Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(1,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.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: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.618034 | −0.233595 | −0.116797 | − | 0.993156i | \(-0.537263\pi\) | ||||
−0.116797 | + | 0.993156i | \(0.537263\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 2.85410 | 0.860544 | 0.430272 | − | 0.902699i | \(-0.358418\pi\) | ||||
0.430272 | + | 0.902699i | \(0.358418\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.09017 | −1.96646 | −0.983230 | − | 0.182372i | \(-0.941623\pi\) | ||||
−0.983230 | + | 0.182372i | \(0.941623\pi\) | |||||||
\(14\) | 0.618034 | 0.165177 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.09017 | −1.47708 | −0.738542 | − | 0.674208i | \(-0.764485\pi\) | ||||
−0.738542 | + | 0.674208i | \(0.764485\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.85410 | 0.425360 | 0.212680 | − | 0.977122i | \(-0.431781\pi\) | ||||
0.212680 | + | 0.977122i | \(0.431781\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.85410 | −0.608497 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 7.09017 | 1.39050 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.618034 | −0.116797 | ||||||||
\(29\) | 9.23607 | 1.71509 | 0.857547 | − | 0.514405i | \(-0.171987\pi\) | ||||
0.857547 | + | 0.514405i | \(0.171987\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.09017 | 1.63264 | 0.816321 | − | 0.577598i | \(-0.196010\pi\) | ||||
0.816321 | + | 0.577598i | \(0.196010\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.09017 | 1.04446 | ||||||||
\(35\) | 0.618034 | 0.104467 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.47214 | 1.06401 | 0.532006 | − | 0.846740i | \(-0.321438\pi\) | ||||
0.532006 | + | 0.846740i | \(0.321438\pi\) | |||||||
\(38\) | −1.85410 | −0.300775 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −3.32624 | −0.519471 | −0.259736 | − | 0.965680i | \(-0.583635\pi\) | ||||
−0.259736 | + | 0.965680i | \(0.583635\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 2.85410 | 0.430272 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 3.70820 | 0.540897 | 0.270449 | − | 0.962734i | \(-0.412828\pi\) | ||||
0.270449 | + | 0.962734i | \(0.412828\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.61803 | −0.945433 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.09017 | −0.983230 | ||||||||
\(53\) | −0.472136 | −0.0648529 | −0.0324264 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324264 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.85410 | −0.384847 | ||||||||
\(56\) | 0.618034 | 0.0825883 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.23607 | −1.21276 | ||||||||
\(59\) | −1.70820 | −0.222389 | −0.111195 | − | 0.993799i | \(-0.535468\pi\) | ||||
−0.111195 | + | 0.993799i | \(0.535468\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.32624 | −1.19410 | −0.597051 | − | 0.802203i | \(-0.703661\pi\) | ||||
−0.597051 | + | 0.802203i | \(0.703661\pi\) | |||||||
\(62\) | −9.09017 | −1.15445 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.09017 | 0.879427 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.4721 | 1.76805 | 0.884026 | − | 0.467437i | \(-0.154823\pi\) | ||||
0.884026 | + | 0.467437i | \(0.154823\pi\) | |||||||
\(68\) | −6.09017 | −0.738542 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.618034 | −0.0738692 | ||||||||
\(71\) | 4.09017 | 0.485414 | 0.242707 | − | 0.970100i | \(-0.421965\pi\) | ||||
0.242707 | + | 0.970100i | \(0.421965\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.23607 | 0.378753 | 0.189377 | − | 0.981905i | \(-0.439353\pi\) | ||||
0.189377 | + | 0.981905i | \(0.439353\pi\) | |||||||
\(74\) | −6.47214 | −0.752371 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.85410 | 0.212680 | ||||||||
\(77\) | −1.76393 | −0.201019 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.52786 | 0.171898 | 0.0859491 | − | 0.996300i | \(-0.472608\pi\) | ||||
0.0859491 | + | 0.996300i | \(0.472608\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.32624 | 0.367322 | ||||||||
\(83\) | 6.94427 | 0.762233 | 0.381116 | − | 0.924527i | \(-0.375540\pi\) | ||||
0.381116 | + | 0.924527i | \(0.375540\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.09017 | 0.660572 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.85410 | −0.304248 | ||||||||
\(89\) | 10.4721 | 1.11004 | 0.555022 | − | 0.831836i | \(-0.312710\pi\) | ||||
0.555022 | + | 0.831836i | \(0.312710\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.38197 | 0.459355 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.70820 | −0.382472 | ||||||||
\(95\) | −1.85410 | −0.190227 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3820 | 1.25720 | 0.628599 | − | 0.777730i | \(-0.283629\pi\) | ||||
0.628599 | + | 0.777730i | \(0.283629\pi\) | |||||||
\(98\) | 6.61803 | 0.668522 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 0.291796 | 0.0290348 | 0.0145174 | − | 0.999895i | \(-0.495379\pi\) | ||||
0.0145174 | + | 0.999895i | \(0.495379\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.5623 | 1.63193 | 0.815966 | − | 0.578100i | \(-0.196205\pi\) | ||||
0.815966 | + | 0.578100i | \(0.196205\pi\) | |||||||
\(104\) | 7.09017 | 0.695248 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.472136 | 0.0458579 | ||||||||
\(107\) | −18.1803 | −1.75756 | −0.878780 | − | 0.477227i | \(-0.841642\pi\) | ||||
−0.878780 | + | 0.477227i | \(0.841642\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.5623 | −1.10747 | −0.553734 | − | 0.832694i | \(-0.686798\pi\) | ||||
−0.553734 | + | 0.832694i | \(0.686798\pi\) | |||||||
\(110\) | 2.85410 | 0.272128 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.618034 | −0.0583987 | ||||||||
\(113\) | −1.05573 | −0.0993145 | −0.0496573 | − | 0.998766i | \(-0.515813\pi\) | ||||
−0.0496573 | + | 0.998766i | \(0.515813\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 9.23607 | 0.857547 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.70820 | 0.157253 | ||||||||
\(119\) | 3.76393 | 0.345039 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.85410 | −0.259464 | ||||||||
\(122\) | 9.32624 | 0.844358 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.09017 | 0.816321 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.1803 | 1.43577 | 0.717886 | − | 0.696160i | \(-0.245110\pi\) | ||||
0.717886 | + | 0.696160i | \(0.245110\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.09017 | −0.621849 | ||||||||
\(131\) | −2.94427 | −0.257242 | −0.128621 | − | 0.991694i | \(-0.541055\pi\) | ||||
−0.128621 | + | 0.991694i | \(0.541055\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.14590 | −0.0993620 | ||||||||
\(134\) | −14.4721 | −1.25020 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.09017 | 0.522228 | ||||||||
\(137\) | 10.3262 | 0.882230 | 0.441115 | − | 0.897451i | \(-0.354583\pi\) | ||||
0.441115 | + | 0.897451i | \(0.354583\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.7639 | 1.08262 | 0.541311 | − | 0.840822i | \(-0.317928\pi\) | ||||
0.541311 | + | 0.840822i | \(0.317928\pi\) | |||||||
\(140\) | 0.618034 | 0.0522334 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.09017 | −0.343239 | ||||||||
\(143\) | −20.2361 | −1.69223 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.23607 | −0.767014 | ||||||||
\(146\) | −3.23607 | −0.267819 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.47214 | 0.532006 | ||||||||
\(149\) | 7.85410 | 0.643433 | 0.321717 | − | 0.946836i | \(-0.395740\pi\) | ||||
0.321717 | + | 0.946836i | \(0.395740\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.56231 | −0.208517 | −0.104259 | − | 0.994550i | \(-0.533247\pi\) | ||||
−0.104259 | + | 0.994550i | \(0.533247\pi\) | |||||||
\(152\) | −1.85410 | −0.150388 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.76393 | 0.142142 | ||||||||
\(155\) | −9.09017 | −0.730140 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.70820 | −0.295947 | −0.147973 | − | 0.988991i | \(-0.547275\pi\) | ||||
−0.147973 | + | 0.988991i | \(0.547275\pi\) | |||||||
\(158\) | −1.52786 | −0.121550 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0.618034 | 0.0487079 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.38197 | 0.108244 | 0.0541220 | − | 0.998534i | \(-0.482764\pi\) | ||||
0.0541220 | + | 0.998534i | \(0.482764\pi\) | |||||||
\(164\) | −3.32624 | −0.259736 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.94427 | −0.538980 | ||||||||
\(167\) | 8.00000 | 0.619059 | 0.309529 | − | 0.950890i | \(-0.399829\pi\) | ||||
0.309529 | + | 0.950890i | \(0.399829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.2705 | 2.86696 | ||||||||
\(170\) | −6.09017 | −0.467095 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.43769 | 0.109306 | 0.0546529 | − | 0.998505i | \(-0.482595\pi\) | ||||
0.0546529 | + | 0.998505i | \(0.482595\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.618034 | −0.0467190 | ||||||||
\(176\) | 2.85410 | 0.215136 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.4721 | −0.784920 | ||||||||
\(179\) | −2.18034 | −0.162966 | −0.0814831 | − | 0.996675i | \(-0.525966\pi\) | ||||
−0.0814831 | + | 0.996675i | \(0.525966\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.1459 | −0.902797 | −0.451399 | − | 0.892322i | \(-0.649075\pi\) | ||||
−0.451399 | + | 0.892322i | \(0.649075\pi\) | |||||||
\(182\) | −4.38197 | −0.324813 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −6.47214 | −0.475841 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.3820 | −1.27110 | ||||||||
\(188\) | 3.70820 | 0.270449 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.85410 | 0.134511 | ||||||||
\(191\) | 13.7082 | 0.991891 | 0.495945 | − | 0.868354i | \(-0.334822\pi\) | ||||
0.495945 | + | 0.868354i | \(0.334822\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.763932 | 0.0549890 | 0.0274945 | − | 0.999622i | \(-0.491247\pi\) | ||||
0.0274945 | + | 0.999622i | \(0.491247\pi\) | |||||||
\(194\) | −12.3820 | −0.888973 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.61803 | −0.472717 | ||||||||
\(197\) | 22.5623 | 1.60750 | 0.803749 | − | 0.594969i | \(-0.202836\pi\) | ||||
0.803749 | + | 0.594969i | \(0.202836\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.291796 | −0.0205307 | ||||||||
\(203\) | −5.70820 | −0.400637 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.32624 | 0.232315 | ||||||||
\(206\) | −16.5623 | −1.15395 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.09017 | −0.491615 | ||||||||
\(209\) | 5.29180 | 0.366041 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0000 | 0.963800 | 0.481900 | − | 0.876226i | \(-0.339947\pi\) | ||||
0.481900 | + | 0.876226i | \(0.339947\pi\) | |||||||
\(212\) | −0.472136 | −0.0324264 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.1803 | 1.24278 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.61803 | −0.381377 | ||||||||
\(218\) | 11.5623 | 0.783098 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.85410 | −0.192424 | ||||||||
\(221\) | 43.1803 | 2.90462 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.9443 | −1.40253 | −0.701266 | − | 0.712900i | \(-0.747382\pi\) | ||||
−0.701266 | + | 0.712900i | \(0.747382\pi\) | |||||||
\(224\) | 0.618034 | 0.0412941 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.05573 | 0.0702260 | ||||||||
\(227\) | 18.7639 | 1.24541 | 0.622703 | − | 0.782458i | \(-0.286035\pi\) | ||||
0.622703 | + | 0.782458i | \(0.286035\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | −1.00000 | −0.0659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.23607 | −0.606378 | ||||||||
\(233\) | −6.29180 | −0.412189 | −0.206095 | − | 0.978532i | \(-0.566075\pi\) | ||||
−0.206095 | + | 0.978532i | \(0.566075\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.70820 | −0.241897 | ||||||||
\(236\) | −1.70820 | −0.111195 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.76393 | −0.243979 | ||||||||
\(239\) | 20.3607 | 1.31702 | 0.658511 | − | 0.752571i | \(-0.271186\pi\) | ||||
0.658511 | + | 0.752571i | \(0.271186\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 2.85410 | 0.183469 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.32624 | −0.597051 | ||||||||
\(245\) | 6.61803 | 0.422811 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.1459 | −0.836453 | ||||||||
\(248\) | −9.09017 | −0.577226 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −6.14590 | −0.387926 | −0.193963 | − | 0.981009i | \(-0.562134\pi\) | ||||
−0.193963 | + | 0.981009i | \(0.562134\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.85410 | −0.179436 | ||||||||
\(254\) | −16.1803 | −1.01524 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.81966 | 0.487777 | 0.243888 | − | 0.969803i | \(-0.421577\pi\) | ||||
0.243888 | + | 0.969803i | \(0.421577\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | −0.248548 | ||||||||
\(260\) | 7.09017 | 0.439714 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.94427 | 0.181898 | ||||||||
\(263\) | −20.7426 | −1.27905 | −0.639523 | − | 0.768772i | \(-0.720868\pi\) | ||||
−0.639523 | + | 0.768772i | \(0.720868\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.472136 | 0.0290031 | ||||||||
\(266\) | 1.14590 | 0.0702595 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.4721 | 0.884026 | ||||||||
\(269\) | 14.1803 | 0.864591 | 0.432295 | − | 0.901732i | \(-0.357704\pi\) | ||||
0.432295 | + | 0.901732i | \(0.357704\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.3262 | −1.84219 | −0.921094 | − | 0.389341i | \(-0.872703\pi\) | ||||
−0.921094 | + | 0.389341i | \(0.872703\pi\) | |||||||
\(272\) | −6.09017 | −0.369271 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.3262 | −0.623831 | ||||||||
\(275\) | 2.85410 | 0.172109 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.4164 | 1.76746 | 0.883730 | − | 0.467996i | \(-0.155024\pi\) | ||||
0.883730 | + | 0.467996i | \(0.155024\pi\) | |||||||
\(278\) | −12.7639 | −0.765530 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.618034 | −0.0369346 | ||||||||
\(281\) | −22.7639 | −1.35798 | −0.678991 | − | 0.734146i | \(-0.737583\pi\) | ||||
−0.678991 | + | 0.734146i | \(0.737583\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.9443 | −1.60167 | −0.800835 | − | 0.598885i | \(-0.795611\pi\) | ||||
−0.800835 | + | 0.598885i | \(0.795611\pi\) | |||||||
\(284\) | 4.09017 | 0.242707 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 20.2361 | 1.19658 | ||||||||
\(287\) | 2.05573 | 0.121346 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.0902 | 1.18177 | ||||||||
\(290\) | 9.23607 | 0.542361 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.23607 | 0.189377 | ||||||||
\(293\) | 19.8885 | 1.16190 | 0.580951 | − | 0.813939i | \(-0.302681\pi\) | ||||
0.580951 | + | 0.813939i | \(0.302681\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.70820 | 0.0994555 | ||||||||
\(296\) | −6.47214 | −0.376185 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.85410 | −0.454976 | ||||||||
\(299\) | 7.09017 | 0.410035 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.56231 | 0.147444 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.85410 | 0.106340 | ||||||||
\(305\) | 9.32624 | 0.534019 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.4508 | −1.62378 | −0.811888 | − | 0.583813i | \(-0.801560\pi\) | ||||
−0.811888 | + | 0.583813i | \(0.801560\pi\) | |||||||
\(308\) | −1.76393 | −0.100509 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.09017 | 0.516287 | ||||||||
\(311\) | −4.00000 | −0.226819 | −0.113410 | − | 0.993548i | \(-0.536177\pi\) | ||||
−0.113410 | + | 0.993548i | \(0.536177\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.7984 | 0.723407 | 0.361703 | − | 0.932293i | \(-0.382195\pi\) | ||||
0.361703 | + | 0.932293i | \(0.382195\pi\) | |||||||
\(314\) | 3.70820 | 0.209266 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.52786 | 0.0859491 | ||||||||
\(317\) | 11.0902 | 0.622886 | 0.311443 | − | 0.950265i | \(-0.399188\pi\) | ||||
0.311443 | + | 0.950265i | \(0.399188\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26.3607 | 1.47591 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.618034 | −0.0344417 | ||||||||
\(323\) | −11.2918 | −0.628292 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.09017 | −0.393292 | ||||||||
\(326\) | −1.38197 | −0.0765400 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.32624 | 0.183661 | ||||||||
\(329\) | −2.29180 | −0.126351 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.2361 | 1.05731 | 0.528655 | − | 0.848837i | \(-0.322697\pi\) | ||||
0.528655 | + | 0.848837i | \(0.322697\pi\) | |||||||
\(332\) | 6.94427 | 0.381116 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | −14.4721 | −0.790697 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.6738 | 0.744857 | 0.372429 | − | 0.928061i | \(-0.378525\pi\) | ||||
0.372429 | + | 0.928061i | \(0.378525\pi\) | |||||||
\(338\) | −37.2705 | −2.02725 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.09017 | 0.330286 | ||||||||
\(341\) | 25.9443 | 1.40496 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.41641 | 0.454443 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.43769 | −0.0772909 | ||||||||
\(347\) | 6.38197 | 0.342602 | 0.171301 | − | 0.985219i | \(-0.445203\pi\) | ||||
0.171301 | + | 0.985219i | \(0.445203\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 0.618034 | 0.0330353 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.85410 | −0.152124 | ||||||||
\(353\) | −24.0000 | −1.27739 | −0.638696 | − | 0.769460i | \(-0.720526\pi\) | ||||
−0.638696 | + | 0.769460i | \(0.720526\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.09017 | −0.217084 | ||||||||
\(356\) | 10.4721 | 0.555022 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.18034 | 0.115235 | ||||||||
\(359\) | −26.3607 | −1.39126 | −0.695632 | − | 0.718399i | \(-0.744875\pi\) | ||||
−0.695632 | + | 0.718399i | \(0.744875\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.5623 | −0.819069 | ||||||||
\(362\) | 12.1459 | 0.638374 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.38197 | 0.229677 | ||||||||
\(365\) | −3.23607 | −0.169384 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.47214 | 0.337843 | 0.168921 | − | 0.985630i | \(-0.445972\pi\) | ||||
0.168921 | + | 0.985630i | \(0.445972\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.47214 | 0.336470 | ||||||||
\(371\) | 0.291796 | 0.0151493 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.1803 | 1.04490 | 0.522449 | − | 0.852670i | \(-0.325018\pi\) | ||||
0.522449 | + | 0.852670i | \(0.325018\pi\) | |||||||
\(374\) | 17.3820 | 0.898800 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.70820 | −0.191236 | ||||||||
\(377\) | −65.4853 | −3.37266 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.4508 | −1.15322 | −0.576611 | − | 0.817019i | \(-0.695625\pi\) | ||||
−0.576611 | + | 0.817019i | \(0.695625\pi\) | |||||||
\(380\) | −1.85410 | −0.0951134 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13.7082 | −0.701373 | ||||||||
\(383\) | 17.8885 | 0.914062 | 0.457031 | − | 0.889451i | \(-0.348913\pi\) | ||||
0.457031 | + | 0.889451i | \(0.348913\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.76393 | 0.0898983 | ||||||||
\(386\) | −0.763932 | −0.0388831 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.3820 | 0.628599 | ||||||||
\(389\) | −21.3262 | −1.08128 | −0.540642 | − | 0.841253i | \(-0.681818\pi\) | ||||
−0.540642 | + | 0.841253i | \(0.681818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.09017 | 0.307993 | ||||||||
\(392\) | 6.61803 | 0.334261 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22.5623 | −1.13667 | ||||||||
\(395\) | −1.52786 | −0.0768752 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.32624 | 0.367693 | 0.183847 | − | 0.982955i | \(-0.441145\pi\) | ||||
0.183847 | + | 0.982955i | \(0.441145\pi\) | |||||||
\(398\) | −2.00000 | −0.100251 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.70820 | 0.0853036 | 0.0426518 | − | 0.999090i | \(-0.486419\pi\) | ||||
0.0426518 | + | 0.999090i | \(0.486419\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −64.4508 | −3.21053 | ||||||||
\(404\) | 0.291796 | 0.0145174 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.70820 | 0.283293 | ||||||||
\(407\) | 18.4721 | 0.915630 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.2148 | −1.49402 | −0.747012 | − | 0.664810i | \(-0.768512\pi\) | ||||
−0.747012 | + | 0.664810i | \(0.768512\pi\) | |||||||
\(410\) | −3.32624 | −0.164271 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.5623 | 0.815966 | ||||||||
\(413\) | 1.05573 | 0.0519490 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.94427 | −0.340881 | ||||||||
\(416\) | 7.09017 | 0.347624 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.29180 | −0.258830 | ||||||||
\(419\) | −14.4721 | −0.707010 | −0.353505 | − | 0.935433i | \(-0.615010\pi\) | ||||
−0.353505 | + | 0.935433i | \(0.615010\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7426 | 0.669776 | 0.334888 | − | 0.942258i | \(-0.391302\pi\) | ||||
0.334888 | + | 0.942258i | \(0.391302\pi\) | |||||||
\(422\) | −14.0000 | −0.681509 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.472136 | 0.0229289 | ||||||||
\(425\) | −6.09017 | −0.295417 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.76393 | 0.278936 | ||||||||
\(428\) | −18.1803 | −0.878780 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.34752 | −0.161245 | −0.0806223 | − | 0.996745i | \(-0.525691\pi\) | ||||
−0.0806223 | + | 0.996745i | \(0.525691\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.50658 | 0.408800 | 0.204400 | − | 0.978887i | \(-0.434476\pi\) | ||||
0.204400 | + | 0.978887i | \(0.434476\pi\) | |||||||
\(434\) | 5.61803 | 0.269674 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.5623 | −0.553734 | ||||||||
\(437\) | −1.85410 | −0.0886937 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.3820 | −0.638686 | −0.319343 | − | 0.947639i | \(-0.603462\pi\) | ||||
−0.319343 | + | 0.947639i | \(0.603462\pi\) | |||||||
\(440\) | 2.85410 | 0.136064 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −43.1803 | −2.05388 | ||||||||
\(443\) | −25.0902 | −1.19207 | −0.596035 | − | 0.802958i | \(-0.703258\pi\) | ||||
−0.596035 | + | 0.802958i | \(0.703258\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.4721 | −0.496427 | ||||||||
\(446\) | 20.9443 | 0.991740 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.618034 | −0.0291994 | ||||||||
\(449\) | 1.56231 | 0.0737298 | 0.0368649 | − | 0.999320i | \(-0.488263\pi\) | ||||
0.0368649 | + | 0.999320i | \(0.488263\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.49342 | −0.447028 | ||||||||
\(452\) | −1.05573 | −0.0496573 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18.7639 | −0.880635 | ||||||||
\(455\) | −4.38197 | −0.205430 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.7771 | −1.76714 | −0.883569 | − | 0.468301i | \(-0.844866\pi\) | ||||
−0.883569 | + | 0.468301i | \(0.844866\pi\) | |||||||
\(458\) | −10.0000 | −0.467269 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.00000 | 0.0466252 | ||||||||
\(461\) | 39.2361 | 1.82741 | 0.913703 | − | 0.406383i | \(-0.133210\pi\) | ||||
0.913703 | + | 0.406383i | \(0.133210\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.00000 | 0.0929479 | 0.0464739 | − | 0.998920i | \(-0.485202\pi\) | ||||
0.0464739 | + | 0.998920i | \(0.485202\pi\) | |||||||
\(464\) | 9.23607 | 0.428774 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.29180 | 0.291462 | ||||||||
\(467\) | 17.1246 | 0.792433 | 0.396216 | − | 0.918157i | \(-0.370323\pi\) | ||||
0.396216 | + | 0.918157i | \(0.370323\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.94427 | −0.413008 | ||||||||
\(470\) | 3.70820 | 0.171047 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.70820 | 0.0786265 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.85410 | 0.0850720 | ||||||||
\(476\) | 3.76393 | 0.172520 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.3607 | −0.931276 | ||||||||
\(479\) | 31.8885 | 1.45702 | 0.728512 | − | 0.685033i | \(-0.240212\pi\) | ||||
0.728512 | + | 0.685033i | \(0.240212\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −45.8885 | −2.09234 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.85410 | −0.129732 | ||||||||
\(485\) | −12.3820 | −0.562236 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.8197 | −0.898115 | −0.449057 | − | 0.893503i | \(-0.648240\pi\) | ||||
−0.449057 | + | 0.893503i | \(0.648240\pi\) | |||||||
\(488\) | 9.32624 | 0.422179 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.61803 | −0.298972 | ||||||||
\(491\) | −6.18034 | −0.278915 | −0.139457 | − | 0.990228i | \(-0.544536\pi\) | ||||
−0.139457 | + | 0.990228i | \(0.544536\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −56.2492 | −2.53334 | ||||||||
\(494\) | 13.1459 | 0.591462 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.09017 | 0.408161 | ||||||||
\(497\) | −2.52786 | −0.113390 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.3607 | 0.553340 | 0.276670 | − | 0.960965i | \(-0.410769\pi\) | ||||
0.276670 | + | 0.960965i | \(0.410769\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.14590 | 0.274305 | ||||||||
\(503\) | −36.3262 | −1.61971 | −0.809853 | − | 0.586632i | \(-0.800453\pi\) | ||||
−0.809853 | + | 0.586632i | \(0.800453\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.291796 | −0.0129848 | ||||||||
\(506\) | 2.85410 | 0.126880 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.1803 | 0.717886 | ||||||||
\(509\) | −36.6525 | −1.62459 | −0.812296 | − | 0.583245i | \(-0.801783\pi\) | ||||
−0.812296 | + | 0.583245i | \(0.801783\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.00000 | −0.0884748 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.81966 | −0.344910 | ||||||||
\(515\) | −16.5623 | −0.729822 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.5836 | 0.465466 | ||||||||
\(518\) | 4.00000 | 0.175750 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.09017 | −0.310925 | ||||||||
\(521\) | 15.5279 | 0.680288 | 0.340144 | − | 0.940373i | \(-0.389524\pi\) | ||||
0.340144 | + | 0.940373i | \(0.389524\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.0000 | −1.13690 | −0.568450 | − | 0.822718i | \(-0.692457\pi\) | ||||
−0.568450 | + | 0.822718i | \(0.692457\pi\) | |||||||
\(524\) | −2.94427 | −0.128621 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.7426 | 0.904422 | ||||||||
\(527\) | −55.3607 | −2.41155 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −0.472136 | −0.0205083 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.14590 | −0.0496810 | ||||||||
\(533\) | 23.5836 | 1.02152 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.1803 | 0.786005 | ||||||||
\(536\) | −14.4721 | −0.625101 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.1803 | −0.611358 | ||||||||
\(539\) | −18.8885 | −0.813587 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.8328 | 0.981659 | 0.490830 | − | 0.871256i | \(-0.336694\pi\) | ||||
0.490830 | + | 0.871256i | \(0.336694\pi\) | |||||||
\(542\) | 30.3262 | 1.30262 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.09017 | 0.261114 | ||||||||
\(545\) | 11.5623 | 0.495275 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.9230 | 1.19390 | 0.596950 | − | 0.802278i | \(-0.296379\pi\) | ||||
0.596950 | + | 0.802278i | \(0.296379\pi\) | |||||||
\(548\) | 10.3262 | 0.441115 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.85410 | −0.121699 | ||||||||
\(551\) | 17.1246 | 0.729533 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.944272 | −0.0401545 | ||||||||
\(554\) | −29.4164 | −1.24978 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.7639 | 0.541311 | ||||||||
\(557\) | 22.8328 | 0.967457 | 0.483729 | − | 0.875218i | \(-0.339282\pi\) | ||||
0.483729 | + | 0.875218i | \(0.339282\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.618034 | 0.0261167 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.7639 | 0.960239 | ||||||||
\(563\) | 13.8885 | 0.585332 | 0.292666 | − | 0.956215i | \(-0.405458\pi\) | ||||
0.292666 | + | 0.956215i | \(0.405458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.05573 | 0.0444148 | ||||||||
\(566\) | 26.9443 | 1.13255 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.09017 | −0.171620 | ||||||||
\(569\) | 2.00000 | 0.0838444 | 0.0419222 | − | 0.999121i | \(-0.486652\pi\) | ||||
0.0419222 | + | 0.999121i | \(0.486652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.9787 | 0.668688 | 0.334344 | − | 0.942451i | \(-0.391485\pi\) | ||||
0.334344 | + | 0.942451i | \(0.391485\pi\) | |||||||
\(572\) | −20.2361 | −0.846113 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.05573 | −0.0858044 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.52786 | −0.146867 | −0.0734335 | − | 0.997300i | \(-0.523396\pi\) | ||||
−0.0734335 | + | 0.997300i | \(0.523396\pi\) | |||||||
\(578\) | −20.0902 | −0.835641 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.23607 | −0.383507 | ||||||||
\(581\) | −4.29180 | −0.178054 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.34752 | −0.0558087 | ||||||||
\(584\) | −3.23607 | −0.133909 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.8885 | −0.821588 | ||||||||
\(587\) | −13.6180 | −0.562076 | −0.281038 | − | 0.959697i | \(-0.590679\pi\) | ||||
−0.281038 | + | 0.959697i | \(0.590679\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.8541 | 0.694461 | ||||||||
\(590\) | −1.70820 | −0.0703256 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.47214 | 0.266003 | ||||||||
\(593\) | −39.2361 | −1.61123 | −0.805616 | − | 0.592438i | \(-0.798166\pi\) | ||||
−0.805616 | + | 0.592438i | \(0.798166\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.76393 | −0.154306 | ||||||||
\(596\) | 7.85410 | 0.321717 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.09017 | −0.289939 | ||||||||
\(599\) | 18.3820 | 0.751067 | 0.375533 | − | 0.926809i | \(-0.377460\pi\) | ||||
0.375533 | + | 0.926809i | \(0.377460\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.2705 | −1.35713 | −0.678566 | − | 0.734539i | \(-0.737398\pi\) | ||||
−0.678566 | + | 0.734539i | \(0.737398\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.56231 | −0.104259 | ||||||||
\(605\) | 2.85410 | 0.116036 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.4721 | 1.07447 | 0.537235 | − | 0.843432i | \(-0.319469\pi\) | ||||
0.537235 | + | 0.843432i | \(0.319469\pi\) | |||||||
\(608\) | −1.85410 | −0.0751938 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.32624 | −0.377608 | ||||||||
\(611\) | −26.2918 | −1.06365 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.3050 | 0.779720 | 0.389860 | − | 0.920874i | \(-0.372523\pi\) | ||||
0.389860 | + | 0.920874i | \(0.372523\pi\) | |||||||
\(614\) | 28.4508 | 1.14818 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.76393 | 0.0710708 | ||||||||
\(617\) | −34.0902 | −1.37242 | −0.686209 | − | 0.727404i | \(-0.740727\pi\) | ||||
−0.686209 | + | 0.727404i | \(0.740727\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.79837 | −0.112476 | −0.0562381 | − | 0.998417i | \(-0.517911\pi\) | ||||
−0.0562381 | + | 0.998417i | \(0.517911\pi\) | |||||||
\(620\) | −9.09017 | −0.365070 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.00000 | 0.160385 | ||||||||
\(623\) | −6.47214 | −0.259301 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −12.7984 | −0.511526 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.70820 | −0.147973 | ||||||||
\(629\) | −39.4164 | −1.57164 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.0689 | 1.67474 | 0.837368 | − | 0.546640i | \(-0.184093\pi\) | ||||
0.837368 | + | 0.546640i | \(0.184093\pi\) | |||||||
\(632\) | −1.52786 | −0.0607752 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.0902 | −0.440447 | ||||||||
\(635\) | −16.1803 | −0.642097 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46.9230 | 1.85916 | ||||||||
\(638\) | −26.3607 | −1.04363 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −0.360680 | −0.0142460 | −0.00712300 | − | 0.999975i | \(-0.502267\pi\) | ||||
−0.00712300 | + | 0.999975i | \(0.502267\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.29180 | −0.326997 | −0.163498 | − | 0.986544i | \(-0.552278\pi\) | ||||
−0.163498 | + | 0.986544i | \(0.552278\pi\) | |||||||
\(644\) | 0.618034 | 0.0243540 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.2918 | 0.444270 | ||||||||
\(647\) | 36.2492 | 1.42510 | 0.712552 | − | 0.701619i | \(-0.247539\pi\) | ||||
0.712552 | + | 0.701619i | \(0.247539\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.87539 | −0.191376 | ||||||||
\(650\) | 7.09017 | 0.278099 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.38197 | 0.0541220 | ||||||||
\(653\) | 8.03444 | 0.314412 | 0.157206 | − | 0.987566i | \(-0.449751\pi\) | ||||
0.157206 | + | 0.987566i | \(0.449751\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.94427 | 0.115042 | ||||||||
\(656\) | −3.32624 | −0.129868 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.29180 | 0.0893435 | ||||||||
\(659\) | 46.2492 | 1.80161 | 0.900807 | − | 0.434220i | \(-0.142976\pi\) | ||||
0.900807 | + | 0.434220i | \(0.142976\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.6738 | 0.726325 | 0.363163 | − | 0.931726i | \(-0.381697\pi\) | ||||
0.363163 | + | 0.931726i | \(0.381697\pi\) | |||||||
\(662\) | −19.2361 | −0.747631 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.94427 | −0.269490 | ||||||||
\(665\) | 1.14590 | 0.0444360 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.23607 | −0.357622 | ||||||||
\(668\) | 8.00000 | 0.309529 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 14.4721 | 0.559107 | ||||||||
\(671\) | −26.6180 | −1.02758 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.9443 | −0.421871 | −0.210935 | − | 0.977500i | \(-0.567651\pi\) | ||||
−0.210935 | + | 0.977500i | \(0.567651\pi\) | |||||||
\(674\) | −13.6738 | −0.526694 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 37.2705 | 1.43348 | ||||||||
\(677\) | 50.9443 | 1.95795 | 0.978974 | − | 0.203986i | \(-0.0653899\pi\) | ||||
0.978974 | + | 0.203986i | \(0.0653899\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.65248 | −0.293675 | ||||||||
\(680\) | −6.09017 | −0.233547 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −25.9443 | −0.993458 | ||||||||
\(683\) | 31.5623 | 1.20770 | 0.603849 | − | 0.797099i | \(-0.293633\pi\) | ||||
0.603849 | + | 0.797099i | \(0.293633\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.3262 | −0.394545 | ||||||||
\(686\) | −8.41641 | −0.321340 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.34752 | 0.127531 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.2361 | −1.11219 | −0.556096 | − | 0.831118i | \(-0.687701\pi\) | ||||
−0.556096 | + | 0.831118i | \(0.687701\pi\) | |||||||
\(692\) | 1.43769 | 0.0546529 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.38197 | −0.242256 | ||||||||
\(695\) | −12.7639 | −0.484164 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.2574 | 0.767302 | ||||||||
\(698\) | 2.00000 | 0.0757011 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.618034 | −0.0233595 | ||||||||
\(701\) | −43.3394 | −1.63691 | −0.818453 | − | 0.574573i | \(-0.805168\pi\) | ||||
−0.818453 | + | 0.574573i | \(0.805168\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000 | 0.452589 | ||||||||
\(704\) | 2.85410 | 0.107568 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.0000 | 0.903252 | ||||||||
\(707\) | −0.180340 | −0.00678238 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.0902 | −0.979837 | −0.489918 | − | 0.871768i | \(-0.662973\pi\) | ||||
−0.489918 | + | 0.871768i | \(0.662973\pi\) | |||||||
\(710\) | 4.09017 | 0.153501 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.4721 | −0.392460 | ||||||||
\(713\) | −9.09017 | −0.340430 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.2361 | 0.756786 | ||||||||
\(716\) | −2.18034 | −0.0814831 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 26.3607 | 0.983772 | ||||||||
\(719\) | −35.2705 | −1.31537 | −0.657684 | − | 0.753294i | \(-0.728464\pi\) | ||||
−0.657684 | + | 0.753294i | \(0.728464\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.2361 | −0.381211 | ||||||||
\(722\) | 15.5623 | 0.579169 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.1459 | −0.451399 | ||||||||
\(725\) | 9.23607 | 0.343019 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.2016 | 1.04594 | 0.522970 | − | 0.852351i | \(-0.324824\pi\) | ||||
0.522970 | + | 0.852351i | \(0.324824\pi\) | |||||||
\(728\) | −4.38197 | −0.162406 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.23607 | 0.119772 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.4164 | −1.08652 | −0.543260 | − | 0.839565i | \(-0.682810\pi\) | ||||
−0.543260 | + | 0.839565i | \(0.682810\pi\) | |||||||
\(734\) | −6.47214 | −0.238891 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 41.3050 | 1.52149 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.8885 | −0.510898 | −0.255449 | − | 0.966822i | \(-0.582223\pi\) | ||||
−0.255449 | + | 0.966822i | \(0.582223\pi\) | |||||||
\(740\) | −6.47214 | −0.237920 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.291796 | −0.0107122 | ||||||||
\(743\) | −33.6312 | −1.23381 | −0.616904 | − | 0.787038i | \(-0.711613\pi\) | ||||
−0.616904 | + | 0.787038i | \(0.711613\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.85410 | −0.287752 | ||||||||
\(746\) | −20.1803 | −0.738855 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −17.3820 | −0.635548 | ||||||||
\(749\) | 11.2361 | 0.410557 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −47.0132 | −1.71553 | −0.857767 | − | 0.514038i | \(-0.828149\pi\) | ||||
−0.857767 | + | 0.514038i | \(0.828149\pi\) | |||||||
\(752\) | 3.70820 | 0.135224 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 65.4853 | 2.38483 | ||||||||
\(755\) | 2.56231 | 0.0932519 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.8885 | −0.650170 | −0.325085 | − | 0.945685i | \(-0.605393\pi\) | ||||
−0.325085 | + | 0.945685i | \(0.605393\pi\) | |||||||
\(758\) | 22.4508 | 0.815452 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.85410 | 0.0672553 | ||||||||
\(761\) | −46.8673 | −1.69894 | −0.849468 | − | 0.527640i | \(-0.823077\pi\) | ||||
−0.849468 | + | 0.527640i | \(0.823077\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.14590 | 0.258699 | ||||||||
\(764\) | 13.7082 | 0.495945 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.8885 | −0.646339 | ||||||||
\(767\) | 12.1115 | 0.437319 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.58359 | −0.237410 | −0.118705 | − | 0.992930i | \(-0.537874\pi\) | ||||
−0.118705 | + | 0.992930i | \(0.537874\pi\) | |||||||
\(770\) | −1.76393 | −0.0635677 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.763932 | 0.0274945 | ||||||||
\(773\) | −28.9443 | −1.04105 | −0.520527 | − | 0.853845i | \(-0.674264\pi\) | ||||
−0.520527 | + | 0.853845i | \(0.674264\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.09017 | 0.326529 | ||||||||
\(776\) | −12.3820 | −0.444487 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21.3262 | 0.764583 | ||||||||
\(779\) | −6.16718 | −0.220962 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.6738 | 0.417720 | ||||||||
\(782\) | −6.09017 | −0.217784 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.61803 | −0.236358 | ||||||||
\(785\) | 3.70820 | 0.132351 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.87539 | −0.102497 | −0.0512483 | − | 0.998686i | \(-0.516320\pi\) | ||||
−0.0512483 | + | 0.998686i | \(0.516320\pi\) | |||||||
\(788\) | 22.5623 | 0.803749 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.52786 | 0.0543590 | ||||||||
\(791\) | 0.652476 | 0.0231994 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 66.1246 | 2.34815 | ||||||||
\(794\) | −7.32624 | −0.259998 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.00000 | 0.0708881 | ||||||||
\(797\) | −13.7082 | −0.485569 | −0.242785 | − | 0.970080i | \(-0.578061\pi\) | ||||
−0.242785 | + | 0.970080i | \(0.578061\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.5836 | −0.798950 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.70820 | −0.0603188 | ||||||||
\(803\) | 9.23607 | 0.325934 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.618034 | −0.0217828 | ||||||||
\(806\) | 64.4508 | 2.27018 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.291796 | −0.0102653 | ||||||||
\(809\) | 46.7426 | 1.64338 | 0.821692 | − | 0.569932i | \(-0.193030\pi\) | ||||
0.821692 | + | 0.569932i | \(0.193030\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.8197 | 0.766192 | 0.383096 | − | 0.923709i | \(-0.374858\pi\) | ||||
0.383096 | + | 0.923709i | \(0.374858\pi\) | |||||||
\(812\) | −5.70820 | −0.200319 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −18.4721 | −0.647448 | ||||||||
\(815\) | −1.38197 | −0.0484082 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 30.2148 | 1.05644 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.32624 | 0.116157 | ||||||||
\(821\) | 33.0557 | 1.15365 | 0.576826 | − | 0.816867i | \(-0.304291\pi\) | ||||
0.576826 | + | 0.816867i | \(0.304291\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.4164 | 0.885960 | 0.442980 | − | 0.896531i | \(-0.353921\pi\) | ||||
0.442980 | + | 0.896531i | \(0.353921\pi\) | |||||||
\(824\) | −16.5623 | −0.576975 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.05573 | −0.0367335 | ||||||||
\(827\) | −21.7082 | −0.754868 | −0.377434 | − | 0.926036i | \(-0.623194\pi\) | ||||
−0.377434 | + | 0.926036i | \(0.623194\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.9443 | 0.657962 | 0.328981 | − | 0.944337i | \(-0.393295\pi\) | ||||
0.328981 | + | 0.944337i | \(0.393295\pi\) | |||||||
\(830\) | 6.94427 | 0.241039 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.09017 | −0.245807 | ||||||||
\(833\) | 40.3050 | 1.39648 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.00000 | −0.276851 | ||||||||
\(836\) | 5.29180 | 0.183021 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.4721 | 0.499932 | ||||||||
\(839\) | −33.0132 | −1.13974 | −0.569870 | − | 0.821735i | \(-0.693007\pi\) | ||||
−0.569870 | + | 0.821735i | \(0.693007\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 56.3050 | 1.94155 | ||||||||
\(842\) | −13.7426 | −0.473603 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.0000 | 0.481900 | ||||||||
\(845\) | −37.2705 | −1.28214 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.76393 | 0.0606094 | ||||||||
\(848\) | −0.472136 | −0.0162132 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.09017 | 0.208891 | ||||||||
\(851\) | −6.47214 | −0.221862 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.7984 | −0.369729 | −0.184865 | − | 0.982764i | \(-0.559185\pi\) | ||||
−0.184865 | + | 0.982764i | \(0.559185\pi\) | |||||||
\(854\) | −5.76393 | −0.197238 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.1803 | 0.621391 | ||||||||
\(857\) | 6.58359 | 0.224891 | 0.112446 | − | 0.993658i | \(-0.464132\pi\) | ||||
0.112446 | + | 0.993658i | \(0.464132\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.0689 | −0.821220 | −0.410610 | − | 0.911811i | \(-0.634684\pi\) | ||||
−0.410610 | + | 0.911811i | \(0.634684\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.34752 | 0.114017 | ||||||||
\(863\) | −32.7639 | −1.11530 | −0.557649 | − | 0.830077i | \(-0.688296\pi\) | ||||
−0.557649 | + | 0.830077i | \(0.688296\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.43769 | −0.0488831 | ||||||||
\(866\) | −8.50658 | −0.289065 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.61803 | −0.190688 | ||||||||
\(869\) | 4.36068 | 0.147926 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −102.610 | −3.47680 | ||||||||
\(872\) | 11.5623 | 0.391549 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.85410 | 0.0627159 | ||||||||
\(875\) | 0.618034 | 0.0208934 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.7426 | 0.632894 | 0.316447 | − | 0.948610i | \(-0.397510\pi\) | ||||
0.316447 | + | 0.948610i | \(0.397510\pi\) | |||||||
\(878\) | 13.3820 | 0.451619 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.85410 | −0.0962118 | ||||||||
\(881\) | −8.58359 | −0.289189 | −0.144594 | − | 0.989491i | \(-0.546188\pi\) | ||||
−0.144594 | + | 0.989491i | \(0.546188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.5623 | 0.523713 | 0.261857 | − | 0.965107i | \(-0.415665\pi\) | ||||
0.261857 | + | 0.965107i | \(0.415665\pi\) | |||||||
\(884\) | 43.1803 | 1.45231 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.0902 | 0.842921 | ||||||||
\(887\) | 5.16718 | 0.173497 | 0.0867485 | − | 0.996230i | \(-0.472352\pi\) | ||||
0.0867485 | + | 0.996230i | \(0.472352\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.0000 | −0.335389 | ||||||||
\(890\) | 10.4721 | 0.351027 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −20.9443 | −0.701266 | ||||||||
\(893\) | 6.87539 | 0.230076 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.18034 | 0.0728807 | ||||||||
\(896\) | 0.618034 | 0.0206471 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.56231 | −0.0521348 | ||||||||
\(899\) | 83.9574 | 2.80014 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.87539 | 0.0957931 | ||||||||
\(902\) | 9.49342 | 0.316096 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.05573 | 0.0351130 | ||||||||
\(905\) | 12.1459 | 0.403743 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.12461 | 0.236569 | 0.118284 | − | 0.992980i | \(-0.462261\pi\) | ||||
0.118284 | + | 0.992980i | \(0.462261\pi\) | |||||||
\(908\) | 18.7639 | 0.622703 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.38197 | 0.145261 | ||||||||
\(911\) | −36.0689 | −1.19502 | −0.597508 | − | 0.801863i | \(-0.703842\pi\) | ||||
−0.597508 | + | 0.801863i | \(0.703842\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.8197 | 0.655935 | ||||||||
\(914\) | 37.7771 | 1.24955 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.0000 | 0.330409 | ||||||||
\(917\) | 1.81966 | 0.0600905 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.0000 | 1.31948 | 0.659739 | − | 0.751495i | \(-0.270667\pi\) | ||||
0.659739 | + | 0.751495i | \(0.270667\pi\) | |||||||
\(920\) | −1.00000 | −0.0329690 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −39.2361 | −1.29217 | ||||||||
\(923\) | −29.0000 | −0.954547 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.47214 | 0.212803 | ||||||||
\(926\) | −2.00000 | −0.0657241 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.23607 | −0.303189 | ||||||||
\(929\) | 3.52786 | 0.115745 | 0.0578727 | − | 0.998324i | \(-0.481568\pi\) | ||||
0.0578727 | + | 0.998324i | \(0.481568\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.2705 | −0.402150 | ||||||||
\(932\) | −6.29180 | −0.206095 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.1246 | −0.560334 | ||||||||
\(935\) | 17.3820 | 0.568451 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.7984 | −1.20215 | −0.601075 | − | 0.799192i | \(-0.705261\pi\) | ||||
−0.601075 | + | 0.799192i | \(0.705261\pi\) | |||||||
\(938\) | 8.94427 | 0.292041 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.70820 | −0.120948 | ||||||||
\(941\) | 22.4934 | 0.733265 | 0.366632 | − | 0.930366i | \(-0.380511\pi\) | ||||
0.366632 | + | 0.930366i | \(0.380511\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.32624 | 0.108317 | ||||||||
\(944\) | −1.70820 | −0.0555973 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54.6869 | 1.77709 | 0.888543 | − | 0.458793i | \(-0.151718\pi\) | ||||
0.888543 | + | 0.458793i | \(0.151718\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.9443 | −0.744803 | ||||||||
\(950\) | −1.85410 | −0.0601550 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.76393 | −0.121990 | ||||||||
\(953\) | −3.79837 | −0.123041 | −0.0615207 | − | 0.998106i | \(-0.519595\pi\) | ||||
−0.0615207 | + | 0.998106i | \(0.519595\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.7082 | −0.443587 | ||||||||
\(956\) | 20.3607 | 0.658511 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −31.8885 | −1.03027 | ||||||||
\(959\) | −6.38197 | −0.206084 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51.6312 | 1.66552 | ||||||||
\(962\) | 45.8885 | 1.47951 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.763932 | −0.0245918 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.5410 | −0.531923 | −0.265962 | − | 0.963984i | \(-0.585689\pi\) | ||||
−0.265962 | + | 0.963984i | \(0.585689\pi\) | |||||||
\(968\) | 2.85410 | 0.0917343 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.3820 | 0.397561 | ||||||||
\(971\) | −34.2705 | −1.09979 | −0.549896 | − | 0.835233i | \(-0.685333\pi\) | ||||
−0.549896 | + | 0.835233i | \(0.685333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.88854 | −0.252895 | ||||||||
\(974\) | 19.8197 | 0.635063 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.32624 | −0.298526 | ||||||||
\(977\) | 23.5623 | 0.753825 | 0.376912 | − | 0.926249i | \(-0.376986\pi\) | ||||
0.376912 | + | 0.926249i | \(0.376986\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.8885 | 0.955242 | ||||||||
\(980\) | 6.61803 | 0.211405 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.18034 | 0.197223 | ||||||||
\(983\) | 14.2705 | 0.455159 | 0.227579 | − | 0.973760i | \(-0.426919\pi\) | ||||
0.227579 | + | 0.973760i | \(0.426919\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.5623 | −0.718895 | ||||||||
\(986\) | 56.2492 | 1.79134 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.1459 | −0.418227 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.5066 | 0.873775 | 0.436888 | − | 0.899516i | \(-0.356081\pi\) | ||||
0.436888 | + | 0.899516i | \(0.356081\pi\) | |||||||
\(992\) | −9.09017 | −0.288613 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.52786 | 0.0801790 | ||||||||
\(995\) | −2.00000 | −0.0634043 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.1935 | 1.81134 | 0.905668 | − | 0.423987i | \(-0.139370\pi\) | ||||
0.905668 | + | 0.423987i | \(0.139370\pi\) | |||||||
\(998\) | −12.3607 | −0.391270 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2070.2.a.u.1.1 | 2 | ||
3.2 | odd | 2 | 230.2.a.c.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 1840.2.a.l.1.1 | 2 | |||
15.2 | even | 4 | 1150.2.b.i.599.3 | 4 | |||
15.8 | even | 4 | 1150.2.b.i.599.2 | 4 | |||
15.14 | odd | 2 | 1150.2.a.j.1.1 | 2 | |||
24.5 | odd | 2 | 7360.2.a.bh.1.1 | 2 | |||
24.11 | even | 2 | 7360.2.a.bn.1.2 | 2 | |||
60.59 | even | 2 | 9200.2.a.bu.1.2 | 2 | |||
69.68 | even | 2 | 5290.2.a.o.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.a.c.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
1150.2.a.j.1.1 | 2 | 15.14 | odd | 2 | |||
1150.2.b.i.599.2 | 4 | 15.8 | even | 4 | |||
1150.2.b.i.599.3 | 4 | 15.2 | even | 4 | |||
1840.2.a.l.1.1 | 2 | 12.11 | even | 2 | |||
2070.2.a.u.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5290.2.a.o.1.2 | 2 | 69.68 | even | 2 | |||
7360.2.a.bh.1.1 | 2 | 24.5 | odd | 2 | |||
7360.2.a.bn.1.2 | 2 | 24.11 | even | 2 | |||
9200.2.a.bu.1.2 | 2 | 60.59 | even | 2 |