Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 49 x^{14} + 130 x^{13} + 932 x^{12} - 2028 x^{11} - 8965 x^{10} + 14400 x^{9} + \cdots + 3888 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.45101\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.45101 | −1.09612 | −0.548062 | − | 0.836437i | \(-0.684634\pi\) | ||||
−0.548062 | + | 0.836437i | \(0.684634\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.23607 | 1.22312 | 0.611559 | − | 0.791199i | \(-0.290543\pi\) | ||||
0.611559 | + | 0.791199i | \(0.290543\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0433085 | 0.0130580 | 0.00652901 | − | 0.999979i | \(-0.497922\pi\) | ||||
0.00652901 | + | 0.999979i | \(0.497922\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.92153 | 1.08764 | 0.543818 | − | 0.839203i | \(-0.316978\pi\) | ||||
0.543818 | + | 0.839203i | \(0.316978\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.45101 | −0.632848 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.01799 | −1.45958 | −0.729788 | − | 0.683674i | \(-0.760381\pi\) | ||||
−0.729788 | + | 0.683674i | \(0.760381\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.13344 | −0.948275 | −0.474138 | − | 0.880451i | \(-0.657240\pi\) | ||||
−0.474138 | + | 0.880451i | \(0.657240\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.23607 | 0.706168 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00745 | 0.201489 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00117 | 0.359421 | 0.179711 | − | 0.983720i | \(-0.442484\pi\) | ||||
0.179711 | + | 0.983720i | \(0.442484\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.0433085 | 0.00753905 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.93163 | −1.34069 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.70187 | 0.608583 | 0.304291 | − | 0.952579i | \(-0.401580\pi\) | ||||
0.304291 | + | 0.952579i | \(0.401580\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.92153 | 0.627947 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.70980 | 1.51642 | 0.758208 | − | 0.652013i | \(-0.226075\pi\) | ||||
0.758208 | + | 0.652013i | \(0.226075\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.70508 | 1.48001 | 0.740005 | − | 0.672601i | \(-0.234823\pi\) | ||||
0.740005 | + | 0.672601i | \(0.234823\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.45101 | −0.365375 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.20139 | −0.321106 | −0.160553 | − | 0.987027i | \(-0.551328\pi\) | ||||
−0.160553 | + | 0.987027i | \(0.551328\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.47213 | 0.496018 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.01799 | −0.842687 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.20613 | −1.12720 | −0.563600 | − | 0.826048i | \(-0.690584\pi\) | ||||
−0.563600 | + | 0.826048i | \(0.690584\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.106150 | −0.0143132 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.13344 | −0.547487 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.1275 | 1.44868 | 0.724339 | − | 0.689444i | \(-0.242145\pi\) | ||||
0.724339 | + | 0.689444i | \(0.242145\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.07501 | 0.521751 | 0.260876 | − | 0.965372i | \(-0.415989\pi\) | ||||
0.260876 | + | 0.965372i | \(0.415989\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.23607 | 0.407706 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.61171 | −1.19219 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.00749010 | 0.000915062 0 | 0.000457531 | − | 1.00000i | \(-0.499854\pi\) | ||||
0.000457531 | 1.00000i | \(0.499854\pi\) | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.37725 | 1.11287 | 0.556437 | − | 0.830889i | \(-0.312168\pi\) | ||||
0.556437 | + | 0.830889i | \(0.312168\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.48676 | −0.408095 | −0.204047 | − | 0.978961i | \(-0.565410\pi\) | ||||
−0.204047 | + | 0.978961i | \(0.565410\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00745 | 0.116330 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.140149 | 0.0159715 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.80589 | 0.540705 | 0.270353 | − | 0.962761i | \(-0.412860\pi\) | ||||
0.270353 | + | 0.962761i | \(0.412860\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.3903 | −1.57954 | −0.789771 | − | 0.613402i | \(-0.789801\pi\) | ||||
−0.789771 | + | 0.613402i | \(0.789801\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.7501 | 1.59988 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.96492 | 0.314281 | 0.157141 | − | 0.987576i | \(-0.449772\pi\) | ||||
0.157141 | + | 0.987576i | \(0.449772\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.6903 | 1.33031 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.00117 | 0.207512 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.1311 | 1.03943 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.26962 | 0.331979 | 0.165990 | − | 0.986127i | \(-0.446918\pi\) | ||||
0.165990 | + | 0.986127i | \(0.446918\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0433085 | 0.00435267 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.7449 | 1.26816 | 0.634082 | − | 0.773266i | \(-0.281378\pi\) | ||||
0.634082 | + | 0.773266i | \(0.281378\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.23760 | −0.417544 | −0.208772 | − | 0.977964i | \(-0.566947\pi\) | ||||
−0.208772 | + | 0.977964i | \(0.566947\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.93163 | −0.774048 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.6453 | −1.22247 | −0.611236 | − | 0.791448i | \(-0.709327\pi\) | ||||
−0.611236 | + | 0.791448i | \(0.709327\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.3055 | 1.08287 | 0.541433 | − | 0.840744i | \(-0.317882\pi\) | ||||
0.541433 | + | 0.840744i | \(0.317882\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.70187 | 0.351366 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.48791 | 0.234042 | 0.117021 | − | 0.993129i | \(-0.462665\pi\) | ||||
0.117021 | + | 0.993129i | \(0.462665\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.45101 | −0.228558 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.92153 | 0.362546 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −19.4746 | −1.78523 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9981 | −0.999829 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.70980 | 0.875503 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.78578 | 0.875267 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.5282 | 1.28917 | 0.644586 | − | 0.764532i | \(-0.277030\pi\) | ||||
0.644586 | + | 0.764532i | \(0.277030\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.70508 | 0.854484 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.41017 | −0.472688 | −0.236344 | − | 0.971669i | \(-0.575949\pi\) | ||||
−0.236344 | + | 0.971669i | \(0.575949\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.3761 | −1.15985 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.45101 | −0.210949 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.81125 | 0.154745 | 0.0773727 | − | 0.997002i | \(-0.475347\pi\) | ||||
0.0773727 | + | 0.997002i | \(0.475347\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.7711 | 1.33769 | 0.668844 | − | 0.743403i | \(-0.266789\pi\) | ||||
0.668844 | + | 0.743403i | \(0.266789\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.20139 | −0.185390 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.169836 | 0.0142024 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.45101 | 0.203545 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.47213 | 0.286376 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.6325 | 1.60836 | 0.804179 | − | 0.594387i | \(-0.202605\pi\) | ||||
0.804179 | + | 0.594387i | \(0.202605\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.8481 | 1.45245 | 0.726227 | − | 0.687455i | \(-0.241272\pi\) | ||||
0.726227 | + | 0.687455i | \(0.241272\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.01799 | −0.486525 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.90489 | −0.393970 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.30848 | −0.742898 | −0.371449 | − | 0.928453i | \(-0.621139\pi\) | ||||
−0.371449 | + | 0.928453i | \(0.621139\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.20613 | −0.650789 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.23607 | 0.255038 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.99734 | 0.234770 | 0.117385 | − | 0.993086i | \(-0.462549\pi\) | ||||
0.117385 | + | 0.993086i | \(0.462549\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.106150 | −0.00826374 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.321484 | −0.0248771 | −0.0124386 | − | 0.999923i | \(-0.503959\pi\) | ||||
−0.0124386 | + | 0.999923i | \(0.503959\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.37840 | 0.182954 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.13344 | −0.316092 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.6090 | −1.79496 | −0.897479 | − | 0.441058i | \(-0.854603\pi\) | ||||
−0.897479 | + | 0.441058i | \(0.854603\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.26017 | 0.246445 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.1275 | 0.836394 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.13868 | −0.533570 | −0.266785 | − | 0.963756i | \(-0.585961\pi\) | ||||
−0.266785 | + | 0.963756i | \(0.585961\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.12027 | 0.231928 | 0.115964 | − | 0.993253i | \(-0.463004\pi\) | ||||
0.115964 | + | 0.993253i | \(0.463004\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.07501 | 0.301233 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.07331 | −0.667083 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.260630 | −0.0190592 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.23607 | 0.235389 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.1136 | −1.02122 | −0.510611 | − | 0.859812i | \(-0.670581\pi\) | ||||
−0.510611 | + | 0.859812i | \(0.670581\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.7712 | −1.20722 | −0.603608 | − | 0.797281i | \(-0.706271\pi\) | ||||
−0.603608 | + | 0.797281i | \(0.706271\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.61171 | −0.688309 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.6105 | 0.755968 | 0.377984 | − | 0.925812i | \(-0.376617\pi\) | ||||
0.377984 | + | 0.925812i | \(0.376617\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.3722 | 1.16059 | 0.580296 | − | 0.814405i | \(-0.302937\pi\) | ||||
0.580296 | + | 0.814405i | \(0.302937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.00749010 | 0.000528311 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.23607 | −0.227127 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −23.7988 | −1.66218 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.179013 | −0.0123826 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.8071 | 1.08820 | 0.544102 | − | 0.839019i | \(-0.316871\pi\) | ||||
0.544102 | + | 0.839019i | \(0.316871\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.37725 | 0.642519 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −23.7872 | −1.62228 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.47593 | 0.439614 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.48676 | −0.235614 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.5997 | −1.58749 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.72822 | 0.450555 | 0.225277 | − | 0.974295i | \(-0.427671\pi\) | ||||
0.225277 | + | 0.974295i | \(0.427671\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00745 | 0.0671632 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.94100 | 0.394318 | 0.197159 | − | 0.980372i | \(-0.436828\pi\) | ||||
0.197159 | + | 0.980372i | \(0.436828\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.95543 | 0.129219 | 0.0646094 | − | 0.997911i | \(-0.479420\pi\) | ||||
0.0646094 | + | 0.997911i | \(0.479420\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.140149 | 0.00922115 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.50808 | 0.229822 | 0.114911 | − | 0.993376i | \(-0.463342\pi\) | ||||
0.114911 | + | 0.993376i | \(0.463342\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.39563 | 0.351972 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.80589 | 0.312176 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.3546 | 1.18726 | 0.593632 | − | 0.804737i | \(-0.297694\pi\) | ||||
0.593632 | + | 0.804737i | \(0.297694\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.4205 | −1.44423 | −0.722115 | − | 0.691773i | \(-0.756830\pi\) | ||||
−0.722115 | + | 0.691773i | \(0.756830\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.51022 | −0.543698 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.2094 | −1.03138 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.3903 | −0.911949 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.2027 | 1.65390 | 0.826949 | − | 0.562276i | \(-0.190074\pi\) | ||||
0.826949 | + | 0.562276i | \(0.190074\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0433085 | 0.00272278 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.7501 | 0.923690 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.42715 | 0.525671 | 0.262836 | − | 0.964841i | \(-0.415342\pi\) | ||||
0.262836 | + | 0.964841i | \(0.415342\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.9795 | 0.744369 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.14464 | 0.255570 | 0.127785 | − | 0.991802i | \(-0.459213\pi\) | ||||
0.127785 | + | 0.991802i | \(0.459213\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.1133 | 1.23555 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.96492 | 0.181450 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.8824 | −1.63905 | −0.819526 | − | 0.573043i | \(-0.805763\pi\) | ||||
−0.819526 | + | 0.573043i | \(0.805763\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.17448 | 0.132090 | 0.0660452 | − | 0.997817i | \(-0.478962\pi\) | ||||
0.0660452 | + | 0.997817i | \(0.478962\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.6903 | 0.768054 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0436311 | 0.00263105 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.82094 | 0.529999 | 0.265000 | − | 0.964249i | \(-0.414628\pi\) | ||||
0.265000 | + | 0.964249i | \(0.414628\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.00117 | 0.119807 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.1754 | −0.726325 | −0.363163 | − | 0.931726i | \(-0.618303\pi\) | ||||
−0.363163 | + | 0.931726i | \(0.618303\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.7446 | 0.638699 | 0.319350 | − | 0.947637i | \(-0.396536\pi\) | ||||
0.319350 | + | 0.947637i | \(0.396536\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.1311 | 0.600114 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 31.4216 | 1.85476 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.2162 | 1.13036 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.26962 | 0.191668 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.55893 | −0.500018 | −0.250009 | − | 0.968243i | \(-0.580434\pi\) | ||||
−0.250009 | + | 0.968243i | \(0.580434\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.2736 | −1.58793 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.0433085 | 0.00251302 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.92153 | 0.226788 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.4063 | 1.81023 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.7449 | 0.732175 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.98788 | −0.571904 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.0895 | 0.632910 | 0.316455 | − | 0.948607i | \(-0.397507\pi\) | ||||
0.316455 | + | 0.948607i | \(0.397507\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.23760 | −0.241069 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.2362 | −1.31760 | −0.658802 | − | 0.752316i | \(-0.728936\pi\) | ||||
−0.658802 | + | 0.752316i | \(0.728936\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.0018 | −1.52623 | −0.763117 | − | 0.646261i | \(-0.776332\pi\) | ||||
−0.763117 | + | 0.646261i | \(0.776332\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.93163 | −0.446897 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.56947 | 0.200481 | 0.100241 | − | 0.994963i | \(-0.468039\pi\) | ||||
0.100241 | + | 0.994963i | \(0.468039\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0433085 | −0.00242481 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.6453 | −0.705794 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.8750 | 1.38408 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.95073 | 0.219147 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.3055 | 0.625194 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.12385 | −0.392750 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.4725 | 1.45506 | 0.727530 | − | 0.686076i | \(-0.240668\pi\) | ||||
0.727530 | + | 0.686076i | \(0.240668\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.70187 | 0.202861 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.0183583 | −0.00100302 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.92885 | 0.322965 | 0.161482 | − | 0.986876i | \(-0.448372\pi\) | ||||
0.161482 | + | 0.986876i | \(0.448372\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.48791 | 0.135124 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.0866678 | 0.00469333 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4164 | −0.616429 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.45101 | −0.131958 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.8239 | 1.43998 | 0.719990 | − | 0.693984i | \(-0.244146\pi\) | ||||
0.719990 | + | 0.693984i | \(0.244146\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.0061 | 0.803258 | 0.401629 | − | 0.915802i | \(-0.368444\pi\) | ||||
0.401629 | + | 0.915802i | \(0.368444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.92153 | 0.209316 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.89223 | −0.100713 | −0.0503567 | − | 0.998731i | \(-0.516036\pi\) | ||||
−0.0503567 | + | 0.998731i | \(0.516036\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.9837 | −1.21985 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.4746 | −1.03071 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.78277 | −0.199647 | −0.0998234 | − | 0.995005i | \(-0.531828\pi\) | ||||
−0.0998234 | + | 0.995005i | \(0.531828\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.91471 | −0.100774 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.9981 | −0.577252 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.54609 | 0.447323 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.2247 | 0.794724 | 0.397362 | − | 0.917662i | \(-0.369926\pi\) | ||||
0.397362 | + | 0.917662i | \(0.369926\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.70980 | 0.505472 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.5556 | −1.37870 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.64921 | 0.137171 | 0.0685854 | − | 0.997645i | \(-0.478151\pi\) | ||||
0.0685854 | + | 0.997645i | \(0.478151\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.78578 | 0.505336 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.92153 | −0.201969 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.7427 | 1.21958 | 0.609790 | − | 0.792563i | \(-0.291254\pi\) | ||||
0.609790 | + | 0.792563i | \(0.291254\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.5282 | 0.744304 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.9829 | 1.12328 | 0.561638 | − | 0.827383i | \(-0.310172\pi\) | ||||
0.561638 | + | 0.827383i | \(0.310172\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.343507 | −0.0175068 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.70508 | 0.493337 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.3962 | −1.08483 | −0.542416 | − | 0.840110i | \(-0.682490\pi\) | ||||
−0.542416 | + | 0.840110i | \(0.682490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.01799 | −0.304343 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.41017 | −0.272907 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.7793 | −0.592680 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.2187 | 1.11512 | 0.557561 | − | 0.830136i | \(-0.311737\pi\) | ||||
0.557561 | + | 0.830136i | \(0.311737\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.3761 | −0.669641 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.5530 | 0.676804 | 0.338402 | − | 0.941002i | \(-0.390114\pi\) | ||||
0.338402 | + | 0.941002i | \(0.390114\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.84766 | 0.390920 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.45101 | −0.121792 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.160322 | 0.00794689 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.7829 | 1.37378 | 0.686888 | − | 0.726763i | \(-0.258976\pi\) | ||||
0.686888 | + | 0.726763i | \(0.258976\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.81125 | 0.0893423 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.0093 | 1.77190 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 35.2708 | 1.73137 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.7711 | 0.772315 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.04791 | 0.246606 | 0.123303 | − | 0.992369i | \(-0.460651\pi\) | ||||
0.123303 | + | 0.992369i | \(0.460651\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.9103 | −1.11658 | −0.558289 | − | 0.829646i | \(-0.688542\pi\) | ||||
−0.558289 | + | 0.829646i | \(0.688542\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.20139 | −0.107035 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.06280 | −0.294089 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.1870 | 0.638163 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.169836 | 0.00819975 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.95827 | −0.190663 | −0.0953315 | − | 0.995446i | \(-0.530391\pi\) | ||||
−0.0953315 | + | 0.995446i | \(0.530391\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.3630 | −0.546073 | −0.273037 | − | 0.962004i | \(-0.588028\pi\) | ||||
−0.273037 | + | 0.962004i | \(0.588028\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.45101 | 0.117517 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.13344 | −0.197729 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.41117 | −0.115079 | −0.0575394 | − | 0.998343i | \(-0.518325\pi\) | ||||
−0.0575394 | + | 0.998343i | \(0.518325\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.47213 | 0.165339 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.17519 | 0.0558349 | 0.0279174 | − | 0.999610i | \(-0.491112\pi\) | ||||
0.0279174 | + | 0.999610i | \(0.491112\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.26705 | −0.344491 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.6325 | 0.928586 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.5786 | 1.15993 | 0.579967 | − | 0.814640i | \(-0.303065\pi\) | ||||
0.579967 | + | 0.814640i | \(0.303065\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.420517 | 0.0198014 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.8481 | 0.838575 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −31.1041 | −1.45818 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.45575 | 0.255209 | 0.127605 | − | 0.991825i | \(-0.459271\pi\) | ||||
0.127605 | + | 0.991825i | \(0.459271\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.01799 | −0.280896 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.9263 | 0.881487 | 0.440744 | − | 0.897633i | \(-0.354715\pi\) | ||||
0.440744 | + | 0.897633i | \(0.354715\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.985702 | −0.0458094 | −0.0229047 | − | 0.999738i | \(-0.507291\pi\) | ||||
−0.0229047 | + | 0.999738i | \(0.507291\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.90489 | −0.227459 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.85204 | 0.455898 | 0.227949 | − | 0.973673i | \(-0.426798\pi\) | ||||
0.227949 | + | 0.973673i | \(0.426798\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0242385 | 0.00111923 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.30848 | −0.428912 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.420313 | 0.0193260 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.16422 | −0.191067 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.20613 | −0.375733 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.9225 | −0.544754 | −0.272377 | − | 0.962191i | \(-0.587810\pi\) | ||||
−0.272377 | + | 0.962191i | \(0.587810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.5170 | 0.661917 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.23607 | 0.147246 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.01386 | −0.363891 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.45791 | 0.247322 | 0.123661 | − | 0.992325i | \(-0.460537\pi\) | ||||
0.123661 | + | 0.992325i | \(0.460537\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.99734 | 0.135544 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.6192 | −1.06592 | −0.532960 | − | 0.846140i | \(-0.678920\pi\) | ||||
−0.532960 | + | 0.846140i | \(0.678920\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.01799 | 0.271036 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.106150 | −0.00477107 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.3454 | 1.36118 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.0659 | −1.21164 | −0.605819 | − | 0.795603i | \(-0.707154\pi\) | ||||
−0.605819 | + | 0.795603i | \(0.707154\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.321484 | −0.0143628 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.8800 | 0.975580 | 0.487790 | − | 0.872961i | \(-0.337803\pi\) | ||||
0.487790 | + | 0.872961i | \(0.337803\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.2378 | −1.39007 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.37840 | 0.105628 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.7019 | 1.58246 | 0.791230 | − | 0.611519i | \(-0.209441\pi\) | ||||
0.791230 | + | 0.611519i | \(0.209441\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.2834 | −0.499148 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.13344 | −0.182496 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.3864 | 0.457680 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.0953390 | −0.00419300 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.6090 | −1.03632 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.9027 | 1.35387 | 0.676936 | − | 0.736042i | \(-0.263307\pi\) | ||||
0.676936 | + | 0.736042i | \(0.263307\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.83309 | 0.429971 | 0.214985 | − | 0.976617i | \(-0.431030\pi\) | ||||
0.214985 | + | 0.976617i | \(0.431030\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.26017 | 0.142285 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.0430 | −0.524602 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.1275 | 0.482893 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38.0773 | 1.64931 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30.9939 | 1.33998 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.13868 | −0.308057 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.150373 | 0.00647702 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.66173 | −0.286410 | −0.143205 | − | 0.989693i | \(-0.545741\pi\) | ||||
−0.143205 | + | 0.989693i | \(0.545741\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.12027 | 0.133904 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −27.7098 | −1.18696 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.3634 | −1.38376 | −0.691879 | − | 0.722013i | \(-0.743217\pi\) | ||||
−0.691879 | + | 0.722013i | \(0.743217\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.07501 | 0.173917 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.13344 | 0.176090 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.5522 | 0.661346 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.07331 | −0.385140 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.1353 | 1.82770 | 0.913850 | − | 0.406052i | \(-0.133095\pi\) | ||||
0.913850 | + | 0.406052i | \(0.133095\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.0588 | 1.60971 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.260630 | −0.0110038 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.3550 | −0.815717 | −0.407858 | − | 0.913045i | \(-0.633724\pi\) | ||||
−0.407858 | + | 0.913045i | \(0.633724\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.09788 | −0.256540 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.23607 | 0.135902 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.73354 | 0.0726736 | 0.0363368 | − | 0.999340i | \(-0.488431\pi\) | ||||
0.0363368 | + | 0.999340i | \(0.488431\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.9638 | 0.751762 | 0.375881 | − | 0.926668i | \(-0.377340\pi\) | ||||
0.375881 | + | 0.926668i | \(0.377340\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.1136 | −0.589603 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00745 | 0.0420135 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.9094 | −1.28677 | −0.643387 | − | 0.765541i | \(-0.722471\pi\) | ||||
−0.643387 | + | 0.765541i | \(0.722471\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.7712 | −0.696987 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −46.5680 | −1.93197 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.355396 | −0.0147190 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.61171 | −0.397395 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.79515 | −0.280466 | −0.140233 | − | 0.990119i | \(-0.544785\pi\) | ||||
−0.140233 | + | 0.990119i | \(0.544785\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.27172 | −0.340830 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.6105 | 0.436459 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.95477 | −0.367728 | −0.183864 | − | 0.982952i | \(-0.558861\pi\) | ||||
−0.183864 | + | 0.982952i | \(0.558861\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 47.7324 | 1.95684 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.3722 | 0.670069 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.8233 | 1.34112 | 0.670562 | − | 0.741854i | \(-0.266053\pi\) | ||||
0.670562 | + | 0.741854i | \(0.266053\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.6404 | 1.86171 | 0.930855 | − | 0.365388i | \(-0.119064\pi\) | ||||
0.930855 | + | 0.365388i | \(0.119064\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.00749010 | 0.000305021 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 26.9565 | 1.09594 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.0597 | 1.09832 | 0.549159 | − | 0.835718i | \(-0.314948\pi\) | ||||
0.549159 | + | 0.835718i | \(0.314948\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.23607 | −0.131132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.63282 | −0.349246 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.03264 | 0.122487 | 0.0612435 | − | 0.998123i | \(-0.480493\pi\) | ||||
0.0612435 | + | 0.998123i | \(0.480493\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −23.7988 | −0.959661 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.4944 | 0.986106 | 0.493053 | − | 0.869999i | \(-0.335881\pi\) | ||||
0.493053 | + | 0.869999i | \(0.335881\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.27879 | −0.332753 | −0.166376 | − | 0.986062i | \(-0.553207\pi\) | ||||
−0.166376 | + | 0.986062i | \(0.553207\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.59469 | 0.384403 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0223 | −1.16089 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.179013 | −0.00714909 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.2778 | −0.888273 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.6197 | −1.25876 | −0.629381 | − | 0.777097i | \(-0.716691\pi\) | ||||
−0.629381 | + | 0.777097i | \(0.716691\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.8071 | 0.628274 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −35.6088 | −1.41309 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.6161 | 0.539488 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.37725 | 0.370958 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.7088 | 0.422971 | 0.211486 | − | 0.977381i | \(-0.432170\pi\) | ||||
0.211486 | + | 0.977381i | \(0.432170\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.2129 | −0.994300 | −0.497150 | − | 0.867664i | \(-0.665620\pi\) | ||||
−0.497150 | + | 0.867664i | \(0.665620\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.7872 | −0.936621 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.0045 | 0.865085 | 0.432542 | − | 0.901614i | \(-0.357617\pi\) | ||||
0.432542 | + | 0.901614i | \(0.357617\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.481916 | 0.0189169 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.47593 | 0.253812 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.3374 | −0.913263 | −0.456631 | − | 0.889656i | \(-0.650944\pi\) | ||||
−0.456631 | + | 0.889656i | \(0.650944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.2604 | 0.518125 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.48676 | −0.136032 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.7470 | 0.457597 | 0.228799 | − | 0.973474i | \(-0.426520\pi\) | ||||
0.228799 | + | 0.973474i | \(0.426520\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.6798 | −0.532082 | −0.266041 | − | 0.963962i | \(-0.585716\pi\) | ||||
−0.266041 | + | 0.963962i | \(0.585716\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −23.5997 | −0.916537 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 32.7849 | 1.27134 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.72822 | 0.260128 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.176483 | 0.00681304 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.7418 | −0.876630 | −0.438315 | − | 0.898821i | \(-0.644425\pi\) | ||||
−0.438315 | + | 0.898821i | \(0.644425\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00745 | 0.0387767 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.6704 | −0.948161 | −0.474080 | − | 0.880482i | \(-0.657219\pi\) | ||||
−0.474080 | + | 0.880482i | \(0.657219\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.5807 | 0.406050 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.94100 | 0.227660 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.8716 | 1.21953 | 0.609767 | − | 0.792581i | \(-0.291263\pi\) | ||||
0.609767 | + | 0.792581i | \(0.291263\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.43939 | −0.169620 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.95543 | 0.0746045 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −32.1806 | −1.22598 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.8968 | −0.642784 | −0.321392 | − | 0.946946i | \(-0.604151\pi\) | ||||
−0.321392 | + | 0.946946i | \(0.604151\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.140149 | 0.00532383 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −38.6552 | −1.46627 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −58.4334 | −2.21332 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.50808 | 0.132688 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.5682 | −1.38116 | −0.690580 | − | 0.723256i | \(-0.742645\pi\) | ||||
−0.690580 | + | 0.723256i | \(0.742645\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.3014 | −0.577104 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.39563 | 0.203211 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 41.2433 | 1.55111 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.1769 | 0.607538 | 0.303769 | − | 0.952746i | \(-0.401755\pi\) | ||||
0.303769 | + | 0.952746i | \(0.401755\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.80589 | 0.180235 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.00117 | 0.0749445 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.416269 | −0.0155676 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.3546 | 0.685467 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.9437 | −1.52694 | −0.763472 | − | 0.645841i | \(-0.776507\pi\) | ||||
−0.763472 | + | 0.645841i | \(0.776507\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.7132 | −0.510705 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.4205 | −0.833827 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.00745 | −0.0374157 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.01933 | −0.111981 | −0.0559904 | − | 0.998431i | \(-0.517832\pi\) | ||||
−0.0559904 | + | 0.998431i | \(0.517832\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −58.4050 | −2.16019 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.34400 | −0.160449 | −0.0802247 | − | 0.996777i | \(-0.525564\pi\) | ||||
−0.0802247 | + | 0.996777i | \(0.525564\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.51022 | −0.313904 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.000324386 0 | 1.19489e−5 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.6178 | −0.942365 | −0.471182 | − | 0.882036i | \(-0.656173\pi\) | ||||
−0.471182 | + | 0.882036i | \(0.656173\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.2094 | −0.595467 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.2924 | −0.377592 | −0.188796 | − | 0.982016i | \(-0.560458\pi\) | ||||
−0.188796 | + | 0.982016i | \(0.560458\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −48.1195 | −1.76296 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.3903 | −0.526514 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −40.9212 | −1.49523 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.1428 | 0.990457 | 0.495228 | − | 0.868763i | \(-0.335084\pi\) | ||||
0.495228 | + | 0.868763i | \(0.335084\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.2027 | 0.954879 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −43.7458 | −1.59207 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.4659 | −0.889227 | −0.444613 | − | 0.895723i | \(-0.646659\pi\) | ||||
−0.444613 | + | 0.895723i | \(0.646659\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0433085 | 0.00157200 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.0747 | −0.691459 | −0.345729 | − | 0.938334i | \(-0.612369\pi\) | ||||
−0.345729 | + | 0.938334i | \(0.612369\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.5852 | 1.32447 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.7501 | 0.533292 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 43.6368 | 1.57564 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.9271 | −0.430101 | −0.215050 | − | 0.976603i | \(-0.568992\pi\) | ||||
−0.215050 | + | 0.976603i | \(0.568992\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.42715 | 0.303496 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.25365 | 0.152993 | 0.0764966 | − | 0.997070i | \(-0.475627\pi\) | ||||
0.0764966 | + | 0.997070i | \(0.475627\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.01608 | 0.0724196 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.9795 | 0.429762 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −40.1348 | −1.43798 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.406115 | 0.0145319 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.8152 | 0.814309 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.7249 | −1.20216 | −0.601081 | − | 0.799188i | \(-0.705263\pi\) | ||||
−0.601081 | + | 0.799188i | \(0.705263\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.14464 | 0.147553 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.05103 | 0.286262 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.9803 | 0.567476 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.1133 | 0.713346 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.2192 | 0.539090 | 0.269545 | − | 0.962988i | \(-0.413127\pi\) | ||||
0.269545 | + | 0.962988i | \(0.413127\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.2479 | 0.468678 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.96492 | 0.104760 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.151007 | −0.00532891 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.93163 | −0.279553 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.8824 | −0.946307 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.6184 | −0.478799 | −0.239399 | − | 0.970921i | \(-0.576951\pi\) | ||||
−0.239399 | + | 0.970921i | \(0.576951\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.8818 | −0.803487 | −0.401743 | − | 0.915752i | \(-0.631596\pi\) | ||||
−0.401743 | + | 0.915752i | \(0.631596\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.17448 | 0.0762624 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.34651 | −0.257337 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.1153 | −1.40346 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.6903 | 0.443436 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.65639 | −0.232310 | −0.116155 | − | 0.993231i | \(-0.537057\pi\) | ||||
−0.116155 | + | 0.993231i | \(0.537057\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.1354 | −0.980739 | −0.490369 | − | 0.871515i | \(-0.663138\pi\) | ||||
−0.490369 | + | 0.871515i | \(0.663138\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.0436311 | 0.00151904 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.959061 | 0.0333498 | 0.0166749 | − | 0.999861i | \(-0.494692\pi\) | ||||
0.0166749 | + | 0.999861i | \(0.494692\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.49176 | 0.225468 | 0.112734 | − | 0.993625i | \(-0.464039\pi\) | ||||
0.112734 | + | 0.993625i | \(0.464039\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.82094 | 0.305995 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.8952 | −0.723976 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.787959 | 0.0272685 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.00117 | 0.0691706 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.7495 | −1.33778 | −0.668890 | − | 0.743362i | \(-0.733230\pi\) | ||||
−0.668890 | + | 0.743362i | \(0.733230\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.1754 | −0.419344 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.82948 | −0.200540 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35.5907 | −1.22291 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.7446 | 0.368753 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.70187 | 0.126898 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.01211 | −0.274329 | −0.137165 | − | 0.990548i | \(-0.543799\pi\) | ||||
−0.137165 | + | 0.990548i | \(0.543799\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.1311 | 0.346476 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.1595 | −0.586157 | −0.293078 | − | 0.956088i | \(-0.594680\pi\) | ||||
−0.293078 | + | 0.956088i | \(0.594680\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.4425 | 0.629251 | 0.314626 | − | 0.949216i | \(-0.398121\pi\) | ||||
0.314626 | + | 0.949216i | \(0.398121\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.4216 | 1.07084 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −56.5433 | −1.92476 | −0.962378 | − | 0.271713i | \(-0.912410\pi\) | ||||
−0.962378 | + | 0.271713i | \(0.912410\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 57.8658 | 1.96750 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.2162 | 0.652615 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.208136 | 0.00706054 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0293727 | 0.000995255 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.26962 | 0.110660 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.6675 | 1.07056 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.9689 | 1.61979 | 0.809897 | − | 0.586572i | \(-0.199523\pi\) | ||||
0.809897 | + | 0.586572i | \(0.199523\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.55893 | −0.288686 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.8070 | 0.667315 | 0.333658 | − | 0.942694i | \(-0.391717\pi\) | ||||
0.333658 | + | 0.942694i | \(0.391717\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.11055 | 0.171984 | 0.0859918 | − | 0.996296i | \(-0.472594\pi\) | ||||
0.0859918 | + | 0.996296i | \(0.472594\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.2736 | −0.916793 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.5325 | −1.22664 | −0.613321 | − | 0.789834i | \(-0.710167\pi\) | ||||
−0.613321 | + | 0.789834i | \(0.710167\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 47.0143 | 1.57681 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.0433085 | 0.00145089 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.09930 | 0.304497 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.4970 | 0.584860 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.92153 | 0.130936 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.00117 | −0.0667428 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 49.3844 | 1.64523 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 31.4063 | 1.04514 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.64781 | −0.254222 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.4816 | 1.31097 | 0.655483 | − | 0.755210i | \(-0.272465\pi\) | ||||
0.655483 | + | 0.755210i | \(0.272465\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.7449 | 0.422721 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.5180 | −0.779186 | −0.389593 | − | 0.920987i | \(-0.627384\pi\) | ||||
−0.389593 | + | 0.920987i | \(0.627384\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.623223 | −0.0206257 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.98788 | −0.330189 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.5077 | −0.578154 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.1970 | −1.58987 | −0.794937 | − | 0.606692i | \(-0.792496\pi\) | ||||
−0.794937 | + | 0.606692i | \(0.792496\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.0895 | 0.365411 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.7732 | 1.21040 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.72943 | 0.122623 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.23760 | −0.139181 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.2944 | 0.501793 | 0.250896 | − | 0.968014i | \(-0.419275\pi\) | ||||
0.250896 | + | 0.968014i | \(0.419275\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.3518 | −0.470362 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.2362 | −0.760719 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.638807 | 0.0208912 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.91415 | 0.193207 | 0.0966034 | − | 0.995323i | \(-0.469202\pi\) | ||||
0.0966034 | + | 0.995323i | \(0.469202\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.0018 | −0.881171 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.8328 | 1.16812 | 0.584058 | − | 0.811712i | \(-0.301464\pi\) | ||||
0.584058 | + | 0.811712i | \(0.301464\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.70980 | 0.316195 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.93163 | −0.258016 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.4015 | 1.41036 | 0.705180 | − | 0.709028i | \(-0.250866\pi\) | ||||
0.705180 | + | 0.709028i | \(0.250866\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.6734 | −0.443859 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.56947 | 0.115748 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.9380 | 0.386711 | 0.193356 | − | 0.981129i | \(-0.438063\pi\) | ||||
0.193356 | + | 0.981129i | \(0.438063\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.5925 | 1.11939 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.0433085 | −0.00139997 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.86132 | 0.189272 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.9953 | −0.870816 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.6453 | −0.407491 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 41.1064 | 1.32326 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.0916 | 1.38573 | 0.692866 | − | 0.721066i | \(-0.256348\pi\) | ||||
0.692866 | + | 0.721066i | \(0.256348\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 24.8750 | 0.799099 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.6354 | −0.726403 | −0.363202 | − | 0.931711i | \(-0.618316\pi\) | ||||
−0.363202 | + | 0.931711i | \(0.618316\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 51.0364 | 1.63615 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.95073 | 0.126525 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.76852 | −0.216544 | −0.108272 | − | 0.994121i | \(-0.534532\pi\) | ||||
−0.108272 | + | 0.994121i | \(0.534532\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.128406 | 0.00410389 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.3055 | 0.360956 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40.8744 | −1.30369 | −0.651846 | − | 0.758352i | \(-0.726005\pi\) | ||||
−0.651846 | + | 0.758352i | \(0.726005\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.0065 | −0.828636 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.12385 | −0.226754 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.70508 | 0.308603 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.79598 | −0.184115 | −0.0920577 | − | 0.995754i | \(-0.529344\pi\) | ||||
−0.0920577 | + | 0.995754i | \(0.529344\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.4725 | 0.840079 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −40.1284 | −1.27215 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.8370 | −1.07163 | −0.535815 | − | 0.844336i | \(-0.679995\pi\) | ||||
−0.535815 | + | 0.844336i | \(0.679995\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.70187 | 0.117122 |
(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 | 8004.2.a.j.1.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.j.1.3 | ✓ | 16 | 1.1 | even | 1 | trivial |