Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | −2.15961 | −1.24685 | −0.623426 | − | 0.781882i | \(-0.714260\pi\) | ||||
−0.623426 | + | 0.781882i | \(0.714260\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.185718 | 0.0830554 | 0.0415277 | − | 0.999137i | \(-0.486778\pi\) | ||||
0.0415277 | + | 0.999137i | \(0.486778\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00693 | 1.13651 | 0.568257 | − | 0.822851i | \(-0.307618\pi\) | ||||
0.568257 | + | 0.822851i | \(0.307618\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.66392 | 0.554641 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.123870 | 0.0373483 | 0.0186741 | − | 0.999826i | \(-0.494055\pi\) | ||||
0.0186741 | + | 0.999826i | \(0.494055\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.56775 | 0.434816 | 0.217408 | − | 0.976081i | \(-0.430240\pi\) | ||||
0.217408 | + | 0.976081i | \(0.430240\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.401078 | −0.103558 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.758557 | 0.183977 | 0.0919885 | − | 0.995760i | \(-0.470678\pi\) | ||||
0.0919885 | + | 0.995760i | \(0.470678\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.18817 | −0.731417 | −0.365708 | − | 0.930730i | \(-0.619173\pi\) | ||||
−0.365708 | + | 0.930730i | \(0.619173\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.49381 | −1.41707 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.97273 | −0.619858 | −0.309929 | − | 0.950760i | \(-0.600305\pi\) | ||||
−0.309929 | + | 0.950760i | \(0.600305\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96551 | −0.993102 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.88541 | 0.555297 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.26058 | 0.605475 | 0.302737 | − | 0.953074i | \(-0.402099\pi\) | ||||
0.302737 | + | 0.953074i | \(0.402099\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.87406 | 1.05501 | 0.527506 | − | 0.849551i | \(-0.323127\pi\) | ||||
0.527506 | + | 0.849551i | \(0.323127\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.267511 | −0.0465678 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.558440 | 0.0943937 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.61053 | −1.57996 | −0.789981 | − | 0.613132i | \(-0.789909\pi\) | ||||
−0.789981 | + | 0.613132i | \(0.789909\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.38573 | −0.542151 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.98093 | 0.934065 | 0.467032 | − | 0.884240i | \(-0.345323\pi\) | ||||
0.467032 | + | 0.884240i | \(0.345323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.323388 | −0.0493162 | −0.0246581 | − | 0.999696i | \(-0.507850\pi\) | ||||
−0.0246581 | + | 0.999696i | \(0.507850\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.309020 | 0.0460660 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.79465 | −1.13697 | −0.568483 | − | 0.822695i | \(-0.692470\pi\) | ||||
−0.568483 | + | 0.822695i | \(0.692470\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.04165 | 0.291664 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.63819 | −0.229392 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.4601 | −1.84889 | −0.924445 | − | 0.381316i | \(-0.875471\pi\) | ||||
−0.924445 | + | 0.381316i | \(0.875471\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0230049 | 0.00310198 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.88521 | 0.911969 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.94483 | 0.253196 | 0.126598 | − | 0.991954i | \(-0.459594\pi\) | ||||
0.126598 | + | 0.991954i | \(0.459594\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.9913 | −1.66337 | −0.831684 | − | 0.555250i | \(-0.812623\pi\) | ||||
−0.831684 | + | 0.555250i | \(0.812623\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.00331 | 0.630357 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.291159 | 0.0361138 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.01188 | 0.978807 | 0.489404 | − | 0.872057i | \(-0.337215\pi\) | ||||
0.489404 | + | 0.872057i | \(0.337215\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.41995 | 0.772872 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.36443 | −0.280606 | −0.140303 | − | 0.990109i | \(-0.544808\pi\) | ||||
−0.140303 | + | 0.990109i | \(0.544808\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.457187 | 0.0535096 | 0.0267548 | − | 0.999642i | \(-0.491483\pi\) | ||||
0.0267548 | + | 0.999642i | \(0.491483\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.7236 | 1.23825 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.372469 | 0.0424468 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.18145 | −0.245433 | −0.122716 | − | 0.992442i | \(-0.539161\pi\) | ||||
−0.122716 | + | 0.992442i | \(0.539161\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2231 | −1.24701 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.917360 | 0.100693 | 0.0503466 | − | 0.998732i | \(-0.483967\pi\) | ||||
0.0503466 | + | 0.998732i | \(0.483967\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.140877 | 0.0152803 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.04159 | −0.754938 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.20797 | 0.870043 | 0.435022 | − | 0.900420i | \(-0.356741\pi\) | ||||
0.435022 | + | 0.900420i | \(0.356741\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.71412 | 0.494174 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.6857 | −1.31544 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.592099 | −0.0607481 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.84686 | −0.898263 | −0.449131 | − | 0.893466i | \(-0.648266\pi\) | ||||
−0.449131 | + | 0.893466i | \(0.648266\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.206110 | 0.0207149 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.07703 | 0.405680 | 0.202840 | − | 0.979212i | \(-0.434983\pi\) | ||||
0.202840 | + | 0.979212i | \(0.434983\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.80357 | 0.177711 | 0.0888553 | − | 0.996045i | \(-0.471679\pi\) | ||||
0.0888553 | + | 0.996045i | \(0.471679\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.20601 | −0.117695 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.35849 | −0.808046 | −0.404023 | − | 0.914749i | \(-0.632388\pi\) | ||||
−0.404023 | + | 0.914749i | \(0.632388\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1134 | 0.968692 | 0.484346 | − | 0.874876i | \(-0.339058\pi\) | ||||
0.484346 | + | 0.874876i | \(0.339058\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 20.7550 | 1.96998 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.3774 | 1.44658 | 0.723290 | − | 0.690545i | \(-0.242629\pi\) | ||||
0.723290 | + | 0.690545i | \(0.242629\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.552089 | −0.0514826 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.60862 | 0.241167 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.28093 | 0.209092 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9847 | −0.998605 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.9165 | −1.16464 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.85077 | −0.165538 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9686 | 1.32825 | 0.664125 | − | 0.747622i | \(-0.268804\pi\) | ||||
0.664125 | + | 0.747622i | \(0.268804\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.698393 | 0.0614901 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.7545 | −1.20173 | −0.600867 | − | 0.799349i | \(-0.705178\pi\) | ||||
−0.600867 | + | 0.799349i | \(0.705178\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.58662 | −0.831265 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.535871 | 0.0461204 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.70396 | −0.743629 | −0.371815 | − | 0.928307i | \(-0.621264\pi\) | ||||
−0.371815 | + | 0.928307i | \(0.621264\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.3690 | 1.38840 | 0.694200 | − | 0.719782i | \(-0.255758\pi\) | ||||
0.694200 | + | 0.719782i | \(0.255758\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.8334 | 1.41763 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.194197 | 0.0162396 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.605548 | 0.0502880 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.40917 | −0.363662 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.29603 | −0.351945 | −0.175972 | − | 0.984395i | \(-0.556307\pi\) | ||||
−0.175972 | + | 0.984395i | \(0.556307\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.9440 | 1.46026 | 0.730132 | − | 0.683306i | \(-0.239459\pi\) | ||||
0.730132 | + | 0.683306i | \(0.239459\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.26218 | 0.102041 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.09092 | 0.0876244 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.0006 | −1.43660 | −0.718301 | − | 0.695733i | \(-0.755080\pi\) | ||||
−0.718301 | + | 0.695733i | \(0.755080\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 29.0686 | 2.30529 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.93882 | −0.704477 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.8287 | −0.848172 | −0.424086 | − | 0.905622i | \(-0.639405\pi\) | ||||
−0.424086 | + | 0.905622i | \(0.639405\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.0496816 | −0.00386771 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.5314 | 1.43401 | 0.717003 | − | 0.697070i | \(-0.245513\pi\) | ||||
0.717003 | + | 0.697070i | \(0.245513\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5422 | −0.810935 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.30487 | −0.405674 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.4296 | 1.78132 | 0.890662 | − | 0.454667i | \(-0.150242\pi\) | ||||
0.890662 | + | 0.454667i | \(0.150242\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.9310 | −1.12867 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.20009 | −0.315698 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.85816 | −0.662090 | −0.331045 | − | 0.943615i | \(-0.607401\pi\) | ||||
−0.331045 | + | 0.943615i | \(0.607401\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.58982 | 0.564147 | 0.282073 | − | 0.959393i | \(-0.408978\pi\) | ||||
0.282073 | + | 0.959393i | \(0.408978\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.0562 | 2.07397 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.78484 | −0.131224 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0939625 | 0.00687122 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.67623 | 0.631103 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.4585 | 1.11854 | 0.559269 | − | 0.828986i | \(-0.311082\pi\) | ||||
0.559269 | + | 0.828986i | \(0.311082\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.7730 | 1.71122 | 0.855611 | − | 0.517620i | \(-0.173182\pi\) | ||||
0.855611 | + | 0.517620i | \(0.173182\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.628790 | −0.0450286 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.5479 | −1.60647 | −0.803237 | − | 0.595660i | \(-0.796891\pi\) | ||||
−0.803237 | + | 0.595660i | \(0.796891\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.63389 | −0.399376 | −0.199688 | − | 0.979860i | \(-0.563993\pi\) | ||||
−0.199688 | + | 0.979860i | \(0.563993\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.3026 | −1.22043 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.80436 | 0.688131 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.11076 | 0.0775792 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.94640 | −0.343799 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.394919 | −0.0273171 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.8158 | −1.57071 | −0.785354 | − | 0.619048i | \(-0.787519\pi\) | ||||
−0.785354 | + | 0.619048i | \(0.787519\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.10625 | 0.349874 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.0600589 | −0.00409598 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.6629 | 1.19904 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.987346 | −0.0667186 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.18923 | 0.0799961 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.7482 | −1.12154 | −0.560770 | − | 0.827972i | \(-0.689495\pi\) | ||||
−0.560770 | + | 0.827972i | \(0.689495\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.26223 | −0.550815 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.46239 | −0.362552 | −0.181276 | − | 0.983432i | \(-0.558023\pi\) | ||||
−0.181276 | + | 0.983432i | \(0.558023\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.83811 | −0.584039 | −0.292019 | − | 0.956412i | \(-0.594327\pi\) | ||||
−0.292019 | + | 0.956412i | \(0.594327\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.804389 | −0.0529249 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.54676 | 0.166844 | 0.0834220 | − | 0.996514i | \(-0.473415\pi\) | ||||
0.0834220 | + | 0.996514i | \(0.473415\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.44760 | −0.0944313 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.71109 | 0.306018 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.96480 | 0.515200 | 0.257600 | − | 0.966252i | \(-0.417068\pi\) | ||||
0.257600 | + | 0.966252i | \(0.417068\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.9559 | −1.41430 | −0.707151 | − | 0.707063i | \(-0.750020\pi\) | ||||
−0.707151 | + | 0.707063i | \(0.750020\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5814 | 0.999546 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.379170 | 0.0242243 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.99825 | −0.318031 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.98114 | −0.125550 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.05711 | −0.0667243 | −0.0333622 | − | 0.999443i | \(-0.510621\pi\) | ||||
−0.0333622 | + | 0.999443i | \(0.510621\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.368233 | −0.0231506 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.304240 | −0.0190523 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.0351 | −0.937863 | −0.468931 | − | 0.883235i | \(-0.655361\pi\) | ||||
−0.468931 | + | 0.883235i | \(0.655361\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −28.8982 | −1.79565 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.42536 | 0.335821 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −31.6009 | −1.94860 | −0.974299 | − | 0.225261i | \(-0.927677\pi\) | ||||
−0.974299 | + | 0.225261i | \(0.927677\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.49978 | −0.153560 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.7260 | −1.08482 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.5039 | −1.55500 | −0.777501 | − | 0.628882i | \(-0.783513\pi\) | ||||
−0.777501 | + | 0.628882i | \(0.783513\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.5125 | −1.85350 | −0.926752 | − | 0.375674i | \(-0.877411\pi\) | ||||
−0.926752 | + | 0.375674i | \(0.877411\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.1807 | −0.616162 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.615078 | −0.0370906 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.8739 | −1.91511 | −0.957557 | − | 0.288243i | \(-0.906929\pi\) | ||||
−0.957557 | + | 0.288243i | \(0.906929\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.77398 | 0.585153 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.5286 | −1.46325 | −0.731627 | − | 0.681705i | \(-0.761239\pi\) | ||||
−0.731627 | + | 0.681705i | \(0.761239\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.0966 | −0.897401 | −0.448701 | − | 0.893682i | \(-0.648113\pi\) | ||||
−0.448701 | + | 0.893682i | \(0.648113\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.27870 | 0.0757439 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.9843 | 1.06158 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4246 | −0.966152 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.1058 | 1.12000 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.51542 | 0.497476 | 0.248738 | − | 0.968571i | \(-0.419984\pi\) | ||||
0.248738 | + | 0.968571i | \(0.419984\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.361190 | 0.0210293 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.357416 | 0.0207394 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.66050 | −0.269524 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.972407 | −0.0560486 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.80480 | −0.505823 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.41272 | −0.138152 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.0858 | 1.88831 | 0.944155 | − | 0.329503i | \(-0.106881\pi\) | ||||
0.944155 | + | 0.329503i | \(0.106881\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.89500 | −0.221579 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.4761 | 0.764162 | 0.382081 | − | 0.924129i | \(-0.375207\pi\) | ||||
0.382081 | + | 0.924129i | \(0.375207\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.22129 | 0.408171 | 0.204086 | − | 0.978953i | \(-0.434578\pi\) | ||||
0.204086 | + | 0.978953i | \(0.434578\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.929202 | 0.0523546 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.30500 | −0.185628 | −0.0928138 | − | 0.995683i | \(-0.529586\pi\) | ||||
−0.0928138 | + | 0.995683i | \(0.529586\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.403889 | 0.0226134 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.0511 | 1.00751 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.41841 | −0.134564 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.78468 | −0.431816 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.8411 | −1.20782 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −23.4380 | −1.29218 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.8668 | 1.42177 | 0.710884 | − | 0.703309i | \(-0.248295\pi\) | ||||
0.710884 | + | 0.703309i | \(0.248295\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.9912 | −0.876311 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.48795 | 0.0812952 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.2463 | −0.612627 | −0.306313 | − | 0.951931i | \(-0.599096\pi\) | ||||
−0.306313 | + | 0.951931i | \(0.599096\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −33.2091 | −1.80367 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.727620 | 0.0394028 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.9094 | −0.805033 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.19230 | 0.0641912 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.9008 | 0.799914 | 0.399957 | − | 0.916534i | \(-0.369025\pi\) | ||||
0.399957 | + | 0.916534i | \(0.369025\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.9580 | −1.49656 | −0.748278 | − | 0.663385i | \(-0.769119\pi\) | ||||
−0.748278 | + | 0.663385i | \(0.769119\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.52360 | 0.241452 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.05626 | 0.162668 | 0.0813341 | − | 0.996687i | \(-0.474082\pi\) | ||||
0.0813341 | + | 0.996687i | \(0.474082\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.439116 | −0.0233059 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.92592 | −0.260707 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.670710 | −0.0353987 | −0.0176994 | − | 0.999843i | \(-0.505634\pi\) | ||||
−0.0176994 | + | 0.999843i | \(0.505634\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.83556 | −0.465030 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 23.7226 | 1.24511 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.0849076 | 0.00444427 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.0680 | 1.77833 | 0.889167 | − | 0.457584i | \(-0.151285\pi\) | ||||
0.889167 | + | 0.457584i | \(0.151285\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.95181 | 0.518071 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −40.4737 | −2.10129 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.42167 | −0.177167 | −0.0885837 | − | 0.996069i | \(-0.528234\pi\) | ||||
−0.0885837 | + | 0.996069i | \(0.528234\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.99695 | 0.206401 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.11178 | 0.263270 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.74129 | −0.500376 | −0.250188 | − | 0.968197i | \(-0.580492\pi\) | ||||
−0.250188 | + | 0.968197i | \(0.580492\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −32.3264 | −1.65613 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.4963 | 1.50719 | 0.753595 | − | 0.657339i | \(-0.228318\pi\) | ||||
0.753595 | + | 0.657339i | \(0.228318\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0691741 | 0.00352544 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.538093 | −0.0273528 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.93654 | −0.453101 | −0.226550 | − | 0.973999i | \(-0.572745\pi\) | ||||
−0.226550 | + | 0.973999i | \(0.572745\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.25499 | −0.114040 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.7043 | 1.49838 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.405134 | −0.0203845 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.4543 | −1.17714 | −0.588569 | − | 0.808447i | \(-0.700308\pi\) | ||||
−0.588569 | + | 0.808447i | \(0.700308\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.7034 | 1.03647 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.22726 | −0.410850 | −0.205425 | − | 0.978673i | \(-0.565858\pi\) | ||||
−0.205425 | + | 0.978673i | \(0.565858\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.20905 | 0.458735 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.08433 | −0.103571 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.19046 | −0.0590088 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.542389 | 0.0268194 | 0.0134097 | − | 0.999910i | \(-0.495731\pi\) | ||||
0.0134097 | + | 0.999910i | \(0.495731\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.7972 | 0.927196 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.84799 | 0.287761 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.170370 | 0.00836312 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −35.3507 | −1.73113 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.7197 | 0.572544 | 0.286272 | − | 0.958148i | \(-0.407584\pi\) | ||||
0.286272 | + | 0.958148i | \(0.407584\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.4556 | −1.33811 | −0.669053 | − | 0.743215i | \(-0.733300\pi\) | ||||
−0.669053 | + | 0.743215i | \(0.733300\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.9697 | −0.630608 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.76662 | −0.182708 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −39.0640 | −1.89044 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.419391 | −0.0202484 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.44537 | −0.358631 | −0.179316 | − | 0.983792i | \(-0.557388\pi\) | ||||
−0.179316 | + | 0.983792i | \(0.557388\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.8573 | −1.09845 | −0.549225 | − | 0.835674i | \(-0.685077\pi\) | ||||
−0.549225 | + | 0.835674i | \(0.685077\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.30775 | −0.0627017 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.47759 | 0.453375 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.9643 | −0.857391 | −0.428696 | − | 0.903449i | \(-0.641027\pi\) | ||||
−0.428696 | + | 0.903449i | \(0.641027\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.39715 | 0.161769 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.1568 | −1.10021 | −0.550106 | − | 0.835095i | \(-0.685413\pi\) | ||||
−0.550106 | + | 0.835095i | \(0.685413\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.52436 | 0.0722618 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.27777 | 0.438823 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.5958 | 0.971974 | 0.485987 | − | 0.873966i | \(-0.338460\pi\) | ||||
0.485987 | + | 0.873966i | \(0.338460\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.740859 | 0.0348857 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −38.7521 | −1.82073 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.875495 | 0.0410438 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.35187 | 0.250350 | 0.125175 | − | 0.992135i | \(-0.460051\pi\) | ||||
0.125175 | + | 0.992135i | \(0.460051\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.18874 | 0.102162 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.14059 | −0.332570 | −0.166285 | − | 0.986078i | \(-0.553177\pi\) | ||||
−0.166285 | + | 0.986078i | \(0.553177\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.45647 | −0.253584 | −0.126792 | − | 0.991929i | \(-0.540468\pi\) | ||||
−0.126792 | + | 0.991929i | \(0.540468\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.35595 | −0.109255 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.0783 | −1.11421 | −0.557105 | − | 0.830442i | \(-0.688088\pi\) | ||||
−0.557105 | + | 0.830442i | \(0.688088\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.0912 | 1.11243 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 38.8742 | 1.79123 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.0400581 | −0.00184188 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.8309 | 0.726371 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.3966 | −1.02547 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.4939 | 1.48468 | 0.742342 | − | 0.670021i | \(-0.233715\pi\) | ||||
0.742342 | + | 0.670021i | \(0.233715\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.0669 | −0.686992 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 19.3044 | 0.878379 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.64302 | −0.0746056 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.4002 | 1.19631 | 0.598154 | − | 0.801381i | \(-0.295901\pi\) | ||||
0.598154 | + | 0.801381i | \(0.295901\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.3859 | 1.05755 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.8605 | 0.896291 | 0.448145 | − | 0.893961i | \(-0.352085\pi\) | ||||
0.448145 | + | 0.893961i | \(0.352085\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.47334 | 0.111393 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.0382783 | 0.00172048 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.10968 | −0.318913 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.8942 | 0.532458 | 0.266229 | − | 0.963910i | \(-0.414222\pi\) | ||||
0.266229 | + | 0.963910i | \(0.414222\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −40.0207 | −1.78799 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.15677 | 0.408280 | 0.204140 | − | 0.978942i | \(-0.434560\pi\) | ||||
0.204140 | + | 0.978942i | \(0.434560\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.757176 | 0.0336939 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.7670 | 1.01112 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.7270 | 0.785737 | 0.392868 | − | 0.919595i | \(-0.371483\pi\) | ||||
0.392868 | + | 0.919595i | \(0.371483\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.37473 | 0.0608145 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.19917 | −0.406153 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.334954 | 0.0147598 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.965525 | −0.0424637 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −50.5989 | −2.22105 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.4733 | 0.634089 | 0.317044 | − | 0.948411i | \(-0.397310\pi\) | ||||
0.317044 | + | 0.948411i | \(0.397310\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −41.8021 | −1.82788 | −0.913938 | − | 0.405854i | \(-0.866974\pi\) | ||||
−0.913938 | + | 0.405854i | \(0.866974\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 32.2451 | 1.40729 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.45580 | 0.194098 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.1628 | −0.615776 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.23606 | 0.140433 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.37661 | 0.406146 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.55232 | −0.0671126 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.1302 | 0.825529 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.252900 | 0.0108932 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0011 | −0.730934 | −0.365467 | − | 0.930824i | \(-0.619091\pi\) | ||||
−0.365467 | + | 0.930824i | \(0.619091\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.3911 | −0.703408 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.87824 | 0.0804552 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.1741 | −1.54669 | −0.773347 | − | 0.633984i | \(-0.781419\pi\) | ||||
−0.773347 | + | 0.633984i | \(0.781419\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.6165 | −0.922572 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.3953 | −0.442854 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.55948 | −0.278938 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.85457 | 0.163617 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.86711 | 0.333340 | 0.166670 | − | 0.986013i | \(-0.446699\pi\) | ||||
0.166670 | + | 0.986013i | \(0.446699\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.506992 | −0.0214435 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.202923 | −0.00856740 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.7498 | −1.71740 | −0.858701 | − | 0.512477i | \(-0.828728\pi\) | ||||
−0.858701 | + | 0.512477i | \(0.828728\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.85585 | 0.120146 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −33.7472 | −1.41725 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.02204 | −0.336302 | −0.168151 | − | 0.985761i | \(-0.553780\pi\) | ||||
−0.168151 | + | 0.985761i | \(0.553780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.97557 | 0.375616 | 0.187808 | − | 0.982206i | \(-0.439862\pi\) | ||||
0.187808 | + | 0.982206i | \(0.439862\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −33.3844 | −1.39465 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.7611 | 0.615582 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.9508 | −0.705670 | −0.352835 | − | 0.935686i | \(-0.614782\pi\) | ||||
−0.352835 | + | 0.935686i | \(0.614782\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −51.3405 | −2.13364 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.75844 | 0.114439 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.66731 | −0.0690528 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.484466 | 0.0200302 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −45.0833 | −1.86079 | −0.930394 | − | 0.366562i | \(-0.880535\pi\) | ||||
−0.930394 | + | 0.366562i | \(0.880535\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.7275 | −0.771653 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 48.6948 | 2.00304 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.3125 | 1.40904 | 0.704522 | − | 0.709682i | \(-0.251161\pi\) | ||||
0.704522 | + | 0.709682i | \(0.251161\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.423609 | 0.0173663 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.1670 | 0.497962 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.5543 | 1.49357 | 0.746783 | − | 0.665068i | \(-0.231597\pi\) | ||||
0.746783 | + | 0.665068i | \(0.231597\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.28152 | 0.174647 | 0.0873235 | − | 0.996180i | \(-0.472169\pi\) | ||||
0.0873235 | + | 0.996180i | \(0.472169\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.3312 | 0.542887 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.04004 | −0.0829396 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.35162 | −0.0548606 | −0.0274303 | − | 0.999624i | \(-0.508732\pi\) | ||||
−0.0274303 | + | 0.999624i | \(0.508732\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.1736 | −0.857998 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.2201 | −0.494371 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.0267 | −1.01082 | −0.505410 | − | 0.862879i | \(-0.668659\pi\) | ||||
−0.505410 | + | 0.862879i | \(0.668659\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.39882 | −0.0967298 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.2952 | 0.937830 | 0.468915 | − | 0.883243i | \(-0.344645\pi\) | ||||
0.468915 | + | 0.883243i | \(0.344645\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.05784 | −0.243485 | −0.121743 | − | 0.992562i | \(-0.538848\pi\) | ||||
−0.121743 | + | 0.992562i | \(0.538848\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.57755 | −0.344205 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.6808 | 0.988817 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.4838 | 0.979353 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.852872 | 0.0340604 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.29013 | −0.290676 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.6830 | −1.42052 | −0.710259 | − | 0.703940i | \(-0.751422\pi\) | ||||
−0.710259 | + | 0.703940i | \(0.751422\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 49.2734 | 1.95844 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.77994 | 0.110318 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.20080 | 0.126820 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.93423 | −0.155636 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.9261 | −1.06352 | −0.531759 | − | 0.846896i | \(-0.678469\pi\) | ||||
−0.531759 | + | 0.846896i | \(0.678469\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.5169 | 0.651363 | 0.325682 | − | 0.945480i | \(-0.394406\pi\) | ||||
0.325682 | + | 0.945480i | \(0.394406\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.129704 | 0.00510709 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.67446 | −0.301714 | −0.150857 | − | 0.988556i | \(-0.548203\pi\) | ||||
−0.150857 | + | 0.988556i | \(0.548203\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.240907 | 0.00945643 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38.1450 | −1.49502 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.7242 | −1.12406 | −0.562032 | − | 0.827115i | \(-0.689980\pi\) | ||||
−0.562032 | + | 0.827115i | \(0.689980\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.55445 | −0.0998105 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.760723 | 0.0296786 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.3867 | 1.26161 | 0.630804 | − | 0.775943i | \(-0.282725\pi\) | ||||
0.630804 | + | 0.775943i | \(0.282725\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.1627 | 1.05651 | 0.528254 | − | 0.849086i | \(-0.322847\pi\) | ||||
0.528254 | + | 0.849086i | \(0.322847\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.56827 | −0.0997433 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.78040 | −0.0690411 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.69285 | −0.375309 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 36.1695 | 1.39839 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.60924 | −0.0621239 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.38022 | 0.130298 | 0.0651489 | − | 0.997876i | \(-0.479248\pi\) | ||||
0.0651489 | + | 0.997876i | \(0.479248\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.3275 | −0.551466 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.2040 | −1.04554 | −0.522768 | − | 0.852475i | \(-0.675101\pi\) | ||||
−0.522768 | + | 0.852475i | \(0.675101\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.6019 | −1.02089 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.7966 | 0.452048 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.0966 | 0.845503 | 0.422751 | − | 0.906246i | \(-0.361064\pi\) | ||||
0.422751 | + | 0.906246i | \(0.361064\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.61648 | −0.0617625 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.0869 | 0.728210 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.1021 | −0.803926 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.9351 | −1.02466 | −0.512330 | − | 0.858788i | \(-0.671218\pi\) | ||||
−0.512330 | + | 0.858788i | \(0.671218\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.619760 | 0.0235427 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.04001 | 0.115314 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.53688 | 0.171846 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.50002 | −0.208030 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.3883 | 0.996673 | 0.498337 | − | 0.866984i | \(-0.333944\pi\) | ||||
0.498337 | + | 0.866984i | \(0.333944\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.6400 | 1.15561 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.12626 | 0.117742 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.2594 | 0.461061 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.3313 | 1.58979 | 0.794893 | − | 0.606750i | \(-0.207527\pi\) | ||||
0.794893 | + | 0.606750i | \(0.207527\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.62977 | −0.136127 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.4620 | −0.653957 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0360659 | 0.00134879 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.2009 | −0.642378 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.7951 | 0.402589 | 0.201295 | − | 0.979531i | \(-0.435485\pi\) | ||||
0.201295 | + | 0.979531i | \(0.435485\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.42320 | 0.201971 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 47.4162 | 1.76343 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.1905 | −0.601298 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.6662 | −1.80493 | −0.902466 | − | 0.430762i | \(-0.858245\pi\) | ||||
−0.902466 | + | 0.430762i | \(0.858245\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.0196552 | 0.000727972 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.245308 | −0.00907305 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.4139 | 1.52966 | 0.764829 | − | 0.644233i | \(-0.222823\pi\) | ||||
0.764829 | + | 0.644233i | \(0.222823\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.818861 | −0.0302041 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.992433 | 0.0365567 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.2022 | 0.816723 | 0.408361 | − | 0.912820i | \(-0.366100\pi\) | ||||
0.408361 | + | 0.912820i | \(0.366100\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.7943 | 0.396538 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.7936 | 0.946276 | 0.473138 | − | 0.880988i | \(-0.343121\pi\) | ||||
0.473138 | + | 0.880988i | \(0.343121\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.797849 | −0.0292309 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.52642 | 0.0558486 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.1334 | −0.918355 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | 0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.28295 | 0.0831954 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.33252 | 0.121283 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.0976 | −1.42103 | −0.710513 | − | 0.703684i | \(-0.751537\pi\) | ||||
−0.710513 | + | 0.703684i | \(0.751537\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.795241 | 0.0288654 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.291090 | −0.0105520 | −0.00527601 | − | 0.999986i | \(-0.501679\pi\) | ||||
−0.00527601 | + | 0.999986i | \(0.501679\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.4105 | 1.10093 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.234409 | 0.00847507 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.04901 | 0.110094 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.941041 | 0.0339348 | 0.0169674 | − | 0.999856i | \(-0.494599\pi\) | ||||
0.0169674 | + | 0.999856i | \(0.494599\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.4700 | 1.16938 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.7263 | −0.781440 | −0.390720 | − | 0.920510i | \(-0.627774\pi\) | ||||
−0.390720 | + | 0.920510i | \(0.627774\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.1677 | −1.04773 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 62.4089 | 2.23891 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.0682 | −0.683191 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.292882 | −0.0104801 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.40811 | 0.336218 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.34302 | −0.119318 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.0634 | −0.643890 | −0.321945 | − | 0.946758i | \(-0.604337\pi\) | ||||
−0.321945 | + | 0.946758i | \(0.604337\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 68.2457 | 2.42961 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 46.2387 | 1.64406 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.3671 | −0.723258 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.39856 | 0.191467 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.92165 | 0.209756 | 0.104878 | − | 0.994485i | \(-0.466555\pi\) | ||||
0.104878 | + | 0.994485i | \(0.466555\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.91268 | −0.209176 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.6574 | 0.482562 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.0566318 | 0.00199849 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.66010 | −0.0585107 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 55.0786 | 1.93886 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.3365 | 1.10173 | 0.550866 | − | 0.834594i | \(-0.314298\pi\) | ||||
0.550866 | + | 0.834594i | \(0.314298\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.5095 | −0.579729 | −0.289864 | − | 0.957068i | \(-0.593610\pi\) | ||||
−0.289864 | + | 0.957068i | \(0.593610\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 65.8952 | 2.31105 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.01109 | −0.0704453 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.03102 | 0.0360707 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.84393 | 0.274089 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.3100 | 0.534324 | 0.267162 | − | 0.963652i | \(-0.413914\pi\) | ||||
0.267162 | + | 0.963652i | \(0.413914\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.7942 | 0.864273 | 0.432137 | − | 0.901808i | \(-0.357760\pi\) | ||||
0.432137 | + | 0.901808i | \(0.357760\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.32833 | 0.0462465 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −50.8640 | −1.76872 | −0.884358 | − | 0.466810i | \(-0.845403\pi\) | ||||
−0.884358 | + | 0.466810i | \(0.845403\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.7297 | 1.31041 | 0.655204 | − | 0.755452i | \(-0.272583\pi\) | ||||
0.655204 | + | 0.755452i | \(0.272583\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 68.8352 | 2.38787 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.54871 | 0.0536595 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.44161 | 0.119102 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.9490 | 0.585845 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.6616 | 1.23117 | 0.615587 | − | 0.788069i | \(-0.288919\pi\) | ||||
0.615587 | + | 0.788069i | \(0.288919\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.3686 | −0.633400 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 52.9722 | 1.82446 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.95786 | −0.0673526 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −33.0301 | −1.13493 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 32.6029 | 1.11893 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.5696 | 0.979352 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.0875 | 0.858979 | 0.429490 | − | 0.903072i | \(-0.358693\pi\) | ||||
0.429490 | + | 0.903072i | \(0.358693\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.985208 | −0.0336934 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43.0907 | −1.47195 | −0.735975 | − | 0.677008i | \(-0.763276\pi\) | ||||
−0.735975 | + | 0.677008i | \(0.763276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.5470 | −1.07637 | −0.538184 | − | 0.842827i | \(-0.680890\pi\) | ||||
−0.538184 | + | 0.842827i | \(0.680890\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −38.8390 | −1.32363 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.2603 | −1.47260 | −0.736298 | − | 0.676657i | \(-0.763428\pi\) | ||||
−0.736298 | + | 0.676657i | \(0.763428\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.35130 | 0.147949 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 35.4707 | 1.20465 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.270217 | −0.00916648 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.5606 | 0.425601 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.7205 | −0.498213 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.56514 | −0.188136 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.6615 | 1.10290 | 0.551450 | − | 0.834208i | \(-0.314075\pi\) | ||||
0.551450 | + | 0.834208i | \(0.314075\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.3900 | −0.620279 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.1491 | 0.914677 | 0.457338 | − | 0.889293i | \(-0.348803\pi\) | ||||
0.457338 | + | 0.889293i | \(0.348803\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.1691 | 1.41910 | 0.709552 | − | 0.704653i | \(-0.248898\pi\) | ||||
0.709552 | + | 0.704653i | \(0.248898\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.780030 | −0.0262204 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.6522 | 0.458397 | 0.229198 | − | 0.973380i | \(-0.426390\pi\) | ||||
0.229198 | + | 0.973380i | \(0.426390\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.0096 | 1.50957 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.39021 | −0.0465738 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.8507 | 0.831596 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.64512 | −0.0549902 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.0649 | 0.336057 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.1528 | 0.638783 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.2103 | −0.340153 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.10002 | 0.0698843 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.40956 | 0.0468555 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.0484 | −1.19697 | −0.598483 | − | 0.801135i | \(-0.704230\pi\) | ||||
−0.598483 | + | 0.801135i | \(0.704230\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.78387 | 0.225007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.3666 | −1.53620 | −0.768098 | − | 0.640333i | \(-0.778796\pi\) | ||||
−0.768098 | + | 0.640333i | \(0.778796\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.113633 | 0.00376072 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.21053 | 0.172255 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −41.3588 | −1.36579 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.2309 | 0.700344 | 0.350172 | − | 0.936685i | \(-0.386123\pi\) | ||||
0.350172 | + | 0.936685i | \(0.386123\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −71.4526 | −2.35444 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.70683 | −0.122012 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 47.7212 | 1.56906 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.00099 | 0.0985656 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.2004 | 0.793989 | 0.396995 | − | 0.917821i | \(-0.370053\pi\) | ||||
0.396995 | + | 0.917821i | \(0.370053\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.50913 | −0.213328 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −29.1032 | −0.952798 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.0174505 | 0.000570692 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.9568 | 0.586623 | 0.293311 | − | 0.956017i | \(-0.405243\pi\) | ||||
0.293311 | + | 0.956017i | \(0.405243\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.5952 | −0.508929 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.2375 | 0.822720 | 0.411360 | − | 0.911473i | \(-0.365054\pi\) | ||||
0.411360 | + | 0.911473i | \(0.365054\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.7797 | −0.578988 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.61133 | 0.0524165 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.2824 | −1.21151 | −0.605757 | − | 0.795650i | \(-0.707130\pi\) | ||||
−0.605757 | + | 0.795650i | \(0.707130\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.716754 | 0.0232668 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.13753 | 0.231450 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.73424 | 0.0885706 | 0.0442853 | − | 0.999019i | \(-0.485899\pi\) | ||||
0.0442853 | + | 0.999019i | \(0.485899\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.87092 | 0.0929007 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.872243 | −0.0281956 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.1722 | −0.845145 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.50453 | 0.113049 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.9079 | −0.448175 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.41507 | 0.142126 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.31745 | 0.235313 | 0.117657 | − | 0.993054i | \(-0.462462\pi\) | ||||
0.117657 | + | 0.993054i | \(0.462462\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.22282 | 0.167781 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.13022 | −0.260911 | −0.130456 | − | 0.991454i | \(-0.541644\pi\) | ||||
−0.130456 | + | 0.991454i | \(0.541644\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 49.2205 | 1.57794 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.8119 | 0.538411 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.0026 | 0.352003 | 0.176002 | − | 0.984390i | \(-0.443684\pi\) | ||||
0.176002 | + | 0.984390i | \(0.443684\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.01672 | 0.0324946 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.8280 | 0.537276 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.2979 | −0.774982 | −0.387491 | − | 0.921874i | \(-0.626658\pi\) | ||||
−0.387491 | + | 0.921874i | \(0.626658\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.18755 | −0.133426 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 50.6170 | 1.61116 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.961348 | 0.0305691 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.9229 | −0.728170 | −0.364085 | − | 0.931366i | \(-0.618618\pi\) | ||||
−0.364085 | + | 0.931366i | \(0.618618\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −55.8623 | −1.77274 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.04631 | −0.0331703 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.3956 | −1.18433 | −0.592165 | − | 0.805817i | \(-0.701726\pi\) | ||||
−0.592165 | + | 0.805817i | \(0.701726\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.7303 | −0.877347 |
(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 | 6008.2.a.c.1.9 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.c.1.9 | ✓ | 44 | 1.1 | even | 1 | trivial |