Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, 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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(0\) |
Dimension: | \(172\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.68534 | −1.89882 | −0.949412 | − | 0.314033i | \(-0.898320\pi\) | ||||
−0.949412 | + | 0.314033i | \(0.898320\pi\) | |||||||
\(3\) | −1.17289 | −0.677169 | −0.338584 | − | 0.940936i | \(-0.609948\pi\) | ||||
−0.338584 | + | 0.940936i | \(0.609948\pi\) | |||||||
\(4\) | 5.21107 | 2.60553 | ||||||||
\(5\) | 0.884422 | 0.395525 | 0.197763 | − | 0.980250i | \(-0.436632\pi\) | ||||
0.197763 | + | 0.980250i | \(0.436632\pi\) | |||||||
\(6\) | 3.14961 | 1.28582 | ||||||||
\(7\) | −0.361098 | −0.136482 | −0.0682411 | − | 0.997669i | \(-0.521739\pi\) | ||||
−0.0682411 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(8\) | −8.62282 | −3.04863 | ||||||||
\(9\) | −1.62433 | −0.541443 | ||||||||
\(10\) | −2.37498 | −0.751033 | ||||||||
\(11\) | −0.487997 | −0.147137 | −0.0735683 | − | 0.997290i | \(-0.523439\pi\) | ||||
−0.0735683 | + | 0.997290i | \(0.523439\pi\) | |||||||
\(12\) | −6.11201 | −1.76439 | ||||||||
\(13\) | 3.81664 | 1.05854 | 0.529272 | − | 0.848452i | \(-0.322465\pi\) | ||||
0.529272 | + | 0.848452i | \(0.322465\pi\) | |||||||
\(14\) | 0.969672 | 0.259156 | ||||||||
\(15\) | −1.03733 | −0.267837 | ||||||||
\(16\) | 12.7331 | 3.18327 | ||||||||
\(17\) | 1.24710 | 0.302466 | 0.151233 | − | 0.988498i | \(-0.451676\pi\) | ||||
0.151233 | + | 0.988498i | \(0.451676\pi\) | |||||||
\(18\) | 4.36188 | 1.02810 | ||||||||
\(19\) | 2.14182 | 0.491367 | 0.245684 | − | 0.969350i | \(-0.420988\pi\) | ||||
0.245684 | + | 0.969350i | \(0.420988\pi\) | |||||||
\(20\) | 4.60878 | 1.03055 | ||||||||
\(21\) | 0.423529 | 0.0924215 | ||||||||
\(22\) | 1.31044 | 0.279386 | ||||||||
\(23\) | −8.74394 | −1.82324 | −0.911619 | − | 0.411036i | \(-0.865167\pi\) | ||||
−0.911619 | + | 0.411036i | \(0.865167\pi\) | |||||||
\(24\) | 10.1136 | 2.06443 | ||||||||
\(25\) | −4.21780 | −0.843560 | ||||||||
\(26\) | −10.2490 | −2.00999 | ||||||||
\(27\) | 5.42383 | 1.04382 | ||||||||
\(28\) | −1.88171 | −0.355609 | ||||||||
\(29\) | −1.05174 | −0.195303 | −0.0976517 | − | 0.995221i | \(-0.531133\pi\) | ||||
−0.0976517 | + | 0.995221i | \(0.531133\pi\) | |||||||
\(30\) | 2.78559 | 0.508576 | ||||||||
\(31\) | 1.50367 | 0.270067 | 0.135034 | − | 0.990841i | \(-0.456886\pi\) | ||||
0.135034 | + | 0.990841i | \(0.456886\pi\) | |||||||
\(32\) | −16.9471 | −2.99585 | ||||||||
\(33\) | 0.572367 | 0.0996362 | ||||||||
\(34\) | −3.34889 | −0.574330 | ||||||||
\(35\) | −0.319363 | −0.0539822 | ||||||||
\(36\) | −8.46448 | −1.41075 | ||||||||
\(37\) | 8.49233 | 1.39613 | 0.698065 | − | 0.716034i | \(-0.254045\pi\) | ||||
0.698065 | + | 0.716034i | \(0.254045\pi\) | |||||||
\(38\) | −5.75152 | −0.933020 | ||||||||
\(39\) | −4.47650 | −0.716813 | ||||||||
\(40\) | −7.62621 | −1.20581 | ||||||||
\(41\) | 9.25630 | 1.44559 | 0.722796 | − | 0.691062i | \(-0.242857\pi\) | ||||
0.722796 | + | 0.691062i | \(0.242857\pi\) | |||||||
\(42\) | −1.13732 | −0.175492 | ||||||||
\(43\) | 7.47251 | 1.13955 | 0.569774 | − | 0.821802i | \(-0.307031\pi\) | ||||
0.569774 | + | 0.821802i | \(0.307031\pi\) | |||||||
\(44\) | −2.54298 | −0.383369 | ||||||||
\(45\) | −1.43659 | −0.214154 | ||||||||
\(46\) | 23.4805 | 3.46201 | ||||||||
\(47\) | −1.75620 | −0.256168 | −0.128084 | − | 0.991763i | \(-0.540883\pi\) | ||||
−0.128084 | + | 0.991763i | \(0.540883\pi\) | |||||||
\(48\) | −14.9345 | −2.15561 | ||||||||
\(49\) | −6.86961 | −0.981373 | ||||||||
\(50\) | 11.3262 | 1.60177 | ||||||||
\(51\) | −1.46271 | −0.204820 | ||||||||
\(52\) | 19.8887 | 2.75807 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | −14.5648 | −1.98202 | ||||||||
\(55\) | −0.431595 | −0.0581962 | ||||||||
\(56\) | 3.11368 | 0.416084 | ||||||||
\(57\) | −2.51212 | −0.332738 | ||||||||
\(58\) | 2.82428 | 0.370847 | ||||||||
\(59\) | −4.21030 | −0.548134 | −0.274067 | − | 0.961711i | \(-0.588369\pi\) | ||||
−0.274067 | + | 0.961711i | \(0.588369\pi\) | |||||||
\(60\) | −5.40559 | −0.697859 | ||||||||
\(61\) | 6.49096 | 0.831083 | 0.415541 | − | 0.909574i | \(-0.363592\pi\) | ||||
0.415541 | + | 0.909574i | \(0.363592\pi\) | |||||||
\(62\) | −4.03787 | −0.512811 | ||||||||
\(63\) | 0.586542 | 0.0738973 | ||||||||
\(64\) | 20.0425 | 2.50532 | ||||||||
\(65\) | 3.37552 | 0.418681 | ||||||||
\(66\) | −1.53700 | −0.189192 | ||||||||
\(67\) | −15.1703 | −1.85334 | −0.926671 | − | 0.375874i | \(-0.877342\pi\) | ||||
−0.926671 | + | 0.375874i | \(0.877342\pi\) | |||||||
\(68\) | 6.49872 | 0.788086 | ||||||||
\(69\) | 10.2557 | 1.23464 | ||||||||
\(70\) | 0.857599 | 0.102503 | ||||||||
\(71\) | −11.2902 | −1.33990 | −0.669949 | − | 0.742407i | \(-0.733684\pi\) | ||||
−0.669949 | + | 0.742407i | \(0.733684\pi\) | |||||||
\(72\) | 14.0063 | 1.65066 | ||||||||
\(73\) | 15.6610 | 1.83298 | 0.916492 | − | 0.400052i | \(-0.131008\pi\) | ||||
0.916492 | + | 0.400052i | \(0.131008\pi\) | |||||||
\(74\) | −22.8048 | −2.65101 | ||||||||
\(75\) | 4.94701 | 0.571232 | ||||||||
\(76\) | 11.1612 | 1.28027 | ||||||||
\(77\) | 0.176215 | 0.0200815 | ||||||||
\(78\) | 12.0209 | 1.36110 | ||||||||
\(79\) | −7.81059 | −0.878760 | −0.439380 | − | 0.898301i | \(-0.644802\pi\) | ||||
−0.439380 | + | 0.898301i | \(0.644802\pi\) | |||||||
\(80\) | 11.2614 | 1.25907 | ||||||||
\(81\) | −1.48857 | −0.165397 | ||||||||
\(82\) | −24.8564 | −2.74492 | ||||||||
\(83\) | 12.9474 | 1.42117 | 0.710583 | − | 0.703613i | \(-0.248431\pi\) | ||||
0.710583 | + | 0.703613i | \(0.248431\pi\) | |||||||
\(84\) | 2.20704 | 0.240807 | ||||||||
\(85\) | 1.10296 | 0.119633 | ||||||||
\(86\) | −20.0663 | −2.16380 | ||||||||
\(87\) | 1.23358 | 0.132253 | ||||||||
\(88\) | 4.20791 | 0.448564 | ||||||||
\(89\) | −7.41778 | −0.786284 | −0.393142 | − | 0.919478i | \(-0.628612\pi\) | ||||
−0.393142 | + | 0.919478i | \(0.628612\pi\) | |||||||
\(90\) | 3.85774 | 0.406642 | ||||||||
\(91\) | −1.37818 | −0.144473 | ||||||||
\(92\) | −45.5653 | −4.75051 | ||||||||
\(93\) | −1.76364 | −0.182881 | ||||||||
\(94\) | 4.71600 | 0.486418 | ||||||||
\(95\) | 1.89427 | 0.194348 | ||||||||
\(96\) | 19.8771 | 2.02869 | ||||||||
\(97\) | −12.2137 | −1.24011 | −0.620055 | − | 0.784558i | \(-0.712890\pi\) | ||||
−0.620055 | + | 0.784558i | \(0.712890\pi\) | |||||||
\(98\) | 18.4473 | 1.86345 | ||||||||
\(99\) | 0.792667 | 0.0796660 | ||||||||
\(100\) | −21.9792 | −2.19792 | ||||||||
\(101\) | −10.0030 | −0.995334 | −0.497667 | − | 0.867368i | \(-0.665810\pi\) | ||||
−0.497667 | + | 0.867368i | \(0.665810\pi\) | |||||||
\(102\) | 3.92788 | 0.388918 | ||||||||
\(103\) | 10.0840 | 0.993608 | 0.496804 | − | 0.867863i | \(-0.334507\pi\) | ||||
0.496804 | + | 0.867863i | \(0.334507\pi\) | |||||||
\(104\) | −32.9102 | −3.22711 | ||||||||
\(105\) | 0.374578 | 0.0365551 | ||||||||
\(106\) | 2.68534 | 0.260824 | ||||||||
\(107\) | −2.87826 | −0.278252 | −0.139126 | − | 0.990275i | \(-0.544429\pi\) | ||||
−0.139126 | + | 0.990275i | \(0.544429\pi\) | |||||||
\(108\) | 28.2639 | 2.71970 | ||||||||
\(109\) | 3.78290 | 0.362337 | 0.181168 | − | 0.983452i | \(-0.442012\pi\) | ||||
0.181168 | + | 0.983452i | \(0.442012\pi\) | |||||||
\(110\) | 1.15898 | 0.110504 | ||||||||
\(111\) | −9.96057 | −0.945416 | ||||||||
\(112\) | −4.59790 | −0.434460 | ||||||||
\(113\) | −0.945287 | −0.0889251 | −0.0444626 | − | 0.999011i | \(-0.514158\pi\) | ||||
−0.0444626 | + | 0.999011i | \(0.514158\pi\) | |||||||
\(114\) | 6.74590 | 0.631812 | ||||||||
\(115\) | −7.73333 | −0.721137 | ||||||||
\(116\) | −5.48069 | −0.508870 | ||||||||
\(117\) | −6.19947 | −0.573141 | ||||||||
\(118\) | 11.3061 | 1.04081 | ||||||||
\(119\) | −0.450325 | −0.0412813 | ||||||||
\(120\) | 8.94471 | 0.816536 | ||||||||
\(121\) | −10.7619 | −0.978351 | ||||||||
\(122\) | −17.4305 | −1.57808 | ||||||||
\(123\) | −10.8566 | −0.978909 | ||||||||
\(124\) | 7.83573 | 0.703670 | ||||||||
\(125\) | −8.15242 | −0.729175 | ||||||||
\(126\) | −1.57507 | −0.140318 | ||||||||
\(127\) | 14.4738 | 1.28434 | 0.642171 | − | 0.766562i | \(-0.278034\pi\) | ||||
0.642171 | + | 0.766562i | \(0.278034\pi\) | |||||||
\(128\) | −19.9269 | −1.76131 | ||||||||
\(129\) | −8.76443 | −0.771665 | ||||||||
\(130\) | −9.06442 | −0.795002 | ||||||||
\(131\) | 1.81293 | 0.158396 | 0.0791980 | − | 0.996859i | \(-0.474764\pi\) | ||||
0.0791980 | + | 0.996859i | \(0.474764\pi\) | |||||||
\(132\) | 2.98264 | 0.259606 | ||||||||
\(133\) | −0.773407 | −0.0670629 | ||||||||
\(134\) | 40.7373 | 3.51917 | ||||||||
\(135\) | 4.79695 | 0.412856 | ||||||||
\(136\) | −10.7535 | −0.922106 | ||||||||
\(137\) | 20.2414 | 1.72934 | 0.864671 | − | 0.502339i | \(-0.167527\pi\) | ||||
0.864671 | + | 0.502339i | \(0.167527\pi\) | |||||||
\(138\) | −27.5400 | −2.34436 | ||||||||
\(139\) | 5.02638 | 0.426332 | 0.213166 | − | 0.977016i | \(-0.431622\pi\) | ||||
0.213166 | + | 0.977016i | \(0.431622\pi\) | |||||||
\(140\) | −1.66422 | −0.140652 | ||||||||
\(141\) | 2.05983 | 0.173469 | ||||||||
\(142\) | 30.3180 | 2.54423 | ||||||||
\(143\) | −1.86251 | −0.155751 | ||||||||
\(144\) | −20.6827 | −1.72356 | ||||||||
\(145\) | −0.930182 | −0.0772474 | ||||||||
\(146\) | −42.0552 | −3.48052 | ||||||||
\(147\) | 8.05730 | 0.664555 | ||||||||
\(148\) | 44.2541 | 3.63767 | ||||||||
\(149\) | 11.8723 | 0.972618 | 0.486309 | − | 0.873787i | \(-0.338343\pi\) | ||||
0.486309 | + | 0.873787i | \(0.338343\pi\) | |||||||
\(150\) | −13.2844 | −1.08467 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | −18.4685 | −1.49800 | ||||||||
\(153\) | −2.02570 | −0.163768 | ||||||||
\(154\) | −0.473197 | −0.0381313 | ||||||||
\(155\) | 1.32988 | 0.106819 | ||||||||
\(156\) | −23.3273 | −1.86768 | ||||||||
\(157\) | −1.16809 | −0.0932236 | −0.0466118 | − | 0.998913i | \(-0.514842\pi\) | ||||
−0.0466118 | + | 0.998913i | \(0.514842\pi\) | |||||||
\(158\) | 20.9741 | 1.66861 | ||||||||
\(159\) | 1.17289 | 0.0930163 | ||||||||
\(160\) | −14.9884 | −1.18493 | ||||||||
\(161\) | 3.15742 | 0.248840 | ||||||||
\(162\) | 3.99733 | 0.314060 | ||||||||
\(163\) | −6.12530 | −0.479770 | −0.239885 | − | 0.970801i | \(-0.577110\pi\) | ||||
−0.239885 | + | 0.970801i | \(0.577110\pi\) | |||||||
\(164\) | 48.2352 | 3.76654 | ||||||||
\(165\) | 0.506213 | 0.0394087 | ||||||||
\(166\) | −34.7683 | −2.69855 | ||||||||
\(167\) | −5.90499 | −0.456942 | −0.228471 | − | 0.973551i | \(-0.573373\pi\) | ||||
−0.228471 | + | 0.973551i | \(0.573373\pi\) | |||||||
\(168\) | −3.65201 | −0.281759 | ||||||||
\(169\) | 1.56671 | 0.120516 | ||||||||
\(170\) | −2.96183 | −0.227162 | ||||||||
\(171\) | −3.47902 | −0.266047 | ||||||||
\(172\) | 38.9398 | 2.96913 | ||||||||
\(173\) | 16.5708 | 1.25985 | 0.629926 | − | 0.776655i | \(-0.283085\pi\) | ||||
0.629926 | + | 0.776655i | \(0.283085\pi\) | |||||||
\(174\) | −3.31258 | −0.251126 | ||||||||
\(175\) | 1.52304 | 0.115131 | ||||||||
\(176\) | −6.21371 | −0.468376 | ||||||||
\(177\) | 4.93822 | 0.371179 | ||||||||
\(178\) | 19.9193 | 1.49301 | ||||||||
\(179\) | −4.28985 | −0.320639 | −0.160319 | − | 0.987065i | \(-0.551252\pi\) | ||||
−0.160319 | + | 0.987065i | \(0.551252\pi\) | |||||||
\(180\) | −7.48617 | −0.557986 | ||||||||
\(181\) | −7.42026 | −0.551543 | −0.275772 | − | 0.961223i | \(-0.588933\pi\) | ||||
−0.275772 | + | 0.961223i | \(0.588933\pi\) | |||||||
\(182\) | 3.70089 | 0.274328 | ||||||||
\(183\) | −7.61319 | −0.562783 | ||||||||
\(184\) | 75.3974 | 5.55837 | ||||||||
\(185\) | 7.51080 | 0.552205 | ||||||||
\(186\) | 4.73598 | 0.347259 | ||||||||
\(187\) | −0.608580 | −0.0445038 | ||||||||
\(188\) | −9.15168 | −0.667455 | ||||||||
\(189\) | −1.95853 | −0.142462 | ||||||||
\(190\) | −5.08677 | −0.369033 | ||||||||
\(191\) | 13.2090 | 0.955766 | 0.477883 | − | 0.878423i | \(-0.341404\pi\) | ||||
0.477883 | + | 0.878423i | \(0.341404\pi\) | |||||||
\(192\) | −23.5077 | −1.69652 | ||||||||
\(193\) | 12.0278 | 0.865778 | 0.432889 | − | 0.901447i | \(-0.357494\pi\) | ||||
0.432889 | + | 0.901447i | \(0.357494\pi\) | |||||||
\(194\) | 32.7979 | 2.35475 | ||||||||
\(195\) | −3.95911 | −0.283518 | ||||||||
\(196\) | −35.7980 | −2.55700 | ||||||||
\(197\) | −22.8987 | −1.63146 | −0.815732 | − | 0.578430i | \(-0.803666\pi\) | ||||
−0.815732 | + | 0.578430i | \(0.803666\pi\) | |||||||
\(198\) | −2.12858 | −0.151272 | ||||||||
\(199\) | 8.38940 | 0.594709 | 0.297355 | − | 0.954767i | \(-0.403896\pi\) | ||||
0.297355 | + | 0.954767i | \(0.403896\pi\) | |||||||
\(200\) | 36.3693 | 2.57170 | ||||||||
\(201\) | 17.7930 | 1.25502 | ||||||||
\(202\) | 26.8614 | 1.88996 | ||||||||
\(203\) | 0.379782 | 0.0266554 | ||||||||
\(204\) | −7.62229 | −0.533667 | ||||||||
\(205\) | 8.18648 | 0.571768 | ||||||||
\(206\) | −27.0790 | −1.88669 | ||||||||
\(207\) | 14.2030 | 0.987179 | ||||||||
\(208\) | 48.5976 | 3.36964 | ||||||||
\(209\) | −1.04520 | −0.0722981 | ||||||||
\(210\) | −1.00587 | −0.0694116 | ||||||||
\(211\) | 8.92553 | 0.614459 | 0.307229 | − | 0.951636i | \(-0.400598\pi\) | ||||
0.307229 | + | 0.951636i | \(0.400598\pi\) | |||||||
\(212\) | −5.21107 | −0.357898 | ||||||||
\(213\) | 13.2422 | 0.907337 | ||||||||
\(214\) | 7.72911 | 0.528351 | ||||||||
\(215\) | 6.60885 | 0.450720 | ||||||||
\(216\) | −46.7687 | −3.18221 | ||||||||
\(217\) | −0.542973 | −0.0368594 | ||||||||
\(218\) | −10.1584 | −0.688013 | ||||||||
\(219\) | −18.3687 | −1.24124 | ||||||||
\(220\) | −2.24907 | −0.151632 | ||||||||
\(221\) | 4.75972 | 0.320174 | ||||||||
\(222\) | 26.7476 | 1.79518 | ||||||||
\(223\) | −15.7402 | −1.05404 | −0.527022 | − | 0.849852i | \(-0.676691\pi\) | ||||
−0.527022 | + | 0.849852i | \(0.676691\pi\) | |||||||
\(224\) | 6.11956 | 0.408880 | ||||||||
\(225\) | 6.85109 | 0.456739 | ||||||||
\(226\) | 2.53842 | 0.168853 | ||||||||
\(227\) | −14.5190 | −0.963659 | −0.481829 | − | 0.876265i | \(-0.660028\pi\) | ||||
−0.481829 | + | 0.876265i | \(0.660028\pi\) | |||||||
\(228\) | −13.0908 | −0.866961 | ||||||||
\(229\) | 10.6816 | 0.705858 | 0.352929 | − | 0.935650i | \(-0.385186\pi\) | ||||
0.352929 | + | 0.935650i | \(0.385186\pi\) | |||||||
\(230\) | 20.7667 | 1.36931 | ||||||||
\(231\) | −0.206681 | −0.0135986 | ||||||||
\(232\) | 9.06897 | 0.595407 | ||||||||
\(233\) | 9.25329 | 0.606203 | 0.303101 | − | 0.952958i | \(-0.401978\pi\) | ||||
0.303101 | + | 0.952958i | \(0.401978\pi\) | |||||||
\(234\) | 16.6477 | 1.08829 | ||||||||
\(235\) | −1.55322 | −0.101321 | ||||||||
\(236\) | −21.9402 | −1.42818 | ||||||||
\(237\) | 9.16096 | 0.595069 | ||||||||
\(238\) | 1.20928 | 0.0783858 | ||||||||
\(239\) | −14.2837 | −0.923939 | −0.461969 | − | 0.886896i | \(-0.652857\pi\) | ||||
−0.461969 | + | 0.886896i | \(0.652857\pi\) | |||||||
\(240\) | −13.2084 | −0.852599 | ||||||||
\(241\) | 13.1156 | 0.844851 | 0.422426 | − | 0.906398i | \(-0.361179\pi\) | ||||
0.422426 | + | 0.906398i | \(0.361179\pi\) | |||||||
\(242\) | 28.8993 | 1.85772 | ||||||||
\(243\) | −14.5256 | −0.931815 | ||||||||
\(244\) | 33.8248 | 2.16541 | ||||||||
\(245\) | −6.07563 | −0.388158 | ||||||||
\(246\) | 29.1538 | 1.85878 | ||||||||
\(247\) | 8.17455 | 0.520134 | ||||||||
\(248\) | −12.9659 | −0.823335 | ||||||||
\(249\) | −15.1859 | −0.962369 | ||||||||
\(250\) | 21.8920 | 1.38457 | ||||||||
\(251\) | −22.1267 | −1.39662 | −0.698312 | − | 0.715794i | \(-0.746065\pi\) | ||||
−0.698312 | + | 0.715794i | \(0.746065\pi\) | |||||||
\(252\) | 3.05651 | 0.192542 | ||||||||
\(253\) | 4.26702 | 0.268265 | ||||||||
\(254\) | −38.8671 | −2.43874 | ||||||||
\(255\) | −1.29365 | −0.0810117 | ||||||||
\(256\) | 13.4256 | 0.839100 | ||||||||
\(257\) | 20.1509 | 1.25698 | 0.628490 | − | 0.777818i | \(-0.283673\pi\) | ||||
0.628490 | + | 0.777818i | \(0.283673\pi\) | |||||||
\(258\) | 23.5355 | 1.46526 | ||||||||
\(259\) | −3.06657 | −0.190547 | ||||||||
\(260\) | 17.5900 | 1.09089 | ||||||||
\(261\) | 1.70837 | 0.105746 | ||||||||
\(262\) | −4.86833 | −0.300766 | ||||||||
\(263\) | 16.1841 | 0.997957 | 0.498978 | − | 0.866614i | \(-0.333709\pi\) | ||||
0.498978 | + | 0.866614i | \(0.333709\pi\) | |||||||
\(264\) | −4.93541 | −0.303754 | ||||||||
\(265\) | −0.884422 | −0.0543296 | ||||||||
\(266\) | 2.07686 | 0.127341 | ||||||||
\(267\) | 8.70025 | 0.532446 | ||||||||
\(268\) | −79.0532 | −4.82894 | ||||||||
\(269\) | 22.3131 | 1.36045 | 0.680227 | − | 0.733001i | \(-0.261881\pi\) | ||||
0.680227 | + | 0.733001i | \(0.261881\pi\) | |||||||
\(270\) | −12.8815 | −0.783941 | ||||||||
\(271\) | −7.62998 | −0.463488 | −0.231744 | − | 0.972777i | \(-0.574443\pi\) | ||||
−0.231744 | + | 0.972777i | \(0.574443\pi\) | |||||||
\(272\) | 15.8794 | 0.962832 | ||||||||
\(273\) | 1.61645 | 0.0978323 | ||||||||
\(274\) | −54.3552 | −3.28372 | ||||||||
\(275\) | 2.05827 | 0.124118 | ||||||||
\(276\) | 53.4431 | 3.21689 | ||||||||
\(277\) | −8.61319 | −0.517516 | −0.258758 | − | 0.965942i | \(-0.583313\pi\) | ||||
−0.258758 | + | 0.965942i | \(0.583313\pi\) | |||||||
\(278\) | −13.4976 | −0.809530 | ||||||||
\(279\) | −2.44246 | −0.146226 | ||||||||
\(280\) | 2.75381 | 0.164572 | ||||||||
\(281\) | 13.4241 | 0.800815 | 0.400408 | − | 0.916337i | \(-0.368869\pi\) | ||||
0.400408 | + | 0.916337i | \(0.368869\pi\) | |||||||
\(282\) | −5.53135 | −0.329387 | ||||||||
\(283\) | 24.0622 | 1.43035 | 0.715176 | − | 0.698945i | \(-0.246347\pi\) | ||||
0.715176 | + | 0.698945i | \(0.246347\pi\) | |||||||
\(284\) | −58.8339 | −3.49115 | ||||||||
\(285\) | −2.22177 | −0.131606 | ||||||||
\(286\) | 5.00147 | 0.295743 | ||||||||
\(287\) | −3.34243 | −0.197298 | ||||||||
\(288\) | 27.5276 | 1.62208 | ||||||||
\(289\) | −15.4447 | −0.908514 | ||||||||
\(290\) | 2.49786 | 0.146679 | ||||||||
\(291\) | 14.3253 | 0.839764 | ||||||||
\(292\) | 81.6107 | 4.77590 | ||||||||
\(293\) | −30.3761 | −1.77459 | −0.887294 | − | 0.461204i | \(-0.847418\pi\) | ||||
−0.887294 | + | 0.461204i | \(0.847418\pi\) | |||||||
\(294\) | −21.6366 | −1.26187 | ||||||||
\(295\) | −3.72368 | −0.216801 | ||||||||
\(296\) | −73.2278 | −4.25628 | ||||||||
\(297\) | −2.64681 | −0.153584 | ||||||||
\(298\) | −31.8812 | −1.84683 | ||||||||
\(299\) | −33.3724 | −1.92998 | ||||||||
\(300\) | 25.7792 | 1.48836 | ||||||||
\(301\) | −2.69831 | −0.155528 | ||||||||
\(302\) | −2.68534 | −0.154524 | ||||||||
\(303\) | 11.7324 | 0.674009 | ||||||||
\(304\) | 27.2720 | 1.56416 | ||||||||
\(305\) | 5.74075 | 0.328714 | ||||||||
\(306\) | 5.43970 | 0.310967 | ||||||||
\(307\) | 2.56443 | 0.146360 | 0.0731800 | − | 0.997319i | \(-0.476685\pi\) | ||||
0.0731800 | + | 0.997319i | \(0.476685\pi\) | |||||||
\(308\) | 0.918267 | 0.0523231 | ||||||||
\(309\) | −11.8274 | −0.672840 | ||||||||
\(310\) | −3.57118 | −0.202830 | ||||||||
\(311\) | 9.57297 | 0.542833 | 0.271417 | − | 0.962462i | \(-0.412508\pi\) | ||||
0.271417 | + | 0.962462i | \(0.412508\pi\) | |||||||
\(312\) | 38.6000 | 2.18530 | ||||||||
\(313\) | 33.9493 | 1.91893 | 0.959465 | − | 0.281829i | \(-0.0909411\pi\) | ||||
0.959465 | + | 0.281829i | \(0.0909411\pi\) | |||||||
\(314\) | 3.13672 | 0.177015 | ||||||||
\(315\) | 0.518750 | 0.0292283 | ||||||||
\(316\) | −40.7015 | −2.28964 | ||||||||
\(317\) | 16.7272 | 0.939492 | 0.469746 | − | 0.882802i | \(-0.344346\pi\) | ||||
0.469746 | + | 0.882802i | \(0.344346\pi\) | |||||||
\(318\) | −3.14961 | −0.176622 | ||||||||
\(319\) | 0.513246 | 0.0287363 | ||||||||
\(320\) | 17.7261 | 0.990917 | ||||||||
\(321\) | 3.37588 | 0.188423 | ||||||||
\(322\) | −8.47876 | −0.472503 | ||||||||
\(323\) | 2.67106 | 0.148622 | ||||||||
\(324\) | −7.75705 | −0.430947 | ||||||||
\(325\) | −16.0978 | −0.892945 | ||||||||
\(326\) | 16.4485 | 0.910999 | ||||||||
\(327\) | −4.43693 | −0.245363 | ||||||||
\(328\) | −79.8154 | −4.40707 | ||||||||
\(329\) | 0.634161 | 0.0349624 | ||||||||
\(330\) | −1.35936 | −0.0748301 | ||||||||
\(331\) | −29.1574 | −1.60264 | −0.801319 | − | 0.598238i | \(-0.795868\pi\) | ||||
−0.801319 | + | 0.598238i | \(0.795868\pi\) | |||||||
\(332\) | 67.4700 | 3.70290 | ||||||||
\(333\) | −13.7943 | −0.755925 | ||||||||
\(334\) | 15.8569 | 0.867652 | ||||||||
\(335\) | −13.4169 | −0.733044 | ||||||||
\(336\) | 5.39283 | 0.294203 | ||||||||
\(337\) | 27.6815 | 1.50791 | 0.753955 | − | 0.656926i | \(-0.228144\pi\) | ||||
0.753955 | + | 0.656926i | \(0.228144\pi\) | |||||||
\(338\) | −4.20716 | −0.228839 | ||||||||
\(339\) | 1.10872 | 0.0602173 | ||||||||
\(340\) | 5.74761 | 0.311708 | ||||||||
\(341\) | −0.733787 | −0.0397368 | ||||||||
\(342\) | 9.34236 | 0.505177 | ||||||||
\(343\) | 5.00829 | 0.270422 | ||||||||
\(344\) | −64.4341 | −3.47405 | ||||||||
\(345\) | 9.07035 | 0.488331 | ||||||||
\(346\) | −44.4982 | −2.39224 | ||||||||
\(347\) | −6.39575 | −0.343342 | −0.171671 | − | 0.985154i | \(-0.554917\pi\) | ||||
−0.171671 | + | 0.985154i | \(0.554917\pi\) | |||||||
\(348\) | 6.42825 | 0.344590 | ||||||||
\(349\) | −17.7946 | −0.952521 | −0.476261 | − | 0.879304i | \(-0.658008\pi\) | ||||
−0.476261 | + | 0.879304i | \(0.658008\pi\) | |||||||
\(350\) | −4.08988 | −0.218613 | ||||||||
\(351\) | 20.7008 | 1.10493 | ||||||||
\(352\) | 8.27012 | 0.440799 | ||||||||
\(353\) | 2.17367 | 0.115693 | 0.0578465 | − | 0.998325i | \(-0.481577\pi\) | ||||
0.0578465 | + | 0.998325i | \(0.481577\pi\) | |||||||
\(354\) | −13.2608 | −0.704804 | ||||||||
\(355\) | −9.98529 | −0.529964 | ||||||||
\(356\) | −38.6546 | −2.04869 | ||||||||
\(357\) | 0.528182 | 0.0279544 | ||||||||
\(358\) | 11.5197 | 0.608837 | ||||||||
\(359\) | −31.3541 | −1.65481 | −0.827404 | − | 0.561607i | \(-0.810183\pi\) | ||||
−0.827404 | + | 0.561607i | \(0.810183\pi\) | |||||||
\(360\) | 12.3875 | 0.652877 | ||||||||
\(361\) | −14.4126 | −0.758558 | ||||||||
\(362\) | 19.9259 | 1.04728 | ||||||||
\(363\) | 12.6225 | 0.662508 | ||||||||
\(364\) | −7.18179 | −0.376428 | ||||||||
\(365\) | 13.8510 | 0.724992 | ||||||||
\(366\) | 20.4440 | 1.06863 | ||||||||
\(367\) | 20.1479 | 1.05171 | 0.525856 | − | 0.850574i | \(-0.323745\pi\) | ||||
0.525856 | + | 0.850574i | \(0.323745\pi\) | |||||||
\(368\) | −111.337 | −5.80386 | ||||||||
\(369\) | −15.0353 | −0.782705 | ||||||||
\(370\) | −20.1691 | −1.04854 | ||||||||
\(371\) | 0.361098 | 0.0187473 | ||||||||
\(372\) | −9.19046 | −0.476503 | ||||||||
\(373\) | −23.9812 | −1.24170 | −0.620849 | − | 0.783930i | \(-0.713212\pi\) | ||||
−0.620849 | + | 0.783930i | \(0.713212\pi\) | |||||||
\(374\) | 1.63425 | 0.0845049 | ||||||||
\(375\) | 9.56190 | 0.493774 | ||||||||
\(376\) | 15.1434 | 0.780961 | ||||||||
\(377\) | −4.01411 | −0.206737 | ||||||||
\(378\) | 5.25934 | 0.270511 | ||||||||
\(379\) | 16.6262 | 0.854030 | 0.427015 | − | 0.904244i | \(-0.359565\pi\) | ||||
0.427015 | + | 0.904244i | \(0.359565\pi\) | |||||||
\(380\) | 9.87118 | 0.506381 | ||||||||
\(381\) | −16.9762 | −0.869716 | ||||||||
\(382\) | −35.4706 | −1.81483 | ||||||||
\(383\) | −26.8236 | −1.37062 | −0.685310 | − | 0.728251i | \(-0.740333\pi\) | ||||
−0.685310 | + | 0.728251i | \(0.740333\pi\) | |||||||
\(384\) | 23.3721 | 1.19270 | ||||||||
\(385\) | 0.155848 | 0.00794276 | ||||||||
\(386\) | −32.2987 | −1.64396 | ||||||||
\(387\) | −12.1378 | −0.617000 | ||||||||
\(388\) | −63.6463 | −3.23115 | ||||||||
\(389\) | 34.1360 | 1.73077 | 0.865383 | − | 0.501111i | \(-0.167075\pi\) | ||||
0.865383 | + | 0.501111i | \(0.167075\pi\) | |||||||
\(390\) | 10.6316 | 0.538350 | ||||||||
\(391\) | −10.9046 | −0.551468 | ||||||||
\(392\) | 59.2354 | 2.99184 | ||||||||
\(393\) | −2.12636 | −0.107261 | ||||||||
\(394\) | 61.4908 | 3.09786 | ||||||||
\(395\) | −6.90785 | −0.347572 | ||||||||
\(396\) | 4.13064 | 0.207573 | ||||||||
\(397\) | −25.8571 | −1.29773 | −0.648867 | − | 0.760902i | \(-0.724757\pi\) | ||||
−0.648867 | + | 0.760902i | \(0.724757\pi\) | |||||||
\(398\) | −22.5284 | −1.12925 | ||||||||
\(399\) | 0.907122 | 0.0454129 | ||||||||
\(400\) | −53.7056 | −2.68528 | ||||||||
\(401\) | −29.5208 | −1.47420 | −0.737100 | − | 0.675784i | \(-0.763805\pi\) | ||||
−0.737100 | + | 0.675784i | \(0.763805\pi\) | |||||||
\(402\) | −47.7804 | −2.38307 | ||||||||
\(403\) | 5.73897 | 0.285878 | ||||||||
\(404\) | −52.1262 | −2.59338 | ||||||||
\(405\) | −1.31653 | −0.0654187 | ||||||||
\(406\) | −1.01984 | −0.0506140 | ||||||||
\(407\) | −4.14423 | −0.205422 | ||||||||
\(408\) | 12.6127 | 0.624421 | ||||||||
\(409\) | −8.24400 | −0.407640 | −0.203820 | − | 0.979008i | \(-0.565336\pi\) | ||||
−0.203820 | + | 0.979008i | \(0.565336\pi\) | |||||||
\(410\) | −21.9835 | −1.08569 | ||||||||
\(411\) | −23.7410 | −1.17106 | ||||||||
\(412\) | 52.5485 | 2.58888 | ||||||||
\(413\) | 1.52033 | 0.0748106 | ||||||||
\(414\) | −38.1400 | −1.87448 | ||||||||
\(415\) | 11.4510 | 0.562108 | ||||||||
\(416\) | −64.6808 | −3.17124 | ||||||||
\(417\) | −5.89540 | −0.288699 | ||||||||
\(418\) | 2.80672 | 0.137281 | ||||||||
\(419\) | −3.03519 | −0.148279 | −0.0741393 | − | 0.997248i | \(-0.523621\pi\) | ||||
−0.0741393 | + | 0.997248i | \(0.523621\pi\) | |||||||
\(420\) | 1.95195 | 0.0952454 | ||||||||
\(421\) | 1.82390 | 0.0888913 | 0.0444457 | − | 0.999012i | \(-0.485848\pi\) | ||||
0.0444457 | + | 0.999012i | \(0.485848\pi\) | |||||||
\(422\) | −23.9681 | −1.16675 | ||||||||
\(423\) | 2.85265 | 0.138700 | ||||||||
\(424\) | 8.62282 | 0.418761 | ||||||||
\(425\) | −5.26001 | −0.255148 | ||||||||
\(426\) | −35.5597 | −1.72287 | ||||||||
\(427\) | −2.34387 | −0.113428 | ||||||||
\(428\) | −14.9988 | −0.724995 | ||||||||
\(429\) | 2.18452 | 0.105469 | ||||||||
\(430\) | −17.7470 | −0.855838 | ||||||||
\(431\) | 12.1740 | 0.586401 | 0.293201 | − | 0.956051i | \(-0.405280\pi\) | ||||
0.293201 | + | 0.956051i | \(0.405280\pi\) | |||||||
\(432\) | 69.0621 | 3.32275 | ||||||||
\(433\) | −16.4391 | −0.790015 | −0.395008 | − | 0.918678i | \(-0.629258\pi\) | ||||
−0.395008 | + | 0.918678i | \(0.629258\pi\) | |||||||
\(434\) | 1.45807 | 0.0699896 | ||||||||
\(435\) | 1.09100 | 0.0523095 | ||||||||
\(436\) | 19.7130 | 0.944080 | ||||||||
\(437\) | −18.7280 | −0.895879 | ||||||||
\(438\) | 49.3262 | 2.35690 | ||||||||
\(439\) | 12.2301 | 0.583709 | 0.291854 | − | 0.956463i | \(-0.405728\pi\) | ||||
0.291854 | + | 0.956463i | \(0.405728\pi\) | |||||||
\(440\) | 3.72156 | 0.177419 | ||||||||
\(441\) | 11.1585 | 0.531357 | ||||||||
\(442\) | −12.7815 | −0.607954 | ||||||||
\(443\) | −37.1334 | −1.76426 | −0.882130 | − | 0.471007i | \(-0.843891\pi\) | ||||
−0.882130 | + | 0.471007i | \(0.843891\pi\) | |||||||
\(444\) | −51.9052 | −2.46331 | ||||||||
\(445\) | −6.56045 | −0.310995 | ||||||||
\(446\) | 42.2679 | 2.00144 | ||||||||
\(447\) | −13.9249 | −0.658626 | ||||||||
\(448\) | −7.23733 | −0.341932 | ||||||||
\(449\) | 3.29013 | 0.155271 | 0.0776354 | − | 0.996982i | \(-0.475263\pi\) | ||||
0.0776354 | + | 0.996982i | \(0.475263\pi\) | |||||||
\(450\) | −18.3975 | −0.867268 | ||||||||
\(451\) | −4.51705 | −0.212699 | ||||||||
\(452\) | −4.92596 | −0.231697 | ||||||||
\(453\) | −1.17289 | −0.0551072 | ||||||||
\(454\) | 38.9885 | 1.82982 | ||||||||
\(455\) | −1.21889 | −0.0571426 | ||||||||
\(456\) | 21.6616 | 1.01440 | ||||||||
\(457\) | −6.13031 | −0.286764 | −0.143382 | − | 0.989667i | \(-0.545798\pi\) | ||||
−0.143382 | + | 0.989667i | \(0.545798\pi\) | |||||||
\(458\) | −28.6837 | −1.34030 | ||||||||
\(459\) | 6.76406 | 0.315719 | ||||||||
\(460\) | −40.2989 | −1.87895 | ||||||||
\(461\) | 1.04742 | 0.0487831 | 0.0243915 | − | 0.999702i | \(-0.492235\pi\) | ||||
0.0243915 | + | 0.999702i | \(0.492235\pi\) | |||||||
\(462\) | 0.555008 | 0.0258213 | ||||||||
\(463\) | 20.6117 | 0.957906 | 0.478953 | − | 0.877841i | \(-0.341016\pi\) | ||||
0.478953 | + | 0.877841i | \(0.341016\pi\) | |||||||
\(464\) | −13.3919 | −0.621704 | ||||||||
\(465\) | −1.55980 | −0.0723341 | ||||||||
\(466\) | −24.8482 | −1.15107 | ||||||||
\(467\) | 2.59284 | 0.119982 | 0.0599911 | − | 0.998199i | \(-0.480893\pi\) | ||||
0.0599911 | + | 0.998199i | \(0.480893\pi\) | |||||||
\(468\) | −32.3059 | −1.49334 | ||||||||
\(469\) | 5.47795 | 0.252948 | ||||||||
\(470\) | 4.17093 | 0.192391 | ||||||||
\(471\) | 1.37004 | 0.0631281 | ||||||||
\(472\) | 36.3047 | 1.67106 | ||||||||
\(473\) | −3.64656 | −0.167669 | ||||||||
\(474\) | −24.6003 | −1.12993 | ||||||||
\(475\) | −9.03376 | −0.414498 | ||||||||
\(476\) | −2.34668 | −0.107560 | ||||||||
\(477\) | 1.62433 | 0.0743729 | ||||||||
\(478\) | 38.3568 | 1.75440 | ||||||||
\(479\) | 31.3486 | 1.43236 | 0.716178 | − | 0.697918i | \(-0.245890\pi\) | ||||
0.716178 | + | 0.697918i | \(0.245890\pi\) | |||||||
\(480\) | 17.5797 | 0.802400 | ||||||||
\(481\) | 32.4121 | 1.47787 | ||||||||
\(482\) | −35.2199 | −1.60422 | ||||||||
\(483\) | −3.70331 | −0.168506 | ||||||||
\(484\) | −56.0808 | −2.54913 | ||||||||
\(485\) | −10.8020 | −0.490495 | ||||||||
\(486\) | 39.0061 | 1.76935 | ||||||||
\(487\) | −18.2798 | −0.828336 | −0.414168 | − | 0.910201i | \(-0.635927\pi\) | ||||
−0.414168 | + | 0.910201i | \(0.635927\pi\) | |||||||
\(488\) | −55.9704 | −2.53366 | ||||||||
\(489\) | 7.18430 | 0.324885 | ||||||||
\(490\) | 16.3152 | 0.737043 | ||||||||
\(491\) | 4.95438 | 0.223588 | 0.111794 | − | 0.993731i | \(-0.464340\pi\) | ||||
0.111794 | + | 0.993731i | \(0.464340\pi\) | |||||||
\(492\) | −56.5746 | −2.55058 | ||||||||
\(493\) | −1.31163 | −0.0590726 | ||||||||
\(494\) | −21.9515 | −0.987643 | ||||||||
\(495\) | 0.701052 | 0.0315099 | ||||||||
\(496\) | 19.1464 | 0.859698 | ||||||||
\(497\) | 4.07687 | 0.182872 | ||||||||
\(498\) | 40.7794 | 1.82737 | ||||||||
\(499\) | 1.73032 | 0.0774596 | 0.0387298 | − | 0.999250i | \(-0.487669\pi\) | ||||
0.0387298 | + | 0.999250i | \(0.487669\pi\) | |||||||
\(500\) | −42.4828 | −1.89989 | ||||||||
\(501\) | 6.92591 | 0.309427 | ||||||||
\(502\) | 59.4177 | 2.65194 | ||||||||
\(503\) | 26.5135 | 1.18218 | 0.591088 | − | 0.806607i | \(-0.298698\pi\) | ||||
0.591088 | + | 0.806607i | \(0.298698\pi\) | |||||||
\(504\) | −5.05764 | −0.225285 | ||||||||
\(505\) | −8.84685 | −0.393680 | ||||||||
\(506\) | −11.4584 | −0.509388 | ||||||||
\(507\) | −1.83758 | −0.0816098 | ||||||||
\(508\) | 75.4239 | 3.34640 | ||||||||
\(509\) | −22.0325 | −0.976573 | −0.488286 | − | 0.872684i | \(-0.662378\pi\) | ||||
−0.488286 | + | 0.872684i | \(0.662378\pi\) | |||||||
\(510\) | 3.47390 | 0.153827 | ||||||||
\(511\) | −5.65517 | −0.250170 | ||||||||
\(512\) | 3.80154 | 0.168006 | ||||||||
\(513\) | 11.6169 | 0.512897 | ||||||||
\(514\) | −54.1121 | −2.38678 | ||||||||
\(515\) | 8.91852 | 0.392997 | ||||||||
\(516\) | −45.6721 | −2.01060 | ||||||||
\(517\) | 0.857020 | 0.0376917 | ||||||||
\(518\) | 8.23478 | 0.361815 | ||||||||
\(519\) | −19.4357 | −0.853133 | ||||||||
\(520\) | −29.1065 | −1.27640 | ||||||||
\(521\) | −24.3157 | −1.06529 | −0.532646 | − | 0.846338i | \(-0.678802\pi\) | ||||
−0.532646 | + | 0.846338i | \(0.678802\pi\) | |||||||
\(522\) | −4.58757 | −0.200792 | ||||||||
\(523\) | −18.7224 | −0.818674 | −0.409337 | − | 0.912383i | \(-0.634240\pi\) | ||||
−0.409337 | + | 0.912383i | \(0.634240\pi\) | |||||||
\(524\) | 9.44728 | 0.412706 | ||||||||
\(525\) | −1.78636 | −0.0779630 | ||||||||
\(526\) | −43.4600 | −1.89494 | ||||||||
\(527\) | 1.87523 | 0.0816862 | ||||||||
\(528\) | 7.28800 | 0.317169 | ||||||||
\(529\) | 53.4565 | 2.32420 | ||||||||
\(530\) | 2.37498 | 0.103162 | ||||||||
\(531\) | 6.83891 | 0.296783 | ||||||||
\(532\) | −4.03028 | −0.174735 | ||||||||
\(533\) | 35.3279 | 1.53022 | ||||||||
\(534\) | −23.3631 | −1.01102 | ||||||||
\(535\) | −2.54560 | −0.110056 | ||||||||
\(536\) | 130.810 | 5.65015 | ||||||||
\(537\) | 5.03153 | 0.217126 | ||||||||
\(538\) | −59.9184 | −2.58326 | ||||||||
\(539\) | 3.35235 | 0.144396 | ||||||||
\(540\) | 24.9972 | 1.07571 | ||||||||
\(541\) | 30.8987 | 1.32844 | 0.664219 | − | 0.747538i | \(-0.268764\pi\) | ||||
0.664219 | + | 0.747538i | \(0.268764\pi\) | |||||||
\(542\) | 20.4891 | 0.880083 | ||||||||
\(543\) | 8.70315 | 0.373488 | ||||||||
\(544\) | −21.1347 | −0.906143 | ||||||||
\(545\) | 3.34568 | 0.143313 | ||||||||
\(546\) | −4.34073 | −0.185766 | ||||||||
\(547\) | 18.2914 | 0.782082 | 0.391041 | − | 0.920373i | \(-0.372115\pi\) | ||||
0.391041 | + | 0.920373i | \(0.372115\pi\) | |||||||
\(548\) | 105.479 | 4.50586 | ||||||||
\(549\) | −10.5435 | −0.449984 | ||||||||
\(550\) | −5.52717 | −0.235679 | ||||||||
\(551\) | −2.25264 | −0.0959657 | ||||||||
\(552\) | −88.4329 | −3.76395 | ||||||||
\(553\) | 2.82039 | 0.119935 | ||||||||
\(554\) | 23.1294 | 0.982673 | ||||||||
\(555\) | −8.80935 | −0.373936 | ||||||||
\(556\) | 26.1928 | 1.11082 | ||||||||
\(557\) | −34.9434 | −1.48060 | −0.740299 | − | 0.672278i | \(-0.765316\pi\) | ||||
−0.740299 | + | 0.672278i | \(0.765316\pi\) | |||||||
\(558\) | 6.55883 | 0.277658 | ||||||||
\(559\) | 28.5199 | 1.20626 | ||||||||
\(560\) | −4.06648 | −0.171840 | ||||||||
\(561\) | 0.713798 | 0.0301366 | ||||||||
\(562\) | −36.0483 | −1.52061 | ||||||||
\(563\) | 9.92320 | 0.418213 | 0.209107 | − | 0.977893i | \(-0.432944\pi\) | ||||
0.209107 | + | 0.977893i | \(0.432944\pi\) | |||||||
\(564\) | 10.7339 | 0.451980 | ||||||||
\(565\) | −0.836032 | −0.0351721 | ||||||||
\(566\) | −64.6154 | −2.71599 | ||||||||
\(567\) | 0.537521 | 0.0225737 | ||||||||
\(568\) | 97.3532 | 4.08485 | ||||||||
\(569\) | −0.327086 | −0.0137121 | −0.00685607 | − | 0.999976i | \(-0.502182\pi\) | ||||
−0.00685607 | + | 0.999976i | \(0.502182\pi\) | |||||||
\(570\) | 5.96622 | 0.249898 | ||||||||
\(571\) | 27.0523 | 1.13211 | 0.566053 | − | 0.824369i | \(-0.308470\pi\) | ||||
0.566053 | + | 0.824369i | \(0.308470\pi\) | |||||||
\(572\) | −9.70564 | −0.405813 | ||||||||
\(573\) | −15.4927 | −0.647215 | ||||||||
\(574\) | 8.97558 | 0.374634 | ||||||||
\(575\) | 36.8802 | 1.53801 | ||||||||
\(576\) | −32.5557 | −1.35649 | ||||||||
\(577\) | 31.8857 | 1.32742 | 0.663709 | − | 0.747991i | \(-0.268981\pi\) | ||||
0.663709 | + | 0.747991i | \(0.268981\pi\) | |||||||
\(578\) | 41.4744 | 1.72511 | ||||||||
\(579\) | −14.1072 | −0.586277 | ||||||||
\(580\) | −4.84724 | −0.201271 | ||||||||
\(581\) | −4.67530 | −0.193964 | ||||||||
\(582\) | −38.4683 | −1.59456 | ||||||||
\(583\) | 0.487997 | 0.0202108 | ||||||||
\(584\) | −135.042 | −5.58809 | ||||||||
\(585\) | −5.48295 | −0.226692 | ||||||||
\(586\) | 81.5702 | 3.36963 | ||||||||
\(587\) | 42.6627 | 1.76088 | 0.880439 | − | 0.474160i | \(-0.157248\pi\) | ||||
0.880439 | + | 0.474160i | \(0.157248\pi\) | |||||||
\(588\) | 41.9871 | 1.73152 | ||||||||
\(589\) | 3.22059 | 0.132702 | ||||||||
\(590\) | 9.99936 | 0.411667 | ||||||||
\(591\) | 26.8576 | 1.10478 | ||||||||
\(592\) | 108.134 | 4.44426 | ||||||||
\(593\) | −17.0411 | −0.699792 | −0.349896 | − | 0.936788i | \(-0.613783\pi\) | ||||
−0.349896 | + | 0.936788i | \(0.613783\pi\) | |||||||
\(594\) | 7.10760 | 0.291628 | ||||||||
\(595\) | −0.398277 | −0.0163278 | ||||||||
\(596\) | 61.8674 | 2.53419 | ||||||||
\(597\) | −9.83985 | −0.402718 | ||||||||
\(598\) | 89.6165 | 3.66469 | ||||||||
\(599\) | 30.2852 | 1.23742 | 0.618710 | − | 0.785620i | \(-0.287656\pi\) | ||||
0.618710 | + | 0.785620i | \(0.287656\pi\) | |||||||
\(600\) | −42.6572 | −1.74147 | ||||||||
\(601\) | −14.5319 | −0.592770 | −0.296385 | − | 0.955069i | \(-0.595781\pi\) | ||||
−0.296385 | + | 0.955069i | \(0.595781\pi\) | |||||||
\(602\) | 7.24589 | 0.295320 | ||||||||
\(603\) | 24.6415 | 1.00348 | ||||||||
\(604\) | 5.21107 | 0.212035 | ||||||||
\(605\) | −9.51802 | −0.386963 | ||||||||
\(606\) | −31.5055 | −1.27982 | ||||||||
\(607\) | 36.4525 | 1.47956 | 0.739781 | − | 0.672848i | \(-0.234929\pi\) | ||||
0.739781 | + | 0.672848i | \(0.234929\pi\) | |||||||
\(608\) | −36.2976 | −1.47206 | ||||||||
\(609\) | −0.445442 | −0.0180502 | ||||||||
\(610\) | −15.4159 | −0.624171 | ||||||||
\(611\) | −6.70278 | −0.271165 | ||||||||
\(612\) | −10.5561 | −0.426703 | ||||||||
\(613\) | 41.6822 | 1.68353 | 0.841765 | − | 0.539844i | \(-0.181517\pi\) | ||||
0.841765 | + | 0.539844i | \(0.181517\pi\) | |||||||
\(614\) | −6.88638 | −0.277912 | ||||||||
\(615\) | −9.60184 | −0.387184 | ||||||||
\(616\) | −1.51947 | −0.0612211 | ||||||||
\(617\) | 36.0920 | 1.45301 | 0.726504 | − | 0.687162i | \(-0.241144\pi\) | ||||
0.726504 | + | 0.687162i | \(0.241144\pi\) | |||||||
\(618\) | 31.7608 | 1.27760 | ||||||||
\(619\) | −10.3980 | −0.417930 | −0.208965 | − | 0.977923i | \(-0.567009\pi\) | ||||
−0.208965 | + | 0.977923i | \(0.567009\pi\) | |||||||
\(620\) | 6.93009 | 0.278319 | ||||||||
\(621\) | −47.4257 | −1.90313 | ||||||||
\(622\) | −25.7067 | −1.03074 | ||||||||
\(623\) | 2.67855 | 0.107314 | ||||||||
\(624\) | −56.9996 | −2.28181 | ||||||||
\(625\) | 13.8788 | 0.555153 | ||||||||
\(626\) | −91.1656 | −3.64371 | ||||||||
\(627\) | 1.22591 | 0.0489580 | ||||||||
\(628\) | −6.08698 | −0.242897 | ||||||||
\(629\) | 10.5908 | 0.422282 | ||||||||
\(630\) | −1.39302 | −0.0554994 | ||||||||
\(631\) | 37.3536 | 1.48702 | 0.743511 | − | 0.668723i | \(-0.233159\pi\) | ||||
0.743511 | + | 0.668723i | \(0.233159\pi\) | |||||||
\(632\) | 67.3493 | 2.67901 | ||||||||
\(633\) | −10.4687 | −0.416092 | ||||||||
\(634\) | −44.9182 | −1.78393 | ||||||||
\(635\) | 12.8009 | 0.507990 | ||||||||
\(636\) | 6.11201 | 0.242357 | ||||||||
\(637\) | −26.2188 | −1.03883 | ||||||||
\(638\) | −1.37824 | −0.0545651 | ||||||||
\(639\) | 18.3390 | 0.725479 | ||||||||
\(640\) | −17.6238 | −0.696643 | ||||||||
\(641\) | −4.30166 | −0.169905 | −0.0849527 | − | 0.996385i | \(-0.527074\pi\) | ||||
−0.0849527 | + | 0.996385i | \(0.527074\pi\) | |||||||
\(642\) | −9.06540 | −0.357783 | ||||||||
\(643\) | 2.21238 | 0.0872476 | 0.0436238 | − | 0.999048i | \(-0.486110\pi\) | ||||
0.0436238 | + | 0.999048i | \(0.486110\pi\) | |||||||
\(644\) | 16.4535 | 0.648360 | ||||||||
\(645\) | −7.75146 | −0.305213 | ||||||||
\(646\) | −7.17272 | −0.282207 | ||||||||
\(647\) | −30.0019 | −1.17950 | −0.589749 | − | 0.807587i | \(-0.700773\pi\) | ||||
−0.589749 | + | 0.807587i | \(0.700773\pi\) | |||||||
\(648\) | 12.8357 | 0.504233 | ||||||||
\(649\) | 2.05461 | 0.0806506 | ||||||||
\(650\) | 43.2281 | 1.69555 | ||||||||
\(651\) | 0.636848 | 0.0249600 | ||||||||
\(652\) | −31.9193 | −1.25006 | ||||||||
\(653\) | 30.8115 | 1.20575 | 0.602874 | − | 0.797836i | \(-0.294022\pi\) | ||||
0.602874 | + | 0.797836i | \(0.294022\pi\) | |||||||
\(654\) | 11.9147 | 0.465901 | ||||||||
\(655\) | 1.60339 | 0.0626497 | ||||||||
\(656\) | 117.861 | 4.60171 | ||||||||
\(657\) | −25.4386 | −0.992456 | ||||||||
\(658\) | −1.70294 | −0.0663875 | ||||||||
\(659\) | −28.4467 | −1.10813 | −0.554063 | − | 0.832475i | \(-0.686923\pi\) | ||||
−0.554063 | + | 0.832475i | \(0.686923\pi\) | |||||||
\(660\) | 2.63791 | 0.102681 | ||||||||
\(661\) | 2.48366 | 0.0966033 | 0.0483017 | − | 0.998833i | \(-0.484619\pi\) | ||||
0.0483017 | + | 0.998833i | \(0.484619\pi\) | |||||||
\(662\) | 78.2977 | 3.04313 | ||||||||
\(663\) | −5.58263 | −0.216812 | ||||||||
\(664\) | −111.643 | −4.33261 | ||||||||
\(665\) | −0.684018 | −0.0265251 | ||||||||
\(666\) | 37.0425 | 1.43537 | ||||||||
\(667\) | 9.19636 | 0.356085 | ||||||||
\(668\) | −30.7713 | −1.19058 | ||||||||
\(669\) | 18.4616 | 0.713765 | ||||||||
\(670\) | 36.0290 | 1.39192 | ||||||||
\(671\) | −3.16757 | −0.122283 | ||||||||
\(672\) | −7.17757 | −0.276881 | ||||||||
\(673\) | 12.8091 | 0.493756 | 0.246878 | − | 0.969047i | \(-0.420595\pi\) | ||||
0.246878 | + | 0.969047i | \(0.420595\pi\) | |||||||
\(674\) | −74.3345 | −2.86326 | ||||||||
\(675\) | −22.8766 | −0.880522 | ||||||||
\(676\) | 8.16423 | 0.314009 | ||||||||
\(677\) | 39.2090 | 1.50692 | 0.753462 | − | 0.657492i | \(-0.228383\pi\) | ||||
0.753462 | + | 0.657492i | \(0.228383\pi\) | |||||||
\(678\) | −2.97729 | −0.114342 | ||||||||
\(679\) | 4.41033 | 0.169253 | ||||||||
\(680\) | −9.51064 | −0.364716 | ||||||||
\(681\) | 17.0292 | 0.652559 | ||||||||
\(682\) | 1.97047 | 0.0754532 | ||||||||
\(683\) | −22.1384 | −0.847101 | −0.423550 | − | 0.905873i | \(-0.639216\pi\) | ||||
−0.423550 | + | 0.905873i | \(0.639216\pi\) | |||||||
\(684\) | −18.1294 | −0.693195 | ||||||||
\(685\) | 17.9020 | 0.683999 | ||||||||
\(686\) | −13.4490 | −0.513484 | ||||||||
\(687\) | −12.5283 | −0.477985 | ||||||||
\(688\) | 95.1482 | 3.62749 | ||||||||
\(689\) | −3.81664 | −0.145402 | ||||||||
\(690\) | −24.3570 | −0.927255 | ||||||||
\(691\) | −16.9735 | −0.645704 | −0.322852 | − | 0.946449i | \(-0.604642\pi\) | ||||
−0.322852 | + | 0.946449i | \(0.604642\pi\) | |||||||
\(692\) | 86.3514 | 3.28259 | ||||||||
\(693\) | −0.286231 | −0.0108730 | ||||||||
\(694\) | 17.1748 | 0.651946 | ||||||||
\(695\) | 4.44544 | 0.168625 | ||||||||
\(696\) | −10.6369 | −0.403191 | ||||||||
\(697\) | 11.5435 | 0.437242 | ||||||||
\(698\) | 47.7845 | 1.80867 | ||||||||
\(699\) | −10.8531 | −0.410501 | ||||||||
\(700\) | 7.93666 | 0.299978 | ||||||||
\(701\) | 1.86972 | 0.0706183 | 0.0353092 | − | 0.999376i | \(-0.488758\pi\) | ||||
0.0353092 | + | 0.999376i | \(0.488758\pi\) | |||||||
\(702\) | −55.5887 | −2.09806 | ||||||||
\(703\) | 18.1890 | 0.686013 | ||||||||
\(704\) | −9.78070 | −0.368624 | ||||||||
\(705\) | 1.82176 | 0.0686114 | ||||||||
\(706\) | −5.83706 | −0.219681 | ||||||||
\(707\) | 3.61206 | 0.135845 | ||||||||
\(708\) | 25.7334 | 0.967120 | ||||||||
\(709\) | −41.4439 | −1.55646 | −0.778230 | − | 0.627980i | \(-0.783882\pi\) | ||||
−0.778230 | + | 0.627980i | \(0.783882\pi\) | |||||||
\(710\) | 26.8139 | 1.00631 | ||||||||
\(711\) | 12.6870 | 0.475798 | ||||||||
\(712\) | 63.9622 | 2.39708 | ||||||||
\(713\) | −13.1480 | −0.492397 | ||||||||
\(714\) | −1.41835 | −0.0530804 | ||||||||
\(715\) | −1.64724 | −0.0616033 | ||||||||
\(716\) | −22.3547 | −0.835435 | ||||||||
\(717\) | 16.7533 | 0.625662 | ||||||||
\(718\) | 84.1966 | 3.14219 | ||||||||
\(719\) | −5.41599 | −0.201982 | −0.100991 | − | 0.994887i | \(-0.532201\pi\) | ||||
−0.100991 | + | 0.994887i | \(0.532201\pi\) | |||||||
\(720\) | −18.2922 | −0.681712 | ||||||||
\(721\) | −3.64132 | −0.135610 | ||||||||
\(722\) | 38.7028 | 1.44037 | ||||||||
\(723\) | −15.3832 | −0.572107 | ||||||||
\(724\) | −38.6675 | −1.43706 | ||||||||
\(725\) | 4.43603 | 0.164750 | ||||||||
\(726\) | −33.8957 | −1.25799 | ||||||||
\(727\) | −22.7235 | −0.842770 | −0.421385 | − | 0.906882i | \(-0.638456\pi\) | ||||
−0.421385 | + | 0.906882i | \(0.638456\pi\) | |||||||
\(728\) | 11.8838 | 0.440443 | ||||||||
\(729\) | 21.5026 | 0.796393 | ||||||||
\(730\) | −37.1946 | −1.37663 | ||||||||
\(731\) | 9.31896 | 0.344674 | ||||||||
\(732\) | −39.6728 | −1.46635 | ||||||||
\(733\) | 34.8033 | 1.28549 | 0.642744 | − | 0.766081i | \(-0.277796\pi\) | ||||
0.642744 | + | 0.766081i | \(0.277796\pi\) | |||||||
\(734\) | −54.1040 | −1.99702 | ||||||||
\(735\) | 7.12605 | 0.262848 | ||||||||
\(736\) | 148.184 | 5.46215 | ||||||||
\(737\) | 7.40303 | 0.272694 | ||||||||
\(738\) | 40.3749 | 1.48622 | ||||||||
\(739\) | 1.86685 | 0.0686732 | 0.0343366 | − | 0.999410i | \(-0.489068\pi\) | ||||
0.0343366 | + | 0.999410i | \(0.489068\pi\) | |||||||
\(740\) | 39.1393 | 1.43879 | ||||||||
\(741\) | −9.58785 | −0.352218 | ||||||||
\(742\) | −0.969672 | −0.0355978 | ||||||||
\(743\) | 42.3785 | 1.55472 | 0.777359 | − | 0.629057i | \(-0.216559\pi\) | ||||
0.777359 | + | 0.629057i | \(0.216559\pi\) | |||||||
\(744\) | 15.2076 | 0.557536 | ||||||||
\(745\) | 10.5001 | 0.384695 | ||||||||
\(746\) | 64.3977 | 2.35777 | ||||||||
\(747\) | −21.0309 | −0.769481 | ||||||||
\(748\) | −3.17135 | −0.115956 | ||||||||
\(749\) | 1.03933 | 0.0379764 | ||||||||
\(750\) | −25.6770 | −0.937590 | ||||||||
\(751\) | −19.2375 | −0.701985 | −0.350993 | − | 0.936378i | \(-0.614156\pi\) | ||||
−0.350993 | + | 0.936378i | \(0.614156\pi\) | |||||||
\(752\) | −22.3619 | −0.815453 | ||||||||
\(753\) | 25.9522 | 0.945749 | ||||||||
\(754\) | 10.7793 | 0.392558 | ||||||||
\(755\) | 0.884422 | 0.0321874 | ||||||||
\(756\) | −10.2061 | −0.371191 | ||||||||
\(757\) | 13.1138 | 0.476631 | 0.238315 | − | 0.971188i | \(-0.423405\pi\) | ||||
0.238315 | + | 0.971188i | \(0.423405\pi\) | |||||||
\(758\) | −44.6470 | −1.62165 | ||||||||
\(759\) | −5.00474 | −0.181661 | ||||||||
\(760\) | −16.3340 | −0.592495 | ||||||||
\(761\) | −35.9168 | −1.30198 | −0.650992 | − | 0.759085i | \(-0.725647\pi\) | ||||
−0.650992 | + | 0.759085i | \(0.725647\pi\) | |||||||
\(762\) | 45.5868 | 1.65144 | ||||||||
\(763\) | −1.36600 | −0.0494525 | ||||||||
\(764\) | 68.8328 | 2.49028 | ||||||||
\(765\) | −1.79157 | −0.0647744 | ||||||||
\(766\) | 72.0305 | 2.60257 | ||||||||
\(767\) | −16.0692 | −0.580225 | ||||||||
\(768\) | −15.7468 | −0.568212 | ||||||||
\(769\) | −9.59014 | −0.345829 | −0.172915 | − | 0.984937i | \(-0.555318\pi\) | ||||
−0.172915 | + | 0.984937i | \(0.555318\pi\) | |||||||
\(770\) | −0.418506 | −0.0150819 | ||||||||
\(771\) | −23.6348 | −0.851187 | ||||||||
\(772\) | 62.6775 | 2.25581 | ||||||||
\(773\) | 40.3150 | 1.45003 | 0.725015 | − | 0.688733i | \(-0.241833\pi\) | ||||
0.725015 | + | 0.688733i | \(0.241833\pi\) | |||||||
\(774\) | 32.5942 | 1.17157 | ||||||||
\(775\) | −6.34218 | −0.227818 | ||||||||
\(776\) | 105.316 | 3.78063 | ||||||||
\(777\) | 3.59674 | 0.129032 | ||||||||
\(778\) | −91.6670 | −3.28642 | ||||||||
\(779\) | 19.8253 | 0.710316 | ||||||||
\(780\) | −20.6312 | −0.738715 | ||||||||
\(781\) | 5.50958 | 0.197148 | ||||||||
\(782\) | 29.2825 | 1.04714 | ||||||||
\(783\) | −5.70446 | −0.203861 | ||||||||
\(784\) | −87.4713 | −3.12398 | ||||||||
\(785\) | −1.03308 | −0.0368723 | ||||||||
\(786\) | 5.71001 | 0.203669 | ||||||||
\(787\) | 4.79720 | 0.171002 | 0.0855009 | − | 0.996338i | \(-0.472751\pi\) | ||||
0.0855009 | + | 0.996338i | \(0.472751\pi\) | |||||||
\(788\) | −119.327 | −4.25083 | ||||||||
\(789\) | −18.9822 | −0.675785 | ||||||||
\(790\) | 18.5500 | 0.659978 | ||||||||
\(791\) | 0.341341 | 0.0121367 | ||||||||
\(792\) | −6.83502 | −0.242872 | ||||||||
\(793\) | 24.7736 | 0.879738 | ||||||||
\(794\) | 69.4353 | 2.46417 | ||||||||
\(795\) | 1.03733 | 0.0367903 | ||||||||
\(796\) | 43.7178 | 1.54953 | ||||||||
\(797\) | −47.4236 | −1.67983 | −0.839915 | − | 0.542719i | \(-0.817395\pi\) | ||||
−0.839915 | + | 0.542719i | \(0.817395\pi\) | |||||||
\(798\) | −2.43593 | −0.0862311 | ||||||||
\(799\) | −2.19016 | −0.0774822 | ||||||||
\(800\) | 71.4794 | 2.52718 | ||||||||
\(801\) | 12.0489 | 0.425728 | ||||||||
\(802\) | 79.2736 | 2.79925 | ||||||||
\(803\) | −7.64253 | −0.269699 | ||||||||
\(804\) | 92.7207 | 3.27001 | ||||||||
\(805\) | 2.79249 | 0.0984224 | ||||||||
\(806\) | −15.4111 | −0.542833 | ||||||||
\(807\) | −26.1708 | −0.921257 | ||||||||
\(808\) | 86.2539 | 3.03440 | ||||||||
\(809\) | 28.1963 | 0.991329 | 0.495665 | − | 0.868514i | \(-0.334925\pi\) | ||||
0.495665 | + | 0.868514i | \(0.334925\pi\) | |||||||
\(810\) | 3.53532 | 0.124219 | ||||||||
\(811\) | 42.8750 | 1.50554 | 0.752772 | − | 0.658281i | \(-0.228716\pi\) | ||||
0.752772 | + | 0.658281i | \(0.228716\pi\) | |||||||
\(812\) | 1.97907 | 0.0694517 | ||||||||
\(813\) | 8.94913 | 0.313860 | ||||||||
\(814\) | 11.1287 | 0.390060 | ||||||||
\(815\) | −5.41734 | −0.189761 | ||||||||
\(816\) | −18.6248 | −0.651999 | ||||||||
\(817\) | 16.0048 | 0.559936 | ||||||||
\(818\) | 22.1380 | 0.774036 | ||||||||
\(819\) | 2.23862 | 0.0782236 | ||||||||
\(820\) | 42.6603 | 1.48976 | ||||||||
\(821\) | 7.52722 | 0.262702 | 0.131351 | − | 0.991336i | \(-0.458069\pi\) | ||||
0.131351 | + | 0.991336i | \(0.458069\pi\) | |||||||
\(822\) | 63.7526 | 2.22363 | ||||||||
\(823\) | −14.1945 | −0.494788 | −0.247394 | − | 0.968915i | \(-0.579574\pi\) | ||||
−0.247394 | + | 0.968915i | \(0.579574\pi\) | |||||||
\(824\) | −86.9527 | −3.02914 | ||||||||
\(825\) | −2.41413 | −0.0840491 | ||||||||
\(826\) | −4.08261 | −0.142052 | ||||||||
\(827\) | 29.4427 | 1.02382 | 0.511911 | − | 0.859039i | \(-0.328938\pi\) | ||||
0.511911 | + | 0.859039i | \(0.328938\pi\) | |||||||
\(828\) | 74.0130 | 2.57213 | ||||||||
\(829\) | 30.6806 | 1.06558 | 0.532791 | − | 0.846247i | \(-0.321143\pi\) | ||||
0.532791 | + | 0.846247i | \(0.321143\pi\) | |||||||
\(830\) | −30.7499 | −1.06734 | ||||||||
\(831\) | 10.1023 | 0.350446 | ||||||||
\(832\) | 76.4951 | 2.65199 | ||||||||
\(833\) | −8.56708 | −0.296832 | ||||||||
\(834\) | 15.8312 | 0.548188 | ||||||||
\(835\) | −5.22250 | −0.180732 | ||||||||
\(836\) | −5.44661 | −0.188375 | ||||||||
\(837\) | 8.15566 | 0.281901 | ||||||||
\(838\) | 8.15052 | 0.281555 | ||||||||
\(839\) | 11.2298 | 0.387694 | 0.193847 | − | 0.981032i | \(-0.437903\pi\) | ||||
0.193847 | + | 0.981032i | \(0.437903\pi\) | |||||||
\(840\) | −3.22992 | −0.111443 | ||||||||
\(841\) | −27.8938 | −0.961857 | ||||||||
\(842\) | −4.89779 | −0.168789 | ||||||||
\(843\) | −15.7450 | −0.542287 | ||||||||
\(844\) | 46.5115 | 1.60099 | ||||||||
\(845\) | 1.38563 | 0.0476672 | ||||||||
\(846\) | −7.66034 | −0.263368 | ||||||||
\(847\) | 3.88609 | 0.133528 | ||||||||
\(848\) | −12.7331 | −0.437256 | ||||||||
\(849\) | −28.2224 | −0.968589 | ||||||||
\(850\) | 14.1249 | 0.484482 | ||||||||
\(851\) | −74.2565 | −2.54548 | ||||||||
\(852\) | 69.0058 | 2.36410 | ||||||||
\(853\) | 27.2043 | 0.931458 | 0.465729 | − | 0.884927i | \(-0.345792\pi\) | ||||
0.465729 | + | 0.884927i | \(0.345792\pi\) | |||||||
\(854\) | 6.29411 | 0.215380 | ||||||||
\(855\) | −3.07692 | −0.105228 | ||||||||
\(856\) | 24.8187 | 0.848286 | ||||||||
\(857\) | −3.25762 | −0.111278 | −0.0556391 | − | 0.998451i | \(-0.517720\pi\) | ||||
−0.0556391 | + | 0.998451i | \(0.517720\pi\) | |||||||
\(858\) | −5.86617 | −0.200268 | ||||||||
\(859\) | −44.2838 | −1.51094 | −0.755472 | − | 0.655181i | \(-0.772592\pi\) | ||||
−0.755472 | + | 0.655181i | \(0.772592\pi\) | |||||||
\(860\) | 34.4392 | 1.17437 | ||||||||
\(861\) | 3.92031 | 0.133604 | ||||||||
\(862\) | −32.6914 | −1.11347 | ||||||||
\(863\) | 54.8601 | 1.86746 | 0.933731 | − | 0.357977i | \(-0.116533\pi\) | ||||
0.933731 | + | 0.357977i | \(0.116533\pi\) | |||||||
\(864\) | −91.9181 | −3.12712 | ||||||||
\(865\) | 14.6556 | 0.498304 | ||||||||
\(866\) | 44.1448 | 1.50010 | ||||||||
\(867\) | 18.1150 | 0.615217 | ||||||||
\(868\) | −2.82947 | −0.0960385 | ||||||||
\(869\) | 3.81154 | 0.129298 | ||||||||
\(870\) | −2.92971 | −0.0993266 | ||||||||
\(871\) | −57.8993 | −1.96184 | ||||||||
\(872\) | −32.6193 | −1.10463 | ||||||||
\(873\) | 19.8390 | 0.671449 | ||||||||
\(874\) | 50.2910 | 1.70112 | ||||||||
\(875\) | 2.94382 | 0.0995194 | ||||||||
\(876\) | −95.7204 | −3.23409 | ||||||||
\(877\) | 14.0994 | 0.476104 | 0.238052 | − | 0.971252i | \(-0.423491\pi\) | ||||
0.238052 | + | 0.971252i | \(0.423491\pi\) | |||||||
\(878\) | −32.8419 | −1.10836 | ||||||||
\(879\) | 35.6278 | 1.20170 | ||||||||
\(880\) | −5.49554 | −0.185255 | ||||||||
\(881\) | −0.786599 | −0.0265012 | −0.0132506 | − | 0.999912i | \(-0.504218\pi\) | ||||
−0.0132506 | + | 0.999912i | \(0.504218\pi\) | |||||||
\(882\) | −29.9644 | −1.00895 | ||||||||
\(883\) | 25.1514 | 0.846413 | 0.423207 | − | 0.906033i | \(-0.360904\pi\) | ||||
0.423207 | + | 0.906033i | \(0.360904\pi\) | |||||||
\(884\) | 24.8032 | 0.834223 | ||||||||
\(885\) | 4.36747 | 0.146811 | ||||||||
\(886\) | 99.7158 | 3.35002 | ||||||||
\(887\) | −30.0873 | −1.01023 | −0.505117 | − | 0.863051i | \(-0.668551\pi\) | ||||
−0.505117 | + | 0.863051i | \(0.668551\pi\) | |||||||
\(888\) | 85.8882 | 2.88222 | ||||||||
\(889\) | −5.22646 | −0.175290 | ||||||||
\(890\) | 17.6171 | 0.590525 | ||||||||
\(891\) | 0.726418 | 0.0243359 | ||||||||
\(892\) | −82.0234 | −2.74635 | ||||||||
\(893\) | −3.76147 | −0.125873 | ||||||||
\(894\) | 37.3932 | 1.25062 | ||||||||
\(895\) | −3.79404 | −0.126821 | ||||||||
\(896\) | 7.19558 | 0.240388 | ||||||||
\(897\) | 39.1422 | 1.30692 | ||||||||
\(898\) | −8.83512 | −0.294832 | ||||||||
\(899\) | −1.58147 | −0.0527451 | ||||||||
\(900\) | 35.7015 | 1.19005 | ||||||||
\(901\) | −1.24710 | −0.0415469 | ||||||||
\(902\) | 12.1298 | 0.403879 | ||||||||
\(903\) | 3.16482 | 0.105319 | ||||||||
\(904\) | 8.15104 | 0.271100 | ||||||||
\(905\) | −6.56264 | −0.218149 | ||||||||
\(906\) | 3.14961 | 0.104639 | ||||||||
\(907\) | −24.1132 | −0.800666 | −0.400333 | − | 0.916370i | \(-0.631106\pi\) | ||||
−0.400333 | + | 0.916370i | \(0.631106\pi\) | |||||||
\(908\) | −75.6594 | −2.51085 | ||||||||
\(909\) | 16.2481 | 0.538916 | ||||||||
\(910\) | 3.27314 | 0.108504 | ||||||||
\(911\) | 10.7343 | 0.355645 | 0.177822 | − | 0.984063i | \(-0.443095\pi\) | ||||
0.177822 | + | 0.984063i | \(0.443095\pi\) | |||||||
\(912\) | −31.9870 | −1.05920 | ||||||||
\(913\) | −6.31831 | −0.209106 | ||||||||
\(914\) | 16.4620 | 0.544514 | ||||||||
\(915\) | −6.73327 | −0.222595 | ||||||||
\(916\) | 55.6624 | 1.83914 | ||||||||
\(917\) | −0.654644 | −0.0216182 | ||||||||
\(918\) | −18.1638 | −0.599495 | ||||||||
\(919\) | 31.9719 | 1.05466 | 0.527328 | − | 0.849662i | \(-0.323194\pi\) | ||||
0.527328 | + | 0.849662i | \(0.323194\pi\) | |||||||
\(920\) | 66.6831 | 2.19848 | ||||||||
\(921\) | −3.00780 | −0.0991103 | ||||||||
\(922\) | −2.81267 | −0.0926305 | ||||||||
\(923\) | −43.0905 | −1.41834 | ||||||||
\(924\) | −1.07703 | −0.0354316 | ||||||||
\(925\) | −35.8189 | −1.17772 | ||||||||
\(926\) | −55.3494 | −1.81889 | ||||||||
\(927\) | −16.3798 | −0.537982 | ||||||||
\(928\) | 17.8239 | 0.585099 | ||||||||
\(929\) | −21.2448 | −0.697018 | −0.348509 | − | 0.937305i | \(-0.613312\pi\) | ||||
−0.348509 | + | 0.937305i | \(0.613312\pi\) | |||||||
\(930\) | 4.18861 | 0.137350 | ||||||||
\(931\) | −14.7135 | −0.482214 | ||||||||
\(932\) | 48.2195 | 1.57948 | ||||||||
\(933\) | −11.2280 | −0.367589 | ||||||||
\(934\) | −6.96266 | −0.227825 | ||||||||
\(935\) | −0.538242 | −0.0176024 | ||||||||
\(936\) | 53.4569 | 1.74729 | ||||||||
\(937\) | 48.1485 | 1.57294 | 0.786471 | − | 0.617627i | \(-0.211906\pi\) | ||||
0.786471 | + | 0.617627i | \(0.211906\pi\) | |||||||
\(938\) | −14.7102 | −0.480304 | ||||||||
\(939\) | −39.8188 | −1.29944 | ||||||||
\(940\) | −8.09395 | −0.263995 | ||||||||
\(941\) | 24.2579 | 0.790785 | 0.395393 | − | 0.918512i | \(-0.370608\pi\) | ||||
0.395393 | + | 0.918512i | \(0.370608\pi\) | |||||||
\(942\) | −3.67902 | −0.119869 | ||||||||
\(943\) | −80.9366 | −2.63566 | ||||||||
\(944\) | −53.6101 | −1.74486 | ||||||||
\(945\) | −1.73217 | −0.0563475 | ||||||||
\(946\) | 9.79227 | 0.318374 | ||||||||
\(947\) | 30.4608 | 0.989841 | 0.494921 | − | 0.868938i | \(-0.335197\pi\) | ||||
0.494921 | + | 0.868938i | \(0.335197\pi\) | |||||||
\(948\) | 47.7384 | 1.55047 | ||||||||
\(949\) | 59.7724 | 1.94030 | ||||||||
\(950\) | 24.2588 | 0.787058 | ||||||||
\(951\) | −19.6191 | −0.636194 | ||||||||
\(952\) | 3.88307 | 0.125851 | ||||||||
\(953\) | 46.5873 | 1.50911 | 0.754555 | − | 0.656236i | \(-0.227853\pi\) | ||||
0.754555 | + | 0.656236i | \(0.227853\pi\) | |||||||
\(954\) | −4.36188 | −0.141221 | ||||||||
\(955\) | 11.6823 | 0.378030 | ||||||||
\(956\) | −74.4336 | −2.40735 | ||||||||
\(957\) | −0.601981 | −0.0194593 | ||||||||
\(958\) | −84.1819 | −2.71979 | ||||||||
\(959\) | −7.30914 | −0.236024 | ||||||||
\(960\) | −20.7907 | −0.671018 | ||||||||
\(961\) | −28.7390 | −0.927064 | ||||||||
\(962\) | −87.0377 | −2.80621 | ||||||||
\(963\) | 4.67524 | 0.150657 | ||||||||
\(964\) | 68.3464 | 2.20129 | ||||||||
\(965\) | 10.6376 | 0.342437 | ||||||||
\(966\) | 9.94466 | 0.319964 | ||||||||
\(967\) | −13.5693 | −0.436360 | −0.218180 | − | 0.975909i | \(-0.570012\pi\) | ||||
−0.218180 | + | 0.975909i | \(0.570012\pi\) | |||||||
\(968\) | 92.7976 | 2.98263 | ||||||||
\(969\) | −3.13286 | −0.100642 | ||||||||
\(970\) | 29.0072 | 0.931364 | ||||||||
\(971\) | −4.24439 | −0.136209 | −0.0681045 | − | 0.997678i | \(-0.521695\pi\) | ||||
−0.0681045 | + | 0.997678i | \(0.521695\pi\) | |||||||
\(972\) | −75.6937 | −2.42788 | ||||||||
\(973\) | −1.81502 | −0.0581868 | ||||||||
\(974\) | 49.0875 | 1.57286 | ||||||||
\(975\) | 18.8810 | 0.604674 | ||||||||
\(976\) | 82.6500 | 2.64556 | ||||||||
\(977\) | 37.1885 | 1.18976 | 0.594882 | − | 0.803813i | \(-0.297199\pi\) | ||||
0.594882 | + | 0.803813i | \(0.297199\pi\) | |||||||
\(978\) | −19.2923 | −0.616900 | ||||||||
\(979\) | 3.61985 | 0.115691 | ||||||||
\(980\) | −31.6605 | −1.01136 | ||||||||
\(981\) | −6.14468 | −0.196185 | ||||||||
\(982\) | −13.3042 | −0.424555 | ||||||||
\(983\) | −37.3592 | −1.19157 | −0.595786 | − | 0.803143i | \(-0.703160\pi\) | ||||
−0.595786 | + | 0.803143i | \(0.703160\pi\) | |||||||
\(984\) | 93.6147 | 2.98433 | ||||||||
\(985\) | −20.2521 | −0.645285 | ||||||||
\(986\) | 3.52216 | 0.112169 | ||||||||
\(987\) | −0.743801 | −0.0236755 | ||||||||
\(988\) | 42.5981 | 1.35523 | ||||||||
\(989\) | −65.3392 | −2.07767 | ||||||||
\(990\) | −1.88256 | −0.0598318 | ||||||||
\(991\) | 41.3444 | 1.31335 | 0.656674 | − | 0.754175i | \(-0.271963\pi\) | ||||
0.656674 | + | 0.754175i | \(0.271963\pi\) | |||||||
\(992\) | −25.4828 | −0.809081 | ||||||||
\(993\) | 34.1985 | 1.08526 | ||||||||
\(994\) | −10.9478 | −0.347243 | ||||||||
\(995\) | 7.41977 | 0.235223 | ||||||||
\(996\) | −79.1349 | −2.50749 | ||||||||
\(997\) | −48.2596 | −1.52840 | −0.764199 | − | 0.644981i | \(-0.776865\pi\) | ||||
−0.764199 | + | 0.644981i | \(0.776865\pi\) | |||||||
\(998\) | −4.64649 | −0.147082 | ||||||||
\(999\) | 46.0610 | 1.45730 |
(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 | 8003.2.a.c.1.5 | ✓ | 172 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.c.1.5 | ✓ | 172 | 1.1 | even | 1 | trivial |