Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(3849,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.3849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.e (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3849.16 | ||
Character | \(\chi\) | \(=\) | 4004.3849 |
Dual form | 4004.2.e.b.3849.33 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4004\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(925\) | \(2003\) | \(3433\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.04079i | − | 0.600900i | −0.953798 | − | 0.300450i | \(-0.902863\pi\) | ||
0.953798 | − | 0.300450i | \(-0.0971368\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 4.22530i | − | 1.88961i | −0.327633 | − | 0.944805i | \(-0.606251\pi\) | ||
0.327633 | − | 0.944805i | \(-0.393749\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.02914 | − | 1.69782i | 0.766941 | − | 0.641717i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.91676 | 0.638919 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.24641 | + | 0.678817i | 0.978831 | + | 0.204671i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.39764 | −1.13547 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.87976 | 0.940981 | 0.470490 | − | 0.882405i | \(-0.344077\pi\) | ||||
0.470490 | + | 0.882405i | \(0.344077\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.23838 | −1.66060 | −0.830299 | − | 0.557319i | \(-0.811830\pi\) | ||||
−0.830299 | + | 0.557319i | \(0.811830\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.76708 | − | 2.11190i | −0.385608 | − | 0.460855i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.94488 | 1.23959 | 0.619797 | − | 0.784762i | \(-0.287215\pi\) | ||||
0.619797 | + | 0.784762i | \(0.287215\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.8531 | −2.57063 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.11731i | − | 0.984826i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.09512i | − | 0.203359i | −0.994817 | − | 0.101679i | \(-0.967578\pi\) | ||
0.994817 | − | 0.101679i | \(-0.0324215\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.22134i | − | 0.937780i | −0.883257 | − | 0.468890i | \(-0.844654\pi\) | ||
0.883257 | − | 0.468890i | \(-0.155346\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.706505 | − | 3.37883i | 0.122987 | − | 0.588179i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.17381 | − | 8.57370i | −1.21259 | − | 1.44922i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.09541 | 0.508882 | 0.254441 | − | 0.967088i | \(-0.418109\pi\) | ||||
0.254441 | + | 0.967088i | \(0.418109\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.04079i | 0.166660i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.53399 | −0.395743 | −0.197871 | − | 0.980228i | \(-0.563403\pi\) | ||||
−0.197871 | + | 0.980228i | \(0.563403\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.88894i | 1.05055i | 0.850931 | + | 0.525277i | \(0.176038\pi\) | ||||
−0.850931 | + | 0.525277i | \(0.823962\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 8.09887i | − | 1.20731i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 5.75983i | − | 0.840157i | −0.907488 | − | 0.420079i | \(-0.862002\pi\) | ||
0.907488 | − | 0.420079i | \(-0.137998\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.23479 | − | 6.89023i | 0.176399 | − | 0.984319i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 4.03802i | − | 0.565435i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.66407 | 1.19010 | 0.595051 | − | 0.803688i | \(-0.297132\pi\) | ||||
0.595051 | + | 0.803688i | \(0.297132\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.86820 | − | 13.7171i | 0.386748 | − | 1.84961i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.53362i | 0.997853i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.74791i | 0.878503i | 0.898364 | + | 0.439251i | \(0.144756\pi\) | ||||
−0.898364 | + | 0.439251i | \(0.855244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.1344 | −1.80972 | −0.904860 | − | 0.425710i | \(-0.860024\pi\) | ||||
−0.904860 | + | 0.425710i | \(0.860024\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.88936 | − | 3.25432i | 0.490014 | − | 0.410005i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.22530i | 0.524084i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.12772 | 0.259942 | 0.129971 | − | 0.991518i | \(-0.458512\pi\) | ||||
0.129971 | + | 0.991518i | \(0.458512\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 6.18737i | − | 0.744872i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.96408 | −0.470450 | −0.235225 | − | 0.971941i | \(-0.575583\pi\) | ||||
−0.235225 | + | 0.971941i | \(0.575583\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.7968 | 1.73183 | 0.865915 | − | 0.500191i | \(-0.166737\pi\) | ||||
0.865915 | + | 0.500191i | \(0.166737\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.3774i | 1.54469i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.73993 | − | 4.13443i | 0.882047 | − | 0.471162i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 15.2582i | − | 1.71668i | −0.513082 | − | 0.858340i | \(-0.671496\pi\) | ||
0.513082 | − | 0.858340i | \(-0.328504\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.424235 | 0.0471372 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.04591 | 0.334332 | 0.167166 | − | 0.985929i | \(-0.446538\pi\) | ||||
0.167166 | + | 0.985929i | \(0.446538\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 16.3932i | − | 1.77809i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.13979 | −0.122198 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.88438i | 0.835742i | 0.908506 | + | 0.417871i | \(0.137224\pi\) | ||||
−0.908506 | + | 0.417871i | \(0.862776\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.02914 | + | 1.69782i | −0.212711 | + | 0.177980i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.43431 | −0.563512 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 30.5843i | 3.13788i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.43823i | 0.755238i | 0.925961 | + | 0.377619i | \(0.123257\pi\) | ||||
−0.925961 | + | 0.377619i | \(0.876743\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.22259 | + | 1.30113i | 0.625394 | + | 0.130768i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.25530 | −0.522922 | −0.261461 | − | 0.965214i | \(-0.584204\pi\) | ||||
−0.261461 | + | 0.965214i | \(0.584204\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 17.6898i | − | 1.74303i | −0.490369 | − | 0.871515i | \(-0.663138\pi\) | ||
0.490369 | − | 0.871515i | \(-0.336862\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.92342 | + | 7.46642i | −0.870836 | + | 0.728648i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.1987i | 0.985946i | 0.870045 | + | 0.492973i | \(0.164090\pi\) | ||||
−0.870045 | + | 0.492973i | \(0.835910\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.9836i | 1.05204i | 0.850473 | + | 0.526019i | \(0.176316\pi\) | ||||
−0.850473 | + | 0.526019i | \(0.823684\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.22167i | − | 0.305787i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.94091 | −0.935162 | −0.467581 | − | 0.883950i | \(-0.654874\pi\) | ||||
−0.467581 | + | 0.883950i | \(0.654874\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 25.1189i | − | 2.34235i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.91676 | −0.177204 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.87257 | − | 6.58716i | 0.721677 | − | 0.603844i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.0784 | + | 4.40744i | 0.916220 | + | 0.400677i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.63735i | 0.237802i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 33.1818i | 2.96787i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.19887i | − | 0.106382i | −0.998584 | − | 0.0531911i | \(-0.983061\pi\) | ||
0.998584 | − | 0.0531911i | \(-0.0169393\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.16994 | 0.631278 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.2740 | 1.42186 | 0.710932 | − | 0.703261i | \(-0.248274\pi\) | ||||
0.710932 | + | 0.703261i | \(0.248274\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.6877 | + | 12.2895i | −1.27358 | + | 1.06563i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −21.6221 | −1.86094 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.65984 | −0.312682 | −0.156341 | − | 0.987703i | \(-0.549970\pi\) | ||||
−0.156341 | + | 0.987703i | \(0.549970\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.1567 | −1.03112 | −0.515558 | − | 0.856855i | \(-0.672415\pi\) | ||||
−0.515558 | + | 0.856855i | \(0.672415\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.99477 | −0.504850 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.24641 | − | 0.678817i | −0.271479 | − | 0.0567655i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.62720 | −0.384268 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.17128 | − | 1.28516i | −0.591477 | − | 0.105998i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 13.6133i | − | 1.11524i | −0.830096 | − | 0.557621i | \(-0.811714\pi\) | ||
0.830096 | − | 0.557621i | \(-0.188286\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.83535i | 0.556253i | 0.960545 | + | 0.278126i | \(0.0897134\pi\) | ||||
−0.960545 | + | 0.278126i | \(0.910287\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.43657 | 0.601211 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.0617 | −1.77204 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.6471i | 1.40839i | 0.710007 | + | 0.704195i | \(0.248692\pi\) | ||||
−0.710007 | + | 0.704195i | \(0.751308\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 9.01747i | − | 0.715132i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0630 | − | 10.0934i | 0.950696 | − | 0.795468i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.69579 | −0.132825 | −0.0664124 | − | 0.997792i | \(-0.521155\pi\) | ||||
−0.0664124 | + | 0.997792i | \(0.521155\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.2766 | − | 2.98519i | −1.11143 | − | 0.232397i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.8023 | 0.990675 | 0.495338 | − | 0.868701i | \(-0.335044\pi\) | ||||
0.495338 | + | 0.868701i | \(0.335044\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.8742 | −1.06099 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.92686 | 0.374582 | 0.187291 | − | 0.982304i | \(-0.440029\pi\) | ||||
0.187291 | + | 0.982304i | \(0.440029\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −26.0808 | + | 21.8223i | −1.97152 | + | 1.64961i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.02315 | 0.527892 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.8659 | −0.812156 | −0.406078 | − | 0.913838i | \(-0.633104\pi\) | ||||
−0.406078 | + | 0.913838i | \(0.633104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.00030i | − | 0.520328i | −0.965564 | − | 0.260164i | \(-0.916223\pi\) | ||
0.965564 | − | 0.260164i | \(-0.0837767\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.7109i | 1.08746i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 13.0790i | − | 0.961589i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.5953 | + | 2.63365i | 0.921061 | + | 0.192592i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.68829 | − | 10.3837i | −0.631980 | − | 0.755304i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25.9684 | −1.87901 | −0.939503 | − | 0.342541i | \(-0.888713\pi\) | ||||
−0.939503 | + | 0.342541i | \(0.888713\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.79949i | 0.633401i | 0.948526 | + | 0.316700i | \(0.102575\pi\) | ||||
−0.948526 | + | 0.316700i | \(0.897425\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.39764 | 0.314922 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.31434i | − | 0.164890i | −0.996596 | − | 0.0824449i | \(-0.973727\pi\) | ||
0.996596 | − | 0.0824449i | \(-0.0262728\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.64625i | 0.542028i | 0.962575 | + | 0.271014i | \(0.0873590\pi\) | ||||
−0.962575 | + | 0.271014i | \(0.912641\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 2.21451i | − | 0.156199i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.85932 | − | 2.22215i | −0.130499 | − | 0.155964i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.7069i | 0.747799i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.3949 | 0.792000 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.4988 | − | 4.91353i | −1.62544 | − | 0.339876i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.8638i | 1.71169i | 0.517228 | + | 0.855847i | \(0.326964\pi\) | ||||
−0.517228 | + | 0.855847i | \(0.673036\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.12578i | 0.282693i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.1078 | 1.98514 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.86491 | − | 10.5948i | −0.601789 | − | 0.719223i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 15.4003i | − | 1.04066i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.87976 | −0.260981 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.2035i | 0.683275i | 0.939832 | + | 0.341638i | \(0.110982\pi\) | ||||
−0.939832 | + | 0.341638i | \(0.889018\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −24.6363 | −1.64242 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.27270 | 0.283589 | 0.141794 | − | 0.989896i | \(-0.454713\pi\) | ||||
0.141794 | + | 0.989896i | \(0.454713\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.23682i | − | 0.147813i | −0.997265 | − | 0.0739066i | \(-0.976453\pi\) | ||
0.997265 | − | 0.0739066i | \(-0.0235467\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.30307 | − | 8.05563i | −0.283121 | − | 0.530022i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 7.75004i | − | 0.507722i | −0.967241 | − | 0.253861i | \(-0.918299\pi\) | ||
0.967241 | − | 0.253861i | \(-0.0817006\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.3370 | −1.58757 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.8806 | −1.03155 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 22.7181i | − | 1.46951i | −0.678332 | − | 0.734756i | \(-0.737297\pi\) | ||
0.678332 | − | 0.734756i | \(-0.262703\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.9004 | 0.766573 | 0.383287 | − | 0.923629i | \(-0.374792\pi\) | ||||
0.383287 | + | 0.923629i | \(0.374792\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 15.7935i | − | 1.01315i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −29.1133 | − | 5.21735i | −1.85998 | − | 0.333324i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.23838 | 0.460567 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 3.17015i | − | 0.200900i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.90988i | − | 0.120551i | −0.998182 | − | 0.0602754i | \(-0.980802\pi\) | ||
0.998182 | − | 0.0602754i | \(-0.0191979\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.2996 | + | 4.03549i | 1.21335 | + | 0.253709i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.0618 | −1.06845 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.52769i | 0.469565i | 0.972048 | + | 0.234782i | \(0.0754377\pi\) | ||||
−0.972048 | + | 0.234782i | \(0.924562\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.28101 | − | 5.25546i | 0.390283 | − | 0.326558i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 2.09908i | − | 0.129930i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 10.6408i | − | 0.656139i | −0.944654 | − | 0.328069i | \(-0.893602\pi\) | ||
0.944654 | − | 0.328069i | \(-0.106398\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 36.6083i | − | 2.24883i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.20597 | 0.502197 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.6510i | 1.56397i | 0.623299 | + | 0.781984i | \(0.285792\pi\) | ||||
−0.623299 | + | 0.781984i | \(0.714208\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.890590 | −0.0540995 | −0.0270497 | − | 0.999634i | \(-0.508611\pi\) | ||||
−0.0270497 | + | 0.999634i | \(0.508611\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.76708 | + | 2.11190i | 0.106948 | + | 0.127818i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −41.7266 | − | 8.72492i | −2.51621 | − | 0.526133i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.75748i | 0.406018i | 0.979177 | + | 0.203009i | \(0.0650720\pi\) | ||||
−0.979177 | + | 0.203009i | \(0.934928\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 10.0080i | − | 0.599166i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.6724i | 1.23321i | 0.787271 | + | 0.616607i | \(0.211493\pi\) | ||||
−0.787271 | + | 0.616607i | \(0.788507\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.0715 | −1.78757 | −0.893783 | − | 0.448499i | \(-0.851959\pi\) | ||||
−0.893783 | + | 0.448499i | \(0.851959\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 31.8318 | 1.88555 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.14181 | + | 4.30227i | −0.303511 | + | 0.253955i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.94743 | −0.114555 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.74163 | 0.453822 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.88089 | −0.343565 | −0.171783 | − | 0.985135i | \(-0.554953\pi\) | ||||
−0.171783 | + | 0.985135i | \(0.554953\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.5119 | 1.66003 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.47372 | − | 16.6129i | 0.201565 | − | 0.963978i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.94488 | −0.343801 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.6962 | + | 13.9786i | 0.674158 | + | 0.805713i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.46966i | 0.314224i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 59.7219i | 3.41966i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.0267 | 1.65664 | 0.828322 | − | 0.560253i | \(-0.189296\pi\) | ||||
0.828322 | + | 0.560253i | \(0.189296\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.4114 | −1.04739 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.7132i | 1.62817i | 0.580743 | + | 0.814087i | \(0.302762\pi\) | ||||
−0.580743 | + | 0.814087i | \(0.697238\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.6871i | 0.717116i | 0.933507 | + | 0.358558i | \(0.116731\pi\) | ||||
−0.933507 | + | 0.358558i | \(0.883269\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −13.7505 | − | 16.4337i | −0.774750 | − | 0.925935i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.52722 | −0.254274 | −0.127137 | − | 0.991885i | \(-0.540579\pi\) | ||||
−0.127137 | + | 0.991885i | \(0.540579\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.743385 | − | 3.55521i | 0.0416216 | − | 0.199054i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.6147 | 0.592455 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.0832 | −1.56259 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.8531 | 0.712963 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.4316 | 0.632169 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.77917 | − | 11.6875i | −0.539143 | − | 0.644352i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.93745 | −0.106492 | −0.0532461 | − | 0.998581i | \(-0.516957\pi\) | ||||
−0.0532461 | + | 0.998581i | \(0.516957\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.93315 | 0.325135 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 8.99024i | − | 0.491189i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 22.5809i | − | 1.23006i | −0.788503 | − | 0.615031i | \(-0.789144\pi\) | ||
0.788503 | − | 0.615031i | \(-0.210856\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.3464i | 0.561939i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.54433 | − | 16.9506i | 0.191936 | − | 0.917928i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.19284 | − | 16.0777i | −0.496367 | − | 0.868113i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −26.1435 | −1.40752 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.6709i | 1.43177i | 0.698219 | + | 0.715884i | \(0.253976\pi\) | ||||
−0.698219 | + | 0.715884i | \(0.746024\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.3350 | 0.767333 | 0.383667 | − | 0.923472i | \(-0.374661\pi\) | ||||
0.383667 | + | 0.923472i | \(0.374661\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.11731i | 0.273142i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 31.0974i | − | 1.65515i | −0.561358 | − | 0.827573i | \(-0.689721\pi\) | ||
0.561358 | − | 0.827573i | \(-0.310279\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.7494i | 0.888967i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.85584 | − | 8.19369i | −0.362850 | − | 0.433656i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 12.0723i | − | 0.637152i | −0.947897 | − | 0.318576i | \(-0.896795\pi\) | ||
0.947897 | − | 0.318576i | \(-0.103205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.3941 | 1.75758 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.58722 | − | 10.4895i | 0.240767 | − | 0.550556i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 62.5207i | − | 3.27248i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 16.2206i | − | 0.846709i | −0.905964 | − | 0.423354i | \(-0.860853\pi\) | ||
0.905964 | − | 0.423354i | \(-0.139147\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.85704 | −0.252848 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.5806 | − | 14.7101i | 0.912738 | − | 0.763709i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.3586i | 0.691681i | 0.938293 | + | 0.345840i | \(0.112406\pi\) | ||||
−0.938293 | + | 0.345840i | \(0.887594\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 34.5353 | 1.78339 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.09512i | 0.0564015i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.6481 | 1.00925 | 0.504627 | − | 0.863338i | \(-0.331630\pi\) | ||||
0.504627 | + | 0.863338i | \(0.331630\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.24777 | −0.0639251 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 24.2656i | − | 1.23991i | −0.784636 | − | 0.619957i | \(-0.787150\pi\) | ||
0.784636 | − | 0.619957i | \(-0.212850\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.4692 | − | 32.7035i | −0.890312 | − | 1.66672i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.2044i | 0.671219i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.5421 | 1.14293 | 0.571464 | − | 0.820627i | \(-0.306375\pi\) | ||||
0.571464 | + | 0.820627i | \(0.306375\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.0647 | 1.16643 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 16.9378i | − | 0.854398i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −64.4703 | −3.24385 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.98437i | − | 0.250158i | −0.992147 | − | 0.125079i | \(-0.960082\pi\) | ||
0.992147 | − | 0.125079i | \(-0.0399185\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.7908 | + | 15.2867i | 0.640339 | + | 0.765295i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.5754 | 1.62674 | 0.813369 | − | 0.581748i | \(-0.197631\pi\) | ||||
0.813369 | + | 0.581748i | \(0.197631\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.22134i | 0.260093i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.79252i | − | 0.0890709i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.0490 | + | 2.10122i | 0.498110 | + | 0.104153i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.9833 | 1.33424 | 0.667119 | − | 0.744951i | \(-0.267527\pi\) | ||||
0.667119 | + | 0.744951i | \(0.267527\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.80913i | 0.187890i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.4568 | + | 13.6924i | 0.563750 | + | 0.673760i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 12.8699i | − | 0.631757i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.6525i | 0.619597i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.7276i | 0.572932i | 0.958090 | + | 0.286466i | \(0.0924806\pi\) | ||||
−0.958090 | + | 0.286466i | \(0.907519\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.3160 | 1.81867 | 0.909335 | − | 0.416065i | \(-0.136591\pi\) | ||||
0.909335 | + | 0.416065i | \(0.136591\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 11.0402i | − | 0.536793i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −49.8671 | −2.41891 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.6805 | + | 23.9976i | −1.38795 | + | 1.16133i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.706505 | + | 3.37883i | −0.0341104 | + | 0.163132i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.43229i | 0.309832i | 0.987928 | + | 0.154916i | \(0.0495108\pi\) | ||||
−0.987928 | + | 0.154916i | \(0.950489\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.5443i | 0.506727i | 0.967371 | + | 0.253364i | \(0.0815369\pi\) | ||||
−0.967371 | + | 0.253364i | \(0.918463\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.81594i | 0.230907i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −43.0313 | −2.05847 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.9053 | −1.14094 | −0.570469 | − | 0.821319i | \(-0.693239\pi\) | ||||
−0.570469 | + | 0.821319i | \(0.693239\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.36679 | − | 13.2069i | 0.112704 | − | 0.628900i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.6603 | −1.02911 | −0.514557 | − | 0.857456i | \(-0.672043\pi\) | ||||
−0.514557 | + | 0.857456i | \(0.672043\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33.3138 | 1.57923 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.1685 | −0.670149 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.4051 | 0.491047 | 0.245524 | − | 0.969391i | \(-0.421040\pi\) | ||||
0.245524 | + | 0.969391i | \(0.421040\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.22638 | − | 1.72011i | −0.387365 | − | 0.0809970i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.11416 | 0.334252 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.17381 | + | 8.57370i | 0.336313 | + | 0.401941i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.1467i | 1.22309i | 0.791209 | + | 0.611546i | \(0.209452\pi\) | ||||
−0.791209 | + | 0.611546i | \(0.790548\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 19.8539i | − | 0.926703i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.4445 | 1.13849 | 0.569247 | − | 0.822166i | \(-0.307235\pi\) | ||||
0.569247 | + | 0.822166i | \(0.307235\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.0519 | 0.606574 | 0.303287 | − | 0.952899i | \(-0.401916\pi\) | ||||
0.303287 | + | 0.952899i | \(0.401916\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.9616i | 1.06482i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 2.52615i | − | 0.116896i | −0.998290 | − | 0.0584480i | \(-0.981385\pi\) | ||
0.998290 | − | 0.0584480i | \(-0.0186152\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.31743 | − | 3.61249i | 0.199360 | − | 0.166809i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.3669 | 0.846301 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.67633 | + | 22.3644i | −0.215018 | + | 1.02831i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 93.0358 | 4.26877 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.6069 | 0.760379 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.6964 | −0.945641 | −0.472821 | − | 0.881159i | \(-0.656764\pi\) | ||||
−0.472821 | + | 0.881159i | \(0.656764\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.09541 | −0.141139 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.5051 | − | 12.5550i | −0.477997 | − | 0.571273i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 31.4287 | 1.42710 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.38430 | 0.0627285 | 0.0313642 | − | 0.999508i | \(-0.490015\pi\) | ||||
0.0313642 | + | 0.999508i | \(0.490015\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.76496i | 0.0798144i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.9851i | 0.811656i | 0.913949 | + | 0.405828i | \(0.133017\pi\) | ||||
−0.913949 | + | 0.405828i | \(0.866983\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.24880i | − | 0.191357i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.49765 | − | 26.2923i | 0.247101 | − | 1.18175i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.04367 | + | 6.73032i | −0.360808 | + | 0.301896i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.7285 | −1.37559 | −0.687797 | − | 0.725903i | \(-0.741422\pi\) | ||||
−0.687797 | + | 0.725903i | \(0.741422\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 13.3245i | − | 0.595297i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.5177 | 0.513547 | 0.256773 | − | 0.966472i | \(-0.417341\pi\) | ||||
0.256773 | + | 0.966472i | \(0.417341\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.2052i | 0.988119i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.04079i | − | 0.0462231i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.5374i | 0.644358i | 0.946679 | + | 0.322179i | \(0.104415\pi\) | ||||
−0.946679 | + | 0.322179i | \(0.895585\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.0247 | − | 25.1223i | 1.32821 | − | 1.11135i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 37.0410i | 1.63540i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −74.7447 | −3.29365 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.90987 | − | 18.6988i | 0.171956 | − | 0.822372i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 5.12782i | − | 0.225086i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.65888i | 0.335542i | 0.985826 | + | 0.167771i | \(0.0536569\pi\) | ||||
−0.985826 | + | 0.167771i | \(0.946343\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.5129 | −1.50914 | −0.754571 | − | 0.656219i | \(-0.772155\pi\) | ||||
−0.754571 | + | 0.656219i | \(0.772155\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 22.7125 | + | 27.1446i | 0.991253 | + | 1.18469i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 20.2576i | − | 0.882433i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.3416 | 0.536593 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.9341i | 0.561292i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.53399 | 0.109759 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 43.0925 | 1.86305 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.3091i | 0.488024i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.68584 | − | 21.5304i | 0.374126 | − | 0.927378i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.8668i | 0.467202i | 0.972333 | + | 0.233601i | \(0.0750510\pi\) | ||||
−0.972333 | + | 0.233601i | \(0.924949\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.28584 | −0.312665 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 46.4089 | 1.98794 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.3846i | 0.828825i | 0.910089 | + | 0.414413i | \(0.136013\pi\) | ||||
−0.910089 | + | 0.414413i | \(0.863987\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −27.0921 | −1.15626 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.92688i | 0.337697i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.9057 | − | 30.9609i | −1.10162 | − | 1.31659i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.6125 | −0.577819 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 39.3119i | − | 1.66570i | −0.553501 | − | 0.832848i | \(-0.686709\pi\) | ||
0.553501 | − | 0.832848i | \(-0.313291\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.88894i | − | 0.291371i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.74107 | − | 13.1091i | 0.115728 | − | 0.553466i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.3326 | −1.69981 | −0.849907 | − | 0.526932i | \(-0.823342\pi\) | ||||
−0.849907 | + | 0.526932i | \(0.823342\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 42.0033i | 1.76709i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.860830 | − | 0.720276i | 0.0361515 | − | 0.0302487i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 18.9039i | − | 0.792494i | −0.918144 | − | 0.396247i | \(-0.870312\pi\) | ||
0.918144 | − | 0.396247i | \(-0.129688\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 21.9985i | − | 0.920608i | −0.887761 | − | 0.460304i | \(-0.847740\pi\) | ||
0.887761 | − | 0.460304i | \(-0.152260\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.0276i | 1.12909i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −76.4104 | −3.18653 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.8565i | 0.576852i | 0.957502 | + | 0.288426i | \(0.0931320\pi\) | ||||
−0.957502 | + | 0.288426i | \(0.906868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.15841 | 0.380611 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.18056 | − | 5.17142i | 0.256413 | − | 0.214546i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.1272 | + | 5.88132i | 1.16491 | + | 0.243579i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.09887i | 0.334847i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 34.9079i | − | 1.44080i | −0.693557 | − | 0.720401i | \(-0.743958\pi\) | ||
0.693557 | − | 0.720401i | \(-0.256042\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37.7940i | 1.55728i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.40874 | −0.0990822 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.4485 | −0.634395 | −0.317198 | − | 0.948359i | \(-0.602742\pi\) | ||||
−0.317198 | + | 0.948359i | \(0.602742\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.8327 | − | 33.2639i | −1.14103 | − | 1.36369i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.95813 | 0.325705 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.57856 | 0.187075 | 0.0935375 | − | 0.995616i | \(-0.470182\pi\) | ||||
0.0935375 | + | 0.995616i | \(0.470182\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.03610 | 0.246218 | 0.123109 | − | 0.992393i | \(-0.460714\pi\) | ||||
0.123109 | + | 0.992393i | \(0.460714\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.07832 | 0.166082 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.6228 | − | 42.5843i | 0.757122 | − | 1.73130i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.8513 | −0.927505 | −0.463753 | − | 0.885965i | \(-0.653497\pi\) | ||||
−0.463753 | + | 0.885965i | \(0.653497\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.31279 | + | 1.93516i | −0.0937188 | + | 0.0784166i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.75983i | 0.233018i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.1407i | 1.58088i | 0.612542 | + | 0.790438i | \(0.290147\pi\) | ||||
−0.612542 | + | 0.790438i | \(0.709853\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.1436 | 0.449353 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.9071 | −0.720913 | −0.360457 | − | 0.932776i | \(-0.617379\pi\) | ||||
−0.360457 | + | 0.932776i | \(0.617379\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 25.0332i | − | 1.00617i | −0.864237 | − | 0.503084i | \(-0.832199\pi\) | ||
0.864237 | − | 0.503084i | \(-0.167801\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 30.4218i | − | 1.22078i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.3863 | + | 15.9985i | 0.536310 | + | 0.640965i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 75.9373 | 3.03749 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.11395 | + | 24.4573i | −0.204232 | + | 0.976729i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.0095 | 0.478848 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.8331 | 0.709926 | 0.354963 | − | 0.934880i | \(-0.384493\pi\) | ||||
0.354963 | + | 0.934880i | \(0.384493\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.8780 | 1.02856 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.06557 | −0.201021 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.23479 | + | 6.89023i | −0.0489241 | + | 0.273001i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.59819 | −0.300580 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.7048 | −0.501808 | −0.250904 | − | 0.968012i | \(-0.580728\pi\) | ||||
−0.250904 | + | 0.968012i | \(0.580728\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 24.9403i | − | 0.983548i | −0.870723 | − | 0.491774i | \(-0.836349\pi\) | ||
0.870723 | − | 0.491774i | \(-0.163651\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 30.2951i | − | 1.19287i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.8931i | 0.506879i | 0.967351 | + | 0.253440i | \(0.0815619\pi\) | ||||
−0.967351 | + | 0.253440i | \(0.918438\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.58059 | + | 21.9065i | −0.179804 | + | 0.859906i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.0270 | + | 9.22651i | −0.432181 | + | 0.361615i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.7356 | 0.928845 | 0.464423 | − | 0.885614i | \(-0.346262\pi\) | ||||
0.464423 | + | 0.885614i | \(0.346262\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 68.7623i | − | 2.68677i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 28.3618 | 1.10650 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.4488i | 0.445983i | 0.974820 | + | 0.222992i | \(0.0715822\pi\) | ||||
−0.974820 | + | 0.222992i | \(0.928418\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.3579i | 0.480668i | 0.970690 | + | 0.240334i | \(0.0772570\pi\) | ||||
−0.970690 | + | 0.240334i | \(0.922743\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.03802i | 0.156824i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 51.9267 | + | 62.0597i | 2.01363 | + | 2.40657i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 6.51035i | − | 0.252082i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.6197 | 0.410580 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −45.8860 | − | 9.59464i | −1.77141 | − | 0.370397i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 16.4465i | − | 0.633967i | −0.948431 | − | 0.316984i | \(-0.897330\pi\) | ||
0.948431 | − | 0.316984i | \(-0.102670\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 65.7734i | 2.53162i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.4667 | 1.09406 | 0.547032 | − | 0.837111i | \(-0.315757\pi\) | ||||
0.547032 | + | 0.837111i | \(0.315757\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.6288 | + | 15.0932i | 0.484649 | + | 0.579223i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.44697i | − | 0.170408i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.2263 | −0.391299 | −0.195649 | − | 0.980674i | \(-0.562681\pi\) | ||||
−0.195649 | + | 0.980674i | \(0.562681\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.4639i | 0.590846i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.32806 | −0.0888210 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.66407 | −0.330075 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2.29224i | − | 0.0872008i | −0.999049 | − | 0.0436004i | \(-0.986117\pi\) | ||
0.999049 | − | 0.0436004i | \(-0.0138828\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.8356 | − | 7.92470i | 0.563557 | − | 0.301034i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 51.3655i | 1.94841i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.83128 | −0.372386 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.06616 | −0.305090 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 25.2242i | − | 0.952706i | −0.879254 | − | 0.476353i | \(-0.841958\pi\) | ||
0.879254 | − | 0.476353i | \(-0.158042\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.4057 | −0.845048 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 25.3297i | 0.953971i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.6637 | + | 8.92258i | −0.401051 | + | 0.335568i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.0689 | −0.678593 | −0.339297 | − | 0.940679i | \(-0.610189\pi\) | ||||
−0.339297 | + | 0.940679i | \(0.610189\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 29.2462i | − | 1.09682i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 31.0402i | − | 1.16247i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.86820 | + | 13.7171i | −0.107265 | + | 0.512989i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.6447 | −0.883029 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35.6934i | 1.33114i | 0.746336 | + | 0.665570i | \(0.231811\pi\) | ||||
−0.746336 | + | 0.665570i | \(0.768189\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.0342 | − | 35.8951i | −1.11853 | − | 1.33680i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 12.3858i | − | 0.460634i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.0757i | 0.522759i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.3618i | 1.08897i | 0.838770 | + | 0.544485i | \(0.183275\pi\) | ||||
−0.838770 | + | 0.544485i | \(0.816725\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.1650 | −0.561665 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.7275i | 0.988551i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.53283 | 0.130488 | 0.0652441 | − | 0.997869i | \(-0.479217\pi\) | ||||
0.0652441 | + | 0.997869i | \(0.479217\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.43016 | + | 30.3008i | −0.200295 | + | 1.11766i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.90745 | + | 1.44433i | 0.254439 | + | 0.0532026i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.6407i | 0.612138i | 0.952009 | + | 0.306069i | \(0.0990138\pi\) | ||||
−0.952009 | + | 0.306069i | \(0.900986\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 7.53362i | − | 0.276755i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.3010i | 1.36844i | 0.729276 | + | 0.684220i | \(0.239857\pi\) | ||||
−0.729276 | + | 0.684220i | \(0.760143\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −57.5201 | −2.10737 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.83827 | 0.213611 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.3156 | + | 20.6946i | 0.632698 | + | 0.756163i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.9852 | 0.510326 | 0.255163 | − | 0.966898i | \(-0.417871\pi\) | ||||
0.255163 | + | 0.966898i | \(0.417871\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.98779 | −0.0724390 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28.8814 | 1.05110 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.2837 | 0.373769 | 0.186884 | − | 0.982382i | \(-0.440161\pi\) | ||||
0.186884 | + | 0.982382i | \(0.440161\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.20009 | − | 20.0868i | 0.152454 | − | 0.729103i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.6121 | −0.602189 | −0.301094 | − | 0.953594i | \(-0.597352\pi\) | ||||
−0.301094 | + | 0.953594i | \(0.597352\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.6482 | + | 22.2872i | 0.675111 | + | 0.806851i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 31.4217i | − | 1.13605i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.74791i | − | 0.243653i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.2510 | 1.19906 | 0.599530 | − | 0.800352i | \(-0.295354\pi\) | ||||
0.599530 | + | 0.800352i | \(0.295354\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.83474 | 0.282161 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.34885i | 0.336255i | 0.985765 | + | 0.168127i | \(0.0537720\pi\) | ||||
−0.985765 | + | 0.168127i | \(0.946228\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 67.1105i | 2.41068i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.46983 | − | 6.53721i | −0.196229 | − | 0.234521i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.3420 | 0.657169 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.8691 | − | 2.69089i | −0.460491 | − | 0.0962875i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.60406 | −0.200273 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 74.5641 | 2.66131 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.23895 | 0.186748 | 0.0933741 | − | 0.995631i | \(-0.470235\pi\) | ||||
0.0933741 | + | 0.995631i | \(0.470235\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.0748 | −0.394274 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.1715 | + | 16.8779i | −0.717214 | + | 0.600109i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.1344 | 0.501926 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −38.1015 | −1.35132 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.0880i | 1.31373i | 0.754010 | + | 0.656863i | \(0.228117\pi\) | ||||
−0.754010 | + | 0.656863i | \(0.771883\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 22.3468i | − | 0.790572i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.1124i | 0.533972i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 48.0364 | + | 10.0443i | 1.69517 | + | 0.354456i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −42.6474 | − | 50.9697i | −1.50313 | − | 1.79644i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.6973 | 0.939788 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 47.2739i | − | 1.66206i | −0.556225 | − | 0.831032i | \(-0.687751\pi\) | ||
0.556225 | − | 0.831032i | \(-0.312249\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.6775 | 0.831430 | 0.415715 | − | 0.909495i | \(-0.363531\pi\) | ||||
0.415715 | + | 0.909495i | \(0.363531\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.926916i | 0.0325084i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.16523i | 0.250987i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 49.8648i | − | 1.74455i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.88936 | + | 3.25432i | −0.135905 | + | 0.113715i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.603496i | 0.0210622i | 0.999945 | + | 0.0105311i | \(0.00335221\pi\) | ||||
−0.999945 | + | 0.0105311i | \(0.996648\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.53514 | 0.297516 | 0.148758 | − | 0.988874i | \(-0.452472\pi\) | ||||
0.148758 | + | 0.988874i | \(0.452472\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.08080 | + | 43.4286i | −0.316153 | + | 1.51199i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 51.4796i | − | 1.79012i | −0.445945 | − | 0.895060i | \(-0.647132\pi\) | ||
0.445945 | − | 0.895060i | \(-0.352868\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.0002i | 1.59765i | 0.601561 | + | 0.798827i | \(0.294546\pi\) | ||||
−0.601561 | + | 0.798827i | \(0.705454\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.03312 | 0.243976 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.79069 | − | 26.7325i | 0.165988 | − | 0.926225i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 54.0937i | − | 1.87199i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −26.7192 | −0.923551 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 11.0223i | − | 0.380533i | −0.981732 | − | 0.190267i | \(-0.939065\pi\) | ||
0.981732 | − | 0.190267i | \(-0.0609352\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.8007 | 0.958645 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.5156 | 0.741038 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 4.22530i | − | 0.145355i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.9335 | − | 8.16807i | 0.959808 | − | 0.280658i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.2981i | 1.07415i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.4018 | 0.630807 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.54541 | −0.326829 | −0.163414 | − | 0.986558i | \(-0.552251\pi\) | ||||
−0.163414 | + | 0.986558i | \(0.552251\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 58.6227i | 2.00485i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 33.0441 | 1.12876 | 0.564382 | − | 0.825514i | \(-0.309114\pi\) | ||||
0.564382 | + | 0.825514i | \(0.309114\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 23.0986i | − | 0.788116i | −0.919086 | − | 0.394058i | \(-0.871071\pi\) | ||
0.919086 | − | 0.394058i | \(-0.128929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.47775 | + | 5.35154i | 0.152601 | + | 0.182380i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.88912 | −0.166427 | −0.0832137 | − | 0.996532i | \(-0.526518\pi\) | ||||
−0.0832137 | + | 0.996532i | \(0.526518\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 20.8174i | − | 0.707814i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.02687i | 0.0688360i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.3575 | − | 49.5344i | 0.351355 | − | 1.68034i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.12772 | −0.0720950 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.2573i | 0.482536i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 56.3368 | + | 67.3304i | 1.90453 | + | 2.27618i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.3368i | 0.349049i | 0.984653 | + | 0.174524i | \(0.0558388\pi\) | ||||
−0.984653 | + | 0.174524i | \(0.944161\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.12076i | 0.206448i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 11.1044i | − | 0.374117i | −0.982349 | − | 0.187058i | \(-0.940105\pi\) | ||
0.982349 | − | 0.187058i | \(-0.0598954\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.6551 | −1.77199 | −0.885993 | − | 0.463700i | \(-0.846522\pi\) | ||||
−0.885993 | + | 0.463700i | \(0.846522\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 29.6749i | − | 0.997510i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.8310 | −0.497978 | −0.248989 | − | 0.968506i | \(-0.580098\pi\) | ||||
−0.248989 | + | 0.968506i | \(0.580098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.03547 | − | 2.43267i | −0.0682673 | − | 0.0815890i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.37724 | + | 0.287978i | 0.0461393 | + | 0.00964761i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 41.6918i | 1.39516i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.9117i | 1.53466i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.18737i | 0.206590i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.71799 | −0.190706 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.6146 | 1.11986 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.5488 | − | 12.1733i | 0.484153 | − | 0.405102i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29.5784 | −0.983218 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.0368692 | −0.00122422 | −0.000612111 | − | 1.00000i | \(-0.500195\pi\) | ||||
−0.000612111 | 1.00000i | \(0.500195\pi\) | ||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.0731 | −0.334105 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.1397 | −0.667259 | −0.333629 | − | 0.942704i | \(-0.608273\pi\) | ||||
−0.333629 | + | 0.942704i | \(0.608273\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.88828 | + | 2.06761i | 0.327254 | + | 0.0684280i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 62.1579 | 2.05488 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 33.0221 | − | 27.6303i | 1.09049 | − | 0.912434i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 35.9160i | − | 1.18476i | −0.805659 | − | 0.592379i | \(-0.798189\pi\) | ||
0.805659 | − | 0.592379i | \(-0.201811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 30.2107i | − | 0.995477i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.96408 | 0.130479 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −39.7857 | −1.30815 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 33.9071i | − | 1.11366i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 50.3872i | − | 1.65315i | −0.562825 | − | 0.826576i | \(-0.690286\pi\) | ||
0.562825 | − | 0.826576i | \(-0.309714\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.93787 | + | 49.8741i | −0.292927 | + | 1.63456i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29.8844 | 0.978370 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.1279 | − | 53.2190i | 0.363923 | − | 1.74045i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.5273 | −0.343910 | −0.171955 | − | 0.985105i | \(-0.555008\pi\) | ||||
−0.171955 | + | 0.985105i | \(0.555008\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.2046 | 0.430915 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.5366 | −0.473880 | −0.236940 | − | 0.971524i | \(-0.576144\pi\) | ||||
−0.236940 | + | 0.971524i | \(0.576144\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.0643 | −0.490560 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −43.8743 | + | 36.7106i | −1.42723 | + | 1.19420i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.0726 | 1.07472 | 0.537358 | − | 0.843354i | \(-0.319423\pi\) | ||||
0.537358 | + | 0.843354i | \(0.319423\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.7968 | −0.480323 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.71189i | 0.152793i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.0937i | 0.424146i | 0.977254 | + | 0.212073i | \(0.0680214\pi\) | ||||
−0.977254 | + | 0.212073i | \(0.931979\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 109.724i | 3.55059i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.70022 | − | 0.773707i | −0.119611 | − | 0.0250104i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.42632 | + | 6.21377i | −0.239808 | + | 0.200653i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.73762 | 0.120568 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.5484i | 0.629940i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 37.1804 | 1.19688 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 34.2317i | − | 1.10082i | −0.834896 | − | 0.550408i | \(-0.814472\pi\) | ||
0.834896 | − | 0.550408i | \(-0.185528\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 29.2287i | 0.938960i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 6.96437i | − | 0.223497i | −0.993737 | − | 0.111749i | \(-0.964355\pi\) | ||
0.993737 | − | 0.111749i | \(-0.0356451\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.6675 | + | 20.6399i | −0.790805 | + | 0.661684i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 13.3774i | − | 0.428420i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 57.1731 | 1.82913 | 0.914565 | − | 0.404438i | \(-0.132533\pi\) | ||||
0.914565 | + | 0.404438i | \(0.132533\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.35205 | + | 25.5960i | −0.171052 | + | 0.818050i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.0529i | 0.672167i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 28.7679i | − | 0.917555i | −0.888551 | − | 0.458777i | \(-0.848288\pi\) | ||
0.888551 | − | 0.458777i | \(-0.151712\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.77876 | −0.311577 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.1642 | + | 10.1781i | −0.387191 | + | 0.323971i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 40.9540i | 1.30226i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.3878 | 1.85475 | 0.927374 | − | 0.374135i | \(-0.122060\pi\) | ||||
0.927374 | + | 0.374135i | \(0.122060\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.01648i | 0.0639911i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32.3077 | 1.02422 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.1774 | −1.30410 | −0.652051 | − | 0.758175i | \(-0.726091\pi\) | ||||
−0.652051 | + | 0.758175i | \(0.726091\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 15.8402i | − | 0.501161i |
(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 | 4004.2.e.b.3849.16 | yes | 48 | |
7.6 | odd | 2 | 4004.2.e.a.3849.33 | yes | 48 | ||
11.10 | odd | 2 | 4004.2.e.a.3849.16 | ✓ | 48 | ||
77.76 | even | 2 | inner | 4004.2.e.b.3849.33 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.e.a.3849.16 | ✓ | 48 | 11.10 | odd | 2 | ||
4004.2.e.a.3849.33 | yes | 48 | 7.6 | odd | 2 | ||
4004.2.e.b.3849.16 | yes | 48 | 1.1 | even | 1 | trivial | |
4004.2.e.b.3849.33 | yes | 48 | 77.76 | even | 2 | inner |