Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(1,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, 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("4004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 18x^{8} + 32x^{7} + 93x^{6} - 119x^{5} - 174x^{4} + 107x^{3} + 51x^{2} - 17x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-3.30965\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4004.1 |
$q$-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 | ||||||||
\(3\) | 3.30965 | 1.91082 | 0.955412 | − | 0.295275i | \(-0.0954112\pi\) | ||||
0.955412 | + | 0.295275i | \(0.0954112\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.14150 | −0.510496 | −0.255248 | − | 0.966876i | \(-0.582157\pi\) | ||||
−0.255248 | + | 0.966876i | \(0.582157\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.95375 | 2.65125 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.77797 | −0.975468 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.91321 | 1.67670 | 0.838350 | − | 0.545133i | \(-0.183521\pi\) | ||||
0.838350 | + | 0.545133i | \(0.183521\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.199068 | −0.0456693 | −0.0228346 | − | 0.999739i | \(-0.507269\pi\) | ||||
−0.0228346 | + | 0.999739i | \(0.507269\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.30965 | −0.722224 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.36118 | 0.700855 | 0.350427 | − | 0.936590i | \(-0.386036\pi\) | ||||
0.350427 | + | 0.936590i | \(0.386036\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.69697 | −0.739394 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 16.3952 | 3.15525 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.35214 | 0.436781 | 0.218391 | − | 0.975861i | \(-0.429919\pi\) | ||||
0.218391 | + | 0.975861i | \(0.429919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.74433 | −0.492896 | −0.246448 | − | 0.969156i | \(-0.579263\pi\) | ||||
−0.246448 | + | 0.969156i | \(0.579263\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.30965 | −0.576135 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.14150 | 0.192949 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.34222 | 0.878256 | 0.439128 | − | 0.898424i | \(-0.355287\pi\) | ||||
0.439128 | + | 0.898424i | \(0.355287\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.30965 | −0.529967 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.92324 | 1.39358 | 0.696788 | − | 0.717277i | \(-0.254612\pi\) | ||||
0.696788 | + | 0.717277i | \(0.254612\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.44857 | −0.220904 | −0.110452 | − | 0.993881i | \(-0.535230\pi\) | ||||
−0.110452 | + | 0.993881i | \(0.535230\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.07924 | −1.35345 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.453744 | −0.0661853 | −0.0330927 | − | 0.999452i | \(-0.510536\pi\) | ||||
−0.0330927 | + | 0.999452i | \(0.510536\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 22.8803 | 3.20388 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.92113 | −0.675969 | −0.337985 | − | 0.941152i | \(-0.609745\pi\) | ||||
−0.337985 | + | 0.941152i | \(0.609745\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.14150 | 0.153920 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.658844 | −0.0872660 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.39219 | −0.311436 | −0.155718 | − | 0.987802i | \(-0.549769\pi\) | ||||
−0.155718 | + | 0.987802i | \(0.549769\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1897 | 1.43269 | 0.716345 | − | 0.697746i | \(-0.245814\pi\) | ||||
0.716345 | + | 0.697746i | \(0.245814\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.95375 | −1.00208 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.14150 | 0.141586 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.28547 | −0.157045 | −0.0785224 | − | 0.996912i | \(-0.525020\pi\) | ||||
−0.0785224 | + | 0.996912i | \(0.525020\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.1243 | 1.33921 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.69296 | −0.912986 | −0.456493 | − | 0.889727i | \(-0.650895\pi\) | ||||
−0.456493 | + | 0.889727i | \(0.650895\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.77768 | 1.14439 | 0.572196 | − | 0.820117i | \(-0.306092\pi\) | ||||
0.572196 | + | 0.820117i | \(0.306092\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.2357 | −1.41285 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.24589 | 0.927735 | 0.463868 | − | 0.885905i | \(-0.346461\pi\) | ||||
0.463868 | + | 0.885905i | \(0.346461\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 30.4009 | 3.37788 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.96589 | 0.215784 | 0.107892 | − | 0.994163i | \(-0.465590\pi\) | ||||
0.107892 | + | 0.994163i | \(0.465590\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.89145 | −0.855948 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.78475 | 0.834612 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.2387 | 1.29730 | 0.648648 | − | 0.761089i | \(-0.275335\pi\) | ||||
0.648648 | + | 0.761089i | \(0.275335\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.08275 | −0.941838 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.227237 | 0.0233140 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.8905 | −1.71497 | −0.857487 | − | 0.514506i | \(-0.827975\pi\) | ||||
−0.857487 | + | 0.514506i | \(0.827975\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.95375 | −0.799382 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.1919 | 1.01414 | 0.507068 | − | 0.861906i | \(-0.330729\pi\) | ||||
0.507068 | + | 0.861906i | \(0.330729\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.9864 | −1.08252 | −0.541262 | − | 0.840854i | \(-0.682053\pi\) | ||||
−0.541262 | + | 0.840854i | \(0.682053\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.77797 | 0.368692 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.39508 | −0.424888 | −0.212444 | − | 0.977173i | \(-0.568142\pi\) | ||||
−0.212444 | + | 0.977173i | \(0.568142\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.90361 | −0.661246 | −0.330623 | − | 0.943763i | \(-0.607259\pi\) | ||||
−0.330623 | + | 0.943763i | \(0.607259\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.6809 | 1.67819 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.2217 | 1.62008 | 0.810041 | − | 0.586373i | \(-0.199445\pi\) | ||||
0.810041 | + | 0.586373i | \(0.199445\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.83680 | −0.357784 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.95375 | −0.735325 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.91321 | −0.633733 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 29.5328 | 2.66288 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.92762 | 0.887954 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.3993 | −1.01153 | −0.505763 | − | 0.862673i | \(-0.668789\pi\) | ||||
−0.505763 | + | 0.862673i | \(0.668789\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.79424 | −0.422109 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5176 | −0.918928 | −0.459464 | − | 0.888196i | \(-0.651959\pi\) | ||||
−0.459464 | + | 0.888196i | \(0.651959\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.199068 | 0.0172614 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −18.7152 | −1.61074 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.53891 | −0.729528 | −0.364764 | − | 0.931100i | \(-0.618850\pi\) | ||||
−0.364764 | + | 0.931100i | \(0.618850\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.9829 | 1.18601 | 0.593007 | − | 0.805197i | \(-0.297941\pi\) | ||||
0.593007 | + | 0.805197i | \(0.297941\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.50173 | −0.126469 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.68498 | −0.222975 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.30965 | 0.272975 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.17868 | −0.670024 | −0.335012 | − | 0.942214i | \(-0.608740\pi\) | ||||
−0.335012 | + | 0.942214i | \(0.608740\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.84020 | 0.312511 | 0.156256 | − | 0.987717i | \(-0.450058\pi\) | ||||
0.156256 | + | 0.987717i | \(0.450058\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 54.9860 | 4.44535 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.13266 | 0.251621 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.86871 | −0.627991 | −0.313996 | − | 0.949424i | \(-0.601668\pi\) | ||||
−0.313996 | + | 0.949424i | \(0.601668\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.2872 | −1.29166 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.36118 | −0.264898 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.588165 | 0.0460686 | 0.0230343 | − | 0.999735i | \(-0.492667\pi\) | ||||
0.0230343 | + | 0.999735i | \(0.492667\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.77797 | 0.294115 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.39033 | −0.494499 | −0.247249 | − | 0.968952i | \(-0.579527\pi\) | ||||
−0.247249 | + | 0.968952i | \(0.579527\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.58334 | −0.121081 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.58075 | −0.424297 | −0.212148 | − | 0.977237i | \(-0.568046\pi\) | ||||
−0.212148 | + | 0.977237i | \(0.568046\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.69697 | 0.279465 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.91730 | −0.595101 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.0557 | 0.826341 | 0.413171 | − | 0.910654i | \(-0.364421\pi\) | ||||
0.413171 | + | 0.910654i | \(0.364421\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.56448 | −0.487934 | −0.243967 | − | 0.969784i | \(-0.578449\pi\) | ||||
−0.243967 | + | 0.969784i | \(0.578449\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 37.0338 | 2.73762 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.09817 | −0.448346 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.91321 | −0.505544 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −16.3952 | −1.19257 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.929315 | 0.0672428 | 0.0336214 | − | 0.999435i | \(-0.489296\pi\) | ||||
0.0336214 | + | 0.999435i | \(0.489296\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.56361 | 0.472459 | 0.236229 | − | 0.971697i | \(-0.424088\pi\) | ||||
0.236229 | + | 0.971697i | \(0.424088\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.77797 | 0.270546 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.8890 | 1.13204 | 0.566021 | − | 0.824391i | \(-0.308482\pi\) | ||||
0.566021 | + | 0.824391i | \(0.308482\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.6387 | −1.25037 | −0.625187 | − | 0.780475i | \(-0.714977\pi\) | ||||
−0.625187 | + | 0.780475i | \(0.714977\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.25444 | −0.300085 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.35214 | −0.165088 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.1859 | −0.711415 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 26.7340 | 1.85814 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.199068 | 0.0137698 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.0928 | 1.24556 | 0.622781 | − | 0.782396i | \(-0.286003\pi\) | ||||
0.622781 | + | 0.782396i | \(0.286003\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −25.4610 | −1.74456 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.65354 | 0.112771 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.74433 | 0.186297 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 32.3607 | 2.18673 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.91321 | −0.465033 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0985 | 0.676244 | 0.338122 | − | 0.941102i | \(-0.390208\pi\) | ||||
0.338122 | + | 0.941102i | \(0.390208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −29.4048 | −1.96032 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.6097 | 1.50066 | 0.750330 | − | 0.661064i | \(-0.229895\pi\) | ||||
0.750330 | + | 0.661064i | \(0.229895\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.52564 | −0.365145 | −0.182572 | − | 0.983192i | \(-0.558442\pi\) | ||||
−0.182572 | + | 0.983192i | \(0.558442\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.30965 | 0.217759 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.0740 | −1.24958 | −0.624790 | − | 0.780793i | \(-0.714815\pi\) | ||||
−0.624790 | + | 0.780793i | \(0.714815\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.517950 | 0.0337874 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.2910 | 1.77274 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.5139 | −1.52099 | −0.760493 | − | 0.649346i | \(-0.775043\pi\) | ||||
−0.760493 | + | 0.649346i | \(0.775043\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.8277 | 1.92137 | 0.960684 | − | 0.277643i | \(-0.0895533\pi\) | ||||
0.960684 | + | 0.277643i | \(0.0895533\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 51.4308 | 3.29929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.14150 | −0.0729280 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.199068 | 0.0126664 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.50640 | 0.412326 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.14866 | 0.261861 | 0.130930 | − | 0.991392i | \(-0.458204\pi\) | ||||
0.130930 | + | 0.991392i | \(0.458204\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.36118 | −0.211316 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −26.1179 | −1.63557 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.8842 | −1.61461 | −0.807305 | − | 0.590134i | \(-0.799075\pi\) | ||||
−0.807305 | + | 0.590134i | \(0.799075\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.34222 | −0.331950 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.7083 | 1.15802 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.8923 | 1.16495 | 0.582475 | − | 0.812849i | \(-0.302085\pi\) | ||||
0.582475 | + | 0.812849i | \(0.302085\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.61749 | 0.345079 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 40.5056 | 2.47890 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.6215 | −1.86702 | −0.933512 | − | 0.358547i | \(-0.883272\pi\) | ||||
−0.933512 | + | 0.358547i | \(0.883272\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.4908 | −1.06249 | −0.531245 | − | 0.847218i | \(-0.678275\pi\) | ||||
−0.531245 | + | 0.847218i | \(0.678275\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.30965 | 0.200309 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.69697 | 0.222936 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.1708 | 1.15186 | 0.575931 | − | 0.817498i | \(-0.304640\pi\) | ||||
0.575931 | + | 0.817498i | \(0.304640\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −21.8277 | −1.30679 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.3917 | −1.69371 | −0.846855 | − | 0.531824i | \(-0.821507\pi\) | ||||
−0.846855 | + | 0.531824i | \(0.821507\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.67320 | 0.575012 | 0.287506 | − | 0.957779i | \(-0.407174\pi\) | ||||
0.287506 | + | 0.957779i | \(0.407174\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.752073 | 0.0445490 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.92324 | −0.526722 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.7925 | 1.81132 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −55.9017 | −3.27701 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.32869 | −0.369726 | −0.184863 | − | 0.982764i | \(-0.559184\pi\) | ||||
−0.184863 | + | 0.982764i | \(0.559184\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.73069 | 0.158987 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.3952 | −0.951344 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.36118 | −0.194382 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.44857 | 0.0834940 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 33.7317 | 1.93784 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.7730 | −0.731382 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.1071 | −1.83245 | −0.916225 | − | 0.400664i | \(-0.868780\pi\) | ||||
−0.916225 | + | 0.400664i | \(0.868780\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −36.3611 | −2.06851 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.4868 | −1.78545 | −0.892725 | − | 0.450602i | \(-0.851209\pi\) | ||||
−0.892725 | + | 0.450602i | \(0.851209\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.67474 | 0.151185 | 0.0755926 | − | 0.997139i | \(-0.475915\pi\) | ||||
0.0755926 | + | 0.997139i | \(0.475915\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.07924 | 0.511557 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.9546 | −0.952266 | −0.476133 | − | 0.879373i | \(-0.657962\pi\) | ||||
−0.476133 | + | 0.879373i | \(0.657962\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.35214 | −0.131694 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.5461 | −0.811887 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.37620 | −0.0765737 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.69697 | 0.205071 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −22.8485 | −1.26353 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.453744 | 0.0250157 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.99776 | −0.219737 | −0.109868 | − | 0.993946i | \(-0.535043\pi\) | ||||
−0.109868 | + | 0.993946i | \(0.535043\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 42.4907 | 2.32848 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.46737 | 0.0801707 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.4860 | −1.22489 | −0.612446 | − | 0.790513i | \(-0.709814\pi\) | ||||
−0.612446 | + | 0.790513i | \(0.709814\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 56.9978 | 3.09569 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.74433 | 0.148614 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.6985 | −0.683662 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.98003 | −0.321025 | −0.160512 | − | 0.987034i | \(-0.551315\pi\) | ||||
−0.160512 | + | 0.987034i | \(0.551315\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.02939 | −0.108631 | −0.0543153 | − | 0.998524i | \(-0.517298\pi\) | ||||
−0.0543153 | + | 0.998524i | \(0.517298\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.3952 | −0.875110 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.77371 | −0.413753 | −0.206876 | − | 0.978367i | \(-0.566330\pi\) | ||||
−0.206876 | + | 0.978367i | \(0.566330\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.78154 | 0.466076 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22.8803 | −1.21095 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.20224 | −0.485675 | −0.242838 | − | 0.970067i | \(-0.578078\pi\) | ||||
−0.242838 | + | 0.970067i | \(0.578078\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9604 | −0.997914 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.30965 | 0.173711 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.1613 | −0.584207 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.2160 | 1.15966 | 0.579832 | − | 0.814736i | \(-0.303118\pi\) | ||||
0.579832 | + | 0.814736i | \(0.303118\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 70.9732 | 3.69472 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.92113 | 0.255492 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.62781 | 0.239619 | 0.119809 | − | 0.992797i | \(-0.461772\pi\) | ||||
0.119809 | + | 0.992797i | \(0.461772\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 32.8569 | 1.69672 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.35214 | −0.121141 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.1619 | 1.44658 | 0.723290 | − | 0.690545i | \(-0.242629\pi\) | ||||
0.723290 | + | 0.690545i | \(0.242629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −37.7277 | −1.93285 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −35.9109 | −1.83496 | −0.917481 | − | 0.397780i | \(-0.869781\pi\) | ||||
−0.917481 | + | 0.397780i | \(0.869781\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.14150 | −0.0581764 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.5215 | −0.585673 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.07346 | −0.409340 | −0.204670 | − | 0.978831i | \(-0.565612\pi\) | ||||
−0.204670 | + | 0.978831i | \(0.565612\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.2365 | 1.17512 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −34.8096 | −1.75591 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.41272 | −0.473605 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.8197 | 1.14529 | 0.572643 | − | 0.819805i | \(-0.305918\pi\) | ||||
0.572643 | + | 0.819805i | \(0.305918\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.658844 | 0.0329835 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −38.7648 | −1.93582 | −0.967911 | − | 0.251294i | \(-0.919144\pi\) | ||||
−0.967911 | + | 0.251294i | \(0.919144\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.74433 | 0.136705 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −34.7028 | −1.72440 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.34222 | −0.264804 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.66784 | −0.329703 | −0.164852 | − | 0.986318i | \(-0.552715\pi\) | ||||
−0.164852 | + | 0.986318i | \(0.552715\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −28.2608 | −1.39400 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.39219 | 0.117712 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.24407 | −0.110157 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 46.2784 | 2.26626 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.45987 | −0.266732 | −0.133366 | − | 0.991067i | \(-0.542579\pi\) | ||||
−0.133366 | + | 0.991067i | \(0.542579\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.23681 | −0.255227 | −0.127613 | − | 0.991824i | \(-0.540732\pi\) | ||||
−0.127613 | + | 0.991824i | \(0.540732\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.60897 | −0.175474 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25.5579 | −1.23974 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.1897 | −0.541506 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.30965 | 0.159791 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.2354 | −1.50456 | −0.752278 | − | 0.658846i | \(-0.771045\pi\) | ||||
−0.752278 | + | 0.658846i | \(0.771045\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.6063 | −1.32667 | −0.663337 | − | 0.748321i | \(-0.730860\pi\) | ||||
−0.663337 | + | 0.748321i | \(0.730860\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.88632 | −0.426066 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.669103 | −0.0320075 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.8992 | −1.28383 | −0.641913 | − | 0.766777i | \(-0.721859\pi\) | ||||
−0.641913 | + | 0.766777i | \(0.721859\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.95375 | 0.378750 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.6967 | 0.508217 | 0.254108 | − | 0.967176i | \(-0.418218\pi\) | ||||
0.254108 | + | 0.967176i | \(0.418218\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.9705 | −0.662264 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −27.0685 | −1.28030 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.8786 | −0.513394 | −0.256697 | − | 0.966492i | \(-0.582634\pi\) | ||||
−0.256697 | + | 0.966492i | \(0.582634\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.92324 | −0.420179 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.7097 | 0.597155 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.14150 | −0.0535145 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.0857 | −0.939569 | −0.469785 | − | 0.882781i | \(-0.655668\pi\) | ||||
−0.469785 | + | 0.882781i | \(0.655668\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 113.343 | 5.29041 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.97216 | 0.324726 | 0.162363 | − | 0.986731i | \(-0.448088\pi\) | ||||
0.162363 | + | 0.986731i | \(0.448088\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.9518 | 0.741342 | 0.370671 | − | 0.928764i | \(-0.379128\pi\) | ||||
0.370671 | + | 0.928764i | \(0.379128\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.3680 | 0.480804 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.2261 | 0.612032 | 0.306016 | − | 0.952026i | \(-0.401004\pi\) | ||||
0.306016 | + | 0.952026i | \(0.401004\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.28547 | 0.0593574 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −26.0426 | −1.19998 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.44857 | 0.0666051 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.735948 | 0.0337676 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −39.1415 | −1.79216 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.70067 | −0.260470 | −0.130235 | − | 0.991483i | \(-0.541573\pi\) | ||||
−0.130235 | + | 0.991483i | \(0.541573\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.34222 | −0.243584 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.1243 | −0.506174 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.2806 | 0.875487 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.8527 | 1.39807 | 0.699034 | − | 0.715088i | \(-0.253614\pi\) | ||||
0.699034 | + | 0.715088i | \(0.253614\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.94662 | 0.0880291 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.8240 | 0.533608 | 0.266804 | − | 0.963751i | \(-0.414032\pi\) | ||||
0.266804 | + | 0.963751i | \(0.414032\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.2608 | 0.732351 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.07924 | 0.408082 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.69296 | 0.345076 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.7360 | −0.570142 | −0.285071 | − | 0.958506i | \(-0.592017\pi\) | ||||
−0.285071 | + | 0.958506i | \(0.592017\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.1497 | −0.944901 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.04582 | −0.0912184 | −0.0456092 | − | 0.998959i | \(-0.514523\pi\) | ||||
−0.0456092 | + | 0.998959i | \(0.514523\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.6341 | −0.517712 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.30965 | 0.146987 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.7165 | 1.18419 | 0.592094 | − | 0.805869i | \(-0.298302\pi\) | ||||
0.592094 | + | 0.805869i | \(0.298302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.77768 | −0.432539 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.26375 | −0.144098 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.5410 | 0.552624 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.453744 | 0.0199556 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.4703 | −0.810757 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.7809 | 0.998049 | 0.499024 | − | 0.866588i | \(-0.333692\pi\) | ||||
0.499024 | + | 0.866588i | \(0.333692\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.6445 | −1.33999 | −0.669994 | − | 0.742366i | \(-0.733703\pi\) | ||||
−0.669994 | + | 0.742366i | \(0.733703\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.2357 | 0.534008 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.9721 | −0.826438 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.7025 | −0.508803 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −19.0269 | −0.825696 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.92324 | −0.386508 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.01700 | 0.216904 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 36.5904 | 1.57899 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.3642 | −1.04750 | −0.523750 | − | 0.851872i | \(-0.675467\pi\) | ||||
−0.523750 | + | 0.851872i | \(0.675467\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.7261 | −0.932357 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.88050 | 0.337564 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.1847 | −1.24785 | −0.623924 | − | 0.781485i | \(-0.714462\pi\) | ||||
−0.623924 | + | 0.781485i | \(0.714462\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 88.9999 | 3.79842 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.468235 | −0.0199475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.24589 | −0.350651 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −20.1828 | −0.856711 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.7830 | 1.00772 | 0.503860 | − | 0.863785i | \(-0.331913\pi\) | ||||
0.503860 | + | 0.863785i | \(0.331913\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.44857 | 0.0612678 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.8803 | −0.966006 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.2314 | 0.557638 | 0.278819 | − | 0.960344i | \(-0.410057\pi\) | ||||
0.278819 | + | 0.960344i | \(0.410057\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.6586 | −0.827045 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −30.4009 | −1.27672 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.5809 | 0.988562 | 0.494281 | − | 0.869302i | \(-0.335431\pi\) | ||||
0.494281 | + | 0.869302i | \(0.335431\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.71844 | −0.364856 | −0.182428 | − | 0.983219i | \(-0.558396\pi\) | ||||
−0.182428 | + | 0.983219i | \(0.558396\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.07570 | 0.128489 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.4262 | −0.518208 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.0480 | 0.501566 | 0.250783 | − | 0.968043i | \(-0.419312\pi\) | ||||
0.250783 | + | 0.968043i | \(0.419312\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.7232 | 0.902786 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.96589 | −0.0815588 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.92113 | 0.203812 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9.07924 | 0.375380 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.65236 | 0.192023 | 0.0960116 | − | 0.995380i | \(-0.469391\pi\) | ||||
0.0960116 | + | 0.995380i | \(0.469391\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.546307 | 0.0225102 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 52.5868 | 2.16313 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.0592 | 0.454146 | 0.227073 | − | 0.973878i | \(-0.427084\pi\) | ||||
0.227073 | + | 0.973878i | \(0.427084\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.89145 | 0.323518 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −58.3779 | −2.38925 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.2328 | −0.499817 | −0.249909 | − | 0.968269i | \(-0.580401\pi\) | ||||
−0.249909 | + | 0.968269i | \(0.580401\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.4471 | 1.48671 | 0.743353 | − | 0.668899i | \(-0.233234\pi\) | ||||
0.743353 | + | 0.668899i | \(0.233234\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.2243 | −0.416365 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.14150 | −0.0464087 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.43071 | −0.0580705 | −0.0290353 | − | 0.999578i | \(-0.509244\pi\) | ||||
−0.0290353 | + | 0.999578i | \(0.509244\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.78475 | −0.315454 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.453744 | 0.0183565 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.88419 | 0.358829 | 0.179414 | − | 0.983774i | \(-0.442580\pi\) | ||||
0.179414 | + | 0.983774i | \(0.442580\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −33.7118 | −1.35939 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.6517 | 0.670371 | 0.335185 | − | 0.942152i | \(-0.391201\pi\) | ||||
0.335185 | + | 0.942152i | \(0.391201\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.8958 | 1.20161 | 0.600807 | − | 0.799394i | \(-0.294846\pi\) | ||||
0.600807 | + | 0.799394i | \(0.294846\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 55.1071 | 2.21137 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.2387 | −0.490332 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.15243 | 0.286097 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.658844 | 0.0263117 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 36.9319 | 1.47257 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.9066 | 1.15075 | 0.575377 | − | 0.817888i | \(-0.304855\pi\) | ||||
0.575377 | + | 0.817888i | \(0.304855\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 59.8809 | 2.38005 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.0124 | 0.516380 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −61.1879 | −2.42056 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.4893 | 1.00677 | 0.503383 | − | 0.864063i | \(-0.332088\pi\) | ||||
0.503383 | + | 0.864063i | \(0.332088\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.9872 | −0.827656 | −0.413828 | − | 0.910355i | \(-0.635809\pi\) | ||||
−0.413828 | + | 0.910355i | \(0.635809\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.47264 | 0.215485 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.9394 | −0.862526 | −0.431263 | − | 0.902226i | \(-0.641932\pi\) | ||||
−0.431263 | + | 0.902226i | \(0.641932\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.39219 | 0.0939016 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.08275 | 0.355981 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.4093 | −1.22914 | −0.614570 | − | 0.788862i | \(-0.710671\pi\) | ||||
−0.614570 | + | 0.788862i | \(0.710671\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0059 | 0.469109 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 77.7693 | 3.03407 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.5256 | −0.916429 | −0.458214 | − | 0.888842i | \(-0.651511\pi\) | ||||
−0.458214 | + | 0.888842i | \(0.651511\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.9217 | 0.852657 | 0.426328 | − | 0.904569i | \(-0.359807\pi\) | ||||
0.426328 | + | 0.904569i | \(0.359807\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.8803 | −0.888596 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.227237 | −0.00881186 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.90596 | 0.306120 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 33.4224 | 1.29218 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.1897 | −0.431972 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.7204 | −0.991448 | −0.495724 | − | 0.868480i | \(-0.665097\pi\) | ||||
−0.495724 | + | 0.868480i | \(0.665097\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −60.6124 | −2.33297 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.9388 | 1.18907 | 0.594537 | − | 0.804068i | \(-0.297335\pi\) | ||||
0.594537 | + | 0.804068i | \(0.297335\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.8905 | 0.648199 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 74.8301 | 2.86750 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.5224 | −0.517419 | −0.258709 | − | 0.965955i | \(-0.583297\pi\) | ||||
−0.258709 | + | 0.965955i | \(0.583297\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.74720 | 0.372421 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.2879 | −0.697727 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.92113 | 0.187480 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.01419 | −0.152707 | −0.0763536 | − | 0.997081i | \(-0.524328\pi\) | ||||
−0.0763536 | + | 0.997081i | \(0.524328\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.95375 | 0.302138 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.9615 | −0.605455 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 61.6882 | 2.33661 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −63.1282 | −2.38773 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.8250 | −0.597701 | −0.298851 | − | 0.954300i | \(-0.596603\pi\) | ||||
−0.298851 | + | 0.954300i | \(0.596603\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.06347 | −0.0401093 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.71423 | 0.0645617 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.1919 | −0.383307 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 52.4075 | 1.96820 | 0.984102 | − | 0.177602i | \(-0.0568338\pi\) | ||||
0.984102 | + | 0.177602i | \(0.0568338\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 65.5858 | 2.45966 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.22418 | −0.345448 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.14150 | −0.0426898 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −77.8226 | −2.90634 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.63927 | 0.247603 | 0.123802 | − | 0.992307i | \(-0.460491\pi\) | ||||
0.123802 | + | 0.992307i | \(0.460491\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.9864 | 0.409155 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 98.7190 | 3.67140 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.69578 | −0.322953 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.7650 | 1.80860 | 0.904298 | − | 0.426902i | \(-0.140395\pi\) | ||||
0.904298 | + | 0.426902i | \(0.140395\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 79.0150 | 2.92648 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.0142 | −0.370390 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.67262 | −0.0617797 | −0.0308899 | − | 0.999523i | \(-0.509834\pi\) | ||||
−0.0308899 | + | 0.999523i | \(0.509834\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.77797 | −0.139353 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.28547 | 0.0473508 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.23012 | 0.339536 | 0.169768 | − | 0.985484i | \(-0.445698\pi\) | ||||
0.169768 | + | 0.985484i | \(0.445698\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.658844 | 0.0242032 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.5606 | 1.26790 | 0.633952 | − | 0.773372i | \(-0.281432\pi\) | ||||
0.633952 | + | 0.773372i | \(0.281432\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.33600 | 0.342044 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.6362 | 0.572099 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.39508 | 0.160593 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.8694 | −1.78327 | −0.891635 | − | 0.452756i | \(-0.850441\pi\) | ||||
−0.891635 | + | 0.452756i | \(0.850441\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.7306 | 0.500370 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.38361 | −0.159536 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.1472 | 0.986682 | 0.493341 | − | 0.869836i | \(-0.335775\pi\) | ||||
0.493341 | + | 0.869836i | \(0.335775\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11.1243 | −0.403787 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.4352 | 1.24827 | 0.624137 | − | 0.781315i | \(-0.285451\pi\) | ||||
0.624137 | + | 0.781315i | \(0.285451\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.90361 | 0.249928 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −62.7667 | −2.26933 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.39219 | 0.0863769 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.46306 | 0.305186 | 0.152593 | − | 0.988289i | \(-0.451238\pi\) | ||||
0.152593 | + | 0.988289i | \(0.451238\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −85.6675 | −3.08524 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.0135 | −1.72693 | −0.863463 | − | 0.504412i | \(-0.831709\pi\) | ||||
−0.863463 | + | 0.504412i | \(0.831709\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.1457 | 0.364444 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.6809 | −0.634298 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.77633 | −0.0636436 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.69296 | 0.275276 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 38.5637 | 1.37815 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.98216 | 0.320587 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.0064 | −1.56866 | −0.784329 | − | 0.620345i | \(-0.786993\pi\) | ||||
−0.784329 | + | 0.620345i | \(0.786993\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 62.5268 | 2.22601 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.2217 | −0.612333 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.1897 | −0.397357 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.5919 | 0.659386 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41.3799 | −1.46575 | −0.732875 | − | 0.680363i | \(-0.761822\pi\) | ||||
−0.732875 | + | 0.680363i | \(0.761822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.13683 | −0.110973 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 97.3433 | 3.43946 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.77768 | −0.345047 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.83680 | 0.135229 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −101.346 | −3.56755 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.7985 | 0.555447 | 0.277724 | − | 0.960661i | \(-0.410420\pi\) | ||||
0.277724 | + | 0.960661i | \(0.410420\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.1077 | 0.390043 | 0.195022 | − | 0.980799i | \(-0.437522\pi\) | ||||
0.195022 | + | 0.980799i | \(0.437522\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −57.8883 | −2.03023 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.671392 | −0.0235179 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.288363 | 0.0100885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.95375 | 0.277927 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.45550 | −0.0856975 | −0.0428488 | − | 0.999082i | \(-0.513643\pi\) | ||||
−0.0428488 | + | 0.999082i | \(0.513643\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.7115 | 0.931103 | 0.465552 | − | 0.885021i | \(-0.345856\pi\) | ||||
0.465552 | + | 0.885021i | \(0.345856\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.2357 | 0.425991 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.7003 | 1.31097 | 0.655484 | − | 0.755209i | \(-0.272465\pi\) | ||||
0.655484 | + | 0.755209i | \(0.272465\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.5698 | 0.992270 | 0.496135 | − | 0.868245i | \(-0.334752\pi\) | ||||
0.496135 | + | 0.868245i | \(0.334752\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 63.4486 | 2.20101 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.91321 | 0.239528 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.29459 | 0.252440 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −44.9937 | −1.55521 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.8409 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4674 | −0.809222 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −93.9666 | −3.23638 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.14150 | −0.0392689 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 32.0149 | 1.09875 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.9562 | 0.615530 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.0852 | −1.40673 | −0.703365 | − | 0.710829i | \(-0.748320\pi\) | ||||
−0.703365 | + | 0.710829i | \(0.748320\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.80739 | 0.0618113 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.3782 | −0.559468 | −0.279734 | − | 0.960078i | \(-0.590246\pi\) | ||||
−0.279734 | + | 0.960078i | \(0.590246\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.9594 | −1.29516 | −0.647579 | − | 0.761998i | \(-0.724218\pi\) | ||||
−0.647579 | + | 0.761998i | \(0.724218\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −29.5328 | −1.00647 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −49.3301 | −1.67922 | −0.839609 | − | 0.543191i | \(-0.817216\pi\) | ||||
−0.839609 | + | 0.543191i | \(0.817216\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.37045 | 0.216602 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 101.912 | 3.46112 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.24589 | −0.279723 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.28547 | 0.0435564 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −134.343 | −4.54683 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.92762 | −0.335615 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.0611 | 0.508576 | 0.254288 | − | 0.967129i | \(-0.418159\pi\) | ||||
0.254288 | + | 0.967129i | \(0.418159\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.9457 | −0.706482 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.7673 | −1.84516 | −0.922578 | − | 0.385809i | \(-0.873922\pi\) | ||||
−0.922578 | + | 0.385809i | \(0.873922\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.7629 | 0.631422 | 0.315711 | − | 0.948855i | \(-0.397757\pi\) | ||||
0.315711 | + | 0.948855i | \(0.397757\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.03763 | 0.303796 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.3836 | 1.12091 | 0.560456 | − | 0.828184i | \(-0.310626\pi\) | ||||
0.560456 | + | 0.828184i | \(0.310626\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.3993 | 0.382321 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −30.4009 | −1.01847 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.0903258 | 0.00302264 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.6201 | −0.421844 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.1243 | −0.371430 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.45504 | −0.215288 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.0208 | −1.13340 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.79424 | 0.159542 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.49338 | 0.249088 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.8818 | −0.527347 | −0.263673 | − | 0.964612i | \(-0.584934\pi\) | ||||
−0.263673 | + | 0.964612i | \(0.584934\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 81.0641 | 2.68873 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.31682 | −0.0436282 | −0.0218141 | − | 0.999762i | \(-0.506944\pi\) | ||||
−0.0218141 | + | 0.999762i | \(0.506944\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.96589 | −0.0650614 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −42.2743 | −1.39754 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.5176 | 0.347322 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.8174 | −0.653715 | −0.326858 | − | 0.945074i | \(-0.605990\pi\) | ||||
−0.326858 | + | 0.945074i | \(0.605990\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −106.263 | −3.50149 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.69296 | 0.253217 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.7500 | −0.649377 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −87.3832 | −2.87004 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −37.1278 | −1.21812 | −0.609062 | − | 0.793122i | \(-0.708454\pi\) | ||||
−0.609062 | + | 0.793122i | \(0.708454\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.199068 | −0.00652419 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −104.210 | −3.41168 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.89145 | 0.258078 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.8888 | −0.453727 | −0.226864 | − | 0.973927i | \(-0.572847\pi\) | ||||
−0.226864 | + | 0.973927i | \(0.572847\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.85244 | 0.288889 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.2735 | −0.530502 | −0.265251 | − | 0.964179i | \(-0.585455\pi\) | ||||
−0.265251 | + | 0.964179i | \(0.585455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.9926 | 0.976694 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.7152 | 0.608804 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.2212 | −1.72946 | −0.864729 | − | 0.502239i | \(-0.832510\pi\) | ||||
−0.864729 | + | 0.502239i | \(0.832510\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.77768 | −0.317397 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −56.1138 | −1.81961 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.2777 | −0.721644 | −0.360822 | − | 0.932635i | \(-0.617504\pi\) | ||||
−0.360822 | + | 0.932635i | \(0.617504\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.06082 | −0.0343272 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.78475 | −0.251645 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.53891 | 0.275736 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.4687 | −0.757054 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34.9574 | −1.12648 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.49238 | −0.241188 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.0297 | −1.25511 | −0.627555 | − | 0.778572i | \(-0.715944\pi\) | ||||
−0.627555 | + | 0.778572i | \(0.715944\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.55473 | −0.146319 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46.2376 | −1.48383 | −0.741917 | − | 0.670491i | \(-0.766083\pi\) | ||||
−0.741917 | + | 0.670491i | \(0.766083\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.9829 | −0.448271 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.2357 | 0.391855 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41.4591 | −1.32639 | −0.663196 | − | 0.748445i | \(-0.730801\pi\) | ||||
−0.663196 | + | 0.748445i | \(0.730801\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.2387 | −0.391149 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −54.9096 | −1.75313 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.9200 | 1.04998 | 0.524992 | − | 0.851107i | \(-0.324068\pi\) | ||||
0.524992 | + | 0.851107i | \(0.324068\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.1373 | −0.577903 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.50173 | 0.0478006 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.86889 | −0.154822 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.21876 | −0.0387150 | −0.0193575 | − | 0.999813i | \(-0.506162\pi\) | ||||
−0.0193575 | + | 0.999813i | \(0.506162\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.2312 | −0.419878 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.1346 | 0.638311 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.8135 | 1.60928 | 0.804640 | − | 0.593763i | \(-0.202358\pi\) | ||||
0.804640 | + | 0.593763i | \(0.202358\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 87.5867 | 2.77112 |
(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 | 4004.2.a.j.1.10 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.a.j.1.10 | ✓ | 10 | 1.1 | even | 1 | trivial |