Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,3,Mod(151,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.9428125571\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 42x^{12} + 677x^{10} + 5313x^{8} + 21125x^{6} + 40138x^{4} + 30565x^{2} + 3675 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.14 | ||
Root | \(3.82982i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.151 |
Dual form | 475.3.c.i.151.1 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.82982i | 1.91491i | 0.288586 | + | 0.957454i | \(0.406815\pi\) | ||||
−0.288586 | + | 0.957454i | \(0.593185\pi\) | |||||||
\(3\) | 0.102062i | 0.0340206i | 0.999855 | + | 0.0170103i | \(0.00541481\pi\) | ||||
−0.999855 | + | 0.0170103i | \(0.994585\pi\) | |||||||
\(4\) | −10.6675 | −2.66687 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.390878 | −0.0651464 | ||||||||
\(7\) | 9.96826 | 1.42404 | 0.712019 | − | 0.702161i | \(-0.247781\pi\) | ||||
0.712019 | + | 0.702161i | \(0.247781\pi\) | |||||||
\(8\) | − | 25.5353i | − | 3.19191i | ||||||
\(9\) | 8.98958 | 0.998843 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.29329 | 0.481208 | 0.240604 | − | 0.970623i | \(-0.422654\pi\) | ||||
0.240604 | + | 0.970623i | \(0.422654\pi\) | |||||||
\(12\) | − | 1.08875i | − | 0.0907288i | ||||||
\(13\) | − | 13.5363i | − | 1.04125i | −0.853785 | − | 0.520625i | \(-0.825699\pi\) | ||
0.853785 | − | 0.520625i | \(-0.174301\pi\) | |||||||
\(14\) | 38.1766i | 2.72690i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 55.1254 | 3.44534 | ||||||||
\(17\) | −5.23391 | −0.307877 | −0.153938 | − | 0.988080i | \(-0.549196\pi\) | ||||
−0.153938 | + | 0.988080i | \(0.549196\pi\) | |||||||
\(18\) | 34.4285i | 1.91269i | ||||||||
\(19\) | 11.7515 | + | 14.9299i | 0.618501 | + | 0.785784i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.01738i | 0.0484467i | ||||||||
\(22\) | 20.2723i | 0.921470i | ||||||||
\(23\) | 37.5555 | 1.63285 | 0.816425 | − | 0.577452i | \(-0.195953\pi\) | ||||
0.816425 | + | 0.577452i | \(0.195953\pi\) | |||||||
\(24\) | 2.60618 | 0.108591 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 51.8414 | 1.99390 | ||||||||
\(27\) | 1.83605i | 0.0680019i | ||||||||
\(28\) | −106.336 | −3.79773 | ||||||||
\(29\) | − | 26.4485i | − | 0.912018i | −0.889975 | − | 0.456009i | \(-0.849278\pi\) | ||
0.889975 | − | 0.456009i | \(-0.150722\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 29.3216i | 0.945859i | 0.881100 | + | 0.472929i | \(0.156803\pi\) | ||||
−0.881100 | + | 0.472929i | \(0.843197\pi\) | |||||||
\(32\) | 108.979i | 3.40560i | ||||||||
\(33\) | 0.540244i | 0.0163710i | ||||||||
\(34\) | − | 20.0449i | − | 0.589556i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −95.8963 | −2.66379 | ||||||||
\(37\) | − | 38.9258i | − | 1.05205i | −0.850470 | − | 0.526024i | \(-0.823682\pi\) | ||
0.850470 | − | 0.526024i | \(-0.176318\pi\) | |||||||
\(38\) | −57.1787 | + | 45.0062i | −1.50470 | + | 1.18437i | ||||
\(39\) | 1.38154 | 0.0354240 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 39.5253i | − | 0.964031i | −0.876163 | − | 0.482015i | \(-0.839905\pi\) | ||
0.876163 | − | 0.482015i | \(-0.160095\pi\) | |||||||
\(42\) | −3.89638 | −0.0927709 | ||||||||
\(43\) | −30.3917 | −0.706784 | −0.353392 | − | 0.935475i | \(-0.614972\pi\) | ||||
−0.353392 | + | 0.935475i | \(0.614972\pi\) | |||||||
\(44\) | −56.4662 | −1.28332 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 143.831i | 3.12676i | ||||||||
\(47\) | −77.0113 | −1.63854 | −0.819270 | − | 0.573409i | \(-0.805621\pi\) | ||||
−0.819270 | + | 0.573409i | \(0.805621\pi\) | |||||||
\(48\) | 5.62621i | 0.117213i | ||||||||
\(49\) | 50.3662 | 1.02788 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 0.534183i | − | 0.0104742i | ||||||
\(52\) | 144.398i | 2.77688i | ||||||||
\(53\) | 41.0262i | 0.774080i | 0.922063 | + | 0.387040i | \(0.126502\pi\) | ||||
−0.922063 | + | 0.387040i | \(0.873498\pi\) | |||||||
\(54\) | −7.03174 | −0.130217 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 254.542i | − | 4.54540i | ||||||
\(57\) | −1.52377 | + | 1.19938i | −0.0267329 | + | 0.0210418i | ||||
\(58\) | 101.293 | 1.74643 | ||||||||
\(59\) | 50.0262i | 0.847902i | 0.905685 | + | 0.423951i | \(0.139357\pi\) | ||||
−0.905685 | + | 0.423951i | \(0.860643\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 32.2395 | 0.528517 | 0.264258 | − | 0.964452i | \(-0.414873\pi\) | ||||
0.264258 | + | 0.964452i | \(0.414873\pi\) | |||||||
\(62\) | −112.296 | −1.81123 | ||||||||
\(63\) | 89.6105 | 1.42239 | ||||||||
\(64\) | −196.869 | −3.07607 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.06903 | −0.0313490 | ||||||||
\(67\) | − | 100.135i | − | 1.49455i | −0.664516 | − | 0.747274i | \(-0.731362\pi\) | ||
0.664516 | − | 0.747274i | \(-0.268638\pi\) | |||||||
\(68\) | 55.8327 | 0.821069 | ||||||||
\(69\) | 3.83299i | 0.0555506i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 90.8238i | 1.27921i | 0.768704 | + | 0.639604i | \(0.220902\pi\) | ||||
−0.768704 | + | 0.639604i | \(0.779098\pi\) | |||||||
\(72\) | − | 229.551i | − | 3.18822i | ||||||
\(73\) | −4.79733 | −0.0657169 | −0.0328584 | − | 0.999460i | \(-0.510461\pi\) | ||||
−0.0328584 | + | 0.999460i | \(0.510461\pi\) | |||||||
\(74\) | 149.079 | 2.01457 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −125.359 | − | 159.265i | −1.64946 | − | 2.09559i | ||||
\(77\) | 52.7649 | 0.685259 | ||||||||
\(78\) | 5.29103i | 0.0678337i | ||||||||
\(79\) | 128.561i | 1.62736i | 0.581314 | + | 0.813679i | \(0.302539\pi\) | ||||
−0.581314 | + | 0.813679i | \(0.697461\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 80.7189 | 0.996529 | ||||||||
\(82\) | 151.374 | 1.84603 | ||||||||
\(83\) | 100.182 | 1.20701 | 0.603503 | − | 0.797360i | \(-0.293771\pi\) | ||||
0.603503 | + | 0.797360i | \(0.293771\pi\) | |||||||
\(84\) | − | 10.8529i | − | 0.129201i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 116.395i | − | 1.35343i | ||||||
\(87\) | 2.69939 | 0.0310274 | ||||||||
\(88\) | − | 135.166i | − | 1.53597i | ||||||
\(89\) | 127.458i | 1.43211i | 0.698043 | + | 0.716056i | \(0.254054\pi\) | ||||
−0.698043 | + | 0.716056i | \(0.745946\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 134.933i | − | 1.48278i | ||||||
\(92\) | −400.623 | −4.35460 | ||||||||
\(93\) | −2.99262 | −0.0321787 | ||||||||
\(94\) | − | 294.939i | − | 3.13765i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −11.1226 | −0.115861 | ||||||||
\(97\) | 14.5978i | 0.150493i | 0.997165 | + | 0.0752464i | \(0.0239743\pi\) | ||||
−0.997165 | + | 0.0752464i | \(0.976026\pi\) | |||||||
\(98\) | 192.893i | 1.96830i | ||||||||
\(99\) | 47.5845 | 0.480651 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.3954 | −0.182132 | −0.0910662 | − | 0.995845i | \(-0.529028\pi\) | ||||
−0.0910662 | + | 0.995845i | \(0.529028\pi\) | |||||||
\(102\) | 2.04582 | 0.0200571 | ||||||||
\(103\) | − | 184.511i | − | 1.79137i | −0.444692 | − | 0.895684i | \(-0.646687\pi\) | ||
0.444692 | − | 0.895684i | \(-0.353313\pi\) | |||||||
\(104\) | −345.652 | −3.32358 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −157.123 | −1.48229 | ||||||||
\(107\) | 131.063i | 1.22489i | 0.790514 | + | 0.612444i | \(0.209814\pi\) | ||||
−0.790514 | + | 0.612444i | \(0.790186\pi\) | |||||||
\(108\) | − | 19.5861i | − | 0.181352i | ||||||
\(109\) | 23.3256i | 0.213996i | 0.994259 | + | 0.106998i | \(0.0341239\pi\) | ||||
−0.994259 | + | 0.106998i | \(0.965876\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.97284 | 0.0357913 | ||||||||
\(112\) | 549.505 | 4.90629 | ||||||||
\(113\) | 130.214i | 1.15234i | 0.817330 | + | 0.576169i | \(0.195453\pi\) | ||||
−0.817330 | + | 0.576169i | \(0.804547\pi\) | |||||||
\(114\) | −4.59342 | − | 5.83577i | −0.0402931 | − | 0.0511910i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 282.139i | 2.43224i | ||||||||
\(117\) | − | 121.685i | − | 1.04004i | ||||||
\(118\) | −191.591 | −1.62366 | ||||||||
\(119\) | −52.1730 | −0.438428 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −92.9811 | −0.768439 | ||||||||
\(122\) | 123.471i | 1.01206i | ||||||||
\(123\) | 4.03402 | 0.0327969 | ||||||||
\(124\) | − | 312.788i | − | 2.52249i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 343.192i | 2.72374i | ||||||||
\(127\) | − | 99.8187i | − | 0.785974i | −0.919544 | − | 0.392987i | \(-0.871442\pi\) | ||
0.919544 | − | 0.392987i | \(-0.128558\pi\) | |||||||
\(128\) | − | 318.054i | − | 2.48480i | ||||||
\(129\) | − | 3.10184i | − | 0.0240452i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 46.5614 | 0.355430 | 0.177715 | − | 0.984082i | \(-0.443129\pi\) | ||||
0.177715 | + | 0.984082i | \(0.443129\pi\) | |||||||
\(132\) | − | 5.76305i | − | 0.0436594i | ||||||
\(133\) | 117.142 | + | 148.825i | 0.880769 | + | 1.11899i | ||||
\(134\) | 383.498 | 2.86192 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 133.649i | 0.982715i | ||||||||
\(137\) | −28.3675 | −0.207062 | −0.103531 | − | 0.994626i | \(-0.533014\pi\) | ||||
−0.103531 | + | 0.994626i | \(0.533014\pi\) | |||||||
\(138\) | −14.6797 | −0.106374 | ||||||||
\(139\) | 155.882 | 1.12146 | 0.560728 | − | 0.828000i | \(-0.310521\pi\) | ||||
0.560728 | + | 0.828000i | \(0.310521\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 7.85993i | − | 0.0557442i | ||||||
\(142\) | −347.838 | −2.44957 | ||||||||
\(143\) | − | 71.6513i | − | 0.501058i | ||||||
\(144\) | 495.555 | 3.44135 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 18.3729i | − | 0.125842i | ||||||
\(147\) | 5.14047i | 0.0349692i | ||||||||
\(148\) | 415.240i | 2.80568i | ||||||||
\(149\) | −42.8941 | −0.287880 | −0.143940 | − | 0.989586i | \(-0.545977\pi\) | ||||
−0.143940 | + | 0.989586i | \(0.545977\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 35.9816i | 0.238289i | 0.992877 | + | 0.119144i | \(0.0380151\pi\) | ||||
−0.992877 | + | 0.119144i | \(0.961985\pi\) | |||||||
\(152\) | 381.239 | − | 300.078i | 2.50815 | − | 1.97420i | ||||
\(153\) | −47.0506 | −0.307521 | ||||||||
\(154\) | 202.080i | 1.31221i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −14.7375 | −0.0944713 | ||||||||
\(157\) | −202.251 | −1.28823 | −0.644113 | − | 0.764931i | \(-0.722773\pi\) | ||||
−0.644113 | + | 0.764931i | \(0.722773\pi\) | |||||||
\(158\) | −492.366 | −3.11624 | ||||||||
\(159\) | −4.18722 | −0.0263347 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 374.363 | 2.32524 | ||||||||
\(162\) | 309.138i | 1.90826i | ||||||||
\(163\) | 99.4595 | 0.610181 | 0.305091 | − | 0.952323i | \(-0.401313\pi\) | ||||
0.305091 | + | 0.952323i | \(0.401313\pi\) | |||||||
\(164\) | 421.635i | 2.57095i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 383.677i | 2.31131i | ||||||||
\(167\) | − | 95.2905i | − | 0.570602i | −0.958438 | − | 0.285301i | \(-0.907906\pi\) | ||
0.958438 | − | 0.285301i | \(-0.0920935\pi\) | |||||||
\(168\) | 25.9791 | 0.154637 | ||||||||
\(169\) | −14.2301 | −0.0842016 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 105.641 | + | 134.214i | 0.617785 | + | 0.784874i | ||||
\(172\) | 324.203 | 1.88490 | ||||||||
\(173\) | − | 245.293i | − | 1.41788i | −0.705269 | − | 0.708940i | \(-0.749174\pi\) | ||
0.705269 | − | 0.708940i | \(-0.250826\pi\) | |||||||
\(174\) | 10.3382i | 0.0594147i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 291.795 | 1.65793 | ||||||||
\(177\) | −5.10578 | −0.0288462 | ||||||||
\(178\) | −488.140 | −2.74236 | ||||||||
\(179\) | − | 81.3066i | − | 0.454227i | −0.973868 | − | 0.227113i | \(-0.927071\pi\) | ||
0.973868 | − | 0.227113i | \(-0.0729288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 257.547i | − | 1.42291i | −0.702730 | − | 0.711457i | \(-0.748036\pi\) | ||
0.702730 | − | 0.711457i | \(-0.251964\pi\) | |||||||
\(182\) | 516.768 | 2.83939 | ||||||||
\(183\) | 3.29043i | 0.0179805i | ||||||||
\(184\) | − | 958.991i | − | 5.21191i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 11.4612i | − | 0.0616193i | ||||||
\(187\) | −27.7046 | −0.148153 | ||||||||
\(188\) | 821.518 | 4.36978 | ||||||||
\(189\) | 18.3022i | 0.0968373i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −236.760 | −1.23958 | −0.619791 | − | 0.784767i | \(-0.712783\pi\) | ||||
−0.619791 | + | 0.784767i | \(0.712783\pi\) | |||||||
\(192\) | − | 20.0928i | − | 0.104650i | ||||||
\(193\) | − | 283.058i | − | 1.46662i | −0.679894 | − | 0.733310i | \(-0.737974\pi\) | ||
0.679894 | − | 0.733310i | \(-0.262026\pi\) | |||||||
\(194\) | −55.9069 | −0.288180 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −537.281 | −2.74123 | ||||||||
\(197\) | 28.6273 | 0.145316 | 0.0726581 | − | 0.997357i | \(-0.476852\pi\) | ||||
0.0726581 | + | 0.997357i | \(0.476852\pi\) | |||||||
\(198\) | 182.240i | 0.920403i | ||||||||
\(199\) | −335.738 | −1.68713 | −0.843564 | − | 0.537029i | \(-0.819547\pi\) | ||||
−0.843564 | + | 0.537029i | \(0.819547\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.2199 | 0.0508455 | ||||||||
\(202\) | − | 70.4509i | − | 0.348767i | ||||||
\(203\) | − | 263.646i | − | 1.29875i | ||||||
\(204\) | 5.69839i | 0.0279333i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 706.643 | 3.43030 | ||||||||
\(207\) | 337.609 | 1.63096 | ||||||||
\(208\) | − | 746.192i | − | 3.58746i | ||||||
\(209\) | 62.2042 | + | 79.0283i | 0.297628 | + | 0.378126i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 116.161i | − | 0.550528i | −0.961369 | − | 0.275264i | \(-0.911235\pi\) | ||
0.961369 | − | 0.275264i | \(-0.0887652\pi\) | |||||||
\(212\) | − | 437.647i | − | 2.06437i | ||||||
\(213\) | −9.26965 | −0.0435195 | ||||||||
\(214\) | −501.947 | −2.34555 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 46.8841 | 0.217056 | ||||||||
\(217\) | 292.286i | 1.34694i | ||||||||
\(218\) | −89.3327 | −0.409783 | ||||||||
\(219\) | − | 0.489625i | − | 0.00223573i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 70.8475i | 0.320577i | ||||||||
\(222\) | 15.2152i | 0.0685371i | ||||||||
\(223\) | 275.634i | 1.23603i | 0.786168 | + | 0.618013i | \(0.212062\pi\) | ||||
−0.786168 | + | 0.618013i | \(0.787938\pi\) | |||||||
\(224\) | 1086.33i | 4.84970i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −498.697 | −2.20662 | ||||||||
\(227\) | 176.419i | 0.777174i | 0.921412 | + | 0.388587i | \(0.127037\pi\) | ||||
−0.921412 | + | 0.388587i | \(0.872963\pi\) | |||||||
\(228\) | 16.2548 | − | 12.7944i | 0.0712932 | − | 0.0561158i | ||||
\(229\) | −89.7773 | −0.392041 | −0.196020 | − | 0.980600i | \(-0.562802\pi\) | ||||
−0.196020 | + | 0.980600i | \(0.562802\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.38529i | 0.0233129i | ||||||||
\(232\) | −675.370 | −2.91108 | ||||||||
\(233\) | 57.1941 | 0.245468 | 0.122734 | − | 0.992440i | \(-0.460834\pi\) | ||||
0.122734 | + | 0.992440i | \(0.460834\pi\) | |||||||
\(234\) | 466.032 | 1.99159 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 533.655i | − | 2.26125i | ||||||
\(237\) | −13.1212 | −0.0553638 | ||||||||
\(238\) | − | 199.813i | − | 0.839550i | ||||||
\(239\) | −30.8457 | −0.129062 | −0.0645308 | − | 0.997916i | \(-0.520555\pi\) | ||||
−0.0645308 | + | 0.997916i | \(0.520555\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 307.041i | − | 1.27403i | −0.770852 | − | 0.637015i | \(-0.780169\pi\) | ||
0.770852 | − | 0.637015i | \(-0.219831\pi\) | |||||||
\(242\) | − | 356.100i | − | 1.47149i | ||||||
\(243\) | 24.7628i | 0.101904i | ||||||||
\(244\) | −343.915 | −1.40949 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 15.4496i | 0.0628031i | ||||||||
\(247\) | 202.095 | − | 159.072i | 0.818197 | − | 0.644014i | ||||
\(248\) | 748.736 | 3.01910 | ||||||||
\(249\) | 10.2247i | 0.0410631i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −252.181 | −1.00470 | −0.502352 | − | 0.864663i | \(-0.667532\pi\) | ||||
−0.502352 | + | 0.864663i | \(0.667532\pi\) | |||||||
\(252\) | −955.919 | −3.79333 | ||||||||
\(253\) | 198.792 | 0.785741 | ||||||||
\(254\) | 382.287 | 1.50507 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 430.613 | 1.68208 | ||||||||
\(257\) | 349.189i | 1.35871i | 0.733808 | + | 0.679356i | \(0.237741\pi\) | ||||
−0.733808 | + | 0.679356i | \(0.762259\pi\) | |||||||
\(258\) | 11.8795 | 0.0460444 | ||||||||
\(259\) | − | 388.022i | − | 1.49815i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 237.761i | − | 0.910962i | ||||||
\(262\) | 178.321i | 0.680616i | ||||||||
\(263\) | −230.049 | −0.874713 | −0.437356 | − | 0.899288i | \(-0.644085\pi\) | ||||
−0.437356 | + | 0.899288i | \(0.644085\pi\) | |||||||
\(264\) | 13.7953 | 0.0522548 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −569.973 | + | 448.633i | −2.14275 | + | 1.68659i | ||||
\(267\) | −13.0086 | −0.0487213 | ||||||||
\(268\) | 1068.19i | 3.98577i | ||||||||
\(269\) | 282.058i | 1.04854i | 0.851551 | + | 0.524272i | \(0.175663\pi\) | ||||
−0.851551 | + | 0.524272i | \(0.824337\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 202.339 | 0.746638 | 0.373319 | − | 0.927703i | \(-0.378220\pi\) | ||||
0.373319 | + | 0.927703i | \(0.378220\pi\) | |||||||
\(272\) | −288.521 | −1.06074 | ||||||||
\(273\) | 13.7715 | 0.0504451 | ||||||||
\(274\) | − | 108.642i | − | 0.396505i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 40.8884i | − | 0.148146i | ||||||
\(277\) | 108.878 | 0.393063 | 0.196531 | − | 0.980498i | \(-0.437032\pi\) | ||||
0.196531 | + | 0.980498i | \(0.437032\pi\) | |||||||
\(278\) | 597.001i | 2.14748i | ||||||||
\(279\) | 263.589i | 0.944764i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 221.302i | 0.787551i | 0.919207 | + | 0.393776i | \(0.128831\pi\) | ||||
−0.919207 | + | 0.393776i | \(0.871169\pi\) | |||||||
\(282\) | 30.1021 | 0.106745 | ||||||||
\(283\) | −148.837 | −0.525927 | −0.262964 | − | 0.964806i | \(-0.584700\pi\) | ||||
−0.262964 | + | 0.964806i | \(0.584700\pi\) | |||||||
\(284\) | − | 968.862i | − | 3.41149i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 274.411 | 0.959481 | ||||||||
\(287\) | − | 393.998i | − | 1.37282i | ||||||
\(288\) | 979.678i | 3.40166i | ||||||||
\(289\) | −261.606 | −0.905212 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.48988 | −0.00511986 | ||||||||
\(292\) | 51.1755 | 0.175259 | ||||||||
\(293\) | − | 68.3191i | − | 0.233171i | −0.993181 | − | 0.116586i | \(-0.962805\pi\) | ||
0.993181 | − | 0.116586i | \(-0.0371949\pi\) | |||||||
\(294\) | −19.6871 | −0.0669628 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −993.980 | −3.35804 | ||||||||
\(297\) | 9.71876i | 0.0327231i | ||||||||
\(298\) | − | 164.276i | − | 0.551263i | ||||||
\(299\) | − | 508.361i | − | 1.70020i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −302.952 | −1.00649 | ||||||||
\(302\) | −137.803 | −0.456301 | ||||||||
\(303\) | − | 1.87747i | − | 0.00619626i | ||||||
\(304\) | 647.808 | + | 823.017i | 2.13095 | + | 2.70729i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 180.195i | − | 0.588874i | ||||||
\(307\) | − | 145.822i | − | 0.474991i | −0.971389 | − | 0.237495i | \(-0.923674\pi\) | ||
0.971389 | − | 0.237495i | \(-0.0763264\pi\) | |||||||
\(308\) | −562.869 | −1.82750 | ||||||||
\(309\) | 18.8315 | 0.0609435 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −43.9351 | −0.141270 | −0.0706351 | − | 0.997502i | \(-0.522503\pi\) | ||||
−0.0706351 | + | 0.997502i | \(0.522503\pi\) | |||||||
\(312\) | − | 35.2779i | − | 0.113070i | ||||||
\(313\) | −204.710 | −0.654026 | −0.327013 | − | 0.945020i | \(-0.606042\pi\) | ||||
−0.327013 | + | 0.945020i | \(0.606042\pi\) | |||||||
\(314\) | − | 774.586i | − | 2.46683i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 1371.43i | − | 4.33996i | ||||||
\(317\) | − | 88.8488i | − | 0.280280i | −0.990132 | − | 0.140140i | \(-0.955245\pi\) | ||
0.990132 | − | 0.140140i | \(-0.0447553\pi\) | |||||||
\(318\) | − | 16.0363i | − | 0.0504285i | ||||||
\(319\) | − | 140.000i | − | 0.438871i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.3765 | −0.0416715 | ||||||||
\(322\) | 1433.74i | 4.45262i | ||||||||
\(323\) | −61.5064 | − | 78.1417i | −0.190422 | − | 0.241925i | ||||
\(324\) | −861.068 | −2.65762 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 380.912i | 1.16844i | ||||||||
\(327\) | −2.38065 | −0.00728029 | ||||||||
\(328\) | −1009.29 | −3.07710 | ||||||||
\(329\) | −767.669 | −2.33334 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 121.098i | − | 0.365854i | −0.983127 | − | 0.182927i | \(-0.941443\pi\) | ||
0.983127 | − | 0.182927i | \(-0.0585572\pi\) | |||||||
\(332\) | −1068.69 | −3.21893 | ||||||||
\(333\) | − | 349.926i | − | 1.05083i | ||||||
\(334\) | 364.945 | 1.09265 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 56.0835i | 0.166915i | ||||||||
\(337\) | 51.4397i | 0.152640i | 0.997083 | + | 0.0763200i | \(0.0243171\pi\) | ||||
−0.997083 | + | 0.0763200i | \(0.975683\pi\) | |||||||
\(338\) | − | 54.4986i | − | 0.161238i | ||||||
\(339\) | −13.2899 | −0.0392033 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 155.208i | 0.455155i | ||||||||
\(342\) | −514.013 | + | 404.587i | −1.50296 | + | 1.18300i | ||||
\(343\) | 13.6188 | 0.0397049 | ||||||||
\(344\) | 776.061i | 2.25599i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 939.428 | 2.71511 | ||||||||
\(347\) | 500.847 | 1.44336 | 0.721682 | − | 0.692225i | \(-0.243369\pi\) | ||||
0.721682 | + | 0.692225i | \(0.243369\pi\) | |||||||
\(348\) | −28.7957 | −0.0827463 | ||||||||
\(349\) | −585.972 | −1.67900 | −0.839501 | − | 0.543357i | \(-0.817153\pi\) | ||||
−0.839501 | + | 0.543357i | \(0.817153\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.8533 | 0.0708070 | ||||||||
\(352\) | 576.859i | 1.63880i | ||||||||
\(353\) | −307.915 | −0.872281 | −0.436140 | − | 0.899879i | \(-0.643655\pi\) | ||||
−0.436140 | + | 0.899879i | \(0.643655\pi\) | |||||||
\(354\) | − | 19.5542i | − | 0.0552378i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 1359.66i | − | 3.81926i | ||||||
\(357\) | − | 5.32487i | − | 0.0149156i | ||||||
\(358\) | 311.389 | 0.869803 | ||||||||
\(359\) | 348.313 | 0.970232 | 0.485116 | − | 0.874450i | \(-0.338777\pi\) | ||||
0.485116 | + | 0.874450i | \(0.338777\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −84.8034 | + | 350.898i | −0.234912 | + | 0.972017i | ||||
\(362\) | 986.359 | 2.72475 | ||||||||
\(363\) | − | 9.48983i | − | 0.0261428i | ||||||
\(364\) | 1439.40i | 3.95438i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −12.6017 | −0.0344310 | ||||||||
\(367\) | 220.044 | 0.599575 | 0.299788 | − | 0.954006i | \(-0.403084\pi\) | ||||
0.299788 | + | 0.954006i | \(0.403084\pi\) | |||||||
\(368\) | 2070.27 | 5.62572 | ||||||||
\(369\) | − | 355.316i | − | 0.962915i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 408.960i | 1.10232i | ||||||||
\(372\) | 31.9238 | 0.0858166 | ||||||||
\(373\) | − | 208.409i | − | 0.558737i | −0.960184 | − | 0.279369i | \(-0.909875\pi\) | ||
0.960184 | − | 0.279369i | \(-0.0901252\pi\) | |||||||
\(374\) | − | 106.104i | − | 0.283699i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1966.51i | 5.23007i | ||||||||
\(377\) | −358.014 | −0.949639 | ||||||||
\(378\) | −70.0942 | −0.185434 | ||||||||
\(379\) | − | 233.504i | − | 0.616104i | −0.951369 | − | 0.308052i | \(-0.900323\pi\) | ||
0.951369 | − | 0.308052i | \(-0.0996771\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.1877 | 0.0267393 | ||||||||
\(382\) | − | 906.748i | − | 2.37368i | ||||||
\(383\) | − | 19.2030i | − | 0.0501385i | −0.999686 | − | 0.0250693i | \(-0.992019\pi\) | ||
0.999686 | − | 0.0250693i | \(-0.00798063\pi\) | |||||||
\(384\) | 32.4612 | 0.0845343 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1084.06 | 2.80844 | ||||||||
\(387\) | −273.209 | −0.705966 | ||||||||
\(388\) | − | 155.722i | − | 0.401345i | ||||||
\(389\) | 385.371 | 0.990672 | 0.495336 | − | 0.868702i | \(-0.335045\pi\) | ||||
0.495336 | + | 0.868702i | \(0.335045\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −196.562 | −0.502717 | ||||||||
\(392\) | − | 1286.12i | − | 3.28091i | ||||||
\(393\) | 4.75214i | 0.0120920i | ||||||||
\(394\) | 109.637i | 0.278267i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −507.607 | −1.28184 | ||||||||
\(397\) | 221.566 | 0.558102 | 0.279051 | − | 0.960276i | \(-0.409980\pi\) | ||||
0.279051 | + | 0.960276i | \(0.409980\pi\) | |||||||
\(398\) | − | 1285.82i | − | 3.23069i | ||||||
\(399\) | −15.1894 | + | 11.9558i | −0.0380686 | + | 0.0299643i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 684.193i | − | 1.70622i | −0.521734 | − | 0.853108i | \(-0.674715\pi\) | ||
0.521734 | − | 0.853108i | \(-0.325285\pi\) | |||||||
\(402\) | 39.1405i | 0.0973644i | ||||||||
\(403\) | 396.905 | 0.984875 | ||||||||
\(404\) | 196.233 | 0.485724 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1009.71 | 2.48698 | ||||||||
\(407\) | − | 206.045i | − | 0.506254i | ||||||
\(408\) | −13.6405 | −0.0334326 | ||||||||
\(409\) | 371.270i | 0.907750i | 0.891065 | + | 0.453875i | \(0.149959\pi\) | ||||
−0.891065 | + | 0.453875i | \(0.850041\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.89525i | − | 0.00704439i | ||||||
\(412\) | 1968.27i | 4.77735i | ||||||||
\(413\) | 498.675i | 1.20744i | ||||||||
\(414\) | 1292.98i | 3.12314i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1475.17 | 3.54608 | ||||||||
\(417\) | 15.9097i | 0.0381526i | ||||||||
\(418\) | −302.664 | + | 238.231i | −0.724076 | + | 0.569930i | ||||
\(419\) | 473.130 | 1.12919 | 0.564595 | − | 0.825368i | \(-0.309033\pi\) | ||||
0.564595 | + | 0.825368i | \(0.309033\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 253.042i | 0.601049i | 0.953774 | + | 0.300524i | \(0.0971617\pi\) | ||||
−0.953774 | + | 0.300524i | \(0.902838\pi\) | |||||||
\(422\) | 444.877 | 1.05421 | ||||||||
\(423\) | −692.300 | −1.63664 | ||||||||
\(424\) | 1047.62 | 2.47079 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 35.5011i | − | 0.0833358i | ||||||
\(427\) | 321.372 | 0.752628 | ||||||||
\(428\) | − | 1398.11i | − | 3.26662i | ||||||
\(429\) | 7.31287 | 0.0170463 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 128.719i | − | 0.298653i | −0.988788 | − | 0.149326i | \(-0.952290\pi\) | ||
0.988788 | − | 0.149326i | \(-0.0477105\pi\) | |||||||
\(432\) | 101.213i | 0.234290i | ||||||||
\(433\) | 161.686i | 0.373409i | 0.982416 | + | 0.186705i | \(0.0597807\pi\) | ||||
−0.982416 | + | 0.186705i | \(0.940219\pi\) | |||||||
\(434\) | −1119.40 | −2.57926 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 248.825i | − | 0.570701i | ||||||
\(437\) | 441.335 | + | 560.700i | 1.00992 | + | 1.28307i | ||||
\(438\) | 1.87517 | 0.00428122 | ||||||||
\(439\) | − | 144.836i | − | 0.329923i | −0.986300 | − | 0.164962i | \(-0.947250\pi\) | ||
0.986300 | − | 0.164962i | \(-0.0527501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 452.771 | 1.02669 | ||||||||
\(442\) | −271.333 | −0.613875 | ||||||||
\(443\) | 236.138 | 0.533042 | 0.266521 | − | 0.963829i | \(-0.414126\pi\) | ||||
0.266521 | + | 0.963829i | \(0.414126\pi\) | |||||||
\(444\) | −42.3802 | −0.0954510 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1055.63 | −2.36688 | ||||||||
\(447\) | − | 4.37785i | − | 0.00979385i | ||||||
\(448\) | −1962.44 | −4.38044 | ||||||||
\(449\) | 392.043i | 0.873147i | 0.899669 | + | 0.436574i | \(0.143808\pi\) | ||||
−0.899669 | + | 0.436574i | \(0.856192\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 209.219i | − | 0.463900i | ||||||
\(452\) | − | 1389.06i | − | 3.07314i | ||||||
\(453\) | −3.67235 | −0.00810673 | ||||||||
\(454\) | −675.651 | −1.48822 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 30.6266 | + | 38.9100i | 0.0671636 | + | 0.0853289i | ||||
\(457\) | −599.374 | −1.31154 | −0.655770 | − | 0.754961i | \(-0.727656\pi\) | ||||
−0.655770 | + | 0.754961i | \(0.727656\pi\) | |||||||
\(458\) | − | 343.831i | − | 0.750722i | ||||||
\(459\) | − | 9.60972i | − | 0.0209362i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −304.936 | −0.661467 | −0.330734 | − | 0.943724i | \(-0.607296\pi\) | ||||
−0.330734 | + | 0.943724i | \(0.607296\pi\) | |||||||
\(462\) | −20.6247 | −0.0446421 | ||||||||
\(463\) | 457.460 | 0.988035 | 0.494018 | − | 0.869452i | \(-0.335528\pi\) | ||||
0.494018 | + | 0.869452i | \(0.335528\pi\) | |||||||
\(464\) | − | 1457.99i | − | 3.14221i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 219.043i | 0.470049i | ||||||||
\(467\) | −211.620 | −0.453147 | −0.226574 | − | 0.973994i | \(-0.572752\pi\) | ||||
−0.226574 | + | 0.973994i | \(0.572752\pi\) | |||||||
\(468\) | 1298.08i | 2.77367i | ||||||||
\(469\) | − | 998.169i | − | 2.12829i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 20.6422i | − | 0.0438263i | ||||||
\(472\) | 1277.43 | 2.70643 | ||||||||
\(473\) | −160.872 | −0.340110 | ||||||||
\(474\) | − | 50.2519i | − | 0.106017i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 556.555 | 1.16923 | ||||||||
\(477\) | 368.809i | 0.773184i | ||||||||
\(478\) | − | 118.133i | − | 0.247141i | ||||||
\(479\) | −116.631 | −0.243488 | −0.121744 | − | 0.992562i | \(-0.538849\pi\) | ||||
−0.121744 | + | 0.992562i | \(0.538849\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −526.909 | −1.09544 | ||||||||
\(482\) | 1175.91 | 2.43965 | ||||||||
\(483\) | 38.2082i | 0.0791061i | ||||||||
\(484\) | 991.875 | 2.04933 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −94.8369 | −0.195138 | ||||||||
\(487\) | − | 86.5090i | − | 0.177637i | −0.996048 | − | 0.0888183i | \(-0.971691\pi\) | ||
0.996048 | − | 0.0888183i | \(-0.0283090\pi\) | |||||||
\(488\) | − | 823.245i | − | 1.68698i | ||||||
\(489\) | 10.1510i | 0.0207588i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 114.292 | 0.232773 | 0.116387 | − | 0.993204i | \(-0.462869\pi\) | ||||
0.116387 | + | 0.993204i | \(0.462869\pi\) | |||||||
\(492\) | −43.0329 | −0.0874653 | ||||||||
\(493\) | 138.429i | 0.280789i | ||||||||
\(494\) | 609.215 | + | 773.986i | 1.23323 | + | 1.56677i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1616.37i | 3.25881i | ||||||||
\(497\) | 905.355i | 1.82164i | ||||||||
\(498\) | −39.1588 | −0.0786322 | ||||||||
\(499\) | 293.641 | 0.588459 | 0.294230 | − | 0.955735i | \(-0.404937\pi\) | ||||
0.294230 | + | 0.955735i | \(0.404937\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.72553 | 0.0194122 | ||||||||
\(502\) | − | 965.805i | − | 1.92391i | ||||||
\(503\) | −67.3735 | −0.133943 | −0.0669717 | − | 0.997755i | \(-0.521334\pi\) | ||||
−0.0669717 | + | 0.997755i | \(0.521334\pi\) | |||||||
\(504\) | − | 2288.23i | − | 4.54014i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 761.338i | 1.50462i | ||||||||
\(507\) | − | 1.45235i | − | 0.00286459i | ||||||
\(508\) | 1064.82i | 2.09609i | ||||||||
\(509\) | 513.534i | 1.00891i | 0.863439 | + | 0.504454i | \(0.168306\pi\) | ||||
−0.863439 | + | 0.504454i | \(0.831694\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −47.8210 | −0.0935833 | ||||||||
\(512\) | 376.954i | 0.736239i | ||||||||
\(513\) | −27.4121 | + | 21.5764i | −0.0534348 | + | 0.0420593i | ||||
\(514\) | −1337.33 | −2.60181 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 33.0888i | 0.0641256i | ||||||||
\(517\) | −407.643 | −0.788479 | ||||||||
\(518\) | 1486.05 | 2.86883 | ||||||||
\(519\) | 25.0351 | 0.0482372 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 294.021i | 0.564340i | 0.959364 | + | 0.282170i | \(0.0910542\pi\) | ||||
−0.959364 | + | 0.282170i | \(0.908946\pi\) | |||||||
\(522\) | 910.582 | 1.74441 | ||||||||
\(523\) | − | 39.6545i | − | 0.0758211i | −0.999281 | − | 0.0379106i | \(-0.987930\pi\) | ||
0.999281 | − | 0.0379106i | \(-0.0120702\pi\) | |||||||
\(524\) | −496.693 | −0.947888 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 881.047i | − | 1.67499i | ||||||
\(527\) | − | 153.467i | − | 0.291208i | ||||||
\(528\) | 29.7812i | 0.0564037i | ||||||||
\(529\) | 881.418 | 1.66620 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 449.715i | 0.846921i | ||||||||
\(532\) | −1249.61 | − | 1587.59i | −2.34890 | − | 2.98419i | ||||
\(533\) | −535.024 | −1.00380 | ||||||||
\(534\) | − | 49.8205i | − | 0.0932969i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2556.97 | −4.77046 | ||||||||
\(537\) | 8.29831 | 0.0154531 | ||||||||
\(538\) | −1080.23 | −2.00787 | ||||||||
\(539\) | 266.603 | 0.494625 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 200.431 | 0.370482 | 0.185241 | − | 0.982693i | \(-0.440693\pi\) | ||||
0.185241 | + | 0.982693i | \(0.440693\pi\) | |||||||
\(542\) | 774.921i | 1.42974i | ||||||||
\(543\) | 26.2858 | 0.0484084 | ||||||||
\(544\) | − | 570.387i | − | 1.04851i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 52.7424i | 0.0965977i | ||||||||
\(547\) | − | 460.716i | − | 0.842260i | −0.907000 | − | 0.421130i | \(-0.861634\pi\) | ||
0.907000 | − | 0.421130i | \(-0.138366\pi\) | |||||||
\(548\) | 302.611 | 0.552209 | ||||||||
\(549\) | 289.820 | 0.527905 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 394.874 | − | 310.810i | 0.716649 | − | 0.564084i | ||||
\(552\) | 97.8765 | 0.177312 | ||||||||
\(553\) | 1281.53i | 2.31742i | ||||||||
\(554\) | 416.984i | 0.752679i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1662.87 | −2.99078 | ||||||||
\(557\) | −920.981 | −1.65347 | −0.826733 | − | 0.562594i | \(-0.809803\pi\) | ||||
−0.826733 | + | 0.562594i | \(0.809803\pi\) | |||||||
\(558\) | −1009.50 | −1.80914 | ||||||||
\(559\) | 411.390i | 0.735939i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 2.82759i | − | 0.00504026i | ||||||
\(562\) | −847.546 | −1.50809 | ||||||||
\(563\) | 90.0804i | 0.160001i | 0.996795 | + | 0.0800004i | \(0.0254921\pi\) | ||||
−0.996795 | + | 0.0800004i | \(0.974508\pi\) | |||||||
\(564\) | 83.8457i | 0.148663i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 570.020i | − | 1.00710i | ||||||
\(567\) | 804.627 | 1.41909 | ||||||||
\(568\) | 2319.21 | 4.08312 | ||||||||
\(569\) | − | 199.974i | − | 0.351448i | −0.984440 | − | 0.175724i | \(-0.943773\pi\) | ||
0.984440 | − | 0.175724i | \(-0.0562266\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.6282 | 0.0256186 | 0.0128093 | − | 0.999918i | \(-0.495923\pi\) | ||||
0.0128093 | + | 0.999918i | \(0.495923\pi\) | |||||||
\(572\) | 764.340i | 1.33626i | ||||||||
\(573\) | − | 24.1642i | − | 0.0421714i | ||||||
\(574\) | 1508.94 | 2.62882 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1769.77 | −3.07251 | ||||||||
\(577\) | −1029.44 | −1.78412 | −0.892062 | − | 0.451912i | \(-0.850742\pi\) | ||||
−0.892062 | + | 0.451912i | \(0.850742\pi\) | |||||||
\(578\) | − | 1001.90i | − | 1.73340i | ||||||
\(579\) | 28.8894 | 0.0498954 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 998.636 | 1.71882 | ||||||||
\(582\) | − | 5.70597i | − | 0.00980406i | ||||||
\(583\) | 217.164i | 0.372494i | ||||||||
\(584\) | 122.501i | 0.209762i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 261.650 | 0.446501 | ||||||||
\(587\) | −904.645 | −1.54113 | −0.770566 | − | 0.637360i | \(-0.780026\pi\) | ||||
−0.770566 | + | 0.637360i | \(0.780026\pi\) | |||||||
\(588\) | − | 54.8360i | − | 0.0932584i | ||||||
\(589\) | −437.769 | + | 344.574i | −0.743240 | + | 0.585015i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.92176i | 0.00494375i | ||||||||
\(592\) | − | 2145.80i | − | 3.62466i | ||||||
\(593\) | −418.448 | −0.705645 | −0.352823 | − | 0.935690i | \(-0.614778\pi\) | ||||
−0.352823 | + | 0.935690i | \(0.614778\pi\) | |||||||
\(594\) | −37.2211 | −0.0626617 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 457.572 | 0.767739 | ||||||||
\(597\) | − | 34.2661i | − | 0.0573972i | ||||||
\(598\) | 1946.93 | 3.25574 | ||||||||
\(599\) | − | 616.270i | − | 1.02883i | −0.857541 | − | 0.514416i | \(-0.828009\pi\) | ||
0.857541 | − | 0.514416i | \(-0.171991\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 618.358i | 1.02888i | 0.857526 | + | 0.514441i | \(0.172000\pi\) | ||||
−0.857526 | + | 0.514441i | \(0.828000\pi\) | |||||||
\(602\) | − | 1160.25i | − | 1.92733i | ||||||
\(603\) | − | 900.169i | − | 1.49282i | ||||||
\(604\) | − | 383.833i | − | 0.635485i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.19036 | 0.0118653 | ||||||||
\(607\) | − | 204.176i | − | 0.336369i | −0.985756 | − | 0.168185i | \(-0.946209\pi\) | ||
0.985756 | − | 0.168185i | \(-0.0537905\pi\) | |||||||
\(608\) | −1627.05 | + | 1280.67i | −2.67607 | + | 2.10637i | ||||
\(609\) | 26.9082 | 0.0441842 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1042.44i | 1.70613i | ||||||||
\(612\) | 501.912 | 0.820118 | ||||||||
\(613\) | 916.966 | 1.49587 | 0.747933 | − | 0.663774i | \(-0.231046\pi\) | ||||
0.747933 | + | 0.663774i | \(0.231046\pi\) | |||||||
\(614\) | 558.472 | 0.909563 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 1347.37i | − | 2.18728i | ||||||
\(617\) | 438.672 | 0.710975 | 0.355488 | − | 0.934681i | \(-0.384315\pi\) | ||||
0.355488 | + | 0.934681i | \(0.384315\pi\) | |||||||
\(618\) | 72.1213i | 0.116701i | ||||||||
\(619\) | −164.123 | −0.265142 | −0.132571 | − | 0.991174i | \(-0.542323\pi\) | ||||
−0.132571 | + | 0.991174i | \(0.542323\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 68.9539i | 0.111037i | ||||||||
\(622\) | − | 168.263i | − | 0.270520i | ||||||
\(623\) | 1270.53i | 2.03938i | ||||||||
\(624\) | 76.1578 | 0.122048 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 784.002i | − | 1.25240i | ||||||
\(627\) | −8.06578 | + | 6.34869i | −0.0128641 | + | 0.0101255i | ||||
\(628\) | 2157.52 | 3.43553 | ||||||||
\(629\) | 203.734i | 0.323901i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1182.36 | −1.87378 | −0.936890 | − | 0.349624i | \(-0.886309\pi\) | ||||
−0.936890 | + | 0.349624i | \(0.886309\pi\) | |||||||
\(632\) | 3282.85 | 5.19438 | ||||||||
\(633\) | 11.8556 | 0.0187293 | ||||||||
\(634\) | 340.275 | 0.536711 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 44.6671 | 0.0702313 | ||||||||
\(637\) | − | 681.770i | − | 1.07028i | ||||||
\(638\) | 536.173 | 0.840397 | ||||||||
\(639\) | 816.468i | 1.27773i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 123.199i | − | 0.192199i | −0.995372 | − | 0.0960993i | \(-0.969363\pi\) | ||
0.995372 | − | 0.0960993i | \(-0.0306366\pi\) | |||||||
\(642\) | − | 51.2297i | − | 0.0797971i | ||||||
\(643\) | 107.069 | 0.166515 | 0.0832577 | − | 0.996528i | \(-0.473468\pi\) | ||||
0.0832577 | + | 0.996528i | \(0.473468\pi\) | |||||||
\(644\) | −3993.52 | −6.20112 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 299.268 | − | 235.558i | 0.463264 | − | 0.364641i | ||||
\(647\) | −277.921 | −0.429553 | −0.214777 | − | 0.976663i | \(-0.568902\pi\) | ||||
−0.214777 | + | 0.976663i | \(0.568902\pi\) | |||||||
\(648\) | − | 2061.18i | − | 3.18083i | ||||||
\(649\) | 264.804i | 0.408018i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −29.8312 | −0.0458237 | ||||||||
\(652\) | −1060.98 | −1.62728 | ||||||||
\(653\) | −500.160 | −0.765942 | −0.382971 | − | 0.923760i | \(-0.625099\pi\) | ||||
−0.382971 | + | 0.923760i | \(0.625099\pi\) | |||||||
\(654\) | − | 9.11747i | − | 0.0139411i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 2178.85i | − | 3.32141i | ||||||
\(657\) | −43.1260 | −0.0656408 | ||||||||
\(658\) | − | 2940.03i | − | 4.46813i | ||||||
\(659\) | − | 154.079i | − | 0.233807i | −0.993143 | − | 0.116903i | \(-0.962703\pi\) | ||
0.993143 | − | 0.116903i | \(-0.0372968\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1164.81i | − | 1.76220i | −0.472933 | − | 0.881099i | \(-0.656805\pi\) | ||
0.472933 | − | 0.881099i | \(-0.343195\pi\) | |||||||
\(662\) | 463.781 | 0.700576 | ||||||||
\(663\) | −7.23083 | −0.0109062 | ||||||||
\(664\) | − | 2558.16i | − | 3.85266i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1340.15 | 2.01224 | ||||||||
\(667\) | − | 993.288i | − | 1.48919i | ||||||
\(668\) | 1016.51i | 1.52172i | ||||||||
\(669\) | −28.1317 | −0.0420504 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 170.653 | 0.254327 | ||||||||
\(672\) | −110.873 | −0.164990 | ||||||||
\(673\) | 943.259i | 1.40157i | 0.713371 | + | 0.700786i | \(0.247167\pi\) | ||||
−0.713371 | + | 0.700786i | \(0.752833\pi\) | |||||||
\(674\) | −197.005 | −0.292292 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 151.799 | 0.224555 | ||||||||
\(677\) | 675.089i | 0.997178i | 0.866839 | + | 0.498589i | \(0.166148\pi\) | ||||
−0.866839 | + | 0.498589i | \(0.833852\pi\) | |||||||
\(678\) | − | 50.8980i | − | 0.0750707i | ||||||
\(679\) | 145.515i | 0.214307i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.0056 | −0.0264400 | ||||||||
\(682\) | −594.418 | −0.871580 | ||||||||
\(683\) | − | 652.171i | − | 0.954863i | −0.878669 | − | 0.477431i | \(-0.841568\pi\) | ||
0.878669 | − | 0.477431i | \(-0.158432\pi\) | |||||||
\(684\) | −1126.93 | − | 1431.72i | −1.64756 | − | 2.09316i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 52.1574i | 0.0760312i | ||||||||
\(687\) | − | 9.16285i | − | 0.0133375i | ||||||
\(688\) | −1675.36 | −2.43511 | ||||||||
\(689\) | 555.341 | 0.806011 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1182.56 | −1.71138 | −0.855688 | − | 0.517491i | \(-0.826866\pi\) | ||||
−0.855688 | + | 0.517491i | \(0.826866\pi\) | |||||||
\(692\) | 2616.66i | 3.78131i | ||||||||
\(693\) | 474.335 | 0.684465 | ||||||||
\(694\) | 1918.15i | 2.76391i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 68.9296i | − | 0.0990368i | ||||||
\(697\) | 206.872i | 0.296803i | ||||||||
\(698\) | − | 2244.17i | − | 3.21514i | ||||||
\(699\) | 5.83734i | 0.00835098i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 935.918 | 1.33512 | 0.667559 | − | 0.744557i | \(-0.267339\pi\) | ||||
0.667559 | + | 0.744557i | \(0.267339\pi\) | |||||||
\(702\) | 95.1834i | 0.135589i | ||||||||
\(703\) | 581.157 | − | 457.437i | 0.826682 | − | 0.650693i | ||||
\(704\) | −1042.08 | −1.48023 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1179.26i | − | 1.67034i | ||||||
\(707\) | −183.370 | −0.259363 | ||||||||
\(708\) | 54.4658 | 0.0769291 | ||||||||
\(709\) | 343.933 | 0.485096 | 0.242548 | − | 0.970139i | \(-0.422017\pi\) | ||||
0.242548 | + | 0.970139i | \(0.422017\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1155.71i | 1.62548i | ||||||||
\(712\) | 3254.67 | 4.57117 | ||||||||
\(713\) | 1101.19i | 1.54444i | ||||||||
\(714\) | 20.3933 | 0.0285620 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 867.338i | 1.21137i | ||||||||
\(717\) | − | 3.14817i | − | 0.00439076i | ||||||
\(718\) | 1333.98i | 1.85790i | ||||||||
\(719\) | 312.031 | 0.433979 | 0.216989 | − | 0.976174i | \(-0.430376\pi\) | ||||
0.216989 | + | 0.976174i | \(0.430376\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1839.25i | − | 2.55097i | ||||||
\(722\) | −1343.87 | − | 324.781i | −1.86132 | − | 0.449836i | ||||
\(723\) | 31.3372 | 0.0433433 | ||||||||
\(724\) | 2747.38i | 3.79473i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 36.3443 | 0.0500610 | ||||||||
\(727\) | 492.307 | 0.677177 | 0.338588 | − | 0.940935i | \(-0.390051\pi\) | ||||
0.338588 | + | 0.940935i | \(0.390051\pi\) | |||||||
\(728\) | −3445.55 | −4.73290 | ||||||||
\(729\) | 723.942 | 0.993062 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 159.067 | 0.217602 | ||||||||
\(732\) | − | 35.1006i | − | 0.0479517i | ||||||
\(733\) | −599.784 | −0.818259 | −0.409130 | − | 0.912476i | \(-0.634168\pi\) | ||||
−0.409130 | + | 0.912476i | \(0.634168\pi\) | |||||||
\(734\) | 842.728i | 1.14813i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4092.77i | 5.56083i | ||||||||
\(737\) | − | 530.042i | − | 0.719189i | ||||||
\(738\) | 1360.79 | 1.84389 | ||||||||
\(739\) | 509.437 | 0.689360 | 0.344680 | − | 0.938720i | \(-0.387987\pi\) | ||||
0.344680 | + | 0.938720i | \(0.387987\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.2352 | + | 20.6262i | 0.0219098 | + | 0.0278356i | ||||
\(742\) | −1566.24 | −2.11084 | ||||||||
\(743\) | 547.250i | 0.736541i | 0.929719 | + | 0.368271i | \(0.120050\pi\) | ||||
−0.929719 | + | 0.368271i | \(0.879950\pi\) | |||||||
\(744\) | 76.4174i | 0.102712i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 798.168 | 1.06993 | ||||||||
\(747\) | 900.590 | 1.20561 | ||||||||
\(748\) | 295.539 | 0.395105 | ||||||||
\(749\) | 1306.47i | 1.74429i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1150.89i | 1.53248i | 0.642554 | + | 0.766240i | \(0.277875\pi\) | ||||
−0.642554 | + | 0.766240i | \(0.722125\pi\) | |||||||
\(752\) | −4245.28 | −5.64532 | ||||||||
\(753\) | − | 25.7380i | − | 0.0341807i | ||||||
\(754\) | − | 1371.13i | − | 1.81847i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 195.239i | − | 0.258253i | ||||||
\(757\) | −600.187 | −0.792849 | −0.396424 | − | 0.918067i | \(-0.629749\pi\) | ||||
−0.396424 | + | 0.918067i | \(0.629749\pi\) | |||||||
\(758\) | 894.276 | 1.17978 | ||||||||
\(759\) | 20.2891i | 0.0267314i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −918.373 | −1.20680 | −0.603399 | − | 0.797440i | \(-0.706187\pi\) | ||||
−0.603399 | + | 0.797440i | \(0.706187\pi\) | |||||||
\(762\) | 39.0170i | 0.0512034i | ||||||||
\(763\) | 232.515i | 0.304738i | ||||||||
\(764\) | 2525.64 | 3.30581 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 73.5441 | 0.0960106 | ||||||||
\(767\) | 677.168 | 0.882878 | ||||||||
\(768\) | 43.9492i | 0.0572255i | ||||||||
\(769\) | 573.628 | 0.745940 | 0.372970 | − | 0.927843i | \(-0.378339\pi\) | ||||
0.372970 | + | 0.927843i | \(0.378339\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.6389 | −0.0462243 | ||||||||
\(772\) | 3019.52i | 3.91129i | ||||||||
\(773\) | 845.816i | 1.09420i | 0.837068 | + | 0.547100i | \(0.184268\pi\) | ||||
−0.837068 | + | 0.547100i | \(0.815732\pi\) | |||||||
\(774\) | − | 1046.34i | − | 1.35186i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 372.759 | 0.480359 | ||||||||
\(777\) | 39.6023 | 0.0509682 | ||||||||
\(778\) | 1475.90i | 1.89705i | ||||||||
\(779\) | 590.108 | − | 464.482i | 0.757520 | − | 0.596254i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 480.757i | 0.615566i | ||||||||
\(782\) | − | 752.797i | − | 0.962656i | ||||||
\(783\) | 48.5609 | 0.0620190 | ||||||||
\(784\) | 2776.46 | 3.54140 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −18.1998 | −0.0231550 | ||||||||
\(787\) | 435.404i | 0.553245i | 0.960979 | + | 0.276623i | \(0.0892152\pi\) | ||||
−0.960979 | + | 0.276623i | \(0.910785\pi\) | |||||||
\(788\) | −305.382 | −0.387540 | ||||||||
\(789\) | − | 23.4793i | − | 0.0297583i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1298.01i | 1.64097i | ||||||||
\(792\) | − | 1215.08i | − | 1.53420i | ||||||
\(793\) | − | 436.402i | − | 0.550318i | ||||||
\(794\) | 848.559i | 1.06871i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3581.49 | 4.49936 | ||||||||
\(797\) | − | 42.1998i | − | 0.0529483i | −0.999649 | − | 0.0264742i | \(-0.991572\pi\) | ||
0.999649 | − | 0.0264742i | \(-0.00842797\pi\) | |||||||
\(798\) | −45.7884 | − | 58.1725i | −0.0573789 | − | 0.0728979i | ||||
\(799\) | 403.070 | 0.504468 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1145.79i | 1.43045i | ||||||||
\(802\) | 2620.33 | 3.26725 | ||||||||
\(803\) | −25.3937 | −0.0316235 | ||||||||
\(804\) | −109.021 | −0.135598 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1520.07i | 1.88595i | ||||||||
\(807\) | −28.7874 | −0.0356722 | ||||||||
\(808\) | 469.731i | 0.581350i | ||||||||
\(809\) | −1054.72 | −1.30374 | −0.651868 | − | 0.758332i | \(-0.726014\pi\) | ||||
−0.651868 | + | 0.758332i | \(0.726014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 388.797i | 0.479404i | 0.970846 | + | 0.239702i | \(0.0770498\pi\) | ||||
−0.970846 | + | 0.239702i | \(0.922950\pi\) | |||||||
\(812\) | 2812.44i | 3.46360i | ||||||||
\(813\) | 20.6511i | 0.0254011i | ||||||||
\(814\) | 789.116 | 0.969430 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 29.4471i | − | 0.0360871i | ||||||
\(817\) | −357.149 | − | 453.745i | −0.437147 | − | 0.555379i | ||||
\(818\) | −1421.89 | −1.73826 | ||||||||
\(819\) | − | 1212.99i | − | 1.48106i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 934.546 | 1.13830 | 0.569151 | − | 0.822233i | \(-0.307272\pi\) | ||||
0.569151 | + | 0.822233i | \(0.307272\pi\) | |||||||
\(822\) | 11.0883 | 0.0134894 | ||||||||
\(823\) | 349.311 | 0.424436 | 0.212218 | − | 0.977222i | \(-0.431931\pi\) | ||||
0.212218 | + | 0.977222i | \(0.431931\pi\) | |||||||
\(824\) | −4711.53 | −5.71788 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1909.83 | −2.31215 | ||||||||
\(827\) | 770.532i | 0.931719i | 0.884859 | + | 0.465860i | \(0.154255\pi\) | ||||
−0.884859 | + | 0.465860i | \(0.845745\pi\) | |||||||
\(828\) | −3601.44 | −4.34956 | ||||||||
\(829\) | 61.0383i | 0.0736288i | 0.999322 | + | 0.0368144i | \(0.0117210\pi\) | ||||
−0.999322 | + | 0.0368144i | \(0.988279\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.1123i | 0.0133723i | ||||||||
\(832\) | 2664.86i | 3.20296i | ||||||||
\(833\) | −263.612 | −0.316461 | ||||||||
\(834\) | −60.9311 | −0.0730588 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −663.563 | − | 843.034i | −0.793736 | − | 1.00841i | ||||
\(837\) | −53.8360 | −0.0643202 | ||||||||
\(838\) | 1812.00i | 2.16229i | ||||||||
\(839\) | − | 1088.98i | − | 1.29795i | −0.760810 | − | 0.648975i | \(-0.775198\pi\) | ||
0.760810 | − | 0.648975i | \(-0.224802\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 141.476 | 0.168223 | ||||||||
\(842\) | −969.103 | −1.15095 | ||||||||
\(843\) | −22.5865 | −0.0267930 | ||||||||
\(844\) | 1239.15i | 1.46819i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 2651.38i | − | 3.13402i | ||||||
\(847\) | −926.859 | −1.09429 | ||||||||
\(848\) | 2261.59i | 2.66697i | ||||||||
\(849\) | − | 15.1906i | − | 0.0178924i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1461.88i | − | 1.71784i | ||||||
\(852\) | 98.8840 | 0.116061 | ||||||||
\(853\) | −1351.24 | −1.58411 | −0.792053 | − | 0.610452i | \(-0.790988\pi\) | ||||
−0.792053 | + | 0.610452i | \(0.790988\pi\) | |||||||
\(854\) | 1230.80i | 1.44121i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3346.73 | 3.90973 | ||||||||
\(857\) | 175.280i | 0.204527i | 0.994757 | + | 0.102264i | \(0.0326085\pi\) | ||||
−0.994757 | + | 0.102264i | \(0.967391\pi\) | |||||||
\(858\) | 28.0070i | 0.0326421i | ||||||||
\(859\) | −567.473 | −0.660620 | −0.330310 | − | 0.943872i | \(-0.607153\pi\) | ||||
−0.330310 | + | 0.943872i | \(0.607153\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 40.2122 | 0.0467041 | ||||||||
\(862\) | 492.971 | 0.571892 | ||||||||
\(863\) | − | 1339.71i | − | 1.55239i | −0.630492 | − | 0.776196i | \(-0.717147\pi\) | ||
0.630492 | − | 0.776196i | \(-0.282853\pi\) | |||||||
\(864\) | −200.091 | −0.231587 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −619.228 | −0.715044 | ||||||||
\(867\) | − | 26.7000i | − | 0.0307959i | ||||||
\(868\) | − | 3117.95i | − | 3.59211i | ||||||
\(869\) | 680.513i | 0.783099i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1355.45 | −1.55620 | ||||||||
\(872\) | 595.625 | 0.683056 | ||||||||
\(873\) | 131.228i | 0.150319i | ||||||||
\(874\) | −2147.38 | + | 1690.23i | −2.45695 | + | 1.93390i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.22307i | 0.00596241i | ||||||||
\(877\) | 1155.71i | 1.31780i | 0.752228 | + | 0.658902i | \(0.228979\pi\) | ||||
−0.752228 | + | 0.658902i | \(0.771021\pi\) | |||||||
\(878\) | 554.697 | 0.631773 | ||||||||
\(879\) | 6.97278 | 0.00793263 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1056.32 | 1.19900 | 0.599500 | − | 0.800374i | \(-0.295366\pi\) | ||||
0.599500 | + | 0.800374i | \(0.295366\pi\) | |||||||
\(882\) | 1734.03i | 1.96602i | ||||||||
\(883\) | −624.622 | −0.707386 | −0.353693 | − | 0.935362i | \(-0.615074\pi\) | ||||
−0.353693 | + | 0.935362i | \(0.615074\pi\) | |||||||
\(884\) | − | 755.765i | − | 0.854938i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 904.364i | 1.02073i | ||||||||
\(887\) | 820.850i | 0.925423i | 0.886509 | + | 0.462711i | \(0.153123\pi\) | ||||
−0.886509 | + | 0.462711i | \(0.846877\pi\) | |||||||
\(888\) | − | 101.448i | − | 0.114243i | ||||||
\(889\) | − | 995.019i | − | 1.11926i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 427.268 | 0.479538 | ||||||||
\(892\) | − | 2940.32i | − | 3.29633i | ||||||
\(893\) | −905.001 | − | 1149.77i | −1.01344 | − | 1.28754i | ||||
\(894\) | 16.7664 | 0.0187543 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 3170.44i | − | 3.53844i | ||||||
\(897\) | 51.8843 | 0.0578421 | ||||||||
\(898\) | −1501.45 | −1.67200 | ||||||||
\(899\) | 775.514 | 0.862640 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 214.727i | − | 0.238321i | ||||||
\(902\) | 801.269 | 0.888325 | ||||||||
\(903\) | − | 30.9199i | − | 0.0342413i | ||||||
\(904\) | 3325.06 | 3.67816 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 14.0644i | − | 0.0155236i | ||||||
\(907\) | − | 1430.19i | − | 1.57684i | −0.615140 | − | 0.788418i | \(-0.710901\pi\) | ||
0.615140 | − | 0.788418i | \(-0.289099\pi\) | |||||||
\(908\) | − | 1881.94i | − | 2.07263i | ||||||
\(909\) | −165.367 | −0.181922 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 436.452i | − | 0.479091i | −0.970885 | − | 0.239546i | \(-0.923001\pi\) | ||
0.970885 | − | 0.239546i | \(-0.0769985\pi\) | |||||||
\(912\) | −83.9987 | + | 66.1165i | −0.0921038 | + | 0.0724962i | ||||
\(913\) | 530.290 | 0.580822 | ||||||||
\(914\) | − | 2295.49i | − | 2.51148i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 957.699 | 1.04552 | ||||||||
\(917\) | 464.136 | 0.506146 | ||||||||
\(918\) | 36.8035 | 0.0400909 | ||||||||
\(919\) | 110.671 | 0.120426 | 0.0602130 | − | 0.998186i | \(-0.480822\pi\) | ||||
0.0602130 | + | 0.998186i | \(0.480822\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.8829 | 0.0161595 | ||||||||
\(922\) | − | 1167.85i | − | 1.26665i | ||||||
\(923\) | 1229.41 | 1.33198 | ||||||||
\(924\) | − | 57.4475i | − | 0.0621727i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1751.99i | 1.89200i | ||||||||
\(927\) | − | 1658.68i | − | 1.78929i | ||||||
\(928\) | 2882.34 | 3.10597 | ||||||||
\(929\) | −1781.29 | −1.91743 | −0.958714 | − | 0.284371i | \(-0.908215\pi\) | ||||
−0.958714 | + | 0.284371i | \(0.908215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 591.880 | + | 751.962i | 0.635746 | + | 0.807693i | ||||
\(932\) | −610.117 | −0.654632 | ||||||||
\(933\) | − | 4.48410i | − | 0.00480611i | ||||||
\(934\) | − | 810.465i | − | 0.867736i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3107.27 | −3.31973 | ||||||||
\(937\) | 400.832 | 0.427782 | 0.213891 | − | 0.976858i | \(-0.431386\pi\) | ||||
0.213891 | + | 0.976858i | \(0.431386\pi\) | |||||||
\(938\) | 3822.80 | 4.07548 | ||||||||
\(939\) | − | 20.8931i | − | 0.0222504i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1092.72i | − | 1.16123i | −0.814177 | − | 0.580617i | \(-0.802812\pi\) | ||
0.814177 | − | 0.580617i | \(-0.197188\pi\) | |||||||
\(942\) | 79.0557 | 0.0839232 | ||||||||
\(943\) | − | 1484.39i | − | 1.57412i | ||||||
\(944\) | 2757.72i | 2.92131i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 616.111i | − | 0.651280i | ||||||
\(947\) | 1260.43 | 1.33097 | 0.665487 | − | 0.746410i | \(-0.268224\pi\) | ||||
0.665487 | + | 0.746410i | \(0.268224\pi\) | |||||||
\(948\) | 139.971 | 0.147648 | ||||||||
\(949\) | 64.9379i | 0.0684277i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.06808 | 0.00953531 | ||||||||
\(952\) | 1332.25i | 1.39942i | ||||||||
\(953\) | − | 381.589i | − | 0.400408i | −0.979754 | − | 0.200204i | \(-0.935839\pi\) | ||
0.979754 | − | 0.200204i | \(-0.0641606\pi\) | |||||||
\(954\) | −1412.47 | −1.48058 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 329.046 | 0.344191 | ||||||||
\(957\) | 14.2886 | 0.0149307 | ||||||||
\(958\) | − | 446.675i | − | 0.466258i | ||||||
\(959\) | −282.775 | −0.294864 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 101.243 | 0.105351 | ||||||||
\(962\) | − | 2017.96i | − | 2.09768i | ||||||
\(963\) | 1178.20i | 1.22347i | ||||||||
\(964\) | 3275.36i | 3.39768i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −146.331 | −0.151481 | ||||||||
\(967\) | −1649.39 | −1.70568 | −0.852840 | − | 0.522172i | \(-0.825122\pi\) | ||||
−0.852840 | + | 0.522172i | \(0.825122\pi\) | |||||||
\(968\) | 2374.30i | 2.45279i | ||||||||
\(969\) | 7.97529 | − | 6.27746i | 0.00823043 | − | 0.00647829i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1246.99i | − | 1.28423i | −0.766607 | − | 0.642116i | \(-0.778057\pi\) | ||
0.766607 | − | 0.642116i | \(-0.221943\pi\) | |||||||
\(972\) | − | 264.157i | − | 0.271766i | ||||||
\(973\) | 1553.88 | 1.59699 | ||||||||
\(974\) | 331.313 | 0.340158 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1777.22 | 1.82092 | ||||||||
\(977\) | 162.841i | 0.166674i | 0.996521 | + | 0.0833372i | \(0.0265578\pi\) | ||||
−0.996521 | + | 0.0833372i | \(0.973442\pi\) | |||||||
\(978\) | −38.8766 | −0.0397511 | ||||||||
\(979\) | 674.672i | 0.689144i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 209.687i | 0.213748i | ||||||||
\(982\) | 437.717i | 0.445740i | ||||||||
\(983\) | 984.880i | 1.00191i | 0.865472 | + | 0.500956i | \(0.167018\pi\) | ||||
−0.865472 | + | 0.500956i | \(0.832982\pi\) | |||||||
\(984\) | − | 103.010i | − | 0.104685i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −530.158 | −0.537686 | ||||||||
\(987\) | − | 78.3498i | − | 0.0793817i | ||||||
\(988\) | −2155.84 | + | 1696.89i | −2.18203 | + | 1.71750i | ||||
\(989\) | −1141.38 | −1.15407 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.4482i | 0.0448518i | 0.999749 | + | 0.0224259i | \(0.00713899\pi\) | ||||
−0.999749 | + | 0.0224259i | \(0.992861\pi\) | |||||||
\(992\) | −3195.45 | −3.22122 | ||||||||
\(993\) | 12.3595 | 0.0124466 | ||||||||
\(994\) | −3467.34 | −3.48827 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 109.072i | − | 0.109510i | ||||||
\(997\) | −666.830 | −0.668836 | −0.334418 | − | 0.942425i | \(-0.608540\pi\) | ||||
−0.334418 | + | 0.942425i | \(0.608540\pi\) | |||||||
\(998\) | 1124.59i | 1.12685i | ||||||||
\(999\) | 71.4697 | 0.0715412 |
(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 | 475.3.c.i.151.14 | yes | 14 | |
5.2 | odd | 4 | 475.3.d.d.474.2 | 28 | |||
5.3 | odd | 4 | 475.3.d.d.474.27 | 28 | |||
5.4 | even | 2 | 475.3.c.h.151.1 | ✓ | 14 | ||
19.18 | odd | 2 | inner | 475.3.c.i.151.1 | yes | 14 | |
95.18 | even | 4 | 475.3.d.d.474.1 | 28 | |||
95.37 | even | 4 | 475.3.d.d.474.28 | 28 | |||
95.94 | odd | 2 | 475.3.c.h.151.14 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.3.c.h.151.1 | ✓ | 14 | 5.4 | even | 2 | ||
475.3.c.h.151.14 | yes | 14 | 95.94 | odd | 2 | ||
475.3.c.i.151.1 | yes | 14 | 19.18 | odd | 2 | inner | |
475.3.c.i.151.14 | yes | 14 | 1.1 | even | 1 | trivial | |
475.3.d.d.474.1 | 28 | 95.18 | even | 4 | |||
475.3.d.d.474.2 | 28 | 5.2 | odd | 4 | |||
475.3.d.d.474.27 | 28 | 5.3 | odd | 4 | |||
475.3.d.d.474.28 | 28 | 95.37 | even | 4 |