Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
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: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.72329.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 9x^{2} + 2x + 15 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.11664\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.59680 | 1.16132 | 0.580662 | − | 0.814145i | \(-0.302794\pi\) | ||||
0.580662 | + | 0.814145i | \(0.302794\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.51984 | 0.574445 | 0.287223 | − | 0.957864i | \(-0.407268\pi\) | ||||
0.287223 | + | 0.957864i | \(0.407268\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.59680 | 0.821180 | ||||||||
\(11\) | 4.86001 | 1.46535 | 0.732674 | − | 0.680579i | \(-0.238272\pi\) | ||||
0.732674 | + | 0.680579i | \(0.238272\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 1.51984 | 0.406194 | ||||||||
\(15\) | 2.59680 | 0.670491 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −6.23328 | −1.43001 | −0.715006 | − | 0.699118i | \(-0.753576\pi\) | ||||
−0.715006 | + | 0.699118i | \(0.753576\pi\) | |||||||
\(20\) | 2.59680 | 0.580662 | ||||||||
\(21\) | 1.51984 | 0.331656 | ||||||||
\(22\) | 4.86001 | 1.03616 | ||||||||
\(23\) | −3.23328 | −0.674185 | −0.337093 | − | 0.941472i | \(-0.609444\pi\) | ||||
−0.337093 | + | 0.941472i | \(0.609444\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.74337 | 0.348674 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.51984 | 0.287223 | ||||||||
\(29\) | 4.97665 | 0.924141 | 0.462070 | − | 0.886843i | \(-0.347107\pi\) | ||||
0.462070 | + | 0.886843i | \(0.347107\pi\) | |||||||
\(30\) | 2.59680 | 0.474109 | ||||||||
\(31\) | 6.23328 | 1.11953 | 0.559765 | − | 0.828651i | \(-0.310891\pi\) | ||||
0.559765 | + | 0.828651i | \(0.310891\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.86001 | 0.846019 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 3.94672 | 0.667117 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.86001 | −1.12778 | −0.563889 | − | 0.825850i | \(-0.690696\pi\) | ||||
−0.563889 | + | 0.825850i | \(0.690696\pi\) | |||||||
\(38\) | −6.23328 | −1.01117 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 2.59680 | 0.410590 | ||||||||
\(41\) | −0.193601 | −0.0302354 | −0.0151177 | − | 0.999886i | \(-0.504812\pi\) | ||||
−0.0151177 | + | 0.999886i | \(0.504812\pi\) | |||||||
\(42\) | 1.51984 | 0.234516 | ||||||||
\(43\) | 3.13999 | 0.478844 | 0.239422 | − | 0.970916i | \(-0.423042\pi\) | ||||
0.239422 | + | 0.970916i | \(0.423042\pi\) | |||||||
\(44\) | 4.86001 | 0.732674 | ||||||||
\(45\) | 2.59680 | 0.387108 | ||||||||
\(46\) | −3.23328 | −0.476721 | ||||||||
\(47\) | −7.83666 | −1.14309 | −0.571547 | − | 0.820569i | \(-0.693657\pi\) | ||||
−0.571547 | + | 0.820569i | \(0.693657\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −4.69009 | −0.670013 | ||||||||
\(50\) | 1.74337 | 0.246550 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 3.47358 | 0.477133 | 0.238566 | − | 0.971126i | \(-0.423323\pi\) | ||||
0.238566 | + | 0.971126i | \(0.423323\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 12.6205 | 1.70175 | ||||||||
\(56\) | 1.51984 | 0.203097 | ||||||||
\(57\) | −6.23328 | −0.825618 | ||||||||
\(58\) | 4.97665 | 0.653466 | ||||||||
\(59\) | 2.65983 | 0.346280 | 0.173140 | − | 0.984897i | \(-0.444609\pi\) | ||||
0.173140 | + | 0.984897i | \(0.444609\pi\) | |||||||
\(60\) | 2.59680 | 0.335245 | ||||||||
\(61\) | 5.09329 | 0.652129 | 0.326064 | − | 0.945348i | \(-0.394277\pi\) | ||||
0.326064 | + | 0.945348i | \(0.394277\pi\) | |||||||
\(62\) | 6.23328 | 0.791627 | ||||||||
\(63\) | 1.51984 | 0.191482 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.59680 | 0.322093 | ||||||||
\(66\) | 4.86001 | 0.598226 | ||||||||
\(67\) | 8.83008 | 1.07877 | 0.539383 | − | 0.842061i | \(-0.318658\pi\) | ||||
0.539383 | + | 0.842061i | \(0.318658\pi\) | |||||||
\(68\) | 2.00000 | 0.242536 | ||||||||
\(69\) | −3.23328 | −0.389241 | ||||||||
\(70\) | 3.94672 | 0.471723 | ||||||||
\(71\) | −12.5404 | −1.48827 | −0.744133 | − | 0.668031i | \(-0.767137\pi\) | ||||
−0.744133 | + | 0.668031i | \(0.767137\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 9.93697 | 1.16303 | 0.581517 | − | 0.813534i | \(-0.302459\pi\) | ||||
0.581517 | + | 0.813534i | \(0.302459\pi\) | |||||||
\(74\) | −6.86001 | −0.797460 | ||||||||
\(75\) | 1.74337 | 0.201307 | ||||||||
\(76\) | −6.23328 | −0.715006 | ||||||||
\(77\) | 7.38643 | 0.841762 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 3.42688 | 0.385554 | 0.192777 | − | 0.981243i | \(-0.438251\pi\) | ||||
0.192777 | + | 0.981243i | \(0.438251\pi\) | |||||||
\(80\) | 2.59680 | 0.290331 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.193601 | −0.0213796 | ||||||||
\(83\) | −6.59680 | −0.724093 | −0.362046 | − | 0.932160i | \(-0.617922\pi\) | ||||
−0.362046 | + | 0.932160i | \(0.617922\pi\) | |||||||
\(84\) | 1.51984 | 0.165828 | ||||||||
\(85\) | 5.19360 | 0.563325 | ||||||||
\(86\) | 3.13999 | 0.338594 | ||||||||
\(87\) | 4.97665 | 0.533553 | ||||||||
\(88\) | 4.86001 | 0.518079 | ||||||||
\(89\) | −12.9136 | −1.36884 | −0.684421 | − | 0.729087i | \(-0.739945\pi\) | ||||
−0.684421 | + | 0.729087i | \(0.739945\pi\) | |||||||
\(90\) | 2.59680 | 0.273727 | ||||||||
\(91\) | 1.51984 | 0.159322 | ||||||||
\(92\) | −3.23328 | −0.337093 | ||||||||
\(93\) | 6.23328 | 0.646361 | ||||||||
\(94\) | −7.83666 | −0.808290 | ||||||||
\(95\) | −16.1866 | −1.66071 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 12.9005 | 1.30984 | 0.654921 | − | 0.755697i | \(-0.272702\pi\) | ||||
0.654921 | + | 0.755697i | \(0.272702\pi\) | |||||||
\(98\) | −4.69009 | −0.473771 | ||||||||
\(99\) | 4.86001 | 0.488450 | ||||||||
\(100\) | 1.74337 | 0.174337 | ||||||||
\(101\) | −10.0069 | −0.995725 | −0.497863 | − | 0.867256i | \(-0.665882\pi\) | ||||
−0.497863 | + | 0.867256i | \(0.665882\pi\) | |||||||
\(102\) | 2.00000 | 0.198030 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 3.94672 | 0.385160 | ||||||||
\(106\) | 3.47358 | 0.337384 | ||||||||
\(107\) | 15.7200 | 1.51971 | 0.759856 | − | 0.650091i | \(-0.225269\pi\) | ||||
0.759856 | + | 0.650091i | \(0.225269\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −17.7138 | −1.69667 | −0.848336 | − | 0.529459i | \(-0.822395\pi\) | ||||
−0.848336 | + | 0.529459i | \(0.822395\pi\) | |||||||
\(110\) | 12.6205 | 1.20332 | ||||||||
\(111\) | −6.86001 | −0.651123 | ||||||||
\(112\) | 1.51984 | 0.143611 | ||||||||
\(113\) | 2.79698 | 0.263118 | 0.131559 | − | 0.991308i | \(-0.458002\pi\) | ||||
0.131559 | + | 0.991308i | \(0.458002\pi\) | |||||||
\(114\) | −6.23328 | −0.583800 | ||||||||
\(115\) | −8.39618 | −0.782948 | ||||||||
\(116\) | 4.97665 | 0.462070 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 2.65983 | 0.244857 | ||||||||
\(119\) | 3.03968 | 0.278647 | ||||||||
\(120\) | 2.59680 | 0.237054 | ||||||||
\(121\) | 12.6197 | 1.14725 | ||||||||
\(122\) | 5.09329 | 0.461125 | ||||||||
\(123\) | −0.193601 | −0.0174564 | ||||||||
\(124\) | 6.23328 | 0.559765 | ||||||||
\(125\) | −8.45681 | −0.756400 | ||||||||
\(126\) | 1.51984 | 0.135398 | ||||||||
\(127\) | −2.55293 | −0.226536 | −0.113268 | − | 0.993564i | \(-0.536132\pi\) | ||||
−0.113268 | + | 0.993564i | \(0.536132\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.13999 | 0.276461 | ||||||||
\(130\) | 2.59680 | 0.227754 | ||||||||
\(131\) | −6.68035 | −0.583665 | −0.291832 | − | 0.956470i | \(-0.594265\pi\) | ||||
−0.291832 | + | 0.956470i | \(0.594265\pi\) | |||||||
\(132\) | 4.86001 | 0.423010 | ||||||||
\(133\) | −9.47358 | −0.821463 | ||||||||
\(134\) | 8.83008 | 0.762803 | ||||||||
\(135\) | 2.59680 | 0.223497 | ||||||||
\(136\) | 2.00000 | 0.171499 | ||||||||
\(137\) | −12.9467 | −1.10611 | −0.553056 | − | 0.833144i | \(-0.686539\pi\) | ||||
−0.553056 | + | 0.833144i | \(0.686539\pi\) | |||||||
\(138\) | −3.23328 | −0.275235 | ||||||||
\(139\) | −7.80015 | −0.661600 | −0.330800 | − | 0.943701i | \(-0.607319\pi\) | ||||
−0.330800 | + | 0.943701i | \(0.607319\pi\) | |||||||
\(140\) | 3.94672 | 0.333559 | ||||||||
\(141\) | −7.83666 | −0.659966 | ||||||||
\(142\) | −12.5404 | −1.05236 | ||||||||
\(143\) | 4.86001 | 0.406415 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 12.9234 | 1.07323 | ||||||||
\(146\) | 9.93697 | 0.822390 | ||||||||
\(147\) | −4.69009 | −0.386832 | ||||||||
\(148\) | −6.86001 | −0.563889 | ||||||||
\(149\) | 6.05361 | 0.495931 | 0.247966 | − | 0.968769i | \(-0.420238\pi\) | ||||
0.247966 | + | 0.968769i | \(0.420238\pi\) | |||||||
\(150\) | 1.74337 | 0.142346 | ||||||||
\(151\) | −22.5738 | −1.83703 | −0.918514 | − | 0.395388i | \(-0.870610\pi\) | ||||
−0.918514 | + | 0.395388i | \(0.870610\pi\) | |||||||
\(152\) | −6.23328 | −0.505586 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 7.38643 | 0.595216 | ||||||||
\(155\) | 16.1866 | 1.30014 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 9.13057 | 0.728699 | 0.364350 | − | 0.931262i | \(-0.381291\pi\) | ||||
0.364350 | + | 0.931262i | \(0.381291\pi\) | |||||||
\(158\) | 3.42688 | 0.272628 | ||||||||
\(159\) | 3.47358 | 0.275473 | ||||||||
\(160\) | 2.59680 | 0.205295 | ||||||||
\(161\) | −4.91406 | −0.387282 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −5.94639 | −0.465757 | −0.232879 | − | 0.972506i | \(-0.574814\pi\) | ||||
−0.232879 | + | 0.972506i | \(0.574814\pi\) | |||||||
\(164\) | −0.193601 | −0.0151177 | ||||||||
\(165\) | 12.6205 | 0.982503 | ||||||||
\(166\) | −6.59680 | −0.512011 | ||||||||
\(167\) | 10.3405 | 0.800172 | 0.400086 | − | 0.916478i | \(-0.368980\pi\) | ||||
0.400086 | + | 0.916478i | \(0.368980\pi\) | |||||||
\(168\) | 1.51984 | 0.117258 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 5.19360 | 0.398331 | ||||||||
\(171\) | −6.23328 | −0.476671 | ||||||||
\(172\) | 3.13999 | 0.239422 | ||||||||
\(173\) | −15.0933 | −1.14752 | −0.573761 | − | 0.819023i | \(-0.694516\pi\) | ||||
−0.573761 | + | 0.819023i | \(0.694516\pi\) | |||||||
\(174\) | 4.97665 | 0.377279 | ||||||||
\(175\) | 2.64964 | 0.200294 | ||||||||
\(176\) | 4.86001 | 0.366337 | ||||||||
\(177\) | 2.65983 | 0.199925 | ||||||||
\(178\) | −12.9136 | −0.967917 | ||||||||
\(179\) | −2.84684 | −0.212783 | −0.106392 | − | 0.994324i | \(-0.533930\pi\) | ||||
−0.106392 | + | 0.994324i | \(0.533930\pi\) | |||||||
\(180\) | 2.59680 | 0.193554 | ||||||||
\(181\) | 8.38720 | 0.623416 | 0.311708 | − | 0.950178i | \(-0.399099\pi\) | ||||
0.311708 | + | 0.950178i | \(0.399099\pi\) | |||||||
\(182\) | 1.51984 | 0.112658 | ||||||||
\(183\) | 5.09329 | 0.376507 | ||||||||
\(184\) | −3.23328 | −0.238360 | ||||||||
\(185\) | −17.8141 | −1.30972 | ||||||||
\(186\) | 6.23328 | 0.457046 | ||||||||
\(187\) | 9.72002 | 0.710798 | ||||||||
\(188\) | −7.83666 | −0.571547 | ||||||||
\(189\) | 1.51984 | 0.110552 | ||||||||
\(190\) | −16.1866 | −1.17430 | ||||||||
\(191\) | 17.9533 | 1.29906 | 0.649528 | − | 0.760338i | \(-0.274967\pi\) | ||||
0.649528 | + | 0.760338i | \(0.274967\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 13.9669 | 1.00536 | 0.502680 | − | 0.864473i | \(-0.332347\pi\) | ||||
0.502680 | + | 0.864473i | \(0.332347\pi\) | |||||||
\(194\) | 12.9005 | 0.926199 | ||||||||
\(195\) | 2.59680 | 0.185961 | ||||||||
\(196\) | −4.69009 | −0.335006 | ||||||||
\(197\) | 7.78305 | 0.554519 | 0.277260 | − | 0.960795i | \(-0.410574\pi\) | ||||
0.277260 | + | 0.960795i | \(0.410574\pi\) | |||||||
\(198\) | 4.86001 | 0.345386 | ||||||||
\(199\) | −4.71344 | −0.334127 | −0.167063 | − | 0.985946i | \(-0.553428\pi\) | ||||
−0.167063 | + | 0.985946i | \(0.553428\pi\) | |||||||
\(200\) | 1.74337 | 0.123275 | ||||||||
\(201\) | 8.83008 | 0.622826 | ||||||||
\(202\) | −10.0069 | −0.704084 | ||||||||
\(203\) | 7.56371 | 0.530868 | ||||||||
\(204\) | 2.00000 | 0.140028 | ||||||||
\(205\) | −0.502743 | −0.0351131 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | −3.23328 | −0.224728 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −30.2938 | −2.09547 | ||||||||
\(210\) | 3.94672 | 0.272349 | ||||||||
\(211\) | −21.4338 | −1.47556 | −0.737782 | − | 0.675040i | \(-0.764127\pi\) | ||||
−0.737782 | + | 0.675040i | \(0.764127\pi\) | |||||||
\(212\) | 3.47358 | 0.238566 | ||||||||
\(213\) | −12.5404 | −0.859251 | ||||||||
\(214\) | 15.7200 | 1.07460 | ||||||||
\(215\) | 8.15392 | 0.556093 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 9.47358 | 0.643108 | ||||||||
\(218\) | −17.7138 | −1.19973 | ||||||||
\(219\) | 9.93697 | 0.671478 | ||||||||
\(220\) | 12.6205 | 0.850873 | ||||||||
\(221\) | 2.00000 | 0.134535 | ||||||||
\(222\) | −6.86001 | −0.460414 | ||||||||
\(223\) | 11.9160 | 0.797956 | 0.398978 | − | 0.916961i | \(-0.369365\pi\) | ||||
0.398978 | + | 0.916961i | \(0.369365\pi\) | |||||||
\(224\) | 1.51984 | 0.101548 | ||||||||
\(225\) | 1.74337 | 0.116225 | ||||||||
\(226\) | 2.79698 | 0.186053 | ||||||||
\(227\) | −11.1469 | −0.739846 | −0.369923 | − | 0.929062i | \(-0.620616\pi\) | ||||
−0.369923 | + | 0.929062i | \(0.620616\pi\) | |||||||
\(228\) | −6.23328 | −0.412809 | ||||||||
\(229\) | 10.4805 | 0.692570 | 0.346285 | − | 0.938129i | \(-0.387443\pi\) | ||||
0.346285 | + | 0.938129i | \(0.387443\pi\) | |||||||
\(230\) | −8.39618 | −0.553628 | ||||||||
\(231\) | 7.38643 | 0.485992 | ||||||||
\(232\) | 4.97665 | 0.326733 | ||||||||
\(233\) | 18.8141 | 1.23255 | 0.616276 | − | 0.787530i | \(-0.288641\pi\) | ||||
0.616276 | + | 0.787530i | \(0.288641\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −20.3502 | −1.32750 | ||||||||
\(236\) | 2.65983 | 0.173140 | ||||||||
\(237\) | 3.42688 | 0.222600 | ||||||||
\(238\) | 3.03968 | 0.197033 | ||||||||
\(239\) | −23.3203 | −1.50847 | −0.754233 | − | 0.656607i | \(-0.771991\pi\) | ||||
−0.754233 | + | 0.656607i | \(0.771991\pi\) | |||||||
\(240\) | 2.59680 | 0.167623 | ||||||||
\(241\) | −9.31263 | −0.599879 | −0.299940 | − | 0.953958i | \(-0.596967\pi\) | ||||
−0.299940 | + | 0.953958i | \(0.596967\pi\) | |||||||
\(242\) | 12.6197 | 0.811226 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 5.09329 | 0.326064 | ||||||||
\(245\) | −12.1792 | −0.778102 | ||||||||
\(246\) | −0.193601 | −0.0123435 | ||||||||
\(247\) | −6.23328 | −0.396614 | ||||||||
\(248\) | 6.23328 | 0.395814 | ||||||||
\(249\) | −6.59680 | −0.418055 | ||||||||
\(250\) | −8.45681 | −0.534856 | ||||||||
\(251\) | −7.04387 | −0.444605 | −0.222302 | − | 0.974978i | \(-0.571357\pi\) | ||||
−0.222302 | + | 0.974978i | \(0.571357\pi\) | |||||||
\(252\) | 1.51984 | 0.0957408 | ||||||||
\(253\) | −15.7138 | −0.987916 | ||||||||
\(254\) | −2.55293 | −0.160185 | ||||||||
\(255\) | 5.19360 | 0.325236 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.04001 | −0.376765 | −0.188383 | − | 0.982096i | \(-0.560325\pi\) | ||||
−0.188383 | + | 0.982096i | \(0.560325\pi\) | |||||||
\(258\) | 3.13999 | 0.195487 | ||||||||
\(259\) | −10.4261 | −0.647847 | ||||||||
\(260\) | 2.59680 | 0.161047 | ||||||||
\(261\) | 4.97665 | 0.308047 | ||||||||
\(262\) | −6.68035 | −0.412713 | ||||||||
\(263\) | −19.5194 | −1.20362 | −0.601809 | − | 0.798640i | \(-0.705553\pi\) | ||||
−0.601809 | + | 0.798640i | \(0.705553\pi\) | |||||||
\(264\) | 4.86001 | 0.299113 | ||||||||
\(265\) | 9.02019 | 0.554106 | ||||||||
\(266\) | −9.47358 | −0.580862 | ||||||||
\(267\) | −12.9136 | −0.790301 | ||||||||
\(268\) | 8.83008 | 0.539383 | ||||||||
\(269\) | −5.23045 | −0.318906 | −0.159453 | − | 0.987206i | \(-0.550973\pi\) | ||||
−0.159453 | + | 0.987206i | \(0.550973\pi\) | |||||||
\(270\) | 2.59680 | 0.158036 | ||||||||
\(271\) | −1.08638 | −0.0659926 | −0.0329963 | − | 0.999455i | \(-0.510505\pi\) | ||||
−0.0329963 | + | 0.999455i | \(0.510505\pi\) | |||||||
\(272\) | 2.00000 | 0.121268 | ||||||||
\(273\) | 1.51984 | 0.0919848 | ||||||||
\(274\) | −12.9467 | −0.782140 | ||||||||
\(275\) | 8.47281 | 0.510930 | ||||||||
\(276\) | −3.23328 | −0.194620 | ||||||||
\(277\) | 7.85343 | 0.471867 | 0.235933 | − | 0.971769i | \(-0.424185\pi\) | ||||
0.235933 | + | 0.971769i | \(0.424185\pi\) | |||||||
\(278\) | −7.80015 | −0.467822 | ||||||||
\(279\) | 6.23328 | 0.373177 | ||||||||
\(280\) | 3.94672 | 0.235862 | ||||||||
\(281\) | 29.0535 | 1.73319 | 0.866593 | − | 0.499015i | \(-0.166305\pi\) | ||||
0.866593 | + | 0.499015i | \(0.166305\pi\) | |||||||
\(282\) | −7.83666 | −0.466666 | ||||||||
\(283\) | −10.6594 | −0.633635 | −0.316817 | − | 0.948487i | \(-0.602614\pi\) | ||||
−0.316817 | + | 0.948487i | \(0.602614\pi\) | |||||||
\(284\) | −12.5404 | −0.744133 | ||||||||
\(285\) | −16.1866 | −0.958810 | ||||||||
\(286\) | 4.86001 | 0.287379 | ||||||||
\(287\) | −0.294242 | −0.0173686 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 12.9234 | 0.758886 | ||||||||
\(291\) | 12.9005 | 0.756238 | ||||||||
\(292\) | 9.93697 | 0.581517 | ||||||||
\(293\) | −18.4143 | −1.07578 | −0.537888 | − | 0.843017i | \(-0.680778\pi\) | ||||
−0.537888 | + | 0.843017i | \(0.680778\pi\) | |||||||
\(294\) | −4.69009 | −0.273532 | ||||||||
\(295\) | 6.90704 | 0.402143 | ||||||||
\(296\) | −6.86001 | −0.398730 | ||||||||
\(297\) | 4.86001 | 0.282006 | ||||||||
\(298\) | 6.05361 | 0.350676 | ||||||||
\(299\) | −3.23328 | −0.186985 | ||||||||
\(300\) | 1.74337 | 0.100654 | ||||||||
\(301\) | 4.77228 | 0.275069 | ||||||||
\(302\) | −22.5738 | −1.29898 | ||||||||
\(303\) | −10.0069 | −0.574882 | ||||||||
\(304\) | −6.23328 | −0.357503 | ||||||||
\(305\) | 13.2263 | 0.757333 | ||||||||
\(306\) | 2.00000 | 0.114332 | ||||||||
\(307\) | −7.92620 | −0.452372 | −0.226186 | − | 0.974084i | \(-0.572626\pi\) | ||||
−0.226186 | + | 0.974084i | \(0.572626\pi\) | |||||||
\(308\) | 7.38643 | 0.420881 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 16.1866 | 0.919336 | ||||||||
\(311\) | 4.06259 | 0.230368 | 0.115184 | − | 0.993344i | \(-0.463254\pi\) | ||||
0.115184 | + | 0.993344i | \(0.463254\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 4.20018 | 0.237408 | 0.118704 | − | 0.992930i | \(-0.462126\pi\) | ||||
0.118704 | + | 0.992930i | \(0.462126\pi\) | |||||||
\(314\) | 9.13057 | 0.515268 | ||||||||
\(315\) | 3.94672 | 0.222372 | ||||||||
\(316\) | 3.42688 | 0.192777 | ||||||||
\(317\) | −6.43390 | −0.361364 | −0.180682 | − | 0.983542i | \(-0.557830\pi\) | ||||
−0.180682 | + | 0.983542i | \(0.557830\pi\) | |||||||
\(318\) | 3.47358 | 0.194789 | ||||||||
\(319\) | 24.1866 | 1.35419 | ||||||||
\(320\) | 2.59680 | 0.145166 | ||||||||
\(321\) | 15.7200 | 0.877406 | ||||||||
\(322\) | −4.91406 | −0.273850 | ||||||||
\(323\) | −12.4666 | −0.693658 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.74337 | 0.0967049 | ||||||||
\(326\) | −5.94639 | −0.329340 | ||||||||
\(327\) | −17.7138 | −0.979574 | ||||||||
\(328\) | −0.193601 | −0.0106898 | ||||||||
\(329\) | −11.9105 | −0.656645 | ||||||||
\(330\) | 12.6205 | 0.694735 | ||||||||
\(331\) | −28.9168 | −1.58941 | −0.794705 | − | 0.606996i | \(-0.792375\pi\) | ||||
−0.794705 | + | 0.606996i | \(0.792375\pi\) | |||||||
\(332\) | −6.59680 | −0.362046 | ||||||||
\(333\) | −6.86001 | −0.375926 | ||||||||
\(334\) | 10.3405 | 0.565807 | ||||||||
\(335\) | 22.9300 | 1.25280 | ||||||||
\(336\) | 1.51984 | 0.0829140 | ||||||||
\(337\) | −6.53344 | −0.355899 | −0.177950 | − | 0.984040i | \(-0.556946\pi\) | ||||
−0.177950 | + | 0.984040i | \(0.556946\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 2.79698 | 0.151911 | ||||||||
\(340\) | 5.19360 | 0.281663 | ||||||||
\(341\) | 30.2938 | 1.64050 | ||||||||
\(342\) | −6.23328 | −0.337057 | ||||||||
\(343\) | −17.7671 | −0.959331 | ||||||||
\(344\) | 3.13999 | 0.169297 | ||||||||
\(345\) | −8.39618 | −0.452035 | ||||||||
\(346\) | −15.0933 | −0.811420 | ||||||||
\(347\) | 33.7931 | 1.81411 | 0.907055 | − | 0.421012i | \(-0.138325\pi\) | ||||
0.907055 | + | 0.421012i | \(0.138325\pi\) | |||||||
\(348\) | 4.97665 | 0.266776 | ||||||||
\(349\) | 21.1748 | 1.13346 | 0.566730 | − | 0.823904i | \(-0.308208\pi\) | ||||
0.566730 | + | 0.823904i | \(0.308208\pi\) | |||||||
\(350\) | 2.64964 | 0.141629 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 4.86001 | 0.259039 | ||||||||
\(353\) | 1.87395 | 0.0997401 | 0.0498701 | − | 0.998756i | \(-0.484119\pi\) | ||||
0.0498701 | + | 0.998756i | \(0.484119\pi\) | |||||||
\(354\) | 2.65983 | 0.141368 | ||||||||
\(355\) | −32.5648 | −1.72836 | ||||||||
\(356\) | −12.9136 | −0.684421 | ||||||||
\(357\) | 3.03968 | 0.160877 | ||||||||
\(358\) | −2.84684 | −0.150460 | ||||||||
\(359\) | 17.7395 | 0.936256 | 0.468128 | − | 0.883661i | \(-0.344929\pi\) | ||||
0.468128 | + | 0.883661i | \(0.344929\pi\) | |||||||
\(360\) | 2.59680 | 0.136863 | ||||||||
\(361\) | 19.8538 | 1.04493 | ||||||||
\(362\) | 8.38720 | 0.440822 | ||||||||
\(363\) | 12.6197 | 0.662363 | ||||||||
\(364\) | 1.51984 | 0.0796612 | ||||||||
\(365\) | 25.8043 | 1.35066 | ||||||||
\(366\) | 5.09329 | 0.266231 | ||||||||
\(367\) | 31.5536 | 1.64708 | 0.823542 | − | 0.567255i | \(-0.191995\pi\) | ||||
0.823542 | + | 0.567255i | \(0.191995\pi\) | |||||||
\(368\) | −3.23328 | −0.168546 | ||||||||
\(369\) | −0.193601 | −0.0100785 | ||||||||
\(370\) | −17.8141 | −0.926110 | ||||||||
\(371\) | 5.27928 | 0.274086 | ||||||||
\(372\) | 6.23328 | 0.323180 | ||||||||
\(373\) | −22.9804 | −1.18988 | −0.594940 | − | 0.803770i | \(-0.702824\pi\) | ||||
−0.594940 | + | 0.803770i | \(0.702824\pi\) | |||||||
\(374\) | 9.72002 | 0.502610 | ||||||||
\(375\) | −8.45681 | −0.436708 | ||||||||
\(376\) | −7.83666 | −0.404145 | ||||||||
\(377\) | 4.97665 | 0.256311 | ||||||||
\(378\) | 1.51984 | 0.0781721 | ||||||||
\(379\) | 34.0810 | 1.75063 | 0.875313 | − | 0.483557i | \(-0.160655\pi\) | ||||
0.875313 | + | 0.483557i | \(0.160655\pi\) | |||||||
\(380\) | −16.1866 | −0.830354 | ||||||||
\(381\) | −2.55293 | −0.130791 | ||||||||
\(382\) | 17.9533 | 0.918571 | ||||||||
\(383\) | 11.2462 | 0.574653 | 0.287327 | − | 0.957833i | \(-0.407234\pi\) | ||||
0.287327 | + | 0.957833i | \(0.407234\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 19.1811 | 0.977559 | ||||||||
\(386\) | 13.9669 | 0.710897 | ||||||||
\(387\) | 3.13999 | 0.159615 | ||||||||
\(388\) | 12.9005 | 0.654921 | ||||||||
\(389\) | 5.06063 | 0.256584 | 0.128292 | − | 0.991736i | \(-0.459050\pi\) | ||||
0.128292 | + | 0.991736i | \(0.459050\pi\) | |||||||
\(390\) | 2.59680 | 0.131494 | ||||||||
\(391\) | −6.46656 | −0.327028 | ||||||||
\(392\) | −4.69009 | −0.236885 | ||||||||
\(393\) | −6.68035 | −0.336979 | ||||||||
\(394\) | 7.78305 | 0.392104 | ||||||||
\(395\) | 8.89892 | 0.447753 | ||||||||
\(396\) | 4.86001 | 0.244225 | ||||||||
\(397\) | 10.7597 | 0.540014 | 0.270007 | − | 0.962858i | \(-0.412974\pi\) | ||||
0.270007 | + | 0.962858i | \(0.412974\pi\) | |||||||
\(398\) | −4.71344 | −0.236263 | ||||||||
\(399\) | −9.47358 | −0.474272 | ||||||||
\(400\) | 1.74337 | 0.0871686 | ||||||||
\(401\) | 5.44048 | 0.271685 | 0.135842 | − | 0.990730i | \(-0.456626\pi\) | ||||
0.135842 | + | 0.990730i | \(0.456626\pi\) | |||||||
\(402\) | 8.83008 | 0.440404 | ||||||||
\(403\) | 6.23328 | 0.310502 | ||||||||
\(404\) | −10.0069 | −0.497863 | ||||||||
\(405\) | 2.59680 | 0.129036 | ||||||||
\(406\) | 7.56371 | 0.375380 | ||||||||
\(407\) | −33.3397 | −1.65259 | ||||||||
\(408\) | 2.00000 | 0.0990148 | ||||||||
\(409\) | 9.94013 | 0.491508 | 0.245754 | − | 0.969332i | \(-0.420964\pi\) | ||||
0.245754 | + | 0.969332i | \(0.420964\pi\) | |||||||
\(410\) | −0.502743 | −0.0248287 | ||||||||
\(411\) | −12.9467 | −0.638614 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 4.04251 | 0.198919 | ||||||||
\(414\) | −3.23328 | −0.158907 | ||||||||
\(415\) | −17.1306 | −0.840907 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −7.80015 | −0.381975 | ||||||||
\(418\) | −30.2938 | −1.48172 | ||||||||
\(419\) | 29.2137 | 1.42718 | 0.713591 | − | 0.700563i | \(-0.247068\pi\) | ||||
0.713591 | + | 0.700563i | \(0.247068\pi\) | |||||||
\(420\) | 3.94672 | 0.192580 | ||||||||
\(421\) | −11.9370 | −0.581772 | −0.290886 | − | 0.956758i | \(-0.593950\pi\) | ||||
−0.290886 | + | 0.956758i | \(0.593950\pi\) | |||||||
\(422\) | −21.4338 | −1.04338 | ||||||||
\(423\) | −7.83666 | −0.381032 | ||||||||
\(424\) | 3.47358 | 0.168692 | ||||||||
\(425\) | 3.48674 | 0.169132 | ||||||||
\(426\) | −12.5404 | −0.607582 | ||||||||
\(427\) | 7.74098 | 0.374612 | ||||||||
\(428\) | 15.7200 | 0.759856 | ||||||||
\(429\) | 4.86001 | 0.234644 | ||||||||
\(430\) | 8.15392 | 0.393217 | ||||||||
\(431\) | 28.4199 | 1.36894 | 0.684468 | − | 0.729043i | \(-0.260034\pi\) | ||||
0.684468 | + | 0.729043i | \(0.260034\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 23.6266 | 1.13542 | 0.567712 | − | 0.823228i | \(-0.307829\pi\) | ||||
0.567712 | + | 0.823228i | \(0.307829\pi\) | |||||||
\(434\) | 9.47358 | 0.454746 | ||||||||
\(435\) | 12.9234 | 0.619628 | ||||||||
\(436\) | −17.7138 | −0.848336 | ||||||||
\(437\) | 20.1539 | 0.964093 | ||||||||
\(438\) | 9.93697 | 0.474807 | ||||||||
\(439\) | −14.9934 | −0.715597 | −0.357798 | − | 0.933799i | \(-0.616472\pi\) | ||||
−0.357798 | + | 0.933799i | \(0.616472\pi\) | |||||||
\(440\) | 12.6205 | 0.601658 | ||||||||
\(441\) | −4.69009 | −0.223338 | ||||||||
\(442\) | 2.00000 | 0.0951303 | ||||||||
\(443\) | −25.5971 | −1.21616 | −0.608078 | − | 0.793877i | \(-0.708059\pi\) | ||||
−0.608078 | + | 0.793877i | \(0.708059\pi\) | |||||||
\(444\) | −6.86001 | −0.325562 | ||||||||
\(445\) | −33.5341 | −1.58967 | ||||||||
\(446\) | 11.9160 | 0.564240 | ||||||||
\(447\) | 6.05361 | 0.286326 | ||||||||
\(448\) | 1.51984 | 0.0718056 | ||||||||
\(449\) | −28.8538 | −1.36169 | −0.680847 | − | 0.732426i | \(-0.738388\pi\) | ||||
−0.680847 | + | 0.732426i | \(0.738388\pi\) | |||||||
\(450\) | 1.74337 | 0.0821834 | ||||||||
\(451\) | −0.940902 | −0.0443054 | ||||||||
\(452\) | 2.79698 | 0.131559 | ||||||||
\(453\) | −22.5738 | −1.06061 | ||||||||
\(454\) | −11.1469 | −0.523150 | ||||||||
\(455\) | 3.94672 | 0.185025 | ||||||||
\(456\) | −6.23328 | −0.291900 | ||||||||
\(457\) | −15.9439 | −0.745824 | −0.372912 | − | 0.927867i | \(-0.621641\pi\) | ||||
−0.372912 | + | 0.927867i | \(0.621641\pi\) | |||||||
\(458\) | 10.4805 | 0.489721 | ||||||||
\(459\) | 2.00000 | 0.0933520 | ||||||||
\(460\) | −8.39618 | −0.391474 | ||||||||
\(461\) | 22.6127 | 1.05318 | 0.526589 | − | 0.850120i | \(-0.323471\pi\) | ||||
0.526589 | + | 0.850120i | \(0.323471\pi\) | |||||||
\(462\) | 7.38643 | 0.343648 | ||||||||
\(463\) | −9.36069 | −0.435028 | −0.217514 | − | 0.976057i | \(-0.569795\pi\) | ||||
−0.217514 | + | 0.976057i | \(0.569795\pi\) | |||||||
\(464\) | 4.97665 | 0.231035 | ||||||||
\(465\) | 16.1866 | 0.750635 | ||||||||
\(466\) | 18.8141 | 0.871545 | ||||||||
\(467\) | 4.53334 | 0.209778 | 0.104889 | − | 0.994484i | \(-0.466551\pi\) | ||||
0.104889 | + | 0.994484i | \(0.466551\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 13.4203 | 0.619692 | ||||||||
\(470\) | −20.3502 | −0.938687 | ||||||||
\(471\) | 9.13057 | 0.420715 | ||||||||
\(472\) | 2.65983 | 0.122428 | ||||||||
\(473\) | 15.2604 | 0.701673 | ||||||||
\(474\) | 3.42688 | 0.157402 | ||||||||
\(475\) | −10.8669 | −0.498609 | ||||||||
\(476\) | 3.03968 | 0.139323 | ||||||||
\(477\) | 3.47358 | 0.159044 | ||||||||
\(478\) | −23.3203 | −1.06665 | ||||||||
\(479\) | −9.66060 | −0.441404 | −0.220702 | − | 0.975341i | \(-0.570835\pi\) | ||||
−0.220702 | + | 0.975341i | \(0.570835\pi\) | |||||||
\(480\) | 2.59680 | 0.118527 | ||||||||
\(481\) | −6.86001 | −0.312790 | ||||||||
\(482\) | −9.31263 | −0.424179 | ||||||||
\(483\) | −4.91406 | −0.223598 | ||||||||
\(484\) | 12.6197 | 0.573623 | ||||||||
\(485\) | 33.4999 | 1.52115 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 28.2938 | 1.28211 | 0.641057 | − | 0.767493i | \(-0.278496\pi\) | ||||
0.641057 | + | 0.767493i | \(0.278496\pi\) | |||||||
\(488\) | 5.09329 | 0.230562 | ||||||||
\(489\) | −5.94639 | −0.268905 | ||||||||
\(490\) | −12.1792 | −0.550201 | ||||||||
\(491\) | 18.5591 | 0.837559 | 0.418780 | − | 0.908088i | \(-0.362458\pi\) | ||||
0.418780 | + | 0.908088i | \(0.362458\pi\) | |||||||
\(492\) | −0.193601 | −0.00872820 | ||||||||
\(493\) | 9.95330 | 0.448274 | ||||||||
\(494\) | −6.23328 | −0.280448 | ||||||||
\(495\) | 12.6205 | 0.567248 | ||||||||
\(496\) | 6.23328 | 0.279882 | ||||||||
\(497\) | −19.0593 | −0.854927 | ||||||||
\(498\) | −6.59680 | −0.295610 | ||||||||
\(499\) | 25.0863 | 1.12302 | 0.561508 | − | 0.827471i | \(-0.310221\pi\) | ||||
0.561508 | + | 0.827471i | \(0.310221\pi\) | |||||||
\(500\) | −8.45681 | −0.378200 | ||||||||
\(501\) | 10.3405 | 0.461980 | ||||||||
\(502\) | −7.04387 | −0.314383 | ||||||||
\(503\) | −43.5320 | −1.94100 | −0.970499 | − | 0.241106i | \(-0.922490\pi\) | ||||
−0.970499 | + | 0.241106i | \(0.922490\pi\) | |||||||
\(504\) | 1.51984 | 0.0676990 | ||||||||
\(505\) | −25.9860 | −1.15636 | ||||||||
\(506\) | −15.7138 | −0.698562 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −2.55293 | −0.113268 | ||||||||
\(509\) | −2.69292 | −0.119362 | −0.0596808 | − | 0.998218i | \(-0.519008\pi\) | ||||
−0.0596808 | + | 0.998218i | \(0.519008\pi\) | |||||||
\(510\) | 5.19360 | 0.229977 | ||||||||
\(511\) | 15.1026 | 0.668100 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.23328 | −0.275206 | ||||||||
\(514\) | −6.04001 | −0.266413 | ||||||||
\(515\) | −2.59680 | −0.114429 | ||||||||
\(516\) | 3.13999 | 0.138230 | ||||||||
\(517\) | −38.0863 | −1.67503 | ||||||||
\(518\) | −10.4261 | −0.458097 | ||||||||
\(519\) | −15.0933 | −0.662522 | ||||||||
\(520\) | 2.59680 | 0.113877 | ||||||||
\(521\) | 31.5142 | 1.38066 | 0.690331 | − | 0.723494i | \(-0.257465\pi\) | ||||
0.690331 | + | 0.723494i | \(0.257465\pi\) | |||||||
\(522\) | 4.97665 | 0.217822 | ||||||||
\(523\) | −2.23012 | −0.0975162 | −0.0487581 | − | 0.998811i | \(-0.515526\pi\) | ||||
−0.0487581 | + | 0.998811i | \(0.515526\pi\) | |||||||
\(524\) | −6.68035 | −0.291832 | ||||||||
\(525\) | 2.64964 | 0.115640 | ||||||||
\(526\) | −19.5194 | −0.851086 | ||||||||
\(527\) | 12.4666 | 0.543052 | ||||||||
\(528\) | 4.86001 | 0.211505 | ||||||||
\(529\) | −12.5459 | −0.545474 | ||||||||
\(530\) | 9.02019 | 0.391812 | ||||||||
\(531\) | 2.65983 | 0.115427 | ||||||||
\(532\) | −9.47358 | −0.410732 | ||||||||
\(533\) | −0.193601 | −0.00838578 | ||||||||
\(534\) | −12.9136 | −0.558827 | ||||||||
\(535\) | 40.8218 | 1.76488 | ||||||||
\(536\) | 8.83008 | 0.381401 | ||||||||
\(537\) | −2.84684 | −0.122850 | ||||||||
\(538\) | −5.23045 | −0.225501 | ||||||||
\(539\) | −22.7939 | −0.981802 | ||||||||
\(540\) | 2.59680 | 0.111748 | ||||||||
\(541\) | 0.256297 | 0.0110191 | 0.00550954 | − | 0.999985i | \(-0.498246\pi\) | ||||
0.00550954 | + | 0.999985i | \(0.498246\pi\) | |||||||
\(542\) | −1.08638 | −0.0466639 | ||||||||
\(543\) | 8.38720 | 0.359929 | ||||||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | −45.9991 | −1.97039 | ||||||||
\(546\) | 1.51984 | 0.0650431 | ||||||||
\(547\) | −30.3175 | −1.29628 | −0.648141 | − | 0.761520i | \(-0.724453\pi\) | ||||
−0.648141 | + | 0.761520i | \(0.724453\pi\) | |||||||
\(548\) | −12.9467 | −0.553056 | ||||||||
\(549\) | 5.09329 | 0.217376 | ||||||||
\(550\) | 8.47281 | 0.361282 | ||||||||
\(551\) | −31.0208 | −1.32153 | ||||||||
\(552\) | −3.23328 | −0.137617 | ||||||||
\(553\) | 5.20830 | 0.221480 | ||||||||
\(554\) | 7.85343 | 0.333660 | ||||||||
\(555\) | −17.8141 | −0.756166 | ||||||||
\(556\) | −7.80015 | −0.330800 | ||||||||
\(557\) | 13.4400 | 0.569473 | 0.284737 | − | 0.958606i | \(-0.408094\pi\) | ||||
0.284737 | + | 0.958606i | \(0.408094\pi\) | |||||||
\(558\) | 6.23328 | 0.263876 | ||||||||
\(559\) | 3.13999 | 0.132807 | ||||||||
\(560\) | 3.94672 | 0.166779 | ||||||||
\(561\) | 9.72002 | 0.410380 | ||||||||
\(562\) | 29.0535 | 1.22555 | ||||||||
\(563\) | 25.0298 | 1.05488 | 0.527441 | − | 0.849592i | \(-0.323152\pi\) | ||||
0.527441 | + | 0.849592i | \(0.323152\pi\) | |||||||
\(564\) | −7.83666 | −0.329983 | ||||||||
\(565\) | 7.26321 | 0.305566 | ||||||||
\(566\) | −10.6594 | −0.448048 | ||||||||
\(567\) | 1.51984 | 0.0638272 | ||||||||
\(568\) | −12.5404 | −0.526182 | ||||||||
\(569\) | −16.6341 | −0.697337 | −0.348669 | − | 0.937246i | \(-0.613366\pi\) | ||||
−0.348669 | + | 0.937246i | \(0.613366\pi\) | |||||||
\(570\) | −16.1866 | −0.677981 | ||||||||
\(571\) | −11.2705 | −0.471654 | −0.235827 | − | 0.971795i | \(-0.575780\pi\) | ||||
−0.235827 | + | 0.971795i | \(0.575780\pi\) | |||||||
\(572\) | 4.86001 | 0.203207 | ||||||||
\(573\) | 17.9533 | 0.750010 | ||||||||
\(574\) | −0.294242 | −0.0122814 | ||||||||
\(575\) | −5.63681 | −0.235071 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −35.5772 | −1.48110 | −0.740549 | − | 0.672002i | \(-0.765435\pi\) | ||||
−0.740549 | + | 0.672002i | \(0.765435\pi\) | |||||||
\(578\) | −13.0000 | −0.540729 | ||||||||
\(579\) | 13.9669 | 0.580445 | ||||||||
\(580\) | 12.9234 | 0.536614 | ||||||||
\(581\) | −10.0261 | −0.415952 | ||||||||
\(582\) | 12.9005 | 0.534741 | ||||||||
\(583\) | 16.8816 | 0.699166 | ||||||||
\(584\) | 9.93697 | 0.411195 | ||||||||
\(585\) | 2.59680 | 0.107364 | ||||||||
\(586\) | −18.4143 | −0.760688 | ||||||||
\(587\) | −8.87009 | −0.366108 | −0.183054 | − | 0.983103i | \(-0.558598\pi\) | ||||
−0.183054 | + | 0.983103i | \(0.558598\pi\) | |||||||
\(588\) | −4.69009 | −0.193416 | ||||||||
\(589\) | −38.8538 | −1.60094 | ||||||||
\(590\) | 6.90704 | 0.284358 | ||||||||
\(591\) | 7.78305 | 0.320152 | ||||||||
\(592\) | −6.86001 | −0.281945 | ||||||||
\(593\) | −45.4874 | −1.86794 | −0.933972 | − | 0.357346i | \(-0.883682\pi\) | ||||
−0.933972 | + | 0.357346i | \(0.883682\pi\) | |||||||
\(594\) | 4.86001 | 0.199409 | ||||||||
\(595\) | 7.89344 | 0.323599 | ||||||||
\(596\) | 6.05361 | 0.247966 | ||||||||
\(597\) | −4.71344 | −0.192908 | ||||||||
\(598\) | −3.23328 | −0.132219 | ||||||||
\(599\) | −5.69369 | −0.232638 | −0.116319 | − | 0.993212i | \(-0.537109\pi\) | ||||
−0.116319 | + | 0.993212i | \(0.537109\pi\) | |||||||
\(600\) | 1.74337 | 0.0711729 | ||||||||
\(601\) | −28.2938 | −1.15413 | −0.577064 | − | 0.816699i | \(-0.695802\pi\) | ||||
−0.577064 | + | 0.816699i | \(0.695802\pi\) | |||||||
\(602\) | 4.77228 | 0.194503 | ||||||||
\(603\) | 8.83008 | 0.359589 | ||||||||
\(604\) | −22.5738 | −0.918514 | ||||||||
\(605\) | 32.7709 | 1.33233 | ||||||||
\(606\) | −10.0069 | −0.406503 | ||||||||
\(607\) | −7.30017 | −0.296305 | −0.148152 | − | 0.988965i | \(-0.547333\pi\) | ||||
−0.148152 | + | 0.988965i | \(0.547333\pi\) | |||||||
\(608\) | −6.23328 | −0.252793 | ||||||||
\(609\) | 7.56371 | 0.306497 | ||||||||
\(610\) | 13.2263 | 0.535515 | ||||||||
\(611\) | −7.83666 | −0.317037 | ||||||||
\(612\) | 2.00000 | 0.0808452 | ||||||||
\(613\) | 23.5070 | 0.949439 | 0.474719 | − | 0.880137i | \(-0.342550\pi\) | ||||
0.474719 | + | 0.880137i | \(0.342550\pi\) | |||||||
\(614\) | −7.92620 | −0.319875 | ||||||||
\(615\) | −0.502743 | −0.0202725 | ||||||||
\(616\) | 7.38643 | 0.297608 | ||||||||
\(617\) | 9.06755 | 0.365046 | 0.182523 | − | 0.983202i | \(-0.441574\pi\) | ||||
0.182523 | + | 0.983202i | \(0.441574\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | −2.64769 | −0.106420 | −0.0532098 | − | 0.998583i | \(-0.516945\pi\) | ||||
−0.0532098 | + | 0.998583i | \(0.516945\pi\) | |||||||
\(620\) | 16.1866 | 0.650069 | ||||||||
\(621\) | −3.23328 | −0.129747 | ||||||||
\(622\) | 4.06259 | 0.162895 | ||||||||
\(623\) | −19.6266 | −0.786324 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −30.6775 | −1.22710 | ||||||||
\(626\) | 4.20018 | 0.167873 | ||||||||
\(627\) | −30.2938 | −1.20982 | ||||||||
\(628\) | 9.13057 | 0.364350 | ||||||||
\(629\) | −13.7200 | −0.547053 | ||||||||
\(630\) | 3.94672 | 0.157241 | ||||||||
\(631\) | 18.0069 | 0.716844 | 0.358422 | − | 0.933560i | \(-0.383315\pi\) | ||||
0.358422 | + | 0.933560i | \(0.383315\pi\) | |||||||
\(632\) | 3.42688 | 0.136314 | ||||||||
\(633\) | −21.4338 | −0.851917 | ||||||||
\(634\) | −6.43390 | −0.255523 | ||||||||
\(635\) | −6.62946 | −0.263082 | ||||||||
\(636\) | 3.47358 | 0.137736 | ||||||||
\(637\) | −4.69009 | −0.185828 | ||||||||
\(638\) | 24.1866 | 0.957556 | ||||||||
\(639\) | −12.5404 | −0.496089 | ||||||||
\(640\) | 2.59680 | 0.102648 | ||||||||
\(641\) | 47.6740 | 1.88301 | 0.941505 | − | 0.337000i | \(-0.109412\pi\) | ||||
0.941505 | + | 0.337000i | \(0.109412\pi\) | |||||||
\(642\) | 15.7200 | 0.620420 | ||||||||
\(643\) | −11.6664 | −0.460078 | −0.230039 | − | 0.973181i | \(-0.573885\pi\) | ||||
−0.230039 | + | 0.973181i | \(0.573885\pi\) | |||||||
\(644\) | −4.91406 | −0.193641 | ||||||||
\(645\) | 8.15392 | 0.321060 | ||||||||
\(646\) | −12.4666 | −0.490490 | ||||||||
\(647\) | 5.01291 | 0.197078 | 0.0985388 | − | 0.995133i | \(-0.468583\pi\) | ||||
0.0985388 | + | 0.995133i | \(0.468583\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 12.9268 | 0.507421 | ||||||||
\(650\) | 1.74337 | 0.0683807 | ||||||||
\(651\) | 9.47358 | 0.371299 | ||||||||
\(652\) | −5.94639 | −0.232879 | ||||||||
\(653\) | −19.8997 | −0.778735 | −0.389368 | − | 0.921082i | \(-0.627306\pi\) | ||||
−0.389368 | + | 0.921082i | \(0.627306\pi\) | |||||||
\(654\) | −17.7138 | −0.692663 | ||||||||
\(655\) | −17.3475 | −0.677824 | ||||||||
\(656\) | −0.193601 | −0.00755884 | ||||||||
\(657\) | 9.93697 | 0.387678 | ||||||||
\(658\) | −11.9105 | −0.464318 | ||||||||
\(659\) | −4.32580 | −0.168509 | −0.0842546 | − | 0.996444i | \(-0.526851\pi\) | ||||
−0.0842546 | + | 0.996444i | \(0.526851\pi\) | |||||||
\(660\) | 12.6205 | 0.491252 | ||||||||
\(661\) | 40.2806 | 1.56674 | 0.783368 | − | 0.621559i | \(-0.213500\pi\) | ||||
0.783368 | + | 0.621559i | \(0.213500\pi\) | |||||||
\(662\) | −28.9168 | −1.12388 | ||||||||
\(663\) | 2.00000 | 0.0776736 | ||||||||
\(664\) | −6.59680 | −0.256006 | ||||||||
\(665\) | −24.6010 | −0.953985 | ||||||||
\(666\) | −6.86001 | −0.265820 | ||||||||
\(667\) | −16.0909 | −0.623042 | ||||||||
\(668\) | 10.3405 | 0.400086 | ||||||||
\(669\) | 11.9160 | 0.460700 | ||||||||
\(670\) | 22.9300 | 0.885861 | ||||||||
\(671\) | 24.7534 | 0.955596 | ||||||||
\(672\) | 1.51984 | 0.0586291 | ||||||||
\(673\) | −12.3573 | −0.476338 | −0.238169 | − | 0.971224i | \(-0.576547\pi\) | ||||
−0.238169 | + | 0.971224i | \(0.576547\pi\) | |||||||
\(674\) | −6.53344 | −0.251659 | ||||||||
\(675\) | 1.74337 | 0.0671024 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −2.16606 | −0.0832485 | −0.0416242 | − | 0.999133i | \(-0.513253\pi\) | ||||
−0.0416242 | + | 0.999133i | \(0.513253\pi\) | |||||||
\(678\) | 2.79698 | 0.107418 | ||||||||
\(679\) | 19.6066 | 0.752433 | ||||||||
\(680\) | 5.19360 | 0.199165 | ||||||||
\(681\) | −11.1469 | −0.427150 | ||||||||
\(682\) | 30.2938 | 1.16001 | ||||||||
\(683\) | 10.8864 | 0.416557 | 0.208279 | − | 0.978070i | \(-0.433214\pi\) | ||||
0.208279 | + | 0.978070i | \(0.433214\pi\) | |||||||
\(684\) | −6.23328 | −0.238335 | ||||||||
\(685\) | −33.6200 | −1.28456 | ||||||||
\(686\) | −17.7671 | −0.678349 | ||||||||
\(687\) | 10.4805 | 0.399856 | ||||||||
\(688\) | 3.13999 | 0.119711 | ||||||||
\(689\) | 3.47358 | 0.132333 | ||||||||
\(690\) | −8.39618 | −0.319637 | ||||||||
\(691\) | 3.94432 | 0.150049 | 0.0750246 | − | 0.997182i | \(-0.476096\pi\) | ||||
0.0750246 | + | 0.997182i | \(0.476096\pi\) | |||||||
\(692\) | −15.0933 | −0.573761 | ||||||||
\(693\) | 7.38643 | 0.280587 | ||||||||
\(694\) | 33.7931 | 1.28277 | ||||||||
\(695\) | −20.2554 | −0.768332 | ||||||||
\(696\) | 4.97665 | 0.188639 | ||||||||
\(697\) | −0.387202 | −0.0146663 | ||||||||
\(698\) | 21.1748 | 0.801477 | ||||||||
\(699\) | 18.8141 | 0.711614 | ||||||||
\(700\) | 2.64964 | 0.100147 | ||||||||
\(701\) | 26.8906 | 1.01564 | 0.507822 | − | 0.861462i | \(-0.330451\pi\) | ||||
0.507822 | + | 0.861462i | \(0.330451\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 42.7604 | 1.61274 | ||||||||
\(704\) | 4.86001 | 0.183169 | ||||||||
\(705\) | −20.3502 | −0.766435 | ||||||||
\(706\) | 1.87395 | 0.0705269 | ||||||||
\(707\) | −15.2089 | −0.571989 | ||||||||
\(708\) | 2.65983 | 0.0999624 | ||||||||
\(709\) | −24.7367 | −0.929006 | −0.464503 | − | 0.885572i | \(-0.653767\pi\) | ||||
−0.464503 | + | 0.885572i | \(0.653767\pi\) | |||||||
\(710\) | −32.5648 | −1.22214 | ||||||||
\(711\) | 3.42688 | 0.128518 | ||||||||
\(712\) | −12.9136 | −0.483959 | ||||||||
\(713\) | −20.1539 | −0.754770 | ||||||||
\(714\) | 3.03968 | 0.113757 | ||||||||
\(715\) | 12.6205 | 0.471979 | ||||||||
\(716\) | −2.84684 | −0.106392 | ||||||||
\(717\) | −23.3203 | −0.870913 | ||||||||
\(718\) | 17.7395 | 0.662033 | ||||||||
\(719\) | −17.4727 | −0.651622 | −0.325811 | − | 0.945435i | \(-0.605637\pi\) | ||||
−0.325811 | + | 0.945435i | \(0.605637\pi\) | |||||||
\(720\) | 2.59680 | 0.0967770 | ||||||||
\(721\) | −1.51984 | −0.0566018 | ||||||||
\(722\) | 19.8538 | 0.738880 | ||||||||
\(723\) | −9.31263 | −0.346341 | ||||||||
\(724\) | 8.38720 | 0.311708 | ||||||||
\(725\) | 8.67616 | 0.322224 | ||||||||
\(726\) | 12.6197 | 0.468361 | ||||||||
\(727\) | −11.2803 | −0.418363 | −0.209182 | − | 0.977877i | \(-0.567080\pi\) | ||||
−0.209182 | + | 0.977877i | \(0.567080\pi\) | |||||||
\(728\) | 1.51984 | 0.0563290 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 25.8043 | 0.955061 | ||||||||
\(731\) | 6.27998 | 0.232273 | ||||||||
\(732\) | 5.09329 | 0.188253 | ||||||||
\(733\) | 7.20051 | 0.265957 | 0.132979 | − | 0.991119i | \(-0.457546\pi\) | ||||
0.132979 | + | 0.991119i | \(0.457546\pi\) | |||||||
\(734\) | 31.5536 | 1.16466 | ||||||||
\(735\) | −12.1792 | −0.449238 | ||||||||
\(736\) | −3.23328 | −0.119180 | ||||||||
\(737\) | 42.9143 | 1.58077 | ||||||||
\(738\) | −0.193601 | −0.00712654 | ||||||||
\(739\) | 11.7931 | 0.433817 | 0.216909 | − | 0.976192i | \(-0.430403\pi\) | ||||
0.216909 | + | 0.976192i | \(0.430403\pi\) | |||||||
\(740\) | −17.8141 | −0.654859 | ||||||||
\(741\) | −6.23328 | −0.228985 | ||||||||
\(742\) | 5.27928 | 0.193808 | ||||||||
\(743\) | −26.8659 | −0.985614 | −0.492807 | − | 0.870139i | \(-0.664029\pi\) | ||||
−0.492807 | + | 0.870139i | \(0.664029\pi\) | |||||||
\(744\) | 6.23328 | 0.228523 | ||||||||
\(745\) | 15.7200 | 0.575937 | ||||||||
\(746\) | −22.9804 | −0.841372 | ||||||||
\(747\) | −6.59680 | −0.241364 | ||||||||
\(748\) | 9.72002 | 0.355399 | ||||||||
\(749\) | 23.8919 | 0.872991 | ||||||||
\(750\) | −8.45681 | −0.308799 | ||||||||
\(751\) | 35.8404 | 1.30784 | 0.653918 | − | 0.756566i | \(-0.273124\pi\) | ||||
0.653918 | + | 0.756566i | \(0.273124\pi\) | |||||||
\(752\) | −7.83666 | −0.285774 | ||||||||
\(753\) | −7.04387 | −0.256693 | ||||||||
\(754\) | 4.97665 | 0.181239 | ||||||||
\(755\) | −58.6196 | −2.13339 | ||||||||
\(756\) | 1.51984 | 0.0552760 | ||||||||
\(757\) | 10.0668 | 0.365883 | 0.182942 | − | 0.983124i | \(-0.441438\pi\) | ||||
0.182942 | + | 0.983124i | \(0.441438\pi\) | |||||||
\(758\) | 34.0810 | 1.23788 | ||||||||
\(759\) | −15.7138 | −0.570374 | ||||||||
\(760\) | −16.1866 | −0.587149 | ||||||||
\(761\) | 20.5411 | 0.744615 | 0.372308 | − | 0.928109i | \(-0.378567\pi\) | ||||
0.372308 | + | 0.928109i | \(0.378567\pi\) | |||||||
\(762\) | −2.55293 | −0.0924830 | ||||||||
\(763\) | −26.9221 | −0.974644 | ||||||||
\(764\) | 17.9533 | 0.649528 | ||||||||
\(765\) | 5.19360 | 0.187775 | ||||||||
\(766\) | 11.2462 | 0.406341 | ||||||||
\(767\) | 2.65983 | 0.0960408 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −9.25869 | −0.333877 | −0.166938 | − | 0.985967i | \(-0.553388\pi\) | ||||
−0.166938 | + | 0.985967i | \(0.553388\pi\) | |||||||
\(770\) | 19.1811 | 0.691239 | ||||||||
\(771\) | −6.04001 | −0.217526 | ||||||||
\(772\) | 13.9669 | 0.502680 | ||||||||
\(773\) | −21.1538 | −0.760850 | −0.380425 | − | 0.924812i | \(-0.624222\pi\) | ||||
−0.380425 | + | 0.924812i | \(0.624222\pi\) | |||||||
\(774\) | 3.13999 | 0.112865 | ||||||||
\(775\) | 10.8669 | 0.390351 | ||||||||
\(776\) | 12.9005 | 0.463099 | ||||||||
\(777\) | −10.4261 | −0.374035 | ||||||||
\(778\) | 5.06063 | 0.181433 | ||||||||
\(779\) | 1.20677 | 0.0432369 | ||||||||
\(780\) | 2.59680 | 0.0929804 | ||||||||
\(781\) | −60.9463 | −2.18083 | ||||||||
\(782\) | −6.46656 | −0.231244 | ||||||||
\(783\) | 4.97665 | 0.177851 | ||||||||
\(784\) | −4.69009 | −0.167503 | ||||||||
\(785\) | 23.7103 | 0.846256 | ||||||||
\(786\) | −6.68035 | −0.238280 | ||||||||
\(787\) | −38.9804 | −1.38950 | −0.694751 | − | 0.719251i | \(-0.744485\pi\) | ||||
−0.694751 | + | 0.719251i | \(0.744485\pi\) | |||||||
\(788\) | 7.78305 | 0.277260 | ||||||||
\(789\) | −19.5194 | −0.694909 | ||||||||
\(790\) | 8.89892 | 0.316609 | ||||||||
\(791\) | 4.25097 | 0.151147 | ||||||||
\(792\) | 4.86001 | 0.172693 | ||||||||
\(793\) | 5.09329 | 0.180868 | ||||||||
\(794\) | 10.7597 | 0.381847 | ||||||||
\(795\) | 9.02019 | 0.319913 | ||||||||
\(796\) | −4.71344 | −0.167063 | ||||||||
\(797\) | −35.4685 | −1.25636 | −0.628180 | − | 0.778068i | \(-0.716200\pi\) | ||||
−0.628180 | + | 0.778068i | \(0.716200\pi\) | |||||||
\(798\) | −9.47358 | −0.335361 | ||||||||
\(799\) | −15.6733 | −0.554482 | ||||||||
\(800\) | 1.74337 | 0.0616375 | ||||||||
\(801\) | −12.9136 | −0.456280 | ||||||||
\(802\) | 5.44048 | 0.192110 | ||||||||
\(803\) | 48.2938 | 1.70425 | ||||||||
\(804\) | 8.83008 | 0.311413 | ||||||||
\(805\) | −12.7608 | −0.449760 | ||||||||
\(806\) | 6.23328 | 0.219558 | ||||||||
\(807\) | −5.23045 | −0.184120 | ||||||||
\(808\) | −10.0069 | −0.352042 | ||||||||
\(809\) | 43.3440 | 1.52389 | 0.761947 | − | 0.647640i | \(-0.224244\pi\) | ||||
0.761947 | + | 0.647640i | \(0.224244\pi\) | |||||||
\(810\) | 2.59680 | 0.0912423 | ||||||||
\(811\) | 15.1101 | 0.530586 | 0.265293 | − | 0.964168i | \(-0.414531\pi\) | ||||
0.265293 | + | 0.964168i | \(0.414531\pi\) | |||||||
\(812\) | 7.56371 | 0.265434 | ||||||||
\(813\) | −1.08638 | −0.0381009 | ||||||||
\(814\) | −33.3397 | −1.16856 | ||||||||
\(815\) | −15.4416 | −0.540895 | ||||||||
\(816\) | 2.00000 | 0.0700140 | ||||||||
\(817\) | −19.5724 | −0.684752 | ||||||||
\(818\) | 9.94013 | 0.347549 | ||||||||
\(819\) | 1.51984 | 0.0531075 | ||||||||
\(820\) | −0.502743 | −0.0175565 | ||||||||
\(821\) | 15.9806 | 0.557726 | 0.278863 | − | 0.960331i | \(-0.410042\pi\) | ||||
0.278863 | + | 0.960331i | \(0.410042\pi\) | |||||||
\(822\) | −12.9467 | −0.451569 | ||||||||
\(823\) | 2.85582 | 0.0995477 | 0.0497738 | − | 0.998761i | \(-0.484150\pi\) | ||||
0.0497738 | + | 0.998761i | \(0.484150\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 8.47281 | 0.294985 | ||||||||
\(826\) | 4.04251 | 0.140657 | ||||||||
\(827\) | −4.50634 | −0.156701 | −0.0783504 | − | 0.996926i | \(-0.524965\pi\) | ||||
−0.0783504 | + | 0.996926i | \(0.524965\pi\) | |||||||
\(828\) | −3.23328 | −0.112364 | ||||||||
\(829\) | −17.7437 | −0.616264 | −0.308132 | − | 0.951344i | \(-0.599704\pi\) | ||||
−0.308132 | + | 0.951344i | \(0.599704\pi\) | |||||||
\(830\) | −17.1306 | −0.594611 | ||||||||
\(831\) | 7.85343 | 0.272432 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −9.38018 | −0.325004 | ||||||||
\(834\) | −7.80015 | −0.270097 | ||||||||
\(835\) | 26.8522 | 0.929259 | ||||||||
\(836\) | −30.2938 | −1.04773 | ||||||||
\(837\) | 6.23328 | 0.215454 | ||||||||
\(838\) | 29.2137 | 1.00917 | ||||||||
\(839\) | −39.9665 | −1.37980 | −0.689898 | − | 0.723907i | \(-0.742345\pi\) | ||||
−0.689898 | + | 0.723907i | \(0.742345\pi\) | |||||||
\(840\) | 3.94672 | 0.136175 | ||||||||
\(841\) | −4.23295 | −0.145964 | ||||||||
\(842\) | −11.9370 | −0.411375 | ||||||||
\(843\) | 29.0535 | 1.00066 | ||||||||
\(844\) | −21.4338 | −0.737782 | ||||||||
\(845\) | 2.59680 | 0.0893326 | ||||||||
\(846\) | −7.83666 | −0.269430 | ||||||||
\(847\) | 19.1799 | 0.659030 | ||||||||
\(848\) | 3.47358 | 0.119283 | ||||||||
\(849\) | −10.6594 | −0.365829 | ||||||||
\(850\) | 3.48674 | 0.119594 | ||||||||
\(851\) | 22.1803 | 0.760332 | ||||||||
\(852\) | −12.5404 | −0.429626 | ||||||||
\(853\) | −7.38437 | −0.252836 | −0.126418 | − | 0.991977i | \(-0.540348\pi\) | ||||
−0.126418 | + | 0.991977i | \(0.540348\pi\) | |||||||
\(854\) | 7.74098 | 0.264891 | ||||||||
\(855\) | −16.1866 | −0.553569 | ||||||||
\(856\) | 15.7200 | 0.537299 | ||||||||
\(857\) | −23.4727 | −0.801812 | −0.400906 | − | 0.916119i | \(-0.631305\pi\) | ||||
−0.400906 | + | 0.916119i | \(0.631305\pi\) | |||||||
\(858\) | 4.86001 | 0.165918 | ||||||||
\(859\) | −16.3474 | −0.557767 | −0.278883 | − | 0.960325i | \(-0.589964\pi\) | ||||
−0.278883 | + | 0.960325i | \(0.589964\pi\) | |||||||
\(860\) | 8.15392 | 0.278046 | ||||||||
\(861\) | −0.294242 | −0.0100277 | ||||||||
\(862\) | 28.4199 | 0.967984 | ||||||||
\(863\) | 0.153332 | 0.00521948 | 0.00260974 | − | 0.999997i | \(-0.499169\pi\) | ||||
0.00260974 | + | 0.999997i | \(0.499169\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −39.1943 | −1.33264 | ||||||||
\(866\) | 23.6266 | 0.802865 | ||||||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | 9.47358 | 0.321554 | ||||||||
\(869\) | 16.6547 | 0.564971 | ||||||||
\(870\) | 12.9234 | 0.438143 | ||||||||
\(871\) | 8.83008 | 0.299196 | ||||||||
\(872\) | −17.7138 | −0.599864 | ||||||||
\(873\) | 12.9005 | 0.436614 | ||||||||
\(874\) | 20.1539 | 0.681717 | ||||||||
\(875\) | −12.8530 | −0.434510 | ||||||||
\(876\) | 9.93697 | 0.335739 | ||||||||
\(877\) | 21.1071 | 0.712737 | 0.356368 | − | 0.934346i | \(-0.384015\pi\) | ||||
0.356368 | + | 0.934346i | \(0.384015\pi\) | |||||||
\(878\) | −14.9934 | −0.506003 | ||||||||
\(879\) | −18.4143 | −0.621099 | ||||||||
\(880\) | 12.6205 | 0.425436 | ||||||||
\(881\) | 22.9937 | 0.774679 | 0.387340 | − | 0.921937i | \(-0.373394\pi\) | ||||
0.387340 | + | 0.921937i | \(0.373394\pi\) | |||||||
\(882\) | −4.69009 | −0.157924 | ||||||||
\(883\) | −44.2152 | −1.48796 | −0.743980 | − | 0.668202i | \(-0.767064\pi\) | ||||
−0.743980 | + | 0.668202i | \(0.767064\pi\) | |||||||
\(884\) | 2.00000 | 0.0672673 | ||||||||
\(885\) | 6.90704 | 0.232178 | ||||||||
\(886\) | −25.5971 | −0.859952 | ||||||||
\(887\) | 34.6988 | 1.16507 | 0.582536 | − | 0.812805i | \(-0.302061\pi\) | ||||
0.582536 | + | 0.812805i | \(0.302061\pi\) | |||||||
\(888\) | −6.86001 | −0.230207 | ||||||||
\(889\) | −3.88005 | −0.130133 | ||||||||
\(890\) | −33.5341 | −1.12407 | ||||||||
\(891\) | 4.86001 | 0.162817 | ||||||||
\(892\) | 11.9160 | 0.398978 | ||||||||
\(893\) | 48.8481 | 1.63464 | ||||||||
\(894\) | 6.05361 | 0.202463 | ||||||||
\(895\) | −7.39269 | −0.247110 | ||||||||
\(896\) | 1.51984 | 0.0507742 | ||||||||
\(897\) | −3.23328 | −0.107956 | ||||||||
\(898\) | −28.8538 | −0.962862 | ||||||||
\(899\) | 31.0208 | 1.03460 | ||||||||
\(900\) | 1.74337 | 0.0581124 | ||||||||
\(901\) | 6.94716 | 0.231443 | ||||||||
\(902\) | −0.940902 | −0.0313286 | ||||||||
\(903\) | 4.77228 | 0.158811 | ||||||||
\(904\) | 2.79698 | 0.0930263 | ||||||||
\(905\) | 21.7799 | 0.723988 | ||||||||
\(906\) | −22.5738 | −0.749964 | ||||||||
\(907\) | −15.4711 | −0.513709 | −0.256854 | − | 0.966450i | \(-0.582686\pi\) | ||||
−0.256854 | + | 0.966450i | \(0.582686\pi\) | |||||||
\(908\) | −11.1469 | −0.369923 | ||||||||
\(909\) | −10.0069 | −0.331908 | ||||||||
\(910\) | 3.94672 | 0.130832 | ||||||||
\(911\) | 13.7137 | 0.454355 | 0.227178 | − | 0.973853i | \(-0.427050\pi\) | ||||
0.227178 | + | 0.973853i | \(0.427050\pi\) | |||||||
\(912\) | −6.23328 | −0.206404 | ||||||||
\(913\) | −32.0605 | −1.06105 | ||||||||
\(914\) | −15.9439 | −0.527377 | ||||||||
\(915\) | 13.2263 | 0.437247 | ||||||||
\(916\) | 10.4805 | 0.346285 | ||||||||
\(917\) | −10.1530 | −0.335283 | ||||||||
\(918\) | 2.00000 | 0.0660098 | ||||||||
\(919\) | −9.67060 | −0.319004 | −0.159502 | − | 0.987198i | \(-0.550989\pi\) | ||||
−0.159502 | + | 0.987198i | \(0.550989\pi\) | |||||||
\(920\) | −8.39618 | −0.276814 | ||||||||
\(921\) | −7.92620 | −0.261177 | ||||||||
\(922\) | 22.6127 | 0.744709 | ||||||||
\(923\) | −12.5404 | −0.412771 | ||||||||
\(924\) | 7.38643 | 0.242996 | ||||||||
\(925\) | −11.9596 | −0.393228 | ||||||||
\(926\) | −9.36069 | −0.307611 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 4.97665 | 0.163367 | ||||||||
\(929\) | −39.0031 | −1.27965 | −0.639824 | − | 0.768521i | \(-0.720993\pi\) | ||||
−0.639824 | + | 0.768521i | \(0.720993\pi\) | |||||||
\(930\) | 16.1866 | 0.530779 | ||||||||
\(931\) | 29.2346 | 0.958127 | ||||||||
\(932\) | 18.8141 | 0.616276 | ||||||||
\(933\) | 4.06259 | 0.133003 | ||||||||
\(934\) | 4.53334 | 0.148335 | ||||||||
\(935\) | 25.2410 | 0.825468 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 50.6538 | 1.65479 | 0.827394 | − | 0.561622i | \(-0.189823\pi\) | ||||
0.827394 | + | 0.561622i | \(0.189823\pi\) | |||||||
\(938\) | 13.4203 | 0.438188 | ||||||||
\(939\) | 4.20018 | 0.137068 | ||||||||
\(940\) | −20.3502 | −0.663752 | ||||||||
\(941\) | −22.0752 | −0.719632 | −0.359816 | − | 0.933023i | \(-0.617161\pi\) | ||||
−0.359816 | + | 0.933023i | \(0.617161\pi\) | |||||||
\(942\) | 9.13057 | 0.297490 | ||||||||
\(943\) | 0.625965 | 0.0203842 | ||||||||
\(944\) | 2.65983 | 0.0865700 | ||||||||
\(945\) | 3.94672 | 0.128387 | ||||||||
\(946\) | 15.2604 | 0.496158 | ||||||||
\(947\) | 9.62125 | 0.312649 | 0.156324 | − | 0.987706i | \(-0.450036\pi\) | ||||
0.156324 | + | 0.987706i | \(0.450036\pi\) | |||||||
\(948\) | 3.42688 | 0.111300 | ||||||||
\(949\) | 9.93697 | 0.322568 | ||||||||
\(950\) | −10.8669 | −0.352570 | ||||||||
\(951\) | −6.43390 | −0.208634 | ||||||||
\(952\) | 3.03968 | 0.0985165 | ||||||||
\(953\) | −11.3670 | −0.368214 | −0.184107 | − | 0.982906i | \(-0.558939\pi\) | ||||
−0.184107 | + | 0.982906i | \(0.558939\pi\) | |||||||
\(954\) | 3.47358 | 0.112461 | ||||||||
\(955\) | 46.6211 | 1.50862 | ||||||||
\(956\) | −23.3203 | −0.754233 | ||||||||
\(957\) | 24.1866 | 0.781841 | ||||||||
\(958\) | −9.66060 | −0.312120 | ||||||||
\(959\) | −19.6769 | −0.635401 | ||||||||
\(960\) | 2.59680 | 0.0838114 | ||||||||
\(961\) | 7.85376 | 0.253347 | ||||||||
\(962\) | −6.86001 | −0.221176 | ||||||||
\(963\) | 15.7200 | 0.506571 | ||||||||
\(964\) | −9.31263 | −0.299940 | ||||||||
\(965\) | 36.2693 | 1.16755 | ||||||||
\(966\) | −4.91406 | −0.158107 | ||||||||
\(967\) | −13.6143 | −0.437807 | −0.218904 | − | 0.975746i | \(-0.570248\pi\) | ||||
−0.218904 | + | 0.975746i | \(0.570248\pi\) | |||||||
\(968\) | 12.6197 | 0.405613 | ||||||||
\(969\) | −12.4666 | −0.400483 | ||||||||
\(970\) | 33.4999 | 1.07562 | ||||||||
\(971\) | 1.45306 | 0.0466309 | 0.0233154 | − | 0.999728i | \(-0.492578\pi\) | ||||
0.0233154 | + | 0.999728i | \(0.492578\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −11.8550 | −0.380053 | ||||||||
\(974\) | 28.2938 | 0.906592 | ||||||||
\(975\) | 1.74337 | 0.0558326 | ||||||||
\(976\) | 5.09329 | 0.163032 | ||||||||
\(977\) | 6.95264 | 0.222435 | 0.111217 | − | 0.993796i | \(-0.464525\pi\) | ||||
0.111217 | + | 0.993796i | \(0.464525\pi\) | |||||||
\(978\) | −5.94639 | −0.190145 | ||||||||
\(979\) | −62.7604 | −2.00583 | ||||||||
\(980\) | −12.1792 | −0.389051 | ||||||||
\(981\) | −17.7138 | −0.565557 | ||||||||
\(982\) | 18.5591 | 0.592244 | ||||||||
\(983\) | −36.9930 | −1.17989 | −0.589946 | − | 0.807442i | \(-0.700851\pi\) | ||||
−0.589946 | + | 0.807442i | \(0.700851\pi\) | |||||||
\(984\) | −0.193601 | −0.00617177 | ||||||||
\(985\) | 20.2110 | 0.643977 | ||||||||
\(986\) | 9.95330 | 0.316978 | ||||||||
\(987\) | −11.9105 | −0.379114 | ||||||||
\(988\) | −6.23328 | −0.198307 | ||||||||
\(989\) | −10.1525 | −0.322829 | ||||||||
\(990\) | 12.6205 | 0.401105 | ||||||||
\(991\) | 50.0465 | 1.58978 | 0.794889 | − | 0.606754i | \(-0.207529\pi\) | ||||
0.794889 | + | 0.606754i | \(0.207529\pi\) | |||||||
\(992\) | 6.23328 | 0.197907 | ||||||||
\(993\) | −28.9168 | −0.917646 | ||||||||
\(994\) | −19.0593 | −0.604525 | ||||||||
\(995\) | −12.2399 | −0.388030 | ||||||||
\(996\) | −6.59680 | −0.209028 | ||||||||
\(997\) | 29.5167 | 0.934805 | 0.467402 | − | 0.884045i | \(-0.345190\pi\) | ||||
0.467402 | + | 0.884045i | \(0.345190\pi\) | |||||||
\(998\) | 25.0863 | 0.794092 | ||||||||
\(999\) | −6.86001 | −0.217041 |
(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 | 8034.2.a.n.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.n.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial |