Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.72902 | −1.92971 | −0.964853 | − | 0.262791i | \(-0.915357\pi\) | ||||
−0.964853 | + | 0.262791i | \(0.915357\pi\) | |||||||
\(3\) | 1.60790 | 0.928322 | 0.464161 | − | 0.885751i | \(-0.346356\pi\) | ||||
0.464161 | + | 0.885751i | \(0.346356\pi\) | |||||||
\(4\) | 5.44753 | 2.72376 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −4.38799 | −1.79139 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −9.40835 | −3.32635 | ||||||||
\(9\) | −0.414653 | −0.138218 | ||||||||
\(10\) | −2.72902 | −0.862990 | ||||||||
\(11\) | −1.93334 | −0.582923 | −0.291462 | − | 0.956583i | \(-0.594142\pi\) | ||||
−0.291462 | + | 0.956583i | \(0.594142\pi\) | |||||||
\(12\) | 8.75908 | 2.52853 | ||||||||
\(13\) | −1.18193 | −0.327808 | −0.163904 | − | 0.986476i | \(-0.552409\pi\) | ||||
−0.163904 | + | 0.986476i | \(0.552409\pi\) | |||||||
\(14\) | 2.72902 | 0.729360 | ||||||||
\(15\) | 1.60790 | 0.415158 | ||||||||
\(16\) | 14.7805 | 3.69512 | ||||||||
\(17\) | −5.40790 | −1.31161 | −0.655804 | − | 0.754931i | \(-0.727670\pi\) | ||||
−0.655804 | + | 0.754931i | \(0.727670\pi\) | |||||||
\(18\) | 1.13159 | 0.266719 | ||||||||
\(19\) | 1.68861 | 0.387394 | 0.193697 | − | 0.981061i | \(-0.437952\pi\) | ||||
0.193697 | + | 0.981061i | \(0.437952\pi\) | |||||||
\(20\) | 5.44753 | 1.21810 | ||||||||
\(21\) | −1.60790 | −0.350873 | ||||||||
\(22\) | 5.27611 | 1.12487 | ||||||||
\(23\) | −7.72119 | −1.60998 | −0.804990 | − | 0.593289i | \(-0.797829\pi\) | ||||
−0.804990 | + | 0.593289i | \(0.797829\pi\) | |||||||
\(24\) | −15.1277 | −3.08793 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.22550 | 0.632573 | ||||||||
\(27\) | −5.49043 | −1.05663 | ||||||||
\(28\) | −5.44753 | −1.02949 | ||||||||
\(29\) | 2.85107 | 0.529431 | 0.264715 | − | 0.964327i | \(-0.414722\pi\) | ||||
0.264715 | + | 0.964327i | \(0.414722\pi\) | |||||||
\(30\) | −4.38799 | −0.801133 | ||||||||
\(31\) | 6.52541 | 1.17200 | 0.585999 | − | 0.810312i | \(-0.300702\pi\) | ||||
0.585999 | + | 0.810312i | \(0.300702\pi\) | |||||||
\(32\) | −21.5195 | −3.80414 | ||||||||
\(33\) | −3.10862 | −0.541141 | ||||||||
\(34\) | 14.7582 | 2.53102 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −2.25883 | −0.376472 | ||||||||
\(37\) | 1.43986 | 0.236712 | 0.118356 | − | 0.992971i | \(-0.462238\pi\) | ||||
0.118356 | + | 0.992971i | \(0.462238\pi\) | |||||||
\(38\) | −4.60824 | −0.747556 | ||||||||
\(39\) | −1.90043 | −0.304312 | ||||||||
\(40\) | −9.40835 | −1.48759 | ||||||||
\(41\) | −9.71007 | −1.51646 | −0.758229 | − | 0.651988i | \(-0.773935\pi\) | ||||
−0.758229 | + | 0.651988i | \(0.773935\pi\) | |||||||
\(42\) | 4.38799 | 0.677081 | ||||||||
\(43\) | 1.65241 | 0.251990 | 0.125995 | − | 0.992031i | \(-0.459788\pi\) | ||||
0.125995 | + | 0.992031i | \(0.459788\pi\) | |||||||
\(44\) | −10.5319 | −1.58774 | ||||||||
\(45\) | −0.414653 | −0.0618128 | ||||||||
\(46\) | 21.0712 | 3.10679 | ||||||||
\(47\) | 3.51255 | 0.512358 | 0.256179 | − | 0.966629i | \(-0.417536\pi\) | ||||
0.256179 | + | 0.966629i | \(0.417536\pi\) | |||||||
\(48\) | 23.7656 | 3.43026 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.72902 | −0.385941 | ||||||||
\(51\) | −8.69537 | −1.21760 | ||||||||
\(52\) | −6.43859 | −0.892871 | ||||||||
\(53\) | 9.58230 | 1.31623 | 0.658115 | − | 0.752917i | \(-0.271354\pi\) | ||||
0.658115 | + | 0.752917i | \(0.271354\pi\) | |||||||
\(54\) | 14.9835 | 2.03899 | ||||||||
\(55\) | −1.93334 | −0.260691 | ||||||||
\(56\) | 9.40835 | 1.25724 | ||||||||
\(57\) | 2.71512 | 0.359626 | ||||||||
\(58\) | −7.78062 | −1.02165 | ||||||||
\(59\) | 5.23923 | 0.682089 | 0.341045 | − | 0.940047i | \(-0.389219\pi\) | ||||
0.341045 | + | 0.940047i | \(0.389219\pi\) | |||||||
\(60\) | 8.75908 | 1.13079 | ||||||||
\(61\) | 3.10438 | 0.397476 | 0.198738 | − | 0.980053i | \(-0.436316\pi\) | ||||
0.198738 | + | 0.980053i | \(0.436316\pi\) | |||||||
\(62\) | −17.8079 | −2.26161 | ||||||||
\(63\) | 0.414653 | 0.0522413 | ||||||||
\(64\) | 29.1660 | 3.64575 | ||||||||
\(65\) | −1.18193 | −0.146600 | ||||||||
\(66\) | 8.48346 | 1.04424 | ||||||||
\(67\) | −4.04904 | −0.494669 | −0.247334 | − | 0.968930i | \(-0.579555\pi\) | ||||
−0.247334 | + | 0.968930i | \(0.579555\pi\) | |||||||
\(68\) | −29.4597 | −3.57251 | ||||||||
\(69\) | −12.4149 | −1.49458 | ||||||||
\(70\) | 2.72902 | 0.326180 | ||||||||
\(71\) | 3.61477 | 0.428995 | 0.214497 | − | 0.976725i | \(-0.431189\pi\) | ||||
0.214497 | + | 0.976725i | \(0.431189\pi\) | |||||||
\(72\) | 3.90120 | 0.459760 | ||||||||
\(73\) | 10.2671 | 1.20167 | 0.600835 | − | 0.799373i | \(-0.294835\pi\) | ||||
0.600835 | + | 0.799373i | \(0.294835\pi\) | |||||||
\(74\) | −3.92940 | −0.456784 | ||||||||
\(75\) | 1.60790 | 0.185664 | ||||||||
\(76\) | 9.19874 | 1.05517 | ||||||||
\(77\) | 1.93334 | 0.220324 | ||||||||
\(78\) | 5.18629 | 0.587232 | ||||||||
\(79\) | 0.905985 | 0.101931 | 0.0509656 | − | 0.998700i | \(-0.483770\pi\) | ||||
0.0509656 | + | 0.998700i | \(0.483770\pi\) | |||||||
\(80\) | 14.7805 | 1.65251 | ||||||||
\(81\) | −7.58411 | −0.842678 | ||||||||
\(82\) | 26.4989 | 2.92632 | ||||||||
\(83\) | −6.61644 | −0.726249 | −0.363125 | − | 0.931741i | \(-0.618290\pi\) | ||||
−0.363125 | + | 0.931741i | \(0.618290\pi\) | |||||||
\(84\) | −8.75908 | −0.955694 | ||||||||
\(85\) | −5.40790 | −0.586569 | ||||||||
\(86\) | −4.50944 | −0.486266 | ||||||||
\(87\) | 4.58424 | 0.491482 | ||||||||
\(88\) | 18.1895 | 1.93901 | ||||||||
\(89\) | −2.60108 | −0.275714 | −0.137857 | − | 0.990452i | \(-0.544021\pi\) | ||||
−0.137857 | + | 0.990452i | \(0.544021\pi\) | |||||||
\(90\) | 1.13159 | 0.119280 | ||||||||
\(91\) | 1.18193 | 0.123900 | ||||||||
\(92\) | −42.0614 | −4.38520 | ||||||||
\(93\) | 10.4922 | 1.08799 | ||||||||
\(94\) | −9.58581 | −0.988701 | ||||||||
\(95\) | 1.68861 | 0.173248 | ||||||||
\(96\) | −34.6012 | −3.53147 | ||||||||
\(97\) | −16.8276 | −1.70858 | −0.854291 | − | 0.519795i | \(-0.826008\pi\) | ||||
−0.854291 | + | 0.519795i | \(0.826008\pi\) | |||||||
\(98\) | −2.72902 | −0.275672 | ||||||||
\(99\) | 0.801663 | 0.0805702 | ||||||||
\(100\) | 5.44753 | 0.544753 | ||||||||
\(101\) | 18.5901 | 1.84978 | 0.924890 | − | 0.380235i | \(-0.124157\pi\) | ||||
0.924890 | + | 0.380235i | \(0.124157\pi\) | |||||||
\(102\) | 23.7298 | 2.34960 | ||||||||
\(103\) | 7.58947 | 0.747813 | 0.373907 | − | 0.927466i | \(-0.378018\pi\) | ||||
0.373907 | + | 0.927466i | \(0.378018\pi\) | |||||||
\(104\) | 11.1200 | 1.09041 | ||||||||
\(105\) | −1.60790 | −0.156915 | ||||||||
\(106\) | −26.1502 | −2.53994 | ||||||||
\(107\) | −13.2571 | −1.28161 | −0.640805 | − | 0.767704i | \(-0.721399\pi\) | ||||
−0.640805 | + | 0.767704i | \(0.721399\pi\) | |||||||
\(108\) | −29.9092 | −2.87802 | ||||||||
\(109\) | 1.70672 | 0.163474 | 0.0817371 | − | 0.996654i | \(-0.473953\pi\) | ||||
0.0817371 | + | 0.996654i | \(0.473953\pi\) | |||||||
\(110\) | 5.27611 | 0.503057 | ||||||||
\(111\) | 2.31515 | 0.219745 | ||||||||
\(112\) | −14.7805 | −1.39662 | ||||||||
\(113\) | 14.1897 | 1.33486 | 0.667428 | − | 0.744675i | \(-0.267395\pi\) | ||||
0.667428 | + | 0.744675i | \(0.267395\pi\) | |||||||
\(114\) | −7.40960 | −0.693973 | ||||||||
\(115\) | −7.72119 | −0.720005 | ||||||||
\(116\) | 15.5313 | 1.44204 | ||||||||
\(117\) | 0.490090 | 0.0453088 | ||||||||
\(118\) | −14.2979 | −1.31623 | ||||||||
\(119\) | 5.40790 | 0.495741 | ||||||||
\(120\) | −15.1277 | −1.38096 | ||||||||
\(121\) | −7.26221 | −0.660201 | ||||||||
\(122\) | −8.47191 | −0.767011 | ||||||||
\(123\) | −15.6128 | −1.40776 | ||||||||
\(124\) | 35.5473 | 3.19224 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.13159 | −0.100810 | ||||||||
\(127\) | 0.00317741 | 0.000281950 0 | 0.000140975 | − | 1.00000i | \(-0.499955\pi\) | ||||
0.000140975 | 1.00000i | \(0.499955\pi\) | ||||||||
\(128\) | −36.5555 | −3.23108 | ||||||||
\(129\) | 2.65691 | 0.233928 | ||||||||
\(130\) | 3.22550 | 0.282895 | ||||||||
\(131\) | −13.2548 | −1.15808 | −0.579040 | − | 0.815299i | \(-0.696573\pi\) | ||||
−0.579040 | + | 0.815299i | \(0.696573\pi\) | |||||||
\(132\) | −16.9343 | −1.47394 | ||||||||
\(133\) | −1.68861 | −0.146421 | ||||||||
\(134\) | 11.0499 | 0.954565 | ||||||||
\(135\) | −5.49043 | −0.472541 | ||||||||
\(136\) | 50.8794 | 4.36287 | ||||||||
\(137\) | −13.3302 | −1.13887 | −0.569437 | − | 0.822035i | \(-0.692839\pi\) | ||||
−0.569437 | + | 0.822035i | \(0.692839\pi\) | |||||||
\(138\) | 33.8805 | 2.88410 | ||||||||
\(139\) | −3.46484 | −0.293884 | −0.146942 | − | 0.989145i | \(-0.546943\pi\) | ||||
−0.146942 | + | 0.989145i | \(0.546943\pi\) | |||||||
\(140\) | −5.44753 | −0.460400 | ||||||||
\(141\) | 5.64784 | 0.475634 | ||||||||
\(142\) | −9.86477 | −0.827833 | ||||||||
\(143\) | 2.28507 | 0.191087 | ||||||||
\(144\) | −6.12876 | −0.510730 | ||||||||
\(145\) | 2.85107 | 0.236769 | ||||||||
\(146\) | −28.0190 | −2.31887 | ||||||||
\(147\) | 1.60790 | 0.132617 | ||||||||
\(148\) | 7.84368 | 0.644746 | ||||||||
\(149\) | 2.92132 | 0.239324 | 0.119662 | − | 0.992815i | \(-0.461819\pi\) | ||||
0.119662 | + | 0.992815i | \(0.461819\pi\) | |||||||
\(150\) | −4.38799 | −0.358278 | ||||||||
\(151\) | 2.32834 | 0.189478 | 0.0947388 | − | 0.995502i | \(-0.469798\pi\) | ||||
0.0947388 | + | 0.995502i | \(0.469798\pi\) | |||||||
\(152\) | −15.8870 | −1.28861 | ||||||||
\(153\) | 2.24240 | 0.181287 | ||||||||
\(154\) | −5.27611 | −0.425161 | ||||||||
\(155\) | 6.52541 | 0.524133 | ||||||||
\(156\) | −10.3526 | −0.828873 | ||||||||
\(157\) | 9.81787 | 0.783551 | 0.391776 | − | 0.920061i | \(-0.371861\pi\) | ||||
0.391776 | + | 0.920061i | \(0.371861\pi\) | |||||||
\(158\) | −2.47245 | −0.196697 | ||||||||
\(159\) | 15.4074 | 1.22189 | ||||||||
\(160\) | −21.5195 | −1.70126 | ||||||||
\(161\) | 7.72119 | 0.608515 | ||||||||
\(162\) | 20.6971 | 1.62612 | ||||||||
\(163\) | 17.5402 | 1.37386 | 0.686928 | − | 0.726725i | \(-0.258959\pi\) | ||||
0.686928 | + | 0.726725i | \(0.258959\pi\) | |||||||
\(164\) | −52.8958 | −4.13047 | ||||||||
\(165\) | −3.10862 | −0.242005 | ||||||||
\(166\) | 18.0564 | 1.40145 | ||||||||
\(167\) | −8.89195 | −0.688079 | −0.344040 | − | 0.938955i | \(-0.611795\pi\) | ||||
−0.344040 | + | 0.938955i | \(0.611795\pi\) | |||||||
\(168\) | 15.1277 | 1.16713 | ||||||||
\(169\) | −11.6030 | −0.892542 | ||||||||
\(170\) | 14.7582 | 1.13191 | ||||||||
\(171\) | −0.700186 | −0.0535446 | ||||||||
\(172\) | 9.00152 | 0.686360 | ||||||||
\(173\) | −8.97034 | −0.682002 | −0.341001 | − | 0.940063i | \(-0.610766\pi\) | ||||
−0.341001 | + | 0.940063i | \(0.610766\pi\) | |||||||
\(174\) | −12.5105 | −0.948416 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −28.5757 | −2.15397 | ||||||||
\(177\) | 8.42416 | 0.633199 | ||||||||
\(178\) | 7.09838 | 0.532046 | ||||||||
\(179\) | 13.0270 | 0.973684 | 0.486842 | − | 0.873490i | \(-0.338149\pi\) | ||||
0.486842 | + | 0.873490i | \(0.338149\pi\) | |||||||
\(180\) | −2.25883 | −0.168363 | ||||||||
\(181\) | 1.09712 | 0.0815480 | 0.0407740 | − | 0.999168i | \(-0.487018\pi\) | ||||
0.0407740 | + | 0.999168i | \(0.487018\pi\) | |||||||
\(182\) | −3.22550 | −0.239090 | ||||||||
\(183\) | 4.99154 | 0.368986 | ||||||||
\(184\) | 72.6437 | 5.35536 | ||||||||
\(185\) | 1.43986 | 0.105861 | ||||||||
\(186\) | −28.6334 | −2.09950 | ||||||||
\(187\) | 10.4553 | 0.764567 | ||||||||
\(188\) | 19.1347 | 1.39554 | ||||||||
\(189\) | 5.49043 | 0.399370 | ||||||||
\(190\) | −4.60824 | −0.334317 | ||||||||
\(191\) | 17.8824 | 1.29393 | 0.646964 | − | 0.762521i | \(-0.276038\pi\) | ||||
0.646964 | + | 0.762521i | \(0.276038\pi\) | |||||||
\(192\) | 46.8960 | 3.38443 | ||||||||
\(193\) | −0.00431391 | −0.000310522 0 | −0.000155261 | − | 1.00000i | \(-0.500049\pi\) | ||||
−0.000155261 | 1.00000i | \(0.500049\pi\) | ||||||||
\(194\) | 45.9227 | 3.29706 | ||||||||
\(195\) | −1.90043 | −0.136092 | ||||||||
\(196\) | 5.44753 | 0.389109 | ||||||||
\(197\) | 20.5601 | 1.46485 | 0.732425 | − | 0.680848i | \(-0.238389\pi\) | ||||
0.732425 | + | 0.680848i | \(0.238389\pi\) | |||||||
\(198\) | −2.18775 | −0.155477 | ||||||||
\(199\) | 26.2122 | 1.85813 | 0.929067 | − | 0.369912i | \(-0.120612\pi\) | ||||
0.929067 | + | 0.369912i | \(0.120612\pi\) | |||||||
\(200\) | −9.40835 | −0.665271 | ||||||||
\(201\) | −6.51046 | −0.459212 | ||||||||
\(202\) | −50.7326 | −3.56953 | ||||||||
\(203\) | −2.85107 | −0.200106 | ||||||||
\(204\) | −47.3682 | −3.31644 | ||||||||
\(205\) | −9.71007 | −0.678181 | ||||||||
\(206\) | −20.7118 | −1.44306 | ||||||||
\(207\) | 3.20161 | 0.222527 | ||||||||
\(208\) | −17.4695 | −1.21129 | ||||||||
\(209\) | −3.26465 | −0.225821 | ||||||||
\(210\) | 4.38799 | 0.302800 | ||||||||
\(211\) | −14.3930 | −0.990856 | −0.495428 | − | 0.868649i | \(-0.664989\pi\) | ||||
−0.495428 | + | 0.868649i | \(0.664989\pi\) | |||||||
\(212\) | 52.1998 | 3.58510 | ||||||||
\(213\) | 5.81220 | 0.398245 | ||||||||
\(214\) | 36.1788 | 2.47313 | ||||||||
\(215\) | 1.65241 | 0.112693 | ||||||||
\(216\) | 51.6558 | 3.51473 | ||||||||
\(217\) | −6.52541 | −0.442973 | ||||||||
\(218\) | −4.65767 | −0.315457 | ||||||||
\(219\) | 16.5084 | 1.11554 | ||||||||
\(220\) | −10.5319 | −0.710061 | ||||||||
\(221\) | 6.39175 | 0.429956 | ||||||||
\(222\) | −6.31809 | −0.424043 | ||||||||
\(223\) | 23.9322 | 1.60262 | 0.801311 | − | 0.598248i | \(-0.204136\pi\) | ||||
0.801311 | + | 0.598248i | \(0.204136\pi\) | |||||||
\(224\) | 21.5195 | 1.43783 | ||||||||
\(225\) | −0.414653 | −0.0276435 | ||||||||
\(226\) | −38.7239 | −2.57588 | ||||||||
\(227\) | −3.42149 | −0.227092 | −0.113546 | − | 0.993533i | \(-0.536221\pi\) | ||||
−0.113546 | + | 0.993533i | \(0.536221\pi\) | |||||||
\(228\) | 14.7907 | 0.979536 | ||||||||
\(229\) | −1.00000 | −0.0660819 | ||||||||
\(230\) | 21.0712 | 1.38940 | ||||||||
\(231\) | 3.10862 | 0.204532 | ||||||||
\(232\) | −26.8239 | −1.76107 | ||||||||
\(233\) | 6.93520 | 0.454340 | 0.227170 | − | 0.973855i | \(-0.427053\pi\) | ||||
0.227170 | + | 0.973855i | \(0.427053\pi\) | |||||||
\(234\) | −1.33746 | −0.0874327 | ||||||||
\(235\) | 3.51255 | 0.229134 | ||||||||
\(236\) | 28.5408 | 1.85785 | ||||||||
\(237\) | 1.45673 | 0.0946250 | ||||||||
\(238\) | −14.7582 | −0.956635 | ||||||||
\(239\) | −3.53951 | −0.228952 | −0.114476 | − | 0.993426i | \(-0.536519\pi\) | ||||
−0.114476 | + | 0.993426i | \(0.536519\pi\) | |||||||
\(240\) | 23.7656 | 1.53406 | ||||||||
\(241\) | 7.76926 | 0.500462 | 0.250231 | − | 0.968186i | \(-0.419493\pi\) | ||||
0.250231 | + | 0.968186i | \(0.419493\pi\) | |||||||
\(242\) | 19.8187 | 1.27399 | ||||||||
\(243\) | 4.27678 | 0.274356 | ||||||||
\(244\) | 16.9112 | 1.08263 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 42.6077 | 2.71657 | ||||||||
\(247\) | −1.99582 | −0.126991 | ||||||||
\(248\) | −61.3933 | −3.89848 | ||||||||
\(249\) | −10.6386 | −0.674193 | ||||||||
\(250\) | −2.72902 | −0.172598 | ||||||||
\(251\) | 9.00810 | 0.568586 | 0.284293 | − | 0.958737i | \(-0.408241\pi\) | ||||
0.284293 | + | 0.958737i | \(0.408241\pi\) | |||||||
\(252\) | 2.25883 | 0.142293 | ||||||||
\(253\) | 14.9277 | 0.938495 | ||||||||
\(254\) | −0.00867121 | −0.000544080 0 | ||||||||
\(255\) | −8.69537 | −0.544525 | ||||||||
\(256\) | 41.4285 | 2.58928 | ||||||||
\(257\) | 22.9201 | 1.42972 | 0.714859 | − | 0.699269i | \(-0.246491\pi\) | ||||
0.714859 | + | 0.699269i | \(0.246491\pi\) | |||||||
\(258\) | −7.25074 | −0.451411 | ||||||||
\(259\) | −1.43986 | −0.0894686 | ||||||||
\(260\) | −6.43859 | −0.399304 | ||||||||
\(261\) | −1.18220 | −0.0731766 | ||||||||
\(262\) | 36.1727 | 2.23475 | ||||||||
\(263\) | 8.91916 | 0.549979 | 0.274990 | − | 0.961447i | \(-0.411326\pi\) | ||||
0.274990 | + | 0.961447i | \(0.411326\pi\) | |||||||
\(264\) | 29.2470 | 1.80003 | ||||||||
\(265\) | 9.58230 | 0.588636 | ||||||||
\(266\) | 4.60824 | 0.282549 | ||||||||
\(267\) | −4.18228 | −0.255951 | ||||||||
\(268\) | −22.0572 | −1.34736 | ||||||||
\(269\) | 10.7485 | 0.655345 | 0.327673 | − | 0.944791i | \(-0.393736\pi\) | ||||
0.327673 | + | 0.944791i | \(0.393736\pi\) | |||||||
\(270\) | 14.9835 | 0.911864 | ||||||||
\(271\) | 27.0770 | 1.64481 | 0.822405 | − | 0.568902i | \(-0.192632\pi\) | ||||
0.822405 | + | 0.568902i | \(0.192632\pi\) | |||||||
\(272\) | −79.9314 | −4.84655 | ||||||||
\(273\) | 1.90043 | 0.115019 | ||||||||
\(274\) | 36.3783 | 2.19769 | ||||||||
\(275\) | −1.93334 | −0.116585 | ||||||||
\(276\) | −67.6306 | −4.07088 | ||||||||
\(277\) | −5.98985 | −0.359895 | −0.179948 | − | 0.983676i | \(-0.557593\pi\) | ||||
−0.179948 | + | 0.983676i | \(0.557593\pi\) | |||||||
\(278\) | 9.45560 | 0.567109 | ||||||||
\(279\) | −2.70578 | −0.161991 | ||||||||
\(280\) | 9.40835 | 0.562256 | ||||||||
\(281\) | 14.7964 | 0.882679 | 0.441339 | − | 0.897340i | \(-0.354503\pi\) | ||||
0.441339 | + | 0.897340i | \(0.354503\pi\) | |||||||
\(282\) | −15.4130 | −0.917833 | ||||||||
\(283\) | −0.143450 | −0.00852722 | −0.00426361 | − | 0.999991i | \(-0.501357\pi\) | ||||
−0.00426361 | + | 0.999991i | \(0.501357\pi\) | |||||||
\(284\) | 19.6916 | 1.16848 | ||||||||
\(285\) | 2.71512 | 0.160830 | ||||||||
\(286\) | −6.23598 | −0.368742 | ||||||||
\(287\) | 9.71007 | 0.573167 | ||||||||
\(288\) | 8.92310 | 0.525799 | ||||||||
\(289\) | 12.2454 | 0.720316 | ||||||||
\(290\) | −7.78062 | −0.456894 | ||||||||
\(291\) | −27.0571 | −1.58612 | ||||||||
\(292\) | 55.9301 | 3.27306 | ||||||||
\(293\) | 28.4691 | 1.66319 | 0.831593 | − | 0.555386i | \(-0.187430\pi\) | ||||
0.831593 | + | 0.555386i | \(0.187430\pi\) | |||||||
\(294\) | −4.38799 | −0.255913 | ||||||||
\(295\) | 5.23923 | 0.305039 | ||||||||
\(296\) | −13.5467 | −0.787387 | ||||||||
\(297\) | 10.6148 | 0.615936 | ||||||||
\(298\) | −7.97232 | −0.461824 | ||||||||
\(299\) | 9.12590 | 0.527764 | ||||||||
\(300\) | 8.75908 | 0.505706 | ||||||||
\(301\) | −1.65241 | −0.0952431 | ||||||||
\(302\) | −6.35408 | −0.365636 | ||||||||
\(303\) | 29.8910 | 1.71719 | ||||||||
\(304\) | 24.9585 | 1.43147 | ||||||||
\(305\) | 3.10438 | 0.177757 | ||||||||
\(306\) | −6.11954 | −0.349831 | ||||||||
\(307\) | −19.9362 | −1.13782 | −0.568909 | − | 0.822400i | \(-0.692634\pi\) | ||||
−0.568909 | + | 0.822400i | \(0.692634\pi\) | |||||||
\(308\) | 10.5319 | 0.600111 | ||||||||
\(309\) | 12.2031 | 0.694212 | ||||||||
\(310\) | −17.8079 | −1.01142 | ||||||||
\(311\) | −29.9567 | −1.69869 | −0.849343 | − | 0.527841i | \(-0.823002\pi\) | ||||
−0.849343 | + | 0.527841i | \(0.823002\pi\) | |||||||
\(312\) | 17.8799 | 1.01225 | ||||||||
\(313\) | 14.0372 | 0.793432 | 0.396716 | − | 0.917941i | \(-0.370150\pi\) | ||||
0.396716 | + | 0.917941i | \(0.370150\pi\) | |||||||
\(314\) | −26.7931 | −1.51202 | ||||||||
\(315\) | 0.414653 | 0.0233630 | ||||||||
\(316\) | 4.93537 | 0.277636 | ||||||||
\(317\) | 31.4565 | 1.76677 | 0.883386 | − | 0.468647i | \(-0.155258\pi\) | ||||
0.883386 | + | 0.468647i | \(0.155258\pi\) | |||||||
\(318\) | −42.0470 | −2.35788 | ||||||||
\(319\) | −5.51209 | −0.308618 | ||||||||
\(320\) | 29.1660 | 1.63043 | ||||||||
\(321\) | −21.3161 | −1.18975 | ||||||||
\(322\) | −21.0712 | −1.17425 | ||||||||
\(323\) | −9.13183 | −0.508109 | ||||||||
\(324\) | −41.3146 | −2.29526 | ||||||||
\(325\) | −1.18193 | −0.0655616 | ||||||||
\(326\) | −47.8675 | −2.65114 | ||||||||
\(327\) | 2.74424 | 0.151757 | ||||||||
\(328\) | 91.3557 | 5.04428 | ||||||||
\(329\) | −3.51255 | −0.193653 | ||||||||
\(330\) | 8.48346 | 0.466999 | ||||||||
\(331\) | 1.60777 | 0.0883708 | 0.0441854 | − | 0.999023i | \(-0.485931\pi\) | ||||
0.0441854 | + | 0.999023i | \(0.485931\pi\) | |||||||
\(332\) | −36.0432 | −1.97813 | ||||||||
\(333\) | −0.597042 | −0.0327177 | ||||||||
\(334\) | 24.2663 | 1.32779 | ||||||||
\(335\) | −4.04904 | −0.221223 | ||||||||
\(336\) | −23.7656 | −1.29652 | ||||||||
\(337\) | 6.83028 | 0.372069 | 0.186035 | − | 0.982543i | \(-0.440436\pi\) | ||||
0.186035 | + | 0.982543i | \(0.440436\pi\) | |||||||
\(338\) | 31.6649 | 1.72234 | ||||||||
\(339\) | 22.8156 | 1.23918 | ||||||||
\(340\) | −29.4597 | −1.59767 | ||||||||
\(341\) | −12.6158 | −0.683185 | ||||||||
\(342\) | 1.91082 | 0.103325 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −15.5464 | −0.838206 | ||||||||
\(345\) | −12.4149 | −0.668397 | ||||||||
\(346\) | 24.4802 | 1.31606 | ||||||||
\(347\) | 9.47567 | 0.508681 | 0.254340 | − | 0.967115i | \(-0.418142\pi\) | ||||
0.254340 | + | 0.967115i | \(0.418142\pi\) | |||||||
\(348\) | 24.9728 | 1.33868 | ||||||||
\(349\) | 23.7418 | 1.27087 | 0.635435 | − | 0.772154i | \(-0.280821\pi\) | ||||
0.635435 | + | 0.772154i | \(0.280821\pi\) | |||||||
\(350\) | 2.72902 | 0.145872 | ||||||||
\(351\) | 6.48929 | 0.346373 | ||||||||
\(352\) | 41.6044 | 2.21752 | ||||||||
\(353\) | −29.4699 | −1.56853 | −0.784263 | − | 0.620429i | \(-0.786958\pi\) | ||||
−0.784263 | + | 0.620429i | \(0.786958\pi\) | |||||||
\(354\) | −22.9897 | −1.22189 | ||||||||
\(355\) | 3.61477 | 0.191852 | ||||||||
\(356\) | −14.1694 | −0.750978 | ||||||||
\(357\) | 8.69537 | 0.460208 | ||||||||
\(358\) | −35.5509 | −1.87892 | ||||||||
\(359\) | −24.7598 | −1.30677 | −0.653387 | − | 0.757024i | \(-0.726653\pi\) | ||||
−0.653387 | + | 0.757024i | \(0.726653\pi\) | |||||||
\(360\) | 3.90120 | 0.205611 | ||||||||
\(361\) | −16.1486 | −0.849926 | ||||||||
\(362\) | −2.99405 | −0.157364 | ||||||||
\(363\) | −11.6769 | −0.612879 | ||||||||
\(364\) | 6.43859 | 0.337474 | ||||||||
\(365\) | 10.2671 | 0.537403 | ||||||||
\(366\) | −13.6220 | −0.712033 | ||||||||
\(367\) | 9.53434 | 0.497688 | 0.248844 | − | 0.968544i | \(-0.419949\pi\) | ||||
0.248844 | + | 0.968544i | \(0.419949\pi\) | |||||||
\(368\) | −114.123 | −5.94907 | ||||||||
\(369\) | 4.02630 | 0.209601 | ||||||||
\(370\) | −3.92940 | −0.204280 | ||||||||
\(371\) | −9.58230 | −0.497488 | ||||||||
\(372\) | 57.1566 | 2.96343 | ||||||||
\(373\) | −21.8553 | −1.13162 | −0.565811 | − | 0.824535i | \(-0.691437\pi\) | ||||
−0.565811 | + | 0.824535i | \(0.691437\pi\) | |||||||
\(374\) | −28.5327 | −1.47539 | ||||||||
\(375\) | 1.60790 | 0.0830317 | ||||||||
\(376\) | −33.0473 | −1.70429 | ||||||||
\(377\) | −3.36976 | −0.173552 | ||||||||
\(378\) | −14.9835 | −0.770666 | ||||||||
\(379\) | 35.6675 | 1.83212 | 0.916059 | − | 0.401044i | \(-0.131352\pi\) | ||||
0.916059 | + | 0.401044i | \(0.131352\pi\) | |||||||
\(380\) | 9.19874 | 0.471886 | ||||||||
\(381\) | 0.00510897 | 0.000261740 0 | ||||||||
\(382\) | −48.8014 | −2.49690 | ||||||||
\(383\) | −0.151027 | −0.00771714 | −0.00385857 | − | 0.999993i | \(-0.501228\pi\) | ||||
−0.00385857 | + | 0.999993i | \(0.501228\pi\) | |||||||
\(384\) | −58.7776 | −2.99948 | ||||||||
\(385\) | 1.93334 | 0.0985320 | ||||||||
\(386\) | 0.0117727 | 0.000599216 0 | ||||||||
\(387\) | −0.685174 | −0.0348294 | ||||||||
\(388\) | −91.6687 | −4.65377 | ||||||||
\(389\) | −34.7515 | −1.76197 | −0.880985 | − | 0.473144i | \(-0.843119\pi\) | ||||
−0.880985 | + | 0.473144i | \(0.843119\pi\) | |||||||
\(390\) | 5.18629 | 0.262618 | ||||||||
\(391\) | 41.7554 | 2.11166 | ||||||||
\(392\) | −9.40835 | −0.475193 | ||||||||
\(393\) | −21.3125 | −1.07507 | ||||||||
\(394\) | −56.1090 | −2.82673 | ||||||||
\(395\) | 0.905985 | 0.0455850 | ||||||||
\(396\) | 4.36708 | 0.219454 | ||||||||
\(397\) | −14.9801 | −0.751827 | −0.375914 | − | 0.926655i | \(-0.622671\pi\) | ||||
−0.375914 | + | 0.926655i | \(0.622671\pi\) | |||||||
\(398\) | −71.5335 | −3.58565 | ||||||||
\(399\) | −2.71512 | −0.135926 | ||||||||
\(400\) | 14.7805 | 0.739024 | ||||||||
\(401\) | 18.2752 | 0.912618 | 0.456309 | − | 0.889821i | \(-0.349171\pi\) | ||||
0.456309 | + | 0.889821i | \(0.349171\pi\) | |||||||
\(402\) | 17.7671 | 0.886144 | ||||||||
\(403\) | −7.71257 | −0.384190 | ||||||||
\(404\) | 101.270 | 5.03836 | ||||||||
\(405\) | −7.58411 | −0.376857 | ||||||||
\(406\) | 7.78062 | 0.386146 | ||||||||
\(407\) | −2.78374 | −0.137985 | ||||||||
\(408\) | 81.8091 | 4.05015 | ||||||||
\(409\) | −9.87371 | −0.488223 | −0.244112 | − | 0.969747i | \(-0.578496\pi\) | ||||
−0.244112 | + | 0.969747i | \(0.578496\pi\) | |||||||
\(410\) | 26.4989 | 1.30869 | ||||||||
\(411\) | −21.4336 | −1.05724 | ||||||||
\(412\) | 41.3439 | 2.03687 | ||||||||
\(413\) | −5.23923 | −0.257805 | ||||||||
\(414\) | −8.73725 | −0.429412 | ||||||||
\(415\) | −6.61644 | −0.324788 | ||||||||
\(416\) | 25.4345 | 1.24703 | ||||||||
\(417\) | −5.57112 | −0.272819 | ||||||||
\(418\) | 8.90929 | 0.435768 | ||||||||
\(419\) | 32.8201 | 1.60337 | 0.801684 | − | 0.597748i | \(-0.203938\pi\) | ||||
0.801684 | + | 0.597748i | \(0.203938\pi\) | |||||||
\(420\) | −8.75908 | −0.427400 | ||||||||
\(421\) | 1.29369 | 0.0630508 | 0.0315254 | − | 0.999503i | \(-0.489963\pi\) | ||||
0.0315254 | + | 0.999503i | \(0.489963\pi\) | |||||||
\(422\) | 39.2788 | 1.91206 | ||||||||
\(423\) | −1.45649 | −0.0708169 | ||||||||
\(424\) | −90.1536 | −4.37825 | ||||||||
\(425\) | −5.40790 | −0.262322 | ||||||||
\(426\) | −15.8616 | −0.768496 | ||||||||
\(427\) | −3.10438 | −0.150232 | ||||||||
\(428\) | −72.2183 | −3.49080 | ||||||||
\(429\) | 3.67416 | 0.177390 | ||||||||
\(430\) | −4.50944 | −0.217465 | ||||||||
\(431\) | 2.79311 | 0.134539 | 0.0672696 | − | 0.997735i | \(-0.478571\pi\) | ||||
0.0672696 | + | 0.997735i | \(0.478571\pi\) | |||||||
\(432\) | −81.1511 | −3.90439 | ||||||||
\(433\) | −38.6032 | −1.85515 | −0.927576 | − | 0.373634i | \(-0.878112\pi\) | ||||
−0.927576 | + | 0.373634i | \(0.878112\pi\) | |||||||
\(434\) | 17.8079 | 0.854808 | ||||||||
\(435\) | 4.58424 | 0.219798 | ||||||||
\(436\) | 9.29740 | 0.445265 | ||||||||
\(437\) | −13.0381 | −0.623696 | ||||||||
\(438\) | −45.0518 | −2.15266 | ||||||||
\(439\) | 31.3298 | 1.49529 | 0.747645 | − | 0.664099i | \(-0.231185\pi\) | ||||
0.747645 | + | 0.664099i | \(0.231185\pi\) | |||||||
\(440\) | 18.1895 | 0.867151 | ||||||||
\(441\) | −0.414653 | −0.0197454 | ||||||||
\(442\) | −17.4432 | −0.829688 | ||||||||
\(443\) | −1.10854 | −0.0526684 | −0.0263342 | − | 0.999653i | \(-0.508383\pi\) | ||||
−0.0263342 | + | 0.999653i | \(0.508383\pi\) | |||||||
\(444\) | 12.6119 | 0.598532 | ||||||||
\(445\) | −2.60108 | −0.123303 | ||||||||
\(446\) | −65.3115 | −3.09259 | ||||||||
\(447\) | 4.69719 | 0.222169 | ||||||||
\(448\) | −29.1660 | −1.37796 | ||||||||
\(449\) | 2.66459 | 0.125750 | 0.0628750 | − | 0.998021i | \(-0.479973\pi\) | ||||
0.0628750 | + | 0.998021i | \(0.479973\pi\) | |||||||
\(450\) | 1.13159 | 0.0533438 | ||||||||
\(451\) | 18.7728 | 0.883979 | ||||||||
\(452\) | 77.2988 | 3.63583 | ||||||||
\(453\) | 3.74374 | 0.175896 | ||||||||
\(454\) | 9.33730 | 0.438221 | ||||||||
\(455\) | 1.18193 | 0.0554097 | ||||||||
\(456\) | −25.5448 | −1.19624 | ||||||||
\(457\) | 30.6840 | 1.43534 | 0.717669 | − | 0.696385i | \(-0.245209\pi\) | ||||
0.717669 | + | 0.696385i | \(0.245209\pi\) | |||||||
\(458\) | 2.72902 | 0.127519 | ||||||||
\(459\) | 29.6917 | 1.38589 | ||||||||
\(460\) | −42.0614 | −1.96112 | ||||||||
\(461\) | 18.9417 | 0.882203 | 0.441102 | − | 0.897457i | \(-0.354588\pi\) | ||||
0.441102 | + | 0.897457i | \(0.354588\pi\) | |||||||
\(462\) | −8.48346 | −0.394686 | ||||||||
\(463\) | −27.4703 | −1.27665 | −0.638326 | − | 0.769766i | \(-0.720373\pi\) | ||||
−0.638326 | + | 0.769766i | \(0.720373\pi\) | |||||||
\(464\) | 42.1402 | 1.95631 | ||||||||
\(465\) | 10.4922 | 0.486565 | ||||||||
\(466\) | −18.9263 | −0.876742 | ||||||||
\(467\) | 22.5405 | 1.04305 | 0.521525 | − | 0.853236i | \(-0.325363\pi\) | ||||
0.521525 | + | 0.853236i | \(0.325363\pi\) | |||||||
\(468\) | 2.66978 | 0.123410 | ||||||||
\(469\) | 4.04904 | 0.186967 | ||||||||
\(470\) | −9.58581 | −0.442160 | ||||||||
\(471\) | 15.7862 | 0.727388 | ||||||||
\(472\) | −49.2925 | −2.26887 | ||||||||
\(473\) | −3.19466 | −0.146891 | ||||||||
\(474\) | −3.97545 | −0.182598 | ||||||||
\(475\) | 1.68861 | 0.0774787 | ||||||||
\(476\) | 29.4597 | 1.35028 | ||||||||
\(477\) | −3.97332 | −0.181926 | ||||||||
\(478\) | 9.65937 | 0.441809 | ||||||||
\(479\) | 1.91492 | 0.0874947 | 0.0437474 | − | 0.999043i | \(-0.486070\pi\) | ||||
0.0437474 | + | 0.999043i | \(0.486070\pi\) | |||||||
\(480\) | −34.6012 | −1.57932 | ||||||||
\(481\) | −1.70181 | −0.0775960 | ||||||||
\(482\) | −21.2024 | −0.965745 | ||||||||
\(483\) | 12.4149 | 0.564898 | ||||||||
\(484\) | −39.5610 | −1.79823 | ||||||||
\(485\) | −16.8276 | −0.764101 | ||||||||
\(486\) | −11.6714 | −0.529425 | ||||||||
\(487\) | 1.96668 | 0.0891187 | 0.0445594 | − | 0.999007i | \(-0.485812\pi\) | ||||
0.0445594 | + | 0.999007i | \(0.485812\pi\) | |||||||
\(488\) | −29.2071 | −1.32214 | ||||||||
\(489\) | 28.2029 | 1.27538 | ||||||||
\(490\) | −2.72902 | −0.123284 | ||||||||
\(491\) | 17.8434 | 0.805260 | 0.402630 | − | 0.915363i | \(-0.368096\pi\) | ||||
0.402630 | + | 0.915363i | \(0.368096\pi\) | |||||||
\(492\) | −85.0513 | −3.83441 | ||||||||
\(493\) | −15.4183 | −0.694406 | ||||||||
\(494\) | 5.44661 | 0.245055 | ||||||||
\(495\) | 0.801663 | 0.0360321 | ||||||||
\(496\) | 96.4486 | 4.33067 | ||||||||
\(497\) | −3.61477 | −0.162145 | ||||||||
\(498\) | 29.0329 | 1.30099 | ||||||||
\(499\) | −5.79248 | −0.259307 | −0.129653 | − | 0.991559i | \(-0.541386\pi\) | ||||
−0.129653 | + | 0.991559i | \(0.541386\pi\) | |||||||
\(500\) | 5.44753 | 0.243621 | ||||||||
\(501\) | −14.2974 | −0.638760 | ||||||||
\(502\) | −24.5833 | −1.09720 | ||||||||
\(503\) | −10.4514 | −0.466006 | −0.233003 | − | 0.972476i | \(-0.574855\pi\) | ||||
−0.233003 | + | 0.972476i | \(0.574855\pi\) | |||||||
\(504\) | −3.90120 | −0.173773 | ||||||||
\(505\) | 18.5901 | 0.827247 | ||||||||
\(506\) | −40.7378 | −1.81102 | ||||||||
\(507\) | −18.6566 | −0.828567 | ||||||||
\(508\) | 0.0173090 | 0.000767965 0 | ||||||||
\(509\) | 26.5478 | 1.17671 | 0.588355 | − | 0.808603i | \(-0.299776\pi\) | ||||
0.588355 | + | 0.808603i | \(0.299776\pi\) | |||||||
\(510\) | 23.7298 | 1.05077 | ||||||||
\(511\) | −10.2671 | −0.454188 | ||||||||
\(512\) | −39.9481 | −1.76547 | ||||||||
\(513\) | −9.27119 | −0.409333 | ||||||||
\(514\) | −62.5493 | −2.75893 | ||||||||
\(515\) | 7.58947 | 0.334432 | ||||||||
\(516\) | 14.4736 | 0.637163 | ||||||||
\(517\) | −6.79095 | −0.298666 | ||||||||
\(518\) | 3.92940 | 0.172648 | ||||||||
\(519\) | −14.4234 | −0.633118 | ||||||||
\(520\) | 11.1200 | 0.487644 | ||||||||
\(521\) | −36.4800 | −1.59822 | −0.799109 | − | 0.601186i | \(-0.794695\pi\) | ||||
−0.799109 | + | 0.601186i | \(0.794695\pi\) | |||||||
\(522\) | 3.22625 | 0.141209 | ||||||||
\(523\) | −24.9843 | −1.09249 | −0.546244 | − | 0.837626i | \(-0.683943\pi\) | ||||
−0.546244 | + | 0.837626i | \(0.683943\pi\) | |||||||
\(524\) | −72.2061 | −3.15434 | ||||||||
\(525\) | −1.60790 | −0.0701746 | ||||||||
\(526\) | −24.3405 | −1.06130 | ||||||||
\(527\) | −35.2887 | −1.53720 | ||||||||
\(528\) | −45.9468 | −1.99958 | ||||||||
\(529\) | 36.6168 | 1.59203 | ||||||||
\(530\) | −26.1502 | −1.13589 | ||||||||
\(531\) | −2.17246 | −0.0942766 | ||||||||
\(532\) | −9.19874 | −0.398816 | ||||||||
\(533\) | 11.4766 | 0.497107 | ||||||||
\(534\) | 11.4135 | 0.493910 | ||||||||
\(535\) | −13.2571 | −0.573154 | ||||||||
\(536\) | 38.0948 | 1.64544 | ||||||||
\(537\) | 20.9461 | 0.903892 | ||||||||
\(538\) | −29.3327 | −1.26462 | ||||||||
\(539\) | −1.93334 | −0.0832747 | ||||||||
\(540\) | −29.9092 | −1.28709 | ||||||||
\(541\) | 12.8237 | 0.551334 | 0.275667 | − | 0.961253i | \(-0.411101\pi\) | ||||
0.275667 | + | 0.961253i | \(0.411101\pi\) | |||||||
\(542\) | −73.8936 | −3.17400 | ||||||||
\(543\) | 1.76405 | 0.0757028 | ||||||||
\(544\) | 116.375 | 4.98954 | ||||||||
\(545\) | 1.70672 | 0.0731079 | ||||||||
\(546\) | −5.18629 | −0.221953 | ||||||||
\(547\) | 43.0760 | 1.84180 | 0.920898 | − | 0.389804i | \(-0.127457\pi\) | ||||
0.920898 | + | 0.389804i | \(0.127457\pi\) | |||||||
\(548\) | −72.6165 | −3.10202 | ||||||||
\(549\) | −1.28724 | −0.0549381 | ||||||||
\(550\) | 5.27611 | 0.224974 | ||||||||
\(551\) | 4.81435 | 0.205098 | ||||||||
\(552\) | 116.804 | 4.97150 | ||||||||
\(553\) | −0.905985 | −0.0385264 | ||||||||
\(554\) | 16.3464 | 0.694491 | ||||||||
\(555\) | 2.31515 | 0.0982728 | ||||||||
\(556\) | −18.8748 | −0.800469 | ||||||||
\(557\) | 25.6989 | 1.08890 | 0.544448 | − | 0.838794i | \(-0.316739\pi\) | ||||
0.544448 | + | 0.838794i | \(0.316739\pi\) | |||||||
\(558\) | 7.38411 | 0.312594 | ||||||||
\(559\) | −1.95303 | −0.0826042 | ||||||||
\(560\) | −14.7805 | −0.624589 | ||||||||
\(561\) | 16.8111 | 0.709765 | ||||||||
\(562\) | −40.3796 | −1.70331 | ||||||||
\(563\) | −26.7824 | −1.12874 | −0.564372 | − | 0.825520i | \(-0.690882\pi\) | ||||
−0.564372 | + | 0.825520i | \(0.690882\pi\) | |||||||
\(564\) | 30.7667 | 1.29551 | ||||||||
\(565\) | 14.1897 | 0.596965 | ||||||||
\(566\) | 0.391477 | 0.0164550 | ||||||||
\(567\) | 7.58411 | 0.318502 | ||||||||
\(568\) | −34.0090 | −1.42699 | ||||||||
\(569\) | −18.7992 | −0.788105 | −0.394052 | − | 0.919088i | \(-0.628927\pi\) | ||||
−0.394052 | + | 0.919088i | \(0.628927\pi\) | |||||||
\(570\) | −7.40960 | −0.310354 | ||||||||
\(571\) | −24.2717 | −1.01574 | −0.507870 | − | 0.861434i | \(-0.669567\pi\) | ||||
−0.507870 | + | 0.861434i | \(0.669567\pi\) | |||||||
\(572\) | 12.4480 | 0.520475 | ||||||||
\(573\) | 28.7532 | 1.20118 | ||||||||
\(574\) | −26.4989 | −1.10604 | ||||||||
\(575\) | −7.72119 | −0.321996 | ||||||||
\(576\) | −12.0937 | −0.503906 | ||||||||
\(577\) | −38.4584 | −1.60105 | −0.800523 | − | 0.599302i | \(-0.795445\pi\) | ||||
−0.800523 | + | 0.599302i | \(0.795445\pi\) | |||||||
\(578\) | −33.4178 | −1.39000 | ||||||||
\(579\) | −0.00693634 | −0.000288264 0 | ||||||||
\(580\) | 15.5313 | 0.644902 | ||||||||
\(581\) | 6.61644 | 0.274496 | ||||||||
\(582\) | 73.8392 | 3.06073 | ||||||||
\(583\) | −18.5258 | −0.767261 | ||||||||
\(584\) | −96.5961 | −3.99718 | ||||||||
\(585\) | 0.490090 | 0.0202627 | ||||||||
\(586\) | −77.6927 | −3.20946 | ||||||||
\(587\) | 23.6255 | 0.975130 | 0.487565 | − | 0.873087i | \(-0.337885\pi\) | ||||
0.487565 | + | 0.873087i | \(0.337885\pi\) | |||||||
\(588\) | 8.75908 | 0.361219 | ||||||||
\(589\) | 11.0189 | 0.454024 | ||||||||
\(590\) | −14.2979 | −0.588636 | ||||||||
\(591\) | 33.0587 | 1.35985 | ||||||||
\(592\) | 21.2818 | 0.874678 | ||||||||
\(593\) | −35.0567 | −1.43961 | −0.719803 | − | 0.694178i | \(-0.755768\pi\) | ||||
−0.719803 | + | 0.694178i | \(0.755768\pi\) | |||||||
\(594\) | −28.9681 | −1.18857 | ||||||||
\(595\) | 5.40790 | 0.221702 | ||||||||
\(596\) | 15.9139 | 0.651861 | ||||||||
\(597\) | 42.1466 | 1.72495 | ||||||||
\(598\) | −24.9047 | −1.01843 | ||||||||
\(599\) | −13.5224 | −0.552511 | −0.276256 | − | 0.961084i | \(-0.589094\pi\) | ||||
−0.276256 | + | 0.961084i | \(0.589094\pi\) | |||||||
\(600\) | −15.1277 | −0.617586 | ||||||||
\(601\) | 10.2777 | 0.419236 | 0.209618 | − | 0.977783i | \(-0.432778\pi\) | ||||
0.209618 | + | 0.977783i | \(0.432778\pi\) | |||||||
\(602\) | 4.50944 | 0.183791 | ||||||||
\(603\) | 1.67894 | 0.0683719 | ||||||||
\(604\) | 12.6837 | 0.516092 | ||||||||
\(605\) | −7.26221 | −0.295251 | ||||||||
\(606\) | −81.5730 | −3.31367 | ||||||||
\(607\) | −39.1510 | −1.58909 | −0.794545 | − | 0.607205i | \(-0.792291\pi\) | ||||
−0.794545 | + | 0.607205i | \(0.792291\pi\) | |||||||
\(608\) | −36.3380 | −1.47370 | ||||||||
\(609\) | −4.58424 | −0.185763 | ||||||||
\(610\) | −8.47191 | −0.343018 | ||||||||
\(611\) | −4.15159 | −0.167955 | ||||||||
\(612\) | 12.2155 | 0.493783 | ||||||||
\(613\) | −6.13092 | −0.247626 | −0.123813 | − | 0.992306i | \(-0.539512\pi\) | ||||
−0.123813 | + | 0.992306i | \(0.539512\pi\) | |||||||
\(614\) | 54.4061 | 2.19565 | ||||||||
\(615\) | −15.6128 | −0.629570 | ||||||||
\(616\) | −18.1895 | −0.732877 | ||||||||
\(617\) | 38.5282 | 1.55109 | 0.775543 | − | 0.631295i | \(-0.217476\pi\) | ||||
0.775543 | + | 0.631295i | \(0.217476\pi\) | |||||||
\(618\) | −33.3025 | −1.33962 | ||||||||
\(619\) | 25.0132 | 1.00537 | 0.502683 | − | 0.864471i | \(-0.332346\pi\) | ||||
0.502683 | + | 0.864471i | \(0.332346\pi\) | |||||||
\(620\) | 35.5473 | 1.42761 | ||||||||
\(621\) | 42.3926 | 1.70116 | ||||||||
\(622\) | 81.7522 | 3.27796 | ||||||||
\(623\) | 2.60108 | 0.104210 | ||||||||
\(624\) | −28.0892 | −1.12447 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −38.3078 | −1.53109 | ||||||||
\(627\) | −5.24924 | −0.209634 | ||||||||
\(628\) | 53.4831 | 2.13421 | ||||||||
\(629\) | −7.78662 | −0.310473 | ||||||||
\(630\) | −1.13159 | −0.0450838 | ||||||||
\(631\) | −36.1897 | −1.44069 | −0.720345 | − | 0.693616i | \(-0.756016\pi\) | ||||
−0.720345 | + | 0.693616i | \(0.756016\pi\) | |||||||
\(632\) | −8.52382 | −0.339059 | ||||||||
\(633\) | −23.1426 | −0.919834 | ||||||||
\(634\) | −85.8452 | −3.40935 | ||||||||
\(635\) | 0.00317741 | 0.000126092 0 | ||||||||
\(636\) | 83.9322 | 3.32813 | ||||||||
\(637\) | −1.18193 | −0.0468297 | ||||||||
\(638\) | 15.0426 | 0.595541 | ||||||||
\(639\) | −1.49887 | −0.0592946 | ||||||||
\(640\) | −36.5555 | −1.44498 | ||||||||
\(641\) | 35.3431 | 1.39597 | 0.697985 | − | 0.716113i | \(-0.254080\pi\) | ||||
0.697985 | + | 0.716113i | \(0.254080\pi\) | |||||||
\(642\) | 58.1719 | 2.29586 | ||||||||
\(643\) | 30.5371 | 1.20427 | 0.602134 | − | 0.798395i | \(-0.294317\pi\) | ||||
0.602134 | + | 0.798395i | \(0.294317\pi\) | |||||||
\(644\) | 42.0614 | 1.65745 | ||||||||
\(645\) | 2.65691 | 0.104616 | ||||||||
\(646\) | 24.9209 | 0.980500 | ||||||||
\(647\) | −7.88287 | −0.309907 | −0.154954 | − | 0.987922i | \(-0.549523\pi\) | ||||
−0.154954 | + | 0.987922i | \(0.549523\pi\) | |||||||
\(648\) | 71.3539 | 2.80305 | ||||||||
\(649\) | −10.1292 | −0.397606 | ||||||||
\(650\) | 3.22550 | 0.126515 | ||||||||
\(651\) | −10.4922 | −0.411222 | ||||||||
\(652\) | 95.5508 | 3.74206 | ||||||||
\(653\) | −31.7326 | −1.24179 | −0.620896 | − | 0.783893i | \(-0.713231\pi\) | ||||
−0.620896 | + | 0.783893i | \(0.713231\pi\) | |||||||
\(654\) | −7.48907 | −0.292846 | ||||||||
\(655\) | −13.2548 | −0.517909 | ||||||||
\(656\) | −143.519 | −5.60349 | ||||||||
\(657\) | −4.25727 | −0.166092 | ||||||||
\(658\) | 9.58581 | 0.373694 | ||||||||
\(659\) | −46.6676 | −1.81791 | −0.908956 | − | 0.416891i | \(-0.863120\pi\) | ||||
−0.908956 | + | 0.416891i | \(0.863120\pi\) | |||||||
\(660\) | −16.9343 | −0.659165 | ||||||||
\(661\) | 8.04132 | 0.312771 | 0.156386 | − | 0.987696i | \(-0.450016\pi\) | ||||
0.156386 | + | 0.987696i | \(0.450016\pi\) | |||||||
\(662\) | −4.38762 | −0.170530 | ||||||||
\(663\) | 10.2773 | 0.399138 | ||||||||
\(664\) | 62.2498 | 2.41576 | ||||||||
\(665\) | −1.68861 | −0.0654815 | ||||||||
\(666\) | 1.62934 | 0.0631355 | ||||||||
\(667\) | −22.0137 | −0.852373 | ||||||||
\(668\) | −48.4391 | −1.87417 | ||||||||
\(669\) | 38.4807 | 1.48775 | ||||||||
\(670\) | 11.0499 | 0.426895 | ||||||||
\(671\) | −6.00182 | −0.231698 | ||||||||
\(672\) | 34.6012 | 1.33477 | ||||||||
\(673\) | 29.5664 | 1.13970 | 0.569851 | − | 0.821748i | \(-0.307001\pi\) | ||||
0.569851 | + | 0.821748i | \(0.307001\pi\) | |||||||
\(674\) | −18.6399 | −0.717984 | ||||||||
\(675\) | −5.49043 | −0.211327 | ||||||||
\(676\) | −63.2079 | −2.43107 | ||||||||
\(677\) | −25.2021 | −0.968595 | −0.484297 | − | 0.874903i | \(-0.660925\pi\) | ||||
−0.484297 | + | 0.874903i | \(0.660925\pi\) | |||||||
\(678\) | −62.2643 | −2.39124 | ||||||||
\(679\) | 16.8276 | 0.645783 | ||||||||
\(680\) | 50.8794 | 1.95114 | ||||||||
\(681\) | −5.50142 | −0.210815 | ||||||||
\(682\) | 34.4288 | 1.31834 | ||||||||
\(683\) | −21.5168 | −0.823319 | −0.411659 | − | 0.911338i | \(-0.635051\pi\) | ||||
−0.411659 | + | 0.911338i | \(0.635051\pi\) | |||||||
\(684\) | −3.81428 | −0.145843 | ||||||||
\(685\) | −13.3302 | −0.509320 | ||||||||
\(686\) | 2.72902 | 0.104194 | ||||||||
\(687\) | −1.60790 | −0.0613453 | ||||||||
\(688\) | 24.4234 | 0.931132 | ||||||||
\(689\) | −11.3256 | −0.431471 | ||||||||
\(690\) | 33.8805 | 1.28981 | ||||||||
\(691\) | 2.71122 | 0.103140 | 0.0515699 | − | 0.998669i | \(-0.483578\pi\) | ||||
0.0515699 | + | 0.998669i | \(0.483578\pi\) | |||||||
\(692\) | −48.8662 | −1.85761 | ||||||||
\(693\) | −0.801663 | −0.0304527 | ||||||||
\(694\) | −25.8592 | −0.981604 | ||||||||
\(695\) | −3.46484 | −0.131429 | ||||||||
\(696\) | −43.1302 | −1.63484 | ||||||||
\(697\) | 52.5111 | 1.98900 | ||||||||
\(698\) | −64.7918 | −2.45241 | ||||||||
\(699\) | 11.1511 | 0.421774 | ||||||||
\(700\) | −5.44753 | −0.205897 | ||||||||
\(701\) | −37.1915 | −1.40470 | −0.702351 | − | 0.711831i | \(-0.747866\pi\) | ||||
−0.702351 | + | 0.711831i | \(0.747866\pi\) | |||||||
\(702\) | −17.7094 | −0.668397 | ||||||||
\(703\) | 2.43136 | 0.0917006 | ||||||||
\(704\) | −56.3877 | −2.12519 | ||||||||
\(705\) | 5.64784 | 0.212710 | ||||||||
\(706\) | 80.4238 | 3.02679 | ||||||||
\(707\) | −18.5901 | −0.699151 | ||||||||
\(708\) | 45.8908 | 1.72468 | ||||||||
\(709\) | 26.9955 | 1.01384 | 0.506920 | − | 0.861993i | \(-0.330784\pi\) | ||||
0.506920 | + | 0.861993i | \(0.330784\pi\) | |||||||
\(710\) | −9.86477 | −0.370218 | ||||||||
\(711\) | −0.375669 | −0.0140887 | ||||||||
\(712\) | 24.4718 | 0.917121 | ||||||||
\(713\) | −50.3839 | −1.88689 | ||||||||
\(714\) | −23.7298 | −0.888065 | ||||||||
\(715\) | 2.28507 | 0.0854567 | ||||||||
\(716\) | 70.9649 | 2.65208 | ||||||||
\(717\) | −5.69118 | −0.212541 | ||||||||
\(718\) | 67.5700 | 2.52169 | ||||||||
\(719\) | 20.9938 | 0.782938 | 0.391469 | − | 0.920191i | \(-0.371967\pi\) | ||||
0.391469 | + | 0.920191i | \(0.371967\pi\) | |||||||
\(720\) | −6.12876 | −0.228406 | ||||||||
\(721\) | −7.58947 | −0.282647 | ||||||||
\(722\) | 44.0698 | 1.64011 | ||||||||
\(723\) | 12.4922 | 0.464590 | ||||||||
\(724\) | 5.97657 | 0.222117 | ||||||||
\(725\) | 2.85107 | 0.105886 | ||||||||
\(726\) | 31.8665 | 1.18268 | ||||||||
\(727\) | −28.3035 | −1.04972 | −0.524859 | − | 0.851189i | \(-0.675882\pi\) | ||||
−0.524859 | + | 0.851189i | \(0.675882\pi\) | |||||||
\(728\) | −11.1200 | −0.412135 | ||||||||
\(729\) | 29.6290 | 1.09737 | ||||||||
\(730\) | −28.0190 | −1.03703 | ||||||||
\(731\) | −8.93604 | −0.330512 | ||||||||
\(732\) | 27.1916 | 1.00503 | ||||||||
\(733\) | 34.1307 | 1.26065 | 0.630324 | − | 0.776333i | \(-0.282922\pi\) | ||||
0.630324 | + | 0.776333i | \(0.282922\pi\) | |||||||
\(734\) | −26.0193 | −0.960392 | ||||||||
\(735\) | 1.60790 | 0.0593083 | ||||||||
\(736\) | 166.156 | 6.12459 | ||||||||
\(737\) | 7.82816 | 0.288354 | ||||||||
\(738\) | −10.9878 | −0.404468 | ||||||||
\(739\) | 37.4808 | 1.37875 | 0.689377 | − | 0.724403i | \(-0.257884\pi\) | ||||
0.689377 | + | 0.724403i | \(0.257884\pi\) | |||||||
\(740\) | 7.84368 | 0.288339 | ||||||||
\(741\) | −3.20908 | −0.117888 | ||||||||
\(742\) | 26.1502 | 0.960005 | ||||||||
\(743\) | 29.0009 | 1.06394 | 0.531970 | − | 0.846763i | \(-0.321452\pi\) | ||||
0.531970 | + | 0.846763i | \(0.321452\pi\) | |||||||
\(744\) | −98.7144 | −3.61905 | ||||||||
\(745\) | 2.92132 | 0.107029 | ||||||||
\(746\) | 59.6434 | 2.18370 | ||||||||
\(747\) | 2.74353 | 0.100380 | ||||||||
\(748\) | 56.9555 | 2.08250 | ||||||||
\(749\) | 13.2571 | 0.484403 | ||||||||
\(750\) | −4.38799 | −0.160227 | ||||||||
\(751\) | 48.8460 | 1.78242 | 0.891208 | − | 0.453596i | \(-0.149859\pi\) | ||||
0.891208 | + | 0.453596i | \(0.149859\pi\) | |||||||
\(752\) | 51.9172 | 1.89323 | ||||||||
\(753\) | 14.4841 | 0.527832 | ||||||||
\(754\) | 9.19614 | 0.334904 | ||||||||
\(755\) | 2.32834 | 0.0847370 | ||||||||
\(756\) | 29.9092 | 1.08779 | ||||||||
\(757\) | −8.41899 | −0.305993 | −0.152997 | − | 0.988227i | \(-0.548892\pi\) | ||||
−0.152997 | + | 0.988227i | \(0.548892\pi\) | |||||||
\(758\) | −97.3372 | −3.53545 | ||||||||
\(759\) | 24.0022 | 0.871225 | ||||||||
\(760\) | −15.8870 | −0.576283 | ||||||||
\(761\) | 26.3088 | 0.953692 | 0.476846 | − | 0.878987i | \(-0.341780\pi\) | ||||
0.476846 | + | 0.878987i | \(0.341780\pi\) | |||||||
\(762\) | −0.0139425 | −0.000505082 0 | ||||||||
\(763\) | −1.70672 | −0.0617874 | ||||||||
\(764\) | 97.4150 | 3.52435 | ||||||||
\(765\) | 2.24240 | 0.0810741 | ||||||||
\(766\) | 0.412156 | 0.0148918 | ||||||||
\(767\) | −6.19239 | −0.223594 | ||||||||
\(768\) | 66.6130 | 2.40369 | ||||||||
\(769\) | 11.2817 | 0.406829 | 0.203415 | − | 0.979093i | \(-0.434796\pi\) | ||||
0.203415 | + | 0.979093i | \(0.434796\pi\) | |||||||
\(770\) | −5.27611 | −0.190138 | ||||||||
\(771\) | 36.8533 | 1.32724 | ||||||||
\(772\) | −0.0235001 | −0.000845788 0 | ||||||||
\(773\) | 17.0963 | 0.614910 | 0.307455 | − | 0.951563i | \(-0.400523\pi\) | ||||
0.307455 | + | 0.951563i | \(0.400523\pi\) | |||||||
\(774\) | 1.86985 | 0.0672104 | ||||||||
\(775\) | 6.52541 | 0.234400 | ||||||||
\(776\) | 158.320 | 5.68335 | ||||||||
\(777\) | −2.31515 | −0.0830557 | ||||||||
\(778\) | 94.8373 | 3.40008 | ||||||||
\(779\) | −16.3965 | −0.587466 | ||||||||
\(780\) | −10.3526 | −0.370683 | ||||||||
\(781\) | −6.98858 | −0.250071 | ||||||||
\(782\) | −113.951 | −4.07489 | ||||||||
\(783\) | −15.6536 | −0.559414 | ||||||||
\(784\) | 14.7805 | 0.527874 | ||||||||
\(785\) | 9.81787 | 0.350415 | ||||||||
\(786\) | 58.1621 | 2.07457 | ||||||||
\(787\) | 30.0966 | 1.07283 | 0.536414 | − | 0.843955i | \(-0.319779\pi\) | ||||
0.536414 | + | 0.843955i | \(0.319779\pi\) | |||||||
\(788\) | 112.002 | 3.98990 | ||||||||
\(789\) | 14.3411 | 0.510558 | ||||||||
\(790\) | −2.47245 | −0.0879657 | ||||||||
\(791\) | −14.1897 | −0.504528 | ||||||||
\(792\) | −7.54233 | −0.268005 | ||||||||
\(793\) | −3.66916 | −0.130296 | ||||||||
\(794\) | 40.8808 | 1.45081 | ||||||||
\(795\) | 15.4074 | 0.546444 | ||||||||
\(796\) | 142.792 | 5.06111 | ||||||||
\(797\) | −0.338746 | −0.0119990 | −0.00599950 | − | 0.999982i | \(-0.501910\pi\) | ||||
−0.00599950 | + | 0.999982i | \(0.501910\pi\) | |||||||
\(798\) | 7.40960 | 0.262297 | ||||||||
\(799\) | −18.9955 | −0.672013 | ||||||||
\(800\) | −21.5195 | −0.760828 | ||||||||
\(801\) | 1.07854 | 0.0381084 | ||||||||
\(802\) | −49.8732 | −1.76108 | ||||||||
\(803\) | −19.8497 | −0.700481 | ||||||||
\(804\) | −35.4659 | −1.25079 | ||||||||
\(805\) | 7.72119 | 0.272136 | ||||||||
\(806\) | 21.0477 | 0.741374 | ||||||||
\(807\) | 17.2825 | 0.608372 | ||||||||
\(808\) | −174.902 | −6.15302 | ||||||||
\(809\) | 35.4946 | 1.24792 | 0.623962 | − | 0.781454i | \(-0.285522\pi\) | ||||
0.623962 | + | 0.781454i | \(0.285522\pi\) | |||||||
\(810\) | 20.6971 | 0.727223 | ||||||||
\(811\) | −7.43222 | −0.260981 | −0.130490 | − | 0.991450i | \(-0.541655\pi\) | ||||
−0.130490 | + | 0.991450i | \(0.541655\pi\) | |||||||
\(812\) | −15.5313 | −0.545041 | ||||||||
\(813\) | 43.5372 | 1.52691 | ||||||||
\(814\) | 7.59686 | 0.266270 | ||||||||
\(815\) | 17.5402 | 0.614407 | ||||||||
\(816\) | −128.522 | −4.49916 | ||||||||
\(817\) | 2.79027 | 0.0976191 | ||||||||
\(818\) | 26.9455 | 0.942127 | ||||||||
\(819\) | −0.490090 | −0.0171251 | ||||||||
\(820\) | −52.8958 | −1.84720 | ||||||||
\(821\) | 29.4532 | 1.02792 | 0.513962 | − | 0.857813i | \(-0.328177\pi\) | ||||
0.513962 | + | 0.857813i | \(0.328177\pi\) | |||||||
\(822\) | 58.4927 | 2.04017 | ||||||||
\(823\) | −1.01650 | −0.0354328 | −0.0177164 | − | 0.999843i | \(-0.505640\pi\) | ||||
−0.0177164 | + | 0.999843i | \(0.505640\pi\) | |||||||
\(824\) | −71.4044 | −2.48749 | ||||||||
\(825\) | −3.10862 | −0.108228 | ||||||||
\(826\) | 14.2979 | 0.497488 | ||||||||
\(827\) | −15.6254 | −0.543350 | −0.271675 | − | 0.962389i | \(-0.587578\pi\) | ||||
−0.271675 | + | 0.962389i | \(0.587578\pi\) | |||||||
\(828\) | 17.4409 | 0.606112 | ||||||||
\(829\) | −11.8091 | −0.410147 | −0.205074 | − | 0.978747i | \(-0.565743\pi\) | ||||
−0.205074 | + | 0.978747i | \(0.565743\pi\) | |||||||
\(830\) | 18.0564 | 0.626746 | ||||||||
\(831\) | −9.63109 | −0.334099 | ||||||||
\(832\) | −34.4721 | −1.19511 | ||||||||
\(833\) | −5.40790 | −0.187373 | ||||||||
\(834\) | 15.2037 | 0.526460 | ||||||||
\(835\) | −8.89195 | −0.307718 | ||||||||
\(836\) | −17.7843 | −0.615082 | ||||||||
\(837\) | −35.8273 | −1.23837 | ||||||||
\(838\) | −89.5666 | −3.09403 | ||||||||
\(839\) | −2.34631 | −0.0810035 | −0.0405018 | − | 0.999179i | \(-0.512896\pi\) | ||||
−0.0405018 | + | 0.999179i | \(0.512896\pi\) | |||||||
\(840\) | 15.1277 | 0.521955 | ||||||||
\(841\) | −20.8714 | −0.719703 | ||||||||
\(842\) | −3.53051 | −0.121669 | ||||||||
\(843\) | 23.7911 | 0.819411 | ||||||||
\(844\) | −78.4063 | −2.69886 | ||||||||
\(845\) | −11.6030 | −0.399157 | ||||||||
\(846\) | 3.97478 | 0.136656 | ||||||||
\(847\) | 7.26221 | 0.249532 | ||||||||
\(848\) | 141.631 | 4.86363 | ||||||||
\(849\) | −0.230654 | −0.00791601 | ||||||||
\(850\) | 14.7582 | 0.506203 | ||||||||
\(851\) | −11.1174 | −0.381101 | ||||||||
\(852\) | 31.6621 | 1.08473 | ||||||||
\(853\) | −31.1950 | −1.06810 | −0.534049 | − | 0.845454i | \(-0.679330\pi\) | ||||
−0.534049 | + | 0.845454i | \(0.679330\pi\) | |||||||
\(854\) | 8.47191 | 0.289903 | ||||||||
\(855\) | −0.700186 | −0.0239459 | ||||||||
\(856\) | 124.727 | 4.26309 | ||||||||
\(857\) | −16.9959 | −0.580569 | −0.290285 | − | 0.956940i | \(-0.593750\pi\) | ||||
−0.290285 | + | 0.956940i | \(0.593750\pi\) | |||||||
\(858\) | −10.0268 | −0.342311 | ||||||||
\(859\) | −8.27192 | −0.282234 | −0.141117 | − | 0.989993i | \(-0.545069\pi\) | ||||
−0.141117 | + | 0.989993i | \(0.545069\pi\) | |||||||
\(860\) | 9.00152 | 0.306949 | ||||||||
\(861\) | 15.6128 | 0.532084 | ||||||||
\(862\) | −7.62243 | −0.259621 | ||||||||
\(863\) | −30.9103 | −1.05220 | −0.526100 | − | 0.850423i | \(-0.676346\pi\) | ||||
−0.526100 | + | 0.850423i | \(0.676346\pi\) | |||||||
\(864\) | 118.151 | 4.01958 | ||||||||
\(865\) | −8.97034 | −0.305001 | ||||||||
\(866\) | 105.349 | 3.57990 | ||||||||
\(867\) | 19.6894 | 0.668686 | ||||||||
\(868\) | −35.5473 | −1.20655 | ||||||||
\(869\) | −1.75157 | −0.0594181 | ||||||||
\(870\) | −12.5105 | −0.424145 | ||||||||
\(871\) | 4.78568 | 0.162156 | ||||||||
\(872\) | −16.0574 | −0.543773 | ||||||||
\(873\) | 6.97760 | 0.236156 | ||||||||
\(874\) | 35.5811 | 1.20355 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 89.9301 | 3.03846 | ||||||||
\(877\) | 35.5998 | 1.20212 | 0.601061 | − | 0.799204i | \(-0.294745\pi\) | ||||
0.601061 | + | 0.799204i | \(0.294745\pi\) | |||||||
\(878\) | −85.4995 | −2.88547 | ||||||||
\(879\) | 45.7756 | 1.54397 | ||||||||
\(880\) | −28.5757 | −0.963285 | ||||||||
\(881\) | −25.9027 | −0.872683 | −0.436341 | − | 0.899781i | \(-0.643726\pi\) | ||||
−0.436341 | + | 0.899781i | \(0.643726\pi\) | |||||||
\(882\) | 1.13159 | 0.0381027 | ||||||||
\(883\) | 10.6533 | 0.358512 | 0.179256 | − | 0.983802i | \(-0.442631\pi\) | ||||
0.179256 | + | 0.983802i | \(0.442631\pi\) | |||||||
\(884\) | 34.8192 | 1.17110 | ||||||||
\(885\) | 8.42416 | 0.283175 | ||||||||
\(886\) | 3.02523 | 0.101635 | ||||||||
\(887\) | −14.5022 | −0.486937 | −0.243468 | − | 0.969909i | \(-0.578285\pi\) | ||||
−0.243468 | + | 0.969909i | \(0.578285\pi\) | |||||||
\(888\) | −21.7818 | −0.730949 | ||||||||
\(889\) | −0.00317741 | −0.000106567 0 | ||||||||
\(890\) | 7.09838 | 0.237938 | ||||||||
\(891\) | 14.6626 | 0.491217 | ||||||||
\(892\) | 130.371 | 4.36516 | ||||||||
\(893\) | 5.93133 | 0.198484 | ||||||||
\(894\) | −12.8187 | −0.428722 | ||||||||
\(895\) | 13.0270 | 0.435445 | ||||||||
\(896\) | 36.5555 | 1.22123 | ||||||||
\(897\) | 14.6735 | 0.489935 | ||||||||
\(898\) | −7.27172 | −0.242660 | ||||||||
\(899\) | 18.6044 | 0.620492 | ||||||||
\(900\) | −2.25883 | −0.0752943 | ||||||||
\(901\) | −51.8201 | −1.72638 | ||||||||
\(902\) | −51.2314 | −1.70582 | ||||||||
\(903\) | −2.65691 | −0.0884163 | ||||||||
\(904\) | −133.502 | −4.44020 | ||||||||
\(905\) | 1.09712 | 0.0364694 | ||||||||
\(906\) | −10.2167 | −0.339428 | ||||||||
\(907\) | 2.11258 | 0.0701470 | 0.0350735 | − | 0.999385i | \(-0.488833\pi\) | ||||
0.0350735 | + | 0.999385i | \(0.488833\pi\) | |||||||
\(908\) | −18.6387 | −0.618546 | ||||||||
\(909\) | −7.70841 | −0.255672 | ||||||||
\(910\) | −3.22550 | −0.106924 | ||||||||
\(911\) | 10.5760 | 0.350398 | 0.175199 | − | 0.984533i | \(-0.443943\pi\) | ||||
0.175199 | + | 0.984533i | \(0.443943\pi\) | |||||||
\(912\) | 40.1308 | 1.32886 | ||||||||
\(913\) | 12.7918 | 0.423347 | ||||||||
\(914\) | −83.7371 | −2.76978 | ||||||||
\(915\) | 4.99154 | 0.165015 | ||||||||
\(916\) | −5.44753 | −0.179991 | ||||||||
\(917\) | 13.2548 | 0.437713 | ||||||||
\(918\) | −81.0290 | −2.67436 | ||||||||
\(919\) | 24.6587 | 0.813416 | 0.406708 | − | 0.913558i | \(-0.366677\pi\) | ||||
0.406708 | + | 0.913558i | \(0.366677\pi\) | |||||||
\(920\) | 72.6437 | 2.39499 | ||||||||
\(921\) | −32.0554 | −1.05626 | ||||||||
\(922\) | −51.6922 | −1.70239 | ||||||||
\(923\) | −4.27240 | −0.140628 | ||||||||
\(924\) | 16.9343 | 0.557097 | ||||||||
\(925\) | 1.43986 | 0.0473423 | ||||||||
\(926\) | 74.9668 | 2.46356 | ||||||||
\(927\) | −3.14699 | −0.103361 | ||||||||
\(928\) | −61.3535 | −2.01403 | ||||||||
\(929\) | 2.58813 | 0.0849139 | 0.0424569 | − | 0.999098i | \(-0.486481\pi\) | ||||
0.0424569 | + | 0.999098i | \(0.486481\pi\) | |||||||
\(930\) | −28.6334 | −0.938926 | ||||||||
\(931\) | 1.68861 | 0.0553419 | ||||||||
\(932\) | 37.7797 | 1.23751 | ||||||||
\(933\) | −48.1674 | −1.57693 | ||||||||
\(934\) | −61.5134 | −2.01278 | ||||||||
\(935\) | 10.4553 | 0.341925 | ||||||||
\(936\) | −4.61094 | −0.150713 | ||||||||
\(937\) | 8.32841 | 0.272077 | 0.136039 | − | 0.990704i | \(-0.456563\pi\) | ||||
0.136039 | + | 0.990704i | \(0.456563\pi\) | |||||||
\(938\) | −11.0499 | −0.360792 | ||||||||
\(939\) | 22.5705 | 0.736560 | ||||||||
\(940\) | 19.1347 | 0.624106 | ||||||||
\(941\) | −57.2964 | −1.86781 | −0.933905 | − | 0.357522i | \(-0.883622\pi\) | ||||
−0.933905 | + | 0.357522i | \(0.883622\pi\) | |||||||
\(942\) | −43.0807 | −1.40364 | ||||||||
\(943\) | 74.9733 | 2.44147 | ||||||||
\(944\) | 77.4383 | 2.52040 | ||||||||
\(945\) | 5.49043 | 0.178604 | ||||||||
\(946\) | 8.71827 | 0.283455 | ||||||||
\(947\) | −4.62095 | −0.150161 | −0.0750803 | − | 0.997177i | \(-0.523921\pi\) | ||||
−0.0750803 | + | 0.997177i | \(0.523921\pi\) | |||||||
\(948\) | 7.93559 | 0.257736 | ||||||||
\(949\) | −12.1349 | −0.393917 | ||||||||
\(950\) | −4.60824 | −0.149511 | ||||||||
\(951\) | 50.5789 | 1.64013 | ||||||||
\(952\) | −50.8794 | −1.64901 | ||||||||
\(953\) | −34.7222 | −1.12476 | −0.562382 | − | 0.826878i | \(-0.690115\pi\) | ||||
−0.562382 | + | 0.826878i | \(0.690115\pi\) | |||||||
\(954\) | 10.8433 | 0.351064 | ||||||||
\(955\) | 17.8824 | 0.578662 | ||||||||
\(956\) | −19.2815 | −0.623610 | ||||||||
\(957\) | −8.86289 | −0.286497 | ||||||||
\(958\) | −5.22583 | −0.168839 | ||||||||
\(959\) | 13.3302 | 0.430454 | ||||||||
\(960\) | 46.8960 | 1.51356 | ||||||||
\(961\) | 11.5809 | 0.373578 | ||||||||
\(962\) | 4.64427 | 0.149737 | ||||||||
\(963\) | 5.49708 | 0.177141 | ||||||||
\(964\) | 42.3233 | 1.36314 | ||||||||
\(965\) | −0.00431391 | −0.000138870 0 | ||||||||
\(966\) | −33.8805 | −1.09009 | ||||||||
\(967\) | −8.99496 | −0.289258 | −0.144629 | − | 0.989486i | \(-0.546199\pi\) | ||||
−0.144629 | + | 0.989486i | \(0.546199\pi\) | |||||||
\(968\) | 68.3254 | 2.19606 | ||||||||
\(969\) | −14.6831 | −0.471689 | ||||||||
\(970\) | 45.9227 | 1.47449 | ||||||||
\(971\) | 41.7337 | 1.33930 | 0.669649 | − | 0.742678i | \(-0.266444\pi\) | ||||
0.669649 | + | 0.742678i | \(0.266444\pi\) | |||||||
\(972\) | 23.2979 | 0.747279 | ||||||||
\(973\) | 3.46484 | 0.111078 | ||||||||
\(974\) | −5.36710 | −0.171973 | ||||||||
\(975\) | −1.90043 | −0.0608623 | ||||||||
\(976\) | 45.8843 | 1.46872 | ||||||||
\(977\) | −6.62613 | −0.211989 | −0.105994 | − | 0.994367i | \(-0.533803\pi\) | ||||
−0.105994 | + | 0.994367i | \(0.533803\pi\) | |||||||
\(978\) | −76.9663 | −2.46111 | ||||||||
\(979\) | 5.02876 | 0.160720 | ||||||||
\(980\) | 5.44753 | 0.174015 | ||||||||
\(981\) | −0.707696 | −0.0225950 | ||||||||
\(982\) | −48.6948 | −1.55391 | ||||||||
\(983\) | 29.1660 | 0.930252 | 0.465126 | − | 0.885244i | \(-0.346009\pi\) | ||||
0.465126 | + | 0.885244i | \(0.346009\pi\) | |||||||
\(984\) | 146.891 | 4.68271 | ||||||||
\(985\) | 20.5601 | 0.655101 | ||||||||
\(986\) | 42.0768 | 1.34000 | ||||||||
\(987\) | −5.64784 | −0.179773 | ||||||||
\(988\) | −10.8723 | −0.345893 | ||||||||
\(989\) | −12.7585 | −0.405698 | ||||||||
\(990\) | −2.18775 | −0.0695313 | ||||||||
\(991\) | 11.0670 | 0.351554 | 0.175777 | − | 0.984430i | \(-0.443756\pi\) | ||||
0.175777 | + | 0.984430i | \(0.443756\pi\) | |||||||
\(992\) | −140.423 | −4.45844 | ||||||||
\(993\) | 2.58513 | 0.0820366 | ||||||||
\(994\) | 9.86477 | 0.312892 | ||||||||
\(995\) | 26.2122 | 0.830982 | ||||||||
\(996\) | −57.9540 | −1.83634 | ||||||||
\(997\) | 3.87204 | 0.122629 | 0.0613143 | − | 0.998119i | \(-0.480471\pi\) | ||||
0.0613143 | + | 0.998119i | \(0.480471\pi\) | |||||||
\(998\) | 15.8078 | 0.500386 | ||||||||
\(999\) | −7.90545 | −0.250117 |
(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 | 8015.2.a.m.1.2 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.m.1.2 | ✓ | 67 | 1.1 | even | 1 | trivial |