Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.74629 | −1.23482 | −0.617408 | − | 0.786643i | \(-0.711817\pi\) | ||||
−0.617408 | + | 0.786643i | \(0.711817\pi\) | |||||||
\(3\) | 2.61915 | 1.51217 | 0.756083 | − | 0.654475i | \(-0.227110\pi\) | ||||
0.756083 | + | 0.654475i | \(0.227110\pi\) | |||||||
\(4\) | 1.04954 | 0.524772 | ||||||||
\(5\) | −0.0450252 | −0.0201359 | −0.0100679 | − | 0.999949i | \(-0.503205\pi\) | ||||
−0.0100679 | + | 0.999949i | \(0.503205\pi\) | |||||||
\(6\) | −4.57381 | −1.86725 | ||||||||
\(7\) | −1.64580 | −0.622055 | −0.311027 | − | 0.950401i | \(-0.600673\pi\) | ||||
−0.311027 | + | 0.950401i | \(0.600673\pi\) | |||||||
\(8\) | 1.65978 | 0.586819 | ||||||||
\(9\) | 3.85995 | 1.28665 | ||||||||
\(10\) | 0.0786272 | 0.0248641 | ||||||||
\(11\) | −1.43541 | −0.432793 | −0.216397 | − | 0.976306i | \(-0.569430\pi\) | ||||
−0.216397 | + | 0.976306i | \(0.569430\pi\) | |||||||
\(12\) | 2.74891 | 0.793543 | ||||||||
\(13\) | 2.18651 | 0.606430 | 0.303215 | − | 0.952922i | \(-0.401940\pi\) | ||||
0.303215 | + | 0.952922i | \(0.401940\pi\) | |||||||
\(14\) | 2.87405 | 0.768123 | ||||||||
\(15\) | −0.117928 | −0.0304488 | ||||||||
\(16\) | −4.99755 | −1.24939 | ||||||||
\(17\) | −4.11109 | −0.997085 | −0.498542 | − | 0.866865i | \(-0.666131\pi\) | ||||
−0.498542 | + | 0.866865i | \(0.666131\pi\) | |||||||
\(18\) | −6.74060 | −1.58878 | ||||||||
\(19\) | −7.92373 | −1.81783 | −0.908914 | − | 0.416983i | \(-0.863087\pi\) | ||||
−0.908914 | + | 0.416983i | \(0.863087\pi\) | |||||||
\(20\) | −0.0472559 | −0.0105667 | ||||||||
\(21\) | −4.31060 | −0.940651 | ||||||||
\(22\) | 2.50665 | 0.534420 | ||||||||
\(23\) | 8.12033 | 1.69321 | 0.846603 | − | 0.532225i | \(-0.178644\pi\) | ||||
0.846603 | + | 0.532225i | \(0.178644\pi\) | |||||||
\(24\) | 4.34720 | 0.887369 | ||||||||
\(25\) | −4.99797 | −0.999595 | ||||||||
\(26\) | −3.81830 | −0.748829 | ||||||||
\(27\) | 2.25233 | 0.433461 | ||||||||
\(28\) | −1.72734 | −0.326437 | ||||||||
\(29\) | 5.25757 | 0.976306 | 0.488153 | − | 0.872758i | \(-0.337671\pi\) | ||||
0.488153 | + | 0.872758i | \(0.337671\pi\) | |||||||
\(30\) | 0.205936 | 0.0375987 | ||||||||
\(31\) | 8.11228 | 1.45701 | 0.728504 | − | 0.685041i | \(-0.240216\pi\) | ||||
0.728504 | + | 0.685041i | \(0.240216\pi\) | |||||||
\(32\) | 5.40763 | 0.955944 | ||||||||
\(33\) | −3.75956 | −0.654456 | ||||||||
\(34\) | 7.17917 | 1.23122 | ||||||||
\(35\) | 0.0741025 | 0.0125256 | ||||||||
\(36\) | 4.05118 | 0.675197 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 13.8372 | 2.24468 | ||||||||
\(39\) | 5.72680 | 0.917023 | ||||||||
\(40\) | −0.0747317 | −0.0118161 | ||||||||
\(41\) | −3.25013 | −0.507584 | −0.253792 | − | 0.967259i | \(-0.581678\pi\) | ||||
−0.253792 | + | 0.967259i | \(0.581678\pi\) | |||||||
\(42\) | 7.52758 | 1.16153 | ||||||||
\(43\) | −1.02152 | −0.155780 | −0.0778899 | − | 0.996962i | \(-0.524818\pi\) | ||||
−0.0778899 | + | 0.996962i | \(0.524818\pi\) | |||||||
\(44\) | −1.50653 | −0.227118 | ||||||||
\(45\) | −0.173795 | −0.0259078 | ||||||||
\(46\) | −14.1805 | −2.09080 | ||||||||
\(47\) | 0.633654 | 0.0924279 | 0.0462140 | − | 0.998932i | \(-0.485284\pi\) | ||||
0.0462140 | + | 0.998932i | \(0.485284\pi\) | |||||||
\(48\) | −13.0893 | −1.88928 | ||||||||
\(49\) | −4.29134 | −0.613048 | ||||||||
\(50\) | 8.72793 | 1.23432 | ||||||||
\(51\) | −10.7676 | −1.50776 | ||||||||
\(52\) | 2.29484 | 0.318237 | ||||||||
\(53\) | −8.79066 | −1.20749 | −0.603745 | − | 0.797178i | \(-0.706325\pi\) | ||||
−0.603745 | + | 0.797178i | \(0.706325\pi\) | |||||||
\(54\) | −3.93323 | −0.535245 | ||||||||
\(55\) | 0.0646297 | 0.00871467 | ||||||||
\(56\) | −2.73166 | −0.365034 | ||||||||
\(57\) | −20.7534 | −2.74886 | ||||||||
\(58\) | −9.18126 | −1.20556 | ||||||||
\(59\) | −7.03026 | −0.915262 | −0.457631 | − | 0.889142i | \(-0.651302\pi\) | ||||
−0.457631 | + | 0.889142i | \(0.651302\pi\) | |||||||
\(60\) | −0.123770 | −0.0159787 | ||||||||
\(61\) | −7.72486 | −0.989067 | −0.494534 | − | 0.869158i | \(-0.664661\pi\) | ||||
−0.494534 | + | 0.869158i | \(0.664661\pi\) | |||||||
\(62\) | −14.1664 | −1.79914 | ||||||||
\(63\) | −6.35271 | −0.800366 | ||||||||
\(64\) | 0.551770 | 0.0689712 | ||||||||
\(65\) | −0.0984481 | −0.0122110 | ||||||||
\(66\) | 6.56530 | 0.808133 | ||||||||
\(67\) | −13.4734 | −1.64603 | −0.823017 | − | 0.568017i | \(-0.807711\pi\) | ||||
−0.823017 | + | 0.568017i | \(0.807711\pi\) | |||||||
\(68\) | −4.31477 | −0.523242 | ||||||||
\(69\) | 21.2684 | 2.56041 | ||||||||
\(70\) | −0.129405 | −0.0154668 | ||||||||
\(71\) | 10.3308 | 1.22604 | 0.613019 | − | 0.790068i | \(-0.289955\pi\) | ||||
0.613019 | + | 0.790068i | \(0.289955\pi\) | |||||||
\(72\) | 6.40665 | 0.755030 | ||||||||
\(73\) | 9.59743 | 1.12329 | 0.561647 | − | 0.827377i | \(-0.310168\pi\) | ||||
0.561647 | + | 0.827377i | \(0.310168\pi\) | |||||||
\(74\) | 1.74629 | 0.203003 | ||||||||
\(75\) | −13.0904 | −1.51155 | ||||||||
\(76\) | −8.31630 | −0.953946 | ||||||||
\(77\) | 2.36241 | 0.269221 | ||||||||
\(78\) | −10.0007 | −1.13235 | ||||||||
\(79\) | 9.98476 | 1.12337 | 0.561686 | − | 0.827350i | \(-0.310153\pi\) | ||||
0.561686 | + | 0.827350i | \(0.310153\pi\) | |||||||
\(80\) | 0.225015 | 0.0251575 | ||||||||
\(81\) | −5.68065 | −0.631184 | ||||||||
\(82\) | 5.67568 | 0.626774 | ||||||||
\(83\) | −1.30660 | −0.143418 | −0.0717092 | − | 0.997426i | \(-0.522845\pi\) | ||||
−0.0717092 | + | 0.997426i | \(0.522845\pi\) | |||||||
\(84\) | −4.52417 | −0.493627 | ||||||||
\(85\) | 0.185102 | 0.0200772 | ||||||||
\(86\) | 1.78387 | 0.192359 | ||||||||
\(87\) | 13.7704 | 1.47634 | ||||||||
\(88\) | −2.38246 | −0.253972 | ||||||||
\(89\) | −7.22191 | −0.765521 | −0.382761 | − | 0.923848i | \(-0.625027\pi\) | ||||
−0.382761 | + | 0.923848i | \(0.625027\pi\) | |||||||
\(90\) | 0.303497 | 0.0319914 | ||||||||
\(91\) | −3.59857 | −0.377232 | ||||||||
\(92\) | 8.52264 | 0.888547 | ||||||||
\(93\) | 21.2473 | 2.20324 | ||||||||
\(94\) | −1.10655 | −0.114132 | ||||||||
\(95\) | 0.356767 | 0.0366035 | ||||||||
\(96\) | 14.1634 | 1.44555 | ||||||||
\(97\) | −9.33511 | −0.947837 | −0.473919 | − | 0.880569i | \(-0.657161\pi\) | ||||
−0.473919 | + | 0.880569i | \(0.657161\pi\) | |||||||
\(98\) | 7.49394 | 0.757002 | ||||||||
\(99\) | −5.54062 | −0.556853 | ||||||||
\(100\) | −5.24559 | −0.524559 | ||||||||
\(101\) | −15.6227 | −1.55451 | −0.777257 | − | 0.629183i | \(-0.783390\pi\) | ||||
−0.777257 | + | 0.629183i | \(0.783390\pi\) | |||||||
\(102\) | 18.8033 | 1.86181 | ||||||||
\(103\) | −10.9414 | −1.07809 | −0.539047 | − | 0.842276i | \(-0.681215\pi\) | ||||
−0.539047 | + | 0.842276i | \(0.681215\pi\) | |||||||
\(104\) | 3.62912 | 0.355865 | ||||||||
\(105\) | 0.194086 | 0.0189408 | ||||||||
\(106\) | 15.3511 | 1.49103 | ||||||||
\(107\) | 5.70963 | 0.551970 | 0.275985 | − | 0.961162i | \(-0.410996\pi\) | ||||
0.275985 | + | 0.961162i | \(0.410996\pi\) | |||||||
\(108\) | 2.36392 | 0.227468 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | −0.112862 | −0.0107610 | ||||||||
\(111\) | −2.61915 | −0.248599 | ||||||||
\(112\) | 8.22497 | 0.777187 | ||||||||
\(113\) | −11.1040 | −1.04457 | −0.522287 | − | 0.852770i | \(-0.674921\pi\) | ||||
−0.522287 | + | 0.852770i | \(0.674921\pi\) | |||||||
\(114\) | 36.2416 | 3.39434 | ||||||||
\(115\) | −0.365619 | −0.0340942 | ||||||||
\(116\) | 5.51805 | 0.512338 | ||||||||
\(117\) | 8.43982 | 0.780262 | ||||||||
\(118\) | 12.2769 | 1.13018 | ||||||||
\(119\) | 6.76603 | 0.620241 | ||||||||
\(120\) | −0.195733 | −0.0178679 | ||||||||
\(121\) | −8.93959 | −0.812690 | ||||||||
\(122\) | 13.4899 | 1.22132 | ||||||||
\(123\) | −8.51257 | −0.767552 | ||||||||
\(124\) | 8.51420 | 0.764597 | ||||||||
\(125\) | 0.450160 | 0.0402636 | ||||||||
\(126\) | 11.0937 | 0.988305 | ||||||||
\(127\) | 11.1808 | 0.992137 | 0.496069 | − | 0.868283i | \(-0.334776\pi\) | ||||
0.496069 | + | 0.868283i | \(0.334776\pi\) | |||||||
\(128\) | −11.7788 | −1.04111 | ||||||||
\(129\) | −2.67550 | −0.235565 | ||||||||
\(130\) | 0.171919 | 0.0150783 | ||||||||
\(131\) | −3.46874 | −0.303065 | −0.151532 | − | 0.988452i | \(-0.548421\pi\) | ||||
−0.151532 | + | 0.988452i | \(0.548421\pi\) | |||||||
\(132\) | −3.94583 | −0.343440 | ||||||||
\(133\) | 13.0409 | 1.13079 | ||||||||
\(134\) | 23.5285 | 2.03255 | ||||||||
\(135\) | −0.101411 | −0.00872811 | ||||||||
\(136\) | −6.82348 | −0.585109 | ||||||||
\(137\) | 2.12643 | 0.181673 | 0.0908365 | − | 0.995866i | \(-0.471046\pi\) | ||||
0.0908365 | + | 0.995866i | \(0.471046\pi\) | |||||||
\(138\) | −37.1408 | −3.16164 | ||||||||
\(139\) | 6.19785 | 0.525695 | 0.262847 | − | 0.964837i | \(-0.415338\pi\) | ||||
0.262847 | + | 0.964837i | \(0.415338\pi\) | |||||||
\(140\) | 0.0777738 | 0.00657309 | ||||||||
\(141\) | 1.65963 | 0.139766 | ||||||||
\(142\) | −18.0406 | −1.51393 | ||||||||
\(143\) | −3.13855 | −0.262459 | ||||||||
\(144\) | −19.2903 | −1.60752 | ||||||||
\(145\) | −0.236723 | −0.0196588 | ||||||||
\(146\) | −16.7599 | −1.38706 | ||||||||
\(147\) | −11.2397 | −0.927031 | ||||||||
\(148\) | −1.04954 | −0.0862720 | ||||||||
\(149\) | −18.8125 | −1.54118 | −0.770590 | − | 0.637332i | \(-0.780038\pi\) | ||||
−0.770590 | + | 0.637332i | \(0.780038\pi\) | |||||||
\(150\) | 22.8598 | 1.86649 | ||||||||
\(151\) | 20.4681 | 1.66567 | 0.832836 | − | 0.553520i | \(-0.186716\pi\) | ||||
0.832836 | + | 0.553520i | \(0.186716\pi\) | |||||||
\(152\) | −13.1516 | −1.06674 | ||||||||
\(153\) | −15.8686 | −1.28290 | ||||||||
\(154\) | −4.12546 | −0.332439 | ||||||||
\(155\) | −0.365257 | −0.0293381 | ||||||||
\(156\) | 6.01053 | 0.481228 | ||||||||
\(157\) | −10.5586 | −0.842669 | −0.421334 | − | 0.906905i | \(-0.638438\pi\) | ||||
−0.421334 | + | 0.906905i | \(0.638438\pi\) | |||||||
\(158\) | −17.4363 | −1.38716 | ||||||||
\(159\) | −23.0241 | −1.82593 | ||||||||
\(160\) | −0.243480 | −0.0192487 | ||||||||
\(161\) | −13.3645 | −1.05327 | ||||||||
\(162\) | 9.92009 | 0.779396 | ||||||||
\(163\) | 16.3370 | 1.27961 | 0.639805 | − | 0.768538i | \(-0.279015\pi\) | ||||
0.639805 | + | 0.768538i | \(0.279015\pi\) | |||||||
\(164\) | −3.41115 | −0.266366 | ||||||||
\(165\) | 0.169275 | 0.0131780 | ||||||||
\(166\) | 2.28171 | 0.177095 | ||||||||
\(167\) | −19.4715 | −1.50675 | −0.753375 | − | 0.657591i | \(-0.771576\pi\) | ||||
−0.753375 | + | 0.657591i | \(0.771576\pi\) | |||||||
\(168\) | −7.15463 | −0.551992 | ||||||||
\(169\) | −8.21916 | −0.632243 | ||||||||
\(170\) | −0.323243 | −0.0247916 | ||||||||
\(171\) | −30.5852 | −2.33891 | ||||||||
\(172\) | −1.07213 | −0.0817489 | ||||||||
\(173\) | 15.2285 | 1.15780 | 0.578899 | − | 0.815399i | \(-0.303483\pi\) | ||||
0.578899 | + | 0.815399i | \(0.303483\pi\) | |||||||
\(174\) | −24.0471 | −1.82301 | ||||||||
\(175\) | 8.22567 | 0.621802 | ||||||||
\(176\) | 7.17354 | 0.540726 | ||||||||
\(177\) | −18.4133 | −1.38403 | ||||||||
\(178\) | 12.6116 | 0.945278 | ||||||||
\(179\) | −15.7451 | −1.17685 | −0.588423 | − | 0.808553i | \(-0.700251\pi\) | ||||
−0.588423 | + | 0.808553i | \(0.700251\pi\) | |||||||
\(180\) | −0.182405 | −0.0135957 | ||||||||
\(181\) | −15.8223 | −1.17606 | −0.588032 | − | 0.808838i | \(-0.700097\pi\) | ||||
−0.588032 | + | 0.808838i | \(0.700097\pi\) | |||||||
\(182\) | 6.28416 | 0.465813 | ||||||||
\(183\) | −20.2326 | −1.49564 | ||||||||
\(184\) | 13.4779 | 0.993606 | ||||||||
\(185\) | 0.0450252 | 0.00331032 | ||||||||
\(186\) | −37.1040 | −2.72060 | ||||||||
\(187\) | 5.90111 | 0.431532 | ||||||||
\(188\) | 0.665048 | 0.0485036 | ||||||||
\(189\) | −3.70689 | −0.269636 | ||||||||
\(190\) | −0.623021 | −0.0451987 | ||||||||
\(191\) | −9.93374 | −0.718780 | −0.359390 | − | 0.933187i | \(-0.617015\pi\) | ||||
−0.359390 | + | 0.933187i | \(0.617015\pi\) | |||||||
\(192\) | 1.44517 | 0.104296 | ||||||||
\(193\) | 3.50234 | 0.252104 | 0.126052 | − | 0.992024i | \(-0.459769\pi\) | ||||
0.126052 | + | 0.992024i | \(0.459769\pi\) | |||||||
\(194\) | 16.3019 | 1.17041 | ||||||||
\(195\) | −0.257850 | −0.0184650 | ||||||||
\(196\) | −4.50395 | −0.321710 | ||||||||
\(197\) | 18.6570 | 1.32926 | 0.664630 | − | 0.747173i | \(-0.268589\pi\) | ||||
0.664630 | + | 0.747173i | \(0.268589\pi\) | |||||||
\(198\) | 9.67555 | 0.687612 | ||||||||
\(199\) | −5.26760 | −0.373410 | −0.186705 | − | 0.982416i | \(-0.559781\pi\) | ||||
−0.186705 | + | 0.982416i | \(0.559781\pi\) | |||||||
\(200\) | −8.29551 | −0.586581 | ||||||||
\(201\) | −35.2888 | −2.48908 | ||||||||
\(202\) | 27.2818 | 1.91954 | ||||||||
\(203\) | −8.65292 | −0.607316 | ||||||||
\(204\) | −11.3010 | −0.791230 | ||||||||
\(205\) | 0.146337 | 0.0102206 | ||||||||
\(206\) | 19.1070 | 1.33125 | ||||||||
\(207\) | 31.3440 | 2.17856 | ||||||||
\(208\) | −10.9272 | −0.757665 | ||||||||
\(209\) | 11.3738 | 0.786744 | ||||||||
\(210\) | −0.338930 | −0.0233884 | ||||||||
\(211\) | −14.0681 | −0.968491 | −0.484245 | − | 0.874932i | \(-0.660906\pi\) | ||||
−0.484245 | + | 0.874932i | \(0.660906\pi\) | |||||||
\(212\) | −9.22618 | −0.633657 | ||||||||
\(213\) | 27.0579 | 1.85398 | ||||||||
\(214\) | −9.97069 | −0.681582 | ||||||||
\(215\) | 0.0459939 | 0.00313676 | ||||||||
\(216\) | 3.73836 | 0.254363 | ||||||||
\(217\) | −13.3512 | −0.906339 | ||||||||
\(218\) | 1.74629 | 0.118274 | ||||||||
\(219\) | 25.1371 | 1.69861 | ||||||||
\(220\) | 0.0678317 | 0.00457321 | ||||||||
\(221\) | −8.98894 | −0.604662 | ||||||||
\(222\) | 4.57381 | 0.306974 | ||||||||
\(223\) | −5.17280 | −0.346397 | −0.173198 | − | 0.984887i | \(-0.555410\pi\) | ||||
−0.173198 | + | 0.984887i | \(0.555410\pi\) | |||||||
\(224\) | −8.89990 | −0.594649 | ||||||||
\(225\) | −19.2919 | −1.28613 | ||||||||
\(226\) | 19.3908 | 1.28986 | ||||||||
\(227\) | 22.4132 | 1.48762 | 0.743809 | − | 0.668392i | \(-0.233017\pi\) | ||||
0.743809 | + | 0.668392i | \(0.233017\pi\) | |||||||
\(228\) | −21.7816 | −1.44252 | ||||||||
\(229\) | 21.2559 | 1.40463 | 0.702313 | − | 0.711868i | \(-0.252151\pi\) | ||||
0.702313 | + | 0.711868i | \(0.252151\pi\) | |||||||
\(230\) | 0.638479 | 0.0421000 | ||||||||
\(231\) | 6.18750 | 0.407107 | ||||||||
\(232\) | 8.72638 | 0.572915 | ||||||||
\(233\) | 28.4334 | 1.86274 | 0.931368 | − | 0.364079i | \(-0.118616\pi\) | ||||
0.931368 | + | 0.364079i | \(0.118616\pi\) | |||||||
\(234\) | −14.7384 | −0.963480 | ||||||||
\(235\) | −0.0285304 | −0.00186112 | ||||||||
\(236\) | −7.37857 | −0.480304 | ||||||||
\(237\) | 26.1516 | 1.69873 | ||||||||
\(238\) | −11.8155 | −0.765884 | ||||||||
\(239\) | −10.4662 | −0.677002 | −0.338501 | − | 0.940966i | \(-0.609920\pi\) | ||||
−0.338501 | + | 0.940966i | \(0.609920\pi\) | |||||||
\(240\) | 0.589349 | 0.0380423 | ||||||||
\(241\) | −4.50370 | −0.290109 | −0.145054 | − | 0.989424i | \(-0.546336\pi\) | ||||
−0.145054 | + | 0.989424i | \(0.546336\pi\) | |||||||
\(242\) | 15.6112 | 1.00352 | ||||||||
\(243\) | −21.6355 | −1.38792 | ||||||||
\(244\) | −8.10759 | −0.519035 | ||||||||
\(245\) | 0.193218 | 0.0123442 | ||||||||
\(246\) | 14.8654 | 0.947786 | ||||||||
\(247\) | −17.3253 | −1.10238 | ||||||||
\(248\) | 13.4646 | 0.855001 | ||||||||
\(249\) | −3.42219 | −0.216872 | ||||||||
\(250\) | −0.786112 | −0.0497181 | ||||||||
\(251\) | −0.600811 | −0.0379229 | −0.0189614 | − | 0.999820i | \(-0.506036\pi\) | ||||
−0.0189614 | + | 0.999820i | \(0.506036\pi\) | |||||||
\(252\) | −6.66745 | −0.420010 | ||||||||
\(253\) | −11.6560 | −0.732808 | ||||||||
\(254\) | −19.5250 | −1.22511 | ||||||||
\(255\) | 0.484811 | 0.0303600 | ||||||||
\(256\) | 19.4657 | 1.21661 | ||||||||
\(257\) | −20.0350 | −1.24975 | −0.624876 | − | 0.780724i | \(-0.714850\pi\) | ||||
−0.624876 | + | 0.780724i | \(0.714850\pi\) | |||||||
\(258\) | 4.67222 | 0.290880 | ||||||||
\(259\) | 1.64580 | 0.102265 | ||||||||
\(260\) | −0.103326 | −0.00640798 | ||||||||
\(261\) | 20.2939 | 1.25616 | ||||||||
\(262\) | 6.05743 | 0.374230 | ||||||||
\(263\) | −9.89890 | −0.610392 | −0.305196 | − | 0.952290i | \(-0.598722\pi\) | ||||
−0.305196 | + | 0.952290i | \(0.598722\pi\) | |||||||
\(264\) | −6.24003 | −0.384047 | ||||||||
\(265\) | 0.395801 | 0.0243138 | ||||||||
\(266\) | −22.7732 | −1.39632 | ||||||||
\(267\) | −18.9153 | −1.15760 | ||||||||
\(268\) | −14.1409 | −0.863793 | ||||||||
\(269\) | 15.2630 | 0.930600 | 0.465300 | − | 0.885153i | \(-0.345946\pi\) | ||||
0.465300 | + | 0.885153i | \(0.345946\pi\) | |||||||
\(270\) | 0.177094 | 0.0107776 | ||||||||
\(271\) | −10.8655 | −0.660030 | −0.330015 | − | 0.943976i | \(-0.607054\pi\) | ||||
−0.330015 | + | 0.943976i | \(0.607054\pi\) | |||||||
\(272\) | 20.5453 | 1.24574 | ||||||||
\(273\) | −9.42519 | −0.570438 | ||||||||
\(274\) | −3.71337 | −0.224333 | ||||||||
\(275\) | 7.17416 | 0.432618 | ||||||||
\(276\) | 22.3221 | 1.34363 | ||||||||
\(277\) | 12.3196 | 0.740213 | 0.370106 | − | 0.928989i | \(-0.379321\pi\) | ||||
0.370106 | + | 0.928989i | \(0.379321\pi\) | |||||||
\(278\) | −10.8233 | −0.649136 | ||||||||
\(279\) | 31.3130 | 1.87466 | ||||||||
\(280\) | 0.122994 | 0.00735027 | ||||||||
\(281\) | −2.82215 | −0.168356 | −0.0841778 | − | 0.996451i | \(-0.526826\pi\) | ||||
−0.0841778 | + | 0.996451i | \(0.526826\pi\) | |||||||
\(282\) | −2.89821 | −0.172586 | ||||||||
\(283\) | 13.7311 | 0.816229 | 0.408114 | − | 0.912931i | \(-0.366186\pi\) | ||||
0.408114 | + | 0.912931i | \(0.366186\pi\) | |||||||
\(284\) | 10.8426 | 0.643391 | ||||||||
\(285\) | 0.934427 | 0.0553507 | ||||||||
\(286\) | 5.48083 | 0.324088 | ||||||||
\(287\) | 5.34906 | 0.315745 | ||||||||
\(288\) | 20.8732 | 1.22996 | ||||||||
\(289\) | −0.0989699 | −0.00582176 | ||||||||
\(290\) | 0.413388 | 0.0242750 | ||||||||
\(291\) | −24.4501 | −1.43329 | ||||||||
\(292\) | 10.0729 | 0.589473 | ||||||||
\(293\) | −15.6542 | −0.914531 | −0.457265 | − | 0.889330i | \(-0.651171\pi\) | ||||
−0.457265 | + | 0.889330i | \(0.651171\pi\) | |||||||
\(294\) | 19.6277 | 1.14471 | ||||||||
\(295\) | 0.316539 | 0.0184296 | ||||||||
\(296\) | −1.65978 | −0.0964725 | ||||||||
\(297\) | −3.23302 | −0.187599 | ||||||||
\(298\) | 32.8521 | 1.90307 | ||||||||
\(299\) | 17.7552 | 1.02681 | ||||||||
\(300\) | −13.7390 | −0.793221 | ||||||||
\(301\) | 1.68121 | 0.0969035 | ||||||||
\(302\) | −35.7434 | −2.05680 | ||||||||
\(303\) | −40.9181 | −2.35069 | ||||||||
\(304\) | 39.5992 | 2.27117 | ||||||||
\(305\) | 0.347813 | 0.0199157 | ||||||||
\(306\) | 27.7112 | 1.58414 | ||||||||
\(307\) | 29.6010 | 1.68942 | 0.844709 | − | 0.535226i | \(-0.179773\pi\) | ||||
0.844709 | + | 0.535226i | \(0.179773\pi\) | |||||||
\(308\) | 2.47945 | 0.141280 | ||||||||
\(309\) | −28.6573 | −1.63026 | ||||||||
\(310\) | 0.637846 | 0.0362272 | ||||||||
\(311\) | −31.4219 | −1.78177 | −0.890887 | − | 0.454225i | \(-0.849916\pi\) | ||||
−0.890887 | + | 0.454225i | \(0.849916\pi\) | |||||||
\(312\) | 9.50521 | 0.538127 | ||||||||
\(313\) | −27.4364 | −1.55080 | −0.775399 | − | 0.631472i | \(-0.782451\pi\) | ||||
−0.775399 | + | 0.631472i | \(0.782451\pi\) | |||||||
\(314\) | 18.4384 | 1.04054 | ||||||||
\(315\) | 0.286032 | 0.0161161 | ||||||||
\(316\) | 10.4794 | 0.589515 | ||||||||
\(317\) | −4.18255 | −0.234915 | −0.117458 | − | 0.993078i | \(-0.537474\pi\) | ||||
−0.117458 | + | 0.993078i | \(0.537474\pi\) | |||||||
\(318\) | 40.2068 | 2.25468 | ||||||||
\(319\) | −7.54678 | −0.422539 | ||||||||
\(320\) | −0.0248435 | −0.00138880 | ||||||||
\(321\) | 14.9544 | 0.834672 | ||||||||
\(322\) | 23.3383 | 1.30059 | ||||||||
\(323\) | 32.5751 | 1.81253 | ||||||||
\(324\) | −5.96209 | −0.331227 | ||||||||
\(325\) | −10.9281 | −0.606184 | ||||||||
\(326\) | −28.5291 | −1.58008 | ||||||||
\(327\) | −2.61915 | −0.144839 | ||||||||
\(328\) | −5.39448 | −0.297860 | ||||||||
\(329\) | −1.04287 | −0.0574952 | ||||||||
\(330\) | −0.295604 | −0.0162725 | ||||||||
\(331\) | −25.3147 | −1.39142 | −0.695710 | − | 0.718322i | \(-0.744910\pi\) | ||||
−0.695710 | + | 0.718322i | \(0.744910\pi\) | |||||||
\(332\) | −1.37134 | −0.0752619 | ||||||||
\(333\) | −3.85995 | −0.211524 | ||||||||
\(334\) | 34.0030 | 1.86056 | ||||||||
\(335\) | 0.606641 | 0.0331443 | ||||||||
\(336\) | 21.5424 | 1.17524 | ||||||||
\(337\) | 14.7711 | 0.804636 | 0.402318 | − | 0.915500i | \(-0.368205\pi\) | ||||
0.402318 | + | 0.915500i | \(0.368205\pi\) | |||||||
\(338\) | 14.3531 | 0.780704 | ||||||||
\(339\) | −29.0830 | −1.57957 | ||||||||
\(340\) | 0.194273 | 0.0105359 | ||||||||
\(341\) | −11.6445 | −0.630584 | ||||||||
\(342\) | 53.4107 | 2.88812 | ||||||||
\(343\) | 18.5833 | 1.00340 | ||||||||
\(344\) | −1.69549 | −0.0914146 | ||||||||
\(345\) | −0.957611 | −0.0515561 | ||||||||
\(346\) | −26.5934 | −1.42967 | ||||||||
\(347\) | −30.6522 | −1.64549 | −0.822747 | − | 0.568407i | \(-0.807560\pi\) | ||||
−0.822747 | + | 0.568407i | \(0.807560\pi\) | |||||||
\(348\) | 14.4526 | 0.774741 | ||||||||
\(349\) | 17.2810 | 0.925030 | 0.462515 | − | 0.886611i | \(-0.346947\pi\) | ||||
0.462515 | + | 0.886611i | \(0.346947\pi\) | |||||||
\(350\) | −14.3644 | −0.767812 | ||||||||
\(351\) | 4.92475 | 0.262864 | ||||||||
\(352\) | −7.76219 | −0.413726 | ||||||||
\(353\) | −10.6330 | −0.565938 | −0.282969 | − | 0.959129i | \(-0.591319\pi\) | ||||
−0.282969 | + | 0.959129i | \(0.591319\pi\) | |||||||
\(354\) | 32.1551 | 1.70902 | ||||||||
\(355\) | −0.465145 | −0.0246873 | ||||||||
\(356\) | −7.57972 | −0.401724 | ||||||||
\(357\) | 17.7213 | 0.937908 | ||||||||
\(358\) | 27.4956 | 1.45319 | ||||||||
\(359\) | −27.8224 | −1.46841 | −0.734205 | − | 0.678928i | \(-0.762445\pi\) | ||||
−0.734205 | + | 0.678928i | \(0.762445\pi\) | |||||||
\(360\) | −0.288460 | −0.0152032 | ||||||||
\(361\) | 43.7855 | 2.30450 | ||||||||
\(362\) | 27.6304 | 1.45222 | ||||||||
\(363\) | −23.4141 | −1.22892 | ||||||||
\(364\) | −3.77686 | −0.197961 | ||||||||
\(365\) | −0.432126 | −0.0226185 | ||||||||
\(366\) | 35.3320 | 1.84684 | ||||||||
\(367\) | 22.7747 | 1.18883 | 0.594415 | − | 0.804159i | \(-0.297384\pi\) | ||||
0.594415 | + | 0.804159i | \(0.297384\pi\) | |||||||
\(368\) | −40.5817 | −2.11547 | ||||||||
\(369\) | −12.5453 | −0.653083 | ||||||||
\(370\) | −0.0786272 | −0.00408763 | ||||||||
\(371\) | 14.4677 | 0.751125 | ||||||||
\(372\) | 22.3000 | 1.15620 | ||||||||
\(373\) | −3.41513 | −0.176829 | −0.0884143 | − | 0.996084i | \(-0.528180\pi\) | ||||
−0.0884143 | + | 0.996084i | \(0.528180\pi\) | |||||||
\(374\) | −10.3051 | −0.532863 | ||||||||
\(375\) | 1.17904 | 0.0608852 | ||||||||
\(376\) | 1.05172 | 0.0542385 | ||||||||
\(377\) | 11.4957 | 0.592061 | ||||||||
\(378\) | 6.47332 | 0.332952 | ||||||||
\(379\) | −23.5744 | −1.21093 | −0.605467 | − | 0.795870i | \(-0.707014\pi\) | ||||
−0.605467 | + | 0.795870i | \(0.707014\pi\) | |||||||
\(380\) | 0.374443 | 0.0192085 | ||||||||
\(381\) | 29.2842 | 1.50028 | ||||||||
\(382\) | 17.3472 | 0.887562 | ||||||||
\(383\) | 7.65425 | 0.391114 | 0.195557 | − | 0.980692i | \(-0.437349\pi\) | ||||
0.195557 | + | 0.980692i | \(0.437349\pi\) | |||||||
\(384\) | −30.8505 | −1.57433 | ||||||||
\(385\) | −0.106368 | −0.00542100 | ||||||||
\(386\) | −6.11611 | −0.311302 | ||||||||
\(387\) | −3.94300 | −0.200434 | ||||||||
\(388\) | −9.79761 | −0.497398 | ||||||||
\(389\) | 18.9416 | 0.960375 | 0.480187 | − | 0.877166i | \(-0.340569\pi\) | ||||
0.480187 | + | 0.877166i | \(0.340569\pi\) | |||||||
\(390\) | 0.450282 | 0.0228009 | ||||||||
\(391\) | −33.3834 | −1.68827 | ||||||||
\(392\) | −7.12265 | −0.359748 | ||||||||
\(393\) | −9.08514 | −0.458285 | ||||||||
\(394\) | −32.5807 | −1.64139 | ||||||||
\(395\) | −0.449565 | −0.0226201 | ||||||||
\(396\) | −5.81512 | −0.292221 | ||||||||
\(397\) | −12.0372 | −0.604131 | −0.302066 | − | 0.953287i | \(-0.597676\pi\) | ||||
−0.302066 | + | 0.953287i | \(0.597676\pi\) | |||||||
\(398\) | 9.19878 | 0.461093 | ||||||||
\(399\) | 34.1561 | 1.70994 | ||||||||
\(400\) | 24.9776 | 1.24888 | ||||||||
\(401\) | −5.39260 | −0.269294 | −0.134647 | − | 0.990894i | \(-0.542990\pi\) | ||||
−0.134647 | + | 0.990894i | \(0.542990\pi\) | |||||||
\(402\) | 61.6246 | 3.07356 | ||||||||
\(403\) | 17.7376 | 0.883573 | ||||||||
\(404\) | −16.3967 | −0.815766 | ||||||||
\(405\) | 0.255772 | 0.0127094 | ||||||||
\(406\) | 15.1105 | 0.749924 | ||||||||
\(407\) | 1.43541 | 0.0711508 | ||||||||
\(408\) | −17.8717 | −0.884782 | ||||||||
\(409\) | 15.6185 | 0.772284 | 0.386142 | − | 0.922439i | \(-0.373807\pi\) | ||||
0.386142 | + | 0.922439i | \(0.373807\pi\) | |||||||
\(410\) | −0.255548 | −0.0126206 | ||||||||
\(411\) | 5.56943 | 0.274720 | ||||||||
\(412\) | −11.4835 | −0.565753 | ||||||||
\(413\) | 11.5704 | 0.569343 | ||||||||
\(414\) | −54.7359 | −2.69012 | ||||||||
\(415\) | 0.0588300 | 0.00288785 | ||||||||
\(416\) | 11.8239 | 0.579712 | ||||||||
\(417\) | 16.2331 | 0.794938 | ||||||||
\(418\) | −19.8621 | −0.971485 | ||||||||
\(419\) | −13.7547 | −0.671960 | −0.335980 | − | 0.941869i | \(-0.609067\pi\) | ||||
−0.335980 | + | 0.941869i | \(0.609067\pi\) | |||||||
\(420\) | 0.203701 | 0.00993961 | ||||||||
\(421\) | 23.6585 | 1.15305 | 0.576523 | − | 0.817081i | \(-0.304409\pi\) | ||||
0.576523 | + | 0.817081i | \(0.304409\pi\) | |||||||
\(422\) | 24.5671 | 1.19591 | ||||||||
\(423\) | 2.44587 | 0.118922 | ||||||||
\(424\) | −14.5905 | −0.708578 | ||||||||
\(425\) | 20.5471 | 0.996681 | ||||||||
\(426\) | −47.2510 | −2.28932 | ||||||||
\(427\) | 12.7136 | 0.615254 | ||||||||
\(428\) | 5.99251 | 0.289659 | ||||||||
\(429\) | −8.22033 | −0.396881 | ||||||||
\(430\) | −0.0803189 | −0.00387332 | ||||||||
\(431\) | −4.35928 | −0.209979 | −0.104989 | − | 0.994473i | \(-0.533481\pi\) | ||||
−0.104989 | + | 0.994473i | \(0.533481\pi\) | |||||||
\(432\) | −11.2561 | −0.541560 | ||||||||
\(433\) | 18.4637 | 0.887310 | 0.443655 | − | 0.896198i | \(-0.353681\pi\) | ||||
0.443655 | + | 0.896198i | \(0.353681\pi\) | |||||||
\(434\) | 23.3151 | 1.11916 | ||||||||
\(435\) | −0.620013 | −0.0297273 | ||||||||
\(436\) | −1.04954 | −0.0502640 | ||||||||
\(437\) | −64.3433 | −3.07796 | ||||||||
\(438\) | −43.8968 | −2.09747 | ||||||||
\(439\) | −28.8537 | −1.37711 | −0.688557 | − | 0.725183i | \(-0.741755\pi\) | ||||
−0.688557 | + | 0.725183i | \(0.741755\pi\) | |||||||
\(440\) | 0.107271 | 0.00511394 | ||||||||
\(441\) | −16.5643 | −0.788777 | ||||||||
\(442\) | 15.6973 | 0.746646 | ||||||||
\(443\) | −18.0891 | −0.859438 | −0.429719 | − | 0.902963i | \(-0.641387\pi\) | ||||
−0.429719 | + | 0.902963i | \(0.641387\pi\) | |||||||
\(444\) | −2.74891 | −0.130458 | ||||||||
\(445\) | 0.325168 | 0.0154144 | ||||||||
\(446\) | 9.03324 | 0.427736 | ||||||||
\(447\) | −49.2727 | −2.33052 | ||||||||
\(448\) | −0.908104 | −0.0429039 | ||||||||
\(449\) | 3.76252 | 0.177564 | 0.0887822 | − | 0.996051i | \(-0.471702\pi\) | ||||
0.0887822 | + | 0.996051i | \(0.471702\pi\) | |||||||
\(450\) | 33.6894 | 1.58813 | ||||||||
\(451\) | 4.66527 | 0.219679 | ||||||||
\(452\) | −11.6541 | −0.548164 | ||||||||
\(453\) | 53.6091 | 2.51877 | ||||||||
\(454\) | −39.1401 | −1.83694 | ||||||||
\(455\) | 0.162026 | 0.00759590 | ||||||||
\(456\) | −34.4461 | −1.61308 | ||||||||
\(457\) | 1.33547 | 0.0624705 | 0.0312352 | − | 0.999512i | \(-0.490056\pi\) | ||||
0.0312352 | + | 0.999512i | \(0.490056\pi\) | |||||||
\(458\) | −37.1190 | −1.73446 | ||||||||
\(459\) | −9.25952 | −0.432197 | ||||||||
\(460\) | −0.383733 | −0.0178917 | ||||||||
\(461\) | 32.9332 | 1.53385 | 0.766927 | − | 0.641734i | \(-0.221785\pi\) | ||||
0.766927 | + | 0.641734i | \(0.221785\pi\) | |||||||
\(462\) | −10.8052 | −0.502703 | ||||||||
\(463\) | 21.3658 | 0.992955 | 0.496478 | − | 0.868050i | \(-0.334626\pi\) | ||||
0.496478 | + | 0.868050i | \(0.334626\pi\) | |||||||
\(464\) | −26.2749 | −1.21978 | ||||||||
\(465\) | −0.956662 | −0.0443641 | ||||||||
\(466\) | −49.6531 | −2.30014 | ||||||||
\(467\) | −8.72214 | −0.403613 | −0.201806 | − | 0.979425i | \(-0.564681\pi\) | ||||
−0.201806 | + | 0.979425i | \(0.564681\pi\) | |||||||
\(468\) | 8.85797 | 0.409460 | ||||||||
\(469\) | 22.1745 | 1.02392 | ||||||||
\(470\) | 0.0498224 | 0.00229814 | ||||||||
\(471\) | −27.6546 | −1.27426 | ||||||||
\(472\) | −11.6687 | −0.537093 | ||||||||
\(473\) | 1.46630 | 0.0674204 | ||||||||
\(474\) | −45.6683 | −2.09762 | ||||||||
\(475\) | 39.6026 | 1.81709 | ||||||||
\(476\) | 7.10125 | 0.325485 | ||||||||
\(477\) | −33.9315 | −1.55362 | ||||||||
\(478\) | 18.2771 | 0.835973 | ||||||||
\(479\) | 29.3328 | 1.34025 | 0.670125 | − | 0.742248i | \(-0.266240\pi\) | ||||
0.670125 | + | 0.742248i | \(0.266240\pi\) | |||||||
\(480\) | −0.637709 | −0.0291073 | ||||||||
\(481\) | −2.18651 | −0.0996964 | ||||||||
\(482\) | 7.86478 | 0.358231 | ||||||||
\(483\) | −35.0035 | −1.59272 | ||||||||
\(484\) | −9.38249 | −0.426477 | ||||||||
\(485\) | 0.420315 | 0.0190855 | ||||||||
\(486\) | 37.7819 | 1.71382 | ||||||||
\(487\) | −34.5610 | −1.56611 | −0.783055 | − | 0.621952i | \(-0.786340\pi\) | ||||
−0.783055 | + | 0.621952i | \(0.786340\pi\) | |||||||
\(488\) | −12.8215 | −0.580404 | ||||||||
\(489\) | 42.7889 | 1.93498 | ||||||||
\(490\) | −0.337416 | −0.0152429 | ||||||||
\(491\) | 11.4040 | 0.514657 | 0.257329 | − | 0.966324i | \(-0.417158\pi\) | ||||
0.257329 | + | 0.966324i | \(0.417158\pi\) | |||||||
\(492\) | −8.93431 | −0.402790 | ||||||||
\(493\) | −21.6143 | −0.973460 | ||||||||
\(494\) | 30.2551 | 1.36124 | ||||||||
\(495\) | 0.249467 | 0.0112127 | ||||||||
\(496\) | −40.5415 | −1.82037 | ||||||||
\(497\) | −17.0024 | −0.762663 | ||||||||
\(498\) | 5.97615 | 0.267798 | ||||||||
\(499\) | 16.0261 | 0.717426 | 0.358713 | − | 0.933448i | \(-0.383216\pi\) | ||||
0.358713 | + | 0.933448i | \(0.383216\pi\) | |||||||
\(500\) | 0.472463 | 0.0211292 | ||||||||
\(501\) | −50.9988 | −2.27846 | ||||||||
\(502\) | 1.04919 | 0.0468278 | ||||||||
\(503\) | −21.5723 | −0.961862 | −0.480931 | − | 0.876758i | \(-0.659701\pi\) | ||||
−0.480931 | + | 0.876758i | \(0.659701\pi\) | |||||||
\(504\) | −10.5441 | −0.469670 | ||||||||
\(505\) | 0.703414 | 0.0313015 | ||||||||
\(506\) | 20.3549 | 0.904884 | ||||||||
\(507\) | −21.5272 | −0.956057 | ||||||||
\(508\) | 11.7348 | 0.520646 | ||||||||
\(509\) | 37.7441 | 1.67298 | 0.836489 | − | 0.547984i | \(-0.184605\pi\) | ||||
0.836489 | + | 0.547984i | \(0.184605\pi\) | |||||||
\(510\) | −0.846622 | −0.0374891 | ||||||||
\(511\) | −15.7955 | −0.698750 | ||||||||
\(512\) | −10.4353 | −0.461179 | ||||||||
\(513\) | −17.8469 | −0.787958 | ||||||||
\(514\) | 34.9871 | 1.54321 | ||||||||
\(515\) | 0.492640 | 0.0217083 | ||||||||
\(516\) | −2.80806 | −0.123618 | ||||||||
\(517\) | −0.909555 | −0.0400022 | ||||||||
\(518\) | −2.87405 | −0.126279 | ||||||||
\(519\) | 39.8856 | 1.75078 | ||||||||
\(520\) | −0.163402 | −0.00716564 | ||||||||
\(521\) | −11.2384 | −0.492362 | −0.246181 | − | 0.969224i | \(-0.579176\pi\) | ||||
−0.246181 | + | 0.969224i | \(0.579176\pi\) | |||||||
\(522\) | −35.4392 | −1.55113 | ||||||||
\(523\) | −1.35953 | −0.0594482 | −0.0297241 | − | 0.999558i | \(-0.509463\pi\) | ||||
−0.0297241 | + | 0.999558i | \(0.509463\pi\) | |||||||
\(524\) | −3.64059 | −0.159040 | ||||||||
\(525\) | 21.5443 | 0.940269 | ||||||||
\(526\) | 17.2864 | 0.753723 | ||||||||
\(527\) | −33.3503 | −1.45276 | ||||||||
\(528\) | 18.7886 | 0.817668 | ||||||||
\(529\) | 42.9398 | 1.86695 | ||||||||
\(530\) | −0.691185 | −0.0300231 | ||||||||
\(531\) | −27.1364 | −1.17762 | ||||||||
\(532\) | 13.6870 | 0.593406 | ||||||||
\(533\) | −7.10644 | −0.307814 | ||||||||
\(534\) | 33.0316 | 1.42942 | ||||||||
\(535\) | −0.257077 | −0.0111144 | ||||||||
\(536\) | −22.3628 | −0.965925 | ||||||||
\(537\) | −41.2388 | −1.77959 | ||||||||
\(538\) | −26.6537 | −1.14912 | ||||||||
\(539\) | 6.15984 | 0.265323 | ||||||||
\(540\) | −0.106436 | −0.00458027 | ||||||||
\(541\) | −5.66000 | −0.243342 | −0.121671 | − | 0.992570i | \(-0.538825\pi\) | ||||
−0.121671 | + | 0.992570i | \(0.538825\pi\) | |||||||
\(542\) | 18.9743 | 0.815017 | ||||||||
\(543\) | −41.4410 | −1.77840 | ||||||||
\(544\) | −22.2312 | −0.953157 | ||||||||
\(545\) | 0.0450252 | 0.00192867 | ||||||||
\(546\) | 16.4592 | 0.704387 | ||||||||
\(547\) | 10.7923 | 0.461444 | 0.230722 | − | 0.973020i | \(-0.425891\pi\) | ||||
0.230722 | + | 0.973020i | \(0.425891\pi\) | |||||||
\(548\) | 2.23178 | 0.0953369 | ||||||||
\(549\) | −29.8176 | −1.27258 | ||||||||
\(550\) | −12.5282 | −0.534204 | ||||||||
\(551\) | −41.6596 | −1.77476 | ||||||||
\(552\) | 35.3007 | 1.50250 | ||||||||
\(553\) | −16.4329 | −0.698799 | ||||||||
\(554\) | −21.5136 | −0.914027 | ||||||||
\(555\) | 0.117928 | 0.00500575 | ||||||||
\(556\) | 6.50491 | 0.275870 | ||||||||
\(557\) | 21.4129 | 0.907294 | 0.453647 | − | 0.891182i | \(-0.350123\pi\) | ||||
0.453647 | + | 0.891182i | \(0.350123\pi\) | |||||||
\(558\) | −54.6817 | −2.31486 | ||||||||
\(559\) | −2.23356 | −0.0944694 | ||||||||
\(560\) | −0.370331 | −0.0156493 | ||||||||
\(561\) | 15.4559 | 0.652548 | ||||||||
\(562\) | 4.92831 | 0.207888 | ||||||||
\(563\) | −35.4522 | −1.49413 | −0.747066 | − | 0.664750i | \(-0.768538\pi\) | ||||
−0.747066 | + | 0.664750i | \(0.768538\pi\) | |||||||
\(564\) | 1.74186 | 0.0733455 | ||||||||
\(565\) | 0.499958 | 0.0210334 | ||||||||
\(566\) | −23.9785 | −1.00789 | ||||||||
\(567\) | 9.34923 | 0.392631 | ||||||||
\(568\) | 17.1468 | 0.719463 | ||||||||
\(569\) | 0.107921 | 0.00452428 | 0.00226214 | − | 0.999997i | \(-0.499280\pi\) | ||||
0.00226214 | + | 0.999997i | \(0.499280\pi\) | |||||||
\(570\) | −1.63178 | −0.0683479 | ||||||||
\(571\) | −11.6760 | −0.488623 | −0.244312 | − | 0.969697i | \(-0.578562\pi\) | ||||
−0.244312 | + | 0.969697i | \(0.578562\pi\) | |||||||
\(572\) | −3.29405 | −0.137731 | ||||||||
\(573\) | −26.0179 | −1.08692 | ||||||||
\(574\) | −9.34104 | −0.389887 | ||||||||
\(575\) | −40.5852 | −1.69252 | ||||||||
\(576\) | 2.12980 | 0.0887418 | ||||||||
\(577\) | −24.9028 | −1.03672 | −0.518358 | − | 0.855164i | \(-0.673457\pi\) | ||||
−0.518358 | + | 0.855164i | \(0.673457\pi\) | |||||||
\(578\) | 0.172831 | 0.00718880 | ||||||||
\(579\) | 9.17315 | 0.381223 | ||||||||
\(580\) | −0.248451 | −0.0103164 | ||||||||
\(581\) | 2.15041 | 0.0892140 | ||||||||
\(582\) | 42.6970 | 1.76985 | ||||||||
\(583\) | 12.6182 | 0.522594 | ||||||||
\(584\) | 15.9296 | 0.659170 | ||||||||
\(585\) | −0.380004 | −0.0157112 | ||||||||
\(586\) | 27.3369 | 1.12928 | ||||||||
\(587\) | −15.4685 | −0.638455 | −0.319228 | − | 0.947678i | \(-0.603423\pi\) | ||||
−0.319228 | + | 0.947678i | \(0.603423\pi\) | |||||||
\(588\) | −11.7965 | −0.486480 | ||||||||
\(589\) | −64.2795 | −2.64859 | ||||||||
\(590\) | −0.552770 | −0.0227572 | ||||||||
\(591\) | 48.8656 | 2.01006 | ||||||||
\(592\) | 4.99755 | 0.205398 | ||||||||
\(593\) | −27.0894 | −1.11243 | −0.556215 | − | 0.831038i | \(-0.687747\pi\) | ||||
−0.556215 | + | 0.831038i | \(0.687747\pi\) | |||||||
\(594\) | 5.64581 | 0.231650 | ||||||||
\(595\) | −0.304642 | −0.0124891 | ||||||||
\(596\) | −19.7445 | −0.808768 | ||||||||
\(597\) | −13.7966 | −0.564659 | ||||||||
\(598\) | −31.0058 | −1.26792 | ||||||||
\(599\) | −9.51041 | −0.388585 | −0.194292 | − | 0.980944i | \(-0.562241\pi\) | ||||
−0.194292 | + | 0.980944i | \(0.562241\pi\) | |||||||
\(600\) | −21.7272 | −0.887009 | ||||||||
\(601\) | −33.4852 | −1.36589 | −0.682944 | − | 0.730470i | \(-0.739301\pi\) | ||||
−0.682944 | + | 0.730470i | \(0.739301\pi\) | |||||||
\(602\) | −2.93589 | −0.119658 | ||||||||
\(603\) | −52.0065 | −2.11787 | ||||||||
\(604\) | 21.4822 | 0.874098 | ||||||||
\(605\) | 0.402506 | 0.0163642 | ||||||||
\(606\) | 71.4551 | 2.90267 | ||||||||
\(607\) | 13.1301 | 0.532934 | 0.266467 | − | 0.963844i | \(-0.414144\pi\) | ||||
0.266467 | + | 0.963844i | \(0.414144\pi\) | |||||||
\(608\) | −42.8486 | −1.73774 | ||||||||
\(609\) | −22.6633 | −0.918363 | ||||||||
\(610\) | −0.607384 | −0.0245923 | ||||||||
\(611\) | 1.38549 | 0.0560510 | ||||||||
\(612\) | −16.6548 | −0.673229 | ||||||||
\(613\) | 20.7261 | 0.837118 | 0.418559 | − | 0.908190i | \(-0.362535\pi\) | ||||
0.418559 | + | 0.908190i | \(0.362535\pi\) | |||||||
\(614\) | −51.6921 | −2.08612 | ||||||||
\(615\) | 0.383280 | 0.0154553 | ||||||||
\(616\) | 3.92106 | 0.157984 | ||||||||
\(617\) | 23.1147 | 0.930561 | 0.465281 | − | 0.885163i | \(-0.345953\pi\) | ||||
0.465281 | + | 0.885163i | \(0.345953\pi\) | |||||||
\(618\) | 50.0441 | 2.01307 | ||||||||
\(619\) | 17.0980 | 0.687225 | 0.343613 | − | 0.939111i | \(-0.388349\pi\) | ||||
0.343613 | + | 0.939111i | \(0.388349\pi\) | |||||||
\(620\) | −0.383353 | −0.0153958 | ||||||||
\(621\) | 18.2897 | 0.733939 | ||||||||
\(622\) | 54.8719 | 2.20016 | ||||||||
\(623\) | 11.8858 | 0.476196 | ||||||||
\(624\) | −28.6200 | −1.14572 | ||||||||
\(625\) | 24.9696 | 0.998784 | ||||||||
\(626\) | 47.9121 | 1.91495 | ||||||||
\(627\) | 29.7898 | 1.18969 | ||||||||
\(628\) | −11.0817 | −0.442209 | ||||||||
\(629\) | 4.11109 | 0.163920 | ||||||||
\(630\) | −0.499495 | −0.0199004 | ||||||||
\(631\) | −8.94391 | −0.356052 | −0.178026 | − | 0.984026i | \(-0.556971\pi\) | ||||
−0.178026 | + | 0.984026i | \(0.556971\pi\) | |||||||
\(632\) | 16.5725 | 0.659217 | ||||||||
\(633\) | −36.8466 | −1.46452 | ||||||||
\(634\) | 7.30396 | 0.290077 | ||||||||
\(635\) | −0.503418 | −0.0199775 | ||||||||
\(636\) | −24.1648 | −0.958195 | ||||||||
\(637\) | −9.38306 | −0.371770 | ||||||||
\(638\) | 13.1789 | 0.521758 | ||||||||
\(639\) | 39.8763 | 1.57748 | ||||||||
\(640\) | 0.530343 | 0.0209637 | ||||||||
\(641\) | −17.5564 | −0.693436 | −0.346718 | − | 0.937969i | \(-0.612704\pi\) | ||||
−0.346718 | + | 0.937969i | \(0.612704\pi\) | |||||||
\(642\) | −26.1147 | −1.03067 | ||||||||
\(643\) | −23.5400 | −0.928328 | −0.464164 | − | 0.885749i | \(-0.653645\pi\) | ||||
−0.464164 | + | 0.885749i | \(0.653645\pi\) | |||||||
\(644\) | −14.0266 | −0.552725 | ||||||||
\(645\) | 0.120465 | 0.00474330 | ||||||||
\(646\) | −56.8858 | −2.23814 | ||||||||
\(647\) | 23.2768 | 0.915104 | 0.457552 | − | 0.889183i | \(-0.348726\pi\) | ||||
0.457552 | + | 0.889183i | \(0.348726\pi\) | |||||||
\(648\) | −9.42861 | −0.370391 | ||||||||
\(649\) | 10.0913 | 0.396119 | ||||||||
\(650\) | 19.0837 | 0.748526 | ||||||||
\(651\) | −34.9688 | −1.37054 | ||||||||
\(652\) | 17.1464 | 0.671503 | ||||||||
\(653\) | 32.6530 | 1.27781 | 0.638905 | − | 0.769286i | \(-0.279388\pi\) | ||||
0.638905 | + | 0.769286i | \(0.279388\pi\) | |||||||
\(654\) | 4.57381 | 0.178850 | ||||||||
\(655\) | 0.156180 | 0.00610247 | ||||||||
\(656\) | 16.2426 | 0.634169 | ||||||||
\(657\) | 37.0455 | 1.44528 | ||||||||
\(658\) | 1.82116 | 0.0709960 | ||||||||
\(659\) | −34.4340 | −1.34136 | −0.670678 | − | 0.741748i | \(-0.733997\pi\) | ||||
−0.670678 | + | 0.741748i | \(0.733997\pi\) | |||||||
\(660\) | 0.177661 | 0.00691546 | ||||||||
\(661\) | −32.2787 | −1.25550 | −0.627748 | − | 0.778417i | \(-0.716023\pi\) | ||||
−0.627748 | + | 0.778417i | \(0.716023\pi\) | |||||||
\(662\) | 44.2069 | 1.71815 | ||||||||
\(663\) | −23.5434 | −0.914349 | ||||||||
\(664\) | −2.16867 | −0.0841606 | ||||||||
\(665\) | −0.587168 | −0.0227694 | ||||||||
\(666\) | 6.74060 | 0.261193 | ||||||||
\(667\) | 42.6932 | 1.65309 | ||||||||
\(668\) | −20.4362 | −0.790700 | ||||||||
\(669\) | −13.5483 | −0.523809 | ||||||||
\(670\) | −1.05937 | −0.0409271 | ||||||||
\(671\) | 11.0884 | 0.428062 | ||||||||
\(672\) | −23.3102 | −0.899209 | ||||||||
\(673\) | 21.6164 | 0.833252 | 0.416626 | − | 0.909078i | \(-0.363213\pi\) | ||||
0.416626 | + | 0.909078i | \(0.363213\pi\) | |||||||
\(674\) | −25.7948 | −0.993578 | ||||||||
\(675\) | −11.2571 | −0.433285 | ||||||||
\(676\) | −8.62637 | −0.331784 | ||||||||
\(677\) | −2.81215 | −0.108080 | −0.0540398 | − | 0.998539i | \(-0.517210\pi\) | ||||
−0.0540398 | + | 0.998539i | \(0.517210\pi\) | |||||||
\(678\) | 50.7875 | 1.95048 | ||||||||
\(679\) | 15.3637 | 0.589607 | ||||||||
\(680\) | 0.307228 | 0.0117817 | ||||||||
\(681\) | 58.7036 | 2.24953 | ||||||||
\(682\) | 20.3347 | 0.778655 | ||||||||
\(683\) | −27.5881 | −1.05563 | −0.527814 | − | 0.849360i | \(-0.676988\pi\) | ||||
−0.527814 | + | 0.849360i | \(0.676988\pi\) | |||||||
\(684\) | −32.1005 | −1.22739 | ||||||||
\(685\) | −0.0957427 | −0.00365814 | ||||||||
\(686\) | −32.4519 | −1.23902 | ||||||||
\(687\) | 55.6723 | 2.12403 | ||||||||
\(688\) | 5.10507 | 0.194629 | ||||||||
\(689\) | −19.2209 | −0.732257 | ||||||||
\(690\) | 1.67227 | 0.0636623 | ||||||||
\(691\) | 17.4897 | 0.665338 | 0.332669 | − | 0.943044i | \(-0.392051\pi\) | ||||
0.332669 | + | 0.943044i | \(0.392051\pi\) | |||||||
\(692\) | 15.9829 | 0.607580 | ||||||||
\(693\) | 9.11876 | 0.346393 | ||||||||
\(694\) | 53.5277 | 2.03188 | ||||||||
\(695\) | −0.279059 | −0.0105853 | ||||||||
\(696\) | 22.8557 | 0.866343 | ||||||||
\(697\) | 13.3615 | 0.506105 | ||||||||
\(698\) | −30.1777 | −1.14224 | ||||||||
\(699\) | 74.4714 | 2.81677 | ||||||||
\(700\) | 8.63321 | 0.326305 | ||||||||
\(701\) | 23.4285 | 0.884882 | 0.442441 | − | 0.896798i | \(-0.354113\pi\) | ||||
0.442441 | + | 0.896798i | \(0.354113\pi\) | |||||||
\(702\) | −8.60006 | −0.324588 | ||||||||
\(703\) | 7.92373 | 0.298849 | ||||||||
\(704\) | −0.792018 | −0.0298503 | ||||||||
\(705\) | −0.0747253 | −0.00281432 | ||||||||
\(706\) | 18.5684 | 0.698830 | ||||||||
\(707\) | 25.7118 | 0.966993 | ||||||||
\(708\) | −19.3256 | −0.726300 | ||||||||
\(709\) | 16.2789 | 0.611366 | 0.305683 | − | 0.952133i | \(-0.401115\pi\) | ||||
0.305683 | + | 0.952133i | \(0.401115\pi\) | |||||||
\(710\) | 0.812281 | 0.0304843 | ||||||||
\(711\) | 38.5406 | 1.44539 | ||||||||
\(712\) | −11.9868 | −0.449223 | ||||||||
\(713\) | 65.8744 | 2.46702 | ||||||||
\(714\) | −30.9465 | −1.15814 | ||||||||
\(715\) | 0.141314 | 0.00528483 | ||||||||
\(716\) | −16.5252 | −0.617576 | ||||||||
\(717\) | −27.4125 | −1.02374 | ||||||||
\(718\) | 48.5861 | 1.81322 | ||||||||
\(719\) | 18.8813 | 0.704155 | 0.352078 | − | 0.935971i | \(-0.385475\pi\) | ||||
0.352078 | + | 0.935971i | \(0.385475\pi\) | |||||||
\(720\) | 0.868547 | 0.0323688 | ||||||||
\(721\) | 18.0075 | 0.670633 | ||||||||
\(722\) | −76.4624 | −2.84564 | ||||||||
\(723\) | −11.7959 | −0.438693 | ||||||||
\(724\) | −16.6062 | −0.617165 | ||||||||
\(725\) | −26.2772 | −0.975910 | ||||||||
\(726\) | 40.8880 | 1.51749 | ||||||||
\(727\) | −6.51462 | −0.241614 | −0.120807 | − | 0.992676i | \(-0.538548\pi\) | ||||
−0.120807 | + | 0.992676i | \(0.538548\pi\) | |||||||
\(728\) | −5.97281 | −0.221367 | ||||||||
\(729\) | −39.6246 | −1.46758 | ||||||||
\(730\) | 0.754618 | 0.0279297 | ||||||||
\(731\) | 4.19954 | 0.155326 | ||||||||
\(732\) | −21.2350 | −0.784868 | ||||||||
\(733\) | 15.2451 | 0.563091 | 0.281546 | − | 0.959548i | \(-0.409153\pi\) | ||||
0.281546 | + | 0.959548i | \(0.409153\pi\) | |||||||
\(734\) | −39.7713 | −1.46799 | ||||||||
\(735\) | 0.506067 | 0.0186666 | ||||||||
\(736\) | 43.9118 | 1.61861 | ||||||||
\(737\) | 19.3399 | 0.712393 | ||||||||
\(738\) | 21.9078 | 0.806437 | ||||||||
\(739\) | 49.1695 | 1.80873 | 0.904365 | − | 0.426759i | \(-0.140345\pi\) | ||||
0.904365 | + | 0.426759i | \(0.140345\pi\) | |||||||
\(740\) | 0.0472559 | 0.00173716 | ||||||||
\(741\) | −45.3777 | −1.66699 | ||||||||
\(742\) | −25.2648 | −0.927501 | ||||||||
\(743\) | −30.5878 | −1.12216 | −0.561079 | − | 0.827762i | \(-0.689614\pi\) | ||||
−0.561079 | + | 0.827762i | \(0.689614\pi\) | |||||||
\(744\) | 35.2657 | 1.29290 | ||||||||
\(745\) | 0.847035 | 0.0310330 | ||||||||
\(746\) | 5.96382 | 0.218351 | ||||||||
\(747\) | −5.04342 | −0.184529 | ||||||||
\(748\) | 6.19347 | 0.226456 | ||||||||
\(749\) | −9.39692 | −0.343356 | ||||||||
\(750\) | −2.05895 | −0.0751821 | ||||||||
\(751\) | −7.57697 | −0.276488 | −0.138244 | − | 0.990398i | \(-0.544146\pi\) | ||||
−0.138244 | + | 0.990398i | \(0.544146\pi\) | |||||||
\(752\) | −3.16671 | −0.115478 | ||||||||
\(753\) | −1.57361 | −0.0573457 | ||||||||
\(754\) | −20.0749 | −0.731086 | ||||||||
\(755\) | −0.921580 | −0.0335397 | ||||||||
\(756\) | −3.89054 | −0.141498 | ||||||||
\(757\) | 32.7115 | 1.18892 | 0.594460 | − | 0.804125i | \(-0.297366\pi\) | ||||
0.594460 | + | 0.804125i | \(0.297366\pi\) | |||||||
\(758\) | 41.1678 | 1.49528 | ||||||||
\(759\) | −30.5289 | −1.10813 | ||||||||
\(760\) | 0.592154 | 0.0214797 | ||||||||
\(761\) | −5.23114 | −0.189629 | −0.0948144 | − | 0.995495i | \(-0.530226\pi\) | ||||
−0.0948144 | + | 0.995495i | \(0.530226\pi\) | |||||||
\(762\) | −51.1389 | −1.85257 | ||||||||
\(763\) | 1.64580 | 0.0595820 | ||||||||
\(764\) | −10.4259 | −0.377196 | ||||||||
\(765\) | 0.714485 | 0.0258323 | ||||||||
\(766\) | −13.3666 | −0.482954 | ||||||||
\(767\) | −15.3718 | −0.555042 | ||||||||
\(768\) | 50.9837 | 1.83972 | ||||||||
\(769\) | −46.9816 | −1.69420 | −0.847101 | − | 0.531432i | \(-0.821654\pi\) | ||||
−0.847101 | + | 0.531432i | \(0.821654\pi\) | |||||||
\(770\) | 0.185749 | 0.00669394 | ||||||||
\(771\) | −52.4748 | −1.88983 | ||||||||
\(772\) | 3.67586 | 0.132297 | ||||||||
\(773\) | 24.2523 | 0.872296 | 0.436148 | − | 0.899875i | \(-0.356342\pi\) | ||||
0.436148 | + | 0.899875i | \(0.356342\pi\) | |||||||
\(774\) | 6.88563 | 0.247499 | ||||||||
\(775\) | −40.5450 | −1.45642 | ||||||||
\(776\) | −15.4942 | −0.556209 | ||||||||
\(777\) | 4.31060 | 0.154642 | ||||||||
\(778\) | −33.0775 | −1.18589 | ||||||||
\(779\) | 25.7531 | 0.922701 | ||||||||
\(780\) | −0.270625 | −0.00968994 | ||||||||
\(781\) | −14.8289 | −0.530621 | ||||||||
\(782\) | 58.2972 | 2.08470 | ||||||||
\(783\) | 11.8418 | 0.423191 | ||||||||
\(784\) | 21.4461 | 0.765934 | ||||||||
\(785\) | 0.475403 | 0.0169679 | ||||||||
\(786\) | 15.8653 | 0.565898 | ||||||||
\(787\) | 3.13846 | 0.111874 | 0.0559369 | − | 0.998434i | \(-0.482185\pi\) | ||||
0.0559369 | + | 0.998434i | \(0.482185\pi\) | |||||||
\(788\) | 19.5814 | 0.697558 | ||||||||
\(789\) | −25.9267 | −0.923015 | ||||||||
\(790\) | 0.785073 | 0.0279316 | ||||||||
\(791\) | 18.2750 | 0.649782 | ||||||||
\(792\) | −9.19618 | −0.326772 | ||||||||
\(793\) | −16.8905 | −0.599800 | ||||||||
\(794\) | 21.0205 | 0.745991 | ||||||||
\(795\) | 1.03666 | 0.0367666 | ||||||||
\(796\) | −5.52858 | −0.195955 | ||||||||
\(797\) | 16.8411 | 0.596544 | 0.298272 | − | 0.954481i | \(-0.403590\pi\) | ||||
0.298272 | + | 0.954481i | \(0.403590\pi\) | |||||||
\(798\) | −59.6465 | −2.11146 | ||||||||
\(799\) | −2.60501 | −0.0921585 | ||||||||
\(800\) | −27.0272 | −0.955556 | ||||||||
\(801\) | −27.8762 | −0.984957 | ||||||||
\(802\) | 9.41707 | 0.332528 | ||||||||
\(803\) | −13.7763 | −0.486154 | ||||||||
\(804\) | −37.0371 | −1.30620 | ||||||||
\(805\) | 0.601737 | 0.0212084 | ||||||||
\(806\) | −30.9751 | −1.09105 | ||||||||
\(807\) | 39.9760 | 1.40722 | ||||||||
\(808\) | −25.9301 | −0.912219 | ||||||||
\(809\) | −7.10227 | −0.249702 | −0.124851 | − | 0.992175i | \(-0.539845\pi\) | ||||
−0.124851 | + | 0.992175i | \(0.539845\pi\) | |||||||
\(810\) | −0.446654 | −0.0156938 | ||||||||
\(811\) | 29.6680 | 1.04179 | 0.520893 | − | 0.853622i | \(-0.325599\pi\) | ||||
0.520893 | + | 0.853622i | \(0.325599\pi\) | |||||||
\(812\) | −9.08162 | −0.318702 | ||||||||
\(813\) | −28.4583 | −0.998076 | ||||||||
\(814\) | −2.50665 | −0.0878582 | ||||||||
\(815\) | −0.735574 | −0.0257660 | ||||||||
\(816\) | 53.8113 | 1.88377 | ||||||||
\(817\) | 8.09422 | 0.283181 | ||||||||
\(818\) | −27.2745 | −0.953630 | ||||||||
\(819\) | −13.8903 | −0.485366 | ||||||||
\(820\) | 0.153588 | 0.00536351 | ||||||||
\(821\) | −48.1826 | −1.68159 | −0.840793 | − | 0.541357i | \(-0.817911\pi\) | ||||
−0.840793 | + | 0.541357i | \(0.817911\pi\) | |||||||
\(822\) | −9.72587 | −0.339229 | ||||||||
\(823\) | −30.1699 | −1.05166 | −0.525829 | − | 0.850590i | \(-0.676245\pi\) | ||||
−0.525829 | + | 0.850590i | \(0.676245\pi\) | |||||||
\(824\) | −18.1604 | −0.632646 | ||||||||
\(825\) | 18.7902 | 0.654191 | ||||||||
\(826\) | −20.2054 | −0.703034 | ||||||||
\(827\) | 22.2195 | 0.772649 | 0.386325 | − | 0.922363i | \(-0.373744\pi\) | ||||
0.386325 | + | 0.922363i | \(0.373744\pi\) | |||||||
\(828\) | 32.8970 | 1.14325 | ||||||||
\(829\) | −55.5836 | −1.93050 | −0.965249 | − | 0.261333i | \(-0.915838\pi\) | ||||
−0.965249 | + | 0.261333i | \(0.915838\pi\) | |||||||
\(830\) | −0.102734 | −0.00356597 | ||||||||
\(831\) | 32.2669 | 1.11933 | ||||||||
\(832\) | 1.20645 | 0.0418262 | ||||||||
\(833\) | 17.6421 | 0.611261 | ||||||||
\(834\) | −28.3478 | −0.981603 | ||||||||
\(835\) | 0.876708 | 0.0303397 | ||||||||
\(836\) | 11.9373 | 0.412861 | ||||||||
\(837\) | 18.2715 | 0.631556 | ||||||||
\(838\) | 24.0197 | 0.829748 | ||||||||
\(839\) | −4.92119 | −0.169898 | −0.0849492 | − | 0.996385i | \(-0.527073\pi\) | ||||
−0.0849492 | + | 0.996385i | \(0.527073\pi\) | |||||||
\(840\) | 0.322138 | 0.0111148 | ||||||||
\(841\) | −1.35797 | −0.0468267 | ||||||||
\(842\) | −41.3148 | −1.42380 | ||||||||
\(843\) | −7.39164 | −0.254582 | ||||||||
\(844\) | −14.7651 | −0.508237 | ||||||||
\(845\) | 0.370069 | 0.0127308 | ||||||||
\(846\) | −4.27121 | −0.146847 | ||||||||
\(847\) | 14.7128 | 0.505538 | ||||||||
\(848\) | 43.9317 | 1.50862 | ||||||||
\(849\) | 35.9638 | 1.23427 | ||||||||
\(850\) | −35.8813 | −1.23072 | ||||||||
\(851\) | −8.12033 | −0.278361 | ||||||||
\(852\) | 28.3984 | 0.972914 | ||||||||
\(853\) | 28.0324 | 0.959812 | 0.479906 | − | 0.877320i | \(-0.340671\pi\) | ||||
0.479906 | + | 0.877320i | \(0.340671\pi\) | |||||||
\(854\) | −22.2017 | −0.759726 | ||||||||
\(855\) | 1.37710 | 0.0470959 | ||||||||
\(856\) | 9.47670 | 0.323907 | ||||||||
\(857\) | −4.28492 | −0.146370 | −0.0731851 | − | 0.997318i | \(-0.523316\pi\) | ||||
−0.0731851 | + | 0.997318i | \(0.523316\pi\) | |||||||
\(858\) | 14.3551 | 0.490076 | ||||||||
\(859\) | 55.0243 | 1.87741 | 0.938703 | − | 0.344728i | \(-0.112029\pi\) | ||||
0.938703 | + | 0.344728i | \(0.112029\pi\) | |||||||
\(860\) | 0.0482726 | 0.00164608 | ||||||||
\(861\) | 14.0100 | 0.477459 | ||||||||
\(862\) | 7.61258 | 0.259285 | ||||||||
\(863\) | −27.3096 | −0.929631 | −0.464815 | − | 0.885408i | \(-0.653879\pi\) | ||||
−0.464815 | + | 0.885408i | \(0.653879\pi\) | |||||||
\(864\) | 12.1798 | 0.414364 | ||||||||
\(865\) | −0.685663 | −0.0233133 | ||||||||
\(866\) | −32.2431 | −1.09567 | ||||||||
\(867\) | −0.259217 | −0.00880347 | ||||||||
\(868\) | −14.0127 | −0.475621 | ||||||||
\(869\) | −14.3323 | −0.486188 | ||||||||
\(870\) | 1.08272 | 0.0367078 | ||||||||
\(871\) | −29.4597 | −0.998204 | ||||||||
\(872\) | −1.65978 | −0.0562071 | ||||||||
\(873\) | −36.0330 | −1.21953 | ||||||||
\(874\) | 112.362 | 3.80071 | ||||||||
\(875\) | −0.740875 | −0.0250461 | ||||||||
\(876\) | 26.3825 | 0.891382 | ||||||||
\(877\) | −36.2740 | −1.22489 | −0.612443 | − | 0.790515i | \(-0.709813\pi\) | ||||
−0.612443 | + | 0.790515i | \(0.709813\pi\) | |||||||
\(878\) | 50.3871 | 1.70048 | ||||||||
\(879\) | −41.0008 | −1.38292 | ||||||||
\(880\) | −0.322990 | −0.0108880 | ||||||||
\(881\) | −27.6231 | −0.930644 | −0.465322 | − | 0.885141i | \(-0.654062\pi\) | ||||
−0.465322 | + | 0.885141i | \(0.654062\pi\) | |||||||
\(882\) | 28.9262 | 0.973995 | ||||||||
\(883\) | −1.50723 | −0.0507223 | −0.0253612 | − | 0.999678i | \(-0.508074\pi\) | ||||
−0.0253612 | + | 0.999678i | \(0.508074\pi\) | |||||||
\(884\) | −9.43429 | −0.317310 | ||||||||
\(885\) | 0.829062 | 0.0278686 | ||||||||
\(886\) | 31.5888 | 1.06125 | ||||||||
\(887\) | −1.36407 | −0.0458011 | −0.0229005 | − | 0.999738i | \(-0.507290\pi\) | ||||
−0.0229005 | + | 0.999738i | \(0.507290\pi\) | |||||||
\(888\) | −4.34720 | −0.145883 | ||||||||
\(889\) | −18.4014 | −0.617164 | ||||||||
\(890\) | −0.567839 | −0.0190340 | ||||||||
\(891\) | 8.15408 | 0.273172 | ||||||||
\(892\) | −5.42909 | −0.181779 | ||||||||
\(893\) | −5.02090 | −0.168018 | ||||||||
\(894\) | 86.0447 | 2.87776 | ||||||||
\(895\) | 0.708927 | 0.0236968 | ||||||||
\(896\) | 19.3856 | 0.647628 | ||||||||
\(897\) | 46.5035 | 1.55271 | ||||||||
\(898\) | −6.57048 | −0.219260 | ||||||||
\(899\) | 42.6509 | 1.42249 | ||||||||
\(900\) | −20.2477 | −0.674924 | ||||||||
\(901\) | 36.1392 | 1.20397 | ||||||||
\(902\) | −8.14694 | −0.271263 | ||||||||
\(903\) | 4.40335 | 0.146534 | ||||||||
\(904\) | −18.4301 | −0.612977 | ||||||||
\(905\) | 0.712402 | 0.0236811 | ||||||||
\(906\) | −93.6172 | −3.11022 | ||||||||
\(907\) | 58.1615 | 1.93122 | 0.965611 | − | 0.259991i | \(-0.0837197\pi\) | ||||
0.965611 | + | 0.259991i | \(0.0837197\pi\) | |||||||
\(908\) | 23.5237 | 0.780660 | ||||||||
\(909\) | −60.3027 | −2.00011 | ||||||||
\(910\) | −0.282945 | −0.00937954 | ||||||||
\(911\) | 45.8785 | 1.52002 | 0.760011 | − | 0.649911i | \(-0.225194\pi\) | ||||
0.760011 | + | 0.649911i | \(0.225194\pi\) | |||||||
\(912\) | 103.716 | 3.43439 | ||||||||
\(913\) | 1.87552 | 0.0620705 | ||||||||
\(914\) | −2.33212 | −0.0771396 | ||||||||
\(915\) | 0.910975 | 0.0301159 | ||||||||
\(916\) | 22.3090 | 0.737109 | ||||||||
\(917\) | 5.70885 | 0.188523 | ||||||||
\(918\) | 16.1698 | 0.533685 | ||||||||
\(919\) | 50.0523 | 1.65107 | 0.825536 | − | 0.564349i | \(-0.190873\pi\) | ||||
0.825536 | + | 0.564349i | \(0.190873\pi\) | |||||||
\(920\) | −0.606846 | −0.0200071 | ||||||||
\(921\) | 77.5295 | 2.55468 | ||||||||
\(922\) | −57.5111 | −1.89403 | ||||||||
\(923\) | 22.5884 | 0.743506 | ||||||||
\(924\) | 6.49405 | 0.213639 | ||||||||
\(925\) | 4.99797 | 0.164332 | ||||||||
\(926\) | −37.3111 | −1.22612 | ||||||||
\(927\) | −42.2334 | −1.38713 | ||||||||
\(928\) | 28.4310 | 0.933293 | ||||||||
\(929\) | −10.1654 | −0.333515 | −0.166757 | − | 0.985998i | \(-0.553330\pi\) | ||||
−0.166757 | + | 0.985998i | \(0.553330\pi\) | |||||||
\(930\) | 1.67061 | 0.0547816 | ||||||||
\(931\) | 34.0034 | 1.11442 | ||||||||
\(932\) | 29.8421 | 0.977512 | ||||||||
\(933\) | −82.2988 | −2.69434 | ||||||||
\(934\) | 15.2314 | 0.498388 | ||||||||
\(935\) | −0.265698 | −0.00868926 | ||||||||
\(936\) | 14.0082 | 0.457873 | ||||||||
\(937\) | 27.8302 | 0.909172 | 0.454586 | − | 0.890703i | \(-0.349787\pi\) | ||||
0.454586 | + | 0.890703i | \(0.349787\pi\) | |||||||
\(938\) | −38.7232 | −1.26436 | ||||||||
\(939\) | −71.8601 | −2.34507 | ||||||||
\(940\) | −0.0299439 | −0.000976661 0 | ||||||||
\(941\) | 50.5334 | 1.64734 | 0.823671 | − | 0.567067i | \(-0.191922\pi\) | ||||
0.823671 | + | 0.567067i | \(0.191922\pi\) | |||||||
\(942\) | 48.2930 | 1.57347 | ||||||||
\(943\) | −26.3921 | −0.859445 | ||||||||
\(944\) | 35.1341 | 1.14352 | ||||||||
\(945\) | 0.166903 | 0.00542936 | ||||||||
\(946\) | −2.56059 | −0.0832519 | ||||||||
\(947\) | 41.6600 | 1.35377 | 0.676884 | − | 0.736090i | \(-0.263330\pi\) | ||||
0.676884 | + | 0.736090i | \(0.263330\pi\) | |||||||
\(948\) | 27.4472 | 0.891445 | ||||||||
\(949\) | 20.9849 | 0.681198 | ||||||||
\(950\) | −69.1578 | −2.24377 | ||||||||
\(951\) | −10.9547 | −0.355231 | ||||||||
\(952\) | 11.2301 | 0.363970 | ||||||||
\(953\) | −2.56093 | −0.0829568 | −0.0414784 | − | 0.999139i | \(-0.513207\pi\) | ||||
−0.0414784 | + | 0.999139i | \(0.513207\pi\) | |||||||
\(954\) | 59.2543 | 1.91843 | ||||||||
\(955\) | 0.447268 | 0.0144733 | ||||||||
\(956\) | −10.9847 | −0.355272 | ||||||||
\(957\) | −19.7662 | −0.638949 | ||||||||
\(958\) | −51.2237 | −1.65496 | ||||||||
\(959\) | −3.49968 | −0.113011 | ||||||||
\(960\) | −0.0650689 | −0.00210009 | ||||||||
\(961\) | 34.8091 | 1.12287 | ||||||||
\(962\) | 3.81830 | 0.123107 | ||||||||
\(963\) | 22.0389 | 0.710192 | ||||||||
\(964\) | −4.72683 | −0.152241 | ||||||||
\(965\) | −0.157693 | −0.00507633 | ||||||||
\(966\) | 61.1264 | 1.96671 | ||||||||
\(967\) | −4.48369 | −0.144186 | −0.0720929 | − | 0.997398i | \(-0.522968\pi\) | ||||
−0.0720929 | + | 0.997398i | \(0.522968\pi\) | |||||||
\(968\) | −14.8377 | −0.476902 | ||||||||
\(969\) | 85.3192 | 2.74085 | ||||||||
\(970\) | −0.733994 | −0.0235671 | ||||||||
\(971\) | −37.6981 | −1.20979 | −0.604895 | − | 0.796305i | \(-0.706785\pi\) | ||||
−0.604895 | + | 0.796305i | \(0.706785\pi\) | |||||||
\(972\) | −22.7074 | −0.728339 | ||||||||
\(973\) | −10.2004 | −0.327011 | ||||||||
\(974\) | 60.3538 | 1.93386 | ||||||||
\(975\) | −28.6224 | −0.916651 | ||||||||
\(976\) | 38.6054 | 1.23573 | ||||||||
\(977\) | −14.1754 | −0.453512 | −0.226756 | − | 0.973952i | \(-0.572812\pi\) | ||||
−0.226756 | + | 0.973952i | \(0.572812\pi\) | |||||||
\(978\) | −74.7221 | −2.38935 | ||||||||
\(979\) | 10.3664 | 0.331313 | ||||||||
\(980\) | 0.202791 | 0.00647792 | ||||||||
\(981\) | −3.85995 | −0.123239 | ||||||||
\(982\) | −19.9148 | −0.635507 | ||||||||
\(983\) | −20.5890 | −0.656687 | −0.328343 | − | 0.944558i | \(-0.606490\pi\) | ||||
−0.328343 | + | 0.944558i | \(0.606490\pi\) | |||||||
\(984\) | −14.1290 | −0.450414 | ||||||||
\(985\) | −0.840036 | −0.0267658 | ||||||||
\(986\) | 37.7450 | 1.20204 | ||||||||
\(987\) | −2.73143 | −0.0869424 | ||||||||
\(988\) | −18.1837 | −0.578501 | ||||||||
\(989\) | −8.29505 | −0.263767 | ||||||||
\(990\) | −0.435643 | −0.0138456 | ||||||||
\(991\) | 34.4809 | 1.09532 | 0.547661 | − | 0.836701i | \(-0.315518\pi\) | ||||
0.547661 | + | 0.836701i | \(0.315518\pi\) | |||||||
\(992\) | 43.8682 | 1.39282 | ||||||||
\(993\) | −66.3029 | −2.10406 | ||||||||
\(994\) | 29.6912 | 0.941749 | ||||||||
\(995\) | 0.237175 | 0.00751894 | ||||||||
\(996\) | −3.59174 | −0.113809 | ||||||||
\(997\) | −62.8352 | −1.99001 | −0.995005 | − | 0.0998249i | \(-0.968172\pi\) | ||||
−0.995005 | + | 0.0998249i | \(0.968172\pi\) | |||||||
\(998\) | −27.9863 | −0.885889 | ||||||||
\(999\) | −2.25233 | −0.0712605 |
(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 | 4033.2.a.d.1.20 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.d.1.20 | ✓ | 79 | 1.1 | even | 1 | trivial |