Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, 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("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 27 x^{18} + 52 x^{17} + 302 x^{16} - 552 x^{15} - 1820 x^{14} + 3090 x^{13} + \cdots + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Root | \(-2.51950\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.51950 | 1.78156 | 0.890779 | − | 0.454436i | \(-0.150159\pi\) | ||||
0.890779 | + | 0.454436i | \(0.150159\pi\) | |||||||
\(3\) | 2.78497 | 1.60790 | 0.803951 | − | 0.594696i | \(-0.202728\pi\) | ||||
0.803951 | + | 0.594696i | \(0.202728\pi\) | |||||||
\(4\) | 4.34790 | 2.17395 | ||||||||
\(5\) | 1.47804 | 0.660998 | 0.330499 | − | 0.943806i | \(-0.392783\pi\) | ||||
0.330499 | + | 0.943806i | \(0.392783\pi\) | |||||||
\(6\) | 7.01674 | 2.86457 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 5.91555 | 2.09146 | ||||||||
\(9\) | 4.75604 | 1.58535 | ||||||||
\(10\) | 3.72392 | 1.17761 | ||||||||
\(11\) | −4.83604 | −1.45812 | −0.729060 | − | 0.684450i | \(-0.760043\pi\) | ||||
−0.729060 | + | 0.684450i | \(0.760043\pi\) | |||||||
\(12\) | 12.1088 | 3.49550 | ||||||||
\(13\) | −4.02077 | −1.11516 | −0.557581 | − | 0.830123i | \(-0.688270\pi\) | ||||
−0.557581 | + | 0.830123i | \(0.688270\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.11628 | 1.06282 | ||||||||
\(16\) | 6.20845 | 1.55211 | ||||||||
\(17\) | −2.82150 | −0.684314 | −0.342157 | − | 0.939643i | \(-0.611157\pi\) | ||||
−0.342157 | + | 0.939643i | \(0.611157\pi\) | |||||||
\(18\) | 11.9829 | 2.82439 | ||||||||
\(19\) | 4.32444 | 0.992096 | 0.496048 | − | 0.868295i | \(-0.334784\pi\) | ||||
0.496048 | + | 0.868295i | \(0.334784\pi\) | |||||||
\(20\) | 6.42636 | 1.43698 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −12.1844 | −2.59773 | ||||||||
\(23\) | −7.27952 | −1.51788 | −0.758942 | − | 0.651158i | \(-0.774283\pi\) | ||||
−0.758942 | + | 0.651158i | \(0.774283\pi\) | |||||||
\(24\) | 16.4746 | 3.36287 | ||||||||
\(25\) | −2.81541 | −0.563082 | ||||||||
\(26\) | −10.1304 | −1.98673 | ||||||||
\(27\) | 4.89052 | 0.941180 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.18920 | 1.33500 | 0.667500 | − | 0.744609i | \(-0.267364\pi\) | ||||
0.667500 | + | 0.744609i | \(0.267364\pi\) | |||||||
\(30\) | 10.3710 | 1.89347 | ||||||||
\(31\) | 7.03562 | 1.26363 | 0.631817 | − | 0.775118i | \(-0.282309\pi\) | ||||
0.631817 | + | 0.775118i | \(0.282309\pi\) | |||||||
\(32\) | 3.81112 | 0.673718 | ||||||||
\(33\) | −13.4682 | −2.34451 | ||||||||
\(34\) | −7.10877 | −1.21914 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 20.6788 | 3.44647 | ||||||||
\(37\) | −8.74950 | −1.43841 | −0.719204 | − | 0.694799i | \(-0.755493\pi\) | ||||
−0.719204 | + | 0.694799i | \(0.755493\pi\) | |||||||
\(38\) | 10.8955 | 1.76748 | ||||||||
\(39\) | −11.1977 | −1.79307 | ||||||||
\(40\) | 8.74340 | 1.38245 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.174038 | 0.0265406 | 0.0132703 | − | 0.999912i | \(-0.495776\pi\) | ||||
0.0132703 | + | 0.999912i | \(0.495776\pi\) | |||||||
\(44\) | −21.0266 | −3.16988 | ||||||||
\(45\) | 7.02960 | 1.04791 | ||||||||
\(46\) | −18.3408 | −2.70420 | ||||||||
\(47\) | 5.63943 | 0.822595 | 0.411298 | − | 0.911501i | \(-0.365076\pi\) | ||||
0.411298 | + | 0.911501i | \(0.365076\pi\) | |||||||
\(48\) | 17.2903 | 2.49565 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.09344 | −1.00316 | ||||||||
\(51\) | −7.85778 | −1.10031 | ||||||||
\(52\) | −17.4819 | −2.42431 | ||||||||
\(53\) | 7.57218 | 1.04012 | 0.520059 | − | 0.854130i | \(-0.325910\pi\) | ||||
0.520059 | + | 0.854130i | \(0.325910\pi\) | |||||||
\(54\) | 12.3217 | 1.67677 | ||||||||
\(55\) | −7.14784 | −0.963814 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.0434 | 1.59519 | ||||||||
\(58\) | 18.1132 | 2.37838 | ||||||||
\(59\) | 3.13471 | 0.408105 | 0.204052 | − | 0.978960i | \(-0.434589\pi\) | ||||
0.204052 | + | 0.978960i | \(0.434589\pi\) | |||||||
\(60\) | 17.8972 | 2.31052 | ||||||||
\(61\) | 4.21867 | 0.540145 | 0.270073 | − | 0.962840i | \(-0.412952\pi\) | ||||
0.270073 | + | 0.962840i | \(0.412952\pi\) | |||||||
\(62\) | 17.7263 | 2.25124 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.81477 | −0.351846 | ||||||||
\(65\) | −5.94285 | −0.737119 | ||||||||
\(66\) | −33.9332 | −4.17689 | ||||||||
\(67\) | −8.79107 | −1.07400 | −0.537000 | − | 0.843582i | \(-0.680442\pi\) | ||||
−0.537000 | + | 0.843582i | \(0.680442\pi\) | |||||||
\(68\) | −12.2676 | −1.48766 | ||||||||
\(69\) | −20.2732 | −2.44061 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.6811 | −1.62365 | −0.811824 | − | 0.583902i | \(-0.801525\pi\) | ||||
−0.811824 | + | 0.583902i | \(0.801525\pi\) | |||||||
\(72\) | 28.1346 | 3.31570 | ||||||||
\(73\) | 2.46761 | 0.288811 | 0.144406 | − | 0.989519i | \(-0.453873\pi\) | ||||
0.144406 | + | 0.989519i | \(0.453873\pi\) | |||||||
\(74\) | −22.0444 | −2.56261 | ||||||||
\(75\) | −7.84083 | −0.905381 | ||||||||
\(76\) | 18.8023 | 2.15677 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −28.2127 | −3.19446 | ||||||||
\(79\) | 16.3988 | 1.84500 | 0.922502 | − | 0.385992i | \(-0.126141\pi\) | ||||
0.922502 | + | 0.385992i | \(0.126141\pi\) | |||||||
\(80\) | 9.17631 | 1.02594 | ||||||||
\(81\) | −0.648197 | −0.0720219 | ||||||||
\(82\) | 2.51950 | 0.278233 | ||||||||
\(83\) | 6.42502 | 0.705238 | 0.352619 | − | 0.935767i | \(-0.385291\pi\) | ||||
0.352619 | + | 0.935767i | \(0.385291\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.17027 | −0.452330 | ||||||||
\(86\) | 0.438490 | 0.0472836 | ||||||||
\(87\) | 20.0217 | 2.14655 | ||||||||
\(88\) | −28.6078 | −3.04960 | ||||||||
\(89\) | 11.4841 | 1.21731 | 0.608655 | − | 0.793435i | \(-0.291709\pi\) | ||||
0.608655 | + | 0.793435i | \(0.291709\pi\) | |||||||
\(90\) | 17.7111 | 1.86691 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −31.6506 | −3.29981 | ||||||||
\(93\) | 19.5940 | 2.03180 | ||||||||
\(94\) | 14.2086 | 1.46550 | ||||||||
\(95\) | 6.39168 | 0.655773 | ||||||||
\(96\) | 10.6138 | 1.08327 | ||||||||
\(97\) | 15.7940 | 1.60364 | 0.801820 | − | 0.597566i | \(-0.203865\pi\) | ||||
0.801820 | + | 0.597566i | \(0.203865\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −23.0004 | −2.31163 | ||||||||
\(100\) | −12.2411 | −1.22411 | ||||||||
\(101\) | −18.0266 | −1.79371 | −0.896856 | − | 0.442322i | \(-0.854155\pi\) | ||||
−0.896856 | + | 0.442322i | \(0.854155\pi\) | |||||||
\(102\) | −19.7977 | −1.96026 | ||||||||
\(103\) | −6.37036 | −0.627691 | −0.313845 | − | 0.949474i | \(-0.601617\pi\) | ||||
−0.313845 | + | 0.949474i | \(0.601617\pi\) | |||||||
\(104\) | −23.7851 | −2.33232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 19.0781 | 1.85303 | ||||||||
\(107\) | 4.47397 | 0.432515 | 0.216257 | − | 0.976336i | \(-0.430615\pi\) | ||||
0.216257 | + | 0.976336i | \(0.430615\pi\) | |||||||
\(108\) | 21.2635 | 2.04608 | ||||||||
\(109\) | 5.49312 | 0.526145 | 0.263073 | − | 0.964776i | \(-0.415264\pi\) | ||||
0.263073 | + | 0.964776i | \(0.415264\pi\) | |||||||
\(110\) | −18.0090 | −1.71709 | ||||||||
\(111\) | −24.3671 | −2.31282 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.20891 | −0.395941 | −0.197970 | − | 0.980208i | \(-0.563435\pi\) | ||||
−0.197970 | + | 0.980208i | \(0.563435\pi\) | |||||||
\(114\) | 30.3435 | 2.84193 | ||||||||
\(115\) | −10.7594 | −1.00332 | ||||||||
\(116\) | 31.2579 | 2.90223 | ||||||||
\(117\) | −19.1230 | −1.76792 | ||||||||
\(118\) | 7.89792 | 0.727063 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 24.3501 | 2.22285 | ||||||||
\(121\) | 12.3873 | 1.12611 | ||||||||
\(122\) | 10.6290 | 0.962301 | ||||||||
\(123\) | 2.78497 | 0.251112 | ||||||||
\(124\) | 30.5902 | 2.74708 | ||||||||
\(125\) | −11.5515 | −1.03319 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.78035 | −0.601658 | −0.300829 | − | 0.953678i | \(-0.597263\pi\) | ||||
−0.300829 | + | 0.953678i | \(0.597263\pi\) | |||||||
\(128\) | −14.7141 | −1.30055 | ||||||||
\(129\) | 0.484691 | 0.0426747 | ||||||||
\(130\) | −14.9730 | −1.31322 | ||||||||
\(131\) | −10.3439 | −0.903752 | −0.451876 | − | 0.892081i | \(-0.649245\pi\) | ||||
−0.451876 | + | 0.892081i | \(0.649245\pi\) | |||||||
\(132\) | −58.5584 | −5.09686 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −22.1491 | −1.91339 | ||||||||
\(135\) | 7.22836 | 0.622118 | ||||||||
\(136\) | −16.6907 | −1.43122 | ||||||||
\(137\) | 5.30605 | 0.453327 | 0.226663 | − | 0.973973i | \(-0.427218\pi\) | ||||
0.226663 | + | 0.973973i | \(0.427218\pi\) | |||||||
\(138\) | −51.0784 | −4.34809 | ||||||||
\(139\) | −0.682588 | −0.0578963 | −0.0289482 | − | 0.999581i | \(-0.509216\pi\) | ||||
−0.0289482 | + | 0.999581i | \(0.509216\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.7056 | 1.32265 | ||||||||
\(142\) | −34.4696 | −2.89263 | ||||||||
\(143\) | 19.4446 | 1.62604 | ||||||||
\(144\) | 29.5277 | 2.46064 | ||||||||
\(145\) | 10.6259 | 0.882432 | ||||||||
\(146\) | 6.21714 | 0.514535 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −38.0420 | −3.12703 | ||||||||
\(149\) | 12.3279 | 1.00994 | 0.504971 | − | 0.863137i | \(-0.331503\pi\) | ||||
0.504971 | + | 0.863137i | \(0.331503\pi\) | |||||||
\(150\) | −19.7550 | −1.61299 | ||||||||
\(151\) | 14.6635 | 1.19330 | 0.596648 | − | 0.802503i | \(-0.296499\pi\) | ||||
0.596648 | + | 0.802503i | \(0.296499\pi\) | |||||||
\(152\) | 25.5815 | 2.07493 | ||||||||
\(153\) | −13.4192 | −1.08487 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.3989 | 0.835259 | ||||||||
\(156\) | −48.6866 | −3.89805 | ||||||||
\(157\) | 7.47508 | 0.596577 | 0.298288 | − | 0.954476i | \(-0.403584\pi\) | ||||
0.298288 | + | 0.954476i | \(0.403584\pi\) | |||||||
\(158\) | 41.3167 | 3.28698 | ||||||||
\(159\) | 21.0883 | 1.67241 | ||||||||
\(160\) | 5.63297 | 0.445326 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.63314 | −0.128311 | ||||||||
\(163\) | 15.2168 | 1.19187 | 0.595935 | − | 0.803033i | \(-0.296782\pi\) | ||||
0.595935 | + | 0.803033i | \(0.296782\pi\) | |||||||
\(164\) | 4.34790 | 0.339514 | ||||||||
\(165\) | −19.9065 | −1.54972 | ||||||||
\(166\) | 16.1879 | 1.25642 | ||||||||
\(167\) | −19.9981 | −1.54750 | −0.773749 | − | 0.633492i | \(-0.781621\pi\) | ||||
−0.773749 | + | 0.633492i | \(0.781621\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.16662 | 0.243586 | ||||||||
\(170\) | −10.5070 | −0.805852 | ||||||||
\(171\) | 20.5672 | 1.57282 | ||||||||
\(172\) | 0.756702 | 0.0576980 | ||||||||
\(173\) | 7.22448 | 0.549267 | 0.274633 | − | 0.961549i | \(-0.411443\pi\) | ||||
0.274633 | + | 0.961549i | \(0.411443\pi\) | |||||||
\(174\) | 50.4447 | 3.82420 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −30.0243 | −2.26317 | ||||||||
\(177\) | 8.73007 | 0.656192 | ||||||||
\(178\) | 28.9342 | 2.16871 | ||||||||
\(179\) | 18.2822 | 1.36648 | 0.683239 | − | 0.730194i | \(-0.260571\pi\) | ||||
0.683239 | + | 0.730194i | \(0.260571\pi\) | |||||||
\(180\) | 30.5640 | 2.27811 | ||||||||
\(181\) | 6.10150 | 0.453521 | 0.226761 | − | 0.973951i | \(-0.427186\pi\) | ||||
0.226761 | + | 0.973951i | \(0.427186\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.7489 | 0.868500 | ||||||||
\(184\) | −43.0624 | −3.17460 | ||||||||
\(185\) | −12.9321 | −0.950785 | ||||||||
\(186\) | 49.3671 | 3.61977 | ||||||||
\(187\) | 13.6449 | 0.997812 | ||||||||
\(188\) | 24.5197 | 1.78828 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.1039 | 1.16830 | ||||||||
\(191\) | 7.22078 | 0.522477 | 0.261239 | − | 0.965274i | \(-0.415869\pi\) | ||||
0.261239 | + | 0.965274i | \(0.415869\pi\) | |||||||
\(192\) | −7.83903 | −0.565734 | ||||||||
\(193\) | −18.4620 | −1.32892 | −0.664461 | − | 0.747323i | \(-0.731339\pi\) | ||||
−0.664461 | + | 0.747323i | \(0.731339\pi\) | |||||||
\(194\) | 39.7931 | 2.85698 | ||||||||
\(195\) | −16.5506 | −1.18522 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.35764 | −0.595457 | −0.297728 | − | 0.954651i | \(-0.596229\pi\) | ||||
−0.297728 | + | 0.954651i | \(0.596229\pi\) | |||||||
\(198\) | −57.9496 | −4.11830 | ||||||||
\(199\) | 27.6030 | 1.95673 | 0.978363 | − | 0.206894i | \(-0.0663356\pi\) | ||||
0.978363 | + | 0.206894i | \(0.0663356\pi\) | |||||||
\(200\) | −16.6547 | −1.17767 | ||||||||
\(201\) | −24.4828 | −1.72689 | ||||||||
\(202\) | −45.4181 | −3.19560 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −34.1648 | −2.39202 | ||||||||
\(205\) | 1.47804 | 0.103230 | ||||||||
\(206\) | −16.0502 | −1.11827 | ||||||||
\(207\) | −34.6217 | −2.40637 | ||||||||
\(208\) | −24.9628 | −1.73086 | ||||||||
\(209\) | −20.9132 | −1.44659 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.43107 | 0.305047 | 0.152524 | − | 0.988300i | \(-0.451260\pi\) | ||||
0.152524 | + | 0.988300i | \(0.451260\pi\) | |||||||
\(212\) | 32.9231 | 2.26117 | ||||||||
\(213\) | −38.1014 | −2.61067 | ||||||||
\(214\) | 11.2722 | 0.770550 | ||||||||
\(215\) | 0.257235 | 0.0175433 | ||||||||
\(216\) | 28.9301 | 1.96844 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 13.8399 | 0.937358 | ||||||||
\(219\) | 6.87220 | 0.464380 | ||||||||
\(220\) | −31.0781 | −2.09528 | ||||||||
\(221\) | 11.3446 | 0.763121 | ||||||||
\(222\) | −61.3929 | −4.12042 | ||||||||
\(223\) | −27.9961 | −1.87476 | −0.937378 | − | 0.348315i | \(-0.886754\pi\) | ||||
−0.937378 | + | 0.348315i | \(0.886754\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.3902 | −0.892681 | ||||||||
\(226\) | −10.6044 | −0.705392 | ||||||||
\(227\) | −10.7502 | −0.713515 | −0.356757 | − | 0.934197i | \(-0.616118\pi\) | ||||
−0.356757 | + | 0.934197i | \(0.616118\pi\) | |||||||
\(228\) | 52.3637 | 3.46787 | ||||||||
\(229\) | 14.0857 | 0.930812 | 0.465406 | − | 0.885097i | \(-0.345908\pi\) | ||||
0.465406 | + | 0.885097i | \(0.345908\pi\) | |||||||
\(230\) | −27.1083 | −1.78747 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 42.5281 | 2.79211 | ||||||||
\(233\) | 6.86735 | 0.449895 | 0.224948 | − | 0.974371i | \(-0.427779\pi\) | ||||
0.224948 | + | 0.974371i | \(0.427779\pi\) | |||||||
\(234\) | −48.1804 | −3.14965 | ||||||||
\(235\) | 8.33528 | 0.543733 | ||||||||
\(236\) | 13.6294 | 0.887200 | ||||||||
\(237\) | 45.6700 | 2.96658 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.467300 | 0.0302271 | 0.0151136 | − | 0.999886i | \(-0.495189\pi\) | ||||
0.0151136 | + | 0.999886i | \(0.495189\pi\) | |||||||
\(240\) | 25.5557 | 1.64962 | ||||||||
\(241\) | −13.9496 | −0.898574 | −0.449287 | − | 0.893387i | \(-0.648322\pi\) | ||||
−0.449287 | + | 0.893387i | \(0.648322\pi\) | |||||||
\(242\) | 31.2098 | 2.00624 | ||||||||
\(243\) | −16.4768 | −1.05698 | ||||||||
\(244\) | 18.3424 | 1.17425 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.01674 | 0.447371 | ||||||||
\(247\) | −17.3876 | −1.10635 | ||||||||
\(248\) | 41.6196 | 2.64284 | ||||||||
\(249\) | 17.8935 | 1.13395 | ||||||||
\(250\) | −29.1039 | −1.84070 | ||||||||
\(251\) | 19.8529 | 1.25311 | 0.626553 | − | 0.779379i | \(-0.284465\pi\) | ||||
0.626553 | + | 0.779379i | \(0.284465\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 35.2040 | 2.21326 | ||||||||
\(254\) | −17.0831 | −1.07189 | ||||||||
\(255\) | −11.6141 | −0.727302 | ||||||||
\(256\) | −31.4426 | −1.96516 | ||||||||
\(257\) | −24.3571 | −1.51935 | −0.759677 | − | 0.650301i | \(-0.774643\pi\) | ||||
−0.759677 | + | 0.650301i | \(0.774643\pi\) | |||||||
\(258\) | 1.22118 | 0.0760274 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −25.8389 | −1.60246 | ||||||||
\(261\) | 34.1921 | 2.11644 | ||||||||
\(262\) | −26.0615 | −1.61009 | ||||||||
\(263\) | −16.4878 | −1.01668 | −0.508341 | − | 0.861156i | \(-0.669741\pi\) | ||||
−0.508341 | + | 0.861156i | \(0.669741\pi\) | |||||||
\(264\) | −79.6719 | −4.90346 | ||||||||
\(265\) | 11.1919 | 0.687516 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 31.9828 | 1.95732 | ||||||||
\(268\) | −38.2227 | −2.33482 | ||||||||
\(269\) | 9.69457 | 0.591088 | 0.295544 | − | 0.955329i | \(-0.404499\pi\) | ||||
0.295544 | + | 0.955329i | \(0.404499\pi\) | |||||||
\(270\) | 18.2119 | 1.10834 | ||||||||
\(271\) | 14.2386 | 0.864933 | 0.432467 | − | 0.901650i | \(-0.357643\pi\) | ||||
0.432467 | + | 0.901650i | \(0.357643\pi\) | |||||||
\(272\) | −17.5171 | −1.06213 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.3686 | 0.807628 | ||||||||
\(275\) | 13.6154 | 0.821041 | ||||||||
\(276\) | −88.1460 | −5.30576 | ||||||||
\(277\) | −15.4775 | −0.929950 | −0.464975 | − | 0.885324i | \(-0.653937\pi\) | ||||
−0.464975 | + | 0.885324i | \(0.653937\pi\) | |||||||
\(278\) | −1.71978 | −0.103146 | ||||||||
\(279\) | 33.4617 | 2.00330 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.5644 | −1.70401 | −0.852005 | − | 0.523534i | \(-0.824613\pi\) | ||||
−0.852005 | + | 0.523534i | \(0.824613\pi\) | |||||||
\(282\) | 39.5704 | 2.35638 | ||||||||
\(283\) | −21.5025 | −1.27819 | −0.639094 | − | 0.769128i | \(-0.720691\pi\) | ||||
−0.639094 | + | 0.769128i | \(0.720691\pi\) | |||||||
\(284\) | −59.4841 | −3.52973 | ||||||||
\(285\) | 17.8006 | 1.05442 | ||||||||
\(286\) | 48.9908 | 2.89689 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 18.1259 | 1.06808 | ||||||||
\(289\) | −9.03915 | −0.531715 | ||||||||
\(290\) | 26.7720 | 1.57210 | ||||||||
\(291\) | 43.9858 | 2.57849 | ||||||||
\(292\) | 10.7289 | 0.627862 | ||||||||
\(293\) | −2.33534 | −0.136432 | −0.0682159 | − | 0.997671i | \(-0.521731\pi\) | ||||
−0.0682159 | + | 0.997671i | \(0.521731\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.63322 | 0.269756 | ||||||||
\(296\) | −51.7581 | −3.00838 | ||||||||
\(297\) | −23.6507 | −1.37235 | ||||||||
\(298\) | 31.0602 | 1.79927 | ||||||||
\(299\) | 29.2693 | 1.69269 | ||||||||
\(300\) | −34.0911 | −1.96825 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 36.9447 | 2.12593 | ||||||||
\(303\) | −50.2034 | −2.88411 | ||||||||
\(304\) | 26.8481 | 1.53984 | ||||||||
\(305\) | 6.23534 | 0.357035 | ||||||||
\(306\) | −33.8096 | −1.93277 | ||||||||
\(307\) | −16.6878 | −0.952422 | −0.476211 | − | 0.879331i | \(-0.657990\pi\) | ||||
−0.476211 | + | 0.879331i | \(0.657990\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.7413 | −1.00926 | ||||||||
\(310\) | 26.2001 | 1.48806 | ||||||||
\(311\) | −2.12955 | −0.120756 | −0.0603779 | − | 0.998176i | \(-0.519231\pi\) | ||||
−0.0603779 | + | 0.998176i | \(0.519231\pi\) | |||||||
\(312\) | −66.2407 | −3.75014 | ||||||||
\(313\) | 31.5460 | 1.78309 | 0.891544 | − | 0.452935i | \(-0.149623\pi\) | ||||
0.891544 | + | 0.452935i | \(0.149623\pi\) | |||||||
\(314\) | 18.8335 | 1.06284 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 71.3002 | 4.01095 | ||||||||
\(317\) | −9.04710 | −0.508136 | −0.254068 | − | 0.967186i | \(-0.581769\pi\) | ||||
−0.254068 | + | 0.967186i | \(0.581769\pi\) | |||||||
\(318\) | 53.1320 | 2.97949 | ||||||||
\(319\) | −34.7672 | −1.94659 | ||||||||
\(320\) | −4.16033 | −0.232569 | ||||||||
\(321\) | 12.4598 | 0.695441 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.2014 | −0.678904 | ||||||||
\(324\) | −2.81830 | −0.156572 | ||||||||
\(325\) | 11.3201 | 0.627928 | ||||||||
\(326\) | 38.3387 | 2.12339 | ||||||||
\(327\) | 15.2981 | 0.845989 | ||||||||
\(328\) | 5.91555 | 0.326632 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −50.1545 | −2.76091 | ||||||||
\(331\) | 6.04330 | 0.332170 | 0.166085 | − | 0.986111i | \(-0.446887\pi\) | ||||
0.166085 | + | 0.986111i | \(0.446887\pi\) | |||||||
\(332\) | 27.9354 | 1.53315 | ||||||||
\(333\) | −41.6130 | −2.28038 | ||||||||
\(334\) | −50.3853 | −2.75696 | ||||||||
\(335\) | −12.9935 | −0.709911 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4122 | −0.621661 | −0.310830 | − | 0.950465i | \(-0.600607\pi\) | ||||
−0.310830 | + | 0.950465i | \(0.600607\pi\) | |||||||
\(338\) | 7.97832 | 0.433963 | ||||||||
\(339\) | −11.7217 | −0.636634 | ||||||||
\(340\) | −18.1319 | −0.983343 | ||||||||
\(341\) | −34.0245 | −1.84253 | ||||||||
\(342\) | 51.8192 | 2.80206 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.02953 | 0.0555087 | ||||||||
\(345\) | −29.9645 | −1.61324 | ||||||||
\(346\) | 18.2021 | 0.978551 | ||||||||
\(347\) | 25.2610 | 1.35608 | 0.678040 | − | 0.735025i | \(-0.262829\pi\) | ||||
0.678040 | + | 0.735025i | \(0.262829\pi\) | |||||||
\(348\) | 87.0523 | 4.66649 | ||||||||
\(349\) | −22.0231 | −1.17887 | −0.589434 | − | 0.807816i | \(-0.700649\pi\) | ||||
−0.589434 | + | 0.807816i | \(0.700649\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.6637 | −1.04957 | ||||||||
\(352\) | −18.4307 | −0.982361 | ||||||||
\(353\) | 0.376661 | 0.0200476 | 0.0100238 | − | 0.999950i | \(-0.496809\pi\) | ||||
0.0100238 | + | 0.999950i | \(0.496809\pi\) | |||||||
\(354\) | 21.9954 | 1.16904 | ||||||||
\(355\) | −20.2212 | −1.07323 | ||||||||
\(356\) | 49.9317 | 2.64637 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 46.0622 | 2.43446 | ||||||||
\(359\) | 27.7277 | 1.46341 | 0.731705 | − | 0.681622i | \(-0.238725\pi\) | ||||
0.731705 | + | 0.681622i | \(0.238725\pi\) | |||||||
\(360\) | 41.5839 | 2.19167 | ||||||||
\(361\) | −0.299182 | −0.0157464 | ||||||||
\(362\) | 15.3728 | 0.807975 | ||||||||
\(363\) | 34.4981 | 1.81068 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.64721 | 0.190904 | ||||||||
\(366\) | 29.6013 | 1.54728 | ||||||||
\(367\) | 15.1846 | 0.792627 | 0.396314 | − | 0.918115i | \(-0.370289\pi\) | ||||
0.396314 | + | 0.918115i | \(0.370289\pi\) | |||||||
\(368\) | −45.1945 | −2.35593 | ||||||||
\(369\) | 4.75604 | 0.247590 | ||||||||
\(370\) | −32.5824 | −1.69388 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 85.1926 | 4.41703 | ||||||||
\(373\) | 9.65905 | 0.500127 | 0.250063 | − | 0.968229i | \(-0.419549\pi\) | ||||
0.250063 | + | 0.968229i | \(0.419549\pi\) | |||||||
\(374\) | 34.3783 | 1.77766 | ||||||||
\(375\) | −32.1704 | −1.66127 | ||||||||
\(376\) | 33.3603 | 1.72043 | ||||||||
\(377\) | −28.9061 | −1.48874 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.8484 | −0.916811 | −0.458406 | − | 0.888743i | \(-0.651579\pi\) | ||||
−0.458406 | + | 0.888743i | \(0.651579\pi\) | |||||||
\(380\) | 27.7904 | 1.42562 | ||||||||
\(381\) | −18.8830 | −0.967407 | ||||||||
\(382\) | 18.1928 | 0.930824 | ||||||||
\(383\) | −3.32996 | −0.170153 | −0.0850765 | − | 0.996374i | \(-0.527113\pi\) | ||||
−0.0850765 | + | 0.996374i | \(0.527113\pi\) | |||||||
\(384\) | −40.9782 | −2.09116 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −46.5150 | −2.36755 | ||||||||
\(387\) | 0.827733 | 0.0420761 | ||||||||
\(388\) | 68.6709 | 3.48624 | ||||||||
\(389\) | 15.6783 | 0.794920 | 0.397460 | − | 0.917620i | \(-0.369892\pi\) | ||||
0.397460 | + | 0.917620i | \(0.369892\pi\) | |||||||
\(390\) | −41.6994 | −2.11153 | ||||||||
\(391\) | 20.5391 | 1.03871 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −28.8075 | −1.45314 | ||||||||
\(394\) | −21.0571 | −1.06084 | ||||||||
\(395\) | 24.2379 | 1.21954 | ||||||||
\(396\) | −100.003 | −5.02536 | ||||||||
\(397\) | −3.32922 | −0.167089 | −0.0835444 | − | 0.996504i | \(-0.526624\pi\) | ||||
−0.0835444 | + | 0.996504i | \(0.526624\pi\) | |||||||
\(398\) | 69.5459 | 3.48602 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.4793 | −0.873967 | ||||||||
\(401\) | 7.17799 | 0.358451 | 0.179226 | − | 0.983808i | \(-0.442641\pi\) | ||||
0.179226 | + | 0.983808i | \(0.442641\pi\) | |||||||
\(402\) | −61.6846 | −3.07655 | ||||||||
\(403\) | −28.2886 | −1.40916 | ||||||||
\(404\) | −78.3778 | −3.89944 | ||||||||
\(405\) | −0.958058 | −0.0476063 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 42.3129 | 2.09737 | ||||||||
\(408\) | −46.4831 | −2.30126 | ||||||||
\(409\) | 9.00790 | 0.445412 | 0.222706 | − | 0.974886i | \(-0.428511\pi\) | ||||
0.222706 | + | 0.974886i | \(0.428511\pi\) | |||||||
\(410\) | 3.72392 | 0.183911 | ||||||||
\(411\) | 14.7772 | 0.728905 | ||||||||
\(412\) | −27.6977 | −1.36457 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −87.2295 | −4.28709 | ||||||||
\(415\) | 9.49641 | 0.466161 | ||||||||
\(416\) | −15.3237 | −0.751304 | ||||||||
\(417\) | −1.90098 | −0.0930916 | ||||||||
\(418\) | −52.6908 | −2.57719 | ||||||||
\(419\) | −3.35984 | −0.164139 | −0.0820694 | − | 0.996627i | \(-0.526153\pi\) | ||||
−0.0820694 | + | 0.996627i | \(0.526153\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.6716 | −1.83600 | −0.918001 | − | 0.396578i | \(-0.870198\pi\) | ||||
−0.918001 | + | 0.396578i | \(0.870198\pi\) | |||||||
\(422\) | 11.1641 | 0.543460 | ||||||||
\(423\) | 26.8214 | 1.30410 | ||||||||
\(424\) | 44.7936 | 2.17537 | ||||||||
\(425\) | 7.94367 | 0.385325 | ||||||||
\(426\) | −95.9967 | −4.65106 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 19.4524 | 0.940266 | ||||||||
\(429\) | 54.1526 | 2.61451 | ||||||||
\(430\) | 0.648104 | 0.0312544 | ||||||||
\(431\) | 12.2998 | 0.592458 | 0.296229 | − | 0.955117i | \(-0.404271\pi\) | ||||
0.296229 | + | 0.955117i | \(0.404271\pi\) | |||||||
\(432\) | 30.3625 | 1.46082 | ||||||||
\(433\) | 0.961159 | 0.0461904 | 0.0230952 | − | 0.999733i | \(-0.492648\pi\) | ||||
0.0230952 | + | 0.999733i | \(0.492648\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 29.5928 | 1.41886 | ||||||||
\(436\) | 23.8835 | 1.14381 | ||||||||
\(437\) | −31.4799 | −1.50589 | ||||||||
\(438\) | 17.3145 | 0.827321 | ||||||||
\(439\) | 17.2056 | 0.821180 | 0.410590 | − | 0.911820i | \(-0.365323\pi\) | ||||
0.410590 | + | 0.911820i | \(0.365323\pi\) | |||||||
\(440\) | −42.2834 | −2.01578 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 28.5828 | 1.35954 | ||||||||
\(443\) | −33.4729 | −1.59035 | −0.795173 | − | 0.606383i | \(-0.792620\pi\) | ||||
−0.795173 | + | 0.606383i | \(0.792620\pi\) | |||||||
\(444\) | −105.946 | −5.02796 | ||||||||
\(445\) | 16.9739 | 0.804640 | ||||||||
\(446\) | −70.5362 | −3.33999 | ||||||||
\(447\) | 34.3328 | 1.62389 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.12640 | −0.194737 | −0.0973685 | − | 0.995248i | \(-0.531043\pi\) | ||||
−0.0973685 | + | 0.995248i | \(0.531043\pi\) | |||||||
\(450\) | −33.7367 | −1.59036 | ||||||||
\(451\) | −4.83604 | −0.227720 | ||||||||
\(452\) | −18.2999 | −0.860756 | ||||||||
\(453\) | 40.8373 | 1.91870 | ||||||||
\(454\) | −27.0851 | −1.27117 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 71.2436 | 3.33629 | ||||||||
\(457\) | 16.2146 | 0.758486 | 0.379243 | − | 0.925297i | \(-0.376184\pi\) | ||||
0.379243 | + | 0.925297i | \(0.376184\pi\) | |||||||
\(458\) | 35.4891 | 1.65830 | ||||||||
\(459\) | −13.7986 | −0.644062 | ||||||||
\(460\) | −46.7808 | −2.18116 | ||||||||
\(461\) | −6.50231 | −0.302843 | −0.151421 | − | 0.988469i | \(-0.548385\pi\) | ||||
−0.151421 | + | 0.988469i | \(0.548385\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.28120 | 0.291912 | 0.145956 | − | 0.989291i | \(-0.453374\pi\) | ||||
0.145956 | + | 0.989291i | \(0.453374\pi\) | |||||||
\(464\) | 44.6338 | 2.07207 | ||||||||
\(465\) | 28.9606 | 1.34301 | ||||||||
\(466\) | 17.3023 | 0.801515 | ||||||||
\(467\) | −32.3281 | −1.49597 | −0.747984 | − | 0.663717i | \(-0.768978\pi\) | ||||
−0.747984 | + | 0.663717i | \(0.768978\pi\) | |||||||
\(468\) | −83.1448 | −3.84337 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 21.0008 | 0.968693 | ||||||||
\(471\) | 20.8179 | 0.959236 | ||||||||
\(472\) | 18.5436 | 0.853536 | ||||||||
\(473\) | −0.841656 | −0.0386994 | ||||||||
\(474\) | 115.066 | 5.28514 | ||||||||
\(475\) | −12.1751 | −0.558631 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 36.0136 | 1.64895 | ||||||||
\(478\) | 1.17736 | 0.0538514 | ||||||||
\(479\) | −6.20951 | −0.283720 | −0.141860 | − | 0.989887i | \(-0.545308\pi\) | ||||
−0.141860 | + | 0.989887i | \(0.545308\pi\) | |||||||
\(480\) | 15.6876 | 0.716040 | ||||||||
\(481\) | 35.1798 | 1.60406 | ||||||||
\(482\) | −35.1461 | −1.60086 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 53.8586 | 2.44812 | ||||||||
\(485\) | 23.3441 | 1.06000 | ||||||||
\(486\) | −41.5133 | −1.88308 | ||||||||
\(487\) | −4.60588 | −0.208712 | −0.104356 | − | 0.994540i | \(-0.533278\pi\) | ||||
−0.104356 | + | 0.994540i | \(0.533278\pi\) | |||||||
\(488\) | 24.9558 | 1.12969 | ||||||||
\(489\) | 42.3782 | 1.91641 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.1445 | −1.22501 | −0.612507 | − | 0.790465i | \(-0.709839\pi\) | ||||
−0.612507 | + | 0.790465i | \(0.709839\pi\) | |||||||
\(492\) | 12.1088 | 0.545905 | ||||||||
\(493\) | −20.2843 | −0.913559 | ||||||||
\(494\) | −43.8082 | −1.97102 | ||||||||
\(495\) | −33.9954 | −1.52798 | ||||||||
\(496\) | 43.6803 | 1.96130 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 45.0827 | 2.02020 | ||||||||
\(499\) | −31.1462 | −1.39430 | −0.697148 | − | 0.716927i | \(-0.745548\pi\) | ||||
−0.697148 | + | 0.716927i | \(0.745548\pi\) | |||||||
\(500\) | −50.2246 | −2.24611 | ||||||||
\(501\) | −55.6940 | −2.48822 | ||||||||
\(502\) | 50.0195 | 2.23248 | ||||||||
\(503\) | 2.38608 | 0.106390 | 0.0531949 | − | 0.998584i | \(-0.483060\pi\) | ||||
0.0531949 | + | 0.998584i | \(0.483060\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.6439 | −1.18564 | ||||||||
\(506\) | 88.6967 | 3.94305 | ||||||||
\(507\) | 8.81894 | 0.391663 | ||||||||
\(508\) | −29.4803 | −1.30798 | ||||||||
\(509\) | 5.11092 | 0.226538 | 0.113269 | − | 0.993564i | \(-0.463868\pi\) | ||||
0.113269 | + | 0.993564i | \(0.463868\pi\) | |||||||
\(510\) | −29.2617 | −1.29573 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −49.7917 | −2.20050 | ||||||||
\(513\) | 21.1488 | 0.933741 | ||||||||
\(514\) | −61.3678 | −2.70682 | ||||||||
\(515\) | −9.41562 | −0.414902 | ||||||||
\(516\) | 2.10739 | 0.0927726 | ||||||||
\(517\) | −27.2725 | −1.19944 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.1199 | 0.883167 | ||||||||
\(520\) | −35.1552 | −1.54166 | ||||||||
\(521\) | −11.9410 | −0.523145 | −0.261573 | − | 0.965184i | \(-0.584241\pi\) | ||||
−0.261573 | + | 0.965184i | \(0.584241\pi\) | |||||||
\(522\) | 86.1472 | 3.77056 | ||||||||
\(523\) | −14.1037 | −0.616710 | −0.308355 | − | 0.951271i | \(-0.599778\pi\) | ||||
−0.308355 | + | 0.951271i | \(0.599778\pi\) | |||||||
\(524\) | −44.9743 | −1.96471 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −41.5411 | −1.81128 | ||||||||
\(527\) | −19.8510 | −0.864722 | ||||||||
\(528\) | −83.6167 | −3.63895 | ||||||||
\(529\) | 29.9914 | 1.30397 | ||||||||
\(530\) | 28.1982 | 1.22485 | ||||||||
\(531\) | 14.9088 | 0.646988 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.02077 | −0.174159 | ||||||||
\(534\) | 80.5808 | 3.48707 | ||||||||
\(535\) | 6.61268 | 0.285891 | ||||||||
\(536\) | −52.0040 | −2.24623 | ||||||||
\(537\) | 50.9154 | 2.19716 | ||||||||
\(538\) | 24.4255 | 1.05306 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 31.4282 | 1.35245 | ||||||||
\(541\) | 2.06663 | 0.0888512 | 0.0444256 | − | 0.999013i | \(-0.485854\pi\) | ||||
0.0444256 | + | 0.999013i | \(0.485854\pi\) | |||||||
\(542\) | 35.8742 | 1.54093 | ||||||||
\(543\) | 16.9925 | 0.729217 | ||||||||
\(544\) | −10.7531 | −0.461034 | ||||||||
\(545\) | 8.11902 | 0.347781 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.6533 | 0.712043 | 0.356022 | − | 0.934478i | \(-0.384133\pi\) | ||||
0.356022 | + | 0.934478i | \(0.384133\pi\) | |||||||
\(548\) | 23.0702 | 0.985510 | ||||||||
\(549\) | 20.0642 | 0.856318 | ||||||||
\(550\) | 34.3041 | 1.46273 | ||||||||
\(551\) | 31.0893 | 1.32445 | ||||||||
\(552\) | −119.927 | −5.10444 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −38.9955 | −1.65676 | ||||||||
\(555\) | −36.0154 | −1.52877 | ||||||||
\(556\) | −2.96782 | −0.125864 | ||||||||
\(557\) | −12.1868 | −0.516373 | −0.258187 | − | 0.966095i | \(-0.583125\pi\) | ||||
−0.258187 | + | 0.966095i | \(0.583125\pi\) | |||||||
\(558\) | 84.3069 | 3.56899 | ||||||||
\(559\) | −0.699769 | −0.0295971 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 38.0005 | 1.60438 | ||||||||
\(562\) | −71.9681 | −3.03579 | ||||||||
\(563\) | 22.8469 | 0.962882 | 0.481441 | − | 0.876479i | \(-0.340114\pi\) | ||||
0.481441 | + | 0.876479i | \(0.340114\pi\) | |||||||
\(564\) | 68.2865 | 2.87538 | ||||||||
\(565\) | −6.22092 | −0.261716 | ||||||||
\(566\) | −54.1755 | −2.27717 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −80.9313 | −3.39580 | ||||||||
\(569\) | −22.9419 | −0.961773 | −0.480886 | − | 0.876783i | \(-0.659685\pi\) | ||||
−0.480886 | + | 0.876783i | \(0.659685\pi\) | |||||||
\(570\) | 44.8488 | 1.87851 | ||||||||
\(571\) | −6.21311 | −0.260010 | −0.130005 | − | 0.991513i | \(-0.541499\pi\) | ||||
−0.130005 | + | 0.991513i | \(0.541499\pi\) | |||||||
\(572\) | 84.5433 | 3.53493 | ||||||||
\(573\) | 20.1096 | 0.840092 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.4948 | 0.854693 | ||||||||
\(576\) | −13.3871 | −0.557798 | ||||||||
\(577\) | 9.46737 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(578\) | −22.7742 | −0.947281 | ||||||||
\(579\) | −51.4160 | −2.13678 | ||||||||
\(580\) | 46.2003 | 1.91836 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 110.822 | 4.59374 | ||||||||
\(583\) | −36.6193 | −1.51662 | ||||||||
\(584\) | 14.5972 | 0.604038 | ||||||||
\(585\) | −28.2644 | −1.16859 | ||||||||
\(586\) | −5.88389 | −0.243061 | ||||||||
\(587\) | 5.16741 | 0.213282 | 0.106641 | − | 0.994298i | \(-0.465990\pi\) | ||||
0.106641 | + | 0.994298i | \(0.465990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.4251 | 1.25365 | ||||||||
\(590\) | 11.6734 | 0.480587 | ||||||||
\(591\) | −23.2757 | −0.957436 | ||||||||
\(592\) | −54.3209 | −2.23257 | ||||||||
\(593\) | −45.0942 | −1.85180 | −0.925898 | − | 0.377774i | \(-0.876690\pi\) | ||||
−0.925898 | + | 0.377774i | \(0.876690\pi\) | |||||||
\(594\) | −59.5881 | −2.44493 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 53.6005 | 2.19556 | ||||||||
\(597\) | 76.8735 | 3.14622 | ||||||||
\(598\) | 73.7441 | 3.01562 | ||||||||
\(599\) | 26.7653 | 1.09360 | 0.546801 | − | 0.837263i | \(-0.315846\pi\) | ||||
0.546801 | + | 0.837263i | \(0.315846\pi\) | |||||||
\(600\) | −46.3828 | −1.89357 | ||||||||
\(601\) | 30.9277 | 1.26157 | 0.630784 | − | 0.775958i | \(-0.282733\pi\) | ||||
0.630784 | + | 0.775958i | \(0.282733\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −41.8107 | −1.70266 | ||||||||
\(604\) | 63.7553 | 2.59417 | ||||||||
\(605\) | 18.3088 | 0.744359 | ||||||||
\(606\) | −126.488 | −5.13822 | ||||||||
\(607\) | −0.361880 | −0.0146883 | −0.00734413 | − | 0.999973i | \(-0.502338\pi\) | ||||
−0.00734413 | + | 0.999973i | \(0.502338\pi\) | |||||||
\(608\) | 16.4810 | 0.668392 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.7100 | 0.636078 | ||||||||
\(611\) | −22.6749 | −0.917327 | ||||||||
\(612\) | −58.3452 | −2.35846 | ||||||||
\(613\) | 23.4574 | 0.947436 | 0.473718 | − | 0.880677i | \(-0.342912\pi\) | ||||
0.473718 | + | 0.880677i | \(0.342912\pi\) | |||||||
\(614\) | −42.0449 | −1.69680 | ||||||||
\(615\) | 4.11628 | 0.165984 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.7266 | 0.834421 | 0.417211 | − | 0.908810i | \(-0.363008\pi\) | ||||
0.417211 | + | 0.908810i | \(0.363008\pi\) | |||||||
\(618\) | −44.6992 | −1.79806 | ||||||||
\(619\) | 15.5058 | 0.623230 | 0.311615 | − | 0.950209i | \(-0.399130\pi\) | ||||
0.311615 | + | 0.950209i | \(0.399130\pi\) | |||||||
\(620\) | 45.2134 | 1.81581 | ||||||||
\(621\) | −35.6006 | −1.42860 | ||||||||
\(622\) | −5.36542 | −0.215134 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −69.5205 | −2.78305 | ||||||||
\(625\) | −2.99641 | −0.119856 | ||||||||
\(626\) | 79.4804 | 3.17667 | ||||||||
\(627\) | −58.2425 | −2.32598 | ||||||||
\(628\) | 32.5009 | 1.29693 | ||||||||
\(629\) | 24.6867 | 0.984323 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.91913 | −0.394874 | −0.197437 | − | 0.980316i | \(-0.563262\pi\) | ||||
−0.197437 | + | 0.980316i | \(0.563262\pi\) | |||||||
\(632\) | 97.0077 | 3.85876 | ||||||||
\(633\) | 12.3404 | 0.490486 | ||||||||
\(634\) | −22.7942 | −0.905274 | ||||||||
\(635\) | −10.0216 | −0.397695 | ||||||||
\(636\) | 91.6897 | 3.63573 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −87.5962 | −3.46797 | ||||||||
\(639\) | −65.0679 | −2.57405 | ||||||||
\(640\) | −21.7479 | −0.859662 | ||||||||
\(641\) | −29.2989 | −1.15724 | −0.578619 | − | 0.815598i | \(-0.696408\pi\) | ||||
−0.578619 | + | 0.815598i | \(0.696408\pi\) | |||||||
\(642\) | 31.3926 | 1.23897 | ||||||||
\(643\) | −15.7181 | −0.619860 | −0.309930 | − | 0.950759i | \(-0.600306\pi\) | ||||
−0.309930 | + | 0.950759i | \(0.600306\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.716390 | 0.0282078 | ||||||||
\(646\) | −30.7415 | −1.20951 | ||||||||
\(647\) | 10.7783 | 0.423738 | 0.211869 | − | 0.977298i | \(-0.432045\pi\) | ||||
0.211869 | + | 0.977298i | \(0.432045\pi\) | |||||||
\(648\) | −3.83444 | −0.150631 | ||||||||
\(649\) | −15.1596 | −0.595066 | ||||||||
\(650\) | 28.5211 | 1.11869 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 66.1611 | 2.59107 | ||||||||
\(653\) | −6.82326 | −0.267015 | −0.133507 | − | 0.991048i | \(-0.542624\pi\) | ||||
−0.133507 | + | 0.991048i | \(0.542624\pi\) | |||||||
\(654\) | 38.5437 | 1.50718 | ||||||||
\(655\) | −15.2887 | −0.597378 | ||||||||
\(656\) | 6.20845 | 0.242399 | ||||||||
\(657\) | 11.7360 | 0.457866 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.9112 | 1.24309 | 0.621543 | − | 0.783380i | \(-0.286506\pi\) | ||||
0.621543 | + | 0.783380i | \(0.286506\pi\) | |||||||
\(660\) | −86.5515 | −3.36901 | ||||||||
\(661\) | 11.6275 | 0.452256 | 0.226128 | − | 0.974098i | \(-0.427393\pi\) | ||||
0.226128 | + | 0.974098i | \(0.427393\pi\) | |||||||
\(662\) | 15.2261 | 0.591780 | ||||||||
\(663\) | 31.5943 | 1.22702 | ||||||||
\(664\) | 38.0076 | 1.47498 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −104.844 | −4.06263 | ||||||||
\(667\) | −52.3339 | −2.02638 | ||||||||
\(668\) | −86.9497 | −3.36419 | ||||||||
\(669\) | −77.9681 | −3.01442 | ||||||||
\(670\) | −32.7372 | −1.26475 | ||||||||
\(671\) | −20.4016 | −0.787597 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.0645 | −1.50582 | −0.752912 | − | 0.658121i | \(-0.771352\pi\) | ||||
−0.752912 | + | 0.658121i | \(0.771352\pi\) | |||||||
\(674\) | −28.7530 | −1.10753 | ||||||||
\(675\) | −13.7688 | −0.529962 | ||||||||
\(676\) | 13.7682 | 0.529545 | ||||||||
\(677\) | −8.82385 | −0.339128 | −0.169564 | − | 0.985519i | \(-0.554236\pi\) | ||||
−0.169564 | + | 0.985519i | \(0.554236\pi\) | |||||||
\(678\) | −29.5328 | −1.13420 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −24.6695 | −0.946031 | ||||||||
\(681\) | −29.9389 | −1.14726 | ||||||||
\(682\) | −85.7249 | −3.28258 | ||||||||
\(683\) | −12.3490 | −0.472522 | −0.236261 | − | 0.971690i | \(-0.575922\pi\) | ||||
−0.236261 | + | 0.971690i | \(0.575922\pi\) | |||||||
\(684\) | 89.4243 | 3.41922 | ||||||||
\(685\) | 7.84254 | 0.299648 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 39.2283 | 1.49665 | ||||||||
\(688\) | 1.08051 | 0.0411940 | ||||||||
\(689\) | −30.4460 | −1.15990 | ||||||||
\(690\) | −75.4958 | −2.87407 | ||||||||
\(691\) | 29.1443 | 1.10870 | 0.554351 | − | 0.832283i | \(-0.312967\pi\) | ||||
0.554351 | + | 0.832283i | \(0.312967\pi\) | |||||||
\(692\) | 31.4113 | 1.19408 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 63.6452 | 2.41594 | ||||||||
\(695\) | −1.00889 | −0.0382693 | ||||||||
\(696\) | 118.439 | 4.48943 | ||||||||
\(697\) | −2.82150 | −0.106872 | ||||||||
\(698\) | −55.4873 | −2.10022 | ||||||||
\(699\) | 19.1254 | 0.723387 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.8243 | −0.635447 | −0.317723 | − | 0.948183i | \(-0.602918\pi\) | ||||
−0.317723 | + | 0.948183i | \(0.602918\pi\) | |||||||
\(702\) | −49.5427 | −1.86987 | ||||||||
\(703\) | −37.8367 | −1.42704 | ||||||||
\(704\) | 13.6123 | 0.513034 | ||||||||
\(705\) | 23.2135 | 0.874270 | ||||||||
\(706\) | 0.948998 | 0.0357160 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 37.9575 | 1.42653 | ||||||||
\(709\) | 23.6356 | 0.887655 | 0.443827 | − | 0.896112i | \(-0.353620\pi\) | ||||
0.443827 | + | 0.896112i | \(0.353620\pi\) | |||||||
\(710\) | −50.9473 | −1.91202 | ||||||||
\(711\) | 77.9932 | 2.92497 | ||||||||
\(712\) | 67.9347 | 2.54596 | ||||||||
\(713\) | −51.2159 | −1.91805 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.7398 | 1.07481 | ||||||||
\(716\) | 79.4894 | 2.97066 | ||||||||
\(717\) | 1.30141 | 0.0486022 | ||||||||
\(718\) | 69.8600 | 2.60715 | ||||||||
\(719\) | 14.5753 | 0.543567 | 0.271784 | − | 0.962358i | \(-0.412386\pi\) | ||||
0.271784 | + | 0.962358i | \(0.412386\pi\) | |||||||
\(720\) | 43.6429 | 1.62648 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.753790 | −0.0280532 | ||||||||
\(723\) | −38.8492 | −1.44482 | ||||||||
\(724\) | 26.5287 | 0.985933 | ||||||||
\(725\) | −20.2405 | −0.751715 | ||||||||
\(726\) | 86.9182 | 3.22584 | ||||||||
\(727\) | 6.71319 | 0.248978 | 0.124489 | − | 0.992221i | \(-0.460271\pi\) | ||||
0.124489 | + | 0.992221i | \(0.460271\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.9426 | −1.62750 | ||||||||
\(730\) | 9.18916 | 0.340106 | ||||||||
\(731\) | −0.491049 | −0.0181621 | ||||||||
\(732\) | 51.0829 | 1.88808 | ||||||||
\(733\) | 7.34544 | 0.271310 | 0.135655 | − | 0.990756i | \(-0.456686\pi\) | ||||
0.135655 | + | 0.990756i | \(0.456686\pi\) | |||||||
\(734\) | 38.2575 | 1.41211 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −27.7431 | −1.02263 | ||||||||
\(737\) | 42.5139 | 1.56602 | ||||||||
\(738\) | 11.9829 | 0.441095 | ||||||||
\(739\) | −41.6009 | −1.53031 | −0.765157 | − | 0.643844i | \(-0.777339\pi\) | ||||
−0.765157 | + | 0.643844i | \(0.777339\pi\) | |||||||
\(740\) | −56.2274 | −2.06696 | ||||||||
\(741\) | −48.4239 | −1.77890 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.8763 | −1.68304 | −0.841519 | − | 0.540228i | \(-0.818338\pi\) | ||||
−0.841519 | + | 0.540228i | \(0.818338\pi\) | |||||||
\(744\) | 115.909 | 4.24943 | ||||||||
\(745\) | 18.2211 | 0.667569 | ||||||||
\(746\) | 24.3360 | 0.891005 | ||||||||
\(747\) | 30.5577 | 1.11805 | ||||||||
\(748\) | 59.3266 | 2.16919 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −81.0535 | −2.95966 | ||||||||
\(751\) | −4.94985 | −0.180623 | −0.0903113 | − | 0.995914i | \(-0.528786\pi\) | ||||
−0.0903113 | + | 0.995914i | \(0.528786\pi\) | |||||||
\(752\) | 35.0121 | 1.27676 | ||||||||
\(753\) | 55.2898 | 2.01487 | ||||||||
\(754\) | −72.8292 | −2.65228 | ||||||||
\(755\) | 21.6731 | 0.788766 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.55579 | −0.201929 | −0.100964 | − | 0.994890i | \(-0.532193\pi\) | ||||
−0.100964 | + | 0.994890i | \(0.532193\pi\) | |||||||
\(758\) | −44.9692 | −1.63335 | ||||||||
\(759\) | 98.0420 | 3.55870 | ||||||||
\(760\) | 37.8103 | 1.37152 | ||||||||
\(761\) | 43.1027 | 1.56247 | 0.781237 | − | 0.624235i | \(-0.214589\pi\) | ||||
0.781237 | + | 0.624235i | \(0.214589\pi\) | |||||||
\(762\) | −47.5759 | −1.72349 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 31.3953 | 1.13584 | ||||||||
\(765\) | −19.8340 | −0.717099 | ||||||||
\(766\) | −8.38985 | −0.303138 | ||||||||
\(767\) | −12.6040 | −0.455103 | ||||||||
\(768\) | −87.5666 | −3.15979 | ||||||||
\(769\) | 40.9910 | 1.47817 | 0.739087 | − | 0.673610i | \(-0.235257\pi\) | ||||
0.739087 | + | 0.673610i | \(0.235257\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −67.8337 | −2.44297 | ||||||||
\(772\) | −80.2709 | −2.88901 | ||||||||
\(773\) | −16.9255 | −0.608769 | −0.304385 | − | 0.952549i | \(-0.598451\pi\) | ||||
−0.304385 | + | 0.952549i | \(0.598451\pi\) | |||||||
\(774\) | 2.08548 | 0.0749610 | ||||||||
\(775\) | −19.8082 | −0.711530 | ||||||||
\(776\) | 93.4303 | 3.35395 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 39.5015 | 1.41620 | ||||||||
\(779\) | 4.32444 | 0.154939 | ||||||||
\(780\) | −71.9605 | −2.57660 | ||||||||
\(781\) | 66.1624 | 2.36748 | ||||||||
\(782\) | 51.7484 | 1.85052 | ||||||||
\(783\) | 35.1589 | 1.25648 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.0484 | 0.394336 | ||||||||
\(786\) | −72.5805 | −2.58886 | ||||||||
\(787\) | −3.43935 | −0.122600 | −0.0612999 | − | 0.998119i | \(-0.519525\pi\) | ||||
−0.0612999 | + | 0.998119i | \(0.519525\pi\) | |||||||
\(788\) | −36.3382 | −1.29449 | ||||||||
\(789\) | −45.9180 | −1.63472 | ||||||||
\(790\) | 61.0676 | 2.17269 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −136.060 | −4.83468 | ||||||||
\(793\) | −16.9623 | −0.602350 | ||||||||
\(794\) | −8.38799 | −0.297679 | ||||||||
\(795\) | 31.1692 | 1.10546 | ||||||||
\(796\) | 120.015 | 4.25383 | ||||||||
\(797\) | 48.0233 | 1.70107 | 0.850536 | − | 0.525917i | \(-0.176278\pi\) | ||||
0.850536 | + | 0.525917i | \(0.176278\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.9116 | −0.562913 | ||||||||
\(800\) | −10.7299 | −0.379358 | ||||||||
\(801\) | 54.6188 | 1.92986 | ||||||||
\(802\) | 18.0850 | 0.638602 | ||||||||
\(803\) | −11.9334 | −0.421122 | ||||||||
\(804\) | −106.449 | −3.75417 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −71.2733 | −2.51050 | ||||||||
\(807\) | 26.9991 | 0.950412 | ||||||||
\(808\) | −106.637 | −3.75148 | ||||||||
\(809\) | −28.9663 | −1.01840 | −0.509200 | − | 0.860648i | \(-0.670059\pi\) | ||||
−0.509200 | + | 0.860648i | \(0.670059\pi\) | |||||||
\(810\) | −2.41383 | −0.0848134 | ||||||||
\(811\) | 15.4521 | 0.542595 | 0.271298 | − | 0.962495i | \(-0.412547\pi\) | ||||
0.271298 | + | 0.962495i | \(0.412547\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 39.6540 | 1.39073 | ||||||||
\(814\) | 106.608 | 3.73659 | ||||||||
\(815\) | 22.4909 | 0.787823 | ||||||||
\(816\) | −48.7846 | −1.70780 | ||||||||
\(817\) | 0.752619 | 0.0263308 | ||||||||
\(818\) | 22.6954 | 0.793527 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.42636 | 0.224418 | ||||||||
\(821\) | 1.92930 | 0.0673329 | 0.0336664 | − | 0.999433i | \(-0.489282\pi\) | ||||
0.0336664 | + | 0.999433i | \(0.489282\pi\) | |||||||
\(822\) | 37.2312 | 1.29859 | ||||||||
\(823\) | 16.1295 | 0.562239 | 0.281120 | − | 0.959673i | \(-0.409294\pi\) | ||||
0.281120 | + | 0.959673i | \(0.409294\pi\) | |||||||
\(824\) | −37.6842 | −1.31279 | ||||||||
\(825\) | 37.9185 | 1.32015 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.3885 | −0.708976 | −0.354488 | − | 0.935060i | \(-0.615345\pi\) | ||||
−0.354488 | + | 0.935060i | \(0.615345\pi\) | |||||||
\(828\) | −150.532 | −5.23134 | ||||||||
\(829\) | −22.6093 | −0.785254 | −0.392627 | − | 0.919698i | \(-0.628434\pi\) | ||||
−0.392627 | + | 0.919698i | \(0.628434\pi\) | |||||||
\(830\) | 23.9263 | 0.830492 | ||||||||
\(831\) | −43.1042 | −1.49527 | ||||||||
\(832\) | 11.3175 | 0.392365 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.78954 | −0.165848 | ||||||||
\(835\) | −29.5579 | −1.02289 | ||||||||
\(836\) | −90.9285 | −3.14483 | ||||||||
\(837\) | 34.4078 | 1.18931 | ||||||||
\(838\) | −8.46513 | −0.292423 | ||||||||
\(839\) | 21.3958 | 0.738665 | 0.369333 | − | 0.929297i | \(-0.379586\pi\) | ||||
0.369333 | + | 0.929297i | \(0.379586\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.6846 | 0.782227 | ||||||||
\(842\) | −94.9138 | −3.27095 | ||||||||
\(843\) | −79.5509 | −2.73988 | ||||||||
\(844\) | 19.2658 | 0.663158 | ||||||||
\(845\) | 4.68038 | 0.161010 | ||||||||
\(846\) | 67.5765 | 2.32333 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 47.0115 | 1.61438 | ||||||||
\(849\) | −59.8836 | −2.05520 | ||||||||
\(850\) | 20.0141 | 0.686479 | ||||||||
\(851\) | 63.6921 | 2.18334 | ||||||||
\(852\) | −165.661 | −5.67546 | ||||||||
\(853\) | 18.6430 | 0.638325 | 0.319163 | − | 0.947700i | \(-0.396598\pi\) | ||||
0.319163 | + | 0.947700i | \(0.396598\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 30.3991 | 1.03963 | ||||||||
\(856\) | 26.4660 | 0.904588 | ||||||||
\(857\) | 13.6233 | 0.465362 | 0.232681 | − | 0.972553i | \(-0.425250\pi\) | ||||
0.232681 | + | 0.972553i | \(0.425250\pi\) | |||||||
\(858\) | 136.438 | 4.65791 | ||||||||
\(859\) | 0.968694 | 0.0330514 | 0.0165257 | − | 0.999863i | \(-0.494739\pi\) | ||||
0.0165257 | + | 0.999863i | \(0.494739\pi\) | |||||||
\(860\) | 1.11843 | 0.0381382 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.9893 | 1.05550 | ||||||||
\(863\) | 5.80688 | 0.197668 | 0.0988342 | − | 0.995104i | \(-0.468489\pi\) | ||||
0.0988342 | + | 0.995104i | \(0.468489\pi\) | |||||||
\(864\) | 18.6384 | 0.634090 | ||||||||
\(865\) | 10.6780 | 0.363064 | ||||||||
\(866\) | 2.42165 | 0.0822909 | ||||||||
\(867\) | −25.1737 | −0.854945 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −79.3050 | −2.69024 | ||||||||
\(870\) | 74.5591 | 2.52779 | ||||||||
\(871\) | 35.3469 | 1.19768 | ||||||||
\(872\) | 32.4948 | 1.10041 | ||||||||
\(873\) | 75.1170 | 2.54233 | ||||||||
\(874\) | −79.3137 | −2.68282 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 29.8797 | 1.00954 | ||||||||
\(877\) | 33.1986 | 1.12104 | 0.560518 | − | 0.828142i | \(-0.310602\pi\) | ||||
0.560518 | + | 0.828142i | \(0.310602\pi\) | |||||||
\(878\) | 43.3497 | 1.46298 | ||||||||
\(879\) | −6.50383 | −0.219369 | ||||||||
\(880\) | −44.3770 | −1.49595 | ||||||||
\(881\) | −43.0324 | −1.44980 | −0.724899 | − | 0.688855i | \(-0.758114\pi\) | ||||
−0.724899 | + | 0.688855i | \(0.758114\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.8894 | 0.871249 | 0.435624 | − | 0.900129i | \(-0.356528\pi\) | ||||
0.435624 | + | 0.900129i | \(0.356528\pi\) | |||||||
\(884\) | 49.3252 | 1.65899 | ||||||||
\(885\) | 12.9034 | 0.433741 | ||||||||
\(886\) | −84.3352 | −2.83330 | ||||||||
\(887\) | −41.8678 | −1.40578 | −0.702891 | − | 0.711297i | \(-0.748108\pi\) | ||||
−0.702891 | + | 0.711297i | \(0.748108\pi\) | |||||||
\(888\) | −144.145 | −4.83718 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 42.7658 | 1.43351 | ||||||||
\(891\) | 3.13471 | 0.105017 | ||||||||
\(892\) | −121.724 | −4.07563 | ||||||||
\(893\) | 24.3874 | 0.816093 | ||||||||
\(894\) | 86.5016 | 2.89305 | ||||||||
\(895\) | 27.0218 | 0.903239 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 81.5140 | 2.72167 | ||||||||
\(898\) | −10.3965 | −0.346935 | ||||||||
\(899\) | 50.5804 | 1.68695 | ||||||||
\(900\) | −58.2193 | −1.94064 | ||||||||
\(901\) | −21.3649 | −0.711767 | ||||||||
\(902\) | −12.1844 | −0.405697 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24.8980 | −0.828096 | ||||||||
\(905\) | 9.01824 | 0.299776 | ||||||||
\(906\) | 102.890 | 3.41828 | ||||||||
\(907\) | −17.7115 | −0.588099 | −0.294050 | − | 0.955790i | \(-0.595003\pi\) | ||||
−0.294050 | + | 0.955790i | \(0.595003\pi\) | |||||||
\(908\) | −46.7408 | −1.55115 | ||||||||
\(909\) | −85.7352 | −2.84366 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.4955 | 0.612783 | 0.306392 | − | 0.951906i | \(-0.400878\pi\) | ||||
0.306392 | + | 0.951906i | \(0.400878\pi\) | |||||||
\(912\) | 74.7711 | 2.47592 | ||||||||
\(913\) | −31.0717 | −1.02832 | ||||||||
\(914\) | 40.8527 | 1.35129 | ||||||||
\(915\) | 17.3652 | 0.574077 | ||||||||
\(916\) | 61.2434 | 2.02354 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −34.7656 | −1.14744 | ||||||||
\(919\) | −36.9355 | −1.21839 | −0.609196 | − | 0.793020i | \(-0.708508\pi\) | ||||
−0.609196 | + | 0.793020i | \(0.708508\pi\) | |||||||
\(920\) | −63.6477 | −2.09840 | ||||||||
\(921\) | −46.4749 | −1.53140 | ||||||||
\(922\) | −16.3826 | −0.539532 | ||||||||
\(923\) | 55.0086 | 1.81063 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.6334 | 0.809942 | ||||||||
\(926\) | 15.8255 | 0.520059 | ||||||||
\(927\) | −30.2977 | −0.995107 | ||||||||
\(928\) | 27.3989 | 0.899413 | ||||||||
\(929\) | 23.0313 | 0.755632 | 0.377816 | − | 0.925881i | \(-0.376675\pi\) | ||||
0.377816 | + | 0.925881i | \(0.376675\pi\) | |||||||
\(930\) | 72.9663 | 2.39266 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 29.8586 | 0.978050 | ||||||||
\(933\) | −5.93074 | −0.194164 | ||||||||
\(934\) | −81.4509 | −2.66515 | ||||||||
\(935\) | 20.1676 | 0.659551 | ||||||||
\(936\) | −113.123 | −3.69754 | ||||||||
\(937\) | −41.7706 | −1.36459 | −0.682293 | − | 0.731078i | \(-0.739017\pi\) | ||||
−0.682293 | + | 0.731078i | \(0.739017\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 87.8547 | 2.86703 | ||||||||
\(940\) | 36.2410 | 1.18205 | ||||||||
\(941\) | 17.1269 | 0.558320 | 0.279160 | − | 0.960245i | \(-0.409944\pi\) | ||||
0.279160 | + | 0.960245i | \(0.409944\pi\) | |||||||
\(942\) | 52.4507 | 1.70894 | ||||||||
\(943\) | −7.27952 | −0.237054 | ||||||||
\(944\) | 19.4617 | 0.633425 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.12056 | −0.0689452 | ||||||||
\(947\) | 6.15920 | 0.200147 | 0.100073 | − | 0.994980i | \(-0.468092\pi\) | ||||
0.100073 | + | 0.994980i | \(0.468092\pi\) | |||||||
\(948\) | 198.569 | 6.44921 | ||||||||
\(949\) | −9.92169 | −0.322072 | ||||||||
\(950\) | −30.6752 | −0.995234 | ||||||||
\(951\) | −25.1959 | −0.817032 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.98600 | −0.0967261 | −0.0483630 | − | 0.998830i | \(-0.515400\pi\) | ||||
−0.0483630 | + | 0.998830i | \(0.515400\pi\) | |||||||
\(954\) | 90.7364 | 2.93770 | ||||||||
\(955\) | 10.6726 | 0.345356 | ||||||||
\(956\) | 2.03177 | 0.0657123 | ||||||||
\(957\) | −96.8256 | −3.12993 | ||||||||
\(958\) | −15.6449 | −0.505463 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −11.5864 | −0.373949 | ||||||||
\(961\) | 18.4999 | 0.596771 | ||||||||
\(962\) | 88.6356 | 2.85772 | ||||||||
\(963\) | 21.2784 | 0.685686 | ||||||||
\(964\) | −60.6516 | −1.95346 | ||||||||
\(965\) | −27.2875 | −0.878414 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.66622 | 0.0857399 | 0.0428699 | − | 0.999081i | \(-0.486350\pi\) | ||||
0.0428699 | + | 0.999081i | \(0.486350\pi\) | |||||||
\(968\) | 73.2775 | 2.35523 | ||||||||
\(969\) | −33.9805 | −1.09161 | ||||||||
\(970\) | 58.8156 | 1.88846 | ||||||||
\(971\) | 6.45629 | 0.207192 | 0.103596 | − | 0.994619i | \(-0.466965\pi\) | ||||
0.103596 | + | 0.994619i | \(0.466965\pi\) | |||||||
\(972\) | −71.6393 | −2.29783 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −11.6045 | −0.371833 | ||||||||
\(975\) | 31.5262 | 1.00965 | ||||||||
\(976\) | 26.1914 | 0.838367 | ||||||||
\(977\) | −21.0479 | −0.673382 | −0.336691 | − | 0.941615i | \(-0.609308\pi\) | ||||
−0.336691 | + | 0.941615i | \(0.609308\pi\) | |||||||
\(978\) | 106.772 | 3.41420 | ||||||||
\(979\) | −55.5375 | −1.77499 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.1255 | 0.834123 | ||||||||
\(982\) | −68.3907 | −2.18243 | ||||||||
\(983\) | 33.1038 | 1.05585 | 0.527924 | − | 0.849292i | \(-0.322971\pi\) | ||||
0.527924 | + | 0.849292i | \(0.322971\pi\) | |||||||
\(984\) | 16.4746 | 0.525192 | ||||||||
\(985\) | −12.3529 | −0.393596 | ||||||||
\(986\) | −51.1064 | −1.62756 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −75.5996 | −2.40515 | ||||||||
\(989\) | −1.26691 | −0.0402855 | ||||||||
\(990\) | −85.6516 | −2.72219 | ||||||||
\(991\) | 33.0725 | 1.05058 | 0.525292 | − | 0.850922i | \(-0.323956\pi\) | ||||
0.525292 | + | 0.850922i | \(0.323956\pi\) | |||||||
\(992\) | 26.8136 | 0.851332 | ||||||||
\(993\) | 16.8304 | 0.534097 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 40.7983 | 1.29339 | ||||||||
\(996\) | 77.7991 | 2.46516 | ||||||||
\(997\) | 11.9187 | 0.377468 | 0.188734 | − | 0.982028i | \(-0.439562\pi\) | ||||
0.188734 | + | 0.982028i | \(0.439562\pi\) | |||||||
\(998\) | −78.4730 | −2.48402 | ||||||||
\(999\) | −42.7896 | −1.35380 |
(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 | 2009.2.a.u.1.19 | yes | 20 | |
7.6 | odd | 2 | 2009.2.a.t.1.19 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2009.2.a.t.1.19 | ✓ | 20 | 7.6 | odd | 2 | ||
2009.2.a.u.1.19 | yes | 20 | 1.1 | even | 1 | trivial |