Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,2,Mod(9,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.n (of order \(8\), degree \(4\), 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: | \(1.08596546749\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 136.49 |
Dual form | 136.2.n.a.25.1 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.292893 | − | 0.707107i | −0.169102 | − | 0.408248i | 0.816497 | − | 0.577350i | \(-0.195913\pi\) |
−0.985599 | + | 0.169102i | \(0.945913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.70711 | − | 0.707107i | 0.763441 | − | 0.316228i | 0.0332288 | − | 0.999448i | \(-0.489421\pi\) |
0.730213 | + | 0.683220i | \(0.239421\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.292893 | − | 0.121320i | −0.110703 | − | 0.0458548i | 0.326644 | − | 0.945147i | \(-0.394082\pi\) |
−0.437348 | + | 0.899293i | \(0.644082\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.70711 | − | 1.70711i | 0.569036 | − | 0.569036i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.292893 | − | 0.707107i | 0.0883106 | − | 0.213201i | −0.873554 | − | 0.486728i | \(-0.838190\pi\) |
0.961864 | + | 0.273527i | \(0.0881903\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | − | 1.00000i | −0.258199 | − | 0.258199i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | + | 4.00000i | 0.242536 | + | 0.970143i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.58579 | − | 1.58579i | −0.363804 | − | 0.363804i | 0.501407 | − | 0.865211i | \(-0.332816\pi\) |
−0.865211 | + | 0.501407i | \(0.832816\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.242641i | 0.0529485i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.53553 | + | 6.12132i | −0.528695 | + | 1.27638i | 0.403683 | + | 0.914899i | \(0.367730\pi\) |
−0.932378 | + | 0.361484i | \(0.882270\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.12132 | + | 1.12132i | −0.224264 | + | 0.224264i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.82843 | − | 1.58579i | −0.736781 | − | 0.305185i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.12132 | + | 2.12132i | −0.951005 | + | 0.393919i | −0.803609 | − | 0.595158i | \(-0.797089\pi\) |
−0.147397 | + | 0.989077i | \(0.547089\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.878680 | + | 2.12132i | 0.157816 | + | 0.381000i | 0.982934 | − | 0.183960i | \(-0.0588916\pi\) |
−0.825118 | + | 0.564960i | \(0.808892\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.585786 | −0.101972 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.585786 | −0.0990160 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.292893 | + | 0.707107i | 0.0481513 | + | 0.116248i | 0.946125 | − | 0.323802i | \(-0.104961\pi\) |
−0.897974 | + | 0.440049i | \(0.854961\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.29289 | − | 0.949747i | −0.358090 | − | 0.148326i | 0.196384 | − | 0.980527i | \(-0.437080\pi\) |
−0.554473 | + | 0.832202i | \(0.687080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.24264 | − | 7.24264i | 1.10449 | − | 1.10449i | 0.110631 | − | 0.993862i | \(-0.464713\pi\) |
0.993862 | − | 0.110631i | \(-0.0352871\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.70711 | − | 4.12132i | 0.254480 | − | 0.614370i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.8284i | 1.87122i | 0.353037 | + | 0.935609i | \(0.385149\pi\) | ||||
−0.353037 | + | 0.935609i | \(0.614851\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.87868 | − | 4.87868i | −0.696954 | − | 0.696954i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.53553 | − | 1.87868i | 0.355046 | − | 0.263068i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.17157 | + | 2.17157i | 0.298288 | + | 0.298288i | 0.840343 | − | 0.542055i | \(-0.182353\pi\) |
−0.542055 | + | 0.840343i | \(0.682353\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.41421i | − | 0.190693i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.656854 | + | 1.58579i | −0.0870025 | + | 0.210043i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.58579 | − | 5.58579i | 0.727207 | − | 0.727207i | −0.242855 | − | 0.970063i | \(-0.578084\pi\) |
0.970063 | + | 0.242855i | \(0.0780840\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.12132 | − | 3.77817i | −1.16787 | − | 0.483746i | −0.287379 | − | 0.957817i | \(-0.592784\pi\) |
−0.880486 | + | 0.474071i | \(0.842784\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.707107 | + | 0.292893i | −0.0890871 | + | 0.0369011i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.65685 | 1.17977 | 0.589886 | − | 0.807486i | \(-0.299173\pi\) | ||||
0.589886 | + | 0.807486i | \(0.299173\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.07107 | 0.610485 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.70711 | + | 8.94975i | 0.439953 | + | 1.06214i | 0.975965 | + | 0.217929i | \(0.0699302\pi\) |
−0.536012 | + | 0.844210i | \(0.680070\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.36396 | − | 3.05025i | 0.861886 | − | 0.357005i | 0.0924414 | − | 0.995718i | \(-0.470533\pi\) |
0.769445 | + | 0.638713i | \(0.220533\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.12132 | + | 0.464466i | 0.129479 | + | 0.0536319i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.171573 | + | 0.171573i | −0.0195525 | + | 0.0195525i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.46447 | − | 13.1924i | 0.614800 | − | 1.48426i | −0.242869 | − | 0.970059i | \(-0.578089\pi\) |
0.857670 | − | 0.514201i | \(-0.171911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 4.07107i | − | 0.452341i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.24264 | − | 7.24264i | −0.794983 | − | 0.794983i | 0.187317 | − | 0.982300i | \(-0.440021\pi\) |
−0.982300 | + | 0.187317i | \(0.940021\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.53553 | + | 6.12132i | 0.491948 | + | 0.663950i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.00000 | + | 3.00000i | 0.321634 | + | 0.321634i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.65685i | 0.175626i | 0.996137 | + | 0.0878131i | \(0.0279878\pi\) | ||||
−0.996137 | + | 0.0878131i | \(0.972012\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.24264 | − | 1.24264i | 0.128856 | − | 0.128856i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.82843 | − | 1.58579i | −0.392788 | − | 0.162698i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.7782 | + | 6.12132i | −1.50050 | + | 0.621526i | −0.973571 | − | 0.228386i | \(-0.926655\pi\) |
−0.526926 | + | 0.849911i | \(0.676655\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.707107 | − | 1.70711i | −0.0710669 | − | 0.171571i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0000 | 0.995037 | 0.497519 | − | 0.867453i | \(-0.334245\pi\) | ||||
0.497519 | + | 0.867453i | \(0.334245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.34315 | −0.230877 | −0.115439 | − | 0.993315i | \(-0.536827\pi\) | ||||
−0.115439 | + | 0.993315i | \(0.536827\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.171573 | + | 0.414214i | 0.0167438 | + | 0.0404231i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.3640 | + | 5.53553i | −1.29194 | + | 0.535140i | −0.919564 | − | 0.392940i | \(-0.871458\pi\) |
−0.372379 | + | 0.928081i | \(0.621458\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.7782 | − | 4.46447i | −1.03236 | − | 0.427618i | −0.198797 | − | 0.980041i | \(-0.563704\pi\) |
−0.833564 | + | 0.552422i | \(0.813704\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.414214 | − | 0.414214i | 0.0393154 | − | 0.0393154i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.12132 | − | 7.53553i | 0.293629 | − | 0.708883i | −0.706370 | − | 0.707842i | \(-0.749669\pi\) |
0.999999 | − | 0.00104094i | \(-0.000331343\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.2426i | 1.14163i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.192388 | − | 1.29289i | 0.0176362 | − | 0.118519i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.36396 | + | 7.36396i | 0.669451 | + | 0.669451i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.89949i | 0.171272i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.65685 | + | 11.2426i | −0.416522 | + | 1.00557i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.24264 | + | 1.24264i | −0.110267 | + | 0.110267i | −0.760087 | − | 0.649821i | \(-0.774844\pi\) |
0.649821 | + | 0.760087i | \(0.274844\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.24264 | − | 3.00000i | −0.637679 | − | 0.264135i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.3640 | + | 5.53553i | −1.16761 | + | 0.483642i | −0.880403 | − | 0.474225i | \(-0.842728\pi\) |
−0.287211 | + | 0.957867i | \(0.592728\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.272078 | + | 0.656854i | 0.0235921 | + | 0.0569565i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.65685 | −0.658997 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.0000 | 1.19610 | 0.598050 | − | 0.801459i | \(-0.295942\pi\) | ||||
0.598050 | + | 0.801459i | \(0.295942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.192388 | + | 0.464466i | 0.0163182 | + | 0.0393955i | 0.931829 | − | 0.362899i | \(-0.118213\pi\) |
−0.915510 | + | 0.402294i | \(0.868213\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.07107 | − | 3.75736i | 0.763922 | − | 0.316427i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.24264 | + | 7.24264i | −0.601469 | + | 0.601469i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.02082 | + | 4.87868i | −0.166674 | + | 0.402387i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 6.34315i | − | 0.519651i | −0.965656 | − | 0.259825i | \(-0.916335\pi\) | ||
0.965656 | − | 0.259825i | \(-0.0836650\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.0711 | − | 14.0711i | −1.14509 | − | 1.14509i | −0.987506 | − | 0.157581i | \(-0.949630\pi\) |
−0.157581 | − | 0.987506i | \(-0.550370\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.53553 | + | 5.12132i | 0.690057 | + | 0.414034i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.00000 | + | 3.00000i | 0.240966 | + | 0.240966i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3137i | 1.22217i | 0.791566 | + | 0.611083i | \(0.209266\pi\) | ||||
−0.791566 | + | 0.611083i | \(0.790734\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.899495 | − | 2.17157i | 0.0713346 | − | 0.172217i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.48528 | − | 1.48528i | 0.117057 | − | 0.117057i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.29289 | − | 1.77817i | −0.336245 | − | 0.139277i | 0.208171 | − | 0.978092i | \(-0.433249\pi\) |
−0.544417 | + | 0.838815i | \(0.683249\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.00000 | + | 0.414214i | −0.0778499 | + | 0.0322465i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.292893 | − | 0.707107i | −0.0226648 | − | 0.0547176i | 0.912142 | − | 0.409874i | \(-0.134427\pi\) |
−0.934807 | + | 0.355157i | \(0.884427\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.41421 | −0.414035 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.22183 | − | 17.4350i | −0.549065 | − | 1.32556i | −0.918175 | − | 0.396175i | \(-0.870337\pi\) |
0.369110 | − | 0.929386i | \(-0.379663\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.464466 | − | 0.192388i | 0.0351103 | − | 0.0145432i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.58579 | − | 2.31371i | −0.419853 | − | 0.173909i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.8995 | − | 12.8995i | 0.964154 | − | 0.964154i | −0.0352259 | − | 0.999379i | \(-0.511215\pi\) |
0.999379 | + | 0.0352259i | \(0.0112151\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.12132 | − | 7.53553i | 0.232006 | − | 0.560112i | −0.764407 | − | 0.644734i | \(-0.776968\pi\) |
0.996413 | + | 0.0846219i | \(0.0269682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.55635i | 0.558581i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.00000 | + | 1.00000i | 0.0735215 | + | 0.0735215i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.12132 | + | 0.464466i | 0.228254 | + | 0.0339651i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.928932 | + | 0.928932i | 0.0675699 | + | 0.0675699i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.82843i | − | 0.638803i | −0.947620 | − | 0.319401i | \(-0.896518\pi\) | ||
0.947620 | − | 0.319401i | \(-0.103482\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.292893 | − | 0.707107i | 0.0210829 | − | 0.0508987i | −0.912987 | − | 0.407988i | \(-0.866231\pi\) |
0.934070 | + | 0.357089i | \(0.116231\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.3640 | + | 4.70711i | 0.809649 | + | 0.335367i | 0.748814 | − | 0.662780i | \(-0.230624\pi\) |
0.0608349 | + | 0.998148i | \(0.480624\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.7782 | − | 8.60660i | 1.47293 | − | 0.610106i | 0.505402 | − | 0.862884i | \(-0.331344\pi\) |
0.967524 | + | 0.252778i | \(0.0813444\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.82843 | − | 6.82843i | −0.199502 | − | 0.481640i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.75736 | 0.123342 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.58579 | −0.320285 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.12132 | + | 14.7782i | 0.425461 | + | 1.02715i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.58579 | + | 0.656854i | −0.109691 | + | 0.0454356i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.1924 | + | 10.0208i | 1.66547 | + | 0.689861i | 0.998475 | − | 0.0551988i | \(-0.0175792\pi\) |
0.666997 | + | 0.745060i | \(0.267579\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.24264 | − | 5.24264i | 0.359220 | − | 0.359220i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.24264 | − | 17.4853i | 0.493944 | − | 1.19249i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.727922i | − | 0.0494146i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.31371 | − | 4.31371i | −0.291493 | − | 0.291493i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.4142 | − | 12.4142i | −0.831317 | − | 0.831317i | 0.156380 | − | 0.987697i | \(-0.450018\pi\) |
−0.987697 | + | 0.156380i | \(0.950018\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.82843i | 0.255228i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.36396 | + | 3.29289i | −0.0905293 | + | 0.218557i | −0.962659 | − | 0.270719i | \(-0.912739\pi\) |
0.872129 | + | 0.489276i | \(0.162739\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | + | 7.00000i | −0.462573 | + | 0.462573i | −0.899498 | − | 0.436925i | \(-0.856068\pi\) |
0.436925 | + | 0.899498i | \(0.356068\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.171573 | + | 0.0710678i | 0.0112887 | + | 0.00467592i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.535534 | − | 0.221825i | 0.0350840 | − | 0.0145323i | −0.365072 | − | 0.930979i | \(-0.618956\pi\) |
0.400156 | + | 0.916447i | \(0.368956\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.07107 | + | 21.8995i | 0.591731 | + | 1.42857i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.9289 | −0.709910 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3137 | 0.731823 | 0.365911 | − | 0.930650i | \(-0.380757\pi\) | ||||
0.365911 | + | 0.930650i | \(0.380757\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.36396 | − | 12.9497i | −0.345523 | − | 0.834167i | −0.997137 | − | 0.0756158i | \(-0.975908\pi\) |
0.651614 | − | 0.758551i | \(-0.274092\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.3640 | + | 5.94975i | −0.921449 | + | 0.381676i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.7782 | − | 4.87868i | −0.752480 | − | 0.311687i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.00000 | + | 7.24264i | −0.190117 | + | 0.458984i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.828427i | 0.0522899i | 0.999658 | + | 0.0261449i | \(0.00832314\pi\) | ||||
−0.999658 | + | 0.0261449i | \(0.991677\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.58579 | + | 3.58579i | 0.225436 | + | 0.225436i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.00000 | − | 5.00000i | 0.187867 | − | 0.313112i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.82843 | − | 5.82843i | −0.363567 | − | 0.363567i | 0.501557 | − | 0.865124i | \(-0.332761\pi\) |
−0.865124 | + | 0.501557i | \(0.832761\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 0.242641i | − | 0.0150770i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.12132 | + | 12.3640i | −0.317002 | + | 0.765310i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.75736 | − | 2.75736i | 0.170026 | − | 0.170026i | −0.616965 | − | 0.786991i | \(-0.711638\pi\) |
0.786991 | + | 0.616965i | \(0.211638\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.24264 | + | 2.17157i | 0.322053 | + | 0.133399i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.17157 | − | 0.485281i | 0.0716991 | − | 0.0296987i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.36396 | − | 12.9497i | −0.327046 | − | 0.789560i | −0.998809 | − | 0.0487934i | \(-0.984462\pi\) |
0.671762 | − | 0.740767i | \(-0.265538\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.3137 | −0.687259 | −0.343629 | − | 0.939105i | \(-0.611656\pi\) | ||||
−0.343629 | + | 0.939105i | \(0.611656\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.464466 | + | 1.12132i | 0.0280084 | + | 0.0676182i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.53553 | − | 3.53553i | 0.512851 | − | 0.212430i | −0.111223 | − | 0.993796i | \(-0.535477\pi\) |
0.624073 | + | 0.781366i | \(0.285477\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.12132 | + | 2.12132i | 0.306605 | + | 0.127000i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.31371 | + | 2.31371i | −0.138024 | + | 0.138024i | −0.772743 | − | 0.634719i | \(-0.781116\pi\) |
0.634719 | + | 0.772743i | \(0.281116\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.0503 | + | 24.2635i | −0.597426 | + | 1.44231i | 0.278770 | + | 0.960358i | \(0.410073\pi\) |
−0.876196 | + | 0.481955i | \(0.839927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.17157i | 0.187868i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.556349 | + | 0.556349i | 0.0328403 | + | 0.0328403i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0000 | + | 8.00000i | −0.882353 | + | 0.470588i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.65685 | + | 8.65685i | 0.507474 | + | 0.507474i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 7.31371i | − | 0.427271i | −0.976913 | − | 0.213636i | \(-0.931469\pi\) | ||
0.976913 | − | 0.213636i | \(-0.0685306\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.58579 | − | 13.4853i | 0.325217 | − | 0.785143i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.24264 | + | 2.24264i | −0.130131 | + | 0.130131i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | + | 1.24264i | −0.172917 | + | 0.0716246i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.92893 | − | 7.07107i | −0.168263 | − | 0.406222i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.2426 | −1.04457 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.6274 | −1.51971 | −0.759853 | − | 0.650094i | \(-0.774729\pi\) | ||||
−0.759853 | + | 0.650094i | \(0.774729\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.686292 | + | 1.65685i | 0.0390418 | + | 0.0942551i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.70711 | + | 1.53553i | −0.210211 | + | 0.0870721i | −0.485304 | − | 0.874345i | \(-0.661291\pi\) |
0.275094 | + | 0.961417i | \(0.411291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.94975 | − | 1.63604i | −0.223253 | − | 0.0924744i | 0.268253 | − | 0.963348i | \(-0.413554\pi\) |
−0.491506 | + | 0.870874i | \(0.663554\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00000 | + | 1.00000i | −0.0563436 | + | 0.0563436i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.05025 | + | 14.6066i | −0.339816 | + | 0.820388i | 0.657917 | + | 0.753091i | \(0.271438\pi\) |
−0.997733 | + | 0.0672979i | \(0.978562\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.24264i | 0.237542i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.82843 | + | 7.82843i | 0.436940 | + | 0.436940i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.75736 | − | 7.92893i | 0.264707 | − | 0.441178i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.92893i | 0.493771i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.55635 | − | 3.75736i | 0.0858043 | − | 0.207150i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.72792 | + | 9.72792i | −0.534695 | + | 0.534695i | −0.921966 | − | 0.387271i | \(-0.873418\pi\) |
0.387271 | + | 0.921966i | \(0.373418\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.70711 | + | 0.707107i | 0.0935489 | + | 0.0387492i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.4853 | − | 6.82843i | 0.900687 | − | 0.373077i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.94975 | + | 14.3640i | 0.324103 | + | 0.782455i | 0.999007 | + | 0.0445491i | \(0.0141851\pi\) |
−0.674904 | + | 0.737906i | \(0.735815\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.24264 | −0.339054 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.75736 | 0.0951663 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.68629 | + | 4.07107i | 0.0910512 | + | 0.219817i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.65685 | − | 3.58579i | 0.466069 | − | 0.193052i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.36396 | + | 2.22183i | 0.287953 | + | 0.119274i | 0.521984 | − | 0.852955i | \(-0.325192\pi\) |
−0.234032 | + | 0.972229i | \(0.575192\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.4853 | + | 15.4853i | −0.828908 | + | 0.828908i | −0.987366 | − | 0.158458i | \(-0.949348\pi\) |
0.158458 | + | 0.987366i | \(0.449348\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 24.9706i | − | 1.32905i | −0.747266 | − | 0.664524i | \(-0.768634\pi\) | ||
0.747266 | − | 0.664524i | \(-0.231366\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.6569 | + | 12.6569i | 0.671756 | + | 0.671756i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.970563 | + | 0.242641i | −0.0513676 | + | 0.0128419i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.7279 | − | 15.7279i | −0.830088 | − | 0.830088i | 0.157440 | − | 0.987528i | \(-0.449676\pi\) |
−0.987528 | + | 0.157440i | \(0.949676\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 13.9706i | − | 0.735293i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.05025 | − | 7.36396i | 0.160097 | − | 0.386508i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.4142 | − | 10.4142i | 0.545105 | − | 0.545105i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.94975 | − | 0.807612i | −0.101776 | − | 0.0421570i | 0.331214 | − | 0.943555i | \(-0.392542\pi\) |
−0.432990 | + | 0.901398i | \(0.642542\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.53553 | + | 2.29289i | −0.288168 | + | 0.119363i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.372583 | − | 0.899495i | −0.0193435 | − | 0.0466995i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.9411 | 1.86096 | 0.930480 | − | 0.366342i | \(-0.119390\pi\) | ||||
0.930480 | + | 0.366342i | \(0.119390\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.31371 | 0.480958 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.9497 | − | 5.77817i | 0.716550 | − | 0.296805i | 0.00553829 | − | 0.999985i | \(-0.498237\pi\) |
0.711012 | + | 0.703180i | \(0.248237\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.24264 | + | 0.514719i | 0.0636624 | + | 0.0263698i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.58579 | + | 7.58579i | −0.387616 | + | 0.387616i | −0.873836 | − | 0.486221i | \(-0.838375\pi\) |
0.486221 | + | 0.873836i | \(0.338375\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.171573 | + | 0.414214i | −0.00874416 | + | 0.0211103i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 24.7279i | − | 1.25699i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.3137 | + | 20.3137i | 1.02995 | + | 1.02995i | 0.999538 | + | 0.0304083i | \(0.00968077\pi\) |
0.0304083 | + | 0.999538i | \(0.490319\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.0208 | − | 4.02082i | −1.36650 | − | 0.203341i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.82843 | + | 7.82843i | 0.394892 | + | 0.394892i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 26.3848i | − | 1.32756i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.1213 | − | 26.8492i | 0.558163 | − | 1.34752i | −0.353056 | − | 0.935602i | \(-0.614857\pi\) |
0.911219 | − | 0.411923i | \(-0.135143\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.384776 | − | 0.384776i | 0.0192629 | − | 0.0192629i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.0208 | + | 10.3640i | 1.24948 | + | 0.517552i | 0.906665 | − | 0.421851i | \(-0.138620\pi\) |
0.342815 | + | 0.939403i | \(0.388620\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.87868 | − | 6.94975i | −0.143043 | − | 0.345336i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.585786 | 0.0290364 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.0000 | 0.890043 | 0.445021 | − | 0.895520i | \(-0.353196\pi\) | ||||
0.445021 | + | 0.895520i | \(0.353196\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.10051 | − | 9.89949i | −0.202263 | − | 0.488306i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.31371 | + | 0.958369i | −0.113850 | + | 0.0471583i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.4853 | − | 7.24264i | −0.858319 | − | 0.355527i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.272078 | − | 0.272078i | 0.0133237 | − | 0.0133237i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.53553 | + | 6.12132i | −0.123869 | + | 0.299046i | −0.973634 | − | 0.228115i | \(-0.926744\pi\) |
0.849765 | + | 0.527161i | \(0.176744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 11.3137i | − | 0.551396i | −0.961244 | − | 0.275698i | \(-0.911091\pi\) | ||
0.961244 | − | 0.275698i | \(-0.0889090\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.8995 | + | 21.8995i | 1.06479 | + | 1.06479i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.60660 | − | 3.36396i | −0.271960 | − | 0.163176i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.21320 | + | 2.21320i | 0.107104 | + | 0.107104i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.878680 | + | 2.12132i | −0.0423245 | + | 0.102180i | −0.943628 | − | 0.331008i | \(-0.892611\pi\) |
0.901304 | + | 0.433188i | \(0.142611\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.82843 | − | 3.82843i | 0.183982 | − | 0.183982i | −0.609106 | − | 0.793089i | \(-0.708472\pi\) |
0.793089 | + | 0.609106i | \(0.208472\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.24264 | + | 3.00000i | 0.347258 | + | 0.143839i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.7279 | − | 5.68629i | 0.656696 | − | 0.272012i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.60660 | − | 8.70711i | −0.172134 | − | 0.415568i | 0.814144 | − | 0.580663i | \(-0.197207\pi\) |
−0.986278 | + | 0.165096i | \(0.947207\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.6569 | −0.793184 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −40.2843 | −1.91396 | −0.956982 | − | 0.290148i | \(-0.906295\pi\) | ||||
−0.956982 | + | 0.290148i | \(0.906295\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.17157 | + | 2.82843i | 0.0555379 | + | 0.134080i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.48528 | + | 1.85786i | −0.212147 | + | 0.0878740i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.5355 | + | 6.84924i | 0.780360 | + | 0.323236i | 0.737061 | − | 0.675826i | \(-0.236213\pi\) |
0.0432993 | + | 0.999062i | \(0.486213\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.34315 | + | 1.34315i | −0.0632463 | + | 0.0632463i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.82843 | + | 14.0711i | −0.273843 | + | 0.661116i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.48528 | − | 3.48528i | −0.163035 | − | 0.163035i | 0.620875 | − | 0.783910i | \(-0.286777\pi\) |
−0.783910 | + | 0.620875i | \(0.786777\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.51472 | − | 16.8995i | 0.117377 | − | 0.788801i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.51472 | − | 2.51472i | −0.117122 | − | 0.117122i | 0.646117 | − | 0.763239i | \(-0.276392\pi\) |
−0.763239 | + | 0.646117i | \(0.776392\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.1421i | 1.12198i | 0.827823 | + | 0.560990i | \(0.189579\pi\) | ||||
−0.827823 | + | 0.560990i | \(0.810421\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.24264 | − | 3.00000i | 0.0576261 | − | 0.139122i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.58579 | − | 9.58579i | 0.443577 | − | 0.443577i | −0.449635 | − | 0.893212i | \(-0.648446\pi\) |
0.893212 | + | 0.449635i | \(0.148446\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.82843 | − | 1.17157i | −0.130605 | − | 0.0540982i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.8284 | − | 4.48528i | 0.498948 | − | 0.206671i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.00000 | − | 7.24264i | −0.137940 | − | 0.333017i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.55635 | 0.163176 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.41421 | 0.339474 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.5355 | + | 35.0919i | 0.664145 | + | 1.60339i | 0.791245 | + | 0.611499i | \(0.209433\pi\) |
−0.127100 | + | 0.991890i | \(0.540567\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.48528 | − | 0.615224i | −0.0675826 | − | 0.0279936i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.8995 | + | 20.8995i | −0.948997 | + | 0.948997i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.73654 | + | 16.2635i | −0.305262 | + | 0.736968i | 0.694584 | + | 0.719412i | \(0.255588\pi\) |
−0.999846 | + | 0.0175559i | \(0.994412\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.55635i | 0.160824i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.4142 | + | 14.4142i | 0.650504 | + | 0.650504i | 0.953114 | − | 0.302610i | \(-0.0978580\pi\) |
−0.302610 | + | 0.953114i | \(0.597858\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.6066 | − | 18.3640i | −0.612811 | − | 0.827071i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.41421 | − | 2.41421i | −0.108511 | − | 0.108511i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 3.07107i | − | 0.137756i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.43503 | − | 15.5355i | 0.288071 | − | 0.695466i | −0.711905 | − | 0.702275i | \(-0.752168\pi\) |
0.999977 | + | 0.00680940i | \(0.00216752\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.414214 | + | 0.414214i | −0.0185057 | + | 0.0185057i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.292893 | − | 0.121320i | −0.0130595 | − | 0.00540941i | 0.376144 | − | 0.926561i | \(-0.377250\pi\) |
−0.389204 | + | 0.921152i | \(0.627250\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.0711 | − | 7.07107i | 0.759653 | − | 0.314658i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.80761 | − | 9.19239i | −0.169102 | − | 0.408248i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.2843 | −1.69692 | −0.848460 | − | 0.529259i | \(-0.822470\pi\) | ||||
−0.848460 | + | 0.529259i | \(0.822470\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.52691 | −0.111784 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.55635 | + | 8.58579i | 0.157017 | + | 0.379072i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.00000 | + | 1.65685i | −0.176261 | + | 0.0730097i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.07107 | + | 3.75736i | 0.398945 | + | 0.165248i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.2132 | + | 10.2132i | −0.448310 | + | 0.448310i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0208 | + | 36.2635i | −0.658074 | + | 1.58873i | 0.142701 | + | 0.989766i | \(0.454421\pi\) |
−0.800775 | + | 0.598965i | \(0.795579\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.14214i | 0.181123i | 0.995891 | + | 0.0905615i | \(0.0288662\pi\) | ||||
−0.995891 | + | 0.0905615i | \(0.971134\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.272078 | − | 0.272078i | −0.0118745 | − | 0.0118745i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.60660 | + | 5.63604i | −0.331349 | + | 0.245510i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.7782 | − | 14.7782i | −0.642529 | − | 0.642529i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 19.0711i | − | 0.827614i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.8995 | + | 18.8995i | −0.817096 | + | 0.817096i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.8995 | − | 5.34315i | −0.556654 | − | 0.230574i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.87868 | + | 2.02082i | −0.210140 | + | 0.0870427i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.94975 | + | 24.0208i | 0.427773 | + | 1.03274i | 0.979992 | + | 0.199036i | \(0.0637812\pi\) |
−0.552219 | + | 0.833699i | \(0.686219\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.24264 | −0.267897 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.5563 | −0.923373 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.2635 | − | 41.6777i | −0.738132 | − | 1.78201i | −0.613330 | − | 0.789827i | \(-0.710170\pi\) |
−0.124802 | − | 0.992182i | \(-0.539830\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.0208 | + | 9.12132i | −0.939825 | + | 0.389288i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.4853 | + | 4.75736i | 0.489289 | + | 0.202670i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.20101 | + | 3.20101i | −0.136121 | + | 0.136121i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.414214 | − | 1.00000i | 0.0175824 | − | 0.0424476i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 16.0000i | − | 0.677942i | −0.940797 | − | 0.338971i | \(-0.889921\pi\) | ||
0.940797 | − | 0.338971i | \(-0.110079\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.585786 | − | 2.34315i | −0.0247319 | − | 0.0989277i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.4142 | + | 18.4142i | 0.776067 | + | 0.776067i | 0.979159 | − | 0.203093i | \(-0.0650993\pi\) |
−0.203093 | + | 0.979159i | \(0.565099\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 15.0711i | − | 0.634045i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.493903 | + | 1.19239i | −0.0207420 | + | 0.0500756i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.3431 | + | 21.3431i | −0.894751 | + | 0.894751i | −0.994966 | − | 0.100215i | \(-0.968047\pi\) |
0.100215 | + | 0.994966i | \(0.468047\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.8492 | + | 12.3640i | 1.24915 | + | 0.517416i | 0.906563 | − | 0.422070i | \(-0.138696\pi\) |
0.342589 | + | 0.939486i | \(0.388696\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.24264 | + | 2.58579i | −0.260790 | + | 0.108023i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.02082 | − | 9.70711i | −0.167680 | − | 0.404814i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0000 | 0.582828 | 0.291414 | − | 0.956597i | \(-0.405874\pi\) | ||||
0.291414 | + | 0.956597i | \(0.405874\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.585786 | −0.0243445 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.24264 | + | 3.00000i | 0.0515534 | + | 0.124461i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.17157 | − | 0.899495i | 0.0899374 | − | 0.0372533i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.27208 | − | 6.27208i | 0.258876 | − | 0.258876i | −0.565721 | − | 0.824597i | \(-0.691402\pi\) |
0.824597 | + | 0.565721i | \(0.191402\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.97056 | − | 4.75736i | 0.0811956 | − | 0.196024i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 9.41421i | − | 0.387249i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.3431 | + | 15.3431i | 0.630067 | + | 0.630067i | 0.948085 | − | 0.318017i | \(-0.103017\pi\) |
−0.318017 | + | 0.948085i | \(0.603017\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.585786 | − | 2.34315i | −0.0240149 | − | 0.0960596i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.1716 | − | 12.1716i | −0.498149 | − | 0.498149i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 44.8284i | 1.83164i | 0.401589 | + | 0.915820i | \(0.368458\pi\) | ||||
−0.401589 | + | 0.915820i | \(0.631542\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.6066 | − | 28.0208i | 0.473443 | − | 1.14299i | −0.489188 | − | 0.872178i | \(-0.662707\pi\) |
0.962631 | − | 0.270815i | \(-0.0872931\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.4853 | − | 16.4853i | 0.671333 | − | 0.671333i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.7782 | + | 7.36396i | 0.722786 | + | 0.299388i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.0919 | − | 14.9497i | 1.46492 | − | 0.606792i | 0.499229 | − | 0.866470i | \(-0.333617\pi\) |
0.965695 | + | 0.259678i | \(0.0836166\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.514719 | − | 1.24264i | −0.0208575 | − | 0.0503543i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.3137 | −1.18397 | −0.591985 | − | 0.805949i | \(-0.701655\pi\) | ||||
−0.591985 | + | 0.805949i | \(0.701655\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.34315 | + | 3.24264i | 0.0541609 | + | 0.130756i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.7782 | + | 9.43503i | −0.917015 | + | 0.379840i | −0.790738 | − | 0.612155i | \(-0.790303\pi\) |
−0.126277 | + | 0.991995i | \(0.540303\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.94975 | − | 0.807612i | −0.0783670 | − | 0.0324607i | 0.343156 | − | 0.939279i | \(-0.388504\pi\) |
−0.421523 | + | 0.906818i | \(0.638504\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19.4142 | − | 19.4142i | 0.779066 | − | 0.779066i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.201010 | − | 0.485281i | 0.00805330 | − | 0.0194424i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5563i | 0.582254i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.928932 | + | 0.928932i | 0.0370980 | + | 0.0370980i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.53553 | + | 1.87868i | −0.101098 | + | 0.0749079i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.3848 | − | 17.3848i | −0.692077 | − | 0.692077i | 0.270612 | − | 0.962689i | \(-0.412774\pi\) |
−0.962689 | + | 0.270612i | \(0.912774\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 20.0416i | − | 0.796583i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.24264 | + | 3.00000i | −0.0493127 | + | 0.119051i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.6066 | + | 8.94975i | 0.854744 | + | 0.354047i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.8787 | − | 4.50610i | 0.429682 | − | 0.177980i | −0.157352 | − | 0.987543i | \(-0.550296\pi\) |
0.587034 | + | 0.809563i | \(0.300296\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.0208 | + | 36.2635i | 0.592363 | + | 1.43009i | 0.881214 | + | 0.472717i | \(0.156727\pi\) |
−0.288851 | + | 0.957374i | \(0.593273\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.4853 | −0.570357 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.2548 | 1.77915 | 0.889576 | − | 0.456788i | \(-0.151000\pi\) | ||||
0.889576 | + | 0.456788i | \(0.151000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.31371 | − | 5.58579i | −0.0908210 | − | 0.219261i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.514719 | + | 0.213203i | −0.0201734 | + | 0.00835610i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.3640 | + | 9.67767i | 0.914302 | + | 0.378716i | 0.789702 | − | 0.613491i | \(-0.210235\pi\) |
0.124600 | + | 0.992207i | \(0.460235\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.8995 | + | 18.8995i | −0.738464 | + | 0.738464i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.36396 | − | 17.7782i | 0.287295 | − | 0.693593i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 22.7696i | − | 0.886976i | −0.896280 | − | 0.443488i | \(-0.853741\pi\) | ||
0.896280 | − | 0.443488i | \(-0.146259\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.7990 | − | 18.7990i | −0.731196 | − | 0.731196i | 0.239661 | − | 0.970857i | \(-0.422964\pi\) |
−0.970857 | + | 0.239661i | \(0.922964\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.928932 | + | 0.928932i | 0.0360224 | + | 0.0360224i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 36.7279i | − | 1.42211i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.14214 | + | 12.4142i | −0.198806 | + | 0.479961i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.34315 | + | 5.34315i | −0.206270 | + | 0.206270i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.1924 | + | 5.87868i | 0.547076 | + | 0.226606i | 0.639064 | − | 0.769154i | \(-0.279322\pi\) |
−0.0919875 | + | 0.995760i | \(0.529322\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.07107 | − | 2.51472i | 0.233676 | − | 0.0967916i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.90812 | − | 9.43503i | −0.150201 | − | 0.362618i | 0.830814 | − | 0.556551i | \(-0.187876\pi\) |
−0.981015 | + | 0.193933i | \(0.937876\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.07107 | 0.194610 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.72792 | 0.104534 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.9792 | − | 31.3345i | −0.496635 | − | 1.19898i | −0.951285 | − | 0.308312i | \(-0.900236\pi\) |
0.454650 | − | 0.890670i | \(-0.349764\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.8995 | − | 9.89949i | 0.913153 | − | 0.378240i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.00000 | + | 2.89949i | 0.267067 | + | 0.110623i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.3934 | + | 29.9203i | −0.471467 | + | 1.13822i | 0.492048 | + | 0.870568i | \(0.336248\pi\) |
−0.963515 | + | 0.267654i | \(0.913752\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.585786i | 0.0222522i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.656854 | + | 0.656854i | 0.0249159 | + | 0.0249159i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.50610 | − | 10.1213i | 0.0570475 | − | 0.383372i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.313708 | − | 0.313708i | −0.0118655 | − | 0.0118655i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.6863i | 1.08347i | 0.840551 | + | 0.541733i | \(0.182232\pi\) | ||||
−0.840551 | + | 0.541733i | \(0.817768\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.656854 | − | 1.58579i | 0.0247737 | − | 0.0598091i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.8284 | − | 12.8284i | 0.483147 | − | 0.483147i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.92893 | − | 1.21320i | −0.110154 | − | 0.0456272i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.1924 | − | 14.1630i | 1.28412 | − | 0.531901i | 0.366894 | − | 0.930263i | \(-0.380421\pi\) |
0.917228 | + | 0.398362i | \(0.130421\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.1924 | − | 31.8492i | −0.494753 | − | 1.19444i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.2132 | −0.569739 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.31371 | − | 8.00000i | −0.123753 | − | 0.298765i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.9497 | − | 7.43503i | 0.669413 | − | 0.277280i | −0.0219807 | − | 0.999758i | \(-0.506997\pi\) |
0.691393 | + | 0.722479i | \(0.256997\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.686292 | + | 0.284271i | 0.0255588 | + | 0.0105868i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.58579 | + | 7.58579i | −0.282118 | + | 0.282118i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.36396 | − | 8.12132i | 0.124934 | − | 0.301618i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 17.7990i | − | 0.660128i | −0.943959 | − | 0.330064i | \(-0.892930\pi\) | ||
0.943959 | − | 0.330064i | \(-0.107070\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.221825 | − | 0.221825i | −0.00821576 | − | 0.00821576i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.2132 | + | 21.7279i | 1.33939 | + | 0.803636i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.4853 | + | 17.4853i | 0.645834 | + | 0.645834i | 0.951983 | − | 0.306150i | \(-0.0990408\pi\) |
−0.306150 | + | 0.951983i | \(0.599041\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.75736i | 0.359906i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.82843 | − | 6.82843i | 0.104186 | − | 0.251528i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.41421 | + | 6.41421i | −0.235951 | + | 0.235951i | −0.815171 | − | 0.579220i | \(-0.803357\pi\) |
0.579220 | + | 0.815171i | \(0.303357\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.8492 | + | 12.3640i | −1.09506 | + | 0.453590i | −0.855769 | − | 0.517358i | \(-0.826916\pi\) |
−0.239293 | + | 0.970947i | \(0.576916\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.48528 | − | 10.8284i | −0.164328 | − | 0.396723i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −24.7279 | −0.904747 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.58579 | 0.167561 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.26346 | − | 22.3640i | −0.338028 | − | 0.816073i | −0.997905 | − | 0.0646985i | \(-0.979391\pi\) |
0.659877 | − | 0.751374i | \(-0.270609\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.585786 | − | 0.242641i | 0.0213472 | − | 0.00884232i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −33.9706 | − | 14.0711i | −1.23632 | − | 0.512099i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.97056 | − | 9.97056i | 0.362386 | − | 0.362386i | −0.502305 | − | 0.864691i | \(-0.667514\pi\) |
0.864691 | + | 0.502305i | \(0.167514\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.48528 | − | 3.58579i | 0.0539123 | − | 0.130156i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3.02944i | − | 0.109817i | −0.998491 | − | 0.0549085i | \(-0.982513\pi\) | ||
0.998491 | − | 0.0549085i | \(-0.0174867\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.61522 | + | 2.61522i | 0.0946775 | + | 0.0946775i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.1924 | + | 2.70711i | 0.657747 | + | 0.0978757i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.5980i | 1.57218i | 0.618110 | + | 0.786092i | \(0.287899\pi\) | ||||
−0.618110 | + | 0.786092i | \(0.712101\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.41421 | + | 5.82843i | −0.0869458 | + | 0.209906i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.2843 | + | 23.2843i | −0.837477 | + | 0.837477i | −0.988526 | − | 0.151049i | \(-0.951735\pi\) |
0.151049 | + | 0.988526i | \(0.451735\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.36396 | − | 1.39340i | −0.120837 | − | 0.0500523i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.171573 | + | 0.0710678i | −0.00615514 | + | 0.00254954i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.12994 | + | 5.14214i | 0.0763131 | + | 0.184236i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.41421 | 0.265301 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.9706 | 0.820901 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.8284 | + | 26.1421i | 0.386483 | + | 0.933053i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.4350 | − | 4.32233i | 0.371969 | − | 0.154074i | −0.188865 | − | 0.982003i | \(-0.560481\pi\) |
0.560833 | + | 0.827929i | \(0.310481\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.75736 | − | 1.14214i | −0.0981646 | − | 0.0406611i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.82843 | + | 1.82843i | −0.0650114 | + | 0.0650114i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 4.34315i | − | 0.154036i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.48528 | + | 9.48528i | 0.335986 | + | 0.335986i | 0.854854 | − | 0.518868i | \(-0.173646\pi\) |
−0.518868 | + | 0.854854i | \(0.673646\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −51.3137 | + | 12.8284i | −1.81535 | + | 0.453837i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.82843 | + | 2.82843i | 0.0999376 | + | 0.0999376i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 6.10051i | − | 0.215282i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.48528 | − | 3.58579i | 0.0523493 | − | 0.126382i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.58579 | + | 7.58579i | −0.267032 | + | 0.267032i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.7782 | − | 6.12132i | −0.519573 | − | 0.215214i | 0.107456 | − | 0.994210i | \(-0.465729\pi\) |
−0.627029 | + | 0.778996i | \(0.715729\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.5061 | + | 16.3640i | −1.38725 | + | 0.574616i | −0.946409 | − | 0.322970i | \(-0.895319\pi\) |
−0.440838 | + | 0.897587i | \(0.645319\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.31371 | + | 8.00000i | 0.116217 | + | 0.280572i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.58579 | −0.300747 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.9706 | −0.803638 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.4350 | + | 18.4056i | −1.55079 | + | 0.642360i | −0.983459 | − | 0.181128i | \(-0.942025\pi\) |
−0.567334 | + | 0.823488i | \(0.692025\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.77817 | − | 3.63604i | −0.305988 | − | 0.126744i | 0.224406 | − | 0.974496i | \(-0.427956\pi\) |
−0.530394 | + | 0.847751i | \(0.677956\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.656854 | − | 0.656854i | 0.0228687 | − | 0.0228687i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.12132 | − | 7.53553i | 0.108539 | − | 0.262036i | −0.860273 | − | 0.509834i | \(-0.829707\pi\) |
0.968812 | + | 0.247798i | \(0.0797068\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 53.9411i | 1.87345i | 0.350062 | + | 0.936726i | \(0.386160\pi\) | ||||
−0.350062 | + | 0.936726i | \(0.613840\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.00000 | − | 5.00000i | −0.173448 | − | 0.173448i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.6360 | − | 24.3934i | 0.507109 | − | 0.845181i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.00000 | − | 1.00000i | −0.0346064 | − | 0.0346064i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 9.51472i | − | 0.328877i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.3640 | + | 32.2635i | −0.461375 | + | 1.11386i | 0.506458 | + | 0.862265i | \(0.330955\pi\) |
−0.967833 | + | 0.251593i | \(0.919045\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.22183 | − | 1.22183i | 0.0421319 | − | 0.0421319i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.31371 | + | 0.958369i | 0.0796884 | + | 0.0330080i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.1924 | − | 9.19239i | 0.763441 | − | 0.316228i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.26346 | − | 3.05025i | −0.0434129 | − | 0.104808i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.1005 | 0.689848 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.07107 | −0.173834 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.05025 | − | 14.6066i | −0.207157 | − | 0.500121i | 0.785817 | − | 0.618460i | \(-0.212243\pi\) |
−0.992973 | + | 0.118339i | \(0.962243\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.24264 | + | 3.82843i | −0.316092 | + | 0.130929i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.36396 | + | 3.05025i | 0.251548 | + | 0.104195i | 0.504895 | − | 0.863181i | \(-0.331531\pi\) |
−0.253347 | + | 0.967376i | \(0.581531\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.7279 | + | 29.7279i | −1.01430 | + | 1.01430i | −0.0144074 | + | 0.999896i | \(0.504586\pi\) |
−0.999896 | + | 0.0144074i | \(0.995414\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.230447 | − | 0.556349i | 0.00785363 | − | 0.0189603i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 15.8579i | − | 0.539808i | −0.962887 | − | 0.269904i | \(-0.913008\pi\) | ||
0.962887 | − | 0.269904i | \(-0.0869920\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.6569 | − | 24.6569i | −0.838358 | − | 0.838358i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.0503 | + | 8.26346i | 0.341324 | + | 0.280642i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.72792 | − | 7.72792i | −0.262152 | − | 0.262152i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.7782 | + | 35.6777i | −0.500165 | + | 1.20751i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.72792 | − | 2.72792i | 0.0922206 | − | 0.0922206i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.77817 | − | 2.80761i | −0.228883 | − | 0.0948063i | 0.265295 | − | 0.964167i | \(-0.414531\pi\) |
−0.494178 | + | 0.869361i | \(0.664531\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.17157 | + | 2.14214i | −0.174433 | + | 0.0722524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.26346 | + | 22.3640i | 0.312094 | + | 0.753461i | 0.999627 | + | 0.0273081i | \(0.00869353\pi\) |
−0.687533 | + | 0.726153i | \(0.741306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.2548 | 1.38834 | 0.694168 | − | 0.719813i | \(-0.255773\pi\) | ||||
0.694168 | + | 0.719813i | \(0.255773\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.1716 | −0.375528 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.84924 | + | 14.1213i | 0.196398 | + | 0.474148i | 0.991143 | − | 0.132796i | \(-0.0423955\pi\) |
−0.794745 | + | 0.606943i | \(0.792395\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.514719 | − | 0.213203i | 0.0172631 | − | 0.00715061i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.87868 | − | 1.19239i | −0.0964394 | − | 0.0399465i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.3431 | − | 20.3431i | 0.680757 | − | 0.680757i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.8995 | − | 31.1421i | 0.431183 | − | 1.04097i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.00000 | − | 9.00000i | −0.300167 | − | 0.300167i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.51472 | + | 10.8579i | −0.217037 | + | 0.361728i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.75736 | + | 1.75736i | 0.0584813 | + | 0.0584813i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 15.0711i | − | 0.500979i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.97918 | − | 21.6777i | 0.298149 | − | 0.719795i | −0.701823 | − | 0.712351i | \(-0.747630\pi\) |
0.999972 | − | 0.00744418i | \(-0.00236958\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.0711 | − | 17.0711i | 0.566212 | − | 0.566212i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.9203 | − | 11.1508i | −0.891910 | − | 0.369441i | −0.110806 | − | 0.993842i | \(-0.535343\pi\) |
−0.781104 | + | 0.624401i | \(0.785343\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.24264 | + | 3.00000i | −0.239696 | + | 0.0992855i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.34315 | + | 12.8995i | 0.176639 | + | 0.426444i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.58579 | 0.151436 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.2843 | 1.46080 | 0.730402 | − | 0.683018i | \(-0.239333\pi\) | ||||
0.730402 | + | 0.683018i | \(0.239333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.79899 | + | 18.8284i | 0.256985 | + | 0.620418i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.12132 | − | 0.464466i | −0.0368688 | − | 0.0152716i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.00000 | + | 4.00000i | −0.131377 | + | 0.131377i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.6360 | − | 25.6777i | 0.348957 | − | 0.842457i | −0.647787 | − | 0.761822i | \(-0.724305\pi\) |
0.996744 | − | 0.0806351i | \(-0.0256949\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.4731i | 0.507110i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.17157 | + | 2.17157i | 0.0710941 | + | 0.0710941i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.65685 | − | 1.41421i | 0.184999 | − | 0.0462497i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.313708 | + | 0.313708i | 0.0102484 | + | 0.0102484i | 0.712212 | − | 0.701964i | \(-0.247693\pi\) |
−0.701964 | + | 0.712212i | \(0.747693\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.27208i | 0.106780i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.9203 | − | 36.0208i | 0.486388 | − | 1.17425i | −0.470136 | − | 0.882594i | \(-0.655795\pi\) |
0.956525 | − | 0.291651i | \(-0.0942047\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.6274 | − | 11.6274i | 0.378641 | − | 0.378641i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.24264 | + | 0.928932i | 0.0729531 | + | 0.0302182i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47.5061 | + | 19.6777i | −1.54374 | + | 0.639438i | −0.982171 | − | 0.187991i | \(-0.939802\pi\) |
−0.561570 | + | 0.827429i | \(0.689802\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.1005 | 0.392386 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −50.0000 | −1.61966 | −0.809829 | − | 0.586665i | \(-0.800440\pi\) | ||||
−0.809829 | + | 0.586665i | \(0.800440\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.24264 | − | 15.0711i | −0.202007 | − | 0.487688i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.00000 | − | 1.24264i | 0.0969762 | − | 0.0401689i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.10051 | − | 1.69848i | −0.132412 | − | 0.0548469i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.1924 | − | 18.1924i | 0.586851 | − | 0.586851i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.3640 | + | 32.2635i | −0.430648 | + | 1.03968i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.41421i | − | 0.0455251i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.4142 | − | 24.4142i | −0.785108 | − | 0.785108i | 0.195580 | − | 0.980688i | \(-0.437341\pi\) |
−0.980688 | + | 0.195580i | \(0.937341\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.00000 | − | 1.04163i | −0.224872 | − | 0.0334620i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.6985 | + | 38.6985i | 1.24189 | + | 1.24189i | 0.959215 | + | 0.282679i | \(0.0912231\pi\) |
0.282679 | + | 0.959215i | \(0.408777\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 0.159380i | − | 0.00510947i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.3137 | − | 24.3137i | 0.777864 | − | 0.777864i | −0.201603 | − | 0.979467i | \(-0.564615\pi\) |
0.979467 | + | 0.201603i | \(0.0646150\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.17157 | + | 0.485281i | 0.0374436 | + | 0.0155097i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.0208 | + | 10.7782i | −0.830781 | + | 0.344121i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.9203 | − | 36.0208i | −0.475884 | − | 1.14889i | −0.961523 | − | 0.274726i | \(-0.911413\pi\) |
0.485639 | − | 0.874160i | \(-0.338587\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.7279 | 0.724172 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.11270 | −0.0990783 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.9706 | + | 62.6985i | 0.825816 | + | 1.99370i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.9203 | − | 19.4350i | 1.49047 | − | 0.617374i | 0.519053 | − | 0.854742i | \(-0.326285\pi\) |
0.971420 | + | 0.237368i | \(0.0762847\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.72792 | + | 4.02944i | 0.308706 | + | 0.127870i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.3848 | − | 29.3848i | 0.931560 | − | 0.931560i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.32233 | − | 8.02082i | 0.105219 | − | 0.254022i | −0.862498 | − | 0.506061i | \(-0.831101\pi\) |
0.967717 | + | 0.252039i | \(0.0811011\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 3.17157i | − | 0.100344i |
(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 | 136.2.n.a.49.1 | yes | 4 | |
3.2 | odd | 2 | 1224.2.bq.a.865.1 | 4 | |||
4.3 | odd | 2 | 272.2.v.e.49.1 | 4 | |||
17.3 | odd | 16 | 2312.2.b.j.577.2 | 4 | |||
17.5 | odd | 16 | 2312.2.a.s.1.3 | 4 | |||
17.8 | even | 8 | inner | 136.2.n.a.25.1 | ✓ | 4 | |
17.12 | odd | 16 | 2312.2.a.s.1.2 | 4 | |||
17.14 | odd | 16 | 2312.2.b.j.577.3 | 4 | |||
51.8 | odd | 8 | 1224.2.bq.a.433.1 | 4 | |||
68.39 | even | 16 | 4624.2.a.bm.1.2 | 4 | |||
68.59 | odd | 8 | 272.2.v.e.161.1 | 4 | |||
68.63 | even | 16 | 4624.2.a.bm.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.2.n.a.25.1 | ✓ | 4 | 17.8 | even | 8 | inner | |
136.2.n.a.49.1 | yes | 4 | 1.1 | even | 1 | trivial | |
272.2.v.e.49.1 | 4 | 4.3 | odd | 2 | |||
272.2.v.e.161.1 | 4 | 68.59 | odd | 8 | |||
1224.2.bq.a.433.1 | 4 | 51.8 | odd | 8 | |||
1224.2.bq.a.865.1 | 4 | 3.2 | odd | 2 | |||
2312.2.a.s.1.2 | 4 | 17.12 | odd | 16 | |||
2312.2.a.s.1.3 | 4 | 17.5 | odd | 16 | |||
2312.2.b.j.577.2 | 4 | 17.3 | odd | 16 | |||
2312.2.b.j.577.3 | 4 | 17.14 | odd | 16 | |||
4624.2.a.bm.1.2 | 4 | 68.39 | even | 16 | |||
4624.2.a.bm.1.3 | 4 | 68.63 | even | 16 |