Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4003,2,Mod(1,4003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4003, 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("4003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4003.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: | \(31.9641159291\) |
Analytic rank: | \(1\) |
Dimension: | \(152\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 4003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.60205 | −1.83993 | −0.919963 | − | 0.392005i | \(-0.871782\pi\) | ||||
−0.919963 | + | 0.392005i | \(0.871782\pi\) | |||||||
\(3\) | 1.48054 | 0.854789 | 0.427395 | − | 0.904065i | \(-0.359431\pi\) | ||||
0.427395 | + | 0.904065i | \(0.359431\pi\) | |||||||
\(4\) | 4.77066 | 2.38533 | ||||||||
\(5\) | 1.31197 | 0.586729 | 0.293365 | − | 0.956001i | \(-0.405225\pi\) | ||||
0.293365 | + | 0.956001i | \(0.405225\pi\) | |||||||
\(6\) | −3.85243 | −1.57275 | ||||||||
\(7\) | 3.44490 | 1.30205 | 0.651026 | − | 0.759056i | \(-0.274339\pi\) | ||||
0.651026 | + | 0.759056i | \(0.274339\pi\) | |||||||
\(8\) | −7.20939 | −2.54890 | ||||||||
\(9\) | −0.808005 | −0.269335 | ||||||||
\(10\) | −3.41380 | −1.07954 | ||||||||
\(11\) | −4.34159 | −1.30904 | −0.654519 | − | 0.756045i | \(-0.727129\pi\) | ||||
−0.654519 | + | 0.756045i | \(0.727129\pi\) | |||||||
\(12\) | 7.06314 | 2.03895 | ||||||||
\(13\) | 1.60278 | 0.444530 | 0.222265 | − | 0.974986i | \(-0.428655\pi\) | ||||
0.222265 | + | 0.974986i | \(0.428655\pi\) | |||||||
\(14\) | −8.96381 | −2.39568 | ||||||||
\(15\) | 1.94242 | 0.501530 | ||||||||
\(16\) | 9.21787 | 2.30447 | ||||||||
\(17\) | −2.68007 | −0.650012 | −0.325006 | − | 0.945712i | \(-0.605366\pi\) | ||||
−0.325006 | + | 0.945712i | \(0.605366\pi\) | |||||||
\(18\) | 2.10247 | 0.495557 | ||||||||
\(19\) | 1.39273 | 0.319514 | 0.159757 | − | 0.987156i | \(-0.448929\pi\) | ||||
0.159757 | + | 0.987156i | \(0.448929\pi\) | |||||||
\(20\) | 6.25894 | 1.39954 | ||||||||
\(21\) | 5.10031 | 1.11298 | ||||||||
\(22\) | 11.2970 | 2.40853 | ||||||||
\(23\) | −1.41743 | −0.295554 | −0.147777 | − | 0.989021i | \(-0.547212\pi\) | ||||
−0.147777 | + | 0.989021i | \(0.547212\pi\) | |||||||
\(24\) | −10.6738 | −2.17878 | ||||||||
\(25\) | −3.27874 | −0.655749 | ||||||||
\(26\) | −4.17050 | −0.817902 | ||||||||
\(27\) | −5.63790 | −1.08501 | ||||||||
\(28\) | 16.4345 | 3.10582 | ||||||||
\(29\) | −9.46568 | −1.75773 | −0.878866 | − | 0.477069i | \(-0.841699\pi\) | ||||
−0.878866 | + | 0.477069i | \(0.841699\pi\) | |||||||
\(30\) | −5.05426 | −0.922778 | ||||||||
\(31\) | −8.88883 | −1.59648 | −0.798241 | − | 0.602338i | \(-0.794236\pi\) | ||||
−0.798241 | + | 0.602338i | \(0.794236\pi\) | |||||||
\(32\) | −9.56656 | −1.69115 | ||||||||
\(33\) | −6.42789 | −1.11895 | ||||||||
\(34\) | 6.97367 | 1.19597 | ||||||||
\(35\) | 4.51960 | 0.763952 | ||||||||
\(36\) | −3.85472 | −0.642453 | ||||||||
\(37\) | 6.69542 | 1.10072 | 0.550360 | − | 0.834927i | \(-0.314490\pi\) | ||||
0.550360 | + | 0.834927i | \(0.314490\pi\) | |||||||
\(38\) | −3.62395 | −0.587882 | ||||||||
\(39\) | 2.37297 | 0.379980 | ||||||||
\(40\) | −9.45848 | −1.49552 | ||||||||
\(41\) | −3.03509 | −0.474001 | −0.237001 | − | 0.971509i | \(-0.576164\pi\) | ||||
−0.237001 | + | 0.971509i | \(0.576164\pi\) | |||||||
\(42\) | −13.2713 | −2.04780 | ||||||||
\(43\) | 11.4209 | 1.74166 | 0.870832 | − | 0.491581i | \(-0.163581\pi\) | ||||
0.870832 | + | 0.491581i | \(0.163581\pi\) | |||||||
\(44\) | −20.7122 | −3.12249 | ||||||||
\(45\) | −1.06008 | −0.158027 | ||||||||
\(46\) | 3.68821 | 0.543797 | ||||||||
\(47\) | 1.90734 | 0.278214 | 0.139107 | − | 0.990277i | \(-0.455577\pi\) | ||||
0.139107 | + | 0.990277i | \(0.455577\pi\) | |||||||
\(48\) | 13.6474 | 1.96983 | ||||||||
\(49\) | 4.86737 | 0.695338 | ||||||||
\(50\) | 8.53145 | 1.20653 | ||||||||
\(51\) | −3.96794 | −0.555623 | ||||||||
\(52\) | 7.64630 | 1.06035 | ||||||||
\(53\) | 9.71534 | 1.33451 | 0.667253 | − | 0.744832i | \(-0.267470\pi\) | ||||
0.667253 | + | 0.744832i | \(0.267470\pi\) | |||||||
\(54\) | 14.6701 | 1.99635 | ||||||||
\(55\) | −5.69602 | −0.768051 | ||||||||
\(56\) | −24.8357 | −3.31880 | ||||||||
\(57\) | 2.06199 | 0.273117 | ||||||||
\(58\) | 24.6302 | 3.23410 | ||||||||
\(59\) | 1.71390 | 0.223131 | 0.111566 | − | 0.993757i | \(-0.464414\pi\) | ||||
0.111566 | + | 0.993757i | \(0.464414\pi\) | |||||||
\(60\) | 9.26661 | 1.19631 | ||||||||
\(61\) | −11.5122 | −1.47398 | −0.736991 | − | 0.675902i | \(-0.763754\pi\) | ||||
−0.736991 | + | 0.675902i | \(0.763754\pi\) | |||||||
\(62\) | 23.1292 | 2.93741 | ||||||||
\(63\) | −2.78350 | −0.350688 | ||||||||
\(64\) | 6.45693 | 0.807117 | ||||||||
\(65\) | 2.10279 | 0.260819 | ||||||||
\(66\) | 16.7257 | 2.05879 | ||||||||
\(67\) | 0.441675 | 0.0539592 | 0.0269796 | − | 0.999636i | \(-0.491411\pi\) | ||||
0.0269796 | + | 0.999636i | \(0.491411\pi\) | |||||||
\(68\) | −12.7857 | −1.55049 | ||||||||
\(69\) | −2.09856 | −0.252636 | ||||||||
\(70\) | −11.7602 | −1.40561 | ||||||||
\(71\) | −7.97411 | −0.946353 | −0.473176 | − | 0.880968i | \(-0.656893\pi\) | ||||
−0.473176 | + | 0.880968i | \(0.656893\pi\) | |||||||
\(72\) | 5.82522 | 0.686509 | ||||||||
\(73\) | −5.45206 | −0.638115 | −0.319057 | − | 0.947735i | \(-0.603366\pi\) | ||||
−0.319057 | + | 0.947735i | \(0.603366\pi\) | |||||||
\(74\) | −17.4218 | −2.02524 | ||||||||
\(75\) | −4.85431 | −0.560527 | ||||||||
\(76\) | 6.64423 | 0.762146 | ||||||||
\(77\) | −14.9564 | −1.70444 | ||||||||
\(78\) | −6.17459 | −0.699134 | ||||||||
\(79\) | 2.73268 | 0.307450 | 0.153725 | − | 0.988114i | \(-0.450873\pi\) | ||||
0.153725 | + | 0.988114i | \(0.450873\pi\) | |||||||
\(80\) | 12.0935 | 1.35210 | ||||||||
\(81\) | −5.92311 | −0.658124 | ||||||||
\(82\) | 7.89745 | 0.872128 | ||||||||
\(83\) | −15.9563 | −1.75143 | −0.875714 | − | 0.482829i | \(-0.839609\pi\) | ||||
−0.875714 | + | 0.482829i | \(0.839609\pi\) | |||||||
\(84\) | 24.3319 | 2.65482 | ||||||||
\(85\) | −3.51616 | −0.381381 | ||||||||
\(86\) | −29.7176 | −3.20453 | ||||||||
\(87\) | −14.0143 | −1.50249 | ||||||||
\(88\) | 31.3002 | 3.33661 | ||||||||
\(89\) | −10.0380 | −1.06403 | −0.532015 | − | 0.846735i | \(-0.678565\pi\) | ||||
−0.532015 | + | 0.846735i | \(0.678565\pi\) | |||||||
\(90\) | 2.75837 | 0.290758 | ||||||||
\(91\) | 5.52141 | 0.578801 | ||||||||
\(92\) | −6.76206 | −0.704993 | ||||||||
\(93\) | −13.1603 | −1.36466 | ||||||||
\(94\) | −4.96299 | −0.511893 | ||||||||
\(95\) | 1.82721 | 0.187468 | ||||||||
\(96\) | −14.1637 | −1.44557 | ||||||||
\(97\) | −0.127111 | −0.0129062 | −0.00645309 | − | 0.999979i | \(-0.502054\pi\) | ||||
−0.00645309 | + | 0.999979i | \(0.502054\pi\) | |||||||
\(98\) | −12.6651 | −1.27937 | ||||||||
\(99\) | 3.50803 | 0.352570 | ||||||||
\(100\) | −15.6418 | −1.56418 | ||||||||
\(101\) | 17.1694 | 1.70842 | 0.854212 | − | 0.519926i | \(-0.174040\pi\) | ||||
0.854212 | + | 0.519926i | \(0.174040\pi\) | |||||||
\(102\) | 10.3248 | 1.02231 | ||||||||
\(103\) | −15.5235 | −1.52958 | −0.764789 | − | 0.644280i | \(-0.777157\pi\) | ||||
−0.764789 | + | 0.644280i | \(0.777157\pi\) | |||||||
\(104\) | −11.5550 | −1.13306 | ||||||||
\(105\) | 6.69144 | 0.653018 | ||||||||
\(106\) | −25.2798 | −2.45539 | ||||||||
\(107\) | −12.5337 | −1.21168 | −0.605841 | − | 0.795586i | \(-0.707163\pi\) | ||||
−0.605841 | + | 0.795586i | \(0.707163\pi\) | |||||||
\(108\) | −26.8965 | −2.58812 | ||||||||
\(109\) | −12.3496 | −1.18287 | −0.591437 | − | 0.806351i | \(-0.701439\pi\) | ||||
−0.591437 | + | 0.806351i | \(0.701439\pi\) | |||||||
\(110\) | 14.8213 | 1.41316 | ||||||||
\(111\) | 9.91283 | 0.940884 | ||||||||
\(112\) | 31.7547 | 3.00053 | ||||||||
\(113\) | 11.0784 | 1.04217 | 0.521086 | − | 0.853504i | \(-0.325527\pi\) | ||||
0.521086 | + | 0.853504i | \(0.325527\pi\) | |||||||
\(114\) | −5.36539 | −0.502515 | ||||||||
\(115\) | −1.85962 | −0.173410 | ||||||||
\(116\) | −45.1575 | −4.19277 | ||||||||
\(117\) | −1.29505 | −0.119728 | ||||||||
\(118\) | −4.45966 | −0.410545 | ||||||||
\(119\) | −9.23258 | −0.846349 | ||||||||
\(120\) | −14.0036 | −1.27835 | ||||||||
\(121\) | 7.84940 | 0.713582 | ||||||||
\(122\) | 29.9552 | 2.71202 | ||||||||
\(123\) | −4.49357 | −0.405171 | ||||||||
\(124\) | −42.4056 | −3.80814 | ||||||||
\(125\) | −10.8614 | −0.971476 | ||||||||
\(126\) | 7.24280 | 0.645240 | ||||||||
\(127\) | −1.19854 | −0.106354 | −0.0531768 | − | 0.998585i | \(-0.516935\pi\) | ||||
−0.0531768 | + | 0.998585i | \(0.516935\pi\) | |||||||
\(128\) | 2.33187 | 0.206111 | ||||||||
\(129\) | 16.9090 | 1.48876 | ||||||||
\(130\) | −5.47156 | −0.479887 | ||||||||
\(131\) | −9.66189 | −0.844164 | −0.422082 | − | 0.906558i | \(-0.638700\pi\) | ||||
−0.422082 | + | 0.906558i | \(0.638700\pi\) | |||||||
\(132\) | −30.6653 | −2.66907 | ||||||||
\(133\) | 4.79782 | 0.416023 | ||||||||
\(134\) | −1.14926 | −0.0992810 | ||||||||
\(135\) | −7.39673 | −0.636609 | ||||||||
\(136\) | 19.3217 | 1.65682 | ||||||||
\(137\) | 3.72997 | 0.318673 | 0.159336 | − | 0.987224i | \(-0.449065\pi\) | ||||
0.159336 | + | 0.987224i | \(0.449065\pi\) | |||||||
\(138\) | 5.46054 | 0.464832 | ||||||||
\(139\) | −0.224646 | −0.0190542 | −0.00952711 | − | 0.999955i | \(-0.503033\pi\) | ||||
−0.00952711 | + | 0.999955i | \(0.503033\pi\) | |||||||
\(140\) | 21.5615 | 1.82228 | ||||||||
\(141\) | 2.82389 | 0.237814 | ||||||||
\(142\) | 20.7490 | 1.74122 | ||||||||
\(143\) | −6.95859 | −0.581907 | ||||||||
\(144\) | −7.44809 | −0.620674 | ||||||||
\(145\) | −12.4186 | −1.03131 | ||||||||
\(146\) | 14.1865 | 1.17408 | ||||||||
\(147\) | 7.20632 | 0.594368 | ||||||||
\(148\) | 31.9416 | 2.62558 | ||||||||
\(149\) | −9.42229 | −0.771904 | −0.385952 | − | 0.922519i | \(-0.626127\pi\) | ||||
−0.385952 | + | 0.922519i | \(0.626127\pi\) | |||||||
\(150\) | 12.6311 | 1.03133 | ||||||||
\(151\) | 0.999601 | 0.0813464 | 0.0406732 | − | 0.999173i | \(-0.487050\pi\) | ||||
0.0406732 | + | 0.999173i | \(0.487050\pi\) | |||||||
\(152\) | −10.0407 | −0.814410 | ||||||||
\(153\) | 2.16551 | 0.175071 | ||||||||
\(154\) | 38.9172 | 3.13604 | ||||||||
\(155\) | −11.6619 | −0.936702 | ||||||||
\(156\) | 11.3206 | 0.906376 | ||||||||
\(157\) | −14.4240 | −1.15116 | −0.575579 | − | 0.817746i | \(-0.695223\pi\) | ||||
−0.575579 | + | 0.817746i | \(0.695223\pi\) | |||||||
\(158\) | −7.11056 | −0.565686 | ||||||||
\(159\) | 14.3839 | 1.14072 | ||||||||
\(160\) | −12.5510 | −0.992244 | ||||||||
\(161\) | −4.88290 | −0.384826 | ||||||||
\(162\) | 15.4122 | 1.21090 | ||||||||
\(163\) | 21.5843 | 1.69061 | 0.845307 | − | 0.534281i | \(-0.179418\pi\) | ||||
0.845307 | + | 0.534281i | \(0.179418\pi\) | |||||||
\(164\) | −14.4794 | −1.13065 | ||||||||
\(165\) | −8.43318 | −0.656522 | ||||||||
\(166\) | 41.5190 | 3.22250 | ||||||||
\(167\) | 0.473361 | 0.0366298 | 0.0183149 | − | 0.999832i | \(-0.494170\pi\) | ||||
0.0183149 | + | 0.999832i | \(0.494170\pi\) | |||||||
\(168\) | −36.7702 | −2.83688 | ||||||||
\(169\) | −10.4311 | −0.802393 | ||||||||
\(170\) | 9.14922 | 0.701713 | ||||||||
\(171\) | −1.12533 | −0.0860563 | ||||||||
\(172\) | 54.4850 | 4.15444 | ||||||||
\(173\) | 18.9142 | 1.43802 | 0.719008 | − | 0.695001i | \(-0.244596\pi\) | ||||
0.719008 | + | 0.695001i | \(0.244596\pi\) | |||||||
\(174\) | 36.4659 | 2.76447 | ||||||||
\(175\) | −11.2950 | −0.853819 | ||||||||
\(176\) | −40.0202 | −3.01664 | ||||||||
\(177\) | 2.53750 | 0.190730 | ||||||||
\(178\) | 26.1194 | 1.95774 | ||||||||
\(179\) | 5.48237 | 0.409772 | 0.204886 | − | 0.978786i | \(-0.434318\pi\) | ||||
0.204886 | + | 0.978786i | \(0.434318\pi\) | |||||||
\(180\) | −5.05726 | −0.376946 | ||||||||
\(181\) | 12.4653 | 0.926535 | 0.463268 | − | 0.886218i | \(-0.346677\pi\) | ||||
0.463268 | + | 0.886218i | \(0.346677\pi\) | |||||||
\(182\) | −14.3670 | −1.06495 | ||||||||
\(183\) | −17.0442 | −1.25994 | ||||||||
\(184\) | 10.2188 | 0.753339 | ||||||||
\(185\) | 8.78417 | 0.645825 | ||||||||
\(186\) | 34.2437 | 2.51087 | ||||||||
\(187\) | 11.6358 | 0.850891 | ||||||||
\(188\) | 9.09926 | 0.663632 | ||||||||
\(189\) | −19.4220 | −1.41274 | ||||||||
\(190\) | −4.75450 | −0.344927 | ||||||||
\(191\) | −3.06566 | −0.221823 | −0.110912 | − | 0.993830i | \(-0.535377\pi\) | ||||
−0.110912 | + | 0.993830i | \(0.535377\pi\) | |||||||
\(192\) | 9.55974 | 0.689915 | ||||||||
\(193\) | 1.51384 | 0.108969 | 0.0544844 | − | 0.998515i | \(-0.482648\pi\) | ||||
0.0544844 | + | 0.998515i | \(0.482648\pi\) | |||||||
\(194\) | 0.330749 | 0.0237464 | ||||||||
\(195\) | 3.11326 | 0.222945 | ||||||||
\(196\) | 23.2205 | 1.65861 | ||||||||
\(197\) | 2.60094 | 0.185309 | 0.0926546 | − | 0.995698i | \(-0.470465\pi\) | ||||
0.0926546 | + | 0.995698i | \(0.470465\pi\) | |||||||
\(198\) | −9.12806 | −0.648703 | ||||||||
\(199\) | 10.1842 | 0.721937 | 0.360968 | − | 0.932578i | \(-0.382446\pi\) | ||||
0.360968 | + | 0.932578i | \(0.382446\pi\) | |||||||
\(200\) | 23.6377 | 1.67144 | ||||||||
\(201\) | 0.653917 | 0.0461238 | ||||||||
\(202\) | −44.6757 | −3.14337 | ||||||||
\(203\) | −32.6083 | −2.28866 | ||||||||
\(204\) | −18.9297 | −1.32534 | ||||||||
\(205\) | −3.98193 | −0.278110 | ||||||||
\(206\) | 40.3930 | 2.81431 | ||||||||
\(207\) | 1.14529 | 0.0796030 | ||||||||
\(208\) | 14.7742 | 1.02440 | ||||||||
\(209\) | −6.04666 | −0.418256 | ||||||||
\(210\) | −17.4115 | −1.20150 | ||||||||
\(211\) | −23.7382 | −1.63421 | −0.817103 | − | 0.576491i | \(-0.804421\pi\) | ||||
−0.817103 | + | 0.576491i | \(0.804421\pi\) | |||||||
\(212\) | 46.3486 | 3.18323 | ||||||||
\(213\) | −11.8060 | −0.808932 | ||||||||
\(214\) | 32.6134 | 2.22941 | ||||||||
\(215\) | 14.9838 | 1.02189 | ||||||||
\(216\) | 40.6458 | 2.76560 | ||||||||
\(217\) | −30.6212 | −2.07870 | ||||||||
\(218\) | 32.1342 | 2.17640 | ||||||||
\(219\) | −8.07198 | −0.545454 | ||||||||
\(220\) | −27.1738 | −1.83205 | ||||||||
\(221\) | −4.29555 | −0.288950 | ||||||||
\(222\) | −25.7937 | −1.73116 | ||||||||
\(223\) | −2.63196 | −0.176249 | −0.0881245 | − | 0.996109i | \(-0.528087\pi\) | ||||
−0.0881245 | + | 0.996109i | \(0.528087\pi\) | |||||||
\(224\) | −32.9559 | −2.20196 | ||||||||
\(225\) | 2.64924 | 0.176616 | ||||||||
\(226\) | −28.8266 | −1.91752 | ||||||||
\(227\) | 13.6806 | 0.908011 | 0.454006 | − | 0.890999i | \(-0.349995\pi\) | ||||
0.454006 | + | 0.890999i | \(0.349995\pi\) | |||||||
\(228\) | 9.83704 | 0.651474 | ||||||||
\(229\) | −13.8201 | −0.913259 | −0.456629 | − | 0.889657i | \(-0.650943\pi\) | ||||
−0.456629 | + | 0.889657i | \(0.650943\pi\) | |||||||
\(230\) | 4.83881 | 0.319062 | ||||||||
\(231\) | −22.1435 | −1.45693 | ||||||||
\(232\) | 68.2417 | 4.48029 | ||||||||
\(233\) | 12.1247 | 0.794315 | 0.397157 | − | 0.917750i | \(-0.369997\pi\) | ||||
0.397157 | + | 0.917750i | \(0.369997\pi\) | |||||||
\(234\) | 3.36979 | 0.220290 | ||||||||
\(235\) | 2.50236 | 0.163236 | ||||||||
\(236\) | 8.17644 | 0.532241 | ||||||||
\(237\) | 4.04584 | 0.262805 | ||||||||
\(238\) | 24.0236 | 1.55722 | ||||||||
\(239\) | 1.62258 | 0.104956 | 0.0524780 | − | 0.998622i | \(-0.483288\pi\) | ||||
0.0524780 | + | 0.998622i | \(0.483288\pi\) | |||||||
\(240\) | 17.9049 | 1.15576 | ||||||||
\(241\) | 0.150756 | 0.00971105 | 0.00485552 | − | 0.999988i | \(-0.498454\pi\) | ||||
0.00485552 | + | 0.999988i | \(0.498454\pi\) | |||||||
\(242\) | −20.4245 | −1.31294 | ||||||||
\(243\) | 8.14430 | 0.522457 | ||||||||
\(244\) | −54.9207 | −3.51593 | ||||||||
\(245\) | 6.38582 | 0.407975 | ||||||||
\(246\) | 11.6925 | 0.745485 | ||||||||
\(247\) | 2.23223 | 0.142033 | ||||||||
\(248\) | 64.0831 | 4.06928 | ||||||||
\(249\) | −23.6239 | −1.49710 | ||||||||
\(250\) | 28.2620 | 1.78744 | ||||||||
\(251\) | 4.44342 | 0.280466 | 0.140233 | − | 0.990119i | \(-0.455215\pi\) | ||||
0.140233 | + | 0.990119i | \(0.455215\pi\) | |||||||
\(252\) | −13.2791 | −0.836507 | ||||||||
\(253\) | 6.15389 | 0.386891 | ||||||||
\(254\) | 3.11867 | 0.195683 | ||||||||
\(255\) | −5.20581 | −0.326000 | ||||||||
\(256\) | −18.9815 | −1.18634 | ||||||||
\(257\) | −21.8189 | −1.36103 | −0.680513 | − | 0.732736i | \(-0.738243\pi\) | ||||
−0.680513 | + | 0.732736i | \(0.738243\pi\) | |||||||
\(258\) | −43.9981 | −2.73920 | ||||||||
\(259\) | 23.0651 | 1.43319 | ||||||||
\(260\) | 10.0317 | 0.622139 | ||||||||
\(261\) | 7.64832 | 0.473419 | ||||||||
\(262\) | 25.1407 | 1.55320 | ||||||||
\(263\) | −11.9036 | −0.734010 | −0.367005 | − | 0.930219i | \(-0.619617\pi\) | ||||
−0.367005 | + | 0.930219i | \(0.619617\pi\) | |||||||
\(264\) | 46.3412 | 2.85210 | ||||||||
\(265\) | 12.7462 | 0.782993 | ||||||||
\(266\) | −12.4842 | −0.765453 | ||||||||
\(267\) | −14.8617 | −0.909521 | ||||||||
\(268\) | 2.10708 | 0.128711 | ||||||||
\(269\) | 22.6301 | 1.37978 | 0.689889 | − | 0.723915i | \(-0.257659\pi\) | ||||
0.689889 | + | 0.723915i | \(0.257659\pi\) | |||||||
\(270\) | 19.2467 | 1.17131 | ||||||||
\(271\) | 19.0156 | 1.15511 | 0.577557 | − | 0.816350i | \(-0.304006\pi\) | ||||
0.577557 | + | 0.816350i | \(0.304006\pi\) | |||||||
\(272\) | −24.7045 | −1.49793 | ||||||||
\(273\) | 8.17466 | 0.494753 | ||||||||
\(274\) | −9.70557 | −0.586335 | ||||||||
\(275\) | 14.2350 | 0.858401 | ||||||||
\(276\) | −10.0115 | −0.602621 | ||||||||
\(277\) | 1.69360 | 0.101758 | 0.0508791 | − | 0.998705i | \(-0.483798\pi\) | ||||
0.0508791 | + | 0.998705i | \(0.483798\pi\) | |||||||
\(278\) | 0.584540 | 0.0350584 | ||||||||
\(279\) | 7.18222 | 0.429989 | ||||||||
\(280\) | −32.5835 | −1.94724 | ||||||||
\(281\) | −11.7182 | −0.699047 | −0.349524 | − | 0.936928i | \(-0.613657\pi\) | ||||
−0.349524 | + | 0.936928i | \(0.613657\pi\) | |||||||
\(282\) | −7.34789 | −0.437561 | ||||||||
\(283\) | −2.12721 | −0.126450 | −0.0632248 | − | 0.997999i | \(-0.520139\pi\) | ||||
−0.0632248 | + | 0.997999i | \(0.520139\pi\) | |||||||
\(284\) | −38.0418 | −2.25736 | ||||||||
\(285\) | 2.70526 | 0.160246 | ||||||||
\(286\) | 18.1066 | 1.07067 | ||||||||
\(287\) | −10.4556 | −0.617174 | ||||||||
\(288\) | 7.72983 | 0.455485 | ||||||||
\(289\) | −9.81724 | −0.577485 | ||||||||
\(290\) | 32.3139 | 1.89754 | ||||||||
\(291\) | −0.188193 | −0.0110321 | ||||||||
\(292\) | −26.0099 | −1.52211 | ||||||||
\(293\) | 26.7323 | 1.56172 | 0.780859 | − | 0.624708i | \(-0.214782\pi\) | ||||
0.780859 | + | 0.624708i | \(0.214782\pi\) | |||||||
\(294\) | −18.7512 | −1.09359 | ||||||||
\(295\) | 2.24858 | 0.130918 | ||||||||
\(296\) | −48.2699 | −2.80563 | ||||||||
\(297\) | 24.4774 | 1.42033 | ||||||||
\(298\) | 24.5173 | 1.42025 | ||||||||
\(299\) | −2.27182 | −0.131383 | ||||||||
\(300\) | −23.1582 | −1.33704 | ||||||||
\(301\) | 39.3438 | 2.26774 | ||||||||
\(302\) | −2.60101 | −0.149671 | ||||||||
\(303\) | 25.4200 | 1.46034 | ||||||||
\(304\) | 12.8380 | 0.736309 | ||||||||
\(305\) | −15.1036 | −0.864829 | ||||||||
\(306\) | −5.63476 | −0.322118 | ||||||||
\(307\) | −11.0660 | −0.631571 | −0.315786 | − | 0.948831i | \(-0.602268\pi\) | ||||
−0.315786 | + | 0.948831i | \(0.602268\pi\) | |||||||
\(308\) | −71.3517 | −4.06564 | ||||||||
\(309\) | −22.9832 | −1.30747 | ||||||||
\(310\) | 30.3447 | 1.72346 | ||||||||
\(311\) | 0.166353 | 0.00943300 | 0.00471650 | − | 0.999989i | \(-0.498499\pi\) | ||||
0.00471650 | + | 0.999989i | \(0.498499\pi\) | |||||||
\(312\) | −17.1077 | −0.968531 | ||||||||
\(313\) | −34.0108 | −1.92241 | −0.961203 | − | 0.275842i | \(-0.911043\pi\) | ||||
−0.961203 | + | 0.275842i | \(0.911043\pi\) | |||||||
\(314\) | 37.5319 | 2.11805 | ||||||||
\(315\) | −3.65186 | −0.205759 | ||||||||
\(316\) | 13.0367 | 0.733370 | ||||||||
\(317\) | −19.8900 | −1.11713 | −0.558567 | − | 0.829459i | \(-0.688649\pi\) | ||||
−0.558567 | + | 0.829459i | \(0.688649\pi\) | |||||||
\(318\) | −37.4277 | −2.09884 | ||||||||
\(319\) | 41.0961 | 2.30094 | ||||||||
\(320\) | 8.47128 | 0.473559 | ||||||||
\(321\) | −18.5567 | −1.03573 | ||||||||
\(322\) | 12.7055 | 0.708052 | ||||||||
\(323\) | −3.73261 | −0.207688 | ||||||||
\(324\) | −28.2571 | −1.56984 | ||||||||
\(325\) | −5.25509 | −0.291500 | ||||||||
\(326\) | −56.1634 | −3.11061 | ||||||||
\(327\) | −18.2840 | −1.01111 | ||||||||
\(328\) | 21.8811 | 1.20818 | ||||||||
\(329\) | 6.57060 | 0.362249 | ||||||||
\(330\) | 21.9435 | 1.20795 | ||||||||
\(331\) | 12.5197 | 0.688144 | 0.344072 | − | 0.938943i | \(-0.388194\pi\) | ||||
0.344072 | + | 0.938943i | \(0.388194\pi\) | |||||||
\(332\) | −76.1220 | −4.17773 | ||||||||
\(333\) | −5.40994 | −0.296463 | ||||||||
\(334\) | −1.23171 | −0.0673961 | ||||||||
\(335\) | 0.579463 | 0.0316595 | ||||||||
\(336\) | 47.0140 | 2.56483 | ||||||||
\(337\) | 35.0463 | 1.90910 | 0.954548 | − | 0.298058i | \(-0.0963389\pi\) | ||||
0.954548 | + | 0.298058i | \(0.0963389\pi\) | |||||||
\(338\) | 27.1423 | 1.47634 | ||||||||
\(339\) | 16.4021 | 0.890837 | ||||||||
\(340\) | −16.7744 | −0.909719 | ||||||||
\(341\) | 38.5917 | 2.08986 | ||||||||
\(342\) | 2.92817 | 0.158337 | ||||||||
\(343\) | −7.34672 | −0.396686 | ||||||||
\(344\) | −82.3374 | −4.43933 | ||||||||
\(345\) | −2.75323 | −0.148229 | ||||||||
\(346\) | −49.2156 | −2.64585 | ||||||||
\(347\) | 9.95569 | 0.534449 | 0.267225 | − | 0.963634i | \(-0.413893\pi\) | ||||
0.267225 | + | 0.963634i | \(0.413893\pi\) | |||||||
\(348\) | −66.8574 | −3.58394 | ||||||||
\(349\) | −5.64792 | −0.302326 | −0.151163 | − | 0.988509i | \(-0.548302\pi\) | ||||
−0.151163 | + | 0.988509i | \(0.548302\pi\) | |||||||
\(350\) | 29.3900 | 1.57096 | ||||||||
\(351\) | −9.03629 | −0.482321 | ||||||||
\(352\) | 41.5341 | 2.21377 | ||||||||
\(353\) | 17.1652 | 0.913613 | 0.456806 | − | 0.889566i | \(-0.348993\pi\) | ||||
0.456806 | + | 0.889566i | \(0.348993\pi\) | |||||||
\(354\) | −6.60270 | −0.350929 | ||||||||
\(355\) | −10.4618 | −0.555253 | ||||||||
\(356\) | −47.8880 | −2.53806 | ||||||||
\(357\) | −13.6692 | −0.723450 | ||||||||
\(358\) | −14.2654 | −0.753950 | ||||||||
\(359\) | −4.59637 | −0.242587 | −0.121294 | − | 0.992617i | \(-0.538704\pi\) | ||||
−0.121294 | + | 0.992617i | \(0.538704\pi\) | |||||||
\(360\) | 7.64250 | 0.402795 | ||||||||
\(361\) | −17.0603 | −0.897911 | ||||||||
\(362\) | −32.4352 | −1.70476 | ||||||||
\(363\) | 11.6213 | 0.609962 | ||||||||
\(364\) | 26.3408 | 1.38063 | ||||||||
\(365\) | −7.15291 | −0.374401 | ||||||||
\(366\) | 44.3499 | 2.31821 | ||||||||
\(367\) | 19.6206 | 1.02419 | 0.512093 | − | 0.858930i | \(-0.328870\pi\) | ||||
0.512093 | + | 0.858930i | \(0.328870\pi\) | |||||||
\(368\) | −13.0657 | −0.681094 | ||||||||
\(369\) | 2.45237 | 0.127665 | ||||||||
\(370\) | −22.8568 | −1.18827 | ||||||||
\(371\) | 33.4684 | 1.73759 | ||||||||
\(372\) | −62.7831 | −3.25515 | ||||||||
\(373\) | 18.1650 | 0.940547 | 0.470274 | − | 0.882521i | \(-0.344155\pi\) | ||||
0.470274 | + | 0.882521i | \(0.344155\pi\) | |||||||
\(374\) | −30.2768 | −1.56558 | ||||||||
\(375\) | −16.0808 | −0.830408 | ||||||||
\(376\) | −13.7507 | −0.709140 | ||||||||
\(377\) | −15.1714 | −0.781365 | ||||||||
\(378\) | 50.5371 | 2.59935 | ||||||||
\(379\) | −29.2836 | −1.50420 | −0.752098 | − | 0.659051i | \(-0.770958\pi\) | ||||
−0.752098 | + | 0.659051i | \(0.770958\pi\) | |||||||
\(380\) | 8.71701 | 0.447173 | ||||||||
\(381\) | −1.77449 | −0.0909100 | ||||||||
\(382\) | 7.97700 | 0.408139 | ||||||||
\(383\) | 6.87287 | 0.351187 | 0.175594 | − | 0.984463i | \(-0.443816\pi\) | ||||
0.175594 | + | 0.984463i | \(0.443816\pi\) | |||||||
\(384\) | 3.45243 | 0.176181 | ||||||||
\(385\) | −19.6222 | −1.00004 | ||||||||
\(386\) | −3.93910 | −0.200495 | ||||||||
\(387\) | −9.22811 | −0.469091 | ||||||||
\(388\) | −0.606404 | −0.0307855 | ||||||||
\(389\) | −2.96440 | −0.150301 | −0.0751506 | − | 0.997172i | \(-0.523944\pi\) | ||||
−0.0751506 | + | 0.997172i | \(0.523944\pi\) | |||||||
\(390\) | −8.10085 | −0.410203 | ||||||||
\(391\) | 3.79880 | 0.192114 | ||||||||
\(392\) | −35.0907 | −1.77235 | ||||||||
\(393\) | −14.3048 | −0.721582 | ||||||||
\(394\) | −6.76777 | −0.340955 | ||||||||
\(395\) | 3.58518 | 0.180390 | ||||||||
\(396\) | 16.7356 | 0.840996 | ||||||||
\(397\) | 11.0763 | 0.555905 | 0.277952 | − | 0.960595i | \(-0.410344\pi\) | ||||
0.277952 | + | 0.960595i | \(0.410344\pi\) | |||||||
\(398\) | −26.4997 | −1.32831 | ||||||||
\(399\) | 7.10335 | 0.355612 | ||||||||
\(400\) | −30.2230 | −1.51115 | ||||||||
\(401\) | −13.5713 | −0.677717 | −0.338859 | − | 0.940837i | \(-0.610041\pi\) | ||||
−0.338859 | + | 0.940837i | \(0.610041\pi\) | |||||||
\(402\) | −1.70153 | −0.0848644 | ||||||||
\(403\) | −14.2468 | −0.709684 | ||||||||
\(404\) | 81.9095 | 4.07515 | ||||||||
\(405\) | −7.77092 | −0.386140 | ||||||||
\(406\) | 84.8485 | 4.21096 | ||||||||
\(407\) | −29.0688 | −1.44089 | ||||||||
\(408\) | 28.6065 | 1.41623 | ||||||||
\(409\) | 14.4605 | 0.715025 | 0.357512 | − | 0.933908i | \(-0.383625\pi\) | ||||
0.357512 | + | 0.933908i | \(0.383625\pi\) | |||||||
\(410\) | 10.3612 | 0.511703 | ||||||||
\(411\) | 5.52237 | 0.272398 | ||||||||
\(412\) | −74.0575 | −3.64855 | ||||||||
\(413\) | 5.90423 | 0.290528 | ||||||||
\(414\) | −2.98010 | −0.146464 | ||||||||
\(415\) | −20.9341 | −1.02761 | ||||||||
\(416\) | −15.3331 | −0.751765 | ||||||||
\(417\) | −0.332597 | −0.0162873 | ||||||||
\(418\) | 15.7337 | 0.769560 | ||||||||
\(419\) | 30.1880 | 1.47478 | 0.737389 | − | 0.675468i | \(-0.236058\pi\) | ||||
0.737389 | + | 0.675468i | \(0.236058\pi\) | |||||||
\(420\) | 31.9226 | 1.55766 | ||||||||
\(421\) | 34.0938 | 1.66163 | 0.830815 | − | 0.556549i | \(-0.187875\pi\) | ||||
0.830815 | + | 0.556549i | \(0.187875\pi\) | |||||||
\(422\) | 61.7680 | 3.00682 | ||||||||
\(423\) | −1.54114 | −0.0749327 | ||||||||
\(424\) | −70.0417 | −3.40153 | ||||||||
\(425\) | 8.78726 | 0.426245 | ||||||||
\(426\) | 30.7197 | 1.48838 | ||||||||
\(427\) | −39.6583 | −1.91920 | ||||||||
\(428\) | −59.7942 | −2.89026 | ||||||||
\(429\) | −10.3025 | −0.497408 | ||||||||
\(430\) | −38.9885 | −1.88019 | ||||||||
\(431\) | −6.56659 | −0.316302 | −0.158151 | − | 0.987415i | \(-0.550553\pi\) | ||||
−0.158151 | + | 0.987415i | \(0.550553\pi\) | |||||||
\(432\) | −51.9694 | −2.50038 | ||||||||
\(433\) | −9.39563 | −0.451525 | −0.225763 | − | 0.974182i | \(-0.572487\pi\) | ||||
−0.225763 | + | 0.974182i | \(0.572487\pi\) | |||||||
\(434\) | 79.6778 | 3.82466 | ||||||||
\(435\) | −18.3863 | −0.881555 | ||||||||
\(436\) | −58.9156 | −2.82155 | ||||||||
\(437\) | −1.97409 | −0.0944336 | ||||||||
\(438\) | 21.0037 | 1.00360 | ||||||||
\(439\) | 22.7287 | 1.08478 | 0.542390 | − | 0.840127i | \(-0.317520\pi\) | ||||
0.542390 | + | 0.840127i | \(0.317520\pi\) | |||||||
\(440\) | 41.0648 | 1.95769 | ||||||||
\(441\) | −3.93286 | −0.187279 | ||||||||
\(442\) | 11.1772 | 0.531646 | ||||||||
\(443\) | 17.7833 | 0.844910 | 0.422455 | − | 0.906384i | \(-0.361168\pi\) | ||||
0.422455 | + | 0.906384i | \(0.361168\pi\) | |||||||
\(444\) | 47.2907 | 2.24432 | ||||||||
\(445\) | −13.1696 | −0.624297 | ||||||||
\(446\) | 6.84848 | 0.324285 | ||||||||
\(447\) | −13.9501 | −0.659816 | ||||||||
\(448\) | 22.2435 | 1.05091 | ||||||||
\(449\) | 1.65386 | 0.0780505 | 0.0390253 | − | 0.999238i | \(-0.487575\pi\) | ||||
0.0390253 | + | 0.999238i | \(0.487575\pi\) | |||||||
\(450\) | −6.89346 | −0.324961 | ||||||||
\(451\) | 13.1771 | 0.620486 | ||||||||
\(452\) | 52.8514 | 2.48592 | ||||||||
\(453\) | 1.47995 | 0.0695340 | ||||||||
\(454\) | −35.5975 | −1.67067 | ||||||||
\(455\) | 7.24390 | 0.339599 | ||||||||
\(456\) | −14.8657 | −0.696149 | ||||||||
\(457\) | −39.0553 | −1.82693 | −0.913464 | − | 0.406919i | \(-0.866603\pi\) | ||||
−0.913464 | + | 0.406919i | \(0.866603\pi\) | |||||||
\(458\) | 35.9606 | 1.68033 | ||||||||
\(459\) | 15.1099 | 0.705272 | ||||||||
\(460\) | −8.87159 | −0.413640 | ||||||||
\(461\) | 22.6274 | 1.05386 | 0.526932 | − | 0.849908i | \(-0.323342\pi\) | ||||
0.526932 | + | 0.849908i | \(0.323342\pi\) | |||||||
\(462\) | 57.6184 | 2.68065 | ||||||||
\(463\) | 36.5371 | 1.69802 | 0.849012 | − | 0.528374i | \(-0.177198\pi\) | ||||
0.849012 | + | 0.528374i | \(0.177198\pi\) | |||||||
\(464\) | −87.2534 | −4.05064 | ||||||||
\(465\) | −17.2658 | −0.800683 | ||||||||
\(466\) | −31.5490 | −1.46148 | ||||||||
\(467\) | −37.2025 | −1.72152 | −0.860762 | − | 0.509007i | \(-0.830013\pi\) | ||||
−0.860762 | + | 0.509007i | \(0.830013\pi\) | |||||||
\(468\) | −6.17825 | −0.285590 | ||||||||
\(469\) | 1.52153 | 0.0702577 | ||||||||
\(470\) | −6.51127 | −0.300343 | ||||||||
\(471\) | −21.3552 | −0.983997 | ||||||||
\(472\) | −12.3562 | −0.568740 | ||||||||
\(473\) | −49.5847 | −2.27991 | ||||||||
\(474\) | −10.5275 | −0.483542 | ||||||||
\(475\) | −4.56640 | −0.209521 | ||||||||
\(476\) | −44.0455 | −2.01882 | ||||||||
\(477\) | −7.85005 | −0.359429 | ||||||||
\(478\) | −4.22203 | −0.193111 | ||||||||
\(479\) | −12.4048 | −0.566788 | −0.283394 | − | 0.959004i | \(-0.591460\pi\) | ||||
−0.283394 | + | 0.959004i | \(0.591460\pi\) | |||||||
\(480\) | −18.5823 | −0.848160 | ||||||||
\(481\) | 10.7313 | 0.489303 | ||||||||
\(482\) | −0.392274 | −0.0178676 | ||||||||
\(483\) | −7.22932 | −0.328946 | ||||||||
\(484\) | 37.4468 | 1.70213 | ||||||||
\(485\) | −0.166765 | −0.00757243 | ||||||||
\(486\) | −21.1919 | −0.961283 | ||||||||
\(487\) | −28.1608 | −1.27609 | −0.638045 | − | 0.769999i | \(-0.720256\pi\) | ||||
−0.638045 | + | 0.769999i | \(0.720256\pi\) | |||||||
\(488\) | 82.9958 | 3.75704 | ||||||||
\(489\) | 31.9564 | 1.44512 | ||||||||
\(490\) | −16.6162 | −0.750644 | ||||||||
\(491\) | −31.2776 | −1.41154 | −0.705769 | − | 0.708443i | \(-0.749398\pi\) | ||||
−0.705769 | + | 0.708443i | \(0.749398\pi\) | |||||||
\(492\) | −21.4373 | −0.966467 | ||||||||
\(493\) | 25.3686 | 1.14255 | ||||||||
\(494\) | −5.80838 | −0.261331 | ||||||||
\(495\) | 4.60241 | 0.206863 | ||||||||
\(496\) | −81.9361 | −3.67904 | ||||||||
\(497\) | −27.4700 | −1.23220 | ||||||||
\(498\) | 61.4705 | 2.75456 | ||||||||
\(499\) | −30.5993 | −1.36981 | −0.684907 | − | 0.728631i | \(-0.740157\pi\) | ||||
−0.684907 | + | 0.728631i | \(0.740157\pi\) | |||||||
\(500\) | −51.8162 | −2.31729 | ||||||||
\(501\) | 0.700829 | 0.0313107 | ||||||||
\(502\) | −11.5620 | −0.516037 | ||||||||
\(503\) | 3.50860 | 0.156441 | 0.0782203 | − | 0.996936i | \(-0.475076\pi\) | ||||
0.0782203 | + | 0.996936i | \(0.475076\pi\) | |||||||
\(504\) | 20.0673 | 0.893870 | ||||||||
\(505\) | 22.5257 | 1.00238 | ||||||||
\(506\) | −16.0127 | −0.711852 | ||||||||
\(507\) | −15.4437 | −0.685877 | ||||||||
\(508\) | −5.71785 | −0.253688 | ||||||||
\(509\) | −0.315424 | −0.0139809 | −0.00699047 | − | 0.999976i | \(-0.502225\pi\) | ||||
−0.00699047 | + | 0.999976i | \(0.502225\pi\) | |||||||
\(510\) | 13.5458 | 0.599817 | ||||||||
\(511\) | −18.7818 | −0.830859 | ||||||||
\(512\) | 44.7271 | 1.97668 | ||||||||
\(513\) | −7.85206 | −0.346677 | ||||||||
\(514\) | 56.7738 | 2.50419 | ||||||||
\(515\) | −20.3663 | −0.897448 | ||||||||
\(516\) | 80.6672 | 3.55117 | ||||||||
\(517\) | −8.28088 | −0.364193 | ||||||||
\(518\) | −60.0165 | −2.63697 | ||||||||
\(519\) | 28.0031 | 1.22920 | ||||||||
\(520\) | −15.1598 | −0.664802 | ||||||||
\(521\) | −37.9517 | −1.66269 | −0.831346 | − | 0.555755i | \(-0.812429\pi\) | ||||
−0.831346 | + | 0.555755i | \(0.812429\pi\) | |||||||
\(522\) | −19.9013 | −0.871056 | ||||||||
\(523\) | −16.5865 | −0.725279 | −0.362639 | − | 0.931930i | \(-0.618124\pi\) | ||||
−0.362639 | + | 0.931930i | \(0.618124\pi\) | |||||||
\(524\) | −46.0936 | −2.01361 | ||||||||
\(525\) | −16.7226 | −0.729835 | ||||||||
\(526\) | 30.9738 | 1.35052 | ||||||||
\(527\) | 23.8227 | 1.03773 | ||||||||
\(528\) | −59.2515 | −2.57859 | ||||||||
\(529\) | −20.9909 | −0.912648 | ||||||||
\(530\) | −33.1662 | −1.44065 | ||||||||
\(531\) | −1.38484 | −0.0600970 | ||||||||
\(532\) | 22.8887 | 0.992353 | ||||||||
\(533\) | −4.86457 | −0.210708 | ||||||||
\(534\) | 38.6709 | 1.67345 | ||||||||
\(535\) | −16.4438 | −0.710929 | ||||||||
\(536\) | −3.18421 | −0.137537 | ||||||||
\(537\) | 8.11686 | 0.350268 | ||||||||
\(538\) | −58.8845 | −2.53869 | ||||||||
\(539\) | −21.1321 | −0.910224 | ||||||||
\(540\) | −35.2873 | −1.51852 | ||||||||
\(541\) | 18.7201 | 0.804838 | 0.402419 | − | 0.915456i | \(-0.368169\pi\) | ||||
0.402419 | + | 0.915456i | \(0.368169\pi\) | |||||||
\(542\) | −49.4795 | −2.12532 | ||||||||
\(543\) | 18.4553 | 0.791992 | ||||||||
\(544\) | 25.6390 | 1.09926 | ||||||||
\(545\) | −16.2022 | −0.694027 | ||||||||
\(546\) | −21.2709 | −0.910309 | ||||||||
\(547\) | 7.78139 | 0.332708 | 0.166354 | − | 0.986066i | \(-0.446801\pi\) | ||||
0.166354 | + | 0.986066i | \(0.446801\pi\) | |||||||
\(548\) | 17.7944 | 0.760140 | ||||||||
\(549\) | 9.30190 | 0.396995 | ||||||||
\(550\) | −37.0401 | −1.57939 | ||||||||
\(551\) | −13.1831 | −0.561620 | ||||||||
\(552\) | 15.1293 | 0.643946 | ||||||||
\(553\) | 9.41381 | 0.400316 | ||||||||
\(554\) | −4.40682 | −0.187228 | ||||||||
\(555\) | 13.0053 | 0.552044 | ||||||||
\(556\) | −1.07171 | −0.0454506 | ||||||||
\(557\) | 4.05324 | 0.171741 | 0.0858707 | − | 0.996306i | \(-0.472633\pi\) | ||||
0.0858707 | + | 0.996306i | \(0.472633\pi\) | |||||||
\(558\) | −18.6885 | −0.791147 | ||||||||
\(559\) | 18.3051 | 0.774222 | ||||||||
\(560\) | 41.6611 | 1.76050 | ||||||||
\(561\) | 17.2272 | 0.727332 | ||||||||
\(562\) | 30.4912 | 1.28620 | ||||||||
\(563\) | 26.2850 | 1.10778 | 0.553891 | − | 0.832589i | \(-0.313142\pi\) | ||||
0.553891 | + | 0.832589i | \(0.313142\pi\) | |||||||
\(564\) | 13.4718 | 0.567265 | ||||||||
\(565\) | 14.5345 | 0.611473 | ||||||||
\(566\) | 5.53511 | 0.232658 | ||||||||
\(567\) | −20.4046 | −0.856911 | ||||||||
\(568\) | 57.4885 | 2.41216 | ||||||||
\(569\) | 43.4456 | 1.82134 | 0.910668 | − | 0.413139i | \(-0.135568\pi\) | ||||
0.910668 | + | 0.413139i | \(0.135568\pi\) | |||||||
\(570\) | −7.03922 | −0.294840 | ||||||||
\(571\) | −12.0931 | −0.506079 | −0.253040 | − | 0.967456i | \(-0.581430\pi\) | ||||
−0.253040 | + | 0.967456i | \(0.581430\pi\) | |||||||
\(572\) | −33.1971 | −1.38804 | ||||||||
\(573\) | −4.53883 | −0.189612 | ||||||||
\(574\) | 27.2060 | 1.13556 | ||||||||
\(575\) | 4.64738 | 0.193809 | ||||||||
\(576\) | −5.21723 | −0.217385 | ||||||||
\(577\) | 27.3145 | 1.13712 | 0.568559 | − | 0.822642i | \(-0.307501\pi\) | ||||
0.568559 | + | 0.822642i | \(0.307501\pi\) | |||||||
\(578\) | 25.5449 | 1.06253 | ||||||||
\(579\) | 2.24130 | 0.0931454 | ||||||||
\(580\) | −59.2451 | −2.46002 | ||||||||
\(581\) | −54.9678 | −2.28045 | ||||||||
\(582\) | 0.489687 | 0.0202982 | ||||||||
\(583\) | −42.1800 | −1.74692 | ||||||||
\(584\) | 39.3060 | 1.62649 | ||||||||
\(585\) | −1.69906 | −0.0702476 | ||||||||
\(586\) | −69.5587 | −2.87345 | ||||||||
\(587\) | −23.6528 | −0.976255 | −0.488128 | − | 0.872772i | \(-0.662320\pi\) | ||||
−0.488128 | + | 0.872772i | \(0.662320\pi\) | |||||||
\(588\) | 34.3789 | 1.41776 | ||||||||
\(589\) | −12.3797 | −0.510098 | ||||||||
\(590\) | −5.85092 | −0.240879 | ||||||||
\(591\) | 3.85079 | 0.158400 | ||||||||
\(592\) | 61.7175 | 2.53657 | ||||||||
\(593\) | 5.32673 | 0.218743 | 0.109371 | − | 0.994001i | \(-0.465116\pi\) | ||||
0.109371 | + | 0.994001i | \(0.465116\pi\) | |||||||
\(594\) | −63.6915 | −2.61329 | ||||||||
\(595\) | −12.1128 | −0.496578 | ||||||||
\(596\) | −44.9505 | −1.84125 | ||||||||
\(597\) | 15.0781 | 0.617104 | ||||||||
\(598\) | 5.91138 | 0.241734 | ||||||||
\(599\) | −10.6513 | −0.435200 | −0.217600 | − | 0.976038i | \(-0.569823\pi\) | ||||
−0.217600 | + | 0.976038i | \(0.569823\pi\) | |||||||
\(600\) | 34.9966 | 1.42873 | ||||||||
\(601\) | −41.2415 | −1.68228 | −0.841139 | − | 0.540820i | \(-0.818114\pi\) | ||||
−0.841139 | + | 0.540820i | \(0.818114\pi\) | |||||||
\(602\) | −102.374 | −4.17247 | ||||||||
\(603\) | −0.356876 | −0.0145331 | ||||||||
\(604\) | 4.76876 | 0.194038 | ||||||||
\(605\) | 10.2982 | 0.418679 | ||||||||
\(606\) | −66.1441 | −2.68692 | ||||||||
\(607\) | 18.8857 | 0.766547 | 0.383273 | − | 0.923635i | \(-0.374797\pi\) | ||||
0.383273 | + | 0.923635i | \(0.374797\pi\) | |||||||
\(608\) | −13.3236 | −0.540344 | ||||||||
\(609\) | −48.2779 | −1.95632 | ||||||||
\(610\) | 39.3003 | 1.59122 | ||||||||
\(611\) | 3.05703 | 0.123674 | ||||||||
\(612\) | 10.3309 | 0.417602 | ||||||||
\(613\) | −10.7188 | −0.432928 | −0.216464 | − | 0.976291i | \(-0.569452\pi\) | ||||
−0.216464 | + | 0.976291i | \(0.569452\pi\) | |||||||
\(614\) | 28.7943 | 1.16204 | ||||||||
\(615\) | −5.89541 | −0.237726 | ||||||||
\(616\) | 107.826 | 4.34444 | ||||||||
\(617\) | −38.2334 | −1.53922 | −0.769609 | − | 0.638515i | \(-0.779549\pi\) | ||||
−0.769609 | + | 0.638515i | \(0.779549\pi\) | |||||||
\(618\) | 59.8034 | 2.40564 | ||||||||
\(619\) | −12.0424 | −0.484024 | −0.242012 | − | 0.970273i | \(-0.577807\pi\) | ||||
−0.242012 | + | 0.970273i | \(0.577807\pi\) | |||||||
\(620\) | −55.6347 | −2.23434 | ||||||||
\(621\) | 7.99131 | 0.320680 | ||||||||
\(622\) | −0.432858 | −0.0173560 | ||||||||
\(623\) | −34.5801 | −1.38542 | ||||||||
\(624\) | 21.8737 | 0.875650 | ||||||||
\(625\) | 2.14389 | 0.0857555 | ||||||||
\(626\) | 88.4978 | 3.53709 | ||||||||
\(627\) | −8.95231 | −0.357521 | ||||||||
\(628\) | −68.8118 | −2.74589 | ||||||||
\(629\) | −17.9442 | −0.715481 | ||||||||
\(630\) | 9.50232 | 0.378581 | ||||||||
\(631\) | −39.6422 | −1.57813 | −0.789065 | − | 0.614310i | \(-0.789435\pi\) | ||||
−0.789065 | + | 0.614310i | \(0.789435\pi\) | |||||||
\(632\) | −19.7009 | −0.783661 | ||||||||
\(633\) | −35.1454 | −1.39690 | ||||||||
\(634\) | 51.7548 | 2.05545 | ||||||||
\(635\) | −1.57245 | −0.0624008 | ||||||||
\(636\) | 68.6209 | 2.72099 | ||||||||
\(637\) | 7.80130 | 0.309099 | ||||||||
\(638\) | −106.934 | −4.23356 | ||||||||
\(639\) | 6.44312 | 0.254886 | ||||||||
\(640\) | 3.05934 | 0.120931 | ||||||||
\(641\) | −35.5559 | −1.40438 | −0.702188 | − | 0.711992i | \(-0.747793\pi\) | ||||
−0.702188 | + | 0.711992i | \(0.747793\pi\) | |||||||
\(642\) | 48.2854 | 1.90567 | ||||||||
\(643\) | 10.1768 | 0.401335 | 0.200667 | − | 0.979659i | \(-0.435689\pi\) | ||||
0.200667 | + | 0.979659i | \(0.435689\pi\) | |||||||
\(644\) | −23.2946 | −0.917938 | ||||||||
\(645\) | 22.1841 | 0.873497 | ||||||||
\(646\) | 9.71242 | 0.382130 | ||||||||
\(647\) | −32.6724 | −1.28449 | −0.642243 | − | 0.766501i | \(-0.721996\pi\) | ||||
−0.642243 | + | 0.766501i | \(0.721996\pi\) | |||||||
\(648\) | 42.7020 | 1.67749 | ||||||||
\(649\) | −7.44106 | −0.292087 | ||||||||
\(650\) | 13.6740 | 0.536339 | ||||||||
\(651\) | −45.3359 | −1.77685 | ||||||||
\(652\) | 102.971 | 4.03267 | ||||||||
\(653\) | −45.5013 | −1.78061 | −0.890303 | − | 0.455369i | \(-0.849507\pi\) | ||||
−0.890303 | + | 0.455369i | \(0.849507\pi\) | |||||||
\(654\) | 47.5759 | 1.86037 | ||||||||
\(655\) | −12.6761 | −0.495295 | ||||||||
\(656\) | −27.9771 | −1.09232 | ||||||||
\(657\) | 4.40529 | 0.171867 | ||||||||
\(658\) | −17.0970 | −0.666511 | ||||||||
\(659\) | 22.6247 | 0.881335 | 0.440667 | − | 0.897670i | \(-0.354742\pi\) | ||||
0.440667 | + | 0.897670i | \(0.354742\pi\) | |||||||
\(660\) | −40.2318 | −1.56602 | ||||||||
\(661\) | 5.20283 | 0.202367 | 0.101183 | − | 0.994868i | \(-0.467737\pi\) | ||||
0.101183 | + | 0.994868i | \(0.467737\pi\) | |||||||
\(662\) | −32.5768 | −1.26613 | ||||||||
\(663\) | −6.35972 | −0.246991 | ||||||||
\(664\) | 115.035 | 4.46422 | ||||||||
\(665\) | 6.29457 | 0.244093 | ||||||||
\(666\) | 14.0769 | 0.545469 | ||||||||
\(667\) | 13.4169 | 0.519505 | ||||||||
\(668\) | 2.25824 | 0.0873741 | ||||||||
\(669\) | −3.89672 | −0.150656 | ||||||||
\(670\) | −1.50779 | −0.0582511 | ||||||||
\(671\) | 49.9811 | 1.92950 | ||||||||
\(672\) | −48.7925 | −1.88221 | ||||||||
\(673\) | −11.2688 | −0.434380 | −0.217190 | − | 0.976129i | \(-0.569689\pi\) | ||||
−0.217190 | + | 0.976129i | \(0.569689\pi\) | |||||||
\(674\) | −91.1923 | −3.51260 | ||||||||
\(675\) | 18.4852 | 0.711497 | ||||||||
\(676\) | −49.7633 | −1.91397 | ||||||||
\(677\) | 30.4679 | 1.17098 | 0.585489 | − | 0.810681i | \(-0.300903\pi\) | ||||
0.585489 | + | 0.810681i | \(0.300903\pi\) | |||||||
\(678\) | −42.6790 | −1.63908 | ||||||||
\(679\) | −0.437886 | −0.0168045 | ||||||||
\(680\) | 25.3494 | 0.972103 | ||||||||
\(681\) | 20.2546 | 0.776158 | ||||||||
\(682\) | −100.417 | −3.84518 | ||||||||
\(683\) | 10.0579 | 0.384855 | 0.192428 | − | 0.981311i | \(-0.438364\pi\) | ||||
0.192428 | + | 0.981311i | \(0.438364\pi\) | |||||||
\(684\) | −5.36857 | −0.205273 | ||||||||
\(685\) | 4.89360 | 0.186975 | ||||||||
\(686\) | 19.1165 | 0.729872 | ||||||||
\(687\) | −20.4612 | −0.780644 | ||||||||
\(688\) | 105.276 | 4.01361 | ||||||||
\(689\) | 15.5715 | 0.593227 | ||||||||
\(690\) | 7.16405 | 0.272731 | ||||||||
\(691\) | 4.87401 | 0.185416 | 0.0927080 | − | 0.995693i | \(-0.470448\pi\) | ||||
0.0927080 | + | 0.995693i | \(0.470448\pi\) | |||||||
\(692\) | 90.2330 | 3.43014 | ||||||||
\(693\) | 12.0848 | 0.459064 | ||||||||
\(694\) | −25.9052 | −0.983348 | ||||||||
\(695\) | −0.294728 | −0.0111797 | ||||||||
\(696\) | 101.035 | 3.82970 | ||||||||
\(697\) | 8.13424 | 0.308106 | ||||||||
\(698\) | 14.6962 | 0.556258 | ||||||||
\(699\) | 17.9511 | 0.678972 | ||||||||
\(700\) | −53.8844 | −2.03664 | ||||||||
\(701\) | 31.7819 | 1.20039 | 0.600193 | − | 0.799855i | \(-0.295090\pi\) | ||||
0.600193 | + | 0.799855i | \(0.295090\pi\) | |||||||
\(702\) | 23.5129 | 0.887436 | ||||||||
\(703\) | 9.32490 | 0.351695 | ||||||||
\(704\) | −28.0334 | −1.05655 | ||||||||
\(705\) | 3.70485 | 0.139533 | ||||||||
\(706\) | −44.6647 | −1.68098 | ||||||||
\(707\) | 59.1471 | 2.22445 | ||||||||
\(708\) | 12.1055 | 0.454954 | ||||||||
\(709\) | 43.1464 | 1.62040 | 0.810199 | − | 0.586155i | \(-0.199359\pi\) | ||||
0.810199 | + | 0.586155i | \(0.199359\pi\) | |||||||
\(710\) | 27.2220 | 1.02162 | ||||||||
\(711\) | −2.20802 | −0.0828071 | ||||||||
\(712\) | 72.3681 | 2.71211 | ||||||||
\(713\) | 12.5993 | 0.471846 | ||||||||
\(714\) | 35.5679 | 1.33109 | ||||||||
\(715\) | −9.12944 | −0.341422 | ||||||||
\(716\) | 26.1545 | 0.977440 | ||||||||
\(717\) | 2.40229 | 0.0897153 | ||||||||
\(718\) | 11.9600 | 0.446343 | ||||||||
\(719\) | −40.5854 | −1.51358 | −0.756790 | − | 0.653658i | \(-0.773234\pi\) | ||||
−0.756790 | + | 0.653658i | \(0.773234\pi\) | |||||||
\(720\) | −9.77164 | −0.364167 | ||||||||
\(721\) | −53.4771 | −1.99159 | ||||||||
\(722\) | 44.3918 | 1.65209 | ||||||||
\(723\) | 0.223200 | 0.00830090 | ||||||||
\(724\) | 59.4675 | 2.21009 | ||||||||
\(725\) | 31.0355 | 1.15263 | ||||||||
\(726\) | −30.2393 | −1.12229 | ||||||||
\(727\) | 41.3587 | 1.53391 | 0.766954 | − | 0.641702i | \(-0.221771\pi\) | ||||
0.766954 | + | 0.641702i | \(0.221771\pi\) | |||||||
\(728\) | −39.8060 | −1.47531 | ||||||||
\(729\) | 29.8273 | 1.10471 | ||||||||
\(730\) | 18.6122 | 0.688870 | ||||||||
\(731\) | −30.6087 | −1.13210 | ||||||||
\(732\) | −81.3122 | −3.00538 | ||||||||
\(733\) | 42.4747 | 1.56884 | 0.784419 | − | 0.620231i | \(-0.212961\pi\) | ||||
0.784419 | + | 0.620231i | \(0.212961\pi\) | |||||||
\(734\) | −51.0537 | −1.88443 | ||||||||
\(735\) | 9.45445 | 0.348733 | ||||||||
\(736\) | 13.5599 | 0.499825 | ||||||||
\(737\) | −1.91757 | −0.0706347 | ||||||||
\(738\) | −6.38118 | −0.234895 | ||||||||
\(739\) | 29.2367 | 1.07549 | 0.537744 | − | 0.843108i | \(-0.319277\pi\) | ||||
0.537744 | + | 0.843108i | \(0.319277\pi\) | |||||||
\(740\) | 41.9063 | 1.54050 | ||||||||
\(741\) | 3.30490 | 0.121409 | ||||||||
\(742\) | −87.0865 | −3.19705 | ||||||||
\(743\) | 21.3907 | 0.784750 | 0.392375 | − | 0.919805i | \(-0.371653\pi\) | ||||
0.392375 | + | 0.919805i | \(0.371653\pi\) | |||||||
\(744\) | 94.8775 | 3.47838 | ||||||||
\(745\) | −12.3617 | −0.452899 | ||||||||
\(746\) | −47.2662 | −1.73054 | ||||||||
\(747\) | 12.8928 | 0.471721 | ||||||||
\(748\) | 55.5102 | 2.02965 | ||||||||
\(749\) | −43.1775 | −1.57767 | ||||||||
\(750\) | 41.8430 | 1.52789 | ||||||||
\(751\) | 45.7959 | 1.67112 | 0.835558 | − | 0.549402i | \(-0.185144\pi\) | ||||
0.835558 | + | 0.549402i | \(0.185144\pi\) | |||||||
\(752\) | 17.5816 | 0.641135 | ||||||||
\(753\) | 6.57865 | 0.239739 | ||||||||
\(754\) | 39.4766 | 1.43765 | ||||||||
\(755\) | 1.31144 | 0.0477283 | ||||||||
\(756\) | −92.6558 | −3.36986 | ||||||||
\(757\) | −42.7929 | −1.55533 | −0.777667 | − | 0.628677i | \(-0.783597\pi\) | ||||
−0.777667 | + | 0.628677i | \(0.783597\pi\) | |||||||
\(758\) | 76.1973 | 2.76761 | ||||||||
\(759\) | 9.11107 | 0.330711 | ||||||||
\(760\) | −13.1731 | −0.477838 | ||||||||
\(761\) | 6.55615 | 0.237660 | 0.118830 | − | 0.992915i | \(-0.462086\pi\) | ||||
0.118830 | + | 0.992915i | \(0.462086\pi\) | |||||||
\(762\) | 4.61731 | 0.167268 | ||||||||
\(763\) | −42.5431 | −1.54016 | ||||||||
\(764\) | −14.6252 | −0.529122 | ||||||||
\(765\) | 2.84107 | 0.102719 | ||||||||
\(766\) | −17.8835 | −0.646158 | ||||||||
\(767\) | 2.74700 | 0.0991885 | ||||||||
\(768\) | −28.1029 | −1.01407 | ||||||||
\(769\) | 25.8243 | 0.931246 | 0.465623 | − | 0.884983i | \(-0.345830\pi\) | ||||
0.465623 | + | 0.884983i | \(0.345830\pi\) | |||||||
\(770\) | 51.0580 | 1.84000 | ||||||||
\(771\) | −32.3037 | −1.16339 | ||||||||
\(772\) | 7.22203 | 0.259927 | ||||||||
\(773\) | −41.8808 | −1.50635 | −0.753174 | − | 0.657822i | \(-0.771478\pi\) | ||||
−0.753174 | + | 0.657822i | \(0.771478\pi\) | |||||||
\(774\) | 24.0120 | 0.863093 | ||||||||
\(775\) | 29.1442 | 1.04689 | ||||||||
\(776\) | 0.916393 | 0.0328966 | ||||||||
\(777\) | 34.1488 | 1.22508 | ||||||||
\(778\) | 7.71353 | 0.276543 | ||||||||
\(779\) | −4.22706 | −0.151450 | ||||||||
\(780\) | 14.8523 | 0.531797 | ||||||||
\(781\) | 34.6203 | 1.23881 | ||||||||
\(782\) | −9.88466 | −0.353475 | ||||||||
\(783\) | 53.3665 | 1.90716 | ||||||||
\(784\) | 44.8667 | 1.60238 | ||||||||
\(785\) | −18.9238 | −0.675418 | ||||||||
\(786\) | 37.2218 | 1.32766 | ||||||||
\(787\) | 1.46512 | 0.0522259 | 0.0261129 | − | 0.999659i | \(-0.491687\pi\) | ||||
0.0261129 | + | 0.999659i | \(0.491687\pi\) | |||||||
\(788\) | 12.4082 | 0.442023 | ||||||||
\(789\) | −17.6238 | −0.627424 | ||||||||
\(790\) | −9.32882 | −0.331904 | ||||||||
\(791\) | 38.1642 | 1.35696 | ||||||||
\(792\) | −25.2907 | −0.898667 | ||||||||
\(793\) | −18.4514 | −0.655230 | ||||||||
\(794\) | −28.8211 | −1.02282 | ||||||||
\(795\) | 18.8712 | 0.669294 | ||||||||
\(796\) | 48.5852 | 1.72206 | ||||||||
\(797\) | −2.22341 | −0.0787572 | −0.0393786 | − | 0.999224i | \(-0.512538\pi\) | ||||
−0.0393786 | + | 0.999224i | \(0.512538\pi\) | |||||||
\(798\) | −18.4833 | −0.654301 | ||||||||
\(799\) | −5.11179 | −0.180842 | ||||||||
\(800\) | 31.3663 | 1.10897 | ||||||||
\(801\) | 8.11078 | 0.286580 | ||||||||
\(802\) | 35.3131 | 1.24695 | ||||||||
\(803\) | 23.6706 | 0.835317 | ||||||||
\(804\) | 3.11962 | 0.110020 | ||||||||
\(805\) | −6.40620 | −0.225789 | ||||||||
\(806\) | 37.0709 | 1.30577 | ||||||||
\(807\) | 33.5047 | 1.17942 | ||||||||
\(808\) | −123.781 | −4.35461 | ||||||||
\(809\) | −1.45886 | −0.0512908 | −0.0256454 | − | 0.999671i | \(-0.508164\pi\) | ||||
−0.0256454 | + | 0.999671i | \(0.508164\pi\) | |||||||
\(810\) | 20.2203 | 0.710470 | ||||||||
\(811\) | −8.64314 | −0.303502 | −0.151751 | − | 0.988419i | \(-0.548491\pi\) | ||||
−0.151751 | + | 0.988419i | \(0.548491\pi\) | |||||||
\(812\) | −155.563 | −5.45920 | ||||||||
\(813\) | 28.1533 | 0.987379 | ||||||||
\(814\) | 75.6384 | 2.65112 | ||||||||
\(815\) | 28.3179 | 0.991932 | ||||||||
\(816\) | −36.5760 | −1.28042 | ||||||||
\(817\) | 15.9061 | 0.556486 | ||||||||
\(818\) | −37.6269 | −1.31559 | ||||||||
\(819\) | −4.46133 | −0.155891 | ||||||||
\(820\) | −18.9965 | −0.663385 | ||||||||
\(821\) | 23.7587 | 0.829185 | 0.414592 | − | 0.910007i | \(-0.363924\pi\) | ||||
0.414592 | + | 0.910007i | \(0.363924\pi\) | |||||||
\(822\) | −14.3695 | −0.501193 | ||||||||
\(823\) | −42.8423 | −1.49339 | −0.746694 | − | 0.665167i | \(-0.768360\pi\) | ||||
−0.746694 | + | 0.665167i | \(0.768360\pi\) | |||||||
\(824\) | 111.915 | 3.89875 | ||||||||
\(825\) | 21.0754 | 0.733752 | ||||||||
\(826\) | −15.3631 | −0.534550 | ||||||||
\(827\) | −14.3999 | −0.500733 | −0.250367 | − | 0.968151i | \(-0.580551\pi\) | ||||
−0.250367 | + | 0.968151i | \(0.580551\pi\) | |||||||
\(828\) | 5.46378 | 0.189879 | ||||||||
\(829\) | −46.3832 | −1.61095 | −0.805477 | − | 0.592627i | \(-0.798091\pi\) | ||||
−0.805477 | + | 0.592627i | \(0.798091\pi\) | |||||||
\(830\) | 54.4715 | 1.89073 | ||||||||
\(831\) | 2.50743 | 0.0869819 | ||||||||
\(832\) | 10.3490 | 0.358787 | ||||||||
\(833\) | −13.0449 | −0.451978 | ||||||||
\(834\) | 0.865434 | 0.0299675 | ||||||||
\(835\) | 0.621034 | 0.0214918 | ||||||||
\(836\) | −28.8465 | −0.997678 | ||||||||
\(837\) | 50.1144 | 1.73221 | ||||||||
\(838\) | −78.5506 | −2.71348 | ||||||||
\(839\) | 18.0317 | 0.622524 | 0.311262 | − | 0.950324i | \(-0.399248\pi\) | ||||
0.311262 | + | 0.950324i | \(0.399248\pi\) | |||||||
\(840\) | −48.2412 | −1.66448 | ||||||||
\(841\) | 60.5990 | 2.08962 | ||||||||
\(842\) | −88.7137 | −3.05728 | ||||||||
\(843\) | −17.3492 | −0.597538 | ||||||||
\(844\) | −113.247 | −3.89812 | ||||||||
\(845\) | −13.6853 | −0.470787 | ||||||||
\(846\) | 4.01012 | 0.137871 | ||||||||
\(847\) | 27.0404 | 0.929121 | ||||||||
\(848\) | 89.5548 | 3.07532 | ||||||||
\(849\) | −3.14942 | −0.108088 | ||||||||
\(850\) | −22.8649 | −0.784259 | ||||||||
\(851\) | −9.49027 | −0.325322 | ||||||||
\(852\) | −56.3223 | −1.92957 | ||||||||
\(853\) | 24.3943 | 0.835245 | 0.417623 | − | 0.908621i | \(-0.362863\pi\) | ||||
0.417623 | + | 0.908621i | \(0.362863\pi\) | |||||||
\(854\) | 103.193 | 3.53119 | ||||||||
\(855\) | −1.47640 | −0.0504917 | ||||||||
\(856\) | 90.3606 | 3.08846 | ||||||||
\(857\) | −18.6142 | −0.635848 | −0.317924 | − | 0.948116i | \(-0.602986\pi\) | ||||
−0.317924 | + | 0.948116i | \(0.602986\pi\) | |||||||
\(858\) | 26.8075 | 0.915194 | ||||||||
\(859\) | 11.9363 | 0.407262 | 0.203631 | − | 0.979048i | \(-0.434726\pi\) | ||||
0.203631 | + | 0.979048i | \(0.434726\pi\) | |||||||
\(860\) | 71.4825 | 2.43753 | ||||||||
\(861\) | −15.4799 | −0.527554 | ||||||||
\(862\) | 17.0866 | 0.581972 | ||||||||
\(863\) | −34.0880 | −1.16037 | −0.580184 | − | 0.814485i | \(-0.697019\pi\) | ||||
−0.580184 | + | 0.814485i | \(0.697019\pi\) | |||||||
\(864\) | 53.9353 | 1.83492 | ||||||||
\(865\) | 24.8147 | 0.843726 | ||||||||
\(866\) | 24.4479 | 0.830773 | ||||||||
\(867\) | −14.5348 | −0.493628 | ||||||||
\(868\) | −146.083 | −4.95839 | ||||||||
\(869\) | −11.8642 | −0.402464 | ||||||||
\(870\) | 47.8420 | 1.62200 | ||||||||
\(871\) | 0.707907 | 0.0239865 | ||||||||
\(872\) | 89.0329 | 3.01503 | ||||||||
\(873\) | 0.102706 | 0.00347609 | ||||||||
\(874\) | 5.13668 | 0.173751 | ||||||||
\(875\) | −37.4166 | −1.26491 | ||||||||
\(876\) | −38.5087 | −1.30109 | ||||||||
\(877\) | 12.6060 | 0.425676 | 0.212838 | − | 0.977088i | \(-0.431729\pi\) | ||||
0.212838 | + | 0.977088i | \(0.431729\pi\) | |||||||
\(878\) | −59.1411 | −1.99591 | ||||||||
\(879\) | 39.5782 | 1.33494 | ||||||||
\(880\) | −52.5052 | −1.76995 | ||||||||
\(881\) | 20.9995 | 0.707491 | 0.353745 | − | 0.935342i | \(-0.384908\pi\) | ||||
0.353745 | + | 0.935342i | \(0.384908\pi\) | |||||||
\(882\) | 10.2335 | 0.344579 | ||||||||
\(883\) | −40.6386 | −1.36760 | −0.683799 | − | 0.729670i | \(-0.739674\pi\) | ||||
−0.683799 | + | 0.729670i | \(0.739674\pi\) | |||||||
\(884\) | −20.4926 | −0.689240 | ||||||||
\(885\) | 3.32911 | 0.111907 | ||||||||
\(886\) | −46.2730 | −1.55457 | ||||||||
\(887\) | 29.8058 | 1.00078 | 0.500390 | − | 0.865800i | \(-0.333190\pi\) | ||||
0.500390 | + | 0.865800i | \(0.333190\pi\) | |||||||
\(888\) | −71.4655 | −2.39822 | ||||||||
\(889\) | −4.12887 | −0.138478 | ||||||||
\(890\) | 34.2678 | 1.14866 | ||||||||
\(891\) | 25.7157 | 0.861509 | ||||||||
\(892\) | −12.5562 | −0.420412 | ||||||||
\(893\) | 2.65640 | 0.0888932 | ||||||||
\(894\) | 36.2988 | 1.21401 | ||||||||
\(895\) | 7.19268 | 0.240425 | ||||||||
\(896\) | 8.03308 | 0.268367 | ||||||||
\(897\) | −3.36351 | −0.112304 | ||||||||
\(898\) | −4.30343 | −0.143607 | ||||||||
\(899\) | 84.1388 | 2.80619 | ||||||||
\(900\) | 12.6386 | 0.421288 | ||||||||
\(901\) | −26.0378 | −0.867444 | ||||||||
\(902\) | −34.2875 | −1.14165 | ||||||||
\(903\) | 58.2499 | 1.93844 | ||||||||
\(904\) | −79.8688 | −2.65640 | ||||||||
\(905\) | 16.3540 | 0.543625 | ||||||||
\(906\) | −3.85090 | −0.127938 | ||||||||
\(907\) | 7.29489 | 0.242223 | 0.121111 | − | 0.992639i | \(-0.461354\pi\) | ||||
0.121111 | + | 0.992639i | \(0.461354\pi\) | |||||||
\(908\) | 65.2653 | 2.16591 | ||||||||
\(909\) | −13.8730 | −0.460138 | ||||||||
\(910\) | −18.8490 | −0.624838 | ||||||||
\(911\) | −41.9506 | −1.38989 | −0.694943 | − | 0.719065i | \(-0.744570\pi\) | ||||
−0.694943 | + | 0.719065i | \(0.744570\pi\) | |||||||
\(912\) | 19.0071 | 0.629389 | ||||||||
\(913\) | 69.2756 | 2.29269 | ||||||||
\(914\) | 101.624 | 3.36141 | ||||||||
\(915\) | −22.3614 | −0.739246 | ||||||||
\(916\) | −65.9310 | −2.17842 | ||||||||
\(917\) | −33.2843 | −1.09914 | ||||||||
\(918\) | −39.3168 | −1.29765 | ||||||||
\(919\) | 16.6118 | 0.547971 | 0.273986 | − | 0.961734i | \(-0.411658\pi\) | ||||
0.273986 | + | 0.961734i | \(0.411658\pi\) | |||||||
\(920\) | 13.4067 | 0.442006 | ||||||||
\(921\) | −16.3837 | −0.539861 | ||||||||
\(922\) | −58.8776 | −1.93903 | ||||||||
\(923\) | −12.7807 | −0.420682 | ||||||||
\(924\) | −105.639 | −3.47527 | ||||||||
\(925\) | −21.9526 | −0.721796 | ||||||||
\(926\) | −95.0714 | −3.12424 | ||||||||
\(927\) | 12.5431 | 0.411969 | ||||||||
\(928\) | 90.5540 | 2.97258 | ||||||||
\(929\) | −8.29258 | −0.272071 | −0.136035 | − | 0.990704i | \(-0.543436\pi\) | ||||
−0.136035 | + | 0.990704i | \(0.543436\pi\) | |||||||
\(930\) | 44.9265 | 1.47320 | ||||||||
\(931\) | 6.77892 | 0.222170 | ||||||||
\(932\) | 57.8428 | 1.89470 | ||||||||
\(933\) | 0.246292 | 0.00806323 | ||||||||
\(934\) | 96.8026 | 3.16748 | ||||||||
\(935\) | 15.2657 | 0.499242 | ||||||||
\(936\) | 9.33653 | 0.305174 | ||||||||
\(937\) | −39.6407 | −1.29500 | −0.647502 | − | 0.762063i | \(-0.724186\pi\) | ||||
−0.647502 | + | 0.762063i | \(0.724186\pi\) | |||||||
\(938\) | −3.95909 | −0.129269 | ||||||||
\(939\) | −50.3543 | −1.64325 | ||||||||
\(940\) | 11.9379 | 0.389372 | ||||||||
\(941\) | 33.5679 | 1.09428 | 0.547141 | − | 0.837040i | \(-0.315716\pi\) | ||||
0.547141 | + | 0.837040i | \(0.315716\pi\) | |||||||
\(942\) | 55.5674 | 1.81048 | ||||||||
\(943\) | 4.30202 | 0.140093 | ||||||||
\(944\) | 15.7985 | 0.514198 | ||||||||
\(945\) | −25.4810 | −0.828898 | ||||||||
\(946\) | 129.022 | 4.19486 | ||||||||
\(947\) | −6.22150 | −0.202172 | −0.101086 | − | 0.994878i | \(-0.532232\pi\) | ||||
−0.101086 | + | 0.994878i | \(0.532232\pi\) | |||||||
\(948\) | 19.3013 | 0.626877 | ||||||||
\(949\) | −8.73842 | −0.283661 | ||||||||
\(950\) | 11.8820 | 0.385503 | ||||||||
\(951\) | −29.4479 | −0.954915 | ||||||||
\(952\) | 66.5612 | 2.15726 | ||||||||
\(953\) | 29.0411 | 0.940732 | 0.470366 | − | 0.882471i | \(-0.344122\pi\) | ||||
0.470366 | + | 0.882471i | \(0.344122\pi\) | |||||||
\(954\) | 20.4262 | 0.661323 | ||||||||
\(955\) | −4.02204 | −0.130150 | ||||||||
\(956\) | 7.74078 | 0.250355 | ||||||||
\(957\) | 60.8443 | 1.96682 | ||||||||
\(958\) | 32.2778 | 1.04285 | ||||||||
\(959\) | 12.8494 | 0.414928 | ||||||||
\(960\) | 12.5421 | 0.404793 | ||||||||
\(961\) | 48.0114 | 1.54875 | ||||||||
\(962\) | −27.9233 | −0.900282 | ||||||||
\(963\) | 10.1273 | 0.326348 | ||||||||
\(964\) | 0.719205 | 0.0231640 | ||||||||
\(965\) | 1.98611 | 0.0639352 | ||||||||
\(966\) | 18.8110 | 0.605236 | ||||||||
\(967\) | 34.5250 | 1.11025 | 0.555125 | − | 0.831767i | \(-0.312670\pi\) | ||||
0.555125 | + | 0.831767i | \(0.312670\pi\) | |||||||
\(968\) | −56.5894 | −1.81885 | ||||||||
\(969\) | −5.52627 | −0.177529 | ||||||||
\(970\) | 0.433932 | 0.0139327 | ||||||||
\(971\) | −14.1435 | −0.453885 | −0.226943 | − | 0.973908i | \(-0.572873\pi\) | ||||
−0.226943 | + | 0.973908i | \(0.572873\pi\) | |||||||
\(972\) | 38.8537 | 1.24623 | ||||||||
\(973\) | −0.773884 | −0.0248096 | ||||||||
\(974\) | 73.2759 | 2.34791 | ||||||||
\(975\) | −7.78037 | −0.249171 | ||||||||
\(976\) | −106.118 | −3.39674 | ||||||||
\(977\) | 25.1451 | 0.804463 | 0.402232 | − | 0.915538i | \(-0.368235\pi\) | ||||
0.402232 | + | 0.915538i | \(0.368235\pi\) | |||||||
\(978\) | −83.1521 | −2.65891 | ||||||||
\(979\) | 43.5810 | 1.39286 | ||||||||
\(980\) | 30.4646 | 0.973155 | ||||||||
\(981\) | 9.97852 | 0.318590 | ||||||||
\(982\) | 81.3858 | 2.59712 | ||||||||
\(983\) | −10.0409 | −0.320254 | −0.160127 | − | 0.987096i | \(-0.551190\pi\) | ||||
−0.160127 | + | 0.987096i | \(0.551190\pi\) | |||||||
\(984\) | 32.3959 | 1.03274 | ||||||||
\(985\) | 3.41234 | 0.108726 | ||||||||
\(986\) | −66.0105 | −2.10220 | ||||||||
\(987\) | 9.72802 | 0.309646 | ||||||||
\(988\) | 10.6492 | 0.338797 | ||||||||
\(989\) | −16.1882 | −0.514756 | ||||||||
\(990\) | −11.9757 | −0.380613 | ||||||||
\(991\) | −29.1337 | −0.925461 | −0.462731 | − | 0.886499i | \(-0.653130\pi\) | ||||
−0.462731 | + | 0.886499i | \(0.653130\pi\) | |||||||
\(992\) | 85.0356 | 2.69988 | ||||||||
\(993\) | 18.5359 | 0.588218 | ||||||||
\(994\) | 71.4784 | 2.26716 | ||||||||
\(995\) | 13.3613 | 0.423581 | ||||||||
\(996\) | −112.701 | −3.57108 | ||||||||
\(997\) | 4.72192 | 0.149545 | 0.0747724 | − | 0.997201i | \(-0.476177\pi\) | ||||
0.0747724 | + | 0.997201i | \(0.476177\pi\) | |||||||
\(998\) | 79.6209 | 2.52036 | ||||||||
\(999\) | −37.7481 | −1.19430 |
(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 | 4003.2.a.b.1.9 | ✓ | 152 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4003.2.a.b.1.9 | ✓ | 152 | 1.1 | even | 1 | trivial |