Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1850,2,Mod(149,1850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1850.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1850 = 2 \cdot 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1850.b (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: | \(14.7723243739\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.37161216.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 15x^{4} + 51x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.4 | ||
Root | \(-3.13264i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1850.149 |
Dual form | 1850.2.b.p.149.3 |
$q$-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 \(\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1777\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − 3.13264i | − 1.80863i | −0.426867 | − | 0.904315i | \(-0.640383\pi\) | ||||
0.426867 | − | 0.904315i | \(-0.359617\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.13264 | 1.27889 | ||||||||
\(7\) | 4.13264i | 1.56199i | 0.624537 | + | 0.780995i | \(0.285288\pi\) | ||||
−0.624537 | + | 0.780995i | \(0.714712\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −6.81342 | −2.27114 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.68078 | −1.10980 | −0.554898 | − | 0.831918i | \(-0.687243\pi\) | ||||
−0.554898 | + | 0.831918i | \(0.687243\pi\) | |||||||
\(12\) | 3.13264i | 0.904315i | ||||||||
\(13\) | 0.132637i | 0.0367870i | 0.999831 | + | 0.0183935i | \(0.00585517\pi\) | ||||
−0.999831 | + | 0.0183935i | \(0.994145\pi\) | |||||||
\(14\) | −4.13264 | −1.10449 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 5.13264i | − 1.24485i | −0.782680 | − | 0.622424i | \(-0.786148\pi\) | ||||
0.782680 | − | 0.622424i | \(-0.213852\pi\) | |||||||
\(18\) | − 6.81342i | − 1.60594i | ||||||||
\(19\) | −0.451857 | −0.103663 | −0.0518316 | − | 0.998656i | \(-0.516506\pi\) | ||||
−0.0518316 | + | 0.998656i | \(0.516506\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.9461 | 2.82506 | ||||||||
\(22\) | − 3.68078i | − 0.784745i | ||||||||
\(23\) | 4.26527i | 0.889371i | 0.895687 | + | 0.444686i | \(0.146685\pi\) | ||||
−0.895687 | + | 0.444686i | \(0.853315\pi\) | |||||||
\(24\) | −3.13264 | −0.639447 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.132637 | −0.0260124 | ||||||||
\(27\) | 11.9461i | 2.29902i | ||||||||
\(28\) | − 4.13264i | − 0.780995i | ||||||||
\(29\) | 10.2653 | 1.90621 | 0.953107 | − | 0.302634i | \(-0.0978660\pi\) | ||||
0.953107 | + | 0.302634i | \(0.0978660\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.58449 | 1.00300 | 0.501502 | − | 0.865156i | \(-0.332781\pi\) | ||||
0.501502 | + | 0.865156i | \(0.332781\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 11.5305i | 2.00721i | ||||||||
\(34\) | 5.13264 | 0.880240 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.81342 | 1.13557 | ||||||||
\(37\) | 1.00000i | 0.164399i | ||||||||
\(38\) | − 0.451857i | − 0.0733009i | ||||||||
\(39\) | 0.415505 | 0.0665341 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.3616 | 1.61820 | 0.809102 | − | 0.587668i | \(-0.199954\pi\) | ||||
0.809102 | + | 0.587668i | \(0.199954\pi\) | |||||||
\(42\) | 12.9461i | 1.99762i | ||||||||
\(43\) | 5.07869i | 0.774493i | 0.921976 | + | 0.387247i | \(0.126574\pi\) | ||||
−0.921976 | + | 0.387247i | \(0.873426\pi\) | |||||||
\(44\) | 3.68078 | 0.554898 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.26527 | −0.628880 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | − 3.13264i | − 0.452157i | ||||||||
\(49\) | −10.0787 | −1.43981 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.0787 | −2.25147 | ||||||||
\(52\) | − 0.132637i | − 0.0183935i | ||||||||
\(53\) | 11.6268i | 1.59707i | 0.601949 | + | 0.798534i | \(0.294391\pi\) | ||||
−0.601949 | + | 0.798534i | \(0.705609\pi\) | |||||||
\(54\) | −11.9461 | −1.62565 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.13264 | 0.552247 | ||||||||
\(57\) | 1.41551i | 0.187488i | ||||||||
\(58\) | 10.2653i | 1.34790i | ||||||||
\(59\) | 13.0787 | 1.70270 | 0.851350 | − | 0.524597i | \(-0.175784\pi\) | ||||
0.851350 | + | 0.524597i | \(0.175784\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.39791 | −0.563095 | −0.281547 | − | 0.959547i | \(-0.590848\pi\) | ||||
−0.281547 | + | 0.959547i | \(0.590848\pi\) | |||||||
\(62\) | 5.58449i | 0.709232i | ||||||||
\(63\) | − 28.1574i | − 3.54750i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −11.5305 | −1.41931 | ||||||||
\(67\) | − 0.228923i | − 0.0279674i | −0.999902 | − | 0.0139837i | \(-0.995549\pi\) | ||||
0.999902 | − | 0.0139837i | \(-0.00445129\pi\) | |||||||
\(68\) | 5.13264i | 0.622424i | ||||||||
\(69\) | 13.3616 | 1.60854 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.49420 | 1.12675 | 0.563377 | − | 0.826200i | \(-0.309502\pi\) | ||||
0.563377 | + | 0.826200i | \(0.309502\pi\) | |||||||
\(72\) | 6.81342i | 0.802969i | ||||||||
\(73\) | − 3.54814i | − 0.415279i | −0.978205 | − | 0.207639i | \(-0.933422\pi\) | ||||
0.978205 | − | 0.207639i | \(-0.0665780\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.451857 | 0.0518316 | ||||||||
\(77\) | − 15.2113i | − 1.73349i | ||||||||
\(78\) | 0.415505i | 0.0470467i | ||||||||
\(79\) | 0.903715 | 0.101676 | 0.0508379 | − | 0.998707i | \(-0.483811\pi\) | ||||
0.0508379 | + | 0.998707i | \(0.483811\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16.9824 | 1.88693 | ||||||||
\(82\) | 10.3616i | 1.14424i | ||||||||
\(83\) | 13.9461i | 1.53078i | 0.643568 | + | 0.765389i | \(0.277454\pi\) | ||||
−0.643568 | + | 0.765389i | \(0.722546\pi\) | |||||||
\(84\) | −12.9461 | −1.41253 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.07869 | −0.547650 | ||||||||
\(87\) | − 32.1574i | − 3.44763i | ||||||||
\(88\) | 3.68078i | 0.392372i | ||||||||
\(89\) | −0.777066 | −0.0823688 | −0.0411844 | − | 0.999152i | \(-0.513113\pi\) | ||||
−0.0411844 | + | 0.999152i | \(0.513113\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.548143 | −0.0574610 | ||||||||
\(92\) | − 4.26527i | − 0.444686i | ||||||||
\(93\) | − 17.4942i | − 1.81406i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.13264 | 0.319723 | ||||||||
\(97\) | 0.638440i | 0.0648237i | 0.999475 | + | 0.0324119i | \(0.0103188\pi\) | ||||
−0.999475 | + | 0.0324119i | \(0.989681\pi\) | |||||||
\(98\) | − 10.0787i | − 1.01810i | ||||||||
\(99\) | 25.0787 | 2.52050 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.62684 | −0.559891 | −0.279946 | − | 0.960016i | \(-0.590316\pi\) | ||||
−0.279946 | + | 0.960016i | \(0.590316\pi\) | |||||||
\(102\) | − 16.0787i | − 1.59203i | ||||||||
\(103\) | − 10.0423i | − 0.989501i | −0.869035 | − | 0.494751i | \(-0.835259\pi\) | ||||
0.869035 | − | 0.494751i | \(-0.164741\pi\) | |||||||
\(104\) | 0.132637 | 0.0130062 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.6268 | −1.12930 | ||||||||
\(107\) | 19.6632i | 1.90091i | 0.310859 | + | 0.950456i | \(0.399383\pi\) | ||||
−0.310859 | + | 0.950456i | \(0.600617\pi\) | |||||||
\(108\) | − 11.9461i | − 1.14951i | ||||||||
\(109\) | −13.6268 | −1.30521 | −0.652607 | − | 0.757697i | \(-0.726325\pi\) | ||||
−0.652607 | + | 0.757697i | \(0.726325\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.13264 | 0.297337 | ||||||||
\(112\) | 4.13264i | 0.390498i | ||||||||
\(113\) | − 7.94606i | − 0.747502i | −0.927529 | − | 0.373751i | \(-0.878071\pi\) | ||||
0.927529 | − | 0.373751i | \(-0.121929\pi\) | |||||||
\(114\) | −1.41551 | −0.132574 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −10.2653 | −0.953107 | ||||||||
\(117\) | − 0.903715i | − 0.0835484i | ||||||||
\(118\) | 13.0787i | 1.20399i | ||||||||
\(119\) | 21.2113 | 1.94444 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.54814 | 0.231649 | ||||||||
\(122\) | − 4.39791i | − 0.398168i | ||||||||
\(123\) | − 32.4590i | − 2.92673i | ||||||||
\(124\) | −5.58449 | −0.501502 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 28.1574 | 2.50846 | ||||||||
\(127\) | 17.4942i | 1.55236i | 0.630512 | + | 0.776180i | \(0.282845\pi\) | ||||
−0.630512 | + | 0.776180i | \(0.717155\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 15.9097 | 1.40077 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.81342 | 0.770032 | 0.385016 | − | 0.922910i | \(-0.374196\pi\) | ||||
0.385016 | + | 0.922910i | \(0.374196\pi\) | |||||||
\(132\) | − 11.5305i | − 1.00361i | ||||||||
\(133\) | − 1.86736i | − 0.161921i | ||||||||
\(134\) | 0.228923 | 0.0197759 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.13264 | −0.440120 | ||||||||
\(137\) | 18.8921i | 1.61406i | 0.590509 | + | 0.807031i | \(0.298927\pi\) | ||||
−0.590509 | + | 0.807031i | \(0.701073\pi\) | |||||||
\(138\) | 13.3616i | 1.13741i | ||||||||
\(139\) | 14.8498 | 1.25954 | 0.629771 | − | 0.776781i | \(-0.283149\pi\) | ||||
0.629771 | + | 0.776781i | \(0.283149\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.49420i | 0.796735i | ||||||||
\(143\) | − 0.488209i | − 0.0408261i | ||||||||
\(144\) | −6.81342 | −0.567785 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.54814 | 0.293646 | ||||||||
\(147\) | 31.5729i | 2.60409i | ||||||||
\(148\) | − 1.00000i | − 0.0821995i | ||||||||
\(149\) | 2.41551 | 0.197886 | 0.0989429 | − | 0.995093i | \(-0.468454\pi\) | ||||
0.0989429 | + | 0.995093i | \(0.468454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.7231 | 0.872635 | 0.436318 | − | 0.899793i | \(-0.356282\pi\) | ||||
0.436318 | + | 0.899793i | \(0.356282\pi\) | |||||||
\(152\) | 0.451857i | 0.0366505i | ||||||||
\(153\) | 34.9708i | 2.82722i | ||||||||
\(154\) | 15.2113 | 1.22576 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.415505 | −0.0332670 | ||||||||
\(157\) | − 3.31922i | − 0.264903i | −0.991190 | − | 0.132451i | \(-0.957715\pi\) | ||||
0.991190 | − | 0.132451i | \(-0.0422848\pi\) | |||||||
\(158\) | 0.903715i | 0.0718957i | ||||||||
\(159\) | 36.4227 | 2.88850 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.6268 | −1.38919 | ||||||||
\(162\) | 16.9824i | 1.33426i | ||||||||
\(163\) | − 15.5481i | − 1.21782i | −0.793238 | − | 0.608912i | \(-0.791606\pi\) | ||||
0.793238 | − | 0.608912i | \(-0.208394\pi\) | |||||||
\(164\) | −10.3616 | −0.809102 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.9461 | −1.08242 | ||||||||
\(167\) | − 3.77707i | − 0.292278i | −0.989264 | − | 0.146139i | \(-0.953315\pi\) | ||||
0.989264 | − | 0.146139i | \(-0.0466847\pi\) | |||||||
\(168\) | − 12.9461i | − 0.998810i | ||||||||
\(169\) | 12.9824 | 0.998647 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.07869 | 0.235434 | ||||||||
\(172\) | − 5.07869i | − 0.387247i | ||||||||
\(173\) | − 20.1574i | − 1.53254i | −0.642520 | − | 0.766269i | \(-0.722111\pi\) | ||||
0.642520 | − | 0.766269i | \(-0.277889\pi\) | |||||||
\(174\) | 32.1574 | 2.43785 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.68078 | −0.277449 | ||||||||
\(177\) | − 40.9708i | − 3.07955i | ||||||||
\(178\) | − 0.777066i | − 0.0582435i | ||||||||
\(179\) | −20.2537 | −1.51383 | −0.756915 | − | 0.653513i | \(-0.773294\pi\) | ||||
−0.756915 | + | 0.653513i | \(0.773294\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.1690 | −1.27616 | −0.638080 | − | 0.769970i | \(-0.720271\pi\) | ||||
−0.638080 | + | 0.769970i | \(0.720271\pi\) | |||||||
\(182\) | − 0.548143i | − 0.0406310i | ||||||||
\(183\) | 13.7771i | 1.01843i | ||||||||
\(184\) | 4.26527 | 0.314440 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 17.4942 | 1.28274 | ||||||||
\(187\) | 18.8921i | 1.38153i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −49.3687 | −3.59105 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.192571 | −0.0139339 | −0.00696696 | − | 0.999976i | \(-0.502218\pi\) | ||||
−0.00696696 | + | 0.999976i | \(0.502218\pi\) | |||||||
\(192\) | 3.13264i | 0.226079i | ||||||||
\(193\) | 14.6692i | 1.05591i | 0.849272 | + | 0.527955i | \(0.177041\pi\) | ||||
−0.849272 | + | 0.527955i | \(0.822959\pi\) | |||||||
\(194\) | −0.638440 | −0.0458373 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.0787 | 0.719907 | ||||||||
\(197\) | − 7.84977i | − 0.559273i | −0.960106 | − | 0.279636i | \(-0.909786\pi\) | ||||
0.960106 | − | 0.279636i | \(-0.0902139\pi\) | |||||||
\(198\) | 25.0787i | 1.78227i | ||||||||
\(199\) | 11.3616 | 0.805400 | 0.402700 | − | 0.915332i | \(-0.368072\pi\) | ||||
0.402700 | + | 0.915332i | \(0.368072\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.717132 | −0.0505826 | ||||||||
\(202\) | − 5.62684i | − 0.395903i | ||||||||
\(203\) | 42.4227i | 2.97749i | ||||||||
\(204\) | 16.0787 | 1.12573 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.0423 | 0.699683 | ||||||||
\(207\) | − 29.0611i | − 2.01989i | ||||||||
\(208\) | 0.132637i | 0.00919676i | ||||||||
\(209\) | 1.66319 | 0.115045 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.2289 | −0.841874 | −0.420937 | − | 0.907090i | \(-0.638299\pi\) | ||||
−0.420937 | + | 0.907090i | \(0.638299\pi\) | |||||||
\(212\) | − 11.6268i | − 0.798534i | ||||||||
\(213\) | − 29.7419i | − 2.03788i | ||||||||
\(214\) | −19.6632 | −1.34415 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 11.9461 | 0.812826 | ||||||||
\(217\) | 23.0787i | 1.56668i | ||||||||
\(218\) | − 13.6268i | − 0.922926i | ||||||||
\(219\) | −11.1150 | −0.751085 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.680780 | 0.0457942 | ||||||||
\(222\) | 3.13264i | 0.210249i | ||||||||
\(223\) | − 28.1574i | − 1.88556i | −0.333418 | − | 0.942779i | \(-0.608202\pi\) | ||||
0.333418 | − | 0.942779i | \(-0.391798\pi\) | |||||||
\(224\) | −4.13264 | −0.276123 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.94606 | 0.528564 | ||||||||
\(227\) | 0.282868i | 0.0187746i | 0.999956 | + | 0.00938729i | \(0.00298811\pi\) | ||||
−0.999956 | + | 0.00938729i | \(0.997012\pi\) | |||||||
\(228\) | − 1.41551i | − 0.0937441i | ||||||||
\(229\) | 8.45785 | 0.558910 | 0.279455 | − | 0.960159i | \(-0.409846\pi\) | ||||
0.279455 | + | 0.960159i | \(0.409846\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −47.6516 | −3.13524 | ||||||||
\(232\) | − 10.2653i | − 0.673948i | ||||||||
\(233\) | 14.2477i | 0.933397i | 0.884417 | + | 0.466698i | \(0.154557\pi\) | ||||
−0.884417 | + | 0.466698i | \(0.845443\pi\) | |||||||
\(234\) | 0.903715 | 0.0590777 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.0787 | −0.851350 | ||||||||
\(237\) | − 2.83101i | − 0.183894i | ||||||||
\(238\) | 21.2113i | 1.37493i | ||||||||
\(239\) | −21.8921 | −1.41608 | −0.708041 | − | 0.706171i | \(-0.750421\pi\) | ||||
−0.708041 | + | 0.706171i | \(0.750421\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.13264 | −0.588285 | −0.294142 | − | 0.955762i | \(-0.595034\pi\) | ||||
−0.294142 | + | 0.955762i | \(0.595034\pi\) | |||||||
\(242\) | 2.54814i | 0.163801i | ||||||||
\(243\) | − 17.3616i | − 1.11374i | ||||||||
\(244\) | 4.39791 | 0.281547 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 32.4590 | 2.06951 | ||||||||
\(247\) | − 0.0599332i | − 0.00381346i | ||||||||
\(248\) | − 5.58449i | − 0.354616i | ||||||||
\(249\) | 43.6879 | 2.76861 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.00000 | −0.568075 | −0.284037 | − | 0.958813i | \(-0.591674\pi\) | ||||
−0.284037 | + | 0.958813i | \(0.591674\pi\) | |||||||
\(252\) | 28.1574i | 1.77375i | ||||||||
\(253\) | − 15.6995i | − 0.987022i | ||||||||
\(254\) | −17.4942 | −1.09768 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 8.90371i | − 0.555398i | −0.960668 | − | 0.277699i | \(-0.910428\pi\) | ||||
0.960668 | − | 0.277699i | \(-0.0895719\pi\) | |||||||
\(258\) | 15.9097i | 0.990495i | ||||||||
\(259\) | −4.13264 | −0.256790 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −69.9416 | −4.32928 | ||||||||
\(262\) | 8.81342i | 0.544495i | ||||||||
\(263\) | 14.9037i | 0.919002i | 0.888177 | + | 0.459501i | \(0.151972\pi\) | ||||
−0.888177 | + | 0.459501i | \(0.848028\pi\) | |||||||
\(264\) | 11.5305 | 0.709656 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.86736 | 0.114495 | ||||||||
\(267\) | 2.43426i | 0.148975i | ||||||||
\(268\) | 0.228923i | 0.0139837i | ||||||||
\(269\) | 1.55413 | 0.0947570 | 0.0473785 | − | 0.998877i | \(-0.484913\pi\) | ||||
0.0473785 | + | 0.998877i | \(0.484913\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.68677 | 0.345447 | 0.172723 | − | 0.984970i | \(-0.444743\pi\) | ||||
0.172723 | + | 0.984970i | \(0.444743\pi\) | |||||||
\(272\) | − 5.13264i | − 0.311212i | ||||||||
\(273\) | 1.71713i | 0.103926i | ||||||||
\(274\) | −18.8921 | −1.14131 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.3616 | −0.804271 | ||||||||
\(277\) | − 12.9037i | − 0.775309i | −0.921805 | − | 0.387655i | \(-0.873285\pi\) | ||||
0.921805 | − | 0.387655i | \(-0.126715\pi\) | |||||||
\(278\) | 14.8498i | 0.890630i | ||||||||
\(279\) | −38.0495 | −2.27796 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.2829 | −0.732734 | −0.366367 | − | 0.930470i | \(-0.619399\pi\) | ||||
−0.366367 | + | 0.930470i | \(0.619399\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.8745i | 1.59752i | 0.601647 | + | 0.798762i | \(0.294511\pi\) | ||||
−0.601647 | + | 0.798762i | \(0.705489\pi\) | |||||||
\(284\) | −9.49420 | −0.563377 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.488209 | 0.0288684 | ||||||||
\(287\) | 42.8206i | 2.52762i | ||||||||
\(288\) | − 6.81342i | − 0.401484i | ||||||||
\(289\) | −9.34397 | −0.549645 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.00000 | 0.117242 | ||||||||
\(292\) | 3.54814i | 0.207639i | ||||||||
\(293\) | 16.7535i | 0.978749i | 0.872074 | + | 0.489375i | \(0.162775\pi\) | ||||
−0.872074 | + | 0.489375i | \(0.837225\pi\) | |||||||
\(294\) | −31.5729 | −1.84137 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | − 43.9708i | − 2.55144i | ||||||||
\(298\) | 2.41551i | 0.139926i | ||||||||
\(299\) | −0.565735 | −0.0327173 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.9884 | −1.20975 | ||||||||
\(302\) | 10.7231i | 0.617046i | ||||||||
\(303\) | 17.6268i | 1.01264i | ||||||||
\(304\) | −0.451857 | −0.0259158 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −34.9708 | −1.99915 | ||||||||
\(307\) | − 8.47661i | − 0.483785i | −0.970303 | − | 0.241893i | \(-0.922232\pi\) | ||||
0.970303 | − | 0.241893i | \(-0.0777682\pi\) | |||||||
\(308\) | 15.2113i | 0.866746i | ||||||||
\(309\) | −31.4590 | −1.78964 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.4650 | 1.84092 | 0.920461 | − | 0.390835i | \(-0.127814\pi\) | ||||
0.920461 | + | 0.390835i | \(0.127814\pi\) | |||||||
\(312\) | − 0.415505i | − 0.0235233i | ||||||||
\(313\) | − 28.8134i | − 1.62863i | −0.580423 | − | 0.814315i | \(-0.697113\pi\) | ||||
0.580423 | − | 0.814315i | \(-0.302887\pi\) | |||||||
\(314\) | 3.31922 | 0.187314 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.903715 | −0.0508379 | ||||||||
\(317\) | − 6.87335i | − 0.386046i | −0.981194 | − | 0.193023i | \(-0.938171\pi\) | ||||
0.981194 | − | 0.193023i | \(-0.0618292\pi\) | |||||||
\(318\) | 36.4227i | 2.04248i | ||||||||
\(319\) | −37.7842 | −2.11551 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 61.5976 | 3.43804 | ||||||||
\(322\) | − 17.6268i | − 0.982305i | ||||||||
\(323\) | 2.31922i | 0.129045i | ||||||||
\(324\) | −16.9824 | −0.943467 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.5481 | 0.861132 | ||||||||
\(327\) | 42.6879i | 2.36065i | ||||||||
\(328\) | − 10.3616i | − 0.572121i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.65603 | −0.0910238 | −0.0455119 | − | 0.998964i | \(-0.514492\pi\) | ||||
−0.0455119 | + | 0.998964i | \(0.514492\pi\) | |||||||
\(332\) | − 13.9461i | − 0.765389i | ||||||||
\(333\) | − 6.81342i | − 0.373373i | ||||||||
\(334\) | 3.77707 | 0.206672 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12.9461 | 0.706265 | ||||||||
\(337\) | 10.2537i | 0.558553i | 0.960211 | + | 0.279277i | \(0.0900946\pi\) | ||||
−0.960211 | + | 0.279277i | \(0.909905\pi\) | |||||||
\(338\) | 12.9824i | 0.706150i | ||||||||
\(339\) | −24.8921 | −1.35195 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.5553 | −1.11313 | ||||||||
\(342\) | 3.07869i | 0.166477i | ||||||||
\(343\) | − 12.7231i | − 0.686984i | ||||||||
\(344\) | 5.07869 | 0.273825 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.1574 | 1.08367 | ||||||||
\(347\) | 25.8805i | 1.38934i | 0.719329 | + | 0.694669i | \(0.244449\pi\) | ||||
−0.719329 | + | 0.694669i | \(0.755551\pi\) | |||||||
\(348\) | 32.1574i | 1.72382i | ||||||||
\(349\) | −12.7535 | −0.682678 | −0.341339 | − | 0.939940i | \(-0.610880\pi\) | ||||
−0.341339 | + | 0.939940i | \(0.610880\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.58449 | −0.0845741 | ||||||||
\(352\) | − 3.68078i | − 0.196186i | ||||||||
\(353\) | − 8.72312i | − 0.464285i | −0.972682 | − | 0.232142i | \(-0.925426\pi\) | ||||
0.972682 | − | 0.232142i | \(-0.0745735\pi\) | |||||||
\(354\) | 40.9708 | 2.17757 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.777066 | 0.0411844 | ||||||||
\(357\) | − 66.4474i | − 3.51677i | ||||||||
\(358\) | − 20.2537i | − 1.07044i | ||||||||
\(359\) | −14.9037 | −0.786588 | −0.393294 | − | 0.919413i | \(-0.628665\pi\) | ||||
−0.393294 | + | 0.919413i | \(0.628665\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7958 | −0.989254 | ||||||||
\(362\) | − 17.1690i | − 0.902382i | ||||||||
\(363\) | − 7.98241i | − 0.418968i | ||||||||
\(364\) | 0.548143 | 0.0287305 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −13.7771 | −0.720139 | ||||||||
\(367\) | − 14.8558i | − 0.775464i | −0.921772 | − | 0.387732i | \(-0.873259\pi\) | ||||
0.921772 | − | 0.387732i | \(-0.126741\pi\) | |||||||
\(368\) | 4.26527i | 0.222343i | ||||||||
\(369\) | −70.5976 | −3.67517 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −48.0495 | −2.49461 | ||||||||
\(372\) | 17.4942i | 0.907032i | ||||||||
\(373\) | 1.77707i | 0.0920130i | 0.998941 | + | 0.0460065i | \(0.0146495\pi\) | ||||
−0.998941 | + | 0.0460065i | \(0.985351\pi\) | |||||||
\(374\) | −18.8921 | −0.976888 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.36156i | 0.0701239i | ||||||||
\(378\) | − 49.3687i | − 2.53925i | ||||||||
\(379\) | 26.3863 | 1.35537 | 0.677687 | − | 0.735351i | \(-0.262983\pi\) | ||||
0.677687 | + | 0.735351i | \(0.262983\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 54.8030 | 2.80764 | ||||||||
\(382\) | − 0.192571i | − 0.00985277i | ||||||||
\(383\) | − 4.57289i | − 0.233664i | −0.993152 | − | 0.116832i | \(-0.962726\pi\) | ||||
0.993152 | − | 0.116832i | \(-0.0372739\pi\) | |||||||
\(384\) | −3.13264 | −0.159862 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.6692 | −0.746641 | ||||||||
\(387\) | − 34.6033i | − 1.75898i | ||||||||
\(388\) | − 0.638440i | − 0.0324119i | ||||||||
\(389\) | −5.03635 | −0.255353 | −0.127677 | − | 0.991816i | \(-0.540752\pi\) | ||||
−0.127677 | + | 0.991816i | \(0.540752\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.8921 | 1.10713 | ||||||||
\(392\) | 10.0787i | 0.509051i | ||||||||
\(393\) | − 27.6092i | − 1.39270i | ||||||||
\(394\) | 7.84977 | 0.395466 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −25.0787 | −1.26025 | ||||||||
\(397\) | 34.4650i | 1.72975i | 0.501988 | + | 0.864874i | \(0.332602\pi\) | ||||
−0.501988 | + | 0.864874i | \(0.667398\pi\) | |||||||
\(398\) | 11.3616i | 0.569504i | ||||||||
\(399\) | −5.84977 | −0.292855 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.47661 | −0.223551 | −0.111775 | − | 0.993733i | \(-0.535654\pi\) | ||||
−0.111775 | + | 0.993733i | \(0.535654\pi\) | |||||||
\(402\) | − 0.717132i | − 0.0357673i | ||||||||
\(403\) | 0.740713i | 0.0368976i | ||||||||
\(404\) | 5.62684 | 0.279946 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −42.4227 | −2.10540 | ||||||||
\(407\) | − 3.68078i | − 0.182449i | ||||||||
\(408\) | 16.0787i | 0.796014i | ||||||||
\(409\) | 34.7243 | 1.71701 | 0.858503 | − | 0.512809i | \(-0.171395\pi\) | ||||
0.858503 | + | 0.512809i | \(0.171395\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 59.1821 | 2.91924 | ||||||||
\(412\) | 10.0423i | 0.494751i | ||||||||
\(413\) | 54.0495i | 2.65960i | ||||||||
\(414\) | 29.0611 | 1.42828 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.132637 | −0.00650309 | ||||||||
\(417\) | − 46.5189i | − 2.27804i | ||||||||
\(418\) | 1.66319i | 0.0813492i | ||||||||
\(419\) | 7.15023 | 0.349312 | 0.174656 | − | 0.984630i | \(-0.444119\pi\) | ||||
0.174656 | + | 0.984630i | \(0.444119\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.6033 | 1.29656 | 0.648282 | − | 0.761401i | \(-0.275488\pi\) | ||||
0.648282 | + | 0.761401i | \(0.275488\pi\) | |||||||
\(422\) | − 12.2289i | − 0.595295i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.6268 | 0.564649 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 29.7419 | 1.44100 | ||||||||
\(427\) | − 18.1750i | − 0.879549i | ||||||||
\(428\) | − 19.6632i | − 0.950456i | ||||||||
\(429\) | −1.52938 | −0.0738393 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.16899 | −0.0563082 | −0.0281541 | − | 0.999604i | \(-0.508963\pi\) | ||||
−0.0281541 | + | 0.999604i | \(0.508963\pi\) | |||||||
\(432\) | 11.9461i | 0.574755i | ||||||||
\(433\) | − 5.00000i | − 0.240285i | −0.992757 | − | 0.120142i | \(-0.961665\pi\) | ||||
0.992757 | − | 0.120142i | \(-0.0383351\pi\) | |||||||
\(434\) | −23.0787 | −1.10781 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.6268 | 0.652607 | ||||||||
\(437\) | − 1.92730i | − 0.0921951i | ||||||||
\(438\) | − 11.1150i | − 0.531097i | ||||||||
\(439\) | 32.3148 | 1.54230 | 0.771150 | − | 0.636654i | \(-0.219682\pi\) | ||||
0.771150 | + | 0.636654i | \(0.219682\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 68.6703 | 3.27002 | ||||||||
\(442\) | 0.680780i | 0.0323814i | ||||||||
\(443\) | 17.4155i | 0.827436i | 0.910405 | + | 0.413718i | \(0.135770\pi\) | ||||
−0.910405 | + | 0.413718i | \(0.864230\pi\) | |||||||
\(444\) | −3.13264 | −0.148668 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 28.1574 | 1.33329 | ||||||||
\(447\) | − 7.56690i | − 0.357902i | ||||||||
\(448\) | − 4.13264i | − 0.195249i | ||||||||
\(449\) | 7.38032 | 0.348299 | 0.174149 | − | 0.984719i | \(-0.444282\pi\) | ||||
0.174149 | + | 0.984719i | \(0.444282\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −38.1386 | −1.79588 | ||||||||
\(452\) | 7.94606i | 0.373751i | ||||||||
\(453\) | − 33.5916i | − 1.57827i | ||||||||
\(454\) | −0.282868 | −0.0132756 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.41551 | 0.0662871 | ||||||||
\(457\) | 22.7419i | 1.06382i | 0.846801 | + | 0.531910i | \(0.178526\pi\) | ||||
−0.846801 | + | 0.531910i | \(0.821474\pi\) | |||||||
\(458\) | 8.45785i | 0.395209i | ||||||||
\(459\) | 61.3148 | 2.86193 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.7115 | 1.84955 | 0.924775 | − | 0.380515i | \(-0.124253\pi\) | ||||
0.924775 | + | 0.380515i | \(0.124253\pi\) | |||||||
\(462\) | − 47.6516i | − 2.21695i | ||||||||
\(463\) | 30.6456i | 1.42422i | 0.702067 | + | 0.712111i | \(0.252261\pi\) | ||||
−0.702067 | + | 0.712111i | \(0.747739\pi\) | |||||||
\(464\) | 10.2653 | 0.476553 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.2477 | −0.660011 | ||||||||
\(467\) | 24.7958i | 1.14741i | 0.819061 | + | 0.573707i | \(0.194495\pi\) | ||||
−0.819061 | + | 0.573707i | \(0.805505\pi\) | |||||||
\(468\) | 0.903715i | 0.0417742i | ||||||||
\(469\) | 0.946055 | 0.0436848 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.3979 | −0.479111 | ||||||||
\(472\) | − 13.0787i | − 0.601996i | ||||||||
\(473\) | − 18.6936i | − 0.859530i | ||||||||
\(474\) | 2.83101 | 0.130033 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −21.2113 | −0.972220 | ||||||||
\(477\) | − 79.2185i | − 3.62717i | ||||||||
\(478\) | − 21.8921i | − 1.00132i | ||||||||
\(479\) | 15.5845 | 0.712074 | 0.356037 | − | 0.934472i | \(-0.384128\pi\) | ||||
0.356037 | + | 0.934472i | \(0.384128\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.132637 | −0.00604775 | ||||||||
\(482\) | − 9.13264i | − 0.415980i | ||||||||
\(483\) | 55.2185i | 2.51253i | ||||||||
\(484\) | −2.54814 | −0.115825 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 17.3616 | 0.787536 | ||||||||
\(487\) | 3.65720i | 0.165724i | 0.996561 | + | 0.0828618i | \(0.0264060\pi\) | ||||
−0.996561 | + | 0.0828618i | \(0.973594\pi\) | |||||||
\(488\) | 4.39791i | 0.199084i | ||||||||
\(489\) | −48.7067 | −2.20259 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.3264 | 1.50400 | 0.751999 | − | 0.659164i | \(-0.229090\pi\) | ||||
0.751999 | + | 0.659164i | \(0.229090\pi\) | |||||||
\(492\) | 32.4590i | 1.46337i | ||||||||
\(493\) | − 52.6879i | − 2.37295i | ||||||||
\(494\) | 0.0599332 | 0.00269652 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.58449 | 0.250751 | ||||||||
\(497\) | 39.2361i | 1.75998i | ||||||||
\(498\) | 43.6879i | 1.95770i | ||||||||
\(499\) | −7.53654 | −0.337382 | −0.168691 | − | 0.985669i | \(-0.553954\pi\) | ||||
−0.168691 | + | 0.985669i | \(0.553954\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.8322 | −0.528623 | ||||||||
\(502\) | − 9.00000i | − 0.401690i | ||||||||
\(503\) | 24.0000i | 1.07011i | 0.844818 | + | 0.535054i | \(0.179709\pi\) | ||||
−0.844818 | + | 0.535054i | \(0.820291\pi\) | |||||||
\(504\) | −28.1574 | −1.25423 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 15.6995 | 0.697930 | ||||||||
\(507\) | − 40.6692i | − 1.80618i | ||||||||
\(508\) | − 17.4942i | − 0.776180i | ||||||||
\(509\) | −24.1150 | −1.06888 | −0.534440 | − | 0.845206i | \(-0.679478\pi\) | ||||
−0.534440 | + | 0.845206i | \(0.679478\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.6632 | 0.648661 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 5.39791i | − 0.238324i | ||||||||
\(514\) | 8.90371 | 0.392726 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −15.9097 | −0.700386 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − 4.13264i | − 0.181578i | ||||||||
\(519\) | −63.1458 | −2.77179 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.8134 | −0.517555 | −0.258778 | − | 0.965937i | \(-0.583320\pi\) | ||||
−0.258778 | + | 0.965937i | \(0.583320\pi\) | |||||||
\(522\) | − 69.9416i | − 3.06126i | ||||||||
\(523\) | 33.9532i | 1.48467i | 0.670029 | + | 0.742335i | \(0.266282\pi\) | ||||
−0.670029 | + | 0.742335i | \(0.733718\pi\) | |||||||
\(524\) | −8.81342 | −0.385016 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.9037 | −0.649833 | ||||||||
\(527\) | − 28.6632i | − 1.24859i | ||||||||
\(528\) | 11.5305i | 0.501803i | ||||||||
\(529\) | 4.80743 | 0.209019 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −89.1106 | −3.86707 | ||||||||
\(532\) | 1.86736i | 0.0809604i | ||||||||
\(533\) | 1.37433i | 0.0595289i | ||||||||
\(534\) | −2.43426 | −0.105341 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.228923 | −0.00988796 | ||||||||
\(537\) | 63.4474i | 2.73796i | ||||||||
\(538\) | 1.55413i | 0.0670033i | ||||||||
\(539\) | 37.0975 | 1.59790 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.4590 | −1.43852 | −0.719258 | − | 0.694743i | \(-0.755518\pi\) | ||||
−0.719258 | + | 0.694743i | \(0.755518\pi\) | |||||||
\(542\) | 5.68677i | 0.244268i | ||||||||
\(543\) | 53.7842i | 2.30810i | ||||||||
\(544\) | 5.13264 | 0.220060 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.71713 | −0.0734865 | ||||||||
\(547\) | − 42.1514i | − 1.80226i | −0.433545 | − | 0.901132i | \(-0.642738\pi\) | ||||
0.433545 | − | 0.901132i | \(-0.357262\pi\) | |||||||
\(548\) | − 18.8921i | − 0.807031i | ||||||||
\(549\) | 29.9648 | 1.27887 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.63844 | −0.197604 | ||||||||
\(552\) | − 13.3616i | − 0.568706i | ||||||||
\(553\) | 3.73473i | 0.158817i | ||||||||
\(554\) | 12.9037 | 0.548226 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.8498 | −0.629771 | ||||||||
\(557\) | 12.3732i | 0.524268i | 0.965032 | + | 0.262134i | \(0.0844262\pi\) | ||||
−0.965032 | + | 0.262134i | \(0.915574\pi\) | |||||||
\(558\) | − 38.0495i | − 1.61076i | ||||||||
\(559\) | −0.673625 | −0.0284913 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 59.1821 | 2.49867 | ||||||||
\(562\) | − 12.2829i | − 0.518122i | ||||||||
\(563\) | − 40.7782i | − 1.71860i | −0.511474 | − | 0.859299i | \(-0.670900\pi\) | ||||
0.511474 | − | 0.859299i | \(-0.329100\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −26.8745 | −1.12962 | ||||||||
\(567\) | 70.1821i | 2.94737i | ||||||||
\(568\) | − 9.49420i | − 0.398368i | ||||||||
\(569\) | 20.7419 | 0.869545 | 0.434772 | − | 0.900540i | \(-0.356829\pi\) | ||||
0.434772 | + | 0.900540i | \(0.356829\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.1458 | −1.55450 | −0.777251 | − | 0.629190i | \(-0.783387\pi\) | ||||
−0.777251 | + | 0.629190i | \(0.783387\pi\) | |||||||
\(572\) | 0.488209i | 0.0204131i | ||||||||
\(573\) | 0.603254i | 0.0252013i | ||||||||
\(574\) | −42.8206 | −1.78730 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.81342 | 0.283892 | ||||||||
\(577\) | − 23.0975i | − 0.961560i | −0.876841 | − | 0.480780i | \(-0.840354\pi\) | ||||
0.876841 | − | 0.480780i | \(-0.159646\pi\) | |||||||
\(578\) | − 9.34397i | − 0.388658i | ||||||||
\(579\) | 45.9532 | 1.90975 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −57.6340 | −2.39106 | ||||||||
\(582\) | 2.00000i | 0.0829027i | ||||||||
\(583\) | − 42.7958i | − 1.77242i | ||||||||
\(584\) | −3.54814 | −0.146823 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.7535 | −0.692080 | ||||||||
\(587\) | 11.0176i | 0.454745i | 0.973808 | + | 0.227372i | \(0.0730134\pi\) | ||||
−0.973808 | + | 0.227372i | \(0.926987\pi\) | |||||||
\(588\) | − 31.5729i | − 1.30204i | ||||||||
\(589\) | −2.52339 | −0.103975 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.5905 | −1.01152 | ||||||||
\(592\) | 1.00000i | 0.0410997i | ||||||||
\(593\) | 0.469450i | 0.0192780i | 0.999954 | + | 0.00963900i | \(0.00306824\pi\) | ||||
−0.999954 | + | 0.00963900i | \(0.996932\pi\) | |||||||
\(594\) | 43.9708 | 1.80414 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.41551 | −0.0989429 | ||||||||
\(597\) | − 35.5916i | − 1.45667i | ||||||||
\(598\) | − 0.565735i | − 0.0231346i | ||||||||
\(599\) | 24.7711 | 1.01212 | 0.506059 | − | 0.862499i | \(-0.331102\pi\) | ||||
0.506059 | + | 0.862499i | \(0.331102\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.4051 | −0.954713 | −0.477356 | − | 0.878710i | \(-0.658405\pi\) | ||||
−0.477356 | + | 0.878710i | \(0.658405\pi\) | |||||||
\(602\) | − 20.9884i | − 0.855423i | ||||||||
\(603\) | 1.55975i | 0.0635178i | ||||||||
\(604\) | −10.7231 | −0.436318 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −17.6268 | −0.716041 | ||||||||
\(607\) | 0.342801i | 0.0139139i | 0.999976 | + | 0.00695693i | \(0.00221448\pi\) | ||||
−0.999976 | + | 0.00695693i | \(0.997786\pi\) | |||||||
\(608\) | − 0.451857i | − 0.0183252i | ||||||||
\(609\) | 132.895 | 5.38517 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | − 34.9708i | − 1.41361i | ||||||||
\(613\) | − 35.8921i | − 1.44967i | −0.688923 | − | 0.724834i | \(-0.741916\pi\) | ||||
0.688923 | − | 0.724834i | \(-0.258084\pi\) | |||||||
\(614\) | 8.47661 | 0.342088 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.2113 | −0.612882 | ||||||||
\(617\) | 7.64443i | 0.307753i | 0.988090 | + | 0.153877i | \(0.0491758\pi\) | ||||
−0.988090 | + | 0.153877i | \(0.950824\pi\) | |||||||
\(618\) | − 31.4590i | − 1.26547i | ||||||||
\(619\) | 10.4227 | 0.418922 | 0.209461 | − | 0.977817i | \(-0.432829\pi\) | ||||
0.209461 | + | 0.977817i | \(0.432829\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −50.9532 | −2.04468 | ||||||||
\(622\) | 32.4650i | 1.30173i | ||||||||
\(623\) | − 3.21133i | − 0.128659i | ||||||||
\(624\) | 0.415505 | 0.0166335 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 28.8134 | 1.15162 | ||||||||
\(627\) | − 5.21016i | − 0.208074i | ||||||||
\(628\) | 3.31922i | 0.132451i | ||||||||
\(629\) | 5.13264 | 0.204652 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.4227 | 1.05187 | 0.525935 | − | 0.850525i | \(-0.323716\pi\) | ||||
0.525935 | + | 0.850525i | \(0.323716\pi\) | |||||||
\(632\) | − 0.903715i | − 0.0359478i | ||||||||
\(633\) | 38.3088i | 1.52264i | ||||||||
\(634\) | 6.87335 | 0.272976 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −36.4227 | −1.44425 | ||||||||
\(637\) | − 1.33681i | − 0.0529664i | ||||||||
\(638\) | − 37.7842i | − 1.49589i | ||||||||
\(639\) | −64.6879 | −2.55902 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.8074 | 0.466365 | 0.233183 | − | 0.972433i | \(-0.425086\pi\) | ||||
0.233183 | + | 0.972433i | \(0.425086\pi\) | |||||||
\(642\) | 61.5976i | 2.43106i | ||||||||
\(643\) | − 18.3556i | − 0.723873i | −0.932203 | − | 0.361937i | \(-0.882116\pi\) | ||||
0.932203 | − | 0.361937i | \(-0.117884\pi\) | |||||||
\(644\) | 17.6268 | 0.694595 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.31922 | −0.0912485 | ||||||||
\(647\) | 33.7771i | 1.32791i | 0.747771 | + | 0.663957i | \(0.231124\pi\) | ||||
−0.747771 | + | 0.663957i | \(0.768876\pi\) | |||||||
\(648\) | − 16.9824i | − 0.667132i | ||||||||
\(649\) | −48.1398 | −1.88965 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 72.2972 | 2.83355 | ||||||||
\(652\) | 15.5481i | 0.608912i | ||||||||
\(653\) | − 18.0247i | − 0.705363i | −0.935743 | − | 0.352681i | \(-0.885270\pi\) | ||||
0.935743 | − | 0.352681i | \(-0.114730\pi\) | |||||||
\(654\) | −42.6879 | −1.66923 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.3616 | 0.404551 | ||||||||
\(657\) | 24.1750i | 0.943156i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.5669 | −0.645355 | −0.322677 | − | 0.946509i | \(-0.604583\pi\) | ||||
−0.322677 | + | 0.946509i | \(0.604583\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.7842 | −0.925099 | −0.462549 | − | 0.886593i | \(-0.653065\pi\) | ||||
−0.462549 | + | 0.886593i | \(0.653065\pi\) | |||||||
\(662\) | − 1.65603i | − 0.0643635i | ||||||||
\(663\) | − 2.13264i | − 0.0828248i | ||||||||
\(664\) | 13.9461 | 0.541212 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.81342 | 0.264015 | ||||||||
\(667\) | 43.7842i | 1.69533i | ||||||||
\(668\) | 3.77707i | 0.146139i | ||||||||
\(669\) | −88.2069 | −3.41028 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.1877 | 0.624921 | ||||||||
\(672\) | 12.9461i | 0.499405i | ||||||||
\(673\) | 12.0551i | 0.464690i | 0.972633 | + | 0.232345i | \(0.0746399\pi\) | ||||
−0.972633 | + | 0.232345i | \(0.925360\pi\) | |||||||
\(674\) | −10.2537 | −0.394957 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.9824 | −0.499323 | ||||||||
\(677\) | − 28.8805i | − 1.10997i | −0.831861 | − | 0.554984i | \(-0.812724\pi\) | ||||
0.831861 | − | 0.554984i | \(-0.187276\pi\) | |||||||
\(678\) | − 24.8921i | − 0.955976i | ||||||||
\(679\) | −2.63844 | −0.101254 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.886122 | 0.0339563 | ||||||||
\(682\) | − 20.5553i | − 0.787103i | ||||||||
\(683\) | − 17.6328i | − 0.674701i | −0.941379 | − | 0.337351i | \(-0.890469\pi\) | ||||
0.941379 | − | 0.337351i | \(-0.109531\pi\) | |||||||
\(684\) | −3.07869 | −0.117717 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12.7231 | 0.485771 | ||||||||
\(687\) | − 26.4954i | − 1.01086i | ||||||||
\(688\) | 5.07869i | 0.193623i | ||||||||
\(689\) | −1.54215 | −0.0587514 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.6572 | −0.785837 | −0.392918 | − | 0.919573i | \(-0.628535\pi\) | ||||
−0.392918 | + | 0.919573i | \(0.628535\pi\) | |||||||
\(692\) | 20.1574i | 0.766269i | ||||||||
\(693\) | 103.641i | 3.93700i | ||||||||
\(694\) | −25.8805 | −0.982411 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −32.1574 | −1.21892 | ||||||||
\(697\) | − 53.1821i | − 2.01442i | ||||||||
\(698\) | − 12.7535i | − 0.482727i | ||||||||
\(699\) | 44.6328 | 1.68817 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.2057 | 1.85847 | 0.929237 | − | 0.369484i | \(-0.120466\pi\) | ||||
0.929237 | + | 0.369484i | \(0.120466\pi\) | |||||||
\(702\) | − 1.58449i | − 0.0598029i | ||||||||
\(703\) | − 0.451857i | − 0.0170421i | ||||||||
\(704\) | 3.68078 | 0.138725 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.72312 | 0.328299 | ||||||||
\(707\) | − 23.2537i | − 0.874544i | ||||||||
\(708\) | 40.9708i | 1.53978i | ||||||||
\(709\) | −3.73473 | −0.140261 | −0.0701303 | − | 0.997538i | \(-0.522341\pi\) | ||||
−0.0701303 | + | 0.997538i | \(0.522341\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.15739 | −0.230920 | ||||||||
\(712\) | 0.777066i | 0.0291218i | ||||||||
\(713\) | 23.8194i | 0.892044i | ||||||||
\(714\) | 66.4474 | 2.48673 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 20.2537 | 0.756915 | ||||||||
\(717\) | 68.5800i | 2.56117i | ||||||||
\(718\) | − 14.9037i | − 0.556202i | ||||||||
\(719\) | 47.0858 | 1.75601 | 0.878003 | − | 0.478655i | \(-0.158876\pi\) | ||||
0.878003 | + | 0.478655i | \(0.158876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.5014 | 1.54559 | ||||||||
\(722\) | − 18.7958i | − 0.699508i | ||||||||
\(723\) | 28.6092i | 1.06399i | ||||||||
\(724\) | 17.1690 | 0.638080 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.98241 | 0.296255 | ||||||||
\(727\) | 27.3616i | 1.01478i | 0.861715 | + | 0.507392i | \(0.169390\pi\) | ||||
−0.861715 | + | 0.507392i | \(0.830610\pi\) | |||||||
\(728\) | 0.548143i | 0.0203155i | ||||||||
\(729\) | −3.44025 | −0.127417 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.0671 | 0.964126 | ||||||||
\(732\) | − 13.7771i | − 0.509215i | ||||||||
\(733\) | − 47.5070i | − 1.75471i | −0.479842 | − | 0.877355i | \(-0.659306\pi\) | ||||
0.479842 | − | 0.877355i | \(-0.340694\pi\) | |||||||
\(734\) | 14.8558 | 0.548336 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.26527 | −0.157220 | ||||||||
\(737\) | 0.842615i | 0.0310381i | ||||||||
\(738\) | − 70.5976i | − 2.59873i | ||||||||
\(739\) | −19.6149 | −0.721544 | −0.360772 | − | 0.932654i | \(-0.617487\pi\) | ||||
−0.360772 | + | 0.932654i | \(0.617487\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.187749 | −0.00689713 | ||||||||
\(742\) | − 48.0495i | − 1.76395i | ||||||||
\(743\) | − 22.3148i | − 0.818650i | −0.912389 | − | 0.409325i | \(-0.865764\pi\) | ||||
0.912389 | − | 0.409325i | \(-0.134236\pi\) | |||||||
\(744\) | −17.4942 | −0.641368 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.77707 | −0.0650630 | ||||||||
\(747\) | − 95.0203i | − 3.47661i | ||||||||
\(748\) | − 18.8921i | − 0.690764i | ||||||||
\(749\) | −81.2608 | −2.96921 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.7958 | 0.758850 | 0.379425 | − | 0.925222i | \(-0.376122\pi\) | ||||
0.379425 | + | 0.925222i | \(0.376122\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.1937i | 1.02744i | ||||||||
\(754\) | −1.36156 | −0.0495851 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 49.3687 | 1.79552 | ||||||||
\(757\) | − 0.530550i | − 0.0192832i | −0.999954 | − | 0.00964158i | \(-0.996931\pi\) | ||||
0.999954 | − | 0.00964158i | \(-0.00306906\pi\) | |||||||
\(758\) | 26.3863i | 0.958394i | ||||||||
\(759\) | −49.1810 | −1.78516 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.63245 | 0.167926 | 0.0839631 | − | 0.996469i | \(-0.473242\pi\) | ||||
0.0839631 | + | 0.996469i | \(0.473242\pi\) | |||||||
\(762\) | 54.8030i | 1.98530i | ||||||||
\(763\) | − 56.3148i | − 2.03873i | ||||||||
\(764\) | 0.192571 | 0.00696696 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.57289 | 0.165225 | ||||||||
\(767\) | 1.73473i | 0.0626373i | ||||||||
\(768\) | − 3.13264i | − 0.113039i | ||||||||
\(769\) | −7.78867 | −0.280867 | −0.140433 | − | 0.990090i | \(-0.544850\pi\) | ||||
−0.140433 | + | 0.990090i | \(0.544850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.8921 | −1.00451 | ||||||||
\(772\) | − 14.6692i | − 0.527955i | ||||||||
\(773\) | 8.04234i | 0.289263i | 0.989486 | + | 0.144631i | \(0.0461997\pi\) | ||||
−0.989486 | + | 0.144631i | \(0.953800\pi\) | |||||||
\(774\) | 34.6033 | 1.24379 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.638440 | 0.0229186 | ||||||||
\(777\) | 12.9461i | 0.464437i | ||||||||
\(778\) | − 5.03635i | − 0.180562i | ||||||||
\(779\) | −4.68195 | −0.167748 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.9461 | −1.25047 | ||||||||
\(782\) | 21.8921i | 0.782860i | ||||||||
\(783\) | 122.630i | 4.38242i | ||||||||
\(784\) | −10.0787 | −0.359953 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 27.6092 | 0.984789 | ||||||||
\(787\) | 25.6268i | 0.913498i | 0.889596 | + | 0.456749i | \(0.150986\pi\) | ||||
−0.889596 | + | 0.456749i | \(0.849014\pi\) | |||||||
\(788\) | 7.84977i | 0.279636i | ||||||||
\(789\) | 46.6879 | 1.66213 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.8382 | 1.16759 | ||||||||
\(792\) | − 25.0787i | − 0.891133i | ||||||||
\(793\) | − 0.583328i | − 0.0207146i | ||||||||
\(794\) | −34.4650 | −1.22312 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.3616 | −0.402700 | ||||||||
\(797\) | 11.4095i | 0.404146i | 0.979370 | + | 0.202073i | \(0.0647678\pi\) | ||||
−0.979370 | + | 0.202073i | \(0.935232\pi\) | |||||||
\(798\) | − 5.84977i | − 0.207080i | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.29447 | 0.187071 | ||||||||
\(802\) | − 4.47661i | − 0.158074i | ||||||||
\(803\) | 13.0599i | 0.460875i | ||||||||
\(804\) | 0.717132 | 0.0252913 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.740713 | −0.0260905 | ||||||||
\(807\) | − 4.86853i | − 0.171380i | ||||||||
\(808\) | 5.62684i | 0.197951i | ||||||||
\(809\) | −21.5189 | −0.756566 | −0.378283 | − | 0.925690i | \(-0.623485\pi\) | ||||
−0.378283 | + | 0.925690i | \(0.623485\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.0847 | −1.54802 | −0.774011 | − | 0.633172i | \(-0.781753\pi\) | ||||
−0.774011 | + | 0.633172i | \(0.781753\pi\) | |||||||
\(812\) | − 42.4227i | − 1.48874i | ||||||||
\(813\) | − 17.8146i | − 0.624785i | ||||||||
\(814\) | 3.68078 | 0.129011 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −16.0787 | −0.562867 | ||||||||
\(817\) | − 2.29484i | − 0.0802864i | ||||||||
\(818\) | 34.7243i | 1.21411i | ||||||||
\(819\) | 3.73473 | 0.130502 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.95766 | −0.347525 | −0.173762 | − | 0.984788i | \(-0.555592\pi\) | ||||
−0.173762 | + | 0.984788i | \(0.555592\pi\) | |||||||
\(822\) | 59.1821i | 2.06421i | ||||||||
\(823\) | − 0.663187i | − 0.0231173i | −0.999933 | − | 0.0115586i | \(-0.996321\pi\) | ||||
0.999933 | − | 0.0115586i | \(-0.00367931\pi\) | |||||||
\(824\) | −10.0423 | −0.349842 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −54.0495 | −1.88062 | ||||||||
\(827\) | − 41.0671i | − 1.42804i | −0.700124 | − | 0.714021i | \(-0.746872\pi\) | ||||
0.700124 | − | 0.714021i | \(-0.253128\pi\) | |||||||
\(828\) | 29.0611i | 1.00994i | ||||||||
\(829\) | −6.48259 | −0.225150 | −0.112575 | − | 0.993643i | \(-0.535910\pi\) | ||||
−0.112575 | + | 0.993643i | \(0.535910\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40.4227 | −1.40225 | ||||||||
\(832\) | − 0.132637i | − 0.00459838i | ||||||||
\(833\) | 51.7303i | 1.79235i | ||||||||
\(834\) | 46.5189 | 1.61082 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.66319 | −0.0575225 | ||||||||
\(837\) | 66.7127i | 2.30593i | ||||||||
\(838\) | 7.15023i | 0.247001i | ||||||||
\(839\) | −0.771077 | −0.0266205 | −0.0133103 | − | 0.999911i | \(-0.504237\pi\) | ||||
−0.0133103 | + | 0.999911i | \(0.504237\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 76.3759 | 2.63365 | ||||||||
\(842\) | 26.6033i | 0.916809i | ||||||||
\(843\) | 38.4778i | 1.32524i | ||||||||
\(844\) | 12.2289 | 0.420937 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.5305i | 0.361834i | ||||||||
\(848\) | 11.6268i | 0.399267i | ||||||||
\(849\) | 84.1881 | 2.88933 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.26527 | −0.146212 | ||||||||
\(852\) | 29.7419i | 1.01894i | ||||||||
\(853\) | − 30.0975i | − 1.03052i | −0.857035 | − | 0.515259i | \(-0.827696\pi\) | ||||
0.857035 | − | 0.515259i | \(-0.172304\pi\) | |||||||
\(854\) | 18.1750 | 0.621935 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.6632 | 0.672074 | ||||||||
\(857\) | 8.22892i | 0.281095i | 0.990074 | + | 0.140547i | \(0.0448862\pi\) | ||||
−0.990074 | + | 0.140547i | \(0.955114\pi\) | |||||||
\(858\) | − 1.52938i | − 0.0522123i | ||||||||
\(859\) | −14.4286 | −0.492299 | −0.246150 | − | 0.969232i | \(-0.579165\pi\) | ||||
−0.246150 | + | 0.969232i | \(0.579165\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 134.141 | 4.57152 | ||||||||
\(862\) | − 1.16899i | − 0.0398159i | ||||||||
\(863\) | − 33.9049i | − 1.15414i | −0.816696 | − | 0.577068i | \(-0.804197\pi\) | ||||
0.816696 | − | 0.577068i | \(-0.195803\pi\) | |||||||
\(864\) | −11.9461 | −0.406413 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.00000 | 0.169907 | ||||||||
\(867\) | 29.2713i | 0.994104i | ||||||||
\(868\) | − 23.0787i | − 0.783342i | ||||||||
\(869\) | −3.32637 | −0.112840 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0303638 | 0.00102884 | ||||||||
\(872\) | 13.6268i | 0.461463i | ||||||||
\(873\) | − 4.34996i | − 0.147224i | ||||||||
\(874\) | 1.92730 | 0.0651918 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.1150 | 0.375543 | ||||||||
\(877\) | 1.36872i | 0.0462182i | 0.999733 | + | 0.0231091i | \(0.00735652\pi\) | ||||
−0.999733 | + | 0.0231091i | \(0.992643\pi\) | |||||||
\(878\) | 32.3148i | 1.09057i | ||||||||
\(879\) | 52.4826 | 1.77019 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.5741 | 1.60281 | 0.801405 | − | 0.598122i | \(-0.204086\pi\) | ||||
0.801405 | + | 0.598122i | \(0.204086\pi\) | |||||||
\(882\) | 68.6703i | 2.31225i | ||||||||
\(883\) | − 9.88051i | − 0.332506i | −0.986083 | − | 0.166253i | \(-0.946833\pi\) | ||||
0.986083 | − | 0.166253i | \(-0.0531668\pi\) | |||||||
\(884\) | −0.680780 | −0.0228971 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.4155 | −0.585085 | ||||||||
\(887\) | 21.8801i | 0.734663i | 0.930090 | + | 0.367331i | \(0.119729\pi\) | ||||
−0.930090 | + | 0.367331i | \(0.880271\pi\) | |||||||
\(888\) | − 3.13264i | − 0.105124i | ||||||||
\(889\) | −72.2972 | −2.42477 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −62.5085 | −2.09411 | ||||||||
\(892\) | 28.1574i | 0.942779i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 7.56690 | 0.253075 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.13264 | 0.138062 | ||||||||
\(897\) | 1.77224i | 0.0591735i | ||||||||
\(898\) | 7.38032i | 0.246284i | ||||||||
\(899\) | 57.3264 | 1.91194 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 59.6763 | 1.98811 | ||||||||
\(902\) | − 38.1386i | − 1.26988i | ||||||||
\(903\) | 65.7490i | 2.18799i | ||||||||
\(904\) | −7.94606 | −0.264282 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 33.5916 | 1.11601 | ||||||||
\(907\) | 8.46346i | 0.281025i | 0.990079 | + | 0.140512i | \(0.0448750\pi\) | ||||
−0.990079 | + | 0.140512i | \(0.955125\pi\) | |||||||
\(908\) | − 0.282868i | − 0.00938729i | ||||||||
\(909\) | 38.3380 | 1.27159 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.1997 | −1.13309 | −0.566544 | − | 0.824032i | \(-0.691720\pi\) | ||||
−0.566544 | + | 0.824032i | \(0.691720\pi\) | |||||||
\(912\) | 1.41551i | 0.0468721i | ||||||||
\(913\) | − 51.3324i | − 1.69885i | ||||||||
\(914\) | −22.7419 | −0.752235 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.45785 | −0.279455 | ||||||||
\(917\) | 36.4227i | 1.20278i | ||||||||
\(918\) | 61.3148i | 2.02369i | ||||||||
\(919\) | 0.723121 | 0.0238536 | 0.0119268 | − | 0.999929i | \(-0.496203\pi\) | ||||
0.0119268 | + | 0.999929i | \(0.496203\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.5541 | −0.874988 | ||||||||
\(922\) | 39.7115i | 1.30783i | ||||||||
\(923\) | 1.25929i | 0.0414499i | ||||||||
\(924\) | 47.6516 | 1.56762 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −30.6456 | −1.00708 | ||||||||
\(927\) | 68.4227i | 2.24730i | ||||||||
\(928\) | 10.2653i | 0.336974i | ||||||||
\(929\) | 16.7902 | 0.550869 | 0.275434 | − | 0.961320i | \(-0.411178\pi\) | ||||
0.275434 | + | 0.961320i | \(0.411178\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.55413 | 0.149256 | ||||||||
\(932\) | − 14.2477i | − 0.466698i | ||||||||
\(933\) | − 101.701i | − 3.32954i | ||||||||
\(934\) | −24.7958 | −0.811344 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.903715 | −0.0295388 | ||||||||
\(937\) | 7.01759i | 0.229255i | 0.993409 | + | 0.114627i | \(0.0365674\pi\) | ||||
−0.993409 | + | 0.114627i | \(0.963433\pi\) | |||||||
\(938\) | 0.946055i | 0.0308898i | ||||||||
\(939\) | −90.2620 | −2.94559 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.7958 | 1.00392 | 0.501958 | − | 0.864892i | \(-0.332613\pi\) | ||||
0.501958 | + | 0.864892i | \(0.332613\pi\) | |||||||
\(942\) | − 10.3979i | − 0.338782i | ||||||||
\(943\) | 44.1949i | 1.43918i | ||||||||
\(944\) | 13.0787 | 0.425675 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.6936 | 0.607780 | ||||||||
\(947\) | 6.19257i | 0.201232i | 0.994925 | + | 0.100616i | \(0.0320813\pi\) | ||||
−0.994925 | + | 0.100616i | \(0.967919\pi\) | |||||||
\(948\) | 2.83101i | 0.0919469i | ||||||||
\(949\) | 0.470617 | 0.0152769 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.5317 | −0.698214 | ||||||||
\(952\) | − 21.2113i | − 0.687463i | ||||||||
\(953\) | 37.1750i | 1.20422i | 0.798415 | + | 0.602108i | \(0.205672\pi\) | ||||
−0.798415 | + | 0.602108i | \(0.794328\pi\) | |||||||
\(954\) | 79.2185 | 2.56479 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 21.8921 | 0.708041 | ||||||||
\(957\) | 118.364i | 3.82617i | ||||||||
\(958\) | 15.5845i | 0.503512i | ||||||||
\(959\) | −78.0742 | −2.52115 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.186582 | 0.00601878 | ||||||||
\(962\) | − 0.132637i | − 0.00427640i | ||||||||
\(963\) | − 133.974i | − 4.31724i | ||||||||
\(964\) | 9.13264 | 0.294142 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −55.2185 | −1.77663 | ||||||||
\(967\) | − 34.4722i | − 1.10855i | −0.832334 | − | 0.554275i | \(-0.812996\pi\) | ||||
0.832334 | − | 0.554275i | \(-0.187004\pi\) | |||||||
\(968\) | − 2.54814i | − 0.0819004i | ||||||||
\(969\) | 7.26527 | 0.233394 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −54.2488 | −1.74093 | −0.870464 | − | 0.492232i | \(-0.836181\pi\) | ||||
−0.870464 | + | 0.492232i | \(0.836181\pi\) | |||||||
\(972\) | 17.3616i | 0.556872i | ||||||||
\(973\) | 61.3687i | 1.96739i | ||||||||
\(974\) | −3.65720 | −0.117184 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.39791 | −0.140774 | ||||||||
\(977\) | − 55.4706i | − 1.77466i | −0.461133 | − | 0.887331i | \(-0.652557\pi\) | ||||
0.461133 | − | 0.887331i | \(-0.347443\pi\) | |||||||
\(978\) | − 48.7067i | − 1.55747i | ||||||||
\(979\) | 2.86021 | 0.0914126 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 92.8453 | 2.96432 | ||||||||
\(982\) | 33.3264i | 1.06349i | ||||||||
\(983\) | 0.422660i | 0.0134808i | 0.999977 | + | 0.00674038i | \(0.00214555\pi\) | ||||
−0.999977 | + | 0.00674038i | \(0.997854\pi\) | |||||||
\(984\) | −32.4590 | −1.03476 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 52.6879 | 1.67793 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.0599332i | 0.00190673i | ||||||||
\(989\) | −21.6620 | −0.688812 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.93445 | 0.252046 | 0.126023 | − | 0.992027i | \(-0.459779\pi\) | ||||
0.126023 | + | 0.992027i | \(0.459779\pi\) | |||||||
\(992\) | 5.58449i | 0.177308i | ||||||||
\(993\) | 5.18775i | 0.164628i | ||||||||
\(994\) | −39.2361 | −1.24449 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −43.6879 | −1.38431 | ||||||||
\(997\) | 48.8933i | 1.54847i | 0.632901 | + | 0.774233i | \(0.281864\pi\) | ||||
−0.632901 | + | 0.774233i | \(0.718136\pi\) | |||||||
\(998\) | − 7.53654i | − 0.238565i | ||||||||
\(999\) | −11.9461 | −0.377956 |
(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 | 1850.2.b.p.149.4 | 6 | ||
5.2 | odd | 4 | 1850.2.a.y.1.1 | ✓ | 3 | ||
5.3 | odd | 4 | 1850.2.a.bc.1.3 | yes | 3 | ||
5.4 | even | 2 | inner | 1850.2.b.p.149.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1850.2.a.y.1.1 | ✓ | 3 | 5.2 | odd | 4 | ||
1850.2.a.bc.1.3 | yes | 3 | 5.3 | odd | 4 | ||
1850.2.b.p.149.3 | 6 | 5.4 | even | 2 | inner | ||
1850.2.b.p.149.4 | 6 | 1.1 | even | 1 | trivial |