Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2169,2,Mod(1,2169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2169, 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("2169.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2169 = 3^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2169.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: | \(17.3195521984\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 14 x^{10} + 44 x^{9} + 65 x^{8} - 219 x^{7} - 123 x^{6} + 444 x^{5} + 105 x^{4} + \cdots - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 241) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-1.32986\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2169.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.32986 | 0.940353 | 0.470176 | − | 0.882572i | \(-0.344190\pi\) | ||||
0.470176 | + | 0.882572i | \(0.344190\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.231473 | −0.115736 | ||||||||
\(5\) | 3.40432 | 1.52246 | 0.761230 | − | 0.648482i | \(-0.224596\pi\) | ||||
0.761230 | + | 0.648482i | \(0.224596\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.83334 | −1.44887 | −0.724434 | − | 0.689344i | \(-0.757899\pi\) | ||||
−0.724434 | + | 0.689344i | \(0.757899\pi\) | |||||||
\(8\) | −2.96755 | −1.04919 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.52727 | 1.43165 | ||||||||
\(11\) | −4.78120 | −1.44159 | −0.720793 | − | 0.693151i | \(-0.756222\pi\) | ||||
−0.720793 | + | 0.693151i | \(0.756222\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.75719 | 0.487356 | 0.243678 | − | 0.969856i | \(-0.421646\pi\) | ||||
0.243678 | + | 0.969856i | \(0.421646\pi\) | |||||||
\(14\) | −5.09781 | −1.36245 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.48347 | −0.870869 | ||||||||
\(17\) | 6.01977 | 1.46001 | 0.730004 | − | 0.683443i | \(-0.239518\pi\) | ||||
0.730004 | + | 0.683443i | \(0.239518\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.20086 | −0.963743 | −0.481871 | − | 0.876242i | \(-0.660043\pi\) | ||||
−0.481871 | + | 0.876242i | \(0.660043\pi\) | |||||||
\(20\) | −0.788008 | −0.176204 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.35832 | −1.35560 | ||||||||
\(23\) | −4.28435 | −0.893348 | −0.446674 | − | 0.894697i | \(-0.647392\pi\) | ||||
−0.446674 | + | 0.894697i | \(0.647392\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.58942 | 1.31788 | ||||||||
\(26\) | 2.33681 | 0.458287 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.887315 | 0.167687 | ||||||||
\(29\) | −4.96202 | −0.921423 | −0.460712 | − | 0.887550i | \(-0.652406\pi\) | ||||
−0.460712 | + | 0.887550i | \(0.652406\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.59803 | 0.825830 | 0.412915 | − | 0.910770i | \(-0.364511\pi\) | ||||
0.412915 | + | 0.910770i | \(0.364511\pi\) | |||||||
\(32\) | 1.30256 | 0.230262 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.00545 | 1.37292 | ||||||||
\(35\) | −13.0499 | −2.20584 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0806 | −1.65723 | −0.828617 | − | 0.559816i | \(-0.810872\pi\) | ||||
−0.828617 | + | 0.559816i | \(0.810872\pi\) | |||||||
\(38\) | −5.58655 | −0.906258 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.1025 | −1.59734 | ||||||||
\(41\) | −1.12501 | −0.175698 | −0.0878488 | − | 0.996134i | \(-0.527999\pi\) | ||||
−0.0878488 | + | 0.996134i | \(0.527999\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.09669 | −1.38723 | −0.693616 | − | 0.720345i | \(-0.743984\pi\) | ||||
−0.693616 | + | 0.720345i | \(0.743984\pi\) | |||||||
\(44\) | 1.10672 | 0.166844 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.69758 | −0.840062 | ||||||||
\(47\) | −7.19156 | −1.04900 | −0.524499 | − | 0.851411i | \(-0.675747\pi\) | ||||
−0.524499 | + | 0.851411i | \(0.675747\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.69453 | 1.09922 | ||||||||
\(50\) | 8.76300 | 1.23928 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.406741 | −0.0564049 | ||||||||
\(53\) | −6.07855 | −0.834953 | −0.417477 | − | 0.908688i | \(-0.637085\pi\) | ||||
−0.417477 | + | 0.908688i | \(0.637085\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.2767 | −2.19475 | ||||||||
\(56\) | 11.3756 | 1.52013 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.59879 | −0.866463 | ||||||||
\(59\) | −1.36242 | −0.177372 | −0.0886862 | − | 0.996060i | \(-0.528267\pi\) | ||||
−0.0886862 | + | 0.996060i | \(0.528267\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.9181 | −1.39791 | −0.698957 | − | 0.715164i | \(-0.746352\pi\) | ||||
−0.698957 | + | 0.715164i | \(0.746352\pi\) | |||||||
\(62\) | 6.11473 | 0.776571 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.69917 | 1.08740 | ||||||||
\(65\) | 5.98204 | 0.741980 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.85684 | 1.20421 | 0.602103 | − | 0.798419i | \(-0.294330\pi\) | ||||
0.602103 | + | 0.798419i | \(0.294330\pi\) | |||||||
\(68\) | −1.39341 | −0.168976 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −17.3546 | −2.07427 | ||||||||
\(71\) | −11.9533 | −1.41859 | −0.709296 | − | 0.704911i | \(-0.750987\pi\) | ||||
−0.709296 | + | 0.704911i | \(0.750987\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.162452 | −0.0190135 | −0.00950676 | − | 0.999955i | \(-0.503026\pi\) | ||||
−0.00950676 | + | 0.999955i | \(0.503026\pi\) | |||||||
\(74\) | −13.4057 | −1.55838 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.972384 | 0.111540 | ||||||||
\(77\) | 18.3280 | 2.08867 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.5772 | 1.64006 | 0.820031 | − | 0.572319i | \(-0.193956\pi\) | ||||
0.820031 | + | 0.572319i | \(0.193956\pi\) | |||||||
\(80\) | −11.8589 | −1.32586 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.49611 | −0.165218 | ||||||||
\(83\) | 5.77030 | 0.633372 | 0.316686 | − | 0.948530i | \(-0.397430\pi\) | ||||
0.316686 | + | 0.948530i | \(0.397430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.4932 | 2.22280 | ||||||||
\(86\) | −12.0973 | −1.30449 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 14.1884 | 1.51249 | ||||||||
\(89\) | −4.73628 | −0.502044 | −0.251022 | − | 0.967981i | \(-0.580767\pi\) | ||||
−0.251022 | + | 0.967981i | \(0.580767\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.73591 | −0.706115 | ||||||||
\(92\) | 0.991709 | 0.103393 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.56377 | −0.986428 | ||||||||
\(95\) | −14.3011 | −1.46726 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.439068 | 0.0445806 | 0.0222903 | − | 0.999752i | \(-0.492904\pi\) | ||||
0.0222903 | + | 0.999752i | \(0.492904\pi\) | |||||||
\(98\) | 10.2326 | 1.03365 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.52527 | −0.152527 | ||||||||
\(101\) | 4.54961 | 0.452703 | 0.226352 | − | 0.974046i | \(-0.427320\pi\) | ||||
0.226352 | + | 0.974046i | \(0.427320\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.9977 | 1.08364 | 0.541819 | − | 0.840495i | \(-0.317736\pi\) | ||||
0.541819 | + | 0.840495i | \(0.317736\pi\) | |||||||
\(104\) | −5.21454 | −0.511327 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.08362 | −0.785151 | ||||||||
\(107\) | −0.634979 | −0.0613858 | −0.0306929 | − | 0.999529i | \(-0.509771\pi\) | ||||
−0.0306929 | + | 0.999529i | \(0.509771\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.56974 | 0.533484 | 0.266742 | − | 0.963768i | \(-0.414053\pi\) | ||||
0.266742 | + | 0.963768i | \(0.414053\pi\) | |||||||
\(110\) | −21.6458 | −2.06384 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 13.3534 | 1.26177 | ||||||||
\(113\) | −4.78347 | −0.449991 | −0.224995 | − | 0.974360i | \(-0.572237\pi\) | ||||
−0.224995 | + | 0.974360i | \(0.572237\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.5853 | −1.36009 | ||||||||
\(116\) | 1.14857 | 0.106642 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.81183 | −0.166793 | ||||||||
\(119\) | −23.0758 | −2.11536 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.8598 | 1.07817 | ||||||||
\(122\) | −14.5195 | −1.31453 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.06432 | −0.0955785 | ||||||||
\(125\) | 5.41088 | 0.483964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.09612 | −0.540944 | −0.270472 | − | 0.962728i | \(-0.587180\pi\) | ||||
−0.270472 | + | 0.962728i | \(0.587180\pi\) | |||||||
\(128\) | 8.96356 | 0.792274 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.95527 | 0.697723 | ||||||||
\(131\) | 6.72698 | 0.587739 | 0.293869 | − | 0.955846i | \(-0.405057\pi\) | ||||
0.293869 | + | 0.955846i | \(0.405057\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.1033 | 1.39634 | ||||||||
\(134\) | 13.1082 | 1.13238 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.8639 | −1.53182 | ||||||||
\(137\) | 9.94109 | 0.849325 | 0.424663 | − | 0.905352i | \(-0.360393\pi\) | ||||
0.424663 | + | 0.905352i | \(0.360393\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.28633 | 0.278743 | 0.139372 | − | 0.990240i | \(-0.455492\pi\) | ||||
0.139372 | + | 0.990240i | \(0.455492\pi\) | |||||||
\(140\) | 3.02071 | 0.255296 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.8962 | −1.33398 | ||||||||
\(143\) | −8.40146 | −0.702566 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.8923 | −1.40283 | ||||||||
\(146\) | −0.216038 | −0.0178794 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.33337 | 0.191802 | ||||||||
\(149\) | −9.42710 | −0.772298 | −0.386149 | − | 0.922436i | \(-0.626195\pi\) | ||||
−0.386149 | + | 0.922436i | \(0.626195\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.34993 | −0.191234 | −0.0956171 | − | 0.995418i | \(-0.530482\pi\) | ||||
−0.0956171 | + | 0.995418i | \(0.530482\pi\) | |||||||
\(152\) | 12.4662 | 1.01115 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 24.3736 | 1.96408 | ||||||||
\(155\) | 15.6532 | 1.25729 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.8666 | 1.58552 | 0.792762 | − | 0.609531i | \(-0.208642\pi\) | ||||
0.792762 | + | 0.609531i | \(0.208642\pi\) | |||||||
\(158\) | 19.3856 | 1.54224 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.43433 | 0.350565 | ||||||||
\(161\) | 16.4234 | 1.29434 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.10105 | −0.164567 | −0.0822836 | − | 0.996609i | \(-0.526221\pi\) | ||||
−0.0822836 | + | 0.996609i | \(0.526221\pi\) | |||||||
\(164\) | 0.260410 | 0.0203346 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.67368 | 0.595593 | ||||||||
\(167\) | −21.9087 | −1.69535 | −0.847673 | − | 0.530518i | \(-0.821997\pi\) | ||||
−0.847673 | + | 0.530518i | \(0.821997\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.91229 | −0.762484 | ||||||||
\(170\) | 27.2531 | 2.09022 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.10564 | 0.160553 | ||||||||
\(173\) | 5.60734 | 0.426318 | 0.213159 | − | 0.977018i | \(-0.431625\pi\) | ||||
0.213159 | + | 0.977018i | \(0.431625\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −25.2595 | −1.90944 | ||||||||
\(176\) | 16.6552 | 1.25543 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.29859 | −0.472099 | ||||||||
\(179\) | 23.8279 | 1.78098 | 0.890492 | − | 0.454999i | \(-0.150360\pi\) | ||||
0.890492 | + | 0.454999i | \(0.150360\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.57832 | 0.488963 | 0.244481 | − | 0.969654i | \(-0.421382\pi\) | ||||
0.244481 | + | 0.969654i | \(0.421382\pi\) | |||||||
\(182\) | −8.95781 | −0.663997 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.7140 | 0.937288 | ||||||||
\(185\) | −34.3175 | −2.52307 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −28.7817 | −2.10473 | ||||||||
\(188\) | 1.66465 | 0.121407 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −19.0184 | −1.37974 | ||||||||
\(191\) | −19.1620 | −1.38652 | −0.693258 | − | 0.720689i | \(-0.743826\pi\) | ||||
−0.693258 | + | 0.720689i | \(0.743826\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.37070 | 0.458573 | 0.229286 | − | 0.973359i | \(-0.426361\pi\) | ||||
0.229286 | + | 0.973359i | \(0.426361\pi\) | |||||||
\(194\) | 0.583899 | 0.0419215 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.78107 | −0.127220 | ||||||||
\(197\) | 12.1752 | 0.867450 | 0.433725 | − | 0.901045i | \(-0.357199\pi\) | ||||
0.433725 | + | 0.901045i | \(0.357199\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.12984 | −0.0800919 | −0.0400459 | − | 0.999198i | \(-0.512750\pi\) | ||||
−0.0400459 | + | 0.999198i | \(0.512750\pi\) | |||||||
\(200\) | −19.5544 | −1.38270 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.05035 | 0.425701 | ||||||||
\(203\) | 19.0211 | 1.33502 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.82991 | −0.267492 | ||||||||
\(206\) | 14.6254 | 1.01900 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.12112 | −0.424423 | ||||||||
\(209\) | 20.0851 | 1.38932 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.7361 | 1.90943 | 0.954716 | − | 0.297520i | \(-0.0961596\pi\) | ||||
0.954716 | + | 0.297520i | \(0.0961596\pi\) | |||||||
\(212\) | 1.40702 | 0.0966345 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.844433 | −0.0577243 | ||||||||
\(215\) | −30.9681 | −2.11201 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.6258 | −1.19652 | ||||||||
\(218\) | 7.40697 | 0.501664 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.76762 | 0.254013 | ||||||||
\(221\) | 10.5779 | 0.711544 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.10518 | −0.609728 | −0.304864 | − | 0.952396i | \(-0.598611\pi\) | ||||
−0.304864 | + | 0.952396i | \(0.598611\pi\) | |||||||
\(224\) | −4.99316 | −0.333619 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.36134 | −0.423150 | ||||||||
\(227\) | −24.1258 | −1.60129 | −0.800644 | − | 0.599141i | \(-0.795509\pi\) | ||||
−0.800644 | + | 0.599141i | \(0.795509\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −29.6552 | −1.95967 | −0.979835 | − | 0.199809i | \(-0.935968\pi\) | ||||
−0.979835 | + | 0.199809i | \(0.935968\pi\) | |||||||
\(230\) | −19.3964 | −1.27896 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.7250 | 0.966744 | ||||||||
\(233\) | 5.36189 | 0.351269 | 0.175635 | − | 0.984455i | \(-0.443802\pi\) | ||||
0.175635 | + | 0.984455i | \(0.443802\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.4824 | −1.59706 | ||||||||
\(236\) | 0.315364 | 0.0205284 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −30.6876 | −1.98918 | ||||||||
\(239\) | −2.14131 | −0.138510 | −0.0692549 | − | 0.997599i | \(-0.522062\pi\) | ||||
−0.0692549 | + | 0.997599i | \(0.522062\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | 15.7719 | 1.01386 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.52723 | 0.161789 | ||||||||
\(245\) | 26.1947 | 1.67352 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.38170 | −0.469686 | ||||||||
\(248\) | −13.6449 | −0.866449 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.19572 | 0.455097 | ||||||||
\(251\) | 28.1462 | 1.77657 | 0.888285 | − | 0.459293i | \(-0.151897\pi\) | ||||
0.888285 | + | 0.459293i | \(0.151897\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.4843 | 1.28784 | ||||||||
\(254\) | −8.10699 | −0.508678 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.47806 | −0.342379 | ||||||||
\(257\) | −1.23067 | −0.0767674 | −0.0383837 | − | 0.999263i | \(-0.512221\pi\) | ||||
−0.0383837 | + | 0.999263i | \(0.512221\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 38.6423 | 2.40111 | ||||||||
\(260\) | −1.38468 | −0.0858741 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.94594 | 0.552682 | ||||||||
\(263\) | 15.0159 | 0.925919 | 0.462960 | − | 0.886379i | \(-0.346787\pi\) | ||||
0.462960 | + | 0.886379i | \(0.346787\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.6934 | −1.27118 | ||||||||
\(266\) | 21.4152 | 1.31305 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.28159 | −0.139370 | ||||||||
\(269\) | 0.940463 | 0.0573410 | 0.0286705 | − | 0.999589i | \(-0.490873\pi\) | ||||
0.0286705 | + | 0.999589i | \(0.490873\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.11230 | 0.310550 | 0.155275 | − | 0.987871i | \(-0.450374\pi\) | ||||
0.155275 | + | 0.987871i | \(0.450374\pi\) | |||||||
\(272\) | −20.9697 | −1.27148 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.2203 | 0.798665 | ||||||||
\(275\) | −31.5053 | −1.89984 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.39186 | 0.143713 | 0.0718565 | − | 0.997415i | \(-0.477108\pi\) | ||||
0.0718565 | + | 0.997415i | \(0.477108\pi\) | |||||||
\(278\) | 4.37036 | 0.262117 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 38.7263 | 2.31434 | ||||||||
\(281\) | −7.49067 | −0.446856 | −0.223428 | − | 0.974720i | \(-0.571725\pi\) | ||||
−0.223428 | + | 0.974720i | \(0.571725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.9408 | −1.06647 | −0.533235 | − | 0.845967i | \(-0.679024\pi\) | ||||
−0.533235 | + | 0.845967i | \(0.679024\pi\) | |||||||
\(284\) | 2.76686 | 0.164183 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.1728 | −0.660660 | ||||||||
\(287\) | 4.31256 | 0.254563 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.2376 | 1.13162 | ||||||||
\(290\) | −22.4644 | −1.31916 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.0376031 | 0.00220056 | ||||||||
\(293\) | −12.6436 | −0.738644 | −0.369322 | − | 0.929301i | \(-0.620410\pi\) | ||||
−0.369322 | + | 0.929301i | \(0.620410\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.63813 | −0.270042 | ||||||||
\(296\) | 29.9145 | 1.73875 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.5367 | −0.726233 | ||||||||
\(299\) | −7.52840 | −0.435379 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 34.8708 | 2.00992 | ||||||||
\(302\) | −3.12507 | −0.179828 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.6336 | 0.839293 | ||||||||
\(305\) | −37.1686 | −2.12827 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.93084 | 0.281418 | 0.140709 | − | 0.990051i | \(-0.455062\pi\) | ||||
0.140709 | + | 0.990051i | \(0.455062\pi\) | |||||||
\(308\) | −4.24243 | −0.241735 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 20.8165 | 1.18230 | ||||||||
\(311\) | −33.2247 | −1.88400 | −0.942001 | − | 0.335609i | \(-0.891058\pi\) | ||||
−0.942001 | + | 0.335609i | \(0.891058\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.2269 | 1.03024 | 0.515122 | − | 0.857117i | \(-0.327747\pi\) | ||||
0.515122 | + | 0.857117i | \(0.327747\pi\) | |||||||
\(314\) | 26.4197 | 1.49095 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.37422 | −0.189815 | ||||||||
\(317\) | −15.7434 | −0.884235 | −0.442117 | − | 0.896957i | \(-0.645773\pi\) | ||||
−0.442117 | + | 0.896957i | \(0.645773\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.7244 | 1.32831 | ||||||||
\(320\) | 29.6148 | 1.65552 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 21.8408 | 1.21714 | ||||||||
\(323\) | −25.2882 | −1.40707 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.5788 | 0.642279 | ||||||||
\(326\) | −2.79411 | −0.154751 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.33853 | 0.184339 | ||||||||
\(329\) | 27.5677 | 1.51986 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.35834 | −0.404451 | −0.202225 | − | 0.979339i | \(-0.564817\pi\) | ||||
−0.202225 | + | 0.979339i | \(0.564817\pi\) | |||||||
\(332\) | −1.33567 | −0.0733042 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −29.1355 | −1.59422 | ||||||||
\(335\) | 33.5559 | 1.83335 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.0122 | −1.14461 | −0.572303 | − | 0.820042i | \(-0.693950\pi\) | ||||
−0.572303 | + | 0.820042i | \(0.693950\pi\) | |||||||
\(338\) | −13.1820 | −0.717004 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.74363 | −0.257259 | ||||||||
\(341\) | −21.9841 | −1.19050 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.66238 | −0.143755 | ||||||||
\(344\) | 26.9949 | 1.45547 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.45697 | 0.400889 | ||||||||
\(347\) | 0.799138 | 0.0429000 | 0.0214500 | − | 0.999770i | \(-0.493172\pi\) | ||||
0.0214500 | + | 0.999770i | \(0.493172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.25641 | −0.0672542 | −0.0336271 | − | 0.999434i | \(-0.510706\pi\) | ||||
−0.0336271 | + | 0.999434i | \(0.510706\pi\) | |||||||
\(350\) | −33.5916 | −1.79555 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.22779 | −0.331942 | ||||||||
\(353\) | −30.7996 | −1.63930 | −0.819649 | − | 0.572865i | \(-0.805832\pi\) | ||||
−0.819649 | + | 0.572865i | \(0.805832\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −40.6928 | −2.15975 | ||||||||
\(356\) | 1.09632 | 0.0581048 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 31.6878 | 1.67475 | ||||||||
\(359\) | 14.3153 | 0.755535 | 0.377768 | − | 0.925900i | \(-0.376692\pi\) | ||||
0.377768 | + | 0.925900i | \(0.376692\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.35280 | −0.0712002 | ||||||||
\(362\) | 8.74825 | 0.459798 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.55918 | 0.0817232 | ||||||||
\(365\) | −0.553038 | −0.0289473 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.37048 | 0.175938 | 0.0879688 | − | 0.996123i | \(-0.471962\pi\) | ||||
0.0879688 | + | 0.996123i | \(0.471962\pi\) | |||||||
\(368\) | 14.9244 | 0.777989 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −45.6374 | −2.37258 | ||||||||
\(371\) | 23.3012 | 1.20974 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.72387 | 0.296371 | 0.148185 | − | 0.988960i | \(-0.452657\pi\) | ||||
0.148185 | + | 0.988960i | \(0.452657\pi\) | |||||||
\(374\) | −38.2756 | −1.97919 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 21.3413 | 1.10059 | ||||||||
\(377\) | −8.71920 | −0.449061 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.963739 | 0.0495040 | 0.0247520 | − | 0.999694i | \(-0.492120\pi\) | ||||
0.0247520 | + | 0.999694i | \(0.492120\pi\) | |||||||
\(380\) | 3.31031 | 0.169815 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −25.4828 | −1.30382 | ||||||||
\(383\) | −17.5403 | −0.896267 | −0.448134 | − | 0.893967i | \(-0.647911\pi\) | ||||
−0.448134 | + | 0.893967i | \(0.647911\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 62.3943 | 3.17991 | ||||||||
\(386\) | 8.47213 | 0.431220 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.101632 | −0.00515960 | ||||||||
\(389\) | 16.8395 | 0.853796 | 0.426898 | − | 0.904300i | \(-0.359606\pi\) | ||||
0.426898 | + | 0.904300i | \(0.359606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.7908 | −1.30429 | ||||||||
\(392\) | −22.8339 | −1.15328 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.1914 | 0.815709 | ||||||||
\(395\) | 49.6254 | 2.49693 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.82968 | −0.142017 | −0.0710087 | − | 0.997476i | \(-0.522622\pi\) | ||||
−0.0710087 | + | 0.997476i | \(0.522622\pi\) | |||||||
\(398\) | −1.50252 | −0.0753146 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −22.9541 | −1.14770 | ||||||||
\(401\) | 13.6028 | 0.679290 | 0.339645 | − | 0.940554i | \(-0.389693\pi\) | ||||
0.339645 | + | 0.940554i | \(0.389693\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.07960 | 0.402473 | ||||||||
\(404\) | −1.05311 | −0.0523943 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 25.2954 | 1.25539 | ||||||||
\(407\) | 48.1971 | 2.38904 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.6420 | 1.21847 | 0.609234 | − | 0.792990i | \(-0.291477\pi\) | ||||
0.609234 | + | 0.792990i | \(0.291477\pi\) | |||||||
\(410\) | −5.09324 | −0.251537 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.54567 | −0.125416 | ||||||||
\(413\) | 5.22264 | 0.256989 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.6439 | 0.964284 | ||||||||
\(416\) | 2.28884 | 0.112220 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 26.7104 | 1.30645 | ||||||||
\(419\) | 7.82622 | 0.382336 | 0.191168 | − | 0.981557i | \(-0.438772\pi\) | ||||
0.191168 | + | 0.981557i | \(0.438772\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.3683 | 1.04143 | 0.520715 | − | 0.853731i | \(-0.325666\pi\) | ||||
0.520715 | + | 0.853731i | \(0.325666\pi\) | |||||||
\(422\) | 36.8851 | 1.79554 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 18.0384 | 0.876021 | ||||||||
\(425\) | 39.6667 | 1.92412 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 41.8527 | 2.02539 | ||||||||
\(428\) | 0.146980 | 0.00710457 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −41.1832 | −1.98603 | ||||||||
\(431\) | −33.9239 | −1.63406 | −0.817028 | − | 0.576598i | \(-0.804380\pi\) | ||||
−0.817028 | + | 0.576598i | \(0.804380\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.5154 | 1.65871 | 0.829353 | − | 0.558725i | \(-0.188709\pi\) | ||||
0.829353 | + | 0.558725i | \(0.188709\pi\) | |||||||
\(434\) | −23.4399 | −1.12515 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.28924 | −0.0617435 | ||||||||
\(437\) | 17.9979 | 0.860957 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.28531 | 0.109072 | 0.0545360 | − | 0.998512i | \(-0.482632\pi\) | ||||
0.0545360 | + | 0.998512i | \(0.482632\pi\) | |||||||
\(440\) | 48.3020 | 2.30271 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.0671 | 0.669103 | ||||||||
\(443\) | −18.3736 | −0.872957 | −0.436478 | − | 0.899715i | \(-0.643774\pi\) | ||||
−0.436478 | + | 0.899715i | \(0.643774\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.1238 | −0.764342 | ||||||||
\(446\) | −12.1086 | −0.573360 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −33.3469 | −1.57549 | ||||||||
\(449\) | −26.0138 | −1.22767 | −0.613833 | − | 0.789436i | \(-0.710373\pi\) | ||||
−0.613833 | + | 0.789436i | \(0.710373\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.37891 | 0.253283 | ||||||||
\(452\) | 1.10724 | 0.0520803 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −32.0840 | −1.50578 | ||||||||
\(455\) | −22.9312 | −1.07503 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.10237 | 0.425791 | 0.212895 | − | 0.977075i | \(-0.431711\pi\) | ||||
0.212895 | + | 0.977075i | \(0.431711\pi\) | |||||||
\(458\) | −39.4372 | −1.84278 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.37610 | 0.157411 | ||||||||
\(461\) | −12.3824 | −0.576708 | −0.288354 | − | 0.957524i | \(-0.593108\pi\) | ||||
−0.288354 | + | 0.957524i | \(0.593108\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.3698 | 1.17904 | 0.589518 | − | 0.807755i | \(-0.299318\pi\) | ||||
0.589518 | + | 0.807755i | \(0.299318\pi\) | |||||||
\(464\) | 17.2851 | 0.802439 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.13057 | 0.330317 | ||||||||
\(467\) | 21.2025 | 0.981137 | 0.490568 | − | 0.871403i | \(-0.336789\pi\) | ||||
0.490568 | + | 0.871403i | \(0.336789\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −37.7847 | −1.74473 | ||||||||
\(470\) | −32.5582 | −1.50180 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.04306 | 0.186097 | ||||||||
\(473\) | 43.4931 | 1.99981 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.6812 | −1.27010 | ||||||||
\(476\) | 5.34143 | 0.244824 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.84764 | −0.130248 | ||||||||
\(479\) | 26.5866 | 1.21477 | 0.607385 | − | 0.794407i | \(-0.292218\pi\) | ||||
0.607385 | + | 0.794407i | \(0.292218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.7134 | −0.807663 | ||||||||
\(482\) | 1.32986 | 0.0605735 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.74523 | −0.124783 | ||||||||
\(485\) | 1.49473 | 0.0678721 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.1209 | −0.775822 | −0.387911 | − | 0.921697i | \(-0.626803\pi\) | ||||
−0.387911 | + | 0.921697i | \(0.626803\pi\) | |||||||
\(488\) | 32.3998 | 1.46667 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 34.8352 | 1.57370 | ||||||||
\(491\) | 5.11790 | 0.230968 | 0.115484 | − | 0.993309i | \(-0.463158\pi\) | ||||
0.115484 | + | 0.993309i | \(0.463158\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −29.8702 | −1.34529 | ||||||||
\(494\) | −9.81662 | −0.441671 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.0171 | −0.719189 | ||||||||
\(497\) | 45.8210 | 2.05535 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.2980 | 1.31156 | 0.655780 | − | 0.754952i | \(-0.272340\pi\) | ||||
0.655780 | + | 0.754952i | \(0.272340\pi\) | |||||||
\(500\) | −1.25247 | −0.0560122 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 37.4305 | 1.67060 | ||||||||
\(503\) | −12.8905 | −0.574761 | −0.287380 | − | 0.957817i | \(-0.592784\pi\) | ||||
−0.287380 | + | 0.957817i | \(0.592784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.4884 | 0.689223 | ||||||||
\(506\) | 27.2412 | 1.21102 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.41109 | 0.0626068 | ||||||||
\(509\) | 11.2706 | 0.499559 | 0.249780 | − | 0.968303i | \(-0.419642\pi\) | ||||
0.249780 | + | 0.968303i | \(0.419642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.622733 | 0.0275481 | ||||||||
\(512\) | −25.2122 | −1.11423 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.63662 | −0.0721884 | ||||||||
\(515\) | 37.4398 | 1.64980 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.3843 | 1.51222 | ||||||||
\(518\) | 51.3888 | 2.25789 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −17.7520 | −0.778475 | ||||||||
\(521\) | −41.5318 | −1.81954 | −0.909771 | − | 0.415110i | \(-0.863743\pi\) | ||||
−0.909771 | + | 0.415110i | \(0.863743\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.02470 | −0.350896 | −0.175448 | − | 0.984489i | \(-0.556137\pi\) | ||||
−0.175448 | + | 0.984489i | \(0.556137\pi\) | |||||||
\(524\) | −1.55711 | −0.0680228 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.9690 | 0.870691 | ||||||||
\(527\) | 27.6790 | 1.20572 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.64439 | −0.201930 | ||||||||
\(530\) | −27.5193 | −1.19536 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.72748 | −0.161607 | ||||||||
\(533\) | −1.97686 | −0.0856273 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.16167 | −0.0934573 | ||||||||
\(536\) | −29.2506 | −1.26344 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.25068 | 0.0539208 | ||||||||
\(539\) | −36.7891 | −1.58462 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.87706 | 0.424648 | 0.212324 | − | 0.977199i | \(-0.431897\pi\) | ||||
0.212324 | + | 0.977199i | \(0.431897\pi\) | |||||||
\(542\) | 6.79864 | 0.292027 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.84110 | 0.336184 | ||||||||
\(545\) | 18.9612 | 0.812208 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.3803 | 0.828641 | 0.414320 | − | 0.910131i | \(-0.364019\pi\) | ||||
0.414320 | + | 0.910131i | \(0.364019\pi\) | |||||||
\(548\) | −2.30109 | −0.0982978 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −41.8976 | −1.78652 | ||||||||
\(551\) | 20.8447 | 0.888015 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −55.8794 | −2.37623 | ||||||||
\(554\) | 3.18084 | 0.135141 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.760696 | −0.0322607 | ||||||||
\(557\) | 18.9414 | 0.802571 | 0.401285 | − | 0.915953i | \(-0.368564\pi\) | ||||
0.401285 | + | 0.915953i | \(0.368564\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.9846 | −0.676077 | ||||||||
\(560\) | 45.4592 | 1.92100 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.96154 | −0.420202 | ||||||||
\(563\) | −12.0839 | −0.509276 | −0.254638 | − | 0.967036i | \(-0.581956\pi\) | ||||
−0.254638 | + | 0.967036i | \(0.581956\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.2845 | −0.685093 | ||||||||
\(566\) | −23.8588 | −1.00286 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 35.4719 | 1.48837 | ||||||||
\(569\) | −8.80054 | −0.368938 | −0.184469 | − | 0.982838i | \(-0.559057\pi\) | ||||
−0.184469 | + | 0.982838i | \(0.559057\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.4541 | −1.48371 | −0.741854 | − | 0.670562i | \(-0.766053\pi\) | ||||
−0.741854 | + | 0.670562i | \(0.766053\pi\) | |||||||
\(572\) | 1.94471 | 0.0813124 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.73511 | 0.239379 | ||||||||
\(575\) | −28.2313 | −1.17733 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.5404 | −0.938368 | −0.469184 | − | 0.883100i | \(-0.655452\pi\) | ||||
−0.469184 | + | 0.883100i | \(0.655452\pi\) | |||||||
\(578\) | 25.5833 | 1.06413 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.91011 | 0.162358 | ||||||||
\(581\) | −22.1195 | −0.917673 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.0628 | 1.20366 | ||||||||
\(584\) | 0.482082 | 0.0199487 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.8142 | −0.694586 | ||||||||
\(587\) | −29.8831 | −1.23341 | −0.616704 | − | 0.787195i | \(-0.711533\pi\) | ||||
−0.616704 | + | 0.787195i | \(0.711533\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.3156 | −0.795887 | ||||||||
\(590\) | −6.16806 | −0.253935 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 35.1154 | 1.44323 | ||||||||
\(593\) | −30.9659 | −1.27162 | −0.635808 | − | 0.771847i | \(-0.719333\pi\) | ||||
−0.635808 | + | 0.771847i | \(0.719333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −78.5576 | −3.22055 | ||||||||
\(596\) | 2.18212 | 0.0893830 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.0117 | −0.409410 | ||||||||
\(599\) | 22.4899 | 0.918912 | 0.459456 | − | 0.888201i | \(-0.348044\pi\) | ||||
0.459456 | + | 0.888201i | \(0.348044\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.2188 | −0.906322 | −0.453161 | − | 0.891429i | \(-0.649704\pi\) | ||||
−0.453161 | + | 0.891429i | \(0.649704\pi\) | |||||||
\(602\) | 46.3732 | 1.89003 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.543944 | 0.0221328 | ||||||||
\(605\) | 40.3747 | 1.64147 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.3047 | 0.702378 | 0.351189 | − | 0.936305i | \(-0.385778\pi\) | ||||
0.351189 | + | 0.936305i | \(0.385778\pi\) | |||||||
\(608\) | −5.47186 | −0.221913 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −49.4290 | −2.00132 | ||||||||
\(611\) | −12.6369 | −0.511235 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.8909 | 0.561050 | 0.280525 | − | 0.959847i | \(-0.409491\pi\) | ||||
0.280525 | + | 0.959847i | \(0.409491\pi\) | |||||||
\(614\) | 6.55732 | 0.264632 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −54.3891 | −2.19140 | ||||||||
\(617\) | −47.6668 | −1.91899 | −0.959496 | − | 0.281722i | \(-0.909094\pi\) | ||||
−0.959496 | + | 0.281722i | \(0.909094\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.3518 | −1.46110 | −0.730551 | − | 0.682858i | \(-0.760737\pi\) | ||||
−0.730551 | + | 0.682858i | \(0.760737\pi\) | |||||||
\(620\) | −3.62328 | −0.145514 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −44.1843 | −1.77163 | ||||||||
\(623\) | 18.1558 | 0.727396 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.5267 | −0.581067 | ||||||||
\(626\) | 24.2392 | 0.968792 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.59857 | −0.183503 | ||||||||
\(629\) | −60.6826 | −2.41957 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.0906 | −1.67560 | −0.837801 | − | 0.545976i | \(-0.816159\pi\) | ||||
−0.837801 | + | 0.545976i | \(0.816159\pi\) | |||||||
\(632\) | −43.2585 | −1.72073 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.9365 | −0.831493 | ||||||||
\(635\) | −20.7532 | −0.823565 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.5207 | 0.535711 | ||||||||
\(638\) | 31.5501 | 1.24908 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 30.5149 | 1.20621 | ||||||||
\(641\) | −13.6204 | −0.537972 | −0.268986 | − | 0.963144i | \(-0.586689\pi\) | ||||
−0.268986 | + | 0.963144i | \(0.586689\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.5929 | −0.614925 | −0.307462 | − | 0.951560i | \(-0.599480\pi\) | ||||
−0.307462 | + | 0.951560i | \(0.599480\pi\) | |||||||
\(644\) | −3.80156 | −0.149803 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −33.6297 | −1.32314 | ||||||||
\(647\) | −30.8612 | −1.21328 | −0.606639 | − | 0.794977i | \(-0.707483\pi\) | ||||
−0.606639 | + | 0.794977i | \(0.707483\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.51402 | 0.255697 | ||||||||
\(650\) | 15.3982 | 0.603969 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.486336 | 0.0190464 | ||||||||
\(653\) | −41.4375 | −1.62157 | −0.810787 | − | 0.585342i | \(-0.800960\pi\) | ||||
−0.810787 | + | 0.585342i | \(0.800960\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.9008 | 0.894809 | ||||||||
\(656\) | 3.91896 | 0.153009 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 36.6612 | 1.42920 | ||||||||
\(659\) | 5.89065 | 0.229467 | 0.114733 | − | 0.993396i | \(-0.463399\pi\) | ||||
0.114733 | + | 0.993396i | \(0.463399\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.1895 | −0.474118 | −0.237059 | − | 0.971495i | \(-0.576184\pi\) | ||||
−0.237059 | + | 0.971495i | \(0.576184\pi\) | |||||||
\(662\) | −9.78556 | −0.380327 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17.1236 | −0.664525 | ||||||||
\(665\) | 54.8209 | 2.12586 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.2590 | 0.823151 | ||||||||
\(668\) | 5.07127 | 0.196213 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 44.6246 | 1.72400 | ||||||||
\(671\) | 52.2014 | 2.01521 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.4033 | −0.516658 | −0.258329 | − | 0.966057i | \(-0.583172\pi\) | ||||
−0.258329 | + | 0.966057i | \(0.583172\pi\) | |||||||
\(674\) | −27.9432 | −1.07633 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.29443 | 0.0882471 | ||||||||
\(677\) | 9.52226 | 0.365970 | 0.182985 | − | 0.983116i | \(-0.441424\pi\) | ||||
0.182985 | + | 0.983116i | \(0.441424\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.68310 | −0.0645914 | ||||||||
\(680\) | −60.8146 | −2.33213 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −29.2357 | −1.11949 | ||||||||
\(683\) | 4.11578 | 0.157486 | 0.0787429 | − | 0.996895i | \(-0.474909\pi\) | ||||
0.0787429 | + | 0.996895i | \(0.474909\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33.8427 | 1.29306 | ||||||||
\(686\) | −3.54059 | −0.135180 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 31.6881 | 1.20810 | ||||||||
\(689\) | −10.6812 | −0.406920 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.0627 | 1.48601 | 0.743007 | − | 0.669283i | \(-0.233399\pi\) | ||||
0.743007 | + | 0.669283i | \(0.233399\pi\) | |||||||
\(692\) | −1.29795 | −0.0493405 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.06274 | 0.0403411 | ||||||||
\(695\) | 11.1877 | 0.424375 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.77232 | −0.256520 | ||||||||
\(698\) | −1.67085 | −0.0632427 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.84689 | 0.220992 | ||||||||
\(701\) | −4.81641 | −0.181913 | −0.0909566 | − | 0.995855i | \(-0.528992\pi\) | ||||
−0.0909566 | + | 0.995855i | \(0.528992\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 42.3470 | 1.59715 | ||||||||
\(704\) | −41.5924 | −1.56757 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −40.9592 | −1.54152 | ||||||||
\(707\) | −17.4402 | −0.655908 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.1628 | 1.47079 | 0.735394 | − | 0.677640i | \(-0.236997\pi\) | ||||
0.735394 | + | 0.677640i | \(0.236997\pi\) | |||||||
\(710\) | −54.1157 | −2.03093 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.0551 | 0.526738 | ||||||||
\(713\) | −19.6995 | −0.737753 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.6013 | −1.06963 | ||||||||
\(716\) | −5.51552 | −0.206125 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.0374 | 0.710470 | ||||||||
\(719\) | 32.1852 | 1.20030 | 0.600152 | − | 0.799886i | \(-0.295107\pi\) | ||||
0.600152 | + | 0.799886i | \(0.295107\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.1581 | −1.57005 | ||||||||
\(722\) | −1.79904 | −0.0669533 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.52270 | −0.0565908 | ||||||||
\(725\) | −32.6968 | −1.21433 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.69429 | −0.0628377 | −0.0314188 | − | 0.999506i | \(-0.510003\pi\) | ||||
−0.0314188 | + | 0.999506i | \(0.510003\pi\) | |||||||
\(728\) | 19.9891 | 0.740846 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.735462 | −0.0272207 | ||||||||
\(731\) | −54.7600 | −2.02537 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.2300 | 0.673340 | 0.336670 | − | 0.941623i | \(-0.390699\pi\) | ||||
0.336670 | + | 0.941623i | \(0.390699\pi\) | |||||||
\(734\) | 4.48226 | 0.165443 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.58061 | −0.205704 | ||||||||
\(737\) | −47.1275 | −1.73596 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.4675 | −0.458623 | −0.229312 | − | 0.973353i | \(-0.573648\pi\) | ||||
−0.229312 | + | 0.973353i | \(0.573648\pi\) | |||||||
\(740\) | 7.94356 | 0.292011 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 30.9873 | 1.13758 | ||||||||
\(743\) | 15.6839 | 0.575385 | 0.287693 | − | 0.957723i | \(-0.407112\pi\) | ||||
0.287693 | + | 0.957723i | \(0.407112\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.0929 | −1.17579 | ||||||||
\(746\) | 7.61194 | 0.278693 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.66218 | 0.243593 | ||||||||
\(749\) | 2.43409 | 0.0889399 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.58156 | −0.130693 | −0.0653465 | − | 0.997863i | \(-0.520815\pi\) | ||||
−0.0653465 | + | 0.997863i | \(0.520815\pi\) | |||||||
\(752\) | 25.0516 | 0.913539 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11.5953 | −0.422276 | ||||||||
\(755\) | −7.99990 | −0.291146 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.7026 | −0.570720 | −0.285360 | − | 0.958420i | \(-0.592113\pi\) | ||||
−0.285360 | + | 0.958420i | \(0.592113\pi\) | |||||||
\(758\) | 1.28164 | 0.0465512 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 42.4391 | 1.53943 | ||||||||
\(761\) | 36.1137 | 1.30912 | 0.654559 | − | 0.756011i | \(-0.272854\pi\) | ||||
0.654559 | + | 0.756011i | \(0.272854\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.3507 | −0.772948 | ||||||||
\(764\) | 4.43549 | 0.160470 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.3261 | −0.842807 | ||||||||
\(767\) | −2.39403 | −0.0864436 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −50.2736 | −1.81291 | −0.906456 | − | 0.422300i | \(-0.861223\pi\) | ||||
−0.906456 | + | 0.422300i | \(0.861223\pi\) | |||||||
\(770\) | 82.9757 | 2.99024 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.47464 | −0.0530736 | ||||||||
\(773\) | 27.4904 | 0.988762 | 0.494381 | − | 0.869245i | \(-0.335395\pi\) | ||||
0.494381 | + | 0.869245i | \(0.335395\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.2983 | 1.08835 | ||||||||
\(776\) | −1.30295 | −0.0467733 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.3942 | 0.802870 | ||||||||
\(779\) | 4.72602 | 0.169327 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 57.1509 | 2.04502 | ||||||||
\(782\) | −34.2981 | −1.22650 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −26.8037 | −0.957275 | ||||||||
\(785\) | 67.6322 | 2.41390 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.4981 | 1.55054 | 0.775271 | − | 0.631629i | \(-0.217614\pi\) | ||||
0.775271 | + | 0.631629i | \(0.217614\pi\) | |||||||
\(788\) | −2.81824 | −0.100396 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 65.9949 | 2.34799 | ||||||||
\(791\) | 18.3367 | 0.651977 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.1851 | −0.681282 | ||||||||
\(794\) | −3.76307 | −0.133547 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.261526 | 0.00926955 | ||||||||
\(797\) | −38.2429 | −1.35463 | −0.677316 | − | 0.735692i | \(-0.736857\pi\) | ||||
−0.677316 | + | 0.735692i | \(0.736857\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.2915 | −1.53154 | ||||||||
\(800\) | 8.58310 | 0.303458 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.0898 | 0.638772 | ||||||||
\(803\) | 0.776713 | 0.0274096 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 55.9105 | 1.97058 | ||||||||
\(806\) | 10.7447 | 0.378467 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.5012 | −0.474970 | ||||||||
\(809\) | 28.3274 | 0.995939 | 0.497969 | − | 0.867195i | \(-0.334079\pi\) | ||||
0.497969 | + | 0.867195i | \(0.334079\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.3902 | −1.38318 | −0.691589 | − | 0.722292i | \(-0.743089\pi\) | ||||
−0.691589 | + | 0.722292i | \(0.743089\pi\) | |||||||
\(812\) | −4.40287 | −0.154510 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 64.0954 | 2.24654 | ||||||||
\(815\) | −7.15266 | −0.250547 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38.2139 | 1.33694 | ||||||||
\(818\) | 32.7704 | 1.14579 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.886519 | 0.0309586 | ||||||||
\(821\) | −39.6673 | −1.38440 | −0.692199 | − | 0.721707i | \(-0.743358\pi\) | ||||
−0.692199 | + | 0.721707i | \(0.743358\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.49313 | −0.330910 | −0.165455 | − | 0.986217i | \(-0.552909\pi\) | ||||
−0.165455 | + | 0.986217i | \(0.552909\pi\) | |||||||
\(824\) | −32.6363 | −1.13694 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.94538 | 0.241661 | ||||||||
\(827\) | 8.26358 | 0.287353 | 0.143676 | − | 0.989625i | \(-0.454108\pi\) | ||||
0.143676 | + | 0.989625i | \(0.454108\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.7576 | −1.13772 | −0.568860 | − | 0.822435i | \(-0.692615\pi\) | ||||
−0.568860 | + | 0.822435i | \(0.692615\pi\) | |||||||
\(830\) | 26.1237 | 0.906767 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 15.2861 | 0.529949 | ||||||||
\(833\) | 46.3193 | 1.60487 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −74.5843 | −2.58110 | ||||||||
\(836\) | −4.64916 | −0.160795 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.4078 | 0.359531 | ||||||||
\(839\) | −28.8263 | −0.995195 | −0.497597 | − | 0.867408i | \(-0.665784\pi\) | ||||
−0.497597 | + | 0.867408i | \(0.665784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.37839 | −0.150979 | ||||||||
\(842\) | 28.4169 | 0.979311 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.42015 | −0.220991 | ||||||||
\(845\) | −33.7446 | −1.16085 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −45.4629 | −1.56212 | ||||||||
\(848\) | 21.1745 | 0.727135 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 52.7512 | 1.80935 | ||||||||
\(851\) | 43.1886 | 1.48049 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.74141 | 0.0596248 | 0.0298124 | − | 0.999556i | \(-0.490509\pi\) | ||||
0.0298124 | + | 0.999556i | \(0.490509\pi\) | |||||||
\(854\) | 55.6582 | 1.90458 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.88433 | 0.0644051 | ||||||||
\(857\) | 23.6164 | 0.806720 | 0.403360 | − | 0.915041i | \(-0.367842\pi\) | ||||
0.403360 | + | 0.915041i | \(0.367842\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.0458 | 0.615714 | 0.307857 | − | 0.951433i | \(-0.400388\pi\) | ||||
0.307857 | + | 0.951433i | \(0.400388\pi\) | |||||||
\(860\) | 7.16827 | 0.244436 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −45.1140 | −1.53659 | ||||||||
\(863\) | −8.06392 | −0.274499 | −0.137249 | − | 0.990537i | \(-0.543826\pi\) | ||||
−0.137249 | + | 0.990537i | \(0.543826\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.0892 | 0.649052 | ||||||||
\(866\) | 45.9007 | 1.55977 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.07990 | 0.138481 | ||||||||
\(869\) | −69.6964 | −2.36429 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.3203 | 0.586877 | ||||||||
\(872\) | −16.5285 | −0.559724 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 23.9347 | 0.809604 | ||||||||
\(875\) | −20.7418 | −0.701200 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.4702 | −0.488625 | −0.244312 | − | 0.969697i | \(-0.578562\pi\) | ||||
−0.244312 | + | 0.969697i | \(0.578562\pi\) | |||||||
\(878\) | 3.03914 | 0.102566 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 56.6996 | 1.91134 | ||||||||
\(881\) | −10.0284 | −0.337867 | −0.168933 | − | 0.985627i | \(-0.554032\pi\) | ||||
−0.168933 | + | 0.985627i | \(0.554032\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.730440 | 0.0245813 | 0.0122906 | − | 0.999924i | \(-0.496088\pi\) | ||||
0.0122906 | + | 0.999924i | \(0.496088\pi\) | |||||||
\(884\) | −2.44849 | −0.0823515 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.4343 | −0.820887 | ||||||||
\(887\) | 29.6147 | 0.994366 | 0.497183 | − | 0.867646i | \(-0.334368\pi\) | ||||
0.497183 | + | 0.867646i | \(0.334368\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.3685 | 0.783756 | ||||||||
\(890\) | −21.4424 | −0.718752 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.10760 | 0.0705677 | ||||||||
\(893\) | 30.2107 | 1.01096 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 81.1180 | 2.71148 | ||||||||
\(896\) | −34.3604 | −1.14790 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −34.5947 | −1.15444 | ||||||||
\(899\) | −22.8155 | −0.760939 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.5915 | −1.21904 | ||||||||
\(902\) | 7.15320 | 0.238175 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.1952 | 0.472124 | ||||||||
\(905\) | 22.3947 | 0.744426 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.96710 | −0.131725 | −0.0658627 | − | 0.997829i | \(-0.520980\pi\) | ||||
−0.0658627 | + | 0.997829i | \(0.520980\pi\) | |||||||
\(908\) | 5.58447 | 0.185327 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −30.4953 | −1.01091 | ||||||||
\(911\) | −25.8759 | −0.857307 | −0.428653 | − | 0.903469i | \(-0.641012\pi\) | ||||
−0.428653 | + | 0.903469i | \(0.641012\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.5889 | −0.913060 | ||||||||
\(914\) | 12.1049 | 0.400394 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.86437 | 0.226805 | ||||||||
\(917\) | −25.7868 | −0.851556 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.5327 | 0.545364 | 0.272682 | − | 0.962104i | \(-0.412089\pi\) | ||||
0.272682 | + | 0.962104i | \(0.412089\pi\) | |||||||
\(920\) | 43.2825 | 1.42698 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.4669 | −0.542309 | ||||||||
\(923\) | −21.0041 | −0.691360 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −66.4250 | −2.18404 | ||||||||
\(926\) | 33.7383 | 1.10871 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.46332 | −0.212169 | ||||||||
\(929\) | 1.50189 | 0.0492755 | 0.0246378 | − | 0.999696i | \(-0.492157\pi\) | ||||
0.0246378 | + | 0.999696i | \(0.492157\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.3236 | −1.05936 | ||||||||
\(932\) | −1.24113 | −0.0406546 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28.1964 | 0.922615 | ||||||||
\(935\) | −97.9822 | −3.20436 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.04782 | −0.262911 | −0.131455 | − | 0.991322i | \(-0.541965\pi\) | ||||
−0.131455 | + | 0.991322i | \(0.541965\pi\) | |||||||
\(938\) | −50.2483 | −1.64067 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.66701 | 0.184837 | ||||||||
\(941\) | 2.66537 | 0.0868887 | 0.0434443 | − | 0.999056i | \(-0.486167\pi\) | ||||
0.0434443 | + | 0.999056i | \(0.486167\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.81995 | 0.156959 | ||||||||
\(944\) | 4.74597 | 0.154468 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 57.8397 | 1.88053 | ||||||||
\(947\) | −39.0257 | −1.26816 | −0.634082 | − | 0.773266i | \(-0.718622\pi\) | ||||
−0.634082 | + | 0.773266i | \(0.718622\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.285458 | −0.00926636 | ||||||||
\(950\) | −36.8121 | −1.19434 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 68.4786 | 2.21941 | ||||||||
\(953\) | 40.4838 | 1.31140 | 0.655700 | − | 0.755022i | \(-0.272374\pi\) | ||||
0.655700 | + | 0.755022i | \(0.272374\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −65.2338 | −2.11092 | ||||||||
\(956\) | 0.495655 | 0.0160306 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 35.3564 | 1.14231 | ||||||||
\(959\) | −38.1076 | −1.23056 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.85816 | −0.318005 | ||||||||
\(962\) | −23.5564 | −0.759489 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.231473 | −0.00745524 | ||||||||
\(965\) | 21.6879 | 0.698159 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.3391 | 0.847009 | 0.423504 | − | 0.905894i | \(-0.360800\pi\) | ||||
0.423504 | + | 0.905894i | \(0.360800\pi\) | |||||||
\(968\) | −35.1946 | −1.13120 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.98778 | 0.0638238 | ||||||||
\(971\) | 9.17879 | 0.294561 | 0.147281 | − | 0.989095i | \(-0.452948\pi\) | ||||
0.147281 | + | 0.989095i | \(0.452948\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.5976 | −0.403862 | ||||||||
\(974\) | −22.7684 | −0.729546 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 38.0328 | 1.21740 | ||||||||
\(977\) | 27.6516 | 0.884653 | 0.442326 | − | 0.896854i | \(-0.354153\pi\) | ||||
0.442326 | + | 0.896854i | \(0.354153\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.6451 | 0.723740 | ||||||||
\(980\) | −6.06335 | −0.193687 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.80610 | 0.217191 | ||||||||
\(983\) | 27.0845 | 0.863861 | 0.431930 | − | 0.901907i | \(-0.357833\pi\) | ||||
0.431930 | + | 0.901907i | \(0.357833\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.4485 | 1.32066 | ||||||||
\(986\) | −39.7232 | −1.26504 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.70866 | 0.0543598 | ||||||||
\(989\) | 38.9734 | 1.23928 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.0027 | −1.30249 | −0.651246 | − | 0.758867i | \(-0.725753\pi\) | ||||
−0.651246 | + | 0.758867i | \(0.725753\pi\) | |||||||
\(992\) | 5.98920 | 0.190157 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 60.9355 | 1.93276 | ||||||||
\(995\) | −3.84632 | −0.121937 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.9223 | −1.20101 | −0.600505 | − | 0.799621i | \(-0.705034\pi\) | ||||
−0.600505 | + | 0.799621i | \(0.705034\pi\) | |||||||
\(998\) | 38.9623 | 1.23333 | ||||||||
\(999\) | 0 | 0 |
(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 | 2169.2.a.h.1.10 | 12 | ||
3.2 | odd | 2 | 241.2.a.b.1.3 | ✓ | 12 | ||
12.11 | even | 2 | 3856.2.a.n.1.10 | 12 | |||
15.14 | odd | 2 | 6025.2.a.h.1.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
241.2.a.b.1.3 | ✓ | 12 | 3.2 | odd | 2 | ||
2169.2.a.h.1.10 | 12 | 1.1 | even | 1 | trivial | ||
3856.2.a.n.1.10 | 12 | 12.11 | even | 2 | |||
6025.2.a.h.1.10 | 12 | 15.14 | odd | 2 |