Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6044,2,Mod(1,6044)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6044, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6044.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6044 = 2^{2} \cdot 1511 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6044.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: | \(48.2615829817\) |
Analytic rank: | \(1\) |
Dimension: | \(63\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6044.1 |
$q$-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 | 0 | ||||||||
\(3\) | −1.98161 | −1.14409 | −0.572043 | − | 0.820224i | \(-0.693849\pi\) | ||||
−0.572043 | + | 0.820224i | \(0.693849\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.75516 | −1.67936 | −0.839679 | − | 0.543084i | \(-0.817257\pi\) | ||||
−0.839679 | + | 0.543084i | \(0.817257\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.03693 | −1.52582 | −0.762908 | − | 0.646507i | \(-0.776229\pi\) | ||||
−0.762908 | + | 0.646507i | \(0.776229\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.926797 | 0.308932 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.98101 | 0.597298 | 0.298649 | − | 0.954363i | \(-0.403464\pi\) | ||||
0.298649 | + | 0.954363i | \(0.403464\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.54356 | −0.428106 | −0.214053 | − | 0.976822i | \(-0.568667\pi\) | ||||
−0.214053 | + | 0.976822i | \(0.568667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.44128 | 1.92133 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.21178 | −0.778971 | −0.389486 | − | 0.921033i | \(-0.627347\pi\) | ||||
−0.389486 | + | 0.921033i | \(0.627347\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.50606 | −1.03376 | −0.516881 | − | 0.856057i | \(-0.672907\pi\) | ||||
−0.516881 | + | 0.856057i | \(0.672907\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.99964 | 1.74566 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.07756 | 0.641716 | 0.320858 | − | 0.947127i | \(-0.396029\pi\) | ||||
0.320858 | + | 0.947127i | \(0.396029\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.10121 | 1.82024 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.10829 | 0.790641 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.71564 | −1.43276 | −0.716379 | − | 0.697711i | \(-0.754202\pi\) | ||||
−0.716379 | + | 0.697711i | \(0.754202\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.10333 | 1.09619 | 0.548095 | − | 0.836416i | \(-0.315353\pi\) | ||||
0.548095 | + | 0.836416i | \(0.315353\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.92561 | −0.683360 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 15.1593 | 2.56239 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.55476 | −1.40639 | −0.703197 | − | 0.710995i | \(-0.748245\pi\) | ||||
−0.703197 | + | 0.710995i | \(0.748245\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.05874 | 0.489790 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.512844 | 0.0800928 | 0.0400464 | − | 0.999198i | \(-0.487249\pi\) | ||||
0.0400464 | + | 0.999198i | \(0.487249\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.00742461 | 0.00113224 | 0.000566121 | − | 1.00000i | \(-0.499820\pi\) | ||||
0.000566121 | 1.00000i | \(0.499820\pi\) | ||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.48027 | −0.518808 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.94533 | 1.15895 | 0.579473 | − | 0.814992i | \(-0.303259\pi\) | ||||
0.579473 | + | 0.814992i | \(0.303259\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.29680 | 1.32811 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.36451 | 0.891210 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.76403 | 1.20383 | 0.601916 | − | 0.798559i | \(-0.294404\pi\) | ||||
0.601916 | + | 0.798559i | \(0.294404\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.43902 | −1.00308 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.92928 | 1.18271 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.0472 | 1.30803 | 0.654016 | − | 0.756480i | \(-0.273083\pi\) | ||||
0.654016 | + | 0.756480i | \(0.273083\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8260 | 1.38613 | 0.693064 | − | 0.720876i | \(-0.256260\pi\) | ||||
0.693064 | + | 0.720876i | \(0.256260\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.74142 | −0.471374 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.79630 | 0.718943 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.290722 | 0.0355174 | 0.0177587 | − | 0.999842i | \(-0.494347\pi\) | ||||
0.0177587 | + | 0.999842i | \(0.494347\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.09854 | −0.734178 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.2769 | −1.21964 | −0.609821 | − | 0.792540i | \(-0.708758\pi\) | ||||
−0.609821 | + | 0.792540i | \(0.708758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.17032 | 0.839222 | 0.419611 | − | 0.907704i | \(-0.362166\pi\) | ||||
0.419611 | + | 0.907704i | \(0.362166\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −18.0351 | −2.08251 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.99721 | −0.911367 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0803 | −1.13412 | −0.567059 | − | 0.823677i | \(-0.691919\pi\) | ||||
−0.567059 | + | 0.823677i | \(0.691919\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.9214 | −1.21349 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.1250 | −1.44065 | −0.720326 | − | 0.693636i | \(-0.756008\pi\) | ||||
−0.720326 | + | 0.693636i | \(0.756008\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0607 | 1.30817 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.2894 | 1.63920 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.9426 | 1.26591 | 0.632957 | − | 0.774187i | \(-0.281841\pi\) | ||||
0.632957 | + | 0.774187i | \(0.281841\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.23124 | 0.653211 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.0945 | −1.25414 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.9210 | 1.73605 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.1591 | 1.74224 | 0.871121 | − | 0.491068i | \(-0.163393\pi\) | ||||
0.871121 | + | 0.491068i | \(0.163393\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.83600 | 0.184525 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.0930 | −1.50181 | −0.750906 | − | 0.660409i | \(-0.770383\pi\) | ||||
−0.750906 | + | 0.660409i | \(0.770383\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.9503 | 1.86723 | 0.933613 | − | 0.358284i | \(-0.116638\pi\) | ||||
0.933613 | + | 0.358284i | \(0.116638\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −30.0399 | −2.93159 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.820531 | 0.0793237 | 0.0396619 | − | 0.999213i | \(-0.487372\pi\) | ||||
0.0396619 | + | 0.999213i | \(0.487372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.4642 | 1.00229 | 0.501144 | − | 0.865364i | \(-0.332913\pi\) | ||||
0.501144 | + | 0.865364i | \(0.332913\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.9522 | 1.60903 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.3388 | 0.972595 | 0.486298 | − | 0.873793i | \(-0.338347\pi\) | ||||
0.486298 | + | 0.873793i | \(0.338347\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.5567 | −1.07767 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.43057 | −0.132256 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.9657 | 1.18857 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.07559 | −0.643235 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.01626 | −0.0916331 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15.4007 | −1.37748 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.30930 | −0.471124 | −0.235562 | − | 0.971859i | \(-0.575693\pi\) | ||||
−0.235562 | + | 0.971859i | \(0.575693\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.0147127 | −0.00129538 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.8227 | −1.03295 | −0.516475 | − | 0.856302i | \(-0.672756\pi\) | ||||
−0.516475 | + | 0.856302i | \(0.672756\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.1907 | 1.57733 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.4273 | −1.32777 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.19520 | 0.529292 | 0.264646 | − | 0.964346i | \(-0.414745\pi\) | ||||
0.264646 | + | 0.964346i | \(0.414745\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.8819 | 1.94081 | 0.970407 | − | 0.241475i | \(-0.0776313\pi\) | ||||
0.970407 | + | 0.241475i | \(0.0776313\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.7446 | −1.32593 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.05781 | −0.255707 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 28.9734 | 2.40611 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −18.4227 | −1.51948 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.5624 | −1.76646 | −0.883229 | − | 0.468942i | \(-0.844635\pi\) | ||||
−0.883229 | + | 0.468942i | \(0.844635\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.6841 | −1.92738 | −0.963691 | − | 0.267022i | \(-0.913960\pi\) | ||||
−0.963691 | + | 0.267022i | \(0.913960\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.97667 | −0.240649 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.9190 | −1.84090 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.11544 | 0.328448 | 0.164224 | − | 0.986423i | \(-0.447488\pi\) | ||||
0.164224 | + | 0.986423i | \(0.447488\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −17.3669 | −1.37729 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.4239 | −0.979140 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.19809 | 0.642124 | 0.321062 | − | 0.947058i | \(-0.395960\pi\) | ||||
0.321062 | + | 0.947058i | \(0.395960\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 14.7413 | 1.14761 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.1489 | −1.01749 | −0.508745 | − | 0.860917i | \(-0.669890\pi\) | ||||
−0.508745 | + | 0.860917i | \(0.669890\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.6174 | −0.816725 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.17621 | −0.319362 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.8651 | 1.35826 | 0.679128 | − | 0.734020i | \(-0.262358\pi\) | ||||
0.679128 | + | 0.734020i | \(0.262358\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −36.7409 | −2.77735 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.9097 | −1.49650 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.0452376 | 0.00338122 | 0.00169061 | − | 0.999999i | \(-0.499462\pi\) | ||||
0.00169061 | + | 0.999999i | \(0.499462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.4560 | −1.29750 | −0.648749 | − | 0.761003i | \(-0.724707\pi\) | ||||
−0.648749 | + | 0.761003i | \(0.724707\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.4530 | −1.58585 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 32.1245 | 2.36184 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.36258 | −0.465278 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −16.5849 | −1.20637 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.77631 | −0.490316 | −0.245158 | − | 0.969483i | \(-0.578840\pi\) | ||||
−0.245158 | + | 0.969483i | \(0.578840\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.1719 | 1.45200 | 0.726002 | − | 0.687693i | \(-0.241376\pi\) | ||||
0.726002 | + | 0.687693i | \(0.241376\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.4860 | −0.822532 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.0795 | 1.00312 | 0.501561 | − | 0.865122i | \(-0.332759\pi\) | ||||
0.501561 | + | 0.865122i | \(0.332759\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.8299 | −1.90192 | −0.950959 | − | 0.309317i | \(-0.899900\pi\) | ||||
−0.950959 | + | 0.309317i | \(0.899900\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.576099 | −0.0406349 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 31.1475 | 2.18613 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.92581 | −0.134504 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.85227 | 0.198247 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.92657 | −0.617464 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.2087 | −1.66659 | −0.833296 | − | 0.552827i | \(-0.813549\pi\) | ||||
−0.833296 | + | 0.552827i | \(0.813549\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.3648 | 1.39537 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.0278806 | −0.00190144 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.6387 | −1.67259 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.2088 | −0.960142 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.95757 | 0.333482 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.2940 | −1.35899 | −0.679495 | − | 0.733680i | \(-0.737801\pi\) | ||||
−0.679495 | + | 0.733680i | \(0.737801\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.43497 | 0.562332 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.65300 | −0.308831 | −0.154415 | − | 0.988006i | \(-0.549349\pi\) | ||||
−0.154415 | + | 0.988006i | \(0.549349\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.4665 | 1.08814 | 0.544069 | − | 0.839041i | \(-0.316883\pi\) | ||||
0.544069 | + | 0.839041i | \(0.316883\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.8474 | 1.04268 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.9380 | 1.69925 | 0.849627 | − | 0.527383i | \(-0.176827\pi\) | ||||
0.849627 | + | 0.527383i | \(0.176827\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.8360 | −1.94628 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.9752 | 1.29753 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.1687 | 1.69271 | 0.846356 | − | 0.532617i | \(-0.178791\pi\) | ||||
0.846356 | + | 0.532617i | \(0.178791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.5894 | −1.00420 | −0.502100 | − | 0.864810i | \(-0.667439\pi\) | ||||
−0.502100 | + | 0.864810i | \(0.667439\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.31722 | 0.597700 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −34.9110 | −2.23038 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.95537 | 0.442559 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 26.0086 | 1.64823 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.73428 | −0.172586 | −0.0862930 | − | 0.996270i | \(-0.527502\pi\) | ||||
−0.0862930 | + | 0.996270i | \(0.527502\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.09669 | 0.383295 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −23.8997 | −1.49666 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.326482 | 0.0203654 | 0.0101827 | − | 0.999948i | \(-0.496759\pi\) | ||||
0.0101827 | + | 0.999948i | \(0.496759\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 34.5350 | 2.14590 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.15083 | −0.442626 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.7711 | 0.664173 | 0.332087 | − | 0.943249i | \(-0.392247\pi\) | ||||
0.332087 | + | 0.943249i | \(0.392247\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −32.9103 | −2.02166 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23.6656 | −1.44831 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.7801 | −1.26699 | −0.633493 | − | 0.773748i | \(-0.718380\pi\) | ||||
−0.633493 | + | 0.773748i | \(0.718380\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.97548 | −0.484476 | −0.242238 | − | 0.970217i | \(-0.577881\pi\) | ||||
−0.242238 | + | 0.970217i | \(0.577881\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.3479 | −0.747329 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.0296 | 1.08723 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.5965 | 1.71820 | 0.859099 | − | 0.511810i | \(-0.171025\pi\) | ||||
0.859099 | + | 0.511810i | \(0.171025\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.65655 | 0.338649 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.04543 | −0.0623651 | −0.0311826 | − | 0.999514i | \(-0.509927\pi\) | ||||
−0.0311826 | + | 0.999514i | \(0.509927\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.591169 | −0.0351413 | −0.0175707 | − | 0.999846i | \(-0.505593\pi\) | ||||
−0.0175707 | + | 0.999846i | \(0.505593\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −33.5308 | −1.98620 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.07032 | −0.122207 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.68447 | −0.393204 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −34.0027 | −1.99328 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.956681 | −0.0558899 | −0.0279449 | − | 0.999609i | \(-0.508896\pi\) | ||||
−0.0279449 | + | 0.999609i | \(0.508896\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −37.7288 | −2.19665 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.13857 | 0.472248 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.75039 | −0.274722 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0299726 | −0.00172759 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 29.9086 | 1.71820 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −40.6534 | −2.32781 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.7592 | −0.899423 | −0.449711 | − | 0.893174i | \(-0.648473\pi\) | ||||
−0.449711 | + | 0.893174i | \(0.648473\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −37.5521 | −2.13627 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.4808 | 1.16136 | 0.580679 | − | 0.814133i | \(-0.302787\pi\) | ||||
0.580679 | + | 0.814133i | \(0.302787\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.57876 | −0.145760 | −0.0728802 | − | 0.997341i | \(-0.523219\pi\) | ||||
−0.0728802 | + | 0.997341i | \(0.523219\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.0496 | 0.791606 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.6486 | −0.878911 | −0.439455 | − | 0.898264i | \(-0.644829\pi\) | ||||
−0.439455 | + | 0.898264i | \(0.644829\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.2848 | −0.855784 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.62598 | −0.0907532 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.4725 | 0.805270 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.0482 | −0.779256 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.7360 | −1.14670 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −32.0747 | −1.76834 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.07476 | 0.278934 | 0.139467 | − | 0.990227i | \(-0.455461\pi\) | ||||
0.139467 | + | 0.990227i | \(0.455461\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.92853 | −0.434481 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.09171 | −0.0596463 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.2593 | −1.86622 | −0.933111 | − | 0.359590i | \(-0.882917\pi\) | ||||
−0.933111 | + | 0.359590i | \(0.882917\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.4876 | −1.11273 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.0908 | 0.654752 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.27203 | −0.500643 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 22.9010 | 1.23295 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.4058 | −1.47122 | −0.735610 | − | 0.677405i | \(-0.763104\pi\) | ||||
−0.735610 | + | 0.677405i | \(0.763104\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.1293 | −1.66632 | −0.833158 | − | 0.553035i | \(-0.813469\pi\) | ||||
−0.833158 | + | 0.553035i | \(0.813469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.34138 | −0.338478 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.376805 | 0.0200553 | 0.0100277 | − | 0.999950i | \(-0.496808\pi\) | ||||
0.0100277 | + | 0.999950i | \(0.496808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 38.5913 | 2.04821 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −25.6931 | −1.35982 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.54113 | 0.450784 | 0.225392 | − | 0.974268i | \(-0.427634\pi\) | ||||
0.225392 | + | 0.974268i | \(0.427634\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.30459 | 0.0686626 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.0211 | 0.735916 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.9257 | −1.40935 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.5264 | 1.64566 | 0.822832 | − | 0.568285i | \(-0.192393\pi\) | ||||
0.822832 | + | 0.568285i | \(0.192393\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.475303 | 0.0247433 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35.3798 | −1.83683 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.8971 | −0.667786 | −0.333893 | − | 0.942611i | \(-0.608362\pi\) | ||||
−0.333893 | + | 0.942611i | \(0.608362\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 30.5182 | 1.57595 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.9095 | 0.613372 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.3680 | 0.738034 | 0.369017 | − | 0.929423i | \(-0.379694\pi\) | ||||
0.369017 | + | 0.929423i | \(0.379694\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.5210 | 0.539007 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.19620 | −0.316611 | −0.158306 | − | 0.987390i | \(-0.550603\pi\) | ||||
−0.158306 | + | 0.987390i | \(0.550603\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 30.0308 | 1.53051 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.00688111 | 0.000349786 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.2489 | 0.519642 | 0.259821 | − | 0.965657i | \(-0.416337\pi\) | ||||
0.259821 | + | 0.965657i | \(0.416337\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.88445 | −0.499878 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.4280 | 1.18178 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 37.8530 | 1.90459 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.9947 | 1.00351 | 0.501754 | − | 0.865011i | \(-0.332688\pi\) | ||||
0.501754 | + | 0.865011i | \(0.332688\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −36.0469 | −1.80460 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.93525 | 0.396267 | 0.198134 | − | 0.980175i | \(-0.436512\pi\) | ||||
0.198134 | + | 0.980175i | \(0.436512\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.42085 | −0.469286 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 41.0117 | 2.03789 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.9471 | −0.840036 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.8734 | 1.13102 | 0.565508 | − | 0.824743i | \(-0.308680\pi\) | ||||
0.565508 | + | 0.824743i | \(0.308680\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.2765 | −0.605555 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −40.5598 | −1.99582 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 49.2863 | 2.41937 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −45.3430 | −2.22046 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 40.1560 | 1.96175 | 0.980875 | − | 0.194637i | \(-0.0623527\pi\) | ||||
0.980875 | + | 0.194637i | \(0.0623527\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.8384 | 1.79540 | 0.897698 | − | 0.440612i | \(-0.145239\pi\) | ||||
0.897698 | + | 0.440612i | \(0.145239\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.36371 | 0.358036 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −29.2311 | −1.41792 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −43.7038 | −2.11498 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.05940 | 0.292551 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.7592 | 0.999937 | 0.499969 | − | 0.866044i | \(-0.333345\pi\) | ||||
0.499969 | + | 0.866044i | \(0.333345\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.900824 | −0.0432908 | −0.0216454 | − | 0.999766i | \(-0.506890\pi\) | ||||
−0.0216454 | + | 0.999766i | \(0.506890\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −57.4142 | −2.75280 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.8677 | −0.663381 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.4142 | −0.497041 | −0.248521 | − | 0.968627i | \(-0.579944\pi\) | ||||
−0.248521 | + | 0.968627i | \(0.579944\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.61625 | 0.410298 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.20294 | 0.199688 | 0.0998438 | − | 0.995003i | \(-0.468166\pi\) | ||||
0.0998438 | + | 0.995003i | \(0.468166\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −44.8464 | −2.12592 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 42.7283 | 2.02098 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.7299 | 1.59181 | 0.795906 | − | 0.605420i | \(-0.206995\pi\) | ||||
0.795906 | + | 0.605420i | \(0.206995\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.01595 | 0.0478393 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 46.9327 | 2.20509 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −23.3993 | −1.09697 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.79665 | −0.317934 | −0.158967 | − | 0.987284i | \(-0.550816\pi\) | ||||
−0.158967 | + | 0.987284i | \(0.550816\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.1949 | −0.615886 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.69822 | 0.0790939 | 0.0395470 | − | 0.999218i | \(-0.487409\pi\) | ||||
0.0395470 | + | 0.999218i | \(0.487409\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.7065 | 0.590519 | 0.295259 | − | 0.955417i | \(-0.404594\pi\) | ||||
0.295259 | + | 0.955417i | \(0.404594\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 45.4166 | 2.10614 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.5427 | −0.858056 | −0.429028 | − | 0.903291i | \(-0.641144\pi\) | ||||
−0.429028 | + | 0.903291i | \(0.641144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.17362 | −0.0541930 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.15521 | −0.375772 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.0147082 | 0.000676286 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −41.0106 | −1.88170 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.12248 | 0.371903 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.7299 | 0.581643 | 0.290822 | − | 0.956777i | \(-0.406071\pi\) | ||||
0.290822 | + | 0.956777i | \(0.406071\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.2048 | 0.602085 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.6194 | 1.12022 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −64.4351 | −2.92585 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.7859 | −1.21378 | −0.606891 | − | 0.794785i | \(-0.707584\pi\) | ||||
−0.606891 | + | 0.794785i | \(0.707584\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.2455 | −0.734645 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.8966 | −1.34921 | −0.674607 | − | 0.738177i | \(-0.735687\pi\) | ||||
−0.674607 | + | 0.738177i | \(0.735687\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.7809 | 1.11608 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.89446 | −0.309883 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 41.4870 | 1.86095 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.1329 | −0.766973 | −0.383487 | − | 0.923546i | \(-0.625277\pi\) | ||||
−0.383487 | + | 0.923546i | \(0.625277\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26.0560 | 1.16410 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.3119 | 1.44072 | 0.720358 | − | 0.693603i | \(-0.243978\pi\) | ||||
0.720358 | + | 0.693603i | \(0.243978\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 56.6767 | 2.52208 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.0397 | 0.934404 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.6430 | 0.959308 | 0.479654 | − | 0.877458i | \(-0.340762\pi\) | ||||
0.479654 | + | 0.877458i | \(0.340762\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.9461 | −1.28050 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.5122 | −0.817334 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −71.1612 | −3.13574 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.7398 | 0.692236 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −35.4017 | −1.55396 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.7723 | 0.515754 | 0.257877 | − | 0.966178i | \(-0.416977\pi\) | ||||
0.257877 | + | 0.966178i | \(0.416977\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.2208 | −1.32146 | −0.660732 | − | 0.750622i | \(-0.729754\pi\) | ||||
−0.660732 | + | 0.750622i | \(0.729754\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 72.8064 | 3.17753 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.6026 | −0.853901 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.5286 | −0.588201 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.31171 | 0.404094 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.791605 | −0.0342882 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.08122 | −0.133213 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.0896434 | −0.00386840 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.4171 | 0.793280 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.78626 | −0.248771 | −0.124385 | − | 0.992234i | \(-0.539696\pi\) | ||||
−0.124385 | + | 0.992234i | \(0.539696\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 34.5911 | 1.48445 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −39.2947 | −1.68320 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.9157 | 1.66392 | 0.831958 | − | 0.554839i | \(-0.187220\pi\) | ||||
0.831958 | + | 0.554839i | \(0.187220\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.0335 | 0.428220 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.7671 | 1.48113 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 40.6933 | 1.73046 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −63.6583 | −2.70214 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.80599 | −0.373122 | −0.186561 | − | 0.982443i | \(-0.559734\pi\) | ||||
−0.186561 | + | 0.982443i | \(0.559734\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.0114603 | −0.000484720 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.6082 | 0.532318 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.5774 | 0.867236 | 0.433618 | − | 0.901097i | \(-0.357237\pi\) | ||||
0.433618 | + | 0.901097i | \(0.357237\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38.8239 | −1.63333 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 44.0891 | 1.85157 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.7000 | 0.490489 | 0.245244 | − | 0.969461i | \(-0.421132\pi\) | ||||
0.245244 | + | 0.969461i | \(0.421132\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.8079 | −1.54036 | −0.770181 | − | 0.637825i | \(-0.779834\pi\) | ||||
−0.770181 | + | 0.637825i | \(0.779834\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.4280 | 0.560964 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.0095 | 1.16808 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.86103 | 0.160737 | 0.0803683 | − | 0.996765i | \(-0.474390\pi\) | ||||
0.0803683 | + | 0.996765i | \(0.474390\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −39.9729 | −1.66122 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 52.9845 | 2.19817 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.3617 | 0.719047 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.37200 | 0.222105 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.6309 | 0.686429 | 0.343215 | − | 0.939257i | \(-0.388484\pi\) | ||||
0.343215 | + | 0.939257i | \(0.388484\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.5020 | −1.13320 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.9001 | −1.14766 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.2687 | 1.24299 | 0.621493 | − | 0.783420i | \(-0.286527\pi\) | ||||
0.621493 | + | 0.783420i | \(0.286527\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −48.6884 | −1.99603 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 53.1664 | 2.17596 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.8264 | 0.932662 | 0.466331 | − | 0.884610i | \(-0.345576\pi\) | ||||
0.466331 | + | 0.884610i | \(0.345576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.2656 | 1.76484 | 0.882421 | − | 0.470461i | \(-0.155913\pi\) | ||||
0.882421 | + | 0.470461i | \(0.155913\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.269440 | 0.0109725 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 26.5699 | 1.08022 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 45.5044 | 1.84697 | 0.923484 | − | 0.383638i | \(-0.125329\pi\) | ||||
0.923484 | + | 0.383638i | \(0.125329\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −61.7223 | −2.50112 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.2641 | −0.496151 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.8696 | −0.802525 | −0.401263 | − | 0.915963i | \(-0.631428\pi\) | ||||
−0.401263 | + | 0.915963i | \(0.631428\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.81622 | 0.153885 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.6405 | −0.911472 | −0.455736 | − | 0.890115i | \(-0.650624\pi\) | ||||
−0.455736 | + | 0.890115i | \(0.650624\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.04376 | 0.363499 | 0.181750 | − | 0.983345i | \(-0.441824\pi\) | ||||
0.181750 | + | 0.983345i | \(0.441824\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.6435 | 0.507366 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −48.2115 | −1.93155 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.3259 | 0.493037 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.6890 | 0.706431 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.4760 | 1.09554 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.2681 | −1.12534 | −0.562668 | − | 0.826683i | \(-0.690225\pi\) | ||||
−0.562668 | + | 0.826683i | \(0.690225\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 47.9722 | 1.90673 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.9373 | 0.791186 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.3502 | −0.568574 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.52458 | −0.376787 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.94615 | 0.116366 | 0.0581830 | − | 0.998306i | \(-0.481469\pi\) | ||||
0.0581830 | + | 0.998306i | \(0.481469\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.6487 | −1.05092 | −0.525461 | − | 0.850818i | \(-0.676107\pi\) | ||||
−0.525461 | + | 0.850818i | \(0.676107\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.0552486 | 0.00217541 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.0182 | −0.865624 | −0.432812 | − | 0.901484i | \(-0.642479\pi\) | ||||
−0.432812 | + | 0.901484i | \(0.642479\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.9036 | 0.781285 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 48.8245 | 1.91358 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.7833 | −0.735049 | −0.367524 | − | 0.930014i | \(-0.619795\pi\) | ||||
−0.367524 | + | 0.930014i | \(0.619795\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 44.3960 | 1.73469 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.64543 | 0.259263 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.5192 | 0.409770 | 0.204885 | − | 0.978786i | \(-0.434318\pi\) | ||||
0.204885 | + | 0.978786i | \(0.434318\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.9363 | −1.28107 | −0.640536 | − | 0.767928i | \(-0.721288\pi\) | ||||
−0.640536 | + | 0.767928i | \(0.721288\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.82399 | −0.381532 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −68.3088 | −2.64890 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.7453 | −0.919423 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 40.2150 | 1.55480 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.4465 | 0.827932 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.8990 | 0.882692 | 0.441346 | − | 0.897337i | \(-0.354501\pi\) | ||||
0.441346 | + | 0.897337i | \(0.354501\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 37.3904 | 1.43916 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.1741 | 1.50558 | 0.752791 | − | 0.658259i | \(-0.228707\pi\) | ||||
0.752791 | + | 0.658259i | \(0.228707\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −69.2701 | −2.65834 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.22046 | 0.353329 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.0617 | −1.26507 | −0.632536 | − | 0.774531i | \(-0.717986\pi\) | ||||
−0.632536 | + | 0.774531i | \(0.717986\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.2640 | −0.888870 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −32.6303 | −1.24492 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.5278 | −0.515368 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.6344 | 0.480634 | 0.240317 | − | 0.970695i | \(-0.422749\pi\) | ||||
0.240317 | + | 0.970695i | \(0.422749\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.41179 | −0.281551 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −85.9250 | −3.25932 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.64714 | −0.0623900 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −51.3991 | −1.94409 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.1698 | −1.59273 | −0.796365 | − | 0.604816i | \(-0.793246\pi\) | ||||
−0.796365 | + | 0.604816i | \(0.793246\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.5483 | 1.45388 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 59.1234 | 2.22672 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 60.9295 | 2.29149 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.3281 | 0.650770 | 0.325385 | − | 0.945582i | \(-0.394506\pi\) | ||||
0.325385 | + | 0.945582i | \(0.394506\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.34236 | −0.350366 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.7834 | 0.703443 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.4826 | 0.429423 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −51.8563 | −1.93661 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.0531 | 0.785146 | 0.392573 | − | 0.919721i | \(-0.371585\pi\) | ||||
0.392573 | + | 0.919721i | \(0.371585\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −76.5009 | −2.84904 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.8921 | 1.14889 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −70.2216 | −2.60797 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −46.4416 | −1.72242 | −0.861211 | − | 0.508247i | \(-0.830294\pi\) | ||||
−0.861211 | + | 0.508247i | \(0.830294\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.3012 | 0.529673 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.0238462 | −0.000881984 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.1293 | −0.411068 | −0.205534 | − | 0.978650i | \(-0.565893\pi\) | ||||
−0.205534 | + | 0.978650i | \(0.565893\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 69.1801 | 2.55175 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.575924 | 0.0212144 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.8979 | 0.695171 | 0.347585 | − | 0.937648i | \(-0.387002\pi\) | ||||
0.347585 | + | 0.937648i | \(0.387002\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.7829 | −0.506326 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.7542 | −0.761397 | −0.380699 | − | 0.924699i | \(-0.624317\pi\) | ||||
−0.380699 | + | 0.924699i | \(0.624317\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 80.9701 | 2.96651 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.1642 | −0.445064 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.31243 | −0.121033 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.9709 | −1.05716 | −0.528582 | − | 0.848882i | \(-0.677276\pi\) | ||||
−0.528582 | + | 0.848882i | \(0.677276\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.41829 | 0.197453 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 88.9374 | 3.23676 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.0656 | −0.656605 | −0.328302 | − | 0.944573i | \(-0.606477\pi\) | ||||
−0.328302 | + | 0.944573i | \(0.606477\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.0813 | −0.438523 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.06197 | −0.292246 | −0.146123 | − | 0.989266i | \(-0.546680\pi\) | ||||
−0.146123 | + | 0.989266i | \(0.546680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42.2432 | −1.52931 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.1779 | 0.404136 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.5084 | −0.559977 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 54.0895 | 1.95052 | 0.975259 | − | 0.221067i | \(-0.0709538\pi\) | ||||
0.975259 | + | 0.221067i | \(0.0709538\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.646961 | −0.0232997 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.44412 | 0.195811 | 0.0979057 | − | 0.995196i | \(-0.468786\pi\) | ||||
0.0979057 | + | 0.995196i | \(0.468786\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 55.5477 | 1.99533 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −68.4350 | −2.45509 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.31091 | −0.0827969 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.3586 | −0.728489 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −31.6981 | −1.13280 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.4541 | −0.551581 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.3518 | −0.903695 | −0.451848 | − | 0.892095i | \(-0.649235\pi\) | ||||
−0.451848 | + | 0.892095i | \(0.649235\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.3441 | −0.759871 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −41.7371 | −1.48400 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.7106 | −0.593410 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 65.2156 | 2.31296 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.06807 | 0.144098 | 0.0720492 | − | 0.997401i | \(-0.477046\pi\) | ||||
0.0720492 | + | 0.997401i | \(0.477046\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.5186 | −0.902785 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.0684 | 0.391082 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.2045 | 0.501266 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 46.6537 | 1.64433 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 41.1782 | 1.44954 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.1759 | 1.55314 | 0.776571 | − | 0.630030i | \(-0.216958\pi\) | ||||
0.776571 | + | 0.630030i | \(0.216958\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.0741 | −0.669781 | −0.334890 | − | 0.942257i | \(-0.608699\pi\) | ||||
−0.334890 | + | 0.942257i | \(0.608699\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.8043 | 0.554282 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.7851 | −1.07836 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.0334557 | −0.00117047 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.77509 | 0.201798 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.6173 | 0.370547 | 0.185274 | − | 0.982687i | \(-0.440683\pi\) | ||||
0.185274 | + | 0.982687i | \(0.440683\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.1191 | −0.457302 | −0.228651 | − | 0.973509i | \(-0.573431\pi\) | ||||
−0.228651 | + | 0.973509i | \(0.573431\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −35.7277 | −1.24388 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.8082 | 0.827891 | 0.413945 | − | 0.910302i | \(-0.364150\pi\) | ||||
0.413945 | + | 0.910302i | \(0.364150\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.6548 | 0.613177 | 0.306588 | − | 0.951842i | \(-0.400813\pi\) | ||||
0.306588 | + | 0.951842i | \(0.400813\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −56.6672 | −1.96576 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29.8593 | −1.03456 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.3761 | 1.70873 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25.0742 | 0.866693 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.2252 | −1.00897 | −0.504484 | − | 0.863421i | \(-0.668317\pi\) | ||||
−0.504484 | + | 0.863421i | \(0.668317\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.5311 | 1.05280 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.07164 | 0.0713511 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 39.8701 | 1.37157 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.5636 | 0.981459 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.17147 | 0.0402047 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.3278 | −0.902505 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36.4350 | −1.24751 | −0.623756 | − | 0.781619i | \(-0.714394\pi\) | ||||
−0.623756 | + | 0.781619i | \(0.714394\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.6823 | 0.536324 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.8969 | −0.406390 | −0.203195 | − | 0.979138i | \(-0.565132\pi\) | ||||
−0.203195 | + | 0.979138i | \(0.565132\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.47013 | −0.0501601 | −0.0250800 | − | 0.999685i | \(-0.507984\pi\) | ||||
−0.0250800 | + | 0.999685i | \(0.507984\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.10257 | 0.139815 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.68482 | 0.329675 | 0.164838 | − | 0.986321i | \(-0.447290\pi\) | ||||
0.164838 | + | 0.986321i | \(0.447290\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −67.0861 | −2.28100 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.2460 | 0.449859 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.9691 | −0.677406 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.448746 | −0.0152052 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.9030 | 0.538235 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 62.1714 | 2.10178 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.0596 | 1.38648 | 0.693242 | − | 0.720705i | \(-0.256182\pi\) | ||||
0.693242 | + | 0.720705i | \(0.256182\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.89577 | 0.0639428 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.4068 | 0.485379 | 0.242689 | − | 0.970104i | \(-0.421970\pi\) | ||||
0.242689 | + | 0.970104i | \(0.421970\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.1639 | −0.644916 | −0.322458 | − | 0.946584i | \(-0.604509\pi\) | ||||
−0.322458 | + | 0.946584i | \(0.604509\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 74.7639 | 2.51316 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.0994 | −0.406258 | −0.203129 | − | 0.979152i | \(-0.565111\pi\) | ||||
−0.203129 | + | 0.979152i | \(0.565111\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.4333 | 0.718849 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.6355 | −0.724817 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −35.8021 | −1.19807 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.169874 | −0.00567827 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.41345 | 0.314306 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −47.0911 | −1.57058 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.1481 | −0.937751 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.0593942 | 0.00197651 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 65.5502 | 2.17896 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.7405 | 0.921109 | 0.460555 | − | 0.887631i | \(-0.347651\pi\) | ||||
0.460555 | + | 0.887631i | \(0.347651\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.9882 | −0.463959 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.4823 | −0.711741 | −0.355870 | − | 0.934535i | \(-0.615816\pi\) | ||||
−0.355870 | + | 0.934535i | \(0.615816\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.0007 | −0.860498 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 80.5593 | 2.66321 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 47.7273 | 1.57609 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.5645 | −1.27213 | −0.636063 | − | 0.771637i | \(-0.719438\pi\) | ||||
−0.636063 | + | 0.771637i | \(0.719438\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.2286 | 1.02902 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.8630 | 0.522136 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −77.8586 | −2.55998 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.5631 | 0.576846 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.84049 | −0.126003 | −0.0630013 | − | 0.998013i | \(-0.520067\pi\) | ||||
−0.0630013 | + | 0.998013i | \(0.520067\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.8920 | −1.37295 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −40.5850 | −1.32869 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23.8925 | 0.781368 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.95905 | 0.227342 | 0.113671 | − | 0.993518i | \(-0.463739\pi\) | ||||
0.113671 | + | 0.993518i | \(0.463739\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.11012 | 0.166762 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.5955 | −1.06258 | −0.531292 | − | 0.847189i | \(-0.678293\pi\) | ||||
−0.531292 | + | 0.847189i | \(0.678293\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.57831 | 0.0513968 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 62.2788 | 2.02593 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −38.6901 | −1.25726 | −0.628630 | − | 0.777705i | \(-0.716384\pi\) | ||||
−0.628630 | + | 0.777705i | \(0.716384\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.0678 | −0.359276 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.0094 | 1.00555 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.1166 | 0.457280 | 0.228640 | − | 0.973511i | \(-0.426572\pi\) | ||||
0.228640 | + | 0.973511i | \(0.426572\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.4461 | 0.823417 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 30.2886 | 0.979090 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.0096 | −0.807602 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.25065 | 0.201634 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.760466 | 0.0245057 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −75.7486 | −2.43843 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.35611 | 0.0436095 | 0.0218047 | − | 0.999762i | \(-0.493059\pi\) | ||||
0.0218047 | + | 0.999762i | \(0.493059\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.6789 | −0.921298 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.3188 | 1.58271 | 0.791357 | − | 0.611354i | \(-0.209375\pi\) | ||||
0.791357 | + | 0.611354i | \(0.209375\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −92.3725 | −2.96132 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27.8382 | 0.891536 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.1966 | −0.518175 | −0.259088 | − | 0.965854i | \(-0.583422\pi\) | ||||
−0.259088 | + | 0.965854i | \(0.583422\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.6585 | 0.756128 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.69819 | 0.309639 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.6120 | 0.689316 | 0.344658 | − | 0.938728i | \(-0.387995\pi\) | ||||
0.344658 | + | 0.938728i | \(0.387995\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.8707 | −1.68460 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 63.5598 | 2.02313 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.0228497 | 0.000726578 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.2359 | −0.388688 | −0.194344 | − | 0.980933i | \(-0.562258\pi\) | ||||
−0.194344 | + | 0.980933i | \(0.562258\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.0562 | −0.319124 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 100.750 | 3.19400 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.1225 | −1.30236 | −0.651182 | − | 0.758922i | \(-0.725726\pi\) | ||||
−0.651182 | + | 0.758922i | \(0.725726\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −35.1454 | −1.11195 |
(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 | 6044.2.a.a.1.14 | ✓ | 63 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6044.2.a.a.1.14 | ✓ | 63 | 1.1 | even | 1 | trivial |