Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4021,2,Mod(1,4021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4021, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4021.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1078466528\) |
Analytic rank: | \(1\) |
Dimension: | \(151\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75476 | −1.94791 | −0.973956 | − | 0.226737i | \(-0.927194\pi\) | ||||
−0.973956 | + | 0.226737i | \(0.927194\pi\) | |||||||
\(3\) | 1.58414 | 0.914605 | 0.457302 | − | 0.889311i | \(-0.348816\pi\) | ||||
0.457302 | + | 0.889311i | \(0.348816\pi\) | |||||||
\(4\) | 5.58872 | 2.79436 | ||||||||
\(5\) | −2.10175 | −0.939930 | −0.469965 | − | 0.882685i | \(-0.655733\pi\) | ||||
−0.469965 | + | 0.882685i | \(0.655733\pi\) | |||||||
\(6\) | −4.36394 | −1.78157 | ||||||||
\(7\) | 2.25410 | 0.851970 | 0.425985 | − | 0.904730i | \(-0.359928\pi\) | ||||
0.425985 | + | 0.904730i | \(0.359928\pi\) | |||||||
\(8\) | −9.88608 | −3.49526 | ||||||||
\(9\) | −0.490495 | −0.163498 | ||||||||
\(10\) | 5.78981 | 1.83090 | ||||||||
\(11\) | 1.94977 | 0.587878 | 0.293939 | − | 0.955824i | \(-0.405034\pi\) | ||||
0.293939 | + | 0.955824i | \(0.405034\pi\) | |||||||
\(12\) | 8.85333 | 2.55574 | ||||||||
\(13\) | −3.92401 | −1.08832 | −0.544162 | − | 0.838980i | \(-0.683152\pi\) | ||||
−0.544162 | + | 0.838980i | \(0.683152\pi\) | |||||||
\(14\) | −6.20952 | −1.65956 | ||||||||
\(15\) | −3.32946 | −0.859664 | ||||||||
\(16\) | 16.0564 | 4.01409 | ||||||||
\(17\) | 1.85363 | 0.449572 | 0.224786 | − | 0.974408i | \(-0.427832\pi\) | ||||
0.224786 | + | 0.974408i | \(0.427832\pi\) | |||||||
\(18\) | 1.35120 | 0.318481 | ||||||||
\(19\) | 2.21776 | 0.508788 | 0.254394 | − | 0.967101i | \(-0.418124\pi\) | ||||
0.254394 | + | 0.967101i | \(0.418124\pi\) | |||||||
\(20\) | −11.7461 | −2.62650 | ||||||||
\(21\) | 3.57082 | 0.779216 | ||||||||
\(22\) | −5.37116 | −1.14514 | ||||||||
\(23\) | −0.662128 | −0.138063 | −0.0690316 | − | 0.997614i | \(-0.521991\pi\) | ||||
−0.0690316 | + | 0.997614i | \(0.521991\pi\) | |||||||
\(24\) | −15.6609 | −3.19678 | ||||||||
\(25\) | −0.582661 | −0.116532 | ||||||||
\(26\) | 10.8097 | 2.11996 | ||||||||
\(27\) | −5.52944 | −1.06414 | ||||||||
\(28\) | 12.5975 | 2.38071 | ||||||||
\(29\) | −0.706007 | −0.131102 | −0.0655511 | − | 0.997849i | \(-0.520881\pi\) | ||||
−0.0655511 | + | 0.997849i | \(0.520881\pi\) | |||||||
\(30\) | 9.17189 | 1.67455 | ||||||||
\(31\) | −0.225375 | −0.0404786 | −0.0202393 | − | 0.999795i | \(-0.506443\pi\) | ||||
−0.0202393 | + | 0.999795i | \(0.506443\pi\) | |||||||
\(32\) | −24.4593 | −4.32384 | ||||||||
\(33\) | 3.08872 | 0.537676 | ||||||||
\(34\) | −5.10632 | −0.875727 | ||||||||
\(35\) | −4.73755 | −0.800792 | ||||||||
\(36\) | −2.74124 | −0.456874 | ||||||||
\(37\) | 7.77252 | 1.27779 | 0.638897 | − | 0.769292i | \(-0.279391\pi\) | ||||
0.638897 | + | 0.769292i | \(0.279391\pi\) | |||||||
\(38\) | −6.10940 | −0.991075 | ||||||||
\(39\) | −6.21619 | −0.995387 | ||||||||
\(40\) | 20.7780 | 3.28530 | ||||||||
\(41\) | −8.00692 | −1.25047 | −0.625235 | − | 0.780436i | \(-0.714997\pi\) | ||||
−0.625235 | + | 0.780436i | \(0.714997\pi\) | |||||||
\(42\) | −9.83675 | −1.51784 | ||||||||
\(43\) | 4.71441 | 0.718941 | 0.359470 | − | 0.933157i | \(-0.382957\pi\) | ||||
0.359470 | + | 0.933157i | \(0.382957\pi\) | |||||||
\(44\) | 10.8967 | 1.64274 | ||||||||
\(45\) | 1.03090 | 0.153677 | ||||||||
\(46\) | 1.82401 | 0.268935 | ||||||||
\(47\) | −4.00297 | −0.583893 | −0.291947 | − | 0.956435i | \(-0.594303\pi\) | ||||
−0.291947 | + | 0.956435i | \(0.594303\pi\) | |||||||
\(48\) | 25.4356 | 3.67131 | ||||||||
\(49\) | −1.91903 | −0.274147 | ||||||||
\(50\) | 1.60509 | 0.226994 | ||||||||
\(51\) | 2.93642 | 0.411181 | ||||||||
\(52\) | −21.9302 | −3.04117 | ||||||||
\(53\) | 3.02515 | 0.415536 | 0.207768 | − | 0.978178i | \(-0.433380\pi\) | ||||
0.207768 | + | 0.978178i | \(0.433380\pi\) | |||||||
\(54\) | 15.2323 | 2.07285 | ||||||||
\(55\) | −4.09793 | −0.552564 | ||||||||
\(56\) | −22.2842 | −2.97785 | ||||||||
\(57\) | 3.51324 | 0.465340 | ||||||||
\(58\) | 1.94488 | 0.255376 | ||||||||
\(59\) | −4.65922 | −0.606578 | −0.303289 | − | 0.952899i | \(-0.598085\pi\) | ||||
−0.303289 | + | 0.952899i | \(0.598085\pi\) | |||||||
\(60\) | −18.6074 | −2.40221 | ||||||||
\(61\) | 0.244526 | 0.0313083 | 0.0156542 | − | 0.999877i | \(-0.495017\pi\) | ||||
0.0156542 | + | 0.999877i | \(0.495017\pi\) | |||||||
\(62\) | 0.620856 | 0.0788488 | ||||||||
\(63\) | −1.10563 | −0.139296 | ||||||||
\(64\) | 35.2669 | 4.40837 | ||||||||
\(65\) | 8.24728 | 1.02295 | ||||||||
\(66\) | −8.50868 | −1.04735 | ||||||||
\(67\) | −1.01244 | −0.123690 | −0.0618449 | − | 0.998086i | \(-0.519698\pi\) | ||||
−0.0618449 | + | 0.998086i | \(0.519698\pi\) | |||||||
\(68\) | 10.3594 | 1.25627 | ||||||||
\(69\) | −1.04890 | −0.126273 | ||||||||
\(70\) | 13.0508 | 1.55987 | ||||||||
\(71\) | −3.47487 | −0.412391 | −0.206196 | − | 0.978511i | \(-0.566108\pi\) | ||||
−0.206196 | + | 0.978511i | \(0.566108\pi\) | |||||||
\(72\) | 4.84907 | 0.571469 | ||||||||
\(73\) | −3.25162 | −0.380574 | −0.190287 | − | 0.981729i | \(-0.560942\pi\) | ||||
−0.190287 | + | 0.981729i | \(0.560942\pi\) | |||||||
\(74\) | −21.4115 | −2.48903 | ||||||||
\(75\) | −0.923017 | −0.106581 | ||||||||
\(76\) | 12.3944 | 1.42174 | ||||||||
\(77\) | 4.39498 | 0.500855 | ||||||||
\(78\) | 17.1241 | 1.93893 | ||||||||
\(79\) | 14.9629 | 1.68346 | 0.841728 | − | 0.539902i | \(-0.181539\pi\) | ||||
0.841728 | + | 0.539902i | \(0.181539\pi\) | |||||||
\(80\) | −33.7464 | −3.77296 | ||||||||
\(81\) | −7.28793 | −0.809770 | ||||||||
\(82\) | 22.0572 | 2.43581 | ||||||||
\(83\) | 7.81484 | 0.857791 | 0.428895 | − | 0.903354i | \(-0.358903\pi\) | ||||
0.428895 | + | 0.903354i | \(0.358903\pi\) | |||||||
\(84\) | 19.9563 | 2.17741 | ||||||||
\(85\) | −3.89587 | −0.422566 | ||||||||
\(86\) | −12.9871 | −1.40043 | ||||||||
\(87\) | −1.11842 | −0.119907 | ||||||||
\(88\) | −19.2756 | −2.05479 | ||||||||
\(89\) | −1.05559 | −0.111892 | −0.0559461 | − | 0.998434i | \(-0.517818\pi\) | ||||
−0.0559461 | + | 0.998434i | \(0.517818\pi\) | |||||||
\(90\) | −2.83988 | −0.299349 | ||||||||
\(91\) | −8.84512 | −0.927221 | ||||||||
\(92\) | −3.70045 | −0.385798 | ||||||||
\(93\) | −0.357027 | −0.0370219 | ||||||||
\(94\) | 11.0272 | 1.13737 | ||||||||
\(95\) | −4.66116 | −0.478225 | ||||||||
\(96\) | −38.7470 | −3.95460 | ||||||||
\(97\) | 10.4961 | 1.06572 | 0.532859 | − | 0.846204i | \(-0.321118\pi\) | ||||
0.532859 | + | 0.846204i | \(0.321118\pi\) | |||||||
\(98\) | 5.28646 | 0.534013 | ||||||||
\(99\) | −0.956354 | −0.0961172 | ||||||||
\(100\) | −3.25633 | −0.325633 | ||||||||
\(101\) | −17.4268 | −1.73404 | −0.867018 | − | 0.498277i | \(-0.833966\pi\) | ||||
−0.867018 | + | 0.498277i | \(0.833966\pi\) | |||||||
\(102\) | −8.08914 | −0.800944 | ||||||||
\(103\) | −10.3766 | −1.02243 | −0.511217 | − | 0.859452i | \(-0.670805\pi\) | ||||
−0.511217 | + | 0.859452i | \(0.670805\pi\) | |||||||
\(104\) | 38.7931 | 3.80397 | ||||||||
\(105\) | −7.50495 | −0.732408 | ||||||||
\(106\) | −8.33356 | −0.809427 | ||||||||
\(107\) | −10.1764 | −0.983785 | −0.491893 | − | 0.870656i | \(-0.663695\pi\) | ||||
−0.491893 | + | 0.870656i | \(0.663695\pi\) | |||||||
\(108\) | −30.9025 | −2.97359 | ||||||||
\(109\) | −7.10750 | −0.680775 | −0.340387 | − | 0.940285i | \(-0.610558\pi\) | ||||
−0.340387 | + | 0.940285i | \(0.610558\pi\) | |||||||
\(110\) | 11.2888 | 1.07635 | ||||||||
\(111\) | 12.3128 | 1.16868 | ||||||||
\(112\) | 36.1927 | 3.41989 | ||||||||
\(113\) | −12.1645 | −1.14434 | −0.572172 | − | 0.820134i | \(-0.693899\pi\) | ||||
−0.572172 | + | 0.820134i | \(0.693899\pi\) | |||||||
\(114\) | −9.67815 | −0.906442 | ||||||||
\(115\) | 1.39162 | 0.129770 | ||||||||
\(116\) | −3.94568 | −0.366347 | ||||||||
\(117\) | 1.92471 | 0.177939 | ||||||||
\(118\) | 12.8350 | 1.18156 | ||||||||
\(119\) | 4.17828 | 0.383022 | ||||||||
\(120\) | 32.9153 | 3.00475 | ||||||||
\(121\) | −7.19839 | −0.654399 | ||||||||
\(122\) | −0.673611 | −0.0609859 | ||||||||
\(123\) | −12.6841 | −1.14369 | ||||||||
\(124\) | −1.25956 | −0.113112 | ||||||||
\(125\) | 11.7333 | 1.04946 | ||||||||
\(126\) | 3.04574 | 0.271336 | ||||||||
\(127\) | 12.9800 | 1.15179 | 0.575894 | − | 0.817524i | \(-0.304654\pi\) | ||||
0.575894 | + | 0.817524i | \(0.304654\pi\) | |||||||
\(128\) | −48.2334 | −4.26327 | ||||||||
\(129\) | 7.46829 | 0.657546 | ||||||||
\(130\) | −22.7193 | −1.99261 | ||||||||
\(131\) | −9.92162 | −0.866856 | −0.433428 | − | 0.901188i | \(-0.642696\pi\) | ||||
−0.433428 | + | 0.901188i | \(0.642696\pi\) | |||||||
\(132\) | 17.2620 | 1.50246 | ||||||||
\(133\) | 4.99905 | 0.433473 | ||||||||
\(134\) | 2.78904 | 0.240937 | ||||||||
\(135\) | 11.6215 | 1.00022 | ||||||||
\(136\) | −18.3252 | −1.57137 | ||||||||
\(137\) | 20.0585 | 1.71371 | 0.856856 | − | 0.515556i | \(-0.172415\pi\) | ||||
0.856856 | + | 0.515556i | \(0.172415\pi\) | |||||||
\(138\) | 2.88948 | 0.245969 | ||||||||
\(139\) | −16.9261 | −1.43565 | −0.717826 | − | 0.696223i | \(-0.754863\pi\) | ||||
−0.717826 | + | 0.696223i | \(0.754863\pi\) | |||||||
\(140\) | −26.4768 | −2.23770 | ||||||||
\(141\) | −6.34127 | −0.534031 | ||||||||
\(142\) | 9.57244 | 0.803301 | ||||||||
\(143\) | −7.65093 | −0.639803 | ||||||||
\(144\) | −7.87557 | −0.656298 | ||||||||
\(145\) | 1.48385 | 0.123227 | ||||||||
\(146\) | 8.95745 | 0.741324 | ||||||||
\(147\) | −3.04001 | −0.250736 | ||||||||
\(148\) | 43.4385 | 3.57062 | ||||||||
\(149\) | −21.3079 | −1.74561 | −0.872804 | − | 0.488071i | \(-0.837701\pi\) | ||||
−0.872804 | + | 0.488071i | \(0.837701\pi\) | |||||||
\(150\) | 2.54269 | 0.207610 | ||||||||
\(151\) | −7.40871 | −0.602913 | −0.301456 | − | 0.953480i | \(-0.597473\pi\) | ||||
−0.301456 | + | 0.953480i | \(0.597473\pi\) | |||||||
\(152\) | −21.9249 | −1.77835 | ||||||||
\(153\) | −0.909199 | −0.0735044 | ||||||||
\(154\) | −12.1071 | −0.975621 | ||||||||
\(155\) | 0.473682 | 0.0380471 | ||||||||
\(156\) | −34.7406 | −2.78147 | ||||||||
\(157\) | −19.1893 | −1.53148 | −0.765738 | − | 0.643153i | \(-0.777626\pi\) | ||||
−0.765738 | + | 0.643153i | \(0.777626\pi\) | |||||||
\(158\) | −41.2192 | −3.27922 | ||||||||
\(159\) | 4.79226 | 0.380051 | ||||||||
\(160\) | 51.4073 | 4.06410 | ||||||||
\(161\) | −1.49250 | −0.117626 | ||||||||
\(162\) | 20.0765 | 1.57736 | ||||||||
\(163\) | −7.57651 | −0.593438 | −0.296719 | − | 0.954965i | \(-0.595892\pi\) | ||||
−0.296719 | + | 0.954965i | \(0.595892\pi\) | |||||||
\(164\) | −44.7484 | −3.49426 | ||||||||
\(165\) | −6.49170 | −0.505378 | ||||||||
\(166\) | −21.5280 | −1.67090 | ||||||||
\(167\) | −0.545012 | −0.0421743 | −0.0210871 | − | 0.999778i | \(-0.506713\pi\) | ||||
−0.0210871 | + | 0.999778i | \(0.506713\pi\) | |||||||
\(168\) | −35.3014 | −2.72356 | ||||||||
\(169\) | 2.39786 | 0.184451 | ||||||||
\(170\) | 10.7322 | 0.823122 | ||||||||
\(171\) | −1.08780 | −0.0831861 | ||||||||
\(172\) | 26.3475 | 2.00898 | ||||||||
\(173\) | 9.50712 | 0.722813 | 0.361407 | − | 0.932408i | \(-0.382297\pi\) | ||||
0.361407 | + | 0.932408i | \(0.382297\pi\) | |||||||
\(174\) | 3.08097 | 0.233568 | ||||||||
\(175\) | −1.31338 | −0.0992819 | ||||||||
\(176\) | 31.3062 | 2.35980 | ||||||||
\(177\) | −7.38086 | −0.554779 | ||||||||
\(178\) | 2.90790 | 0.217956 | ||||||||
\(179\) | −0.675918 | −0.0505205 | −0.0252602 | − | 0.999681i | \(-0.508041\pi\) | ||||
−0.0252602 | + | 0.999681i | \(0.508041\pi\) | |||||||
\(180\) | 5.76140 | 0.429429 | ||||||||
\(181\) | −10.9761 | −0.815848 | −0.407924 | − | 0.913016i | \(-0.633747\pi\) | ||||
−0.407924 | + | 0.913016i | \(0.633747\pi\) | |||||||
\(182\) | 24.3662 | 1.80614 | ||||||||
\(183\) | 0.387364 | 0.0286348 | ||||||||
\(184\) | 6.54585 | 0.482566 | ||||||||
\(185\) | −16.3359 | −1.20104 | ||||||||
\(186\) | 0.983524 | 0.0721155 | ||||||||
\(187\) | 3.61417 | 0.264294 | ||||||||
\(188\) | −22.3715 | −1.63161 | ||||||||
\(189\) | −12.4639 | −0.906617 | ||||||||
\(190\) | 12.8404 | 0.931541 | ||||||||
\(191\) | 3.99182 | 0.288838 | 0.144419 | − | 0.989517i | \(-0.453869\pi\) | ||||
0.144419 | + | 0.989517i | \(0.453869\pi\) | |||||||
\(192\) | 55.8678 | 4.03191 | ||||||||
\(193\) | 8.26413 | 0.594865 | 0.297433 | − | 0.954743i | \(-0.403870\pi\) | ||||
0.297433 | + | 0.954743i | \(0.403870\pi\) | |||||||
\(194\) | −28.9143 | −2.07593 | ||||||||
\(195\) | 13.0649 | 0.935594 | ||||||||
\(196\) | −10.7249 | −0.766064 | ||||||||
\(197\) | −12.1040 | −0.862371 | −0.431185 | − | 0.902263i | \(-0.641905\pi\) | ||||
−0.431185 | + | 0.902263i | \(0.641905\pi\) | |||||||
\(198\) | 2.63453 | 0.187228 | ||||||||
\(199\) | 0.810514 | 0.0574558 | 0.0287279 | − | 0.999587i | \(-0.490854\pi\) | ||||
0.0287279 | + | 0.999587i | \(0.490854\pi\) | |||||||
\(200\) | 5.76023 | 0.407310 | ||||||||
\(201\) | −1.60385 | −0.113127 | ||||||||
\(202\) | 48.0068 | 3.37775 | ||||||||
\(203\) | −1.59141 | −0.111695 | ||||||||
\(204\) | 16.4108 | 1.14899 | ||||||||
\(205\) | 16.8285 | 1.17535 | ||||||||
\(206\) | 28.5850 | 1.99161 | ||||||||
\(207\) | 0.324771 | 0.0225731 | ||||||||
\(208\) | −63.0053 | −4.36863 | ||||||||
\(209\) | 4.32412 | 0.299106 | ||||||||
\(210\) | 20.6744 | 1.42667 | ||||||||
\(211\) | −3.07713 | −0.211838 | −0.105919 | − | 0.994375i | \(-0.533778\pi\) | ||||
−0.105919 | + | 0.994375i | \(0.533778\pi\) | |||||||
\(212\) | 16.9067 | 1.16116 | ||||||||
\(213\) | −5.50468 | −0.377175 | ||||||||
\(214\) | 28.0334 | 1.91633 | ||||||||
\(215\) | −9.90849 | −0.675754 | ||||||||
\(216\) | 54.6645 | 3.71945 | ||||||||
\(217\) | −0.508019 | −0.0344866 | ||||||||
\(218\) | 19.5795 | 1.32609 | ||||||||
\(219\) | −5.15103 | −0.348074 | ||||||||
\(220\) | −22.9022 | −1.54406 | ||||||||
\(221\) | −7.27368 | −0.489281 | ||||||||
\(222\) | −33.9188 | −2.27648 | ||||||||
\(223\) | −1.25069 | −0.0837521 | −0.0418761 | − | 0.999123i | \(-0.513333\pi\) | ||||
−0.0418761 | + | 0.999123i | \(0.513333\pi\) | |||||||
\(224\) | −55.1338 | −3.68378 | ||||||||
\(225\) | 0.285792 | 0.0190528 | ||||||||
\(226\) | 33.5104 | 2.22908 | ||||||||
\(227\) | 17.4474 | 1.15803 | 0.579013 | − | 0.815319i | \(-0.303438\pi\) | ||||
0.579013 | + | 0.815319i | \(0.303438\pi\) | |||||||
\(228\) | 19.6345 | 1.30033 | ||||||||
\(229\) | 2.10943 | 0.139395 | 0.0696977 | − | 0.997568i | \(-0.477797\pi\) | ||||
0.0696977 | + | 0.997568i | \(0.477797\pi\) | |||||||
\(230\) | −3.83360 | −0.252780 | ||||||||
\(231\) | 6.96228 | 0.458084 | ||||||||
\(232\) | 6.97964 | 0.458236 | ||||||||
\(233\) | −12.7769 | −0.837045 | −0.418523 | − | 0.908206i | \(-0.637452\pi\) | ||||
−0.418523 | + | 0.908206i | \(0.637452\pi\) | |||||||
\(234\) | −5.30212 | −0.346610 | ||||||||
\(235\) | 8.41323 | 0.548818 | ||||||||
\(236\) | −26.0391 | −1.69500 | ||||||||
\(237\) | 23.7033 | 1.53970 | ||||||||
\(238\) | −11.5102 | −0.746094 | ||||||||
\(239\) | 4.69844 | 0.303917 | 0.151959 | − | 0.988387i | \(-0.451442\pi\) | ||||
0.151959 | + | 0.988387i | \(0.451442\pi\) | |||||||
\(240\) | −53.4591 | −3.45077 | ||||||||
\(241\) | 8.00368 | 0.515563 | 0.257781 | − | 0.966203i | \(-0.417009\pi\) | ||||
0.257781 | + | 0.966203i | \(0.417009\pi\) | |||||||
\(242\) | 19.8299 | 1.27471 | ||||||||
\(243\) | 5.04321 | 0.323522 | ||||||||
\(244\) | 1.36659 | 0.0874868 | ||||||||
\(245\) | 4.03331 | 0.257679 | ||||||||
\(246\) | 34.9417 | 2.22780 | ||||||||
\(247\) | −8.70250 | −0.553727 | ||||||||
\(248\) | 2.22808 | 0.141483 | ||||||||
\(249\) | 12.3798 | 0.784539 | ||||||||
\(250\) | −32.3226 | −2.04426 | ||||||||
\(251\) | 24.1329 | 1.52325 | 0.761627 | − | 0.648016i | \(-0.224401\pi\) | ||||
0.761627 | + | 0.648016i | \(0.224401\pi\) | |||||||
\(252\) | −6.17904 | −0.389243 | ||||||||
\(253\) | −1.29100 | −0.0811644 | ||||||||
\(254\) | −35.7568 | −2.24358 | ||||||||
\(255\) | −6.17161 | −0.386481 | ||||||||
\(256\) | 62.3377 | 3.89611 | ||||||||
\(257\) | −7.46681 | −0.465767 | −0.232883 | − | 0.972505i | \(-0.574816\pi\) | ||||
−0.232883 | + | 0.972505i | \(0.574816\pi\) | |||||||
\(258\) | −20.5734 | −1.28084 | ||||||||
\(259\) | 17.5201 | 1.08864 | ||||||||
\(260\) | 46.0917 | 2.85849 | ||||||||
\(261\) | 0.346293 | 0.0214350 | ||||||||
\(262\) | 27.3317 | 1.68856 | ||||||||
\(263\) | −5.94621 | −0.366659 | −0.183330 | − | 0.983051i | \(-0.558688\pi\) | ||||
−0.183330 | + | 0.983051i | \(0.558688\pi\) | |||||||
\(264\) | −30.5353 | −1.87932 | ||||||||
\(265\) | −6.35809 | −0.390574 | ||||||||
\(266\) | −13.7712 | −0.844366 | ||||||||
\(267\) | −1.67220 | −0.102337 | ||||||||
\(268\) | −5.65827 | −0.345634 | ||||||||
\(269\) | 11.6823 | 0.712281 | 0.356141 | − | 0.934432i | \(-0.384092\pi\) | ||||
0.356141 | + | 0.934432i | \(0.384092\pi\) | |||||||
\(270\) | −32.0144 | −1.94834 | ||||||||
\(271\) | 15.8375 | 0.962062 | 0.481031 | − | 0.876703i | \(-0.340262\pi\) | ||||
0.481031 | + | 0.876703i | \(0.340262\pi\) | |||||||
\(272\) | 29.7626 | 1.80462 | ||||||||
\(273\) | −14.0119 | −0.848040 | ||||||||
\(274\) | −55.2564 | −3.33816 | ||||||||
\(275\) | −1.13606 | −0.0685067 | ||||||||
\(276\) | −5.86203 | −0.352853 | ||||||||
\(277\) | −8.37907 | −0.503450 | −0.251725 | − | 0.967799i | \(-0.580998\pi\) | ||||
−0.251725 | + | 0.967799i | \(0.580998\pi\) | |||||||
\(278\) | 46.6273 | 2.79652 | ||||||||
\(279\) | 0.110546 | 0.00661819 | ||||||||
\(280\) | 46.8358 | 2.79897 | ||||||||
\(281\) | −21.6480 | −1.29141 | −0.645705 | − | 0.763587i | \(-0.723436\pi\) | ||||
−0.645705 | + | 0.763587i | \(0.723436\pi\) | |||||||
\(282\) | 17.4687 | 1.04025 | ||||||||
\(283\) | 0.399452 | 0.0237450 | 0.0118725 | − | 0.999930i | \(-0.496221\pi\) | ||||
0.0118725 | + | 0.999930i | \(0.496221\pi\) | |||||||
\(284\) | −19.4201 | −1.15237 | ||||||||
\(285\) | −7.38394 | −0.437387 | ||||||||
\(286\) | 21.0765 | 1.24628 | ||||||||
\(287\) | −18.0484 | −1.06536 | ||||||||
\(288\) | 11.9972 | 0.706941 | ||||||||
\(289\) | −13.5640 | −0.797885 | ||||||||
\(290\) | −4.08765 | −0.240035 | ||||||||
\(291\) | 16.6273 | 0.974711 | ||||||||
\(292\) | −18.1724 | −1.06346 | ||||||||
\(293\) | −10.1754 | −0.594454 | −0.297227 | − | 0.954807i | \(-0.596062\pi\) | ||||
−0.297227 | + | 0.954807i | \(0.596062\pi\) | |||||||
\(294\) | 8.37451 | 0.488411 | ||||||||
\(295\) | 9.79249 | 0.570141 | ||||||||
\(296\) | −76.8398 | −4.46622 | ||||||||
\(297\) | −10.7811 | −0.625586 | ||||||||
\(298\) | 58.6981 | 3.40029 | ||||||||
\(299\) | 2.59820 | 0.150258 | ||||||||
\(300\) | −5.15848 | −0.297825 | ||||||||
\(301\) | 10.6268 | 0.612516 | ||||||||
\(302\) | 20.4093 | 1.17442 | ||||||||
\(303\) | −27.6066 | −1.58596 | ||||||||
\(304\) | 35.6091 | 2.04232 | ||||||||
\(305\) | −0.513932 | −0.0294276 | ||||||||
\(306\) | 2.50463 | 0.143180 | ||||||||
\(307\) | 22.0773 | 1.26002 | 0.630008 | − | 0.776588i | \(-0.283051\pi\) | ||||
0.630008 | + | 0.776588i | \(0.283051\pi\) | |||||||
\(308\) | 24.5623 | 1.39957 | ||||||||
\(309\) | −16.4379 | −0.935122 | ||||||||
\(310\) | −1.30488 | −0.0741123 | ||||||||
\(311\) | −11.4692 | −0.650357 | −0.325179 | − | 0.945653i | \(-0.605424\pi\) | ||||
−0.325179 | + | 0.945653i | \(0.605424\pi\) | |||||||
\(312\) | 61.4537 | 3.47913 | ||||||||
\(313\) | 5.19668 | 0.293734 | 0.146867 | − | 0.989156i | \(-0.453081\pi\) | ||||
0.146867 | + | 0.989156i | \(0.453081\pi\) | |||||||
\(314\) | 52.8621 | 2.98318 | ||||||||
\(315\) | 2.32375 | 0.130928 | ||||||||
\(316\) | 83.6234 | 4.70418 | ||||||||
\(317\) | −1.99594 | −0.112103 | −0.0560516 | − | 0.998428i | \(-0.517851\pi\) | ||||
−0.0560516 | + | 0.998428i | \(0.517851\pi\) | |||||||
\(318\) | −13.2015 | −0.740306 | ||||||||
\(319\) | −1.37655 | −0.0770722 | ||||||||
\(320\) | −74.1221 | −4.14355 | ||||||||
\(321\) | −16.1208 | −0.899774 | ||||||||
\(322\) | 4.11149 | 0.229125 | ||||||||
\(323\) | 4.11091 | 0.228737 | ||||||||
\(324\) | −40.7302 | −2.26279 | ||||||||
\(325\) | 2.28637 | 0.126825 | ||||||||
\(326\) | 20.8715 | 1.15597 | ||||||||
\(327\) | −11.2593 | −0.622640 | ||||||||
\(328\) | 79.1570 | 4.37071 | ||||||||
\(329\) | −9.02310 | −0.497460 | ||||||||
\(330\) | 17.8831 | 0.984432 | ||||||||
\(331\) | −1.27496 | −0.0700784 | −0.0350392 | − | 0.999386i | \(-0.511156\pi\) | ||||
−0.0350392 | + | 0.999386i | \(0.511156\pi\) | |||||||
\(332\) | 43.6750 | 2.39698 | ||||||||
\(333\) | −3.81239 | −0.208917 | ||||||||
\(334\) | 1.50138 | 0.0821518 | ||||||||
\(335\) | 2.12790 | 0.116260 | ||||||||
\(336\) | 57.3343 | 3.12784 | ||||||||
\(337\) | −3.24412 | −0.176719 | −0.0883593 | − | 0.996089i | \(-0.528162\pi\) | ||||
−0.0883593 | + | 0.996089i | \(0.528162\pi\) | |||||||
\(338\) | −6.60555 | −0.359294 | ||||||||
\(339\) | −19.2703 | −1.04662 | ||||||||
\(340\) | −21.7729 | −1.18080 | ||||||||
\(341\) | −0.439431 | −0.0237965 | ||||||||
\(342\) | 2.99663 | 0.162039 | ||||||||
\(343\) | −20.1044 | −1.08554 | ||||||||
\(344\) | −46.6070 | −2.51288 | ||||||||
\(345\) | 2.20453 | 0.118688 | ||||||||
\(346\) | −26.1899 | −1.40798 | ||||||||
\(347\) | 1.25044 | 0.0671271 | 0.0335635 | − | 0.999437i | \(-0.489314\pi\) | ||||
0.0335635 | + | 0.999437i | \(0.489314\pi\) | |||||||
\(348\) | −6.25051 | −0.335063 | ||||||||
\(349\) | 7.77303 | 0.416081 | 0.208040 | − | 0.978120i | \(-0.433291\pi\) | ||||
0.208040 | + | 0.978120i | \(0.433291\pi\) | |||||||
\(350\) | 3.61804 | 0.193392 | ||||||||
\(351\) | 21.6976 | 1.15813 | ||||||||
\(352\) | −47.6901 | −2.54189 | ||||||||
\(353\) | −13.4663 | −0.716738 | −0.358369 | − | 0.933580i | \(-0.616667\pi\) | ||||
−0.358369 | + | 0.933580i | \(0.616667\pi\) | |||||||
\(354\) | 20.3325 | 1.08066 | ||||||||
\(355\) | 7.30329 | 0.387619 | ||||||||
\(356\) | −5.89939 | −0.312667 | ||||||||
\(357\) | 6.61899 | 0.350314 | ||||||||
\(358\) | 1.86199 | 0.0984094 | ||||||||
\(359\) | 26.0038 | 1.37243 | 0.686214 | − | 0.727400i | \(-0.259271\pi\) | ||||
0.686214 | + | 0.727400i | \(0.259271\pi\) | |||||||
\(360\) | −10.1915 | −0.537141 | ||||||||
\(361\) | −14.0816 | −0.741134 | ||||||||
\(362\) | 30.2366 | 1.58920 | ||||||||
\(363\) | −11.4033 | −0.598516 | ||||||||
\(364\) | −49.4329 | −2.59099 | ||||||||
\(365\) | 6.83409 | 0.357712 | ||||||||
\(366\) | −1.06710 | −0.0557780 | ||||||||
\(367\) | −29.0687 | −1.51738 | −0.758688 | − | 0.651455i | \(-0.774159\pi\) | ||||
−0.758688 | + | 0.651455i | \(0.774159\pi\) | |||||||
\(368\) | −10.6314 | −0.554198 | ||||||||
\(369\) | 3.92736 | 0.204450 | ||||||||
\(370\) | 45.0015 | 2.33952 | ||||||||
\(371\) | 6.81899 | 0.354024 | ||||||||
\(372\) | −1.99532 | −0.103453 | ||||||||
\(373\) | −5.10946 | −0.264558 | −0.132279 | − | 0.991213i | \(-0.542229\pi\) | ||||
−0.132279 | + | 0.991213i | \(0.542229\pi\) | |||||||
\(374\) | −9.95617 | −0.514821 | ||||||||
\(375\) | 18.5873 | 0.959843 | ||||||||
\(376\) | 39.5737 | 2.04086 | ||||||||
\(377\) | 2.77038 | 0.142682 | ||||||||
\(378\) | 34.3351 | 1.76601 | ||||||||
\(379\) | −5.37268 | −0.275976 | −0.137988 | − | 0.990434i | \(-0.544064\pi\) | ||||
−0.137988 | + | 0.990434i | \(0.544064\pi\) | |||||||
\(380\) | −26.0499 | −1.33633 | ||||||||
\(381\) | 20.5621 | 1.05343 | ||||||||
\(382\) | −10.9965 | −0.562630 | ||||||||
\(383\) | 24.4970 | 1.25174 | 0.625869 | − | 0.779928i | \(-0.284745\pi\) | ||||
0.625869 | + | 0.779928i | \(0.284745\pi\) | |||||||
\(384\) | −76.4085 | −3.89921 | ||||||||
\(385\) | −9.23714 | −0.470768 | ||||||||
\(386\) | −22.7657 | −1.15875 | ||||||||
\(387\) | −2.31240 | −0.117546 | ||||||||
\(388\) | 58.6598 | 2.97800 | ||||||||
\(389\) | −35.8596 | −1.81815 | −0.909077 | − | 0.416627i | \(-0.863212\pi\) | ||||
−0.909077 | + | 0.416627i | \(0.863212\pi\) | |||||||
\(390\) | −35.9906 | −1.82245 | ||||||||
\(391\) | −1.22734 | −0.0620694 | ||||||||
\(392\) | 18.9716 | 0.958213 | ||||||||
\(393\) | −15.7173 | −0.792830 | ||||||||
\(394\) | 33.3435 | 1.67982 | ||||||||
\(395\) | −31.4482 | −1.58233 | ||||||||
\(396\) | −5.34480 | −0.268586 | ||||||||
\(397\) | 9.23466 | 0.463474 | 0.231737 | − | 0.972778i | \(-0.425559\pi\) | ||||
0.231737 | + | 0.972778i | \(0.425559\pi\) | |||||||
\(398\) | −2.23277 | −0.111919 | ||||||||
\(399\) | 7.91920 | 0.396456 | ||||||||
\(400\) | −9.35541 | −0.467771 | ||||||||
\(401\) | −18.6576 | −0.931716 | −0.465858 | − | 0.884859i | \(-0.654254\pi\) | ||||
−0.465858 | + | 0.884859i | \(0.654254\pi\) | |||||||
\(402\) | 4.41824 | 0.220362 | ||||||||
\(403\) | 0.884376 | 0.0440539 | ||||||||
\(404\) | −97.3938 | −4.84552 | ||||||||
\(405\) | 15.3174 | 0.761127 | ||||||||
\(406\) | 4.38396 | 0.217572 | ||||||||
\(407\) | 15.1546 | 0.751188 | ||||||||
\(408\) | −29.0297 | −1.43718 | ||||||||
\(409\) | −5.67821 | −0.280770 | −0.140385 | − | 0.990097i | \(-0.544834\pi\) | ||||
−0.140385 | + | 0.990097i | \(0.544834\pi\) | |||||||
\(410\) | −46.3586 | −2.28949 | ||||||||
\(411\) | 31.7755 | 1.56737 | ||||||||
\(412\) | −57.9917 | −2.85705 | ||||||||
\(413\) | −10.5023 | −0.516787 | ||||||||
\(414\) | −0.894666 | −0.0439704 | ||||||||
\(415\) | −16.4248 | −0.806263 | ||||||||
\(416\) | 95.9787 | 4.70574 | ||||||||
\(417\) | −26.8133 | −1.31305 | ||||||||
\(418\) | −11.9119 | −0.582632 | ||||||||
\(419\) | −6.67056 | −0.325878 | −0.162939 | − | 0.986636i | \(-0.552097\pi\) | ||||
−0.162939 | + | 0.986636i | \(0.552097\pi\) | |||||||
\(420\) | −41.9431 | −2.04661 | ||||||||
\(421\) | −7.82208 | −0.381225 | −0.190612 | − | 0.981665i | \(-0.561047\pi\) | ||||
−0.190612 | + | 0.981665i | \(0.561047\pi\) | |||||||
\(422\) | 8.47677 | 0.412643 | ||||||||
\(423\) | 1.96344 | 0.0954656 | ||||||||
\(424\) | −29.9068 | −1.45240 | ||||||||
\(425\) | −1.08004 | −0.0523896 | ||||||||
\(426\) | 15.1641 | 0.734703 | ||||||||
\(427\) | 0.551186 | 0.0266738 | ||||||||
\(428\) | −56.8728 | −2.74905 | ||||||||
\(429\) | −12.1202 | −0.585167 | ||||||||
\(430\) | 27.2956 | 1.31631 | ||||||||
\(431\) | −4.51099 | −0.217287 | −0.108643 | − | 0.994081i | \(-0.534651\pi\) | ||||
−0.108643 | + | 0.994081i | \(0.534651\pi\) | |||||||
\(432\) | −88.7827 | −4.27156 | ||||||||
\(433\) | −37.0679 | −1.78137 | −0.890684 | − | 0.454623i | \(-0.849774\pi\) | ||||
−0.890684 | + | 0.454623i | \(0.849774\pi\) | |||||||
\(434\) | 1.39947 | 0.0671768 | ||||||||
\(435\) | 2.35063 | 0.112704 | ||||||||
\(436\) | −39.7218 | −1.90233 | ||||||||
\(437\) | −1.46844 | −0.0702449 | ||||||||
\(438\) | 14.1899 | 0.678018 | ||||||||
\(439\) | 24.0995 | 1.15020 | 0.575102 | − | 0.818082i | \(-0.304962\pi\) | ||||
0.575102 | + | 0.818082i | \(0.304962\pi\) | |||||||
\(440\) | 40.5124 | 1.93135 | ||||||||
\(441\) | 0.941273 | 0.0448225 | ||||||||
\(442\) | 20.0373 | 0.953076 | ||||||||
\(443\) | −6.29590 | −0.299127 | −0.149564 | − | 0.988752i | \(-0.547787\pi\) | ||||
−0.149564 | + | 0.988752i | \(0.547787\pi\) | |||||||
\(444\) | 68.8127 | 3.26571 | ||||||||
\(445\) | 2.21858 | 0.105171 | ||||||||
\(446\) | 3.44534 | 0.163142 | ||||||||
\(447\) | −33.7547 | −1.59654 | ||||||||
\(448\) | 79.4952 | 3.75580 | ||||||||
\(449\) | −6.24008 | −0.294488 | −0.147244 | − | 0.989100i | \(-0.547040\pi\) | ||||
−0.147244 | + | 0.989100i | \(0.547040\pi\) | |||||||
\(450\) | −0.787290 | −0.0371132 | ||||||||
\(451\) | −15.6117 | −0.735125 | ||||||||
\(452\) | −67.9842 | −3.19771 | ||||||||
\(453\) | −11.7365 | −0.551427 | ||||||||
\(454\) | −48.0635 | −2.25573 | ||||||||
\(455\) | 18.5902 | 0.871522 | ||||||||
\(456\) | −34.7322 | −1.62648 | ||||||||
\(457\) | −36.9888 | −1.73026 | −0.865131 | − | 0.501547i | \(-0.832765\pi\) | ||||
−0.865131 | + | 0.501547i | \(0.832765\pi\) | |||||||
\(458\) | −5.81099 | −0.271530 | ||||||||
\(459\) | −10.2496 | −0.478408 | ||||||||
\(460\) | 7.77740 | 0.362623 | ||||||||
\(461\) | −27.5069 | −1.28112 | −0.640561 | − | 0.767907i | \(-0.721298\pi\) | ||||
−0.640561 | + | 0.767907i | \(0.721298\pi\) | |||||||
\(462\) | −19.1794 | −0.892308 | ||||||||
\(463\) | 0.453593 | 0.0210802 | 0.0105401 | − | 0.999944i | \(-0.496645\pi\) | ||||
0.0105401 | + | 0.999944i | \(0.496645\pi\) | |||||||
\(464\) | −11.3359 | −0.526256 | ||||||||
\(465\) | 0.750380 | 0.0347980 | ||||||||
\(466\) | 35.1974 | 1.63049 | ||||||||
\(467\) | 11.9808 | 0.554404 | 0.277202 | − | 0.960812i | \(-0.410593\pi\) | ||||
0.277202 | + | 0.960812i | \(0.410593\pi\) | |||||||
\(468\) | 10.7567 | 0.497227 | ||||||||
\(469\) | −2.28215 | −0.105380 | ||||||||
\(470\) | −23.1765 | −1.06905 | ||||||||
\(471\) | −30.3986 | −1.40069 | ||||||||
\(472\) | 46.0614 | 2.12015 | ||||||||
\(473\) | 9.19202 | 0.422650 | ||||||||
\(474\) | −65.2970 | −2.99919 | ||||||||
\(475\) | −1.29220 | −0.0592902 | ||||||||
\(476\) | 23.3512 | 1.07030 | ||||||||
\(477\) | −1.48382 | −0.0679394 | ||||||||
\(478\) | −12.9431 | −0.592004 | ||||||||
\(479\) | 26.3778 | 1.20523 | 0.602617 | − | 0.798031i | \(-0.294125\pi\) | ||||
0.602617 | + | 0.798031i | \(0.294125\pi\) | |||||||
\(480\) | 81.4365 | 3.71705 | ||||||||
\(481\) | −30.4995 | −1.39066 | ||||||||
\(482\) | −22.0483 | −1.00427 | ||||||||
\(483\) | −2.36434 | −0.107581 | ||||||||
\(484\) | −40.2298 | −1.82863 | ||||||||
\(485\) | −22.0602 | −1.00170 | ||||||||
\(486\) | −13.8928 | −0.630192 | ||||||||
\(487\) | −33.1185 | −1.50074 | −0.750371 | − | 0.661017i | \(-0.770125\pi\) | ||||
−0.750371 | + | 0.661017i | \(0.770125\pi\) | |||||||
\(488\) | −2.41740 | −0.109431 | ||||||||
\(489\) | −12.0023 | −0.542761 | ||||||||
\(490\) | −11.1108 | −0.501935 | ||||||||
\(491\) | 6.44472 | 0.290846 | 0.145423 | − | 0.989370i | \(-0.453546\pi\) | ||||
0.145423 | + | 0.989370i | \(0.453546\pi\) | |||||||
\(492\) | −70.8878 | −3.19587 | ||||||||
\(493\) | −1.30868 | −0.0589399 | ||||||||
\(494\) | 23.9733 | 1.07861 | ||||||||
\(495\) | 2.01001 | 0.0903434 | ||||||||
\(496\) | −3.61871 | −0.162485 | ||||||||
\(497\) | −7.83271 | −0.351345 | ||||||||
\(498\) | −34.1035 | −1.52821 | ||||||||
\(499\) | −28.2725 | −1.26565 | −0.632824 | − | 0.774295i | \(-0.718104\pi\) | ||||
−0.632824 | + | 0.774295i | \(0.718104\pi\) | |||||||
\(500\) | 65.5744 | 2.93257 | ||||||||
\(501\) | −0.863376 | −0.0385728 | ||||||||
\(502\) | −66.4803 | −2.96716 | ||||||||
\(503\) | 20.2084 | 0.901046 | 0.450523 | − | 0.892765i | \(-0.351237\pi\) | ||||
0.450523 | + | 0.892765i | \(0.351237\pi\) | |||||||
\(504\) | 10.9303 | 0.486875 | ||||||||
\(505\) | 36.6268 | 1.62987 | ||||||||
\(506\) | 3.55639 | 0.158101 | ||||||||
\(507\) | 3.79856 | 0.168700 | ||||||||
\(508\) | 72.5416 | 3.21851 | ||||||||
\(509\) | −7.80824 | −0.346094 | −0.173047 | − | 0.984914i | \(-0.555361\pi\) | ||||
−0.173047 | + | 0.984914i | \(0.555361\pi\) | |||||||
\(510\) | 17.0013 | 0.752831 | ||||||||
\(511\) | −7.32949 | −0.324237 | ||||||||
\(512\) | −75.2589 | −3.32600 | ||||||||
\(513\) | −12.2630 | −0.541423 | ||||||||
\(514\) | 20.5693 | 0.907273 | ||||||||
\(515\) | 21.8089 | 0.961015 | ||||||||
\(516\) | 41.7382 | 1.83742 | ||||||||
\(517\) | −7.80488 | −0.343258 | ||||||||
\(518\) | −48.2636 | −2.12058 | ||||||||
\(519\) | 15.0606 | 0.661088 | ||||||||
\(520\) | −81.5332 | −3.57547 | ||||||||
\(521\) | −3.21561 | −0.140878 | −0.0704392 | − | 0.997516i | \(-0.522440\pi\) | ||||
−0.0704392 | + | 0.997516i | \(0.522440\pi\) | |||||||
\(522\) | −0.953956 | −0.0417535 | ||||||||
\(523\) | 20.3437 | 0.889567 | 0.444784 | − | 0.895638i | \(-0.353281\pi\) | ||||
0.444784 | + | 0.895638i | \(0.353281\pi\) | |||||||
\(524\) | −55.4492 | −2.42231 | ||||||||
\(525\) | −2.08057 | −0.0908037 | ||||||||
\(526\) | 16.3804 | 0.714220 | ||||||||
\(527\) | −0.417764 | −0.0181981 | ||||||||
\(528\) | 49.5935 | 2.15828 | ||||||||
\(529\) | −22.5616 | −0.980939 | ||||||||
\(530\) | 17.5150 | 0.760805 | ||||||||
\(531\) | 2.28532 | 0.0991746 | ||||||||
\(532\) | 27.9383 | 1.21128 | ||||||||
\(533\) | 31.4192 | 1.36092 | ||||||||
\(534\) | 4.60652 | 0.199344 | ||||||||
\(535\) | 21.3881 | 0.924689 | ||||||||
\(536\) | 10.0091 | 0.432327 | ||||||||
\(537\) | −1.07075 | −0.0462063 | ||||||||
\(538\) | −32.1819 | −1.38746 | ||||||||
\(539\) | −3.74166 | −0.161165 | ||||||||
\(540\) | 64.9492 | 2.79497 | ||||||||
\(541\) | 2.48117 | 0.106674 | 0.0533368 | − | 0.998577i | \(-0.483014\pi\) | ||||
0.0533368 | + | 0.998577i | \(0.483014\pi\) | |||||||
\(542\) | −43.6287 | −1.87401 | ||||||||
\(543\) | −17.3877 | −0.746179 | ||||||||
\(544\) | −45.3386 | −1.94388 | ||||||||
\(545\) | 14.9382 | 0.639881 | ||||||||
\(546\) | 38.5995 | 1.65191 | ||||||||
\(547\) | 9.48989 | 0.405758 | 0.202879 | − | 0.979204i | \(-0.434970\pi\) | ||||
0.202879 | + | 0.979204i | \(0.434970\pi\) | |||||||
\(548\) | 112.101 | 4.78873 | ||||||||
\(549\) | −0.119939 | −0.00511887 | ||||||||
\(550\) | 3.12956 | 0.133445 | ||||||||
\(551\) | −1.56575 | −0.0667033 | ||||||||
\(552\) | 10.3695 | 0.441357 | ||||||||
\(553\) | 33.7279 | 1.43425 | ||||||||
\(554\) | 23.0824 | 0.980675 | ||||||||
\(555\) | −25.8783 | −1.09847 | ||||||||
\(556\) | −94.5951 | −4.01173 | ||||||||
\(557\) | 39.1678 | 1.65959 | 0.829796 | − | 0.558067i | \(-0.188457\pi\) | ||||
0.829796 | + | 0.558067i | \(0.188457\pi\) | |||||||
\(558\) | −0.304527 | −0.0128917 | ||||||||
\(559\) | −18.4994 | −0.782441 | ||||||||
\(560\) | −76.0678 | −3.21445 | ||||||||
\(561\) | 5.72535 | 0.241724 | ||||||||
\(562\) | 59.6350 | 2.51555 | ||||||||
\(563\) | 36.2205 | 1.52651 | 0.763256 | − | 0.646096i | \(-0.223599\pi\) | ||||
0.763256 | + | 0.646096i | \(0.223599\pi\) | |||||||
\(564\) | −35.4396 | −1.49228 | ||||||||
\(565\) | 25.5668 | 1.07560 | ||||||||
\(566\) | −1.10040 | −0.0462531 | ||||||||
\(567\) | −16.4277 | −0.689900 | ||||||||
\(568\) | 34.3528 | 1.44141 | ||||||||
\(569\) | −23.1789 | −0.971709 | −0.485854 | − | 0.874040i | \(-0.661491\pi\) | ||||
−0.485854 | + | 0.874040i | \(0.661491\pi\) | |||||||
\(570\) | 20.3410 | 0.851992 | ||||||||
\(571\) | −44.0770 | −1.84456 | −0.922282 | − | 0.386517i | \(-0.873678\pi\) | ||||
−0.922282 | + | 0.386517i | \(0.873678\pi\) | |||||||
\(572\) | −42.7589 | −1.78784 | ||||||||
\(573\) | 6.32360 | 0.264172 | ||||||||
\(574\) | 49.7191 | 2.07523 | ||||||||
\(575\) | 0.385796 | 0.0160888 | ||||||||
\(576\) | −17.2983 | −0.720761 | ||||||||
\(577\) | −11.0652 | −0.460651 | −0.230325 | − | 0.973114i | \(-0.573979\pi\) | ||||
−0.230325 | + | 0.973114i | \(0.573979\pi\) | |||||||
\(578\) | 37.3657 | 1.55421 | ||||||||
\(579\) | 13.0916 | 0.544066 | ||||||||
\(580\) | 8.29281 | 0.344340 | ||||||||
\(581\) | 17.6155 | 0.730812 | ||||||||
\(582\) | −45.8043 | −1.89865 | ||||||||
\(583\) | 5.89835 | 0.244285 | ||||||||
\(584\) | 32.1458 | 1.33020 | ||||||||
\(585\) | −4.04525 | −0.167251 | ||||||||
\(586\) | 28.0309 | 1.15794 | ||||||||
\(587\) | −7.22525 | −0.298218 | −0.149109 | − | 0.988821i | \(-0.547641\pi\) | ||||
−0.149109 | + | 0.988821i | \(0.547641\pi\) | |||||||
\(588\) | −16.9898 | −0.700646 | ||||||||
\(589\) | −0.499828 | −0.0205951 | ||||||||
\(590\) | −26.9760 | −1.11058 | ||||||||
\(591\) | −19.1744 | −0.788728 | ||||||||
\(592\) | 124.798 | 5.12918 | ||||||||
\(593\) | −19.1197 | −0.785154 | −0.392577 | − | 0.919719i | \(-0.628416\pi\) | ||||
−0.392577 | + | 0.919719i | \(0.628416\pi\) | |||||||
\(594\) | 29.6995 | 1.21859 | ||||||||
\(595\) | −8.78169 | −0.360014 | ||||||||
\(596\) | −119.084 | −4.87786 | ||||||||
\(597\) | 1.28397 | 0.0525493 | ||||||||
\(598\) | −7.15742 | −0.292689 | ||||||||
\(599\) | −9.04350 | −0.369507 | −0.184754 | − | 0.982785i | \(-0.559149\pi\) | ||||
−0.184754 | + | 0.982785i | \(0.559149\pi\) | |||||||
\(600\) | 9.12502 | 0.372527 | ||||||||
\(601\) | −11.8006 | −0.481356 | −0.240678 | − | 0.970605i | \(-0.577370\pi\) | ||||
−0.240678 | + | 0.970605i | \(0.577370\pi\) | |||||||
\(602\) | −29.2742 | −1.19313 | ||||||||
\(603\) | 0.496599 | 0.0202231 | ||||||||
\(604\) | −41.4052 | −1.68476 | ||||||||
\(605\) | 15.1292 | 0.615089 | ||||||||
\(606\) | 76.0496 | 3.08931 | ||||||||
\(607\) | −20.5982 | −0.836054 | −0.418027 | − | 0.908435i | \(-0.637278\pi\) | ||||
−0.418027 | + | 0.908435i | \(0.637278\pi\) | |||||||
\(608\) | −54.2448 | −2.19992 | ||||||||
\(609\) | −2.52102 | −0.102157 | ||||||||
\(610\) | 1.41576 | 0.0573225 | ||||||||
\(611\) | 15.7077 | 0.635465 | ||||||||
\(612\) | −5.08126 | −0.205398 | ||||||||
\(613\) | 1.51954 | 0.0613735 | 0.0306868 | − | 0.999529i | \(-0.490231\pi\) | ||||
0.0306868 | + | 0.999529i | \(0.490231\pi\) | |||||||
\(614\) | −60.8177 | −2.45440 | ||||||||
\(615\) | 26.6587 | 1.07498 | ||||||||
\(616\) | −43.4492 | −1.75062 | ||||||||
\(617\) | −34.1749 | −1.37583 | −0.687914 | − | 0.725792i | \(-0.741473\pi\) | ||||
−0.687914 | + | 0.725792i | \(0.741473\pi\) | |||||||
\(618\) | 45.2827 | 1.82154 | ||||||||
\(619\) | 10.5551 | 0.424246 | 0.212123 | − | 0.977243i | \(-0.431962\pi\) | ||||
0.212123 | + | 0.977243i | \(0.431962\pi\) | |||||||
\(620\) | 2.64728 | 0.106317 | ||||||||
\(621\) | 3.66119 | 0.146919 | ||||||||
\(622\) | 31.5949 | 1.26684 | ||||||||
\(623\) | −2.37941 | −0.0953289 | ||||||||
\(624\) | −99.8094 | −3.99557 | ||||||||
\(625\) | −21.7472 | −0.869888 | ||||||||
\(626\) | −14.3156 | −0.572168 | ||||||||
\(627\) | 6.85002 | 0.273563 | ||||||||
\(628\) | −107.244 | −4.27950 | ||||||||
\(629\) | 14.4074 | 0.574461 | ||||||||
\(630\) | −6.40137 | −0.255037 | ||||||||
\(631\) | −0.429836 | −0.0171115 | −0.00855576 | − | 0.999963i | \(-0.502723\pi\) | ||||
−0.00855576 | + | 0.999963i | \(0.502723\pi\) | |||||||
\(632\) | −147.924 | −5.88411 | ||||||||
\(633\) | −4.87461 | −0.193748 | ||||||||
\(634\) | 5.49835 | 0.218367 | ||||||||
\(635\) | −27.2807 | −1.08260 | ||||||||
\(636\) | 26.7826 | 1.06200 | ||||||||
\(637\) | 7.53028 | 0.298361 | ||||||||
\(638\) | 3.79208 | 0.150130 | ||||||||
\(639\) | 1.70441 | 0.0674253 | ||||||||
\(640\) | 101.374 | 4.00717 | ||||||||
\(641\) | −45.8583 | −1.81129 | −0.905647 | − | 0.424033i | \(-0.860614\pi\) | ||||
−0.905647 | + | 0.424033i | \(0.860614\pi\) | |||||||
\(642\) | 44.4089 | 1.75268 | ||||||||
\(643\) | 19.4843 | 0.768385 | 0.384193 | − | 0.923253i | \(-0.374480\pi\) | ||||
0.384193 | + | 0.923253i | \(0.374480\pi\) | |||||||
\(644\) | −8.34118 | −0.328689 | ||||||||
\(645\) | −15.6965 | −0.618047 | ||||||||
\(646\) | −11.3246 | −0.445560 | ||||||||
\(647\) | −38.8760 | −1.52837 | −0.764186 | − | 0.644996i | \(-0.776859\pi\) | ||||
−0.764186 | + | 0.644996i | \(0.776859\pi\) | |||||||
\(648\) | 72.0490 | 2.83035 | ||||||||
\(649\) | −9.08441 | −0.356594 | ||||||||
\(650\) | −6.29840 | −0.247044 | ||||||||
\(651\) | −0.804774 | −0.0315416 | ||||||||
\(652\) | −42.3430 | −1.65828 | ||||||||
\(653\) | −18.4729 | −0.722900 | −0.361450 | − | 0.932392i | \(-0.617718\pi\) | ||||
−0.361450 | + | 0.932392i | \(0.617718\pi\) | |||||||
\(654\) | 31.0167 | 1.21285 | ||||||||
\(655\) | 20.8527 | 0.814784 | ||||||||
\(656\) | −128.562 | −5.01950 | ||||||||
\(657\) | 1.59491 | 0.0622232 | ||||||||
\(658\) | 24.8565 | 0.969007 | ||||||||
\(659\) | 3.69443 | 0.143915 | 0.0719574 | − | 0.997408i | \(-0.477075\pi\) | ||||
0.0719574 | + | 0.997408i | \(0.477075\pi\) | |||||||
\(660\) | −36.2803 | −1.41221 | ||||||||
\(661\) | 24.7906 | 0.964243 | 0.482121 | − | 0.876104i | \(-0.339866\pi\) | ||||
0.482121 | + | 0.876104i | \(0.339866\pi\) | |||||||
\(662\) | 3.51223 | 0.136507 | ||||||||
\(663\) | −11.5225 | −0.447499 | ||||||||
\(664\) | −77.2582 | −2.99820 | ||||||||
\(665\) | −10.5067 | −0.407434 | ||||||||
\(666\) | 10.5022 | 0.406953 | ||||||||
\(667\) | 0.467467 | 0.0181004 | ||||||||
\(668\) | −3.04592 | −0.117850 | ||||||||
\(669\) | −1.98126 | −0.0766001 | ||||||||
\(670\) | −5.86186 | −0.226464 | ||||||||
\(671\) | 0.476770 | 0.0184055 | ||||||||
\(672\) | −87.3397 | −3.36920 | ||||||||
\(673\) | −4.47142 | −0.172361 | −0.0861803 | − | 0.996280i | \(-0.527466\pi\) | ||||
−0.0861803 | + | 0.996280i | \(0.527466\pi\) | |||||||
\(674\) | 8.93679 | 0.344232 | ||||||||
\(675\) | 3.22179 | 0.124007 | ||||||||
\(676\) | 13.4010 | 0.515423 | ||||||||
\(677\) | 46.4166 | 1.78394 | 0.891968 | − | 0.452099i | \(-0.149325\pi\) | ||||
0.891968 | + | 0.452099i | \(0.149325\pi\) | |||||||
\(678\) | 53.0853 | 2.03873 | ||||||||
\(679\) | 23.6593 | 0.907960 | ||||||||
\(680\) | 38.5149 | 1.47698 | ||||||||
\(681\) | 27.6392 | 1.05914 | ||||||||
\(682\) | 1.21053 | 0.0463535 | ||||||||
\(683\) | −17.4545 | −0.667879 | −0.333939 | − | 0.942595i | \(-0.608378\pi\) | ||||
−0.333939 | + | 0.942595i | \(0.608378\pi\) | |||||||
\(684\) | −6.07941 | −0.232452 | ||||||||
\(685\) | −42.1578 | −1.61077 | ||||||||
\(686\) | 55.3828 | 2.11453 | ||||||||
\(687\) | 3.34164 | 0.127492 | ||||||||
\(688\) | 75.6963 | 2.88589 | ||||||||
\(689\) | −11.8707 | −0.452238 | ||||||||
\(690\) | −6.07296 | −0.231194 | ||||||||
\(691\) | −44.5591 | −1.69511 | −0.847554 | − | 0.530709i | \(-0.821926\pi\) | ||||
−0.847554 | + | 0.530709i | \(0.821926\pi\) | |||||||
\(692\) | 53.1327 | 2.01980 | ||||||||
\(693\) | −2.15572 | −0.0818890 | ||||||||
\(694\) | −3.44466 | −0.130758 | ||||||||
\(695\) | 35.5743 | 1.34941 | ||||||||
\(696\) | 11.0567 | 0.419105 | ||||||||
\(697\) | −14.8419 | −0.562177 | ||||||||
\(698\) | −21.4129 | −0.810489 | ||||||||
\(699\) | −20.2405 | −0.765565 | ||||||||
\(700\) | −7.34009 | −0.277429 | ||||||||
\(701\) | −12.4062 | −0.468577 | −0.234288 | − | 0.972167i | \(-0.575276\pi\) | ||||
−0.234288 | + | 0.972167i | \(0.575276\pi\) | |||||||
\(702\) | −59.7717 | −2.25594 | ||||||||
\(703\) | 17.2376 | 0.650127 | ||||||||
\(704\) | 68.7625 | 2.59158 | ||||||||
\(705\) | 13.3277 | 0.501952 | ||||||||
\(706\) | 37.0964 | 1.39614 | ||||||||
\(707\) | −39.2819 | −1.47735 | ||||||||
\(708\) | −41.2496 | −1.55025 | ||||||||
\(709\) | −36.2791 | −1.36249 | −0.681245 | − | 0.732056i | \(-0.738561\pi\) | ||||
−0.681245 | + | 0.732056i | \(0.738561\pi\) | |||||||
\(710\) | −20.1188 | −0.755047 | ||||||||
\(711\) | −7.33922 | −0.275242 | ||||||||
\(712\) | 10.4356 | 0.391092 | ||||||||
\(713\) | 0.149227 | 0.00558861 | ||||||||
\(714\) | −18.2337 | −0.682381 | ||||||||
\(715\) | 16.0803 | 0.601370 | ||||||||
\(716\) | −3.77752 | −0.141172 | ||||||||
\(717\) | 7.44300 | 0.277964 | ||||||||
\(718\) | −71.6343 | −2.67337 | ||||||||
\(719\) | 3.53151 | 0.131703 | 0.0658516 | − | 0.997829i | \(-0.479024\pi\) | ||||
0.0658516 | + | 0.997829i | \(0.479024\pi\) | |||||||
\(720\) | 16.5525 | 0.616874 | ||||||||
\(721\) | −23.3898 | −0.871083 | ||||||||
\(722\) | 38.7913 | 1.44366 | ||||||||
\(723\) | 12.6790 | 0.471536 | ||||||||
\(724\) | −61.3425 | −2.27977 | ||||||||
\(725\) | 0.411363 | 0.0152776 | ||||||||
\(726\) | 31.4133 | 1.16586 | ||||||||
\(727\) | 18.5251 | 0.687058 | 0.343529 | − | 0.939142i | \(-0.388378\pi\) | ||||
0.343529 | + | 0.939142i | \(0.388378\pi\) | |||||||
\(728\) | 87.4435 | 3.24087 | ||||||||
\(729\) | 29.8529 | 1.10566 | ||||||||
\(730\) | −18.8263 | −0.696792 | ||||||||
\(731\) | 8.73879 | 0.323216 | ||||||||
\(732\) | 2.16487 | 0.0800158 | ||||||||
\(733\) | 1.15451 | 0.0426427 | 0.0213213 | − | 0.999773i | \(-0.493213\pi\) | ||||
0.0213213 | + | 0.999773i | \(0.493213\pi\) | |||||||
\(734\) | 80.0775 | 2.95571 | ||||||||
\(735\) | 6.38933 | 0.235674 | ||||||||
\(736\) | 16.1952 | 0.596963 | ||||||||
\(737\) | −1.97404 | −0.0727145 | ||||||||
\(738\) | −10.8189 | −0.398250 | ||||||||
\(739\) | 6.62022 | 0.243529 | 0.121764 | − | 0.992559i | \(-0.461145\pi\) | ||||
0.121764 | + | 0.992559i | \(0.461145\pi\) | |||||||
\(740\) | −91.2967 | −3.35613 | ||||||||
\(741\) | −13.7860 | −0.506441 | ||||||||
\(742\) | −18.7847 | −0.689608 | ||||||||
\(743\) | 9.02942 | 0.331257 | 0.165629 | − | 0.986188i | \(-0.447035\pi\) | ||||
0.165629 | + | 0.986188i | \(0.447035\pi\) | |||||||
\(744\) | 3.52959 | 0.129401 | ||||||||
\(745\) | 44.7837 | 1.64075 | ||||||||
\(746\) | 14.0754 | 0.515336 | ||||||||
\(747\) | −3.83314 | −0.140247 | ||||||||
\(748\) | 20.1986 | 0.738533 | ||||||||
\(749\) | −22.9385 | −0.838156 | ||||||||
\(750\) | −51.2035 | −1.86969 | ||||||||
\(751\) | 50.9157 | 1.85794 | 0.928971 | − | 0.370153i | \(-0.120695\pi\) | ||||
0.928971 | + | 0.370153i | \(0.120695\pi\) | |||||||
\(752\) | −64.2731 | −2.34380 | ||||||||
\(753\) | 38.2299 | 1.39317 | ||||||||
\(754\) | −7.63174 | −0.277932 | ||||||||
\(755\) | 15.5712 | 0.566695 | ||||||||
\(756\) | −69.6574 | −2.53341 | ||||||||
\(757\) | −0.0654002 | −0.00237701 | −0.00118851 | − | 0.999999i | \(-0.500378\pi\) | ||||
−0.00118851 | + | 0.999999i | \(0.500378\pi\) | |||||||
\(758\) | 14.8004 | 0.537577 | ||||||||
\(759\) | −2.04512 | −0.0742333 | ||||||||
\(760\) | 46.0806 | 1.67152 | ||||||||
\(761\) | 47.6467 | 1.72719 | 0.863596 | − | 0.504184i | \(-0.168207\pi\) | ||||
0.863596 | + | 0.504184i | \(0.168207\pi\) | |||||||
\(762\) | −56.6439 | −2.05199 | ||||||||
\(763\) | −16.0210 | −0.580000 | ||||||||
\(764\) | 22.3092 | 0.807117 | ||||||||
\(765\) | 1.91091 | 0.0690890 | ||||||||
\(766\) | −67.4834 | −2.43827 | ||||||||
\(767\) | 18.2828 | 0.660154 | ||||||||
\(768\) | 98.7518 | 3.56340 | ||||||||
\(769\) | −25.3168 | −0.912947 | −0.456473 | − | 0.889737i | \(-0.650888\pi\) | ||||
−0.456473 | + | 0.889737i | \(0.650888\pi\) | |||||||
\(770\) | 25.4461 | 0.917016 | ||||||||
\(771\) | −11.8285 | −0.425993 | ||||||||
\(772\) | 46.1859 | 1.66227 | ||||||||
\(773\) | −17.7503 | −0.638433 | −0.319217 | − | 0.947682i | \(-0.603420\pi\) | ||||
−0.319217 | + | 0.947682i | \(0.603420\pi\) | |||||||
\(774\) | 6.37010 | 0.228969 | ||||||||
\(775\) | 0.131317 | 0.00471706 | ||||||||
\(776\) | −103.765 | −3.72496 | ||||||||
\(777\) | 27.7543 | 0.995678 | ||||||||
\(778\) | 98.7848 | 3.54160 | ||||||||
\(779\) | −17.7574 | −0.636225 | ||||||||
\(780\) | 73.0158 | 2.61439 | ||||||||
\(781\) | −6.77520 | −0.242436 | ||||||||
\(782\) | 3.38104 | 0.120906 | ||||||||
\(783\) | 3.90382 | 0.139511 | ||||||||
\(784\) | −30.8126 | −1.10045 | ||||||||
\(785\) | 40.3311 | 1.43948 | ||||||||
\(786\) | 43.2973 | 1.54436 | ||||||||
\(787\) | 39.7731 | 1.41776 | 0.708879 | − | 0.705330i | \(-0.249201\pi\) | ||||
0.708879 | + | 0.705330i | \(0.249201\pi\) | |||||||
\(788\) | −67.6456 | −2.40978 | ||||||||
\(789\) | −9.41965 | −0.335348 | ||||||||
\(790\) | 86.6323 | 3.08224 | ||||||||
\(791\) | −27.4201 | −0.974947 | ||||||||
\(792\) | 9.45459 | 0.335954 | ||||||||
\(793\) | −0.959523 | −0.0340736 | ||||||||
\(794\) | −25.4393 | −0.902807 | ||||||||
\(795\) | −10.0721 | −0.357221 | ||||||||
\(796\) | 4.52974 | 0.160552 | ||||||||
\(797\) | 51.4986 | 1.82417 | 0.912087 | − | 0.409997i | \(-0.134470\pi\) | ||||
0.912087 | + | 0.409997i | \(0.134470\pi\) | |||||||
\(798\) | −21.8155 | −0.772261 | ||||||||
\(799\) | −7.42004 | −0.262502 | ||||||||
\(800\) | 14.2515 | 0.503866 | ||||||||
\(801\) | 0.517762 | 0.0182942 | ||||||||
\(802\) | 51.3973 | 1.81490 | ||||||||
\(803\) | −6.33992 | −0.223731 | ||||||||
\(804\) | −8.96350 | −0.316118 | ||||||||
\(805\) | 3.13686 | 0.110560 | ||||||||
\(806\) | −2.43625 | −0.0858131 | ||||||||
\(807\) | 18.5064 | 0.651456 | ||||||||
\(808\) | 172.283 | 6.06090 | ||||||||
\(809\) | 36.6592 | 1.28887 | 0.644434 | − | 0.764660i | \(-0.277093\pi\) | ||||
0.644434 | + | 0.764660i | \(0.277093\pi\) | |||||||
\(810\) | −42.1958 | −1.48261 | ||||||||
\(811\) | 16.2061 | 0.569074 | 0.284537 | − | 0.958665i | \(-0.408160\pi\) | ||||
0.284537 | + | 0.958665i | \(0.408160\pi\) | |||||||
\(812\) | −8.89396 | −0.312117 | ||||||||
\(813\) | 25.0889 | 0.879907 | ||||||||
\(814\) | −41.7475 | −1.46325 | ||||||||
\(815\) | 15.9239 | 0.557790 | ||||||||
\(816\) | 47.1482 | 1.65052 | ||||||||
\(817\) | 10.4554 | 0.365789 | ||||||||
\(818\) | 15.6421 | 0.546915 | ||||||||
\(819\) | 4.33849 | 0.151599 | ||||||||
\(820\) | 94.0499 | 3.28436 | ||||||||
\(821\) | 3.96186 | 0.138270 | 0.0691350 | − | 0.997607i | \(-0.477976\pi\) | ||||
0.0691350 | + | 0.997607i | \(0.477976\pi\) | |||||||
\(822\) | −87.5339 | −3.05310 | ||||||||
\(823\) | 6.21540 | 0.216655 | 0.108328 | − | 0.994115i | \(-0.465450\pi\) | ||||
0.108328 | + | 0.994115i | \(0.465450\pi\) | |||||||
\(824\) | 102.584 | 3.57367 | ||||||||
\(825\) | −1.79967 | −0.0626566 | ||||||||
\(826\) | 28.9315 | 1.00666 | ||||||||
\(827\) | −29.2952 | −1.01869 | −0.509347 | − | 0.860561i | \(-0.670113\pi\) | ||||
−0.509347 | + | 0.860561i | \(0.670113\pi\) | |||||||
\(828\) | 1.81505 | 0.0630774 | ||||||||
\(829\) | −9.97765 | −0.346538 | −0.173269 | − | 0.984875i | \(-0.555433\pi\) | ||||
−0.173269 | + | 0.984875i | \(0.555433\pi\) | |||||||
\(830\) | 45.2465 | 1.57053 | ||||||||
\(831\) | −13.2736 | −0.460457 | ||||||||
\(832\) | −138.388 | −4.79773 | ||||||||
\(833\) | −3.55717 | −0.123249 | ||||||||
\(834\) | 73.8643 | 2.55771 | ||||||||
\(835\) | 1.14548 | 0.0396409 | ||||||||
\(836\) | 24.1663 | 0.835809 | ||||||||
\(837\) | 1.24620 | 0.0430750 | ||||||||
\(838\) | 18.3758 | 0.634782 | ||||||||
\(839\) | 11.9561 | 0.412772 | 0.206386 | − | 0.978471i | \(-0.433830\pi\) | ||||
0.206386 | + | 0.978471i | \(0.433830\pi\) | |||||||
\(840\) | 74.1945 | 2.55995 | ||||||||
\(841\) | −28.5016 | −0.982812 | ||||||||
\(842\) | 21.5480 | 0.742592 | ||||||||
\(843\) | −34.2935 | −1.18113 | ||||||||
\(844\) | −17.1972 | −0.591953 | ||||||||
\(845\) | −5.03970 | −0.173371 | ||||||||
\(846\) | −5.40881 | −0.185959 | ||||||||
\(847\) | −16.2259 | −0.557528 | ||||||||
\(848\) | 48.5728 | 1.66800 | ||||||||
\(849\) | 0.632789 | 0.0217173 | ||||||||
\(850\) | 2.97525 | 0.102050 | ||||||||
\(851\) | −5.14640 | −0.176416 | ||||||||
\(852\) | −30.7641 | −1.05396 | ||||||||
\(853\) | 49.9164 | 1.70911 | 0.854553 | − | 0.519364i | \(-0.173831\pi\) | ||||
0.854553 | + | 0.519364i | \(0.173831\pi\) | |||||||
\(854\) | −1.51839 | −0.0519582 | ||||||||
\(855\) | 2.28628 | 0.0781891 | ||||||||
\(856\) | 100.604 | 3.43858 | ||||||||
\(857\) | −1.79790 | −0.0614151 | −0.0307076 | − | 0.999528i | \(-0.509776\pi\) | ||||
−0.0307076 | + | 0.999528i | \(0.509776\pi\) | |||||||
\(858\) | 33.3882 | 1.13985 | ||||||||
\(859\) | 14.5095 | 0.495058 | 0.247529 | − | 0.968881i | \(-0.420381\pi\) | ||||
0.247529 | + | 0.968881i | \(0.420381\pi\) | |||||||
\(860\) | −55.3758 | −1.88830 | ||||||||
\(861\) | −28.5912 | −0.974386 | ||||||||
\(862\) | 12.4267 | 0.423255 | ||||||||
\(863\) | 49.0226 | 1.66875 | 0.834375 | − | 0.551197i | \(-0.185829\pi\) | ||||
0.834375 | + | 0.551197i | \(0.185829\pi\) | |||||||
\(864\) | 135.246 | 4.60117 | ||||||||
\(865\) | −19.9816 | −0.679393 | ||||||||
\(866\) | 102.113 | 3.46995 | ||||||||
\(867\) | −21.4874 | −0.729749 | ||||||||
\(868\) | −2.83918 | −0.0963680 | ||||||||
\(869\) | 29.1742 | 0.989667 | ||||||||
\(870\) | −6.47542 | −0.219537 | ||||||||
\(871\) | 3.97284 | 0.134615 | ||||||||
\(872\) | 70.2653 | 2.37948 | ||||||||
\(873\) | −5.14829 | −0.174243 | ||||||||
\(874\) | 4.04520 | 0.136831 | ||||||||
\(875\) | 26.4481 | 0.894110 | ||||||||
\(876\) | −28.7877 | −0.972645 | ||||||||
\(877\) | −0.662079 | −0.0223568 | −0.0111784 | − | 0.999938i | \(-0.503558\pi\) | ||||
−0.0111784 | + | 0.999938i | \(0.503558\pi\) | |||||||
\(878\) | −66.3883 | −2.24050 | ||||||||
\(879\) | −16.1193 | −0.543691 | ||||||||
\(880\) | −65.7978 | −2.21804 | ||||||||
\(881\) | 35.5742 | 1.19853 | 0.599263 | − | 0.800552i | \(-0.295460\pi\) | ||||
0.599263 | + | 0.800552i | \(0.295460\pi\) | |||||||
\(882\) | −2.59299 | −0.0873104 | ||||||||
\(883\) | −37.5465 | −1.26354 | −0.631770 | − | 0.775156i | \(-0.717671\pi\) | ||||
−0.631770 | + | 0.775156i | \(0.717671\pi\) | |||||||
\(884\) | −40.6506 | −1.36723 | ||||||||
\(885\) | 15.5127 | 0.521454 | ||||||||
\(886\) | 17.3437 | 0.582673 | ||||||||
\(887\) | 9.07790 | 0.304806 | 0.152403 | − | 0.988318i | \(-0.451299\pi\) | ||||
0.152403 | + | 0.988318i | \(0.451299\pi\) | |||||||
\(888\) | −121.725 | −4.08483 | ||||||||
\(889\) | 29.2582 | 0.981289 | ||||||||
\(890\) | −6.11167 | −0.204863 | ||||||||
\(891\) | −14.2098 | −0.476046 | ||||||||
\(892\) | −6.98974 | −0.234034 | ||||||||
\(893\) | −8.87761 | −0.297078 | ||||||||
\(894\) | 92.9861 | 3.10992 | ||||||||
\(895\) | 1.42061 | 0.0474857 | ||||||||
\(896\) | −108.723 | −3.63218 | ||||||||
\(897\) | 4.11591 | 0.137426 | ||||||||
\(898\) | 17.1899 | 0.573636 | ||||||||
\(899\) | 0.159117 | 0.00530684 | ||||||||
\(900\) | 1.59721 | 0.0532405 | ||||||||
\(901\) | 5.60752 | 0.186813 | ||||||||
\(902\) | 43.0064 | 1.43196 | ||||||||
\(903\) | 16.8343 | 0.560210 | ||||||||
\(904\) | 120.260 | 3.99977 | ||||||||
\(905\) | 23.0690 | 0.766840 | ||||||||
\(906\) | 32.3311 | 1.07413 | ||||||||
\(907\) | −43.5644 | −1.44653 | −0.723266 | − | 0.690570i | \(-0.757360\pi\) | ||||
−0.723266 | + | 0.690570i | \(0.757360\pi\) | |||||||
\(908\) | 97.5087 | 3.23594 | ||||||||
\(909\) | 8.54779 | 0.283512 | ||||||||
\(910\) | −51.2116 | −1.69765 | ||||||||
\(911\) | 45.7729 | 1.51652 | 0.758262 | − | 0.651950i | \(-0.226049\pi\) | ||||
0.758262 | + | 0.651950i | \(0.226049\pi\) | |||||||
\(912\) | 56.4099 | 1.86792 | ||||||||
\(913\) | 15.2372 | 0.504277 | ||||||||
\(914\) | 101.895 | 3.37040 | ||||||||
\(915\) | −0.814141 | −0.0269147 | ||||||||
\(916\) | 11.7890 | 0.389521 | ||||||||
\(917\) | −22.3643 | −0.738536 | ||||||||
\(918\) | 28.2351 | 0.931898 | ||||||||
\(919\) | −28.9616 | −0.955354 | −0.477677 | − | 0.878535i | \(-0.658521\pi\) | ||||
−0.477677 | + | 0.878535i | \(0.658521\pi\) | |||||||
\(920\) | −13.7577 | −0.453578 | ||||||||
\(921\) | 34.9735 | 1.15242 | ||||||||
\(922\) | 75.7749 | 2.49551 | ||||||||
\(923\) | 13.6354 | 0.448815 | ||||||||
\(924\) | 38.9102 | 1.28005 | ||||||||
\(925\) | −4.52874 | −0.148904 | ||||||||
\(926\) | −1.24954 | −0.0410625 | ||||||||
\(927\) | 5.08966 | 0.167166 | ||||||||
\(928\) | 17.2685 | 0.566865 | ||||||||
\(929\) | 37.4242 | 1.22785 | 0.613924 | − | 0.789365i | \(-0.289590\pi\) | ||||
0.613924 | + | 0.789365i | \(0.289590\pi\) | |||||||
\(930\) | −2.06712 | −0.0677835 | ||||||||
\(931\) | −4.25593 | −0.139483 | ||||||||
\(932\) | −71.4067 | −2.33901 | ||||||||
\(933\) | −18.1688 | −0.594820 | ||||||||
\(934\) | −33.0042 | −1.07993 | ||||||||
\(935\) | −7.59606 | −0.248418 | ||||||||
\(936\) | −19.0278 | −0.621944 | ||||||||
\(937\) | −56.4941 | −1.84558 | −0.922791 | − | 0.385301i | \(-0.874097\pi\) | ||||
−0.922791 | + | 0.385301i | \(0.874097\pi\) | |||||||
\(938\) | 6.28679 | 0.205271 | ||||||||
\(939\) | 8.23228 | 0.268650 | ||||||||
\(940\) | 47.0192 | 1.53360 | ||||||||
\(941\) | −25.8171 | −0.841614 | −0.420807 | − | 0.907150i | \(-0.638253\pi\) | ||||
−0.420807 | + | 0.907150i | \(0.638253\pi\) | |||||||
\(942\) | 83.7410 | 2.72843 | ||||||||
\(943\) | 5.30160 | 0.172644 | ||||||||
\(944\) | −74.8101 | −2.43486 | ||||||||
\(945\) | 26.1960 | 0.852156 | ||||||||
\(946\) | −25.3218 | −0.823284 | ||||||||
\(947\) | 9.17193 | 0.298048 | 0.149024 | − | 0.988834i | \(-0.452387\pi\) | ||||
0.149024 | + | 0.988834i | \(0.452387\pi\) | |||||||
\(948\) | 132.471 | 4.30247 | ||||||||
\(949\) | 12.7594 | 0.414188 | ||||||||
\(950\) | 3.55971 | 0.115492 | ||||||||
\(951\) | −3.16186 | −0.102530 | ||||||||
\(952\) | −41.3068 | −1.33876 | ||||||||
\(953\) | 22.2148 | 0.719609 | 0.359805 | − | 0.933028i | \(-0.382843\pi\) | ||||
0.359805 | + | 0.933028i | \(0.382843\pi\) | |||||||
\(954\) | 4.08757 | 0.132340 | ||||||||
\(955\) | −8.38979 | −0.271487 | ||||||||
\(956\) | 26.2583 | 0.849254 | ||||||||
\(957\) | −2.18065 | −0.0704906 | ||||||||
\(958\) | −72.6647 | −2.34769 | ||||||||
\(959\) | 45.2139 | 1.46003 | ||||||||
\(960\) | −117.420 | −3.78971 | ||||||||
\(961\) | −30.9492 | −0.998361 | ||||||||
\(962\) | 84.0188 | 2.70888 | ||||||||
\(963\) | 4.99145 | 0.160847 | ||||||||
\(964\) | 44.7304 | 1.44067 | ||||||||
\(965\) | −17.3691 | −0.559132 | ||||||||
\(966\) | 6.51319 | 0.209558 | ||||||||
\(967\) | 38.6726 | 1.24363 | 0.621814 | − | 0.783165i | \(-0.286396\pi\) | ||||
0.621814 | + | 0.783165i | \(0.286396\pi\) | |||||||
\(968\) | 71.1638 | 2.28729 | ||||||||
\(969\) | 6.51227 | 0.209204 | ||||||||
\(970\) | 60.7705 | 1.95122 | ||||||||
\(971\) | 56.6430 | 1.81776 | 0.908881 | − | 0.417056i | \(-0.136938\pi\) | ||||
0.908881 | + | 0.417056i | \(0.136938\pi\) | |||||||
\(972\) | 28.1851 | 0.904037 | ||||||||
\(973\) | −38.1531 | −1.22313 | ||||||||
\(974\) | 91.2336 | 2.92331 | ||||||||
\(975\) | 3.62193 | 0.115995 | ||||||||
\(976\) | 3.92620 | 0.125675 | ||||||||
\(977\) | −11.6553 | −0.372888 | −0.186444 | − | 0.982466i | \(-0.559696\pi\) | ||||
−0.186444 | + | 0.982466i | \(0.559696\pi\) | |||||||
\(978\) | 33.0634 | 1.05725 | ||||||||
\(979\) | −2.05816 | −0.0657790 | ||||||||
\(980\) | 22.5410 | 0.720047 | ||||||||
\(981\) | 3.48620 | 0.111306 | ||||||||
\(982\) | −17.7537 | −0.566542 | ||||||||
\(983\) | 29.3978 | 0.937643 | 0.468822 | − | 0.883293i | \(-0.344679\pi\) | ||||
0.468822 | + | 0.883293i | \(0.344679\pi\) | |||||||
\(984\) | 125.396 | 3.99748 | ||||||||
\(985\) | 25.4394 | 0.810568 | ||||||||
\(986\) | 3.60510 | 0.114810 | ||||||||
\(987\) | −14.2939 | −0.454979 | ||||||||
\(988\) | −48.6359 | −1.54731 | ||||||||
\(989\) | −3.12154 | −0.0992592 | ||||||||
\(990\) | −5.53711 | −0.175981 | ||||||||
\(991\) | 36.4480 | 1.15781 | 0.578905 | − | 0.815395i | \(-0.303480\pi\) | ||||
0.578905 | + | 0.815395i | \(0.303480\pi\) | |||||||
\(992\) | 5.51253 | 0.175023 | ||||||||
\(993\) | −2.01972 | −0.0640940 | ||||||||
\(994\) | 21.5773 | 0.684389 | ||||||||
\(995\) | −1.70349 | −0.0540044 | ||||||||
\(996\) | 69.1874 | 2.19229 | ||||||||
\(997\) | 9.94513 | 0.314966 | 0.157483 | − | 0.987522i | \(-0.449662\pi\) | ||||
0.157483 | + | 0.987522i | \(0.449662\pi\) | |||||||
\(998\) | 77.8839 | 2.46537 | ||||||||
\(999\) | −42.9777 | −1.35975 |
(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 | 4021.2.a.b.1.1 | ✓ | 151 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4021.2.a.b.1.1 | ✓ | 151 | 1.1 | even | 1 | trivial |