Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} - 699 x^{6} - 297 x^{5} + 394 x^{4} + 89 x^{3} - 57 x^{2} - 17 x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.596683\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.596683 | −0.421919 | −0.210959 | − | 0.977495i | \(-0.567659\pi\) | ||||
−0.210959 | + | 0.977495i | \(0.567659\pi\) | |||||||
\(3\) | 3.22200 | 1.86022 | 0.930112 | − | 0.367276i | \(-0.119710\pi\) | ||||
0.930112 | + | 0.367276i | \(0.119710\pi\) | |||||||
\(4\) | −1.64397 | −0.821984 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.92252 | −0.784864 | ||||||||
\(7\) | −0.0914365 | −0.0345597 | −0.0172799 | − | 0.999851i | \(-0.505501\pi\) | ||||
−0.0172799 | + | 0.999851i | \(0.505501\pi\) | |||||||
\(8\) | 2.17430 | 0.768730 | ||||||||
\(9\) | 7.38130 | 2.46043 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.938184 | 0.282873 | 0.141437 | − | 0.989947i | \(-0.454828\pi\) | ||||
0.141437 | + | 0.989947i | \(0.454828\pi\) | |||||||
\(12\) | −5.29687 | −1.52908 | ||||||||
\(13\) | −6.40952 | −1.77768 | −0.888840 | − | 0.458218i | \(-0.848488\pi\) | ||||
−0.888840 | + | 0.458218i | \(0.848488\pi\) | |||||||
\(14\) | 0.0545586 | 0.0145814 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.99057 | 0.497643 | ||||||||
\(17\) | 5.47227 | 1.32722 | 0.663610 | − | 0.748079i | \(-0.269023\pi\) | ||||
0.663610 | + | 0.748079i | \(0.269023\pi\) | |||||||
\(18\) | −4.40430 | −1.03810 | ||||||||
\(19\) | −4.62417 | −1.06086 | −0.530429 | − | 0.847729i | \(-0.677969\pi\) | ||||
−0.530429 | + | 0.847729i | \(0.677969\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.294609 | −0.0642889 | ||||||||
\(22\) | −0.559799 | −0.119349 | ||||||||
\(23\) | −9.45757 | −1.97204 | −0.986020 | − | 0.166626i | \(-0.946713\pi\) | ||||
−0.986020 | + | 0.166626i | \(0.946713\pi\) | |||||||
\(24\) | 7.00559 | 1.43001 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.82445 | 0.750037 | ||||||||
\(27\) | 14.1166 | 2.71673 | ||||||||
\(28\) | 0.150319 | 0.0284076 | ||||||||
\(29\) | −0.666961 | −0.123852 | −0.0619258 | − | 0.998081i | \(-0.519724\pi\) | ||||
−0.0619258 | + | 0.998081i | \(0.519724\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.51445 | −1.34964 | −0.674818 | − | 0.737985i | \(-0.735778\pi\) | ||||
−0.674818 | + | 0.737985i | \(0.735778\pi\) | |||||||
\(32\) | −5.53633 | −0.978695 | ||||||||
\(33\) | 3.02283 | 0.526207 | ||||||||
\(34\) | −3.26521 | −0.559979 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −12.1346 | −2.02244 | ||||||||
\(37\) | −5.97202 | −0.981793 | −0.490897 | − | 0.871218i | \(-0.663331\pi\) | ||||
−0.490897 | + | 0.871218i | \(0.663331\pi\) | |||||||
\(38\) | 2.75917 | 0.447596 | ||||||||
\(39\) | −20.6515 | −3.30688 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.82336 | −0.284761 | −0.142380 | − | 0.989812i | \(-0.545476\pi\) | ||||
−0.142380 | + | 0.989812i | \(0.545476\pi\) | |||||||
\(42\) | 0.175788 | 0.0271247 | ||||||||
\(43\) | −2.41367 | −0.368081 | −0.184041 | − | 0.982919i | \(-0.558918\pi\) | ||||
−0.184041 | + | 0.982919i | \(0.558918\pi\) | |||||||
\(44\) | −1.54234 | −0.232517 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.64318 | 0.832041 | ||||||||
\(47\) | −1.50928 | −0.220151 | −0.110075 | − | 0.993923i | \(-0.535109\pi\) | ||||
−0.110075 | + | 0.993923i | \(0.535109\pi\) | |||||||
\(48\) | 6.41363 | 0.925727 | ||||||||
\(49\) | −6.99164 | −0.998806 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 17.6317 | 2.46893 | ||||||||
\(52\) | 10.5370 | 1.46123 | ||||||||
\(53\) | 3.52075 | 0.483612 | 0.241806 | − | 0.970325i | \(-0.422260\pi\) | ||||
0.241806 | + | 0.970325i | \(0.422260\pi\) | |||||||
\(54\) | −8.42312 | −1.14624 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.198810 | −0.0265671 | ||||||||
\(57\) | −14.8991 | −1.97343 | ||||||||
\(58\) | 0.397965 | 0.0522553 | ||||||||
\(59\) | −14.3795 | −1.87206 | −0.936028 | − | 0.351926i | \(-0.885527\pi\) | ||||
−0.936028 | + | 0.351926i | \(0.885527\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.52207 | −0.835065 | −0.417533 | − | 0.908662i | \(-0.637105\pi\) | ||||
−0.417533 | + | 0.908662i | \(0.637105\pi\) | |||||||
\(62\) | 4.48375 | 0.569437 | ||||||||
\(63\) | −0.674920 | −0.0850320 | ||||||||
\(64\) | −0.677704 | −0.0847130 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.80367 | −0.222017 | ||||||||
\(67\) | 15.3694 | 1.87767 | 0.938835 | − | 0.344369i | \(-0.111907\pi\) | ||||
0.938835 | + | 0.344369i | \(0.111907\pi\) | |||||||
\(68\) | −8.99624 | −1.09095 | ||||||||
\(69\) | −30.4723 | −3.66844 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.49472 | 0.770782 | 0.385391 | − | 0.922753i | \(-0.374067\pi\) | ||||
0.385391 | + | 0.922753i | \(0.374067\pi\) | |||||||
\(72\) | 16.0491 | 1.89141 | ||||||||
\(73\) | 2.73165 | 0.319716 | 0.159858 | − | 0.987140i | \(-0.448896\pi\) | ||||
0.159858 | + | 0.987140i | \(0.448896\pi\) | |||||||
\(74\) | 3.56340 | 0.414237 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.60200 | 0.872009 | ||||||||
\(77\) | −0.0857842 | −0.00977602 | ||||||||
\(78\) | 12.3224 | 1.39524 | ||||||||
\(79\) | −8.80094 | −0.990184 | −0.495092 | − | 0.868841i | \(-0.664866\pi\) | ||||
−0.495092 | + | 0.868841i | \(0.664866\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 23.3397 | 2.59330 | ||||||||
\(82\) | 1.08797 | 0.120146 | ||||||||
\(83\) | 0.402706 | 0.0442028 | 0.0221014 | − | 0.999756i | \(-0.492964\pi\) | ||||
0.0221014 | + | 0.999756i | \(0.492964\pi\) | |||||||
\(84\) | 0.484327 | 0.0528444 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.44020 | 0.155300 | ||||||||
\(87\) | −2.14895 | −0.230392 | ||||||||
\(88\) | 2.03989 | 0.217453 | ||||||||
\(89\) | 17.9570 | 1.90344 | 0.951721 | − | 0.306964i | \(-0.0993132\pi\) | ||||
0.951721 | + | 0.306964i | \(0.0993132\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.586064 | 0.0614362 | ||||||||
\(92\) | 15.5480 | 1.62099 | ||||||||
\(93\) | −24.2116 | −2.51062 | ||||||||
\(94\) | 0.900560 | 0.0928857 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −17.8381 | −1.82059 | ||||||||
\(97\) | −17.4995 | −1.77680 | −0.888401 | − | 0.459068i | \(-0.848184\pi\) | ||||
−0.888401 | + | 0.459068i | \(0.848184\pi\) | |||||||
\(98\) | 4.17180 | 0.421415 | ||||||||
\(99\) | 6.92502 | 0.695990 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.0553 | 1.59757 | 0.798783 | − | 0.601619i | \(-0.205477\pi\) | ||||
0.798783 | + | 0.601619i | \(0.205477\pi\) | |||||||
\(102\) | −10.5205 | −1.04169 | ||||||||
\(103\) | 9.85176 | 0.970722 | 0.485361 | − | 0.874314i | \(-0.338688\pi\) | ||||
0.485361 | + | 0.874314i | \(0.338688\pi\) | |||||||
\(104\) | −13.9362 | −1.36656 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.10077 | −0.204045 | ||||||||
\(107\) | 5.96114 | 0.576285 | 0.288143 | − | 0.957588i | \(-0.406962\pi\) | ||||
0.288143 | + | 0.957588i | \(0.406962\pi\) | |||||||
\(108\) | −23.2072 | −2.23311 | ||||||||
\(109\) | −8.70283 | −0.833580 | −0.416790 | − | 0.909003i | \(-0.636845\pi\) | ||||
−0.416790 | + | 0.909003i | \(0.636845\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.2418 | −1.82636 | ||||||||
\(112\) | −0.182011 | −0.0171984 | ||||||||
\(113\) | −12.3991 | −1.16640 | −0.583202 | − | 0.812327i | \(-0.698201\pi\) | ||||
−0.583202 | + | 0.812327i | \(0.698201\pi\) | |||||||
\(114\) | 8.89004 | 0.832629 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.09646 | 0.101804 | ||||||||
\(117\) | −47.3106 | −4.37386 | ||||||||
\(118\) | 8.58003 | 0.789856 | ||||||||
\(119\) | −0.500365 | −0.0458684 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1198 | −0.919983 | ||||||||
\(122\) | 3.89161 | 0.352330 | ||||||||
\(123\) | −5.87486 | −0.529718 | ||||||||
\(124\) | 12.3535 | 1.10938 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.402714 | 0.0358766 | ||||||||
\(127\) | −12.6594 | −1.12334 | −0.561671 | − | 0.827361i | \(-0.689841\pi\) | ||||
−0.561671 | + | 0.827361i | \(0.689841\pi\) | |||||||
\(128\) | 11.4770 | 1.01444 | ||||||||
\(129\) | −7.77685 | −0.684714 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.79459 | 0.681017 | 0.340508 | − | 0.940242i | \(-0.389401\pi\) | ||||
0.340508 | + | 0.940242i | \(0.389401\pi\) | |||||||
\(132\) | −4.96944 | −0.432534 | ||||||||
\(133\) | 0.422818 | 0.0366630 | ||||||||
\(134\) | −9.17066 | −0.792224 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.8983 | 1.02027 | ||||||||
\(137\) | 11.1891 | 0.955948 | 0.477974 | − | 0.878374i | \(-0.341371\pi\) | ||||
0.477974 | + | 0.878374i | \(0.341371\pi\) | |||||||
\(138\) | 18.1823 | 1.54778 | ||||||||
\(139\) | −13.2779 | −1.12622 | −0.563110 | − | 0.826382i | \(-0.690395\pi\) | ||||
−0.563110 | + | 0.826382i | \(0.690395\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.86289 | −0.409529 | ||||||||
\(142\) | −3.87529 | −0.325207 | ||||||||
\(143\) | −6.01330 | −0.502858 | ||||||||
\(144\) | 14.6930 | 1.22442 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.62993 | −0.134894 | ||||||||
\(147\) | −22.5271 | −1.85800 | ||||||||
\(148\) | 9.81781 | 0.807019 | ||||||||
\(149\) | −13.4293 | −1.10017 | −0.550084 | − | 0.835109i | \(-0.685404\pi\) | ||||
−0.550084 | + | 0.835109i | \(0.685404\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.2454 | −1.07789 | −0.538947 | − | 0.842340i | \(-0.681178\pi\) | ||||
−0.538947 | + | 0.842340i | \(0.681178\pi\) | |||||||
\(152\) | −10.0543 | −0.815513 | ||||||||
\(153\) | 40.3925 | 3.26554 | ||||||||
\(154\) | 0.0511860 | 0.00412469 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 33.9504 | 2.71821 | ||||||||
\(157\) | 11.4227 | 0.911634 | 0.455817 | − | 0.890074i | \(-0.349347\pi\) | ||||
0.455817 | + | 0.890074i | \(0.349347\pi\) | |||||||
\(158\) | 5.25138 | 0.417777 | ||||||||
\(159\) | 11.3439 | 0.899628 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.864767 | 0.0681532 | ||||||||
\(162\) | −13.9264 | −1.09416 | ||||||||
\(163\) | −4.17420 | −0.326949 | −0.163474 | − | 0.986548i | \(-0.552270\pi\) | ||||
−0.163474 | + | 0.986548i | \(0.552270\pi\) | |||||||
\(164\) | 2.99754 | 0.234069 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.240288 | −0.0186500 | ||||||||
\(167\) | 22.4429 | 1.73668 | 0.868340 | − | 0.495969i | \(-0.165187\pi\) | ||||
0.868340 | + | 0.495969i | \(0.165187\pi\) | |||||||
\(168\) | −0.640566 | −0.0494208 | ||||||||
\(169\) | 28.0819 | 2.16015 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −34.1324 | −2.61017 | ||||||||
\(172\) | 3.96800 | 0.302557 | ||||||||
\(173\) | 19.0621 | 1.44926 | 0.724632 | − | 0.689136i | \(-0.242010\pi\) | ||||
0.724632 | + | 0.689136i | \(0.242010\pi\) | |||||||
\(174\) | 1.28224 | 0.0972066 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.86752 | 0.140770 | ||||||||
\(177\) | −46.3309 | −3.48244 | ||||||||
\(178\) | −10.7147 | −0.803098 | ||||||||
\(179\) | 6.78903 | 0.507436 | 0.253718 | − | 0.967278i | \(-0.418346\pi\) | ||||
0.253718 | + | 0.967278i | \(0.418346\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.650357 | −0.0483406 | −0.0241703 | − | 0.999708i | \(-0.507694\pi\) | ||||
−0.0241703 | + | 0.999708i | \(0.507694\pi\) | |||||||
\(182\) | −0.349694 | −0.0259211 | ||||||||
\(183\) | −21.0141 | −1.55341 | ||||||||
\(184\) | −20.5636 | −1.51597 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 14.4466 | 1.05928 | ||||||||
\(187\) | 5.13399 | 0.375435 | ||||||||
\(188\) | 2.48120 | 0.180960 | ||||||||
\(189\) | −1.29077 | −0.0938896 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.4770 | −0.975161 | −0.487580 | − | 0.873078i | \(-0.662120\pi\) | ||||
−0.487580 | + | 0.873078i | \(0.662120\pi\) | |||||||
\(192\) | −2.18356 | −0.157585 | ||||||||
\(193\) | −5.46458 | −0.393349 | −0.196675 | − | 0.980469i | \(-0.563014\pi\) | ||||
−0.196675 | + | 0.980469i | \(0.563014\pi\) | |||||||
\(194\) | 10.4416 | 0.749667 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.4940 | 0.821003 | ||||||||
\(197\) | 20.7161 | 1.47596 | 0.737981 | − | 0.674822i | \(-0.235780\pi\) | ||||
0.737981 | + | 0.674822i | \(0.235780\pi\) | |||||||
\(198\) | −4.13204 | −0.293651 | ||||||||
\(199\) | −25.7071 | −1.82233 | −0.911165 | − | 0.412041i | \(-0.864816\pi\) | ||||
−0.911165 | + | 0.412041i | \(0.864816\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 49.5202 | 3.49289 | ||||||||
\(202\) | −9.57996 | −0.674043 | ||||||||
\(203\) | 0.0609846 | 0.00428028 | ||||||||
\(204\) | −28.9859 | −2.02942 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.87838 | −0.409566 | ||||||||
\(207\) | −69.8092 | −4.85207 | ||||||||
\(208\) | −12.7586 | −0.884649 | ||||||||
\(209\) | −4.33832 | −0.300088 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.6358 | 0.732195 | 0.366098 | − | 0.930576i | \(-0.380694\pi\) | ||||
0.366098 | + | 0.930576i | \(0.380694\pi\) | |||||||
\(212\) | −5.78801 | −0.397522 | ||||||||
\(213\) | 20.9260 | 1.43383 | ||||||||
\(214\) | −3.55691 | −0.243146 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 30.6936 | 2.08843 | ||||||||
\(217\) | 0.687095 | 0.0466430 | ||||||||
\(218\) | 5.19283 | 0.351703 | ||||||||
\(219\) | 8.80139 | 0.594743 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −35.0746 | −2.35937 | ||||||||
\(222\) | 11.4813 | 0.770574 | ||||||||
\(223\) | −11.7045 | −0.783791 | −0.391896 | − | 0.920010i | \(-0.628181\pi\) | ||||
−0.391896 | + | 0.920010i | \(0.628181\pi\) | |||||||
\(224\) | 0.506223 | 0.0338234 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.39831 | 0.492128 | ||||||||
\(227\) | 4.74976 | 0.315253 | 0.157626 | − | 0.987499i | \(-0.449616\pi\) | ||||
0.157626 | + | 0.987499i | \(0.449616\pi\) | |||||||
\(228\) | 24.4937 | 1.62213 | ||||||||
\(229\) | 3.91733 | 0.258864 | 0.129432 | − | 0.991588i | \(-0.458685\pi\) | ||||
0.129432 | + | 0.991588i | \(0.458685\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.276397 | −0.0181856 | ||||||||
\(232\) | −1.45017 | −0.0952084 | ||||||||
\(233\) | −2.05639 | −0.134719 | −0.0673593 | − | 0.997729i | \(-0.521457\pi\) | ||||
−0.0673593 | + | 0.997729i | \(0.521457\pi\) | |||||||
\(234\) | 28.2294 | 1.84542 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 23.6395 | 1.53880 | ||||||||
\(237\) | −28.3567 | −1.84196 | ||||||||
\(238\) | 0.298560 | 0.0193527 | ||||||||
\(239\) | −4.37294 | −0.282862 | −0.141431 | − | 0.989948i | \(-0.545170\pi\) | ||||
−0.141431 | + | 0.989948i | \(0.545170\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 6.03832 | 0.388158 | ||||||||
\(243\) | 32.8509 | 2.10739 | ||||||||
\(244\) | 10.7221 | 0.686410 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.50543 | 0.223498 | ||||||||
\(247\) | 29.6387 | 1.88587 | ||||||||
\(248\) | −16.3386 | −1.03750 | ||||||||
\(249\) | 1.29752 | 0.0822271 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.1344 | −0.639677 | −0.319839 | − | 0.947472i | \(-0.603629\pi\) | ||||
−0.319839 | + | 0.947472i | \(0.603629\pi\) | |||||||
\(252\) | 1.10955 | 0.0698949 | ||||||||
\(253\) | −8.87294 | −0.557837 | ||||||||
\(254\) | 7.55367 | 0.473959 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.49275 | −0.343297 | ||||||||
\(257\) | 7.65793 | 0.477689 | 0.238844 | − | 0.971058i | \(-0.423231\pi\) | ||||
0.238844 | + | 0.971058i | \(0.423231\pi\) | |||||||
\(258\) | 4.64032 | 0.288894 | ||||||||
\(259\) | 0.546060 | 0.0339305 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.92304 | −0.304729 | ||||||||
\(262\) | −4.65090 | −0.287334 | ||||||||
\(263\) | 7.22289 | 0.445382 | 0.222691 | − | 0.974889i | \(-0.428516\pi\) | ||||
0.222691 | + | 0.974889i | \(0.428516\pi\) | |||||||
\(264\) | 6.57253 | 0.404511 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.252289 | −0.0154688 | ||||||||
\(267\) | 57.8576 | 3.54083 | ||||||||
\(268\) | −25.2668 | −1.54341 | ||||||||
\(269\) | −3.86388 | −0.235585 | −0.117793 | − | 0.993038i | \(-0.537582\pi\) | ||||
−0.117793 | + | 0.993038i | \(0.537582\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.9680 | −1.88117 | −0.940587 | − | 0.339554i | \(-0.889724\pi\) | ||||
−0.940587 | + | 0.339554i | \(0.889724\pi\) | |||||||
\(272\) | 10.8929 | 0.660482 | ||||||||
\(273\) | 1.88830 | 0.114285 | ||||||||
\(274\) | −6.67634 | −0.403333 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 50.0956 | 3.01540 | ||||||||
\(277\) | 3.23714 | 0.194501 | 0.0972503 | − | 0.995260i | \(-0.468995\pi\) | ||||
0.0972503 | + | 0.995260i | \(0.468995\pi\) | |||||||
\(278\) | 7.92272 | 0.475173 | ||||||||
\(279\) | −55.4664 | −3.32069 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.7837 | 0.941577 | 0.470788 | − | 0.882246i | \(-0.343970\pi\) | ||||
0.470788 | + | 0.882246i | \(0.343970\pi\) | |||||||
\(282\) | 2.90161 | 0.172788 | ||||||||
\(283\) | −17.7210 | −1.05340 | −0.526702 | − | 0.850050i | \(-0.676571\pi\) | ||||
−0.526702 | + | 0.850050i | \(0.676571\pi\) | |||||||
\(284\) | −10.6771 | −0.633571 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.58804 | 0.212165 | ||||||||
\(287\) | 0.166721 | 0.00984125 | ||||||||
\(288\) | −40.8653 | −2.40801 | ||||||||
\(289\) | 12.9457 | 0.761514 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −56.3834 | −3.30525 | ||||||||
\(292\) | −4.49075 | −0.262801 | ||||||||
\(293\) | −17.6430 | −1.03072 | −0.515358 | − | 0.856975i | \(-0.672341\pi\) | ||||
−0.515358 | + | 0.856975i | \(0.672341\pi\) | |||||||
\(294\) | 13.4415 | 0.783926 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −12.9849 | −0.754734 | ||||||||
\(297\) | 13.2439 | 0.768491 | ||||||||
\(298\) | 8.01302 | 0.464182 | ||||||||
\(299\) | 60.6185 | 3.50566 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.220697 | 0.0127208 | ||||||||
\(302\) | 7.90330 | 0.454784 | ||||||||
\(303\) | 51.7304 | 2.97183 | ||||||||
\(304\) | −9.20474 | −0.527928 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −24.1015 | −1.37779 | ||||||||
\(307\) | −10.5635 | −0.602891 | −0.301445 | − | 0.953483i | \(-0.597469\pi\) | ||||
−0.301445 | + | 0.953483i | \(0.597469\pi\) | |||||||
\(308\) | 0.141027 | 0.00803574 | ||||||||
\(309\) | 31.7424 | 1.80576 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.5162 | 0.879843 | 0.439922 | − | 0.898036i | \(-0.355006\pi\) | ||||
0.439922 | + | 0.898036i | \(0.355006\pi\) | |||||||
\(312\) | −44.9024 | −2.54210 | ||||||||
\(313\) | 16.0089 | 0.904874 | 0.452437 | − | 0.891796i | \(-0.350555\pi\) | ||||
0.452437 | + | 0.891796i | \(0.350555\pi\) | |||||||
\(314\) | −6.81576 | −0.384636 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.4685 | 0.813915 | ||||||||
\(317\) | 5.93621 | 0.333411 | 0.166705 | − | 0.986007i | \(-0.446687\pi\) | ||||
0.166705 | + | 0.986007i | \(0.446687\pi\) | |||||||
\(318\) | −6.76870 | −0.379570 | ||||||||
\(319\) | −0.625732 | −0.0350343 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.2068 | 1.07202 | ||||||||
\(322\) | −0.515992 | −0.0287551 | ||||||||
\(323\) | −25.3047 | −1.40799 | ||||||||
\(324\) | −38.3697 | −2.13165 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.49068 | 0.137946 | ||||||||
\(327\) | −28.0405 | −1.55064 | ||||||||
\(328\) | −3.96452 | −0.218904 | ||||||||
\(329\) | 0.138003 | 0.00760835 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.4916 | −1.34618 | −0.673091 | − | 0.739560i | \(-0.735034\pi\) | ||||
−0.673091 | + | 0.739560i | \(0.735034\pi\) | |||||||
\(332\) | −0.662037 | −0.0363340 | ||||||||
\(333\) | −44.0812 | −2.41564 | ||||||||
\(334\) | −13.3913 | −0.732738 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.586439 | −0.0319929 | ||||||||
\(337\) | −4.60431 | −0.250813 | −0.125406 | − | 0.992105i | \(-0.540023\pi\) | ||||
−0.125406 | + | 0.992105i | \(0.540023\pi\) | |||||||
\(338\) | −16.7560 | −0.911406 | ||||||||
\(339\) | −39.9498 | −2.16977 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.04993 | −0.381775 | ||||||||
\(342\) | 20.3662 | 1.10128 | ||||||||
\(343\) | 1.27935 | 0.0690782 | ||||||||
\(344\) | −5.24803 | −0.282955 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.3740 | −0.611472 | ||||||||
\(347\) | −6.59915 | −0.354261 | −0.177131 | − | 0.984187i | \(-0.556681\pi\) | ||||
−0.177131 | + | 0.984187i | \(0.556681\pi\) | |||||||
\(348\) | 3.53281 | 0.189378 | ||||||||
\(349\) | −9.00022 | −0.481770 | −0.240885 | − | 0.970554i | \(-0.577438\pi\) | ||||
−0.240885 | + | 0.970554i | \(0.577438\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −90.4803 | −4.82948 | ||||||||
\(352\) | −5.19410 | −0.276846 | ||||||||
\(353\) | −19.2510 | −1.02463 | −0.512313 | − | 0.858799i | \(-0.671211\pi\) | ||||
−0.512313 | + | 0.858799i | \(0.671211\pi\) | |||||||
\(354\) | 27.6449 | 1.46931 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −29.5208 | −1.56460 | ||||||||
\(357\) | −1.61218 | −0.0853255 | ||||||||
\(358\) | −4.05091 | −0.214097 | ||||||||
\(359\) | −6.46996 | −0.341472 | −0.170736 | − | 0.985317i | \(-0.554614\pi\) | ||||
−0.170736 | + | 0.985317i | \(0.554614\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.38297 | 0.125420 | ||||||||
\(362\) | 0.388057 | 0.0203958 | ||||||||
\(363\) | −32.6061 | −1.71137 | ||||||||
\(364\) | −0.963470 | −0.0504996 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 12.5388 | 0.655412 | ||||||||
\(367\) | −7.33529 | −0.382899 | −0.191450 | − | 0.981502i | \(-0.561319\pi\) | ||||
−0.191450 | + | 0.981502i | \(0.561319\pi\) | |||||||
\(368\) | −18.8260 | −0.981372 | ||||||||
\(369\) | −13.4587 | −0.700634 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.321925 | −0.0167135 | ||||||||
\(372\) | 39.8031 | 2.06369 | ||||||||
\(373\) | 19.9506 | 1.03300 | 0.516500 | − | 0.856287i | \(-0.327234\pi\) | ||||
0.516500 | + | 0.856287i | \(0.327234\pi\) | |||||||
\(374\) | −3.06337 | −0.158403 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.28161 | −0.169236 | ||||||||
\(377\) | 4.27490 | 0.220169 | ||||||||
\(378\) | 0.770181 | 0.0396138 | ||||||||
\(379\) | −23.4451 | −1.20430 | −0.602148 | − | 0.798384i | \(-0.705688\pi\) | ||||
−0.602148 | + | 0.798384i | \(0.705688\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −40.7887 | −2.08967 | ||||||||
\(382\) | 8.04150 | 0.411439 | ||||||||
\(383\) | −15.0980 | −0.771472 | −0.385736 | − | 0.922609i | \(-0.626052\pi\) | ||||
−0.385736 | + | 0.922609i | \(0.626052\pi\) | |||||||
\(384\) | 36.9791 | 1.88708 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.26063 | 0.165962 | ||||||||
\(387\) | −17.8160 | −0.905639 | ||||||||
\(388\) | 28.7686 | 1.46050 | ||||||||
\(389\) | −30.5029 | −1.54656 | −0.773279 | − | 0.634066i | \(-0.781385\pi\) | ||||
−0.773279 | + | 0.634066i | \(0.781385\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −51.7544 | −2.61733 | ||||||||
\(392\) | −15.2019 | −0.767812 | ||||||||
\(393\) | 25.1142 | 1.26684 | ||||||||
\(394\) | −12.3610 | −0.622736 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −11.3845 | −0.572093 | ||||||||
\(397\) | 13.3211 | 0.668569 | 0.334284 | − | 0.942472i | \(-0.391505\pi\) | ||||
0.334284 | + | 0.942472i | \(0.391505\pi\) | |||||||
\(398\) | 15.3390 | 0.768876 | ||||||||
\(399\) | 1.36232 | 0.0682014 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.04724 | −0.102234 | −0.0511171 | − | 0.998693i | \(-0.516278\pi\) | ||||
−0.0511171 | + | 0.998693i | \(0.516278\pi\) | |||||||
\(402\) | −29.5479 | −1.47371 | ||||||||
\(403\) | 48.1640 | 2.39922 | ||||||||
\(404\) | −26.3945 | −1.31317 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0363885 | −0.00180593 | ||||||||
\(407\) | −5.60285 | −0.277723 | ||||||||
\(408\) | 38.3365 | 1.89794 | ||||||||
\(409\) | −13.4604 | −0.665575 | −0.332787 | − | 0.943002i | \(-0.607989\pi\) | ||||
−0.332787 | + | 0.943002i | \(0.607989\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 36.0513 | 1.77828 | ||||||||
\(412\) | −16.1960 | −0.797919 | ||||||||
\(413\) | 1.31481 | 0.0646978 | ||||||||
\(414\) | 41.6540 | 2.04718 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 35.4852 | 1.73981 | ||||||||
\(417\) | −42.7815 | −2.09502 | ||||||||
\(418\) | 2.58861 | 0.126613 | ||||||||
\(419\) | −11.6546 | −0.569366 | −0.284683 | − | 0.958622i | \(-0.591888\pi\) | ||||
−0.284683 | + | 0.958622i | \(0.591888\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.83090 | −0.332918 | −0.166459 | − | 0.986048i | \(-0.553233\pi\) | ||||
−0.166459 | + | 0.986048i | \(0.553233\pi\) | |||||||
\(422\) | −6.34618 | −0.308927 | ||||||||
\(423\) | −11.1404 | −0.541666 | ||||||||
\(424\) | 7.65516 | 0.371767 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.4862 | −0.604959 | ||||||||
\(427\) | 0.596355 | 0.0288596 | ||||||||
\(428\) | −9.79993 | −0.473697 | ||||||||
\(429\) | −19.3749 | −0.935428 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.6002 | 0.944109 | 0.472054 | − | 0.881569i | \(-0.343513\pi\) | ||||
0.472054 | + | 0.881569i | \(0.343513\pi\) | |||||||
\(432\) | 28.1000 | 1.35196 | ||||||||
\(433\) | 8.10862 | 0.389676 | 0.194838 | − | 0.980835i | \(-0.437582\pi\) | ||||
0.194838 | + | 0.980835i | \(0.437582\pi\) | |||||||
\(434\) | −0.409978 | −0.0196796 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 14.3072 | 0.685189 | ||||||||
\(437\) | 43.7335 | 2.09205 | ||||||||
\(438\) | −5.25164 | −0.250933 | ||||||||
\(439\) | 34.0684 | 1.62600 | 0.812998 | − | 0.582267i | \(-0.197834\pi\) | ||||
0.812998 | + | 0.582267i | \(0.197834\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −51.6074 | −2.45750 | ||||||||
\(442\) | 20.9284 | 0.995464 | ||||||||
\(443\) | −12.5494 | −0.596240 | −0.298120 | − | 0.954528i | \(-0.596360\pi\) | ||||
−0.298120 | + | 0.954528i | \(0.596360\pi\) | |||||||
\(444\) | 31.6330 | 1.50124 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.98388 | 0.330696 | ||||||||
\(447\) | −43.2691 | −2.04656 | ||||||||
\(448\) | 0.0619669 | 0.00292766 | ||||||||
\(449\) | 23.2022 | 1.09498 | 0.547489 | − | 0.836813i | \(-0.315584\pi\) | ||||
0.547489 | + | 0.836813i | \(0.315584\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.71064 | −0.0805511 | ||||||||
\(452\) | 20.3837 | 0.958766 | ||||||||
\(453\) | −42.6766 | −2.00512 | ||||||||
\(454\) | −2.83410 | −0.133011 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −32.3950 | −1.51704 | ||||||||
\(457\) | 12.7868 | 0.598140 | 0.299070 | − | 0.954231i | \(-0.403324\pi\) | ||||
0.299070 | + | 0.954231i | \(0.403324\pi\) | |||||||
\(458\) | −2.33740 | −0.109220 | ||||||||
\(459\) | 77.2496 | 3.60570 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.71560 | −0.126478 | −0.0632389 | − | 0.997998i | \(-0.520143\pi\) | ||||
−0.0632389 | + | 0.997998i | \(0.520143\pi\) | |||||||
\(462\) | 0.164922 | 0.00767284 | ||||||||
\(463\) | 29.7362 | 1.38196 | 0.690979 | − | 0.722875i | \(-0.257180\pi\) | ||||
0.690979 | + | 0.722875i | \(0.257180\pi\) | |||||||
\(464\) | −1.32763 | −0.0616339 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.22701 | 0.0568403 | ||||||||
\(467\) | 6.90067 | 0.319325 | 0.159662 | − | 0.987172i | \(-0.448959\pi\) | ||||
0.159662 | + | 0.987172i | \(0.448959\pi\) | |||||||
\(468\) | 77.7771 | 3.59525 | ||||||||
\(469\) | −1.40532 | −0.0648918 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.8041 | 1.69584 | ||||||||
\(472\) | −31.2654 | −1.43911 | ||||||||
\(473\) | −2.26447 | −0.104120 | ||||||||
\(474\) | 16.9200 | 0.777159 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.822585 | 0.0377031 | ||||||||
\(477\) | 25.9877 | 1.18990 | ||||||||
\(478\) | 2.60926 | 0.119345 | ||||||||
\(479\) | 33.1760 | 1.51585 | 0.757924 | − | 0.652342i | \(-0.226214\pi\) | ||||
0.757924 | + | 0.652342i | \(0.226214\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 38.2777 | 1.74531 | ||||||||
\(482\) | 0.596683 | 0.0271782 | ||||||||
\(483\) | 2.78628 | 0.126780 | ||||||||
\(484\) | 16.6367 | 0.756212 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.6016 | −0.889146 | ||||||||
\(487\) | 3.24933 | 0.147241 | 0.0736207 | − | 0.997286i | \(-0.476545\pi\) | ||||
0.0736207 | + | 0.997286i | \(0.476545\pi\) | |||||||
\(488\) | −14.1809 | −0.641939 | ||||||||
\(489\) | −13.4493 | −0.608198 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.81775 | −0.0820340 | −0.0410170 | − | 0.999158i | \(-0.513060\pi\) | ||||
−0.0410170 | + | 0.999158i | \(0.513060\pi\) | |||||||
\(492\) | 9.65809 | 0.435420 | ||||||||
\(493\) | −3.64979 | −0.164378 | ||||||||
\(494\) | −17.6849 | −0.795682 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.9580 | −0.671636 | ||||||||
\(497\) | −0.593855 | −0.0266380 | ||||||||
\(498\) | −0.774209 | −0.0346932 | ||||||||
\(499\) | −12.2563 | −0.548667 | −0.274333 | − | 0.961635i | \(-0.588457\pi\) | ||||
−0.274333 | + | 0.961635i | \(0.588457\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 72.3109 | 3.23061 | ||||||||
\(502\) | 6.04702 | 0.269892 | ||||||||
\(503\) | 5.24664 | 0.233936 | 0.116968 | − | 0.993136i | \(-0.462682\pi\) | ||||
0.116968 | + | 0.993136i | \(0.462682\pi\) | |||||||
\(504\) | −1.46748 | −0.0653666 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.29434 | 0.235362 | ||||||||
\(507\) | 90.4799 | 4.01835 | ||||||||
\(508\) | 20.8117 | 0.923370 | ||||||||
\(509\) | −38.3672 | −1.70060 | −0.850298 | − | 0.526301i | \(-0.823579\pi\) | ||||
−0.850298 | + | 0.526301i | \(0.823579\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.249773 | −0.0110493 | ||||||||
\(512\) | −19.6766 | −0.869593 | ||||||||
\(513\) | −65.2774 | −2.88207 | ||||||||
\(514\) | −4.56936 | −0.201546 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 12.7849 | 0.562824 | ||||||||
\(517\) | −1.41598 | −0.0622746 | ||||||||
\(518\) | −0.325825 | −0.0143159 | ||||||||
\(519\) | 61.4181 | 2.69596 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.6227 | 0.815876 | 0.407938 | − | 0.913010i | \(-0.366248\pi\) | ||||
0.407938 | + | 0.913010i | \(0.366248\pi\) | |||||||
\(522\) | 2.93750 | 0.128571 | ||||||||
\(523\) | 26.1292 | 1.14255 | 0.571274 | − | 0.820759i | \(-0.306449\pi\) | ||||
0.571274 | + | 0.820759i | \(0.306449\pi\) | |||||||
\(524\) | −12.8141 | −0.559785 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.30978 | −0.187915 | ||||||||
\(527\) | −41.1211 | −1.79126 | ||||||||
\(528\) | 6.01716 | 0.261863 | ||||||||
\(529\) | 66.4457 | 2.88894 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −106.140 | −4.60607 | ||||||||
\(532\) | −0.695100 | −0.0301364 | ||||||||
\(533\) | 11.6868 | 0.506213 | ||||||||
\(534\) | −34.5227 | −1.49394 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 33.4176 | 1.44342 | ||||||||
\(537\) | 21.8743 | 0.943945 | ||||||||
\(538\) | 2.30552 | 0.0993978 | ||||||||
\(539\) | −6.55944 | −0.282535 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.4175 | 1.17877 | 0.589386 | − | 0.807852i | \(-0.299370\pi\) | ||||
0.589386 | + | 0.807852i | \(0.299370\pi\) | |||||||
\(542\) | 18.4781 | 0.793703 | ||||||||
\(543\) | −2.09545 | −0.0899244 | ||||||||
\(544\) | −30.2963 | −1.29894 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.12672 | −0.0482190 | ||||||||
\(547\) | −7.78442 | −0.332838 | −0.166419 | − | 0.986055i | \(-0.553220\pi\) | ||||
−0.166419 | + | 0.986055i | \(0.553220\pi\) | |||||||
\(548\) | −18.3945 | −0.785775 | ||||||||
\(549\) | −48.1413 | −2.05462 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.08414 | 0.131389 | ||||||||
\(552\) | −66.2559 | −2.82004 | ||||||||
\(553\) | 0.804727 | 0.0342205 | ||||||||
\(554\) | −1.93155 | −0.0820635 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21.8285 | 0.925735 | ||||||||
\(557\) | −31.6184 | −1.33971 | −0.669857 | − | 0.742490i | \(-0.733645\pi\) | ||||
−0.669857 | + | 0.742490i | \(0.733645\pi\) | |||||||
\(558\) | 33.0959 | 1.40106 | ||||||||
\(559\) | 15.4705 | 0.654330 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.5417 | 0.698393 | ||||||||
\(562\) | −9.41788 | −0.397269 | ||||||||
\(563\) | 13.8213 | 0.582498 | 0.291249 | − | 0.956647i | \(-0.405929\pi\) | ||||
0.291249 | + | 0.956647i | \(0.405929\pi\) | |||||||
\(564\) | 7.99444 | 0.336627 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.5738 | 0.444451 | ||||||||
\(567\) | −2.13410 | −0.0896238 | ||||||||
\(568\) | 14.1215 | 0.592523 | ||||||||
\(569\) | 8.73989 | 0.366395 | 0.183198 | − | 0.983076i | \(-0.441355\pi\) | ||||
0.183198 | + | 0.983076i | \(0.441355\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.5163 | −0.481944 | −0.240972 | − | 0.970532i | \(-0.577466\pi\) | ||||
−0.240972 | + | 0.970532i | \(0.577466\pi\) | |||||||
\(572\) | 9.88568 | 0.413341 | ||||||||
\(573\) | −43.4229 | −1.81402 | ||||||||
\(574\) | −0.0994799 | −0.00415221 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.00234 | −0.208431 | ||||||||
\(577\) | 6.75615 | 0.281262 | 0.140631 | − | 0.990062i | \(-0.455087\pi\) | ||||
0.140631 | + | 0.990062i | \(0.455087\pi\) | |||||||
\(578\) | −7.72451 | −0.321297 | ||||||||
\(579\) | −17.6069 | −0.731718 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0368221 | −0.00152764 | ||||||||
\(582\) | 33.6430 | 1.39455 | ||||||||
\(583\) | 3.30311 | 0.136801 | ||||||||
\(584\) | 5.93942 | 0.245775 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.5273 | 0.434879 | ||||||||
\(587\) | 1.71413 | 0.0707498 | 0.0353749 | − | 0.999374i | \(-0.488737\pi\) | ||||
0.0353749 | + | 0.999374i | \(0.488737\pi\) | |||||||
\(588\) | 37.0338 | 1.52725 | ||||||||
\(589\) | 34.7481 | 1.43177 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 66.7473 | 2.74562 | ||||||||
\(592\) | −11.8877 | −0.488582 | ||||||||
\(593\) | −27.1227 | −1.11380 | −0.556898 | − | 0.830581i | \(-0.688008\pi\) | ||||
−0.556898 | + | 0.830581i | \(0.688008\pi\) | |||||||
\(594\) | −7.90243 | −0.324241 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.0773 | 0.904321 | ||||||||
\(597\) | −82.8285 | −3.38994 | ||||||||
\(598\) | −36.1700 | −1.47910 | ||||||||
\(599\) | 29.0181 | 1.18565 | 0.592824 | − | 0.805332i | \(-0.298013\pi\) | ||||
0.592824 | + | 0.805332i | \(0.298013\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.46669 | −0.263782 | −0.131891 | − | 0.991264i | \(-0.542105\pi\) | ||||
−0.131891 | + | 0.991264i | \(0.542105\pi\) | |||||||
\(602\) | −0.131687 | −0.00536714 | ||||||||
\(603\) | 113.446 | 4.61988 | ||||||||
\(604\) | 21.7750 | 0.886012 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −30.8666 | −1.25387 | ||||||||
\(607\) | −16.5728 | −0.672669 | −0.336335 | − | 0.941743i | \(-0.609187\pi\) | ||||
−0.336335 | + | 0.941743i | \(0.609187\pi\) | |||||||
\(608\) | 25.6010 | 1.03826 | ||||||||
\(609\) | 0.196493 | 0.00796228 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.67373 | 0.391357 | ||||||||
\(612\) | −66.4040 | −2.68422 | ||||||||
\(613\) | −21.8721 | −0.883407 | −0.441704 | − | 0.897161i | \(-0.645626\pi\) | ||||
−0.441704 | + | 0.897161i | \(0.645626\pi\) | |||||||
\(614\) | 6.30306 | 0.254371 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.186520 | −0.00751512 | ||||||||
\(617\) | −10.5044 | −0.422891 | −0.211446 | − | 0.977390i | \(-0.567817\pi\) | ||||
−0.211446 | + | 0.977390i | \(0.567817\pi\) | |||||||
\(618\) | −18.9402 | −0.761885 | ||||||||
\(619\) | 23.9195 | 0.961406 | 0.480703 | − | 0.876884i | \(-0.340382\pi\) | ||||
0.480703 | + | 0.876884i | \(0.340382\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −133.508 | −5.35751 | ||||||||
\(622\) | −9.25826 | −0.371222 | ||||||||
\(623\) | −1.64193 | −0.0657825 | ||||||||
\(624\) | −41.1082 | −1.64565 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.55222 | −0.381783 | ||||||||
\(627\) | −13.9781 | −0.558231 | ||||||||
\(628\) | −18.7786 | −0.749349 | ||||||||
\(629\) | −32.6805 | −1.30306 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.4550 | −0.575444 | −0.287722 | − | 0.957714i | \(-0.592898\pi\) | ||||
−0.287722 | + | 0.957714i | \(0.592898\pi\) | |||||||
\(632\) | −19.1359 | −0.761184 | ||||||||
\(633\) | 34.2684 | 1.36205 | ||||||||
\(634\) | −3.54204 | −0.140672 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −18.6490 | −0.739480 | ||||||||
\(637\) | 44.8130 | 1.77556 | ||||||||
\(638\) | 0.373364 | 0.0147816 | ||||||||
\(639\) | 47.9395 | 1.89646 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.0263 | 0.396017 | 0.198008 | − | 0.980200i | \(-0.436553\pi\) | ||||
0.198008 | + | 0.980200i | \(0.436553\pi\) | |||||||
\(642\) | −11.4604 | −0.452305 | ||||||||
\(643\) | 22.8415 | 0.900781 | 0.450391 | − | 0.892832i | \(-0.351285\pi\) | ||||
0.450391 | + | 0.892832i | \(0.351285\pi\) | |||||||
\(644\) | −1.42165 | −0.0560209 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.0989 | 0.594059 | ||||||||
\(647\) | −5.91891 | −0.232697 | −0.116348 | − | 0.993208i | \(-0.537119\pi\) | ||||
−0.116348 | + | 0.993208i | \(0.537119\pi\) | |||||||
\(648\) | 50.7474 | 1.99355 | ||||||||
\(649\) | −13.4906 | −0.529554 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.21382 | 0.0867665 | ||||||||
\(652\) | 6.86226 | 0.268747 | ||||||||
\(653\) | 7.83832 | 0.306737 | 0.153369 | − | 0.988169i | \(-0.450988\pi\) | ||||
0.153369 | + | 0.988169i | \(0.450988\pi\) | |||||||
\(654\) | 16.7313 | 0.654246 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.62952 | −0.141709 | ||||||||
\(657\) | 20.1631 | 0.786639 | ||||||||
\(658\) | −0.0823441 | −0.00321011 | ||||||||
\(659\) | 8.38247 | 0.326535 | 0.163267 | − | 0.986582i | \(-0.447797\pi\) | ||||
0.163267 | + | 0.986582i | \(0.447797\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.45841 | 0.173412 | 0.0867060 | − | 0.996234i | \(-0.472366\pi\) | ||||
0.0867060 | + | 0.996234i | \(0.472366\pi\) | |||||||
\(662\) | 14.6138 | 0.567980 | ||||||||
\(663\) | −113.010 | −4.38896 | ||||||||
\(664\) | 0.875603 | 0.0339800 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 26.3026 | 1.01920 | ||||||||
\(667\) | 6.30784 | 0.244240 | ||||||||
\(668\) | −36.8954 | −1.42752 | ||||||||
\(669\) | −37.7119 | −1.45803 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.11890 | −0.236217 | ||||||||
\(672\) | 1.63105 | 0.0629192 | ||||||||
\(673\) | 31.5701 | 1.21694 | 0.608470 | − | 0.793577i | \(-0.291784\pi\) | ||||
0.608470 | + | 0.793577i | \(0.291784\pi\) | |||||||
\(674\) | 2.74732 | 0.105823 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −46.1657 | −1.77561 | ||||||||
\(677\) | 15.6023 | 0.599645 | 0.299823 | − | 0.953995i | \(-0.403072\pi\) | ||||
0.299823 | + | 0.953995i | \(0.403072\pi\) | |||||||
\(678\) | 23.8374 | 0.915469 | ||||||||
\(679\) | 1.60009 | 0.0614058 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.3037 | 0.586441 | ||||||||
\(682\) | 4.20658 | 0.161078 | ||||||||
\(683\) | 24.0372 | 0.919756 | 0.459878 | − | 0.887982i | \(-0.347893\pi\) | ||||
0.459878 | + | 0.887982i | \(0.347893\pi\) | |||||||
\(684\) | 56.1126 | 2.14552 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.763365 | −0.0291454 | ||||||||
\(687\) | 12.6216 | 0.481546 | ||||||||
\(688\) | −4.80458 | −0.183173 | ||||||||
\(689\) | −22.5663 | −0.859708 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.8219 | −0.830143 | −0.415072 | − | 0.909789i | \(-0.636243\pi\) | ||||
−0.415072 | + | 0.909789i | \(0.636243\pi\) | |||||||
\(692\) | −31.3375 | −1.19127 | ||||||||
\(693\) | −0.633199 | −0.0240532 | ||||||||
\(694\) | 3.93761 | 0.149469 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.67246 | −0.177109 | ||||||||
\(697\) | −9.97790 | −0.377940 | ||||||||
\(698\) | 5.37028 | 0.203268 | ||||||||
\(699\) | −6.62569 | −0.250607 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.9054 | −1.39390 | −0.696949 | − | 0.717120i | \(-0.745460\pi\) | ||||
−0.696949 | + | 0.717120i | \(0.745460\pi\) | |||||||
\(702\) | 53.9881 | 2.03765 | ||||||||
\(703\) | 27.6156 | 1.04154 | ||||||||
\(704\) | −0.635811 | −0.0239630 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.4867 | 0.432309 | ||||||||
\(707\) | −1.46804 | −0.0552115 | ||||||||
\(708\) | 76.1666 | 2.86251 | ||||||||
\(709\) | 18.5895 | 0.698145 | 0.349072 | − | 0.937096i | \(-0.386497\pi\) | ||||
0.349072 | + | 0.937096i | \(0.386497\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −64.9624 | −2.43628 | ||||||||
\(712\) | 39.0439 | 1.46323 | ||||||||
\(713\) | 71.0685 | 2.66154 | ||||||||
\(714\) | 0.961960 | 0.0360004 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.1610 | −0.417105 | ||||||||
\(717\) | −14.0896 | −0.526187 | ||||||||
\(718\) | 3.86052 | 0.144073 | ||||||||
\(719\) | 21.3723 | 0.797052 | 0.398526 | − | 0.917157i | \(-0.369522\pi\) | ||||
0.398526 | + | 0.917157i | \(0.369522\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.900810 | −0.0335479 | ||||||||
\(722\) | −1.42188 | −0.0529169 | ||||||||
\(723\) | −3.22200 | −0.119828 | ||||||||
\(724\) | 1.06917 | 0.0397353 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 19.4555 | 0.722061 | ||||||||
\(727\) | −4.55494 | −0.168933 | −0.0844667 | − | 0.996426i | \(-0.526919\pi\) | ||||
−0.0844667 | + | 0.996426i | \(0.526919\pi\) | |||||||
\(728\) | 1.27428 | 0.0472278 | ||||||||
\(729\) | 35.8266 | 1.32691 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.2083 | −0.488525 | ||||||||
\(732\) | 34.5466 | 1.27688 | ||||||||
\(733\) | 6.73245 | 0.248669 | 0.124334 | − | 0.992240i | \(-0.460320\pi\) | ||||
0.124334 | + | 0.992240i | \(0.460320\pi\) | |||||||
\(734\) | 4.37685 | 0.161552 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 52.3603 | 1.93003 | ||||||||
\(737\) | 14.4193 | 0.531142 | ||||||||
\(738\) | 8.03061 | 0.295611 | ||||||||
\(739\) | −7.18344 | −0.264247 | −0.132124 | − | 0.991233i | \(-0.542180\pi\) | ||||
−0.132124 | + | 0.991233i | \(0.542180\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 95.4960 | 3.50813 | ||||||||
\(742\) | 0.192087 | 0.00705175 | ||||||||
\(743\) | −30.4874 | −1.11847 | −0.559237 | − | 0.829008i | \(-0.688906\pi\) | ||||
−0.559237 | + | 0.829008i | \(0.688906\pi\) | |||||||
\(744\) | −52.6431 | −1.92999 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11.9042 | −0.435843 | ||||||||
\(747\) | 2.97250 | 0.108758 | ||||||||
\(748\) | −8.44013 | −0.308602 | ||||||||
\(749\) | −0.545066 | −0.0199163 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.4839 | 1.07588 | 0.537942 | − | 0.842982i | \(-0.319202\pi\) | ||||
0.537942 | + | 0.842982i | \(0.319202\pi\) | |||||||
\(752\) | −3.00432 | −0.109556 | ||||||||
\(753\) | −32.6530 | −1.18994 | ||||||||
\(754\) | −2.55076 | −0.0928933 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.12198 | 0.0771758 | ||||||||
\(757\) | 7.20199 | 0.261761 | 0.130880 | − | 0.991398i | \(-0.458220\pi\) | ||||
0.130880 | + | 0.991398i | \(0.458220\pi\) | |||||||
\(758\) | 13.9893 | 0.508115 | ||||||||
\(759\) | −28.5886 | −1.03770 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.55723 | −0.128950 | −0.0644748 | − | 0.997919i | \(-0.520537\pi\) | ||||
−0.0644748 | + | 0.997919i | \(0.520537\pi\) | |||||||
\(762\) | 24.3379 | 0.881671 | ||||||||
\(763\) | 0.795756 | 0.0288083 | ||||||||
\(764\) | 22.1558 | 0.801567 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.00873 | 0.325499 | ||||||||
\(767\) | 92.1659 | 3.32792 | ||||||||
\(768\) | −17.6977 | −0.638609 | ||||||||
\(769\) | −9.11046 | −0.328532 | −0.164266 | − | 0.986416i | \(-0.552525\pi\) | ||||
−0.164266 | + | 0.986416i | \(0.552525\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.6739 | 0.888608 | ||||||||
\(772\) | 8.98361 | 0.323327 | ||||||||
\(773\) | −14.7015 | −0.528777 | −0.264388 | − | 0.964416i | \(-0.585170\pi\) | ||||
−0.264388 | + | 0.964416i | \(0.585170\pi\) | |||||||
\(774\) | 10.6305 | 0.382106 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −38.0490 | −1.36588 | ||||||||
\(777\) | 1.75941 | 0.0631184 | ||||||||
\(778\) | 18.2006 | 0.652522 | ||||||||
\(779\) | 8.43152 | 0.302090 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.09324 | 0.218033 | ||||||||
\(782\) | 30.8810 | 1.10430 | ||||||||
\(783\) | −9.41520 | −0.336472 | ||||||||
\(784\) | −13.9174 | −0.497048 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −14.9852 | −0.534505 | ||||||||
\(787\) | −41.7194 | −1.48713 | −0.743567 | − | 0.668661i | \(-0.766868\pi\) | ||||
−0.743567 | + | 0.668661i | \(0.766868\pi\) | |||||||
\(788\) | −34.0566 | −1.21322 | ||||||||
\(789\) | 23.2722 | 0.828511 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.13373 | 0.0403106 | ||||||||
\(792\) | 15.0570 | 0.535028 | ||||||||
\(793\) | 41.8033 | 1.48448 | ||||||||
\(794\) | −7.94850 | −0.282082 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 42.2617 | 1.49793 | ||||||||
\(797\) | −39.9649 | −1.41563 | −0.707815 | − | 0.706398i | \(-0.750319\pi\) | ||||
−0.707815 | + | 0.706398i | \(0.750319\pi\) | |||||||
\(798\) | −0.812874 | −0.0287754 | ||||||||
\(799\) | −8.25917 | −0.292188 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 132.546 | 4.68329 | ||||||||
\(802\) | 1.22155 | 0.0431346 | ||||||||
\(803\) | 2.56279 | 0.0904389 | ||||||||
\(804\) | −81.4097 | −2.87110 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −28.7387 | −1.01228 | ||||||||
\(807\) | −12.4494 | −0.438241 | ||||||||
\(808\) | 34.9091 | 1.22810 | ||||||||
\(809\) | 48.1327 | 1.69226 | 0.846128 | − | 0.532980i | \(-0.178928\pi\) | ||||
0.846128 | + | 0.532980i | \(0.178928\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.1641 | −1.34012 | −0.670061 | − | 0.742306i | \(-0.733732\pi\) | ||||
−0.670061 | + | 0.742306i | \(0.733732\pi\) | |||||||
\(812\) | −0.100257 | −0.00351832 | ||||||||
\(813\) | −99.7790 | −3.49940 | ||||||||
\(814\) | 3.34313 | 0.117177 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 35.0971 | 1.22864 | ||||||||
\(817\) | 11.1612 | 0.390482 | ||||||||
\(818\) | 8.03161 | 0.280819 | ||||||||
\(819\) | 4.32591 | 0.151160 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.8745 | 0.903025 | 0.451512 | − | 0.892265i | \(-0.350885\pi\) | ||||
0.451512 | + | 0.892265i | \(0.350885\pi\) | |||||||
\(822\) | −21.5112 | −0.750289 | ||||||||
\(823\) | 0.237610 | 0.00828258 | 0.00414129 | − | 0.999991i | \(-0.498682\pi\) | ||||
0.00414129 | + | 0.999991i | \(0.498682\pi\) | |||||||
\(824\) | 21.4206 | 0.746223 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.784528 | −0.0272972 | ||||||||
\(827\) | 22.1323 | 0.769615 | 0.384807 | − | 0.922997i | \(-0.374268\pi\) | ||||
0.384807 | + | 0.922997i | \(0.374268\pi\) | |||||||
\(828\) | 114.764 | 3.98833 | ||||||||
\(829\) | −17.4722 | −0.606834 | −0.303417 | − | 0.952858i | \(-0.598128\pi\) | ||||
−0.303417 | + | 0.952858i | \(0.598128\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.4301 | 0.361815 | ||||||||
\(832\) | 4.34375 | 0.150593 | ||||||||
\(833\) | −38.2601 | −1.32564 | ||||||||
\(834\) | 25.5270 | 0.883929 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.13207 | 0.246668 | ||||||||
\(837\) | −106.078 | −3.66660 | ||||||||
\(838\) | 6.95412 | 0.240226 | ||||||||
\(839\) | 2.59302 | 0.0895208 | 0.0447604 | − | 0.998998i | \(-0.485748\pi\) | ||||
0.0447604 | + | 0.998998i | \(0.485748\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5552 | −0.984661 | ||||||||
\(842\) | 4.07589 | 0.140464 | ||||||||
\(843\) | 50.8551 | 1.75154 | ||||||||
\(844\) | −17.4848 | −0.601853 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.64731 | 0.228539 | ||||||||
\(847\) | 0.925320 | 0.0317944 | ||||||||
\(848\) | 7.00831 | 0.240666 | ||||||||
\(849\) | −57.0971 | −1.95957 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 56.4808 | 1.93614 | ||||||||
\(852\) | −34.4017 | −1.17858 | ||||||||
\(853\) | 14.2813 | 0.488984 | 0.244492 | − | 0.969651i | \(-0.421379\pi\) | ||||
0.244492 | + | 0.969651i | \(0.421379\pi\) | |||||||
\(854\) | −0.355835 | −0.0121764 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.9613 | 0.443008 | ||||||||
\(857\) | −5.29985 | −0.181039 | −0.0905196 | − | 0.995895i | \(-0.528853\pi\) | ||||
−0.0905196 | + | 0.995895i | \(0.528853\pi\) | |||||||
\(858\) | 11.5607 | 0.394675 | ||||||||
\(859\) | −46.6430 | −1.59144 | −0.795719 | − | 0.605666i | \(-0.792907\pi\) | ||||
−0.795719 | + | 0.605666i | \(0.792907\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.537177 | 0.0183069 | ||||||||
\(862\) | −11.6951 | −0.398337 | ||||||||
\(863\) | −7.04585 | −0.239843 | −0.119922 | − | 0.992783i | \(-0.538264\pi\) | ||||
−0.119922 | + | 0.992783i | \(0.538264\pi\) | |||||||
\(864\) | −78.1540 | −2.65885 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.83828 | −0.164411 | ||||||||
\(867\) | 41.7112 | 1.41659 | ||||||||
\(868\) | −1.12956 | −0.0383399 | ||||||||
\(869\) | −8.25690 | −0.280096 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −98.5103 | −3.33789 | ||||||||
\(872\) | −18.9225 | −0.640797 | ||||||||
\(873\) | −129.169 | −4.37171 | ||||||||
\(874\) | −26.0950 | −0.882678 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14.4692 | −0.488869 | ||||||||
\(877\) | 9.94520 | 0.335825 | 0.167913 | − | 0.985802i | \(-0.446297\pi\) | ||||
0.167913 | + | 0.985802i | \(0.446297\pi\) | |||||||
\(878\) | −20.3280 | −0.686038 | ||||||||
\(879\) | −56.8459 | −1.91736 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.95289 | 0.0994854 | 0.0497427 | − | 0.998762i | \(-0.484160\pi\) | ||||
0.0497427 | + | 0.998762i | \(0.484160\pi\) | |||||||
\(882\) | 30.7933 | 1.03686 | ||||||||
\(883\) | −47.0985 | −1.58499 | −0.792495 | − | 0.609878i | \(-0.791219\pi\) | ||||
−0.792495 | + | 0.609878i | \(0.791219\pi\) | |||||||
\(884\) | 57.6615 | 1.93937 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.48803 | 0.251565 | ||||||||
\(887\) | −30.3790 | −1.02003 | −0.510013 | − | 0.860167i | \(-0.670360\pi\) | ||||
−0.510013 | + | 0.860167i | \(0.670360\pi\) | |||||||
\(888\) | −41.8375 | −1.40397 | ||||||||
\(889\) | 1.15753 | 0.0388224 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.8969 | 0.733575 | ||||||||
\(892\) | 19.2418 | 0.644264 | ||||||||
\(893\) | 6.97915 | 0.233548 | ||||||||
\(894\) | 25.8180 | 0.863482 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.04942 | −0.0350587 | ||||||||
\(897\) | 195.313 | 6.52131 | ||||||||
\(898\) | −13.8444 | −0.461992 | ||||||||
\(899\) | 5.01185 | 0.167154 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.2665 | 0.641860 | ||||||||
\(902\) | 1.02071 | 0.0339860 | ||||||||
\(903\) | 0.711088 | 0.0236635 | ||||||||
\(904\) | −26.9592 | −0.896650 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 25.4644 | 0.845999 | ||||||||
\(907\) | −3.94698 | −0.131057 | −0.0655287 | − | 0.997851i | \(-0.520873\pi\) | ||||
−0.0655287 | + | 0.997851i | \(0.520873\pi\) | |||||||
\(908\) | −7.80846 | −0.259133 | ||||||||
\(909\) | 118.509 | 3.93071 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.1864 | −1.06638 | −0.533192 | − | 0.845994i | \(-0.679008\pi\) | ||||
−0.533192 | + | 0.845994i | \(0.679008\pi\) | |||||||
\(912\) | −29.6577 | −0.982065 | ||||||||
\(913\) | 0.377813 | 0.0125038 | ||||||||
\(914\) | −7.62965 | −0.252366 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.43996 | −0.212782 | ||||||||
\(917\) | −0.712710 | −0.0235358 | ||||||||
\(918\) | −46.0936 | −1.52132 | ||||||||
\(919\) | −22.6485 | −0.747106 | −0.373553 | − | 0.927609i | \(-0.621861\pi\) | ||||
−0.373553 | + | 0.927609i | \(0.621861\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −34.0356 | −1.12151 | ||||||||
\(922\) | 1.62035 | 0.0533634 | ||||||||
\(923\) | −41.6280 | −1.37020 | ||||||||
\(924\) | 0.454388 | 0.0149483 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −17.7431 | −0.583074 | ||||||||
\(927\) | 72.7188 | 2.38840 | ||||||||
\(928\) | 3.69252 | 0.121213 | ||||||||
\(929\) | 9.27409 | 0.304273 | 0.152137 | − | 0.988359i | \(-0.451385\pi\) | ||||
0.152137 | + | 0.988359i | \(0.451385\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.3305 | 1.05959 | ||||||||
\(932\) | 3.38064 | 0.110737 | ||||||||
\(933\) | 49.9932 | 1.63671 | ||||||||
\(934\) | −4.11751 | −0.134729 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −102.867 | −3.36232 | ||||||||
\(937\) | 37.3432 | 1.21995 | 0.609975 | − | 0.792420i | \(-0.291179\pi\) | ||||
0.609975 | + | 0.792420i | \(0.291179\pi\) | |||||||
\(938\) | 0.838533 | 0.0273791 | ||||||||
\(939\) | 51.5806 | 1.68327 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.4044 | 1.21935 | 0.609674 | − | 0.792652i | \(-0.291300\pi\) | ||||
0.609674 | + | 0.792652i | \(0.291300\pi\) | |||||||
\(942\) | −21.9604 | −0.715508 | ||||||||
\(943\) | 17.2445 | 0.561559 | ||||||||
\(944\) | −28.6235 | −0.931615 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.35117 | 0.0439303 | ||||||||
\(947\) | 38.2457 | 1.24282 | 0.621409 | − | 0.783486i | \(-0.286560\pi\) | ||||
0.621409 | + | 0.783486i | \(0.286560\pi\) | |||||||
\(948\) | 46.6175 | 1.51407 | ||||||||
\(949\) | −17.5086 | −0.568352 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.1265 | 0.620218 | ||||||||
\(952\) | −1.08794 | −0.0352604 | ||||||||
\(953\) | 16.0014 | 0.518336 | 0.259168 | − | 0.965832i | \(-0.416552\pi\) | ||||
0.259168 | + | 0.965832i | \(0.416552\pi\) | |||||||
\(954\) | −15.5064 | −0.502040 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.18898 | 0.232508 | ||||||||
\(957\) | −2.01611 | −0.0651716 | ||||||||
\(958\) | −19.7956 | −0.639565 | ||||||||
\(959\) | −1.02309 | −0.0330373 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.4670 | 0.821515 | ||||||||
\(962\) | −22.8397 | −0.736381 | ||||||||
\(963\) | 44.0010 | 1.41791 | ||||||||
\(964\) | 1.64397 | 0.0529487 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.66253 | −0.0534910 | ||||||||
\(967\) | −57.3667 | −1.84479 | −0.922394 | − | 0.386251i | \(-0.873770\pi\) | ||||
−0.922394 | + | 0.386251i | \(0.873770\pi\) | |||||||
\(968\) | −22.0035 | −0.707218 | ||||||||
\(969\) | −81.5319 | −2.61918 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.3616 | −0.749711 | −0.374855 | − | 0.927083i | \(-0.622308\pi\) | ||||
−0.374855 | + | 0.927083i | \(0.622308\pi\) | |||||||
\(972\) | −54.0059 | −1.73224 | ||||||||
\(973\) | 1.21409 | 0.0389218 | ||||||||
\(974\) | −1.93882 | −0.0621239 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.9826 | −0.415564 | ||||||||
\(977\) | −21.2763 | −0.680690 | −0.340345 | − | 0.940301i | \(-0.610544\pi\) | ||||
−0.340345 | + | 0.940301i | \(0.610544\pi\) | |||||||
\(978\) | 8.02497 | 0.256610 | ||||||||
\(979\) | 16.8470 | 0.538432 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −64.2382 | −2.05097 | ||||||||
\(982\) | 1.08462 | 0.0346117 | ||||||||
\(983\) | −20.2377 | −0.645481 | −0.322741 | − | 0.946487i | \(-0.604604\pi\) | ||||
−0.322741 | + | 0.946487i | \(0.604604\pi\) | |||||||
\(984\) | −12.7737 | −0.407210 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.17777 | 0.0693544 | ||||||||
\(987\) | 0.444646 | 0.0141532 | ||||||||
\(988\) | −48.7251 | −1.55015 | ||||||||
\(989\) | 22.8275 | 0.725871 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.318692 | −0.0101236 | −0.00506179 | − | 0.999987i | \(-0.501611\pi\) | ||||
−0.00506179 | + | 0.999987i | \(0.501611\pi\) | |||||||
\(992\) | 41.6025 | 1.32088 | ||||||||
\(993\) | −78.9121 | −2.50420 | ||||||||
\(994\) | 0.354343 | 0.0112391 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.13308 | −0.0675894 | ||||||||
\(997\) | −44.7214 | −1.41634 | −0.708170 | − | 0.706042i | \(-0.750479\pi\) | ||||
−0.708170 | + | 0.706042i | \(0.750479\pi\) | |||||||
\(998\) | 7.31312 | 0.231493 | ||||||||
\(999\) | −84.3043 | −2.66727 |
(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 | 6025.2.a.i.1.7 | 15 | ||
5.4 | even | 2 | 1205.2.a.c.1.9 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.a.c.1.9 | ✓ | 15 | 5.4 | even | 2 | ||
6025.2.a.i.1.7 | 15 | 1.1 | even | 1 | trivial |