Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(214,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.214");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.s (of order \(16\), degree \(8\), 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: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{16})\) |
Coefficient field: | 16.0.3289935900927224469054816256.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10319x^{8} + 214358881 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{16}]$ |
Embedding invariants
Embedding label | 343.1 | ||
Root | \(-3.22048 + 0.792772i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 731.343 |
Dual form | 731.2.s.a.601.1 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(e\left(\frac{1}{16}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(3\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(4\) | 1.41421 | − | 1.41421i | 0.707107 | − | 0.707107i | ||||
\(5\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.77164 | + | 1.14805i | 0.923880 | + | 0.382683i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.955307 | − | 4.80265i | −0.288036 | − | 1.44805i | −0.805626 | − | 0.592425i | \(-0.798171\pi\) |
0.517590 | − | 0.855629i | \(-0.326829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.77872 | − | 4.77872i | −1.32538 | − | 1.32538i | −0.909353 | − | 0.416025i | \(-0.863423\pi\) |
−0.416025 | − | 0.909353i | \(-0.636577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | − | 4.00000i | − | 1.00000i | ||||||
\(17\) | 2.07243 | + | 3.56441i | 0.502639 | + | 0.864496i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.47887 | − | 1.08981i | 1.14242 | − | 0.227242i | 0.412622 | − | 0.910902i | \(-0.364613\pi\) |
0.729800 | + | 0.683660i | \(0.239613\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.91342 | + | 4.61940i | −0.382683 | + | 0.923880i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.749168 | − | 3.76632i | 0.134555 | − | 0.676451i | −0.853344 | − | 0.521349i | \(-0.825429\pi\) |
0.987898 | − | 0.155103i | \(-0.0495709\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.54328 | − | 2.29610i | 0.923880 | − | 0.382683i | ||||
\(37\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.38087 | + | 3.56322i | −0.371829 | + | 0.556481i | −0.969447 | − | 0.245299i | \(-0.921114\pi\) |
0.597619 | + | 0.801781i | \(0.296114\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.05828 | + | 2.50942i | 0.923880 | + | 0.382683i | ||||
\(44\) | −8.14298 | − | 5.44097i | −1.22760 | − | 0.820257i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.16199 | − | 6.16199i | −0.898818 | − | 0.898818i | 0.0965136 | − | 0.995332i | \(-0.469231\pi\) |
−0.995332 | + | 0.0965136i | \(0.969231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.67878 | − | 6.46716i | −0.382683 | − | 0.923880i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.5163 | −1.87437 | ||||||||
\(53\) | 10.1933 | − | 4.22221i | 1.40016 | − | 0.579965i | 0.450367 | − | 0.892844i | \(-0.351293\pi\) |
0.949793 | + | 0.312878i | \(0.101293\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.46524 | − | 8.36582i | 0.451135 | − | 1.08914i | −0.520756 | − | 0.853706i | \(-0.674350\pi\) |
0.971891 | − | 0.235431i | \(-0.0756503\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.65685 | − | 5.65685i | −0.707107 | − | 0.707107i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3488i | 1.38647i | 0.720710 | + | 0.693236i | \(0.243816\pi\) | ||||
−0.720710 | + | 0.693236i | \(0.756184\pi\) | |||||||
\(68\) | 7.97170 | + | 2.10997i | 0.966711 | + | 0.255872i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.96615 | + | 14.9118i | 0.333717 | + | 1.67771i | 0.675053 | + | 0.737769i | \(0.264121\pi\) |
−0.341335 | + | 0.939942i | \(0.610879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.36396 | + | 6.36396i | 0.707107 | + | 0.707107i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.50942 | + | 6.05828i | 0.275445 | + | 0.664983i | 0.999699 | − | 0.0245507i | \(-0.00781552\pi\) |
−0.724254 | + | 0.689534i | \(0.757816\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.20706 | − | 9.28952i | 0.647130 | − | 0.968499i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.2049 | + | 10.8277i | −1.64535 | + | 1.09939i | −0.742093 | + | 0.670297i | \(0.766167\pi\) |
−0.903260 | + | 0.429093i | \(0.858833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.86592 | − | 14.4080i | 0.288036 | − | 1.44805i | ||||
\(100\) | 3.82683 | + | 9.23880i | 0.382683 | + | 0.923880i | ||||
\(101\) | − | 20.0631i | − | 1.99636i | −0.0603342 | − | 0.998178i | \(-0.519217\pi\) | ||
0.0603342 | − | 0.998178i | \(-0.480783\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 20.0883 | 1.97936 | 0.989678 | − | 0.143310i | \(-0.0457745\pi\) | ||||
0.989678 | + | 0.143310i | \(0.0457745\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.4391 | + | 17.1198i | 1.10585 | + | 1.65503i | 0.633932 | + | 0.773389i | \(0.281440\pi\) |
0.471923 | + | 0.881640i | \(0.343560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.30560 | + | 13.9268i | −0.891315 | + | 1.33395i | 0.0508181 | + | 0.998708i | \(0.483817\pi\) |
−0.942133 | + | 0.335239i | \(0.891183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.75867 | − | 18.7311i | −0.717290 | − | 1.73169i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.9902 | + | 4.96649i | −1.09002 | + | 0.451499i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.26690 | − | 6.38587i | −0.383179 | − | 0.573468i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00814 | + | 2.43387i | −0.0894583 | + | 0.215971i | −0.962276 | − | 0.272075i | \(-0.912290\pi\) |
0.872818 | + | 0.488046i | \(0.162290\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.2694 | − | 3.23618i | −1.37995 | − | 0.274489i | −0.551323 | − | 0.834292i | \(-0.685877\pi\) |
−0.828626 | + | 0.559803i | \(0.810877\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.3854 | + | 27.5157i | −1.53746 | + | 2.30098i | ||||
\(144\) | 4.59220 | − | 11.0866i | 0.382683 | − | 0.923880i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.65191 | + | 12.2585i | 0.133549 | + | 0.991042i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(164\) | 1.67210 | + | 8.40620i | 0.130569 | + | 0.656414i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.76603 | + | 23.9604i | −0.368806 | + | 1.85411i | 0.135760 | + | 0.990742i | \(0.456653\pi\) |
−0.504566 | + | 0.863373i | \(0.668347\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.6723i | 2.51326i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.1166 | − | 5.01885i | 0.923880 | − | 0.382683i | ||||
\(173\) | 12.6615 | + | 2.51852i | 0.962634 | + | 0.191480i | 0.651300 | − | 0.758820i | \(-0.274224\pi\) |
0.311335 | + | 0.950300i | \(0.399224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −19.2106 | + | 3.82123i | −1.44805 | + | 0.288036i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.14636 | + | 10.7905i | 0.159538 | + | 0.802050i | 0.974821 | + | 0.222988i | \(0.0715812\pi\) |
−0.815283 | + | 0.579062i | \(0.803419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.1388 | − | 13.3583i | 1.10706 | − | 0.976854i | ||||
\(188\) | −17.4287 | −1.27112 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −27.2271 | + | 5.41580i | −1.95985 | + | 0.389838i | −0.971751 | + | 0.236007i | \(0.924161\pi\) |
−0.988097 | + | 0.153831i | \(0.950839\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.9343 | − | 5.35757i | −0.923880 | − | 0.382683i | ||||
\(197\) | 19.7681 | + | 13.2086i | 1.40842 | + | 0.941074i | 0.999595 | + | 0.0284595i | \(0.00906017\pi\) |
0.408822 | + | 0.912614i | \(0.365940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.4366 | + | 3.26944i | 1.14242 | + | 0.227242i | ||||
\(208\) | −19.1149 | + | 19.1149i | −1.32538 | + | 1.32538i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(212\) | 8.44442 | − | 20.3866i | 0.579965 | − | 1.40016i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.12974 | − | 26.9369i | 0.479598 | − | 1.81197i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.6066 | + | 10.6066i | −0.707107 | + | 0.707107i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.0127 | − | 26.5869i | 0.727738 | − | 1.75691i | 0.0777462 | − | 0.996973i | \(-0.475228\pi\) |
0.649992 | − | 0.759941i | \(-0.274772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.93047 | − | 16.7316i | −0.451135 | − | 1.08914i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.5254 | 0.680830 | 0.340415 | − | 0.940275i | \(-0.389432\pi\) | ||||
0.340415 | + | 0.940275i | \(0.389432\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.2213 | + | 12.2213i | 0.771400 | + | 0.771400i | 0.978351 | − | 0.206951i | \(-0.0663540\pi\) |
−0.206951 | + | 0.978351i | \(0.566354\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.4680 | − | 25.2720i | −0.658117 | − | 1.58884i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.0000 | −1.00000 | ||||||||
\(257\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16.0496 | + | 16.0496i | 0.980384 | + | 0.980384i | ||||
\(269\) | 1.05655 | − | 5.31162i | 0.0644188 | − | 0.323855i | −0.935116 | − | 0.354341i | \(-0.884705\pi\) |
0.999535 | + | 0.0304855i | \(0.00970535\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.1434i | 1.77033i | 0.465274 | + | 0.885167i | \(0.345956\pi\) | ||||
−0.465274 | + | 0.885167i | \(0.654044\pi\) | |||||||
\(272\) | 14.2576 | − | 8.28973i | 0.864496 | − | 0.502639i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 24.0133 | + | 4.77653i | 1.44805 | + | 0.288036i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.40035 | − | 9.57880i | 0.383179 | − | 0.573468i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.61715 | + | 2.32670i | 0.335091 | + | 0.138799i | 0.543884 | − | 0.839161i | \(-0.316953\pi\) |
−0.208792 | + | 0.977960i | \(0.566953\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.64044 | − | 23.3291i | −0.275846 | − | 1.38677i | −0.831578 | − | 0.555409i | \(-0.812562\pi\) |
0.555732 | − | 0.831362i | \(-0.312438\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.41004 | + | 14.7740i | −0.494708 | + | 0.869059i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.11488 | + | 2.11488i | −0.123552 | + | 0.123552i | −0.766179 | − | 0.642627i | \(-0.777845\pi\) |
0.642627 | + | 0.766179i | \(0.277845\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31.3899 | − | 20.9740i | −1.81532 | − | 1.21296i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.07703 | 0.403907 | 0.201954 | − | 0.979395i | \(-0.435271\pi\) | ||||
0.201954 | + | 0.979395i | \(0.435271\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.2746 | − | 28.8465i | −1.09296 | − | 1.63573i | −0.696265 | − | 0.717784i | \(-0.745156\pi\) |
−0.396697 | − | 0.917950i | \(-0.629844\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 25.2833 | + | 16.8937i | 1.42229 | + | 0.950347i | ||||
\(317\) | 2.72983 | + | 13.7238i | 0.153323 | + | 0.770804i | 0.978551 | + | 0.206005i | \(0.0660464\pi\) |
−0.825228 | + | 0.564799i | \(0.808954\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 18.0000 | 1.00000 | ||||||||
\(325\) | 31.2185 | − | 12.9311i | 1.73169 | − | 0.717290i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(332\) | 12.1166 | + | 5.01885i | 0.664983 | + | 0.275445i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.55106 | − | 32.9344i | 0.356859 | − | 1.79405i | −0.218163 | − | 0.975912i | \(-0.570006\pi\) |
0.575022 | − | 0.818138i | \(-0.304994\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.8040 | −1.01829 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.7787 | − | 21.7787i | −1.15916 | − | 1.15916i | −0.984656 | − | 0.174509i | \(-0.944166\pi\) |
−0.174509 | − | 0.984656i | \(-0.555834\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.00692 | − | 3.73079i | 0.475367 | − | 0.196903i | −0.132119 | − | 0.991234i | \(-0.542178\pi\) |
0.607486 | + | 0.794330i | \(0.292178\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.4350 | − | 13.4350i | 0.707107 | − | 0.707107i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.56297 | + | 5.05341i | 0.394784 | + | 0.263786i | 0.737079 | − | 0.675806i | \(-0.236204\pi\) |
−0.342296 | + | 0.939592i | \(0.611204\pi\) | |||||||
\(368\) | −4.35926 | − | 21.9155i | −0.227242 | − | 1.14242i | ||||
\(369\) | −10.6897 | + | 7.14260i | −0.556481 | + | 0.371829i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.5895 | − | 23.3313i | −0.800777 | − | 1.19845i | −0.976819 | − | 0.214065i | \(-0.931330\pi\) |
0.176042 | − | 0.984383i | \(-0.443670\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.9104 | + | 13.9104i | 0.707107 | + | 0.707107i | ||||
\(388\) | −7.60439 | + | 38.2298i | −0.386054 | + | 1.94083i | ||||
\(389\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.2391 | + | 17.2704i | 0.770676 | + | 0.873400i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −16.3229 | − | 24.4289i | −0.820257 | − | 1.22760i | ||||
\(397\) | −37.7370 | + | 7.50636i | −1.89397 | + | 0.376734i | −0.997760 | − | 0.0669005i | \(-0.978689\pi\) |
−0.896208 | + | 0.443634i | \(0.853689\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.4776 | + | 7.65367i | 0.923880 | + | 0.382683i | ||||
\(401\) | −31.0466 | − | 20.7447i | −1.55039 | − | 1.03594i | −0.976109 | − | 0.217281i | \(-0.930281\pi\) |
−0.574283 | − | 0.818657i | \(-0.694719\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.5783 | + | 14.4181i | −1.07489 | + | 0.718218i | ||||
\(404\) | −28.3736 | − | 28.3736i | −1.41164 | − | 1.41164i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 28.4091 | − | 28.4091i | 1.39962 | − | 1.39962i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.0045 | − | 24.1531i | −0.486437 | − | 1.17436i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.4309 | + | 2.75319i | −0.991042 | + | 0.133549i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 40.3882 | + | 8.03372i | 1.95224 | + | 0.388325i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.1848 | − | 7.59543i | 1.83930 | − | 0.365859i | 0.851848 | − | 0.523789i | \(-0.175482\pi\) |
0.987450 | + | 0.157930i | \(0.0504821\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.53539 | + | 32.8556i | 0.312988 | + | 1.57350i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.819217 | + | 4.11848i | −0.0390991 | + | 0.196564i | −0.995398 | − | 0.0958262i | \(-0.969451\pi\) |
0.956299 | + | 0.292391i | \(0.0944507\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 21.0000i | − | 1.00000i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.5579 | −1.78443 | −0.892215 | − | 0.451612i | \(-0.850849\pi\) | ||||
−0.892215 | + | 0.451612i | \(0.850849\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.3873 | + | 8.03050i | 0.912915 | + | 0.378142i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.2331 | − | 10.0377i | 1.12865 | − | 0.467502i | 0.261328 | − | 0.965250i | \(-0.415840\pi\) |
0.867322 | + | 0.497748i | \(0.165840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(468\) | −37.4622 | − | 15.5173i | −1.73169 | − | 0.717290i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.26437 | − | 31.4931i | 0.288036 | − | 1.44805i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 33.0995 | 1.51552 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 42.5397 | + | 8.46167i | 1.94369 | + | 0.386624i | 0.998127 | + | 0.0611793i | \(0.0194862\pi\) |
0.945561 | + | 0.325444i | \(0.105514\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.93298 | + | 23.9803i | −0.451499 | + | 1.09002i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.02019 | + | 5.12883i | 0.0462292 | + | 0.232410i | 0.996991 | − | 0.0775113i | \(-0.0246974\pi\) |
−0.950762 | + | 0.309921i | \(0.899697\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.0653 | − | 2.99667i | −0.676451 | − | 0.134555i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.01629 | + | 4.86775i | 0.0894583 | + | 0.215971i | ||||
\(509\) | 42.1546i | 1.86847i | 0.356658 | + | 0.934235i | \(0.383916\pi\) | ||||
−0.356658 | + | 0.934235i | \(0.616084\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.7073 | + | 35.4805i | −1.04265 | + | 1.56043i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.9773 | − | 5.13511i | 0.652422 | − | 0.223689i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.58106 | − | 3.14018i | 0.329611 | − | 0.136529i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.2088 | − | 19.2088i | 0.833589 | − | 0.833589i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.4051 | − | 5.65013i | 1.23036 | − | 0.244734i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −28.5004 | + | 19.0434i | −1.22760 | + | 0.820257i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.56216 | − | 38.0176i | 0.325123 | − | 1.63450i | −0.379693 | − | 0.925113i | \(-0.623970\pi\) |
0.704816 | − | 0.709390i | \(-0.251030\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 42.4330 | + | 8.44044i | 1.81430 | + | 0.360887i | 0.981315 | − | 0.192406i | \(-0.0616291\pi\) |
0.832987 | + | 0.553293i | \(0.186629\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −27.5850 | + | 18.4317i | −1.16986 | + | 0.781678i | ||||
\(557\) | −27.0104 | − | 27.0104i | −1.14447 | − | 1.14447i | −0.987623 | − | 0.156844i | \(-0.949868\pi\) |
−0.156844 | − | 0.987623i | \(-0.550132\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.9590 | − | 40.9427i | −0.717290 | − | 1.73169i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.2141 | − | 9.20140i | 0.936214 | − | 0.387793i | 0.138182 | − | 0.990407i | \(-0.455874\pi\) |
0.798033 | + | 0.602614i | \(0.205874\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.90324 | + | 21.4943i | −0.373243 | + | 0.901088i | 0.619953 | + | 0.784639i | \(0.287151\pi\) |
−0.993197 | + | 0.116450i | \(0.962849\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(572\) | 12.9122 | + | 64.9139i | 0.539885 | + | 2.71419i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.44907 | + | 27.3943i | −0.227242 | + | 1.14242i | ||||
\(576\) | −9.18440 | − | 22.1731i | −0.382683 | − | 0.923880i | ||||
\(577\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.0155 | − | 44.9214i | −1.24312 | − | 1.86046i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.4577 | − | 32.4577i | 1.32618 | − | 1.32618i | 0.417514 | − | 0.908671i | \(-0.362902\pi\) |
0.908671 | − | 0.417514i | \(-0.137098\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.0290 | + | 31.4547i | −0.530580 | + | 1.28093i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 58.8928i | 2.38255i | ||||||||
\(612\) | 19.6723 | + | 15.0000i | 0.795206 | + | 0.606339i | ||||
\(613\) | −48.8406 | −1.97265 | −0.986327 | − | 0.164798i | \(-0.947303\pi\) | ||||
−0.986327 | + | 0.164798i | \(0.947303\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.3282 | + | 22.9402i | 0.617089 | + | 0.923539i | 1.00000 | 0.000246592i | \(-7.84928e-5\pi\) | |
−0.382911 | + | 0.923785i | \(0.625078\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.7335 | − | 37.0163i | 0.994123 | − | 1.48781i | 0.125649 | − | 0.992075i | \(-0.459899\pi\) |
0.868474 | − | 0.495735i | \(-0.165101\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.6777 | − | 17.6777i | −0.707107 | − | 0.707107i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.1036 | + | 43.7059i | −0.717290 | + | 1.73169i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.31034 | + | 31.7242i | −0.248856 | + | 1.25108i | 0.630978 | + | 0.775800i | \(0.282654\pi\) |
−0.879834 | + | 0.475281i | \(0.842346\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −43.4885 | − | 8.65040i | −1.70707 | − | 0.339558i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 14.2529 | + | 9.52346i | 0.556481 | + | 0.371829i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.2107 | − | 36.2107i | −1.41057 | − | 1.41057i | −0.756013 | − | 0.654557i | \(-0.772855\pi\) |
−0.654557 | − | 0.756013i | \(-0.727145\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.50942 | + | 6.05828i | 0.0976052 | + | 0.235640i | 0.965139 | − | 0.261739i | \(-0.0842959\pi\) |
−0.867533 | + | 0.497379i | \(0.834296\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 27.1450 | + | 40.6254i | 1.05027 | + | 1.57184i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 46.2056 | + | 46.2056i | 1.77714 | + | 1.77714i | ||||
\(677\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 48.9386 | + | 9.73449i | 1.87258 | + | 0.372480i | 0.994385 | − | 0.105819i | \(-0.0337466\pi\) |
0.878197 | + | 0.478299i | \(0.158747\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.0377 | − | 24.2331i | 0.382683 | − | 0.923880i | ||||
\(689\) | −68.8878 | − | 28.5342i | −2.62441 | − | 1.08707i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(692\) | 21.4678 | − | 14.3443i | 0.816082 | − | 0.545289i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.6350 | − | 1.10185i | −0.667972 | − | 0.0417357i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.1149 | + | 36.1149i | −1.36404 | + | 1.36404i | −0.495342 | + | 0.868698i | \(0.664957\pi\) |
−0.868698 | + | 0.495342i | \(0.835043\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −21.7639 | + | 32.5719i | −0.820257 | + | 1.22760i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.2064 | + | 29.5378i | −1.66021 | + | 1.10931i | −0.798262 | + | 0.602311i | \(0.794247\pi\) |
−0.861944 | + | 0.507003i | \(0.830753\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.89844 | + | 44.7355i | −0.333717 | + | 1.67771i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 21.4516i | − | 0.803370i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.9729 | − | 29.8915i | −0.744862 | − | 1.11476i | −0.989413 | − | 0.145128i | \(-0.953641\pi\) |
0.244551 | − | 0.969636i | \(-0.421359\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.2955 | + | 12.2246i | 0.679946 | + | 0.454325i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.3325 | + | 24.9447i | 0.382683 | + | 0.923880i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.61077 | + | 26.7948i | 0.133549 | + | 0.991042i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 54.5042 | − | 10.8416i | 2.00769 | − | 0.399354i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.6723i | 0.719772i | ||||||||
\(748\) | 2.51805 | − | 40.3010i | 0.0920691 | − | 1.47355i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(752\) | −24.6479 | + | 24.6479i | −0.898818 | + | 0.898818i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −56.5373 | + | 23.4185i | −2.04144 | + | 0.845594i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.43637 | + | 2.43637i | −0.0878579 | + | 0.0878579i | −0.749670 | − | 0.661812i | \(-0.769788\pi\) |
0.661812 | + | 0.749670i | \(0.269788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −30.8458 | + | 46.1640i | −1.11016 | + | 1.66148i | ||||
\(773\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.9647 | + | 10.6673i | 0.573468 | + | 0.383179i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −25.8686 | + | 10.7151i | −0.923880 | + | 0.382683i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.82852 | − | 8.72299i | −0.207764 | − | 0.310941i | 0.712923 | − | 0.701242i | \(-0.247371\pi\) |
−0.920687 | + | 0.390301i | \(0.872371\pi\) | |||||||
\(788\) | 46.6361 | − | 9.27649i | 1.66134 | − | 0.330461i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.95129 | − | 4.71083i | −0.0691182 | − | 0.166866i | 0.885545 | − | 0.464553i | \(-0.153785\pi\) |
−0.954664 | + | 0.297687i | \(0.903785\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.19354 | − | 34.7342i | 0.325244 | − | 1.22881i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.43130 | − | 6.30180i | −0.331587 | − | 0.221559i | 0.378620 | − | 0.925552i | \(-0.376399\pi\) |
−0.710207 | + | 0.703993i | \(0.751399\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.9597 | − | 34.3617i | −0.801300 | − | 1.19923i | −0.976674 | − | 0.214729i | \(-0.931113\pi\) |
0.175373 | − | 0.984502i | \(-0.443887\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.75114 | + | 14.5936i | −0.339903 | + | 0.508701i | −0.961562 | − | 0.274587i | \(-0.911459\pi\) |
0.621659 | + | 0.783288i | \(0.286459\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.378050 | + | 1.90059i | 0.0131461 | + | 0.0660898i | 0.986801 | − | 0.161935i | \(-0.0517734\pi\) |
−0.973655 | + | 0.228024i | \(0.926773\pi\) | |||||||
\(828\) | 27.8686 | − | 18.6212i | 0.968499 | − | 0.647130i | ||||
\(829\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 54.0650i | 1.87437i | ||||||||
\(833\) | 17.5000 | − | 22.9510i | 0.606339 | − | 0.795206i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0978 | − | 26.7925i | 0.382683 | − | 0.923880i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −16.8888 | − | 40.7733i | −0.579965 | − | 1.40016i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.1426 | + | 9.77506i | 1.68261 | + | 0.334692i | 0.941582 | − | 0.336784i | \(-0.109339\pi\) |
0.741027 | + | 0.671475i | \(0.234339\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.2582 | + | 48.2779i | −1.10192 | + | 1.64914i | −0.444072 | + | 0.895991i | \(0.646466\pi\) |
−0.657849 | + | 0.753150i | \(0.728534\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 68.7827 | − | 28.4907i | 2.33329 | − | 0.966482i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.2326 | − | 54.2326i | 1.83760 | − | 1.83760i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −57.3448 | + | 11.4066i | −1.94083 | + | 0.386054i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.6507 | − | 9.12111i | −0.460952 | − | 0.307998i | 0.303324 | − | 0.952887i | \(-0.401903\pi\) |
−0.764276 | + | 0.644889i | \(0.776903\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.2812 | + | 51.6872i | −0.346383 | + | 1.74139i | 0.278287 | + | 0.960498i | \(0.410233\pi\) |
−0.624670 | + | 0.780889i | \(0.714767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 36.7815i | − | 1.23780i | −0.785471 | − | 0.618899i | \(-0.787579\pi\) | ||
0.785471 | − | 0.618899i | \(-0.212421\pi\) | |||||||
\(884\) | −28.0115 | − | 48.1775i | −0.942130 | − | 1.62038i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.4844 | − | 36.6434i | 0.820257 | − | 1.22760i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 30.0000i | 1.00000i | ||||||||
\(901\) | 36.1747 | + | 27.5829i | 1.20515 | + | 0.918920i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.8160 | − | 11.3014i | 1.88655 | − | 0.375257i | 0.889834 | − | 0.456284i | \(-0.150820\pi\) |
0.996712 | + | 0.0810272i | \(0.0258201\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23.0335 | − | 55.6078i | 0.763973 | − | 1.84439i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.6986 | − | 17.8394i | 0.883593 | − | 0.590398i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.0253 | − | 53.1739i | −0.727738 | − | 1.75691i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.7872 | −1.08155 | −0.540775 | − | 0.841167i | \(-0.681869\pi\) | ||||
−0.540775 | + | 0.841167i | \(0.681869\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 55.6774 | + | 23.0623i | 1.82869 | + | 0.757467i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −59.9330 | + | 11.9214i | −1.95376 | + | 0.388627i | −0.959490 | + | 0.281744i | \(0.909087\pi\) |
−0.994272 | + | 0.106883i | \(0.965913\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.16120 | + | 22.1171i | −0.298330 | + | 0.720232i | ||||
\(944\) | −33.4633 | − | 13.8609i | −1.08914 | − | 0.451135i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.7945 | + | 8.54900i | −0.415765 | + | 0.277805i | −0.745808 | − | 0.666160i | \(-0.767937\pi\) |
0.330044 | + | 0.943966i | \(0.392937\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.8851 | − | 14.8851i | 0.481419 | − | 0.481419i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0163 | + | 6.21997i | 0.484398 | + | 0.200644i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.0506 | + | 60.5824i | 0.388325 | + | 1.95224i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.6420 | + | 25.6920i | 0.342223 | + | 0.826201i | 0.997490 | + | 0.0708031i | \(0.0225562\pi\) |
−0.655267 | + | 0.755397i | \(0.727444\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.2047 | + | 5.46955i | −0.423757 | + | 0.175526i | −0.584363 | − | 0.811493i | \(-0.698655\pi\) |
0.160605 | + | 0.987019i | \(0.448655\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.0754 | − | 48.4663i | 0.642268 | − | 1.55057i | −0.181344 | − | 0.983420i | \(-0.558045\pi\) |
0.823612 | − | 0.567153i | \(-0.191955\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −41.7805 | + | 27.9168i | −1.33395 | + | 0.891315i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 35.9273 | + | 7.14639i | 1.14242 | + | 0.227242i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 731.2.s.a.343.1 | ✓ | 16 | |
17.6 | odd | 16 | inner | 731.2.s.a.601.1 | yes | 16 | |
43.42 | odd | 2 | CM | 731.2.s.a.343.1 | ✓ | 16 | |
731.601 | even | 16 | inner | 731.2.s.a.601.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.s.a.343.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
731.2.s.a.343.1 | ✓ | 16 | 43.42 | odd | 2 | CM | |
731.2.s.a.601.1 | yes | 16 | 17.6 | odd | 16 | inner | |
731.2.s.a.601.1 | yes | 16 | 731.601 | even | 16 | inner |