Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(506,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.506");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.c (of order \(2\), degree \(1\), not 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: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 506.1 | ||
Root | \(0.665665 + 1.24775i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.506 |
Dual form | 845.2.c.g.506.8 |
$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.49551i | − 1.76459i | −0.470696 | − | 0.882295i | \(-0.655997\pi\) | ||||
0.470696 | − | 0.882295i | \(-0.344003\pi\) | |||||||
\(3\) | −2.82684 | −1.63208 | −0.816038 | − | 0.577998i | \(-0.803834\pi\) | ||||
−0.816038 | + | 0.577998i | \(0.803834\pi\) | |||||||
\(4\) | −4.22756 | −2.11378 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 7.05440i | 2.87995i | ||||||||
\(7\) | 1.90521i | 0.720103i | 0.932933 | + | 0.360051i | \(0.117241\pi\) | ||||
−0.932933 | + | 0.360051i | \(0.882759\pi\) | |||||||
\(8\) | 5.55889i | 1.96536i | ||||||||
\(9\) | 4.99102 | 1.66367 | ||||||||
\(10\) | 2.49551 | 0.789149 | ||||||||
\(11\) | 1.06939i | 0.322433i | 0.986919 | + | 0.161217i | \(0.0515417\pi\) | ||||
−0.986919 | + | 0.161217i | \(0.948458\pi\) | |||||||
\(12\) | 11.9506 | 3.44985 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.75447 | 1.27069 | ||||||||
\(15\) | − 2.82684i | − 0.729887i | ||||||||
\(16\) | 5.41713 | 1.35428 | ||||||||
\(17\) | −0.637263 | −0.154559 | −0.0772795 | − | 0.997009i | \(-0.524623\pi\) | ||||
−0.0772795 | + | 0.997009i | \(0.524623\pi\) | |||||||
\(18\) | − 12.4551i | − 2.93570i | ||||||||
\(19\) | − 5.73205i | − 1.31502i | −0.753445 | − | 0.657511i | \(-0.771609\pi\) | ||||
0.753445 | − | 0.657511i | \(-0.228391\pi\) | |||||||
\(20\) | − 4.22756i | − 0.945311i | ||||||||
\(21\) | − 5.38573i | − 1.17526i | ||||||||
\(22\) | 2.66867 | 0.568962 | ||||||||
\(23\) | −3.81785 | −0.796078 | −0.398039 | − | 0.917369i | \(-0.630309\pi\) | ||||
−0.398039 | + | 0.917369i | \(0.630309\pi\) | |||||||
\(24\) | − 15.7141i | − 3.20762i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.62828 | −1.08316 | ||||||||
\(28\) | − 8.05440i | − 1.52214i | ||||||||
\(29\) | 9.45512 | 1.75577 | 0.877886 | − | 0.478870i | \(-0.158954\pi\) | ||||
0.877886 | + | 0.478870i | \(0.158954\pi\) | |||||||
\(30\) | −7.05440 | −1.28795 | ||||||||
\(31\) | 1.46410i | 0.262960i | 0.991319 | + | 0.131480i | \(0.0419730\pi\) | ||||
−0.991319 | + | 0.131480i | \(0.958027\pi\) | |||||||
\(32\) | − 2.40072i | − 0.424391i | ||||||||
\(33\) | − 3.02299i | − 0.526235i | ||||||||
\(34\) | 1.59030i | 0.272733i | ||||||||
\(35\) | −1.90521 | −0.322040 | ||||||||
\(36\) | −21.0998 | −3.51663 | ||||||||
\(37\) | 0.757449i | 0.124524i | 0.998060 | + | 0.0622619i | \(0.0198314\pi\) | ||||
−0.998060 | + | 0.0622619i | \(0.980169\pi\) | |||||||
\(38\) | −14.3044 | −2.32048 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.55889 | −0.878938 | ||||||||
\(41\) | − 0.267949i | − 0.0418466i | −0.999781 | − | 0.0209233i | \(-0.993339\pi\) | ||||
0.999781 | − | 0.0209233i | \(-0.00666058\pi\) | |||||||
\(42\) | −13.4401 | −2.07386 | ||||||||
\(43\) | −0.637263 | −0.0971817 | −0.0485909 | − | 0.998819i | \(-0.515473\pi\) | ||||
−0.0485909 | + | 0.998819i | \(0.515473\pi\) | |||||||
\(44\) | − 4.52091i | − 0.681552i | ||||||||
\(45\) | 4.99102i | 0.744017i | ||||||||
\(46\) | 9.52748i | 1.40475i | ||||||||
\(47\) | − 9.44613i | − 1.37786i | −0.724828 | − | 0.688930i | \(-0.758081\pi\) | ||||
0.724828 | − | 0.688930i | \(-0.241919\pi\) | |||||||
\(48\) | −15.3134 | −2.21029 | ||||||||
\(49\) | 3.37017 | 0.481452 | ||||||||
\(50\) | 2.49551i | 0.352918i | ||||||||
\(51\) | 1.80144 | 0.252252 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.99102 | −0.960290 | −0.480145 | − | 0.877189i | \(-0.659416\pi\) | ||||
−0.480145 | + | 0.877189i | \(0.659416\pi\) | |||||||
\(54\) | 14.0454i | 1.91134i | ||||||||
\(55\) | −1.06939 | −0.144196 | ||||||||
\(56\) | −10.5909 | −1.41526 | ||||||||
\(57\) | 16.2036i | 2.14622i | ||||||||
\(58\) | − 23.5953i | − 3.09822i | ||||||||
\(59\) | 0.741035i | 0.0964746i | 0.998836 | + | 0.0482373i | \(0.0153604\pi\) | ||||
−0.998836 | + | 0.0482373i | \(0.984640\pi\) | |||||||
\(60\) | 11.9506i | 1.54282i | ||||||||
\(61\) | 4.19856 | 0.537571 | 0.268785 | − | 0.963200i | \(-0.413378\pi\) | ||||
0.268785 | + | 0.963200i | \(0.413378\pi\) | |||||||
\(62\) | 3.65368 | 0.464017 | ||||||||
\(63\) | 9.50894i | 1.19801i | ||||||||
\(64\) | 4.84325 | 0.605406 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.54390 | −0.928589 | ||||||||
\(67\) | − 8.09479i | − 0.988936i | −0.869196 | − | 0.494468i | \(-0.835363\pi\) | ||||
0.869196 | − | 0.494468i | \(-0.164637\pi\) | |||||||
\(68\) | 2.69407 | 0.326704 | ||||||||
\(69\) | 10.7925 | 1.29926 | ||||||||
\(70\) | 4.75447i | 0.568268i | ||||||||
\(71\) | − 9.76488i | − 1.15888i | −0.815016 | − | 0.579439i | \(-0.803272\pi\) | ||||
0.815016 | − | 0.579439i | \(-0.196728\pi\) | |||||||
\(72\) | 27.7445i | 3.26972i | ||||||||
\(73\) | − 3.71649i | − 0.434982i | −0.976062 | − | 0.217491i | \(-0.930213\pi\) | ||||
0.976062 | − | 0.217491i | \(-0.0697873\pi\) | |||||||
\(74\) | 1.89022 | 0.219734 | ||||||||
\(75\) | 2.82684 | 0.326415 | ||||||||
\(76\) | 24.2326i | 2.77967i | ||||||||
\(77\) | −2.03741 | −0.232185 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.31937 | −1.04851 | −0.524255 | − | 0.851561i | \(-0.675656\pi\) | ||||
−0.524255 | + | 0.851561i | \(0.675656\pi\) | |||||||
\(80\) | 5.41713i | 0.605654i | ||||||||
\(81\) | 0.937188 | 0.104132 | ||||||||
\(82\) | −0.668669 | −0.0738422 | ||||||||
\(83\) | − 5.11778i | − 0.561749i | −0.959744 | − | 0.280875i | \(-0.909376\pi\) | ||||
0.959744 | − | 0.280875i | \(-0.0906245\pi\) | |||||||
\(84\) | 22.7685i | 2.48424i | ||||||||
\(85\) | − 0.637263i | − 0.0691209i | ||||||||
\(86\) | 1.59030i | 0.171486i | ||||||||
\(87\) | −26.7281 | −2.86555 | ||||||||
\(88\) | −5.94462 | −0.633698 | ||||||||
\(89\) | − 12.5783i | − 1.33330i | −0.745371 | − | 0.666650i | \(-0.767727\pi\) | ||||
0.745371 | − | 0.666650i | \(-0.232273\pi\) | |||||||
\(90\) | 12.4551 | 1.31288 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 16.1402 | 1.68273 | ||||||||
\(93\) | − 4.13878i | − 0.429171i | ||||||||
\(94\) | −23.5729 | −2.43136 | ||||||||
\(95\) | 5.73205 | 0.588096 | ||||||||
\(96\) | 6.78645i | 0.692639i | ||||||||
\(97\) | 4.22155i | 0.428634i | 0.976764 | + | 0.214317i | \(0.0687525\pi\) | ||||
−0.976764 | + | 0.214317i | \(0.931248\pi\) | |||||||
\(98\) | − 8.41027i | − 0.849566i | ||||||||
\(99\) | 5.33734i | 0.536423i | ||||||||
\(100\) | 4.22756 | 0.422756 | ||||||||
\(101\) | 15.2476 | 1.51719 | 0.758595 | − | 0.651562i | \(-0.225886\pi\) | ||||
0.758595 | + | 0.651562i | \(0.225886\pi\) | |||||||
\(102\) | − 4.49551i | − 0.445122i | ||||||||
\(103\) | 13.5269 | 1.33285 | 0.666423 | − | 0.745574i | \(-0.267824\pi\) | ||||
0.666423 | + | 0.745574i | \(0.267824\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.38573 | 0.525593 | ||||||||
\(106\) | 17.4461i | 1.69452i | ||||||||
\(107\) | −7.36274 | −0.711783 | −0.355891 | − | 0.934527i | \(-0.615823\pi\) | ||||
−0.355891 | + | 0.934527i | \(0.615823\pi\) | |||||||
\(108\) | 23.7939 | 2.28957 | ||||||||
\(109\) | − 10.0760i | − 0.965103i | −0.875868 | − | 0.482551i | \(-0.839710\pi\) | ||||
0.875868 | − | 0.482551i | \(-0.160290\pi\) | |||||||
\(110\) | 2.66867i | 0.254448i | ||||||||
\(111\) | − 2.14119i | − 0.203232i | ||||||||
\(112\) | 10.3208i | 0.975223i | ||||||||
\(113\) | −6.68806 | −0.629160 | −0.314580 | − | 0.949231i | \(-0.601864\pi\) | ||||
−0.314580 | + | 0.949231i | \(0.601864\pi\) | |||||||
\(114\) | 40.4362 | 3.78719 | ||||||||
\(115\) | − 3.81785i | − 0.356017i | ||||||||
\(116\) | −39.9721 | −3.71131 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.84926 | 0.170238 | ||||||||
\(119\) | − 1.21412i | − 0.111298i | ||||||||
\(120\) | 15.7141 | 1.43449 | ||||||||
\(121\) | 9.85641 | 0.896037 | ||||||||
\(122\) | − 10.4775i | − 0.948592i | ||||||||
\(123\) | 0.757449i | 0.0682969i | ||||||||
\(124\) | − 6.18958i | − 0.555840i | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 23.7296 | 2.11400 | ||||||||
\(127\) | −1.48950 | −0.132172 | −0.0660859 | − | 0.997814i | \(-0.521051\pi\) | ||||
−0.0660859 | + | 0.997814i | \(0.521051\pi\) | |||||||
\(128\) | − 16.8878i | − 1.49269i | ||||||||
\(129\) | 1.80144 | 0.158608 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.12676 | 0.360557 | 0.180278 | − | 0.983616i | \(-0.442300\pi\) | ||||
0.180278 | + | 0.983616i | \(0.442300\pi\) | |||||||
\(132\) | 12.7799i | 1.11234i | ||||||||
\(133\) | 10.9208 | 0.946951 | ||||||||
\(134\) | −20.2006 | −1.74507 | ||||||||
\(135\) | − 5.62828i | − 0.484405i | ||||||||
\(136\) | − 3.54248i | − 0.303765i | ||||||||
\(137\) | − 20.1096i | − 1.71808i | −0.511906 | − | 0.859041i | \(-0.671060\pi\) | ||||
0.511906 | − | 0.859041i | \(-0.328940\pi\) | |||||||
\(138\) | − 26.9327i | − 2.29266i | ||||||||
\(139\) | 20.8253 | 1.76638 | 0.883189 | − | 0.469018i | \(-0.155392\pi\) | ||||
0.883189 | + | 0.469018i | \(0.155392\pi\) | |||||||
\(140\) | 8.05440 | 0.680721 | ||||||||
\(141\) | 26.7027i | 2.24877i | ||||||||
\(142\) | −24.3683 | −2.04494 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 27.0370 | 2.25308 | ||||||||
\(145\) | 9.45512i | 0.785205i | ||||||||
\(146\) | −9.27453 | −0.767565 | ||||||||
\(147\) | −9.52691 | −0.785767 | ||||||||
\(148\) | − 3.20216i | − 0.263216i | ||||||||
\(149\) | − 13.3678i | − 1.09513i | −0.836763 | − | 0.547565i | \(-0.815555\pi\) | ||||
0.836763 | − | 0.547565i | \(-0.184445\pi\) | |||||||
\(150\) | − 7.05440i | − 0.575989i | ||||||||
\(151\) | 18.2984i | 1.48910i | 0.667567 | + | 0.744550i | \(0.267336\pi\) | ||||
−0.667567 | + | 0.744550i | \(0.732664\pi\) | |||||||
\(152\) | 31.8638 | 2.58450 | ||||||||
\(153\) | −3.18059 | −0.257136 | ||||||||
\(154\) | 5.08438i | 0.409711i | ||||||||
\(155\) | −1.46410 | −0.117599 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.42229 | 0.193320 | 0.0966599 | − | 0.995317i | \(-0.469184\pi\) | ||||
0.0966599 | + | 0.995317i | \(0.469184\pi\) | |||||||
\(158\) | 23.2566i | 1.85019i | ||||||||
\(159\) | 19.7625 | 1.56727 | ||||||||
\(160\) | 2.40072 | 0.189794 | ||||||||
\(161\) | − 7.27382i | − 0.573258i | ||||||||
\(162\) | − 2.33876i | − 0.183750i | ||||||||
\(163\) | 15.9829i | 1.25188i | 0.779873 | + | 0.625938i | \(0.215284\pi\) | ||||
−0.779873 | + | 0.625938i | \(0.784716\pi\) | |||||||
\(164\) | 1.13277i | 0.0884545i | ||||||||
\(165\) | 3.02299 | 0.235340 | ||||||||
\(166\) | −12.7715 | −0.991257 | ||||||||
\(167\) | − 14.3932i | − 1.11378i | −0.830588 | − | 0.556888i | \(-0.811995\pi\) | ||||
0.830588 | − | 0.556888i | \(-0.188005\pi\) | |||||||
\(168\) | 29.9387 | 2.30982 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.59030 | −0.121970 | ||||||||
\(171\) | − 28.6088i | − 2.18777i | ||||||||
\(172\) | 2.69407 | 0.205421 | ||||||||
\(173\) | 24.3489 | 1.85122 | 0.925608 | − | 0.378484i | \(-0.123555\pi\) | ||||
0.925608 | + | 0.378484i | \(0.123555\pi\) | |||||||
\(174\) | 66.7001i | 5.05653i | ||||||||
\(175\) | − 1.90521i | − 0.144021i | ||||||||
\(176\) | 5.79302i | 0.436666i | ||||||||
\(177\) | − 2.09479i | − 0.157454i | ||||||||
\(178\) | −31.3893 | −2.35273 | ||||||||
\(179\) | −3.78829 | −0.283150 | −0.141575 | − | 0.989928i | \(-0.545217\pi\) | ||||
−0.141575 | + | 0.989928i | \(0.545217\pi\) | |||||||
\(180\) | − 21.0998i | − 1.57269i | ||||||||
\(181\) | 8.48794 | 0.630904 | 0.315452 | − | 0.948942i | \(-0.397844\pi\) | ||||
0.315452 | + | 0.948942i | \(0.397844\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.8687 | −0.877356 | ||||||||
\(184\) | − 21.2230i | − 1.56458i | ||||||||
\(185\) | −0.757449 | −0.0556888 | ||||||||
\(186\) | −10.3284 | −0.757312 | ||||||||
\(187\) | − 0.681482i | − 0.0498349i | ||||||||
\(188\) | 39.9341i | 2.91249i | ||||||||
\(189\) | − 10.7231i | − 0.779988i | ||||||||
\(190\) | − 14.3044i | − 1.03775i | ||||||||
\(191\) | −5.44310 | −0.393849 | −0.196924 | − | 0.980419i | \(-0.563095\pi\) | ||||
−0.196924 | + | 0.980419i | \(0.563095\pi\) | |||||||
\(192\) | −13.6911 | −0.988069 | ||||||||
\(193\) | 12.1576i | 0.875123i | 0.899188 | + | 0.437562i | \(0.144158\pi\) | ||||
−0.899188 | + | 0.437562i | \(0.855842\pi\) | |||||||
\(194\) | 10.5349 | 0.756363 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.2476 | −1.01768 | ||||||||
\(197\) | 4.37830i | 0.311941i | 0.987762 | + | 0.155970i | \(0.0498505\pi\) | ||||
−0.987762 | + | 0.155970i | \(0.950150\pi\) | |||||||
\(198\) | 13.3194 | 0.946566 | ||||||||
\(199\) | −20.8373 | −1.47712 | −0.738558 | − | 0.674189i | \(-0.764493\pi\) | ||||
−0.738558 | + | 0.674189i | \(0.764493\pi\) | |||||||
\(200\) | − 5.55889i | − 0.393073i | ||||||||
\(201\) | 22.8827i | 1.61402i | ||||||||
\(202\) | − 38.0504i | − 2.67722i | ||||||||
\(203\) | 18.0140i | 1.26434i | ||||||||
\(204\) | −7.61569 | −0.533205 | ||||||||
\(205\) | 0.267949 | 0.0187144 | ||||||||
\(206\) | − 33.7565i | − 2.35193i | ||||||||
\(207\) | −19.0550 | −1.32441 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.12979 | 0.424007 | ||||||||
\(210\) | − 13.4401i | − 0.927457i | ||||||||
\(211\) | −10.6537 | −0.733429 | −0.366715 | − | 0.930333i | \(-0.619517\pi\) | ||||
−0.366715 | + | 0.930333i | \(0.619517\pi\) | |||||||
\(212\) | 29.5549 | 2.02984 | ||||||||
\(213\) | 27.6037i | 1.89138i | ||||||||
\(214\) | 18.3738i | 1.25600i | ||||||||
\(215\) | − 0.637263i | − 0.0434610i | ||||||||
\(216\) | − 31.2870i | − 2.12881i | ||||||||
\(217\) | −2.78942 | −0.189358 | ||||||||
\(218\) | −25.1447 | −1.70301 | ||||||||
\(219\) | 10.5059i | 0.709924i | ||||||||
\(220\) | 4.52091 | 0.304799 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.34335 | −0.358622 | ||||||||
\(223\) | − 21.3393i | − 1.42899i | −0.699642 | − | 0.714494i | \(-0.746657\pi\) | ||||
0.699642 | − | 0.714494i | \(-0.253343\pi\) | |||||||
\(224\) | 4.57388 | 0.305605 | ||||||||
\(225\) | −4.99102 | −0.332734 | ||||||||
\(226\) | 16.6901i | 1.11021i | ||||||||
\(227\) | − 15.6857i | − 1.04109i | −0.853833 | − | 0.520547i | \(-0.825728\pi\) | ||||
0.853833 | − | 0.520547i | \(-0.174272\pi\) | |||||||
\(228\) | − 68.5016i | − 4.53663i | ||||||||
\(229\) | − 7.62085i | − 0.503600i | −0.967779 | − | 0.251800i | \(-0.918977\pi\) | ||||
0.967779 | − | 0.251800i | \(-0.0810225\pi\) | |||||||
\(230\) | −9.52748 | −0.628224 | ||||||||
\(231\) | 5.75944 | 0.378943 | ||||||||
\(232\) | 52.5599i | 3.45073i | ||||||||
\(233\) | 19.0550 | 1.24833 | 0.624166 | − | 0.781292i | \(-0.285439\pi\) | ||||
0.624166 | + | 0.781292i | \(0.285439\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.44613 | 0.616198 | ||||||||
\(236\) | − 3.13277i | − 0.203926i | ||||||||
\(237\) | 26.3444 | 1.71125 | ||||||||
\(238\) | −3.02985 | −0.196396 | ||||||||
\(239\) | − 12.7535i | − 0.824954i | −0.910968 | − | 0.412477i | \(-0.864664\pi\) | ||||
0.910968 | − | 0.412477i | \(-0.135336\pi\) | |||||||
\(240\) | − 15.3134i | − 0.988473i | ||||||||
\(241\) | 25.9288i | 1.67022i | 0.550081 | + | 0.835111i | \(0.314597\pi\) | ||||
−0.550081 | + | 0.835111i | \(0.685403\pi\) | |||||||
\(242\) | − 24.5967i | − 1.58114i | ||||||||
\(243\) | 14.2356 | 0.913211 | ||||||||
\(244\) | −17.7497 | −1.13631 | ||||||||
\(245\) | 3.37017i | 0.215312i | ||||||||
\(246\) | 1.89022 | 0.120516 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8.13878 | −0.516813 | ||||||||
\(249\) | 14.4671i | 0.916817i | ||||||||
\(250\) | −2.49551 | −0.157830 | ||||||||
\(251\) | −7.61186 | −0.480457 | −0.240228 | − | 0.970716i | \(-0.577222\pi\) | ||||
−0.240228 | + | 0.970716i | \(0.577222\pi\) | |||||||
\(252\) | − 40.1996i | − 2.53234i | ||||||||
\(253\) | − 4.08277i | − 0.256682i | ||||||||
\(254\) | 3.71706i | 0.233229i | ||||||||
\(255\) | 1.80144i | 0.112811i | ||||||||
\(256\) | −32.4572 | −2.02857 | ||||||||
\(257\) | −0.335783 | −0.0209456 | −0.0104728 | − | 0.999945i | \(-0.503334\pi\) | ||||
−0.0104728 | + | 0.999945i | \(0.503334\pi\) | |||||||
\(258\) | − 4.49551i | − 0.279878i | ||||||||
\(259\) | −1.44310 | −0.0896700 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 47.1906 | 2.92103 | ||||||||
\(262\) | − 10.2984i | − 0.636235i | ||||||||
\(263\) | −5.37589 | −0.331492 | −0.165746 | − | 0.986169i | \(-0.553003\pi\) | ||||
−0.165746 | + | 0.986169i | \(0.553003\pi\) | |||||||
\(264\) | 16.8045 | 1.03424 | ||||||||
\(265\) | − 6.99102i | − 0.429455i | ||||||||
\(266\) | − 27.2529i | − 1.67098i | ||||||||
\(267\) | 35.5569i | 2.17605i | ||||||||
\(268\) | 34.2212i | 2.09039i | ||||||||
\(269\) | −1.31038 | −0.0798956 | −0.0399478 | − | 0.999202i | \(-0.512719\pi\) | ||||
−0.0399478 | + | 0.999202i | \(0.512719\pi\) | |||||||
\(270\) | −14.0454 | −0.854777 | ||||||||
\(271\) | − 11.6453i | − 0.707403i | −0.935358 | − | 0.353701i | \(-0.884923\pi\) | ||||
0.935358 | − | 0.353701i | \(-0.115077\pi\) | |||||||
\(272\) | −3.45214 | −0.209317 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −50.1838 | −3.03171 | ||||||||
\(275\) | − 1.06939i | − 0.0644866i | ||||||||
\(276\) | −45.6257 | −2.74635 | ||||||||
\(277\) | 20.3161 | 1.22068 | 0.610338 | − | 0.792141i | \(-0.291033\pi\) | ||||
0.610338 | + | 0.792141i | \(0.291033\pi\) | |||||||
\(278\) | − 51.9697i | − 3.11693i | ||||||||
\(279\) | 7.30735i | 0.437480i | ||||||||
\(280\) | − 10.5909i | − 0.632925i | ||||||||
\(281\) | − 11.8744i | − 0.708366i | −0.935176 | − | 0.354183i | \(-0.884759\pi\) | ||||
0.935176 | − | 0.354183i | \(-0.115241\pi\) | |||||||
\(282\) | 66.6368 | 3.96816 | ||||||||
\(283\) | 22.6521 | 1.34653 | 0.673264 | − | 0.739402i | \(-0.264892\pi\) | ||||
0.673264 | + | 0.739402i | \(0.264892\pi\) | |||||||
\(284\) | 41.2816i | 2.44961i | ||||||||
\(285\) | −16.2036 | −0.959817 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.510500 | 0.0301339 | ||||||||
\(288\) | − 11.9820i | − 0.706048i | ||||||||
\(289\) | −16.5939 | −0.976112 | ||||||||
\(290\) | 23.5953 | 1.38556 | ||||||||
\(291\) | − 11.9336i | − 0.699562i | ||||||||
\(292\) | 15.7117i | 0.919456i | ||||||||
\(293\) | 18.6127i | 1.08737i | 0.839290 | + | 0.543683i | \(0.182971\pi\) | ||||
−0.839290 | + | 0.543683i | \(0.817029\pi\) | |||||||
\(294\) | 23.7745i | 1.38656i | ||||||||
\(295\) | −0.741035 | −0.0431448 | ||||||||
\(296\) | −4.21058 | −0.244735 | ||||||||
\(297\) | − 6.01882i | − 0.349247i | ||||||||
\(298\) | −33.3593 | −1.93245 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −11.9506 | −0.689970 | ||||||||
\(301\) | − 1.21412i | − 0.0699808i | ||||||||
\(302\) | 45.6637 | 2.62765 | ||||||||
\(303\) | −43.1024 | −2.47617 | ||||||||
\(304\) | − 31.0513i | − 1.78091i | ||||||||
\(305\) | 4.19856i | 0.240409i | ||||||||
\(306\) | 7.93719i | 0.453739i | ||||||||
\(307\) | 3.14776i | 0.179652i | 0.995957 | + | 0.0898262i | \(0.0286311\pi\) | ||||
−0.995957 | + | 0.0898262i | \(0.971369\pi\) | |||||||
\(308\) | 8.61329 | 0.490788 | ||||||||
\(309\) | −38.2384 | −2.17531 | ||||||||
\(310\) | 3.65368i | 0.207515i | ||||||||
\(311\) | 3.18059 | 0.180355 | 0.0901774 | − | 0.995926i | \(-0.471257\pi\) | ||||
0.0901774 | + | 0.995926i | \(0.471257\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 35.3533 | 1.99829 | 0.999144 | − | 0.0413596i | \(-0.0131689\pi\) | ||||
0.999144 | + | 0.0413596i | \(0.0131689\pi\) | |||||||
\(314\) | − 6.04484i | − 0.341130i | ||||||||
\(315\) | −9.50894 | −0.535768 | ||||||||
\(316\) | 39.3982 | 2.21632 | ||||||||
\(317\) | 13.6357i | 0.765858i | 0.923778 | + | 0.382929i | \(0.125085\pi\) | ||||
−0.923778 | + | 0.382929i | \(0.874915\pi\) | |||||||
\(318\) | − 49.3174i | − 2.76558i | ||||||||
\(319\) | 10.1112i | 0.566119i | ||||||||
\(320\) | 4.84325i | 0.270746i | ||||||||
\(321\) | 20.8133 | 1.16168 | ||||||||
\(322\) | −18.1519 | −1.01156 | ||||||||
\(323\) | 3.65283i | 0.203249i | ||||||||
\(324\) | −3.96202 | −0.220112 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 39.8854 | 2.20905 | ||||||||
\(327\) | 28.4831i | 1.57512i | ||||||||
\(328\) | 1.48950 | 0.0822439 | ||||||||
\(329\) | 17.9969 | 0.992201 | ||||||||
\(330\) | − 7.54390i | − 0.415278i | ||||||||
\(331\) | 28.7959i | 1.58277i | 0.611320 | + | 0.791383i | \(0.290639\pi\) | ||||
−0.611320 | + | 0.791383i | \(0.709361\pi\) | |||||||
\(332\) | 21.6357i | 1.18741i | ||||||||
\(333\) | 3.78044i | 0.207167i | ||||||||
\(334\) | −35.9182 | −1.96536 | ||||||||
\(335\) | 8.09479 | 0.442265 | ||||||||
\(336\) | − 29.1752i | − 1.59164i | ||||||||
\(337\) | −11.7493 | −0.640026 | −0.320013 | − | 0.947413i | \(-0.603687\pi\) | ||||
−0.320013 | + | 0.947413i | \(0.603687\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.9061 | 1.02684 | ||||||||
\(340\) | 2.69407i | 0.146106i | ||||||||
\(341\) | −1.56569 | −0.0847871 | ||||||||
\(342\) | −71.3934 | −3.86051 | ||||||||
\(343\) | 19.7574i | 1.06680i | ||||||||
\(344\) | − 3.54248i | − 0.190997i | ||||||||
\(345\) | 10.7925i | 0.581046i | ||||||||
\(346\) | − 60.7630i | − 3.26664i | ||||||||
\(347\) | 1.89977 | 0.101985 | 0.0509926 | − | 0.998699i | \(-0.483762\pi\) | ||||
0.0509926 | + | 0.998699i | \(0.483762\pi\) | |||||||
\(348\) | 112.995 | 6.05714 | ||||||||
\(349\) | − 10.2691i | − 0.549692i | −0.961488 | − | 0.274846i | \(-0.911373\pi\) | ||||
0.961488 | − | 0.274846i | \(-0.0886268\pi\) | |||||||
\(350\) | −4.75447 | −0.254137 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.56730 | 0.136838 | ||||||||
\(353\) | − 0.800589i | − 0.0426110i | −0.999773 | − | 0.0213055i | \(-0.993218\pi\) | ||||
0.999773 | − | 0.0213055i | \(-0.00678227\pi\) | |||||||
\(354\) | −5.22756 | −0.277842 | ||||||||
\(355\) | 9.76488 | 0.518266 | ||||||||
\(356\) | 53.1756i | 2.81830i | ||||||||
\(357\) | 3.43213i | 0.181647i | ||||||||
\(358\) | 9.45370i | 0.499643i | ||||||||
\(359\) | 8.13272i | 0.429228i | 0.976699 | + | 0.214614i | \(0.0688494\pi\) | ||||
−0.976699 | + | 0.214614i | \(0.931151\pi\) | |||||||
\(360\) | −27.7445 | −1.46226 | ||||||||
\(361\) | −13.8564 | −0.729285 | ||||||||
\(362\) | − 21.1817i | − 1.11329i | ||||||||
\(363\) | −27.8625 | −1.46240 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.71649 | 0.194530 | ||||||||
\(366\) | 29.6183i | 1.54817i | ||||||||
\(367\) | −20.5265 | −1.07147 | −0.535737 | − | 0.844385i | \(-0.679966\pi\) | ||||
−0.535737 | + | 0.844385i | \(0.679966\pi\) | |||||||
\(368\) | −20.6818 | −1.07811 | ||||||||
\(369\) | − 1.33734i | − 0.0696191i | ||||||||
\(370\) | 1.89022i | 0.0982679i | ||||||||
\(371\) | − 13.3194i | − 0.691507i | ||||||||
\(372\) | 17.4969i | 0.907173i | ||||||||
\(373\) | −17.8058 | −0.921951 | −0.460976 | − | 0.887413i | \(-0.652500\pi\) | ||||
−0.460976 | + | 0.887413i | \(0.652500\pi\) | |||||||
\(374\) | −1.70064 | −0.0879382 | ||||||||
\(375\) | 2.82684i | 0.145977i | ||||||||
\(376\) | 52.5100 | 2.70800 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −26.7595 | −1.37636 | ||||||||
\(379\) | − 2.04555i | − 0.105073i | −0.998619 | − | 0.0525363i | \(-0.983269\pi\) | ||||
0.998619 | − | 0.0525363i | \(-0.0167305\pi\) | |||||||
\(380\) | −24.2326 | −1.24311 | ||||||||
\(381\) | 4.21058 | 0.215714 | ||||||||
\(382\) | 13.5833i | 0.694982i | ||||||||
\(383\) | 7.90521i | 0.403937i | 0.979392 | + | 0.201969i | \(0.0647339\pi\) | ||||
−0.979392 | + | 0.201969i | \(0.935266\pi\) | |||||||
\(384\) | 47.7391i | 2.43618i | ||||||||
\(385\) | − 2.03741i | − 0.103836i | ||||||||
\(386\) | 30.3394 | 1.54423 | ||||||||
\(387\) | −3.18059 | −0.161679 | ||||||||
\(388\) | − 17.8469i | − 0.906037i | ||||||||
\(389\) | 9.21171 | 0.467052 | 0.233526 | − | 0.972351i | \(-0.424974\pi\) | ||||
0.233526 | + | 0.972351i | \(0.424974\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.43298 | 0.123041 | ||||||||
\(392\) | 18.7344i | 0.946229i | ||||||||
\(393\) | −11.6657 | −0.588456 | ||||||||
\(394\) | 10.9261 | 0.550448 | ||||||||
\(395\) | − 9.31937i | − 0.468908i | ||||||||
\(396\) | − 22.5639i | − 1.13388i | ||||||||
\(397\) | − 6.35438i | − 0.318917i | −0.987205 | − | 0.159458i | \(-0.949025\pi\) | ||||
0.987205 | − | 0.159458i | \(-0.0509748\pi\) | |||||||
\(398\) | 51.9996i | 2.60651i | ||||||||
\(399\) | −30.8713 | −1.54550 | ||||||||
\(400\) | −5.41713 | −0.270857 | ||||||||
\(401\) | 4.16920i | 0.208200i | 0.994567 | + | 0.104100i | \(0.0331962\pi\) | ||||
−0.994567 | + | 0.104100i | \(0.966804\pi\) | |||||||
\(402\) | 57.1038 | 2.84808 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −64.4600 | −3.20701 | ||||||||
\(405\) | 0.937188i | 0.0465692i | ||||||||
\(406\) | 44.9541 | 2.23103 | ||||||||
\(407\) | −0.810008 | −0.0401506 | ||||||||
\(408\) | 10.0140i | 0.495767i | ||||||||
\(409\) | − 10.1681i | − 0.502778i | −0.967886 | − | 0.251389i | \(-0.919113\pi\) | ||||
0.967886 | − | 0.251389i | \(-0.0808874\pi\) | |||||||
\(410\) | − 0.668669i | − 0.0330232i | ||||||||
\(411\) | 56.8467i | 2.80404i | ||||||||
\(412\) | −57.1858 | −2.81734 | ||||||||
\(413\) | −1.41183 | −0.0694716 | ||||||||
\(414\) | 47.5518i | 2.33704i | ||||||||
\(415\) | 5.11778 | 0.251222 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −58.8697 | −2.88286 | ||||||||
\(418\) | − 15.2969i | − 0.748198i | ||||||||
\(419\) | 28.5909 | 1.39676 | 0.698378 | − | 0.715730i | \(-0.253906\pi\) | ||||
0.698378 | + | 0.715730i | \(0.253906\pi\) | |||||||
\(420\) | −22.7685 | −1.11099 | ||||||||
\(421\) | − 2.01797i | − 0.0983498i | −0.998790 | − | 0.0491749i | \(-0.984341\pi\) | ||||
0.998790 | − | 0.0491749i | \(-0.0156592\pi\) | |||||||
\(422\) | 26.5863i | 1.29420i | ||||||||
\(423\) | − 47.1458i | − 2.29231i | ||||||||
\(424\) | − 38.8623i | − 1.88732i | ||||||||
\(425\) | 0.637263 | 0.0309118 | ||||||||
\(426\) | 68.8853 | 3.33750 | ||||||||
\(427\) | 7.99915i | 0.387106i | ||||||||
\(428\) | 31.1264 | 1.50455 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.59030 | −0.0766908 | ||||||||
\(431\) | 20.6123i | 0.992860i | 0.868077 | + | 0.496430i | \(0.165356\pi\) | ||||
−0.868077 | + | 0.496430i | \(0.834644\pi\) | |||||||
\(432\) | −30.4891 | −1.46691 | ||||||||
\(433\) | −29.4356 | −1.41458 | −0.707292 | − | 0.706921i | \(-0.750083\pi\) | ||||
−0.707292 | + | 0.706921i | \(0.750083\pi\) | |||||||
\(434\) | 6.96103i | 0.334140i | ||||||||
\(435\) | − 26.7281i | − 1.28151i | ||||||||
\(436\) | 42.5967i | 2.04001i | ||||||||
\(437\) | 21.8841i | 1.04686i | ||||||||
\(438\) | 26.2176 | 1.25272 | ||||||||
\(439\) | −16.9520 | −0.809077 | −0.404538 | − | 0.914521i | \(-0.632568\pi\) | ||||
−0.404538 | + | 0.914521i | \(0.632568\pi\) | |||||||
\(440\) | − 5.94462i | − 0.283398i | ||||||||
\(441\) | 16.8205 | 0.800978 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.1399 | −1.14692 | −0.573461 | − | 0.819233i | \(-0.694400\pi\) | ||||
−0.573461 | + | 0.819233i | \(0.694400\pi\) | |||||||
\(444\) | 9.05199i | 0.429588i | ||||||||
\(445\) | 12.5783 | 0.596270 | ||||||||
\(446\) | −53.2525 | −2.52158 | ||||||||
\(447\) | 37.7885i | 1.78733i | ||||||||
\(448\) | 9.22742i | 0.435955i | ||||||||
\(449\) | − 20.8630i | − 0.984585i | −0.870430 | − | 0.492293i | \(-0.836159\pi\) | ||||
0.870430 | − | 0.492293i | \(-0.163841\pi\) | |||||||
\(450\) | 12.4551i | 0.587140i | ||||||||
\(451\) | 0.286542 | 0.0134927 | ||||||||
\(452\) | 28.2742 | 1.32990 | ||||||||
\(453\) | − 51.7265i | − 2.43032i | ||||||||
\(454\) | −39.1437 | −1.83710 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −90.0739 | −4.21810 | ||||||||
\(457\) | 30.5659i | 1.42981i | 0.699220 | + | 0.714906i | \(0.253531\pi\) | ||||
−0.699220 | + | 0.714906i | \(0.746469\pi\) | |||||||
\(458\) | −19.0179 | −0.888648 | ||||||||
\(459\) | 3.58669 | 0.167413 | ||||||||
\(460\) | 16.1402i | 0.752541i | ||||||||
\(461\) | − 4.67822i | − 0.217887i | −0.994048 | − | 0.108943i | \(-0.965253\pi\) | ||||
0.994048 | − | 0.108943i | \(-0.0347467\pi\) | |||||||
\(462\) | − 14.3727i | − 0.668680i | ||||||||
\(463\) | − 14.0011i | − 0.650688i | −0.945596 | − | 0.325344i | \(-0.894520\pi\) | ||||
0.945596 | − | 0.325344i | \(-0.105480\pi\) | |||||||
\(464\) | 51.2196 | 2.37781 | ||||||||
\(465\) | 4.13878 | 0.191931 | ||||||||
\(466\) | − 47.5518i | − 2.20280i | ||||||||
\(467\) | 6.98506 | 0.323230 | 0.161615 | − | 0.986854i | \(-0.448330\pi\) | ||||
0.161615 | + | 0.986854i | \(0.448330\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.4223 | 0.712135 | ||||||||
\(470\) | − 23.5729i | − 1.08734i | ||||||||
\(471\) | −6.84742 | −0.315513 | ||||||||
\(472\) | −4.11933 | −0.189608 | ||||||||
\(473\) | − 0.681482i | − 0.0313346i | ||||||||
\(474\) | − 65.7425i | − 3.01965i | ||||||||
\(475\) | 5.73205i | 0.263005i | ||||||||
\(476\) | 5.13277i | 0.235260i | ||||||||
\(477\) | −34.8923 | −1.59761 | ||||||||
\(478\) | −31.8264 | −1.45571 | ||||||||
\(479\) | − 16.2888i | − 0.744252i | −0.928182 | − | 0.372126i | \(-0.878629\pi\) | ||||
0.928182 | − | 0.372126i | \(-0.121371\pi\) | |||||||
\(480\) | −6.78645 | −0.309758 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 64.7056 | 2.94726 | ||||||||
\(483\) | 20.5619i | 0.935600i | ||||||||
\(484\) | −41.6685 | −1.89402 | ||||||||
\(485\) | −4.22155 | −0.191691 | ||||||||
\(486\) | − 35.5249i | − 1.61144i | ||||||||
\(487\) | − 20.0409i | − 0.908139i | −0.890966 | − | 0.454069i | \(-0.849972\pi\) | ||||
0.890966 | − | 0.454069i | \(-0.150028\pi\) | |||||||
\(488\) | 23.3393i | 1.05652i | ||||||||
\(489\) | − 45.1810i | − 2.04316i | ||||||||
\(490\) | 8.41027 | 0.379937 | ||||||||
\(491\) | 15.7983 | 0.712969 | 0.356484 | − | 0.934301i | \(-0.383975\pi\) | ||||
0.356484 | + | 0.934301i | \(0.383975\pi\) | |||||||
\(492\) | − 3.20216i | − 0.144365i | ||||||||
\(493\) | −6.02540 | −0.271370 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.33734 | −0.239896 | ||||||||
\(496\) | 7.93123i | 0.356123i | ||||||||
\(497\) | 18.6042 | 0.834511 | ||||||||
\(498\) | 36.1028 | 1.61781 | ||||||||
\(499\) | − 1.24651i | − 0.0558016i | −0.999611 | − | 0.0279008i | \(-0.991118\pi\) | ||||
0.999611 | − | 0.0279008i | \(-0.00888226\pi\) | |||||||
\(500\) | 4.22756i | 0.189062i | ||||||||
\(501\) | 40.6871i | 1.81777i | ||||||||
\(502\) | 18.9955i | 0.847809i | ||||||||
\(503\) | −7.65345 | −0.341250 | −0.170625 | − | 0.985336i | \(-0.554579\pi\) | ||||
−0.170625 | + | 0.985336i | \(0.554579\pi\) | |||||||
\(504\) | −52.8592 | −2.35453 | ||||||||
\(505\) | 15.2476i | 0.678508i | ||||||||
\(506\) | −10.1886 | −0.452938 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.29695 | 0.279382 | ||||||||
\(509\) | − 25.7241i | − 1.14020i | −0.821575 | − | 0.570101i | \(-0.806904\pi\) | ||||
0.821575 | − | 0.570101i | \(-0.193096\pi\) | |||||||
\(510\) | 4.49551 | 0.199064 | ||||||||
\(511\) | 7.08070 | 0.313232 | ||||||||
\(512\) | 47.2215i | 2.08691i | ||||||||
\(513\) | 32.2616i | 1.42438i | ||||||||
\(514\) | 0.837948i | 0.0369603i | ||||||||
\(515\) | 13.5269i | 0.596067i | ||||||||
\(516\) | −7.61569 | −0.335262 | ||||||||
\(517\) | 10.1016 | 0.444268 | ||||||||
\(518\) | 3.60127i | 0.158231i | ||||||||
\(519\) | −68.8305 | −3.02132 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.1519 | −1.32098 | −0.660490 | − | 0.750835i | \(-0.729651\pi\) | ||||
−0.660490 | + | 0.750835i | \(0.729651\pi\) | |||||||
\(522\) | − 117.765i | − 5.15442i | ||||||||
\(523\) | 3.93752 | 0.172176 | 0.0860880 | − | 0.996288i | \(-0.472563\pi\) | ||||
0.0860880 | + | 0.996288i | \(0.472563\pi\) | |||||||
\(524\) | −17.4461 | −0.762138 | ||||||||
\(525\) | 5.38573i | 0.235052i | ||||||||
\(526\) | 13.4156i | 0.584947i | ||||||||
\(527\) | − 0.933018i | − 0.0406429i | ||||||||
\(528\) | − 16.3759i | − 0.712672i | ||||||||
\(529\) | −8.42399 | −0.366261 | ||||||||
\(530\) | −17.4461 | −0.757812 | ||||||||
\(531\) | 3.69852i | 0.160502i | ||||||||
\(532\) | −46.1682 | −2.00165 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 88.7326 | 3.83983 | ||||||||
\(535\) | − 7.36274i | − 0.318319i | ||||||||
\(536\) | 44.9980 | 1.94362 | ||||||||
\(537\) | 10.7089 | 0.462122 | ||||||||
\(538\) | 3.27007i | 0.140983i | ||||||||
\(539\) | 3.60402i | 0.155236i | ||||||||
\(540\) | 23.7939i | 1.02393i | ||||||||
\(541\) | − 15.8881i | − 0.683083i | −0.939867 | − | 0.341541i | \(-0.889051\pi\) | ||||
0.939867 | − | 0.341541i | \(-0.110949\pi\) | |||||||
\(542\) | −29.0610 | −1.24828 | ||||||||
\(543\) | −23.9940 | −1.02968 | ||||||||
\(544\) | 1.52989i | 0.0655935i | ||||||||
\(545\) | 10.0760 | 0.431607 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.56107 | −0.280531 | −0.140266 | − | 0.990114i | \(-0.544796\pi\) | ||||
−0.140266 | + | 0.990114i | \(0.544796\pi\) | |||||||
\(548\) | 85.0147i | 3.63165i | ||||||||
\(549\) | 20.9551 | 0.894341 | ||||||||
\(550\) | −2.66867 | −0.113792 | ||||||||
\(551\) | − 54.1972i | − 2.30888i | ||||||||
\(552\) | 59.9941i | 2.55352i | ||||||||
\(553\) | − 17.7554i | − 0.755035i | ||||||||
\(554\) | − 50.6990i | − 2.15399i | ||||||||
\(555\) | 2.14119 | 0.0908883 | ||||||||
\(556\) | −88.0401 | −3.73373 | ||||||||
\(557\) | 7.85006i | 0.332618i | 0.986074 | + | 0.166309i | \(0.0531849\pi\) | ||||
−0.986074 | + | 0.166309i | \(0.946815\pi\) | |||||||
\(558\) | 18.2356 | 0.771973 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −10.3208 | −0.436133 | ||||||||
\(561\) | 1.92644i | 0.0813344i | ||||||||
\(562\) | −29.6326 | −1.24998 | ||||||||
\(563\) | 15.5595 | 0.655755 | 0.327878 | − | 0.944720i | \(-0.393667\pi\) | ||||
0.327878 | + | 0.944720i | \(0.393667\pi\) | |||||||
\(564\) | − 112.887i | − 4.75341i | ||||||||
\(565\) | − 6.68806i | − 0.281369i | ||||||||
\(566\) | − 56.5285i | − 2.37607i | ||||||||
\(567\) | 1.78554i | 0.0749857i | ||||||||
\(568\) | 54.2819 | 2.27762 | ||||||||
\(569\) | −3.47915 | −0.145853 | −0.0729267 | − | 0.997337i | \(-0.523234\pi\) | ||||
−0.0729267 | + | 0.997337i | \(0.523234\pi\) | |||||||
\(570\) | 40.4362i | 1.69368i | ||||||||
\(571\) | 21.5118 | 0.900240 | 0.450120 | − | 0.892968i | \(-0.351381\pi\) | ||||
0.450120 | + | 0.892968i | \(0.351381\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.3868 | 0.642791 | ||||||||
\(574\) | − 1.27396i | − 0.0531739i | ||||||||
\(575\) | 3.81785 | 0.159216 | ||||||||
\(576\) | 24.1727 | 1.00720 | ||||||||
\(577\) | − 9.97608i | − 0.415310i | −0.978202 | − | 0.207655i | \(-0.933417\pi\) | ||||
0.978202 | − | 0.207655i | \(-0.0665831\pi\) | |||||||
\(578\) | 41.4102i | 1.72244i | ||||||||
\(579\) | − 34.3676i | − 1.42827i | ||||||||
\(580\) | − 39.9721i | − 1.65975i | ||||||||
\(581\) | 9.75045 | 0.404517 | ||||||||
\(582\) | −29.7805 | −1.23444 | ||||||||
\(583\) | − 7.47612i | − 0.309629i | ||||||||
\(584\) | 20.6595 | 0.854898 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 46.4482 | 1.91876 | ||||||||
\(587\) | 24.0571i | 0.992945i | 0.868053 | + | 0.496472i | \(0.165372\pi\) | ||||
−0.868053 | + | 0.496472i | \(0.834628\pi\) | |||||||
\(588\) | 40.2756 | 1.66094 | ||||||||
\(589\) | 8.39230 | 0.345799 | ||||||||
\(590\) | 1.84926i | 0.0761328i | ||||||||
\(591\) | − 12.3767i | − 0.509111i | ||||||||
\(592\) | 4.10320i | 0.168641i | ||||||||
\(593\) | 0.940219i | 0.0386102i | 0.999814 | + | 0.0193051i | \(0.00614538\pi\) | ||||
−0.999814 | + | 0.0193051i | \(0.993855\pi\) | |||||||
\(594\) | −15.0200 | −0.616279 | ||||||||
\(595\) | 1.21412 | 0.0497741 | ||||||||
\(596\) | 56.5130i | 2.31486i | ||||||||
\(597\) | 58.9037 | 2.41077 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.4270 | −0.466896 | −0.233448 | − | 0.972369i | \(-0.575001\pi\) | ||||
−0.233448 | + | 0.972369i | \(0.575001\pi\) | |||||||
\(600\) | 15.7141i | 0.641525i | ||||||||
\(601\) | −36.0431 | −1.47023 | −0.735114 | − | 0.677944i | \(-0.762871\pi\) | ||||
−0.735114 | + | 0.677944i | \(0.762871\pi\) | |||||||
\(602\) | −3.02985 | −0.123487 | ||||||||
\(603\) | − 40.4012i | − 1.64526i | ||||||||
\(604\) | − 77.3574i | − 3.14763i | ||||||||
\(605\) | 9.85641i | 0.400720i | ||||||||
\(606\) | 107.562i | 4.36942i | ||||||||
\(607\) | 39.8907 | 1.61911 | 0.809557 | − | 0.587041i | \(-0.199707\pi\) | ||||
0.809557 | + | 0.587041i | \(0.199707\pi\) | |||||||
\(608\) | −13.7610 | −0.558084 | ||||||||
\(609\) | − 50.9227i | − 2.06349i | ||||||||
\(610\) | 10.4775 | 0.424223 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 13.4461 | 0.543528 | ||||||||
\(613\) | 0.345472i | 0.0139535i | 0.999976 | + | 0.00697673i | \(0.00222078\pi\) | ||||
−0.999976 | + | 0.00697673i | \(0.997779\pi\) | |||||||
\(614\) | 7.85527 | 0.317013 | ||||||||
\(615\) | −0.757449 | −0.0305433 | ||||||||
\(616\) | − 11.3258i | − 0.456328i | ||||||||
\(617\) | − 38.6850i | − 1.55740i | −0.627397 | − | 0.778700i | \(-0.715879\pi\) | ||||
0.627397 | − | 0.778700i | \(-0.284121\pi\) | |||||||
\(618\) | 95.4242i | 3.83852i | ||||||||
\(619\) | 14.8971i | 0.598764i | 0.954133 | + | 0.299382i | \(0.0967805\pi\) | ||||
−0.954133 | + | 0.299382i | \(0.903219\pi\) | |||||||
\(620\) | 6.18958 | 0.248579 | ||||||||
\(621\) | 21.4879 | 0.862281 | ||||||||
\(622\) | − 7.93719i | − 0.318252i | ||||||||
\(623\) | 23.9644 | 0.960113 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | − 88.2245i | − 3.52616i | ||||||||
\(627\) | −17.3279 | −0.692011 | ||||||||
\(628\) | −10.2404 | −0.408635 | ||||||||
\(629\) | − 0.482694i | − 0.0192463i | ||||||||
\(630\) | 23.7296i | 0.945412i | ||||||||
\(631\) | − 38.8450i | − 1.54640i | −0.634165 | − | 0.773198i | \(-0.718656\pi\) | ||||
0.634165 | − | 0.773198i | \(-0.281344\pi\) | |||||||
\(632\) | − 51.8053i | − 2.06071i | ||||||||
\(633\) | 30.1162 | 1.19701 | ||||||||
\(634\) | 34.0280 | 1.35143 | ||||||||
\(635\) | − 1.48950i | − 0.0591090i | ||||||||
\(636\) | −83.5470 | −3.31285 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 25.2326 | 0.998967 | ||||||||
\(639\) | − 48.7367i | − 1.92799i | ||||||||
\(640\) | 16.8878 | 0.667549 | ||||||||
\(641\) | −37.1816 | −1.46859 | −0.734293 | − | 0.678832i | \(-0.762486\pi\) | ||||
−0.734293 | + | 0.678832i | \(0.762486\pi\) | |||||||
\(642\) | − 51.9397i | − 2.04990i | ||||||||
\(643\) | − 9.10377i | − 0.359018i | −0.983756 | − | 0.179509i | \(-0.942549\pi\) | ||||
0.983756 | − | 0.179509i | \(-0.0574509\pi\) | |||||||
\(644\) | 30.7505i | 1.21174i | ||||||||
\(645\) | 1.80144i | 0.0709316i | ||||||||
\(646\) | 9.11565 | 0.358651 | ||||||||
\(647\) | 19.1224 | 0.751778 | 0.375889 | − | 0.926665i | \(-0.377337\pi\) | ||||
0.375889 | + | 0.926665i | \(0.377337\pi\) | |||||||
\(648\) | 5.20972i | 0.204657i | ||||||||
\(649\) | −0.792455 | −0.0311066 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.88525 | 0.309047 | ||||||||
\(652\) | − 67.5686i | − 2.64619i | ||||||||
\(653\) | 34.6324 | 1.35527 | 0.677636 | − | 0.735397i | \(-0.263004\pi\) | ||||
0.677636 | + | 0.735397i | \(0.263004\pi\) | |||||||
\(654\) | 71.0799 | 2.77944 | ||||||||
\(655\) | 4.12676i | 0.161246i | ||||||||
\(656\) | − 1.45152i | − 0.0566722i | ||||||||
\(657\) | − 18.5491i | − 0.723667i | ||||||||
\(658\) | − 44.9114i | − 1.75083i | ||||||||
\(659\) | −6.69852 | −0.260937 | −0.130469 | − | 0.991452i | \(-0.541648\pi\) | ||||
−0.130469 | + | 0.991452i | \(0.541648\pi\) | |||||||
\(660\) | −12.7799 | −0.497456 | ||||||||
\(661\) | 6.02758i | 0.234446i | 0.993106 | + | 0.117223i | \(0.0373992\pi\) | ||||
−0.993106 | + | 0.117223i | \(0.962601\pi\) | |||||||
\(662\) | 71.8604 | 2.79294 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 28.4492 | 1.10404 | ||||||||
\(665\) | 10.9208i | 0.423489i | ||||||||
\(666\) | 9.43412 | 0.365565 | ||||||||
\(667\) | −36.0983 | −1.39773 | ||||||||
\(668\) | 60.8479i | 2.35428i | ||||||||
\(669\) | 60.3228i | 2.33222i | ||||||||
\(670\) | − 20.2006i | − 0.780417i | ||||||||
\(671\) | 4.48990i | 0.173330i | ||||||||
\(672\) | −12.9296 | −0.498771 | ||||||||
\(673\) | −23.3568 | −0.900338 | −0.450169 | − | 0.892943i | \(-0.648636\pi\) | ||||
−0.450169 | + | 0.892943i | \(0.648636\pi\) | |||||||
\(674\) | 29.3205i | 1.12938i | ||||||||
\(675\) | 5.62828 | 0.216633 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.4042 | −1.74503 | −0.872513 | − | 0.488590i | \(-0.837511\pi\) | ||||
−0.872513 | + | 0.488590i | \(0.837511\pi\) | |||||||
\(678\) | − 47.1802i | − 1.81195i | ||||||||
\(679\) | −8.04295 | −0.308660 | ||||||||
\(680\) | 3.54248 | 0.135848 | ||||||||
\(681\) | 44.3408i | 1.69914i | ||||||||
\(682\) | 3.90720i | 0.149615i | ||||||||
\(683\) | − 25.4978i | − 0.975645i | −0.872943 | − | 0.487823i | \(-0.837791\pi\) | ||||
0.872943 | − | 0.487823i | \(-0.162209\pi\) | |||||||
\(684\) | 120.945i | 4.62445i | ||||||||
\(685\) | 20.1096 | 0.768350 | ||||||||
\(686\) | 49.3047 | 1.88246 | ||||||||
\(687\) | 21.5429i | 0.821913i | ||||||||
\(688\) | −3.45214 | −0.131612 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 26.9327 | 1.02531 | ||||||||
\(691\) | 6.59630i | 0.250935i | 0.992098 | + | 0.125468i | \(0.0400431\pi\) | ||||
−0.992098 | + | 0.125468i | \(0.959957\pi\) | |||||||
\(692\) | −102.937 | −3.91306 | ||||||||
\(693\) | −10.1688 | −0.386279 | ||||||||
\(694\) | − 4.74090i | − 0.179962i | ||||||||
\(695\) | 20.8253i | 0.789948i | ||||||||
\(696\) | − 148.578i | − 5.63185i | ||||||||
\(697\) | 0.170754i | 0.00646778i | ||||||||
\(698\) | −25.6266 | −0.969981 | ||||||||
\(699\) | −53.8653 | −2.03737 | ||||||||
\(700\) | 8.05440i | 0.304428i | ||||||||
\(701\) | −29.2474 | −1.10466 | −0.552329 | − | 0.833626i | \(-0.686261\pi\) | ||||
−0.552329 | + | 0.833626i | \(0.686261\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.34174 | 0.163752 | ||||||||
\(704\) | 5.17932i | 0.195203i | ||||||||
\(705\) | −26.7027 | −1.00568 | ||||||||
\(706\) | −1.99787 | −0.0751910 | ||||||||
\(707\) | 29.0499i | 1.09253i | ||||||||
\(708\) | 8.85584i | 0.332823i | ||||||||
\(709\) | 10.9335i | 0.410614i | 0.978698 | + | 0.205307i | \(0.0658194\pi\) | ||||
−0.978698 | + | 0.205307i | \(0.934181\pi\) | |||||||
\(710\) | − 24.3683i | − 0.914527i | ||||||||
\(711\) | −46.5131 | −1.74438 | ||||||||
\(712\) | 69.9216 | 2.62042 | ||||||||
\(713\) | − 5.58973i | − 0.209337i | ||||||||
\(714\) | 8.56490 | 0.320533 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.0152 | 0.598516 | ||||||||
\(717\) | 36.0520i | 1.34639i | ||||||||
\(718\) | 20.2953 | 0.757412 | ||||||||
\(719\) | −16.0598 | −0.598929 | −0.299464 | − | 0.954107i | \(-0.596808\pi\) | ||||
−0.299464 | + | 0.954107i | \(0.596808\pi\) | |||||||
\(720\) | 27.0370i | 1.00761i | ||||||||
\(721\) | 25.7716i | 0.959786i | ||||||||
\(722\) | 34.5788i | 1.28689i | ||||||||
\(723\) | − 73.2966i | − 2.72593i | ||||||||
\(724\) | −35.8833 | −1.33359 | ||||||||
\(725\) | −9.45512 | −0.351154 | ||||||||
\(726\) | 69.5310i | 2.58054i | ||||||||
\(727\) | −51.3754 | −1.90541 | −0.952704 | − | 0.303900i | \(-0.901711\pi\) | ||||
−0.952704 | + | 0.303900i | \(0.901711\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.0532 | −1.59456 | ||||||||
\(730\) | − 9.27453i | − 0.343266i | ||||||||
\(731\) | 0.406104 | 0.0150203 | ||||||||
\(732\) | 50.1754 | 1.85454 | ||||||||
\(733\) | 9.82358i | 0.362842i | 0.983406 | + | 0.181421i | \(0.0580697\pi\) | ||||
−0.983406 | + | 0.181421i | \(0.941930\pi\) | |||||||
\(734\) | 51.2240i | 1.89071i | ||||||||
\(735\) | − 9.52691i | − 0.351406i | ||||||||
\(736\) | 9.16560i | 0.337848i | ||||||||
\(737\) | 8.65648 | 0.318866 | ||||||||
\(738\) | −3.33734 | −0.122849 | ||||||||
\(739\) | 49.0842i | 1.80559i | 0.430068 | + | 0.902797i | \(0.358490\pi\) | ||||
−0.430068 | + | 0.902797i | \(0.641510\pi\) | |||||||
\(740\) | 3.20216 | 0.117714 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −33.2386 | −1.22023 | ||||||||
\(743\) | − 40.8375i | − 1.49818i | −0.662467 | − | 0.749091i | \(-0.730490\pi\) | ||||
0.662467 | − | 0.749091i | \(-0.269510\pi\) | |||||||
\(744\) | 23.0070 | 0.843478 | ||||||||
\(745\) | 13.3678 | 0.489757 | ||||||||
\(746\) | 44.4346i | 1.62687i | ||||||||
\(747\) | − 25.5429i | − 0.934566i | ||||||||
\(748\) | 2.88101i | 0.105340i | ||||||||
\(749\) | − 14.0276i | − 0.512557i | ||||||||
\(750\) | 7.05440 | 0.257590 | ||||||||
\(751\) | 2.72680 | 0.0995024 | 0.0497512 | − | 0.998762i | \(-0.484157\pi\) | ||||
0.0497512 | + | 0.998762i | \(0.484157\pi\) | |||||||
\(752\) | − 51.1710i | − 1.86601i | ||||||||
\(753\) | 21.5175 | 0.784142 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.2984 | −0.665946 | ||||||||
\(756\) | 45.3324i | 1.64872i | ||||||||
\(757\) | 14.8060 | 0.538134 | 0.269067 | − | 0.963121i | \(-0.413285\pi\) | ||||
0.269067 | + | 0.963121i | \(0.413285\pi\) | |||||||
\(758\) | −5.10468 | −0.185410 | ||||||||
\(759\) | 11.5413i | 0.418924i | ||||||||
\(760\) | 31.8638i | 1.15582i | ||||||||
\(761\) | − 11.3689i | − 0.412122i | −0.978539 | − | 0.206061i | \(-0.933935\pi\) | ||||
0.978539 | − | 0.206061i | \(-0.0660646\pi\) | |||||||
\(762\) | − 10.5075i | − 0.380647i | ||||||||
\(763\) | 19.1969 | 0.694973 | ||||||||
\(764\) | 23.0110 | 0.832510 | ||||||||
\(765\) | − 3.18059i | − 0.114994i | ||||||||
\(766\) | 19.7275 | 0.712784 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 91.7512 | 3.31078 | ||||||||
\(769\) | 21.0562i | 0.759307i | 0.925129 | + | 0.379654i | \(0.123957\pi\) | ||||
−0.925129 | + | 0.379654i | \(0.876043\pi\) | |||||||
\(770\) | −5.08438 | −0.183228 | ||||||||
\(771\) | 0.949203 | 0.0341847 | ||||||||
\(772\) | − 51.3970i | − 1.84982i | ||||||||
\(773\) | − 14.0829i | − 0.506526i | −0.967397 | − | 0.253263i | \(-0.918496\pi\) | ||||
0.967397 | − | 0.253263i | \(-0.0815038\pi\) | |||||||
\(774\) | 7.93719i | 0.285296i | ||||||||
\(775\) | − 1.46410i | − 0.0525921i | ||||||||
\(776\) | −23.4671 | −0.842421 | ||||||||
\(777\) | 4.07941 | 0.146348 | ||||||||
\(778\) | − 22.9879i | − 0.824156i | ||||||||
\(779\) | −1.53590 | −0.0550293 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.4425 | 0.373660 | ||||||||
\(782\) | − 6.07151i | − 0.217117i | ||||||||
\(783\) | −53.2160 | −1.90179 | ||||||||
\(784\) | 18.2566 | 0.652023 | ||||||||
\(785\) | 2.42229i | 0.0864552i | ||||||||
\(786\) | 29.1118i | 1.03838i | ||||||||
\(787\) | 33.0242i | 1.17719i | 0.808429 | + | 0.588593i | \(0.200318\pi\) | ||||
−0.808429 | + | 0.588593i | \(0.799682\pi\) | |||||||
\(788\) | − 18.5095i | − 0.659374i | ||||||||
\(789\) | 15.1968 | 0.541020 | ||||||||
\(790\) | −23.2566 | −0.827431 | ||||||||
\(791\) | − 12.7422i | − 0.453060i | ||||||||
\(792\) | −29.6697 | −1.05427 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −15.8574 | −0.562758 | ||||||||
\(795\) | 19.7625i | 0.700903i | ||||||||
\(796\) | 88.0909 | 3.12230 | ||||||||
\(797\) | 16.9416 | 0.600102 | 0.300051 | − | 0.953923i | \(-0.402996\pi\) | ||||
0.300051 | + | 0.953923i | \(0.402996\pi\) | |||||||
\(798\) | 77.0395i | 2.72717i | ||||||||
\(799\) | 6.01967i | 0.212961i | ||||||||
\(800\) | 2.40072i | 0.0848783i | ||||||||
\(801\) | − 62.7787i | − 2.21817i | ||||||||
\(802\) | 10.4043 | 0.367387 | ||||||||
\(803\) | 3.97437 | 0.140253 | ||||||||
\(804\) | − 96.7378i | − 3.41168i | ||||||||
\(805\) | 7.27382 | 0.256369 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.70425 | 0.130396 | ||||||||
\(808\) | 84.7596i | 2.98183i | ||||||||
\(809\) | −51.7635 | −1.81991 | −0.909954 | − | 0.414708i | \(-0.863884\pi\) | ||||
−0.909954 | + | 0.414708i | \(0.863884\pi\) | |||||||
\(810\) | 2.33876 | 0.0821756 | ||||||||
\(811\) | − 22.6699i | − 0.796047i | −0.917375 | − | 0.398023i | \(-0.869696\pi\) | ||||
0.917375 | − | 0.398023i | \(-0.130304\pi\) | |||||||
\(812\) | − 76.1553i | − 2.67253i | ||||||||
\(813\) | 32.9194i | 1.15453i | ||||||||
\(814\) | 2.02138i | 0.0708494i | ||||||||
\(815\) | −15.9829 | −0.559856 | ||||||||
\(816\) | 9.75864 | 0.341621 | ||||||||
\(817\) | 3.65283i | 0.127796i | ||||||||
\(818\) | −25.3745 | −0.887198 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.13277 | −0.0395581 | ||||||||
\(821\) | − 28.6631i | − 1.00035i | −0.865925 | − | 0.500174i | \(-0.833269\pi\) | ||||
0.865925 | − | 0.500174i | \(-0.166731\pi\) | |||||||
\(822\) | 141.861 | 4.94799 | ||||||||
\(823\) | 25.8327 | 0.900472 | 0.450236 | − | 0.892910i | \(-0.351340\pi\) | ||||
0.450236 | + | 0.892910i | \(0.351340\pi\) | |||||||
\(824\) | 75.1946i | 2.61953i | ||||||||
\(825\) | 3.02299i | 0.105247i | ||||||||
\(826\) | 3.52323i | 0.122589i | ||||||||
\(827\) | − 16.0820i | − 0.559227i | −0.960113 | − | 0.279613i | \(-0.909794\pi\) | ||||
0.960113 | − | 0.279613i | \(-0.0902063\pi\) | |||||||
\(828\) | 80.5560 | 2.79951 | ||||||||
\(829\) | 22.5818 | 0.784298 | 0.392149 | − | 0.919902i | \(-0.371732\pi\) | ||||
0.392149 | + | 0.919902i | \(0.371732\pi\) | |||||||
\(830\) | − 12.7715i | − 0.443304i | ||||||||
\(831\) | −57.4304 | −1.99224 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.14768 | −0.0744128 | ||||||||
\(834\) | 146.910i | 5.08707i | ||||||||
\(835\) | 14.3932 | 0.498096 | ||||||||
\(836\) | −25.9141 | −0.896257 | ||||||||
\(837\) | − 8.24037i | − 0.284829i | ||||||||
\(838\) | − 71.3487i | − 2.46470i | ||||||||
\(839\) | − 17.8440i | − 0.616042i | −0.951380 | − | 0.308021i | \(-0.900333\pi\) | ||||
0.951380 | − | 0.308021i | \(-0.0996667\pi\) | |||||||
\(840\) | 29.9387i | 1.03298i | ||||||||
\(841\) | 60.3992 | 2.08273 | ||||||||
\(842\) | −5.03586 | −0.173547 | ||||||||
\(843\) | 33.5669i | 1.15611i | ||||||||
\(844\) | 45.0390 | 1.55031 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −117.653 | −4.04498 | ||||||||
\(847\) | 18.7785i | 0.645239i | ||||||||
\(848\) | −37.8713 | −1.30050 | ||||||||
\(849\) | −64.0339 | −2.19764 | ||||||||
\(850\) | − 1.59030i | − 0.0545467i | ||||||||
\(851\) | − 2.89183i | − 0.0991306i | ||||||||
\(852\) | − 116.696i | − 3.99795i | ||||||||
\(853\) | 19.7936i | 0.677720i | 0.940837 | + | 0.338860i | \(0.110041\pi\) | ||||
−0.940837 | + | 0.338860i | \(0.889959\pi\) | |||||||
\(854\) | 19.9619 | 0.683083 | ||||||||
\(855\) | 28.6088 | 0.978399 | ||||||||
\(856\) | − 40.9286i | − 1.39891i | ||||||||
\(857\) | 11.7302 | 0.400696 | 0.200348 | − | 0.979725i | \(-0.435793\pi\) | ||||
0.200348 | + | 0.979725i | \(0.435793\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.37452 | 0.183376 | 0.0916882 | − | 0.995788i | \(-0.470774\pi\) | ||||
0.0916882 | + | 0.995788i | \(0.470774\pi\) | |||||||
\(860\) | 2.69407i | 0.0918669i | ||||||||
\(861\) | −1.44310 | −0.0491808 | ||||||||
\(862\) | 51.4382 | 1.75199 | ||||||||
\(863\) | 25.3234i | 0.862017i | 0.902348 | + | 0.431008i | \(0.141842\pi\) | ||||
−0.902348 | + | 0.431008i | \(0.858158\pi\) | |||||||
\(864\) | 13.5119i | 0.459685i | ||||||||
\(865\) | 24.3489i | 0.827889i | ||||||||
\(866\) | 73.4567i | 2.49616i | ||||||||
\(867\) | 46.9083 | 1.59309 | ||||||||
\(868\) | 11.7925 | 0.400262 | ||||||||
\(869\) | − 9.96603i | − 0.338075i | ||||||||
\(870\) | −66.7001 | −2.26135 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 56.0112 | 1.89678 | ||||||||
\(873\) | 21.0698i | 0.713106i | ||||||||
\(874\) | 54.6120 | 1.84728 | ||||||||
\(875\) | 1.90521 | 0.0644079 | ||||||||
\(876\) | − 44.4144i | − 1.50062i | ||||||||
\(877\) | − 20.6915i | − 0.698703i | −0.936992 | − | 0.349352i | \(-0.886402\pi\) | ||||
0.936992 | − | 0.349352i | \(-0.113598\pi\) | |||||||
\(878\) | 42.3040i | 1.42769i | ||||||||
\(879\) | − 52.6151i | − 1.77466i | ||||||||
\(880\) | −5.79302 | −0.195283 | ||||||||
\(881\) | −48.3993 | −1.63061 | −0.815307 | − | 0.579029i | \(-0.803432\pi\) | ||||
−0.815307 | + | 0.579029i | \(0.803432\pi\) | |||||||
\(882\) | − 41.9758i | − 1.41340i | ||||||||
\(883\) | −45.8550 | −1.54314 | −0.771572 | − | 0.636142i | \(-0.780529\pi\) | ||||
−0.771572 | + | 0.636142i | \(0.780529\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.09479 | 0.0704155 | ||||||||
\(886\) | 60.2413i | 2.02385i | ||||||||
\(887\) | −1.08234 | −0.0363413 | −0.0181707 | − | 0.999835i | \(-0.505784\pi\) | ||||
−0.0181707 | + | 0.999835i | \(0.505784\pi\) | |||||||
\(888\) | 11.9026 | 0.399426 | ||||||||
\(889\) | − 2.83781i | − 0.0951772i | ||||||||
\(890\) | − 31.3893i | − 1.05217i | ||||||||
\(891\) | 1.00222i | 0.0335756i | ||||||||
\(892\) | 90.2133i | 3.02056i | ||||||||
\(893\) | −54.1457 | −1.81192 | ||||||||
\(894\) | 94.3015 | 3.15391 | ||||||||
\(895\) | − 3.78829i | − 0.126628i | ||||||||
\(896\) | 32.1749 | 1.07489 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −52.0637 | −1.73739 | ||||||||
\(899\) | 13.8433i | 0.461698i | ||||||||
\(900\) | 21.0998 | 0.703327 | ||||||||
\(901\) | 4.45512 | 0.148421 | ||||||||
\(902\) | − 0.715068i | − 0.0238092i | ||||||||
\(903\) | 3.43213i | 0.114214i | ||||||||
\(904\) | − 37.1782i | − 1.23653i | ||||||||
\(905\) | 8.48794i | 0.282149i | ||||||||
\(906\) | −129.084 | −4.28853 | ||||||||
\(907\) | 45.5307 | 1.51182 | 0.755910 | − | 0.654675i | \(-0.227195\pi\) | ||||
0.755910 | + | 0.654675i | \(0.227195\pi\) | |||||||
\(908\) | 66.3120i | 2.20064i | ||||||||
\(909\) | 76.1009 | 2.52411 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.7417 | 1.31670 | 0.658350 | − | 0.752712i | \(-0.271255\pi\) | ||||
0.658350 | + | 0.752712i | \(0.271255\pi\) | |||||||
\(912\) | 87.7770i | 2.90659i | ||||||||
\(913\) | 5.47290 | 0.181126 | ||||||||
\(914\) | 76.2774 | 2.52303 | ||||||||
\(915\) | − 11.8687i | − 0.392365i | ||||||||
\(916\) | 32.2176i | 1.06450i | ||||||||
\(917\) | 7.86236i | 0.259638i | ||||||||
\(918\) | − 8.95062i | − 0.295415i | ||||||||
\(919\) | 46.9938 | 1.55018 | 0.775091 | − | 0.631850i | \(-0.217704\pi\) | ||||
0.775091 | + | 0.631850i | \(0.217704\pi\) | |||||||
\(920\) | 21.2230 | 0.699702 | ||||||||
\(921\) | − 8.89822i | − 0.293206i | ||||||||
\(922\) | −11.6745 | −0.384481 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −24.3484 | −0.801002 | ||||||||
\(925\) | − 0.757449i | − 0.0249048i | ||||||||
\(926\) | −34.9399 | −1.14820 | ||||||||
\(927\) | 67.5130 | 2.21742 | ||||||||
\(928\) | − 22.6991i | − 0.745134i | ||||||||
\(929\) | 15.2213i | 0.499395i | 0.968324 | + | 0.249698i | \(0.0803312\pi\) | ||||
−0.968324 | + | 0.249698i | \(0.919669\pi\) | |||||||
\(930\) | − 10.3284i | − 0.338680i | ||||||||
\(931\) | − 19.3180i | − 0.633121i | ||||||||
\(932\) | −80.5560 | −2.63870 | ||||||||
\(933\) | −8.99102 | −0.294353 | ||||||||
\(934\) | − 17.4313i | − 0.570369i | ||||||||
\(935\) | 0.681482 | 0.0222869 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.07285 | 0.198392 | 0.0991958 | − | 0.995068i | \(-0.468373\pi\) | ||||
0.0991958 | + | 0.995068i | \(0.468373\pi\) | |||||||
\(938\) | − 38.4864i | − 1.25663i | ||||||||
\(939\) | −99.9382 | −3.26136 | ||||||||
\(940\) | −39.9341 | −1.30251 | ||||||||
\(941\) | 0.0496576i | 0.00161879i | 1.00000 | 0.000809396i | \(0.000257639\pi\) | |||||
−1.00000 | 0.000809396i | \(0.999742\pi\) | ||||||||
\(942\) | 17.0878i | 0.556750i | ||||||||
\(943\) | 1.02299i | 0.0333132i | ||||||||
\(944\) | 4.01429i | 0.130654i | ||||||||
\(945\) | 10.7231 | 0.348821 | ||||||||
\(946\) | −1.70064 | −0.0552927 | ||||||||
\(947\) | − 18.6581i | − 0.606308i | −0.952942 | − | 0.303154i | \(-0.901960\pi\) | ||||
0.952942 | − | 0.303154i | \(-0.0980396\pi\) | |||||||
\(948\) | −111.372 | −3.61720 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 14.3044 | 0.464095 | ||||||||
\(951\) | − 38.5459i | − 1.24994i | ||||||||
\(952\) | 6.74917 | 0.218742 | ||||||||
\(953\) | 1.52953 | 0.0495463 | 0.0247731 | − | 0.999693i | \(-0.492114\pi\) | ||||
0.0247731 | + | 0.999693i | \(0.492114\pi\) | |||||||
\(954\) | 87.0739i | 2.81912i | ||||||||
\(955\) | − 5.44310i | − 0.176135i | ||||||||
\(956\) | 53.9161i | 1.74377i | ||||||||
\(957\) | − 28.5827i | − 0.923948i | ||||||||
\(958\) | −40.6487 | −1.31330 | ||||||||
\(959\) | 38.3131 | 1.23720 | ||||||||
\(960\) | − 13.6911i | − 0.441878i | ||||||||
\(961\) | 28.8564 | 0.930852 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36.7475 | −1.18417 | ||||||||
\(964\) | − 109.616i | − 3.53048i | ||||||||
\(965\) | −12.1576 | −0.391367 | ||||||||
\(966\) | 51.3124 | 1.65095 | ||||||||
\(967\) | − 32.1716i | − 1.03457i | −0.855813 | − | 0.517285i | \(-0.826943\pi\) | ||||
0.855813 | − | 0.517285i | \(-0.173057\pi\) | |||||||
\(968\) | 54.7907i | 1.76104i | ||||||||
\(969\) | − 10.3259i | − 0.331717i | ||||||||
\(970\) | 10.5349i | 0.338256i | ||||||||
\(971\) | −17.2541 | −0.553710 | −0.276855 | − | 0.960912i | \(-0.589292\pi\) | ||||
−0.276855 | + | 0.960912i | \(0.589292\pi\) | |||||||
\(972\) | −60.1816 | −1.93033 | ||||||||
\(973\) | 39.6766i | 1.27197i | ||||||||
\(974\) | −50.0122 | −1.60249 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.7442 | 0.728023 | ||||||||
\(977\) | − 15.7228i | − 0.503018i | −0.967855 | − | 0.251509i | \(-0.919073\pi\) | ||||
0.967855 | − | 0.251509i | \(-0.0809268\pi\) | |||||||
\(978\) | −112.750 | −3.60533 | ||||||||
\(979\) | 13.4511 | 0.429900 | ||||||||
\(980\) | − 14.2476i | − 0.455122i | ||||||||
\(981\) | − 50.2893i | − 1.60561i | ||||||||
\(982\) | − 39.4248i | − 1.25810i | ||||||||
\(983\) | 38.5356i | 1.22910i | 0.788880 | + | 0.614548i | \(0.210662\pi\) | ||||
−0.788880 | + | 0.614548i | \(0.789338\pi\) | |||||||
\(984\) | −4.21058 | −0.134228 | ||||||||
\(985\) | −4.37830 | −0.139504 | ||||||||
\(986\) | 15.0364i | 0.478857i | ||||||||
\(987\) | −50.8743 | −1.61935 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.43298 | 0.0773642 | ||||||||
\(990\) | 13.3194i | 0.423317i | ||||||||
\(991\) | 8.59143 | 0.272916 | 0.136458 | − | 0.990646i | \(-0.456428\pi\) | ||||
0.136458 | + | 0.990646i | \(0.456428\pi\) | |||||||
\(992\) | 3.51490 | 0.111598 | ||||||||
\(993\) | − 81.4014i | − 2.58320i | ||||||||
\(994\) | − 46.4268i | − 1.47257i | ||||||||
\(995\) | − 20.8373i | − 0.660587i | ||||||||
\(996\) | − 61.1606i | − 1.93795i | ||||||||
\(997\) | −20.5374 | −0.650425 | −0.325213 | − | 0.945641i | \(-0.605436\pi\) | ||||
−0.325213 | + | 0.945641i | \(0.605436\pi\) | |||||||
\(998\) | −3.11069 | −0.0984670 | ||||||||
\(999\) | − 4.26313i | − 0.134880i |
(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 | 845.2.c.g.506.1 | 8 | ||
13.2 | odd | 12 | 845.2.e.n.191.4 | 8 | |||
13.3 | even | 3 | 845.2.m.g.316.4 | 8 | |||
13.4 | even | 6 | 845.2.m.g.361.4 | 8 | |||
13.5 | odd | 4 | 845.2.a.l.1.1 | 4 | |||
13.6 | odd | 12 | 845.2.e.n.146.4 | 8 | |||
13.7 | odd | 12 | 845.2.e.m.146.1 | 8 | |||
13.8 | odd | 4 | 845.2.a.m.1.4 | 4 | |||
13.9 | even | 3 | 65.2.m.a.36.1 | ✓ | 8 | ||
13.10 | even | 6 | 65.2.m.a.56.1 | yes | 8 | ||
13.11 | odd | 12 | 845.2.e.m.191.1 | 8 | |||
13.12 | even | 2 | inner | 845.2.c.g.506.8 | 8 | ||
39.5 | even | 4 | 7605.2.a.cj.1.4 | 4 | |||
39.8 | even | 4 | 7605.2.a.cf.1.1 | 4 | |||
39.23 | odd | 6 | 585.2.bu.c.316.4 | 8 | |||
39.35 | odd | 6 | 585.2.bu.c.361.4 | 8 | |||
52.23 | odd | 6 | 1040.2.da.b.641.1 | 8 | |||
52.35 | odd | 6 | 1040.2.da.b.881.1 | 8 | |||
65.9 | even | 6 | 325.2.n.d.101.4 | 8 | |||
65.22 | odd | 12 | 325.2.m.b.49.1 | 8 | |||
65.23 | odd | 12 | 325.2.m.b.199.1 | 8 | |||
65.34 | odd | 4 | 4225.2.a.bi.1.1 | 4 | |||
65.44 | odd | 4 | 4225.2.a.bl.1.4 | 4 | |||
65.48 | odd | 12 | 325.2.m.c.49.4 | 8 | |||
65.49 | even | 6 | 325.2.n.d.251.4 | 8 | |||
65.62 | odd | 12 | 325.2.m.c.199.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.1 | ✓ | 8 | 13.9 | even | 3 | ||
65.2.m.a.56.1 | yes | 8 | 13.10 | even | 6 | ||
325.2.m.b.49.1 | 8 | 65.22 | odd | 12 | |||
325.2.m.b.199.1 | 8 | 65.23 | odd | 12 | |||
325.2.m.c.49.4 | 8 | 65.48 | odd | 12 | |||
325.2.m.c.199.4 | 8 | 65.62 | odd | 12 | |||
325.2.n.d.101.4 | 8 | 65.9 | even | 6 | |||
325.2.n.d.251.4 | 8 | 65.49 | even | 6 | |||
585.2.bu.c.316.4 | 8 | 39.23 | odd | 6 | |||
585.2.bu.c.361.4 | 8 | 39.35 | odd | 6 | |||
845.2.a.l.1.1 | 4 | 13.5 | odd | 4 | |||
845.2.a.m.1.4 | 4 | 13.8 | odd | 4 | |||
845.2.c.g.506.1 | 8 | 1.1 | even | 1 | trivial | ||
845.2.c.g.506.8 | 8 | 13.12 | even | 2 | inner | ||
845.2.e.m.146.1 | 8 | 13.7 | odd | 12 | |||
845.2.e.m.191.1 | 8 | 13.11 | odd | 12 | |||
845.2.e.n.146.4 | 8 | 13.6 | odd | 12 | |||
845.2.e.n.191.4 | 8 | 13.2 | odd | 12 | |||
845.2.m.g.316.4 | 8 | 13.3 | even | 3 | |||
845.2.m.g.361.4 | 8 | 13.4 | even | 6 | |||
1040.2.da.b.641.1 | 8 | 52.23 | odd | 6 | |||
1040.2.da.b.881.1 | 8 | 52.35 | odd | 6 | |||
4225.2.a.bi.1.1 | 4 | 65.34 | odd | 4 | |||
4225.2.a.bl.1.4 | 4 | 65.44 | odd | 4 | |||
7605.2.a.cf.1.1 | 4 | 39.8 | even | 4 | |||
7605.2.a.cj.1.4 | 4 | 39.5 | even | 4 |