3.06621 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.605551 | 0.0259390 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.4500 | 1.08816 | 0.544081 | − | 0.839033i | \(-0.316878\pi\) | ||||
0.544081 | + | 0.839033i | \(0.316878\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.51388 | 0.235327 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.36669 | −0.356433 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.21110 | 0.306094 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.21110 | −0.136059 | −0.0680294 | − | 0.997683i | \(-0.521671\pi\) | ||||
−0.0680294 | + | 0.997683i | \(0.521671\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.422205 | 0.0178574 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.60555 | −0.363327 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.2389 | 0.768676 | 0.384338 | − | 0.923192i | \(-0.374430\pi\) | ||||
0.384338 | + | 0.923192i | \(0.374430\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.44996 | −0.0610003 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.4861 | −0.984589 | −0.492295 | − | 0.870429i | \(-0.663842\pi\) | ||||
−0.492295 | + | 0.870429i | \(0.663842\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.63331 | 0.403141 | 0.201571 | − | 0.979474i | \(-0.435395\pi\) | ||||
0.201571 | + | 0.979474i | \(0.435395\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 28.8167 | 1.20383 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.6056 | −0.942717 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.97224 | −0.123736 | −0.0618681 | − | 0.998084i | \(-0.519706\pi\) | ||||
−0.0618681 | + | 0.998084i | \(0.519706\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −41.6333 | −1.73022 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.2111 | −0.464316 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.44996 | 0.0599485 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.78890 | 0.115110 | 0.0575551 | − | 0.998342i | \(-0.481670\pi\) | ||||
0.0575551 | + | 0.998342i | \(0.481670\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 61.8167 | 2.54711 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 43.0278 | 1.76993 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.6333 | 1.38115 | 0.690577 | − | 0.723259i | \(-0.257357\pi\) | ||||
0.690577 | + | 0.723259i | \(0.257357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.9083 | 0.610157 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.5416 | 0.880167 | 0.440084 | − | 0.897957i | \(-0.354949\pi\) | ||||
0.440084 | + | 0.897957i | \(0.354949\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.78890 | −0.195343 | −0.0976716 | − | 0.995219i | \(-0.531139\pi\) | ||||
−0.0976716 | + | 0.995219i | \(0.531139\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 49.8444 | 2.02982 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.27502 | 0.0518369 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.9083 | 1.09218 | 0.546088 | − | 0.837728i | \(-0.316117\pi\) | ||||
0.546088 | + | 0.837728i | \(0.316117\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.05551 | 0.244980 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.9361 | 0.643652 | 0.321826 | − | 0.946799i | \(-0.395703\pi\) | ||||
0.321826 | + | 0.946799i | \(0.395703\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.51388 | −0.343313 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.60555 | −0.104896 | −0.0524478 | − | 0.998624i | \(-0.516702\pi\) | ||||
−0.0524478 | + | 0.998624i | \(0.516702\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.00000 | 0.321547 | 0.160774 | − | 0.986991i | \(-0.448601\pi\) | ||||
0.160774 | + | 0.986991i | \(0.448601\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 74.6611 | 2.99605 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.6333 | 0.945332 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −51.6333 | −2.06204 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.21110 | −0.287525 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.1194 | −0.482467 | −0.241233 | − | 0.970467i | \(-0.577552\pi\) | ||||
−0.241233 | + | 0.970467i | \(0.577552\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 29.8167 | 1.18511 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.09167 | −0.241741 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.8167 | −0.625697 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.4222 | −1.43859 | −0.719295 | − | 0.694704i | \(-0.755535\pi\) | ||||
−0.719295 | + | 0.694704i | \(0.755535\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.3305 | 0.486269 | 0.243134 | − | 0.969993i | \(-0.421824\pi\) | ||||
0.243134 | + | 0.969993i | \(0.421824\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.697224 | 0.0274532 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.6056 | 1.36048 | 0.680242 | − | 0.732987i | \(-0.261875\pi\) | ||||
0.680242 | + | 0.732987i | \(0.261875\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.00000 | 0.0782660 | 0.0391330 | − | 0.999234i | \(-0.487540\pi\) | ||||
0.0391330 | + | 0.999234i | \(0.487540\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.57779 | 0.217942 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −35.6972 | −1.39268 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.5416 | −1.81300 | −0.906502 | − | 0.422201i | \(-0.861258\pi\) | ||||
−0.906502 | + | 0.422201i | \(0.861258\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.6333 | 1.07481 | 0.537406 | − | 0.843324i | \(-0.319404\pi\) | ||||
0.537406 | + | 0.843324i | \(0.319404\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.00000 | −0.0776736 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.42221 | −0.248669 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −71.4500 | −2.76242 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.81665 | −0.0701311 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.8444 | 1.42025 | 0.710124 | − | 0.704077i | \(-0.248639\pi\) | ||||
0.710124 | + | 0.704077i | \(0.248639\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −79.5694 | −3.06263 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.0000 | −0.845529 | −0.422764 | − | 0.906240i | \(-0.638940\pi\) | ||||
−0.422764 | + | 0.906240i | \(0.638940\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −36.0278 | −1.38059 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.0278 | 0.957660 | 0.478830 | − | 0.877908i | \(-0.341061\pi\) | ||||
0.478830 | + | 0.877908i | \(0.341061\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.21110 | 0.160898 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −52.2389 | −1.99304 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.60555 | −0.0992636 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.697224 | −0.0265237 | −0.0132618 | − | 0.999912i | \(-0.504221\pi\) | ||||
−0.0132618 | + | 0.999912i | \(0.504221\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.90833 | −0.224116 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.51388 | 0.322486 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.00000 | −0.151294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.21110 | 0.121282 | 0.0606408 | − | 0.998160i | \(-0.480686\pi\) | ||||
0.0606408 | + | 0.998160i | \(0.480686\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −43.2666 | −1.63183 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.0000 | 0.376622 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.8167 | −1.72068 | −0.860340 | − | 0.509720i | \(-0.829749\pi\) | ||||
−0.860340 | + | 0.509720i | \(0.829749\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −47.4500 | −1.77951 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 47.4500 | 1.77702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.477718 | −0.0178656 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28.7250 | −1.07275 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.5139 | 0.765039 | 0.382519 | − | 0.923948i | \(-0.375057\pi\) | ||||
0.382519 | + | 0.923948i | \(0.375057\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.2111 | −0.379755 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.84441 | 0.254195 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.2666 | 1.38214 | 0.691071 | − | 0.722787i | \(-0.257139\pi\) | ||||
0.691071 | + | 0.722787i | \(0.257139\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 75.1749 | 2.78426 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.697224 | −0.0257878 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.6333 | −1.02066 | −0.510330 | − | 0.859979i | \(-0.670477\pi\) | ||||
−0.510330 | + | 0.859979i | \(0.670477\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.4222 | −0.604920 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.0917 | −0.518371 | −0.259185 | − | 0.965828i | \(-0.583454\pi\) | ||||
−0.259185 | + | 0.965828i | \(0.583454\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.0000 | −0.440831 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.6056 | −1.48967 | −0.744837 | − | 0.667247i | \(-0.767473\pi\) | ||||
−0.744837 | + | 0.667247i | \(0.767473\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.78890 | 0.0655401 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 41.2111 | 1.50784 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.7889 | −1.34245 | −0.671223 | − | 0.741256i | \(-0.734231\pi\) | ||||
−0.671223 | + | 0.741256i | \(0.734231\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −76.6611 | −2.79368 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.36669 | 0.122526 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.9083 | 1.23242 | 0.616210 | − | 0.787582i | \(-0.288667\pi\) | ||||
0.616210 | + | 0.787582i | \(0.288667\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −39.6333 | −1.43860 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.3944 | −1.42805 | −0.714024 | − | 0.700121i | \(-0.753129\pi\) | ||||
−0.714024 | + | 0.700121i | \(0.753129\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.39445 | −0.0865715 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.57779 | −0.201403 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.81665 | 0.353998 | 0.176999 | − | 0.984211i | \(-0.443361\pi\) | ||||
0.176999 | + | 0.984211i | \(0.443361\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.8167 | −0.929764 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −50.8444 | −1.82875 | −0.914373 | − | 0.404872i | \(-0.867316\pi\) | ||||
−0.914373 | + | 0.404872i | \(0.867316\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −50.5694 | −1.81651 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 51.0833 | 1.83025 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.21110 | 0.186468 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.6056 | −0.807856 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.60555 | −0.235762 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.4222 | −0.514096 | −0.257048 | − | 0.966399i | \(-0.582750\pi\) | ||||
−0.257048 | + | 0.966399i | \(0.582750\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.2111 | −0.755135 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.422205 | −0.0149929 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.30278 | −0.152604 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.2111 | −1.03471 | −0.517355 | − | 0.855771i | \(-0.673083\pi\) | ||||
−0.517355 | + | 0.855771i | \(0.673083\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.0000 | −0.353775 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.8167 | 0.558854 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.7611 | 0.415042 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.8167 | 0.697579 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.4500 | −0.683824 | −0.341912 | − | 0.939732i | \(-0.611075\pi\) | ||||
−0.341912 | + | 0.939732i | \(0.611075\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.3583 | −1.31183 | −0.655913 | − | 0.754836i | \(-0.727716\pi\) | ||||
−0.655913 | + | 0.754836i | \(0.727716\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 33.6333 | 1.17957 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.0555128 | 0.00194453 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.18335 | −0.146357 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.5778 | 0.404068 | 0.202034 | − | 0.979379i | \(-0.435245\pi\) | ||||
0.202034 | + | 0.979379i | \(0.435245\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.0278 | 1.08156 | 0.540780 | − | 0.841164i | \(-0.318129\pi\) | ||||
0.540780 | + | 0.841164i | \(0.318129\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 42.2389 | 1.47057 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.8444 | −1.35075 | −0.675376 | − | 0.737473i | \(-0.736019\pi\) | ||||
−0.675376 | + | 0.737473i | \(0.736019\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.6056 | 1.27136 | 0.635682 | − | 0.771951i | \(-0.280719\pi\) | ||||
0.635682 | + | 0.771951i | \(0.280719\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.4222 | −1.26347 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.00000 | 0.242245 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 167.019 | 5.77303 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.78890 | −0.234379 | −0.117189 | − | 0.993110i | \(-0.537388\pi\) | ||||
−0.117189 | + | 0.993110i | \(0.537388\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0555 | −0.932949 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −67.0555 | −2.30951 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.82506 | 0.131586 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −34.0278 | −1.16783 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.2111 | −1.13846 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.78890 | 0.163969 | 0.0819844 | − | 0.996634i | \(-0.473874\pi\) | ||||
0.0819844 | + | 0.996634i | \(0.473874\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.3667 | −0.491331 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.51388 | 0.188350 | 0.0941752 | − | 0.995556i | \(-0.469979\pi\) | ||||
0.0941752 | + | 0.995556i | \(0.469979\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.36669 | 0.0807505 | 0.0403753 | − | 0.999185i | \(-0.487145\pi\) | ||||
0.0403753 | + | 0.999185i | \(0.487145\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.9361 | −1.29136 | −0.645680 | − | 0.763608i | \(-0.723426\pi\) | ||||
−0.645680 | + | 0.763608i | \(0.723426\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.78890 | −0.0608243 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.30278 | 0.112168 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.6333 | 0.530324 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.81665 | −0.129322 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 102.083 | 3.45500 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.8167 | −0.939302 | −0.469651 | − | 0.882852i | \(-0.655620\pi\) | ||||
−0.469651 | + | 0.882852i | \(0.655620\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 65.4500 | 2.20757 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.1194 | −0.610459 | −0.305230 | − | 0.952279i | \(-0.598733\pi\) | ||||
−0.305230 | + | 0.952279i | \(0.598733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.2750 | 0.783267 | 0.391633 | − | 0.920121i | \(-0.371910\pi\) | ||||
0.391633 | + | 0.920121i | \(0.371910\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.21110 | −0.309628 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.7250 | 1.50172 | 0.750859 | − | 0.660463i | \(-0.229640\pi\) | ||||
0.750859 | + | 0.660463i | \(0.229640\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −77.6888 | −2.60267 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −60.0000 | −2.00782 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.63331 | −0.221727 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.21110 | −0.307550 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.3667 | −0.479156 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.30278 | 0.143346 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.55004 | 0.217731 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.4222 | −1.07656 | −0.538281 | − | 0.842766i | \(-0.680926\pi\) | ||||
−0.538281 | + | 0.842766i | \(0.680926\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −129.872 | −4.30759 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.4222 | 0.610355 | 0.305177 | − | 0.952296i | \(-0.401284\pi\) | ||||
0.305177 | + | 0.952296i | \(0.401284\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.5778 | −0.449359 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.697224 | −0.0230495 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.5139 | −0.940586 | −0.470293 | − | 0.882510i | \(-0.655852\pi\) | ||||
−0.470293 | + | 0.882510i | \(0.655852\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 85.8722 | 2.82958 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.21110 | 0.0398639 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.3944 | 1.16376 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.57779 | 0.314576 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.3028 | 0.928584 | 0.464292 | − | 0.885682i | \(-0.346309\pi\) | ||||
0.464292 | + | 0.885682i | \(0.346309\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −55.2389 | −1.80844 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.788897 | 0.0257997 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.7889 | 0.352458 | 0.176229 | − | 0.984349i | \(-0.443610\pi\) | ||||
0.176229 | + | 0.984349i | \(0.443610\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −88.2666 | −2.88047 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40.3305 | 1.31474 | 0.657369 | − | 0.753569i | \(-0.271669\pi\) | ||||
0.657369 | + | 0.753569i | \(0.271669\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.2111 | 1.27689 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.2389 | −0.982631 | −0.491315 | − | 0.870982i | \(-0.663484\pi\) | ||||
−0.491315 | + | 0.870982i | \(0.663484\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.73338 | 0.0887294 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.8167 | −0.577745 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.7527 | −1.35250 | −0.676252 | − | 0.736670i | \(-0.736397\pi\) | ||||
−0.676252 | + | 0.736670i | \(0.736397\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.64171 | −0.0854838 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.0000 | 0.387905 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 75.1472 | 2.42410 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −131.322 | −4.23180 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.81665 | 0.122862 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.6972 | −0.536947 | −0.268473 | − | 0.963287i | \(-0.586519\pi\) | ||||
−0.268473 | + | 0.963287i | \(0.586519\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.8167 | 0.636603 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.2389 | −0.970411 | −0.485206 | − | 0.874400i | \(-0.661255\pi\) | ||||
−0.485206 | + | 0.874400i | \(0.661255\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.81665 | 0.314385 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.51388 | −0.176405 | −0.0882023 | − | 0.996103i | \(-0.528112\pi\) | ||||
−0.0882023 | + | 0.996103i | \(0.528112\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.21110 | −0.166548 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.8167 | −0.504987 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.51388 | 0.112075 | 0.0560377 | − | 0.998429i | \(-0.482153\pi\) | ||||
0.0560377 | + | 0.998429i | \(0.482153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.94449 | −0.125682 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.21110 | −0.102107 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.00000 | 0.190596 | 0.0952981 | − | 0.995449i | \(-0.469620\pi\) | ||||
0.0952981 | + | 0.995449i | \(0.469620\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −108.083 | −3.42992 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.36669 | −0.0433271 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.0917 | −0.699650 | −0.349825 | − | 0.936815i | \(-0.613759\pi\) | ||||
−0.349825 | + | 0.936815i | \(0.613759\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −116.900 | −3.69855 |
(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 | 3332.2.a.n.1.2 | 2 | ||
7.6 | odd | 2 | 476.2.a.a.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 4284.2.a.p.1.1 | 2 | |||
28.27 | even | 2 | 1904.2.a.l.1.2 | 2 | |||
56.13 | odd | 2 | 7616.2.a.z.1.2 | 2 | |||
56.27 | even | 2 | 7616.2.a.m.1.1 | 2 | |||
119.118 | odd | 2 | 8092.2.a.n.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
476.2.a.a.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
1904.2.a.l.1.2 | 2 | 28.27 | even | 2 | |||
3332.2.a.n.1.2 | 2 | 1.1 | even | 1 | trivial | ||
4284.2.a.p.1.1 | 2 | 21.20 | even | 2 | |||
7616.2.a.m.1.1 | 2 | 56.27 | even | 2 | |||
7616.2.a.z.1.2 | 2 | 56.13 | odd | 2 | |||
8092.2.a.n.1.2 | 2 | 119.118 | odd | 2 |