Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.26509 | −1.60166 | −0.800829 | − | 0.598894i | \(-0.795607\pi\) | ||||
−0.800829 | + | 0.598894i | \(0.795607\pi\) | |||||||
\(3\) | 0.846807 | 0.488904 | 0.244452 | − | 0.969661i | \(-0.421392\pi\) | ||||
0.244452 | + | 0.969661i | \(0.421392\pi\) | |||||||
\(4\) | 3.13061 | 1.56531 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.91809 | −0.783057 | ||||||||
\(7\) | −3.17432 | −1.19978 | −0.599891 | − | 0.800082i | \(-0.704789\pi\) | ||||
−0.599891 | + | 0.800082i | \(0.704789\pi\) | |||||||
\(8\) | −2.56093 | −0.905426 | ||||||||
\(9\) | −2.28292 | −0.760973 | ||||||||
\(10\) | −2.26509 | −0.716283 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 2.65102 | 0.765285 | ||||||||
\(13\) | 0.106703 | 0.0295940 | 0.0147970 | − | 0.999891i | \(-0.495290\pi\) | ||||
0.0147970 | + | 0.999891i | \(0.495290\pi\) | |||||||
\(14\) | 7.19011 | 1.92164 | ||||||||
\(15\) | 0.846807 | 0.218645 | ||||||||
\(16\) | −0.460493 | −0.115123 | ||||||||
\(17\) | −6.41831 | −1.55667 | −0.778334 | − | 0.627851i | \(-0.783935\pi\) | ||||
−0.778334 | + | 0.627851i | \(0.783935\pi\) | |||||||
\(18\) | 5.17100 | 1.21882 | ||||||||
\(19\) | −4.21256 | −0.966428 | −0.483214 | − | 0.875502i | \(-0.660531\pi\) | ||||
−0.483214 | + | 0.875502i | \(0.660531\pi\) | |||||||
\(20\) | 3.13061 | 0.700026 | ||||||||
\(21\) | −2.68804 | −0.586578 | ||||||||
\(22\) | 2.26509 | 0.482918 | ||||||||
\(23\) | −5.49690 | −1.14618 | −0.573091 | − | 0.819492i | \(-0.694256\pi\) | ||||
−0.573091 | + | 0.819492i | \(0.694256\pi\) | |||||||
\(24\) | −2.16862 | −0.442667 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.241691 | −0.0473995 | ||||||||
\(27\) | −4.47361 | −0.860947 | ||||||||
\(28\) | −9.93757 | −1.87802 | ||||||||
\(29\) | 5.93442 | 1.10199 | 0.550997 | − | 0.834507i | \(-0.314248\pi\) | ||||
0.550997 | + | 0.834507i | \(0.314248\pi\) | |||||||
\(30\) | −1.91809 | −0.350194 | ||||||||
\(31\) | −2.85181 | −0.512200 | −0.256100 | − | 0.966650i | \(-0.582438\pi\) | ||||
−0.256100 | + | 0.966650i | \(0.582438\pi\) | |||||||
\(32\) | 6.16492 | 1.08981 | ||||||||
\(33\) | −0.846807 | −0.147410 | ||||||||
\(34\) | 14.5380 | 2.49325 | ||||||||
\(35\) | −3.17432 | −0.536558 | ||||||||
\(36\) | −7.14693 | −1.19115 | ||||||||
\(37\) | 6.54343 | 1.07573 | 0.537866 | − | 0.843030i | \(-0.319231\pi\) | ||||
0.537866 | + | 0.843030i | \(0.319231\pi\) | |||||||
\(38\) | 9.54181 | 1.54789 | ||||||||
\(39\) | 0.0903567 | 0.0144686 | ||||||||
\(40\) | −2.56093 | −0.404919 | ||||||||
\(41\) | −9.34825 | −1.45995 | −0.729976 | − | 0.683473i | \(-0.760469\pi\) | ||||
−0.729976 | + | 0.683473i | \(0.760469\pi\) | |||||||
\(42\) | 6.08864 | 0.939497 | ||||||||
\(43\) | −3.06128 | −0.466840 | −0.233420 | − | 0.972376i | \(-0.574992\pi\) | ||||
−0.233420 | + | 0.972376i | \(0.574992\pi\) | |||||||
\(44\) | −3.13061 | −0.471957 | ||||||||
\(45\) | −2.28292 | −0.340317 | ||||||||
\(46\) | 12.4509 | 1.83579 | ||||||||
\(47\) | 2.53298 | 0.369474 | 0.184737 | − | 0.982788i | \(-0.440857\pi\) | ||||
0.184737 | + | 0.982788i | \(0.440857\pi\) | |||||||
\(48\) | −0.389949 | −0.0562843 | ||||||||
\(49\) | 3.07633 | 0.439475 | ||||||||
\(50\) | −2.26509 | −0.320331 | ||||||||
\(51\) | −5.43507 | −0.761062 | ||||||||
\(52\) | 0.334045 | 0.0463237 | ||||||||
\(53\) | 0.824356 | 0.113234 | 0.0566170 | − | 0.998396i | \(-0.481969\pi\) | ||||
0.0566170 | + | 0.998396i | \(0.481969\pi\) | |||||||
\(54\) | 10.1331 | 1.37894 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 8.12923 | 1.08631 | ||||||||
\(57\) | −3.56723 | −0.472491 | ||||||||
\(58\) | −13.4420 | −1.76502 | ||||||||
\(59\) | 6.89047 | 0.897063 | 0.448531 | − | 0.893767i | \(-0.351947\pi\) | ||||
0.448531 | + | 0.893767i | \(0.351947\pi\) | |||||||
\(60\) | 2.65102 | 0.342246 | ||||||||
\(61\) | 5.77749 | 0.739732 | 0.369866 | − | 0.929085i | \(-0.379404\pi\) | ||||
0.369866 | + | 0.929085i | \(0.379404\pi\) | |||||||
\(62\) | 6.45959 | 0.820369 | ||||||||
\(63\) | 7.24672 | 0.913001 | ||||||||
\(64\) | −13.0431 | −1.63039 | ||||||||
\(65\) | 0.106703 | 0.0132348 | ||||||||
\(66\) | 1.91809 | 0.236101 | ||||||||
\(67\) | −9.02101 | −1.10209 | −0.551046 | − | 0.834475i | \(-0.685771\pi\) | ||||
−0.551046 | + | 0.834475i | \(0.685771\pi\) | |||||||
\(68\) | −20.0932 | −2.43666 | ||||||||
\(69\) | −4.65481 | −0.560374 | ||||||||
\(70\) | 7.19011 | 0.859383 | ||||||||
\(71\) | 14.2526 | 1.69147 | 0.845735 | − | 0.533602i | \(-0.179162\pi\) | ||||
0.845735 | + | 0.533602i | \(0.179162\pi\) | |||||||
\(72\) | 5.84640 | 0.689005 | ||||||||
\(73\) | −1.00000 | −0.117041 | ||||||||
\(74\) | −14.8214 | −1.72295 | ||||||||
\(75\) | 0.846807 | 0.0977809 | ||||||||
\(76\) | −13.1879 | −1.51276 | ||||||||
\(77\) | 3.17432 | 0.361748 | ||||||||
\(78\) | −0.204666 | −0.0231738 | ||||||||
\(79\) | 15.0952 | 1.69834 | 0.849172 | − | 0.528116i | \(-0.177102\pi\) | ||||
0.849172 | + | 0.528116i | \(0.177102\pi\) | |||||||
\(80\) | −0.460493 | −0.0514847 | ||||||||
\(81\) | 3.06047 | 0.340052 | ||||||||
\(82\) | 21.1746 | 2.33834 | ||||||||
\(83\) | −15.3194 | −1.68152 | −0.840762 | − | 0.541405i | \(-0.817893\pi\) | ||||
−0.840762 | + | 0.541405i | \(0.817893\pi\) | |||||||
\(84\) | −8.41521 | −0.918174 | ||||||||
\(85\) | −6.41831 | −0.696163 | ||||||||
\(86\) | 6.93405 | 0.747718 | ||||||||
\(87\) | 5.02530 | 0.538769 | ||||||||
\(88\) | 2.56093 | 0.272996 | ||||||||
\(89\) | 13.1552 | 1.39444 | 0.697222 | − | 0.716856i | \(-0.254419\pi\) | ||||
0.697222 | + | 0.716856i | \(0.254419\pi\) | |||||||
\(90\) | 5.17100 | 0.545072 | ||||||||
\(91\) | −0.338709 | −0.0355063 | ||||||||
\(92\) | −17.2087 | −1.79413 | ||||||||
\(93\) | −2.41493 | −0.250417 | ||||||||
\(94\) | −5.73743 | −0.591770 | ||||||||
\(95\) | −4.21256 | −0.432200 | ||||||||
\(96\) | 5.22050 | 0.532815 | ||||||||
\(97\) | 7.14280 | 0.725241 | 0.362621 | − | 0.931937i | \(-0.381882\pi\) | ||||
0.362621 | + | 0.931937i | \(0.381882\pi\) | |||||||
\(98\) | −6.96814 | −0.703888 | ||||||||
\(99\) | 2.28292 | 0.229442 | ||||||||
\(100\) | 3.13061 | 0.313061 | ||||||||
\(101\) | −1.85103 | −0.184185 | −0.0920923 | − | 0.995750i | \(-0.529355\pi\) | ||||
−0.0920923 | + | 0.995750i | \(0.529355\pi\) | |||||||
\(102\) | 12.3109 | 1.21896 | ||||||||
\(103\) | 11.0094 | 1.08478 | 0.542392 | − | 0.840126i | \(-0.317519\pi\) | ||||
0.542392 | + | 0.840126i | \(0.317519\pi\) | |||||||
\(104\) | −0.273259 | −0.0267952 | ||||||||
\(105\) | −2.68804 | −0.262326 | ||||||||
\(106\) | −1.86724 | −0.181362 | ||||||||
\(107\) | −9.27940 | −0.897074 | −0.448537 | − | 0.893764i | \(-0.648055\pi\) | ||||
−0.448537 | + | 0.893764i | \(0.648055\pi\) | |||||||
\(108\) | −14.0051 | −1.34765 | ||||||||
\(109\) | −1.19923 | −0.114866 | −0.0574329 | − | 0.998349i | \(-0.518292\pi\) | ||||
−0.0574329 | + | 0.998349i | \(0.518292\pi\) | |||||||
\(110\) | 2.26509 | 0.215967 | ||||||||
\(111\) | 5.54102 | 0.525930 | ||||||||
\(112\) | 1.46175 | 0.138123 | ||||||||
\(113\) | 9.65051 | 0.907843 | 0.453922 | − | 0.891042i | \(-0.350025\pi\) | ||||
0.453922 | + | 0.891042i | \(0.350025\pi\) | |||||||
\(114\) | 8.08008 | 0.756768 | ||||||||
\(115\) | −5.49690 | −0.512588 | ||||||||
\(116\) | 18.5783 | 1.72496 | ||||||||
\(117\) | −0.243594 | −0.0225202 | ||||||||
\(118\) | −15.6075 | −1.43679 | ||||||||
\(119\) | 20.3738 | 1.86766 | ||||||||
\(120\) | −2.16862 | −0.197967 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −13.0865 | −1.18480 | ||||||||
\(123\) | −7.91617 | −0.713777 | ||||||||
\(124\) | −8.92790 | −0.801749 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −16.4144 | −1.46231 | ||||||||
\(127\) | 9.49076 | 0.842169 | 0.421084 | − | 0.907022i | \(-0.361650\pi\) | ||||
0.421084 | + | 0.907022i | \(0.361650\pi\) | |||||||
\(128\) | 17.2139 | 1.52150 | ||||||||
\(129\) | −2.59231 | −0.228240 | ||||||||
\(130\) | −0.241691 | −0.0211977 | ||||||||
\(131\) | 14.4570 | 1.26311 | 0.631555 | − | 0.775331i | \(-0.282417\pi\) | ||||
0.631555 | + | 0.775331i | \(0.282417\pi\) | |||||||
\(132\) | −2.65102 | −0.230742 | ||||||||
\(133\) | 13.3720 | 1.15950 | ||||||||
\(134\) | 20.4334 | 1.76517 | ||||||||
\(135\) | −4.47361 | −0.385027 | ||||||||
\(136\) | 16.4368 | 1.40945 | ||||||||
\(137\) | 17.7950 | 1.52033 | 0.760166 | − | 0.649729i | \(-0.225118\pi\) | ||||
0.760166 | + | 0.649729i | \(0.225118\pi\) | |||||||
\(138\) | 10.5435 | 0.897526 | ||||||||
\(139\) | −0.0888487 | −0.00753605 | −0.00376802 | − | 0.999993i | \(-0.501199\pi\) | ||||
−0.00376802 | + | 0.999993i | \(0.501199\pi\) | |||||||
\(140\) | −9.93757 | −0.839878 | ||||||||
\(141\) | 2.14495 | 0.180637 | ||||||||
\(142\) | −32.2833 | −2.70916 | ||||||||
\(143\) | −0.106703 | −0.00892293 | ||||||||
\(144\) | 1.05127 | 0.0876057 | ||||||||
\(145\) | 5.93442 | 0.492826 | ||||||||
\(146\) | 2.26509 | 0.187460 | ||||||||
\(147\) | 2.60505 | 0.214861 | ||||||||
\(148\) | 20.4849 | 1.68385 | ||||||||
\(149\) | 12.9622 | 1.06190 | 0.530951 | − | 0.847402i | \(-0.321835\pi\) | ||||
0.530951 | + | 0.847402i | \(0.321835\pi\) | |||||||
\(150\) | −1.91809 | −0.156611 | ||||||||
\(151\) | −11.7110 | −0.953025 | −0.476512 | − | 0.879168i | \(-0.658099\pi\) | ||||
−0.476512 | + | 0.879168i | \(0.658099\pi\) | |||||||
\(152\) | 10.7881 | 0.875029 | ||||||||
\(153\) | 14.6525 | 1.18458 | ||||||||
\(154\) | −7.19011 | −0.579396 | ||||||||
\(155\) | −2.85181 | −0.229063 | ||||||||
\(156\) | 0.282872 | 0.0226479 | ||||||||
\(157\) | 17.1979 | 1.37254 | 0.686272 | − | 0.727345i | \(-0.259246\pi\) | ||||
0.686272 | + | 0.727345i | \(0.259246\pi\) | |||||||
\(158\) | −34.1919 | −2.72017 | ||||||||
\(159\) | 0.698071 | 0.0553606 | ||||||||
\(160\) | 6.16492 | 0.487380 | ||||||||
\(161\) | 17.4489 | 1.37517 | ||||||||
\(162\) | −6.93222 | −0.544646 | ||||||||
\(163\) | −4.50983 | −0.353237 | −0.176619 | − | 0.984279i | \(-0.556516\pi\) | ||||
−0.176619 | + | 0.984279i | \(0.556516\pi\) | |||||||
\(164\) | −29.2657 | −2.28527 | ||||||||
\(165\) | −0.846807 | −0.0659238 | ||||||||
\(166\) | 34.6998 | 2.69323 | ||||||||
\(167\) | −18.6018 | −1.43945 | −0.719724 | − | 0.694261i | \(-0.755731\pi\) | ||||
−0.719724 | + | 0.694261i | \(0.755731\pi\) | |||||||
\(168\) | 6.88389 | 0.531103 | ||||||||
\(169\) | −12.9886 | −0.999124 | ||||||||
\(170\) | 14.5380 | 1.11501 | ||||||||
\(171\) | 9.61693 | 0.735425 | ||||||||
\(172\) | −9.58366 | −0.730748 | ||||||||
\(173\) | −9.42803 | −0.716800 | −0.358400 | − | 0.933568i | \(-0.616678\pi\) | ||||
−0.358400 | + | 0.933568i | \(0.616678\pi\) | |||||||
\(174\) | −11.3827 | −0.862924 | ||||||||
\(175\) | −3.17432 | −0.239956 | ||||||||
\(176\) | 0.460493 | 0.0347110 | ||||||||
\(177\) | 5.83490 | 0.438578 | ||||||||
\(178\) | −29.7975 | −2.23342 | ||||||||
\(179\) | 4.43582 | 0.331549 | 0.165774 | − | 0.986164i | \(-0.446988\pi\) | ||||
0.165774 | + | 0.986164i | \(0.446988\pi\) | |||||||
\(180\) | −7.14693 | −0.532701 | ||||||||
\(181\) | −9.38468 | −0.697557 | −0.348779 | − | 0.937205i | \(-0.613404\pi\) | ||||
−0.348779 | + | 0.937205i | \(0.613404\pi\) | |||||||
\(182\) | 0.767205 | 0.0568690 | ||||||||
\(183\) | 4.89242 | 0.361658 | ||||||||
\(184\) | 14.0772 | 1.03778 | ||||||||
\(185\) | 6.54343 | 0.481082 | ||||||||
\(186\) | 5.47003 | 0.401082 | ||||||||
\(187\) | 6.41831 | 0.469353 | ||||||||
\(188\) | 7.92979 | 0.578340 | ||||||||
\(189\) | 14.2007 | 1.03295 | ||||||||
\(190\) | 9.54181 | 0.692236 | ||||||||
\(191\) | 1.30115 | 0.0941478 | 0.0470739 | − | 0.998891i | \(-0.485010\pi\) | ||||
0.0470739 | + | 0.998891i | \(0.485010\pi\) | |||||||
\(192\) | −11.0450 | −0.797103 | ||||||||
\(193\) | −15.7852 | −1.13625 | −0.568123 | − | 0.822944i | \(-0.692330\pi\) | ||||
−0.568123 | + | 0.822944i | \(0.692330\pi\) | |||||||
\(194\) | −16.1790 | −1.16159 | ||||||||
\(195\) | 0.0903567 | 0.00647057 | ||||||||
\(196\) | 9.63078 | 0.687913 | ||||||||
\(197\) | 3.26661 | 0.232736 | 0.116368 | − | 0.993206i | \(-0.462875\pi\) | ||||
0.116368 | + | 0.993206i | \(0.462875\pi\) | |||||||
\(198\) | −5.17100 | −0.367487 | ||||||||
\(199\) | 4.37603 | 0.310208 | 0.155104 | − | 0.987898i | \(-0.450429\pi\) | ||||
0.155104 | + | 0.987898i | \(0.450429\pi\) | |||||||
\(200\) | −2.56093 | −0.181085 | ||||||||
\(201\) | −7.63905 | −0.538817 | ||||||||
\(202\) | 4.19275 | 0.295001 | ||||||||
\(203\) | −18.8377 | −1.32215 | ||||||||
\(204\) | −17.0151 | −1.19129 | ||||||||
\(205\) | −9.34825 | −0.652910 | ||||||||
\(206\) | −24.9371 | −1.73745 | ||||||||
\(207\) | 12.5490 | 0.872214 | ||||||||
\(208\) | −0.0491359 | −0.00340696 | ||||||||
\(209\) | 4.21256 | 0.291389 | ||||||||
\(210\) | 6.08864 | 0.420156 | ||||||||
\(211\) | −4.42716 | −0.304779 | −0.152389 | − | 0.988321i | \(-0.548697\pi\) | ||||
−0.152389 | + | 0.988321i | \(0.548697\pi\) | |||||||
\(212\) | 2.58074 | 0.177246 | ||||||||
\(213\) | 12.0692 | 0.826967 | ||||||||
\(214\) | 21.0186 | 1.43680 | ||||||||
\(215\) | −3.06128 | −0.208777 | ||||||||
\(216\) | 11.4566 | 0.779524 | ||||||||
\(217\) | 9.05256 | 0.614528 | ||||||||
\(218\) | 2.71637 | 0.183976 | ||||||||
\(219\) | −0.846807 | −0.0572219 | ||||||||
\(220\) | −3.13061 | −0.211066 | ||||||||
\(221\) | −0.684851 | −0.0460681 | ||||||||
\(222\) | −12.5509 | −0.842360 | ||||||||
\(223\) | −25.3843 | −1.69986 | −0.849928 | − | 0.526899i | \(-0.823355\pi\) | ||||
−0.849928 | + | 0.526899i | \(0.823355\pi\) | |||||||
\(224\) | −19.5695 | −1.30754 | ||||||||
\(225\) | −2.28292 | −0.152195 | ||||||||
\(226\) | −21.8592 | −1.45405 | ||||||||
\(227\) | −0.216301 | −0.0143564 | −0.00717819 | − | 0.999974i | \(-0.502285\pi\) | ||||
−0.00717819 | + | 0.999974i | \(0.502285\pi\) | |||||||
\(228\) | −11.1676 | −0.739593 | ||||||||
\(229\) | −3.28796 | −0.217275 | −0.108637 | − | 0.994081i | \(-0.534649\pi\) | ||||
−0.108637 | + | 0.994081i | \(0.534649\pi\) | |||||||
\(230\) | 12.4509 | 0.820991 | ||||||||
\(231\) | 2.68804 | 0.176860 | ||||||||
\(232\) | −15.1976 | −0.997774 | ||||||||
\(233\) | −13.3046 | −0.871614 | −0.435807 | − | 0.900040i | \(-0.643537\pi\) | ||||
−0.435807 | + | 0.900040i | \(0.643537\pi\) | |||||||
\(234\) | 0.551760 | 0.0360697 | ||||||||
\(235\) | 2.53298 | 0.165234 | ||||||||
\(236\) | 21.5714 | 1.40418 | ||||||||
\(237\) | 12.7827 | 0.830328 | ||||||||
\(238\) | −46.1483 | −2.99135 | ||||||||
\(239\) | 23.6381 | 1.52902 | 0.764509 | − | 0.644613i | \(-0.222981\pi\) | ||||
0.764509 | + | 0.644613i | \(0.222981\pi\) | |||||||
\(240\) | −0.389949 | −0.0251711 | ||||||||
\(241\) | −10.5637 | −0.680467 | −0.340234 | − | 0.940341i | \(-0.610506\pi\) | ||||
−0.340234 | + | 0.940341i | \(0.610506\pi\) | |||||||
\(242\) | −2.26509 | −0.145605 | ||||||||
\(243\) | 16.0125 | 1.02720 | ||||||||
\(244\) | 18.0871 | 1.15791 | ||||||||
\(245\) | 3.07633 | 0.196539 | ||||||||
\(246\) | 17.9308 | 1.14323 | ||||||||
\(247\) | −0.449492 | −0.0286005 | ||||||||
\(248\) | 7.30329 | 0.463759 | ||||||||
\(249\) | −12.9726 | −0.822104 | ||||||||
\(250\) | −2.26509 | −0.143257 | ||||||||
\(251\) | −23.8074 | −1.50271 | −0.751356 | − | 0.659897i | \(-0.770600\pi\) | ||||
−0.751356 | + | 0.659897i | \(0.770600\pi\) | |||||||
\(252\) | 22.6867 | 1.42913 | ||||||||
\(253\) | 5.49690 | 0.345587 | ||||||||
\(254\) | −21.4974 | −1.34887 | ||||||||
\(255\) | −5.43507 | −0.340357 | ||||||||
\(256\) | −12.9047 | −0.806543 | ||||||||
\(257\) | −22.5855 | −1.40885 | −0.704423 | − | 0.709780i | \(-0.748794\pi\) | ||||
−0.704423 | + | 0.709780i | \(0.748794\pi\) | |||||||
\(258\) | 5.87180 | 0.365562 | ||||||||
\(259\) | −20.7709 | −1.29064 | ||||||||
\(260\) | 0.334045 | 0.0207166 | ||||||||
\(261\) | −13.5478 | −0.838587 | ||||||||
\(262\) | −32.7463 | −2.02307 | ||||||||
\(263\) | −21.1197 | −1.30230 | −0.651148 | − | 0.758951i | \(-0.725712\pi\) | ||||
−0.651148 | + | 0.758951i | \(0.725712\pi\) | |||||||
\(264\) | 2.16862 | 0.133469 | ||||||||
\(265\) | 0.824356 | 0.0506398 | ||||||||
\(266\) | −30.2888 | −1.85713 | ||||||||
\(267\) | 11.1399 | 0.681749 | ||||||||
\(268\) | −28.2413 | −1.72511 | ||||||||
\(269\) | 27.8043 | 1.69526 | 0.847628 | − | 0.530591i | \(-0.178030\pi\) | ||||
0.847628 | + | 0.530591i | \(0.178030\pi\) | |||||||
\(270\) | 10.1331 | 0.616682 | ||||||||
\(271\) | −6.10517 | −0.370863 | −0.185431 | − | 0.982657i | \(-0.559368\pi\) | ||||
−0.185431 | + | 0.982657i | \(0.559368\pi\) | |||||||
\(272\) | 2.95559 | 0.179209 | ||||||||
\(273\) | −0.286821 | −0.0173592 | ||||||||
\(274\) | −40.3072 | −2.43505 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −14.5724 | −0.877156 | ||||||||
\(277\) | −19.2588 | −1.15715 | −0.578575 | − | 0.815629i | \(-0.696391\pi\) | ||||
−0.578575 | + | 0.815629i | \(0.696391\pi\) | |||||||
\(278\) | 0.201250 | 0.0120702 | ||||||||
\(279\) | 6.51044 | 0.389770 | ||||||||
\(280\) | 8.12923 | 0.485814 | ||||||||
\(281\) | 13.1655 | 0.785387 | 0.392694 | − | 0.919669i | \(-0.371543\pi\) | ||||
0.392694 | + | 0.919669i | \(0.371543\pi\) | |||||||
\(282\) | −4.85849 | −0.289319 | ||||||||
\(283\) | −27.1971 | −1.61670 | −0.808351 | − | 0.588701i | \(-0.799640\pi\) | ||||
−0.808351 | + | 0.588701i | \(0.799640\pi\) | |||||||
\(284\) | 44.6193 | 2.64767 | ||||||||
\(285\) | −3.56723 | −0.211304 | ||||||||
\(286\) | 0.241691 | 0.0142915 | ||||||||
\(287\) | 29.6744 | 1.75162 | ||||||||
\(288\) | −14.0740 | −0.829319 | ||||||||
\(289\) | 24.1946 | 1.42321 | ||||||||
\(290\) | −13.4420 | −0.789339 | ||||||||
\(291\) | 6.04857 | 0.354574 | ||||||||
\(292\) | −3.13061 | −0.183205 | ||||||||
\(293\) | 28.9691 | 1.69239 | 0.846197 | − | 0.532871i | \(-0.178887\pi\) | ||||
0.846197 | + | 0.532871i | \(0.178887\pi\) | |||||||
\(294\) | −5.90067 | −0.344134 | ||||||||
\(295\) | 6.89047 | 0.401179 | ||||||||
\(296\) | −16.7573 | −0.973996 | ||||||||
\(297\) | 4.47361 | 0.259585 | ||||||||
\(298\) | −29.3604 | −1.70080 | ||||||||
\(299\) | −0.586534 | −0.0339202 | ||||||||
\(300\) | 2.65102 | 0.153057 | ||||||||
\(301\) | 9.71748 | 0.560106 | ||||||||
\(302\) | 26.5263 | 1.52642 | ||||||||
\(303\) | −1.56747 | −0.0900487 | ||||||||
\(304\) | 1.93986 | 0.111258 | ||||||||
\(305\) | 5.77749 | 0.330818 | ||||||||
\(306\) | −33.1891 | −1.89729 | ||||||||
\(307\) | 11.9936 | 0.684509 | 0.342255 | − | 0.939607i | \(-0.388809\pi\) | ||||
0.342255 | + | 0.939607i | \(0.388809\pi\) | |||||||
\(308\) | 9.93757 | 0.566246 | ||||||||
\(309\) | 9.32280 | 0.530355 | ||||||||
\(310\) | 6.45959 | 0.366880 | ||||||||
\(311\) | 16.6020 | 0.941415 | 0.470707 | − | 0.882289i | \(-0.343999\pi\) | ||||
0.470707 | + | 0.882289i | \(0.343999\pi\) | |||||||
\(312\) | −0.231397 | −0.0131003 | ||||||||
\(313\) | −32.0017 | −1.80884 | −0.904421 | − | 0.426640i | \(-0.859697\pi\) | ||||
−0.904421 | + | 0.426640i | \(0.859697\pi\) | |||||||
\(314\) | −38.9548 | −2.19834 | ||||||||
\(315\) | 7.24672 | 0.408306 | ||||||||
\(316\) | 47.2572 | 2.65843 | ||||||||
\(317\) | 9.38752 | 0.527256 | 0.263628 | − | 0.964624i | \(-0.415081\pi\) | ||||
0.263628 | + | 0.964624i | \(0.415081\pi\) | |||||||
\(318\) | −1.58119 | −0.0886687 | ||||||||
\(319\) | −5.93442 | −0.332263 | ||||||||
\(320\) | −13.0431 | −0.729131 | ||||||||
\(321\) | −7.85786 | −0.438583 | ||||||||
\(322\) | −39.5233 | −2.20255 | ||||||||
\(323\) | 27.0375 | 1.50441 | ||||||||
\(324\) | 9.58113 | 0.532285 | ||||||||
\(325\) | 0.106703 | 0.00591880 | ||||||||
\(326\) | 10.2151 | 0.565765 | ||||||||
\(327\) | −1.01552 | −0.0561584 | ||||||||
\(328\) | 23.9402 | 1.32188 | ||||||||
\(329\) | −8.04051 | −0.443288 | ||||||||
\(330\) | 1.91809 | 0.105587 | ||||||||
\(331\) | −19.1415 | −1.05211 | −0.526056 | − | 0.850450i | \(-0.676330\pi\) | ||||
−0.526056 | + | 0.850450i | \(0.676330\pi\) | |||||||
\(332\) | −47.9591 | −2.63210 | ||||||||
\(333\) | −14.9381 | −0.818603 | ||||||||
\(334\) | 42.1346 | 2.30550 | ||||||||
\(335\) | −9.02101 | −0.492870 | ||||||||
\(336\) | 1.23782 | 0.0675289 | ||||||||
\(337\) | 19.4662 | 1.06039 | 0.530197 | − | 0.847874i | \(-0.322118\pi\) | ||||
0.530197 | + | 0.847874i | \(0.322118\pi\) | |||||||
\(338\) | 29.4203 | 1.60025 | ||||||||
\(339\) | 8.17212 | 0.443848 | ||||||||
\(340\) | −20.0932 | −1.08971 | ||||||||
\(341\) | 2.85181 | 0.154434 | ||||||||
\(342\) | −21.7832 | −1.17790 | ||||||||
\(343\) | 12.4550 | 0.672507 | ||||||||
\(344\) | 7.83972 | 0.422689 | ||||||||
\(345\) | −4.65481 | −0.250607 | ||||||||
\(346\) | 21.3553 | 1.14807 | ||||||||
\(347\) | 1.02228 | 0.0548789 | 0.0274395 | − | 0.999623i | \(-0.491265\pi\) | ||||
0.0274395 | + | 0.999623i | \(0.491265\pi\) | |||||||
\(348\) | 15.7323 | 0.843339 | ||||||||
\(349\) | 13.4592 | 0.720454 | 0.360227 | − | 0.932865i | \(-0.382699\pi\) | ||||
0.360227 | + | 0.932865i | \(0.382699\pi\) | |||||||
\(350\) | 7.19011 | 0.384328 | ||||||||
\(351\) | −0.477347 | −0.0254789 | ||||||||
\(352\) | −6.16492 | −0.328591 | ||||||||
\(353\) | 16.1934 | 0.861885 | 0.430943 | − | 0.902379i | \(-0.358181\pi\) | ||||
0.430943 | + | 0.902379i | \(0.358181\pi\) | |||||||
\(354\) | −13.2165 | −0.702451 | ||||||||
\(355\) | 14.2526 | 0.756449 | ||||||||
\(356\) | 41.1837 | 2.18273 | ||||||||
\(357\) | 17.2527 | 0.913107 | ||||||||
\(358\) | −10.0475 | −0.531027 | ||||||||
\(359\) | −11.1725 | −0.589664 | −0.294832 | − | 0.955549i | \(-0.595264\pi\) | ||||
−0.294832 | + | 0.955549i | \(0.595264\pi\) | |||||||
\(360\) | 5.84640 | 0.308132 | ||||||||
\(361\) | −1.25431 | −0.0660166 | ||||||||
\(362\) | 21.2571 | 1.11725 | ||||||||
\(363\) | 0.846807 | 0.0444458 | ||||||||
\(364\) | −1.06037 | −0.0555783 | ||||||||
\(365\) | −1.00000 | −0.0523424 | ||||||||
\(366\) | −11.0818 | −0.579253 | ||||||||
\(367\) | 28.1766 | 1.47081 | 0.735404 | − | 0.677629i | \(-0.236993\pi\) | ||||
0.735404 | + | 0.677629i | \(0.236993\pi\) | |||||||
\(368\) | 2.53129 | 0.131952 | ||||||||
\(369\) | 21.3413 | 1.11098 | ||||||||
\(370\) | −14.8214 | −0.770529 | ||||||||
\(371\) | −2.61677 | −0.135856 | ||||||||
\(372\) | −7.56021 | −0.391979 | ||||||||
\(373\) | 16.5111 | 0.854912 | 0.427456 | − | 0.904036i | \(-0.359410\pi\) | ||||
0.427456 | + | 0.904036i | \(0.359410\pi\) | |||||||
\(374\) | −14.5380 | −0.751743 | ||||||||
\(375\) | 0.846807 | 0.0437289 | ||||||||
\(376\) | −6.48680 | −0.334531 | ||||||||
\(377\) | 0.633218 | 0.0326124 | ||||||||
\(378\) | −32.1658 | −1.65443 | ||||||||
\(379\) | 29.4953 | 1.51507 | 0.757537 | − | 0.652792i | \(-0.226403\pi\) | ||||
0.757537 | + | 0.652792i | \(0.226403\pi\) | |||||||
\(380\) | −13.1879 | −0.676525 | ||||||||
\(381\) | 8.03684 | 0.411740 | ||||||||
\(382\) | −2.94721 | −0.150793 | ||||||||
\(383\) | 24.2535 | 1.23929 | 0.619647 | − | 0.784880i | \(-0.287276\pi\) | ||||
0.619647 | + | 0.784880i | \(0.287276\pi\) | |||||||
\(384\) | 14.5768 | 0.743870 | ||||||||
\(385\) | 3.17432 | 0.161778 | ||||||||
\(386\) | 35.7549 | 1.81988 | ||||||||
\(387\) | 6.98864 | 0.355253 | ||||||||
\(388\) | 22.3613 | 1.13522 | ||||||||
\(389\) | 19.6390 | 0.995736 | 0.497868 | − | 0.867253i | \(-0.334116\pi\) | ||||
0.497868 | + | 0.867253i | \(0.334116\pi\) | |||||||
\(390\) | −0.204666 | −0.0103636 | ||||||||
\(391\) | 35.2808 | 1.78423 | ||||||||
\(392\) | −7.87826 | −0.397912 | ||||||||
\(393\) | 12.2423 | 0.617540 | ||||||||
\(394\) | −7.39914 | −0.372763 | ||||||||
\(395\) | 15.0952 | 0.759523 | ||||||||
\(396\) | 7.14693 | 0.359147 | ||||||||
\(397\) | −5.46015 | −0.274037 | −0.137019 | − | 0.990568i | \(-0.543752\pi\) | ||||
−0.137019 | + | 0.990568i | \(0.543752\pi\) | |||||||
\(398\) | −9.91208 | −0.496848 | ||||||||
\(399\) | 11.3235 | 0.566886 | ||||||||
\(400\) | −0.460493 | −0.0230247 | ||||||||
\(401\) | −30.1486 | −1.50555 | −0.752776 | − | 0.658277i | \(-0.771285\pi\) | ||||
−0.752776 | + | 0.658277i | \(0.771285\pi\) | |||||||
\(402\) | 17.3031 | 0.863001 | ||||||||
\(403\) | −0.304296 | −0.0151581 | ||||||||
\(404\) | −5.79487 | −0.288305 | ||||||||
\(405\) | 3.06047 | 0.152076 | ||||||||
\(406\) | 42.6691 | 2.11763 | ||||||||
\(407\) | −6.54343 | −0.324346 | ||||||||
\(408\) | 13.9188 | 0.689085 | ||||||||
\(409\) | −26.7960 | −1.32498 | −0.662489 | − | 0.749072i | \(-0.730500\pi\) | ||||
−0.662489 | + | 0.749072i | \(0.730500\pi\) | |||||||
\(410\) | 21.1746 | 1.04574 | ||||||||
\(411\) | 15.0689 | 0.743296 | ||||||||
\(412\) | 34.4660 | 1.69802 | ||||||||
\(413\) | −21.8726 | −1.07628 | ||||||||
\(414\) | −28.4245 | −1.39699 | ||||||||
\(415\) | −15.3194 | −0.752000 | ||||||||
\(416\) | 0.657814 | 0.0322520 | ||||||||
\(417\) | −0.0752377 | −0.00368441 | ||||||||
\(418\) | −9.54181 | −0.466705 | ||||||||
\(419\) | 7.95612 | 0.388682 | 0.194341 | − | 0.980934i | \(-0.437743\pi\) | ||||
0.194341 | + | 0.980934i | \(0.437743\pi\) | |||||||
\(420\) | −8.41521 | −0.410620 | ||||||||
\(421\) | 6.16353 | 0.300392 | 0.150196 | − | 0.988656i | \(-0.452010\pi\) | ||||
0.150196 | + | 0.988656i | \(0.452010\pi\) | |||||||
\(422\) | 10.0279 | 0.488151 | ||||||||
\(423\) | −5.78260 | −0.281159 | ||||||||
\(424\) | −2.11112 | −0.102525 | ||||||||
\(425\) | −6.41831 | −0.311334 | ||||||||
\(426\) | −27.3377 | −1.32452 | ||||||||
\(427\) | −18.3396 | −0.887517 | ||||||||
\(428\) | −29.0502 | −1.40419 | ||||||||
\(429\) | −0.0903567 | −0.00436246 | ||||||||
\(430\) | 6.93405 | 0.334390 | ||||||||
\(431\) | −3.80907 | −0.183477 | −0.0917383 | − | 0.995783i | \(-0.529242\pi\) | ||||
−0.0917383 | + | 0.995783i | \(0.529242\pi\) | |||||||
\(432\) | 2.06007 | 0.0991151 | ||||||||
\(433\) | −29.1987 | −1.40320 | −0.701600 | − | 0.712571i | \(-0.747531\pi\) | ||||
−0.701600 | + | 0.712571i | \(0.747531\pi\) | |||||||
\(434\) | −20.5048 | −0.984263 | ||||||||
\(435\) | 5.02530 | 0.240945 | ||||||||
\(436\) | −3.75434 | −0.179800 | ||||||||
\(437\) | 23.1560 | 1.10770 | ||||||||
\(438\) | 1.91809 | 0.0916499 | ||||||||
\(439\) | −0.821251 | −0.0391962 | −0.0195981 | − | 0.999808i | \(-0.506239\pi\) | ||||
−0.0195981 | + | 0.999808i | \(0.506239\pi\) | |||||||
\(440\) | 2.56093 | 0.122088 | ||||||||
\(441\) | −7.02300 | −0.334428 | ||||||||
\(442\) | 1.55125 | 0.0737852 | ||||||||
\(443\) | −10.6512 | −0.506053 | −0.253026 | − | 0.967459i | \(-0.581426\pi\) | ||||
−0.253026 | + | 0.967459i | \(0.581426\pi\) | |||||||
\(444\) | 17.3468 | 0.823242 | ||||||||
\(445\) | 13.1552 | 0.623614 | ||||||||
\(446\) | 57.4975 | 2.72259 | ||||||||
\(447\) | 10.9765 | 0.519169 | ||||||||
\(448\) | 41.4030 | 1.95611 | ||||||||
\(449\) | −2.51675 | −0.118773 | −0.0593864 | − | 0.998235i | \(-0.518914\pi\) | ||||
−0.0593864 | + | 0.998235i | \(0.518914\pi\) | |||||||
\(450\) | 5.17100 | 0.243763 | ||||||||
\(451\) | 9.34825 | 0.440192 | ||||||||
\(452\) | 30.2120 | 1.42105 | ||||||||
\(453\) | −9.91693 | −0.465938 | ||||||||
\(454\) | 0.489940 | 0.0229940 | ||||||||
\(455\) | −0.338709 | −0.0158789 | ||||||||
\(456\) | 9.13543 | 0.427806 | ||||||||
\(457\) | −18.8119 | −0.879985 | −0.439993 | − | 0.898001i | \(-0.645019\pi\) | ||||
−0.439993 | + | 0.898001i | \(0.645019\pi\) | |||||||
\(458\) | 7.44752 | 0.348000 | ||||||||
\(459\) | 28.7130 | 1.34021 | ||||||||
\(460\) | −17.2087 | −0.802358 | ||||||||
\(461\) | 36.5827 | 1.70383 | 0.851914 | − | 0.523682i | \(-0.175442\pi\) | ||||
0.851914 | + | 0.523682i | \(0.175442\pi\) | |||||||
\(462\) | −6.08864 | −0.283269 | ||||||||
\(463\) | 1.05788 | 0.0491641 | 0.0245820 | − | 0.999698i | \(-0.492175\pi\) | ||||
0.0245820 | + | 0.999698i | \(0.492175\pi\) | |||||||
\(464\) | −2.73276 | −0.126865 | ||||||||
\(465\) | −2.41493 | −0.111990 | ||||||||
\(466\) | 30.1361 | 1.39603 | ||||||||
\(467\) | −1.23362 | −0.0570851 | −0.0285426 | − | 0.999593i | \(-0.509087\pi\) | ||||
−0.0285426 | + | 0.999593i | \(0.509087\pi\) | |||||||
\(468\) | −0.762597 | −0.0352511 | ||||||||
\(469\) | 28.6356 | 1.32227 | ||||||||
\(470\) | −5.73743 | −0.264648 | ||||||||
\(471\) | 14.5633 | 0.671042 | ||||||||
\(472\) | −17.6460 | −0.812224 | ||||||||
\(473\) | 3.06128 | 0.140758 | ||||||||
\(474\) | −28.9540 | −1.32990 | ||||||||
\(475\) | −4.21256 | −0.193286 | ||||||||
\(476\) | 63.7824 | 2.92346 | ||||||||
\(477\) | −1.88194 | −0.0861680 | ||||||||
\(478\) | −53.5422 | −2.44896 | ||||||||
\(479\) | 7.11688 | 0.325179 | 0.162589 | − | 0.986694i | \(-0.448015\pi\) | ||||
0.162589 | + | 0.986694i | \(0.448015\pi\) | |||||||
\(480\) | 5.22050 | 0.238282 | ||||||||
\(481\) | 0.698201 | 0.0318352 | ||||||||
\(482\) | 23.9277 | 1.08988 | ||||||||
\(483\) | 14.7759 | 0.672326 | ||||||||
\(484\) | 3.13061 | 0.142301 | ||||||||
\(485\) | 7.14280 | 0.324338 | ||||||||
\(486\) | −36.2696 | −1.64522 | ||||||||
\(487\) | −39.5101 | −1.79037 | −0.895186 | − | 0.445693i | \(-0.852957\pi\) | ||||
−0.895186 | + | 0.445693i | \(0.852957\pi\) | |||||||
\(488\) | −14.7958 | −0.669773 | ||||||||
\(489\) | −3.81895 | −0.172699 | ||||||||
\(490\) | −6.96814 | −0.314788 | ||||||||
\(491\) | 37.1038 | 1.67447 | 0.837235 | − | 0.546844i | \(-0.184171\pi\) | ||||
0.837235 | + | 0.546844i | \(0.184171\pi\) | |||||||
\(492\) | −24.7824 | −1.11728 | ||||||||
\(493\) | −38.0889 | −1.71544 | ||||||||
\(494\) | 1.01814 | 0.0458082 | ||||||||
\(495\) | 2.28292 | 0.102610 | ||||||||
\(496\) | 1.31324 | 0.0589662 | ||||||||
\(497\) | −45.2423 | −2.02939 | ||||||||
\(498\) | 29.3840 | 1.31673 | ||||||||
\(499\) | −21.6772 | −0.970404 | −0.485202 | − | 0.874402i | \(-0.661254\pi\) | ||||
−0.485202 | + | 0.874402i | \(0.661254\pi\) | |||||||
\(500\) | 3.13061 | 0.140005 | ||||||||
\(501\) | −15.7521 | −0.703752 | ||||||||
\(502\) | 53.9259 | 2.40683 | ||||||||
\(503\) | 7.26725 | 0.324031 | 0.162015 | − | 0.986788i | \(-0.448201\pi\) | ||||
0.162015 | + | 0.986788i | \(0.448201\pi\) | |||||||
\(504\) | −18.5584 | −0.826655 | ||||||||
\(505\) | −1.85103 | −0.0823699 | ||||||||
\(506\) | −12.4509 | −0.553512 | ||||||||
\(507\) | −10.9989 | −0.488476 | ||||||||
\(508\) | 29.7119 | 1.31825 | ||||||||
\(509\) | 26.1909 | 1.16089 | 0.580446 | − | 0.814299i | \(-0.302878\pi\) | ||||
0.580446 | + | 0.814299i | \(0.302878\pi\) | |||||||
\(510\) | 12.3109 | 0.545135 | ||||||||
\(511\) | 3.17432 | 0.140424 | ||||||||
\(512\) | −5.19749 | −0.229699 | ||||||||
\(513\) | 18.8454 | 0.832044 | ||||||||
\(514\) | 51.1582 | 2.25649 | ||||||||
\(515\) | 11.0094 | 0.485130 | ||||||||
\(516\) | −8.11552 | −0.357266 | ||||||||
\(517\) | −2.53298 | −0.111401 | ||||||||
\(518\) | 47.0480 | 2.06717 | ||||||||
\(519\) | −7.98373 | −0.350447 | ||||||||
\(520\) | −0.273259 | −0.0119832 | ||||||||
\(521\) | 16.2995 | 0.714095 | 0.357047 | − | 0.934086i | \(-0.383783\pi\) | ||||
0.357047 | + | 0.934086i | \(0.383783\pi\) | |||||||
\(522\) | 30.6869 | 1.34313 | ||||||||
\(523\) | 39.0185 | 1.70616 | 0.853079 | − | 0.521781i | \(-0.174732\pi\) | ||||
0.853079 | + | 0.521781i | \(0.174732\pi\) | |||||||
\(524\) | 45.2591 | 1.97715 | ||||||||
\(525\) | −2.68804 | −0.117316 | ||||||||
\(526\) | 47.8379 | 2.08583 | ||||||||
\(527\) | 18.3038 | 0.797325 | ||||||||
\(528\) | 0.389949 | 0.0169704 | ||||||||
\(529\) | 7.21590 | 0.313735 | ||||||||
\(530\) | −1.86724 | −0.0811076 | ||||||||
\(531\) | −15.7304 | −0.682640 | ||||||||
\(532\) | 41.8626 | 1.81498 | ||||||||
\(533\) | −0.997484 | −0.0432058 | ||||||||
\(534\) | −25.2328 | −1.09193 | ||||||||
\(535\) | −9.27940 | −0.401184 | ||||||||
\(536\) | 23.1022 | 0.997863 | ||||||||
\(537\) | 3.75628 | 0.162096 | ||||||||
\(538\) | −62.9790 | −2.71522 | ||||||||
\(539\) | −3.07633 | −0.132507 | ||||||||
\(540\) | −14.0051 | −0.602685 | ||||||||
\(541\) | 27.4700 | 1.18103 | 0.590514 | − | 0.807028i | \(-0.298925\pi\) | ||||
0.590514 | + | 0.807028i | \(0.298925\pi\) | |||||||
\(542\) | 13.8287 | 0.593995 | ||||||||
\(543\) | −7.94701 | −0.341039 | ||||||||
\(544\) | −39.5683 | −1.69648 | ||||||||
\(545\) | −1.19923 | −0.0513695 | ||||||||
\(546\) | 0.649674 | 0.0278035 | ||||||||
\(547\) | 7.64867 | 0.327034 | 0.163517 | − | 0.986541i | \(-0.447716\pi\) | ||||
0.163517 | + | 0.986541i | \(0.447716\pi\) | |||||||
\(548\) | 55.7093 | 2.37978 | ||||||||
\(549\) | −13.1895 | −0.562916 | ||||||||
\(550\) | 2.26509 | 0.0965836 | ||||||||
\(551\) | −24.9991 | −1.06500 | ||||||||
\(552\) | 11.9207 | 0.507377 | ||||||||
\(553\) | −47.9171 | −2.03764 | ||||||||
\(554\) | 43.6229 | 1.85336 | ||||||||
\(555\) | 5.54102 | 0.235203 | ||||||||
\(556\) | −0.278151 | −0.0117962 | ||||||||
\(557\) | −1.94096 | −0.0822411 | −0.0411206 | − | 0.999154i | \(-0.513093\pi\) | ||||
−0.0411206 | + | 0.999154i | \(0.513093\pi\) | |||||||
\(558\) | −14.7467 | −0.624278 | ||||||||
\(559\) | −0.326647 | −0.0138157 | ||||||||
\(560\) | 1.46175 | 0.0617704 | ||||||||
\(561\) | 5.43507 | 0.229469 | ||||||||
\(562\) | −29.8210 | −1.25792 | ||||||||
\(563\) | −24.0918 | −1.01535 | −0.507674 | − | 0.861549i | \(-0.669495\pi\) | ||||
−0.507674 | + | 0.861549i | \(0.669495\pi\) | |||||||
\(564\) | 6.71500 | 0.282753 | ||||||||
\(565\) | 9.65051 | 0.406000 | ||||||||
\(566\) | 61.6038 | 2.58940 | ||||||||
\(567\) | −9.71491 | −0.407988 | ||||||||
\(568\) | −36.4999 | −1.53150 | ||||||||
\(569\) | 28.1093 | 1.17840 | 0.589202 | − | 0.807986i | \(-0.299442\pi\) | ||||
0.589202 | + | 0.807986i | \(0.299442\pi\) | |||||||
\(570\) | 8.08008 | 0.338437 | ||||||||
\(571\) | 1.39775 | 0.0584940 | 0.0292470 | − | 0.999572i | \(-0.490689\pi\) | ||||
0.0292470 | + | 0.999572i | \(0.490689\pi\) | |||||||
\(572\) | −0.334045 | −0.0139671 | ||||||||
\(573\) | 1.10182 | 0.0460293 | ||||||||
\(574\) | −67.2150 | −2.80550 | ||||||||
\(575\) | −5.49690 | −0.229237 | ||||||||
\(576\) | 29.7763 | 1.24068 | ||||||||
\(577\) | −15.7186 | −0.654373 | −0.327187 | − | 0.944960i | \(-0.606101\pi\) | ||||
−0.327187 | + | 0.944960i | \(0.606101\pi\) | |||||||
\(578\) | −54.8029 | −2.27950 | ||||||||
\(579\) | −13.3670 | −0.555515 | ||||||||
\(580\) | 18.5783 | 0.771424 | ||||||||
\(581\) | 48.6288 | 2.01746 | ||||||||
\(582\) | −13.7005 | −0.567905 | ||||||||
\(583\) | −0.824356 | −0.0341414 | ||||||||
\(584\) | 2.56093 | 0.105972 | ||||||||
\(585\) | −0.243594 | −0.0100714 | ||||||||
\(586\) | −65.6175 | −2.71063 | ||||||||
\(587\) | 16.4309 | 0.678177 | 0.339089 | − | 0.940754i | \(-0.389881\pi\) | ||||
0.339089 | + | 0.940754i | \(0.389881\pi\) | |||||||
\(588\) | 8.15541 | 0.336324 | ||||||||
\(589\) | 12.0134 | 0.495004 | ||||||||
\(590\) | −15.6075 | −0.642551 | ||||||||
\(591\) | 2.76619 | 0.113786 | ||||||||
\(592\) | −3.01320 | −0.123842 | ||||||||
\(593\) | 46.1092 | 1.89348 | 0.946738 | − | 0.322004i | \(-0.104356\pi\) | ||||
0.946738 | + | 0.322004i | \(0.104356\pi\) | |||||||
\(594\) | −10.1331 | −0.415767 | ||||||||
\(595\) | 20.3738 | 0.835243 | ||||||||
\(596\) | 40.5795 | 1.66220 | ||||||||
\(597\) | 3.70565 | 0.151662 | ||||||||
\(598\) | 1.32855 | 0.0543285 | ||||||||
\(599\) | 15.4687 | 0.632034 | 0.316017 | − | 0.948753i | \(-0.397654\pi\) | ||||
0.316017 | + | 0.948753i | \(0.397654\pi\) | |||||||
\(600\) | −2.16862 | −0.0885334 | ||||||||
\(601\) | 39.6969 | 1.61927 | 0.809634 | − | 0.586935i | \(-0.199665\pi\) | ||||
0.809634 | + | 0.586935i | \(0.199665\pi\) | |||||||
\(602\) | −22.0109 | −0.897098 | ||||||||
\(603\) | 20.5942 | 0.838661 | ||||||||
\(604\) | −36.6625 | −1.49178 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 3.55045 | 0.144227 | ||||||||
\(607\) | 14.5226 | 0.589454 | 0.294727 | − | 0.955581i | \(-0.404771\pi\) | ||||
0.294727 | + | 0.955581i | \(0.404771\pi\) | |||||||
\(608\) | −25.9701 | −1.05323 | ||||||||
\(609\) | −15.9519 | −0.646405 | ||||||||
\(610\) | −13.0865 | −0.529858 | ||||||||
\(611\) | 0.270276 | 0.0109342 | ||||||||
\(612\) | 45.8712 | 1.85423 | ||||||||
\(613\) | −22.2083 | −0.896987 | −0.448493 | − | 0.893786i | \(-0.648039\pi\) | ||||
−0.448493 | + | 0.893786i | \(0.648039\pi\) | |||||||
\(614\) | −27.1665 | −1.09635 | ||||||||
\(615\) | −7.91617 | −0.319211 | ||||||||
\(616\) | −8.12923 | −0.327536 | ||||||||
\(617\) | 9.91147 | 0.399021 | 0.199510 | − | 0.979896i | \(-0.436065\pi\) | ||||
0.199510 | + | 0.979896i | \(0.436065\pi\) | |||||||
\(618\) | −21.1169 | −0.849447 | ||||||||
\(619\) | −3.68563 | −0.148138 | −0.0740691 | − | 0.997253i | \(-0.523599\pi\) | ||||
−0.0740691 | + | 0.997253i | \(0.523599\pi\) | |||||||
\(620\) | −8.92790 | −0.358553 | ||||||||
\(621\) | 24.5910 | 0.986803 | ||||||||
\(622\) | −37.6050 | −1.50782 | ||||||||
\(623\) | −41.7587 | −1.67303 | ||||||||
\(624\) | −0.0416086 | −0.00166568 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 72.4866 | 2.89715 | ||||||||
\(627\) | 3.56723 | 0.142461 | ||||||||
\(628\) | 53.8400 | 2.14845 | ||||||||
\(629\) | −41.9977 | −1.67456 | ||||||||
\(630\) | −16.4144 | −0.653967 | ||||||||
\(631\) | −26.2854 | −1.04640 | −0.523202 | − | 0.852209i | \(-0.675263\pi\) | ||||
−0.523202 | + | 0.852209i | \(0.675263\pi\) | |||||||
\(632\) | −38.6578 | −1.53773 | ||||||||
\(633\) | −3.74895 | −0.149008 | ||||||||
\(634\) | −21.2635 | −0.844483 | ||||||||
\(635\) | 9.49076 | 0.376629 | ||||||||
\(636\) | 2.18539 | 0.0866563 | ||||||||
\(637\) | 0.328252 | 0.0130058 | ||||||||
\(638\) | 13.4420 | 0.532172 | ||||||||
\(639\) | −32.5375 | −1.28716 | ||||||||
\(640\) | 17.2139 | 0.680438 | ||||||||
\(641\) | −35.0939 | −1.38612 | −0.693062 | − | 0.720878i | \(-0.743739\pi\) | ||||
−0.693062 | + | 0.720878i | \(0.743739\pi\) | |||||||
\(642\) | 17.7987 | 0.702460 | ||||||||
\(643\) | 34.6132 | 1.36501 | 0.682505 | − | 0.730881i | \(-0.260891\pi\) | ||||
0.682505 | + | 0.730881i | \(0.260891\pi\) | |||||||
\(644\) | 54.6258 | 2.15256 | ||||||||
\(645\) | −2.59231 | −0.102072 | ||||||||
\(646\) | −61.2423 | −2.40955 | ||||||||
\(647\) | −3.17606 | −0.124864 | −0.0624319 | − | 0.998049i | \(-0.519886\pi\) | ||||
−0.0624319 | + | 0.998049i | \(0.519886\pi\) | |||||||
\(648\) | −7.83765 | −0.307892 | ||||||||
\(649\) | −6.89047 | −0.270475 | ||||||||
\(650\) | −0.241691 | −0.00947989 | ||||||||
\(651\) | 7.66577 | 0.300445 | ||||||||
\(652\) | −14.1185 | −0.552924 | ||||||||
\(653\) | 26.0647 | 1.01999 | 0.509996 | − | 0.860177i | \(-0.329647\pi\) | ||||
0.509996 | + | 0.860177i | \(0.329647\pi\) | |||||||
\(654\) | 2.30024 | 0.0899465 | ||||||||
\(655\) | 14.4570 | 0.564880 | ||||||||
\(656\) | 4.30481 | 0.168075 | ||||||||
\(657\) | 2.28292 | 0.0890651 | ||||||||
\(658\) | 18.2124 | 0.709995 | ||||||||
\(659\) | −25.3185 | −0.986269 | −0.493135 | − | 0.869953i | \(-0.664149\pi\) | ||||
−0.493135 | + | 0.869953i | \(0.664149\pi\) | |||||||
\(660\) | −2.65102 | −0.103191 | ||||||||
\(661\) | −47.9428 | −1.86476 | −0.932379 | − | 0.361482i | \(-0.882271\pi\) | ||||
−0.932379 | + | 0.361482i | \(0.882271\pi\) | |||||||
\(662\) | 43.3572 | 1.68512 | ||||||||
\(663\) | −0.579937 | −0.0225229 | ||||||||
\(664\) | 39.2320 | 1.52250 | ||||||||
\(665\) | 13.3720 | 0.518545 | ||||||||
\(666\) | 33.8361 | 1.31112 | ||||||||
\(667\) | −32.6209 | −1.26309 | ||||||||
\(668\) | −58.2349 | −2.25318 | ||||||||
\(669\) | −21.4956 | −0.831067 | ||||||||
\(670\) | 20.4334 | 0.789409 | ||||||||
\(671\) | −5.77749 | −0.223038 | ||||||||
\(672\) | −16.5716 | −0.639261 | ||||||||
\(673\) | −47.4326 | −1.82839 | −0.914196 | − | 0.405273i | \(-0.867177\pi\) | ||||
−0.914196 | + | 0.405273i | \(0.867177\pi\) | |||||||
\(674\) | −44.0927 | −1.69839 | ||||||||
\(675\) | −4.47361 | −0.172189 | ||||||||
\(676\) | −40.6623 | −1.56393 | ||||||||
\(677\) | 36.7758 | 1.41341 | 0.706704 | − | 0.707510i | \(-0.250181\pi\) | ||||
0.706704 | + | 0.707510i | \(0.250181\pi\) | |||||||
\(678\) | −18.5105 | −0.710893 | ||||||||
\(679\) | −22.6735 | −0.870131 | ||||||||
\(680\) | 16.4368 | 0.630324 | ||||||||
\(681\) | −0.183165 | −0.00701890 | ||||||||
\(682\) | −6.45959 | −0.247350 | ||||||||
\(683\) | 27.1590 | 1.03921 | 0.519606 | − | 0.854406i | \(-0.326079\pi\) | ||||
0.519606 | + | 0.854406i | \(0.326079\pi\) | |||||||
\(684\) | 30.1069 | 1.15117 | ||||||||
\(685\) | 17.7950 | 0.679913 | ||||||||
\(686\) | −28.2117 | −1.07713 | ||||||||
\(687\) | −2.78427 | −0.106227 | ||||||||
\(688\) | 1.40970 | 0.0537442 | ||||||||
\(689\) | 0.0879611 | 0.00335105 | ||||||||
\(690\) | 10.5435 | 0.401386 | ||||||||
\(691\) | 16.3924 | 0.623598 | 0.311799 | − | 0.950148i | \(-0.399068\pi\) | ||||
0.311799 | + | 0.950148i | \(0.399068\pi\) | |||||||
\(692\) | −29.5155 | −1.12201 | ||||||||
\(693\) | −7.24672 | −0.275280 | ||||||||
\(694\) | −2.31555 | −0.0878972 | ||||||||
\(695\) | −0.0888487 | −0.00337022 | ||||||||
\(696\) | −12.8695 | −0.487816 | ||||||||
\(697\) | 59.9999 | 2.27266 | ||||||||
\(698\) | −30.4862 | −1.15392 | ||||||||
\(699\) | −11.2664 | −0.426136 | ||||||||
\(700\) | −9.93757 | −0.375605 | ||||||||
\(701\) | −17.4670 | −0.659718 | −0.329859 | − | 0.944030i | \(-0.607001\pi\) | ||||
−0.329859 | + | 0.944030i | \(0.607001\pi\) | |||||||
\(702\) | 1.08123 | 0.0408084 | ||||||||
\(703\) | −27.5646 | −1.03962 | ||||||||
\(704\) | 13.0431 | 0.491580 | ||||||||
\(705\) | 2.14495 | 0.0807835 | ||||||||
\(706\) | −36.6793 | −1.38044 | ||||||||
\(707\) | 5.87578 | 0.220981 | ||||||||
\(708\) | 18.2668 | 0.686509 | ||||||||
\(709\) | 16.4184 | 0.616606 | 0.308303 | − | 0.951288i | \(-0.400239\pi\) | ||||
0.308303 | + | 0.951288i | \(0.400239\pi\) | |||||||
\(710\) | −32.2833 | −1.21157 | ||||||||
\(711\) | −34.4611 | −1.29239 | ||||||||
\(712\) | −33.6894 | −1.26257 | ||||||||
\(713\) | 15.6761 | 0.587075 | ||||||||
\(714\) | −39.0787 | −1.46249 | ||||||||
\(715\) | −0.106703 | −0.00399046 | ||||||||
\(716\) | 13.8868 | 0.518975 | ||||||||
\(717\) | 20.0169 | 0.747544 | ||||||||
\(718\) | 25.3067 | 0.944439 | ||||||||
\(719\) | −17.2489 | −0.643275 | −0.321638 | − | 0.946863i | \(-0.604233\pi\) | ||||
−0.321638 | + | 0.946863i | \(0.604233\pi\) | |||||||
\(720\) | 1.05127 | 0.0391785 | ||||||||
\(721\) | −34.9472 | −1.30150 | ||||||||
\(722\) | 2.84113 | 0.105736 | ||||||||
\(723\) | −8.94541 | −0.332683 | ||||||||
\(724\) | −29.3798 | −1.09189 | ||||||||
\(725\) | 5.93442 | 0.220399 | ||||||||
\(726\) | −1.91809 | −0.0711870 | ||||||||
\(727\) | −18.3674 | −0.681210 | −0.340605 | − | 0.940206i | \(-0.610632\pi\) | ||||
−0.340605 | + | 0.940206i | \(0.610632\pi\) | |||||||
\(728\) | 0.867411 | 0.0321484 | ||||||||
\(729\) | 4.37807 | 0.162151 | ||||||||
\(730\) | 2.26509 | 0.0838346 | ||||||||
\(731\) | 19.6482 | 0.726715 | ||||||||
\(732\) | 15.3163 | 0.566106 | ||||||||
\(733\) | 31.1376 | 1.15009 | 0.575047 | − | 0.818120i | \(-0.304984\pi\) | ||||
0.575047 | + | 0.818120i | \(0.304984\pi\) | |||||||
\(734\) | −63.8225 | −2.35573 | ||||||||
\(735\) | 2.60505 | 0.0960889 | ||||||||
\(736\) | −33.8879 | −1.24913 | ||||||||
\(737\) | 9.02101 | 0.332293 | ||||||||
\(738\) | −48.3398 | −1.77941 | ||||||||
\(739\) | −29.5518 | −1.08708 | −0.543541 | − | 0.839383i | \(-0.682917\pi\) | ||||
−0.543541 | + | 0.839383i | \(0.682917\pi\) | |||||||
\(740\) | 20.4849 | 0.753041 | ||||||||
\(741\) | −0.380633 | −0.0139829 | ||||||||
\(742\) | 5.92721 | 0.217595 | ||||||||
\(743\) | 19.6679 | 0.721547 | 0.360773 | − | 0.932653i | \(-0.382513\pi\) | ||||
0.360773 | + | 0.932653i | \(0.382513\pi\) | |||||||
\(744\) | 6.18448 | 0.226734 | ||||||||
\(745\) | 12.9622 | 0.474897 | ||||||||
\(746\) | −37.3990 | −1.36928 | ||||||||
\(747\) | 34.9730 | 1.27959 | ||||||||
\(748\) | 20.0932 | 0.734681 | ||||||||
\(749\) | 29.4558 | 1.07629 | ||||||||
\(750\) | −1.91809 | −0.0700388 | ||||||||
\(751\) | 25.5937 | 0.933928 | 0.466964 | − | 0.884276i | \(-0.345348\pi\) | ||||
0.466964 | + | 0.884276i | \(0.345348\pi\) | |||||||
\(752\) | −1.16642 | −0.0425351 | ||||||||
\(753\) | −20.1603 | −0.734682 | ||||||||
\(754\) | −1.43429 | −0.0522339 | ||||||||
\(755\) | −11.7110 | −0.426206 | ||||||||
\(756\) | 44.4568 | 1.61688 | ||||||||
\(757\) | −52.4842 | −1.90757 | −0.953785 | − | 0.300491i | \(-0.902849\pi\) | ||||
−0.953785 | + | 0.300491i | \(0.902849\pi\) | |||||||
\(758\) | −66.8095 | −2.42663 | ||||||||
\(759\) | 4.65481 | 0.168959 | ||||||||
\(760\) | 10.7881 | 0.391325 | ||||||||
\(761\) | 33.1709 | 1.20244 | 0.601222 | − | 0.799082i | \(-0.294681\pi\) | ||||
0.601222 | + | 0.799082i | \(0.294681\pi\) | |||||||
\(762\) | −18.2041 | −0.659466 | ||||||||
\(763\) | 3.80676 | 0.137814 | ||||||||
\(764\) | 4.07339 | 0.147370 | ||||||||
\(765\) | 14.6525 | 0.529761 | ||||||||
\(766\) | −54.9362 | −1.98492 | ||||||||
\(767\) | 0.735232 | 0.0265477 | ||||||||
\(768\) | −10.9278 | −0.394323 | ||||||||
\(769\) | −16.9060 | −0.609646 | −0.304823 | − | 0.952409i | \(-0.598597\pi\) | ||||
−0.304823 | + | 0.952409i | \(0.598597\pi\) | |||||||
\(770\) | −7.19011 | −0.259114 | ||||||||
\(771\) | −19.1256 | −0.688791 | ||||||||
\(772\) | −49.4174 | −1.77857 | ||||||||
\(773\) | 15.5282 | 0.558511 | 0.279255 | − | 0.960217i | \(-0.409912\pi\) | ||||
0.279255 | + | 0.960217i | \(0.409912\pi\) | |||||||
\(774\) | −15.8299 | −0.568993 | ||||||||
\(775\) | −2.85181 | −0.102440 | ||||||||
\(776\) | −18.2922 | −0.656652 | ||||||||
\(777\) | −17.5890 | −0.631001 | ||||||||
\(778\) | −44.4840 | −1.59483 | ||||||||
\(779\) | 39.3801 | 1.41094 | ||||||||
\(780\) | 0.282872 | 0.0101284 | ||||||||
\(781\) | −14.2526 | −0.509998 | ||||||||
\(782\) | −79.9140 | −2.85772 | ||||||||
\(783\) | −26.5483 | −0.948758 | ||||||||
\(784\) | −1.41663 | −0.0505938 | ||||||||
\(785\) | 17.1979 | 0.613820 | ||||||||
\(786\) | −27.7298 | −0.989088 | ||||||||
\(787\) | 33.7886 | 1.20443 | 0.602216 | − | 0.798333i | \(-0.294284\pi\) | ||||
0.602216 | + | 0.798333i | \(0.294284\pi\) | |||||||
\(788\) | 10.2265 | 0.364303 | ||||||||
\(789\) | −17.8843 | −0.636698 | ||||||||
\(790\) | −34.1919 | −1.21649 | ||||||||
\(791\) | −30.6338 | −1.08921 | ||||||||
\(792\) | −5.84640 | −0.207743 | ||||||||
\(793\) | 0.616475 | 0.0218917 | ||||||||
\(794\) | 12.3677 | 0.438913 | ||||||||
\(795\) | 0.698071 | 0.0247580 | ||||||||
\(796\) | 13.6996 | 0.485571 | ||||||||
\(797\) | 34.8460 | 1.23431 | 0.617154 | − | 0.786843i | \(-0.288286\pi\) | ||||
0.617154 | + | 0.786843i | \(0.288286\pi\) | |||||||
\(798\) | −25.6488 | −0.907957 | ||||||||
\(799\) | −16.2575 | −0.575148 | ||||||||
\(800\) | 6.16492 | 0.217963 | ||||||||
\(801\) | −30.0321 | −1.06113 | ||||||||
\(802\) | 68.2892 | 2.41138 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | −23.9149 | −0.843414 | ||||||||
\(805\) | 17.4489 | 0.614994 | ||||||||
\(806\) | 0.689256 | 0.0242780 | ||||||||
\(807\) | 23.5449 | 0.828818 | ||||||||
\(808\) | 4.74037 | 0.166766 | ||||||||
\(809\) | −3.17918 | −0.111774 | −0.0558870 | − | 0.998437i | \(-0.517799\pi\) | ||||
−0.0558870 | + | 0.998437i | \(0.517799\pi\) | |||||||
\(810\) | −6.93222 | −0.243573 | ||||||||
\(811\) | 27.1513 | 0.953411 | 0.476706 | − | 0.879063i | \(-0.341831\pi\) | ||||
0.476706 | + | 0.879063i | \(0.341831\pi\) | |||||||
\(812\) | −58.9737 | −2.06957 | ||||||||
\(813\) | −5.16990 | −0.181316 | ||||||||
\(814\) | 14.8214 | 0.519490 | ||||||||
\(815\) | −4.50983 | −0.157972 | ||||||||
\(816\) | 2.50281 | 0.0876160 | ||||||||
\(817\) | 12.8958 | 0.451167 | ||||||||
\(818\) | 60.6952 | 2.12216 | ||||||||
\(819\) | 0.773245 | 0.0270194 | ||||||||
\(820\) | −29.2657 | −1.02200 | ||||||||
\(821\) | −38.5388 | −1.34501 | −0.672507 | − | 0.740091i | \(-0.734783\pi\) | ||||
−0.672507 | + | 0.740091i | \(0.734783\pi\) | |||||||
\(822\) | −34.1325 | −1.19051 | ||||||||
\(823\) | 3.34786 | 0.116699 | 0.0583495 | − | 0.998296i | \(-0.481416\pi\) | ||||
0.0583495 | + | 0.998296i | \(0.481416\pi\) | |||||||
\(824\) | −28.1942 | −0.982191 | ||||||||
\(825\) | −0.846807 | −0.0294820 | ||||||||
\(826\) | 49.5433 | 1.72383 | ||||||||
\(827\) | −47.2016 | −1.64136 | −0.820681 | − | 0.571387i | \(-0.806406\pi\) | ||||
−0.820681 | + | 0.571387i | \(0.806406\pi\) | |||||||
\(828\) | 39.2859 | 1.36528 | ||||||||
\(829\) | 8.59558 | 0.298537 | 0.149268 | − | 0.988797i | \(-0.452308\pi\) | ||||
0.149268 | + | 0.988797i | \(0.452308\pi\) | |||||||
\(830\) | 34.6998 | 1.20445 | ||||||||
\(831\) | −16.3085 | −0.565736 | ||||||||
\(832\) | −1.39173 | −0.0482497 | ||||||||
\(833\) | −19.7448 | −0.684117 | ||||||||
\(834\) | 0.170420 | 0.00590115 | ||||||||
\(835\) | −18.6018 | −0.643740 | ||||||||
\(836\) | 13.1879 | 0.456113 | ||||||||
\(837\) | 12.7579 | 0.440977 | ||||||||
\(838\) | −18.0213 | −0.622535 | ||||||||
\(839\) | 16.5948 | 0.572915 | 0.286458 | − | 0.958093i | \(-0.407522\pi\) | ||||
0.286458 | + | 0.958093i | \(0.407522\pi\) | |||||||
\(840\) | 6.88389 | 0.237517 | ||||||||
\(841\) | 6.21728 | 0.214389 | ||||||||
\(842\) | −13.9609 | −0.481125 | ||||||||
\(843\) | 11.1486 | 0.383979 | ||||||||
\(844\) | −13.8597 | −0.477072 | ||||||||
\(845\) | −12.9886 | −0.446822 | ||||||||
\(846\) | 13.0981 | 0.450321 | ||||||||
\(847\) | −3.17432 | −0.109071 | ||||||||
\(848\) | −0.379611 | −0.0130359 | ||||||||
\(849\) | −23.0307 | −0.790413 | ||||||||
\(850\) | 14.5380 | 0.498650 | ||||||||
\(851\) | −35.9685 | −1.23299 | ||||||||
\(852\) | 37.7840 | 1.29446 | ||||||||
\(853\) | 38.7402 | 1.32644 | 0.663219 | − | 0.748425i | \(-0.269190\pi\) | ||||
0.663219 | + | 0.748425i | \(0.269190\pi\) | |||||||
\(854\) | 41.5408 | 1.42150 | ||||||||
\(855\) | 9.61693 | 0.328892 | ||||||||
\(856\) | 23.7639 | 0.812234 | ||||||||
\(857\) | −9.09153 | −0.310561 | −0.155280 | − | 0.987870i | \(-0.549628\pi\) | ||||
−0.155280 | + | 0.987870i | \(0.549628\pi\) | |||||||
\(858\) | 0.204666 | 0.00698717 | ||||||||
\(859\) | 38.9948 | 1.33048 | 0.665242 | − | 0.746628i | \(-0.268328\pi\) | ||||
0.665242 | + | 0.746628i | \(0.268328\pi\) | |||||||
\(860\) | −9.58366 | −0.326800 | ||||||||
\(861\) | 25.1285 | 0.856376 | ||||||||
\(862\) | 8.62787 | 0.293866 | ||||||||
\(863\) | −37.1356 | −1.26411 | −0.632055 | − | 0.774924i | \(-0.717788\pi\) | ||||
−0.632055 | + | 0.774924i | \(0.717788\pi\) | |||||||
\(864\) | −27.5795 | −0.938273 | ||||||||
\(865\) | −9.42803 | −0.320563 | ||||||||
\(866\) | 66.1375 | 2.24744 | ||||||||
\(867\) | 20.4882 | 0.695816 | ||||||||
\(868\) | 28.3400 | 0.961924 | ||||||||
\(869\) | −15.0952 | −0.512070 | ||||||||
\(870\) | −11.3827 | −0.385911 | ||||||||
\(871\) | −0.962566 | −0.0326153 | ||||||||
\(872\) | 3.07116 | 0.104003 | ||||||||
\(873\) | −16.3064 | −0.551889 | ||||||||
\(874\) | −52.4504 | −1.77416 | ||||||||
\(875\) | −3.17432 | −0.107312 | ||||||||
\(876\) | −2.65102 | −0.0895698 | ||||||||
\(877\) | 16.0179 | 0.540885 | 0.270442 | − | 0.962736i | \(-0.412830\pi\) | ||||
0.270442 | + | 0.962736i | \(0.412830\pi\) | |||||||
\(878\) | 1.86020 | 0.0627788 | ||||||||
\(879\) | 24.5312 | 0.827418 | ||||||||
\(880\) | 0.460493 | 0.0155232 | ||||||||
\(881\) | 43.1627 | 1.45419 | 0.727095 | − | 0.686537i | \(-0.240870\pi\) | ||||
0.727095 | + | 0.686537i | \(0.240870\pi\) | |||||||
\(882\) | 15.9077 | 0.535640 | ||||||||
\(883\) | 24.2300 | 0.815404 | 0.407702 | − | 0.913115i | \(-0.366330\pi\) | ||||
0.407702 | + | 0.913115i | \(0.366330\pi\) | |||||||
\(884\) | −2.14400 | −0.0721106 | ||||||||
\(885\) | 5.83490 | 0.196138 | ||||||||
\(886\) | 24.1258 | 0.810523 | ||||||||
\(887\) | −55.5713 | −1.86590 | −0.932951 | − | 0.360004i | \(-0.882775\pi\) | ||||
−0.932951 | + | 0.360004i | \(0.882775\pi\) | |||||||
\(888\) | −14.1902 | −0.476191 | ||||||||
\(889\) | −30.1267 | −1.01042 | ||||||||
\(890\) | −29.7975 | −0.998816 | ||||||||
\(891\) | −3.06047 | −0.102529 | ||||||||
\(892\) | −79.4683 | −2.66079 | ||||||||
\(893\) | −10.6704 | −0.357070 | ||||||||
\(894\) | −24.8626 | −0.831530 | ||||||||
\(895\) | 4.43582 | 0.148273 | ||||||||
\(896\) | −54.6424 | −1.82547 | ||||||||
\(897\) | −0.496681 | −0.0165837 | ||||||||
\(898\) | 5.70066 | 0.190233 | ||||||||
\(899\) | −16.9238 | −0.564441 | ||||||||
\(900\) | −7.14693 | −0.238231 | ||||||||
\(901\) | −5.29097 | −0.176268 | ||||||||
\(902\) | −21.1746 | −0.705037 | ||||||||
\(903\) | 8.22883 | 0.273838 | ||||||||
\(904\) | −24.7143 | −0.821985 | ||||||||
\(905\) | −9.38468 | −0.311957 | ||||||||
\(906\) | 22.4627 | 0.746273 | ||||||||
\(907\) | 19.3917 | 0.643890 | 0.321945 | − | 0.946758i | \(-0.395663\pi\) | ||||
0.321945 | + | 0.946758i | \(0.395663\pi\) | |||||||
\(908\) | −0.677154 | −0.0224721 | ||||||||
\(909\) | 4.22576 | 0.140159 | ||||||||
\(910\) | 0.767205 | 0.0254326 | ||||||||
\(911\) | −29.5602 | −0.979375 | −0.489687 | − | 0.871898i | \(-0.662889\pi\) | ||||
−0.489687 | + | 0.871898i | \(0.662889\pi\) | |||||||
\(912\) | 1.64269 | 0.0543947 | ||||||||
\(913\) | 15.3194 | 0.506999 | ||||||||
\(914\) | 42.6106 | 1.40943 | ||||||||
\(915\) | 4.89242 | 0.161739 | ||||||||
\(916\) | −10.2933 | −0.340102 | ||||||||
\(917\) | −45.8911 | −1.51546 | ||||||||
\(918\) | −65.0374 | −2.14655 | ||||||||
\(919\) | −3.75963 | −0.124019 | −0.0620095 | − | 0.998076i | \(-0.519751\pi\) | ||||
−0.0620095 | + | 0.998076i | \(0.519751\pi\) | |||||||
\(920\) | 14.0772 | 0.464111 | ||||||||
\(921\) | 10.1562 | 0.334659 | ||||||||
\(922\) | −82.8630 | −2.72895 | ||||||||
\(923\) | 1.52079 | 0.0500574 | ||||||||
\(924\) | 8.41521 | 0.276840 | ||||||||
\(925\) | 6.54343 | 0.215146 | ||||||||
\(926\) | −2.39620 | −0.0787440 | ||||||||
\(927\) | −25.1334 | −0.825490 | ||||||||
\(928\) | 36.5852 | 1.20097 | ||||||||
\(929\) | 49.2103 | 1.61454 | 0.807268 | − | 0.590185i | \(-0.200945\pi\) | ||||
0.807268 | + | 0.590185i | \(0.200945\pi\) | |||||||
\(930\) | 5.47003 | 0.179369 | ||||||||
\(931\) | −12.9592 | −0.424721 | ||||||||
\(932\) | −41.6516 | −1.36434 | ||||||||
\(933\) | 14.0587 | 0.460262 | ||||||||
\(934\) | 2.79426 | 0.0914308 | ||||||||
\(935\) | 6.41831 | 0.209901 | ||||||||
\(936\) | 0.623827 | 0.0203904 | ||||||||
\(937\) | 32.7620 | 1.07029 | 0.535144 | − | 0.844761i | \(-0.320257\pi\) | ||||
0.535144 | + | 0.844761i | \(0.320257\pi\) | |||||||
\(938\) | −64.8621 | −2.11782 | ||||||||
\(939\) | −27.0993 | −0.884351 | ||||||||
\(940\) | 7.92979 | 0.258641 | ||||||||
\(941\) | 54.8721 | 1.78878 | 0.894389 | − | 0.447289i | \(-0.147611\pi\) | ||||
0.894389 | + | 0.447289i | \(0.147611\pi\) | |||||||
\(942\) | −32.9872 | −1.07478 | ||||||||
\(943\) | 51.3864 | 1.67337 | ||||||||
\(944\) | −3.17302 | −0.103273 | ||||||||
\(945\) | 14.2007 | 0.461948 | ||||||||
\(946\) | −6.93405 | −0.225445 | ||||||||
\(947\) | 26.0152 | 0.845379 | 0.422690 | − | 0.906275i | \(-0.361086\pi\) | ||||
0.422690 | + | 0.906275i | \(0.361086\pi\) | |||||||
\(948\) | 40.0178 | 1.29972 | ||||||||
\(949\) | −0.106703 | −0.00346372 | ||||||||
\(950\) | 9.54181 | 0.309577 | ||||||||
\(951\) | 7.94942 | 0.257777 | ||||||||
\(952\) | −52.1759 | −1.69103 | ||||||||
\(953\) | −6.79895 | −0.220240 | −0.110120 | − | 0.993918i | \(-0.535123\pi\) | ||||
−0.110120 | + | 0.993918i | \(0.535123\pi\) | |||||||
\(954\) | 4.26275 | 0.138012 | ||||||||
\(955\) | 1.30115 | 0.0421042 | ||||||||
\(956\) | 74.0016 | 2.39338 | ||||||||
\(957\) | −5.02530 | −0.162445 | ||||||||
\(958\) | −16.1203 | −0.520825 | ||||||||
\(959\) | −56.4871 | −1.82406 | ||||||||
\(960\) | −11.0450 | −0.356475 | ||||||||
\(961\) | −22.8672 | −0.737651 | ||||||||
\(962\) | −1.58149 | −0.0509892 | ||||||||
\(963\) | 21.1841 | 0.682648 | ||||||||
\(964\) | −33.0708 | −1.06514 | ||||||||
\(965\) | −15.7852 | −0.508144 | ||||||||
\(966\) | −33.4686 | −1.07684 | ||||||||
\(967\) | 37.8667 | 1.21771 | 0.608856 | − | 0.793281i | \(-0.291629\pi\) | ||||
0.608856 | + | 0.793281i | \(0.291629\pi\) | |||||||
\(968\) | −2.56093 | −0.0823115 | ||||||||
\(969\) | 22.8956 | 0.735511 | ||||||||
\(970\) | −16.1790 | −0.519478 | ||||||||
\(971\) | −17.5825 | −0.564251 | −0.282125 | − | 0.959378i | \(-0.591039\pi\) | ||||
−0.282125 | + | 0.959378i | \(0.591039\pi\) | |||||||
\(972\) | 50.1288 | 1.60788 | ||||||||
\(973\) | 0.282034 | 0.00904161 | ||||||||
\(974\) | 89.4937 | 2.86756 | ||||||||
\(975\) | 0.0903567 | 0.00289373 | ||||||||
\(976\) | −2.66050 | −0.0851605 | ||||||||
\(977\) | −14.4533 | −0.462401 | −0.231201 | − | 0.972906i | \(-0.574265\pi\) | ||||
−0.231201 | + | 0.972906i | \(0.574265\pi\) | |||||||
\(978\) | 8.65026 | 0.276605 | ||||||||
\(979\) | −13.1552 | −0.420440 | ||||||||
\(980\) | 9.63078 | 0.307644 | ||||||||
\(981\) | 2.73775 | 0.0874097 | ||||||||
\(982\) | −84.0432 | −2.68193 | ||||||||
\(983\) | 16.9165 | 0.539554 | 0.269777 | − | 0.962923i | \(-0.413050\pi\) | ||||
0.269777 | + | 0.962923i | \(0.413050\pi\) | |||||||
\(984\) | 20.2728 | 0.646272 | ||||||||
\(985\) | 3.26661 | 0.104083 | ||||||||
\(986\) | 86.2746 | 2.74754 | ||||||||
\(987\) | −6.80876 | −0.216725 | ||||||||
\(988\) | −1.40719 | −0.0447685 | ||||||||
\(989\) | 16.8275 | 0.535084 | ||||||||
\(990\) | −5.17100 | −0.164345 | ||||||||
\(991\) | −29.9769 | −0.952248 | −0.476124 | − | 0.879378i | \(-0.657959\pi\) | ||||
−0.476124 | + | 0.879378i | \(0.657959\pi\) | |||||||
\(992\) | −17.5812 | −0.558203 | ||||||||
\(993\) | −16.2092 | −0.514383 | ||||||||
\(994\) | 102.478 | 3.25040 | ||||||||
\(995\) | 4.37603 | 0.138729 | ||||||||
\(996\) | −40.6121 | −1.28684 | ||||||||
\(997\) | −14.0000 | −0.443384 | −0.221692 | − | 0.975117i | \(-0.571158\pi\) | ||||
−0.221692 | + | 0.975117i | \(0.571158\pi\) | |||||||
\(998\) | 49.1007 | 1.55426 | ||||||||
\(999\) | −29.2727 | −0.926149 |
(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 | 4015.2.a.i.1.6 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.i.1.6 | ✓ | 38 | 1.1 | even | 1 | trivial |