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: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.08661 | −1.47545 | −0.737727 | − | 0.675099i | \(-0.764101\pi\) | ||||
−0.737727 | + | 0.675099i | \(0.764101\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.35393 | 1.17696 | ||||||||
\(5\) | −1.43041 | −0.639698 | −0.319849 | − | 0.947468i | \(-0.603632\pi\) | ||||
−0.319849 | + | 0.947468i | \(0.603632\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.274571 | −0.103778 | −0.0518890 | − | 0.998653i | \(-0.516524\pi\) | ||||
−0.0518890 | + | 0.998653i | \(0.516524\pi\) | |||||||
\(8\) | −0.738503 | −0.261100 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.98470 | 0.943845 | ||||||||
\(11\) | 6.10520 | 1.84079 | 0.920394 | − | 0.390993i | \(-0.127868\pi\) | ||||
0.920394 | + | 0.390993i | \(0.127868\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.188265 | 0.0522152 | 0.0261076 | − | 0.999659i | \(-0.491689\pi\) | ||||
0.0261076 | + | 0.999659i | \(0.491689\pi\) | |||||||
\(14\) | 0.572921 | 0.153120 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.16689 | −0.791721 | ||||||||
\(17\) | 2.24526 | 0.544554 | 0.272277 | − | 0.962219i | \(-0.412223\pi\) | ||||
0.272277 | + | 0.962219i | \(0.412223\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.65245 | 0.837929 | 0.418965 | − | 0.908003i | \(-0.362393\pi\) | ||||
0.418965 | + | 0.908003i | \(0.362393\pi\) | |||||||
\(20\) | −3.36708 | −0.752901 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −12.7391 | −2.71600 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.95393 | −0.590786 | ||||||||
\(26\) | −0.392834 | −0.0770412 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.646319 | −0.122143 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.05707 | −0.728671 | −0.364336 | − | 0.931268i | \(-0.618704\pi\) | ||||
−0.364336 | + | 0.931268i | \(0.618704\pi\) | |||||||
\(32\) | 8.08505 | 1.42925 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.68496 | −0.803465 | ||||||||
\(35\) | 0.392749 | 0.0663866 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.16777 | −0.685178 | −0.342589 | − | 0.939485i | \(-0.611304\pi\) | ||||
−0.342589 | + | 0.939485i | \(0.611304\pi\) | |||||||
\(38\) | −7.62122 | −1.23633 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.05636 | 0.167025 | ||||||||
\(41\) | 3.24174 | 0.506275 | 0.253138 | − | 0.967430i | \(-0.418537\pi\) | ||||
0.253138 | + | 0.967430i | \(0.418537\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.69667 | −0.716236 | −0.358118 | − | 0.933676i | \(-0.616581\pi\) | ||||
−0.358118 | + | 0.933676i | \(0.616581\pi\) | |||||||
\(44\) | 14.3712 | 2.16654 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.08661 | 0.307653 | ||||||||
\(47\) | −6.10569 | −0.890606 | −0.445303 | − | 0.895380i | \(-0.646904\pi\) | ||||
−0.445303 | + | 0.895380i | \(0.646904\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.92461 | −0.989230 | ||||||||
\(50\) | 6.16369 | 0.871677 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.443161 | 0.0614554 | ||||||||
\(53\) | −3.87730 | −0.532588 | −0.266294 | − | 0.963892i | \(-0.585799\pi\) | ||||
−0.266294 | + | 0.963892i | \(0.585799\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.73294 | −1.17755 | ||||||||
\(56\) | 0.202771 | 0.0270965 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.08661 | 0.273985 | ||||||||
\(59\) | −2.91676 | −0.379730 | −0.189865 | − | 0.981810i | \(-0.560805\pi\) | ||||
−0.189865 | + | 0.981810i | \(0.560805\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.77700 | −0.355559 | −0.177779 | − | 0.984070i | \(-0.556891\pi\) | ||||
−0.177779 | + | 0.984070i | \(0.556891\pi\) | |||||||
\(62\) | 8.46551 | 1.07512 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.5365 | −1.31707 | ||||||||
\(65\) | −0.269296 | −0.0334020 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.02715 | 0.858502 | 0.429251 | − | 0.903185i | \(-0.358778\pi\) | ||||
0.429251 | + | 0.903185i | \(0.358778\pi\) | |||||||
\(68\) | 5.28516 | 0.640920 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.819512 | −0.0979504 | ||||||||
\(71\) | 3.49275 | 0.414514 | 0.207257 | − | 0.978287i | \(-0.433546\pi\) | ||||
0.207257 | + | 0.978287i | \(0.433546\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.1979 | −1.42766 | −0.713830 | − | 0.700319i | \(-0.753041\pi\) | ||||
−0.713830 | + | 0.700319i | \(0.753041\pi\) | |||||||
\(74\) | 8.69650 | 1.01095 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.59759 | 0.986211 | ||||||||
\(77\) | −1.67631 | −0.191033 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.81856 | −0.992165 | −0.496083 | − | 0.868275i | \(-0.665229\pi\) | ||||
−0.496083 | + | 0.868275i | \(0.665229\pi\) | |||||||
\(80\) | 4.52994 | 0.506463 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.76424 | −0.746986 | ||||||||
\(83\) | 2.42899 | 0.266616 | 0.133308 | − | 0.991075i | \(-0.457440\pi\) | ||||
0.133308 | + | 0.991075i | \(0.457440\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.21163 | −0.348351 | ||||||||
\(86\) | 9.80011 | 1.05677 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.50871 | −0.480630 | ||||||||
\(89\) | 1.75647 | 0.186185 | 0.0930926 | − | 0.995657i | \(-0.470325\pi\) | ||||
0.0930926 | + | 0.995657i | \(0.470325\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0516920 | −0.00541879 | ||||||||
\(92\) | −2.35393 | −0.245414 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.7402 | 1.31405 | ||||||||
\(95\) | −5.22450 | −0.536022 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.73211 | −0.582008 | −0.291004 | − | 0.956722i | \(-0.593989\pi\) | ||||
−0.291004 | + | 0.956722i | \(0.593989\pi\) | |||||||
\(98\) | 14.4489 | 1.45956 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.95333 | −0.695333 | ||||||||
\(101\) | −9.23902 | −0.919317 | −0.459659 | − | 0.888096i | \(-0.652028\pi\) | ||||
−0.459659 | + | 0.888096i | \(0.652028\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.23178 | −0.712568 | −0.356284 | − | 0.934378i | \(-0.615957\pi\) | ||||
−0.356284 | + | 0.934378i | \(0.615957\pi\) | |||||||
\(104\) | −0.139034 | −0.0136334 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.09040 | 0.785809 | ||||||||
\(107\) | 3.16077 | 0.305563 | 0.152781 | − | 0.988260i | \(-0.451177\pi\) | ||||
0.152781 | + | 0.988260i | \(0.451177\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.56401 | 0.916066 | 0.458033 | − | 0.888935i | \(-0.348554\pi\) | ||||
0.458033 | + | 0.888935i | \(0.348554\pi\) | |||||||
\(110\) | 18.2222 | 1.73742 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.869534 | 0.0821633 | ||||||||
\(113\) | 19.3625 | 1.82147 | 0.910734 | − | 0.412994i | \(-0.135517\pi\) | ||||
0.910734 | + | 0.412994i | \(0.135517\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.43041 | 0.133386 | ||||||||
\(116\) | −2.35393 | −0.218556 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.08613 | 0.560274 | ||||||||
\(119\) | −0.616482 | −0.0565128 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.2735 | 2.38850 | ||||||||
\(122\) | 5.79451 | 0.524610 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.55004 | −0.857619 | ||||||||
\(125\) | 11.3774 | 1.01762 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.6479 | −1.12232 | −0.561161 | − | 0.827706i | \(-0.689645\pi\) | ||||
−0.561161 | + | 0.827706i | \(0.689645\pi\) | |||||||
\(128\) | 5.81552 | 0.514024 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.561914 | 0.0492831 | ||||||||
\(131\) | −7.81787 | −0.683050 | −0.341525 | − | 0.939873i | \(-0.610943\pi\) | ||||
−0.341525 | + | 0.939873i | \(0.610943\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00286 | −0.0869586 | ||||||||
\(134\) | −14.6629 | −1.26668 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.65813 | −0.142183 | ||||||||
\(137\) | 2.22227 | 0.189861 | 0.0949305 | − | 0.995484i | \(-0.469737\pi\) | ||||
0.0949305 | + | 0.995484i | \(0.469737\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.7510 | 1.16635 | 0.583174 | − | 0.812347i | \(-0.301811\pi\) | ||||
0.583174 | + | 0.812347i | \(0.301811\pi\) | |||||||
\(140\) | 0.924501 | 0.0781346 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.28800 | −0.611595 | ||||||||
\(143\) | 1.14939 | 0.0961171 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.43041 | 0.118789 | ||||||||
\(146\) | 25.4523 | 2.10645 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.81063 | −0.806428 | ||||||||
\(149\) | −6.77408 | −0.554954 | −0.277477 | − | 0.960732i | \(-0.589498\pi\) | ||||
−0.277477 | + | 0.960732i | \(0.589498\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.6096 | −0.863395 | −0.431698 | − | 0.902018i | \(-0.642085\pi\) | ||||
−0.431698 | + | 0.902018i | \(0.642085\pi\) | |||||||
\(152\) | −2.69734 | −0.218784 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.49780 | 0.281861 | ||||||||
\(155\) | 5.80327 | 0.466130 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.0603 | 1.36156 | 0.680778 | − | 0.732489i | \(-0.261642\pi\) | ||||
0.680778 | + | 0.732489i | \(0.261642\pi\) | |||||||
\(158\) | 18.4009 | 1.46389 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −11.5649 | −0.914288 | ||||||||
\(161\) | 0.274571 | 0.0216392 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.0671 | −1.88508 | −0.942539 | − | 0.334096i | \(-0.891569\pi\) | ||||
−0.942539 | + | 0.334096i | \(0.891569\pi\) | |||||||
\(164\) | 7.63082 | 0.595867 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.06835 | −0.393380 | ||||||||
\(167\) | −4.02327 | −0.311330 | −0.155665 | − | 0.987810i | \(-0.549752\pi\) | ||||
−0.155665 | + | 0.987810i | \(0.549752\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9646 | −0.997274 | ||||||||
\(170\) | 6.70141 | 0.513975 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.0556 | −0.842983 | ||||||||
\(173\) | 0.0249861 | 0.00189966 | 0.000949830 | − | 1.00000i | \(-0.499698\pi\) | ||||
0.000949830 | 1.00000i | \(0.499698\pi\) | ||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.811063 | 0.0613106 | ||||||||
\(176\) | −19.3345 | −1.45739 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.66506 | −0.274707 | ||||||||
\(179\) | 1.00959 | 0.0754606 | 0.0377303 | − | 0.999288i | \(-0.487987\pi\) | ||||
0.0377303 | + | 0.999288i | \(0.487987\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.8161 | 1.69591 | 0.847955 | − | 0.530069i | \(-0.177834\pi\) | ||||
0.847955 | + | 0.530069i | \(0.177834\pi\) | |||||||
\(182\) | 0.107861 | 0.00799518 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.738503 | 0.0544432 | ||||||||
\(185\) | 5.96162 | 0.438307 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.7077 | 1.00241 | ||||||||
\(188\) | −14.3723 | −1.04821 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.9015 | 0.790875 | ||||||||
\(191\) | −2.91312 | −0.210786 | −0.105393 | − | 0.994431i | \(-0.533610\pi\) | ||||
−0.105393 | + | 0.994431i | \(0.533610\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.51894 | −0.253299 | −0.126650 | − | 0.991948i | \(-0.540422\pi\) | ||||
−0.126650 | + | 0.991948i | \(0.540422\pi\) | |||||||
\(194\) | 11.9607 | 0.858725 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16.3000 | −1.16429 | ||||||||
\(197\) | −14.7731 | −1.05254 | −0.526272 | − | 0.850317i | \(-0.676410\pi\) | ||||
−0.526272 | + | 0.850317i | \(0.676410\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.7774 | 1.68553 | 0.842767 | − | 0.538278i | \(-0.180925\pi\) | ||||
0.842767 | + | 0.538278i | \(0.180925\pi\) | |||||||
\(200\) | 2.18149 | 0.154254 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 19.2782 | 1.35641 | ||||||||
\(203\) | 0.274571 | 0.0192711 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.63702 | −0.323864 | ||||||||
\(206\) | 15.0899 | 1.05136 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.596213 | −0.0413399 | ||||||||
\(209\) | 22.2989 | 1.54245 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.588832 | 0.0405369 | 0.0202684 | − | 0.999795i | \(-0.493548\pi\) | ||||
0.0202684 | + | 0.999795i | \(0.493548\pi\) | |||||||
\(212\) | −9.12688 | −0.626837 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.59527 | −0.450844 | ||||||||
\(215\) | 6.71817 | 0.458175 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.11395 | 0.0756201 | ||||||||
\(218\) | −19.9563 | −1.35161 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −20.5567 | −1.38593 | ||||||||
\(221\) | 0.422702 | 0.0284340 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.5937 | −1.17816 | −0.589079 | − | 0.808075i | \(-0.700509\pi\) | ||||
−0.589079 | + | 0.808075i | \(0.700509\pi\) | |||||||
\(224\) | −2.21992 | −0.148325 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −40.4018 | −2.68749 | ||||||||
\(227\) | −27.3659 | −1.81634 | −0.908169 | − | 0.418603i | \(-0.862520\pi\) | ||||
−0.908169 | + | 0.418603i | \(0.862520\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.2749 | −1.33980 | −0.669900 | − | 0.742451i | \(-0.733663\pi\) | ||||
−0.669900 | + | 0.742451i | \(0.733663\pi\) | |||||||
\(230\) | −2.98470 | −0.196805 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.738503 | 0.0484851 | ||||||||
\(233\) | 3.03886 | 0.199082 | 0.0995412 | − | 0.995033i | \(-0.468263\pi\) | ||||
0.0995412 | + | 0.995033i | \(0.468263\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.73363 | 0.569719 | ||||||||
\(236\) | −6.86584 | −0.446928 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.28635 | 0.0833820 | ||||||||
\(239\) | 1.74365 | 0.112787 | 0.0563936 | − | 0.998409i | \(-0.482040\pi\) | ||||
0.0563936 | + | 0.998409i | \(0.482040\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.99474 | 0.257324 | 0.128662 | − | 0.991689i | \(-0.458932\pi\) | ||||
0.128662 | + | 0.991689i | \(0.458932\pi\) | |||||||
\(242\) | −54.8224 | −3.52412 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.53685 | −0.418479 | ||||||||
\(245\) | 9.90503 | 0.632809 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.687627 | 0.0437527 | ||||||||
\(248\) | 2.99616 | 0.190256 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −23.7401 | −1.50146 | ||||||||
\(251\) | 7.41675 | 0.468141 | 0.234070 | − | 0.972220i | \(-0.424795\pi\) | ||||
0.234070 | + | 0.972220i | \(0.424795\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.10520 | −0.383831 | ||||||||
\(254\) | 26.3913 | 1.65594 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.93839 | 0.558649 | ||||||||
\(257\) | −19.0615 | −1.18902 | −0.594512 | − | 0.804087i | \(-0.702655\pi\) | ||||
−0.594512 | + | 0.804087i | \(0.702655\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.14435 | 0.0711064 | ||||||||
\(260\) | −0.633902 | −0.0393129 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.3128 | 1.00781 | ||||||||
\(263\) | −2.53582 | −0.156365 | −0.0781827 | − | 0.996939i | \(-0.524912\pi\) | ||||
−0.0781827 | + | 0.996939i | \(0.524912\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.54613 | 0.340696 | ||||||||
\(266\) | 2.09257 | 0.128303 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16.5414 | 1.01043 | ||||||||
\(269\) | 4.13080 | 0.251859 | 0.125930 | − | 0.992039i | \(-0.459809\pi\) | ||||
0.125930 | + | 0.992039i | \(0.459809\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.10014 | −0.249066 | −0.124533 | − | 0.992215i | \(-0.539743\pi\) | ||||
−0.124533 | + | 0.992215i | \(0.539743\pi\) | |||||||
\(272\) | −7.11047 | −0.431135 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.63700 | −0.280131 | ||||||||
\(275\) | −18.0343 | −1.08751 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.14419 | 0.429253 | 0.214626 | − | 0.976696i | \(-0.431147\pi\) | ||||
0.214626 | + | 0.976696i | \(0.431147\pi\) | |||||||
\(278\) | −28.6930 | −1.72089 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.290046 | −0.0173336 | ||||||||
\(281\) | 15.6506 | 0.933635 | 0.466817 | − | 0.884354i | \(-0.345401\pi\) | ||||
0.466817 | + | 0.884354i | \(0.345401\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.24117 | 0.489887 | 0.244943 | − | 0.969537i | \(-0.421231\pi\) | ||||
0.244943 | + | 0.969537i | \(0.421231\pi\) | |||||||
\(284\) | 8.22168 | 0.487867 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.39833 | −0.141816 | ||||||||
\(287\) | −0.890088 | −0.0525403 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.9588 | −0.703461 | ||||||||
\(290\) | −2.98470 | −0.175268 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −28.7130 | −1.68030 | ||||||||
\(293\) | −20.9302 | −1.22275 | −0.611377 | − | 0.791340i | \(-0.709384\pi\) | ||||
−0.611377 | + | 0.791340i | \(0.709384\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.17216 | 0.242913 | ||||||||
\(296\) | 3.07791 | 0.178900 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.1348 | 0.818809 | ||||||||
\(299\) | −0.188265 | −0.0108876 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.28957 | 0.0743296 | ||||||||
\(302\) | 22.1380 | 1.27390 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.5669 | −0.663406 | ||||||||
\(305\) | 3.97225 | 0.227450 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.1315 | 1.09189 | 0.545947 | − | 0.837819i | \(-0.316170\pi\) | ||||
0.545947 | + | 0.837819i | \(0.316170\pi\) | |||||||
\(308\) | −3.94591 | −0.224839 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.1091 | −0.687753 | ||||||||
\(311\) | −30.8388 | −1.74871 | −0.874353 | − | 0.485291i | \(-0.838714\pi\) | ||||
−0.874353 | + | 0.485291i | \(0.838714\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.287106 | 0.0162282 | 0.00811409 | − | 0.999967i | \(-0.497417\pi\) | ||||
0.00811409 | + | 0.999967i | \(0.497417\pi\) | |||||||
\(314\) | −35.5980 | −2.00891 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.7582 | −1.16774 | ||||||||
\(317\) | −4.79550 | −0.269342 | −0.134671 | − | 0.990890i | \(-0.542998\pi\) | ||||
−0.134671 | + | 0.990890i | \(0.542998\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.10520 | −0.341826 | ||||||||
\(320\) | 15.0716 | 0.842526 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.572921 | −0.0319276 | ||||||||
\(323\) | 8.20068 | 0.456298 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.556121 | −0.0308480 | ||||||||
\(326\) | 50.2185 | 2.78134 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.39404 | −0.132189 | ||||||||
\(329\) | 1.67644 | 0.0924253 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.68460 | −0.422384 | −0.211192 | − | 0.977445i | \(-0.567735\pi\) | ||||
−0.211192 | + | 0.977445i | \(0.567735\pi\) | |||||||
\(332\) | 5.71766 | 0.313798 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.39498 | 0.459353 | ||||||||
\(335\) | −10.0517 | −0.549183 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.712372 | 0.0388054 | 0.0194027 | − | 0.999812i | \(-0.493824\pi\) | ||||
0.0194027 | + | 0.999812i | \(0.493824\pi\) | |||||||
\(338\) | 27.0519 | 1.47143 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.55995 | −0.409996 | ||||||||
\(341\) | −24.7692 | −1.34133 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.82329 | 0.206438 | ||||||||
\(344\) | 3.46851 | 0.187009 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.0521362 | −0.00280286 | ||||||||
\(347\) | 20.4402 | 1.09729 | 0.548645 | − | 0.836056i | \(-0.315144\pi\) | ||||
0.548645 | + | 0.836056i | \(0.315144\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.84665 | 0.205907 | 0.102953 | − | 0.994686i | \(-0.467171\pi\) | ||||
0.102953 | + | 0.994686i | \(0.467171\pi\) | |||||||
\(350\) | −1.69237 | −0.0904609 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 49.3608 | 2.63094 | ||||||||
\(353\) | −6.68615 | −0.355868 | −0.177934 | − | 0.984042i | \(-0.556941\pi\) | ||||
−0.177934 | + | 0.984042i | \(0.556941\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.99607 | −0.265164 | ||||||||
\(356\) | 4.13459 | 0.219133 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.10662 | −0.111339 | ||||||||
\(359\) | 25.6460 | 1.35355 | 0.676773 | − | 0.736191i | \(-0.263378\pi\) | ||||
0.676773 | + | 0.736191i | \(0.263378\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.65962 | −0.297875 | ||||||||
\(362\) | −47.6083 | −2.50223 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.121679 | −0.00637772 | ||||||||
\(365\) | 17.4480 | 0.913272 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.3016 | 0.642141 | 0.321070 | − | 0.947055i | \(-0.395957\pi\) | ||||
0.321070 | + | 0.947055i | \(0.395957\pi\) | |||||||
\(368\) | 3.16689 | 0.165085 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.4396 | −0.646702 | ||||||||
\(371\) | 1.06459 | 0.0552710 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.4264 | −1.16120 | −0.580598 | − | 0.814190i | \(-0.697181\pi\) | ||||
−0.580598 | + | 0.814190i | \(0.697181\pi\) | |||||||
\(374\) | −28.6026 | −1.47901 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.50907 | 0.232537 | ||||||||
\(377\) | −0.188265 | −0.00969613 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.7025 | 1.73118 | 0.865590 | − | 0.500754i | \(-0.166944\pi\) | ||||
0.865590 | + | 0.500754i | \(0.166944\pi\) | |||||||
\(380\) | −12.2981 | −0.630878 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.07853 | 0.311004 | ||||||||
\(383\) | −21.0513 | −1.07567 | −0.537836 | − | 0.843050i | \(-0.680758\pi\) | ||||
−0.537836 | + | 0.843050i | \(0.680758\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.39781 | 0.122204 | ||||||||
\(386\) | 7.34265 | 0.373731 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.4930 | −0.685001 | ||||||||
\(389\) | 34.5723 | 1.75288 | 0.876442 | − | 0.481507i | \(-0.159910\pi\) | ||||
0.876442 | + | 0.481507i | \(0.159910\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.24526 | −0.113547 | ||||||||
\(392\) | 5.11385 | 0.258288 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 30.8257 | 1.55298 | ||||||||
\(395\) | 12.6141 | 0.634686 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.2736 | 0.615995 | 0.307997 | − | 0.951387i | \(-0.400341\pi\) | ||||
0.307997 | + | 0.951387i | \(0.400341\pi\) | |||||||
\(398\) | −49.6140 | −2.48693 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.35476 | 0.467738 | ||||||||
\(401\) | 9.95916 | 0.497337 | 0.248668 | − | 0.968589i | \(-0.420007\pi\) | ||||
0.248668 | + | 0.968589i | \(0.420007\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.763803 | −0.0380478 | ||||||||
\(404\) | −21.7480 | −1.08200 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.572921 | −0.0284336 | ||||||||
\(407\) | −25.4451 | −1.26127 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.5666 | −1.41253 | −0.706264 | − | 0.707949i | \(-0.749621\pi\) | ||||
−0.706264 | + | 0.707949i | \(0.749621\pi\) | |||||||
\(410\) | 9.67564 | 0.477846 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.0231 | −0.838666 | ||||||||
\(413\) | 0.800858 | 0.0394076 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.47445 | −0.170554 | ||||||||
\(416\) | 1.52213 | 0.0746285 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −46.5291 | −2.27581 | ||||||||
\(419\) | −7.55392 | −0.369033 | −0.184517 | − | 0.982829i | \(-0.559072\pi\) | ||||
−0.184517 | + | 0.982829i | \(0.559072\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.74446 | −0.377442 | −0.188721 | − | 0.982031i | \(-0.560434\pi\) | ||||
−0.188721 | + | 0.982031i | \(0.560434\pi\) | |||||||
\(422\) | −1.22866 | −0.0598103 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.86340 | 0.139059 | ||||||||
\(425\) | −6.63233 | −0.321715 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.762484 | 0.0368992 | ||||||||
\(428\) | 7.44021 | 0.359636 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.0182 | −0.676016 | ||||||||
\(431\) | −38.6217 | −1.86034 | −0.930172 | − | 0.367124i | \(-0.880342\pi\) | ||||
−0.930172 | + | 0.367124i | \(0.880342\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.41271 | −0.260118 | −0.130059 | − | 0.991506i | \(-0.541517\pi\) | ||||
−0.130059 | + | 0.991506i | \(0.541517\pi\) | |||||||
\(434\) | −2.32438 | −0.111574 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 22.5130 | 1.07818 | ||||||||
\(437\) | −3.65245 | −0.174720 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.2447 | −0.584407 | −0.292203 | − | 0.956356i | \(-0.594388\pi\) | ||||
−0.292203 | + | 0.956356i | \(0.594388\pi\) | |||||||
\(440\) | 6.44930 | 0.307458 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.882013 | −0.0419531 | ||||||||
\(443\) | 11.2775 | 0.535808 | 0.267904 | − | 0.963446i | \(-0.413669\pi\) | ||||
0.267904 | + | 0.963446i | \(0.413669\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.51247 | −0.119102 | ||||||||
\(446\) | 36.7110 | 1.73832 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.89303 | 0.136683 | ||||||||
\(449\) | 20.3814 | 0.961858 | 0.480929 | − | 0.876760i | \(-0.340300\pi\) | ||||
0.480929 | + | 0.876760i | \(0.340300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.7915 | 0.931945 | ||||||||
\(452\) | 45.5778 | 2.14380 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 57.1019 | 2.67992 | ||||||||
\(455\) | 0.0739407 | 0.00346639 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.2683 | −0.667442 | −0.333721 | − | 0.942672i | \(-0.608304\pi\) | ||||
−0.333721 | + | 0.942672i | \(0.608304\pi\) | |||||||
\(458\) | 42.3057 | 1.97681 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.36708 | 0.156991 | ||||||||
\(461\) | 28.9224 | 1.34705 | 0.673525 | − | 0.739164i | \(-0.264779\pi\) | ||||
0.673525 | + | 0.739164i | \(0.264779\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.8540 | −0.504429 | −0.252215 | − | 0.967671i | \(-0.581159\pi\) | ||||
−0.252215 | + | 0.967671i | \(0.581159\pi\) | |||||||
\(464\) | 3.16689 | 0.147019 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.34090 | −0.293737 | ||||||||
\(467\) | 18.3096 | 0.847267 | 0.423633 | − | 0.905834i | \(-0.360755\pi\) | ||||
0.423633 | + | 0.905834i | \(0.360755\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.92945 | −0.0890937 | ||||||||
\(470\) | −18.2236 | −0.840594 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.15404 | 0.0991476 | ||||||||
\(473\) | −28.6741 | −1.31844 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.7891 | −0.495037 | ||||||||
\(476\) | −1.45115 | −0.0665134 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.63831 | −0.166412 | ||||||||
\(479\) | −29.2790 | −1.33779 | −0.668896 | − | 0.743356i | \(-0.733233\pi\) | ||||
−0.668896 | + | 0.743356i | \(0.733233\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.784645 | −0.0357767 | ||||||||
\(482\) | −8.33544 | −0.379669 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 61.8458 | 2.81117 | ||||||||
\(485\) | 8.19926 | 0.372309 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.51914 | 0.114153 | 0.0570766 | − | 0.998370i | \(-0.481822\pi\) | ||||
0.0570766 | + | 0.998370i | \(0.481822\pi\) | |||||||
\(488\) | 2.05082 | 0.0928365 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −20.6679 | −0.933680 | ||||||||
\(491\) | 18.0791 | 0.815896 | 0.407948 | − | 0.913005i | \(-0.366244\pi\) | ||||
0.407948 | + | 0.913005i | \(0.366244\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.24526 | −0.101121 | ||||||||
\(494\) | −1.43481 | −0.0645550 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.8483 | 0.576905 | ||||||||
\(497\) | −0.959008 | −0.0430174 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.8082 | 0.886736 | 0.443368 | − | 0.896340i | \(-0.353784\pi\) | ||||
0.443368 | + | 0.896340i | \(0.353784\pi\) | |||||||
\(500\) | 26.7815 | 1.19770 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.4758 | −0.690720 | ||||||||
\(503\) | −12.8927 | −0.574855 | −0.287428 | − | 0.957802i | \(-0.592800\pi\) | ||||
−0.287428 | + | 0.957802i | \(0.592800\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.2156 | 0.588086 | ||||||||
\(506\) | 12.7391 | 0.566324 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −29.7723 | −1.32093 | ||||||||
\(509\) | −8.87677 | −0.393456 | −0.196728 | − | 0.980458i | \(-0.563032\pi\) | ||||
−0.196728 | + | 0.980458i | \(0.563032\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.34920 | 0.148160 | ||||||||
\(512\) | −30.2819 | −1.33829 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 39.7739 | 1.75435 | ||||||||
\(515\) | 10.3444 | 0.455829 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −37.2764 | −1.63942 | ||||||||
\(518\) | −2.38780 | −0.104914 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.198876 | 0.00872127 | ||||||||
\(521\) | −4.07848 | −0.178681 | −0.0893407 | − | 0.996001i | \(-0.528476\pi\) | ||||
−0.0893407 | + | 0.996001i | \(0.528476\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −41.7215 | −1.82436 | −0.912178 | − | 0.409795i | \(-0.865600\pi\) | ||||
−0.912178 | + | 0.409795i | \(0.865600\pi\) | |||||||
\(524\) | −18.4027 | −0.803925 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.29126 | 0.230710 | ||||||||
\(527\) | −9.10916 | −0.396801 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −11.5726 | −0.502681 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.36065 | −0.102347 | ||||||||
\(533\) | 0.610306 | 0.0264353 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.52119 | −0.195468 | ||||||||
\(536\) | −5.18957 | −0.224155 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.61935 | −0.371607 | ||||||||
\(539\) | −42.2761 | −1.82096 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.0737 | −0.863038 | −0.431519 | − | 0.902104i | \(-0.642022\pi\) | ||||
−0.431519 | + | 0.902104i | \(0.642022\pi\) | |||||||
\(542\) | 8.55538 | 0.367485 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.1530 | 0.778303 | ||||||||
\(545\) | −13.6804 | −0.586006 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.2512 | −0.566583 | −0.283291 | − | 0.959034i | \(-0.591426\pi\) | ||||
−0.283291 | + | 0.959034i | \(0.591426\pi\) | |||||||
\(548\) | 5.23105 | 0.223459 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 37.6305 | 1.60457 | ||||||||
\(551\) | −3.65245 | −0.155600 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.42132 | 0.102965 | ||||||||
\(554\) | −14.9071 | −0.633342 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 32.3689 | 1.37275 | ||||||||
\(557\) | 29.8454 | 1.26459 | 0.632295 | − | 0.774727i | \(-0.282113\pi\) | ||||
0.632295 | + | 0.774727i | \(0.282113\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.884218 | −0.0373984 | ||||||||
\(560\) | −1.24379 | −0.0525597 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −32.6566 | −1.37753 | ||||||||
\(563\) | 6.32526 | 0.266578 | 0.133289 | − | 0.991077i | \(-0.457446\pi\) | ||||
0.133289 | + | 0.991077i | \(0.457446\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.6962 | −1.16519 | ||||||||
\(566\) | −17.1961 | −0.722805 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.57941 | −0.108230 | ||||||||
\(569\) | 13.4246 | 0.562788 | 0.281394 | − | 0.959592i | \(-0.409203\pi\) | ||||
0.281394 | + | 0.959592i | \(0.409203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.9335 | −1.33638 | −0.668188 | − | 0.743992i | \(-0.732930\pi\) | ||||
−0.668188 | + | 0.743992i | \(0.732930\pi\) | |||||||
\(572\) | 2.70559 | 0.113126 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.85726 | 0.0775207 | ||||||||
\(575\) | 2.95393 | 0.123187 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.4350 | 0.517677 | 0.258838 | − | 0.965921i | \(-0.416660\pi\) | ||||
0.258838 | + | 0.965921i | \(0.416660\pi\) | |||||||
\(578\) | 24.9534 | 1.03792 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.36708 | 0.139810 | ||||||||
\(581\) | −0.666930 | −0.0276689 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.6717 | −0.980382 | ||||||||
\(584\) | 9.00821 | 0.372762 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 43.6730 | 1.80412 | ||||||||
\(587\) | −24.0000 | −0.990586 | −0.495293 | − | 0.868726i | \(-0.664939\pi\) | ||||
−0.495293 | + | 0.868726i | \(0.664939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.8182 | −0.610575 | ||||||||
\(590\) | −8.70566 | −0.358406 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13.1989 | 0.542470 | ||||||||
\(593\) | 19.4433 | 0.798441 | 0.399221 | − | 0.916855i | \(-0.369281\pi\) | ||||
0.399221 | + | 0.916855i | \(0.369281\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.881821 | 0.0361511 | ||||||||
\(596\) | −15.9457 | −0.653161 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.392834 | 0.0160642 | ||||||||
\(599\) | −13.7703 | −0.562640 | −0.281320 | − | 0.959614i | \(-0.590772\pi\) | ||||
−0.281320 | + | 0.959614i | \(0.590772\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.23499 | −0.0503764 | −0.0251882 | − | 0.999683i | \(-0.508018\pi\) | ||||
−0.0251882 | + | 0.999683i | \(0.508018\pi\) | |||||||
\(602\) | −2.69082 | −0.109670 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −24.9742 | −1.01618 | ||||||||
\(605\) | −37.5818 | −1.52792 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.5165 | −1.19804 | −0.599019 | − | 0.800735i | \(-0.704443\pi\) | ||||
−0.599019 | + | 0.800735i | \(0.704443\pi\) | |||||||
\(608\) | 29.5302 | 1.19761 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.28852 | −0.335592 | ||||||||
\(611\) | −1.14949 | −0.0465032 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.7152 | 0.473172 | 0.236586 | − | 0.971611i | \(-0.423972\pi\) | ||||
0.236586 | + | 0.971611i | \(0.423972\pi\) | |||||||
\(614\) | −39.9200 | −1.61104 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.23796 | 0.0498788 | ||||||||
\(617\) | −29.9849 | −1.20715 | −0.603573 | − | 0.797308i | \(-0.706257\pi\) | ||||
−0.603573 | + | 0.797308i | \(0.706257\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.17569 | 0.288415 | 0.144208 | − | 0.989547i | \(-0.453937\pi\) | ||||
0.144208 | + | 0.989547i | \(0.453937\pi\) | |||||||
\(620\) | 13.6605 | 0.548618 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 64.3484 | 2.58013 | ||||||||
\(623\) | −0.482275 | −0.0193219 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.50465 | −0.0601861 | ||||||||
\(626\) | −0.599077 | −0.0239439 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 40.1586 | 1.60250 | ||||||||
\(629\) | −9.35771 | −0.373116 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.8076 | −0.907955 | −0.453977 | − | 0.891013i | \(-0.649995\pi\) | ||||
−0.453977 | + | 0.891013i | \(0.649995\pi\) | |||||||
\(632\) | 6.51253 | 0.259055 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.0063 | 0.397402 | ||||||||
\(635\) | 18.0917 | 0.717948 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.30366 | −0.0516529 | ||||||||
\(638\) | 12.7391 | 0.504348 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.31857 | −0.328820 | ||||||||
\(641\) | −2.68538 | −0.106066 | −0.0530331 | − | 0.998593i | \(-0.516889\pi\) | ||||
−0.0530331 | + | 0.998593i | \(0.516889\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.39727 | 0.331156 | 0.165578 | − | 0.986197i | \(-0.447051\pi\) | ||||
0.165578 | + | 0.986197i | \(0.447051\pi\) | |||||||
\(644\) | 0.646319 | 0.0254685 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.1116 | −0.673246 | ||||||||
\(647\) | 13.2389 | 0.520476 | 0.260238 | − | 0.965545i | \(-0.416199\pi\) | ||||
0.260238 | + | 0.965545i | \(0.416199\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.8074 | −0.699002 | ||||||||
\(650\) | 1.16040 | 0.0455148 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −56.6521 | −2.21867 | ||||||||
\(653\) | −30.6244 | −1.19842 | −0.599212 | − | 0.800591i | \(-0.704519\pi\) | ||||
−0.599212 | + | 0.800591i | \(0.704519\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.1827 | 0.436946 | ||||||||
\(656\) | −10.2662 | −0.400829 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.49808 | −0.136369 | ||||||||
\(659\) | −33.9602 | −1.32290 | −0.661450 | − | 0.749989i | \(-0.730059\pi\) | ||||
−0.661450 | + | 0.749989i | \(0.730059\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.1979 | 0.630027 | 0.315013 | − | 0.949087i | \(-0.397991\pi\) | ||||
0.315013 | + | 0.949087i | \(0.397991\pi\) | |||||||
\(662\) | 16.0347 | 0.623208 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.79382 | −0.0696136 | ||||||||
\(665\) | 1.43449 | 0.0556273 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −9.47047 | −0.366424 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 20.9739 | 0.810293 | ||||||||
\(671\) | −16.9542 | −0.654508 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.7576 | −1.49400 | −0.746998 | − | 0.664827i | \(-0.768505\pi\) | ||||
−0.746998 | + | 0.664827i | \(0.768505\pi\) | |||||||
\(674\) | −1.48644 | −0.0572555 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −30.5176 | −1.17375 | ||||||||
\(677\) | −34.2894 | −1.31785 | −0.658925 | − | 0.752208i | \(-0.728989\pi\) | ||||
−0.658925 | + | 0.752208i | \(0.728989\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.57387 | 0.0603996 | ||||||||
\(680\) | 2.37180 | 0.0909544 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 51.6836 | 1.97907 | ||||||||
\(683\) | −7.15688 | −0.273851 | −0.136925 | − | 0.990581i | \(-0.543722\pi\) | ||||
−0.136925 | + | 0.990581i | \(0.543722\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.17875 | −0.121454 | ||||||||
\(686\) | −7.97770 | −0.304590 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 14.8738 | 0.567060 | ||||||||
\(689\) | −0.729959 | −0.0278092 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.4957 | −1.04599 | −0.522993 | − | 0.852337i | \(-0.675184\pi\) | ||||
−0.522993 | + | 0.852337i | \(0.675184\pi\) | |||||||
\(692\) | 0.0588155 | 0.00223583 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −42.6507 | −1.61900 | ||||||||
\(695\) | −19.6696 | −0.746111 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.27854 | 0.275694 | ||||||||
\(698\) | −8.02645 | −0.303806 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.90918 | 0.0721603 | ||||||||
\(701\) | 13.8109 | 0.521630 | 0.260815 | − | 0.965389i | \(-0.416009\pi\) | ||||
0.260815 | + | 0.965389i | \(0.416009\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.2226 | −0.574130 | ||||||||
\(704\) | −64.3277 | −2.42444 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.9514 | 0.525067 | ||||||||
\(707\) | 2.53677 | 0.0954049 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.924764 | −0.0347303 | −0.0173651 | − | 0.999849i | \(-0.505528\pi\) | ||||
−0.0173651 | + | 0.999849i | \(0.505528\pi\) | |||||||
\(710\) | 10.4248 | 0.391237 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.29716 | −0.0486130 | ||||||||
\(713\) | 4.05707 | 0.151938 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.64410 | −0.0614860 | ||||||||
\(716\) | 2.37651 | 0.0888143 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −53.5132 | −1.99709 | ||||||||
\(719\) | −20.1522 | −0.751552 | −0.375776 | − | 0.926711i | \(-0.622624\pi\) | ||||
−0.375776 | + | 0.926711i | \(0.622624\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.98564 | 0.0739489 | ||||||||
\(722\) | 11.8094 | 0.439500 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 53.7075 | 1.99602 | ||||||||
\(725\) | 2.95393 | 0.109706 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.08270 | 0.0772429 | 0.0386215 | − | 0.999254i | \(-0.487703\pi\) | ||||
0.0386215 | + | 0.999254i | \(0.487703\pi\) | |||||||
\(728\) | 0.0381747 | 0.00141485 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −36.4072 | −1.34749 | ||||||||
\(731\) | −10.5452 | −0.390030 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.15634 | 0.301261 | 0.150631 | − | 0.988590i | \(-0.451870\pi\) | ||||
0.150631 | + | 0.988590i | \(0.451870\pi\) | |||||||
\(734\) | −25.6687 | −0.947449 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.08505 | −0.298019 | ||||||||
\(737\) | 42.9021 | 1.58032 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.8699 | −0.951638 | −0.475819 | − | 0.879543i | \(-0.657848\pi\) | ||||
−0.475819 | + | 0.879543i | \(0.657848\pi\) | |||||||
\(740\) | 14.0332 | 0.515871 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.22139 | −0.0815497 | ||||||||
\(743\) | −34.9391 | −1.28179 | −0.640896 | − | 0.767628i | \(-0.721437\pi\) | ||||
−0.640896 | + | 0.767628i | \(0.721437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.68971 | 0.355003 | ||||||||
\(746\) | 46.7951 | 1.71329 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 32.2670 | 1.17980 | ||||||||
\(749\) | −0.867854 | −0.0317107 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.4297 | 0.380585 | 0.190293 | − | 0.981727i | \(-0.439056\pi\) | ||||
0.190293 | + | 0.981727i | \(0.439056\pi\) | |||||||
\(752\) | 19.3360 | 0.705112 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.392834 | 0.0143062 | ||||||||
\(755\) | 15.1760 | 0.552313 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.0068 | 1.67215 | 0.836073 | − | 0.548619i | \(-0.184846\pi\) | ||||
0.836073 | + | 0.548619i | \(0.184846\pi\) | |||||||
\(758\) | −70.3238 | −2.55428 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.85831 | 0.139956 | ||||||||
\(761\) | 33.1684 | 1.20235 | 0.601177 | − | 0.799116i | \(-0.294699\pi\) | ||||
0.601177 | + | 0.799116i | \(0.294699\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.62600 | −0.0950675 | ||||||||
\(764\) | −6.85726 | −0.248087 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 43.9258 | 1.58710 | ||||||||
\(767\) | −0.549123 | −0.0198277 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.9544 | −0.863816 | −0.431908 | − | 0.901918i | \(-0.642159\pi\) | ||||
−0.431908 | + | 0.901918i | \(0.642159\pi\) | |||||||
\(770\) | −5.00328 | −0.180306 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.28333 | −0.298124 | ||||||||
\(773\) | 37.4046 | 1.34535 | 0.672674 | − | 0.739939i | \(-0.265146\pi\) | ||||
0.672674 | + | 0.739939i | \(0.265146\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.9843 | 0.430489 | ||||||||
\(776\) | 4.23318 | 0.151962 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −72.1387 | −2.58630 | ||||||||
\(779\) | 11.8403 | 0.424223 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.3240 | 0.763031 | ||||||||
\(782\) | 4.68496 | 0.167534 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 21.9295 | 0.783195 | ||||||||
\(785\) | −24.4032 | −0.870986 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.05977 | 0.144715 | 0.0723576 | − | 0.997379i | \(-0.476948\pi\) | ||||
0.0723576 | + | 0.997379i | \(0.476948\pi\) | |||||||
\(788\) | −34.7749 | −1.23880 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −26.3208 | −0.936450 | ||||||||
\(791\) | −5.31637 | −0.189028 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.522811 | −0.0185656 | ||||||||
\(794\) | −25.6102 | −0.908871 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 55.9702 | 1.98381 | ||||||||
\(797\) | 1.56174 | 0.0553196 | 0.0276598 | − | 0.999617i | \(-0.491194\pi\) | ||||
0.0276598 | + | 0.999617i | \(0.491194\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.7088 | −0.484983 | ||||||||
\(800\) | −23.8827 | −0.844380 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.7808 | −0.733797 | ||||||||
\(803\) | −74.4708 | −2.62802 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.392749 | −0.0138426 | ||||||||
\(806\) | 1.59376 | 0.0561377 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.82305 | 0.240034 | ||||||||
\(809\) | 9.09173 | 0.319648 | 0.159824 | − | 0.987146i | \(-0.448907\pi\) | ||||
0.159824 | + | 0.987146i | \(0.448907\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.07851 | 0.213445 | 0.106723 | − | 0.994289i | \(-0.465964\pi\) | ||||
0.106723 | + | 0.994289i | \(0.465964\pi\) | |||||||
\(812\) | 0.646319 | 0.0226814 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 53.0939 | 1.86094 | ||||||||
\(815\) | 34.4257 | 1.20588 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.1544 | −0.600155 | ||||||||
\(818\) | 59.6073 | 2.08412 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.9152 | −0.381175 | ||||||||
\(821\) | −29.7440 | −1.03807 | −0.519036 | − | 0.854752i | \(-0.673709\pi\) | ||||
−0.519036 | + | 0.854752i | \(0.673709\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.8740 | 0.448758 | 0.224379 | − | 0.974502i | \(-0.427965\pi\) | ||||
0.224379 | + | 0.974502i | \(0.427965\pi\) | |||||||
\(824\) | 5.34069 | 0.186052 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.67107 | −0.0581441 | ||||||||
\(827\) | −36.2049 | −1.25897 | −0.629484 | − | 0.777014i | \(-0.716734\pi\) | ||||
−0.629484 | + | 0.777014i | \(0.716734\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.7283 | −1.10197 | −0.550985 | − | 0.834515i | \(-0.685748\pi\) | ||||
−0.550985 | + | 0.834515i | \(0.685748\pi\) | |||||||
\(830\) | 7.24981 | 0.251645 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.98366 | −0.0687710 | ||||||||
\(833\) | −15.5475 | −0.538690 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.75492 | 0.199157 | ||||||||
\(836\) | 52.4900 | 1.81541 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.7621 | 0.544491 | ||||||||
\(839\) | 29.9699 | 1.03468 | 0.517338 | − | 0.855781i | \(-0.326923\pi\) | ||||
0.517338 | + | 0.855781i | \(0.326923\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 16.1596 | 0.556898 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.38607 | 0.0477104 | ||||||||
\(845\) | 18.5446 | 0.637954 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.21393 | −0.247874 | ||||||||
\(848\) | 12.2790 | 0.421662 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13.8391 | 0.474676 | ||||||||
\(851\) | 4.16777 | 0.142869 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.0788 | −1.47499 | −0.737495 | − | 0.675352i | \(-0.763992\pi\) | ||||
−0.737495 | + | 0.675352i | \(0.763992\pi\) | |||||||
\(854\) | −1.59100 | −0.0544430 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.33424 | −0.0797825 | ||||||||
\(857\) | 56.4937 | 1.92979 | 0.964895 | − | 0.262637i | \(-0.0845921\pi\) | ||||
0.964895 | + | 0.262637i | \(0.0845921\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.8657 | 0.473093 | 0.236547 | − | 0.971620i | \(-0.423984\pi\) | ||||
0.236547 | + | 0.971620i | \(0.423984\pi\) | |||||||
\(860\) | 15.8141 | 0.539255 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 80.5884 | 2.74485 | ||||||||
\(863\) | −12.0348 | −0.409669 | −0.204835 | − | 0.978797i | \(-0.565666\pi\) | ||||
−0.204835 | + | 0.978797i | \(0.565666\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.0357404 | −0.00121521 | ||||||||
\(866\) | 11.2942 | 0.383792 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.62216 | 0.0890020 | ||||||||
\(869\) | −53.8391 | −1.82636 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.32296 | 0.0448269 | ||||||||
\(872\) | −7.06305 | −0.239185 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.62122 | 0.257792 | ||||||||
\(875\) | −3.12389 | −0.105607 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.0150 | −0.878463 | −0.439232 | − | 0.898374i | \(-0.644749\pi\) | ||||
−0.439232 | + | 0.898374i | \(0.644749\pi\) | |||||||
\(878\) | 25.5498 | 0.862265 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 27.6562 | 0.932291 | ||||||||
\(881\) | −18.7821 | −0.632785 | −0.316392 | − | 0.948628i | \(-0.602472\pi\) | ||||
−0.316392 | + | 0.948628i | \(0.602472\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.62443 | −0.290235 | −0.145118 | − | 0.989414i | \(-0.546356\pi\) | ||||
−0.145118 | + | 0.989414i | \(0.546356\pi\) | |||||||
\(884\) | 0.995010 | 0.0334658 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23.5316 | −0.790560 | ||||||||
\(887\) | −39.3782 | −1.32219 | −0.661095 | − | 0.750302i | \(-0.729908\pi\) | ||||
−0.661095 | + | 0.750302i | \(0.729908\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.47275 | 0.116472 | ||||||||
\(890\) | 5.24253 | 0.175730 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −41.4142 | −1.38665 | ||||||||
\(893\) | −22.3007 | −0.746265 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.44413 | −0.0482720 | ||||||||
\(896\) | −1.59677 | −0.0533444 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −42.5280 | −1.41918 | ||||||||
\(899\) | 4.05707 | 0.135311 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.70553 | −0.290023 | ||||||||
\(902\) | −41.2971 | −1.37504 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.2992 | −0.475586 | ||||||||
\(905\) | −32.6364 | −1.08487 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.33324 | 0.276701 | 0.138350 | − | 0.990383i | \(-0.455820\pi\) | ||||
0.138350 | + | 0.990383i | \(0.455820\pi\) | |||||||
\(908\) | −64.4173 | −2.13776 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.154285 | −0.00511450 | ||||||||
\(911\) | −40.2510 | −1.33358 | −0.666788 | − | 0.745247i | \(-0.732331\pi\) | ||||
−0.666788 | + | 0.745247i | \(0.732331\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.8295 | 0.490784 | ||||||||
\(914\) | 29.7723 | 0.984780 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −47.7255 | −1.57690 | ||||||||
\(917\) | 2.14656 | 0.0708856 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.7016 | 1.14470 | 0.572351 | − | 0.820009i | \(-0.306032\pi\) | ||||
0.572351 | + | 0.820009i | \(0.306032\pi\) | |||||||
\(920\) | −1.05636 | −0.0348272 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −60.3497 | −1.98751 | ||||||||
\(923\) | 0.657562 | 0.0216439 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.3113 | 0.404793 | ||||||||
\(926\) | 22.6481 | 0.744262 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.08505 | −0.265405 | ||||||||
\(929\) | −25.0656 | −0.822376 | −0.411188 | − | 0.911551i | \(-0.634886\pi\) | ||||
−0.411188 | + | 0.911551i | \(0.634886\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.2918 | −0.828905 | ||||||||
\(932\) | 7.15325 | 0.234313 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −38.2049 | −1.25010 | ||||||||
\(935\) | −19.6077 | −0.641239 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.2923 | −1.57764 | −0.788821 | − | 0.614623i | \(-0.789308\pi\) | ||||
−0.788821 | + | 0.614623i | \(0.789308\pi\) | |||||||
\(938\) | 4.02600 | 0.131454 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 20.5583 | 0.670538 | ||||||||
\(941\) | −16.0613 | −0.523582 | −0.261791 | − | 0.965125i | \(-0.584313\pi\) | ||||
−0.261791 | + | 0.965125i | \(0.584313\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.24174 | −0.105566 | ||||||||
\(944\) | 9.23705 | 0.300640 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 59.8316 | 1.94529 | ||||||||
\(947\) | −36.9475 | −1.20063 | −0.600316 | − | 0.799763i | \(-0.704959\pi\) | ||||
−0.600316 | + | 0.799763i | \(0.704959\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.29644 | −0.0745456 | ||||||||
\(950\) | 22.5126 | 0.730404 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.455274 | 0.0147555 | ||||||||
\(953\) | −31.1650 | −1.00953 | −0.504766 | − | 0.863256i | \(-0.668421\pi\) | ||||
−0.504766 | + | 0.863256i | \(0.668421\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.16695 | 0.134839 | ||||||||
\(956\) | 4.10442 | 0.132746 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 61.0938 | 1.97385 | ||||||||
\(959\) | −0.610170 | −0.0197034 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.5402 | −0.469038 | ||||||||
\(962\) | 1.63724 | 0.0527869 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.40331 | 0.302860 | ||||||||
\(965\) | 5.03353 | 0.162035 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.2912 | 1.84236 | 0.921181 | − | 0.389134i | \(-0.127226\pi\) | ||||
0.921181 | + | 0.389134i | \(0.127226\pi\) | |||||||
\(968\) | −19.4030 | −0.623637 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −17.1086 | −0.549325 | ||||||||
\(971\) | 36.2034 | 1.16182 | 0.580912 | − | 0.813966i | \(-0.302696\pi\) | ||||
0.580912 | + | 0.813966i | \(0.302696\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.77563 | −0.121041 | ||||||||
\(974\) | −5.25646 | −0.168428 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.79445 | 0.281503 | ||||||||
\(977\) | 36.0090 | 1.15203 | 0.576015 | − | 0.817439i | \(-0.304607\pi\) | ||||
0.576015 | + | 0.817439i | \(0.304607\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.7236 | 0.342727 | ||||||||
\(980\) | 23.3157 | 0.744793 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −37.7239 | −1.20382 | ||||||||
\(983\) | −14.3777 | −0.458576 | −0.229288 | − | 0.973359i | \(-0.573640\pi\) | ||||
−0.229288 | + | 0.973359i | \(0.573640\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.1316 | 0.673310 | ||||||||
\(986\) | 4.68496 | 0.149200 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.61862 | 0.0514953 | ||||||||
\(989\) | 4.69667 | 0.149346 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.18303 | 0.164644 | 0.0823221 | − | 0.996606i | \(-0.473766\pi\) | ||||
0.0823221 | + | 0.996606i | \(0.473766\pi\) | |||||||
\(992\) | −32.8016 | −1.04145 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.00107 | 0.0634702 | ||||||||
\(995\) | −34.0114 | −1.07823 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.0974 | −1.58660 | −0.793301 | − | 0.608830i | \(-0.791639\pi\) | ||||
−0.793301 | + | 0.608830i | \(0.791639\pi\) | |||||||
\(998\) | −41.3319 | −1.30834 | ||||||||
\(999\) | 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.u.1.3 | yes | 22 | |
3.2 | odd | 2 | 6003.2.a.t.1.20 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.t.1.20 | ✓ | 22 | 3.2 | odd | 2 | ||
6003.2.a.u.1.3 | yes | 22 | 1.1 | even | 1 | trivial |