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 | 515.1 | ||
Root | \(-1.71665 - 2.83780i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 731.515 |
Dual form | 731.2.s.a.687.1 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(e\left(\frac{5}{16}\right)\) | \(-1\) |
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 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(4\) | −1.41421 | + | 1.41421i | −0.707107 | + | 0.707107i | ||||
\(5\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.14805 | + | 2.77164i | −0.382683 | + | 0.923880i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.18533 | − | 3.46473i | −1.56344 | − | 1.04466i | −0.971012 | − | 0.239030i | \(-0.923171\pi\) |
−0.592425 | − | 0.805626i | \(-0.701829\pi\) | |||||||
\(12\) | 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 | ||||||||
\(23\) | 5.18975 | − | 7.76701i | 1.08214 | − | 1.61953i | 0.352337 | − | 0.935873i | \(-0.385387\pi\) |
0.729800 | − | 0.683660i | \(-0.239613\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.61940 | − | 1.91342i | −0.923880 | − | 0.382683i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.27575 | + | 4.19332i | −1.12716 | + | 0.753142i | −0.972054 | − | 0.234756i | \(-0.924571\pi\) |
−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 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.49507 | + | 12.5435i | 0.389664 | + | 1.95897i | 0.245299 | + | 0.969447i | \(0.421114\pi\) |
0.144364 | + | 0.989525i | \(0.453886\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.50942 | − | 6.05828i | 0.382683 | − | 0.923880i | ||||
\(44\) | 12.2330 | − | 2.43330i | 1.84420 | − | 0.366834i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.65010 | − | 9.65010i | −1.40761 | − | 1.40761i | −0.772051 | − | 0.635560i | \(-0.780769\pi\) |
−0.635560 | − | 0.772051i | \(-0.719231\pi\) | |||||||
\(48\) | 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 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(62\) | 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 | \(0.00618416\pi\) | ||||
−0.999811 | + | 0.0194269i | \(0.993816\pi\) | |||||||
\(68\) | 7.12882 | + | 4.14487i | 0.864496 | + | 0.502639i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.23782 | + | 1.49526i | 0.251774 | + | 0.168230i | 0.675053 | − | 0.737769i | \(-0.264121\pi\) |
−0.423279 | + | 0.906000i | \(0.639121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.36396 | − | 6.36396i | −0.707107 | − | 0.707107i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.05828 | + | 2.50942i | −0.664983 | + | 0.275445i | −0.689534 | − | 0.724254i | \(-0.742184\pi\) |
0.0245507 | + | 0.999699i | \(0.492184\pi\) | |||||||
\(84\) | 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 | ||||||||
\(92\) | 3.64480 | + | 18.3236i | 0.379996 | + | 1.91037i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.90386 | − | 1.97000i | −1.00558 | − | 0.200023i | −0.335287 | − | 0.942116i | \(-0.608833\pi\) |
−0.670297 | + | 0.742093i | \(0.733833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.5560 | − | 10.3942i | 1.56344 | − | 1.04466i | ||||
\(100\) | 9.23880 | − | 3.82683i | 0.923880 | − | 0.382683i | ||||
\(101\) | 13.3293i | 1.32631i | 0.748481 | + | 0.663156i | \(0.230783\pi\) | ||||
−0.748481 | + | 0.663156i | \(0.769217\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.1477 | 1.19695 | 0.598473 | − | 0.801143i | \(-0.295775\pi\) | ||||
0.598473 | + | 0.801143i | \(0.295775\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.56062 | + | 17.9005i | −0.344218 | + | 1.73050i | 0.289713 | + | 0.957114i | \(0.406440\pi\) |
−0.633932 | + | 0.773389i | \(0.718560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.08812 | + | 10.4977i | 0.200006 | + | 1.00550i | 0.942133 | + | 0.335239i | \(0.108817\pi\) |
−0.742127 | + | 0.670259i | \(0.766183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(114\) | 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 | ||||||||
\(121\) | 10.6738 | + | 25.7689i | 0.970348 | + | 2.34263i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.94500 | − | 14.8055i | 0.264468 | − | 1.32957i | ||||
\(125\) | 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 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(132\) | 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 | ||||||||
\(139\) | 5.07487 | + | 7.59508i | 0.430445 | + | 0.644206i | 0.981767 | − | 0.190086i | \(-0.0608767\pi\) |
−0.551323 | + | 0.834292i | \(0.685877\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.06047 | − | 15.3860i | −0.255930 | − | 1.28664i | ||||
\(144\) | 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 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(164\) | −21.2678 | − | 14.2107i | −1.66074 | − | 1.10967i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.4510 | − | 14.3331i | 1.65993 | − | 1.10913i | 0.796557 | − | 0.604564i | \(-0.206653\pi\) |
0.863373 | − | 0.504566i | \(-0.168347\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 6.67232i | − | 0.513255i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.01885 | + | 12.1166i | 0.382683 | + | 0.923880i | ||||
\(173\) | −1.75316 | − | 2.62379i | −0.133290 | − | 0.199483i | 0.758820 | − | 0.651300i | \(-0.225776\pi\) |
−0.892111 | + | 0.451817i | \(0.850776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.8589 | + | 20.7413i | −1.04466 | + | 1.56344i | ||||
\(177\) | 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 | ||||||||
\(181\) | −15.3621 | − | 10.2646i | −1.14185 | − | 0.762963i | −0.167034 | − | 0.985951i | \(-0.553419\pi\) |
−0.974821 | + | 0.222988i | \(0.928419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.33943 | + | 24.3232i | −0.609840 | + | 1.77869i | ||||
\(188\) | 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 | ||||||||
\(193\) | −5.30463 | + | 7.93894i | −0.381836 | + | 0.571458i | −0.971751 | − | 0.236007i | \(-0.924161\pi\) |
0.589915 | + | 0.807465i | \(0.299161\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.35757 | − | 12.9343i | 0.382683 | − | 0.923880i | ||||
\(197\) | 22.4474 | − | 4.46506i | 1.59931 | − | 0.318123i | 0.686696 | − | 0.726944i | \(-0.259060\pi\) |
0.912614 | + | 0.408822i | \(0.134060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.5692 | + | 23.3010i | 1.08214 | + | 1.61953i | ||||
\(208\) | 7.11488 | − | 7.11488i | 0.493328 | − | 0.493328i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(212\) | 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 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(228\) | 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 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(234\) | 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 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(242\) | 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 | ||||||||
\(253\) | −53.8212 | + | 22.2935i | −3.38371 | + | 1.40158i | ||||
\(254\) | 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 | ||||
\(269\) | −23.1291 | + | 15.4544i | −1.41021 | + | 0.942269i | −0.410671 | + | 0.911784i | \(0.634705\pi\) |
−0.999535 | + | 0.0304855i | \(0.990295\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.77548i | 0.593818i | 0.954906 | + | 0.296909i | \(0.0959558\pi\) | ||||
−0.954906 | + | 0.296909i | \(0.904044\pi\) | |||||||
\(272\) | −15.9434 | + | 4.21995i | −0.966711 | + | 0.255872i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.3236 | + | 25.9267i | 1.04466 | + | 1.56344i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.41749 | − | 22.2082i | −0.264468 | − | 1.32957i | ||||
\(280\) | 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 | ||||||||
\(283\) | −10.7005 | − | 7.14987i | −0.636081 | − | 0.425015i | 0.195281 | − | 0.980747i | \(-0.437438\pi\) |
−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 | ||||||||
\(299\) | 23.0464 | − | 4.58422i | 1.33281 | − | 0.265112i | ||||
\(300\) | 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 | \(-0.685271\pi\) | ||||
−0.549734 | + | 0.835340i | \(0.685271\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.44493 | − | 7.26417i | 0.0819346 | − | 0.411913i | −0.917950 | − | 0.396697i | \(-0.870156\pi\) |
0.999884 | − | 0.0152162i | \(-0.00484366\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.27937 | + | 1.05013i | −0.296988 | + | 0.0590746i | ||||
\(317\) | 0.329862 | + | 0.220407i | 0.0185269 | + | 0.0123793i | 0.564799 | − | 0.825228i | \(-0.308954\pi\) |
−0.546272 | + | 0.837608i | \(0.683954\pi\) | |||||||
\(318\) | 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 | ||||||||
\(337\) | 21.0712 | − | 14.0793i | 1.14782 | − | 0.766950i | 0.171909 | − | 0.985113i | \(-0.445006\pi\) |
0.975912 | + | 0.218163i | \(0.0700065\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 47.0706 | 2.54901 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(348\) | 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 | \(-0.707822\pi\) |
−0.132119 | − | 0.991234i | \(-0.542178\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | 5.72742 | − | 1.13925i | 0.298969 | − | 0.0594686i | −0.0433266 | − | 0.999061i | \(-0.513796\pi\) |
0.342296 | + | 0.939592i | \(0.388796\pi\) | |||||||
\(368\) | −31.0680 | − | 20.7590i | −1.61953 | − | 1.08214i | ||||
\(369\) | −37.6306 | − | 7.48520i | −1.95897 | − | 0.389664i | ||||
\(370\) | 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 | ||||||||
\(379\) | 6.96013 | − | 34.9909i | 0.357518 | − | 1.79736i | −0.214065 | − | 0.976819i | \(-0.568670\pi\) |
0.571583 | − | 0.820544i | \(-0.306330\pi\) | |||||||
\(380\) | 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 | ||||
\(388\) | 16.7922 | − | 11.2202i | 0.852493 | − | 0.569618i | ||||
\(389\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.4333 | − | 12.4915i | −1.84251 | − | 0.631721i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.29991 | + | 36.6991i | −0.366834 | + | 1.84420i | ||||
\(397\) | −17.5441 | + | 26.2565i | −0.880511 | + | 1.31778i | 0.0669005 | + | 0.997760i | \(0.478689\pi\) |
−0.947411 | + | 0.320018i | \(0.896311\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.65367 | + | 18.4776i | −0.382683 | + | 0.923880i | ||||
\(401\) | −28.3982 | + | 5.64875i | −1.41814 | + | 0.282085i | −0.843854 | − | 0.536572i | \(-0.819719\pi\) |
−0.574283 | + | 0.818657i | \(0.694719\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.6215 | − | 3.70405i | −0.927604 | − | 0.184512i | ||||
\(404\) | −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 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(420\) | 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 | ||||||||
\(428\) | −20.2796 | − | 30.3506i | −0.980251 | − | 1.46705i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.6841 | − | 23.4730i | 0.755478 | − | 1.13065i | −0.231972 | − | 0.972722i | \(-0.574518\pi\) |
0.987450 | − | 0.157930i | \(-0.0504821\pi\) | |||||||
\(432\) | 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 | ||||||||
\(436\) | −17.7991 | − | 11.8930i | −0.852421 | − | 0.569569i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.0408 | − | 6.70905i | 0.479222 | − | 0.320206i | −0.292391 | − | 0.956299i | \(-0.594451\pi\) |
0.771612 | + | 0.636093i | \(0.219451\pi\) | |||||||
\(440\) | 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 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.5222 | − | 73.6872i | 1.43724 | − | 3.46979i | ||||
\(452\) | 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 | \(0.0841604\pi\) |
−0.497748 | + | 0.867322i | \(0.665840\pi\) | |||||||
\(462\) | 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 | ||||||||
\(473\) | −34.0025 | + | 22.7198i | −1.56344 | + | 1.04466i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 43.5596 | 1.99446 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.0088 | + | 31.4419i | 0.959916 | + | 1.43662i | 0.898737 | + | 0.438489i | \(0.144486\pi\) |
0.0611793 | + | 0.998127i | \(0.480514\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −51.5378 | − | 21.3476i | −2.34263 | − | 0.970348i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.92770 | + | 6.63348i | 0.449867 | + | 0.300592i | 0.759788 | − | 0.650171i | \(-0.225303\pi\) |
−0.309921 | + | 0.950762i | \(0.600303\pi\) | |||||||
\(488\) | 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 | ||||||||
\(496\) | 16.7733 | + | 25.1030i | 0.753142 | + | 1.12716i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(504\) | 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 | \(0.366084\pi\) | ||||
−0.408408 | + | 0.912799i | \(0.633916\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.6040 | + | 83.4740i | 0.730243 | + | 3.67118i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(522\) | 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 | ||||||||
\(527\) | 23.3348 | + | 20.5903i | 1.01648 | + | 0.896927i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −24.5912 | − | 59.3684i | −1.06918 | − | 2.58124i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.03218 | − | 5.03218i | 0.218378 | − | 0.218378i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.8734 | + | 26.7495i | −0.774184 | + | 1.15865i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 42.8156 | + | 8.51656i | 1.84420 | + | 0.366834i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.42314 | + | 4.95998i | −0.319146 | + | 0.213246i | −0.704816 | − | 0.709390i | \(-0.748970\pi\) |
0.385670 | + | 0.922637i | \(0.373970\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.3255 | − | 27.4261i | −0.783542 | − | 1.17265i | −0.981315 | − | 0.192406i | \(-0.938371\pi\) |
0.197773 | − | 0.980248i | \(-0.436629\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.9180 | − | 3.56411i | −0.759893 | − | 0.151152i | ||||
\(557\) | 5.23491 | + | 5.23491i | 0.221810 | + | 0.221810i | 0.809260 | − | 0.587450i | \(-0.199868\pi\) |
−0.587450 | + | 0.809260i | \(0.699868\pi\) | |||||||
\(558\) | 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 | −0.619953 | − | 0.784639i | \(-0.712849\pi\) |
−0.993197 | + | 0.116450i | \(0.962849\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(572\) | 26.0873 | + | 17.4310i | 1.09076 | + | 0.728826i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.8350 | + | 25.9487i | −1.61953 | + | 1.08214i | ||||
\(576\) | −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 | ||||||||
\(583\) | −17.6656 | + | 88.8110i | −0.731635 | + | 3.67818i | ||||
\(584\) | 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 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.881469 | − | 0.365116i | −0.0358962 | − | 0.0148687i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(608\) | 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 | \(-0.197303\pi\) | ||||
0.813969 | + | 0.580909i | \(0.197303\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.38651 | + | 27.0798i | −0.216853 | + | 1.09019i | 0.706932 | + | 0.707281i | \(0.250078\pi\) |
−0.923785 | + | 0.382911i | \(0.874922\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.32993 | + | 36.8501i | 0.294615 | + | 1.48113i | 0.790350 | + | 0.612655i | \(0.209899\pi\) |
−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 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.2978 | − | 26.9261i | 1.58919 | − | 1.06186i | 0.630978 | − | 0.775800i | \(-0.282654\pi\) |
0.958211 | − | 0.286062i | \(-0.0923464\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.21900 | + | 12.3006i | 0.322624 | + | 0.482841i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 50.1742 | − | 9.98026i | 1.95897 | − | 0.389664i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.4465 | + | 27.4465i | 1.06916 | + | 1.06916i | 0.997423 | + | 0.0717399i | \(0.0228551\pi\) |
0.0717399 | + | 0.997423i | \(0.477145\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.05828 | + | 2.50942i | −0.235640 | + | 0.0976052i | −0.497379 | − | 0.867533i | \(-0.665704\pi\) |
0.261739 | + | 0.965139i | \(0.415704\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −10.0662 | + | 50.6064i | −0.389475 | + | 1.95802i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.43608 | + | 9.43608i | 0.362926 | + | 0.362926i | ||||
\(677\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.61956 | − | 3.92045i | −0.100235 | − | 0.150012i | 0.777962 | − | 0.628311i | \(-0.216253\pi\) |
−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 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(692\) | 6.18993 | + | 1.23125i | 0.235306 | + | 0.0468053i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 47.3644 | − | 23.1782i | 1.79406 | − | 0.877938i | ||||
\(698\) | 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 | ||||||||
\(704\) | −9.73321 | − | 48.9322i | −0.366834 | − | 1.84420i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.3213 | + | 9.81061i | 1.85230 | + | 0.368445i | 0.990354 | − | 0.138558i | \(-0.0442468\pi\) |
0.861944 | + | 0.507003i | \(0.169247\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.71345 | + | 4.48579i | −0.251774 | + | 0.168230i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 70.5060i | 2.64047i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.45061 | − | 47.5114i | 0.352448 | − | 1.77188i | −0.244551 | − | 0.969636i | \(-0.578641\pi\) |
0.597000 | − | 0.802242i | \(-0.296359\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 36.2416 | − | 7.20891i | 1.34691 | − | 0.267917i | ||||
\(725\) | 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 | ||||||||
\(737\) | 1.10189 | − | 1.64910i | 0.0405888 | − | 0.0607454i | ||||
\(738\) | 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 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 19.6723i | − | 0.719772i | ||||||
\(748\) | −22.6045 | − | 46.1920i | −0.826502 | − | 1.68895i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(752\) | −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 | \(0.519788\pi\) |
−0.998068 | + | 0.0621249i | \(0.980212\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.72548 | − | 18.7292i | −0.134083 | − | 0.674080i | ||||
\(773\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37.0137 | − | 7.36249i | 1.32957 | − | 0.264468i | ||||
\(776\) | 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 | ||||||||
\(787\) | −6.00586 | + | 30.1935i | −0.214086 | + | 1.07628i | 0.712923 | + | 0.701242i | \(0.247371\pi\) |
−0.927009 | + | 0.375040i | \(0.877629\pi\) | |||||||
\(788\) | −25.4309 | + | 38.0600i | −0.905937 | + | 1.35583i | ||||
\(789\) | 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 | ||||||||
\(809\) | 54.7681 | − | 10.8940i | 1.92554 | − | 0.383014i | 0.925552 | − | 0.378620i | \(-0.123601\pi\) |
0.999990 | − | 0.00439415i | \(-0.00139871\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(812\) | 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 | ||||||||
\(821\) | −4.07026 | + | 20.4626i | −0.142053 | + | 0.714150i | 0.842449 | + | 0.538776i | \(0.181113\pi\) |
−0.984502 | + | 0.175373i | \(0.943887\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.53533 | − | 42.9100i | −0.297523 | − | 1.49575i | −0.783288 | − | 0.621659i | \(-0.786459\pi\) |
0.485765 | − | 0.874089i | \(-0.338541\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.7734 | − | 29.9166i | −1.55692 | − | 1.04030i | −0.973655 | − | 0.228024i | \(-0.926773\pi\) |
−0.583269 | − | 0.812279i | \(-0.698227\pi\) | |||||||
\(828\) | −54.9709 | − | 10.9344i | −1.91037 | − | 0.379996i | ||||
\(829\) | 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 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(840\) | 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 | ||||||||
\(853\) | 26.0636 | + | 39.0070i | 0.892402 | + | 1.33557i | 0.941582 | + | 0.336784i | \(0.109339\pi\) |
−0.0491804 | + | 0.998790i | \(0.515661\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.0273 | − | 55.4378i | −0.376684 | − | 1.89372i | −0.444072 | − | 0.895991i | \(-0.646466\pi\) |
0.0673876 | − | 0.997727i | \(-0.478534\pi\) | |||||||
\(858\) | 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 | ||||||||
\(869\) | −6.42315 | − | 15.5069i | −0.217891 | − | 0.526034i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.565689 | + | 0.565689i | −0.0191676 | + | 0.0191676i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.8303 | − | 25.1882i | 0.569618 | − | 0.852493i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.4034 | + | 9.03131i | −1.53317 | + | 0.304966i | −0.888276 | − | 0.459310i | \(-0.848097\pi\) |
−0.644889 | + | 0.764276i | \(0.723097\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.1778 | − | 32.8595i | 1.65684 | − | 1.10707i | 0.780889 | − | 0.624670i | \(-0.214767\pi\) |
0.875953 | − | 0.482396i | \(-0.160233\pi\) | |||||||
\(882\) | 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 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.9499 | + | 55.0487i | 0.366834 | + | 1.84420i | ||||
\(892\) | 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 | ||||||||
\(907\) | −26.2261 | + | 39.2501i | −0.870822 | + | 1.30328i | 0.0810272 | + | 0.996712i | \(0.474180\pi\) |
−0.951849 | + | 0.306566i | \(0.900820\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −36.9439 | − | 15.3027i | −1.22535 | − | 0.507558i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.1087 | + | 7.97812i | 1.32740 | + | 0.264037i | ||||
\(914\) | 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 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(930\) | 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 | ||||||||
\(941\) | −15.7990 | + | 23.6449i | −0.515033 | + | 0.770802i | −0.994272 | − | 0.106883i | \(-0.965913\pi\) |
0.479238 | + | 0.877685i | \(0.340913\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 110.375 | + | 45.7186i | 3.59429 | + | 1.48880i | ||||
\(944\) | −3.63119 | + | 8.76647i | −0.118185 | + | 0.285324i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.3100 | + | 7.22251i | 1.17992 | + | 0.234700i | 0.745808 | − | 0.666160i | \(-0.232063\pi\) |
0.434109 | + | 0.900861i | \(0.357063\pi\) | |||||||
\(948\) | 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 | ||||||||
\(961\) | 9.93787 | − | 23.9921i | 0.320576 | − | 0.773940i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −45.5258 | − | 30.4194i | −1.46705 | − | 0.980251i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51.3952 | + | 21.2886i | −1.65276 | + | 0.684594i | −0.997490 | − | 0.0708031i | \(-0.977444\pi\) |
−0.655267 | + | 0.755397i | \(0.727444\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.2138 | − | 56.0432i | −0.744968 | − | 1.79851i | −0.584363 | − | 0.811493i | \(-0.698655\pi\) |
−0.160605 | − | 0.987019i | \(-0.551345\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.4663 | − | 20.0754i | −1.55057 | − | 0.642268i | −0.567153 | − | 0.823612i | \(-0.691955\pi\) |
−0.983420 | + | 0.181344i | \(0.941955\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31.4931 | − | 6.26437i | −1.00550 | − | 0.200006i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −34.0315 | − | 50.9317i | −1.08214 | − | 1.61953i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(998\) | 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.515.1 | ✓ | 16 | |
17.7 | odd | 16 | inner | 731.2.s.a.687.1 | yes | 16 | |
43.42 | odd | 2 | CM | 731.2.s.a.515.1 | ✓ | 16 | |
731.687 | even | 16 | inner | 731.2.s.a.687.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.s.a.515.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
731.2.s.a.515.1 | ✓ | 16 | 43.42 | odd | 2 | CM | |
731.2.s.a.687.1 | yes | 16 | 17.7 | odd | 16 | inner | |
731.2.s.a.687.1 | yes | 16 | 731.687 | even | 16 | inner |