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 | 386.2 | ||
Root | \(1.71665 + 2.83780i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 731.386 |
Dual form | 731.2.s.a.214.2 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(e\left(\frac{13}{16}\right)\) | \(-1\) |
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 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(3\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(4\) | −1.41421 | + | 1.41421i | −0.707107 | + | 0.707107i | ||||
\(5\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.14805 | − | 2.77164i | 0.382683 | − | 0.923880i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.25563 | − | 1.87919i | 0.378587 | − | 0.566596i | −0.592425 | − | 0.805626i | \(-0.701829\pi\) |
0.971012 | + | 0.239030i | \(0.0768293\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.77872 | + | 1.77872i | 0.493328 | + | 0.493328i | 0.909353 | − | 0.416025i | \(-0.136577\pi\) |
−0.416025 | + | 0.909353i | \(0.636577\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | − | 4.00000i | − | 1.00000i | ||||||
\(17\) | 1.05499 | + | 3.98585i | 0.255872 | + | 0.966711i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.81025 | + | 1.20957i | 0.377463 | + | 0.252213i | 0.729800 | − | 0.683660i | \(-0.239613\pi\) |
−0.352337 | + | 0.935873i | \(0.614613\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.61940 | + | 1.91342i | 0.923880 | + | 0.382683i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.54859 | + | 6.80745i | 0.816952 | + | 1.22265i | 0.972054 | + | 0.234756i | \(0.0754291\pi\) |
−0.155103 | + | 0.987898i | \(0.549571\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.29610 | + | 5.54328i | 0.382683 | + | 0.923880i | ||||
\(37\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.646300 | − | 0.128557i | 0.100935 | − | 0.0200772i | −0.144364 | − | 0.989525i | \(-0.546114\pi\) |
0.245299 | + | 0.969447i | \(0.421114\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.50942 | + | 6.05828i | −0.382683 | + | 0.923880i | ||||
\(44\) | 0.881839 | + | 4.43330i | 0.132942 | + | 0.668346i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.65010 | + | 9.65010i | 1.40761 | + | 1.40761i | 0.772051 | + | 0.635560i | \(0.219231\pi\) |
0.635560 | + | 0.772051i | \(0.280769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.46716 | − | 2.67878i | 0.923880 | − | 0.382683i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.03098 | −0.697671 | ||||||||
\(53\) | −5.55651 | − | 13.4146i | −0.763245 | − | 1.84264i | −0.450367 | − | 0.892844i | \(-0.648707\pi\) |
−0.312878 | − | 0.949793i | \(-0.601293\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.19162 | − | 0.907798i | −0.285324 | − | 0.118185i | 0.235431 | − | 0.971891i | \(-0.424350\pi\) |
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.65685 | + | 5.65685i | 0.707107 | + | 0.707107i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.318032i | − | 0.0388538i | −0.999811 | − | 0.0194269i | \(-0.993816\pi\) | ||
0.999811 | − | 0.0194269i | \(-0.00618416\pi\) | |||||||
\(68\) | −7.12882 | − | 4.14487i | −0.864496 | − | 0.502639i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.76218 | − | 14.6101i | 1.09833 | − | 1.64377i | 0.423279 | − | 0.906000i | \(-0.360879\pi\) |
0.675053 | − | 0.737769i | \(-0.264121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.36396 | − | 6.36396i | −0.707107 | − | 0.707107i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.05828 | − | 2.50942i | 0.664983 | − | 0.275445i | −0.0245507 | − | 0.999699i | \(-0.507816\pi\) |
0.689534 | + | 0.724254i | \(0.257816\pi\) | |||||||
\(84\) | 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 | ||||||||
\(92\) | −4.27067 | + | 0.849489i | −0.445248 | + | 0.0885654i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.29947 | + | 16.5875i | −0.335010 | + | 1.68421i | 0.335287 | + | 0.942116i | \(0.391167\pi\) |
−0.670297 | + | 0.742093i | \(0.733833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.76690 | − | 5.63756i | −0.378587 | − | 0.566596i | ||||
\(100\) | −9.23880 | + | 3.82683i | −0.923880 | + | 0.382683i | ||||
\(101\) | − | 13.3293i | − | 1.32631i | −0.748481 | − | 0.663156i | \(-0.769217\pi\) | ||
0.748481 | − | 0.663156i | \(-0.230783\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.1477 | −1.19695 | −0.598473 | − | 0.801143i | \(-0.704225\pi\) | ||||
−0.598473 | + | 0.801143i | \(0.704225\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.55425 | − | 1.90046i | −0.923645 | − | 0.183724i | −0.289713 | − | 0.957114i | \(-0.593560\pi\) |
−0.633932 | + | 0.773389i | \(0.718560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.5842 | − | 3.49771i | 1.68426 | − | 0.335020i | 0.742127 | − | 0.670259i | \(-0.233817\pi\) |
0.942133 | + | 0.335239i | \(0.108817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.97203 | − | 2.88791i | 0.644564 | − | 0.266987i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.25479 | + | 5.44354i | 0.204981 | + | 0.494867i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −16.0599 | − | 3.19451i | −1.44222 | − | 0.286875i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9023 | − | 5.34430i | −1.14489 | − | 0.474230i | −0.272075 | − | 0.962276i | \(-0.587710\pi\) |
−0.872818 | + | 0.488046i | \(0.837710\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(132\) | 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 | ||||||||
\(139\) | −18.0749 | + | 12.0772i | −1.53309 | + | 1.02438i | −0.551323 | + | 0.834292i | \(0.685877\pi\) |
−0.981767 | + | 0.190086i | \(0.939123\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.57596 | − | 1.10913i | 0.466285 | − | 0.0927499i | ||||
\(144\) | −11.0866 | − | 4.59220i | −0.923880 | − | 0.382683i | ||||
\(145\) | 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 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.2585 | + | 1.65191i | 0.991042 | + | 0.133549i | ||||
\(154\) | 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 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(164\) | −0.732199 | + | 1.09581i | −0.0571751 | + | 0.0855686i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.863457 | + | 1.29225i | 0.0668163 | + | 0.0999976i | 0.863373 | − | 0.504566i | \(-0.168347\pi\) |
−0.796557 | + | 0.604564i | \(0.793347\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 6.67232i | − | 0.513255i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.01885 | − | 12.1166i | −0.382683 | − | 0.923880i | ||||
\(173\) | 21.7146 | − | 14.5092i | 1.65093 | − | 1.10312i | 0.758820 | − | 0.651300i | \(-0.225776\pi\) |
0.892111 | − | 0.451817i | \(-0.149224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.51674 | − | 5.02253i | −0.566596 | − | 0.378587i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.8677 | + | 16.2646i | −0.807788 | + | 1.20894i | 0.167034 | + | 0.985951i | \(0.446581\pi\) |
−0.974821 | + | 0.222988i | \(0.928419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.81483 | + | 3.02224i | 0.644604 | + | 0.221008i | ||||
\(188\) | −27.2946 | −1.99066 | ||||||||
\(189\) | 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 | ||||||||
\(193\) | −21.6954 | − | 14.4964i | −1.56167 | − | 1.04347i | −0.971751 | − | 0.236007i | \(-0.924161\pi\) |
−0.589915 | − | 0.807465i | \(-0.700839\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.35757 | + | 12.9343i | −0.382683 | + | 0.923880i | ||||
\(197\) | 3.17091 | + | 15.9412i | 0.225918 | + | 1.13577i | 0.912614 | + | 0.408822i | \(0.134060\pi\) |
−0.686696 | + | 0.726944i | \(0.740940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.43075 | − | 3.62871i | 0.377463 | − | 0.252213i | ||||
\(208\) | 7.11488 | − | 7.11488i | 0.493328 | − | 0.493328i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(212\) | 26.8292 | + | 11.1130i | 1.84264 | + | 0.763245i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.21318 | + | 8.96623i | −0.350677 | + | 0.603134i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.6066 | − | 10.6066i | 0.707107 | − | 0.707107i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.9231 | − | 10.3235i | −1.64696 | − | 0.682195i | −0.649992 | − | 0.759941i | \(-0.725228\pi\) |
−0.996973 | + | 0.0777462i | \(0.975228\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.38324 | − | 1.81560i | 0.285324 | − | 0.118185i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −29.0726 | −1.88055 | −0.940275 | − | 0.340415i | \(-0.889432\pi\) | ||||
−0.940275 | + | 0.340415i | \(0.889432\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(242\) | 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 | ||||||||
\(251\) | 18.7787 | + | 18.7787i | 1.18530 | + | 1.18530i | 0.978351 | + | 0.206951i | \(0.0663540\pi\) |
0.206951 | + | 0.978351i | \(0.433646\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.54602 | − | 1.88302i | 0.285806 | − | 0.118385i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.0000 | −1.00000 | ||||||||
\(257\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.449765 | + | 0.449765i | 0.0274738 | + | 0.0274738i | ||||
\(269\) | −9.65810 | − | 14.4544i | −0.588865 | − | 0.881298i | 0.410671 | − | 0.911784i | \(-0.365295\pi\) |
−0.999535 | + | 0.0304855i | \(0.990295\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 9.77548i | − | 0.593818i | −0.954906 | − | 0.296909i | \(-0.904044\pi\) | ||
0.954906 | − | 0.296909i | \(-0.0959558\pi\) | |||||||
\(272\) | 15.9434 | − | 4.21995i | 0.966711 | − | 0.255872i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.39593 | − | 6.27816i | 0.566596 | − | 0.378587i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.0898 | − | 4.79176i | 1.44222 | − | 0.286875i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.5669 | − | 25.5107i | 0.630368 | − | 1.52184i | −0.208792 | − | 0.977960i | \(-0.566953\pi\) |
0.839161 | − | 0.543884i | \(-0.183047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.2708 | + | 25.8476i | −1.02664 | + | 1.53648i | −0.195281 | + | 0.980747i | \(0.562562\pi\) |
−0.831362 | + | 0.555732i | \(0.812438\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.7740 | + | 8.41004i | −0.869059 | + | 0.494708i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.1149 | − | 24.1149i | 1.40881 | − | 1.40881i | 0.642627 | − | 0.766179i | \(-0.277845\pi\) |
0.766179 | − | 0.642627i | \(-0.222155\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.06844 | + | 5.37141i | 0.0617895 | + | 0.310637i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.2642 | 1.09947 | 0.549734 | − | 0.835340i | \(-0.314729\pi\) | ||||
0.549734 | + | 0.835340i | \(0.314729\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −33.8214 | − | 6.72749i | −1.91783 | − | 0.381481i | −0.917950 | − | 0.396697i | \(-0.870156\pi\) |
−0.999884 | + | 0.0152162i | \(0.995156\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.85605 | + | 34.4677i | 0.385683 | + | 1.93896i | ||||
\(317\) | 19.7821 | − | 29.6060i | 1.11107 | − | 1.66284i | 0.546272 | − | 0.837608i | \(-0.316046\pi\) |
0.564799 | − | 0.825228i | \(-0.308954\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 18.0000 | 1.00000 | ||||||||
\(325\) | 4.81318 | + | 11.6200i | 0.266987 | + | 0.644564i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(332\) | −5.01885 | + | 12.1166i | −0.275445 | + | 0.664983i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.7595 | + | 22.0892i | 0.804003 | + | 1.20328i | 0.975912 | + | 0.218163i | \(0.0700065\pi\) |
−0.171909 | + | 0.985113i | \(0.554994\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.5038 | 1.00204 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.2213 | − | 15.2213i | −0.810147 | − | 0.810147i | 0.174509 | − | 0.984656i | \(-0.444166\pi\) |
−0.984656 | + | 0.174509i | \(0.944166\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.0135 | + | 33.8316i | 0.739605 | + | 1.78556i | 0.607486 | + | 0.794330i | \(0.292178\pi\) |
0.132119 | + | 0.991234i | \(0.457822\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | 7.38746 | + | 37.1393i | 0.385622 | + | 1.93865i | 0.342296 | + | 0.939592i | \(0.388796\pi\) |
0.0433266 | + | 0.999061i | \(0.486204\pi\) | |||||||
\(368\) | 4.83828 | − | 7.24100i | 0.252213 | − | 0.377463i | ||||
\(369\) | 0.385671 | − | 1.93890i | 0.0200772 | − | 0.100935i | ||||
\(370\) | 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 | ||||||||
\(379\) | −15.2949 | − | 3.04235i | −0.785648 | − | 0.156275i | −0.214065 | − | 0.976819i | \(-0.568670\pi\) |
−0.571583 | + | 0.820544i | \(0.693670\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.9104 | + | 13.9104i | 0.707107 | + | 0.707107i | ||||
\(388\) | −18.7922 | − | 28.1245i | −0.954028 | − | 1.42780i | ||||
\(389\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.91138 | + | 8.49147i | −0.147235 | + | 0.429432i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 13.2999 | + | 2.64552i | 0.668346 | + | 0.132942i | ||||
\(397\) | 20.2100 | + | 13.5039i | 1.01431 | + | 0.677742i | 0.947411 | − | 0.320018i | \(-0.103689\pi\) |
0.0669005 | + | 0.997760i | \(0.478689\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.65367 | − | 18.4776i | 0.382683 | − | 0.923880i | ||||
\(401\) | 5.39817 | + | 27.1384i | 0.269572 | + | 1.35523i | 0.843854 | + | 0.536572i | \(0.180281\pi\) |
−0.574283 | + | 0.818657i | \(0.694719\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.01787 | + | 20.1992i | −0.200145 | + | 1.00619i | ||||
\(404\) | 18.8504 | + | 18.8504i | 0.937844 | + | 0.937844i | ||||
\(405\) | 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 | ||||||||
\(412\) | 17.1794 | − | 17.1794i | 0.846368 | − | 0.846368i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 37.8254 | − | 15.6678i | 1.83913 | − | 0.761794i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.75319 | + | 20.4309i | −0.133549 | + | 0.991042i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 16.1994 | − | 10.8241i | 0.783028 | − | 0.523203i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.3159 | + | 16.9155i | 1.21942 | + | 0.814792i | 0.987450 | − | 0.157930i | \(-0.0504821\pi\) |
0.231972 | + | 0.972722i | \(0.425482\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.9213 | + | 29.8143i | −0.954057 | + | 1.42785i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.2933 | − | 33.3643i | −1.06400 | − | 1.59239i | −0.771612 | − | 0.636093i | \(-0.780549\pi\) |
−0.292391 | − | 0.956299i | \(-0.594451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 21.0000i | − | 1.00000i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.0107 | 0.903223 | 0.451612 | − | 0.892215i | \(-0.350849\pi\) | ||||
0.451612 | + | 0.892215i | \(0.350849\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.569932 | − | 1.37594i | 0.0268371 | − | 0.0647904i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0377 | − | 24.2331i | −0.467502 | − | 1.12865i | −0.965250 | − | 0.261328i | \(-0.915840\pi\) |
0.497748 | − | 0.867322i | \(-0.334160\pi\) | |||||||
\(462\) | 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 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(468\) | −5.77582 | + | 13.9441i | −0.266987 | + | 0.644564i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.23373 | + | 12.3226i | 0.378587 | + | 0.566596i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −43.5596 | −1.99446 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.3308 | + | 12.2483i | −0.837557 | + | 0.559638i | −0.898737 | − | 0.438489i | \(-0.855514\pi\) |
0.0611793 | + | 0.998127i | \(0.480514\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.8871 | − | 4.50958i | −0.494867 | − | 0.204981i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.6064 | + | 35.3295i | −1.06971 | + | 1.60093i | −0.309921 | + | 0.950762i | \(0.600303\pi\) |
−0.759788 | + | 0.650171i | \(0.774697\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 27.2298 | − | 18.1944i | 1.22265 | − | 0.816952i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 25.8046 | − | 10.6886i | 1.14489 | − | 0.474230i | ||||
\(509\) | − | 41.1874i | − | 1.82560i | −0.408408 | − | 0.912799i | \(-0.633916\pi\) | ||
0.408408 | − | 0.912799i | \(-0.366084\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.2513 | − | 6.01736i | 1.33045 | − | 0.264643i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(522\) | 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 | ||||||||
\(527\) | −22.3348 | + | 25.3118i | −0.972918 | + | 1.10260i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.98777 | − | 16.8700i | −0.303816 | − | 0.733477i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.03218 | + | 5.03218i | −0.218378 | + | 0.218378i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.37825 | + | 0.920919i | 0.0596988 | + | 0.0398894i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.08644 | − | 15.5166i | 0.132942 | − | 0.668346i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.3641 | − | 37.9600i | −1.09049 | − | 1.63203i | −0.704816 | − | 0.709390i | \(-0.748970\pi\) |
−0.385670 | − | 0.922637i | \(-0.626030\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.5766 | + | 18.4261i | −1.17909 | + | 0.787842i | −0.981315 | − | 0.192406i | \(-0.938371\pi\) |
−0.197773 | + | 0.980248i | \(0.563371\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.48193 | − | 42.6415i | 0.359714 | − | 1.80840i | ||||
\(557\) | −5.23491 | − | 5.23491i | −0.221810 | − | 0.221810i | 0.587450 | − | 0.809260i | \(-0.300132\pi\) |
−0.809260 | + | 0.587450i | \(0.800132\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.2395 | + | 6.31243i | −0.644564 | + | 0.266987i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.5773 | − | 42.4354i | −0.740796 | − | 1.78844i | −0.602614 | − | 0.798033i | \(-0.705874\pi\) |
−0.138182 | − | 0.990407i | \(-0.544126\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 38.4796 | + | 15.9388i | 1.61315 | + | 0.668189i | 0.993197 | − | 0.116450i | \(-0.0371515\pi\) |
0.619953 | + | 0.784639i | \(0.287151\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(572\) | −6.31706 | + | 9.45414i | −0.264129 | + | 0.395298i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.04785 | + | 9.05125i | 0.252213 | + | 0.377463i | ||||
\(576\) | 22.1731 | − | 9.18440i | 0.923880 | − | 0.382683i | ||||
\(577\) | 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 | ||||||||
\(583\) | −32.1855 | − | 6.40209i | −1.33299 | − | 0.265147i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(594\) | 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 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.881469 | − | 0.365116i | −0.0358962 | − | 0.0148687i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.3296i | 1.38883i | ||||||||
\(612\) | −19.6723 | + | 15.0000i | −0.795206 | + | 0.606339i | ||||
\(613\) | −40.3058 | −1.62794 | −0.813969 | − | 0.580909i | \(-0.802697\pi\) | ||||
−0.813969 | + | 0.580909i | \(0.802697\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.5062 | − | 8.05718i | −1.63072 | − | 0.324370i | −0.706932 | − | 0.707281i | \(-0.749922\pi\) |
−0.923785 | + | 0.382911i | \(0.874922\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.9974 | + | 6.36469i | −1.28609 | + | 0.255818i | −0.790350 | − | 0.612655i | \(-0.790101\pi\) |
−0.495735 | + | 0.868474i | \(0.665101\pi\) | |||||||
\(620\) | 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 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.2681 | + | 6.73845i | 0.644564 | + | 0.266987i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.29778 | − | 12.4185i | −0.327233 | − | 0.489738i | 0.630978 | − | 0.775800i | \(-0.282654\pi\) |
−0.958211 | + | 0.286062i | \(0.907654\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.45779 | + | 2.97860i | −0.174983 | + | 0.116920i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.514228 | − | 2.58520i | −0.0200772 | − | 0.100935i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.4465 | − | 27.4465i | −1.06916 | − | 1.06916i | −0.997423 | − | 0.0717399i | \(-0.977145\pi\) |
−0.0717399 | − | 0.997423i | \(-0.522855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.05828 | − | 2.50942i | 0.235640 | − | 0.0976052i | −0.261739 | − | 0.965139i | \(-0.584296\pi\) |
0.497379 | + | 0.867533i | \(0.334296\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −3.04864 | − | 0.606411i | −0.117955 | − | 0.0234628i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.43608 | + | 9.43608i | 0.362926 | + | 0.362926i | ||||
\(677\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.2825 | + | 28.9204i | −1.65616 | + | 1.10661i | −0.777962 | + | 0.628311i | \(0.783747\pi\) |
−0.878197 | + | 0.478299i | \(0.841253\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 24.2331 | + | 10.0377i | 0.923880 | + | 0.382683i | ||||
\(689\) | 13.9773 | − | 33.7443i | 0.532494 | − | 1.28555i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(692\) | −10.1899 | + | 51.2283i | −0.387363 | + | 1.94741i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.19425 | + | 2.44043i | 0.0452353 | + | 0.0924378i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.88512 | + | 9.88512i | −0.373356 | + | 0.373356i | −0.868698 | − | 0.495342i | \(-0.835043\pi\) |
0.495342 | + | 0.868698i | \(0.335043\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 17.7332 | − | 3.52735i | 0.668346 | − | 0.132942i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.41918 | + | 17.1894i | −0.128410 | + | 0.645561i | 0.861944 | + | 0.507003i | \(0.169247\pi\) |
−0.990354 | + | 0.138558i | \(0.955753\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.2865 | − | 43.8304i | −1.09833 | − | 1.64377i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.8250i | 0.667553i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.5655 | − | 4.48856i | −0.841551 | − | 0.167395i | −0.244551 | − | 0.969636i | \(-0.578641\pi\) |
−0.597000 | + | 0.802242i | \(0.703641\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.63244 | − | 38.3708i | −0.283657 | − | 1.42604i | ||||
\(725\) | 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 | ||||||||
\(729\) | −24.9447 | + | 10.3325i | −0.923880 | + | 0.382683i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.7948 | − | 3.61077i | −0.991042 | − | 0.133549i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.597641 | − | 0.399331i | −0.0220144 | − | 0.0147095i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 19.6723i | − | 0.719772i | ||||||
\(748\) | −16.7402 | + | 8.19195i | −0.612081 | + | 0.299528i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(752\) | 38.6004 | − | 38.6004i | 1.40761 | − | 1.40761i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(758\) | 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 | ||||||||
\(767\) | −2.28356 | − | 5.51299i | −0.0824544 | − | 0.199063i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.4001 | − | 29.4001i | 1.06019 | − | 1.06019i | 0.0621249 | − | 0.998068i | \(-0.480212\pi\) |
0.998068 | − | 0.0621249i | \(-0.0197877\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 51.1829 | − | 10.1809i | 1.84211 | − | 0.366419i | ||||
\(773\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.98627 | + | 40.1497i | 0.286875 | + | 1.44222i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10.7151 | − | 25.8686i | −0.382683 | − | 0.923880i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.0059 | + | 9.15113i | 1.63993 | + | 0.326203i | 0.927009 | − | 0.375040i | \(-0.122371\pi\) |
0.712923 | + | 0.701242i | \(0.247371\pi\) | |||||||
\(788\) | −27.0287 | − | 18.0600i | −0.962856 | − | 0.643360i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.4041 | − | 13.8364i | 1.18323 | − | 0.490111i | 0.297687 | − | 0.954664i | \(-0.403785\pi\) |
0.885545 | + | 0.464553i | \(0.153785\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.2831 | + | 48.6446i | −1.00058 | + | 1.72092i | ||||
\(800\) | 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 | ||||||||
\(809\) | −2.11724 | − | 10.6441i | −0.0744382 | − | 0.374226i | 0.925552 | − | 0.378620i | \(-0.123601\pi\) |
−0.999990 | + | 0.00439415i | \(0.998601\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(812\) | 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 | ||||||||
\(821\) | −52.3478 | − | 10.4126i | −1.82695 | − | 0.363403i | −0.842449 | − | 0.538776i | \(-0.818887\pi\) |
−0.984502 | + | 0.175373i | \(0.943887\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.4066 | + | 7.24172i | −1.26905 | + | 0.252430i | −0.783288 | − | 0.621659i | \(-0.786459\pi\) |
−0.485765 | + | 0.874089i | \(0.661459\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.2266 | + | 16.8018i | −0.390386 | + | 0.584255i | −0.973655 | − | 0.228024i | \(-0.926773\pi\) |
0.583269 | + | 0.812279i | \(0.301773\pi\) | |||||||
\(828\) | −2.54847 | + | 12.8120i | −0.0885654 | + | 0.445248i | ||||
\(829\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 20.1239i | 0.697671i | ||||||||
\(833\) | 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 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.7925 | − | 11.0978i | −0.923880 | − | 0.382683i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −53.6584 | + | 22.2260i | −1.84264 | + | 0.763245i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.9364 | − | 19.3347i | 0.990762 | − | 0.662006i | 0.0491804 | − | 0.998790i | \(-0.484339\pi\) |
0.941582 | + | 0.336784i | \(0.109339\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.9727 | + | 2.97826i | −0.511459 | + | 0.101736i | −0.444072 | − | 0.895991i | \(-0.646466\pi\) |
−0.0673876 | + | 0.997727i | \(0.521466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(860\) | 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 | ||||||||
\(869\) | −15.1975 | − | 36.6899i | −0.515539 | − | 1.24462i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.565689 | − | 0.565689i | 0.0191676 | − | 0.0191676i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 42.1867 | + | 28.1882i | 1.42780 | + | 0.954028i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.20769 | + | 36.2355i | 0.243386 | + | 1.22359i | 0.888276 | + | 0.459310i | \(0.151903\pi\) |
−0.644889 | + | 0.764276i | \(0.723097\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.82168 | − | 4.22294i | −0.0950648 | − | 0.142275i | 0.780889 | − | 0.624670i | \(-0.214767\pi\) |
−0.875953 | + | 0.482396i | \(0.839767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 46.6810i | − | 1.57094i | −0.618899 | − | 0.785471i | \(-0.712421\pi\) | ||
0.618899 | − | 0.785471i | \(-0.287579\pi\) | |||||||
\(884\) | −5.30762 | − | 20.0527i | −0.178514 | − | 0.674446i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.9499 | + | 3.96827i | −0.668346 | + | 0.132942i | ||||
\(892\) | 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 | ||||||||
\(901\) | 47.6065 | − | 36.2996i | 1.58600 | − | 1.20932i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.1066 | + | 20.7847i | 1.03288 | + | 0.690146i | 0.951849 | − | 0.306566i | \(-0.0991799\pi\) |
0.0810272 | + | 0.996712i | \(0.474180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −36.9439 | − | 15.3027i | −1.22535 | − | 0.507558i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.89130 | − | 14.5356i | 0.0956881 | − | 0.481057i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 49.8462 | − | 20.6470i | 1.64696 | − | 0.682195i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.7872 | 1.08155 | 0.540775 | − | 0.841167i | \(-0.318131\pi\) | ||||
0.540775 | + | 0.841167i | \(0.318131\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.9461 | + | 33.6689i | −0.458051 | + | 1.10583i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.2010 | − | 30.2023i | −1.47351 | − | 0.984568i | −0.994272 | − | 0.106883i | \(-0.965913\pi\) |
−0.479238 | − | 0.877685i | \(-0.659087\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.32546 | + | 0.549025i | 0.0431630 | + | 0.0178787i | ||||
\(944\) | −3.63119 | + | 8.76647i | −0.118185 | + | 0.285324i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.59205 | − | 48.2225i | 0.311700 | − | 1.56702i | −0.434109 | − | 0.900861i | \(-0.642937\pi\) |
0.745808 | − | 0.666160i | \(-0.232063\pi\) | |||||||
\(948\) | 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 | ||||||||
\(956\) | 41.1149 | − | 41.1149i | 1.32975 | − | 1.32975i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.7885 | + | 33.2884i | −0.444790 | + | 1.07382i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.2362 | + | 24.2991i | −0.523203 | + | 0.783028i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51.3952 | − | 21.2886i | 1.65276 | − | 0.684594i | 0.655267 | − | 0.755397i | \(-0.272556\pi\) |
0.997490 | + | 0.0708031i | \(0.0225562\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.2138 | + | 56.0432i | 0.744968 | + | 1.79851i | 0.584363 | + | 0.811493i | \(0.301345\pi\) |
0.160605 | + | 0.987019i | \(0.448655\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.4663 | + | 20.0754i | 1.55057 | + | 0.642268i | 0.983420 | − | 0.181344i | \(-0.0580446\pi\) |
0.567153 | + | 0.823612i | \(0.308045\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.4931 | − | 52.7526i | 0.335020 | − | 1.68426i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.8706 | + | 7.93169i | −0.377463 | + | 0.252213i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(998\) | 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.386.2 | yes | 16 | |
17.10 | odd | 16 | inner | 731.2.s.a.214.2 | ✓ | 16 | |
43.42 | odd | 2 | CM | 731.2.s.a.386.2 | yes | 16 | |
731.214 | even | 16 | inner | 731.2.s.a.214.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.s.a.214.2 | ✓ | 16 | 17.10 | odd | 16 | inner | |
731.2.s.a.214.2 | ✓ | 16 | 731.214 | even | 16 | inner | |
731.2.s.a.386.2 | yes | 16 | 1.1 | even | 1 | trivial | |
731.2.s.a.386.2 | yes | 16 | 43.42 | odd | 2 | CM |