Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(77,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.k (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 533.6 | ||
Character | \(\chi\) | \(=\) | 570.533 |
Dual form | 570.2.k.a.77.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0.668751 | + | 1.59774i | 0.386104 | + | 0.922455i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −0.595769 | − | 2.15524i | −0.266436 | − | 0.963853i | ||||
\(6\) | 0.656894 | − | 1.60265i | 0.268176 | − | 0.654280i | ||||
\(7\) | −0.0702822 | + | 0.0702822i | −0.0265642 | + | 0.0265642i | −0.720264 | − | 0.693700i | \(-0.755979\pi\) |
0.693700 | + | 0.720264i | \(0.255979\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | −2.10554 | + | 2.13698i | −0.701848 | + | 0.712327i | ||||
\(10\) | −1.10271 | + | 1.94526i | −0.348708 | + | 0.615144i | ||||
\(11\) | 3.25490i | 0.981388i | 0.871332 | + | 0.490694i | \(0.163257\pi\) | ||||
−0.871332 | + | 0.490694i | \(0.836743\pi\) | |||||||
\(12\) | −1.59774 | + | 0.668751i | −0.461228 | + | 0.193052i | ||||
\(13\) | 1.84783 | + | 1.84783i | 0.512496 | + | 0.512496i | 0.915290 | − | 0.402795i | \(-0.131961\pi\) |
−0.402795 | + | 0.915290i | \(0.631961\pi\) | |||||||
\(14\) | 0.0993940 | 0.0265642 | ||||||||
\(15\) | 3.04509 | − | 2.39320i | 0.786239 | − | 0.617923i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.76548 | + | 3.76548i | 0.913262 | + | 0.913262i | 0.996527 | − | 0.0832653i | \(-0.0265349\pi\) |
−0.0832653 | + | 0.996527i | \(0.526535\pi\) | |||||||
\(18\) | 2.99992 | − | 0.0222303i | 0.707087 | − | 0.00523973i | ||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | 2.15524 | − | 0.595769i | 0.481926 | − | 0.133218i | ||||
\(21\) | −0.159294 | − | 0.0652913i | −0.0347608 | − | 0.0142477i | ||||
\(22\) | 2.30156 | − | 2.30156i | 0.490694 | − | 0.490694i | ||||
\(23\) | −1.02394 | + | 1.02394i | −0.213506 | + | 0.213506i | −0.805755 | − | 0.592249i | \(-0.798240\pi\) |
0.592249 | + | 0.805755i | \(0.298240\pi\) | |||||||
\(24\) | 1.60265 | + | 0.656894i | 0.327140 | + | 0.134088i | ||||
\(25\) | −4.29012 | + | 2.56805i | −0.858024 | + | 0.513610i | ||||
\(26\) | − | 2.61323i | − | 0.512496i | ||||||
\(27\) | −4.82242 | − | 1.93500i | −0.928076 | − | 0.372391i | ||||
\(28\) | −0.0702822 | − | 0.0702822i | −0.0132821 | − | 0.0132821i | ||||
\(29\) | 6.98010 | 1.29617 | 0.648086 | − | 0.761567i | \(-0.275570\pi\) | ||||
0.648086 | + | 0.761567i | \(0.275570\pi\) | |||||||
\(30\) | −3.84545 | − | 0.460953i | −0.702081 | − | 0.0841582i | ||||
\(31\) | 9.93413 | 1.78422 | 0.892111 | − | 0.451816i | \(-0.149224\pi\) | ||||
0.892111 | + | 0.451816i | \(0.149224\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −5.20048 | + | 2.17672i | −0.905287 | + | 0.378918i | ||||
\(34\) | − | 5.32519i | − | 0.913262i | ||||||
\(35\) | 0.193347 | + | 0.109603i | 0.0326816 | + | 0.0185263i | ||||
\(36\) | −2.13698 | − | 2.10554i | −0.356164 | − | 0.350924i | ||||
\(37\) | −3.00157 | + | 3.00157i | −0.493456 | + | 0.493456i | −0.909393 | − | 0.415938i | \(-0.863453\pi\) |
0.415938 | + | 0.909393i | \(0.363453\pi\) | |||||||
\(38\) | −0.707107 | + | 0.707107i | −0.114708 | + | 0.114708i | ||||
\(39\) | −1.71661 | + | 4.18809i | −0.274878 | + | 0.670631i | ||||
\(40\) | −1.94526 | − | 1.10271i | −0.307572 | − | 0.174354i | ||||
\(41\) | 8.72182i | 1.36212i | 0.732228 | + | 0.681059i | \(0.238480\pi\) | ||||
−0.732228 | + | 0.681059i | \(0.761520\pi\) | |||||||
\(42\) | 0.0664699 | + | 0.158806i | 0.0102565 | + | 0.0245043i | ||||
\(43\) | −2.35540 | − | 2.35540i | −0.359195 | − | 0.359195i | 0.504321 | − | 0.863516i | \(-0.331743\pi\) |
−0.863516 | + | 0.504321i | \(0.831743\pi\) | |||||||
\(44\) | −3.25490 | −0.490694 | ||||||||
\(45\) | 5.86012 | + | 3.26480i | 0.873576 | + | 0.486688i | ||||
\(46\) | 1.44807 | 0.213506 | ||||||||
\(47\) | −0.871132 | − | 0.871132i | −0.127068 | − | 0.127068i | 0.640713 | − | 0.767781i | \(-0.278639\pi\) |
−0.767781 | + | 0.640713i | \(0.778639\pi\) | |||||||
\(48\) | −0.668751 | − | 1.59774i | −0.0965260 | − | 0.230614i | ||||
\(49\) | 6.99012i | 0.998589i | ||||||||
\(50\) | 4.84946 | + | 1.21769i | 0.685817 | + | 0.172207i | ||||
\(51\) | −3.49808 | + | 8.53442i | −0.489829 | + | 1.19506i | ||||
\(52\) | −1.84783 | + | 1.84783i | −0.256248 | + | 0.256248i | ||||
\(53\) | −8.49654 | + | 8.49654i | −1.16709 | + | 1.16709i | −0.184201 | + | 0.982889i | \(0.558970\pi\) |
−0.982889 | + | 0.184201i | \(0.941030\pi\) | |||||||
\(54\) | 2.04172 | + | 4.77822i | 0.277843 | + | 0.650233i | ||||
\(55\) | 7.01508 | − | 1.93917i | 0.945914 | − | 0.261477i | ||||
\(56\) | 0.0993940i | 0.0132821i | ||||||||
\(57\) | 1.59774 | − | 0.668751i | 0.211626 | − | 0.0885783i | ||||
\(58\) | −4.93568 | − | 4.93568i | −0.648086 | − | 0.648086i | ||||
\(59\) | −2.24875 | −0.292762 | −0.146381 | − | 0.989228i | \(-0.546763\pi\) | ||||
−0.146381 | + | 0.989228i | \(0.546763\pi\) | |||||||
\(60\) | 2.39320 | + | 3.04509i | 0.308961 | + | 0.393119i | ||||
\(61\) | 8.33970 | 1.06779 | 0.533895 | − | 0.845551i | \(-0.320728\pi\) | ||||
0.533895 | + | 0.845551i | \(0.320728\pi\) | |||||||
\(62\) | −7.02449 | − | 7.02449i | −0.892111 | − | 0.892111i | ||||
\(63\) | −0.00220956 | − | 0.298174i | −0.000278378 | − | 0.0375664i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 2.88164 | − | 5.08340i | 0.357423 | − | 0.630518i | ||||
\(66\) | 5.21646 | + | 2.13812i | 0.642102 | + | 0.263185i | ||||
\(67\) | 2.25310 | − | 2.25310i | 0.275260 | − | 0.275260i | −0.555954 | − | 0.831213i | \(-0.687647\pi\) |
0.831213 | + | 0.555954i | \(0.187647\pi\) | |||||||
\(68\) | −3.76548 | + | 3.76548i | −0.456631 | + | 0.456631i | ||||
\(69\) | −2.32074 | − | 0.951225i | −0.279385 | − | 0.114514i | ||||
\(70\) | −0.0592159 | − | 0.214218i | −0.00707765 | − | 0.0256039i | ||||
\(71\) | − | 6.67876i | − | 0.792623i | −0.918116 | − | 0.396311i | \(-0.870290\pi\) | ||
0.918116 | − | 0.396311i | \(-0.129710\pi\) | |||||||
\(72\) | 0.0222303 | + | 2.99992i | 0.00261986 | + | 0.353544i | ||||
\(73\) | −4.70997 | − | 4.70997i | −0.551260 | − | 0.551260i | 0.375544 | − | 0.926805i | \(-0.377456\pi\) |
−0.926805 | + | 0.375544i | \(0.877456\pi\) | |||||||
\(74\) | 4.24487 | 0.493456 | ||||||||
\(75\) | −6.97210 | − | 5.13710i | −0.805069 | − | 0.593182i | ||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −0.228761 | − | 0.228761i | −0.0260698 | − | 0.0260698i | ||||
\(78\) | 4.17525 | − | 1.74760i | 0.472754 | − | 0.197877i | ||||
\(79\) | − | 9.81442i | − | 1.10421i | −0.833775 | − | 0.552104i | \(-0.813825\pi\) | ||
0.833775 | − | 0.552104i | \(-0.186175\pi\) | |||||||
\(80\) | 0.595769 | + | 2.15524i | 0.0666090 | + | 0.240963i | ||||
\(81\) | −0.133378 | − | 8.99901i | −0.0148198 | − | 0.999890i | ||||
\(82\) | 6.16725 | − | 6.16725i | 0.681059 | − | 0.681059i | ||||
\(83\) | 10.5506 | − | 10.5506i | 1.15808 | − | 1.15808i | 0.173188 | − | 0.984889i | \(-0.444593\pi\) |
0.984889 | − | 0.173188i | \(-0.0554067\pi\) | |||||||
\(84\) | 0.0652913 | − | 0.159294i | 0.00712387 | − | 0.0173804i | ||||
\(85\) | 5.87215 | − | 10.3589i | 0.636924 | − | 1.12358i | ||||
\(86\) | 3.33103i | 0.359195i | ||||||||
\(87\) | 4.66795 | + | 11.1524i | 0.500457 | + | 1.19566i | ||||
\(88\) | 2.30156 | + | 2.30156i | 0.245347 | + | 0.245347i | ||||
\(89\) | 0.330099 | 0.0349904 | 0.0174952 | − | 0.999847i | \(-0.494431\pi\) | ||||
0.0174952 | + | 0.999847i | \(0.494431\pi\) | |||||||
\(90\) | −1.83517 | − | 6.45230i | −0.193444 | − | 0.680132i | ||||
\(91\) | −0.259739 | −0.0272280 | ||||||||
\(92\) | −1.02394 | − | 1.02394i | −0.106753 | − | 0.106753i | ||||
\(93\) | 6.64346 | + | 15.8722i | 0.688895 | + | 1.64587i | ||||
\(94\) | 1.23197i | 0.127068i | ||||||||
\(95\) | −2.15524 | + | 0.595769i | −0.221123 | + | 0.0611246i | ||||
\(96\) | −0.656894 | + | 1.60265i | −0.0670439 | + | 0.163570i | ||||
\(97\) | −3.68496 | + | 3.68496i | −0.374151 | + | 0.374151i | −0.868986 | − | 0.494836i | \(-0.835228\pi\) |
0.494836 | + | 0.868986i | \(0.335228\pi\) | |||||||
\(98\) | 4.94276 | − | 4.94276i | 0.499294 | − | 0.499294i | ||||
\(99\) | −6.95565 | − | 6.85333i | −0.699070 | − | 0.688785i | ||||
\(100\) | −2.56805 | − | 4.29012i | −0.256805 | − | 0.429012i | ||||
\(101\) | 10.2407i | 1.01898i | 0.860475 | + | 0.509492i | \(0.170167\pi\) | ||||
−0.860475 | + | 0.509492i | \(0.829833\pi\) | |||||||
\(102\) | 8.50826 | − | 3.56123i | 0.842443 | − | 0.352614i | ||||
\(103\) | −6.21848 | − | 6.21848i | −0.612725 | − | 0.612725i | 0.330930 | − | 0.943655i | \(-0.392638\pi\) |
−0.943655 | + | 0.330930i | \(0.892638\pi\) | |||||||
\(104\) | 2.61323 | 0.256248 | ||||||||
\(105\) | −0.0458160 | + | 0.382215i | −0.00447119 | + | 0.0373004i | ||||
\(106\) | 12.0159 | 1.16709 | ||||||||
\(107\) | −8.75189 | − | 8.75189i | −0.846077 | − | 0.846077i | 0.143564 | − | 0.989641i | \(-0.454144\pi\) |
−0.989641 | + | 0.143564i | \(0.954144\pi\) | |||||||
\(108\) | 1.93500 | − | 4.82242i | 0.186195 | − | 0.464038i | ||||
\(109\) | − | 13.5040i | − | 1.29345i | −0.762725 | − | 0.646723i | \(-0.776139\pi\) | ||
0.762725 | − | 0.646723i | \(-0.223861\pi\) | |||||||
\(110\) | −6.33161 | − | 3.58922i | −0.603696 | − | 0.342218i | ||||
\(111\) | −6.80304 | − | 2.78843i | −0.645716 | − | 0.264666i | ||||
\(112\) | 0.0702822 | − | 0.0702822i | 0.00664104 | − | 0.00664104i | ||||
\(113\) | 1.54982 | − | 1.54982i | 0.145794 | − | 0.145794i | −0.630442 | − | 0.776236i | \(-0.717126\pi\) |
0.776236 | + | 0.630442i | \(0.217126\pi\) | |||||||
\(114\) | −1.60265 | − | 0.656894i | −0.150102 | − | 0.0615237i | ||||
\(115\) | 2.81686 | + | 1.59680i | 0.262674 | + | 0.148902i | ||||
\(116\) | 6.98010i | 0.648086i | ||||||||
\(117\) | −7.83946 | + | 0.0580928i | −0.724758 | + | 0.00537068i | ||||
\(118\) | 1.59010 | + | 1.59010i | 0.146381 | + | 0.146381i | ||||
\(119\) | −0.529292 | −0.0485201 | ||||||||
\(120\) | 0.460953 | − | 3.84545i | 0.0420791 | − | 0.351040i | ||||
\(121\) | 0.405644 | 0.0368767 | ||||||||
\(122\) | −5.89706 | − | 5.89706i | −0.533895 | − | 0.533895i | ||||
\(123\) | −13.9352 | + | 5.83273i | −1.25649 | + | 0.525919i | ||||
\(124\) | 9.93413i | 0.892111i | ||||||||
\(125\) | 8.09069 | + | 7.71627i | 0.723653 | + | 0.690164i | ||||
\(126\) | −0.209278 | + | 0.212403i | −0.0186440 | + | 0.0189224i | ||||
\(127\) | −15.2603 | + | 15.2603i | −1.35413 | + | 1.35413i | −0.473148 | + | 0.880983i | \(0.656882\pi\) |
−0.880983 | + | 0.473148i | \(0.843118\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 2.18814 | − | 5.33849i | 0.192655 | − | 0.470028i | ||||
\(130\) | −5.63213 | + | 1.55688i | −0.493970 | + | 0.136547i | ||||
\(131\) | 3.07551i | 0.268709i | 0.990933 | + | 0.134354i | \(0.0428960\pi\) | ||||
−0.990933 | + | 0.134354i | \(0.957104\pi\) | |||||||
\(132\) | −2.17672 | − | 5.20048i | −0.189459 | − | 0.452643i | ||||
\(133\) | 0.0702822 | + | 0.0702822i | 0.00609424 | + | 0.00609424i | ||||
\(134\) | −3.18636 | −0.275260 | ||||||||
\(135\) | −1.29734 | + | 11.5463i | −0.111657 | + | 0.993747i | ||||
\(136\) | 5.32519 | 0.456631 | ||||||||
\(137\) | −8.96502 | − | 8.96502i | −0.765934 | − | 0.765934i | 0.211454 | − | 0.977388i | \(-0.432180\pi\) |
−0.977388 | + | 0.211454i | \(0.932180\pi\) | |||||||
\(138\) | 0.968396 | + | 2.31363i | 0.0824354 | + | 0.196949i | ||||
\(139\) | − | 8.80702i | − | 0.747002i | −0.927630 | − | 0.373501i | \(-0.878157\pi\) | ||
0.927630 | − | 0.373501i | \(-0.121843\pi\) | |||||||
\(140\) | −0.109603 | + | 0.193347i | −0.00926315 | + | 0.0163408i | ||||
\(141\) | 0.809272 | − | 1.97441i | 0.0681530 | − | 0.166276i | ||||
\(142\) | −4.72260 | + | 4.72260i | −0.396311 | + | 0.396311i | ||||
\(143\) | −6.01449 | + | 6.01449i | −0.502957 | + | 0.502957i | ||||
\(144\) | 2.10554 | − | 2.13698i | 0.175462 | − | 0.178082i | ||||
\(145\) | −4.15853 | − | 15.0438i | −0.345347 | − | 1.24932i | ||||
\(146\) | 6.66091i | 0.551260i | ||||||||
\(147\) | −11.1684 | + | 4.67465i | −0.921153 | + | 0.385559i | ||||
\(148\) | −3.00157 | − | 3.00157i | −0.246728 | − | 0.246728i | ||||
\(149\) | 19.3731 | 1.58710 | 0.793552 | − | 0.608503i | \(-0.208230\pi\) | ||||
0.793552 | + | 0.608503i | \(0.208230\pi\) | |||||||
\(150\) | 1.29754 | + | 8.56250i | 0.105944 | + | 0.699125i | ||||
\(151\) | 15.4311 | 1.25577 | 0.627883 | − | 0.778308i | \(-0.283922\pi\) | ||||
0.627883 | + | 0.778308i | \(0.283922\pi\) | |||||||
\(152\) | −0.707107 | − | 0.707107i | −0.0573539 | − | 0.0573539i | ||||
\(153\) | −15.9751 | + | 0.118380i | −1.29151 | + | 0.00957049i | ||||
\(154\) | 0.323517i | 0.0260698i | ||||||||
\(155\) | −5.91845 | − | 21.4104i | −0.475381 | − | 1.71973i | ||||
\(156\) | −4.18809 | − | 1.71661i | −0.335315 | − | 0.137439i | ||||
\(157\) | 13.5743 | − | 13.5743i | 1.08335 | − | 1.08335i | 0.0871534 | − | 0.996195i | \(-0.472223\pi\) |
0.996195 | − | 0.0871534i | \(-0.0277770\pi\) | |||||||
\(158\) | −6.93985 | + | 6.93985i | −0.552104 | + | 0.552104i | ||||
\(159\) | −19.2573 | − | 7.89318i | −1.52721 | − | 0.625970i | ||||
\(160\) | 1.10271 | − | 1.94526i | 0.0871771 | − | 0.153786i | ||||
\(161\) | − | 0.143929i | − | 0.0113432i | ||||||
\(162\) | −6.26895 | + | 6.45757i | −0.492535 | + | 0.507355i | ||||
\(163\) | −1.79928 | − | 1.79928i | −0.140930 | − | 0.140930i | 0.633122 | − | 0.774052i | \(-0.281773\pi\) |
−0.774052 | + | 0.633122i | \(0.781773\pi\) | |||||||
\(164\) | −8.72182 | −0.681059 | ||||||||
\(165\) | 7.78963 | + | 9.91146i | 0.606422 | + | 0.771606i | ||||
\(166\) | −14.9208 | −1.15808 | ||||||||
\(167\) | −3.31894 | − | 3.31894i | −0.256827 | − | 0.256827i | 0.566935 | − | 0.823762i | \(-0.308129\pi\) |
−0.823762 | + | 0.566935i | \(0.808129\pi\) | |||||||
\(168\) | −0.158806 | + | 0.0664699i | −0.0122521 | + | 0.00512826i | ||||
\(169\) | − | 6.17105i | − | 0.474696i | ||||||
\(170\) | −11.4771 | + | 3.17258i | −0.880250 | + | 0.243326i | ||||
\(171\) | 2.13698 | + | 2.10554i | 0.163419 | + | 0.161015i | ||||
\(172\) | 2.35540 | − | 2.35540i | 0.179597 | − | 0.179597i | ||||
\(173\) | −2.84866 | + | 2.84866i | −0.216580 | + | 0.216580i | −0.807056 | − | 0.590476i | \(-0.798940\pi\) |
0.590476 | + | 0.807056i | \(0.298940\pi\) | |||||||
\(174\) | 4.58518 | − | 11.1867i | 0.347602 | − | 0.848059i | ||||
\(175\) | 0.121031 | − | 0.482007i | 0.00914906 | − | 0.0364363i | ||||
\(176\) | − | 3.25490i | − | 0.245347i | ||||||
\(177\) | −1.50385 | − | 3.59291i | −0.113037 | − | 0.270060i | ||||
\(178\) | −0.233415 | − | 0.233415i | −0.0174952 | − | 0.0174952i | ||||
\(179\) | 7.34939 | 0.549319 | 0.274660 | − | 0.961541i | \(-0.411435\pi\) | ||||
0.274660 | + | 0.961541i | \(0.411435\pi\) | |||||||
\(180\) | −3.26480 | + | 5.86012i | −0.243344 | + | 0.436788i | ||||
\(181\) | −24.4774 | −1.81939 | −0.909695 | − | 0.415277i | \(-0.863685\pi\) | ||||
−0.909695 | + | 0.415277i | \(0.863685\pi\) | |||||||
\(182\) | 0.183663 | + | 0.183663i | 0.0136140 | + | 0.0136140i | ||||
\(183\) | 5.57719 | + | 13.3247i | 0.412278 | + | 0.984988i | ||||
\(184\) | 1.44807i | 0.106753i | ||||||||
\(185\) | 8.25736 | + | 4.68087i | 0.607093 | + | 0.344144i | ||||
\(186\) | 6.52567 | − | 15.9209i | 0.478485 | − | 1.16738i | ||||
\(187\) | −12.2562 | + | 12.2562i | −0.896265 | + | 0.896265i | ||||
\(188\) | 0.871132 | − | 0.871132i | 0.0635339 | − | 0.0635339i | ||||
\(189\) | 0.474927 | − | 0.202935i | 0.0345458 | − | 0.0147613i | ||||
\(190\) | 1.94526 | + | 1.10271i | 0.141124 | + | 0.0799992i | ||||
\(191\) | − | 1.13422i | − | 0.0820694i | −0.999158 | − | 0.0410347i | \(-0.986935\pi\) | ||
0.999158 | − | 0.0410347i | \(-0.0130654\pi\) | |||||||
\(192\) | 1.59774 | − | 0.668751i | 0.115307 | − | 0.0482630i | ||||
\(193\) | 6.15920 | + | 6.15920i | 0.443349 | + | 0.443349i | 0.893136 | − | 0.449787i | \(-0.148500\pi\) |
−0.449787 | + | 0.893136i | \(0.648500\pi\) | |||||||
\(194\) | 5.21132 | 0.374151 | ||||||||
\(195\) | 10.0490 | + | 1.20458i | 0.719627 | + | 0.0862614i | ||||
\(196\) | −6.99012 | −0.499294 | ||||||||
\(197\) | −7.62320 | − | 7.62320i | −0.543130 | − | 0.543130i | 0.381315 | − | 0.924445i | \(-0.375471\pi\) |
−0.924445 | + | 0.381315i | \(0.875471\pi\) | |||||||
\(198\) | 0.0723573 | + | 9.76442i | 0.00514221 | + | 0.693927i | ||||
\(199\) | − | 1.98374i | − | 0.140624i | −0.997525 | − | 0.0703119i | \(-0.977601\pi\) | ||
0.997525 | − | 0.0703119i | \(-0.0223994\pi\) | |||||||
\(200\) | −1.21769 | + | 4.84946i | −0.0861034 | + | 0.342908i | ||||
\(201\) | 5.10663 | + | 2.09310i | 0.360194 | + | 0.147636i | ||||
\(202\) | 7.24125 | − | 7.24125i | 0.509492 | − | 0.509492i | ||||
\(203\) | −0.490577 | + | 0.490577i | −0.0344317 | + | 0.0344317i | ||||
\(204\) | −8.53442 | − | 3.49808i | −0.597529 | − | 0.244915i | ||||
\(205\) | 18.7976 | − | 5.19619i | 1.31288 | − | 0.362918i | ||||
\(206\) | 8.79426i | 0.612725i | ||||||||
\(207\) | −0.0321909 | − | 4.34408i | −0.00223742 | − | 0.301934i | ||||
\(208\) | −1.84783 | − | 1.84783i | −0.128124 | − | 0.128124i | ||||
\(209\) | 3.25490 | 0.225146 | ||||||||
\(210\) | 0.302664 | − | 0.237870i | 0.0208858 | − | 0.0164146i | ||||
\(211\) | −9.94617 | −0.684723 | −0.342361 | − | 0.939568i | \(-0.611227\pi\) | ||||
−0.342361 | + | 0.939568i | \(0.611227\pi\) | |||||||
\(212\) | −8.49654 | − | 8.49654i | −0.583545 | − | 0.583545i | ||||
\(213\) | 10.6709 | − | 4.46643i | 0.731159 | − | 0.306035i | ||||
\(214\) | 12.3770i | 0.846077i | ||||||||
\(215\) | −3.67317 | + | 6.47972i | −0.250508 | + | 0.441913i | ||||
\(216\) | −4.77822 | + | 2.04172i | −0.325117 | + | 0.138921i | ||||
\(217\) | −0.698192 | + | 0.698192i | −0.0473964 | + | 0.0473964i | ||||
\(218\) | −9.54875 | + | 9.54875i | −0.646723 | + | 0.646723i | ||||
\(219\) | 4.37551 | − | 10.6751i | 0.295669 | − | 0.721357i | ||||
\(220\) | 1.93917 | + | 7.01508i | 0.130739 | + | 0.472957i | ||||
\(221\) | 13.9159i | 0.936086i | ||||||||
\(222\) | 2.83876 | + | 6.78219i | 0.190525 | + | 0.455191i | ||||
\(223\) | 10.6374 | + | 10.6374i | 0.712332 | + | 0.712332i | 0.967023 | − | 0.254691i | \(-0.0819736\pi\) |
−0.254691 | + | 0.967023i | \(0.581974\pi\) | |||||||
\(224\) | −0.0993940 | −0.00664104 | ||||||||
\(225\) | 3.54515 | − | 14.5750i | 0.236343 | − | 0.971670i | ||||
\(226\) | −2.19177 | −0.145794 | ||||||||
\(227\) | −0.315490 | − | 0.315490i | −0.0209398 | − | 0.0209398i | 0.696559 | − | 0.717499i | \(-0.254713\pi\) |
−0.717499 | + | 0.696559i | \(0.754713\pi\) | |||||||
\(228\) | 0.668751 | + | 1.59774i | 0.0442891 | + | 0.105813i | ||||
\(229\) | 2.55362i | 0.168748i | 0.996434 | + | 0.0843740i | \(0.0268890\pi\) | ||||
−0.996434 | + | 0.0843740i | \(0.973111\pi\) | |||||||
\(230\) | −0.862713 | − | 3.12093i | −0.0568856 | − | 0.205788i | ||||
\(231\) | 0.212517 | − | 0.518485i | 0.0139826 | − | 0.0341138i | ||||
\(232\) | 4.93568 | − | 4.93568i | 0.324043 | − | 0.324043i | ||||
\(233\) | 16.5030 | − | 16.5030i | 1.08115 | − | 1.08115i | 0.0847454 | − | 0.996403i | \(-0.472992\pi\) |
0.996403 | − | 0.0847454i | \(-0.0270077\pi\) | |||||||
\(234\) | 5.58441 | + | 5.50226i | 0.365065 | + | 0.359694i | ||||
\(235\) | −1.35851 | + | 2.39649i | −0.0886191 | + | 0.156330i | ||||
\(236\) | − | 2.24875i | − | 0.146381i | ||||||
\(237\) | 15.6809 | − | 6.56341i | 1.01858 | − | 0.426339i | ||||
\(238\) | 0.374266 | + | 0.374266i | 0.0242600 | + | 0.0242600i | ||||
\(239\) | 12.9423 | 0.837167 | 0.418583 | − | 0.908178i | \(-0.362527\pi\) | ||||
0.418583 | + | 0.908178i | \(0.362527\pi\) | |||||||
\(240\) | −3.04509 | + | 2.39320i | −0.196560 | + | 0.154481i | ||||
\(241\) | −27.2768 | −1.75705 | −0.878526 | − | 0.477694i | \(-0.841473\pi\) | ||||
−0.878526 | + | 0.477694i | \(0.841473\pi\) | |||||||
\(242\) | −0.286834 | − | 0.286834i | −0.0184384 | − | 0.0184384i | ||||
\(243\) | 14.2889 | − | 6.23121i | 0.916632 | − | 0.399732i | ||||
\(244\) | 8.33970i | 0.533895i | ||||||||
\(245\) | 15.0654 | − | 4.16450i | 0.962492 | − | 0.266060i | ||||
\(246\) | 13.9780 | + | 5.72931i | 0.891206 | + | 0.365287i | ||||
\(247\) | 1.84783 | − | 1.84783i | 0.117575 | − | 0.117575i | ||||
\(248\) | 7.02449 | − | 7.02449i | 0.446056 | − | 0.446056i | ||||
\(249\) | 23.9128 | + | 9.80136i | 1.51541 | + | 0.621136i | ||||
\(250\) | −0.264753 | − | 11.1772i | −0.0167444 | − | 0.706908i | ||||
\(251\) | − | 3.84899i | − | 0.242946i | −0.992595 | − | 0.121473i | \(-0.961238\pi\) | ||
0.992595 | − | 0.121473i | \(-0.0387618\pi\) | |||||||
\(252\) | 0.298174 | − | 0.00220956i | 0.0187832 | − | 0.000139189i | ||||
\(253\) | −3.33281 | − | 3.33281i | −0.209532 | − | 0.209532i | ||||
\(254\) | 21.5813 | 1.35413 | ||||||||
\(255\) | 20.4778 | + | 2.45466i | 1.28237 | + | 0.153717i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.91882 | + | 1.91882i | 0.119693 | + | 0.119693i | 0.764416 | − | 0.644723i | \(-0.223027\pi\) |
−0.644723 | + | 0.764416i | \(0.723027\pi\) | |||||||
\(258\) | −5.32213 | + | 2.22763i | −0.331341 | + | 0.138686i | ||||
\(259\) | − | 0.421914i | − | 0.0262165i | ||||||
\(260\) | 5.08340 | + | 2.88164i | 0.315259 | + | 0.178711i | ||||
\(261\) | −14.6969 | + | 14.9163i | −0.909715 | + | 0.923298i | ||||
\(262\) | 2.17471 | − | 2.17471i | 0.134354 | − | 0.134354i | ||||
\(263\) | −1.90216 | + | 1.90216i | −0.117292 | + | 0.117292i | −0.763317 | − | 0.646024i | \(-0.776430\pi\) |
0.646024 | + | 0.763317i | \(0.276430\pi\) | |||||||
\(264\) | −2.13812 | + | 5.21646i | −0.131592 | + | 0.321051i | ||||
\(265\) | 23.3741 | + | 13.2501i | 1.43586 | + | 0.813948i | ||||
\(266\) | − | 0.0993940i | − | 0.00609424i | ||||||
\(267\) | 0.220754 | + | 0.527412i | 0.0135099 | + | 0.0322771i | ||||
\(268\) | 2.25310 | + | 2.25310i | 0.137630 | + | 0.137630i | ||||
\(269\) | 11.5783 | 0.705939 | 0.352970 | − | 0.935635i | \(-0.385172\pi\) | ||||
0.352970 | + | 0.935635i | \(0.385172\pi\) | |||||||
\(270\) | 9.08182 | − | 7.24711i | 0.552702 | − | 0.441045i | ||||
\(271\) | 10.6701 | 0.648161 | 0.324081 | − | 0.946029i | \(-0.394945\pi\) | ||||
0.324081 | + | 0.946029i | \(0.394945\pi\) | |||||||
\(272\) | −3.76548 | − | 3.76548i | −0.228316 | − | 0.228316i | ||||
\(273\) | −0.173701 | − | 0.414995i | −0.0105129 | − | 0.0251167i | ||||
\(274\) | 12.6785i | 0.765934i | ||||||||
\(275\) | −8.35874 | − | 13.9639i | −0.504051 | − | 0.842054i | ||||
\(276\) | 0.951225 | − | 2.32074i | 0.0572570 | − | 0.139692i | ||||
\(277\) | −14.7968 | + | 14.7968i | −0.889056 | + | 0.889056i | −0.994432 | − | 0.105376i | \(-0.966395\pi\) |
0.105376 | + | 0.994432i | \(0.466395\pi\) | |||||||
\(278\) | −6.22750 | + | 6.22750i | −0.373501 | + | 0.373501i | ||||
\(279\) | −20.9167 | + | 21.2290i | −1.25225 | + | 1.27095i | ||||
\(280\) | 0.214218 | − | 0.0592159i | 0.0128020 | − | 0.00353883i | ||||
\(281\) | 3.17823i | 0.189597i | 0.995496 | + | 0.0947985i | \(0.0302207\pi\) | ||||
−0.995496 | + | 0.0947985i | \(0.969779\pi\) | |||||||
\(282\) | −1.96836 | + | 0.823880i | −0.117214 | + | 0.0490613i | ||||
\(283\) | 12.7639 | + | 12.7639i | 0.758734 | + | 0.758734i | 0.976092 | − | 0.217358i | \(-0.0697439\pi\) |
−0.217358 | + | 0.976092i | \(0.569744\pi\) | |||||||
\(284\) | 6.67876 | 0.396311 | ||||||||
\(285\) | −2.39320 | − | 3.04509i | −0.141761 | − | 0.180376i | ||||
\(286\) | 8.50578 | 0.502957 | ||||||||
\(287\) | −0.612988 | − | 0.612988i | −0.0361836 | − | 0.0361836i | ||||
\(288\) | −2.99992 | + | 0.0222303i | −0.176772 | + | 0.00130993i | ||||
\(289\) | 11.3576i | 0.668095i | ||||||||
\(290\) | −7.69704 | + | 13.5781i | −0.451986 | + | 0.797333i | ||||
\(291\) | −8.35192 | − | 3.42328i | −0.489598 | − | 0.200676i | ||||
\(292\) | 4.70997 | − | 4.70997i | 0.275630 | − | 0.275630i | ||||
\(293\) | 19.9916 | − | 19.9916i | 1.16792 | − | 1.16792i | 0.185226 | − | 0.982696i | \(-0.440698\pi\) |
0.982696 | − | 0.185226i | \(-0.0593017\pi\) | |||||||
\(294\) | 11.2027 | + | 4.59177i | 0.653356 | + | 0.267797i | ||||
\(295\) | 1.33973 | + | 4.84659i | 0.0780023 | + | 0.282179i | ||||
\(296\) | 4.24487i | 0.246728i | ||||||||
\(297\) | 6.29822 | − | 15.6965i | 0.365460 | − | 0.910803i | ||||
\(298\) | −13.6988 | − | 13.6988i | −0.793552 | − | 0.793552i | ||||
\(299\) | −3.78412 | −0.218841 | ||||||||
\(300\) | 5.13710 | − | 6.97210i | 0.296591 | − | 0.402534i | ||||
\(301\) | 0.331085 | 0.0190834 | ||||||||
\(302\) | −10.9114 | − | 10.9114i | −0.627883 | − | 0.627883i | ||||
\(303\) | −16.3619 | + | 6.84846i | −0.939968 | + | 0.393434i | ||||
\(304\) | 1.00000i | 0.0573539i | ||||||||
\(305\) | −4.96854 | − | 17.9741i | −0.284498 | − | 1.02919i | ||||
\(306\) | 11.3798 | + | 11.2124i | 0.650541 | + | 0.640971i | ||||
\(307\) | −22.8303 | + | 22.8303i | −1.30299 | + | 1.30299i | −0.376629 | + | 0.926364i | \(0.622917\pi\) |
−0.926364 | + | 0.376629i | \(0.877083\pi\) | |||||||
\(308\) | 0.228761 | − | 0.228761i | 0.0130349 | − | 0.0130349i | ||||
\(309\) | 5.77689 | − | 14.0941i | 0.328636 | − | 0.801787i | ||||
\(310\) | −10.9545 | + | 19.3244i | −0.622173 | + | 1.09755i | ||||
\(311\) | − | 23.6135i | − | 1.33900i | −0.742814 | − | 0.669498i | \(-0.766509\pi\) | ||
0.742814 | − | 0.669498i | \(-0.233491\pi\) | |||||||
\(312\) | 1.74760 | + | 4.17525i | 0.0989383 | + | 0.236377i | ||||
\(313\) | 17.4841 | + | 17.4841i | 0.988260 | + | 0.988260i | 0.999932 | − | 0.0116720i | \(-0.00371538\pi\) |
−0.0116720 | + | 0.999932i | \(0.503715\pi\) | |||||||
\(314\) | −19.1970 | −1.08335 | ||||||||
\(315\) | −0.641320 | + | 0.182405i | −0.0361343 | + | 0.0102774i | ||||
\(316\) | 9.81442 | 0.552104 | ||||||||
\(317\) | 7.39204 | + | 7.39204i | 0.415178 | + | 0.415178i | 0.883538 | − | 0.468360i | \(-0.155155\pi\) |
−0.468360 | + | 0.883538i | \(0.655155\pi\) | |||||||
\(318\) | 8.03567 | + | 19.1983i | 0.450618 | + | 1.07659i | ||||
\(319\) | 22.7195i | 1.27205i | ||||||||
\(320\) | −2.15524 | + | 0.595769i | −0.120482 | + | 0.0333045i | ||||
\(321\) | 8.13040 | − | 19.8361i | 0.453795 | − | 1.10714i | ||||
\(322\) | −0.101773 | + | 0.101773i | −0.00567160 | + | 0.00567160i | ||||
\(323\) | 3.76548 | − | 3.76548i | 0.209517 | − | 0.209517i | ||||
\(324\) | 8.99901 | − | 0.133378i | 0.499945 | − | 0.00740989i | ||||
\(325\) | −12.6727 | − | 3.18209i | −0.702956 | − | 0.176510i | ||||
\(326\) | 2.54457i | 0.140930i | ||||||||
\(327\) | 21.5758 | − | 9.03080i | 1.19315 | − | 0.499404i | ||||
\(328\) | 6.16725 | + | 6.16725i | 0.340530 | + | 0.340530i | ||||
\(329\) | 0.122450 | 0.00675090 | ||||||||
\(330\) | 1.50036 | − | 12.5166i | 0.0825919 | − | 0.689014i | ||||
\(331\) | 2.95830 | 0.162603 | 0.0813014 | − | 0.996690i | \(-0.474092\pi\) | ||||
0.0813014 | + | 0.996690i | \(0.474092\pi\) | |||||||
\(332\) | 10.5506 | + | 10.5506i | 0.579038 | + | 0.579038i | ||||
\(333\) | −0.0943646 | − | 12.7342i | −0.00517115 | − | 0.697833i | ||||
\(334\) | 4.69368i | 0.256827i | ||||||||
\(335\) | −6.19829 | − | 3.51364i | −0.338649 | − | 0.191971i | ||||
\(336\) | 0.159294 | + | 0.0652913i | 0.00869020 | + | 0.00356193i | ||||
\(337\) | −7.56158 | + | 7.56158i | −0.411905 | + | 0.411905i | −0.882402 | − | 0.470497i | \(-0.844075\pi\) |
0.470497 | + | 0.882402i | \(0.344075\pi\) | |||||||
\(338\) | −4.36359 | + | 4.36359i | −0.237348 | + | 0.237348i | ||||
\(339\) | 3.51264 | + | 1.43976i | 0.190781 | + | 0.0781970i | ||||
\(340\) | 10.3589 | + | 5.87215i | 0.561788 | + | 0.318462i | ||||
\(341\) | 32.3346i | 1.75102i | ||||||||
\(342\) | −0.0222303 | − | 2.99992i | −0.00120208 | − | 0.162217i | ||||
\(343\) | −0.983256 | − | 0.983256i | −0.0530909 | − | 0.0530909i | ||||
\(344\) | −3.33103 | −0.179597 | ||||||||
\(345\) | −0.667491 | + | 5.56847i | −0.0359365 | + | 0.299796i | ||||
\(346\) | 4.02862 | 0.216580 | ||||||||
\(347\) | −1.03476 | − | 1.03476i | −0.0555491 | − | 0.0555491i | 0.678787 | − | 0.734336i | \(-0.262506\pi\) |
−0.734336 | + | 0.678787i | \(0.762506\pi\) | |||||||
\(348\) | −11.1524 | + | 4.66795i | −0.597830 | + | 0.250228i | ||||
\(349\) | − | 3.40331i | − | 0.182175i | −0.995843 | − | 0.0910876i | \(-0.970966\pi\) | ||
0.995843 | − | 0.0910876i | \(-0.0290343\pi\) | |||||||
\(350\) | −0.426412 | + | 0.255249i | −0.0227927 | + | 0.0136436i | ||||
\(351\) | −5.33547 | − | 12.4866i | −0.284786 | − | 0.666484i | ||||
\(352\) | −2.30156 | + | 2.30156i | −0.122674 | + | 0.122674i | ||||
\(353\) | 11.6964 | − | 11.6964i | 0.622536 | − | 0.622536i | −0.323643 | − | 0.946179i | \(-0.604908\pi\) |
0.946179 | + | 0.323643i | \(0.104908\pi\) | |||||||
\(354\) | −1.47719 | + | 3.60396i | −0.0785117 | + | 0.191548i | ||||
\(355\) | −14.3943 | + | 3.97900i | −0.763972 | + | 0.211183i | ||||
\(356\) | 0.330099i | 0.0174952i | ||||||||
\(357\) | −0.353965 | − | 0.845670i | −0.0187338 | − | 0.0447576i | ||||
\(358\) | −5.19681 | − | 5.19681i | −0.274660 | − | 0.274660i | ||||
\(359\) | −17.2125 | −0.908438 | −0.454219 | − | 0.890890i | \(-0.650082\pi\) | ||||
−0.454219 | + | 0.890890i | \(0.650082\pi\) | |||||||
\(360\) | 6.45230 | − | 1.83517i | 0.340066 | − | 0.0967219i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 17.3081 | + | 17.3081i | 0.909695 | + | 0.909695i | ||||
\(363\) | 0.271275 | + | 0.648114i | 0.0142383 | + | 0.0340171i | ||||
\(364\) | − | 0.259739i | − | 0.0136140i | ||||||
\(365\) | −7.34506 | + | 12.9572i | −0.384458 | + | 0.678210i | ||||
\(366\) | 5.47830 | − | 13.3656i | 0.286355 | − | 0.698633i | ||||
\(367\) | −9.63368 | + | 9.63368i | −0.502874 | + | 0.502874i | −0.912330 | − | 0.409456i | \(-0.865719\pi\) |
0.409456 | + | 0.912330i | \(0.365719\pi\) | |||||||
\(368\) | 1.02394 | − | 1.02394i | 0.0533764 | − | 0.0533764i | ||||
\(369\) | −18.6384 | − | 18.3642i | −0.970274 | − | 0.956000i | ||||
\(370\) | −2.52896 | − | 9.14871i | −0.131474 | − | 0.475619i | ||||
\(371\) | − | 1.19431i | − | 0.0620055i | ||||||
\(372\) | −15.8722 | + | 6.64346i | −0.822933 | + | 0.344448i | ||||
\(373\) | −9.07273 | − | 9.07273i | −0.469768 | − | 0.469768i | 0.432071 | − | 0.901839i | \(-0.357783\pi\) |
−0.901839 | + | 0.432071i | \(0.857783\pi\) | |||||||
\(374\) | 17.3329 | 0.896265 | ||||||||
\(375\) | −6.91793 | + | 18.0871i | −0.357240 | + | 0.934012i | ||||
\(376\) | −1.23197 | −0.0635339 | ||||||||
\(377\) | 12.8980 | + | 12.8980i | 0.664282 | + | 0.664282i | ||||
\(378\) | −0.479320 | − | 0.192327i | −0.0246536 | − | 0.00989225i | ||||
\(379\) | − | 9.80779i | − | 0.503792i | −0.967754 | − | 0.251896i | \(-0.918946\pi\) | ||
0.967754 | − | 0.251896i | \(-0.0810542\pi\) | |||||||
\(380\) | −0.595769 | − | 2.15524i | −0.0305623 | − | 0.110561i | ||||
\(381\) | −34.5873 | − | 14.1766i | −1.77196 | − | 0.726290i | ||||
\(382\) | −0.802016 | + | 0.802016i | −0.0410347 | + | 0.0410347i | ||||
\(383\) | 4.82382 | − | 4.82382i | 0.246486 | − | 0.246486i | −0.573041 | − | 0.819527i | \(-0.694236\pi\) |
0.819527 | + | 0.573041i | \(0.194236\pi\) | |||||||
\(384\) | −1.60265 | − | 0.656894i | −0.0817849 | − | 0.0335220i | ||||
\(385\) | −0.356747 | + | 0.629324i | −0.0181815 | + | 0.0320733i | ||||
\(386\) | − | 8.71042i | − | 0.443349i | ||||||
\(387\) | 9.99283 | − | 0.0740499i | 0.507964 | − | 0.00376417i | ||||
\(388\) | −3.68496 | − | 3.68496i | −0.187075 | − | 0.187075i | ||||
\(389\) | −12.4320 | −0.630330 | −0.315165 | − | 0.949037i | \(-0.602060\pi\) | ||||
−0.315165 | + | 0.949037i | \(0.602060\pi\) | |||||||
\(390\) | −6.25398 | − | 7.95751i | −0.316683 | − | 0.402944i | ||||
\(391\) | −7.71122 | −0.389973 | ||||||||
\(392\) | 4.94276 | + | 4.94276i | 0.249647 | + | 0.249647i | ||||
\(393\) | −4.91386 | + | 2.05675i | −0.247872 | + | 0.103749i | ||||
\(394\) | 10.7808i | 0.543130i | ||||||||
\(395\) | −21.1524 | + | 5.84713i | −1.06429 | + | 0.294201i | ||||
\(396\) | 6.85333 | − | 6.95565i | 0.344393 | − | 0.349535i | ||||
\(397\) | 24.5965 | − | 24.5965i | 1.23446 | − | 1.23446i | 0.272234 | − | 0.962231i | \(-0.412238\pi\) |
0.962231 | − | 0.272234i | \(-0.0877623\pi\) | |||||||
\(398\) | −1.40272 | + | 1.40272i | −0.0703119 | + | 0.0703119i | ||||
\(399\) | −0.0652913 | + | 0.159294i | −0.00326865 | + | 0.00797467i | ||||
\(400\) | 4.29012 | − | 2.56805i | 0.214506 | − | 0.128403i | ||||
\(401\) | 31.8360i | 1.58981i | 0.606731 | + | 0.794907i | \(0.292480\pi\) | ||||
−0.606731 | + | 0.794907i | \(0.707520\pi\) | |||||||
\(402\) | −2.13088 | − | 5.09098i | −0.106279 | − | 0.253915i | ||||
\(403\) | 18.3566 | + | 18.3566i | 0.914406 | + | 0.914406i | ||||
\(404\) | −10.2407 | −0.509492 | ||||||||
\(405\) | −19.3156 | + | 5.64880i | −0.959798 | + | 0.280691i | ||||
\(406\) | 0.693780 | 0.0344317 | ||||||||
\(407\) | −9.76981 | − | 9.76981i | −0.484272 | − | 0.484272i | ||||
\(408\) | 3.56123 | + | 8.50826i | 0.176307 | + | 0.421222i | ||||
\(409\) | 18.0144i | 0.890754i | 0.895343 | + | 0.445377i | \(0.146930\pi\) | ||||
−0.895343 | + | 0.445377i | \(0.853070\pi\) | |||||||
\(410\) | −16.9662 | − | 9.61765i | −0.837900 | − | 0.474982i | ||||
\(411\) | 8.32840 | − | 20.3191i | 0.410810 | − | 1.00227i | ||||
\(412\) | 6.21848 | − | 6.21848i | 0.306363 | − | 0.306363i | ||||
\(413\) | 0.158047 | − | 0.158047i | 0.00777698 | − | 0.00777698i | ||||
\(414\) | −3.04897 | + | 3.09449i | −0.149848 | + | 0.152086i | ||||
\(415\) | −29.0247 | − | 16.4533i | −1.42477 | − | 0.807662i | ||||
\(416\) | 2.61323i | 0.128124i | ||||||||
\(417\) | 14.0713 | − | 5.88971i | 0.689076 | − | 0.288420i | ||||
\(418\) | −2.30156 | − | 2.30156i | −0.112573 | − | 0.112573i | ||||
\(419\) | 18.0752 | 0.883032 | 0.441516 | − | 0.897253i | \(-0.354441\pi\) | ||||
0.441516 | + | 0.897253i | \(0.354441\pi\) | |||||||
\(420\) | −0.382215 | − | 0.0458160i | −0.0186502 | − | 0.00223559i | ||||
\(421\) | 34.7735 | 1.69475 | 0.847377 | − | 0.530991i | \(-0.178180\pi\) | ||||
0.847377 | + | 0.530991i | \(0.178180\pi\) | |||||||
\(422\) | 7.03301 | + | 7.03301i | 0.342361 | + | 0.342361i | ||||
\(423\) | 3.69580 | − | 0.0273870i | 0.179696 | − | 0.00133160i | ||||
\(424\) | 12.0159i | 0.583545i | ||||||||
\(425\) | −25.8243 | − | 6.48440i | −1.25266 | − | 0.314540i | ||||
\(426\) | −10.7037 | − | 4.38724i | −0.518597 | − | 0.212562i | ||||
\(427\) | −0.586133 | + | 0.586133i | −0.0283649 | + | 0.0283649i | ||||
\(428\) | 8.75189 | − | 8.75189i | 0.423038 | − | 0.423038i | ||||
\(429\) | −13.6318 | − | 5.58739i | −0.658149 | − | 0.269762i | ||||
\(430\) | 7.17918 | − | 1.98453i | 0.346211 | − | 0.0957024i | ||||
\(431\) | 23.0890i | 1.11216i | 0.831130 | + | 0.556079i | \(0.187695\pi\) | ||||
−0.831130 | + | 0.556079i | \(0.812305\pi\) | |||||||
\(432\) | 4.82242 | + | 1.93500i | 0.232019 | + | 0.0930977i | ||||
\(433\) | −27.1524 | − | 27.1524i | −1.30486 | − | 1.30486i | −0.925073 | − | 0.379790i | \(-0.875996\pi\) |
−0.379790 | − | 0.925073i | \(-0.624004\pi\) | |||||||
\(434\) | 0.987393 | 0.0473964 | ||||||||
\(435\) | 21.2550 | − | 16.7048i | 1.01910 | − | 0.800934i | ||||
\(436\) | 13.5040 | 0.646723 | ||||||||
\(437\) | 1.02394 | + | 1.02394i | 0.0489816 | + | 0.0489816i | ||||
\(438\) | −10.6424 | + | 4.45449i | −0.508513 | + | 0.212844i | ||||
\(439\) | − | 4.16128i | − | 0.198607i | −0.995057 | − | 0.0993035i | \(-0.968339\pi\) | ||
0.995057 | − | 0.0993035i | \(-0.0316615\pi\) | |||||||
\(440\) | 3.58922 | − | 6.33161i | 0.171109 | − | 0.301848i | ||||
\(441\) | −14.9378 | − | 14.7180i | −0.711322 | − | 0.700857i | ||||
\(442\) | 9.84004 | − | 9.84004i | 0.468043 | − | 0.468043i | ||||
\(443\) | 7.44535 | − | 7.44535i | 0.353739 | − | 0.353739i | −0.507760 | − | 0.861499i | \(-0.669526\pi\) |
0.861499 | + | 0.507760i | \(0.169526\pi\) | |||||||
\(444\) | 2.78843 | − | 6.80304i | 0.132333 | − | 0.322858i | ||||
\(445\) | −0.196663 | − | 0.711442i | −0.00932270 | − | 0.0337256i | ||||
\(446\) | − | 15.0435i | − | 0.712332i | ||||||
\(447\) | 12.9558 | + | 30.9531i | 0.612787 | + | 1.46403i | ||||
\(448\) | 0.0702822 | + | 0.0702822i | 0.00332052 | + | 0.00332052i | ||||
\(449\) | −11.6674 | −0.550618 | −0.275309 | − | 0.961356i | \(-0.588780\pi\) | ||||
−0.275309 | + | 0.961356i | \(0.588780\pi\) | |||||||
\(450\) | −12.8129 | + | 7.79931i | −0.604007 | + | 0.367663i | ||||
\(451\) | −28.3886 | −1.33677 | ||||||||
\(452\) | 1.54982 | + | 1.54982i | 0.0728972 | + | 0.0728972i | ||||
\(453\) | 10.3196 | + | 24.6549i | 0.484856 | + | 1.15839i | ||||
\(454\) | 0.446170i | 0.0209398i | ||||||||
\(455\) | 0.154744 | + | 0.559800i | 0.00725453 | + | 0.0262438i | ||||
\(456\) | 0.656894 | − | 1.60265i | 0.0307619 | − | 0.0750510i | ||||
\(457\) | −13.3405 | + | 13.3405i | −0.624041 | + | 0.624041i | −0.946562 | − | 0.322521i | \(-0.895470\pi\) |
0.322521 | + | 0.946562i | \(0.395470\pi\) | |||||||
\(458\) | 1.80568 | − | 1.80568i | 0.0843740 | − | 0.0843740i | ||||
\(459\) | −10.8725 | − | 25.4449i | −0.507486 | − | 1.18767i | ||||
\(460\) | −1.59680 | + | 2.81686i | −0.0744512 | + | 0.131337i | ||||
\(461\) | 11.7687i | 0.548122i | 0.961712 | + | 0.274061i | \(0.0883670\pi\) | ||||
−0.961712 | + | 0.274061i | \(0.911633\pi\) | |||||||
\(462\) | −0.516896 | + | 0.216353i | −0.0240482 | + | 0.0100656i | ||||
\(463\) | 17.0577 | + | 17.0577i | 0.792739 | + | 0.792739i | 0.981939 | − | 0.189200i | \(-0.0605894\pi\) |
−0.189200 | + | 0.981939i | \(0.560589\pi\) | |||||||
\(464\) | −6.98010 | −0.324043 | ||||||||
\(465\) | 30.2503 | − | 23.7744i | 1.40283 | − | 1.10251i | ||||
\(466\) | −23.3388 | −1.08115 | ||||||||
\(467\) | −20.8943 | − | 20.8943i | −0.966874 | − | 0.966874i | 0.0325947 | − | 0.999469i | \(-0.489623\pi\) |
−0.999469 | + | 0.0325947i | \(0.989623\pi\) | |||||||
\(468\) | −0.0580928 | − | 7.83946i | −0.00268534 | − | 0.362379i | ||||
\(469\) | 0.316705i | 0.0146241i | ||||||||
\(470\) | 2.65519 | − | 0.733968i | 0.122475 | − | 0.0338554i | ||||
\(471\) | 30.7661 | + | 12.6104i | 1.41763 | + | 0.581055i | ||||
\(472\) | −1.59010 | + | 1.59010i | −0.0731905 | + | 0.0731905i | ||||
\(473\) | 7.66658 | − | 7.66658i | 0.352510 | − | 0.352510i | ||||
\(474\) | −15.7291 | − | 6.44703i | −0.722461 | − | 0.296122i | ||||
\(475\) | 2.56805 | + | 4.29012i | 0.117830 | + | 0.196844i | ||||
\(476\) | − | 0.529292i | − | 0.0242600i | ||||||
\(477\) | −0.267117 | − | 36.0468i | −0.0122305 | − | 1.65047i | ||||
\(478\) | −9.15158 | − | 9.15158i | −0.418583 | − | 0.418583i | ||||
\(479\) | −27.6237 | −1.26216 | −0.631079 | − | 0.775718i | \(-0.717388\pi\) | ||||
−0.631079 | + | 0.775718i | \(0.717388\pi\) | |||||||
\(480\) | 3.84545 | + | 0.460953i | 0.175520 | + | 0.0210396i | ||||
\(481\) | −11.0928 | −0.505788 | ||||||||
\(482\) | 19.2876 | + | 19.2876i | 0.878526 | + | 0.878526i | ||||
\(483\) | 0.229961 | − | 0.0962528i | 0.0104636 | − | 0.00437965i | ||||
\(484\) | 0.405644i | 0.0184384i | ||||||||
\(485\) | 10.1373 | + | 5.74658i | 0.460313 | + | 0.260939i | ||||
\(486\) | −14.5099 | − | 5.69764i | −0.658182 | − | 0.258450i | ||||
\(487\) | −15.5968 | + | 15.5968i | −0.706757 | + | 0.706757i | −0.965852 | − | 0.259095i | \(-0.916576\pi\) |
0.259095 | + | 0.965852i | \(0.416576\pi\) | |||||||
\(488\) | 5.89706 | − | 5.89706i | 0.266947 | − | 0.266947i | ||||
\(489\) | 1.67151 | − | 4.07805i | 0.0755883 | − | 0.184416i | ||||
\(490\) | −13.5976 | − | 7.70809i | −0.614276 | − | 0.348216i | ||||
\(491\) | − | 36.7768i | − | 1.65971i | −0.557978 | − | 0.829856i | \(-0.688422\pi\) | ||
0.557978 | − | 0.829856i | \(-0.311578\pi\) | |||||||
\(492\) | −5.83273 | − | 13.9352i | −0.262960 | − | 0.628247i | ||||
\(493\) | 26.2834 | + | 26.2834i | 1.18374 | + | 1.18374i | ||||
\(494\) | −2.61323 | −0.117575 | ||||||||
\(495\) | −10.6266 | + | 19.0741i | −0.477630 | + | 0.857317i | ||||
\(496\) | −9.93413 | −0.446056 | ||||||||
\(497\) | 0.469398 | + | 0.469398i | 0.0210554 | + | 0.0210554i | ||||
\(498\) | −9.97829 | − | 23.8395i | −0.447138 | − | 1.06827i | ||||
\(499\) | − | 27.0776i | − | 1.21216i | −0.795404 | − | 0.606080i | \(-0.792741\pi\) | ||
0.795404 | − | 0.606080i | \(-0.207259\pi\) | |||||||
\(500\) | −7.71627 | + | 8.09069i | −0.345082 | + | 0.361826i | ||||
\(501\) | 3.08325 | − | 7.52234i | 0.137749 | − | 0.336073i | ||||
\(502\) | −2.72165 | + | 2.72165i | −0.121473 | + | 0.121473i | ||||
\(503\) | −22.6492 | + | 22.6492i | −1.00988 | + | 1.00988i | −0.00992738 | + | 0.999951i | \(0.503160\pi\) |
−0.999951 | + | 0.00992738i | \(0.996840\pi\) | |||||||
\(504\) | −0.212403 | − | 0.209278i | −0.00946119 | − | 0.00932200i | ||||
\(505\) | 22.0711 | − | 6.10108i | 0.982151 | − | 0.271494i | ||||
\(506\) | 4.71331i | 0.209532i | ||||||||
\(507\) | 9.85973 | − | 4.12690i | 0.437886 | − | 0.183282i | ||||
\(508\) | −15.2603 | − | 15.2603i | −0.677065 | − | 0.677065i | ||||
\(509\) | 24.2312 | 1.07403 | 0.537015 | − | 0.843572i | \(-0.319552\pi\) | ||||
0.537015 | + | 0.843572i | \(0.319552\pi\) | |||||||
\(510\) | −12.7443 | − | 16.2157i | −0.564325 | − | 0.718042i | ||||
\(511\) | 0.662054 | 0.0292876 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −1.93500 | + | 4.82242i | −0.0854323 | + | 0.212915i | ||||
\(514\) | − | 2.71362i | − | 0.119693i | ||||||
\(515\) | −9.69754 | + | 17.1071i | −0.427325 | + | 0.753829i | ||||
\(516\) | 5.33849 | + | 2.18814i | 0.235014 | + | 0.0963273i | ||||
\(517\) | 2.83545 | − | 2.83545i | 0.124703 | − | 0.124703i | ||||
\(518\) | −0.298338 | + | 0.298338i | −0.0131082 | + | 0.0131082i | ||||
\(519\) | −6.45647 | − | 2.64637i | −0.283408 | − | 0.116163i | ||||
\(520\) | −1.55688 | − | 5.63213i | −0.0682737 | − | 0.246985i | ||||
\(521\) | 36.4402i | 1.59647i | 0.602343 | + | 0.798237i | \(0.294234\pi\) | ||||
−0.602343 | + | 0.798237i | \(0.705766\pi\) | |||||||
\(522\) | 20.9397 | − | 0.155170i | 0.916507 | − | 0.00679159i | ||||
\(523\) | −7.87242 | − | 7.87242i | −0.344237 | − | 0.344237i | 0.513721 | − | 0.857957i | \(-0.328267\pi\) |
−0.857957 | + | 0.513721i | \(0.828267\pi\) | |||||||
\(524\) | −3.07551 | −0.134354 | ||||||||
\(525\) | 0.851061 | − | 0.128968i | 0.0371434 | − | 0.00562860i | ||||
\(526\) | 2.69006 | 0.117292 | ||||||||
\(527\) | 37.4067 | + | 37.4067i | 1.62946 | + | 1.62946i | ||||
\(528\) | 5.20048 | − | 2.17672i | 0.226322 | − | 0.0947295i | ||||
\(529\) | 20.9031i | 0.908831i | ||||||||
\(530\) | −7.15872 | − | 25.8972i | −0.310955 | − | 1.12490i | ||||
\(531\) | 4.73483 | − | 4.80553i | 0.205474 | − | 0.208542i | ||||
\(532\) | −0.0702822 | + | 0.0702822i | −0.00304712 | + | 0.00304712i | ||||
\(533\) | −16.1164 | + | 16.1164i | −0.698080 | + | 0.698080i | ||||
\(534\) | 0.216840 | − | 0.529033i | 0.00938358 | − | 0.0228935i | ||||
\(535\) | −13.6483 | + | 24.0765i | −0.590068 | + | 1.04092i | ||||
\(536\) | − | 3.18636i | − | 0.137630i | ||||||
\(537\) | 4.91492 | + | 11.7424i | 0.212094 | + | 0.506723i | ||||
\(538\) | −8.18707 | − | 8.18707i | −0.352970 | − | 0.352970i | ||||
\(539\) | −22.7521 | −0.980003 | ||||||||
\(540\) | −11.5463 | − | 1.29734i | −0.496873 | − | 0.0558285i | ||||
\(541\) | −22.5624 | −0.970033 | −0.485017 | − | 0.874505i | \(-0.661186\pi\) | ||||
−0.485017 | + | 0.874505i | \(0.661186\pi\) | |||||||
\(542\) | −7.54489 | − | 7.54489i | −0.324081 | − | 0.324081i | ||||
\(543\) | −16.3693 | − | 39.1085i | −0.702474 | − | 1.67831i | ||||
\(544\) | 5.32519i | 0.228316i | ||||||||
\(545\) | −29.1043 | + | 8.04525i | −1.24669 | + | 0.344620i | ||||
\(546\) | −0.170621 | + | 0.416271i | −0.00730190 | + | 0.0178148i | ||||
\(547\) | 30.2103 | − | 30.2103i | 1.29170 | − | 1.29170i | 0.357966 | − | 0.933735i | \(-0.383470\pi\) |
0.933735 | − | 0.357966i | \(-0.116530\pi\) | |||||||
\(548\) | 8.96502 | − | 8.96502i | 0.382967 | − | 0.382967i | ||||
\(549\) | −17.5596 | + | 17.8218i | −0.749426 | + | 0.760615i | ||||
\(550\) | −3.96344 | + | 15.7845i | −0.169002 | + | 0.673053i | ||||
\(551\) | − | 6.98010i | − | 0.297362i | ||||||
\(552\) | −2.31363 | + | 0.968396i | −0.0984747 | + | 0.0412177i | ||||
\(553\) | 0.689779 | + | 0.689779i | 0.0293324 | + | 0.0293324i | ||||
\(554\) | 20.9259 | 0.889056 | ||||||||
\(555\) | −1.95669 | + | 16.3234i | −0.0830567 | + | 0.692891i | ||||
\(556\) | 8.80702 | 0.373501 | ||||||||
\(557\) | 26.8130 | + | 26.8130i | 1.13610 | + | 1.13610i | 0.989142 | + | 0.146962i | \(0.0469495\pi\) |
0.146962 | + | 0.989142i | \(0.453050\pi\) | |||||||
\(558\) | 29.8016 | − | 0.220839i | 1.26160 | − | 0.00934884i | ||||
\(559\) | − | 8.70474i | − | 0.368171i | ||||||
\(560\) | −0.193347 | − | 0.109603i | −0.00817040 | − | 0.00463157i | ||||
\(561\) | −27.7787 | − | 11.3859i | −1.17282 | − | 0.480713i | ||||
\(562\) | 2.24735 | − | 2.24735i | 0.0947985 | − | 0.0947985i | ||||
\(563\) | 20.9853 | − | 20.9853i | 0.884426 | − | 0.884426i | −0.109555 | − | 0.993981i | \(-0.534942\pi\) |
0.993981 | + | 0.109555i | \(0.0349425\pi\) | |||||||
\(564\) | 1.97441 | + | 0.809272i | 0.0831378 | + | 0.0340765i | ||||
\(565\) | −4.26356 | − | 2.41689i | −0.179369 | − | 0.101679i | ||||
\(566\) | − | 18.0509i | − | 0.758734i | ||||||
\(567\) | 0.641844 | + | 0.623096i | 0.0269549 | + | 0.0261676i | ||||
\(568\) | −4.72260 | − | 4.72260i | −0.198156 | − | 0.198156i | ||||
\(569\) | 10.5079 | 0.440513 | 0.220257 | − | 0.975442i | \(-0.429311\pi\) | ||||
0.220257 | + | 0.975442i | \(0.429311\pi\) | |||||||
\(570\) | −0.460953 | + | 3.84545i | −0.0193072 | + | 0.161068i | ||||
\(571\) | 43.4684 | 1.81910 | 0.909548 | − | 0.415598i | \(-0.136428\pi\) | ||||
0.909548 | + | 0.415598i | \(0.136428\pi\) | |||||||
\(572\) | −6.01449 | − | 6.01449i | −0.251479 | − | 0.251479i | ||||
\(573\) | 1.81219 | − | 0.758513i | 0.0757054 | − | 0.0316873i | ||||
\(574\) | 0.866896i | 0.0361836i | ||||||||
\(575\) | 1.76329 | − | 7.02234i | 0.0735342 | − | 0.292852i | ||||
\(576\) | 2.13698 | + | 2.10554i | 0.0890409 | + | 0.0877310i | ||||
\(577\) | 17.9007 | − | 17.9007i | 0.745215 | − | 0.745215i | −0.228362 | − | 0.973576i | \(-0.573337\pi\) |
0.973576 | + | 0.228362i | \(0.0733369\pi\) | |||||||
\(578\) | 8.03105 | − | 8.03105i | 0.334048 | − | 0.334048i | ||||
\(579\) | −5.72182 | + | 13.9598i | −0.237791 | + | 0.580148i | ||||
\(580\) | 15.0438 | − | 4.15853i | 0.624659 | − | 0.172673i | ||||
\(581\) | 1.48304i | 0.0615267i | ||||||||
\(582\) | 3.48507 | + | 8.32632i | 0.144461 | + | 0.345137i | ||||
\(583\) | −27.6554 | − | 27.6554i | −1.14537 | − | 1.14537i | ||||
\(584\) | −6.66091 | −0.275630 | ||||||||
\(585\) | 4.79571 | + | 16.8613i | 0.198278 | + | 0.697129i | ||||
\(586\) | −28.2724 | −1.16792 | ||||||||
\(587\) | 13.5624 | + | 13.5624i | 0.559781 | + | 0.559781i | 0.929245 | − | 0.369464i | \(-0.120459\pi\) |
−0.369464 | + | 0.929245i | \(0.620459\pi\) | |||||||
\(588\) | −4.67465 | − | 11.1684i | −0.192779 | − | 0.460577i | ||||
\(589\) | − | 9.93413i | − | 0.409329i | ||||||
\(590\) | 2.47972 | − | 4.37439i | 0.102089 | − | 0.180091i | ||||
\(591\) | 7.08186 | − | 17.2779i | 0.291309 | − | 0.710718i | ||||
\(592\) | 3.00157 | − | 3.00157i | 0.123364 | − | 0.123364i | ||||
\(593\) | −7.39960 | + | 7.39960i | −0.303865 | + | 0.303865i | −0.842524 | − | 0.538659i | \(-0.818931\pi\) |
0.538659 | + | 0.842524i | \(0.318931\pi\) | |||||||
\(594\) | −15.5526 | + | 6.64558i | −0.638132 | + | 0.272671i | ||||
\(595\) | 0.315336 | + | 1.14075i | 0.0129275 | + | 0.0467662i | ||||
\(596\) | 19.3731i | 0.793552i | ||||||||
\(597\) | 3.16950 | − | 1.32663i | 0.129719 | − | 0.0542954i | ||||
\(598\) | 2.67578 | + | 2.67578i | 0.109421 | + | 0.109421i | ||||
\(599\) | −20.8602 | −0.852326 | −0.426163 | − | 0.904646i | \(-0.640135\pi\) | ||||
−0.426163 | + | 0.904646i | \(0.640135\pi\) | |||||||
\(600\) | −8.56250 | + | 1.29754i | −0.349563 | + | 0.0529718i | ||||
\(601\) | −15.2975 | −0.624000 | −0.312000 | − | 0.950082i | \(-0.600999\pi\) | ||||
−0.312000 | + | 0.950082i | \(0.600999\pi\) | |||||||
\(602\) | −0.234112 | − | 0.234112i | −0.00954171 | − | 0.00954171i | ||||
\(603\) | 0.0708337 | + | 9.55882i | 0.00288457 | + | 0.389265i | ||||
\(604\) | 15.4311i | 0.627883i | ||||||||
\(605\) | −0.241670 | − | 0.874261i | −0.00982529 | − | 0.0355437i | ||||
\(606\) | 16.4122 | + | 6.72703i | 0.666701 | + | 0.273267i | ||||
\(607\) | 33.6117 | − | 33.6117i | 1.36426 | − | 1.36426i | 0.495849 | − | 0.868409i | \(-0.334857\pi\) |
0.868409 | − | 0.495849i | \(-0.165143\pi\) | |||||||
\(608\) | 0.707107 | − | 0.707107i | 0.0286770 | − | 0.0286770i | ||||
\(609\) | −1.11189 | − | 0.455740i | −0.0450560 | − | 0.0184675i | ||||
\(610\) | −9.19629 | + | 16.2229i | −0.372347 | + | 0.656845i | ||||
\(611\) | − | 3.21941i | − | 0.130243i | ||||||
\(612\) | −0.118380 | − | 15.9751i | −0.00478525 | − | 0.645756i | ||||
\(613\) | −7.47342 | − | 7.47342i | −0.301849 | − | 0.301849i | 0.539888 | − | 0.841737i | \(-0.318467\pi\) |
−0.841737 | + | 0.539888i | \(0.818467\pi\) | |||||||
\(614\) | 32.2869 | 1.30299 | ||||||||
\(615\) | 20.8731 | + | 26.5587i | 0.841684 | + | 1.07095i | ||||
\(616\) | −0.323517 | −0.0130349 | ||||||||
\(617\) | −5.02881 | − | 5.02881i | −0.202452 | − | 0.202452i | 0.598598 | − | 0.801050i | \(-0.295725\pi\) |
−0.801050 | + | 0.598598i | \(0.795725\pi\) | |||||||
\(618\) | −14.0509 | + | 5.88117i | −0.565211 | + | 0.236575i | ||||
\(619\) | − | 40.6819i | − | 1.63514i | −0.575826 | − | 0.817572i | \(-0.695319\pi\) | ||
0.575826 | − | 0.817572i | \(-0.304681\pi\) | |||||||
\(620\) | 21.4104 | − | 5.91845i | 0.859864 | − | 0.237691i | ||||
\(621\) | 6.91918 | − | 2.95654i | 0.277657 | − | 0.118642i | ||||
\(622\) | −16.6972 | + | 16.6972i | −0.669498 | + | 0.669498i | ||||
\(623\) | −0.0232001 | + | 0.0232001i | −0.000929491 | + | 0.000929491i | ||||
\(624\) | 1.71661 | − | 4.18809i | 0.0687195 | − | 0.167658i | ||||
\(625\) | 11.8102 | − | 22.0345i | 0.472409 | − | 0.881379i | ||||
\(626\) | − | 24.7263i | − | 0.988260i | ||||||
\(627\) | 2.17672 | + | 5.20048i | 0.0869297 | + | 0.207687i | ||||
\(628\) | 13.5743 | + | 13.5743i | 0.541674 | + | 0.541674i | ||||
\(629\) | −22.6047 | −0.901309 | ||||||||
\(630\) | 0.582461 | + | 0.324502i | 0.0232058 | + | 0.0129285i | ||||
\(631\) | 37.2313 | 1.48215 | 0.741077 | − | 0.671420i | \(-0.234315\pi\) | ||||
0.741077 | + | 0.671420i | \(0.234315\pi\) | |||||||
\(632\) | −6.93985 | − | 6.93985i | −0.276052 | − | 0.276052i | ||||
\(633\) | −6.65152 | − | 15.8914i | −0.264374 | − | 0.631626i | ||||
\(634\) | − | 10.4539i | − | 0.415178i | ||||||
\(635\) | 41.9812 | + | 23.7980i | 1.66597 | + | 0.944393i | ||||
\(636\) | 7.89318 | − | 19.2573i | 0.312985 | − | 0.763603i | ||||
\(637\) | −12.9166 | + | 12.9166i | −0.511772 | + | 0.511772i | ||||
\(638\) | 16.0651 | − | 16.0651i | 0.636024 | − | 0.636024i | ||||
\(639\) | 14.2724 | + | 14.0624i | 0.564607 | + | 0.556301i | ||||
\(640\) | 1.94526 | + | 1.10271i | 0.0768930 | + | 0.0435885i | ||||
\(641\) | 19.9142i | 0.786564i | 0.919418 | + | 0.393282i | \(0.128660\pi\) | ||||
−0.919418 | + | 0.393282i | \(0.871340\pi\) | |||||||
\(642\) | −19.7753 | + | 8.27716i | −0.780468 | + | 0.326674i | ||||
\(643\) | −30.9151 | − | 30.9151i | −1.21917 | − | 1.21917i | −0.967922 | − | 0.251251i | \(-0.919158\pi\) |
−0.251251 | − | 0.967922i | \(-0.580842\pi\) | |||||||
\(644\) | 0.143929 | 0.00567160 | ||||||||
\(645\) | −12.8093 | − | 1.53545i | −0.504367 | − | 0.0604584i | ||||
\(646\) | −5.32519 | −0.209517 | ||||||||
\(647\) | −2.55700 | − | 2.55700i | −0.100526 | − | 0.100526i | 0.655055 | − | 0.755581i | \(-0.272645\pi\) |
−0.755581 | + | 0.655055i | \(0.772645\pi\) | |||||||
\(648\) | −6.45757 | − | 6.26895i | −0.253677 | − | 0.246268i | ||||
\(649\) | − | 7.31944i | − | 0.287313i | ||||||
\(650\) | 6.71090 | + | 11.2110i | 0.263223 | + | 0.439733i | ||||
\(651\) | −1.58245 | − | 0.648612i | −0.0620210 | − | 0.0254211i | ||||
\(652\) | 1.79928 | − | 1.79928i | 0.0704652 | − | 0.0704652i | ||||
\(653\) | 2.83582 | − | 2.83582i | 0.110974 | − | 0.110974i | −0.649439 | − | 0.760413i | \(-0.724996\pi\) |
0.760413 | + | 0.649439i | \(0.224996\pi\) | |||||||
\(654\) | −21.6421 | − | 8.87067i | −0.846275 | − | 0.346871i | ||||
\(655\) | 6.62846 | − | 1.83229i | 0.258995 | − | 0.0715936i | ||||
\(656\) | − | 8.72182i | − | 0.340530i | ||||||
\(657\) | 19.9822 | − | 0.148074i | 0.779579 | − | 0.00577691i | ||||
\(658\) | −0.0865854 | − | 0.0865854i | −0.00337545 | − | 0.00337545i | ||||
\(659\) | −19.5551 | −0.761760 | −0.380880 | − | 0.924624i | \(-0.624379\pi\) | ||||
−0.380880 | + | 0.924624i | \(0.624379\pi\) | |||||||
\(660\) | −9.91146 | + | 7.78963i | −0.385803 | + | 0.303211i | ||||
\(661\) | 4.07898 | 0.158654 | 0.0793269 | − | 0.996849i | \(-0.474723\pi\) | ||||
0.0793269 | + | 0.996849i | \(0.474723\pi\) | |||||||
\(662\) | −2.09183 | − | 2.09183i | −0.0813014 | − | 0.0813014i | ||||
\(663\) | −22.2340 | + | 9.30629i | −0.863497 | + | 0.361426i | ||||
\(664\) | − | 14.9208i | − | 0.579038i | ||||||
\(665\) | 0.109603 | − | 0.193347i | 0.00425022 | − | 0.00749767i | ||||
\(666\) | −8.93775 | + | 9.07120i | −0.346331 | + | 0.351502i | ||||
\(667\) | −7.14718 | + | 7.14718i | −0.276740 | + | 0.276740i | ||||
\(668\) | 3.31894 | − | 3.31894i | 0.128413 | − | 0.128413i | ||||
\(669\) | −9.88200 | + | 24.1095i | −0.382060 | + | 0.932129i | ||||
\(670\) | 1.89834 | + | 6.86737i | 0.0733391 | + | 0.265310i | ||||
\(671\) | 27.1449i | 1.04792i | ||||||||
\(672\) | −0.0664699 | − | 0.158806i | −0.00256413 | − | 0.00612607i | ||||
\(673\) | 3.90944 | + | 3.90944i | 0.150698 | + | 0.150698i | 0.778430 | − | 0.627732i | \(-0.216017\pi\) |
−0.627732 | + | 0.778430i | \(0.716017\pi\) | |||||||
\(674\) | 10.6937 | 0.411905 | ||||||||
\(675\) | 25.6579 | − | 4.08285i | 0.987575 | − | 0.157149i | ||||
\(676\) | 6.17105 | 0.237348 | ||||||||
\(677\) | −12.6939 | − | 12.6939i | −0.487866 | − | 0.487866i | 0.419766 | − | 0.907632i | \(-0.362112\pi\) |
−0.907632 | + | 0.419766i | \(0.862112\pi\) | |||||||
\(678\) | −1.46575 | − | 3.50188i | −0.0562918 | − | 0.134489i | ||||
\(679\) | − | 0.517974i | − | 0.0198780i | ||||||
\(680\) | −3.17258 | − | 11.4771i | −0.121663 | − | 0.440125i | ||||
\(681\) | 0.293086 | − | 0.715054i | 0.0112311 | − | 0.0274009i | ||||
\(682\) | 22.8640 | − | 22.8640i | 0.875508 | − | 0.875508i | ||||
\(683\) | 21.0801 | − | 21.0801i | 0.806609 | − | 0.806609i | −0.177510 | − | 0.984119i | \(-0.556804\pi\) |
0.984119 | + | 0.177510i | \(0.0568041\pi\) | |||||||
\(684\) | −2.10554 | + | 2.13698i | −0.0805074 | + | 0.0817095i | ||||
\(685\) | −13.9807 | + | 24.6629i | −0.534175 | + | 0.942320i | ||||
\(686\) | 1.39053i | 0.0530909i | ||||||||
\(687\) | −4.08002 | + | 1.70774i | −0.155662 | + | 0.0651542i | ||||
\(688\) | 2.35540 | + | 2.35540i | 0.0897987 | + | 0.0897987i | ||||
\(689\) | −31.4003 | −1.19626 | ||||||||
\(690\) | 4.40949 | − | 3.46552i | 0.167866 | − | 0.131930i | ||||
\(691\) | 13.9849 | 0.532010 | 0.266005 | − | 0.963972i | \(-0.414296\pi\) | ||||
0.266005 | + | 0.963972i | \(0.414296\pi\) | |||||||
\(692\) | −2.84866 | − | 2.84866i | −0.108290 | − | 0.108290i | ||||
\(693\) | 0.970525 | − | 0.00719188i | 0.0368672 | − | 0.000273197i | ||||
\(694\) | 1.46338i | 0.0555491i | ||||||||
\(695\) | −18.9812 | + | 5.24695i | −0.719999 | + | 0.199028i | ||||
\(696\) | 11.1867 | + | 4.58518i | 0.424029 | + | 0.173801i | ||||
\(697\) | −32.8418 | + | 32.8418i | −1.24397 | + | 1.24397i | ||||
\(698\) | −2.40651 | + | 2.40651i | −0.0910876 | + | 0.0910876i | ||||
\(699\) | 37.4039 | + | 15.3311i | 1.41475 | + | 0.579875i | ||||
\(700\) | 0.482007 | + | 0.121031i | 0.0182182 | + | 0.00457453i | ||||
\(701\) | − | 45.3072i | − | 1.71123i | −0.517614 | − | 0.855614i | \(-0.673180\pi\) | ||
0.517614 | − | 0.855614i | \(-0.326820\pi\) | |||||||
\(702\) | −5.05659 | + | 12.6021i | −0.190849 | + | 0.475635i | ||||
\(703\) | 3.00157 | + | 3.00157i | 0.113206 | + | 0.113206i | ||||
\(704\) | 3.25490 | 0.122674 | ||||||||
\(705\) | −4.73747 | − | 0.567880i | −0.178424 | − | 0.0213876i | ||||
\(706\) | −16.5412 | −0.622536 | ||||||||
\(707\) | −0.719737 | − | 0.719737i | −0.0270685 | − | 0.0270685i | ||||
\(708\) | 3.59291 | − | 1.50385i | 0.135030 | − | 0.0565183i | ||||
\(709\) | 34.5259i | 1.29665i | 0.761365 | + | 0.648323i | \(0.224530\pi\) | ||||
−0.761365 | + | 0.648323i | \(0.775470\pi\) | |||||||
\(710\) | 12.9919 | + | 7.36475i | 0.487577 | + | 0.276394i | ||||
\(711\) | 20.9732 | + | 20.6647i | 0.786558 | + | 0.774986i | ||||
\(712\) | 0.233415 | − | 0.233415i | 0.00874760 | − | 0.00874760i | ||||
\(713\) | −10.1719 | + | 10.1719i | −0.380942 | + | 0.380942i | ||||
\(714\) | −0.347688 | + | 0.848270i | −0.0130119 | + | 0.0317457i | ||||
\(715\) | 16.5459 | + | 9.37943i | 0.618783 | + | 0.350771i | ||||
\(716\) | 7.34939i | 0.274660i | ||||||||
\(717\) | 8.65517 | + | 20.6784i | 0.323233 | + | 0.772249i | ||||
\(718\) | 12.1710 | + | 12.1710i | 0.454219 | + | 0.454219i | ||||
\(719\) | −2.64921 | −0.0987990 | −0.0493995 | − | 0.998779i | \(-0.515731\pi\) | ||||
−0.0493995 | + | 0.998779i | \(0.515731\pi\) | |||||||
\(720\) | −5.86012 | − | 3.26480i | −0.218394 | − | 0.121672i | ||||
\(721\) | 0.874097 | 0.0325531 | ||||||||
\(722\) | 0.707107 | + | 0.707107i | 0.0263158 | + | 0.0263158i | ||||
\(723\) | −18.2414 | − | 43.5812i | −0.678405 | − | 1.62080i | ||||
\(724\) | − | 24.4774i | − | 0.909695i | ||||||
\(725\) | −29.9455 | + | 17.9252i | −1.11215 | + | 0.665727i | ||||
\(726\) | 0.266465 | − | 0.650106i | 0.00988945 | − | 0.0241277i | ||||
\(727\) | 2.05295 | − | 2.05295i | 0.0761398 | − | 0.0761398i | −0.668011 | − | 0.744151i | \(-0.732854\pi\) |
0.744151 | + | 0.668011i | \(0.232854\pi\) | |||||||
\(728\) | −0.183663 | + | 0.183663i | −0.00680701 | + | 0.00680701i | ||||
\(729\) | 19.5116 | + | 18.6628i | 0.722650 | + | 0.691214i | ||||
\(730\) | 14.3559 | − | 3.96836i | 0.531334 | − | 0.146876i | ||||
\(731\) | − | 17.7384i | − | 0.656078i | ||||||
\(732\) | −13.3247 | + | 5.57719i | −0.492494 | + | 0.206139i | ||||
\(733\) | −1.89006 | − | 1.89006i | −0.0698111 | − | 0.0698111i | 0.671339 | − | 0.741150i | \(-0.265719\pi\) |
−0.741150 | + | 0.671339i | \(0.765719\pi\) | |||||||
\(734\) | 13.6241 | 0.502874 | ||||||||
\(735\) | 16.7288 | + | 21.2856i | 0.617050 | + | 0.785129i | ||||
\(736\) | −1.44807 | −0.0533764 | ||||||||
\(737\) | 7.33360 | + | 7.33360i | 0.270137 | + | 0.270137i | ||||
\(738\) | 0.193888 | + | 26.1647i | 0.00713713 | + | 0.963137i | ||||
\(739\) | − | 16.9189i | − | 0.622373i | −0.950349 | − | 0.311187i | \(-0.899274\pi\) | ||
0.950349 | − | 0.311187i | \(-0.100726\pi\) | |||||||
\(740\) | −4.68087 | + | 8.25736i | −0.172072 | + | 0.303546i | ||||
\(741\) | 4.18809 | + | 1.71661i | 0.153853 | + | 0.0630613i | ||||
\(742\) | −0.844505 | + | 0.844505i | −0.0310028 | + | 0.0310028i | ||||
\(743\) | −13.2213 | + | 13.2213i | −0.485044 | + | 0.485044i | −0.906738 | − | 0.421694i | \(-0.861436\pi\) |
0.421694 | + | 0.906738i | \(0.361436\pi\) | |||||||
\(744\) | 15.9209 | + | 6.52567i | 0.583690 | + | 0.239243i | ||||
\(745\) | −11.5419 | − | 41.7536i | −0.422862 | − | 1.52973i | ||||
\(746\) | 12.8308i | 0.469768i | ||||||||
\(747\) | 0.331693 | + | 44.7611i | 0.0121360 | + | 1.63772i | ||||
\(748\) | −12.2562 | − | 12.2562i | −0.448132 | − | 0.448132i | ||||
\(749\) | 1.23020 | 0.0449507 | ||||||||
\(750\) | 17.6812 | − | 7.89778i | 0.645626 | − | 0.288386i | ||||
\(751\) | 9.73721 | 0.355316 | 0.177658 | − | 0.984092i | \(-0.443148\pi\) | ||||
0.177658 | + | 0.984092i | \(0.443148\pi\) | |||||||
\(752\) | 0.871132 | + | 0.871132i | 0.0317669 | + | 0.0317669i | ||||
\(753\) | 6.14968 | − | 2.57402i | 0.224107 | − | 0.0938024i | ||||
\(754\) | − | 18.2406i | − | 0.664282i | ||||||
\(755\) | −9.19338 | − | 33.2577i | −0.334581 | − | 1.21037i | ||||
\(756\) | 0.202935 | + | 0.474927i | 0.00738066 | + | 0.0172729i | ||||
\(757\) | 23.5741 | − | 23.5741i | 0.856814 | − | 0.856814i | −0.134148 | − | 0.990961i | \(-0.542830\pi\) |
0.990961 | + | 0.134148i | \(0.0428296\pi\) | |||||||
\(758\) | −6.93516 | + | 6.93516i | −0.251896 | + | 0.251896i | ||||
\(759\) | 3.09614 | − | 7.55379i | 0.112383 | − | 0.274185i | ||||
\(760\) | −1.10271 | + | 1.94526i | −0.0399996 | + | 0.0705619i | ||||
\(761\) | 6.55642i | 0.237670i | 0.992914 | + | 0.118835i | \(0.0379160\pi\) | ||||
−0.992914 | + | 0.118835i | \(0.962084\pi\) | |||||||
\(762\) | 14.4325 | + | 34.4813i | 0.522835 | + | 1.24913i | ||||
\(763\) | 0.949088 | + | 0.949088i | 0.0343593 | + | 0.0343593i | ||||
\(764\) | 1.13422 | 0.0410347 | ||||||||
\(765\) | 9.77262 | + | 34.3597i | 0.353330 | + | 1.24228i | ||||
\(766\) | −6.82192 | −0.246486 | ||||||||
\(767\) | −4.15530 | − | 4.15530i | −0.150039 | − | 0.150039i | ||||
\(768\) | 0.668751 | + | 1.59774i | 0.0241315 | + | 0.0576535i | ||||
\(769\) | 3.44513i | 0.124235i | 0.998069 | + | 0.0621173i | \(0.0197853\pi\) | ||||
−0.998069 | + | 0.0621173i | \(0.980215\pi\) | |||||||
\(770\) | 0.697257 | − | 0.192742i | 0.0251274 | − | 0.00694593i | ||||
\(771\) | −1.78256 | + | 4.34899i | −0.0641974 | + | 0.156625i | ||||
\(772\) | −6.15920 | + | 6.15920i | −0.221674 | + | 0.221674i | ||||
\(773\) | 28.7349 | − | 28.7349i | 1.03352 | − | 1.03352i | 0.0341034 | − | 0.999418i | \(-0.489142\pi\) |
0.999418 | − | 0.0341034i | \(-0.0108576\pi\) | |||||||
\(774\) | −7.11836 | − | 7.01364i | −0.255864 | − | 0.252100i | ||||
\(775\) | −42.6186 | + | 25.5113i | −1.53090 | + | 0.916395i | ||||
\(776\) | 5.21132i | 0.187075i | ||||||||
\(777\) | 0.674109 | − | 0.282156i | 0.0241835 | − | 0.0101223i | ||||
\(778\) | 8.79079 | + | 8.79079i | 0.315165 | + | 0.315165i | ||||
\(779\) | 8.72182 | 0.312491 | ||||||||
\(780\) | −1.20458 | + | 10.0490i | −0.0431307 | + | 0.359813i | ||||
\(781\) | 21.7387 | 0.777871 | ||||||||
\(782\) | 5.45266 | + | 5.45266i | 0.194987 | + | 0.194987i | ||||
\(783\) | −33.6610 | − | 13.5065i | −1.20295 | − | 0.482683i | ||||
\(784\) | − | 6.99012i | − | 0.249647i | ||||||
\(785\) | −37.3431 | − | 21.1687i | −1.33283 | − | 0.755545i | ||||
\(786\) | 4.92897 | + | 2.02028i | 0.175810 | + | 0.0720611i | ||||
\(787\) | −16.5690 | + | 16.5690i | −0.590622 | + | 0.590622i | −0.937800 | − | 0.347177i | \(-0.887140\pi\) |
0.347177 | + | 0.937800i | \(0.387140\pi\) | |||||||
\(788\) | 7.62320 | − | 7.62320i | 0.271565 | − | 0.271565i | ||||
\(789\) | −4.31123 | − | 1.76708i | −0.153484 | − | 0.0629098i | ||||
\(790\) | 19.0916 | + | 10.8225i | 0.679248 | + | 0.385047i | ||||
\(791\) | 0.217849i | 0.00774581i | ||||||||
\(792\) | −9.76442 | + | 0.0723573i | −0.346964 | + | 0.00257111i | ||||
\(793\) | 15.4103 | + | 15.4103i | 0.547238 | + | 0.547238i | ||||
\(794\) | −34.7848 | −1.23446 | ||||||||
\(795\) | −5.53878 | + | 46.2067i | −0.196440 | + | 1.63878i | ||||
\(796\) | 1.98374 | 0.0703119 | ||||||||
\(797\) | −26.0034 | − | 26.0034i | −0.921088 | − | 0.921088i | 0.0760180 | − | 0.997106i | \(-0.475779\pi\) |
−0.997106 | + | 0.0760180i | \(0.975779\pi\) | |||||||
\(798\) | 0.158806 | − | 0.0664699i | 0.00562166 | − | 0.00235301i | ||||
\(799\) | − | 6.56046i | − | 0.232092i | ||||||
\(800\) | −4.84946 | − | 1.21769i | −0.171454 | − | 0.0430517i | ||||
\(801\) | −0.695037 | + | 0.705415i | −0.0245579 | + | 0.0249246i | ||||
\(802\) | 22.5115 | − | 22.5115i | 0.794907 | − | 0.794907i | ||||
\(803\) | 15.3305 | − | 15.3305i | 0.541001 | − | 0.541001i | ||||
\(804\) | −2.09310 | + | 5.10663i | −0.0738180 | + | 0.180097i | ||||
\(805\) | −0.310202 | + | 0.0857485i | −0.0109332 | + | 0.00302224i | ||||
\(806\) | − | 25.9601i | − | 0.914406i | ||||||
\(807\) | 7.74298 | + | 18.4991i | 0.272566 | + | 0.651197i | ||||
\(808\) | 7.24125 | + | 7.24125i | 0.254746 | + | 0.254746i | ||||
\(809\) | −35.7156 | −1.25569 | −0.627847 | − | 0.778337i | \(-0.716063\pi\) | ||||
−0.627847 | + | 0.778337i | \(0.716063\pi\) | |||||||
\(810\) | 17.6525 | + | 9.66387i | 0.620245 | + | 0.339554i | ||||
\(811\) | −45.2298 | −1.58823 | −0.794116 | − | 0.607766i | \(-0.792066\pi\) | ||||
−0.794116 | + | 0.607766i | \(0.792066\pi\) | |||||||
\(812\) | −0.490577 | − | 0.490577i | −0.0172159 | − | 0.0172159i | ||||
\(813\) | 7.13563 | + | 17.0480i | 0.250258 | + | 0.597900i | ||||
\(814\) | 13.8166i | 0.484272i | ||||||||
\(815\) | −2.80592 | + | 4.94984i | −0.0982873 | + | 0.173385i | ||||
\(816\) | 3.49808 | − | 8.53442i | 0.122457 | − | 0.298764i | ||||
\(817\) | −2.35540 | + | 2.35540i | −0.0824049 | + | 0.0824049i | ||||
\(818\) | 12.7381 | − | 12.7381i | 0.445377 | − | 0.445377i | ||||
\(819\) | 0.546892 | − | 0.555057i | 0.0191099 | − | 0.0193953i | ||||
\(820\) | 5.19619 | + | 18.7976i | 0.181459 | + | 0.656441i | ||||
\(821\) | − | 43.7380i | − | 1.52647i | −0.646123 | − | 0.763234i | \(-0.723611\pi\) | ||
0.646123 | − | 0.763234i | \(-0.276389\pi\) | |||||||
\(822\) | −20.2569 | + | 8.47874i | −0.706540 | + | 0.295730i | ||||
\(823\) | 19.4288 | + | 19.4288i | 0.677246 | + | 0.677246i | 0.959376 | − | 0.282130i | \(-0.0910410\pi\) |
−0.282130 | + | 0.959376i | \(0.591041\pi\) | |||||||
\(824\) | −8.79426 | −0.306363 | ||||||||
\(825\) | 16.7207 | − | 22.6935i | 0.582142 | − | 0.790085i | ||||
\(826\) | −0.223512 | −0.00777698 | ||||||||
\(827\) | 29.2247 | + | 29.2247i | 1.01624 | + | 1.01624i | 0.999866 | + | 0.0163748i | \(0.00521250\pi\) |
0.0163748 | + | 0.999866i | \(0.494788\pi\) | |||||||
\(828\) | 4.34408 | − | 0.0321909i | 0.150967 | − | 0.00111871i | ||||
\(829\) | − | 3.38851i | − | 0.117688i | −0.998267 | − | 0.0588439i | \(-0.981259\pi\) | ||
0.998267 | − | 0.0588439i | \(-0.0187414\pi\) | |||||||
\(830\) | 8.88933 | + | 32.1578i | 0.308553 | + | 1.11621i | ||||
\(831\) | −33.5369 | − | 13.7461i | −1.16338 | − | 0.476847i | ||||
\(832\) | 1.84783 | − | 1.84783i | 0.0640620 | − | 0.0640620i | ||||
\(833\) | −26.3211 | + | 26.3211i | −0.911973 | + | 0.911973i | ||||
\(834\) | −14.1146 | − | 5.78527i | −0.488748 | − | 0.200328i | ||||
\(835\) | −5.17578 | + | 9.13042i | −0.179115 | + | 0.315971i | ||||
\(836\) | 3.25490i | 0.112573i | ||||||||
\(837\) | −47.9066 | − | 19.2225i | −1.65589 | − | 0.664428i | ||||
\(838\) | −12.7811 | − | 12.7811i | −0.441516 | − | 0.441516i | ||||
\(839\) | 12.7144 | 0.438949 | 0.219475 | − | 0.975618i | \(-0.429566\pi\) | ||||
0.219475 | + | 0.975618i | \(0.429566\pi\) | |||||||
\(840\) | 0.237870 | + | 0.302664i | 0.00820730 | + | 0.0104429i | ||||
\(841\) | 19.7218 | 0.680062 | ||||||||
\(842\) | −24.5885 | − | 24.5885i | −0.847377 | − | 0.847377i | ||||
\(843\) | −5.07798 | + | 2.12544i | −0.174895 | + | 0.0732042i | ||||
\(844\) | − | 9.94617i | − | 0.342361i | ||||||
\(845\) | −13.3001 | + | 3.67652i | −0.457537 | + | 0.126476i | ||||
\(846\) | −2.63269 | − | 2.59396i | −0.0905138 | − | 0.0891822i | ||||
\(847\) | −0.0285096 | + | 0.0285096i | −0.000979600 | + | 0.000979600i | ||||
\(848\) | 8.49654 | − | 8.49654i | 0.291772 | − | 0.291772i | ||||
\(849\) | −11.8575 | + | 28.9292i | −0.406948 | + | 0.992848i | ||||
\(850\) | 13.6754 | + | 22.8457i | 0.469061 | + | 0.783600i | ||||
\(851\) | − | 6.14685i | − | 0.210711i | ||||||
\(852\) | 4.46643 | + | 10.6709i | 0.153017 | + | 0.365580i | ||||
\(853\) | 10.2291 | + | 10.2291i | 0.350239 | + | 0.350239i | 0.860199 | − | 0.509959i | \(-0.170340\pi\) |
−0.509959 | + | 0.860199i | \(0.670340\pi\) | |||||||
\(854\) | 0.828917 | 0.0283649 | ||||||||
\(855\) | 3.26480 | − | 5.86012i | 0.111654 | − | 0.200412i | ||||
\(856\) | −12.3770 | −0.423038 | ||||||||
\(857\) | −24.0991 | − | 24.0991i | −0.823210 | − | 0.823210i | 0.163357 | − | 0.986567i | \(-0.447768\pi\) |
−0.986567 | + | 0.163357i | \(0.947768\pi\) | |||||||
\(858\) | 5.68825 | + | 13.5900i | 0.194194 | + | 0.463956i | ||||
\(859\) | 57.7511i | 1.97044i | 0.171286 | + | 0.985221i | \(0.445208\pi\) | ||||
−0.171286 | + | 0.985221i | \(0.554792\pi\) | |||||||
\(860\) | −6.47972 | − | 3.67317i | −0.220957 | − | 0.125254i | ||||
\(861\) | 0.569459 | − | 1.38933i | 0.0194071 | − | 0.0473483i | ||||
\(862\) | 16.3264 | − | 16.3264i | 0.556079 | − | 0.556079i | ||||
\(863\) | −5.94787 | + | 5.94787i | −0.202468 | + | 0.202468i | −0.801057 | − | 0.598589i | \(-0.795728\pi\) |
0.598589 | + | 0.801057i | \(0.295728\pi\) | |||||||
\(864\) | −2.04172 | − | 4.77822i | −0.0694606 | − | 0.162558i | ||||
\(865\) | 7.83670 | + | 4.44241i | 0.266456 | + | 0.151046i | ||||
\(866\) | 38.3993i | 1.30486i | ||||||||
\(867\) | −18.1465 | + | 7.59542i | −0.616288 | + | 0.257954i | ||||
\(868\) | −0.698192 | − | 0.698192i | −0.0236982 | − | 0.0236982i | ||||
\(869\) | 31.9449 | 1.08366 | ||||||||
\(870\) | −26.8417 | − | 3.21750i | −0.910017 | − | 0.109084i | ||||
\(871\) | 8.32668 | 0.282139 | ||||||||
\(872\) | −9.54875 | − | 9.54875i | −0.323361 | − | 0.323361i | ||||
\(873\) | −0.115849 | − | 15.6335i | −0.00392090 | − | 0.529114i | ||||
\(874\) | − | 1.44807i | − | 0.0489816i | ||||||
\(875\) | −1.11095 | + | 0.0263148i | −0.0375569 | + | 0.000889604i | ||||
\(876\) | 10.6751 | + | 4.37551i | 0.360678 | + | 0.147835i | ||||
\(877\) | 21.5348 | − | 21.5348i | 0.727178 | − | 0.727178i | −0.242879 | − | 0.970057i | \(-0.578092\pi\) |
0.970057 | + | 0.242879i | \(0.0780917\pi\) | |||||||
\(878\) | −2.94247 | + | 2.94247i | −0.0993035 | + | 0.0993035i | ||||
\(879\) | 45.3108 | + | 18.5720i | 1.52830 | + | 0.626417i | ||||
\(880\) | −7.01508 | + | 1.93917i | −0.236478 | + | 0.0653693i | ||||
\(881\) | − | 25.6283i | − | 0.863440i | −0.902008 | − | 0.431720i | \(-0.857907\pi\) | ||
0.902008 | − | 0.431720i | \(-0.142093\pi\) | |||||||
\(882\) | 0.155392 | + | 20.9698i | 0.00523233 | + | 0.706089i | ||||
\(883\) | 22.5479 | + | 22.5479i | 0.758798 | + | 0.758798i | 0.976104 | − | 0.217306i | \(-0.0697269\pi\) |
−0.217306 | + | 0.976104i | \(0.569727\pi\) | |||||||
\(884\) | −13.9159 | −0.468043 | ||||||||
\(885\) | −6.84764 | + | 5.38171i | −0.230181 | + | 0.180904i | ||||
\(886\) | −10.5293 | −0.353739 | ||||||||
\(887\) | −28.8045 | − | 28.8045i | −0.967161 | − | 0.967161i | 0.0323163 | − | 0.999478i | \(-0.489712\pi\) |
−0.999478 | + | 0.0323163i | \(0.989712\pi\) | |||||||
\(888\) | −6.78219 | + | 2.83876i | −0.227595 | + | 0.0952626i | ||||
\(889\) | − | 2.14505i | − | 0.0719427i | ||||||
\(890\) | −0.364004 | + | 0.642127i | −0.0122014 | + | 0.0215241i | ||||
\(891\) | 29.2909 | − | 0.434132i | 0.981281 | − | 0.0145440i | ||||
\(892\) | −10.6374 | + | 10.6374i | −0.356166 | + | 0.356166i | ||||
\(893\) | −0.871132 | + | 0.871132i | −0.0291513 | + | 0.0291513i | ||||
\(894\) | 12.7260 | − | 31.0483i | 0.425623 | − | 1.03841i | ||||
\(895\) | −4.37854 | − | 15.8397i | −0.146359 | − | 0.529463i | ||||
\(896\) | − | 0.0993940i | − | 0.00332052i | ||||||
\(897\) | −2.53064 | − | 6.04604i | −0.0844955 | − | 0.201871i | ||||
\(898\) | 8.25008 | + | 8.25008i | 0.275309 | + | 0.275309i | ||||
\(899\) | 69.3412 | 2.31266 | ||||||||
\(900\) | 14.5750 | + | 3.54515i | 0.485835 | + | 0.118172i | ||||
\(901\) | −63.9870 | −2.13172 | ||||||||
\(902\) | 20.0738 | + | 20.0738i | 0.668384 | + | 0.668384i | ||||
\(903\) | 0.221414 | + | 0.528987i | 0.00736818 | + | 0.0176036i | ||||
\(904\) | − | 2.19177i | − | 0.0728972i | ||||||
\(905\) | 14.5829 | + | 52.7547i | 0.484751 | + | 1.75362i | ||||
\(906\) | 10.1366 | − | 24.7307i | 0.336766 | − | 0.821622i | ||||
\(907\) | 2.94946 | − | 2.94946i | 0.0979353 | − | 0.0979353i | −0.656442 | − | 0.754377i | \(-0.727939\pi\) |
0.754377 | + | 0.656442i | \(0.227939\pi\) | |||||||
\(908\) | 0.315490 | − | 0.315490i | 0.0104699 | − | 0.0104699i | ||||
\(909\) | −21.8841 | − | 21.5622i | −0.725851 | − | 0.715172i | ||||
\(910\) | 0.286417 | − | 0.505259i | 0.00949464 | − | 0.0167492i | ||||
\(911\) | − | 45.2345i | − | 1.49869i | −0.662182 | − | 0.749343i | \(-0.730370\pi\) | ||
0.662182 | − | 0.749343i | \(-0.269630\pi\) | |||||||
\(912\) | −1.59774 | + | 0.668751i | −0.0529064 | + | 0.0221446i | ||||
\(913\) | 34.3410 | + | 34.3410i | 1.13652 | + | 1.13652i | ||||
\(914\) | 18.8663 | 0.624041 | ||||||||
\(915\) | 25.3952 | − | 19.9586i | 0.839538 | − | 0.659811i | ||||
\(916\) | −2.55362 | −0.0843740 | ||||||||
\(917\) | −0.216154 | − | 0.216154i | −0.00713802 | − | 0.00713802i | ||||
\(918\) | −10.3042 | + | 25.6803i | −0.340090 | + | 0.847577i | ||||
\(919\) | − | 28.8919i | − | 0.953056i | −0.879159 | − | 0.476528i | \(-0.841895\pi\) | ||
0.879159 | − | 0.476528i | \(-0.158105\pi\) | |||||||
\(920\) | 3.12093 | − | 0.862713i | 0.102894 | − | 0.0284428i | ||||
\(921\) | −51.7446 | − | 21.2091i | −1.70504 | − | 0.698862i | ||||
\(922\) | 8.32171 | − | 8.32171i | 0.274061 | − | 0.274061i | ||||
\(923\) | 12.3412 | − | 12.3412i | 0.406216 | − | 0.406216i | ||||
\(924\) | 0.518485 | + | 0.212517i | 0.0170569 | + | 0.00699128i | ||||
\(925\) | 5.16891 | − | 20.5853i | 0.169953 | − | 0.676840i | ||||
\(926\) | − | 24.1232i | − | 0.792739i | ||||||
\(927\) | 26.3821 | − | 0.195499i | 0.866500 | − | 0.00642103i | ||||
\(928\) | 4.93568 | + | 4.93568i | 0.162021 | + | 0.162021i | ||||
\(929\) | 27.0120 | 0.886235 | 0.443117 | − | 0.896464i | \(-0.353873\pi\) | ||||
0.443117 | + | 0.896464i | \(0.353873\pi\) | |||||||
\(930\) | −38.2012 | − | 4.57917i | −1.25267 | − | 0.150157i | ||||
\(931\) | 6.99012 | 0.229092 | ||||||||
\(932\) | 16.5030 | + | 16.5030i | 0.540574 | + | 0.540574i | ||||
\(933\) | 37.7282 | − | 15.7915i | 1.23516 | − | 0.516992i | ||||
\(934\) | 29.5490i | 0.966874i | ||||||||
\(935\) | 33.7170 | + | 19.1132i | 1.10266 | + | 0.625070i | ||||
\(936\) | −5.50226 | + | 5.58441i | −0.179847 | + | 0.182532i | ||||
\(937\) | 4.28218 | − | 4.28218i | 0.139893 | − | 0.139893i | −0.633692 | − | 0.773585i | \(-0.718462\pi\) |
0.773585 | + | 0.633692i | \(0.218462\pi\) | |||||||
\(938\) | 0.223944 | − | 0.223944i | 0.00731205 | − | 0.00731205i | ||||
\(939\) | −16.2425 | + | 39.6276i | −0.530055 | + | 1.29320i | ||||
\(940\) | −2.39649 | − | 1.35851i | −0.0781650 | − | 0.0443096i | ||||
\(941\) | − | 15.4501i | − | 0.503659i | −0.967772 | − | 0.251830i | \(-0.918968\pi\) | ||
0.967772 | − | 0.251830i | \(-0.0810323\pi\) | |||||||
\(942\) | −12.8380 | − | 30.6718i | −0.418285 | − | 0.999340i | ||||
\(943\) | −8.93059 | − | 8.93059i | −0.290820 | − | 0.290820i | ||||
\(944\) | 2.24875 | 0.0731905 | ||||||||
\(945\) | −0.720319 | − | 0.902679i | −0.0234320 | − | 0.0293641i | ||||
\(946\) | −10.8422 | −0.352510 | ||||||||
\(947\) | 20.6794 | + | 20.6794i | 0.671989 | + | 0.671989i | 0.958174 | − | 0.286185i | \(-0.0923873\pi\) |
−0.286185 | + | 0.958174i | \(0.592387\pi\) | |||||||
\(948\) | 6.56341 | + | 15.6809i | 0.213170 | + | 0.509292i | ||||
\(949\) | − | 17.4064i | − | 0.565037i | ||||||
\(950\) | 1.21769 | − | 4.84946i | 0.0395069 | − | 0.157337i | ||||
\(951\) | −6.86712 | + | 16.7540i | −0.222682 | + | 0.543285i | ||||
\(952\) | −0.374266 | + | 0.374266i | −0.0121300 | + | 0.0121300i | ||||
\(953\) | −39.5523 | + | 39.5523i | −1.28122 | + | 1.28122i | −0.341253 | + | 0.939971i | \(0.610851\pi\) |
−0.939971 | + | 0.341253i | \(0.889149\pi\) | |||||||
\(954\) | −25.3000 | + | 25.6778i | −0.819119 | + | 0.831349i | ||||
\(955\) | −2.44452 | + | 0.675735i | −0.0791028 | + | 0.0218663i | ||||
\(956\) | 12.9423i | 0.418583i | ||||||||
\(957\) | −36.2999 | + | 15.1937i | −1.17341 | + | 0.491143i | ||||
\(958\) | 19.5329 | + | 19.5329i | 0.631079 | + | 0.631079i | ||||
\(959\) | 1.26016 | 0.0406928 | ||||||||
\(960\) | −2.39320 | − | 3.04509i | −0.0772403 | − | 0.0982799i | ||||
\(961\) | 67.6869 | 2.18345 | ||||||||
\(962\) | 7.84379 | + | 7.84379i | 0.252894 | + | 0.252894i | ||||
\(963\) | 37.1301 | − | 0.275145i | 1.19650 | − | 0.00886643i | ||||
\(964\) | − | 27.2768i | − | 0.878526i | ||||||
\(965\) | 9.60509 | − | 16.9440i | 0.309199 | − | 0.545447i | ||||
\(966\) | −0.230668 | − | 0.0945461i | −0.00742163 | − | 0.00304197i | ||||
\(967\) | −2.80525 | + | 2.80525i | −0.0902106 | + | 0.0902106i | −0.750772 | − | 0.660561i | \(-0.770318\pi\) |
0.660561 | + | 0.750772i | \(0.270318\pi\) | |||||||
\(968\) | 0.286834 | − | 0.286834i | 0.00921919 | − | 0.00921919i | ||||
\(969\) | 8.53442 | + | 3.49808i | 0.274165 | + | 0.112375i | ||||
\(970\) | −3.10474 | − | 11.2316i | −0.0996872 | − | 0.360626i | ||||
\(971\) | − | 38.2865i | − | 1.22867i | −0.789044 | − | 0.614336i | \(-0.789424\pi\) | ||
0.789044 | − | 0.614336i | \(-0.210576\pi\) | |||||||
\(972\) | 6.23121 | + | 14.2889i | 0.199866 | + | 0.458316i | ||||
\(973\) | 0.618976 | + | 0.618976i | 0.0198435 | + | 0.0198435i | ||||
\(974\) | 22.0572 | 0.706757 | ||||||||
\(975\) | −3.39076 | − | 22.3757i | −0.108591 | − | 0.716597i | ||||
\(976\) | −8.33970 | −0.266947 | ||||||||
\(977\) | −7.27269 | − | 7.27269i | −0.232674 | − | 0.232674i | 0.581134 | − | 0.813808i | \(-0.302609\pi\) |
−0.813808 | + | 0.581134i | \(0.802609\pi\) | |||||||
\(978\) | −4.06555 | + | 1.70168i | −0.130002 | + | 0.0544138i | ||||
\(979\) | 1.07444i | 0.0343392i | ||||||||
\(980\) | 4.16450 | + | 15.0654i | 0.133030 | + | 0.481246i | ||||
\(981\) | 28.8577 | + | 28.4332i | 0.921356 | + | 0.907802i | ||||
\(982\) | −26.0051 | + | 26.0051i | −0.829856 | + | 0.829856i | ||||
\(983\) | −1.11513 | + | 1.11513i | −0.0355670 | + | 0.0355670i | −0.724667 | − | 0.689100i | \(-0.758006\pi\) |
0.689100 | + | 0.724667i | \(0.258006\pi\) | |||||||
\(984\) | −5.72931 | + | 13.9780i | −0.182644 | + | 0.445603i | ||||
\(985\) | −11.8882 | + | 20.9715i | −0.378788 | + | 0.668207i | ||||
\(986\) | − | 37.1703i | − | 1.18374i | ||||||
\(987\) | 0.0818887 | + | 0.195644i | 0.00260655 | + | 0.00622740i | ||||
\(988\) | 1.84783 | + | 1.84783i | 0.0587873 | + | 0.0587873i | ||||
\(989\) | 4.82356 | 0.153380 | ||||||||
\(990\) | 21.0016 | − | 5.97329i | 0.667474 | − | 0.189844i | ||||
\(991\) | 55.9333 | 1.77678 | 0.888390 | − | 0.459090i | \(-0.151824\pi\) | ||||
0.888390 | + | 0.459090i | \(0.151824\pi\) | |||||||
\(992\) | 7.02449 | + | 7.02449i | 0.223028 | + | 0.223028i | ||||
\(993\) | 1.97837 | + | 4.72659i | 0.0627816 | + | 0.149994i | ||||
\(994\) | − | 0.663829i | − | 0.0210554i | ||||||
\(995\) | −4.27544 | + | 1.18185i | −0.135541 | + | 0.0374672i | ||||
\(996\) | −9.80136 | + | 23.9128i | −0.310568 | + | 0.757706i | ||||
\(997\) | −12.1505 | + | 12.1505i | −0.384809 | + | 0.384809i | −0.872831 | − | 0.488022i | \(-0.837719\pi\) |
0.488022 | + | 0.872831i | \(0.337719\pi\) | |||||||
\(998\) | −19.1468 | + | 19.1468i | −0.606080 | + | 0.606080i | ||||
\(999\) | 20.2829 | − | 8.66682i | 0.641723 | − | 0.274206i |
(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 | 570.2.k.a.533.6 | yes | 36 | |
3.2 | odd | 2 | inner | 570.2.k.a.533.17 | yes | 36 | |
5.2 | odd | 4 | inner | 570.2.k.a.77.17 | yes | 36 | |
15.2 | even | 4 | inner | 570.2.k.a.77.6 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.k.a.77.6 | ✓ | 36 | 15.2 | even | 4 | inner | |
570.2.k.a.77.17 | yes | 36 | 5.2 | odd | 4 | inner | |
570.2.k.a.533.6 | yes | 36 | 1.1 | even | 1 | trivial | |
570.2.k.a.533.17 | yes | 36 | 3.2 | odd | 2 | inner |