Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6033,2,Mod(1,6033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6033 = 3 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6033.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: | \(48.1737475394\) |
Analytic rank: | \(1\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.86532 | −1.31898 | −0.659491 | − | 0.751712i | \(-0.729228\pi\) | ||||
−0.659491 | + | 0.751712i | \(0.729228\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.47943 | 0.739715 | ||||||||
\(5\) | −0.830382 | −0.371358 | −0.185679 | − | 0.982610i | \(-0.559448\pi\) | ||||
−0.185679 | + | 0.982610i | \(0.559448\pi\) | |||||||
\(6\) | 1.86532 | 0.761515 | ||||||||
\(7\) | −1.56075 | −0.589910 | −0.294955 | − | 0.955511i | \(-0.595305\pi\) | ||||
−0.294955 | + | 0.955511i | \(0.595305\pi\) | |||||||
\(8\) | 0.971032 | 0.343312 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.54893 | 0.489815 | ||||||||
\(11\) | −0.963587 | −0.290532 | −0.145266 | − | 0.989393i | \(-0.546404\pi\) | ||||
−0.145266 | + | 0.989393i | \(0.546404\pi\) | |||||||
\(12\) | −1.47943 | −0.427075 | ||||||||
\(13\) | 2.49116 | 0.690922 | 0.345461 | − | 0.938433i | \(-0.387723\pi\) | ||||
0.345461 | + | 0.938433i | \(0.387723\pi\) | |||||||
\(14\) | 2.91131 | 0.778081 | ||||||||
\(15\) | 0.830382 | 0.214404 | ||||||||
\(16\) | −4.77015 | −1.19254 | ||||||||
\(17\) | −7.01663 | −1.70178 | −0.850892 | − | 0.525341i | \(-0.823938\pi\) | ||||
−0.850892 | + | 0.525341i | \(0.823938\pi\) | |||||||
\(18\) | −1.86532 | −0.439661 | ||||||||
\(19\) | 7.71862 | 1.77077 | 0.885386 | − | 0.464856i | \(-0.153894\pi\) | ||||
0.885386 | + | 0.464856i | \(0.153894\pi\) | |||||||
\(20\) | −1.22849 | −0.274699 | ||||||||
\(21\) | 1.56075 | 0.340585 | ||||||||
\(22\) | 1.79740 | 0.383207 | ||||||||
\(23\) | 4.98467 | 1.03938 | 0.519688 | − | 0.854356i | \(-0.326048\pi\) | ||||
0.519688 | + | 0.854356i | \(0.326048\pi\) | |||||||
\(24\) | −0.971032 | −0.198211 | ||||||||
\(25\) | −4.31047 | −0.862093 | ||||||||
\(26\) | −4.64681 | −0.911314 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.30903 | −0.436365 | ||||||||
\(29\) | −5.27328 | −0.979224 | −0.489612 | − | 0.871940i | \(-0.662862\pi\) | ||||
−0.489612 | + | 0.871940i | \(0.662862\pi\) | |||||||
\(30\) | −1.54893 | −0.282795 | ||||||||
\(31\) | 7.06097 | 1.26819 | 0.634094 | − | 0.773256i | \(-0.281373\pi\) | ||||
0.634094 | + | 0.773256i | \(0.281373\pi\) | |||||||
\(32\) | 6.95580 | 1.22962 | ||||||||
\(33\) | 0.963587 | 0.167739 | ||||||||
\(34\) | 13.0883 | 2.24462 | ||||||||
\(35\) | 1.29602 | 0.219068 | ||||||||
\(36\) | 1.47943 | 0.246572 | ||||||||
\(37\) | −6.02292 | −0.990163 | −0.495081 | − | 0.868847i | \(-0.664862\pi\) | ||||
−0.495081 | + | 0.868847i | \(0.664862\pi\) | |||||||
\(38\) | −14.3977 | −2.33562 | ||||||||
\(39\) | −2.49116 | −0.398904 | ||||||||
\(40\) | −0.806327 | −0.127492 | ||||||||
\(41\) | −3.69659 | −0.577311 | −0.288656 | − | 0.957433i | \(-0.593208\pi\) | ||||
−0.288656 | + | 0.957433i | \(0.593208\pi\) | |||||||
\(42\) | −2.91131 | −0.449225 | ||||||||
\(43\) | −2.56589 | −0.391294 | −0.195647 | − | 0.980674i | \(-0.562681\pi\) | ||||
−0.195647 | + | 0.980674i | \(0.562681\pi\) | |||||||
\(44\) | −1.42556 | −0.214911 | ||||||||
\(45\) | −0.830382 | −0.123786 | ||||||||
\(46\) | −9.29802 | −1.37092 | ||||||||
\(47\) | 3.50021 | 0.510558 | 0.255279 | − | 0.966867i | \(-0.417833\pi\) | ||||
0.255279 | + | 0.966867i | \(0.417833\pi\) | |||||||
\(48\) | 4.77015 | 0.688511 | ||||||||
\(49\) | −4.56405 | −0.652006 | ||||||||
\(50\) | 8.04041 | 1.13709 | ||||||||
\(51\) | 7.01663 | 0.982525 | ||||||||
\(52\) | 3.68549 | 0.511085 | ||||||||
\(53\) | 2.99589 | 0.411516 | 0.205758 | − | 0.978603i | \(-0.434034\pi\) | ||||
0.205758 | + | 0.978603i | \(0.434034\pi\) | |||||||
\(54\) | 1.86532 | 0.253838 | ||||||||
\(55\) | 0.800146 | 0.107892 | ||||||||
\(56\) | −1.51554 | −0.202523 | ||||||||
\(57\) | −7.71862 | −1.02236 | ||||||||
\(58\) | 9.83638 | 1.29158 | ||||||||
\(59\) | 4.80183 | 0.625145 | 0.312573 | − | 0.949894i | \(-0.398809\pi\) | ||||
0.312573 | + | 0.949894i | \(0.398809\pi\) | |||||||
\(60\) | 1.22849 | 0.158598 | ||||||||
\(61\) | 0.592250 | 0.0758298 | 0.0379149 | − | 0.999281i | \(-0.487928\pi\) | ||||
0.0379149 | + | 0.999281i | \(0.487928\pi\) | |||||||
\(62\) | −13.1710 | −1.67272 | ||||||||
\(63\) | −1.56075 | −0.196637 | ||||||||
\(64\) | −3.43452 | −0.429315 | ||||||||
\(65\) | −2.06861 | −0.256580 | ||||||||
\(66\) | −1.79740 | −0.221245 | ||||||||
\(67\) | 2.76615 | 0.337939 | 0.168969 | − | 0.985621i | \(-0.445956\pi\) | ||||
0.168969 | + | 0.985621i | \(0.445956\pi\) | |||||||
\(68\) | −10.3806 | −1.25883 | ||||||||
\(69\) | −4.98467 | −0.600084 | ||||||||
\(70\) | −2.41750 | −0.288947 | ||||||||
\(71\) | −0.539467 | −0.0640229 | −0.0320115 | − | 0.999488i | \(-0.510191\pi\) | ||||
−0.0320115 | + | 0.999488i | \(0.510191\pi\) | |||||||
\(72\) | 0.971032 | 0.114437 | ||||||||
\(73\) | 8.09331 | 0.947250 | 0.473625 | − | 0.880727i | \(-0.342945\pi\) | ||||
0.473625 | + | 0.880727i | \(0.342945\pi\) | |||||||
\(74\) | 11.2347 | 1.30601 | ||||||||
\(75\) | 4.31047 | 0.497730 | ||||||||
\(76\) | 11.4192 | 1.30987 | ||||||||
\(77\) | 1.50392 | 0.171388 | ||||||||
\(78\) | 4.64681 | 0.526148 | ||||||||
\(79\) | 8.49130 | 0.955346 | 0.477673 | − | 0.878538i | \(-0.341480\pi\) | ||||
0.477673 | + | 0.878538i | \(0.341480\pi\) | |||||||
\(80\) | 3.96105 | 0.442858 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.89534 | 0.761463 | ||||||||
\(83\) | −13.3674 | −1.46726 | −0.733632 | − | 0.679547i | \(-0.762176\pi\) | ||||
−0.733632 | + | 0.679547i | \(0.762176\pi\) | |||||||
\(84\) | 2.30903 | 0.251935 | ||||||||
\(85\) | 5.82649 | 0.631971 | ||||||||
\(86\) | 4.78620 | 0.516110 | ||||||||
\(87\) | 5.27328 | 0.565355 | ||||||||
\(88\) | −0.935674 | −0.0997431 | ||||||||
\(89\) | −4.97649 | −0.527507 | −0.263753 | − | 0.964590i | \(-0.584961\pi\) | ||||
−0.263753 | + | 0.964590i | \(0.584961\pi\) | |||||||
\(90\) | 1.54893 | 0.163272 | ||||||||
\(91\) | −3.88808 | −0.407582 | ||||||||
\(92\) | 7.37447 | 0.768841 | ||||||||
\(93\) | −7.06097 | −0.732189 | ||||||||
\(94\) | −6.52903 | −0.673418 | ||||||||
\(95\) | −6.40940 | −0.657591 | ||||||||
\(96\) | −6.95580 | −0.709924 | ||||||||
\(97\) | −8.51266 | −0.864329 | −0.432165 | − | 0.901795i | \(-0.642250\pi\) | ||||
−0.432165 | + | 0.901795i | \(0.642250\pi\) | |||||||
\(98\) | 8.51342 | 0.859985 | ||||||||
\(99\) | −0.963587 | −0.0968441 | ||||||||
\(100\) | −6.37703 | −0.637703 | ||||||||
\(101\) | 7.85984 | 0.782083 | 0.391042 | − | 0.920373i | \(-0.372115\pi\) | ||||
0.391042 | + | 0.920373i | \(0.372115\pi\) | |||||||
\(102\) | −13.0883 | −1.29593 | ||||||||
\(103\) | −9.63873 | −0.949732 | −0.474866 | − | 0.880058i | \(-0.657504\pi\) | ||||
−0.474866 | + | 0.880058i | \(0.657504\pi\) | |||||||
\(104\) | 2.41899 | 0.237202 | ||||||||
\(105\) | −1.29602 | −0.126479 | ||||||||
\(106\) | −5.58829 | −0.542783 | ||||||||
\(107\) | −6.35949 | −0.614795 | −0.307398 | − | 0.951581i | \(-0.599458\pi\) | ||||
−0.307398 | + | 0.951581i | \(0.599458\pi\) | |||||||
\(108\) | −1.47943 | −0.142358 | ||||||||
\(109\) | 14.1151 | 1.35198 | 0.675992 | − | 0.736909i | \(-0.263715\pi\) | ||||
0.675992 | + | 0.736909i | \(0.263715\pi\) | |||||||
\(110\) | −1.49253 | −0.142307 | ||||||||
\(111\) | 6.02292 | 0.571671 | ||||||||
\(112\) | 7.44503 | 0.703489 | ||||||||
\(113\) | 1.62567 | 0.152931 | 0.0764653 | − | 0.997072i | \(-0.475637\pi\) | ||||
0.0764653 | + | 0.997072i | \(0.475637\pi\) | |||||||
\(114\) | 14.3977 | 1.34847 | ||||||||
\(115\) | −4.13918 | −0.385981 | ||||||||
\(116\) | −7.80145 | −0.724347 | ||||||||
\(117\) | 2.49116 | 0.230307 | ||||||||
\(118\) | −8.95696 | −0.824555 | ||||||||
\(119\) | 10.9512 | 1.00390 | ||||||||
\(120\) | 0.806327 | 0.0736073 | ||||||||
\(121\) | −10.0715 | −0.915591 | ||||||||
\(122\) | −1.10474 | −0.100018 | ||||||||
\(123\) | 3.69659 | 0.333311 | ||||||||
\(124\) | 10.4462 | 0.938098 | ||||||||
\(125\) | 7.73124 | 0.691504 | ||||||||
\(126\) | 2.91131 | 0.259360 | ||||||||
\(127\) | 20.7987 | 1.84559 | 0.922793 | − | 0.385295i | \(-0.125900\pi\) | ||||
0.922793 | + | 0.385295i | \(0.125900\pi\) | |||||||
\(128\) | −7.50511 | −0.663364 | ||||||||
\(129\) | 2.56589 | 0.225914 | ||||||||
\(130\) | 3.85863 | 0.338424 | ||||||||
\(131\) | −2.35111 | −0.205417 | −0.102709 | − | 0.994711i | \(-0.532751\pi\) | ||||
−0.102709 | + | 0.994711i | \(0.532751\pi\) | |||||||
\(132\) | 1.42556 | 0.124079 | ||||||||
\(133\) | −12.0469 | −1.04460 | ||||||||
\(134\) | −5.15976 | −0.445735 | ||||||||
\(135\) | 0.830382 | 0.0714679 | ||||||||
\(136\) | −6.81337 | −0.584242 | ||||||||
\(137\) | −9.94169 | −0.849376 | −0.424688 | − | 0.905340i | \(-0.639616\pi\) | ||||
−0.424688 | + | 0.905340i | \(0.639616\pi\) | |||||||
\(138\) | 9.29802 | 0.791500 | ||||||||
\(139\) | 2.50975 | 0.212874 | 0.106437 | − | 0.994319i | \(-0.466056\pi\) | ||||
0.106437 | + | 0.994319i | \(0.466056\pi\) | |||||||
\(140\) | 1.91737 | 0.162048 | ||||||||
\(141\) | −3.50021 | −0.294771 | ||||||||
\(142\) | 1.00628 | 0.0844451 | ||||||||
\(143\) | −2.40045 | −0.200735 | ||||||||
\(144\) | −4.77015 | −0.397512 | ||||||||
\(145\) | 4.37884 | 0.363643 | ||||||||
\(146\) | −15.0966 | −1.24941 | ||||||||
\(147\) | 4.56405 | 0.376436 | ||||||||
\(148\) | −8.91049 | −0.732438 | ||||||||
\(149\) | 11.2473 | 0.921417 | 0.460709 | − | 0.887551i | \(-0.347595\pi\) | ||||
0.460709 | + | 0.887551i | \(0.347595\pi\) | |||||||
\(150\) | −8.04041 | −0.656497 | ||||||||
\(151\) | 11.9413 | 0.971765 | 0.485883 | − | 0.874024i | \(-0.338498\pi\) | ||||
0.485883 | + | 0.874024i | \(0.338498\pi\) | |||||||
\(152\) | 7.49502 | 0.607927 | ||||||||
\(153\) | −7.01663 | −0.567261 | ||||||||
\(154\) | −2.80530 | −0.226058 | ||||||||
\(155\) | −5.86331 | −0.470952 | ||||||||
\(156\) | −3.68549 | −0.295075 | ||||||||
\(157\) | 22.0003 | 1.75581 | 0.877907 | − | 0.478831i | \(-0.158939\pi\) | ||||
0.877907 | + | 0.478831i | \(0.158939\pi\) | |||||||
\(158\) | −15.8390 | −1.26008 | ||||||||
\(159\) | −2.99589 | −0.237589 | ||||||||
\(160\) | −5.77597 | −0.456631 | ||||||||
\(161\) | −7.77984 | −0.613138 | ||||||||
\(162\) | −1.86532 | −0.146554 | ||||||||
\(163\) | −7.54504 | −0.590973 | −0.295487 | − | 0.955347i | \(-0.595482\pi\) | ||||
−0.295487 | + | 0.955347i | \(0.595482\pi\) | |||||||
\(164\) | −5.46885 | −0.427046 | ||||||||
\(165\) | −0.800146 | −0.0622912 | ||||||||
\(166\) | 24.9345 | 1.93529 | ||||||||
\(167\) | 13.4737 | 1.04262 | 0.521312 | − | 0.853366i | \(-0.325443\pi\) | ||||
0.521312 | + | 0.853366i | \(0.325443\pi\) | |||||||
\(168\) | 1.51554 | 0.116927 | ||||||||
\(169\) | −6.79414 | −0.522626 | ||||||||
\(170\) | −10.8683 | −0.833559 | ||||||||
\(171\) | 7.71862 | 0.590258 | ||||||||
\(172\) | −3.79605 | −0.289446 | ||||||||
\(173\) | −20.0283 | −1.52272 | −0.761362 | − | 0.648327i | \(-0.775469\pi\) | ||||
−0.761362 | + | 0.648327i | \(0.775469\pi\) | |||||||
\(174\) | −9.83638 | −0.745694 | ||||||||
\(175\) | 6.72758 | 0.508557 | ||||||||
\(176\) | 4.59645 | 0.346471 | ||||||||
\(177\) | −4.80183 | −0.360928 | ||||||||
\(178\) | 9.28276 | 0.695772 | ||||||||
\(179\) | 8.16777 | 0.610488 | 0.305244 | − | 0.952274i | \(-0.401262\pi\) | ||||
0.305244 | + | 0.952274i | \(0.401262\pi\) | |||||||
\(180\) | −1.22849 | −0.0915664 | ||||||||
\(181\) | 12.5430 | 0.932315 | 0.466158 | − | 0.884702i | \(-0.345638\pi\) | ||||
0.466158 | + | 0.884702i | \(0.345638\pi\) | |||||||
\(182\) | 7.25253 | 0.537593 | ||||||||
\(183\) | −0.592250 | −0.0437804 | ||||||||
\(184\) | 4.84027 | 0.356830 | ||||||||
\(185\) | 5.00133 | 0.367705 | ||||||||
\(186\) | 13.1710 | 0.965744 | ||||||||
\(187\) | 6.76114 | 0.494423 | ||||||||
\(188\) | 5.17832 | 0.377668 | ||||||||
\(189\) | 1.56075 | 0.113528 | ||||||||
\(190\) | 11.9556 | 0.867351 | ||||||||
\(191\) | 8.52547 | 0.616881 | 0.308441 | − | 0.951244i | \(-0.400193\pi\) | ||||
0.308441 | + | 0.951244i | \(0.400193\pi\) | |||||||
\(192\) | 3.43452 | 0.247865 | ||||||||
\(193\) | 4.74772 | 0.341748 | 0.170874 | − | 0.985293i | \(-0.445341\pi\) | ||||
0.170874 | + | 0.985293i | \(0.445341\pi\) | |||||||
\(194\) | 15.8789 | 1.14004 | ||||||||
\(195\) | 2.06861 | 0.148136 | ||||||||
\(196\) | −6.75218 | −0.482299 | ||||||||
\(197\) | 8.15451 | 0.580985 | 0.290492 | − | 0.956877i | \(-0.406181\pi\) | ||||
0.290492 | + | 0.956877i | \(0.406181\pi\) | |||||||
\(198\) | 1.79740 | 0.127736 | ||||||||
\(199\) | −0.508875 | −0.0360732 | −0.0180366 | − | 0.999837i | \(-0.505742\pi\) | ||||
−0.0180366 | + | 0.999837i | \(0.505742\pi\) | |||||||
\(200\) | −4.18560 | −0.295967 | ||||||||
\(201\) | −2.76615 | −0.195109 | ||||||||
\(202\) | −14.6611 | −1.03155 | ||||||||
\(203\) | 8.23030 | 0.577654 | ||||||||
\(204\) | 10.3806 | 0.726788 | ||||||||
\(205\) | 3.06959 | 0.214389 | ||||||||
\(206\) | 17.9793 | 1.25268 | ||||||||
\(207\) | 4.98467 | 0.346458 | ||||||||
\(208\) | −11.8832 | −0.823950 | ||||||||
\(209\) | −7.43756 | −0.514467 | ||||||||
\(210\) | 2.41750 | 0.166823 | ||||||||
\(211\) | 3.64195 | 0.250722 | 0.125361 | − | 0.992111i | \(-0.459991\pi\) | ||||
0.125361 | + | 0.992111i | \(0.459991\pi\) | |||||||
\(212\) | 4.43220 | 0.304405 | ||||||||
\(213\) | 0.539467 | 0.0369637 | ||||||||
\(214\) | 11.8625 | 0.810904 | ||||||||
\(215\) | 2.13067 | 0.145310 | ||||||||
\(216\) | −0.971032 | −0.0660703 | ||||||||
\(217\) | −11.0204 | −0.748117 | ||||||||
\(218\) | −26.3293 | −1.78324 | ||||||||
\(219\) | −8.09331 | −0.546895 | ||||||||
\(220\) | 1.18376 | 0.0798090 | ||||||||
\(221\) | −17.4795 | −1.17580 | ||||||||
\(222\) | −11.2347 | −0.754024 | ||||||||
\(223\) | 19.2756 | 1.29079 | 0.645396 | − | 0.763848i | \(-0.276692\pi\) | ||||
0.645396 | + | 0.763848i | \(0.276692\pi\) | |||||||
\(224\) | −10.8563 | −0.725367 | ||||||||
\(225\) | −4.31047 | −0.287364 | ||||||||
\(226\) | −3.03241 | −0.201713 | ||||||||
\(227\) | −15.2177 | −1.01003 | −0.505017 | − | 0.863109i | \(-0.668514\pi\) | ||||
−0.505017 | + | 0.863109i | \(0.668514\pi\) | |||||||
\(228\) | −11.4192 | −0.756252 | ||||||||
\(229\) | −20.4128 | −1.34892 | −0.674458 | − | 0.738313i | \(-0.735623\pi\) | ||||
−0.674458 | + | 0.738313i | \(0.735623\pi\) | |||||||
\(230\) | 7.72091 | 0.509102 | ||||||||
\(231\) | −1.50392 | −0.0989509 | ||||||||
\(232\) | −5.12053 | −0.336179 | ||||||||
\(233\) | 8.60588 | 0.563790 | 0.281895 | − | 0.959445i | \(-0.409037\pi\) | ||||
0.281895 | + | 0.959445i | \(0.409037\pi\) | |||||||
\(234\) | −4.64681 | −0.303771 | ||||||||
\(235\) | −2.90651 | −0.189600 | ||||||||
\(236\) | 7.10397 | 0.462429 | ||||||||
\(237\) | −8.49130 | −0.551569 | ||||||||
\(238\) | −20.4276 | −1.32412 | ||||||||
\(239\) | −10.2583 | −0.663556 | −0.331778 | − | 0.943358i | \(-0.607648\pi\) | ||||
−0.331778 | + | 0.943358i | \(0.607648\pi\) | |||||||
\(240\) | −3.96105 | −0.255684 | ||||||||
\(241\) | −14.6332 | −0.942608 | −0.471304 | − | 0.881971i | \(-0.656216\pi\) | ||||
−0.471304 | + | 0.881971i | \(0.656216\pi\) | |||||||
\(242\) | 18.7866 | 1.20765 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.876192 | 0.0560924 | ||||||||
\(245\) | 3.78990 | 0.242128 | ||||||||
\(246\) | −6.89534 | −0.439631 | ||||||||
\(247\) | 19.2283 | 1.22347 | ||||||||
\(248\) | 6.85643 | 0.435384 | ||||||||
\(249\) | 13.3674 | 0.847125 | ||||||||
\(250\) | −14.4213 | −0.912081 | ||||||||
\(251\) | −16.7486 | −1.05716 | −0.528582 | − | 0.848882i | \(-0.677276\pi\) | ||||
−0.528582 | + | 0.848882i | \(0.677276\pi\) | |||||||
\(252\) | −2.30903 | −0.145455 | ||||||||
\(253\) | −4.80316 | −0.301972 | ||||||||
\(254\) | −38.7963 | −2.43430 | ||||||||
\(255\) | −5.82649 | −0.364869 | ||||||||
\(256\) | 20.8685 | 1.30428 | ||||||||
\(257\) | 4.89131 | 0.305111 | 0.152556 | − | 0.988295i | \(-0.451250\pi\) | ||||
0.152556 | + | 0.988295i | \(0.451250\pi\) | |||||||
\(258\) | −4.78620 | −0.297976 | ||||||||
\(259\) | 9.40031 | 0.584107 | ||||||||
\(260\) | −3.06036 | −0.189796 | ||||||||
\(261\) | −5.27328 | −0.326408 | ||||||||
\(262\) | 4.38558 | 0.270942 | ||||||||
\(263\) | 1.80979 | 0.111596 | 0.0557982 | − | 0.998442i | \(-0.482230\pi\) | ||||
0.0557982 | + | 0.998442i | \(0.482230\pi\) | |||||||
\(264\) | 0.935674 | 0.0575867 | ||||||||
\(265\) | −2.48773 | −0.152820 | ||||||||
\(266\) | 22.4713 | 1.37780 | ||||||||
\(267\) | 4.97649 | 0.304556 | ||||||||
\(268\) | 4.09232 | 0.249978 | ||||||||
\(269\) | 3.71262 | 0.226363 | 0.113181 | − | 0.993574i | \(-0.463896\pi\) | ||||
0.113181 | + | 0.993574i | \(0.463896\pi\) | |||||||
\(270\) | −1.54893 | −0.0942649 | ||||||||
\(271\) | −4.45630 | −0.270701 | −0.135350 | − | 0.990798i | \(-0.543216\pi\) | ||||
−0.135350 | + | 0.990798i | \(0.543216\pi\) | |||||||
\(272\) | 33.4704 | 2.02944 | ||||||||
\(273\) | 3.88808 | 0.235317 | ||||||||
\(274\) | 18.5445 | 1.12031 | ||||||||
\(275\) | 4.15351 | 0.250466 | ||||||||
\(276\) | −7.37447 | −0.443891 | ||||||||
\(277\) | 9.13295 | 0.548746 | 0.274373 | − | 0.961623i | \(-0.411530\pi\) | ||||
0.274373 | + | 0.961623i | \(0.411530\pi\) | |||||||
\(278\) | −4.68150 | −0.280778 | ||||||||
\(279\) | 7.06097 | 0.422729 | ||||||||
\(280\) | 1.25848 | 0.0752085 | ||||||||
\(281\) | −22.5769 | −1.34682 | −0.673412 | − | 0.739267i | \(-0.735172\pi\) | ||||
−0.673412 | + | 0.739267i | \(0.735172\pi\) | |||||||
\(282\) | 6.52903 | 0.388798 | ||||||||
\(283\) | −6.41224 | −0.381168 | −0.190584 | − | 0.981671i | \(-0.561038\pi\) | ||||
−0.190584 | + | 0.981671i | \(0.561038\pi\) | |||||||
\(284\) | −0.798103 | −0.0473587 | ||||||||
\(285\) | 6.40940 | 0.379660 | ||||||||
\(286\) | 4.47761 | 0.264766 | ||||||||
\(287\) | 5.76948 | 0.340561 | ||||||||
\(288\) | 6.95580 | 0.409875 | ||||||||
\(289\) | 32.2331 | 1.89607 | ||||||||
\(290\) | −8.16795 | −0.479639 | ||||||||
\(291\) | 8.51266 | 0.499021 | ||||||||
\(292\) | 11.9735 | 0.700695 | ||||||||
\(293\) | −3.55312 | −0.207576 | −0.103788 | − | 0.994599i | \(-0.533096\pi\) | ||||
−0.103788 | + | 0.994599i | \(0.533096\pi\) | |||||||
\(294\) | −8.51342 | −0.496513 | ||||||||
\(295\) | −3.98735 | −0.232153 | ||||||||
\(296\) | −5.84845 | −0.339934 | ||||||||
\(297\) | 0.963587 | 0.0559130 | ||||||||
\(298\) | −20.9799 | −1.21533 | ||||||||
\(299\) | 12.4176 | 0.718128 | ||||||||
\(300\) | 6.37703 | 0.368178 | ||||||||
\(301\) | 4.00472 | 0.230828 | ||||||||
\(302\) | −22.2743 | −1.28174 | ||||||||
\(303\) | −7.85984 | −0.451536 | ||||||||
\(304\) | −36.8189 | −2.11171 | ||||||||
\(305\) | −0.491794 | −0.0281600 | ||||||||
\(306\) | 13.0883 | 0.748207 | ||||||||
\(307\) | −27.0815 | −1.54562 | −0.772812 | − | 0.634635i | \(-0.781150\pi\) | ||||
−0.772812 | + | 0.634635i | \(0.781150\pi\) | |||||||
\(308\) | 2.22495 | 0.126778 | ||||||||
\(309\) | 9.63873 | 0.548328 | ||||||||
\(310\) | 10.9370 | 0.621178 | ||||||||
\(311\) | 17.1629 | 0.973219 | 0.486609 | − | 0.873620i | \(-0.338233\pi\) | ||||
0.486609 | + | 0.873620i | \(0.338233\pi\) | |||||||
\(312\) | −2.41899 | −0.136948 | ||||||||
\(313\) | −4.58545 | −0.259185 | −0.129593 | − | 0.991567i | \(-0.541367\pi\) | ||||
−0.129593 | + | 0.991567i | \(0.541367\pi\) | |||||||
\(314\) | −41.0377 | −2.31589 | ||||||||
\(315\) | 1.29602 | 0.0730226 | ||||||||
\(316\) | 12.5623 | 0.706683 | ||||||||
\(317\) | −24.8545 | −1.39597 | −0.697984 | − | 0.716113i | \(-0.745919\pi\) | ||||
−0.697984 | + | 0.716113i | \(0.745919\pi\) | |||||||
\(318\) | 5.58829 | 0.313376 | ||||||||
\(319\) | 5.08127 | 0.284496 | ||||||||
\(320\) | 2.85197 | 0.159430 | ||||||||
\(321\) | 6.35949 | 0.354952 | ||||||||
\(322\) | 14.5119 | 0.808718 | ||||||||
\(323\) | −54.1587 | −3.01347 | ||||||||
\(324\) | 1.47943 | 0.0821905 | ||||||||
\(325\) | −10.7380 | −0.595639 | ||||||||
\(326\) | 14.0739 | 0.779483 | ||||||||
\(327\) | −14.1151 | −0.780569 | ||||||||
\(328\) | −3.58951 | −0.198198 | ||||||||
\(329\) | −5.46297 | −0.301183 | ||||||||
\(330\) | 1.49253 | 0.0821611 | ||||||||
\(331\) | −23.1335 | −1.27153 | −0.635765 | − | 0.771882i | \(-0.719315\pi\) | ||||
−0.635765 | + | 0.771882i | \(0.719315\pi\) | |||||||
\(332\) | −19.7761 | −1.08536 | ||||||||
\(333\) | −6.02292 | −0.330054 | ||||||||
\(334\) | −25.1327 | −1.37520 | ||||||||
\(335\) | −2.29696 | −0.125496 | ||||||||
\(336\) | −7.44503 | −0.406160 | ||||||||
\(337\) | 13.9613 | 0.760522 | 0.380261 | − | 0.924879i | \(-0.375834\pi\) | ||||
0.380261 | + | 0.924879i | \(0.375834\pi\) | |||||||
\(338\) | 12.6733 | 0.689335 | ||||||||
\(339\) | −1.62567 | −0.0882945 | ||||||||
\(340\) | 8.61988 | 0.467478 | ||||||||
\(341\) | −6.80386 | −0.368450 | ||||||||
\(342\) | −14.3977 | −0.778539 | ||||||||
\(343\) | 18.0486 | 0.974535 | ||||||||
\(344\) | −2.49156 | −0.134336 | ||||||||
\(345\) | 4.13918 | 0.222846 | ||||||||
\(346\) | 37.3593 | 2.00845 | ||||||||
\(347\) | −13.3009 | −0.714032 | −0.357016 | − | 0.934098i | \(-0.616206\pi\) | ||||
−0.357016 | + | 0.934098i | \(0.616206\pi\) | |||||||
\(348\) | 7.80145 | 0.418202 | ||||||||
\(349\) | 25.4322 | 1.36136 | 0.680678 | − | 0.732583i | \(-0.261685\pi\) | ||||
0.680678 | + | 0.732583i | \(0.261685\pi\) | |||||||
\(350\) | −12.5491 | −0.670778 | ||||||||
\(351\) | −2.49116 | −0.132968 | ||||||||
\(352\) | −6.70252 | −0.357246 | ||||||||
\(353\) | −27.3285 | −1.45455 | −0.727273 | − | 0.686348i | \(-0.759213\pi\) | ||||
−0.727273 | + | 0.686348i | \(0.759213\pi\) | |||||||
\(354\) | 8.95696 | 0.476057 | ||||||||
\(355\) | 0.447964 | 0.0237754 | ||||||||
\(356\) | −7.36237 | −0.390205 | ||||||||
\(357\) | −10.9512 | −0.579601 | ||||||||
\(358\) | −15.2355 | −0.805223 | ||||||||
\(359\) | 4.39233 | 0.231818 | 0.115909 | − | 0.993260i | \(-0.463022\pi\) | ||||
0.115909 | + | 0.993260i | \(0.463022\pi\) | |||||||
\(360\) | −0.806327 | −0.0424972 | ||||||||
\(361\) | 40.5771 | 2.13564 | ||||||||
\(362\) | −23.3968 | −1.22971 | ||||||||
\(363\) | 10.0715 | 0.528617 | ||||||||
\(364\) | −5.75214 | −0.301494 | ||||||||
\(365\) | −6.72054 | −0.351769 | ||||||||
\(366\) | 1.10474 | 0.0577455 | ||||||||
\(367\) | 27.9324 | 1.45806 | 0.729029 | − | 0.684482i | \(-0.239972\pi\) | ||||
0.729029 | + | 0.684482i | \(0.239972\pi\) | |||||||
\(368\) | −23.7776 | −1.23949 | ||||||||
\(369\) | −3.69659 | −0.192437 | ||||||||
\(370\) | −9.32909 | −0.484997 | ||||||||
\(371\) | −4.67584 | −0.242758 | ||||||||
\(372\) | −10.4462 | −0.541611 | ||||||||
\(373\) | −5.12249 | −0.265232 | −0.132616 | − | 0.991167i | \(-0.542338\pi\) | ||||
−0.132616 | + | 0.991167i | \(0.542338\pi\) | |||||||
\(374\) | −12.6117 | −0.652136 | ||||||||
\(375\) | −7.73124 | −0.399240 | ||||||||
\(376\) | 3.39882 | 0.175281 | ||||||||
\(377\) | −13.1366 | −0.676568 | ||||||||
\(378\) | −2.91131 | −0.149742 | ||||||||
\(379\) | 13.9046 | 0.714230 | 0.357115 | − | 0.934060i | \(-0.383760\pi\) | ||||
0.357115 | + | 0.934060i | \(0.383760\pi\) | |||||||
\(380\) | −9.48226 | −0.486430 | ||||||||
\(381\) | −20.7987 | −1.06555 | ||||||||
\(382\) | −15.9028 | −0.813656 | ||||||||
\(383\) | −5.78300 | −0.295498 | −0.147749 | − | 0.989025i | \(-0.547203\pi\) | ||||
−0.147749 | + | 0.989025i | \(0.547203\pi\) | |||||||
\(384\) | 7.50511 | 0.382994 | ||||||||
\(385\) | −1.24883 | −0.0636463 | ||||||||
\(386\) | −8.85603 | −0.450760 | ||||||||
\(387\) | −2.56589 | −0.130431 | ||||||||
\(388\) | −12.5939 | −0.639357 | ||||||||
\(389\) | −21.4651 | −1.08832 | −0.544161 | − | 0.838981i | \(-0.683152\pi\) | ||||
−0.544161 | + | 0.838981i | \(0.683152\pi\) | |||||||
\(390\) | −3.85863 | −0.195389 | ||||||||
\(391\) | −34.9756 | −1.76879 | ||||||||
\(392\) | −4.43183 | −0.223841 | ||||||||
\(393\) | 2.35111 | 0.118598 | ||||||||
\(394\) | −15.2108 | −0.766309 | ||||||||
\(395\) | −7.05102 | −0.354775 | ||||||||
\(396\) | −1.42556 | −0.0716371 | ||||||||
\(397\) | −11.1495 | −0.559577 | −0.279788 | − | 0.960062i | \(-0.590264\pi\) | ||||
−0.279788 | + | 0.960062i | \(0.590264\pi\) | |||||||
\(398\) | 0.949216 | 0.0475799 | ||||||||
\(399\) | 12.0469 | 0.603098 | ||||||||
\(400\) | 20.5616 | 1.02808 | ||||||||
\(401\) | 26.8528 | 1.34096 | 0.670482 | − | 0.741926i | \(-0.266087\pi\) | ||||
0.670482 | + | 0.741926i | \(0.266087\pi\) | |||||||
\(402\) | 5.15976 | 0.257345 | ||||||||
\(403\) | 17.5900 | 0.876220 | ||||||||
\(404\) | 11.6281 | 0.578519 | ||||||||
\(405\) | −0.830382 | −0.0412620 | ||||||||
\(406\) | −15.3522 | −0.761915 | ||||||||
\(407\) | 5.80361 | 0.287674 | ||||||||
\(408\) | 6.81337 | 0.337312 | ||||||||
\(409\) | 12.3151 | 0.608943 | 0.304472 | − | 0.952521i | \(-0.401520\pi\) | ||||
0.304472 | + | 0.952521i | \(0.401520\pi\) | |||||||
\(410\) | −5.72577 | −0.282776 | ||||||||
\(411\) | 9.94169 | 0.490387 | ||||||||
\(412\) | −14.2598 | −0.702531 | ||||||||
\(413\) | −7.49448 | −0.368779 | ||||||||
\(414\) | −9.29802 | −0.456973 | ||||||||
\(415\) | 11.1001 | 0.544880 | ||||||||
\(416\) | 17.3280 | 0.849574 | ||||||||
\(417\) | −2.50975 | −0.122903 | ||||||||
\(418\) | 13.8735 | 0.678573 | ||||||||
\(419\) | −0.482802 | −0.0235864 | −0.0117932 | − | 0.999930i | \(-0.503754\pi\) | ||||
−0.0117932 | + | 0.999930i | \(0.503754\pi\) | |||||||
\(420\) | −1.91737 | −0.0935583 | ||||||||
\(421\) | 4.20660 | 0.205017 | 0.102509 | − | 0.994732i | \(-0.467313\pi\) | ||||
0.102509 | + | 0.994732i | \(0.467313\pi\) | |||||||
\(422\) | −6.79341 | −0.330698 | ||||||||
\(423\) | 3.50021 | 0.170186 | ||||||||
\(424\) | 2.90910 | 0.141278 | ||||||||
\(425\) | 30.2450 | 1.46710 | ||||||||
\(426\) | −1.00628 | −0.0487544 | ||||||||
\(427\) | −0.924357 | −0.0447328 | ||||||||
\(428\) | −9.40842 | −0.454773 | ||||||||
\(429\) | 2.40045 | 0.115895 | ||||||||
\(430\) | −3.97438 | −0.191662 | ||||||||
\(431\) | −37.7930 | −1.82043 | −0.910213 | − | 0.414141i | \(-0.864082\pi\) | ||||
−0.910213 | + | 0.414141i | \(0.864082\pi\) | |||||||
\(432\) | 4.77015 | 0.229504 | ||||||||
\(433\) | 26.2119 | 1.25966 | 0.629832 | − | 0.776731i | \(-0.283124\pi\) | ||||
0.629832 | + | 0.776731i | \(0.283124\pi\) | |||||||
\(434\) | 20.5567 | 0.986753 | ||||||||
\(435\) | −4.37884 | −0.209949 | ||||||||
\(436\) | 20.8823 | 1.00008 | ||||||||
\(437\) | 38.4748 | 1.84050 | ||||||||
\(438\) | 15.0966 | 0.721345 | ||||||||
\(439\) | −2.27776 | −0.108712 | −0.0543558 | − | 0.998522i | \(-0.517311\pi\) | ||||
−0.0543558 | + | 0.998522i | \(0.517311\pi\) | |||||||
\(440\) | 0.776967 | 0.0370404 | ||||||||
\(441\) | −4.56405 | −0.217335 | ||||||||
\(442\) | 32.6050 | 1.55086 | ||||||||
\(443\) | −32.7283 | −1.55497 | −0.777485 | − | 0.628901i | \(-0.783505\pi\) | ||||
−0.777485 | + | 0.628901i | \(0.783505\pi\) | |||||||
\(444\) | 8.91049 | 0.422873 | ||||||||
\(445\) | 4.13239 | 0.195894 | ||||||||
\(446\) | −35.9553 | −1.70253 | ||||||||
\(447\) | −11.2473 | −0.531980 | ||||||||
\(448\) | 5.36045 | 0.253257 | ||||||||
\(449\) | −3.52134 | −0.166182 | −0.0830911 | − | 0.996542i | \(-0.526479\pi\) | ||||
−0.0830911 | + | 0.996542i | \(0.526479\pi\) | |||||||
\(450\) | 8.04041 | 0.379029 | ||||||||
\(451\) | 3.56199 | 0.167728 | ||||||||
\(452\) | 2.40507 | 0.113125 | ||||||||
\(453\) | −11.9413 | −0.561049 | ||||||||
\(454\) | 28.3859 | 1.33222 | ||||||||
\(455\) | 3.22859 | 0.151359 | ||||||||
\(456\) | −7.49502 | −0.350987 | ||||||||
\(457\) | 35.8412 | 1.67658 | 0.838290 | − | 0.545224i | \(-0.183556\pi\) | ||||
0.838290 | + | 0.545224i | \(0.183556\pi\) | |||||||
\(458\) | 38.0765 | 1.77920 | ||||||||
\(459\) | 7.01663 | 0.327508 | ||||||||
\(460\) | −6.12363 | −0.285516 | ||||||||
\(461\) | −34.6163 | −1.61224 | −0.806121 | − | 0.591750i | \(-0.798437\pi\) | ||||
−0.806121 | + | 0.591750i | \(0.798437\pi\) | |||||||
\(462\) | 2.80530 | 0.130514 | ||||||||
\(463\) | −36.0446 | −1.67513 | −0.837567 | − | 0.546334i | \(-0.816023\pi\) | ||||
−0.837567 | + | 0.546334i | \(0.816023\pi\) | |||||||
\(464\) | 25.1543 | 1.16776 | ||||||||
\(465\) | 5.86331 | 0.271904 | ||||||||
\(466\) | −16.0527 | −0.743629 | ||||||||
\(467\) | −0.946926 | −0.0438185 | −0.0219092 | − | 0.999760i | \(-0.506974\pi\) | ||||
−0.0219092 | + | 0.999760i | \(0.506974\pi\) | |||||||
\(468\) | 3.68549 | 0.170362 | ||||||||
\(469\) | −4.31728 | −0.199353 | ||||||||
\(470\) | 5.42159 | 0.250079 | ||||||||
\(471\) | −22.0003 | −1.01372 | ||||||||
\(472\) | 4.66273 | 0.214620 | ||||||||
\(473\) | 2.47245 | 0.113684 | ||||||||
\(474\) | 15.8390 | 0.727510 | ||||||||
\(475\) | −33.2708 | −1.52657 | ||||||||
\(476\) | 16.2016 | 0.742599 | ||||||||
\(477\) | 2.99589 | 0.137172 | ||||||||
\(478\) | 19.1351 | 0.875218 | ||||||||
\(479\) | −12.7304 | −0.581667 | −0.290834 | − | 0.956774i | \(-0.593933\pi\) | ||||
−0.290834 | + | 0.956774i | \(0.593933\pi\) | |||||||
\(480\) | 5.77597 | 0.263636 | ||||||||
\(481\) | −15.0040 | −0.684125 | ||||||||
\(482\) | 27.2957 | 1.24328 | ||||||||
\(483\) | 7.77984 | 0.353995 | ||||||||
\(484\) | −14.9001 | −0.677276 | ||||||||
\(485\) | 7.06876 | 0.320976 | ||||||||
\(486\) | 1.86532 | 0.0846128 | ||||||||
\(487\) | −35.9217 | −1.62777 | −0.813885 | − | 0.581027i | \(-0.802651\pi\) | ||||
−0.813885 | + | 0.581027i | \(0.802651\pi\) | |||||||
\(488\) | 0.575093 | 0.0260333 | ||||||||
\(489\) | 7.54504 | 0.341198 | ||||||||
\(490\) | −7.06939 | −0.319363 | ||||||||
\(491\) | 34.4343 | 1.55400 | 0.776999 | − | 0.629502i | \(-0.216741\pi\) | ||||
0.776999 | + | 0.629502i | \(0.216741\pi\) | |||||||
\(492\) | 5.46885 | 0.246555 | ||||||||
\(493\) | 37.0007 | 1.66643 | ||||||||
\(494\) | −35.8670 | −1.61373 | ||||||||
\(495\) | 0.800146 | 0.0359639 | ||||||||
\(496\) | −33.6819 | −1.51236 | ||||||||
\(497\) | 0.841975 | 0.0377678 | ||||||||
\(498\) | −24.9345 | −1.11734 | ||||||||
\(499\) | −18.8783 | −0.845111 | −0.422555 | − | 0.906337i | \(-0.638867\pi\) | ||||
−0.422555 | + | 0.906337i | \(0.638867\pi\) | |||||||
\(500\) | 11.4378 | 0.511515 | ||||||||
\(501\) | −13.4737 | −0.601959 | ||||||||
\(502\) | 31.2416 | 1.39438 | ||||||||
\(503\) | −19.3504 | −0.862794 | −0.431397 | − | 0.902162i | \(-0.641979\pi\) | ||||
−0.431397 | + | 0.902162i | \(0.641979\pi\) | |||||||
\(504\) | −1.51554 | −0.0675076 | ||||||||
\(505\) | −6.52667 | −0.290433 | ||||||||
\(506\) | 8.95945 | 0.398296 | ||||||||
\(507\) | 6.79414 | 0.301739 | ||||||||
\(508\) | 30.7702 | 1.36521 | ||||||||
\(509\) | 21.1614 | 0.937961 | 0.468981 | − | 0.883208i | \(-0.344621\pi\) | ||||
0.468981 | + | 0.883208i | \(0.344621\pi\) | |||||||
\(510\) | 10.8683 | 0.481255 | ||||||||
\(511\) | −12.6317 | −0.558792 | ||||||||
\(512\) | −23.9163 | −1.05696 | ||||||||
\(513\) | −7.71862 | −0.340785 | ||||||||
\(514\) | −9.12387 | −0.402436 | ||||||||
\(515\) | 8.00383 | 0.352691 | ||||||||
\(516\) | 3.79605 | 0.167112 | ||||||||
\(517\) | −3.37276 | −0.148334 | ||||||||
\(518\) | −17.5346 | −0.770426 | ||||||||
\(519\) | 20.0283 | 0.879145 | ||||||||
\(520\) | −2.00869 | −0.0880868 | ||||||||
\(521\) | −1.70720 | −0.0747938 | −0.0373969 | − | 0.999300i | \(-0.511907\pi\) | ||||
−0.0373969 | + | 0.999300i | \(0.511907\pi\) | |||||||
\(522\) | 9.83638 | 0.430527 | ||||||||
\(523\) | −34.0337 | −1.48819 | −0.744095 | − | 0.668073i | \(-0.767119\pi\) | ||||
−0.744095 | + | 0.668073i | \(0.767119\pi\) | |||||||
\(524\) | −3.47830 | −0.151950 | ||||||||
\(525\) | −6.72758 | −0.293616 | ||||||||
\(526\) | −3.37584 | −0.147194 | ||||||||
\(527\) | −49.5443 | −2.15818 | ||||||||
\(528\) | −4.59645 | −0.200035 | ||||||||
\(529\) | 1.84692 | 0.0803010 | ||||||||
\(530\) | 4.64042 | 0.201567 | ||||||||
\(531\) | 4.80183 | 0.208382 | ||||||||
\(532\) | −17.8225 | −0.772703 | ||||||||
\(533\) | −9.20879 | −0.398877 | ||||||||
\(534\) | −9.28276 | −0.401704 | ||||||||
\(535\) | 5.28081 | 0.228309 | ||||||||
\(536\) | 2.68602 | 0.116018 | ||||||||
\(537\) | −8.16777 | −0.352465 | ||||||||
\(538\) | −6.92524 | −0.298568 | ||||||||
\(539\) | 4.39786 | 0.189429 | ||||||||
\(540\) | 1.22849 | 0.0528659 | ||||||||
\(541\) | −19.5570 | −0.840822 | −0.420411 | − | 0.907334i | \(-0.638114\pi\) | ||||
−0.420411 | + | 0.907334i | \(0.638114\pi\) | |||||||
\(542\) | 8.31243 | 0.357050 | ||||||||
\(543\) | −12.5430 | −0.538272 | ||||||||
\(544\) | −48.8063 | −2.09255 | ||||||||
\(545\) | −11.7210 | −0.502070 | ||||||||
\(546\) | −7.25253 | −0.310380 | ||||||||
\(547\) | 18.2043 | 0.778361 | 0.389180 | − | 0.921162i | \(-0.372758\pi\) | ||||
0.389180 | + | 0.921162i | \(0.372758\pi\) | |||||||
\(548\) | −14.7080 | −0.628296 | ||||||||
\(549\) | 0.592250 | 0.0252766 | ||||||||
\(550\) | −7.74764 | −0.330360 | ||||||||
\(551\) | −40.7025 | −1.73398 | ||||||||
\(552\) | −4.84027 | −0.206016 | ||||||||
\(553\) | −13.2528 | −0.563568 | ||||||||
\(554\) | −17.0359 | −0.723786 | ||||||||
\(555\) | −5.00133 | −0.212295 | ||||||||
\(556\) | 3.71300 | 0.157466 | ||||||||
\(557\) | −27.1202 | −1.14912 | −0.574559 | − | 0.818463i | \(-0.694826\pi\) | ||||
−0.574559 | + | 0.818463i | \(0.694826\pi\) | |||||||
\(558\) | −13.1710 | −0.557573 | ||||||||
\(559\) | −6.39202 | −0.270354 | ||||||||
\(560\) | −6.18222 | −0.261246 | ||||||||
\(561\) | −6.76114 | −0.285455 | ||||||||
\(562\) | 42.1132 | 1.77644 | ||||||||
\(563\) | −33.3968 | −1.40751 | −0.703753 | − | 0.710445i | \(-0.748494\pi\) | ||||
−0.703753 | + | 0.710445i | \(0.748494\pi\) | |||||||
\(564\) | −5.17832 | −0.218047 | ||||||||
\(565\) | −1.34993 | −0.0567920 | ||||||||
\(566\) | 11.9609 | 0.502754 | ||||||||
\(567\) | −1.56075 | −0.0655455 | ||||||||
\(568\) | −0.523839 | −0.0219798 | ||||||||
\(569\) | 1.70655 | 0.0715423 | 0.0357712 | − | 0.999360i | \(-0.488611\pi\) | ||||
0.0357712 | + | 0.999360i | \(0.488611\pi\) | |||||||
\(570\) | −11.9556 | −0.500765 | ||||||||
\(571\) | −13.1200 | −0.549056 | −0.274528 | − | 0.961579i | \(-0.588522\pi\) | ||||
−0.274528 | + | 0.961579i | \(0.588522\pi\) | |||||||
\(572\) | −3.55129 | −0.148487 | ||||||||
\(573\) | −8.52547 | −0.356157 | ||||||||
\(574\) | −10.7619 | −0.449195 | ||||||||
\(575\) | −21.4862 | −0.896038 | ||||||||
\(576\) | −3.43452 | −0.143105 | ||||||||
\(577\) | −26.7845 | −1.11505 | −0.557526 | − | 0.830159i | \(-0.688249\pi\) | ||||
−0.557526 | + | 0.830159i | \(0.688249\pi\) | |||||||
\(578\) | −60.1252 | −2.50088 | ||||||||
\(579\) | −4.74772 | −0.197308 | ||||||||
\(580\) | 6.47819 | 0.268992 | ||||||||
\(581\) | 20.8632 | 0.865553 | ||||||||
\(582\) | −15.8789 | −0.658200 | ||||||||
\(583\) | −2.88680 | −0.119559 | ||||||||
\(584\) | 7.85886 | 0.325202 | ||||||||
\(585\) | −2.06861 | −0.0855265 | ||||||||
\(586\) | 6.62772 | 0.273788 | ||||||||
\(587\) | 15.6518 | 0.646019 | 0.323009 | − | 0.946396i | \(-0.395305\pi\) | ||||
0.323009 | + | 0.946396i | \(0.395305\pi\) | |||||||
\(588\) | 6.75218 | 0.278455 | ||||||||
\(589\) | 54.5010 | 2.24567 | ||||||||
\(590\) | 7.43770 | 0.306205 | ||||||||
\(591\) | −8.15451 | −0.335432 | ||||||||
\(592\) | 28.7302 | 1.18081 | ||||||||
\(593\) | −28.9905 | −1.19050 | −0.595249 | − | 0.803541i | \(-0.702947\pi\) | ||||
−0.595249 | + | 0.803541i | \(0.702947\pi\) | |||||||
\(594\) | −1.79740 | −0.0737483 | ||||||||
\(595\) | −9.09371 | −0.372806 | ||||||||
\(596\) | 16.6396 | 0.681586 | ||||||||
\(597\) | 0.508875 | 0.0208269 | ||||||||
\(598\) | −23.1628 | −0.947198 | ||||||||
\(599\) | −31.6792 | −1.29438 | −0.647188 | − | 0.762330i | \(-0.724055\pi\) | ||||
−0.647188 | + | 0.762330i | \(0.724055\pi\) | |||||||
\(600\) | 4.18560 | 0.170876 | ||||||||
\(601\) | −18.5474 | −0.756565 | −0.378283 | − | 0.925690i | \(-0.623485\pi\) | ||||
−0.378283 | + | 0.925690i | \(0.623485\pi\) | |||||||
\(602\) | −7.47009 | −0.304458 | ||||||||
\(603\) | 2.76615 | 0.112646 | ||||||||
\(604\) | 17.6662 | 0.718829 | ||||||||
\(605\) | 8.36319 | 0.340012 | ||||||||
\(606\) | 14.6611 | 0.595568 | ||||||||
\(607\) | −44.8061 | −1.81862 | −0.909312 | − | 0.416115i | \(-0.863391\pi\) | ||||
−0.909312 | + | 0.416115i | \(0.863391\pi\) | |||||||
\(608\) | 53.6892 | 2.17738 | ||||||||
\(609\) | −8.23030 | −0.333509 | ||||||||
\(610\) | 0.917354 | 0.0371426 | ||||||||
\(611\) | 8.71957 | 0.352756 | ||||||||
\(612\) | −10.3806 | −0.419611 | ||||||||
\(613\) | −8.42647 | −0.340342 | −0.170171 | − | 0.985415i | \(-0.554432\pi\) | ||||
−0.170171 | + | 0.985415i | \(0.554432\pi\) | |||||||
\(614\) | 50.5158 | 2.03865 | ||||||||
\(615\) | −3.06959 | −0.123778 | ||||||||
\(616\) | 1.46036 | 0.0588395 | ||||||||
\(617\) | 10.1002 | 0.406618 | 0.203309 | − | 0.979115i | \(-0.434830\pi\) | ||||
0.203309 | + | 0.979115i | \(0.434830\pi\) | |||||||
\(618\) | −17.9793 | −0.723235 | ||||||||
\(619\) | 15.9945 | 0.642874 | 0.321437 | − | 0.946931i | \(-0.395834\pi\) | ||||
0.321437 | + | 0.946931i | \(0.395834\pi\) | |||||||
\(620\) | −8.67435 | −0.348370 | ||||||||
\(621\) | −4.98467 | −0.200028 | ||||||||
\(622\) | −32.0144 | −1.28366 | ||||||||
\(623\) | 7.76708 | 0.311181 | ||||||||
\(624\) | 11.8832 | 0.475708 | ||||||||
\(625\) | 15.1324 | 0.605298 | ||||||||
\(626\) | 8.55335 | 0.341861 | ||||||||
\(627\) | 7.43756 | 0.297028 | ||||||||
\(628\) | 32.5479 | 1.29880 | ||||||||
\(629\) | 42.2606 | 1.68504 | ||||||||
\(630\) | −2.41750 | −0.0963155 | ||||||||
\(631\) | −47.1827 | −1.87831 | −0.939157 | − | 0.343488i | \(-0.888391\pi\) | ||||
−0.939157 | + | 0.343488i | \(0.888391\pi\) | |||||||
\(632\) | 8.24532 | 0.327981 | ||||||||
\(633\) | −3.64195 | −0.144754 | ||||||||
\(634\) | 46.3617 | 1.84126 | ||||||||
\(635\) | −17.2709 | −0.685374 | ||||||||
\(636\) | −4.43220 | −0.175748 | ||||||||
\(637\) | −11.3697 | −0.450486 | ||||||||
\(638\) | −9.47821 | −0.375246 | ||||||||
\(639\) | −0.539467 | −0.0213410 | ||||||||
\(640\) | 6.23211 | 0.246346 | ||||||||
\(641\) | −12.9023 | −0.509608 | −0.254804 | − | 0.966993i | \(-0.582011\pi\) | ||||
−0.254804 | + | 0.966993i | \(0.582011\pi\) | |||||||
\(642\) | −11.8625 | −0.468176 | ||||||||
\(643\) | −24.7744 | −0.977005 | −0.488503 | − | 0.872562i | \(-0.662457\pi\) | ||||
−0.488503 | + | 0.872562i | \(0.662457\pi\) | |||||||
\(644\) | −11.5097 | −0.453547 | ||||||||
\(645\) | −2.13067 | −0.0838949 | ||||||||
\(646\) | 101.023 | 3.97472 | ||||||||
\(647\) | 32.0696 | 1.26079 | 0.630394 | − | 0.776275i | \(-0.282893\pi\) | ||||
0.630394 | + | 0.776275i | \(0.282893\pi\) | |||||||
\(648\) | 0.971032 | 0.0381457 | ||||||||
\(649\) | −4.62698 | −0.181625 | ||||||||
\(650\) | 20.0299 | 0.785638 | ||||||||
\(651\) | 11.0204 | 0.431925 | ||||||||
\(652\) | −11.1624 | −0.437152 | ||||||||
\(653\) | −35.0193 | −1.37041 | −0.685205 | − | 0.728350i | \(-0.740287\pi\) | ||||
−0.685205 | + | 0.728350i | \(0.740287\pi\) | |||||||
\(654\) | 26.3293 | 1.02956 | ||||||||
\(655\) | 1.95232 | 0.0762835 | ||||||||
\(656\) | 17.6333 | 0.688465 | ||||||||
\(657\) | 8.09331 | 0.315750 | ||||||||
\(658\) | 10.1902 | 0.397256 | ||||||||
\(659\) | −44.2560 | −1.72397 | −0.861985 | − | 0.506933i | \(-0.830779\pi\) | ||||
−0.861985 | + | 0.506933i | \(0.830779\pi\) | |||||||
\(660\) | −1.18376 | −0.0460778 | ||||||||
\(661\) | 50.3174 | 1.95712 | 0.978560 | − | 0.205962i | \(-0.0660323\pi\) | ||||
0.978560 | + | 0.205962i | \(0.0660323\pi\) | |||||||
\(662\) | 43.1514 | 1.67713 | ||||||||
\(663\) | 17.4795 | 0.678848 | ||||||||
\(664\) | −12.9802 | −0.503729 | ||||||||
\(665\) | 10.0035 | 0.387919 | ||||||||
\(666\) | 11.2347 | 0.435336 | ||||||||
\(667\) | −26.2856 | −1.01778 | ||||||||
\(668\) | 19.9333 | 0.771244 | ||||||||
\(669\) | −19.2756 | −0.745240 | ||||||||
\(670\) | 4.28457 | 0.165527 | ||||||||
\(671\) | −0.570684 | −0.0220310 | ||||||||
\(672\) | 10.8563 | 0.418791 | ||||||||
\(673\) | −44.4153 | −1.71209 | −0.856043 | − | 0.516905i | \(-0.827084\pi\) | ||||
−0.856043 | + | 0.516905i | \(0.827084\pi\) | |||||||
\(674\) | −26.0424 | −1.00312 | ||||||||
\(675\) | 4.31047 | 0.165910 | ||||||||
\(676\) | −10.0515 | −0.386595 | ||||||||
\(677\) | −21.3928 | −0.822192 | −0.411096 | − | 0.911592i | \(-0.634854\pi\) | ||||
−0.411096 | + | 0.911592i | \(0.634854\pi\) | |||||||
\(678\) | 3.03241 | 0.116459 | ||||||||
\(679\) | 13.2862 | 0.509876 | ||||||||
\(680\) | 5.65770 | 0.216963 | ||||||||
\(681\) | 15.2177 | 0.583143 | ||||||||
\(682\) | 12.6914 | 0.485979 | ||||||||
\(683\) | 15.4896 | 0.592693 | 0.296347 | − | 0.955080i | \(-0.404232\pi\) | ||||
0.296347 | + | 0.955080i | \(0.404232\pi\) | |||||||
\(684\) | 11.4192 | 0.436622 | ||||||||
\(685\) | 8.25540 | 0.315423 | ||||||||
\(686\) | −33.6665 | −1.28539 | ||||||||
\(687\) | 20.4128 | 0.778798 | ||||||||
\(688\) | 12.2397 | 0.466632 | ||||||||
\(689\) | 7.46322 | 0.284326 | ||||||||
\(690\) | −7.72091 | −0.293930 | ||||||||
\(691\) | −0.436168 | −0.0165926 | −0.00829630 | − | 0.999966i | \(-0.502641\pi\) | ||||
−0.00829630 | + | 0.999966i | \(0.502641\pi\) | |||||||
\(692\) | −29.6305 | −1.12638 | ||||||||
\(693\) | 1.50392 | 0.0571293 | ||||||||
\(694\) | 24.8106 | 0.941796 | ||||||||
\(695\) | −2.08405 | −0.0790527 | ||||||||
\(696\) | 5.12053 | 0.194093 | ||||||||
\(697\) | 25.9376 | 0.982458 | ||||||||
\(698\) | −47.4393 | −1.79560 | ||||||||
\(699\) | −8.60588 | −0.325504 | ||||||||
\(700\) | 9.95298 | 0.376187 | ||||||||
\(701\) | 47.9348 | 1.81047 | 0.905237 | − | 0.424908i | \(-0.139694\pi\) | ||||
0.905237 | + | 0.424908i | \(0.139694\pi\) | |||||||
\(702\) | 4.64681 | 0.175383 | ||||||||
\(703\) | −46.4887 | −1.75335 | ||||||||
\(704\) | 3.30946 | 0.124730 | ||||||||
\(705\) | 2.90651 | 0.109466 | ||||||||
\(706\) | 50.9764 | 1.91852 | ||||||||
\(707\) | −12.2673 | −0.461358 | ||||||||
\(708\) | −7.10397 | −0.266984 | ||||||||
\(709\) | 49.0171 | 1.84088 | 0.920438 | − | 0.390888i | \(-0.127832\pi\) | ||||
0.920438 | + | 0.390888i | \(0.127832\pi\) | |||||||
\(710\) | −0.835597 | −0.0313594 | ||||||||
\(711\) | 8.49130 | 0.318449 | ||||||||
\(712\) | −4.83233 | −0.181099 | ||||||||
\(713\) | 35.1966 | 1.31812 | ||||||||
\(714\) | 20.4276 | 0.764484 | ||||||||
\(715\) | 1.99329 | 0.0745447 | ||||||||
\(716\) | 12.0836 | 0.451587 | ||||||||
\(717\) | 10.2583 | 0.383104 | ||||||||
\(718\) | −8.19312 | −0.305764 | ||||||||
\(719\) | −21.7427 | −0.810868 | −0.405434 | − | 0.914124i | \(-0.632880\pi\) | ||||
−0.405434 | + | 0.914124i | \(0.632880\pi\) | |||||||
\(720\) | 3.96105 | 0.147619 | ||||||||
\(721\) | 15.0437 | 0.560256 | ||||||||
\(722\) | −75.6893 | −2.81687 | ||||||||
\(723\) | 14.6332 | 0.544215 | ||||||||
\(724\) | 18.5565 | 0.689647 | ||||||||
\(725\) | 22.7303 | 0.844182 | ||||||||
\(726\) | −18.7866 | −0.697236 | ||||||||
\(727\) | −5.78142 | −0.214421 | −0.107211 | − | 0.994236i | \(-0.534192\pi\) | ||||
−0.107211 | + | 0.994236i | \(0.534192\pi\) | |||||||
\(728\) | −3.77545 | −0.139928 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.5360 | 0.463977 | ||||||||
\(731\) | 18.0039 | 0.665897 | ||||||||
\(732\) | −0.876192 | −0.0323850 | ||||||||
\(733\) | −31.0088 | −1.14534 | −0.572668 | − | 0.819788i | \(-0.694091\pi\) | ||||
−0.572668 | + | 0.819788i | \(0.694091\pi\) | |||||||
\(734\) | −52.1029 | −1.92315 | ||||||||
\(735\) | −3.78990 | −0.139793 | ||||||||
\(736\) | 34.6724 | 1.27804 | ||||||||
\(737\) | −2.66542 | −0.0981821 | ||||||||
\(738\) | 6.89534 | 0.253821 | ||||||||
\(739\) | 47.3776 | 1.74281 | 0.871406 | − | 0.490563i | \(-0.163209\pi\) | ||||
0.871406 | + | 0.490563i | \(0.163209\pi\) | |||||||
\(740\) | 7.39912 | 0.271997 | ||||||||
\(741\) | −19.2283 | −0.706369 | ||||||||
\(742\) | 8.72195 | 0.320193 | ||||||||
\(743\) | −23.4684 | −0.860972 | −0.430486 | − | 0.902597i | \(-0.641658\pi\) | ||||
−0.430486 | + | 0.902597i | \(0.641658\pi\) | |||||||
\(744\) | −6.85643 | −0.251369 | ||||||||
\(745\) | −9.33958 | −0.342176 | ||||||||
\(746\) | 9.55509 | 0.349837 | ||||||||
\(747\) | −13.3674 | −0.489088 | ||||||||
\(748\) | 10.0026 | 0.365732 | ||||||||
\(749\) | 9.92560 | 0.362674 | ||||||||
\(750\) | 14.4213 | 0.526590 | ||||||||
\(751\) | 10.5901 | 0.386437 | 0.193218 | − | 0.981156i | \(-0.438107\pi\) | ||||
0.193218 | + | 0.981156i | \(0.438107\pi\) | |||||||
\(752\) | −16.6965 | −0.608860 | ||||||||
\(753\) | 16.7486 | 0.610354 | ||||||||
\(754\) | 24.5039 | 0.892381 | ||||||||
\(755\) | −9.91580 | −0.360873 | ||||||||
\(756\) | 2.30903 | 0.0839785 | ||||||||
\(757\) | −44.7414 | −1.62615 | −0.813076 | − | 0.582157i | \(-0.802209\pi\) | ||||
−0.813076 | + | 0.582157i | \(0.802209\pi\) | |||||||
\(758\) | −25.9365 | −0.942057 | ||||||||
\(759\) | 4.80316 | 0.174344 | ||||||||
\(760\) | −6.22373 | −0.225759 | ||||||||
\(761\) | −37.1182 | −1.34553 | −0.672767 | − | 0.739855i | \(-0.734894\pi\) | ||||
−0.672767 | + | 0.739855i | \(0.734894\pi\) | |||||||
\(762\) | 38.7963 | 1.40544 | ||||||||
\(763\) | −22.0303 | −0.797549 | ||||||||
\(764\) | 12.6128 | 0.456316 | ||||||||
\(765\) | 5.82649 | 0.210657 | ||||||||
\(766\) | 10.7872 | 0.389756 | ||||||||
\(767\) | 11.9621 | 0.431927 | ||||||||
\(768\) | −20.8685 | −0.753027 | ||||||||
\(769\) | −31.4382 | −1.13369 | −0.566845 | − | 0.823825i | \(-0.691836\pi\) | ||||
−0.566845 | + | 0.823825i | \(0.691836\pi\) | |||||||
\(770\) | 2.32947 | 0.0839484 | ||||||||
\(771\) | −4.89131 | −0.176156 | ||||||||
\(772\) | 7.02392 | 0.252796 | ||||||||
\(773\) | −16.5463 | −0.595129 | −0.297564 | − | 0.954702i | \(-0.596174\pi\) | ||||
−0.297564 | + | 0.954702i | \(0.596174\pi\) | |||||||
\(774\) | 4.78620 | 0.172037 | ||||||||
\(775\) | −30.4361 | −1.09330 | ||||||||
\(776\) | −8.26606 | −0.296734 | ||||||||
\(777\) | −9.40031 | −0.337234 | ||||||||
\(778\) | 40.0393 | 1.43548 | ||||||||
\(779\) | −28.5326 | −1.02229 | ||||||||
\(780\) | 3.06036 | 0.109579 | ||||||||
\(781\) | 0.519823 | 0.0186007 | ||||||||
\(782\) | 65.2408 | 2.33301 | ||||||||
\(783\) | 5.27328 | 0.188452 | ||||||||
\(784\) | 21.7712 | 0.777542 | ||||||||
\(785\) | −18.2687 | −0.652036 | ||||||||
\(786\) | −4.38558 | −0.156428 | ||||||||
\(787\) | −13.6570 | −0.486818 | −0.243409 | − | 0.969924i | \(-0.578266\pi\) | ||||
−0.243409 | + | 0.969924i | \(0.578266\pi\) | |||||||
\(788\) | 12.0640 | 0.429763 | ||||||||
\(789\) | −1.80979 | −0.0644302 | ||||||||
\(790\) | 13.1524 | 0.467943 | ||||||||
\(791\) | −2.53728 | −0.0902153 | ||||||||
\(792\) | −0.935674 | −0.0332477 | ||||||||
\(793\) | 1.47539 | 0.0523925 | ||||||||
\(794\) | 20.7974 | 0.738072 | ||||||||
\(795\) | 2.48773 | 0.0882307 | ||||||||
\(796\) | −0.752845 | −0.0266839 | ||||||||
\(797\) | −27.4397 | −0.971962 | −0.485981 | − | 0.873969i | \(-0.661538\pi\) | ||||
−0.485981 | + | 0.873969i | \(0.661538\pi\) | |||||||
\(798\) | −22.4713 | −0.795475 | ||||||||
\(799\) | −24.5597 | −0.868860 | ||||||||
\(800\) | −29.9827 | −1.06005 | ||||||||
\(801\) | −4.97649 | −0.175836 | ||||||||
\(802\) | −50.0891 | −1.76871 | ||||||||
\(803\) | −7.79861 | −0.275207 | ||||||||
\(804\) | −4.09232 | −0.144325 | ||||||||
\(805\) | 6.46024 | 0.227694 | ||||||||
\(806\) | −32.8110 | −1.15572 | ||||||||
\(807\) | −3.71262 | −0.130691 | ||||||||
\(808\) | 7.63215 | 0.268498 | ||||||||
\(809\) | −3.14162 | −0.110454 | −0.0552268 | − | 0.998474i | \(-0.517588\pi\) | ||||
−0.0552268 | + | 0.998474i | \(0.517588\pi\) | |||||||
\(810\) | 1.54893 | 0.0544239 | ||||||||
\(811\) | −50.4489 | −1.77150 | −0.885750 | − | 0.464162i | \(-0.846356\pi\) | ||||
−0.885750 | + | 0.464162i | \(0.846356\pi\) | |||||||
\(812\) | 12.1762 | 0.427299 | ||||||||
\(813\) | 4.45630 | 0.156289 | ||||||||
\(814\) | −10.8256 | −0.379437 | ||||||||
\(815\) | 6.26527 | 0.219463 | ||||||||
\(816\) | −33.4704 | −1.17170 | ||||||||
\(817\) | −19.8051 | −0.692892 | ||||||||
\(818\) | −22.9717 | −0.803185 | ||||||||
\(819\) | −3.88808 | −0.135861 | ||||||||
\(820\) | 4.54124 | 0.158587 | ||||||||
\(821\) | −13.8898 | −0.484758 | −0.242379 | − | 0.970182i | \(-0.577928\pi\) | ||||
−0.242379 | + | 0.970182i | \(0.577928\pi\) | |||||||
\(822\) | −18.5445 | −0.646812 | ||||||||
\(823\) | 34.1194 | 1.18933 | 0.594664 | − | 0.803974i | \(-0.297285\pi\) | ||||
0.594664 | + | 0.803974i | \(0.297285\pi\) | |||||||
\(824\) | −9.35951 | −0.326054 | ||||||||
\(825\) | −4.15351 | −0.144607 | ||||||||
\(826\) | 13.9796 | 0.486413 | ||||||||
\(827\) | 47.0110 | 1.63473 | 0.817366 | − | 0.576119i | \(-0.195433\pi\) | ||||
0.817366 | + | 0.576119i | \(0.195433\pi\) | |||||||
\(828\) | 7.37447 | 0.256280 | ||||||||
\(829\) | 9.52320 | 0.330754 | 0.165377 | − | 0.986230i | \(-0.447116\pi\) | ||||
0.165377 | + | 0.986230i | \(0.447116\pi\) | |||||||
\(830\) | −20.7052 | −0.718688 | ||||||||
\(831\) | −9.13295 | −0.316819 | ||||||||
\(832\) | −8.55593 | −0.296623 | ||||||||
\(833\) | 32.0242 | 1.10957 | ||||||||
\(834\) | 4.68150 | 0.162107 | ||||||||
\(835\) | −11.1883 | −0.387187 | ||||||||
\(836\) | −11.0033 | −0.380559 | ||||||||
\(837\) | −7.06097 | −0.244063 | ||||||||
\(838\) | 0.900582 | 0.0311101 | ||||||||
\(839\) | 25.9901 | 0.897277 | 0.448639 | − | 0.893713i | \(-0.351909\pi\) | ||||
0.448639 | + | 0.893713i | \(0.351909\pi\) | |||||||
\(840\) | −1.25848 | −0.0434217 | ||||||||
\(841\) | −1.19248 | −0.0411199 | ||||||||
\(842\) | −7.84666 | −0.270414 | ||||||||
\(843\) | 22.5769 | 0.777589 | ||||||||
\(844\) | 5.38801 | 0.185463 | ||||||||
\(845\) | 5.64174 | 0.194082 | ||||||||
\(846\) | −6.52903 | −0.224473 | ||||||||
\(847\) | 15.7191 | 0.540116 | ||||||||
\(848\) | −14.2908 | −0.490749 | ||||||||
\(849\) | 6.41224 | 0.220068 | ||||||||
\(850\) | −56.4166 | −1.93507 | ||||||||
\(851\) | −30.0223 | −1.02915 | ||||||||
\(852\) | 0.798103 | 0.0273426 | ||||||||
\(853\) | −40.4602 | −1.38533 | −0.692666 | − | 0.721259i | \(-0.743564\pi\) | ||||
−0.692666 | + | 0.721259i | \(0.743564\pi\) | |||||||
\(854\) | 1.72422 | 0.0590017 | ||||||||
\(855\) | −6.40940 | −0.219197 | ||||||||
\(856\) | −6.17527 | −0.211066 | ||||||||
\(857\) | −12.6625 | −0.432541 | −0.216271 | − | 0.976333i | \(-0.569389\pi\) | ||||
−0.216271 | + | 0.976333i | \(0.569389\pi\) | |||||||
\(858\) | −4.47761 | −0.152863 | ||||||||
\(859\) | −34.0940 | −1.16327 | −0.581636 | − | 0.813449i | \(-0.697587\pi\) | ||||
−0.581636 | + | 0.813449i | \(0.697587\pi\) | |||||||
\(860\) | 3.15217 | 0.107488 | ||||||||
\(861\) | −5.76948 | −0.196623 | ||||||||
\(862\) | 70.4962 | 2.40111 | ||||||||
\(863\) | −18.1693 | −0.618490 | −0.309245 | − | 0.950982i | \(-0.600076\pi\) | ||||
−0.309245 | + | 0.950982i | \(0.600076\pi\) | |||||||
\(864\) | −6.95580 | −0.236641 | ||||||||
\(865\) | 16.6311 | 0.565476 | ||||||||
\(866\) | −48.8937 | −1.66148 | ||||||||
\(867\) | −32.2331 | −1.09469 | ||||||||
\(868\) | −16.3040 | −0.553393 | ||||||||
\(869\) | −8.18211 | −0.277559 | ||||||||
\(870\) | 8.16795 | 0.276920 | ||||||||
\(871\) | 6.89090 | 0.233489 | ||||||||
\(872\) | 13.7062 | 0.464152 | ||||||||
\(873\) | −8.51266 | −0.288110 | ||||||||
\(874\) | −71.7678 | −2.42758 | ||||||||
\(875\) | −12.0666 | −0.407925 | ||||||||
\(876\) | −11.9735 | −0.404546 | ||||||||
\(877\) | −26.5456 | −0.896381 | −0.448190 | − | 0.893938i | \(-0.647931\pi\) | ||||
−0.448190 | + | 0.893938i | \(0.647931\pi\) | |||||||
\(878\) | 4.24876 | 0.143389 | ||||||||
\(879\) | 3.55312 | 0.119844 | ||||||||
\(880\) | −3.81681 | −0.128665 | ||||||||
\(881\) | −36.1912 | −1.21931 | −0.609657 | − | 0.792665i | \(-0.708693\pi\) | ||||
−0.609657 | + | 0.792665i | \(0.708693\pi\) | |||||||
\(882\) | 8.51342 | 0.286662 | ||||||||
\(883\) | 2.52755 | 0.0850587 | 0.0425293 | − | 0.999095i | \(-0.486458\pi\) | ||||
0.0425293 | + | 0.999095i | \(0.486458\pi\) | |||||||
\(884\) | −25.8597 | −0.869757 | ||||||||
\(885\) | 3.98735 | 0.134033 | ||||||||
\(886\) | 61.0489 | 2.05098 | ||||||||
\(887\) | 6.35333 | 0.213324 | 0.106662 | − | 0.994295i | \(-0.465984\pi\) | ||||
0.106662 | + | 0.994295i | \(0.465984\pi\) | |||||||
\(888\) | 5.84845 | 0.196261 | ||||||||
\(889\) | −32.4617 | −1.08873 | ||||||||
\(890\) | −7.70824 | −0.258381 | ||||||||
\(891\) | −0.963587 | −0.0322814 | ||||||||
\(892\) | 28.5170 | 0.954819 | ||||||||
\(893\) | 27.0168 | 0.904083 | ||||||||
\(894\) | 20.9799 | 0.701673 | ||||||||
\(895\) | −6.78237 | −0.226710 | ||||||||
\(896\) | 11.7136 | 0.391325 | ||||||||
\(897\) | −12.4176 | −0.414611 | ||||||||
\(898\) | 6.56844 | 0.219192 | ||||||||
\(899\) | −37.2345 | −1.24184 | ||||||||
\(900\) | −6.37703 | −0.212568 | ||||||||
\(901\) | −21.0210 | −0.700312 | ||||||||
\(902\) | −6.64426 | −0.221230 | ||||||||
\(903\) | −4.00472 | −0.133269 | ||||||||
\(904\) | 1.57858 | 0.0525028 | ||||||||
\(905\) | −10.4155 | −0.346223 | ||||||||
\(906\) | 22.2743 | 0.740014 | ||||||||
\(907\) | −24.3919 | −0.809919 | −0.404960 | − | 0.914335i | \(-0.632714\pi\) | ||||
−0.404960 | + | 0.914335i | \(0.632714\pi\) | |||||||
\(908\) | −22.5135 | −0.747137 | ||||||||
\(909\) | 7.85984 | 0.260694 | ||||||||
\(910\) | −6.02237 | −0.199640 | ||||||||
\(911\) | −10.3397 | −0.342569 | −0.171285 | − | 0.985222i | \(-0.554792\pi\) | ||||
−0.171285 | + | 0.985222i | \(0.554792\pi\) | |||||||
\(912\) | 36.8189 | 1.21920 | ||||||||
\(913\) | 12.8807 | 0.426288 | ||||||||
\(914\) | −66.8554 | −2.21138 | ||||||||
\(915\) | 0.491794 | 0.0162582 | ||||||||
\(916\) | −30.1993 | −0.997814 | ||||||||
\(917\) | 3.66951 | 0.121178 | ||||||||
\(918\) | −13.0883 | −0.431978 | ||||||||
\(919\) | 0.529162 | 0.0174555 | 0.00872773 | − | 0.999962i | \(-0.497222\pi\) | ||||
0.00872773 | + | 0.999962i | \(0.497222\pi\) | |||||||
\(920\) | −4.01927 | −0.132512 | ||||||||
\(921\) | 27.0815 | 0.892366 | ||||||||
\(922\) | 64.5706 | 2.12652 | ||||||||
\(923\) | −1.34390 | −0.0442349 | ||||||||
\(924\) | −2.22495 | −0.0731954 | ||||||||
\(925\) | 25.9616 | 0.853612 | ||||||||
\(926\) | 67.2348 | 2.20947 | ||||||||
\(927\) | −9.63873 | −0.316577 | ||||||||
\(928\) | −36.6799 | −1.20408 | ||||||||
\(929\) | 49.8368 | 1.63509 | 0.817546 | − | 0.575863i | \(-0.195334\pi\) | ||||
0.817546 | + | 0.575863i | \(0.195334\pi\) | |||||||
\(930\) | −10.9370 | −0.358637 | ||||||||
\(931\) | −35.2281 | −1.15456 | ||||||||
\(932\) | 12.7318 | 0.417044 | ||||||||
\(933\) | −17.1629 | −0.561888 | ||||||||
\(934\) | 1.76632 | 0.0577958 | ||||||||
\(935\) | −5.61433 | −0.183608 | ||||||||
\(936\) | 2.41899 | 0.0790672 | ||||||||
\(937\) | 14.9564 | 0.488605 | 0.244302 | − | 0.969699i | \(-0.421441\pi\) | ||||
0.244302 | + | 0.969699i | \(0.421441\pi\) | |||||||
\(938\) | 8.05311 | 0.262944 | ||||||||
\(939\) | 4.58545 | 0.149641 | ||||||||
\(940\) | −4.29998 | −0.140250 | ||||||||
\(941\) | −6.38382 | −0.208106 | −0.104053 | − | 0.994572i | \(-0.533181\pi\) | ||||
−0.104053 | + | 0.994572i | \(0.533181\pi\) | |||||||
\(942\) | 41.0377 | 1.33708 | ||||||||
\(943\) | −18.4263 | −0.600043 | ||||||||
\(944\) | −22.9054 | −0.745508 | ||||||||
\(945\) | −1.29602 | −0.0421596 | ||||||||
\(946\) | −4.61193 | −0.149947 | ||||||||
\(947\) | 15.8841 | 0.516164 | 0.258082 | − | 0.966123i | \(-0.416910\pi\) | ||||
0.258082 | + | 0.966123i | \(0.416910\pi\) | |||||||
\(948\) | −12.5623 | −0.408004 | ||||||||
\(949\) | 20.1617 | 0.654476 | ||||||||
\(950\) | 62.0609 | 2.01352 | ||||||||
\(951\) | 24.8545 | 0.805963 | ||||||||
\(952\) | 10.6340 | 0.344650 | ||||||||
\(953\) | −12.9998 | −0.421104 | −0.210552 | − | 0.977583i | \(-0.567526\pi\) | ||||
−0.210552 | + | 0.977583i | \(0.567526\pi\) | |||||||
\(954\) | −5.58829 | −0.180928 | ||||||||
\(955\) | −7.07940 | −0.229084 | ||||||||
\(956\) | −15.1765 | −0.490842 | ||||||||
\(957\) | −5.08127 | −0.164254 | ||||||||
\(958\) | 23.7463 | 0.767209 | ||||||||
\(959\) | 15.5165 | 0.501055 | ||||||||
\(960\) | −2.85197 | −0.0920468 | ||||||||
\(961\) | 18.8574 | 0.608302 | ||||||||
\(962\) | 27.9874 | 0.902350 | ||||||||
\(963\) | −6.35949 | −0.204932 | ||||||||
\(964\) | −21.6488 | −0.697261 | ||||||||
\(965\) | −3.94242 | −0.126911 | ||||||||
\(966\) | −14.5119 | −0.466913 | ||||||||
\(967\) | −11.7867 | −0.379036 | −0.189518 | − | 0.981877i | \(-0.560693\pi\) | ||||
−0.189518 | + | 0.981877i | \(0.560693\pi\) | |||||||
\(968\) | −9.77975 | −0.314333 | ||||||||
\(969\) | 54.1587 | 1.73983 | ||||||||
\(970\) | −13.1855 | −0.423361 | ||||||||
\(971\) | 24.1526 | 0.775095 | 0.387548 | − | 0.921850i | \(-0.373322\pi\) | ||||
0.387548 | + | 0.921850i | \(0.373322\pi\) | |||||||
\(972\) | −1.47943 | −0.0474527 | ||||||||
\(973\) | −3.91711 | −0.125577 | ||||||||
\(974\) | 67.0056 | 2.14700 | ||||||||
\(975\) | 10.7380 | 0.343893 | ||||||||
\(976\) | −2.82512 | −0.0904299 | ||||||||
\(977\) | 15.4450 | 0.494129 | 0.247065 | − | 0.968999i | \(-0.420534\pi\) | ||||
0.247065 | + | 0.968999i | \(0.420534\pi\) | |||||||
\(978\) | −14.0739 | −0.450035 | ||||||||
\(979\) | 4.79528 | 0.153258 | ||||||||
\(980\) | 5.60689 | 0.179106 | ||||||||
\(981\) | 14.1151 | 0.450661 | ||||||||
\(982\) | −64.2311 | −2.04970 | ||||||||
\(983\) | −11.3002 | −0.360421 | −0.180210 | − | 0.983628i | \(-0.557678\pi\) | ||||
−0.180210 | + | 0.983628i | \(0.557678\pi\) | |||||||
\(984\) | 3.58951 | 0.114429 | ||||||||
\(985\) | −6.77136 | −0.215753 | ||||||||
\(986\) | −69.0182 | −2.19799 | ||||||||
\(987\) | 5.46297 | 0.173888 | ||||||||
\(988\) | 28.4469 | 0.905016 | ||||||||
\(989\) | −12.7901 | −0.406701 | ||||||||
\(990\) | −1.49253 | −0.0474357 | ||||||||
\(991\) | −39.0925 | −1.24182 | −0.620908 | − | 0.783884i | \(-0.713236\pi\) | ||||
−0.620908 | + | 0.783884i | \(0.713236\pi\) | |||||||
\(992\) | 49.1147 | 1.55939 | ||||||||
\(993\) | 23.1335 | 0.734119 | ||||||||
\(994\) | −1.57056 | −0.0498150 | ||||||||
\(995\) | 0.422561 | 0.0133961 | ||||||||
\(996\) | 19.7761 | 0.626631 | ||||||||
\(997\) | −17.8388 | −0.564962 | −0.282481 | − | 0.959273i | \(-0.591157\pi\) | ||||
−0.282481 | + | 0.959273i | \(0.591157\pi\) | |||||||
\(998\) | 35.2142 | 1.11469 | ||||||||
\(999\) | 6.02292 | 0.190557 |
(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 | 6033.2.a.d.1.19 | ✓ | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6033.2.a.d.1.19 | ✓ | 84 | 1.1 | even | 1 | trivial |