Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.480943 | −0.340078 | −0.170039 | − | 0.985437i | \(-0.554389\pi\) | ||||
−0.170039 | + | 0.985437i | \(0.554389\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.76869 | −0.884347 | ||||||||
\(5\) | −1.51137 | −0.675903 | −0.337952 | − | 0.941164i | \(-0.609734\pi\) | ||||
−0.337952 | + | 0.941164i | \(0.609734\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.82960 | 1.44745 | 0.723727 | − | 0.690087i | \(-0.242428\pi\) | ||||
0.723727 | + | 0.690087i | \(0.242428\pi\) | |||||||
\(8\) | 1.81253 | 0.640825 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.726880 | 0.229860 | ||||||||
\(11\) | −4.55830 | −1.37438 | −0.687190 | − | 0.726478i | \(-0.741156\pi\) | ||||
−0.687190 | + | 0.726478i | \(0.741156\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.03350 | −0.563992 | −0.281996 | − | 0.959416i | \(-0.590996\pi\) | ||||
−0.281996 | + | 0.959416i | \(0.590996\pi\) | |||||||
\(14\) | −1.84182 | −0.492247 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.66567 | 0.666417 | ||||||||
\(17\) | −3.09482 | −0.750604 | −0.375302 | − | 0.926903i | \(-0.622461\pi\) | ||||
−0.375302 | + | 0.926903i | \(0.622461\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.07355 | −1.16395 | −0.581976 | − | 0.813206i | \(-0.697720\pi\) | ||||
−0.581976 | + | 0.813206i | \(0.697720\pi\) | |||||||
\(20\) | 2.67314 | 0.597733 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.19228 | 0.467396 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.71578 | −0.543155 | ||||||||
\(26\) | 0.977997 | 0.191801 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.77339 | −1.28005 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.30853 | 0.594229 | 0.297115 | − | 0.954842i | \(-0.403976\pi\) | ||||
0.297115 | + | 0.954842i | \(0.403976\pi\) | |||||||
\(32\) | −4.90709 | −0.867458 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.48843 | 0.255264 | ||||||||
\(35\) | −5.78793 | −0.978338 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.63233 | 1.58355 | 0.791773 | − | 0.610816i | \(-0.209158\pi\) | ||||
0.791773 | + | 0.610816i | \(0.209158\pi\) | |||||||
\(38\) | 2.44008 | 0.395834 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.73939 | −0.433135 | ||||||||
\(41\) | −7.83947 | −1.22432 | −0.612160 | − | 0.790734i | \(-0.709699\pi\) | ||||
−0.612160 | + | 0.790734i | \(0.709699\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.74208 | 0.265665 | 0.132832 | − | 0.991139i | \(-0.457593\pi\) | ||||
0.132832 | + | 0.991139i | \(0.457593\pi\) | |||||||
\(44\) | 8.06224 | 1.21543 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.480943 | 0.0709111 | ||||||||
\(47\) | −6.78144 | −0.989175 | −0.494587 | − | 0.869128i | \(-0.664681\pi\) | ||||
−0.494587 | + | 0.869128i | \(0.664681\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.66585 | 1.09512 | ||||||||
\(50\) | 1.30613 | 0.184715 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.59664 | 0.498764 | ||||||||
\(53\) | 8.59890 | 1.18115 | 0.590575 | − | 0.806983i | \(-0.298901\pi\) | ||||
0.590575 | + | 0.806983i | \(0.298901\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.88926 | 0.928948 | ||||||||
\(56\) | 6.94125 | 0.927564 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.480943 | −0.0631509 | ||||||||
\(59\) | −2.86760 | −0.373330 | −0.186665 | − | 0.982424i | \(-0.559768\pi\) | ||||
−0.186665 | + | 0.982424i | \(0.559768\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.14004 | −0.402041 | −0.201021 | − | 0.979587i | \(-0.564426\pi\) | ||||
−0.201021 | + | 0.979587i | \(0.564426\pi\) | |||||||
\(62\) | −1.59121 | −0.202084 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.97131 | −0.371413 | ||||||||
\(65\) | 3.07336 | 0.381204 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.13434 | −0.382921 | −0.191460 | − | 0.981500i | \(-0.561322\pi\) | ||||
−0.191460 | + | 0.981500i | \(0.561322\pi\) | |||||||
\(68\) | 5.47379 | 0.663794 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.78366 | 0.332711 | ||||||||
\(71\) | 5.22684 | 0.620312 | 0.310156 | − | 0.950686i | \(-0.399619\pi\) | ||||
0.310156 | + | 0.950686i | \(0.399619\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.0074 | 1.63944 | 0.819721 | − | 0.572763i | \(-0.194128\pi\) | ||||
0.819721 | + | 0.572763i | \(0.194128\pi\) | |||||||
\(74\) | −4.63260 | −0.538529 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.97355 | 1.02934 | ||||||||
\(77\) | −17.4565 | −1.98935 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.01553 | −0.226764 | −0.113382 | − | 0.993551i | \(-0.536168\pi\) | ||||
−0.113382 | + | 0.993551i | \(0.536168\pi\) | |||||||
\(80\) | −4.02880 | −0.450433 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.77034 | 0.416364 | ||||||||
\(83\) | −0.169808 | −0.0186388 | −0.00931941 | − | 0.999957i | \(-0.502967\pi\) | ||||
−0.00931941 | + | 0.999957i | \(0.502967\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.67740 | 0.507335 | ||||||||
\(86\) | −0.837841 | −0.0903467 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.26204 | −0.880737 | ||||||||
\(89\) | 4.44668 | 0.471347 | 0.235673 | − | 0.971832i | \(-0.424270\pi\) | ||||
0.235673 | + | 0.971832i | \(0.424270\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.78750 | −0.816351 | ||||||||
\(92\) | 1.76869 | 0.184399 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.26148 | 0.336396 | ||||||||
\(95\) | 7.66798 | 0.786718 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.6221 | −1.28158 | −0.640792 | − | 0.767715i | \(-0.721394\pi\) | ||||
−0.640792 | + | 0.767715i | \(0.721394\pi\) | |||||||
\(98\) | −3.68683 | −0.372426 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.80338 | 0.480338 | ||||||||
\(101\) | −2.61569 | −0.260271 | −0.130135 | − | 0.991496i | \(-0.541541\pi\) | ||||
−0.130135 | + | 0.991496i | \(0.541541\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.4221 | −1.51958 | −0.759792 | − | 0.650166i | \(-0.774699\pi\) | ||||
−0.759792 | + | 0.650166i | \(0.774699\pi\) | |||||||
\(104\) | −3.68577 | −0.361420 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.13558 | −0.401683 | ||||||||
\(107\) | −7.44129 | −0.719376 | −0.359688 | − | 0.933073i | \(-0.617117\pi\) | ||||
−0.359688 | + | 0.933073i | \(0.617117\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.35061 | 0.320931 | 0.160465 | − | 0.987041i | \(-0.448701\pi\) | ||||
0.160465 | + | 0.987041i | \(0.448701\pi\) | |||||||
\(110\) | −3.31334 | −0.315915 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.2084 | 0.964607 | ||||||||
\(113\) | 3.11687 | 0.293211 | 0.146605 | − | 0.989195i | \(-0.453165\pi\) | ||||
0.146605 | + | 0.989195i | \(0.453165\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.51137 | 0.140936 | ||||||||
\(116\) | −1.76869 | −0.164219 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.37915 | 0.126961 | ||||||||
\(119\) | −11.8519 | −1.08646 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.77813 | 0.888921 | ||||||||
\(122\) | 1.51018 | 0.136725 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.85177 | −0.525505 | ||||||||
\(125\) | 11.6614 | 1.04302 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.1857 | 1.17004 | 0.585022 | − | 0.811018i | \(-0.301086\pi\) | ||||
0.585022 | + | 0.811018i | \(0.301086\pi\) | |||||||
\(128\) | 11.2432 | 0.993768 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.47811 | −0.129639 | ||||||||
\(131\) | −0.293403 | −0.0256347 | −0.0128174 | − | 0.999918i | \(-0.504080\pi\) | ||||
−0.0128174 | + | 0.999918i | \(0.504080\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.4297 | −1.68477 | ||||||||
\(134\) | 1.50744 | 0.130223 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.60944 | −0.481005 | ||||||||
\(137\) | 9.42909 | 0.805581 | 0.402791 | − | 0.915292i | \(-0.368040\pi\) | ||||
0.402791 | + | 0.915292i | \(0.368040\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.18681 | 0.355120 | 0.177560 | − | 0.984110i | \(-0.443180\pi\) | ||||
0.177560 | + | 0.984110i | \(0.443180\pi\) | |||||||
\(140\) | 10.2371 | 0.865190 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.51381 | −0.210954 | ||||||||
\(143\) | 9.26931 | 0.775139 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.51137 | −0.125512 | ||||||||
\(146\) | −6.73676 | −0.557538 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −17.0366 | −1.40040 | ||||||||
\(149\) | −3.07017 | −0.251518 | −0.125759 | − | 0.992061i | \(-0.540137\pi\) | ||||
−0.125759 | + | 0.992061i | \(0.540137\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00783 | −0.326153 | −0.163076 | − | 0.986613i | \(-0.552142\pi\) | ||||
−0.163076 | + | 0.986613i | \(0.552142\pi\) | |||||||
\(152\) | −9.19593 | −0.745889 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.39557 | 0.676534 | ||||||||
\(155\) | −5.00039 | −0.401641 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.32743 | 0.504984 | 0.252492 | − | 0.967599i | \(-0.418750\pi\) | ||||
0.252492 | + | 0.967599i | \(0.418750\pi\) | |||||||
\(158\) | 0.969353 | 0.0771176 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.41640 | 0.586318 | ||||||||
\(161\) | −3.82960 | −0.301815 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.6695 | 1.14900 | 0.574501 | − | 0.818504i | \(-0.305196\pi\) | ||||
0.574501 | + | 0.818504i | \(0.305196\pi\) | |||||||
\(164\) | 13.8656 | 1.08272 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0816678 | 0.00633865 | ||||||||
\(167\) | 9.34863 | 0.723419 | 0.361709 | − | 0.932291i | \(-0.382193\pi\) | ||||
0.361709 | + | 0.932291i | \(0.382193\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.86488 | −0.681914 | ||||||||
\(170\) | −2.24956 | −0.172534 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.08121 | −0.234940 | ||||||||
\(173\) | 5.41582 | 0.411757 | 0.205879 | − | 0.978578i | \(-0.433995\pi\) | ||||
0.205879 | + | 0.978578i | \(0.433995\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.4003 | −0.786192 | ||||||||
\(176\) | −12.1509 | −0.915910 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.13860 | −0.160295 | ||||||||
\(179\) | 7.39935 | 0.553054 | 0.276527 | − | 0.961006i | \(-0.410817\pi\) | ||||
0.276527 | + | 0.961006i | \(0.410817\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.51076 | 0.558270 | 0.279135 | − | 0.960252i | \(-0.409952\pi\) | ||||
0.279135 | + | 0.960252i | \(0.409952\pi\) | |||||||
\(182\) | 3.74534 | 0.277623 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.81253 | −0.133621 | ||||||||
\(185\) | −14.5580 | −1.07032 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.1071 | 1.03161 | ||||||||
\(188\) | 11.9943 | 0.874774 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.68786 | −0.267545 | ||||||||
\(191\) | −22.8811 | −1.65562 | −0.827810 | − | 0.561008i | \(-0.810414\pi\) | ||||
−0.827810 | + | 0.561008i | \(0.810414\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.40826 | −0.245332 | −0.122666 | − | 0.992448i | \(-0.539144\pi\) | ||||
−0.122666 | + | 0.992448i | \(0.539144\pi\) | |||||||
\(194\) | 6.07052 | 0.435838 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.5585 | −0.968467 | ||||||||
\(197\) | −19.0599 | −1.35796 | −0.678982 | − | 0.734155i | \(-0.737578\pi\) | ||||
−0.678982 | + | 0.734155i | \(0.737578\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.1967 | 0.935492 | 0.467746 | − | 0.883863i | \(-0.345066\pi\) | ||||
0.467746 | + | 0.883863i | \(0.345066\pi\) | |||||||
\(200\) | −4.92241 | −0.348067 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.25800 | 0.0885123 | ||||||||
\(203\) | 3.82960 | 0.268785 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.8483 | 0.827521 | ||||||||
\(206\) | 7.41714 | 0.516777 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.42064 | −0.375853 | ||||||||
\(209\) | 23.1268 | 1.59971 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.2487 | 0.774393 | 0.387197 | − | 0.921997i | \(-0.373443\pi\) | ||||
0.387197 | + | 0.921997i | \(0.373443\pi\) | |||||||
\(212\) | −15.2088 | −1.04455 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.57883 | 0.244644 | ||||||||
\(215\) | −2.63292 | −0.179564 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.6703 | 0.860119 | ||||||||
\(218\) | −1.61145 | −0.109141 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.1850 | −0.821512 | ||||||||
\(221\) | 6.29332 | 0.423334 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.42434 | −0.363240 | −0.181620 | − | 0.983369i | \(-0.558134\pi\) | ||||
−0.181620 | + | 0.983369i | \(0.558134\pi\) | |||||||
\(224\) | −18.7922 | −1.25561 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.49904 | −0.0997145 | ||||||||
\(227\) | 14.2301 | 0.944488 | 0.472244 | − | 0.881468i | \(-0.343444\pi\) | ||||
0.472244 | + | 0.881468i | \(0.343444\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.6452 | 1.16603 | 0.583013 | − | 0.812463i | \(-0.301874\pi\) | ||||
0.583013 | + | 0.812463i | \(0.301874\pi\) | |||||||
\(230\) | −0.726880 | −0.0479291 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.81253 | 0.118998 | ||||||||
\(233\) | −27.1596 | −1.77929 | −0.889643 | − | 0.456657i | \(-0.849047\pi\) | ||||
−0.889643 | + | 0.456657i | \(0.849047\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.2492 | 0.668586 | ||||||||
\(236\) | 5.07192 | 0.330154 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.70010 | 0.369482 | ||||||||
\(239\) | −23.7211 | −1.53439 | −0.767196 | − | 0.641412i | \(-0.778349\pi\) | ||||
−0.767196 | + | 0.641412i | \(0.778349\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.4044 | 1.37878 | 0.689390 | − | 0.724390i | \(-0.257878\pi\) | ||||
0.689390 | + | 0.724390i | \(0.257878\pi\) | |||||||
\(242\) | −4.70272 | −0.302302 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.55378 | 0.355544 | ||||||||
\(245\) | −11.5859 | −0.740196 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.3171 | 0.656459 | ||||||||
\(248\) | 5.99679 | 0.380797 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.60844 | −0.354709 | ||||||||
\(251\) | −1.11929 | −0.0706487 | −0.0353243 | − | 0.999376i | \(-0.511246\pi\) | ||||
−0.0353243 | + | 0.999376i | \(0.511246\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.55830 | 0.286578 | ||||||||
\(254\) | −6.34158 | −0.397906 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.535280 | 0.0334550 | ||||||||
\(257\) | 5.99320 | 0.373846 | 0.186923 | − | 0.982375i | \(-0.440149\pi\) | ||||
0.186923 | + | 0.982375i | \(0.440149\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 36.8880 | 2.29211 | ||||||||
\(260\) | −5.43584 | −0.337116 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.141110 | 0.00871780 | ||||||||
\(263\) | −22.6606 | −1.39732 | −0.698658 | − | 0.715456i | \(-0.746219\pi\) | ||||
−0.698658 | + | 0.715456i | \(0.746219\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.9961 | −0.798342 | ||||||||
\(266\) | 9.34455 | 0.572951 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.54369 | 0.338635 | ||||||||
\(269\) | 15.1575 | 0.924169 | 0.462084 | − | 0.886836i | \(-0.347102\pi\) | ||||
0.462084 | + | 0.886836i | \(0.347102\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.95810 | 0.604912 | 0.302456 | − | 0.953163i | \(-0.402194\pi\) | ||||
0.302456 | + | 0.953163i | \(0.402194\pi\) | |||||||
\(272\) | −8.24976 | −0.500215 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.53485 | −0.273960 | ||||||||
\(275\) | 12.3793 | 0.746502 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.33062 | −0.320286 | −0.160143 | − | 0.987094i | \(-0.551196\pi\) | ||||
−0.160143 | + | 0.987094i | \(0.551196\pi\) | |||||||
\(278\) | −2.01361 | −0.120769 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.4908 | −0.626943 | ||||||||
\(281\) | 5.27221 | 0.314513 | 0.157257 | − | 0.987558i | \(-0.449735\pi\) | ||||
0.157257 | + | 0.987558i | \(0.449735\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.8471 | 1.53645 | 0.768225 | − | 0.640180i | \(-0.221140\pi\) | ||||
0.768225 | + | 0.640180i | \(0.221140\pi\) | |||||||
\(284\) | −9.24468 | −0.548571 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.45801 | −0.263608 | ||||||||
\(287\) | −30.0220 | −1.77215 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.42210 | −0.436594 | ||||||||
\(290\) | 0.726880 | 0.0426839 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −24.7748 | −1.44984 | ||||||||
\(293\) | 3.67536 | 0.214717 | 0.107358 | − | 0.994220i | \(-0.465761\pi\) | ||||
0.107358 | + | 0.994220i | \(0.465761\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.33400 | 0.252335 | ||||||||
\(296\) | 17.4589 | 1.01478 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.47658 | 0.0855358 | ||||||||
\(299\) | 2.03350 | 0.117600 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.67148 | 0.384538 | ||||||||
\(302\) | 1.92754 | 0.110917 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −13.5244 | −0.775677 | ||||||||
\(305\) | 4.74575 | 0.271741 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.5203 | 1.85603 | 0.928016 | − | 0.372540i | \(-0.121513\pi\) | ||||
0.928016 | + | 0.372540i | \(0.121513\pi\) | |||||||
\(308\) | 30.8752 | 1.75928 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.40490 | 0.136589 | ||||||||
\(311\) | 7.24369 | 0.410752 | 0.205376 | − | 0.978683i | \(-0.434158\pi\) | ||||
0.205376 | + | 0.978683i | \(0.434158\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.1361 | −1.64687 | −0.823434 | − | 0.567412i | \(-0.807945\pi\) | ||||
−0.823434 | + | 0.567412i | \(0.807945\pi\) | |||||||
\(314\) | −3.04313 | −0.171734 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.56485 | 0.200539 | ||||||||
\(317\) | 22.2779 | 1.25125 | 0.625626 | − | 0.780123i | \(-0.284844\pi\) | ||||
0.625626 | + | 0.780123i | \(0.284844\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.55830 | −0.255216 | ||||||||
\(320\) | 4.49073 | 0.251039 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.84182 | 0.102641 | ||||||||
\(323\) | 15.7017 | 0.873666 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.52253 | 0.306335 | ||||||||
\(326\) | −7.05518 | −0.390750 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14.2092 | −0.784574 | ||||||||
\(329\) | −25.9702 | −1.43178 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.57404 | 0.141482 | 0.0707409 | − | 0.997495i | \(-0.477464\pi\) | ||||
0.0707409 | + | 0.997495i | \(0.477464\pi\) | |||||||
\(332\) | 0.300338 | 0.0164832 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.49616 | −0.246019 | ||||||||
\(335\) | 4.73714 | 0.258817 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.9240 | 1.63007 | 0.815033 | − | 0.579415i | \(-0.196719\pi\) | ||||
0.815033 | + | 0.579415i | \(0.196719\pi\) | |||||||
\(338\) | 4.26350 | 0.231904 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.27289 | −0.448661 | ||||||||
\(341\) | −15.0813 | −0.816696 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.54993 | 0.137683 | ||||||||
\(344\) | 3.15757 | 0.170245 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.60470 | −0.140030 | ||||||||
\(347\) | 28.3110 | 1.51981 | 0.759906 | − | 0.650033i | \(-0.225245\pi\) | ||||
0.759906 | + | 0.650033i | \(0.225245\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.2588 | 1.72678 | 0.863388 | − | 0.504540i | \(-0.168338\pi\) | ||||
0.863388 | + | 0.504540i | \(0.168338\pi\) | |||||||
\(350\) | 5.00197 | 0.267366 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 22.3680 | 1.19222 | ||||||||
\(353\) | 27.3821 | 1.45740 | 0.728701 | − | 0.684832i | \(-0.240124\pi\) | ||||
0.728701 | + | 0.684832i | \(0.240124\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.89966 | −0.419271 | ||||||||
\(356\) | −7.86481 | −0.416834 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.55866 | −0.188081 | ||||||||
\(359\) | 22.3917 | 1.18179 | 0.590893 | − | 0.806750i | \(-0.298775\pi\) | ||||
0.590893 | + | 0.806750i | \(0.298775\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.74087 | 0.354783 | ||||||||
\(362\) | −3.61224 | −0.189855 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.7737 | 0.721938 | ||||||||
\(365\) | −21.1703 | −1.10810 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.55651 | 0.394447 | 0.197223 | − | 0.980359i | \(-0.436808\pi\) | ||||
0.197223 | + | 0.980359i | \(0.436808\pi\) | |||||||
\(368\) | −2.66567 | −0.138958 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.00155 | 0.363993 | ||||||||
\(371\) | 32.9304 | 1.70966 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.61281 | −0.238842 | −0.119421 | − | 0.992844i | \(-0.538104\pi\) | ||||
−0.119421 | + | 0.992844i | \(0.538104\pi\) | |||||||
\(374\) | −6.78472 | −0.350829 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.2915 | −0.633888 | ||||||||
\(377\) | −2.03350 | −0.104731 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.3480 | 1.45614 | 0.728069 | − | 0.685504i | \(-0.240418\pi\) | ||||
0.728069 | + | 0.685504i | \(0.240418\pi\) | |||||||
\(380\) | −13.5623 | −0.695732 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.0045 | 0.563040 | ||||||||
\(383\) | −17.9810 | −0.918786 | −0.459393 | − | 0.888233i | \(-0.651933\pi\) | ||||
−0.459393 | + | 0.888233i | \(0.651933\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26.3831 | 1.34461 | ||||||||
\(386\) | 1.63918 | 0.0834321 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 22.3247 | 1.13336 | ||||||||
\(389\) | 17.4058 | 0.882507 | 0.441254 | − | 0.897382i | \(-0.354534\pi\) | ||||
0.441254 | + | 0.897382i | \(0.354534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.09482 | 0.156512 | ||||||||
\(392\) | 13.8945 | 0.701781 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.16673 | 0.461813 | ||||||||
\(395\) | 3.04620 | 0.153271 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.3372 | 1.07088 | 0.535441 | − | 0.844573i | \(-0.320145\pi\) | ||||
0.535441 | + | 0.844573i | \(0.320145\pi\) | |||||||
\(398\) | −6.34688 | −0.318140 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.23935 | −0.361968 | ||||||||
\(401\) | 14.1561 | 0.706920 | 0.353460 | − | 0.935450i | \(-0.385005\pi\) | ||||
0.353460 | + | 0.935450i | \(0.385005\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.72789 | −0.335140 | ||||||||
\(404\) | 4.62635 | 0.230170 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.84182 | −0.0914079 | ||||||||
\(407\) | −43.9071 | −2.17639 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.840710 | −0.0415704 | −0.0207852 | − | 0.999784i | \(-0.506617\pi\) | ||||
−0.0207852 | + | 0.999784i | \(0.506617\pi\) | |||||||
\(410\) | −5.69835 | −0.281422 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 27.2770 | 1.34384 | ||||||||
\(413\) | −10.9818 | −0.540378 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.256641 | 0.0125980 | ||||||||
\(416\) | 9.97856 | 0.489239 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.1226 | −0.544026 | ||||||||
\(419\) | −5.72839 | −0.279850 | −0.139925 | − | 0.990162i | \(-0.544686\pi\) | ||||
−0.139925 | + | 0.990162i | \(0.544686\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.4014 | −0.555672 | −0.277836 | − | 0.960629i | \(-0.589617\pi\) | ||||
−0.277836 | + | 0.960629i | \(0.589617\pi\) | |||||||
\(422\) | −5.40999 | −0.263354 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 15.5857 | 0.756910 | ||||||||
\(425\) | 8.40483 | 0.407694 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.0251 | −0.581936 | ||||||||
\(428\) | 13.1614 | 0.636178 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.26628 | 0.0610656 | ||||||||
\(431\) | 13.3430 | 0.642710 | 0.321355 | − | 0.946959i | \(-0.395862\pi\) | ||||
0.321355 | + | 0.946959i | \(0.395862\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.77877 | 0.181596 | 0.0907980 | − | 0.995869i | \(-0.471058\pi\) | ||||
0.0907980 | + | 0.995869i | \(0.471058\pi\) | |||||||
\(434\) | −6.09371 | −0.292507 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.92621 | −0.283814 | ||||||||
\(437\) | 5.07355 | 0.242701 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.3726 | 0.495060 | 0.247530 | − | 0.968880i | \(-0.420381\pi\) | ||||
0.247530 | + | 0.968880i | \(0.420381\pi\) | |||||||
\(440\) | 12.4870 | 0.595293 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.02672 | −0.143967 | ||||||||
\(443\) | 10.7478 | 0.510645 | 0.255322 | − | 0.966856i | \(-0.417818\pi\) | ||||
0.255322 | + | 0.966856i | \(0.417818\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.72055 | −0.318585 | ||||||||
\(446\) | 2.60879 | 0.123530 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11.3789 | −0.537604 | ||||||||
\(449\) | −16.4083 | −0.774357 | −0.387178 | − | 0.922005i | \(-0.626550\pi\) | ||||
−0.387178 | + | 0.922005i | \(0.626550\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.7347 | 1.68268 | ||||||||
\(452\) | −5.51279 | −0.259300 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.84389 | −0.321199 | ||||||||
\(455\) | 11.7698 | 0.551774 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.278452 | −0.0130254 | −0.00651272 | − | 0.999979i | \(-0.502073\pi\) | ||||
−0.00651272 | + | 0.999979i | \(0.502073\pi\) | |||||||
\(458\) | −8.48632 | −0.396540 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.67314 | −0.124636 | ||||||||
\(461\) | 18.6860 | 0.870294 | 0.435147 | − | 0.900360i | \(-0.356696\pi\) | ||||
0.435147 | + | 0.900360i | \(0.356696\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.8292 | −1.61865 | −0.809325 | − | 0.587361i | \(-0.800167\pi\) | ||||
−0.809325 | + | 0.587361i | \(0.800167\pi\) | |||||||
\(464\) | 2.66567 | 0.123750 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.0622 | 0.605096 | ||||||||
\(467\) | 22.6213 | 1.04679 | 0.523395 | − | 0.852090i | \(-0.324665\pi\) | ||||
0.523395 | + | 0.852090i | \(0.324665\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.0033 | −0.554260 | ||||||||
\(470\) | −4.92929 | −0.227371 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.19761 | −0.239239 | ||||||||
\(473\) | −7.94093 | −0.365125 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.7786 | 0.632206 | ||||||||
\(476\) | 20.9624 | 0.960811 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.4085 | 0.521813 | ||||||||
\(479\) | 27.8673 | 1.27329 | 0.636644 | − | 0.771158i | \(-0.280322\pi\) | ||||
0.636644 | + | 0.771158i | \(0.280322\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.5874 | −0.893106 | ||||||||
\(482\) | −10.2943 | −0.468893 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.2945 | −0.786114 | ||||||||
\(485\) | 19.0767 | 0.866226 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.4508 | −0.518885 | −0.259443 | − | 0.965759i | \(-0.583539\pi\) | ||||
−0.259443 | + | 0.965759i | \(0.583539\pi\) | |||||||
\(488\) | −5.69141 | −0.257638 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.57215 | 0.251724 | ||||||||
\(491\) | −22.6586 | −1.02257 | −0.511285 | − | 0.859411i | \(-0.670830\pi\) | ||||
−0.511285 | + | 0.859411i | \(0.670830\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.09482 | −0.139384 | ||||||||
\(494\) | −4.96191 | −0.223247 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.81943 | 0.396004 | ||||||||
\(497\) | 20.0167 | 0.897872 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.8400 | 0.530032 | 0.265016 | − | 0.964244i | \(-0.414623\pi\) | ||||
0.265016 | + | 0.964244i | \(0.414623\pi\) | |||||||
\(500\) | −20.6254 | −0.922394 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.538312 | 0.0240261 | ||||||||
\(503\) | 33.5152 | 1.49437 | 0.747185 | − | 0.664616i | \(-0.231405\pi\) | ||||
0.747185 | + | 0.664616i | \(0.231405\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.95326 | 0.175918 | ||||||||
\(506\) | −2.19228 | −0.0974588 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23.3215 | −1.03472 | ||||||||
\(509\) | −7.92984 | −0.351484 | −0.175742 | − | 0.984436i | \(-0.556232\pi\) | ||||
−0.175742 | + | 0.984436i | \(0.556232\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 53.6428 | 2.37302 | ||||||||
\(512\) | −22.7438 | −1.00515 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.88239 | −0.127137 | ||||||||
\(515\) | 23.3084 | 1.02709 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.9119 | 1.35950 | ||||||||
\(518\) | −17.7410 | −0.779495 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.57055 | 0.244285 | ||||||||
\(521\) | 45.1228 | 1.97687 | 0.988433 | − | 0.151661i | \(-0.0484621\pi\) | ||||
0.988433 | + | 0.151661i | \(0.0484621\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.7131 | 0.905720 | 0.452860 | − | 0.891582i | \(-0.350404\pi\) | ||||
0.452860 | + | 0.891582i | \(0.350404\pi\) | |||||||
\(524\) | 0.518940 | 0.0226700 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.8985 | 0.475196 | ||||||||
\(527\) | −10.2393 | −0.446031 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 6.25037 | 0.271499 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 34.3651 | 1.48992 | ||||||||
\(533\) | 15.9416 | 0.690506 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.2465 | 0.486229 | ||||||||
\(536\) | −5.68108 | −0.245385 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.28989 | −0.314289 | ||||||||
\(539\) | −34.9433 | −1.50511 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.2474 | −0.698528 | −0.349264 | − | 0.937024i | \(-0.613568\pi\) | ||||
−0.349264 | + | 0.937024i | \(0.613568\pi\) | |||||||
\(542\) | −4.78928 | −0.205717 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15.1865 | 0.651118 | ||||||||
\(545\) | −5.06400 | −0.216918 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.7363 | 0.843864 | 0.421932 | − | 0.906627i | \(-0.361352\pi\) | ||||
0.421932 | + | 0.906627i | \(0.361352\pi\) | |||||||
\(548\) | −16.6772 | −0.712414 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.95375 | −0.253869 | ||||||||
\(551\) | −5.07355 | −0.216140 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.71866 | −0.328231 | ||||||||
\(554\) | 2.56372 | 0.108922 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.40518 | −0.314050 | ||||||||
\(557\) | −35.9309 | −1.52244 | −0.761221 | − | 0.648492i | \(-0.775400\pi\) | ||||
−0.761221 | + | 0.648492i | \(0.775400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.54252 | −0.149833 | ||||||||
\(560\) | −15.4287 | −0.651981 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.53563 | −0.106959 | ||||||||
\(563\) | −42.8625 | −1.80644 | −0.903220 | − | 0.429178i | \(-0.858803\pi\) | ||||
−0.903220 | + | 0.429178i | \(0.858803\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.71073 | −0.198182 | ||||||||
\(566\) | −12.4310 | −0.522513 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.47378 | 0.397511 | ||||||||
\(569\) | −2.91112 | −0.122040 | −0.0610202 | − | 0.998137i | \(-0.519435\pi\) | ||||
−0.0610202 | + | 0.998137i | \(0.519435\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.2792 | −1.18345 | −0.591724 | − | 0.806141i | \(-0.701552\pi\) | ||||
−0.591724 | + | 0.806141i | \(0.701552\pi\) | |||||||
\(572\) | −16.3946 | −0.685492 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.4389 | 0.602667 | ||||||||
\(575\) | 2.71578 | 0.113256 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.4164 | 0.974837 | 0.487419 | − | 0.873168i | \(-0.337939\pi\) | ||||
0.487419 | + | 0.873168i | \(0.337939\pi\) | |||||||
\(578\) | 3.56960 | 0.148476 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.67314 | 0.110996 | ||||||||
\(581\) | −0.650296 | −0.0269788 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −39.1964 | −1.62335 | ||||||||
\(584\) | 25.3888 | 1.05059 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.76764 | −0.0730204 | ||||||||
\(587\) | −9.90376 | −0.408772 | −0.204386 | − | 0.978890i | \(-0.565520\pi\) | ||||
−0.204386 | + | 0.978890i | \(0.565520\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.7860 | −0.691654 | ||||||||
\(590\) | −2.08440 | −0.0858136 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 25.6766 | 1.05530 | ||||||||
\(593\) | −39.4781 | −1.62117 | −0.810585 | − | 0.585621i | \(-0.800851\pi\) | ||||
−0.810585 | + | 0.585621i | \(0.800851\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.9126 | 0.734344 | ||||||||
\(596\) | 5.43019 | 0.222429 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.977997 | −0.0399933 | ||||||||
\(599\) | 28.8979 | 1.18074 | 0.590369 | − | 0.807134i | \(-0.298982\pi\) | ||||
0.590369 | + | 0.807134i | \(0.298982\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.30294 | −0.338684 | −0.169342 | − | 0.985557i | \(-0.554164\pi\) | ||||
−0.169342 | + | 0.985557i | \(0.554164\pi\) | |||||||
\(602\) | −3.20860 | −0.130773 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.08863 | 0.288432 | ||||||||
\(605\) | −14.7783 | −0.600824 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.6030 | −0.876840 | −0.438420 | − | 0.898770i | \(-0.644462\pi\) | ||||
−0.438420 | + | 0.898770i | \(0.644462\pi\) | |||||||
\(608\) | 24.8963 | 1.00968 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.28244 | −0.0924131 | ||||||||
\(611\) | 13.7901 | 0.557886 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.82158 | −0.154352 | −0.0771761 | − | 0.997017i | \(-0.524590\pi\) | ||||
−0.0771761 | + | 0.997017i | \(0.524590\pi\) | |||||||
\(614\) | −15.6404 | −0.631195 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −31.6403 | −1.27483 | ||||||||
\(617\) | 30.6641 | 1.23449 | 0.617246 | − | 0.786770i | \(-0.288248\pi\) | ||||
0.617246 | + | 0.786770i | \(0.288248\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.05425 | 0.323728 | 0.161864 | − | 0.986813i | \(-0.448249\pi\) | ||||
0.161864 | + | 0.986813i | \(0.448249\pi\) | |||||||
\(620\) | 8.84416 | 0.355190 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.48380 | −0.139688 | ||||||||
\(623\) | 17.0290 | 0.682253 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.04569 | −0.161827 | ||||||||
\(626\) | 14.0128 | 0.560063 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.1913 | −0.446581 | ||||||||
\(629\) | −29.8103 | −1.18862 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.6692 | −0.942257 | −0.471128 | − | 0.882065i | \(-0.656153\pi\) | ||||
−0.471128 | + | 0.882065i | \(0.656153\pi\) | |||||||
\(632\) | −3.65319 | −0.145316 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.7144 | −0.425523 | ||||||||
\(635\) | −19.9284 | −0.790836 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.5885 | −0.617639 | ||||||||
\(638\) | 2.19228 | 0.0867933 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.9926 | −0.671691 | ||||||||
\(641\) | 41.6923 | 1.64674 | 0.823372 | − | 0.567501i | \(-0.192090\pi\) | ||||
0.823372 | + | 0.567501i | \(0.192090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.2442 | −1.03497 | −0.517486 | − | 0.855692i | \(-0.673132\pi\) | ||||
−0.517486 | + | 0.855692i | \(0.673132\pi\) | |||||||
\(644\) | 6.77339 | 0.266909 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.55162 | −0.297115 | ||||||||
\(647\) | 8.24798 | 0.324262 | 0.162131 | − | 0.986769i | \(-0.448163\pi\) | ||||
0.162131 | + | 0.986769i | \(0.448163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.0714 | 0.513098 | ||||||||
\(650\) | −2.65602 | −0.104178 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −25.9458 | −1.01612 | ||||||||
\(653\) | −0.574006 | −0.0224626 | −0.0112313 | − | 0.999937i | \(-0.503575\pi\) | ||||
−0.0112313 | + | 0.999937i | \(0.503575\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.443439 | 0.0173266 | ||||||||
\(656\) | −20.8974 | −0.815907 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.4902 | 0.486918 | ||||||||
\(659\) | 50.4367 | 1.96474 | 0.982368 | − | 0.186957i | \(-0.0598624\pi\) | ||||
0.982368 | + | 0.186957i | \(0.0598624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.5906 | 0.800880 | 0.400440 | − | 0.916323i | \(-0.368857\pi\) | ||||
0.400440 | + | 0.916323i | \(0.368857\pi\) | |||||||
\(662\) | −1.23796 | −0.0481149 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.307781 | −0.0119442 | ||||||||
\(665\) | 29.3653 | 1.13874 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −16.5349 | −0.639753 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.27829 | −0.0880181 | ||||||||
\(671\) | 14.3133 | 0.552558 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.0937 | −1.73823 | −0.869117 | − | 0.494607i | \(-0.835312\pi\) | ||||
−0.869117 | + | 0.494607i | \(0.835312\pi\) | |||||||
\(674\) | −14.3917 | −0.554349 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.6793 | 0.603048 | ||||||||
\(677\) | −33.5470 | −1.28932 | −0.644658 | − | 0.764471i | \(-0.723000\pi\) | ||||
−0.644658 | + | 0.764471i | \(0.723000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −48.3377 | −1.85503 | ||||||||
\(680\) | 8.47791 | 0.325113 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.25323 | 0.277740 | ||||||||
\(683\) | −25.6859 | −0.982844 | −0.491422 | − | 0.870922i | \(-0.663523\pi\) | ||||
−0.491422 | + | 0.870922i | \(0.663523\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.2508 | −0.544495 | ||||||||
\(686\) | −1.22637 | −0.0468231 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.64381 | 0.177044 | ||||||||
\(689\) | −17.4859 | −0.666158 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.3465 | 0.850101 | 0.425050 | − | 0.905170i | \(-0.360256\pi\) | ||||
0.425050 | + | 0.905170i | \(0.360256\pi\) | |||||||
\(692\) | −9.57893 | −0.364136 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.6160 | −0.516855 | ||||||||
\(695\) | −6.32779 | −0.240027 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.2617 | 0.918979 | ||||||||
\(698\) | −15.5147 | −0.587238 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 18.3950 | 0.695266 | ||||||||
\(701\) | −33.6787 | −1.27203 | −0.636013 | − | 0.771678i | \(-0.719418\pi\) | ||||
−0.636013 | + | 0.771678i | \(0.719418\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −48.8701 | −1.84317 | ||||||||
\(704\) | 13.5441 | 0.510463 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.1692 | −0.495630 | ||||||||
\(707\) | −10.0170 | −0.376730 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.22302 | 0.271266 | 0.135633 | − | 0.990759i | \(-0.456693\pi\) | ||||
0.135633 | + | 0.990759i | \(0.456693\pi\) | |||||||
\(710\) | 3.79928 | 0.142585 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.05972 | 0.302051 | ||||||||
\(713\) | −3.30853 | −0.123905 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.0093 | −0.523919 | ||||||||
\(716\) | −13.0872 | −0.489091 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.7691 | −0.401900 | ||||||||
\(719\) | 27.3138 | 1.01863 | 0.509316 | − | 0.860579i | \(-0.329898\pi\) | ||||
0.509316 | + | 0.860579i | \(0.329898\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −59.0605 | −2.19953 | ||||||||
\(722\) | −3.24197 | −0.120654 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.2842 | −0.493705 | ||||||||
\(725\) | −2.71578 | −0.100861 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.5084 | −1.53946 | −0.769730 | − | 0.638370i | \(-0.779609\pi\) | ||||
−0.769730 | + | 0.638370i | \(0.779609\pi\) | |||||||
\(728\) | −14.1150 | −0.523138 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.1817 | 0.376842 | ||||||||
\(731\) | −5.39143 | −0.199409 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.4918 | −0.461394 | −0.230697 | − | 0.973026i | \(-0.574101\pi\) | ||||
−0.230697 | + | 0.973026i | \(0.574101\pi\) | |||||||
\(734\) | −3.63425 | −0.134143 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.90709 | 0.180878 | ||||||||
\(737\) | 14.2873 | 0.526279 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.0795 | −1.10649 | −0.553246 | − | 0.833018i | \(-0.686611\pi\) | ||||
−0.553246 | + | 0.833018i | \(0.686611\pi\) | |||||||
\(740\) | 25.7486 | 0.946537 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.8376 | −0.581417 | ||||||||
\(743\) | −19.8015 | −0.726445 | −0.363223 | − | 0.931702i | \(-0.618324\pi\) | ||||
−0.363223 | + | 0.931702i | \(0.618324\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.64015 | 0.170002 | ||||||||
\(746\) | 2.21850 | 0.0812249 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −24.9512 | −0.912306 | ||||||||
\(749\) | −28.4972 | −1.04126 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.1667 | −0.699405 | −0.349702 | − | 0.936861i | \(-0.613717\pi\) | ||||
−0.349702 | + | 0.936861i | \(0.613717\pi\) | |||||||
\(752\) | −18.0771 | −0.659203 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.977997 | 0.0356166 | ||||||||
\(755\) | 6.05730 | 0.220448 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.95766 | −0.180189 | −0.0900946 | − | 0.995933i | \(-0.528717\pi\) | ||||
−0.0900946 | + | 0.995933i | \(0.528717\pi\) | |||||||
\(758\) | −13.6338 | −0.495200 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.8984 | 0.504148 | ||||||||
\(761\) | −21.5501 | −0.781189 | −0.390595 | − | 0.920563i | \(-0.627731\pi\) | ||||
−0.390595 | + | 0.920563i | \(0.627731\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.8315 | 0.464532 | ||||||||
\(764\) | 40.4697 | 1.46414 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.64783 | 0.312459 | ||||||||
\(767\) | 5.83128 | 0.210555 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.5390 | 1.38975 | 0.694876 | − | 0.719130i | \(-0.255459\pi\) | ||||
0.694876 | + | 0.719130i | \(0.255459\pi\) | |||||||
\(770\) | −12.6888 | −0.457272 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.02818 | 0.216959 | ||||||||
\(773\) | 39.8782 | 1.43432 | 0.717160 | − | 0.696909i | \(-0.245442\pi\) | ||||
0.717160 | + | 0.696909i | \(0.245442\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.98522 | −0.322759 | ||||||||
\(776\) | −22.8779 | −0.821270 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.37118 | −0.300121 | ||||||||
\(779\) | 39.7739 | 1.42505 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.8255 | −0.852544 | ||||||||
\(782\) | −1.48843 | −0.0532262 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20.4346 | 0.729807 | ||||||||
\(785\) | −9.56306 | −0.341320 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −54.2889 | −1.93519 | −0.967595 | − | 0.252506i | \(-0.918745\pi\) | ||||
−0.967595 | + | 0.252506i | \(0.918745\pi\) | |||||||
\(788\) | 33.7112 | 1.20091 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.46505 | −0.0521240 | ||||||||
\(791\) | 11.9364 | 0.424409 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.38528 | 0.226748 | ||||||||
\(794\) | −10.2620 | −0.364183 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −23.3410 | −0.827300 | ||||||||
\(797\) | 6.62914 | 0.234816 | 0.117408 | − | 0.993084i | \(-0.462541\pi\) | ||||
0.117408 | + | 0.993084i | \(0.462541\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.9873 | 0.742478 | ||||||||
\(800\) | 13.3265 | 0.471164 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.80825 | −0.240408 | ||||||||
\(803\) | −63.8500 | −2.25322 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.78793 | 0.203998 | ||||||||
\(806\) | 3.23573 | 0.113974 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.74100 | −0.166788 | ||||||||
\(809\) | −18.7279 | −0.658439 | −0.329219 | − | 0.944253i | \(-0.606786\pi\) | ||||
−0.329219 | + | 0.944253i | \(0.606786\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.1555 | 0.918443 | 0.459222 | − | 0.888322i | \(-0.348128\pi\) | ||||
0.459222 | + | 0.888322i | \(0.348128\pi\) | |||||||
\(812\) | −6.77339 | −0.237700 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 21.1168 | 0.740143 | ||||||||
\(815\) | −22.1710 | −0.776615 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.83853 | −0.309221 | ||||||||
\(818\) | 0.404333 | 0.0141372 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.9560 | −0.731816 | ||||||||
\(821\) | −37.4288 | −1.30628 | −0.653138 | − | 0.757239i | \(-0.726548\pi\) | ||||
−0.653138 | + | 0.757239i | \(0.726548\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.8575 | 1.11048 | 0.555241 | − | 0.831690i | \(-0.312626\pi\) | ||||
0.555241 | + | 0.831690i | \(0.312626\pi\) | |||||||
\(824\) | −27.9529 | −0.973787 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.28161 | 0.183771 | ||||||||
\(827\) | 39.9645 | 1.38970 | 0.694851 | − | 0.719154i | \(-0.255470\pi\) | ||||
0.694851 | + | 0.719154i | \(0.255470\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.3349 | −0.602066 | −0.301033 | − | 0.953614i | \(-0.597331\pi\) | ||||
−0.301033 | + | 0.953614i | \(0.597331\pi\) | |||||||
\(830\) | −0.123430 | −0.00428431 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.04215 | 0.209474 | ||||||||
\(833\) | −23.7244 | −0.822002 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.1292 | −0.488961 | ||||||||
\(836\) | −40.9042 | −1.41470 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.75503 | 0.0951709 | ||||||||
\(839\) | 17.4594 | 0.602765 | 0.301382 | − | 0.953503i | \(-0.402552\pi\) | ||||
0.301382 | + | 0.953503i | \(0.402552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 5.48344 | 0.188972 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −19.8955 | −0.684833 | ||||||||
\(845\) | 13.3981 | 0.460907 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.4463 | 1.28667 | ||||||||
\(848\) | 22.9218 | 0.787138 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.04224 | −0.138648 | ||||||||
\(851\) | −9.63233 | −0.330192 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.0237 | 1.09647 | 0.548235 | − | 0.836324i | \(-0.315300\pi\) | ||||
0.548235 | + | 0.836324i | \(0.315300\pi\) | |||||||
\(854\) | 5.78339 | 0.197904 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.4875 | −0.460994 | ||||||||
\(857\) | 6.53401 | 0.223197 | 0.111599 | − | 0.993753i | \(-0.464403\pi\) | ||||
0.111599 | + | 0.993753i | \(0.464403\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.81937 | −0.0961958 | −0.0480979 | − | 0.998843i | \(-0.515316\pi\) | ||||
−0.0480979 | + | 0.998843i | \(0.515316\pi\) | |||||||
\(860\) | 4.65683 | 0.158797 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.41722 | −0.218571 | ||||||||
\(863\) | 1.36845 | 0.0465825 | 0.0232913 | − | 0.999729i | \(-0.492585\pi\) | ||||
0.0232913 | + | 0.999729i | \(0.492585\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.18528 | −0.278308 | ||||||||
\(866\) | −1.81737 | −0.0617567 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −22.4100 | −0.760644 | ||||||||
\(869\) | 9.18738 | 0.311661 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.37369 | 0.215964 | ||||||||
\(872\) | 6.07307 | 0.205660 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.44008 | −0.0825371 | ||||||||
\(875\) | 44.6583 | 1.50973 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.4787 | −1.02919 | −0.514597 | − | 0.857432i | \(-0.672058\pi\) | ||||
−0.514597 | + | 0.857432i | \(0.672058\pi\) | |||||||
\(878\) | −4.98865 | −0.168359 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 18.3645 | 0.619066 | ||||||||
\(881\) | −26.0641 | −0.878122 | −0.439061 | − | 0.898457i | \(-0.644689\pi\) | ||||
−0.439061 | + | 0.898457i | \(0.644689\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.7473 | −1.23664 | −0.618322 | − | 0.785925i | \(-0.712187\pi\) | ||||
−0.618322 | + | 0.785925i | \(0.712187\pi\) | |||||||
\(884\) | −11.1310 | −0.374374 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.16909 | −0.173659 | ||||||||
\(887\) | 24.6091 | 0.826293 | 0.413147 | − | 0.910665i | \(-0.364430\pi\) | ||||
0.413147 | + | 0.910665i | \(0.364430\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 50.4961 | 1.69358 | ||||||||
\(890\) | 3.23220 | 0.108344 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.59399 | 0.321231 | ||||||||
\(893\) | 34.4059 | 1.15135 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.1831 | −0.373811 | ||||||||
\(896\) | 43.0570 | 1.43843 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.89147 | 0.263342 | ||||||||
\(899\) | 3.30853 | 0.110346 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.6120 | −0.886575 | ||||||||
\(902\) | −17.1863 | −0.572242 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.64941 | 0.187897 | ||||||||
\(905\) | −11.3515 | −0.377336 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 53.1771 | 1.76572 | 0.882859 | − | 0.469638i | \(-0.155616\pi\) | ||||
0.882859 | + | 0.469638i | \(0.155616\pi\) | |||||||
\(908\) | −25.1688 | −0.835255 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.66058 | −0.187646 | ||||||||
\(911\) | −32.6481 | −1.08168 | −0.540840 | − | 0.841126i | \(-0.681893\pi\) | ||||
−0.540840 | + | 0.841126i | \(0.681893\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.774035 | 0.0256168 | ||||||||
\(914\) | 0.133920 | 0.00442966 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −31.2089 | −1.03117 | ||||||||
\(917\) | −1.12362 | −0.0371051 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.2070 | 1.65618 | 0.828089 | − | 0.560597i | \(-0.189428\pi\) | ||||
0.828089 | + | 0.560597i | \(0.189428\pi\) | |||||||
\(920\) | 2.73939 | 0.0903150 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.98689 | −0.295968 | ||||||||
\(923\) | −10.6288 | −0.349851 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.1593 | −0.860111 | ||||||||
\(926\) | 16.7509 | 0.550467 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.90709 | −0.161083 | ||||||||
\(929\) | 4.68086 | 0.153574 | 0.0767870 | − | 0.997048i | \(-0.475534\pi\) | ||||
0.0767870 | + | 0.997048i | \(0.475534\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38.8930 | −1.27467 | ||||||||
\(932\) | 48.0371 | 1.57351 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.8796 | −0.355990 | ||||||||
\(935\) | −21.3210 | −0.697272 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56.6795 | −1.85164 | −0.925819 | − | 0.377966i | \(-0.876624\pi\) | ||||
−0.925819 | + | 0.377966i | \(0.876624\pi\) | |||||||
\(938\) | 5.77289 | 0.188492 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.1278 | −0.591262 | ||||||||
\(941\) | −5.57428 | −0.181716 | −0.0908582 | − | 0.995864i | \(-0.528961\pi\) | ||||
−0.0908582 | + | 0.995864i | \(0.528961\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.83947 | 0.255288 | ||||||||
\(944\) | −7.64408 | −0.248794 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.81913 | 0.124171 | ||||||||
\(947\) | −25.1058 | −0.815828 | −0.407914 | − | 0.913020i | \(-0.633744\pi\) | ||||
−0.407914 | + | 0.913020i | \(0.633744\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.4841 | −0.924631 | ||||||||
\(950\) | −6.62672 | −0.214999 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −21.4819 | −0.696233 | ||||||||
\(953\) | 18.7777 | 0.608269 | 0.304134 | − | 0.952629i | \(-0.401633\pi\) | ||||
0.304134 | + | 0.952629i | \(0.401633\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34.5817 | 1.11904 | ||||||||
\(956\) | 41.9554 | 1.35694 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.4026 | −0.433017 | ||||||||
\(959\) | 36.1097 | 1.16604 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.0536 | −0.646892 | ||||||||
\(962\) | 9.42039 | 0.303726 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −37.8579 | −1.21932 | ||||||||
\(965\) | 5.15113 | 0.165821 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.19383 | −0.134864 | −0.0674322 | − | 0.997724i | \(-0.521481\pi\) | ||||
−0.0674322 | + | 0.997724i | \(0.521481\pi\) | |||||||
\(968\) | 17.7231 | 0.569642 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.17478 | −0.294584 | ||||||||
\(971\) | −5.18080 | −0.166260 | −0.0831300 | − | 0.996539i | \(-0.526492\pi\) | ||||
−0.0831300 | + | 0.996539i | \(0.526492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.0338 | 0.514020 | ||||||||
\(974\) | 5.50718 | 0.176461 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.37031 | −0.267927 | ||||||||
\(977\) | −22.3619 | −0.715421 | −0.357711 | − | 0.933832i | \(-0.616443\pi\) | ||||
−0.357711 | + | 0.933832i | \(0.616443\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.2693 | −0.647810 | ||||||||
\(980\) | 20.4919 | 0.654590 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.8975 | 0.347753 | ||||||||
\(983\) | −29.6255 | −0.944907 | −0.472454 | − | 0.881355i | \(-0.656632\pi\) | ||||
−0.472454 | + | 0.881355i | \(0.656632\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.8065 | 0.917852 | ||||||||
\(986\) | 1.48843 | 0.0474013 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18.2477 | −0.580537 | ||||||||
\(989\) | −1.74208 | −0.0553950 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.5311 | −1.03339 | −0.516693 | − | 0.856171i | \(-0.672837\pi\) | ||||
−0.516693 | + | 0.856171i | \(0.672837\pi\) | |||||||
\(992\) | −16.2352 | −0.515469 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.62689 | −0.305346 | ||||||||
\(995\) | −19.9451 | −0.632302 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.00782078 | 0.000247687 0 | 0.000123843 | − | 1.00000i | \(-0.499961\pi\) | ||||
0.000123843 | 1.00000i | \(0.499961\pi\) | ||||||||
\(998\) | −5.69437 | −0.180252 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.w.1.14 | yes | 30 | |
3.2 | odd | 2 | 6003.2.a.v.1.17 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.v.1.17 | ✓ | 30 | 3.2 | odd | 2 | ||
6003.2.a.w.1.14 | yes | 30 | 1.1 | even | 1 | trivial |