Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, 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("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.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: | \(31.9481458487\) |
Analytic rank: | \(0\) |
Dimension: | \(184\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.109 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.635075 | 0.449066 | 0.224533 | − | 0.974467i | \(-0.427914\pi\) | ||||
0.224533 | + | 0.974467i | \(0.427914\pi\) | |||||||
\(3\) | 2.40773 | 1.39010 | 0.695051 | − | 0.718960i | \(-0.255382\pi\) | ||||
0.695051 | + | 0.718960i | \(0.255382\pi\) | |||||||
\(4\) | −1.59668 | −0.798340 | ||||||||
\(5\) | −0.176134 | −0.0787695 | −0.0393847 | − | 0.999224i | \(-0.512540\pi\) | ||||
−0.0393847 | + | 0.999224i | \(0.512540\pi\) | |||||||
\(6\) | 1.52909 | 0.624247 | ||||||||
\(7\) | 0.607658 | 0.229673 | 0.114837 | − | 0.993384i | \(-0.463366\pi\) | ||||
0.114837 | + | 0.993384i | \(0.463366\pi\) | |||||||
\(8\) | −2.28416 | −0.807573 | ||||||||
\(9\) | 2.79716 | 0.932385 | ||||||||
\(10\) | −0.111858 | −0.0353726 | ||||||||
\(11\) | 0.724171 | 0.218346 | 0.109173 | − | 0.994023i | \(-0.465180\pi\) | ||||
0.109173 | + | 0.994023i | \(0.465180\pi\) | |||||||
\(12\) | −3.84437 | −1.10977 | ||||||||
\(13\) | −3.12375 | −0.866371 | −0.433186 | − | 0.901305i | \(-0.642611\pi\) | ||||
−0.433186 | + | 0.901305i | \(0.642611\pi\) | |||||||
\(14\) | 0.385908 | 0.103138 | ||||||||
\(15\) | −0.424082 | −0.109498 | ||||||||
\(16\) | 1.74275 | 0.435687 | ||||||||
\(17\) | −1.81722 | −0.440742 | −0.220371 | − | 0.975416i | \(-0.570727\pi\) | ||||
−0.220371 | + | 0.975416i | \(0.570727\pi\) | |||||||
\(18\) | 1.77640 | 0.418702 | ||||||||
\(19\) | 3.76611 | 0.864006 | 0.432003 | − | 0.901872i | \(-0.357807\pi\) | ||||
0.432003 | + | 0.901872i | \(0.357807\pi\) | |||||||
\(20\) | 0.281229 | 0.0628848 | ||||||||
\(21\) | 1.46307 | 0.319269 | ||||||||
\(22\) | 0.459903 | 0.0980516 | ||||||||
\(23\) | 4.76589 | 0.993757 | 0.496879 | − | 0.867820i | \(-0.334479\pi\) | ||||
0.496879 | + | 0.867820i | \(0.334479\pi\) | |||||||
\(24\) | −5.49964 | −1.12261 | ||||||||
\(25\) | −4.96898 | −0.993795 | ||||||||
\(26\) | −1.98381 | −0.389057 | ||||||||
\(27\) | −0.488393 | −0.0939912 | ||||||||
\(28\) | −0.970235 | −0.183357 | ||||||||
\(29\) | 9.17023 | 1.70287 | 0.851434 | − | 0.524462i | \(-0.175733\pi\) | ||||
0.851434 | + | 0.524462i | \(0.175733\pi\) | |||||||
\(30\) | −0.269324 | −0.0491716 | ||||||||
\(31\) | 10.3551 | 1.85983 | 0.929916 | − | 0.367773i | \(-0.119880\pi\) | ||||
0.929916 | + | 0.367773i | \(0.119880\pi\) | |||||||
\(32\) | 5.67510 | 1.00322 | ||||||||
\(33\) | 1.74361 | 0.303523 | ||||||||
\(34\) | −1.15407 | −0.197922 | ||||||||
\(35\) | −0.107029 | −0.0180912 | ||||||||
\(36\) | −4.46616 | −0.744361 | ||||||||
\(37\) | −4.97256 | −0.817484 | −0.408742 | − | 0.912650i | \(-0.634032\pi\) | ||||
−0.408742 | + | 0.912650i | \(0.634032\pi\) | |||||||
\(38\) | 2.39176 | 0.387995 | ||||||||
\(39\) | −7.52113 | −1.20434 | ||||||||
\(40\) | 0.402318 | 0.0636120 | ||||||||
\(41\) | 6.40622 | 1.00048 | 0.500241 | − | 0.865886i | \(-0.333245\pi\) | ||||
0.500241 | + | 0.865886i | \(0.333245\pi\) | |||||||
\(42\) | 0.929162 | 0.143373 | ||||||||
\(43\) | 12.8602 | 1.96117 | 0.980584 | − | 0.196098i | \(-0.0628271\pi\) | ||||
0.980584 | + | 0.196098i | \(0.0628271\pi\) | |||||||
\(44\) | −1.15627 | −0.174314 | ||||||||
\(45\) | −0.492674 | −0.0734435 | ||||||||
\(46\) | 3.02670 | 0.446262 | ||||||||
\(47\) | −8.43691 | −1.23065 | −0.615325 | − | 0.788274i | \(-0.710975\pi\) | ||||
−0.615325 | + | 0.788274i | \(0.710975\pi\) | |||||||
\(48\) | 4.19607 | 0.605650 | ||||||||
\(49\) | −6.63075 | −0.947250 | ||||||||
\(50\) | −3.15567 | −0.446279 | ||||||||
\(51\) | −4.37538 | −0.612676 | ||||||||
\(52\) | 4.98762 | 0.691659 | ||||||||
\(53\) | −1.37242 | −0.188517 | −0.0942583 | − | 0.995548i | \(-0.530048\pi\) | ||||
−0.0942583 | + | 0.995548i | \(0.530048\pi\) | |||||||
\(54\) | −0.310166 | −0.0422082 | ||||||||
\(55\) | −0.127551 | −0.0171990 | ||||||||
\(56\) | −1.38799 | −0.185478 | ||||||||
\(57\) | 9.06778 | 1.20106 | ||||||||
\(58\) | 5.82378 | 0.764699 | ||||||||
\(59\) | −3.41084 | −0.444053 | −0.222027 | − | 0.975041i | \(-0.571267\pi\) | ||||
−0.222027 | + | 0.975041i | \(0.571267\pi\) | |||||||
\(60\) | 0.677124 | 0.0874163 | ||||||||
\(61\) | 12.6507 | 1.61976 | 0.809881 | − | 0.586594i | \(-0.199532\pi\) | ||||
0.809881 | + | 0.586594i | \(0.199532\pi\) | |||||||
\(62\) | 6.57626 | 0.835186 | ||||||||
\(63\) | 1.69971 | 0.214144 | ||||||||
\(64\) | 0.118612 | 0.0148264 | ||||||||
\(65\) | 0.550197 | 0.0682436 | ||||||||
\(66\) | 1.10732 | 0.136302 | ||||||||
\(67\) | 3.00526 | 0.367151 | 0.183576 | − | 0.983006i | \(-0.441233\pi\) | ||||
0.183576 | + | 0.983006i | \(0.441233\pi\) | |||||||
\(68\) | 2.90153 | 0.351862 | ||||||||
\(69\) | 11.4750 | 1.38142 | ||||||||
\(70\) | −0.0679714 | −0.00812414 | ||||||||
\(71\) | 14.7122 | 1.74602 | 0.873008 | − | 0.487706i | \(-0.162166\pi\) | ||||
0.873008 | + | 0.487706i | \(0.162166\pi\) | |||||||
\(72\) | −6.38915 | −0.752969 | ||||||||
\(73\) | 7.69266 | 0.900358 | 0.450179 | − | 0.892938i | \(-0.351360\pi\) | ||||
0.450179 | + | 0.892938i | \(0.351360\pi\) | |||||||
\(74\) | −3.15795 | −0.367104 | ||||||||
\(75\) | −11.9639 | −1.38148 | ||||||||
\(76\) | −6.01328 | −0.689770 | ||||||||
\(77\) | 0.440048 | 0.0501481 | ||||||||
\(78\) | −4.77648 | −0.540830 | ||||||||
\(79\) | −6.27366 | −0.705842 | −0.352921 | − | 0.935653i | \(-0.614812\pi\) | ||||
−0.352921 | + | 0.935653i | \(0.614812\pi\) | |||||||
\(80\) | −0.306957 | −0.0343188 | ||||||||
\(81\) | −9.56739 | −1.06304 | ||||||||
\(82\) | 4.06843 | 0.449282 | ||||||||
\(83\) | 13.4465 | 1.47595 | 0.737975 | − | 0.674828i | \(-0.235782\pi\) | ||||
0.737975 | + | 0.674828i | \(0.235782\pi\) | |||||||
\(84\) | −2.33606 | −0.254885 | ||||||||
\(85\) | 0.320075 | 0.0347170 | ||||||||
\(86\) | 8.16721 | 0.880693 | ||||||||
\(87\) | 22.0794 | 2.36716 | ||||||||
\(88\) | −1.65412 | −0.176330 | ||||||||
\(89\) | −0.176694 | −0.0187295 | −0.00936477 | − | 0.999956i | \(-0.502981\pi\) | ||||
−0.00936477 | + | 0.999956i | \(0.502981\pi\) | |||||||
\(90\) | −0.312885 | −0.0329809 | ||||||||
\(91\) | −1.89817 | −0.198982 | ||||||||
\(92\) | −7.60960 | −0.793356 | ||||||||
\(93\) | 24.9323 | 2.58536 | ||||||||
\(94\) | −5.35806 | −0.552642 | ||||||||
\(95\) | −0.663340 | −0.0680572 | ||||||||
\(96\) | 13.6641 | 1.39459 | ||||||||
\(97\) | 8.88739 | 0.902378 | 0.451189 | − | 0.892428i | \(-0.351000\pi\) | ||||
0.451189 | + | 0.892428i | \(0.351000\pi\) | |||||||
\(98\) | −4.21102 | −0.425377 | ||||||||
\(99\) | 2.02562 | 0.203582 | ||||||||
\(100\) | 7.93387 | 0.793387 | ||||||||
\(101\) | −12.9674 | −1.29031 | −0.645154 | − | 0.764053i | \(-0.723207\pi\) | ||||
−0.645154 | + | 0.764053i | \(0.723207\pi\) | |||||||
\(102\) | −2.77869 | −0.275132 | ||||||||
\(103\) | −19.8336 | −1.95427 | −0.977133 | − | 0.212629i | \(-0.931798\pi\) | ||||
−0.977133 | + | 0.212629i | \(0.931798\pi\) | |||||||
\(104\) | 7.13513 | 0.699658 | ||||||||
\(105\) | −0.257697 | −0.0251486 | ||||||||
\(106\) | −0.871590 | −0.0846563 | ||||||||
\(107\) | 7.83410 | 0.757351 | 0.378676 | − | 0.925529i | \(-0.376380\pi\) | ||||
0.378676 | + | 0.925529i | \(0.376380\pi\) | |||||||
\(108\) | 0.779807 | 0.0750370 | ||||||||
\(109\) | 14.6274 | 1.40105 | 0.700525 | − | 0.713627i | \(-0.252949\pi\) | ||||
0.700525 | + | 0.713627i | \(0.252949\pi\) | |||||||
\(110\) | −0.0810044 | −0.00772347 | ||||||||
\(111\) | −11.9726 | −1.13639 | ||||||||
\(112\) | 1.05899 | 0.100066 | ||||||||
\(113\) | 9.61490 | 0.904493 | 0.452247 | − | 0.891893i | \(-0.350623\pi\) | ||||
0.452247 | + | 0.891893i | \(0.350623\pi\) | |||||||
\(114\) | 5.75871 | 0.539353 | ||||||||
\(115\) | −0.839435 | −0.0782777 | ||||||||
\(116\) | −14.6419 | −1.35947 | ||||||||
\(117\) | −8.73760 | −0.807792 | ||||||||
\(118\) | −2.16614 | −0.199409 | ||||||||
\(119\) | −1.10425 | −0.101226 | ||||||||
\(120\) | 0.968672 | 0.0884273 | ||||||||
\(121\) | −10.4756 | −0.952325 | ||||||||
\(122\) | 8.03417 | 0.727379 | ||||||||
\(123\) | 15.4244 | 1.39077 | ||||||||
\(124\) | −16.5338 | −1.48478 | ||||||||
\(125\) | 1.75587 | 0.157050 | ||||||||
\(126\) | 1.07944 | 0.0961646 | ||||||||
\(127\) | −18.8576 | −1.67334 | −0.836672 | − | 0.547704i | \(-0.815502\pi\) | ||||
−0.836672 | + | 0.547704i | \(0.815502\pi\) | |||||||
\(128\) | −11.2749 | −0.996567 | ||||||||
\(129\) | 30.9640 | 2.72623 | ||||||||
\(130\) | 0.349416 | 0.0306458 | ||||||||
\(131\) | −2.73047 | −0.238563 | −0.119281 | − | 0.992860i | \(-0.538059\pi\) | ||||
−0.119281 | + | 0.992860i | \(0.538059\pi\) | |||||||
\(132\) | −2.78398 | −0.242315 | ||||||||
\(133\) | 2.28851 | 0.198439 | ||||||||
\(134\) | 1.90857 | 0.164875 | ||||||||
\(135\) | 0.0860225 | 0.00740364 | ||||||||
\(136\) | 4.15083 | 0.355931 | ||||||||
\(137\) | 7.27473 | 0.621522 | 0.310761 | − | 0.950488i | \(-0.399416\pi\) | ||||
0.310761 | + | 0.950488i | \(0.399416\pi\) | |||||||
\(138\) | 7.28746 | 0.620350 | ||||||||
\(139\) | 0.817790 | 0.0693640 | 0.0346820 | − | 0.999398i | \(-0.488958\pi\) | ||||
0.0346820 | + | 0.999398i | \(0.488958\pi\) | |||||||
\(140\) | 0.170891 | 0.0144429 | ||||||||
\(141\) | −20.3138 | −1.71073 | ||||||||
\(142\) | 9.34334 | 0.784075 | ||||||||
\(143\) | −2.26213 | −0.189168 | ||||||||
\(144\) | 4.87474 | 0.406228 | ||||||||
\(145\) | −1.61519 | −0.134134 | ||||||||
\(146\) | 4.88541 | 0.404320 | ||||||||
\(147\) | −15.9651 | −1.31678 | ||||||||
\(148\) | 7.93959 | 0.652630 | ||||||||
\(149\) | 14.2722 | 1.16923 | 0.584613 | − | 0.811312i | \(-0.301246\pi\) | ||||
0.584613 | + | 0.811312i | \(0.301246\pi\) | |||||||
\(150\) | −7.59800 | −0.620374 | ||||||||
\(151\) | 17.4665 | 1.42140 | 0.710700 | − | 0.703495i | \(-0.248378\pi\) | ||||
0.710700 | + | 0.703495i | \(0.248378\pi\) | |||||||
\(152\) | −8.60240 | −0.697747 | ||||||||
\(153\) | −5.08306 | −0.410941 | ||||||||
\(154\) | 0.279463 | 0.0225198 | ||||||||
\(155\) | −1.82388 | −0.146498 | ||||||||
\(156\) | 12.0088 | 0.961477 | ||||||||
\(157\) | −5.24052 | −0.418239 | −0.209119 | − | 0.977890i | \(-0.567060\pi\) | ||||
−0.209119 | + | 0.977890i | \(0.567060\pi\) | |||||||
\(158\) | −3.98424 | −0.316969 | ||||||||
\(159\) | −3.30442 | −0.262057 | ||||||||
\(160\) | −0.999576 | −0.0790235 | ||||||||
\(161\) | 2.89603 | 0.228239 | ||||||||
\(162\) | −6.07600 | −0.477376 | ||||||||
\(163\) | −2.26445 | −0.177366 | −0.0886828 | − | 0.996060i | \(-0.528266\pi\) | ||||
−0.0886828 | + | 0.996060i | \(0.528266\pi\) | |||||||
\(164\) | −10.2287 | −0.798726 | ||||||||
\(165\) | −0.307108 | −0.0239083 | ||||||||
\(166\) | 8.53956 | 0.662799 | ||||||||
\(167\) | −0.734105 | −0.0568068 | −0.0284034 | − | 0.999597i | \(-0.509042\pi\) | ||||
−0.0284034 | + | 0.999597i | \(0.509042\pi\) | |||||||
\(168\) | −3.34190 | −0.257833 | ||||||||
\(169\) | −3.24221 | −0.249401 | ||||||||
\(170\) | 0.203271 | 0.0155902 | ||||||||
\(171\) | 10.5344 | 0.805586 | ||||||||
\(172\) | −20.5337 | −1.56568 | ||||||||
\(173\) | 0.151447 | 0.0115143 | 0.00575716 | − | 0.999983i | \(-0.498167\pi\) | ||||
0.00575716 | + | 0.999983i | \(0.498167\pi\) | |||||||
\(174\) | 14.0221 | 1.06301 | ||||||||
\(175\) | −3.01944 | −0.228248 | ||||||||
\(176\) | 1.26205 | 0.0951304 | ||||||||
\(177\) | −8.21237 | −0.617280 | ||||||||
\(178\) | −0.112214 | −0.00841079 | ||||||||
\(179\) | −16.2761 | −1.21653 | −0.608267 | − | 0.793733i | \(-0.708135\pi\) | ||||
−0.608267 | + | 0.793733i | \(0.708135\pi\) | |||||||
\(180\) | 0.786643 | 0.0586329 | ||||||||
\(181\) | 0.272612 | 0.0202631 | 0.0101315 | − | 0.999949i | \(-0.496775\pi\) | ||||
0.0101315 | + | 0.999949i | \(0.496775\pi\) | |||||||
\(182\) | −1.20548 | −0.0893560 | ||||||||
\(183\) | 30.4596 | 2.25164 | ||||||||
\(184\) | −10.8861 | −0.802531 | ||||||||
\(185\) | 0.875836 | 0.0643928 | ||||||||
\(186\) | 15.8339 | 1.16099 | ||||||||
\(187\) | −1.31598 | −0.0962341 | ||||||||
\(188\) | 13.4710 | 0.982477 | ||||||||
\(189\) | −0.296776 | −0.0215873 | ||||||||
\(190\) | −0.421270 | −0.0305622 | ||||||||
\(191\) | −20.1278 | −1.45640 | −0.728199 | − | 0.685366i | \(-0.759642\pi\) | ||||
−0.728199 | + | 0.685366i | \(0.759642\pi\) | |||||||
\(192\) | 0.285584 | 0.0206103 | ||||||||
\(193\) | −5.05542 | −0.363897 | −0.181949 | − | 0.983308i | \(-0.558240\pi\) | ||||
−0.181949 | + | 0.983308i | \(0.558240\pi\) | |||||||
\(194\) | 5.64416 | 0.405227 | ||||||||
\(195\) | 1.32473 | 0.0948656 | ||||||||
\(196\) | 10.5872 | 0.756228 | ||||||||
\(197\) | 2.29838 | 0.163753 | 0.0818765 | − | 0.996642i | \(-0.473909\pi\) | ||||
0.0818765 | + | 0.996642i | \(0.473909\pi\) | |||||||
\(198\) | 1.28642 | 0.0914218 | ||||||||
\(199\) | 18.0824 | 1.28183 | 0.640913 | − | 0.767614i | \(-0.278556\pi\) | ||||
0.640913 | + | 0.767614i | \(0.278556\pi\) | |||||||
\(200\) | 11.3499 | 0.802562 | ||||||||
\(201\) | 7.23586 | 0.510378 | ||||||||
\(202\) | −8.23528 | −0.579432 | ||||||||
\(203\) | 5.57236 | 0.391103 | ||||||||
\(204\) | 6.98609 | 0.489124 | ||||||||
\(205\) | −1.12835 | −0.0788075 | ||||||||
\(206\) | −12.5958 | −0.877594 | ||||||||
\(207\) | 13.3309 | 0.926565 | ||||||||
\(208\) | −5.44390 | −0.377467 | ||||||||
\(209\) | 2.72731 | 0.188652 | ||||||||
\(210\) | −0.163657 | −0.0112934 | ||||||||
\(211\) | −14.4216 | −0.992824 | −0.496412 | − | 0.868087i | \(-0.665350\pi\) | ||||
−0.496412 | + | 0.868087i | \(0.665350\pi\) | |||||||
\(212\) | 2.19132 | 0.150500 | ||||||||
\(213\) | 35.4230 | 2.42714 | ||||||||
\(214\) | 4.97524 | 0.340100 | ||||||||
\(215\) | −2.26512 | −0.154480 | ||||||||
\(216\) | 1.11557 | 0.0759048 | ||||||||
\(217\) | 6.29236 | 0.427153 | ||||||||
\(218\) | 9.28949 | 0.629164 | ||||||||
\(219\) | 18.5218 | 1.25159 | ||||||||
\(220\) | 0.203658 | 0.0137306 | ||||||||
\(221\) | 5.67655 | 0.381846 | ||||||||
\(222\) | −7.60348 | −0.510312 | ||||||||
\(223\) | −24.4696 | −1.63861 | −0.819303 | − | 0.573361i | \(-0.805639\pi\) | ||||
−0.819303 | + | 0.573361i | \(0.805639\pi\) | |||||||
\(224\) | 3.44852 | 0.230414 | ||||||||
\(225\) | −13.8990 | −0.926600 | ||||||||
\(226\) | 6.10618 | 0.406177 | ||||||||
\(227\) | −10.9184 | −0.724681 | −0.362340 | − | 0.932046i | \(-0.618022\pi\) | ||||
−0.362340 | + | 0.932046i | \(0.618022\pi\) | |||||||
\(228\) | −14.4783 | −0.958852 | ||||||||
\(229\) | 19.7809 | 1.30716 | 0.653579 | − | 0.756858i | \(-0.273267\pi\) | ||||
0.653579 | + | 0.756858i | \(0.273267\pi\) | |||||||
\(230\) | −0.533104 | −0.0351518 | ||||||||
\(231\) | 1.05952 | 0.0697111 | ||||||||
\(232\) | −20.9463 | −1.37519 | ||||||||
\(233\) | −13.7176 | −0.898671 | −0.449335 | − | 0.893363i | \(-0.648339\pi\) | ||||
−0.449335 | + | 0.893363i | \(0.648339\pi\) | |||||||
\(234\) | −5.54903 | −0.362751 | ||||||||
\(235\) | 1.48602 | 0.0969376 | ||||||||
\(236\) | 5.44602 | 0.354506 | ||||||||
\(237\) | −15.1053 | −0.981193 | ||||||||
\(238\) | −0.701281 | −0.0454573 | ||||||||
\(239\) | −5.54277 | −0.358532 | −0.179266 | − | 0.983801i | \(-0.557372\pi\) | ||||
−0.179266 | + | 0.983801i | \(0.557372\pi\) | |||||||
\(240\) | −0.739069 | −0.0477067 | ||||||||
\(241\) | 8.06605 | 0.519580 | 0.259790 | − | 0.965665i | \(-0.416347\pi\) | ||||
0.259790 | + | 0.965665i | \(0.416347\pi\) | |||||||
\(242\) | −6.65277 | −0.427656 | ||||||||
\(243\) | −21.5705 | −1.38375 | ||||||||
\(244\) | −20.1992 | −1.29312 | ||||||||
\(245\) | 1.16790 | 0.0746144 | ||||||||
\(246\) | 9.79566 | 0.624549 | ||||||||
\(247\) | −11.7644 | −0.748549 | ||||||||
\(248\) | −23.6527 | −1.50195 | ||||||||
\(249\) | 32.3756 | 2.05172 | ||||||||
\(250\) | 1.11511 | 0.0705258 | ||||||||
\(251\) | 5.73783 | 0.362168 | 0.181084 | − | 0.983468i | \(-0.442039\pi\) | ||||
0.181084 | + | 0.983468i | \(0.442039\pi\) | |||||||
\(252\) | −2.71390 | −0.170960 | ||||||||
\(253\) | 3.45132 | 0.216983 | ||||||||
\(254\) | −11.9760 | −0.751441 | ||||||||
\(255\) | 0.770653 | 0.0482602 | ||||||||
\(256\) | −7.39760 | −0.462350 | ||||||||
\(257\) | −24.2566 | −1.51308 | −0.756541 | − | 0.653946i | \(-0.773112\pi\) | ||||
−0.756541 | + | 0.653946i | \(0.773112\pi\) | |||||||
\(258\) | 19.6644 | 1.22425 | ||||||||
\(259\) | −3.02161 | −0.187754 | ||||||||
\(260\) | −0.878489 | −0.0544816 | ||||||||
\(261\) | 25.6506 | 1.58773 | ||||||||
\(262\) | −1.73405 | −0.107130 | ||||||||
\(263\) | 2.32155 | 0.143153 | 0.0715764 | − | 0.997435i | \(-0.477197\pi\) | ||||
0.0715764 | + | 0.997435i | \(0.477197\pi\) | |||||||
\(264\) | −3.98268 | −0.245117 | ||||||||
\(265\) | 0.241730 | 0.0148494 | ||||||||
\(266\) | 1.45337 | 0.0891120 | ||||||||
\(267\) | −0.425431 | −0.0260360 | ||||||||
\(268\) | −4.79844 | −0.293112 | ||||||||
\(269\) | −4.95698 | −0.302232 | −0.151116 | − | 0.988516i | \(-0.548287\pi\) | ||||
−0.151116 | + | 0.988516i | \(0.548287\pi\) | |||||||
\(270\) | 0.0546307 | 0.00332472 | ||||||||
\(271\) | −20.5983 | −1.25126 | −0.625630 | − | 0.780120i | \(-0.715158\pi\) | ||||
−0.625630 | + | 0.780120i | \(0.715158\pi\) | |||||||
\(272\) | −3.16697 | −0.192025 | ||||||||
\(273\) | −4.57027 | −0.276606 | ||||||||
\(274\) | 4.61999 | 0.279104 | ||||||||
\(275\) | −3.59839 | −0.216991 | ||||||||
\(276\) | −18.3219 | −1.10285 | ||||||||
\(277\) | 32.4420 | 1.94925 | 0.974625 | − | 0.223846i | \(-0.0718612\pi\) | ||||
0.974625 | + | 0.223846i | \(0.0718612\pi\) | |||||||
\(278\) | 0.519357 | 0.0311490 | ||||||||
\(279\) | 28.9648 | 1.73408 | ||||||||
\(280\) | 0.244472 | 0.0146100 | ||||||||
\(281\) | 26.8662 | 1.60270 | 0.801352 | − | 0.598193i | \(-0.204114\pi\) | ||||
0.801352 | + | 0.598193i | \(0.204114\pi\) | |||||||
\(282\) | −12.9008 | −0.768229 | ||||||||
\(283\) | 19.4549 | 1.15647 | 0.578237 | − | 0.815869i | \(-0.303741\pi\) | ||||
0.578237 | + | 0.815869i | \(0.303741\pi\) | |||||||
\(284\) | −23.4907 | −1.39391 | ||||||||
\(285\) | −1.59714 | −0.0946066 | ||||||||
\(286\) | −1.43662 | −0.0849490 | ||||||||
\(287\) | 3.89279 | 0.229784 | ||||||||
\(288\) | 15.8741 | 0.935392 | ||||||||
\(289\) | −13.6977 | −0.805747 | ||||||||
\(290\) | −1.02576 | −0.0602349 | ||||||||
\(291\) | 21.3984 | 1.25440 | ||||||||
\(292\) | −12.2827 | −0.718792 | ||||||||
\(293\) | −6.12616 | −0.357894 | −0.178947 | − | 0.983859i | \(-0.557269\pi\) | ||||
−0.178947 | + | 0.983859i | \(0.557269\pi\) | |||||||
\(294\) | −10.1390 | −0.591318 | ||||||||
\(295\) | 0.600764 | 0.0349778 | ||||||||
\(296\) | 11.3581 | 0.660178 | ||||||||
\(297\) | −0.353680 | −0.0205226 | ||||||||
\(298\) | 9.06393 | 0.525059 | ||||||||
\(299\) | −14.8874 | −0.860962 | ||||||||
\(300\) | 19.1026 | 1.10289 | ||||||||
\(301\) | 7.81462 | 0.450427 | ||||||||
\(302\) | 11.0925 | 0.638302 | ||||||||
\(303\) | −31.2220 | −1.79366 | ||||||||
\(304\) | 6.56339 | 0.376436 | ||||||||
\(305\) | −2.22822 | −0.127588 | ||||||||
\(306\) | −3.22812 | −0.184539 | ||||||||
\(307\) | 3.75293 | 0.214191 | 0.107095 | − | 0.994249i | \(-0.465845\pi\) | ||||
0.107095 | + | 0.994249i | \(0.465845\pi\) | |||||||
\(308\) | −0.702616 | −0.0400353 | ||||||||
\(309\) | −47.7540 | −2.71663 | ||||||||
\(310\) | −1.15830 | −0.0657871 | ||||||||
\(311\) | 26.5046 | 1.50294 | 0.751470 | − | 0.659767i | \(-0.229345\pi\) | ||||
0.751470 | + | 0.659767i | \(0.229345\pi\) | |||||||
\(312\) | 17.1795 | 0.972596 | ||||||||
\(313\) | 12.0658 | 0.682000 | 0.341000 | − | 0.940063i | \(-0.389234\pi\) | ||||
0.341000 | + | 0.940063i | \(0.389234\pi\) | |||||||
\(314\) | −3.32812 | −0.187817 | ||||||||
\(315\) | −0.299377 | −0.0168680 | ||||||||
\(316\) | 10.0170 | 0.563502 | ||||||||
\(317\) | 13.5511 | 0.761107 | 0.380554 | − | 0.924759i | \(-0.375733\pi\) | ||||
0.380554 | + | 0.924759i | \(0.375733\pi\) | |||||||
\(318\) | −2.09855 | −0.117681 | ||||||||
\(319\) | 6.64081 | 0.371814 | ||||||||
\(320\) | −0.0208915 | −0.00116787 | ||||||||
\(321\) | 18.8624 | 1.05280 | ||||||||
\(322\) | 1.83920 | 0.102494 | ||||||||
\(323\) | −6.84387 | −0.380803 | ||||||||
\(324\) | 15.2761 | 0.848670 | ||||||||
\(325\) | 15.5218 | 0.860996 | ||||||||
\(326\) | −1.43810 | −0.0796487 | ||||||||
\(327\) | 35.2188 | 1.94760 | ||||||||
\(328\) | −14.6328 | −0.807963 | ||||||||
\(329\) | −5.12675 | −0.282647 | ||||||||
\(330\) | −0.195037 | −0.0107364 | ||||||||
\(331\) | 28.6918 | 1.57705 | 0.788523 | − | 0.615005i | \(-0.210846\pi\) | ||||
0.788523 | + | 0.615005i | \(0.210846\pi\) | |||||||
\(332\) | −21.4698 | −1.17831 | ||||||||
\(333\) | −13.9090 | −0.762210 | ||||||||
\(334\) | −0.466211 | −0.0255100 | ||||||||
\(335\) | −0.529328 | −0.0289203 | ||||||||
\(336\) | 2.54977 | 0.139101 | ||||||||
\(337\) | 8.58771 | 0.467803 | 0.233901 | − | 0.972260i | \(-0.424851\pi\) | ||||
0.233901 | + | 0.972260i | \(0.424851\pi\) | |||||||
\(338\) | −2.05905 | −0.111997 | ||||||||
\(339\) | 23.1501 | 1.25734 | ||||||||
\(340\) | −0.511057 | −0.0277160 | ||||||||
\(341\) | 7.49886 | 0.406086 | ||||||||
\(342\) | 6.69013 | 0.361761 | ||||||||
\(343\) | −8.28283 | −0.447231 | ||||||||
\(344\) | −29.3749 | −1.58379 | ||||||||
\(345\) | −2.02113 | −0.108814 | ||||||||
\(346\) | 0.0961802 | 0.00517068 | ||||||||
\(347\) | −15.2240 | −0.817265 | −0.408633 | − | 0.912699i | \(-0.633994\pi\) | ||||
−0.408633 | + | 0.912699i | \(0.633994\pi\) | |||||||
\(348\) | −35.2538 | −1.88980 | ||||||||
\(349\) | 17.8082 | 0.953252 | 0.476626 | − | 0.879106i | \(-0.341860\pi\) | ||||
0.476626 | + | 0.879106i | \(0.341860\pi\) | |||||||
\(350\) | −1.91757 | −0.102498 | ||||||||
\(351\) | 1.52561 | 0.0814313 | ||||||||
\(352\) | 4.10974 | 0.219050 | ||||||||
\(353\) | 16.6349 | 0.885387 | 0.442693 | − | 0.896673i | \(-0.354023\pi\) | ||||
0.442693 | + | 0.896673i | \(0.354023\pi\) | |||||||
\(354\) | −5.21547 | −0.277199 | ||||||||
\(355\) | −2.59131 | −0.137533 | ||||||||
\(356\) | 0.282124 | 0.0149525 | ||||||||
\(357\) | −2.65874 | −0.140715 | ||||||||
\(358\) | −10.3365 | −0.546303 | ||||||||
\(359\) | 16.4374 | 0.867535 | 0.433767 | − | 0.901025i | \(-0.357184\pi\) | ||||
0.433767 | + | 0.901025i | \(0.357184\pi\) | |||||||
\(360\) | 1.12535 | 0.0593109 | ||||||||
\(361\) | −4.81639 | −0.253494 | ||||||||
\(362\) | 0.173129 | 0.00909945 | ||||||||
\(363\) | −25.2223 | −1.32383 | ||||||||
\(364\) | 3.03077 | 0.158855 | ||||||||
\(365\) | −1.35494 | −0.0709207 | ||||||||
\(366\) | 19.3441 | 1.01113 | ||||||||
\(367\) | −7.72221 | −0.403096 | −0.201548 | − | 0.979479i | \(-0.564597\pi\) | ||||
−0.201548 | + | 0.979479i | \(0.564597\pi\) | |||||||
\(368\) | 8.30575 | 0.432967 | ||||||||
\(369\) | 17.9192 | 0.932836 | ||||||||
\(370\) | 0.556221 | 0.0289166 | ||||||||
\(371\) | −0.833963 | −0.0432972 | ||||||||
\(372\) | −39.8089 | −2.06399 | ||||||||
\(373\) | 1.70082 | 0.0880650 | 0.0440325 | − | 0.999030i | \(-0.485979\pi\) | ||||
0.0440325 | + | 0.999030i | \(0.485979\pi\) | |||||||
\(374\) | −0.835746 | −0.0432154 | ||||||||
\(375\) | 4.22767 | 0.218316 | ||||||||
\(376\) | 19.2712 | 0.993838 | ||||||||
\(377\) | −28.6454 | −1.47532 | ||||||||
\(378\) | −0.188475 | −0.00969409 | ||||||||
\(379\) | 15.6176 | 0.802224 | 0.401112 | − | 0.916029i | \(-0.368624\pi\) | ||||
0.401112 | + | 0.916029i | \(0.368624\pi\) | |||||||
\(380\) | 1.05914 | 0.0543328 | ||||||||
\(381\) | −45.4041 | −2.32612 | ||||||||
\(382\) | −12.7827 | −0.654018 | ||||||||
\(383\) | −4.30563 | −0.220008 | −0.110004 | − | 0.993931i | \(-0.535086\pi\) | ||||
−0.110004 | + | 0.993931i | \(0.535086\pi\) | |||||||
\(384\) | −27.1468 | −1.38533 | ||||||||
\(385\) | −0.0775074 | −0.00395014 | ||||||||
\(386\) | −3.21057 | −0.163414 | ||||||||
\(387\) | 35.9721 | 1.82856 | ||||||||
\(388\) | −14.1903 | −0.720404 | ||||||||
\(389\) | −34.1729 | −1.73264 | −0.866318 | − | 0.499492i | \(-0.833520\pi\) | ||||
−0.866318 | + | 0.499492i | \(0.833520\pi\) | |||||||
\(390\) | 0.841300 | 0.0426009 | ||||||||
\(391\) | −8.66069 | −0.437990 | ||||||||
\(392\) | 15.1457 | 0.764973 | ||||||||
\(393\) | −6.57424 | −0.331627 | ||||||||
\(394\) | 1.45965 | 0.0735359 | ||||||||
\(395\) | 1.10500 | 0.0555988 | ||||||||
\(396\) | −3.23427 | −0.162528 | ||||||||
\(397\) | 12.3301 | 0.618829 | 0.309414 | − | 0.950927i | \(-0.399867\pi\) | ||||
0.309414 | + | 0.950927i | \(0.399867\pi\) | |||||||
\(398\) | 11.4837 | 0.575624 | ||||||||
\(399\) | 5.51010 | 0.275850 | ||||||||
\(400\) | −8.65968 | −0.432984 | ||||||||
\(401\) | −35.2145 | −1.75853 | −0.879265 | − | 0.476333i | \(-0.841966\pi\) | ||||
−0.879265 | + | 0.476333i | \(0.841966\pi\) | |||||||
\(402\) | 4.59531 | 0.229193 | ||||||||
\(403\) | −32.3467 | −1.61130 | ||||||||
\(404\) | 20.7048 | 1.03010 | ||||||||
\(405\) | 1.68514 | 0.0837353 | ||||||||
\(406\) | 3.53886 | 0.175631 | ||||||||
\(407\) | −3.60098 | −0.178494 | ||||||||
\(408\) | 9.99408 | 0.494780 | ||||||||
\(409\) | −7.35670 | −0.363766 | −0.181883 | − | 0.983320i | \(-0.558219\pi\) | ||||
−0.181883 | + | 0.983320i | \(0.558219\pi\) | |||||||
\(410\) | −0.716587 | −0.0353897 | ||||||||
\(411\) | 17.5156 | 0.863979 | ||||||||
\(412\) | 31.6680 | 1.56017 | ||||||||
\(413\) | −2.07262 | −0.101987 | ||||||||
\(414\) | 8.46614 | 0.416088 | ||||||||
\(415\) | −2.36839 | −0.116260 | ||||||||
\(416\) | −17.7276 | −0.869165 | ||||||||
\(417\) | 1.96902 | 0.0964231 | ||||||||
\(418\) | 1.73204 | 0.0847171 | ||||||||
\(419\) | 17.0403 | 0.832471 | 0.416236 | − | 0.909257i | \(-0.363349\pi\) | ||||
0.416236 | + | 0.909257i | \(0.363349\pi\) | |||||||
\(420\) | 0.411460 | 0.0200772 | ||||||||
\(421\) | −18.9374 | −0.922951 | −0.461476 | − | 0.887153i | \(-0.652680\pi\) | ||||
−0.461476 | + | 0.887153i | \(0.652680\pi\) | |||||||
\(422\) | −9.15880 | −0.445843 | ||||||||
\(423\) | −23.5993 | −1.14744 | ||||||||
\(424\) | 3.13483 | 0.152241 | ||||||||
\(425\) | 9.02975 | 0.438007 | ||||||||
\(426\) | 22.4962 | 1.08995 | ||||||||
\(427\) | 7.68732 | 0.372016 | ||||||||
\(428\) | −12.5086 | −0.604624 | ||||||||
\(429\) | −5.44658 | −0.262964 | ||||||||
\(430\) | −1.43852 | −0.0693717 | ||||||||
\(431\) | −20.6409 | −0.994238 | −0.497119 | − | 0.867682i | \(-0.665609\pi\) | ||||
−0.497119 | + | 0.867682i | \(0.665609\pi\) | |||||||
\(432\) | −0.851146 | −0.0409508 | ||||||||
\(433\) | −30.0335 | −1.44332 | −0.721660 | − | 0.692248i | \(-0.756620\pi\) | ||||
−0.721660 | + | 0.692248i | \(0.756620\pi\) | |||||||
\(434\) | 3.99612 | 0.191820 | ||||||||
\(435\) | −3.88893 | −0.186460 | ||||||||
\(436\) | −23.3553 | −1.11852 | ||||||||
\(437\) | 17.9489 | 0.858612 | ||||||||
\(438\) | 11.7628 | 0.562046 | ||||||||
\(439\) | −7.91987 | −0.377995 | −0.188997 | − | 0.981978i | \(-0.560524\pi\) | ||||
−0.188997 | + | 0.981978i | \(0.560524\pi\) | |||||||
\(440\) | 0.291347 | 0.0138894 | ||||||||
\(441\) | −18.5472 | −0.883202 | ||||||||
\(442\) | 3.60503 | 0.171474 | ||||||||
\(443\) | −31.6434 | −1.50342 | −0.751712 | − | 0.659491i | \(-0.770772\pi\) | ||||
−0.751712 | + | 0.659491i | \(0.770772\pi\) | |||||||
\(444\) | 19.1164 | 0.907223 | ||||||||
\(445\) | 0.0311218 | 0.00147531 | ||||||||
\(446\) | −15.5400 | −0.735841 | ||||||||
\(447\) | 34.3637 | 1.62535 | ||||||||
\(448\) | 0.0720752 | 0.00340523 | ||||||||
\(449\) | 17.3272 | 0.817720 | 0.408860 | − | 0.912597i | \(-0.365926\pi\) | ||||
0.408860 | + | 0.912597i | \(0.365926\pi\) | |||||||
\(450\) | −8.82690 | −0.416104 | ||||||||
\(451\) | 4.63920 | 0.218451 | ||||||||
\(452\) | −15.3519 | −0.722093 | ||||||||
\(453\) | 42.0545 | 1.97589 | ||||||||
\(454\) | −6.93401 | −0.325429 | ||||||||
\(455\) | 0.334332 | 0.0156737 | ||||||||
\(456\) | −20.7123 | −0.969940 | ||||||||
\(457\) | −14.1405 | −0.661467 | −0.330733 | − | 0.943724i | \(-0.607296\pi\) | ||||
−0.330733 | + | 0.943724i | \(0.607296\pi\) | |||||||
\(458\) | 12.5623 | 0.587000 | ||||||||
\(459\) | 0.887519 | 0.0414259 | ||||||||
\(460\) | 1.34031 | 0.0624922 | ||||||||
\(461\) | 1.42940 | 0.0665736 | 0.0332868 | − | 0.999446i | \(-0.489403\pi\) | ||||
0.0332868 | + | 0.999446i | \(0.489403\pi\) | |||||||
\(462\) | 0.672872 | 0.0313048 | ||||||||
\(463\) | 0.337105 | 0.0156666 | 0.00783330 | − | 0.999969i | \(-0.497507\pi\) | ||||
0.00783330 | + | 0.999969i | \(0.497507\pi\) | |||||||
\(464\) | 15.9814 | 0.741918 | ||||||||
\(465\) | −4.39142 | −0.203647 | ||||||||
\(466\) | −8.71171 | −0.403562 | ||||||||
\(467\) | −20.7741 | −0.961308 | −0.480654 | − | 0.876910i | \(-0.659601\pi\) | ||||
−0.480654 | + | 0.876910i | \(0.659601\pi\) | |||||||
\(468\) | 13.9512 | 0.644893 | ||||||||
\(469\) | 1.82617 | 0.0843247 | ||||||||
\(470\) | 0.943736 | 0.0435313 | ||||||||
\(471\) | −12.6177 | −0.581395 | ||||||||
\(472\) | 7.79090 | 0.358605 | ||||||||
\(473\) | 9.31301 | 0.428213 | ||||||||
\(474\) | −9.59297 | −0.440620 | ||||||||
\(475\) | −18.7137 | −0.858645 | ||||||||
\(476\) | 1.76313 | 0.0808132 | ||||||||
\(477\) | −3.83888 | −0.175770 | ||||||||
\(478\) | −3.52007 | −0.161004 | ||||||||
\(479\) | 6.13427 | 0.280282 | 0.140141 | − | 0.990132i | \(-0.455244\pi\) | ||||
0.140141 | + | 0.990132i | \(0.455244\pi\) | |||||||
\(480\) | −2.40671 | −0.109851 | ||||||||
\(481\) | 15.5330 | 0.708244 | ||||||||
\(482\) | 5.12254 | 0.233325 | ||||||||
\(483\) | 6.97286 | 0.317276 | ||||||||
\(484\) | 16.7261 | 0.760279 | ||||||||
\(485\) | −1.56537 | −0.0710798 | ||||||||
\(486\) | −13.6989 | −0.621393 | ||||||||
\(487\) | −29.9065 | −1.35519 | −0.677596 | − | 0.735434i | \(-0.736978\pi\) | ||||
−0.677596 | + | 0.735434i | \(0.736978\pi\) | |||||||
\(488\) | −28.8963 | −1.30808 | ||||||||
\(489\) | −5.45218 | −0.246556 | ||||||||
\(490\) | 0.741703 | 0.0335067 | ||||||||
\(491\) | 6.47968 | 0.292424 | 0.146212 | − | 0.989253i | \(-0.453292\pi\) | ||||
0.146212 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(492\) | −24.6279 | −1.11031 | ||||||||
\(493\) | −16.6644 | −0.750525 | ||||||||
\(494\) | −7.47126 | −0.336148 | ||||||||
\(495\) | −0.356780 | −0.0160361 | ||||||||
\(496\) | 18.0463 | 0.810305 | ||||||||
\(497\) | 8.93998 | 0.401013 | ||||||||
\(498\) | 20.5609 | 0.921358 | ||||||||
\(499\) | −31.0634 | −1.39059 | −0.695294 | − | 0.718726i | \(-0.744726\pi\) | ||||
−0.695294 | + | 0.718726i | \(0.744726\pi\) | |||||||
\(500\) | −2.80357 | −0.125379 | ||||||||
\(501\) | −1.76753 | −0.0789672 | ||||||||
\(502\) | 3.64395 | 0.162637 | ||||||||
\(503\) | −5.69577 | −0.253962 | −0.126981 | − | 0.991905i | \(-0.540529\pi\) | ||||
−0.126981 | + | 0.991905i | \(0.540529\pi\) | |||||||
\(504\) | −3.88242 | −0.172937 | ||||||||
\(505\) | 2.28400 | 0.101637 | ||||||||
\(506\) | 2.19185 | 0.0974394 | ||||||||
\(507\) | −7.80637 | −0.346693 | ||||||||
\(508\) | 30.1096 | 1.33590 | ||||||||
\(509\) | −12.1525 | −0.538649 | −0.269325 | − | 0.963049i | \(-0.586800\pi\) | ||||
−0.269325 | + | 0.963049i | \(0.586800\pi\) | |||||||
\(510\) | 0.489422 | 0.0216720 | ||||||||
\(511\) | 4.67451 | 0.206788 | ||||||||
\(512\) | 17.8517 | 0.788941 | ||||||||
\(513\) | −1.83934 | −0.0812090 | ||||||||
\(514\) | −15.4047 | −0.679473 | ||||||||
\(515\) | 3.49337 | 0.153936 | ||||||||
\(516\) | −49.4396 | −2.17646 | ||||||||
\(517\) | −6.10976 | −0.268707 | ||||||||
\(518\) | −1.91895 | −0.0843138 | ||||||||
\(519\) | 0.364644 | 0.0160061 | ||||||||
\(520\) | −1.25674 | −0.0551116 | ||||||||
\(521\) | −1.56247 | −0.0684529 | −0.0342264 | − | 0.999414i | \(-0.510897\pi\) | ||||
−0.0342264 | + | 0.999414i | \(0.510897\pi\) | |||||||
\(522\) | 16.2900 | 0.712995 | ||||||||
\(523\) | −3.02707 | −0.132365 | −0.0661823 | − | 0.997808i | \(-0.521082\pi\) | ||||
−0.0661823 | + | 0.997808i | \(0.521082\pi\) | |||||||
\(524\) | 4.35970 | 0.190454 | ||||||||
\(525\) | −7.26998 | −0.317288 | ||||||||
\(526\) | 1.47436 | 0.0642850 | ||||||||
\(527\) | −18.8175 | −0.819705 | ||||||||
\(528\) | 3.03867 | 0.132241 | ||||||||
\(529\) | −0.286279 | −0.0124469 | ||||||||
\(530\) | 0.153517 | 0.00666833 | ||||||||
\(531\) | −9.54065 | −0.414029 | ||||||||
\(532\) | −3.65401 | −0.158422 | ||||||||
\(533\) | −20.0114 | −0.866790 | ||||||||
\(534\) | −0.270181 | −0.0116919 | ||||||||
\(535\) | −1.37985 | −0.0596562 | ||||||||
\(536\) | −6.86450 | −0.296501 | ||||||||
\(537\) | −39.1884 | −1.69111 | ||||||||
\(538\) | −3.14805 | −0.135722 | ||||||||
\(539\) | −4.80180 | −0.206828 | ||||||||
\(540\) | −0.137350 | −0.00591062 | ||||||||
\(541\) | −26.5451 | −1.14126 | −0.570631 | − | 0.821207i | \(-0.693301\pi\) | ||||
−0.570631 | + | 0.821207i | \(0.693301\pi\) | |||||||
\(542\) | −13.0815 | −0.561897 | ||||||||
\(543\) | 0.656375 | 0.0281678 | ||||||||
\(544\) | −10.3129 | −0.442163 | ||||||||
\(545\) | −2.57638 | −0.110360 | ||||||||
\(546\) | −2.90246 | −0.124214 | ||||||||
\(547\) | −34.7992 | −1.48790 | −0.743952 | − | 0.668233i | \(-0.767051\pi\) | ||||
−0.743952 | + | 0.668233i | \(0.767051\pi\) | |||||||
\(548\) | −11.6154 | −0.496186 | ||||||||
\(549\) | 35.3861 | 1.51024 | ||||||||
\(550\) | −2.28525 | −0.0974432 | ||||||||
\(551\) | 34.5361 | 1.47129 | ||||||||
\(552\) | −26.2107 | −1.11560 | ||||||||
\(553\) | −3.81224 | −0.162113 | ||||||||
\(554\) | 20.6031 | 0.875341 | ||||||||
\(555\) | 2.10878 | 0.0895125 | ||||||||
\(556\) | −1.30575 | −0.0553761 | ||||||||
\(557\) | −41.3801 | −1.75333 | −0.876665 | − | 0.481102i | \(-0.840237\pi\) | ||||
−0.876665 | + | 0.481102i | \(0.840237\pi\) | |||||||
\(558\) | 18.3948 | 0.778715 | ||||||||
\(559\) | −40.1721 | −1.69910 | ||||||||
\(560\) | −0.186525 | −0.00788211 | ||||||||
\(561\) | −3.16853 | −0.133775 | ||||||||
\(562\) | 17.0621 | 0.719719 | ||||||||
\(563\) | 24.8102 | 1.04562 | 0.522812 | − | 0.852448i | \(-0.324883\pi\) | ||||
0.522812 | + | 0.852448i | \(0.324883\pi\) | |||||||
\(564\) | 32.4346 | 1.36574 | ||||||||
\(565\) | −1.69351 | −0.0712464 | ||||||||
\(566\) | 12.3553 | 0.519332 | ||||||||
\(567\) | −5.81370 | −0.244152 | ||||||||
\(568\) | −33.6050 | −1.41003 | ||||||||
\(569\) | 23.5407 | 0.986876 | 0.493438 | − | 0.869781i | \(-0.335740\pi\) | ||||
0.493438 | + | 0.869781i | \(0.335740\pi\) | |||||||
\(570\) | −1.01430 | −0.0424845 | ||||||||
\(571\) | 11.2932 | 0.472608 | 0.236304 | − | 0.971679i | \(-0.424064\pi\) | ||||
0.236304 | + | 0.971679i | \(0.424064\pi\) | |||||||
\(572\) | 3.61189 | 0.151021 | ||||||||
\(573\) | −48.4623 | −2.02454 | ||||||||
\(574\) | 2.47221 | 0.103188 | ||||||||
\(575\) | −23.6816 | −0.987591 | ||||||||
\(576\) | 0.331775 | 0.0138240 | ||||||||
\(577\) | −14.3977 | −0.599384 | −0.299692 | − | 0.954036i | \(-0.596884\pi\) | ||||
−0.299692 | + | 0.954036i | \(0.596884\pi\) | |||||||
\(578\) | −8.69906 | −0.361833 | ||||||||
\(579\) | −12.1721 | −0.505855 | ||||||||
\(580\) | 2.57894 | 0.107085 | ||||||||
\(581\) | 8.17090 | 0.338986 | ||||||||
\(582\) | 13.5896 | 0.563307 | ||||||||
\(583\) | −0.993868 | −0.0411618 | ||||||||
\(584\) | −17.5713 | −0.727104 | ||||||||
\(585\) | 1.53899 | 0.0636293 | ||||||||
\(586\) | −3.89057 | −0.160718 | ||||||||
\(587\) | 27.9863 | 1.15512 | 0.577560 | − | 0.816348i | \(-0.304005\pi\) | ||||
0.577560 | + | 0.816348i | \(0.304005\pi\) | |||||||
\(588\) | 25.4911 | 1.05123 | ||||||||
\(589\) | 38.9985 | 1.60690 | ||||||||
\(590\) | 0.381530 | 0.0157073 | ||||||||
\(591\) | 5.53388 | 0.227634 | ||||||||
\(592\) | −8.66592 | −0.356167 | ||||||||
\(593\) | 15.3065 | 0.628561 | 0.314281 | − | 0.949330i | \(-0.398237\pi\) | ||||
0.314281 | + | 0.949330i | \(0.398237\pi\) | |||||||
\(594\) | −0.224613 | −0.00921599 | ||||||||
\(595\) | 0.194496 | 0.00797355 | ||||||||
\(596\) | −22.7882 | −0.933441 | ||||||||
\(597\) | 43.5374 | 1.78187 | ||||||||
\(598\) | −9.45463 | −0.386629 | ||||||||
\(599\) | −17.5465 | −0.716930 | −0.358465 | − | 0.933543i | \(-0.616700\pi\) | ||||
−0.358465 | + | 0.933543i | \(0.616700\pi\) | |||||||
\(600\) | 27.3276 | 1.11564 | ||||||||
\(601\) | 39.5400 | 1.61287 | 0.806434 | − | 0.591324i | \(-0.201394\pi\) | ||||
0.806434 | + | 0.591324i | \(0.201394\pi\) | |||||||
\(602\) | 4.96287 | 0.202271 | ||||||||
\(603\) | 8.40619 | 0.342326 | ||||||||
\(604\) | −27.8884 | −1.13476 | ||||||||
\(605\) | 1.84510 | 0.0750141 | ||||||||
\(606\) | −19.8283 | −0.805471 | ||||||||
\(607\) | 25.8799 | 1.05043 | 0.525216 | − | 0.850969i | \(-0.323985\pi\) | ||||
0.525216 | + | 0.850969i | \(0.323985\pi\) | |||||||
\(608\) | 21.3731 | 0.866792 | ||||||||
\(609\) | 13.4167 | 0.543673 | ||||||||
\(610\) | −1.41509 | −0.0572953 | ||||||||
\(611\) | 26.3547 | 1.06620 | ||||||||
\(612\) | 8.11602 | 0.328071 | ||||||||
\(613\) | 11.3209 | 0.457246 | 0.228623 | − | 0.973515i | \(-0.426578\pi\) | ||||
0.228623 | + | 0.973515i | \(0.426578\pi\) | |||||||
\(614\) | 2.38339 | 0.0961857 | ||||||||
\(615\) | −2.71676 | −0.109551 | ||||||||
\(616\) | −1.00514 | −0.0404983 | ||||||||
\(617\) | −32.2416 | −1.29800 | −0.648999 | − | 0.760789i | \(-0.724812\pi\) | ||||
−0.648999 | + | 0.760789i | \(0.724812\pi\) | |||||||
\(618\) | −30.3274 | −1.21995 | ||||||||
\(619\) | −10.9416 | −0.439778 | −0.219889 | − | 0.975525i | \(-0.570570\pi\) | ||||
−0.219889 | + | 0.975525i | \(0.570570\pi\) | |||||||
\(620\) | 2.91216 | 0.116955 | ||||||||
\(621\) | −2.32763 | −0.0934045 | ||||||||
\(622\) | 16.8324 | 0.674919 | ||||||||
\(623\) | −0.107369 | −0.00430167 | ||||||||
\(624\) | −13.1074 | −0.524718 | ||||||||
\(625\) | 24.5356 | 0.981425 | ||||||||
\(626\) | 7.66269 | 0.306263 | ||||||||
\(627\) | 6.56662 | 0.262246 | ||||||||
\(628\) | 8.36743 | 0.333897 | ||||||||
\(629\) | 9.03626 | 0.360299 | ||||||||
\(630\) | −0.190127 | −0.00757483 | ||||||||
\(631\) | −0.302984 | −0.0120616 | −0.00603081 | − | 0.999982i | \(-0.501920\pi\) | ||||
−0.00603081 | + | 0.999982i | \(0.501920\pi\) | |||||||
\(632\) | 14.3300 | 0.570018 | ||||||||
\(633\) | −34.7233 | −1.38013 | ||||||||
\(634\) | 8.60598 | 0.341787 | ||||||||
\(635\) | 3.32147 | 0.131808 | ||||||||
\(636\) | 5.27610 | 0.209211 | ||||||||
\(637\) | 20.7128 | 0.820670 | ||||||||
\(638\) | 4.21741 | 0.166969 | ||||||||
\(639\) | 41.1523 | 1.62796 | ||||||||
\(640\) | 1.98589 | 0.0784990 | ||||||||
\(641\) | 44.3485 | 1.75166 | 0.875831 | − | 0.482619i | \(-0.160314\pi\) | ||||
0.875831 | + | 0.482619i | \(0.160314\pi\) | |||||||
\(642\) | 11.9790 | 0.472775 | ||||||||
\(643\) | −24.9513 | −0.983982 | −0.491991 | − | 0.870600i | \(-0.663731\pi\) | ||||
−0.491991 | + | 0.870600i | \(0.663731\pi\) | |||||||
\(644\) | −4.62404 | −0.182213 | ||||||||
\(645\) | −5.45380 | −0.214743 | ||||||||
\(646\) | −4.34637 | −0.171006 | ||||||||
\(647\) | 35.1007 | 1.37995 | 0.689976 | − | 0.723832i | \(-0.257621\pi\) | ||||
0.689976 | + | 0.723832i | \(0.257621\pi\) | |||||||
\(648\) | 21.8534 | 0.858484 | ||||||||
\(649\) | −2.47003 | −0.0969571 | ||||||||
\(650\) | 9.85751 | 0.386643 | ||||||||
\(651\) | 15.1503 | 0.593787 | ||||||||
\(652\) | 3.61560 | 0.141598 | ||||||||
\(653\) | 40.8715 | 1.59943 | 0.799713 | − | 0.600383i | \(-0.204985\pi\) | ||||
0.799713 | + | 0.600383i | \(0.204985\pi\) | |||||||
\(654\) | 22.3666 | 0.874602 | ||||||||
\(655\) | 0.480929 | 0.0187915 | ||||||||
\(656\) | 11.1644 | 0.435898 | ||||||||
\(657\) | 21.5176 | 0.839481 | ||||||||
\(658\) | −3.25587 | −0.126927 | ||||||||
\(659\) | 34.1506 | 1.33032 | 0.665159 | − | 0.746702i | \(-0.268364\pi\) | ||||
0.665159 | + | 0.746702i | \(0.268364\pi\) | |||||||
\(660\) | 0.490354 | 0.0190870 | ||||||||
\(661\) | −3.68626 | −0.143379 | −0.0716895 | − | 0.997427i | \(-0.522839\pi\) | ||||
−0.0716895 | + | 0.997427i | \(0.522839\pi\) | |||||||
\(662\) | 18.2215 | 0.708197 | ||||||||
\(663\) | 13.6676 | 0.530805 | ||||||||
\(664\) | −30.7141 | −1.19194 | ||||||||
\(665\) | −0.403084 | −0.0156309 | ||||||||
\(666\) | −8.83327 | −0.342282 | ||||||||
\(667\) | 43.7043 | 1.69224 | ||||||||
\(668\) | 1.17213 | 0.0453511 | ||||||||
\(669\) | −58.9161 | −2.27783 | ||||||||
\(670\) | −0.336163 | −0.0129871 | ||||||||
\(671\) | 9.16130 | 0.353668 | ||||||||
\(672\) | 8.30309 | 0.320299 | ||||||||
\(673\) | −19.1692 | −0.738919 | −0.369460 | − | 0.929247i | \(-0.620457\pi\) | ||||
−0.369460 | + | 0.929247i | \(0.620457\pi\) | |||||||
\(674\) | 5.45384 | 0.210074 | ||||||||
\(675\) | 2.42681 | 0.0934081 | ||||||||
\(676\) | 5.17678 | 0.199107 | ||||||||
\(677\) | −28.1525 | −1.08199 | −0.540994 | − | 0.841026i | \(-0.681952\pi\) | ||||
−0.540994 | + | 0.841026i | \(0.681952\pi\) | |||||||
\(678\) | 14.7020 | 0.564627 | ||||||||
\(679\) | 5.40049 | 0.207252 | ||||||||
\(680\) | −0.731102 | −0.0280365 | ||||||||
\(681\) | −26.2886 | −1.00738 | ||||||||
\(682\) | 4.76234 | 0.182359 | ||||||||
\(683\) | −35.9956 | −1.37734 | −0.688668 | − | 0.725077i | \(-0.741804\pi\) | ||||
−0.688668 | + | 0.725077i | \(0.741804\pi\) | |||||||
\(684\) | −16.8201 | −0.643132 | ||||||||
\(685\) | −1.28133 | −0.0489569 | ||||||||
\(686\) | −5.26022 | −0.200836 | ||||||||
\(687\) | 47.6270 | 1.81708 | ||||||||
\(688\) | 22.4122 | 0.854456 | ||||||||
\(689\) | 4.28710 | 0.163325 | ||||||||
\(690\) | −1.28357 | −0.0488646 | ||||||||
\(691\) | 7.55169 | 0.287280 | 0.143640 | − | 0.989630i | \(-0.454119\pi\) | ||||
0.143640 | + | 0.989630i | \(0.454119\pi\) | |||||||
\(692\) | −0.241813 | −0.00919234 | ||||||||
\(693\) | 1.23088 | 0.0467574 | ||||||||
\(694\) | −9.66835 | −0.367006 | ||||||||
\(695\) | −0.144040 | −0.00546377 | ||||||||
\(696\) | −50.4329 | −1.91165 | ||||||||
\(697\) | −11.6415 | −0.440955 | ||||||||
\(698\) | 11.3095 | 0.428072 | ||||||||
\(699\) | −33.0283 | −1.24924 | ||||||||
\(700\) | 4.82108 | 0.182220 | ||||||||
\(701\) | −6.15196 | −0.232356 | −0.116178 | − | 0.993228i | \(-0.537064\pi\) | ||||
−0.116178 | + | 0.993228i | \(0.537064\pi\) | |||||||
\(702\) | 0.968879 | 0.0365680 | ||||||||
\(703\) | −18.7272 | −0.706311 | ||||||||
\(704\) | 0.0858950 | 0.00323729 | ||||||||
\(705\) | 3.57794 | 0.134753 | ||||||||
\(706\) | 10.5644 | 0.397597 | ||||||||
\(707\) | −7.87976 | −0.296349 | ||||||||
\(708\) | 13.1125 | 0.492799 | ||||||||
\(709\) | 48.5620 | 1.82378 | 0.911892 | − | 0.410430i | \(-0.134621\pi\) | ||||
0.911892 | + | 0.410430i | \(0.134621\pi\) | |||||||
\(710\) | −1.64568 | −0.0617612 | ||||||||
\(711\) | −17.5484 | −0.658117 | ||||||||
\(712\) | 0.403597 | 0.0151255 | ||||||||
\(713\) | 49.3513 | 1.84822 | ||||||||
\(714\) | −1.68850 | −0.0631903 | ||||||||
\(715\) | 0.398437 | 0.0149007 | ||||||||
\(716\) | 25.9877 | 0.971207 | ||||||||
\(717\) | −13.3455 | −0.498396 | ||||||||
\(718\) | 10.4390 | 0.389580 | ||||||||
\(719\) | 28.8372 | 1.07545 | 0.537724 | − | 0.843121i | \(-0.319284\pi\) | ||||
0.537724 | + | 0.843121i | \(0.319284\pi\) | |||||||
\(720\) | −0.858607 | −0.0319984 | ||||||||
\(721\) | −12.0521 | −0.448842 | ||||||||
\(722\) | −3.05877 | −0.113836 | ||||||||
\(723\) | 19.4209 | 0.722269 | ||||||||
\(724\) | −0.435274 | −0.0161768 | ||||||||
\(725\) | −45.5666 | −1.69230 | ||||||||
\(726\) | −16.0181 | −0.594486 | ||||||||
\(727\) | −13.8642 | −0.514194 | −0.257097 | − | 0.966386i | \(-0.582766\pi\) | ||||
−0.257097 | + | 0.966386i | \(0.582766\pi\) | |||||||
\(728\) | 4.33572 | 0.160692 | ||||||||
\(729\) | −23.2337 | −0.860508 | ||||||||
\(730\) | −0.860487 | −0.0318480 | ||||||||
\(731\) | −23.3699 | −0.864369 | ||||||||
\(732\) | −48.6342 | −1.79757 | ||||||||
\(733\) | 36.1980 | 1.33700 | 0.668501 | − | 0.743711i | \(-0.266936\pi\) | ||||
0.668501 | + | 0.743711i | \(0.266936\pi\) | |||||||
\(734\) | −4.90418 | −0.181016 | ||||||||
\(735\) | 2.81199 | 0.103722 | ||||||||
\(736\) | 27.0469 | 0.996962 | ||||||||
\(737\) | 2.17632 | 0.0801659 | ||||||||
\(738\) | 11.3800 | 0.418904 | ||||||||
\(739\) | 12.6074 | 0.463769 | 0.231885 | − | 0.972743i | \(-0.425511\pi\) | ||||
0.231885 | + | 0.972743i | \(0.425511\pi\) | |||||||
\(740\) | −1.39843 | −0.0514073 | ||||||||
\(741\) | −28.3254 | −1.04056 | ||||||||
\(742\) | −0.529628 | −0.0194433 | ||||||||
\(743\) | −1.17912 | −0.0432577 | −0.0216288 | − | 0.999766i | \(-0.506885\pi\) | ||||
−0.0216288 | + | 0.999766i | \(0.506885\pi\) | |||||||
\(744\) | −56.9493 | −2.08786 | ||||||||
\(745\) | −2.51382 | −0.0920993 | ||||||||
\(746\) | 1.08015 | 0.0395470 | ||||||||
\(747\) | 37.6121 | 1.37615 | ||||||||
\(748\) | 2.10120 | 0.0768275 | ||||||||
\(749\) | 4.76045 | 0.173943 | ||||||||
\(750\) | 2.68488 | 0.0980381 | ||||||||
\(751\) | 40.8675 | 1.49128 | 0.745638 | − | 0.666351i | \(-0.232145\pi\) | ||||
0.745638 | + | 0.666351i | \(0.232145\pi\) | |||||||
\(752\) | −14.7034 | −0.536178 | ||||||||
\(753\) | 13.8151 | 0.503451 | ||||||||
\(754\) | −18.1920 | −0.662513 | ||||||||
\(755\) | −3.07643 | −0.111963 | ||||||||
\(756\) | 0.473856 | 0.0172340 | ||||||||
\(757\) | −37.7187 | −1.37091 | −0.685455 | − | 0.728115i | \(-0.740397\pi\) | ||||
−0.685455 | + | 0.728115i | \(0.740397\pi\) | |||||||
\(758\) | 9.91836 | 0.360251 | ||||||||
\(759\) | 8.30984 | 0.301628 | ||||||||
\(760\) | 1.51517 | 0.0549612 | ||||||||
\(761\) | −37.0936 | −1.34464 | −0.672320 | − | 0.740260i | \(-0.734702\pi\) | ||||
−0.672320 | + | 0.740260i | \(0.734702\pi\) | |||||||
\(762\) | −28.8350 | −1.04458 | ||||||||
\(763\) | 8.88845 | 0.321784 | ||||||||
\(764\) | 32.1377 | 1.16270 | ||||||||
\(765\) | 0.895299 | 0.0323696 | ||||||||
\(766\) | −2.73440 | −0.0987978 | ||||||||
\(767\) | 10.6546 | 0.384715 | ||||||||
\(768\) | −17.8114 | −0.642714 | ||||||||
\(769\) | −42.7296 | −1.54087 | −0.770434 | − | 0.637519i | \(-0.779961\pi\) | ||||
−0.770434 | + | 0.637519i | \(0.779961\pi\) | |||||||
\(770\) | −0.0492230 | −0.00177387 | ||||||||
\(771\) | −58.4032 | −2.10334 | ||||||||
\(772\) | 8.07189 | 0.290514 | ||||||||
\(773\) | 47.5229 | 1.70928 | 0.854640 | − | 0.519220i | \(-0.173778\pi\) | ||||
0.854640 | + | 0.519220i | \(0.173778\pi\) | |||||||
\(774\) | 22.8450 | 0.821145 | ||||||||
\(775\) | −51.4543 | −1.84829 | ||||||||
\(776\) | −20.3002 | −0.728736 | ||||||||
\(777\) | −7.27523 | −0.260997 | ||||||||
\(778\) | −21.7024 | −0.778067 | ||||||||
\(779\) | 24.1265 | 0.864423 | ||||||||
\(780\) | −2.11516 | −0.0757350 | ||||||||
\(781\) | 10.6541 | 0.381235 | ||||||||
\(782\) | −5.50019 | −0.196686 | ||||||||
\(783\) | −4.47867 | −0.160055 | ||||||||
\(784\) | −11.5557 | −0.412705 | ||||||||
\(785\) | 0.923033 | 0.0329445 | ||||||||
\(786\) | −4.17513 | −0.148922 | ||||||||
\(787\) | 25.3634 | 0.904106 | 0.452053 | − | 0.891991i | \(-0.350692\pi\) | ||||
0.452053 | + | 0.891991i | \(0.350692\pi\) | |||||||
\(788\) | −3.66978 | −0.130731 | ||||||||
\(789\) | 5.58966 | 0.198997 | ||||||||
\(790\) | 0.701760 | 0.0249675 | ||||||||
\(791\) | 5.84257 | 0.207738 | ||||||||
\(792\) | −4.62684 | −0.164408 | ||||||||
\(793\) | −39.5177 | −1.40331 | ||||||||
\(794\) | 7.83052 | 0.277895 | ||||||||
\(795\) | 0.582020 | 0.0206421 | ||||||||
\(796\) | −28.8718 | −1.02333 | ||||||||
\(797\) | −12.4440 | −0.440791 | −0.220395 | − | 0.975411i | \(-0.570735\pi\) | ||||
−0.220395 | + | 0.975411i | \(0.570735\pi\) | |||||||
\(798\) | 3.49933 | 0.123875 | ||||||||
\(799\) | 15.3318 | 0.542398 | ||||||||
\(800\) | −28.1994 | −0.997000 | ||||||||
\(801\) | −0.494241 | −0.0174631 | ||||||||
\(802\) | −22.3639 | −0.789695 | ||||||||
\(803\) | 5.57080 | 0.196589 | ||||||||
\(804\) | −11.5533 | −0.407455 | ||||||||
\(805\) | −0.510089 | −0.0179783 | ||||||||
\(806\) | −20.5426 | −0.723581 | ||||||||
\(807\) | −11.9351 | −0.420134 | ||||||||
\(808\) | 29.6197 | 1.04202 | ||||||||
\(809\) | −37.2615 | −1.31004 | −0.655022 | − | 0.755610i | \(-0.727341\pi\) | ||||
−0.655022 | + | 0.755610i | \(0.727341\pi\) | |||||||
\(810\) | 1.07019 | 0.0376026 | ||||||||
\(811\) | −32.5136 | −1.14171 | −0.570853 | − | 0.821052i | \(-0.693387\pi\) | ||||
−0.570853 | + | 0.821052i | \(0.693387\pi\) | |||||||
\(812\) | −8.89727 | −0.312233 | ||||||||
\(813\) | −49.5952 | −1.73938 | ||||||||
\(814\) | −2.28689 | −0.0801556 | ||||||||
\(815\) | 0.398846 | 0.0139710 | ||||||||
\(816\) | −7.62519 | −0.266935 | ||||||||
\(817\) | 48.4331 | 1.69446 | ||||||||
\(818\) | −4.67206 | −0.163355 | ||||||||
\(819\) | −5.30947 | −0.185528 | ||||||||
\(820\) | 1.80162 | 0.0629152 | ||||||||
\(821\) | 26.9597 | 0.940899 | 0.470449 | − | 0.882427i | \(-0.344092\pi\) | ||||
0.470449 | + | 0.882427i | \(0.344092\pi\) | |||||||
\(822\) | 11.1237 | 0.387983 | ||||||||
\(823\) | −34.6716 | −1.20858 | −0.604288 | − | 0.796766i | \(-0.706542\pi\) | ||||
−0.604288 | + | 0.796766i | \(0.706542\pi\) | |||||||
\(824\) | 45.3032 | 1.57821 | ||||||||
\(825\) | −8.66394 | −0.301640 | ||||||||
\(826\) | −1.31627 | −0.0457989 | ||||||||
\(827\) | −10.3523 | −0.359983 | −0.179992 | − | 0.983668i | \(-0.557607\pi\) | ||||
−0.179992 | + | 0.983668i | \(0.557607\pi\) | |||||||
\(828\) | −21.2853 | −0.739714 | ||||||||
\(829\) | 37.8331 | 1.31400 | 0.656998 | − | 0.753892i | \(-0.271826\pi\) | ||||
0.656998 | + | 0.753892i | \(0.271826\pi\) | |||||||
\(830\) | −1.50411 | −0.0522083 | ||||||||
\(831\) | 78.1115 | 2.70966 | ||||||||
\(832\) | −0.370512 | −0.0128452 | ||||||||
\(833\) | 12.0496 | 0.417493 | ||||||||
\(834\) | 1.25047 | 0.0433003 | ||||||||
\(835\) | 0.129301 | 0.00447464 | ||||||||
\(836\) | −4.35464 | −0.150608 | ||||||||
\(837\) | −5.05736 | −0.174808 | ||||||||
\(838\) | 10.8218 | 0.373834 | ||||||||
\(839\) | 34.8243 | 1.20227 | 0.601134 | − | 0.799148i | \(-0.294716\pi\) | ||||
0.601134 | + | 0.799148i | \(0.294716\pi\) | |||||||
\(840\) | 0.588621 | 0.0203094 | ||||||||
\(841\) | 55.0930 | 1.89976 | ||||||||
\(842\) | −12.0266 | −0.414466 | ||||||||
\(843\) | 64.6866 | 2.22792 | ||||||||
\(844\) | 23.0267 | 0.792612 | ||||||||
\(845\) | 0.571064 | 0.0196452 | ||||||||
\(846\) | −14.9873 | −0.515275 | ||||||||
\(847\) | −6.36556 | −0.218723 | ||||||||
\(848\) | −2.39179 | −0.0821343 | ||||||||
\(849\) | 46.8421 | 1.60762 | ||||||||
\(850\) | 5.73456 | 0.196694 | ||||||||
\(851\) | −23.6987 | −0.812380 | ||||||||
\(852\) | −56.5591 | −1.93768 | ||||||||
\(853\) | −39.5421 | −1.35389 | −0.676947 | − | 0.736032i | \(-0.736697\pi\) | ||||
−0.676947 | + | 0.736032i | \(0.736697\pi\) | |||||||
\(854\) | 4.88202 | 0.167059 | ||||||||
\(855\) | −1.85547 | −0.0634556 | ||||||||
\(856\) | −17.8943 | −0.611616 | ||||||||
\(857\) | −31.8063 | −1.08648 | −0.543242 | − | 0.839576i | \(-0.682803\pi\) | ||||
−0.543242 | + | 0.839576i | \(0.682803\pi\) | |||||||
\(858\) | −3.45899 | −0.118088 | ||||||||
\(859\) | −46.6429 | −1.59144 | −0.795718 | − | 0.605668i | \(-0.792906\pi\) | ||||
−0.795718 | + | 0.605668i | \(0.792906\pi\) | |||||||
\(860\) | 3.61668 | 0.123328 | ||||||||
\(861\) | 9.37277 | 0.319423 | ||||||||
\(862\) | −13.1085 | −0.446478 | ||||||||
\(863\) | 1.38859 | 0.0472681 | 0.0236341 | − | 0.999721i | \(-0.492476\pi\) | ||||
0.0236341 | + | 0.999721i | \(0.492476\pi\) | |||||||
\(864\) | −2.77168 | −0.0942943 | ||||||||
\(865\) | −0.0266750 | −0.000906976 0 | ||||||||
\(866\) | −19.0735 | −0.648145 | ||||||||
\(867\) | −32.9803 | −1.12007 | ||||||||
\(868\) | −10.0469 | −0.341013 | ||||||||
\(869\) | −4.54320 | −0.154118 | ||||||||
\(870\) | −2.46976 | −0.0837328 | ||||||||
\(871\) | −9.38768 | −0.318089 | ||||||||
\(872\) | −33.4113 | −1.13145 | ||||||||
\(873\) | 24.8594 | 0.841364 | ||||||||
\(874\) | 11.3989 | 0.385573 | ||||||||
\(875\) | 1.06697 | 0.0360702 | ||||||||
\(876\) | −29.5735 | −0.999195 | ||||||||
\(877\) | −16.7394 | −0.565249 | −0.282624 | − | 0.959231i | \(-0.591205\pi\) | ||||
−0.282624 | + | 0.959231i | \(0.591205\pi\) | |||||||
\(878\) | −5.02971 | −0.169744 | ||||||||
\(879\) | −14.7501 | −0.497510 | ||||||||
\(880\) | −0.222289 | −0.00749337 | ||||||||
\(881\) | −35.2674 | −1.18819 | −0.594095 | − | 0.804395i | \(-0.702490\pi\) | ||||
−0.594095 | + | 0.804395i | \(0.702490\pi\) | |||||||
\(882\) | −11.7789 | −0.396616 | ||||||||
\(883\) | −12.2091 | −0.410870 | −0.205435 | − | 0.978671i | \(-0.565861\pi\) | ||||
−0.205435 | + | 0.978671i | \(0.565861\pi\) | |||||||
\(884\) | −9.06363 | −0.304843 | ||||||||
\(885\) | 1.44648 | 0.0486228 | ||||||||
\(886\) | −20.0959 | −0.675136 | ||||||||
\(887\) | −54.0998 | −1.81649 | −0.908247 | − | 0.418435i | \(-0.862579\pi\) | ||||
−0.908247 | + | 0.418435i | \(0.862579\pi\) | |||||||
\(888\) | 27.3473 | 0.917715 | ||||||||
\(889\) | −11.4590 | −0.384322 | ||||||||
\(890\) | 0.0197647 | 0.000662513 0 | ||||||||
\(891\) | −6.92842 | −0.232111 | ||||||||
\(892\) | 39.0701 | 1.30816 | ||||||||
\(893\) | −31.7743 | −1.06329 | ||||||||
\(894\) | 21.8235 | 0.729887 | ||||||||
\(895\) | 2.86677 | 0.0958257 | ||||||||
\(896\) | −6.85126 | −0.228884 | ||||||||
\(897\) | −35.8449 | −1.19683 | ||||||||
\(898\) | 11.0040 | 0.367210 | ||||||||
\(899\) | 94.9586 | 3.16705 | ||||||||
\(900\) | 22.1923 | 0.739742 | ||||||||
\(901\) | 2.49400 | 0.0830871 | ||||||||
\(902\) | 2.94624 | 0.0980989 | ||||||||
\(903\) | 18.8155 | 0.626140 | ||||||||
\(904\) | −21.9620 | −0.730444 | ||||||||
\(905\) | −0.0480162 | −0.00159611 | ||||||||
\(906\) | 26.7077 | 0.887305 | ||||||||
\(907\) | 10.3854 | 0.344842 | 0.172421 | − | 0.985023i | \(-0.444841\pi\) | ||||
0.172421 | + | 0.985023i | \(0.444841\pi\) | |||||||
\(908\) | 17.4332 | 0.578542 | ||||||||
\(909\) | −36.2719 | −1.20306 | ||||||||
\(910\) | 0.212326 | 0.00703852 | ||||||||
\(911\) | 38.4824 | 1.27498 | 0.637490 | − | 0.770459i | \(-0.279973\pi\) | ||||
0.637490 | + | 0.770459i | \(0.279973\pi\) | |||||||
\(912\) | 15.8029 | 0.523285 | ||||||||
\(913\) | 9.73760 | 0.322268 | ||||||||
\(914\) | −8.98030 | −0.297042 | ||||||||
\(915\) | −5.36496 | −0.177360 | ||||||||
\(916\) | −31.5838 | −1.04356 | ||||||||
\(917\) | −1.65919 | −0.0547914 | ||||||||
\(918\) | 0.563641 | 0.0186029 | ||||||||
\(919\) | 13.5106 | 0.445675 | 0.222837 | − | 0.974856i | \(-0.428468\pi\) | ||||
0.222837 | + | 0.974856i | \(0.428468\pi\) | |||||||
\(920\) | 1.91740 | 0.0632149 | ||||||||
\(921\) | 9.03603 | 0.297747 | ||||||||
\(922\) | 0.907773 | 0.0298959 | ||||||||
\(923\) | −45.9571 | −1.51270 | ||||||||
\(924\) | −1.69171 | −0.0556531 | ||||||||
\(925\) | 24.7085 | 0.812412 | ||||||||
\(926\) | 0.214087 | 0.00703533 | ||||||||
\(927\) | −55.4778 | −1.82213 | ||||||||
\(928\) | 52.0419 | 1.70836 | ||||||||
\(929\) | −6.58540 | −0.216060 | −0.108030 | − | 0.994148i | \(-0.534454\pi\) | ||||
−0.108030 | + | 0.994148i | \(0.534454\pi\) | |||||||
\(930\) | −2.78888 | −0.0914509 | ||||||||
\(931\) | −24.9722 | −0.818430 | ||||||||
\(932\) | 21.9026 | 0.717445 | ||||||||
\(933\) | 63.8160 | 2.08924 | ||||||||
\(934\) | −13.1931 | −0.431690 | ||||||||
\(935\) | 0.231789 | 0.00758031 | ||||||||
\(936\) | 19.9581 | 0.652350 | ||||||||
\(937\) | −33.4636 | −1.09321 | −0.546604 | − | 0.837391i | \(-0.684080\pi\) | ||||
−0.546604 | + | 0.837391i | \(0.684080\pi\) | |||||||
\(938\) | 1.15975 | 0.0378673 | ||||||||
\(939\) | 29.0512 | 0.948050 | ||||||||
\(940\) | −2.37271 | −0.0773891 | ||||||||
\(941\) | 29.6727 | 0.967303 | 0.483651 | − | 0.875261i | \(-0.339310\pi\) | ||||
0.483651 | + | 0.875261i | \(0.339310\pi\) | |||||||
\(942\) | −8.01321 | −0.261085 | ||||||||
\(943\) | 30.5313 | 0.994237 | ||||||||
\(944\) | −5.94423 | −0.193468 | ||||||||
\(945\) | 0.0522722 | 0.00170042 | ||||||||
\(946\) | 5.91446 | 0.192296 | ||||||||
\(947\) | −38.4749 | −1.25027 | −0.625133 | − | 0.780518i | \(-0.714955\pi\) | ||||
−0.625133 | + | 0.780518i | \(0.714955\pi\) | |||||||
\(948\) | 24.1183 | 0.783325 | ||||||||
\(949\) | −24.0299 | −0.780044 | ||||||||
\(950\) | −11.8846 | −0.385588 | ||||||||
\(951\) | 32.6274 | 1.05802 | ||||||||
\(952\) | 2.52228 | 0.0817477 | ||||||||
\(953\) | 20.7040 | 0.670669 | 0.335335 | − | 0.942099i | \(-0.391151\pi\) | ||||
0.335335 | + | 0.942099i | \(0.391151\pi\) | |||||||
\(954\) | −2.43797 | −0.0789323 | ||||||||
\(955\) | 3.54519 | 0.114720 | ||||||||
\(956\) | 8.85003 | 0.286230 | ||||||||
\(957\) | 15.9893 | 0.516860 | ||||||||
\(958\) | 3.89572 | 0.125865 | ||||||||
\(959\) | 4.42054 | 0.142747 | ||||||||
\(960\) | −0.0503011 | −0.00162346 | ||||||||
\(961\) | 76.2281 | 2.45897 | ||||||||
\(962\) | 9.86462 | 0.318048 | ||||||||
\(963\) | 21.9132 | 0.706143 | ||||||||
\(964\) | −12.8789 | −0.414801 | ||||||||
\(965\) | 0.890431 | 0.0286640 | ||||||||
\(966\) | 4.42828 | 0.142478 | ||||||||
\(967\) | 6.81229 | 0.219069 | 0.109534 | − | 0.993983i | \(-0.465064\pi\) | ||||
0.109534 | + | 0.993983i | \(0.465064\pi\) | |||||||
\(968\) | 23.9279 | 0.769072 | ||||||||
\(969\) | −16.4782 | −0.529356 | ||||||||
\(970\) | −0.994127 | −0.0319195 | ||||||||
\(971\) | −43.2325 | −1.38740 | −0.693698 | − | 0.720266i | \(-0.744020\pi\) | ||||
−0.693698 | + | 0.720266i | \(0.744020\pi\) | |||||||
\(972\) | 34.4412 | 1.10470 | ||||||||
\(973\) | 0.496936 | 0.0159310 | ||||||||
\(974\) | −18.9929 | −0.608570 | ||||||||
\(975\) | 37.3723 | 1.19687 | ||||||||
\(976\) | 22.0471 | 0.705709 | ||||||||
\(977\) | −45.3628 | −1.45128 | −0.725642 | − | 0.688073i | \(-0.758457\pi\) | ||||
−0.725642 | + | 0.688073i | \(0.758457\pi\) | |||||||
\(978\) | −3.46254 | −0.110720 | ||||||||
\(979\) | −0.127957 | −0.00408951 | ||||||||
\(980\) | −1.86476 | −0.0595677 | ||||||||
\(981\) | 40.9151 | 1.30632 | ||||||||
\(982\) | 4.11508 | 0.131317 | ||||||||
\(983\) | −1.32516 | −0.0422661 | −0.0211331 | − | 0.999777i | \(-0.506727\pi\) | ||||
−0.0211331 | + | 0.999777i | \(0.506727\pi\) | |||||||
\(984\) | −35.2319 | −1.12315 | ||||||||
\(985\) | −0.404823 | −0.0128987 | ||||||||
\(986\) | −10.5831 | −0.337035 | ||||||||
\(987\) | −12.3438 | −0.392908 | ||||||||
\(988\) | 18.7840 | 0.597597 | ||||||||
\(989\) | 61.2905 | 1.94893 | ||||||||
\(990\) | −0.226582 | −0.00720125 | ||||||||
\(991\) | 0.415651 | 0.0132036 | 0.00660180 | − | 0.999978i | \(-0.497899\pi\) | ||||
0.00660180 | + | 0.999978i | \(0.497899\pi\) | |||||||
\(992\) | 58.7662 | 1.86583 | ||||||||
\(993\) | 69.0822 | 2.19226 | ||||||||
\(994\) | 5.67755 | 0.180081 | ||||||||
\(995\) | −3.18492 | −0.100969 | ||||||||
\(996\) | −51.6935 | −1.63797 | ||||||||
\(997\) | 54.8267 | 1.73638 | 0.868190 | − | 0.496232i | \(-0.165283\pi\) | ||||
0.868190 | + | 0.496232i | \(0.165283\pi\) | |||||||
\(998\) | −19.7276 | −0.624465 | ||||||||
\(999\) | 2.42856 | 0.0768363 |
(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 | 4001.2.a.b.1.109 | ✓ | 184 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.b.1.109 | ✓ | 184 | 1.1 | even | 1 | trivial |