Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, 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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(59\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.67397 | −1.18368 | −0.591839 | − | 0.806056i | \(-0.701598\pi\) | ||||
−0.591839 | + | 0.806056i | \(0.701598\pi\) | |||||||
\(3\) | −0.759884 | −0.438719 | −0.219360 | − | 0.975644i | \(-0.570397\pi\) | ||||
−0.219360 | + | 0.975644i | \(0.570397\pi\) | |||||||
\(4\) | 0.802190 | 0.401095 | ||||||||
\(5\) | 2.08858 | 0.934041 | 0.467020 | − | 0.884247i | \(-0.345327\pi\) | ||||
0.467020 | + | 0.884247i | \(0.345327\pi\) | |||||||
\(6\) | 1.27203 | 0.519302 | ||||||||
\(7\) | −1.20948 | −0.457142 | −0.228571 | − | 0.973527i | \(-0.573405\pi\) | ||||
−0.228571 | + | 0.973527i | \(0.573405\pi\) | |||||||
\(8\) | 2.00510 | 0.708911 | ||||||||
\(9\) | −2.42258 | −0.807526 | ||||||||
\(10\) | −3.49623 | −1.10560 | ||||||||
\(11\) | 0.872783 | 0.263154 | 0.131577 | − | 0.991306i | \(-0.457996\pi\) | ||||
0.131577 | + | 0.991306i | \(0.457996\pi\) | |||||||
\(12\) | −0.609571 | −0.175968 | ||||||||
\(13\) | −1.63350 | −0.453050 | −0.226525 | − | 0.974005i | \(-0.572737\pi\) | ||||
−0.226525 | + | 0.974005i | \(0.572737\pi\) | |||||||
\(14\) | 2.02464 | 0.541109 | ||||||||
\(15\) | −1.58708 | −0.409781 | ||||||||
\(16\) | −4.96087 | −1.24022 | ||||||||
\(17\) | 4.07334 | 0.987931 | 0.493965 | − | 0.869482i | \(-0.335547\pi\) | ||||
0.493965 | + | 0.869482i | \(0.335547\pi\) | |||||||
\(18\) | 4.05533 | 0.955851 | ||||||||
\(19\) | 0.346683 | 0.0795345 | 0.0397673 | − | 0.999209i | \(-0.487338\pi\) | ||||
0.0397673 | + | 0.999209i | \(0.487338\pi\) | |||||||
\(20\) | 1.67544 | 0.374639 | ||||||||
\(21\) | 0.919067 | 0.200557 | ||||||||
\(22\) | −1.46102 | −0.311490 | ||||||||
\(23\) | −5.88362 | −1.22682 | −0.613409 | − | 0.789765i | \(-0.710202\pi\) | ||||
−0.613409 | + | 0.789765i | \(0.710202\pi\) | |||||||
\(24\) | −1.52365 | −0.311013 | ||||||||
\(25\) | −0.637840 | −0.127568 | ||||||||
\(26\) | 2.73443 | 0.536266 | ||||||||
\(27\) | 4.12053 | 0.792996 | ||||||||
\(28\) | −0.970236 | −0.183357 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 2.65673 | 0.485050 | ||||||||
\(31\) | 6.54222 | 1.17502 | 0.587509 | − | 0.809218i | \(-0.300109\pi\) | ||||
0.587509 | + | 0.809218i | \(0.300109\pi\) | |||||||
\(32\) | 4.29416 | 0.759108 | ||||||||
\(33\) | −0.663214 | −0.115451 | ||||||||
\(34\) | −6.81867 | −1.16939 | ||||||||
\(35\) | −2.52610 | −0.426989 | ||||||||
\(36\) | −1.94337 | −0.323894 | ||||||||
\(37\) | 2.25609 | 0.370898 | 0.185449 | − | 0.982654i | \(-0.440626\pi\) | ||||
0.185449 | + | 0.982654i | \(0.440626\pi\) | |||||||
\(38\) | −0.580338 | −0.0941433 | ||||||||
\(39\) | 1.24127 | 0.198762 | ||||||||
\(40\) | 4.18782 | 0.662152 | ||||||||
\(41\) | 5.30697 | 0.828810 | 0.414405 | − | 0.910093i | \(-0.363990\pi\) | ||||
0.414405 | + | 0.910093i | \(0.363990\pi\) | |||||||
\(42\) | −1.53849 | −0.237395 | ||||||||
\(43\) | 6.40472 | 0.976710 | 0.488355 | − | 0.872645i | \(-0.337597\pi\) | ||||
0.488355 | + | 0.872645i | \(0.337597\pi\) | |||||||
\(44\) | 0.700138 | 0.105550 | ||||||||
\(45\) | −5.05974 | −0.754262 | ||||||||
\(46\) | 9.84902 | 1.45216 | ||||||||
\(47\) | −4.58648 | −0.669007 | −0.334503 | − | 0.942395i | \(-0.608569\pi\) | ||||
−0.334503 | + | 0.942395i | \(0.608569\pi\) | |||||||
\(48\) | 3.76969 | 0.544107 | ||||||||
\(49\) | −5.53715 | −0.791021 | ||||||||
\(50\) | 1.06773 | 0.151000 | ||||||||
\(51\) | −3.09527 | −0.433424 | ||||||||
\(52\) | −1.31037 | −0.181716 | ||||||||
\(53\) | −13.1227 | −1.80255 | −0.901273 | − | 0.433253i | \(-0.857366\pi\) | ||||
−0.901273 | + | 0.433253i | \(0.857366\pi\) | |||||||
\(54\) | −6.89766 | −0.938652 | ||||||||
\(55\) | 1.82288 | 0.245796 | ||||||||
\(56\) | −2.42514 | −0.324073 | ||||||||
\(57\) | −0.263439 | −0.0348933 | ||||||||
\(58\) | −1.67397 | −0.219804 | ||||||||
\(59\) | −1.64556 | −0.214234 | −0.107117 | − | 0.994246i | \(-0.534162\pi\) | ||||
−0.107117 | + | 0.994246i | \(0.534162\pi\) | |||||||
\(60\) | −1.27314 | −0.164361 | ||||||||
\(61\) | −12.3423 | −1.58028 | −0.790138 | − | 0.612930i | \(-0.789991\pi\) | ||||
−0.790138 | + | 0.612930i | \(0.789991\pi\) | |||||||
\(62\) | −10.9515 | −1.39084 | ||||||||
\(63\) | 2.93007 | 0.369154 | ||||||||
\(64\) | 2.73342 | 0.341678 | ||||||||
\(65\) | −3.41168 | −0.423167 | ||||||||
\(66\) | 1.11020 | 0.136656 | ||||||||
\(67\) | 2.98614 | 0.364815 | 0.182407 | − | 0.983223i | \(-0.441611\pi\) | ||||
0.182407 | + | 0.983223i | \(0.441611\pi\) | |||||||
\(68\) | 3.26759 | 0.396254 | ||||||||
\(69\) | 4.47087 | 0.538229 | ||||||||
\(70\) | 4.22863 | 0.505418 | ||||||||
\(71\) | −11.8995 | −1.41221 | −0.706105 | − | 0.708107i | \(-0.749549\pi\) | ||||
−0.706105 | + | 0.708107i | \(0.749549\pi\) | |||||||
\(72\) | −4.85752 | −0.572464 | ||||||||
\(73\) | 7.78542 | 0.911215 | 0.455607 | − | 0.890181i | \(-0.349422\pi\) | ||||
0.455607 | + | 0.890181i | \(0.349422\pi\) | |||||||
\(74\) | −3.77663 | −0.439024 | ||||||||
\(75\) | 0.484685 | 0.0559665 | ||||||||
\(76\) | 0.278106 | 0.0319009 | ||||||||
\(77\) | −1.05562 | −0.120299 | ||||||||
\(78\) | −2.07785 | −0.235270 | ||||||||
\(79\) | 9.99150 | 1.12413 | 0.562066 | − | 0.827093i | \(-0.310007\pi\) | ||||
0.562066 | + | 0.827093i | \(0.310007\pi\) | |||||||
\(80\) | −10.3612 | −1.15841 | ||||||||
\(81\) | 4.13661 | 0.459623 | ||||||||
\(82\) | −8.88374 | −0.981044 | ||||||||
\(83\) | 6.27488 | 0.688758 | 0.344379 | − | 0.938831i | \(-0.388090\pi\) | ||||
0.344379 | + | 0.938831i | \(0.388090\pi\) | |||||||
\(84\) | 0.737266 | 0.0804424 | ||||||||
\(85\) | 8.50750 | 0.922768 | ||||||||
\(86\) | −10.7213 | −1.15611 | ||||||||
\(87\) | −0.759884 | −0.0814681 | ||||||||
\(88\) | 1.75002 | 0.186553 | ||||||||
\(89\) | −4.35379 | −0.461501 | −0.230750 | − | 0.973013i | \(-0.574118\pi\) | ||||
−0.230750 | + | 0.973013i | \(0.574118\pi\) | |||||||
\(90\) | 8.46988 | 0.892803 | ||||||||
\(91\) | 1.97569 | 0.207108 | ||||||||
\(92\) | −4.71978 | −0.492071 | ||||||||
\(93\) | −4.97133 | −0.515503 | ||||||||
\(94\) | 7.67765 | 0.791889 | ||||||||
\(95\) | 0.724075 | 0.0742885 | ||||||||
\(96\) | −3.26307 | −0.333035 | ||||||||
\(97\) | 10.3985 | 1.05580 | 0.527902 | − | 0.849306i | \(-0.322979\pi\) | ||||
0.527902 | + | 0.849306i | \(0.322979\pi\) | |||||||
\(98\) | 9.26904 | 0.936315 | ||||||||
\(99\) | −2.11438 | −0.212504 | ||||||||
\(100\) | −0.511669 | −0.0511669 | ||||||||
\(101\) | 10.1672 | 1.01168 | 0.505839 | − | 0.862628i | \(-0.331183\pi\) | ||||
0.505839 | + | 0.862628i | \(0.331183\pi\) | |||||||
\(102\) | 5.18140 | 0.513035 | ||||||||
\(103\) | −14.3815 | −1.41706 | −0.708528 | − | 0.705683i | \(-0.750640\pi\) | ||||
−0.708528 | + | 0.705683i | \(0.750640\pi\) | |||||||
\(104\) | −3.27533 | −0.321172 | ||||||||
\(105\) | 1.91954 | 0.187328 | ||||||||
\(106\) | 21.9671 | 2.13363 | ||||||||
\(107\) | −3.57358 | −0.345471 | −0.172736 | − | 0.984968i | \(-0.555261\pi\) | ||||
−0.172736 | + | 0.984968i | \(0.555261\pi\) | |||||||
\(108\) | 3.30545 | 0.318067 | ||||||||
\(109\) | 5.67750 | 0.543806 | 0.271903 | − | 0.962325i | \(-0.412347\pi\) | ||||
0.271903 | + | 0.962325i | \(0.412347\pi\) | |||||||
\(110\) | −3.05145 | −0.290944 | ||||||||
\(111\) | −1.71436 | −0.162720 | ||||||||
\(112\) | 6.00009 | 0.566956 | ||||||||
\(113\) | 0.177433 | 0.0166915 | 0.00834576 | − | 0.999965i | \(-0.497343\pi\) | ||||
0.00834576 | + | 0.999965i | \(0.497343\pi\) | |||||||
\(114\) | 0.440990 | 0.0413025 | ||||||||
\(115\) | −12.2884 | −1.14590 | ||||||||
\(116\) | 0.802190 | 0.0744815 | ||||||||
\(117\) | 3.95727 | 0.365850 | ||||||||
\(118\) | 2.75463 | 0.253584 | ||||||||
\(119\) | −4.92664 | −0.451625 | ||||||||
\(120\) | −3.18225 | −0.290499 | ||||||||
\(121\) | −10.2383 | −0.930750 | ||||||||
\(122\) | 20.6608 | 1.87054 | ||||||||
\(123\) | −4.03268 | −0.363615 | ||||||||
\(124\) | 5.24810 | 0.471294 | ||||||||
\(125\) | −11.7751 | −1.05319 | ||||||||
\(126\) | −4.90486 | −0.436959 | ||||||||
\(127\) | 6.85541 | 0.608319 | 0.304159 | − | 0.952621i | \(-0.401624\pi\) | ||||
0.304159 | + | 0.952621i | \(0.401624\pi\) | |||||||
\(128\) | −13.1640 | −1.16354 | ||||||||
\(129\) | −4.86684 | −0.428501 | ||||||||
\(130\) | 5.71107 | 0.500894 | ||||||||
\(131\) | −13.3584 | −1.16713 | −0.583566 | − | 0.812066i | \(-0.698343\pi\) | ||||
−0.583566 | + | 0.812066i | \(0.698343\pi\) | |||||||
\(132\) | −0.532023 | −0.0463067 | ||||||||
\(133\) | −0.419307 | −0.0363586 | ||||||||
\(134\) | −4.99872 | −0.431824 | ||||||||
\(135\) | 8.60605 | 0.740690 | ||||||||
\(136\) | 8.16747 | 0.700355 | ||||||||
\(137\) | −11.3302 | −0.968002 | −0.484001 | − | 0.875068i | \(-0.660817\pi\) | ||||
−0.484001 | + | 0.875068i | \(0.660817\pi\) | |||||||
\(138\) | −7.48411 | −0.637090 | ||||||||
\(139\) | 1.00000 | 0.0848189 | ||||||||
\(140\) | −2.02641 | −0.171263 | ||||||||
\(141\) | 3.48519 | 0.293506 | ||||||||
\(142\) | 19.9194 | 1.67160 | ||||||||
\(143\) | −1.42569 | −0.119222 | ||||||||
\(144\) | 12.0181 | 1.00151 | ||||||||
\(145\) | 2.08858 | 0.173447 | ||||||||
\(146\) | −13.0326 | −1.07859 | ||||||||
\(147\) | 4.20759 | 0.347036 | ||||||||
\(148\) | 1.80981 | 0.148765 | ||||||||
\(149\) | 12.4387 | 1.01902 | 0.509508 | − | 0.860466i | \(-0.329827\pi\) | ||||
0.509508 | + | 0.860466i | \(0.329827\pi\) | |||||||
\(150\) | −0.811349 | −0.0662464 | ||||||||
\(151\) | −13.8962 | −1.13086 | −0.565428 | − | 0.824798i | \(-0.691289\pi\) | ||||
−0.565428 | + | 0.824798i | \(0.691289\pi\) | |||||||
\(152\) | 0.695135 | 0.0563829 | ||||||||
\(153\) | −9.86799 | −0.797779 | ||||||||
\(154\) | 1.76708 | 0.142395 | ||||||||
\(155\) | 13.6639 | 1.09751 | ||||||||
\(156\) | 0.995732 | 0.0797223 | ||||||||
\(157\) | 0.999786 | 0.0797916 | 0.0398958 | − | 0.999204i | \(-0.487297\pi\) | ||||
0.0398958 | + | 0.999204i | \(0.487297\pi\) | |||||||
\(158\) | −16.7255 | −1.33061 | ||||||||
\(159\) | 9.97175 | 0.790811 | ||||||||
\(160\) | 8.96870 | 0.709038 | ||||||||
\(161\) | 7.11614 | 0.560830 | ||||||||
\(162\) | −6.92457 | −0.544046 | ||||||||
\(163\) | −9.52993 | −0.746441 | −0.373221 | − | 0.927743i | \(-0.621747\pi\) | ||||
−0.373221 | + | 0.927743i | \(0.621747\pi\) | |||||||
\(164\) | 4.25720 | 0.332431 | ||||||||
\(165\) | −1.38517 | −0.107836 | ||||||||
\(166\) | −10.5040 | −0.815268 | ||||||||
\(167\) | 13.9715 | 1.08114 | 0.540572 | − | 0.841298i | \(-0.318208\pi\) | ||||
0.540572 | + | 0.841298i | \(0.318208\pi\) | |||||||
\(168\) | 1.84282 | 0.142177 | ||||||||
\(169\) | −10.3317 | −0.794746 | ||||||||
\(170\) | −14.2413 | −1.09226 | ||||||||
\(171\) | −0.839866 | −0.0642262 | ||||||||
\(172\) | 5.13780 | 0.391754 | ||||||||
\(173\) | −2.50021 | −0.190088 | −0.0950438 | − | 0.995473i | \(-0.530299\pi\) | ||||
−0.0950438 | + | 0.995473i | \(0.530299\pi\) | |||||||
\(174\) | 1.27203 | 0.0964320 | ||||||||
\(175\) | 0.771458 | 0.0583167 | ||||||||
\(176\) | −4.32976 | −0.326368 | ||||||||
\(177\) | 1.25044 | 0.0939886 | ||||||||
\(178\) | 7.28813 | 0.546268 | ||||||||
\(179\) | 9.25085 | 0.691441 | 0.345720 | − | 0.938338i | \(-0.387635\pi\) | ||||
0.345720 | + | 0.938338i | \(0.387635\pi\) | |||||||
\(180\) | −4.05887 | −0.302531 | ||||||||
\(181\) | 13.7001 | 1.01832 | 0.509160 | − | 0.860672i | \(-0.329956\pi\) | ||||
0.509160 | + | 0.860672i | \(0.329956\pi\) | |||||||
\(182\) | −3.30725 | −0.245150 | ||||||||
\(183\) | 9.37875 | 0.693297 | ||||||||
\(184\) | −11.7973 | −0.869706 | ||||||||
\(185\) | 4.71201 | 0.346434 | ||||||||
\(186\) | 8.32187 | 0.610189 | ||||||||
\(187\) | 3.55514 | 0.259978 | ||||||||
\(188\) | −3.67923 | −0.268335 | ||||||||
\(189\) | −4.98371 | −0.362512 | ||||||||
\(190\) | −1.21208 | −0.0879337 | ||||||||
\(191\) | 12.1621 | 0.880019 | 0.440009 | − | 0.897993i | \(-0.354975\pi\) | ||||
0.440009 | + | 0.897993i | \(0.354975\pi\) | |||||||
\(192\) | −2.07708 | −0.149901 | ||||||||
\(193\) | −16.2564 | −1.17016 | −0.585080 | − | 0.810976i | \(-0.698937\pi\) | ||||
−0.585080 | + | 0.810976i | \(0.698937\pi\) | |||||||
\(194\) | −17.4067 | −1.24973 | ||||||||
\(195\) | 2.59248 | 0.185652 | ||||||||
\(196\) | −4.44184 | −0.317275 | ||||||||
\(197\) | 15.2507 | 1.08657 | 0.543283 | − | 0.839550i | \(-0.317181\pi\) | ||||
0.543283 | + | 0.839550i | \(0.317181\pi\) | |||||||
\(198\) | 3.53942 | 0.251536 | ||||||||
\(199\) | 4.04089 | 0.286451 | 0.143225 | − | 0.989690i | \(-0.454253\pi\) | ||||
0.143225 | + | 0.989690i | \(0.454253\pi\) | |||||||
\(200\) | −1.27894 | −0.0904344 | ||||||||
\(201\) | −2.26912 | −0.160051 | ||||||||
\(202\) | −17.0197 | −1.19750 | ||||||||
\(203\) | −1.20948 | −0.0848891 | ||||||||
\(204\) | −2.48299 | −0.173844 | ||||||||
\(205\) | 11.0840 | 0.774142 | ||||||||
\(206\) | 24.0743 | 1.67734 | ||||||||
\(207\) | 14.2535 | 0.990688 | ||||||||
\(208\) | 8.10356 | 0.561881 | ||||||||
\(209\) | 0.302579 | 0.0209298 | ||||||||
\(210\) | −3.21327 | −0.221736 | ||||||||
\(211\) | −8.10689 | −0.558101 | −0.279051 | − | 0.960276i | \(-0.590020\pi\) | ||||
−0.279051 | + | 0.960276i | \(0.590020\pi\) | |||||||
\(212\) | −10.5269 | −0.722992 | ||||||||
\(213\) | 9.04223 | 0.619563 | ||||||||
\(214\) | 5.98209 | 0.408927 | ||||||||
\(215\) | 13.3768 | 0.912287 | ||||||||
\(216\) | 8.26208 | 0.562164 | ||||||||
\(217\) | −7.91271 | −0.537150 | ||||||||
\(218\) | −9.50399 | −0.643692 | ||||||||
\(219\) | −5.91602 | −0.399767 | ||||||||
\(220\) | 1.46229 | 0.0985877 | ||||||||
\(221\) | −6.65379 | −0.447582 | ||||||||
\(222\) | 2.86980 | 0.192608 | ||||||||
\(223\) | −7.51629 | −0.503328 | −0.251664 | − | 0.967815i | \(-0.580978\pi\) | ||||
−0.251664 | + | 0.967815i | \(0.580978\pi\) | |||||||
\(224\) | −5.19372 | −0.347020 | ||||||||
\(225\) | 1.54522 | 0.103014 | ||||||||
\(226\) | −0.297019 | −0.0197574 | ||||||||
\(227\) | 8.78542 | 0.583109 | 0.291554 | − | 0.956554i | \(-0.405828\pi\) | ||||
0.291554 | + | 0.956554i | \(0.405828\pi\) | |||||||
\(228\) | −0.211328 | −0.0139955 | ||||||||
\(229\) | −11.9938 | −0.792570 | −0.396285 | − | 0.918127i | \(-0.629701\pi\) | ||||
−0.396285 | + | 0.918127i | \(0.629701\pi\) | |||||||
\(230\) | 20.5705 | 1.35638 | ||||||||
\(231\) | 0.802146 | 0.0527773 | ||||||||
\(232\) | 2.00510 | 0.131641 | ||||||||
\(233\) | 16.5917 | 1.08696 | 0.543479 | − | 0.839423i | \(-0.317107\pi\) | ||||
0.543479 | + | 0.839423i | \(0.317107\pi\) | |||||||
\(234\) | −6.62437 | −0.433048 | ||||||||
\(235\) | −9.57922 | −0.624879 | ||||||||
\(236\) | −1.32005 | −0.0859282 | ||||||||
\(237\) | −7.59238 | −0.493178 | ||||||||
\(238\) | 8.24707 | 0.534578 | ||||||||
\(239\) | 3.32189 | 0.214875 | 0.107437 | − | 0.994212i | \(-0.465735\pi\) | ||||
0.107437 | + | 0.994212i | \(0.465735\pi\) | |||||||
\(240\) | 7.87328 | 0.508218 | ||||||||
\(241\) | −2.65657 | −0.171125 | −0.0855624 | − | 0.996333i | \(-0.527269\pi\) | ||||
−0.0855624 | + | 0.996333i | \(0.527269\pi\) | |||||||
\(242\) | 17.1386 | 1.10171 | ||||||||
\(243\) | −15.5049 | −0.994641 | ||||||||
\(244\) | −9.90090 | −0.633840 | ||||||||
\(245\) | −11.5648 | −0.738846 | ||||||||
\(246\) | 6.75061 | 0.430403 | ||||||||
\(247\) | −0.566305 | −0.0360331 | ||||||||
\(248\) | 13.1178 | 0.832983 | ||||||||
\(249\) | −4.76818 | −0.302171 | ||||||||
\(250\) | 19.7112 | 1.24664 | ||||||||
\(251\) | −6.68508 | −0.421959 | −0.210979 | − | 0.977491i | \(-0.567665\pi\) | ||||
−0.210979 | + | 0.977491i | \(0.567665\pi\) | |||||||
\(252\) | 2.35047 | 0.148066 | ||||||||
\(253\) | −5.13512 | −0.322842 | ||||||||
\(254\) | −11.4758 | −0.720054 | ||||||||
\(255\) | −6.46471 | −0.404836 | ||||||||
\(256\) | 16.5694 | 1.03559 | ||||||||
\(257\) | −17.9037 | −1.11680 | −0.558402 | − | 0.829571i | \(-0.688585\pi\) | ||||
−0.558402 | + | 0.829571i | \(0.688585\pi\) | |||||||
\(258\) | 8.14697 | 0.507208 | ||||||||
\(259\) | −2.72870 | −0.169553 | ||||||||
\(260\) | −2.73682 | −0.169730 | ||||||||
\(261\) | −2.42258 | −0.149954 | ||||||||
\(262\) | 22.3617 | 1.38151 | ||||||||
\(263\) | 10.9077 | 0.672598 | 0.336299 | − | 0.941755i | \(-0.390825\pi\) | ||||
0.336299 | + | 0.941755i | \(0.390825\pi\) | |||||||
\(264\) | −1.32981 | −0.0818442 | ||||||||
\(265\) | −27.4078 | −1.68365 | ||||||||
\(266\) | 0.701910 | 0.0430369 | ||||||||
\(267\) | 3.30837 | 0.202469 | ||||||||
\(268\) | 2.39545 | 0.146325 | ||||||||
\(269\) | −28.9344 | −1.76416 | −0.882081 | − | 0.471098i | \(-0.843858\pi\) | ||||
−0.882081 | + | 0.471098i | \(0.843858\pi\) | |||||||
\(270\) | −14.4063 | −0.876739 | ||||||||
\(271\) | 11.5432 | 0.701197 | 0.350599 | − | 0.936526i | \(-0.385978\pi\) | ||||
0.350599 | + | 0.936526i | \(0.385978\pi\) | |||||||
\(272\) | −20.2073 | −1.22525 | ||||||||
\(273\) | −1.50129 | −0.0908623 | ||||||||
\(274\) | 18.9664 | 1.14580 | ||||||||
\(275\) | −0.556696 | −0.0335700 | ||||||||
\(276\) | 3.58648 | 0.215881 | ||||||||
\(277\) | −17.2086 | −1.03396 | −0.516982 | − | 0.855996i | \(-0.672945\pi\) | ||||
−0.516982 | + | 0.855996i | \(0.672945\pi\) | |||||||
\(278\) | −1.67397 | −0.100398 | ||||||||
\(279\) | −15.8490 | −0.948856 | ||||||||
\(280\) | −5.06510 | −0.302697 | ||||||||
\(281\) | −29.3962 | −1.75363 | −0.876814 | − | 0.480830i | \(-0.840336\pi\) | ||||
−0.876814 | + | 0.480830i | \(0.840336\pi\) | |||||||
\(282\) | −5.83412 | −0.347417 | ||||||||
\(283\) | −3.53239 | −0.209979 | −0.104989 | − | 0.994473i | \(-0.533481\pi\) | ||||
−0.104989 | + | 0.994473i | \(0.533481\pi\) | |||||||
\(284\) | −9.54565 | −0.566430 | ||||||||
\(285\) | −0.550212 | −0.0325918 | ||||||||
\(286\) | 2.38656 | 0.141120 | ||||||||
\(287\) | −6.41870 | −0.378884 | ||||||||
\(288\) | −10.4029 | −0.612999 | ||||||||
\(289\) | −0.407875 | −0.0239927 | ||||||||
\(290\) | −3.49623 | −0.205305 | ||||||||
\(291\) | −7.90162 | −0.463201 | ||||||||
\(292\) | 6.24539 | 0.365484 | ||||||||
\(293\) | −20.7708 | −1.21344 | −0.606721 | − | 0.794915i | \(-0.707515\pi\) | ||||
−0.606721 | + | 0.794915i | \(0.707515\pi\) | |||||||
\(294\) | −7.04340 | −0.410779 | ||||||||
\(295\) | −3.43689 | −0.200103 | ||||||||
\(296\) | 4.52369 | 0.262934 | ||||||||
\(297\) | 3.59633 | 0.208680 | ||||||||
\(298\) | −20.8220 | −1.20619 | ||||||||
\(299\) | 9.61086 | 0.555811 | ||||||||
\(300\) | 0.388809 | 0.0224479 | ||||||||
\(301\) | −7.74640 | −0.446495 | ||||||||
\(302\) | 23.2619 | 1.33857 | ||||||||
\(303\) | −7.72592 | −0.443843 | ||||||||
\(304\) | −1.71985 | −0.0986401 | ||||||||
\(305\) | −25.7780 | −1.47604 | ||||||||
\(306\) | 16.5188 | 0.944314 | ||||||||
\(307\) | −7.44444 | −0.424877 | −0.212438 | − | 0.977174i | \(-0.568140\pi\) | ||||
−0.212438 | + | 0.977174i | \(0.568140\pi\) | |||||||
\(308\) | −0.846805 | −0.0482512 | ||||||||
\(309\) | 10.9283 | 0.621689 | ||||||||
\(310\) | −22.8731 | −1.29910 | ||||||||
\(311\) | 4.48859 | 0.254525 | 0.127262 | − | 0.991869i | \(-0.459381\pi\) | ||||
0.127262 | + | 0.991869i | \(0.459381\pi\) | |||||||
\(312\) | 2.48887 | 0.140904 | ||||||||
\(313\) | 3.71574 | 0.210026 | 0.105013 | − | 0.994471i | \(-0.466512\pi\) | ||||
0.105013 | + | 0.994471i | \(0.466512\pi\) | |||||||
\(314\) | −1.67362 | −0.0944476 | ||||||||
\(315\) | 6.11968 | 0.344805 | ||||||||
\(316\) | 8.01508 | 0.450883 | ||||||||
\(317\) | 1.56109 | 0.0876795 | 0.0438397 | − | 0.999039i | \(-0.486041\pi\) | ||||
0.0438397 | + | 0.999039i | \(0.486041\pi\) | |||||||
\(318\) | −16.6924 | −0.936066 | ||||||||
\(319\) | 0.872783 | 0.0488665 | ||||||||
\(320\) | 5.70897 | 0.319141 | ||||||||
\(321\) | 2.71551 | 0.151565 | ||||||||
\(322\) | −11.9122 | −0.663843 | ||||||||
\(323\) | 1.41216 | 0.0785746 | ||||||||
\(324\) | 3.31834 | 0.184352 | ||||||||
\(325\) | 1.04191 | 0.0577947 | ||||||||
\(326\) | 15.9529 | 0.883547 | ||||||||
\(327\) | −4.31424 | −0.238578 | ||||||||
\(328\) | 10.6410 | 0.587552 | ||||||||
\(329\) | 5.54727 | 0.305831 | ||||||||
\(330\) | 2.31874 | 0.127643 | ||||||||
\(331\) | −28.0632 | −1.54249 | −0.771246 | − | 0.636538i | \(-0.780366\pi\) | ||||
−0.771246 | + | 0.636538i | \(0.780366\pi\) | |||||||
\(332\) | 5.03365 | 0.276257 | ||||||||
\(333\) | −5.46554 | −0.299510 | ||||||||
\(334\) | −23.3879 | −1.27973 | ||||||||
\(335\) | 6.23678 | 0.340752 | ||||||||
\(336\) | −4.55937 | −0.248734 | ||||||||
\(337\) | −15.6029 | −0.849943 | −0.424971 | − | 0.905207i | \(-0.639716\pi\) | ||||
−0.424971 | + | 0.905207i | \(0.639716\pi\) | |||||||
\(338\) | 17.2950 | 0.940723 | ||||||||
\(339\) | −0.134829 | −0.00732289 | ||||||||
\(340\) | 6.82463 | 0.370117 | ||||||||
\(341\) | 5.70994 | 0.309210 | ||||||||
\(342\) | 1.40591 | 0.0760231 | ||||||||
\(343\) | 15.1635 | 0.818751 | ||||||||
\(344\) | 12.8421 | 0.692401 | ||||||||
\(345\) | 9.33775 | 0.502728 | ||||||||
\(346\) | 4.18529 | 0.225003 | ||||||||
\(347\) | −15.8776 | −0.852355 | −0.426177 | − | 0.904640i | \(-0.640140\pi\) | ||||
−0.426177 | + | 0.904640i | \(0.640140\pi\) | |||||||
\(348\) | −0.609571 | −0.0326764 | ||||||||
\(349\) | −1.14394 | −0.0612337 | −0.0306168 | − | 0.999531i | \(-0.509747\pi\) | ||||
−0.0306168 | + | 0.999531i | \(0.509747\pi\) | |||||||
\(350\) | −1.29140 | −0.0690282 | ||||||||
\(351\) | −6.73087 | −0.359267 | ||||||||
\(352\) | 3.74787 | 0.199762 | ||||||||
\(353\) | −24.5164 | −1.30487 | −0.652437 | − | 0.757843i | \(-0.726253\pi\) | ||||
−0.652437 | + | 0.757843i | \(0.726253\pi\) | |||||||
\(354\) | −2.09320 | −0.111252 | ||||||||
\(355\) | −24.8530 | −1.31906 | ||||||||
\(356\) | −3.49257 | −0.185106 | ||||||||
\(357\) | 3.74368 | 0.198136 | ||||||||
\(358\) | −15.4857 | −0.818443 | ||||||||
\(359\) | 20.4331 | 1.07842 | 0.539210 | − | 0.842171i | \(-0.318723\pi\) | ||||
0.539210 | + | 0.842171i | \(0.318723\pi\) | |||||||
\(360\) | −10.1453 | −0.534704 | ||||||||
\(361\) | −18.8798 | −0.993674 | ||||||||
\(362\) | −22.9336 | −1.20536 | ||||||||
\(363\) | 7.77988 | 0.408338 | ||||||||
\(364\) | 1.58488 | 0.0830701 | ||||||||
\(365\) | 16.2605 | 0.851112 | ||||||||
\(366\) | −15.6998 | −0.820641 | ||||||||
\(367\) | 5.93878 | 0.310002 | 0.155001 | − | 0.987914i | \(-0.450462\pi\) | ||||
0.155001 | + | 0.987914i | \(0.450462\pi\) | |||||||
\(368\) | 29.1879 | 1.52152 | ||||||||
\(369\) | −12.8565 | −0.669285 | ||||||||
\(370\) | −7.88779 | −0.410067 | ||||||||
\(371\) | 15.8717 | 0.824019 | ||||||||
\(372\) | −3.98795 | −0.206765 | ||||||||
\(373\) | −15.4008 | −0.797425 | −0.398713 | − | 0.917076i | \(-0.630543\pi\) | ||||
−0.398713 | + | 0.917076i | \(0.630543\pi\) | |||||||
\(374\) | −5.95122 | −0.307730 | ||||||||
\(375\) | 8.94769 | 0.462057 | ||||||||
\(376\) | −9.19636 | −0.474266 | ||||||||
\(377\) | −1.63350 | −0.0841293 | ||||||||
\(378\) | 8.34261 | 0.429097 | ||||||||
\(379\) | 6.48943 | 0.333340 | 0.166670 | − | 0.986013i | \(-0.446699\pi\) | ||||
0.166670 | + | 0.986013i | \(0.446699\pi\) | |||||||
\(380\) | 0.580845 | 0.0297967 | ||||||||
\(381\) | −5.20931 | −0.266881 | ||||||||
\(382\) | −20.3590 | −1.04166 | ||||||||
\(383\) | −0.835621 | −0.0426982 | −0.0213491 | − | 0.999772i | \(-0.506796\pi\) | ||||
−0.0213491 | + | 0.999772i | \(0.506796\pi\) | |||||||
\(384\) | 10.0031 | 0.510469 | ||||||||
\(385\) | −2.20474 | −0.112364 | ||||||||
\(386\) | 27.2128 | 1.38509 | ||||||||
\(387\) | −15.5159 | −0.788718 | ||||||||
\(388\) | 8.34153 | 0.423477 | ||||||||
\(389\) | −12.0363 | −0.610264 | −0.305132 | − | 0.952310i | \(-0.598701\pi\) | ||||
−0.305132 | + | 0.952310i | \(0.598701\pi\) | |||||||
\(390\) | −4.33975 | −0.219752 | ||||||||
\(391\) | −23.9660 | −1.21201 | ||||||||
\(392\) | −11.1026 | −0.560764 | ||||||||
\(393\) | 10.1509 | 0.512043 | ||||||||
\(394\) | −25.5292 | −1.28614 | ||||||||
\(395\) | 20.8680 | 1.04998 | ||||||||
\(396\) | −1.69614 | −0.0852341 | ||||||||
\(397\) | −20.2501 | −1.01632 | −0.508162 | − | 0.861262i | \(-0.669675\pi\) | ||||
−0.508162 | + | 0.861262i | \(0.669675\pi\) | |||||||
\(398\) | −6.76434 | −0.339066 | ||||||||
\(399\) | 0.318625 | 0.0159512 | ||||||||
\(400\) | 3.16424 | 0.158212 | ||||||||
\(401\) | −30.3838 | −1.51729 | −0.758646 | − | 0.651503i | \(-0.774139\pi\) | ||||
−0.758646 | + | 0.651503i | \(0.774139\pi\) | |||||||
\(402\) | 3.79845 | 0.189449 | ||||||||
\(403\) | −10.6867 | −0.532342 | ||||||||
\(404\) | 8.15606 | 0.405779 | ||||||||
\(405\) | 8.63963 | 0.429307 | ||||||||
\(406\) | 2.02464 | 0.100481 | ||||||||
\(407\) | 1.96907 | 0.0976034 | ||||||||
\(408\) | −6.20633 | −0.307259 | ||||||||
\(409\) | −12.4439 | −0.615310 | −0.307655 | − | 0.951498i | \(-0.599544\pi\) | ||||
−0.307655 | + | 0.951498i | \(0.599544\pi\) | |||||||
\(410\) | −18.5544 | −0.916335 | ||||||||
\(411\) | 8.60961 | 0.424681 | ||||||||
\(412\) | −11.5367 | −0.568374 | ||||||||
\(413\) | 1.99028 | 0.0979354 | ||||||||
\(414\) | −23.8600 | −1.17266 | ||||||||
\(415\) | 13.1056 | 0.643328 | ||||||||
\(416\) | −7.01450 | −0.343914 | ||||||||
\(417\) | −0.759884 | −0.0372117 | ||||||||
\(418\) | −0.506509 | −0.0247742 | ||||||||
\(419\) | −33.7887 | −1.65069 | −0.825344 | − | 0.564630i | \(-0.809019\pi\) | ||||
−0.825344 | + | 0.564630i | \(0.809019\pi\) | |||||||
\(420\) | 1.53984 | 0.0751364 | ||||||||
\(421\) | 2.15341 | 0.104951 | 0.0524755 | − | 0.998622i | \(-0.483289\pi\) | ||||
0.0524755 | + | 0.998622i | \(0.483289\pi\) | |||||||
\(422\) | 13.5707 | 0.660613 | ||||||||
\(423\) | 11.1111 | 0.540240 | ||||||||
\(424\) | −26.3124 | −1.27784 | ||||||||
\(425\) | −2.59814 | −0.126028 | ||||||||
\(426\) | −15.1365 | −0.733364 | ||||||||
\(427\) | 14.9279 | 0.722410 | ||||||||
\(428\) | −2.86669 | −0.138567 | ||||||||
\(429\) | 1.08336 | 0.0523049 | ||||||||
\(430\) | −22.3923 | −1.07985 | ||||||||
\(431\) | −4.77353 | −0.229933 | −0.114966 | − | 0.993369i | \(-0.536676\pi\) | ||||
−0.114966 | + | 0.993369i | \(0.536676\pi\) | |||||||
\(432\) | −20.4414 | −0.983488 | ||||||||
\(433\) | −15.3770 | −0.738972 | −0.369486 | − | 0.929236i | \(-0.620466\pi\) | ||||
−0.369486 | + | 0.929236i | \(0.620466\pi\) | |||||||
\(434\) | 13.2457 | 0.635813 | ||||||||
\(435\) | −1.58708 | −0.0760945 | ||||||||
\(436\) | 4.55443 | 0.218118 | ||||||||
\(437\) | −2.03975 | −0.0975745 | ||||||||
\(438\) | 9.90326 | 0.473196 | ||||||||
\(439\) | −15.7132 | −0.749951 | −0.374975 | − | 0.927035i | \(-0.622349\pi\) | ||||
−0.374975 | + | 0.927035i | \(0.622349\pi\) | |||||||
\(440\) | 3.65505 | 0.174248 | ||||||||
\(441\) | 13.4142 | 0.638770 | ||||||||
\(442\) | 11.1383 | 0.529794 | ||||||||
\(443\) | 13.8342 | 0.657281 | 0.328640 | − | 0.944455i | \(-0.393410\pi\) | ||||
0.328640 | + | 0.944455i | \(0.393410\pi\) | |||||||
\(444\) | −1.37525 | −0.0652662 | ||||||||
\(445\) | −9.09323 | −0.431060 | ||||||||
\(446\) | 12.5821 | 0.595779 | ||||||||
\(447\) | −9.45195 | −0.447062 | ||||||||
\(448\) | −3.30603 | −0.156195 | ||||||||
\(449\) | −8.41440 | −0.397100 | −0.198550 | − | 0.980091i | \(-0.563623\pi\) | ||||
−0.198550 | + | 0.980091i | \(0.563623\pi\) | |||||||
\(450\) | −2.58665 | −0.121936 | ||||||||
\(451\) | 4.63183 | 0.218105 | ||||||||
\(452\) | 0.142335 | 0.00669489 | ||||||||
\(453\) | 10.5595 | 0.496128 | ||||||||
\(454\) | −14.7066 | −0.690213 | ||||||||
\(455\) | 4.12638 | 0.193448 | ||||||||
\(456\) | −0.528222 | −0.0247363 | ||||||||
\(457\) | 17.7081 | 0.828350 | 0.414175 | − | 0.910197i | \(-0.364070\pi\) | ||||
0.414175 | + | 0.910197i | \(0.364070\pi\) | |||||||
\(458\) | 20.0773 | 0.938149 | ||||||||
\(459\) | 16.7843 | 0.783425 | ||||||||
\(460\) | −9.85763 | −0.459614 | ||||||||
\(461\) | −24.6462 | −1.14789 | −0.573945 | − | 0.818894i | \(-0.694588\pi\) | ||||
−0.573945 | + | 0.818894i | \(0.694588\pi\) | |||||||
\(462\) | −1.34277 | −0.0624714 | ||||||||
\(463\) | 4.02078 | 0.186862 | 0.0934308 | − | 0.995626i | \(-0.470217\pi\) | ||||
0.0934308 | + | 0.995626i | \(0.470217\pi\) | |||||||
\(464\) | −4.96087 | −0.230303 | ||||||||
\(465\) | −10.3830 | −0.481500 | ||||||||
\(466\) | −27.7741 | −1.28661 | ||||||||
\(467\) | −21.2936 | −0.985349 | −0.492675 | − | 0.870214i | \(-0.663981\pi\) | ||||
−0.492675 | + | 0.870214i | \(0.663981\pi\) | |||||||
\(468\) | 3.17448 | 0.146740 | ||||||||
\(469\) | −3.61169 | −0.166772 | ||||||||
\(470\) | 16.0354 | 0.739656 | ||||||||
\(471\) | −0.759721 | −0.0350061 | ||||||||
\(472\) | −3.29953 | −0.151873 | ||||||||
\(473\) | 5.58993 | 0.257025 | ||||||||
\(474\) | 12.7094 | 0.583764 | ||||||||
\(475\) | −0.221128 | −0.0101461 | ||||||||
\(476\) | −3.95210 | −0.181144 | ||||||||
\(477\) | 31.7908 | 1.45560 | ||||||||
\(478\) | −5.56075 | −0.254343 | ||||||||
\(479\) | −8.63347 | −0.394473 | −0.197237 | − | 0.980356i | \(-0.563197\pi\) | ||||
−0.197237 | + | 0.980356i | \(0.563197\pi\) | |||||||
\(480\) | −6.81517 | −0.311068 | ||||||||
\(481\) | −3.68531 | −0.168036 | ||||||||
\(482\) | 4.44703 | 0.202557 | ||||||||
\(483\) | −5.40744 | −0.246047 | ||||||||
\(484\) | −8.21302 | −0.373319 | ||||||||
\(485\) | 21.7180 | 0.986163 | ||||||||
\(486\) | 25.9548 | 1.17734 | ||||||||
\(487\) | −40.5928 | −1.83944 | −0.919718 | − | 0.392579i | \(-0.871583\pi\) | ||||
−0.919718 | + | 0.392579i | \(0.871583\pi\) | |||||||
\(488\) | −24.7477 | −1.12027 | ||||||||
\(489\) | 7.24164 | 0.327478 | ||||||||
\(490\) | 19.3591 | 0.874556 | ||||||||
\(491\) | 8.35307 | 0.376969 | 0.188484 | − | 0.982076i | \(-0.439643\pi\) | ||||
0.188484 | + | 0.982076i | \(0.439643\pi\) | |||||||
\(492\) | −3.23498 | −0.145844 | ||||||||
\(493\) | 4.07334 | 0.183454 | ||||||||
\(494\) | 0.947980 | 0.0426516 | ||||||||
\(495\) | −4.41606 | −0.198487 | ||||||||
\(496\) | −32.4551 | −1.45728 | ||||||||
\(497\) | 14.3922 | 0.645580 | ||||||||
\(498\) | 7.98181 | 0.357673 | ||||||||
\(499\) | 21.2676 | 0.952067 | 0.476033 | − | 0.879427i | \(-0.342074\pi\) | ||||
0.476033 | + | 0.879427i | \(0.342074\pi\) | |||||||
\(500\) | −9.44584 | −0.422431 | ||||||||
\(501\) | −10.6167 | −0.474319 | ||||||||
\(502\) | 11.1907 | 0.499463 | ||||||||
\(503\) | 11.3840 | 0.507586 | 0.253793 | − | 0.967259i | \(-0.418322\pi\) | ||||
0.253793 | + | 0.967259i | \(0.418322\pi\) | |||||||
\(504\) | 5.87509 | 0.261697 | ||||||||
\(505\) | 21.2351 | 0.944949 | ||||||||
\(506\) | 8.59606 | 0.382141 | ||||||||
\(507\) | 7.85089 | 0.348670 | ||||||||
\(508\) | 5.49934 | 0.243994 | ||||||||
\(509\) | −15.4472 | −0.684684 | −0.342342 | − | 0.939575i | \(-0.611220\pi\) | ||||
−0.342342 | + | 0.939575i | \(0.611220\pi\) | |||||||
\(510\) | 10.8218 | 0.479195 | ||||||||
\(511\) | −9.41634 | −0.416555 | ||||||||
\(512\) | −1.40868 | −0.0622553 | ||||||||
\(513\) | 1.42852 | 0.0630706 | ||||||||
\(514\) | 29.9704 | 1.32194 | ||||||||
\(515\) | −30.0370 | −1.32359 | ||||||||
\(516\) | −3.90413 | −0.171870 | ||||||||
\(517\) | −4.00300 | −0.176052 | ||||||||
\(518\) | 4.56777 | 0.200696 | ||||||||
\(519\) | 1.89987 | 0.0833950 | ||||||||
\(520\) | −6.84078 | −0.299988 | ||||||||
\(521\) | −14.0644 | −0.616172 | −0.308086 | − | 0.951359i | \(-0.599688\pi\) | ||||
−0.308086 | + | 0.951359i | \(0.599688\pi\) | |||||||
\(522\) | 4.05533 | 0.177497 | ||||||||
\(523\) | 25.5680 | 1.11801 | 0.559006 | − | 0.829164i | \(-0.311183\pi\) | ||||
0.559006 | + | 0.829164i | \(0.311183\pi\) | |||||||
\(524\) | −10.7160 | −0.468131 | ||||||||
\(525\) | −0.586218 | −0.0255847 | ||||||||
\(526\) | −18.2592 | −0.796140 | ||||||||
\(527\) | 26.6487 | 1.16084 | ||||||||
\(528\) | 3.29012 | 0.143184 | ||||||||
\(529\) | 11.6169 | 0.505085 | ||||||||
\(530\) | 45.8800 | 1.99290 | ||||||||
\(531\) | 3.98650 | 0.173000 | ||||||||
\(532\) | −0.336364 | −0.0145832 | ||||||||
\(533\) | −8.66892 | −0.375492 | ||||||||
\(534\) | −5.53813 | −0.239658 | ||||||||
\(535\) | −7.46371 | −0.322684 | ||||||||
\(536\) | 5.98752 | 0.258621 | ||||||||
\(537\) | −7.02957 | −0.303348 | ||||||||
\(538\) | 48.4354 | 2.08820 | ||||||||
\(539\) | −4.83273 | −0.208160 | ||||||||
\(540\) | 6.90368 | 0.297087 | ||||||||
\(541\) | −11.4275 | −0.491308 | −0.245654 | − | 0.969358i | \(-0.579003\pi\) | ||||
−0.245654 | + | 0.969358i | \(0.579003\pi\) | |||||||
\(542\) | −19.3230 | −0.829992 | ||||||||
\(543\) | −10.4105 | −0.446756 | ||||||||
\(544\) | 17.4916 | 0.749946 | ||||||||
\(545\) | 11.8579 | 0.507937 | ||||||||
\(546\) | 2.51312 | 0.107552 | ||||||||
\(547\) | −38.3109 | −1.63806 | −0.819028 | − | 0.573754i | \(-0.805487\pi\) | ||||
−0.819028 | + | 0.573754i | \(0.805487\pi\) | |||||||
\(548\) | −9.08895 | −0.388261 | ||||||||
\(549\) | 29.9003 | 1.27611 | ||||||||
\(550\) | 0.931895 | 0.0397361 | ||||||||
\(551\) | 0.346683 | 0.0147692 | ||||||||
\(552\) | 8.96455 | 0.381556 | ||||||||
\(553\) | −12.0846 | −0.513888 | ||||||||
\(554\) | 28.8068 | 1.22388 | ||||||||
\(555\) | −3.58058 | −0.151987 | ||||||||
\(556\) | 0.802190 | 0.0340204 | ||||||||
\(557\) | 25.2205 | 1.06863 | 0.534314 | − | 0.845286i | \(-0.320570\pi\) | ||||
0.534314 | + | 0.845286i | \(0.320570\pi\) | |||||||
\(558\) | 26.5309 | 1.12314 | ||||||||
\(559\) | −10.4621 | −0.442499 | ||||||||
\(560\) | 12.5317 | 0.529560 | ||||||||
\(561\) | −2.70150 | −0.114057 | ||||||||
\(562\) | 49.2084 | 2.07573 | ||||||||
\(563\) | 3.33057 | 0.140367 | 0.0701835 | − | 0.997534i | \(-0.477642\pi\) | ||||
0.0701835 | + | 0.997534i | \(0.477642\pi\) | |||||||
\(564\) | 2.79578 | 0.117724 | ||||||||
\(565\) | 0.370583 | 0.0155906 | ||||||||
\(566\) | 5.91313 | 0.248547 | ||||||||
\(567\) | −5.00316 | −0.210113 | ||||||||
\(568\) | −23.8597 | −1.00113 | ||||||||
\(569\) | −10.4526 | −0.438197 | −0.219099 | − | 0.975703i | \(-0.570312\pi\) | ||||
−0.219099 | + | 0.975703i | \(0.570312\pi\) | |||||||
\(570\) | 0.921042 | 0.0385782 | ||||||||
\(571\) | 16.7258 | 0.699953 | 0.349977 | − | 0.936758i | \(-0.386190\pi\) | ||||
0.349977 | + | 0.936758i | \(0.386190\pi\) | |||||||
\(572\) | −1.14367 | −0.0478193 | ||||||||
\(573\) | −9.24178 | −0.386081 | ||||||||
\(574\) | 10.7447 | 0.448477 | ||||||||
\(575\) | 3.75281 | 0.156503 | ||||||||
\(576\) | −6.62192 | −0.275914 | ||||||||
\(577\) | 23.3282 | 0.971164 | 0.485582 | − | 0.874191i | \(-0.338608\pi\) | ||||
0.485582 | + | 0.874191i | \(0.338608\pi\) | |||||||
\(578\) | 0.682773 | 0.0283996 | ||||||||
\(579\) | 12.3530 | 0.513371 | ||||||||
\(580\) | 1.67544 | 0.0695687 | ||||||||
\(581\) | −7.58937 | −0.314860 | ||||||||
\(582\) | 13.2271 | 0.548281 | ||||||||
\(583\) | −11.4533 | −0.474347 | ||||||||
\(584\) | 15.6106 | 0.645970 | ||||||||
\(585\) | 8.26507 | 0.341718 | ||||||||
\(586\) | 34.7697 | 1.43632 | ||||||||
\(587\) | −16.7347 | −0.690715 | −0.345358 | − | 0.938471i | \(-0.612242\pi\) | ||||
−0.345358 | + | 0.938471i | \(0.612242\pi\) | |||||||
\(588\) | 3.37529 | 0.139194 | ||||||||
\(589\) | 2.26808 | 0.0934544 | ||||||||
\(590\) | 5.75326 | 0.236858 | ||||||||
\(591\) | −11.5887 | −0.476697 | ||||||||
\(592\) | −11.1922 | −0.459995 | ||||||||
\(593\) | −30.1399 | −1.23770 | −0.618849 | − | 0.785510i | \(-0.712401\pi\) | ||||
−0.618849 | + | 0.785510i | \(0.712401\pi\) | |||||||
\(594\) | −6.02016 | −0.247010 | ||||||||
\(595\) | −10.2897 | −0.421836 | ||||||||
\(596\) | 9.97818 | 0.408722 | ||||||||
\(597\) | −3.07060 | −0.125671 | ||||||||
\(598\) | −16.0883 | −0.657901 | ||||||||
\(599\) | 32.7389 | 1.33768 | 0.668838 | − | 0.743409i | \(-0.266792\pi\) | ||||
0.668838 | + | 0.743409i | \(0.266792\pi\) | |||||||
\(600\) | 0.971843 | 0.0396753 | ||||||||
\(601\) | −6.47379 | −0.264071 | −0.132036 | − | 0.991245i | \(-0.542151\pi\) | ||||
−0.132036 | + | 0.991245i | \(0.542151\pi\) | |||||||
\(602\) | 12.9673 | 0.528507 | ||||||||
\(603\) | −7.23415 | −0.294597 | ||||||||
\(604\) | −11.1474 | −0.453580 | ||||||||
\(605\) | −21.3834 | −0.869358 | ||||||||
\(606\) | 12.9330 | 0.525367 | ||||||||
\(607\) | −11.3125 | −0.459161 | −0.229580 | − | 0.973290i | \(-0.573735\pi\) | ||||
−0.229580 | + | 0.973290i | \(0.573735\pi\) | |||||||
\(608\) | 1.48871 | 0.0603753 | ||||||||
\(609\) | 0.919067 | 0.0372425 | ||||||||
\(610\) | 43.1516 | 1.74716 | ||||||||
\(611\) | 7.49199 | 0.303094 | ||||||||
\(612\) | −7.91600 | −0.319985 | ||||||||
\(613\) | −10.2075 | −0.412276 | −0.206138 | − | 0.978523i | \(-0.566090\pi\) | ||||
−0.206138 | + | 0.978523i | \(0.566090\pi\) | |||||||
\(614\) | 12.4618 | 0.502917 | ||||||||
\(615\) | −8.42257 | −0.339631 | ||||||||
\(616\) | −2.11662 | −0.0852811 | ||||||||
\(617\) | 37.7087 | 1.51810 | 0.759049 | − | 0.651034i | \(-0.225664\pi\) | ||||
0.759049 | + | 0.651034i | \(0.225664\pi\) | |||||||
\(618\) | −18.2937 | −0.735880 | ||||||||
\(619\) | −43.1665 | −1.73501 | −0.867505 | − | 0.497429i | \(-0.834278\pi\) | ||||
−0.867505 | + | 0.497429i | \(0.834278\pi\) | |||||||
\(620\) | 10.9611 | 0.440207 | ||||||||
\(621\) | −24.2436 | −0.972862 | ||||||||
\(622\) | −7.51379 | −0.301275 | ||||||||
\(623\) | 5.26584 | 0.210971 | ||||||||
\(624\) | −6.15777 | −0.246508 | ||||||||
\(625\) | −21.4040 | −0.856158 | ||||||||
\(626\) | −6.22005 | −0.248603 | ||||||||
\(627\) | −0.229925 | −0.00918231 | ||||||||
\(628\) | 0.802018 | 0.0320040 | ||||||||
\(629\) | 9.18982 | 0.366422 | ||||||||
\(630\) | −10.2442 | −0.408138 | ||||||||
\(631\) | −23.0180 | −0.916331 | −0.458166 | − | 0.888867i | \(-0.651493\pi\) | ||||
−0.458166 | + | 0.888867i | \(0.651493\pi\) | |||||||
\(632\) | 20.0340 | 0.796909 | ||||||||
\(633\) | 6.16030 | 0.244850 | ||||||||
\(634\) | −2.61322 | −0.103784 | ||||||||
\(635\) | 14.3181 | 0.568195 | ||||||||
\(636\) | 7.99923 | 0.317190 | ||||||||
\(637\) | 9.04491 | 0.358372 | ||||||||
\(638\) | −1.46102 | −0.0578422 | ||||||||
\(639\) | 28.8274 | 1.14040 | ||||||||
\(640\) | −27.4941 | −1.08680 | ||||||||
\(641\) | −13.2100 | −0.521765 | −0.260883 | − | 0.965371i | \(-0.584014\pi\) | ||||
−0.260883 | + | 0.965371i | \(0.584014\pi\) | |||||||
\(642\) | −4.54569 | −0.179404 | ||||||||
\(643\) | 3.88059 | 0.153036 | 0.0765178 | − | 0.997068i | \(-0.475620\pi\) | ||||
0.0765178 | + | 0.997068i | \(0.475620\pi\) | |||||||
\(644\) | 5.70850 | 0.224946 | ||||||||
\(645\) | −10.1648 | −0.400238 | ||||||||
\(646\) | −2.36392 | −0.0930071 | ||||||||
\(647\) | −6.45540 | −0.253788 | −0.126894 | − | 0.991916i | \(-0.540501\pi\) | ||||
−0.126894 | + | 0.991916i | \(0.540501\pi\) | |||||||
\(648\) | 8.29433 | 0.325832 | ||||||||
\(649\) | −1.43622 | −0.0563766 | ||||||||
\(650\) | −1.74413 | −0.0684104 | ||||||||
\(651\) | 6.01274 | 0.235658 | ||||||||
\(652\) | −7.64481 | −0.299394 | ||||||||
\(653\) | −11.8397 | −0.463325 | −0.231662 | − | 0.972796i | \(-0.574416\pi\) | ||||
−0.231662 | + | 0.972796i | \(0.574416\pi\) | |||||||
\(654\) | 7.22193 | 0.282400 | ||||||||
\(655\) | −27.9001 | −1.09015 | ||||||||
\(656\) | −26.3272 | −1.02790 | ||||||||
\(657\) | −18.8608 | −0.735829 | ||||||||
\(658\) | −9.28599 | −0.362006 | ||||||||
\(659\) | 31.9996 | 1.24653 | 0.623263 | − | 0.782012i | \(-0.285806\pi\) | ||||
0.623263 | + | 0.782012i | \(0.285806\pi\) | |||||||
\(660\) | −1.11117 | −0.0432523 | ||||||||
\(661\) | 9.86037 | 0.383524 | 0.191762 | − | 0.981441i | \(-0.438580\pi\) | ||||
0.191762 | + | 0.981441i | \(0.438580\pi\) | |||||||
\(662\) | 46.9770 | 1.82581 | ||||||||
\(663\) | 5.05611 | 0.196363 | ||||||||
\(664\) | 12.5818 | 0.488268 | ||||||||
\(665\) | −0.875756 | −0.0339604 | ||||||||
\(666\) | 9.14918 | 0.354523 | ||||||||
\(667\) | −5.88362 | −0.227815 | ||||||||
\(668\) | 11.2078 | 0.433642 | ||||||||
\(669\) | 5.71151 | 0.220820 | ||||||||
\(670\) | −10.4402 | −0.403341 | ||||||||
\(671\) | −10.7722 | −0.415856 | ||||||||
\(672\) | 3.94663 | 0.152244 | ||||||||
\(673\) | 15.1686 | 0.584707 | 0.292353 | − | 0.956310i | \(-0.405562\pi\) | ||||
0.292353 | + | 0.956310i | \(0.405562\pi\) | |||||||
\(674\) | 26.1188 | 1.00606 | ||||||||
\(675\) | −2.62824 | −0.101161 | ||||||||
\(676\) | −8.28798 | −0.318768 | ||||||||
\(677\) | 51.5127 | 1.97979 | 0.989897 | − | 0.141787i | \(-0.0452849\pi\) | ||||
0.989897 | + | 0.141787i | \(0.0452849\pi\) | |||||||
\(678\) | 0.225700 | 0.00866795 | ||||||||
\(679\) | −12.5768 | −0.482652 | ||||||||
\(680\) | 17.0584 | 0.654160 | ||||||||
\(681\) | −6.67590 | −0.255821 | ||||||||
\(682\) | −9.55829 | −0.366006 | ||||||||
\(683\) | 6.90419 | 0.264182 | 0.132091 | − | 0.991238i | \(-0.457831\pi\) | ||||
0.132091 | + | 0.991238i | \(0.457831\pi\) | |||||||
\(684\) | −0.673732 | −0.0257608 | ||||||||
\(685\) | −23.6639 | −0.904153 | ||||||||
\(686\) | −25.3833 | −0.969138 | ||||||||
\(687\) | 9.11387 | 0.347716 | ||||||||
\(688\) | −31.7730 | −1.21133 | ||||||||
\(689\) | 21.4359 | 0.816643 | ||||||||
\(690\) | −15.6312 | −0.595068 | ||||||||
\(691\) | −39.5370 | −1.50406 | −0.752029 | − | 0.659130i | \(-0.770925\pi\) | ||||
−0.752029 | + | 0.659130i | \(0.770925\pi\) | |||||||
\(692\) | −2.00564 | −0.0762432 | ||||||||
\(693\) | 2.55731 | 0.0971443 | ||||||||
\(694\) | 26.5787 | 1.00891 | ||||||||
\(695\) | 2.08858 | 0.0792243 | ||||||||
\(696\) | −1.52365 | −0.0577536 | ||||||||
\(697\) | 21.6171 | 0.818807 | ||||||||
\(698\) | 1.91492 | 0.0724810 | ||||||||
\(699\) | −12.6078 | −0.476869 | ||||||||
\(700\) | 0.618855 | 0.0233905 | ||||||||
\(701\) | −36.3238 | −1.37193 | −0.685966 | − | 0.727634i | \(-0.740620\pi\) | ||||
−0.685966 | + | 0.727634i | \(0.740620\pi\) | |||||||
\(702\) | 11.2673 | 0.425257 | ||||||||
\(703\) | 0.782147 | 0.0294992 | ||||||||
\(704\) | 2.38568 | 0.0899138 | ||||||||
\(705\) | 7.27909 | 0.274147 | ||||||||
\(706\) | 41.0398 | 1.54455 | ||||||||
\(707\) | −12.2971 | −0.462481 | ||||||||
\(708\) | 1.00309 | 0.0376984 | ||||||||
\(709\) | −21.1318 | −0.793622 | −0.396811 | − | 0.917900i | \(-0.629883\pi\) | ||||
−0.396811 | + | 0.917900i | \(0.629883\pi\) | |||||||
\(710\) | 41.6033 | 1.56134 | ||||||||
\(711\) | −24.2052 | −0.907765 | ||||||||
\(712\) | −8.72980 | −0.327163 | ||||||||
\(713\) | −38.4919 | −1.44153 | ||||||||
\(714\) | −6.26682 | −0.234530 | ||||||||
\(715\) | −2.97766 | −0.111358 | ||||||||
\(716\) | 7.42093 | 0.277333 | ||||||||
\(717\) | −2.52425 | −0.0942697 | ||||||||
\(718\) | −34.2046 | −1.27650 | ||||||||
\(719\) | 36.4633 | 1.35985 | 0.679925 | − | 0.733281i | \(-0.262012\pi\) | ||||
0.679925 | + | 0.733281i | \(0.262012\pi\) | |||||||
\(720\) | 25.1007 | 0.935449 | ||||||||
\(721\) | 17.3942 | 0.647795 | ||||||||
\(722\) | 31.6043 | 1.17619 | ||||||||
\(723\) | 2.01869 | 0.0750758 | ||||||||
\(724\) | 10.9901 | 0.408443 | ||||||||
\(725\) | −0.637840 | −0.0236888 | ||||||||
\(726\) | −13.0233 | −0.483341 | ||||||||
\(727\) | 29.3420 | 1.08823 | 0.544117 | − | 0.839009i | \(-0.316865\pi\) | ||||
0.544117 | + | 0.839009i | \(0.316865\pi\) | |||||||
\(728\) | 3.96146 | 0.146821 | ||||||||
\(729\) | −0.627881 | −0.0232548 | ||||||||
\(730\) | −27.2196 | −1.00744 | ||||||||
\(731\) | 26.0886 | 0.964922 | ||||||||
\(732\) | 7.52354 | 0.278078 | ||||||||
\(733\) | 7.76498 | 0.286806 | 0.143403 | − | 0.989664i | \(-0.454196\pi\) | ||||
0.143403 | + | 0.989664i | \(0.454196\pi\) | |||||||
\(734\) | −9.94136 | −0.366942 | ||||||||
\(735\) | 8.78788 | 0.324146 | ||||||||
\(736\) | −25.2652 | −0.931288 | ||||||||
\(737\) | 2.60625 | 0.0960025 | ||||||||
\(738\) | 21.5215 | 0.792218 | ||||||||
\(739\) | −1.63864 | −0.0602782 | −0.0301391 | − | 0.999546i | \(-0.509595\pi\) | ||||
−0.0301391 | + | 0.999546i | \(0.509595\pi\) | |||||||
\(740\) | 3.77993 | 0.138953 | ||||||||
\(741\) | 0.430326 | 0.0158084 | ||||||||
\(742\) | −26.5689 | −0.975374 | ||||||||
\(743\) | 5.50482 | 0.201952 | 0.100976 | − | 0.994889i | \(-0.467803\pi\) | ||||
0.100976 | + | 0.994889i | \(0.467803\pi\) | |||||||
\(744\) | −9.96802 | −0.365445 | ||||||||
\(745\) | 25.9791 | 0.951802 | ||||||||
\(746\) | 25.7806 | 0.943895 | ||||||||
\(747\) | −15.2014 | −0.556189 | ||||||||
\(748\) | 2.85190 | 0.104276 | ||||||||
\(749\) | 4.32219 | 0.157929 | ||||||||
\(750\) | −14.9782 | −0.546926 | ||||||||
\(751\) | 3.06691 | 0.111913 | 0.0559566 | − | 0.998433i | \(-0.482179\pi\) | ||||
0.0559566 | + | 0.998433i | \(0.482179\pi\) | |||||||
\(752\) | 22.7529 | 0.829714 | ||||||||
\(753\) | 5.07989 | 0.185121 | ||||||||
\(754\) | 2.73443 | 0.0995821 | ||||||||
\(755\) | −29.0233 | −1.05626 | ||||||||
\(756\) | −3.99788 | −0.145402 | ||||||||
\(757\) | 17.6180 | 0.640338 | 0.320169 | − | 0.947360i | \(-0.396260\pi\) | ||||
0.320169 | + | 0.947360i | \(0.396260\pi\) | |||||||
\(758\) | −10.8631 | −0.394567 | ||||||||
\(759\) | 3.90209 | 0.141637 | ||||||||
\(760\) | 1.45184 | 0.0526639 | ||||||||
\(761\) | −30.6175 | −1.10988 | −0.554942 | − | 0.831889i | \(-0.687260\pi\) | ||||
−0.554942 | + | 0.831889i | \(0.687260\pi\) | |||||||
\(762\) | 8.72025 | 0.315901 | ||||||||
\(763\) | −6.86685 | −0.248597 | ||||||||
\(764\) | 9.75632 | 0.352971 | ||||||||
\(765\) | −20.6101 | −0.745158 | ||||||||
\(766\) | 1.39881 | 0.0505410 | ||||||||
\(767\) | 2.68802 | 0.0970588 | ||||||||
\(768\) | −12.5908 | −0.454331 | ||||||||
\(769\) | 43.9852 | 1.58615 | 0.793074 | − | 0.609125i | \(-0.208479\pi\) | ||||
0.793074 | + | 0.609125i | \(0.208479\pi\) | |||||||
\(770\) | 3.69068 | 0.133003 | ||||||||
\(771\) | 13.6048 | 0.489963 | ||||||||
\(772\) | −13.0407 | −0.469345 | ||||||||
\(773\) | 16.9500 | 0.609650 | 0.304825 | − | 0.952408i | \(-0.401402\pi\) | ||||
0.304825 | + | 0.952408i | \(0.401402\pi\) | |||||||
\(774\) | 25.9732 | 0.933589 | ||||||||
\(775\) | −4.17289 | −0.149895 | ||||||||
\(776\) | 20.8500 | 0.748470 | ||||||||
\(777\) | 2.07350 | 0.0743862 | ||||||||
\(778\) | 20.1484 | 0.722357 | ||||||||
\(779\) | 1.83984 | 0.0659190 | ||||||||
\(780\) | 2.07966 | 0.0744639 | ||||||||
\(781\) | −10.3857 | −0.371629 | ||||||||
\(782\) | 40.1185 | 1.43463 | ||||||||
\(783\) | 4.12053 | 0.147256 | ||||||||
\(784\) | 27.4691 | 0.981039 | ||||||||
\(785\) | 2.08813 | 0.0745286 | ||||||||
\(786\) | −16.9923 | −0.606094 | ||||||||
\(787\) | −3.40678 | −0.121439 | −0.0607193 | − | 0.998155i | \(-0.519339\pi\) | ||||
−0.0607193 | + | 0.998155i | \(0.519339\pi\) | |||||||
\(788\) | 12.2339 | 0.435816 | ||||||||
\(789\) | −8.28859 | −0.295082 | ||||||||
\(790\) | −34.9325 | −1.24284 | ||||||||
\(791\) | −0.214603 | −0.00763040 | ||||||||
\(792\) | −4.23956 | −0.150646 | ||||||||
\(793\) | 20.1612 | 0.715944 | ||||||||
\(794\) | 33.8981 | 1.20300 | ||||||||
\(795\) | 20.8268 | 0.738650 | ||||||||
\(796\) | 3.24156 | 0.114894 | ||||||||
\(797\) | 5.19269 | 0.183935 | 0.0919673 | − | 0.995762i | \(-0.470684\pi\) | ||||
0.0919673 | + | 0.995762i | \(0.470684\pi\) | |||||||
\(798\) | −0.533370 | −0.0188811 | ||||||||
\(799\) | −18.6823 | −0.660932 | ||||||||
\(800\) | −2.73899 | −0.0968380 | ||||||||
\(801\) | 10.5474 | 0.372674 | ||||||||
\(802\) | 50.8616 | 1.79599 | ||||||||
\(803\) | 6.79498 | 0.239790 | ||||||||
\(804\) | −1.82026 | −0.0641958 | ||||||||
\(805\) | 14.8626 | 0.523838 | ||||||||
\(806\) | 17.8892 | 0.630122 | ||||||||
\(807\) | 21.9868 | 0.773971 | ||||||||
\(808\) | 20.3864 | 0.717190 | ||||||||
\(809\) | 45.4054 | 1.59637 | 0.798184 | − | 0.602414i | \(-0.205794\pi\) | ||||
0.798184 | + | 0.602414i | \(0.205794\pi\) | |||||||
\(810\) | −14.4625 | −0.508161 | ||||||||
\(811\) | −13.2067 | −0.463749 | −0.231875 | − | 0.972746i | \(-0.574486\pi\) | ||||
−0.231875 | + | 0.972746i | \(0.574486\pi\) | |||||||
\(812\) | −0.970236 | −0.0340486 | ||||||||
\(813\) | −8.77146 | −0.307629 | ||||||||
\(814\) | −3.29618 | −0.115531 | ||||||||
\(815\) | −19.9040 | −0.697207 | ||||||||
\(816\) | 15.3552 | 0.537540 | ||||||||
\(817\) | 2.22041 | 0.0776822 | ||||||||
\(818\) | 20.8307 | 0.728329 | ||||||||
\(819\) | −4.78625 | −0.167245 | ||||||||
\(820\) | 8.89150 | 0.310504 | ||||||||
\(821\) | 3.31312 | 0.115629 | 0.0578144 | − | 0.998327i | \(-0.481587\pi\) | ||||
0.0578144 | + | 0.998327i | \(0.481587\pi\) | |||||||
\(822\) | −14.4123 | −0.502686 | ||||||||
\(823\) | −12.8389 | −0.447537 | −0.223768 | − | 0.974642i | \(-0.571836\pi\) | ||||
−0.223768 | + | 0.974642i | \(0.571836\pi\) | |||||||
\(824\) | −28.8365 | −1.00457 | ||||||||
\(825\) | 0.423024 | 0.0147278 | ||||||||
\(826\) | −3.33168 | −0.115924 | ||||||||
\(827\) | 29.4914 | 1.02552 | 0.512758 | − | 0.858533i | \(-0.328624\pi\) | ||||
0.512758 | + | 0.858533i | \(0.328624\pi\) | |||||||
\(828\) | 11.4340 | 0.397360 | ||||||||
\(829\) | 24.8497 | 0.863065 | 0.431533 | − | 0.902097i | \(-0.357973\pi\) | ||||
0.431533 | + | 0.902097i | \(0.357973\pi\) | |||||||
\(830\) | −21.9384 | −0.761493 | ||||||||
\(831\) | 13.0765 | 0.453620 | ||||||||
\(832\) | −4.46503 | −0.154797 | ||||||||
\(833\) | −22.5547 | −0.781474 | ||||||||
\(834\) | 1.27203 | 0.0440467 | ||||||||
\(835\) | 29.1805 | 1.00983 | ||||||||
\(836\) | 0.242726 | 0.00839485 | ||||||||
\(837\) | 26.9574 | 0.931784 | ||||||||
\(838\) | 56.5615 | 1.95388 | ||||||||
\(839\) | 28.8276 | 0.995240 | 0.497620 | − | 0.867395i | \(-0.334207\pi\) | ||||
0.497620 | + | 0.867395i | \(0.334207\pi\) | |||||||
\(840\) | 3.84888 | 0.132799 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −3.60476 | −0.124228 | ||||||||
\(843\) | 22.3377 | 0.769350 | ||||||||
\(844\) | −6.50327 | −0.223852 | ||||||||
\(845\) | −21.5785 | −0.742325 | ||||||||
\(846\) | −18.5997 | −0.639470 | ||||||||
\(847\) | 12.3830 | 0.425485 | ||||||||
\(848\) | 65.1002 | 2.23555 | ||||||||
\(849\) | 2.68420 | 0.0921217 | ||||||||
\(850\) | 4.34922 | 0.149177 | ||||||||
\(851\) | −13.2739 | −0.455025 | ||||||||
\(852\) | 7.25359 | 0.248504 | ||||||||
\(853\) | −33.1368 | −1.13458 | −0.567291 | − | 0.823517i | \(-0.692009\pi\) | ||||
−0.567291 | + | 0.823517i | \(0.692009\pi\) | |||||||
\(854\) | −24.9889 | −0.855101 | ||||||||
\(855\) | −1.75413 | −0.0599898 | ||||||||
\(856\) | −7.16540 | −0.244908 | ||||||||
\(857\) | 6.64178 | 0.226879 | 0.113439 | − | 0.993545i | \(-0.463813\pi\) | ||||
0.113439 | + | 0.993545i | \(0.463813\pi\) | |||||||
\(858\) | −1.81351 | −0.0619122 | ||||||||
\(859\) | 21.1222 | 0.720681 | 0.360341 | − | 0.932821i | \(-0.382660\pi\) | ||||
0.360341 | + | 0.932821i | \(0.382660\pi\) | |||||||
\(860\) | 10.7307 | 0.365914 | ||||||||
\(861\) | 4.87746 | 0.166224 | ||||||||
\(862\) | 7.99077 | 0.272167 | ||||||||
\(863\) | 52.1404 | 1.77488 | 0.887440 | − | 0.460924i | \(-0.152482\pi\) | ||||
0.887440 | + | 0.460924i | \(0.152482\pi\) | |||||||
\(864\) | 17.6942 | 0.601970 | ||||||||
\(865\) | −5.22189 | −0.177550 | ||||||||
\(866\) | 25.7407 | 0.874705 | ||||||||
\(867\) | 0.309938 | 0.0105260 | ||||||||
\(868\) | −6.34749 | −0.215448 | ||||||||
\(869\) | 8.72041 | 0.295820 | ||||||||
\(870\) | 2.65673 | 0.0900714 | ||||||||
\(871\) | −4.87784 | −0.165279 | ||||||||
\(872\) | 11.3840 | 0.385510 | ||||||||
\(873\) | −25.1911 | −0.852588 | ||||||||
\(874\) | 3.41449 | 0.115497 | ||||||||
\(875\) | 14.2418 | 0.481459 | ||||||||
\(876\) | −4.74577 | −0.160345 | ||||||||
\(877\) | −16.9905 | −0.573729 | −0.286864 | − | 0.957971i | \(-0.592613\pi\) | ||||
−0.286864 | + | 0.957971i | \(0.592613\pi\) | |||||||
\(878\) | 26.3035 | 0.887701 | ||||||||
\(879\) | 15.7834 | 0.532360 | ||||||||
\(880\) | −9.04305 | −0.304841 | ||||||||
\(881\) | −26.8442 | −0.904404 | −0.452202 | − | 0.891915i | \(-0.649361\pi\) | ||||
−0.452202 | + | 0.891915i | \(0.649361\pi\) | |||||||
\(882\) | −22.4550 | −0.756098 | ||||||||
\(883\) | 20.0172 | 0.673631 | 0.336815 | − | 0.941571i | \(-0.390650\pi\) | ||||
0.336815 | + | 0.941571i | \(0.390650\pi\) | |||||||
\(884\) | −5.33760 | −0.179523 | ||||||||
\(885\) | 2.61164 | 0.0877892 | ||||||||
\(886\) | −23.1580 | −0.778009 | ||||||||
\(887\) | 13.8251 | 0.464202 | 0.232101 | − | 0.972692i | \(-0.425440\pi\) | ||||
0.232101 | + | 0.972692i | \(0.425440\pi\) | |||||||
\(888\) | −3.43748 | −0.115354 | ||||||||
\(889\) | −8.29150 | −0.278088 | ||||||||
\(890\) | 15.2218 | 0.510237 | ||||||||
\(891\) | 3.61036 | 0.120952 | ||||||||
\(892\) | −6.02949 | −0.201882 | ||||||||
\(893\) | −1.59005 | −0.0532091 | ||||||||
\(894\) | 15.8223 | 0.529177 | ||||||||
\(895\) | 19.3211 | 0.645834 | ||||||||
\(896\) | 15.9217 | 0.531905 | ||||||||
\(897\) | −7.30314 | −0.243845 | ||||||||
\(898\) | 14.0855 | 0.470039 | ||||||||
\(899\) | 6.54222 | 0.218195 | ||||||||
\(900\) | 1.23956 | 0.0413186 | ||||||||
\(901\) | −53.4534 | −1.78079 | ||||||||
\(902\) | −7.75357 | −0.258166 | ||||||||
\(903\) | 5.88637 | 0.195886 | ||||||||
\(904\) | 0.355772 | 0.0118328 | ||||||||
\(905\) | 28.6137 | 0.951152 | ||||||||
\(906\) | −17.6763 | −0.587256 | ||||||||
\(907\) | 22.4747 | 0.746261 | 0.373131 | − | 0.927779i | \(-0.378284\pi\) | ||||
0.373131 | + | 0.927779i | \(0.378284\pi\) | |||||||
\(908\) | 7.04757 | 0.233882 | ||||||||
\(909\) | −24.6309 | −0.816956 | ||||||||
\(910\) | −6.90745 | −0.228980 | ||||||||
\(911\) | −23.7277 | −0.786133 | −0.393067 | − | 0.919510i | \(-0.628586\pi\) | ||||
−0.393067 | + | 0.919510i | \(0.628586\pi\) | |||||||
\(912\) | 1.30689 | 0.0432753 | ||||||||
\(913\) | 5.47661 | 0.181249 | ||||||||
\(914\) | −29.6429 | −0.980500 | ||||||||
\(915\) | 19.5882 | 0.647567 | ||||||||
\(916\) | −9.62128 | −0.317896 | ||||||||
\(917\) | 16.1568 | 0.533545 | ||||||||
\(918\) | −28.0965 | −0.927324 | ||||||||
\(919\) | −6.97296 | −0.230017 | −0.115008 | − | 0.993365i | \(-0.536690\pi\) | ||||
−0.115008 | + | 0.993365i | \(0.536690\pi\) | |||||||
\(920\) | −24.6395 | −0.812340 | ||||||||
\(921\) | 5.65691 | 0.186402 | ||||||||
\(922\) | 41.2572 | 1.35873 | ||||||||
\(923\) | 19.4378 | 0.639802 | ||||||||
\(924\) | 0.643473 | 0.0211687 | ||||||||
\(925\) | −1.43902 | −0.0473148 | ||||||||
\(926\) | −6.73069 | −0.221184 | ||||||||
\(927\) | 34.8404 | 1.14431 | ||||||||
\(928\) | 4.29416 | 0.140963 | ||||||||
\(929\) | −5.95024 | −0.195221 | −0.0976106 | − | 0.995225i | \(-0.531120\pi\) | ||||
−0.0976106 | + | 0.995225i | \(0.531120\pi\) | |||||||
\(930\) | 17.3809 | 0.569942 | ||||||||
\(931\) | −1.91964 | −0.0629135 | ||||||||
\(932\) | 13.3097 | 0.435973 | ||||||||
\(933\) | −3.41081 | −0.111665 | ||||||||
\(934\) | 35.6449 | 1.16634 | ||||||||
\(935\) | 7.42520 | 0.242830 | ||||||||
\(936\) | 7.93473 | 0.259355 | ||||||||
\(937\) | −17.5059 | −0.571891 | −0.285946 | − | 0.958246i | \(-0.592308\pi\) | ||||
−0.285946 | + | 0.958246i | \(0.592308\pi\) | |||||||
\(938\) | 6.04587 | 0.197405 | ||||||||
\(939\) | −2.82353 | −0.0921423 | ||||||||
\(940\) | −7.68435 | −0.250636 | ||||||||
\(941\) | 12.7580 | 0.415900 | 0.207950 | − | 0.978139i | \(-0.433321\pi\) | ||||
0.207950 | + | 0.978139i | \(0.433321\pi\) | |||||||
\(942\) | 1.27175 | 0.0414360 | ||||||||
\(943\) | −31.2242 | −1.01680 | ||||||||
\(944\) | 8.16343 | 0.265697 | ||||||||
\(945\) | −10.4089 | −0.338601 | ||||||||
\(946\) | −9.35739 | −0.304235 | ||||||||
\(947\) | 38.5393 | 1.25236 | 0.626179 | − | 0.779680i | \(-0.284618\pi\) | ||||
0.626179 | + | 0.779680i | \(0.284618\pi\) | |||||||
\(948\) | −6.09053 | −0.197811 | ||||||||
\(949\) | −12.7175 | −0.412826 | ||||||||
\(950\) | 0.370163 | 0.0120097 | ||||||||
\(951\) | −1.18625 | −0.0384667 | ||||||||
\(952\) | −9.87843 | −0.320162 | ||||||||
\(953\) | 47.9766 | 1.55411 | 0.777057 | − | 0.629430i | \(-0.216711\pi\) | ||||
0.777057 | + | 0.629430i | \(0.216711\pi\) | |||||||
\(954\) | −53.2170 | −1.72296 | ||||||||
\(955\) | 25.4015 | 0.821973 | ||||||||
\(956\) | 2.66478 | 0.0861852 | ||||||||
\(957\) | −0.663214 | −0.0214386 | ||||||||
\(958\) | 14.4522 | 0.466930 | ||||||||
\(959\) | 13.7037 | 0.442514 | ||||||||
\(960\) | −4.33815 | −0.140013 | ||||||||
\(961\) | 11.8006 | 0.380666 | ||||||||
\(962\) | 6.16911 | 0.198900 | ||||||||
\(963\) | 8.65728 | 0.278977 | ||||||||
\(964\) | −2.13108 | −0.0686373 | ||||||||
\(965\) | −33.9527 | −1.09298 | ||||||||
\(966\) | 9.05191 | 0.291241 | ||||||||
\(967\) | −27.2849 | −0.877422 | −0.438711 | − | 0.898628i | \(-0.644565\pi\) | ||||
−0.438711 | + | 0.898628i | \(0.644565\pi\) | |||||||
\(968\) | −20.5287 | −0.659819 | ||||||||
\(969\) | −1.07308 | −0.0344722 | ||||||||
\(970\) | −36.3554 | −1.16730 | ||||||||
\(971\) | −43.8382 | −1.40683 | −0.703417 | − | 0.710777i | \(-0.748343\pi\) | ||||
−0.703417 | + | 0.710777i | \(0.748343\pi\) | |||||||
\(972\) | −12.4379 | −0.398946 | ||||||||
\(973\) | −1.20948 | −0.0387743 | ||||||||
\(974\) | 67.9514 | 2.17730 | ||||||||
\(975\) | −0.791730 | −0.0253557 | ||||||||
\(976\) | 61.2288 | 1.95989 | ||||||||
\(977\) | −4.66520 | −0.149253 | −0.0746264 | − | 0.997212i | \(-0.523776\pi\) | ||||
−0.0746264 | + | 0.997212i | \(0.523776\pi\) | |||||||
\(978\) | −12.1223 | −0.387629 | ||||||||
\(979\) | −3.79991 | −0.121446 | ||||||||
\(980\) | −9.27714 | −0.296347 | ||||||||
\(981\) | −13.7542 | −0.439137 | ||||||||
\(982\) | −13.9828 | −0.446210 | ||||||||
\(983\) | 36.8388 | 1.17498 | 0.587488 | − | 0.809233i | \(-0.300117\pi\) | ||||
0.587488 | + | 0.809233i | \(0.300117\pi\) | |||||||
\(984\) | −8.08594 | −0.257771 | ||||||||
\(985\) | 31.8522 | 1.01490 | ||||||||
\(986\) | −6.81867 | −0.217151 | ||||||||
\(987\) | −4.21528 | −0.134174 | ||||||||
\(988\) | −0.454284 | −0.0144527 | ||||||||
\(989\) | −37.6829 | −1.19825 | ||||||||
\(990\) | 7.39236 | 0.234945 | ||||||||
\(991\) | 5.51410 | 0.175161 | 0.0875806 | − | 0.996157i | \(-0.472086\pi\) | ||||
0.0875806 | + | 0.996157i | \(0.472086\pi\) | |||||||
\(992\) | 28.0934 | 0.891965 | ||||||||
\(993\) | 21.3248 | 0.676720 | ||||||||
\(994\) | −24.0922 | −0.764160 | ||||||||
\(995\) | 8.43971 | 0.267557 | ||||||||
\(996\) | −3.82499 | −0.121199 | ||||||||
\(997\) | −57.9820 | −1.83631 | −0.918155 | − | 0.396222i | \(-0.870321\pi\) | ||||
−0.918155 | + | 0.396222i | \(0.870321\pi\) | |||||||
\(998\) | −35.6013 | −1.12694 | ||||||||
\(999\) | 9.29627 | 0.294121 |
(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 | 4031.2.a.b.1.14 | ✓ | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.b.1.14 | ✓ | 59 | 1.1 | even | 1 | trivial |