Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [931,2,Mod(1,931)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(931, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("931.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 931 = 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 931.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: | \(7.43407242818\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 133) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 931.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | −0.437016 | −0.218508 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | −2.61803 | −1.51152 | −0.755761 | − | 0.654847i | \(-0.772733\pi\) | ||||
−0.755761 | + | 0.654847i | \(0.772733\pi\) | |||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | −1.00000 | −0.447214 | −0.223607 | − | 0.974679i | \(-0.571783\pi\) | ||||
−0.223607 | + | 0.974679i | \(0.571783\pi\) | |||||||
\(6\) | 1.61803 | 0.660560 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 3.85410 | 1.28470 | ||||||||
\(10\) | 0.618034 | 0.195440 | ||||||||
\(11\) | −1.61803 | −0.487856 | −0.243928 | − | 0.969793i | \(-0.578436\pi\) | ||||
−0.243928 | + | 0.969793i | \(0.578436\pi\) | |||||||
\(12\) | 4.23607 | 1.22285 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.61803 | 0.675973 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | 2.85410 | 0.692221 | 0.346111 | − | 0.938194i | \(-0.387502\pi\) | ||||
0.346111 | + | 0.938194i | \(0.387502\pi\) | |||||||
\(18\) | −2.38197 | −0.561435 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 1.61803 | 0.361803 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 3.47214 | 0.723990 | 0.361995 | − | 0.932180i | \(-0.382096\pi\) | ||||
0.361995 | + | 0.932180i | \(0.382096\pi\) | |||||||
\(24\) | −5.85410 | −1.19496 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | −0.618034 | −0.121206 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.61803 | 0.671852 | 0.335926 | − | 0.941888i | \(-0.390951\pi\) | ||||
0.335926 | + | 0.941888i | \(0.390951\pi\) | |||||||
\(30\) | −1.61803 | −0.295411 | ||||||||
\(31\) | 10.5623 | 1.89705 | 0.948523 | − | 0.316708i | \(-0.102578\pi\) | ||||
0.948523 | + | 0.316708i | \(0.102578\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | 4.23607 | 0.737405 | ||||||||
\(34\) | −1.76393 | −0.302512 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.23607 | −1.03934 | ||||||||
\(37\) | −11.4721 | −1.88601 | −0.943004 | − | 0.332782i | \(-0.892013\pi\) | ||||
−0.943004 | + | 0.332782i | \(0.892013\pi\) | |||||||
\(38\) | −0.618034 | −0.100258 | ||||||||
\(39\) | −2.61803 | −0.419221 | ||||||||
\(40\) | −2.23607 | −0.353553 | ||||||||
\(41\) | −10.0902 | −1.57582 | −0.787910 | − | 0.615791i | \(-0.788837\pi\) | ||||
−0.787910 | + | 0.615791i | \(0.788837\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.472136 | −0.0720001 | −0.0360000 | − | 0.999352i | \(-0.511462\pi\) | ||||
−0.0360000 | + | 0.999352i | \(0.511462\pi\) | |||||||
\(44\) | 2.61803 | 0.394683 | ||||||||
\(45\) | −3.85410 | −0.574536 | ||||||||
\(46\) | −2.14590 | −0.316395 | ||||||||
\(47\) | 1.47214 | 0.214733 | 0.107367 | − | 0.994220i | \(-0.465758\pi\) | ||||
0.107367 | + | 0.994220i | \(0.465758\pi\) | |||||||
\(48\) | −4.85410 | −0.700629 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.47214 | 0.349613 | ||||||||
\(51\) | −7.47214 | −1.04631 | ||||||||
\(52\) | −1.61803 | −0.224381 | ||||||||
\(53\) | −1.85410 | −0.254680 | −0.127340 | − | 0.991859i | \(-0.540644\pi\) | ||||
−0.127340 | + | 0.991859i | \(0.540644\pi\) | |||||||
\(54\) | 1.38197 | 0.188062 | ||||||||
\(55\) | 1.61803 | 0.218176 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.61803 | −0.346767 | ||||||||
\(58\) | −2.23607 | −0.293610 | ||||||||
\(59\) | −12.2361 | −1.59300 | −0.796500 | − | 0.604638i | \(-0.793318\pi\) | ||||
−0.796500 | + | 0.604638i | \(0.793318\pi\) | |||||||
\(60\) | −4.23607 | −0.546874 | ||||||||
\(61\) | −5.94427 | −0.761086 | −0.380543 | − | 0.924763i | \(-0.624263\pi\) | ||||
−0.380543 | + | 0.924763i | \(0.624263\pi\) | |||||||
\(62\) | −6.52786 | −0.829040 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | −2.61803 | −0.322258 | ||||||||
\(67\) | 13.3262 | 1.62806 | 0.814030 | − | 0.580823i | \(-0.197269\pi\) | ||||
0.814030 | + | 0.580823i | \(0.197269\pi\) | |||||||
\(68\) | −4.61803 | −0.560019 | ||||||||
\(69\) | −9.09017 | −1.09433 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.70820 | −0.558761 | −0.279381 | − | 0.960180i | \(-0.590129\pi\) | ||||
−0.279381 | + | 0.960180i | \(0.590129\pi\) | |||||||
\(72\) | 8.61803 | 1.01565 | ||||||||
\(73\) | −4.32624 | −0.506348 | −0.253174 | − | 0.967421i | \(-0.581474\pi\) | ||||
−0.253174 | + | 0.967421i | \(0.581474\pi\) | |||||||
\(74\) | 7.09017 | 0.824216 | ||||||||
\(75\) | 10.4721 | 1.20922 | ||||||||
\(76\) | −1.61803 | −0.185601 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.61803 | 0.183206 | ||||||||
\(79\) | 4.47214 | 0.503155 | 0.251577 | − | 0.967837i | \(-0.419051\pi\) | ||||
0.251577 | + | 0.967837i | \(0.419051\pi\) | |||||||
\(80\) | −1.85410 | −0.207295 | ||||||||
\(81\) | −5.70820 | −0.634245 | ||||||||
\(82\) | 6.23607 | 0.688659 | ||||||||
\(83\) | −9.85410 | −1.08163 | −0.540814 | − | 0.841142i | \(-0.681884\pi\) | ||||
−0.540814 | + | 0.841142i | \(0.681884\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.85410 | −0.309571 | ||||||||
\(86\) | 0.291796 | 0.0314652 | ||||||||
\(87\) | −9.47214 | −1.01552 | ||||||||
\(88\) | −3.61803 | −0.385684 | ||||||||
\(89\) | −7.23607 | −0.767022 | −0.383511 | − | 0.923536i | \(-0.625285\pi\) | ||||
−0.383511 | + | 0.923536i | \(0.625285\pi\) | |||||||
\(90\) | 2.38197 | 0.251081 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.61803 | −0.585721 | ||||||||
\(93\) | −27.6525 | −2.86743 | ||||||||
\(94\) | −0.909830 | −0.0938418 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 14.7082 | 1.50115 | ||||||||
\(97\) | 1.47214 | 0.149473 | 0.0747364 | − | 0.997203i | \(-0.476188\pi\) | ||||
0.0747364 | + | 0.997203i | \(0.476188\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.23607 | −0.626748 | ||||||||
\(100\) | 6.47214 | 0.647214 | ||||||||
\(101\) | 19.1803 | 1.90852 | 0.954258 | − | 0.298986i | \(-0.0966483\pi\) | ||||
0.954258 | + | 0.298986i | \(0.0966483\pi\) | |||||||
\(102\) | 4.61803 | 0.457254 | ||||||||
\(103\) | −0.708204 | −0.0697814 | −0.0348907 | − | 0.999391i | \(-0.511108\pi\) | ||||
−0.0348907 | + | 0.999391i | \(0.511108\pi\) | |||||||
\(104\) | 2.23607 | 0.219265 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.14590 | 0.111299 | ||||||||
\(107\) | 10.2361 | 0.989558 | 0.494779 | − | 0.869019i | \(-0.335249\pi\) | ||||
0.494779 | + | 0.869019i | \(0.335249\pi\) | |||||||
\(108\) | 3.61803 | 0.348145 | ||||||||
\(109\) | −7.76393 | −0.743650 | −0.371825 | − | 0.928303i | \(-0.621268\pi\) | ||||
−0.371825 | + | 0.928303i | \(0.621268\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 30.0344 | 2.85074 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.2705 | 1.24838 | 0.624192 | − | 0.781271i | \(-0.285428\pi\) | ||||
0.624192 | + | 0.781271i | \(0.285428\pi\) | |||||||
\(114\) | 1.61803 | 0.151543 | ||||||||
\(115\) | −3.47214 | −0.323778 | ||||||||
\(116\) | −5.85410 | −0.543540 | ||||||||
\(117\) | 3.85410 | 0.356312 | ||||||||
\(118\) | 7.56231 | 0.696167 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.85410 | 0.534404 | ||||||||
\(121\) | −8.38197 | −0.761997 | ||||||||
\(122\) | 3.67376 | 0.332607 | ||||||||
\(123\) | 26.4164 | 2.38189 | ||||||||
\(124\) | −17.0902 | −1.53474 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.70820 | 0.861464 | 0.430732 | − | 0.902480i | \(-0.358255\pi\) | ||||
0.430732 | + | 0.902480i | \(0.358255\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | 1.23607 | 0.108830 | ||||||||
\(130\) | 0.618034 | 0.0542052 | ||||||||
\(131\) | −14.5623 | −1.27231 | −0.636157 | − | 0.771559i | \(-0.719477\pi\) | ||||
−0.636157 | + | 0.771559i | \(0.719477\pi\) | |||||||
\(132\) | −6.85410 | −0.596573 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.23607 | −0.711488 | ||||||||
\(135\) | 2.23607 | 0.192450 | ||||||||
\(136\) | 6.38197 | 0.547249 | ||||||||
\(137\) | −10.9443 | −0.935032 | −0.467516 | − | 0.883985i | \(-0.654851\pi\) | ||||
−0.467516 | + | 0.883985i | \(0.654851\pi\) | |||||||
\(138\) | 5.61803 | 0.478239 | ||||||||
\(139\) | 0.527864 | 0.0447728 | 0.0223864 | − | 0.999749i | \(-0.492874\pi\) | ||||
0.0223864 | + | 0.999749i | \(0.492874\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.85410 | −0.324574 | ||||||||
\(142\) | 2.90983 | 0.244188 | ||||||||
\(143\) | −1.61803 | −0.135307 | ||||||||
\(144\) | 7.14590 | 0.595492 | ||||||||
\(145\) | −3.61803 | −0.300461 | ||||||||
\(146\) | 2.67376 | 0.221282 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 18.5623 | 1.52581 | ||||||||
\(149\) | −19.4721 | −1.59522 | −0.797610 | − | 0.603174i | \(-0.793903\pi\) | ||||
−0.797610 | + | 0.603174i | \(0.793903\pi\) | |||||||
\(150\) | −6.47214 | −0.528448 | ||||||||
\(151\) | 19.0344 | 1.54900 | 0.774500 | − | 0.632573i | \(-0.218001\pi\) | ||||
0.774500 | + | 0.632573i | \(0.218001\pi\) | |||||||
\(152\) | 2.23607 | 0.181369 | ||||||||
\(153\) | 11.0000 | 0.889297 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.5623 | −0.848385 | ||||||||
\(156\) | 4.23607 | 0.339157 | ||||||||
\(157\) | −3.32624 | −0.265463 | −0.132731 | − | 0.991152i | \(-0.542375\pi\) | ||||
−0.132731 | + | 0.991152i | \(0.542375\pi\) | |||||||
\(158\) | −2.76393 | −0.219887 | ||||||||
\(159\) | 4.85410 | 0.384955 | ||||||||
\(160\) | 5.61803 | 0.444145 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.52786 | 0.277175 | ||||||||
\(163\) | −20.7984 | −1.62905 | −0.814527 | − | 0.580125i | \(-0.803004\pi\) | ||||
−0.814527 | + | 0.580125i | \(0.803004\pi\) | |||||||
\(164\) | 16.3262 | 1.27486 | ||||||||
\(165\) | −4.23607 | −0.329777 | ||||||||
\(166\) | 6.09017 | 0.472689 | ||||||||
\(167\) | 1.47214 | 0.113917 | 0.0569587 | − | 0.998377i | \(-0.481860\pi\) | ||||
0.0569587 | + | 0.998377i | \(0.481860\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 1.76393 | 0.135287 | ||||||||
\(171\) | 3.85410 | 0.294731 | ||||||||
\(172\) | 0.763932 | 0.0582493 | ||||||||
\(173\) | −16.7639 | −1.27454 | −0.637269 | − | 0.770641i | \(-0.719936\pi\) | ||||
−0.637269 | + | 0.770641i | \(0.719936\pi\) | |||||||
\(174\) | 5.85410 | 0.443798 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | 32.0344 | 2.40786 | ||||||||
\(178\) | 4.47214 | 0.335201 | ||||||||
\(179\) | −18.7426 | −1.40089 | −0.700446 | − | 0.713706i | \(-0.747015\pi\) | ||||
−0.700446 | + | 0.713706i | \(0.747015\pi\) | |||||||
\(180\) | 6.23607 | 0.464809 | ||||||||
\(181\) | 16.0902 | 1.19597 | 0.597986 | − | 0.801506i | \(-0.295968\pi\) | ||||
0.597986 | + | 0.801506i | \(0.295968\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.5623 | 1.15040 | ||||||||
\(184\) | 7.76393 | 0.572365 | ||||||||
\(185\) | 11.4721 | 0.843448 | ||||||||
\(186\) | 17.0902 | 1.25311 | ||||||||
\(187\) | −4.61803 | −0.337704 | ||||||||
\(188\) | −2.38197 | −0.173723 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.618034 | 0.0448369 | ||||||||
\(191\) | 14.0344 | 1.01550 | 0.507748 | − | 0.861505i | \(-0.330478\pi\) | ||||
0.507748 | + | 0.861505i | \(0.330478\pi\) | |||||||
\(192\) | 0.618034 | 0.0446028 | ||||||||
\(193\) | 5.90983 | 0.425399 | 0.212699 | − | 0.977118i | \(-0.431774\pi\) | ||||
0.212699 | + | 0.977118i | \(0.431774\pi\) | |||||||
\(194\) | −0.909830 | −0.0653220 | ||||||||
\(195\) | 2.61803 | 0.187481 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.5623 | −1.39376 | −0.696878 | − | 0.717189i | \(-0.745428\pi\) | ||||
−0.696878 | + | 0.717189i | \(0.745428\pi\) | |||||||
\(198\) | 3.85410 | 0.273899 | ||||||||
\(199\) | −10.5279 | −0.746300 | −0.373150 | − | 0.927771i | \(-0.621722\pi\) | ||||
−0.373150 | + | 0.927771i | \(0.621722\pi\) | |||||||
\(200\) | −8.94427 | −0.632456 | ||||||||
\(201\) | −34.8885 | −2.46085 | ||||||||
\(202\) | −11.8541 | −0.834052 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 12.0902 | 0.846481 | ||||||||
\(205\) | 10.0902 | 0.704728 | ||||||||
\(206\) | 0.437694 | 0.0304956 | ||||||||
\(207\) | 13.3820 | 0.930111 | ||||||||
\(208\) | 1.85410 | 0.128559 | ||||||||
\(209\) | −1.61803 | −0.111922 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.67376 | 0.115227 | 0.0576133 | − | 0.998339i | \(-0.481651\pi\) | ||||
0.0576133 | + | 0.998339i | \(0.481651\pi\) | |||||||
\(212\) | 3.00000 | 0.206041 | ||||||||
\(213\) | 12.3262 | 0.844580 | ||||||||
\(214\) | −6.32624 | −0.432453 | ||||||||
\(215\) | 0.472136 | 0.0321994 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.79837 | 0.324987 | ||||||||
\(219\) | 11.3262 | 0.765356 | ||||||||
\(220\) | −2.61803 | −0.176508 | ||||||||
\(221\) | 2.85410 | 0.191988 | ||||||||
\(222\) | −18.5623 | −1.24582 | ||||||||
\(223\) | −2.41641 | −0.161815 | −0.0809073 | − | 0.996722i | \(-0.525782\pi\) | ||||
−0.0809073 | + | 0.996722i | \(0.525782\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15.4164 | −1.02776 | ||||||||
\(226\) | −8.20163 | −0.545564 | ||||||||
\(227\) | −5.43769 | −0.360912 | −0.180456 | − | 0.983583i | \(-0.557757\pi\) | ||||
−0.180456 | + | 0.983583i | \(0.557757\pi\) | |||||||
\(228\) | 4.23607 | 0.280540 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 2.14590 | 0.141496 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.09017 | 0.531146 | ||||||||
\(233\) | 6.56231 | 0.429911 | 0.214955 | − | 0.976624i | \(-0.431039\pi\) | ||||
0.214955 | + | 0.976624i | \(0.431039\pi\) | |||||||
\(234\) | −2.38197 | −0.155714 | ||||||||
\(235\) | −1.47214 | −0.0960316 | ||||||||
\(236\) | 19.7984 | 1.28876 | ||||||||
\(237\) | −11.7082 | −0.760530 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.0000 | −1.61712 | −0.808558 | − | 0.588417i | \(-0.799751\pi\) | ||||
−0.808558 | + | 0.588417i | \(0.799751\pi\) | |||||||
\(240\) | 4.85410 | 0.313331 | ||||||||
\(241\) | 8.65248 | 0.557355 | 0.278677 | − | 0.960385i | \(-0.410104\pi\) | ||||
0.278677 | + | 0.960385i | \(0.410104\pi\) | |||||||
\(242\) | 5.18034 | 0.333005 | ||||||||
\(243\) | 21.6525 | 1.38901 | ||||||||
\(244\) | 9.61803 | 0.615732 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −16.3262 | −1.04092 | ||||||||
\(247\) | 1.00000 | 0.0636285 | ||||||||
\(248\) | 23.6180 | 1.49975 | ||||||||
\(249\) | 25.7984 | 1.63491 | ||||||||
\(250\) | −5.56231 | −0.351791 | ||||||||
\(251\) | −26.2705 | −1.65818 | −0.829090 | − | 0.559115i | \(-0.811141\pi\) | ||||
−0.829090 | + | 0.559115i | \(0.811141\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.61803 | −0.353203 | ||||||||
\(254\) | −6.00000 | −0.376473 | ||||||||
\(255\) | 7.47214 | 0.467923 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | 2.32624 | 0.145107 | 0.0725534 | − | 0.997365i | \(-0.476885\pi\) | ||||
0.0725534 | + | 0.997365i | \(0.476885\pi\) | |||||||
\(258\) | −0.763932 | −0.0475603 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.61803 | 0.100346 | ||||||||
\(261\) | 13.9443 | 0.863129 | ||||||||
\(262\) | 9.00000 | 0.556022 | ||||||||
\(263\) | −3.56231 | −0.219661 | −0.109831 | − | 0.993950i | \(-0.535031\pi\) | ||||
−0.109831 | + | 0.993950i | \(0.535031\pi\) | |||||||
\(264\) | 9.47214 | 0.582970 | ||||||||
\(265\) | 1.85410 | 0.113897 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.9443 | 1.15937 | ||||||||
\(268\) | −21.5623 | −1.31713 | ||||||||
\(269\) | −20.9787 | −1.27909 | −0.639547 | − | 0.768752i | \(-0.720878\pi\) | ||||
−0.639547 | + | 0.768752i | \(0.720878\pi\) | |||||||
\(270\) | −1.38197 | −0.0841038 | ||||||||
\(271\) | 5.43769 | 0.330316 | 0.165158 | − | 0.986267i | \(-0.447187\pi\) | ||||
0.165158 | + | 0.986267i | \(0.447187\pi\) | |||||||
\(272\) | 5.29180 | 0.320862 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.76393 | 0.408624 | ||||||||
\(275\) | 6.47214 | 0.390284 | ||||||||
\(276\) | 14.7082 | 0.885330 | ||||||||
\(277\) | 23.1246 | 1.38942 | 0.694712 | − | 0.719288i | \(-0.255532\pi\) | ||||
0.694712 | + | 0.719288i | \(0.255532\pi\) | |||||||
\(278\) | −0.326238 | −0.0195665 | ||||||||
\(279\) | 40.7082 | 2.43714 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.7082 | −1.47397 | −0.736984 | − | 0.675910i | \(-0.763751\pi\) | ||||
−0.736984 | + | 0.675910i | \(0.763751\pi\) | |||||||
\(282\) | 2.38197 | 0.141844 | ||||||||
\(283\) | −27.0902 | −1.61034 | −0.805172 | − | 0.593042i | \(-0.797927\pi\) | ||||
−0.805172 | + | 0.593042i | \(0.797927\pi\) | |||||||
\(284\) | 7.61803 | 0.452047 | ||||||||
\(285\) | 2.61803 | 0.155079 | ||||||||
\(286\) | 1.00000 | 0.0591312 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −21.6525 | −1.27588 | ||||||||
\(289\) | −8.85410 | −0.520830 | ||||||||
\(290\) | 2.23607 | 0.131306 | ||||||||
\(291\) | −3.85410 | −0.225931 | ||||||||
\(292\) | 7.00000 | 0.409644 | ||||||||
\(293\) | −21.7639 | −1.27146 | −0.635731 | − | 0.771910i | \(-0.719301\pi\) | ||||
−0.635731 | + | 0.771910i | \(0.719301\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2361 | 0.712411 | ||||||||
\(296\) | −25.6525 | −1.49102 | ||||||||
\(297\) | 3.61803 | 0.209940 | ||||||||
\(298\) | 12.0344 | 0.697136 | ||||||||
\(299\) | 3.47214 | 0.200799 | ||||||||
\(300\) | −16.9443 | −0.978278 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −11.7639 | −0.676938 | ||||||||
\(303\) | −50.2148 | −2.88476 | ||||||||
\(304\) | 1.85410 | 0.106340 | ||||||||
\(305\) | 5.94427 | 0.340368 | ||||||||
\(306\) | −6.79837 | −0.388637 | ||||||||
\(307\) | 10.7426 | 0.613115 | 0.306558 | − | 0.951852i | \(-0.400823\pi\) | ||||
0.306558 | + | 0.951852i | \(0.400823\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.85410 | 0.105476 | ||||||||
\(310\) | 6.52786 | 0.370758 | ||||||||
\(311\) | −22.4508 | −1.27307 | −0.636535 | − | 0.771247i | \(-0.719633\pi\) | ||||
−0.636535 | + | 0.771247i | \(0.719633\pi\) | |||||||
\(312\) | −5.85410 | −0.331423 | ||||||||
\(313\) | 25.5967 | 1.44681 | 0.723407 | − | 0.690422i | \(-0.242575\pi\) | ||||
0.723407 | + | 0.690422i | \(0.242575\pi\) | |||||||
\(314\) | 2.05573 | 0.116011 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.23607 | −0.407061 | ||||||||
\(317\) | −5.41641 | −0.304216 | −0.152108 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152108 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(318\) | −3.00000 | −0.168232 | ||||||||
\(319\) | −5.85410 | −0.327767 | ||||||||
\(320\) | 0.236068 | 0.0131966 | ||||||||
\(321\) | −26.7984 | −1.49574 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.85410 | 0.158806 | ||||||||
\(324\) | 9.23607 | 0.513115 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 12.8541 | 0.711923 | ||||||||
\(327\) | 20.3262 | 1.12404 | ||||||||
\(328\) | −22.5623 | −1.24579 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.61803 | 0.144118 | ||||||||
\(331\) | 7.85410 | 0.431700 | 0.215850 | − | 0.976426i | \(-0.430748\pi\) | ||||
0.215850 | + | 0.976426i | \(0.430748\pi\) | |||||||
\(332\) | 15.9443 | 0.875056 | ||||||||
\(333\) | −44.2148 | −2.42296 | ||||||||
\(334\) | −0.909830 | −0.0497837 | ||||||||
\(335\) | −13.3262 | −0.728090 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.7984 | 0.969539 | 0.484770 | − | 0.874642i | \(-0.338903\pi\) | ||||
0.484770 | + | 0.874642i | \(0.338903\pi\) | |||||||
\(338\) | 7.41641 | 0.403399 | ||||||||
\(339\) | −34.7426 | −1.88696 | ||||||||
\(340\) | 4.61803 | 0.250448 | ||||||||
\(341\) | −17.0902 | −0.925485 | ||||||||
\(342\) | −2.38197 | −0.128802 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.05573 | −0.0569210 | ||||||||
\(345\) | 9.09017 | 0.489398 | ||||||||
\(346\) | 10.3607 | 0.556994 | ||||||||
\(347\) | 22.7984 | 1.22388 | 0.611940 | − | 0.790904i | \(-0.290389\pi\) | ||||
0.611940 | + | 0.790904i | \(0.290389\pi\) | |||||||
\(348\) | 15.3262 | 0.821573 | ||||||||
\(349\) | 10.9787 | 0.587677 | 0.293839 | − | 0.955855i | \(-0.405067\pi\) | ||||
0.293839 | + | 0.955855i | \(0.405067\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.23607 | −0.119352 | ||||||||
\(352\) | 9.09017 | 0.484508 | ||||||||
\(353\) | 20.2705 | 1.07889 | 0.539445 | − | 0.842021i | \(-0.318634\pi\) | ||||
0.539445 | + | 0.842021i | \(0.318634\pi\) | |||||||
\(354\) | −19.7984 | −1.05227 | ||||||||
\(355\) | 4.70820 | 0.249886 | ||||||||
\(356\) | 11.7082 | 0.620534 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.5836 | 0.612212 | ||||||||
\(359\) | −22.5623 | −1.19079 | −0.595396 | − | 0.803432i | \(-0.703005\pi\) | ||||
−0.595396 | + | 0.803432i | \(0.703005\pi\) | |||||||
\(360\) | −8.61803 | −0.454210 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −9.94427 | −0.522659 | ||||||||
\(363\) | 21.9443 | 1.15178 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.32624 | 0.226446 | ||||||||
\(366\) | −9.61803 | −0.502743 | ||||||||
\(367\) | 14.2361 | 0.743117 | 0.371558 | − | 0.928410i | \(-0.378824\pi\) | ||||
0.371558 | + | 0.928410i | \(0.378824\pi\) | |||||||
\(368\) | 6.43769 | 0.335588 | ||||||||
\(369\) | −38.8885 | −2.02446 | ||||||||
\(370\) | −7.09017 | −0.368600 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 44.7426 | 2.31980 | ||||||||
\(373\) | 15.3820 | 0.796448 | 0.398224 | − | 0.917288i | \(-0.369627\pi\) | ||||
0.398224 | + | 0.917288i | \(0.369627\pi\) | |||||||
\(374\) | 2.85410 | 0.147582 | ||||||||
\(375\) | −23.5623 | −1.21675 | ||||||||
\(376\) | 3.29180 | 0.169761 | ||||||||
\(377\) | 3.61803 | 0.186338 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.0000 | −0.770498 | −0.385249 | − | 0.922813i | \(-0.625884\pi\) | ||||
−0.385249 | + | 0.922813i | \(0.625884\pi\) | |||||||
\(380\) | 1.61803 | 0.0830034 | ||||||||
\(381\) | −25.4164 | −1.30212 | ||||||||
\(382\) | −8.67376 | −0.443788 | ||||||||
\(383\) | 12.7082 | 0.649359 | 0.324679 | − | 0.945824i | \(-0.394744\pi\) | ||||
0.324679 | + | 0.945824i | \(0.394744\pi\) | |||||||
\(384\) | −29.7984 | −1.52064 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.65248 | −0.185906 | ||||||||
\(387\) | −1.81966 | −0.0924985 | ||||||||
\(388\) | −2.38197 | −0.120926 | ||||||||
\(389\) | −17.4377 | −0.884126 | −0.442063 | − | 0.896984i | \(-0.645753\pi\) | ||||
−0.442063 | + | 0.896984i | \(0.645753\pi\) | |||||||
\(390\) | −1.61803 | −0.0819323 | ||||||||
\(391\) | 9.90983 | 0.501162 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 38.1246 | 1.92313 | ||||||||
\(394\) | 12.0902 | 0.609094 | ||||||||
\(395\) | −4.47214 | −0.225018 | ||||||||
\(396\) | 10.0902 | 0.507050 | ||||||||
\(397\) | 4.76393 | 0.239095 | 0.119547 | − | 0.992828i | \(-0.461856\pi\) | ||||
0.119547 | + | 0.992828i | \(0.461856\pi\) | |||||||
\(398\) | 6.50658 | 0.326145 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.41641 | −0.370820 | ||||||||
\(401\) | −23.9787 | −1.19744 | −0.598720 | − | 0.800958i | \(-0.704324\pi\) | ||||
−0.598720 | + | 0.800958i | \(0.704324\pi\) | |||||||
\(402\) | 21.5623 | 1.07543 | ||||||||
\(403\) | 10.5623 | 0.526146 | ||||||||
\(404\) | −31.0344 | −1.54402 | ||||||||
\(405\) | 5.70820 | 0.283643 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.5623 | 0.920099 | ||||||||
\(408\) | −16.7082 | −0.827179 | ||||||||
\(409\) | −28.2148 | −1.39513 | −0.697566 | − | 0.716521i | \(-0.745733\pi\) | ||||
−0.697566 | + | 0.716521i | \(0.745733\pi\) | |||||||
\(410\) | −6.23607 | −0.307977 | ||||||||
\(411\) | 28.6525 | 1.41332 | ||||||||
\(412\) | 1.14590 | 0.0564543 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.27051 | −0.406473 | ||||||||
\(415\) | 9.85410 | 0.483719 | ||||||||
\(416\) | −5.61803 | −0.275447 | ||||||||
\(417\) | −1.38197 | −0.0676752 | ||||||||
\(418\) | 1.00000 | 0.0489116 | ||||||||
\(419\) | −0.527864 | −0.0257878 | −0.0128939 | − | 0.999917i | \(-0.504104\pi\) | ||||
−0.0128939 | + | 0.999917i | \(0.504104\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.4164 | 1.48241 | 0.741203 | − | 0.671281i | \(-0.234256\pi\) | ||||
0.741203 | + | 0.671281i | \(0.234256\pi\) | |||||||
\(422\) | −1.03444 | −0.0503558 | ||||||||
\(423\) | 5.67376 | 0.275868 | ||||||||
\(424\) | −4.14590 | −0.201343 | ||||||||
\(425\) | −11.4164 | −0.553777 | ||||||||
\(426\) | −7.61803 | −0.369095 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −16.5623 | −0.800569 | ||||||||
\(429\) | 4.23607 | 0.204519 | ||||||||
\(430\) | −0.291796 | −0.0140717 | ||||||||
\(431\) | −23.5279 | −1.13330 | −0.566649 | − | 0.823960i | \(-0.691760\pi\) | ||||
−0.566649 | + | 0.823960i | \(0.691760\pi\) | |||||||
\(432\) | −4.14590 | −0.199470 | ||||||||
\(433\) | −24.1246 | −1.15935 | −0.579677 | − | 0.814846i | \(-0.696821\pi\) | ||||
−0.579677 | + | 0.814846i | \(0.696821\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.47214 | 0.454154 | ||||||||
\(436\) | 12.5623 | 0.601625 | ||||||||
\(437\) | 3.47214 | 0.166095 | ||||||||
\(438\) | −7.00000 | −0.334473 | ||||||||
\(439\) | 23.4164 | 1.11760 | 0.558802 | − | 0.829301i | \(-0.311261\pi\) | ||||
0.558802 | + | 0.829301i | \(0.311261\pi\) | |||||||
\(440\) | 3.61803 | 0.172483 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.76393 | −0.0839017 | ||||||||
\(443\) | 10.9098 | 0.518342 | 0.259171 | − | 0.965831i | \(-0.416551\pi\) | ||||
0.259171 | + | 0.965831i | \(0.416551\pi\) | |||||||
\(444\) | −48.5967 | −2.30630 | ||||||||
\(445\) | 7.23607 | 0.343023 | ||||||||
\(446\) | 1.49342 | 0.0707156 | ||||||||
\(447\) | 50.9787 | 2.41121 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.3820 | −0.537148 | −0.268574 | − | 0.963259i | \(-0.586552\pi\) | ||||
−0.268574 | + | 0.963259i | \(0.586552\pi\) | |||||||
\(450\) | 9.52786 | 0.449148 | ||||||||
\(451\) | 16.3262 | 0.768773 | ||||||||
\(452\) | −21.4721 | −1.00996 | ||||||||
\(453\) | −49.8328 | −2.34135 | ||||||||
\(454\) | 3.36068 | 0.157725 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.85410 | −0.274143 | ||||||||
\(457\) | 14.9098 | 0.697452 | 0.348726 | − | 0.937225i | \(-0.386614\pi\) | ||||
0.348726 | + | 0.937225i | \(0.386614\pi\) | |||||||
\(458\) | 6.18034 | 0.288788 | ||||||||
\(459\) | −6.38197 | −0.297885 | ||||||||
\(460\) | 5.61803 | 0.261942 | ||||||||
\(461\) | −26.1459 | −1.21774 | −0.608868 | − | 0.793272i | \(-0.708376\pi\) | ||||
−0.608868 | + | 0.793272i | \(0.708376\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.0689 | −1.62979 | −0.814895 | − | 0.579609i | \(-0.803205\pi\) | ||||
−0.814895 | + | 0.579609i | \(0.803205\pi\) | |||||||
\(464\) | 6.70820 | 0.311421 | ||||||||
\(465\) | 27.6525 | 1.28235 | ||||||||
\(466\) | −4.05573 | −0.187878 | ||||||||
\(467\) | 8.90983 | 0.412298 | 0.206149 | − | 0.978521i | \(-0.433907\pi\) | ||||
0.206149 | + | 0.978521i | \(0.433907\pi\) | |||||||
\(468\) | −6.23607 | −0.288262 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.909830 | 0.0419673 | ||||||||
\(471\) | 8.70820 | 0.401253 | ||||||||
\(472\) | −27.3607 | −1.25938 | ||||||||
\(473\) | 0.763932 | 0.0351256 | ||||||||
\(474\) | 7.23607 | 0.332364 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.14590 | −0.327188 | ||||||||
\(478\) | 15.4508 | 0.706705 | ||||||||
\(479\) | −9.79837 | −0.447699 | −0.223850 | − | 0.974624i | \(-0.571862\pi\) | ||||
−0.223850 | + | 0.974624i | \(0.571862\pi\) | |||||||
\(480\) | −14.7082 | −0.671335 | ||||||||
\(481\) | −11.4721 | −0.523084 | ||||||||
\(482\) | −5.34752 | −0.243573 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.5623 | 0.616468 | ||||||||
\(485\) | −1.47214 | −0.0668463 | ||||||||
\(486\) | −13.3820 | −0.607018 | ||||||||
\(487\) | −14.2361 | −0.645098 | −0.322549 | − | 0.946553i | \(-0.604540\pi\) | ||||
−0.322549 | + | 0.946553i | \(0.604540\pi\) | |||||||
\(488\) | −13.2918 | −0.601691 | ||||||||
\(489\) | 54.4508 | 2.46235 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.5279 | 0.791021 | 0.395511 | − | 0.918461i | \(-0.370568\pi\) | ||||
0.395511 | + | 0.918461i | \(0.370568\pi\) | |||||||
\(492\) | −42.7426 | −1.92699 | ||||||||
\(493\) | 10.3262 | 0.465070 | ||||||||
\(494\) | −0.618034 | −0.0278067 | ||||||||
\(495\) | 6.23607 | 0.280290 | ||||||||
\(496\) | 19.5836 | 0.879329 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −15.9443 | −0.714480 | ||||||||
\(499\) | −28.6180 | −1.28112 | −0.640560 | − | 0.767908i | \(-0.721298\pi\) | ||||
−0.640560 | + | 0.767908i | \(0.721298\pi\) | |||||||
\(500\) | −14.5623 | −0.651246 | ||||||||
\(501\) | −3.85410 | −0.172189 | ||||||||
\(502\) | 16.2361 | 0.724651 | ||||||||
\(503\) | 4.94427 | 0.220454 | 0.110227 | − | 0.993906i | \(-0.464842\pi\) | ||||
0.110227 | + | 0.993906i | \(0.464842\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.1803 | −0.853514 | ||||||||
\(506\) | 3.47214 | 0.154355 | ||||||||
\(507\) | 31.4164 | 1.39525 | ||||||||
\(508\) | −15.7082 | −0.696939 | ||||||||
\(509\) | 10.0000 | 0.443242 | 0.221621 | − | 0.975133i | \(-0.428865\pi\) | ||||
0.221621 | + | 0.975133i | \(0.428865\pi\) | |||||||
\(510\) | −4.61803 | −0.204490 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | −2.23607 | −0.0987248 | ||||||||
\(514\) | −1.43769 | −0.0634140 | ||||||||
\(515\) | 0.708204 | 0.0312072 | ||||||||
\(516\) | −2.00000 | −0.0880451 | ||||||||
\(517\) | −2.38197 | −0.104759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 43.8885 | 1.92649 | ||||||||
\(520\) | −2.23607 | −0.0980581 | ||||||||
\(521\) | 9.18034 | 0.402198 | 0.201099 | − | 0.979571i | \(-0.435549\pi\) | ||||
0.201099 | + | 0.979571i | \(0.435549\pi\) | |||||||
\(522\) | −8.61803 | −0.377201 | ||||||||
\(523\) | 3.11146 | 0.136054 | 0.0680272 | − | 0.997683i | \(-0.478330\pi\) | ||||
0.0680272 | + | 0.997683i | \(0.478330\pi\) | |||||||
\(524\) | 23.5623 | 1.02932 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.20163 | 0.0959955 | ||||||||
\(527\) | 30.1459 | 1.31318 | ||||||||
\(528\) | 7.85410 | 0.341806 | ||||||||
\(529\) | −10.9443 | −0.475838 | ||||||||
\(530\) | −1.14590 | −0.0497746 | ||||||||
\(531\) | −47.1591 | −2.04653 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.0902 | −0.437054 | ||||||||
\(534\) | −11.7082 | −0.506664 | ||||||||
\(535\) | −10.2361 | −0.442544 | ||||||||
\(536\) | 29.7984 | 1.28709 | ||||||||
\(537\) | 49.0689 | 2.11748 | ||||||||
\(538\) | 12.9656 | 0.558985 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.61803 | −0.155695 | ||||||||
\(541\) | −35.8885 | −1.54297 | −0.771485 | − | 0.636248i | \(-0.780485\pi\) | ||||
−0.771485 | + | 0.636248i | \(0.780485\pi\) | |||||||
\(542\) | −3.36068 | −0.144354 | ||||||||
\(543\) | −42.1246 | −1.80774 | ||||||||
\(544\) | −16.0344 | −0.687471 | ||||||||
\(545\) | 7.76393 | 0.332570 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.3820 | −0.572172 | −0.286086 | − | 0.958204i | \(-0.592354\pi\) | ||||
−0.286086 | + | 0.958204i | \(0.592354\pi\) | |||||||
\(548\) | 17.7082 | 0.756457 | ||||||||
\(549\) | −22.9098 | −0.977768 | ||||||||
\(550\) | −4.00000 | −0.170561 | ||||||||
\(551\) | 3.61803 | 0.154133 | ||||||||
\(552\) | −20.3262 | −0.865142 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14.2918 | −0.607200 | ||||||||
\(555\) | −30.0344 | −1.27489 | ||||||||
\(556\) | −0.854102 | −0.0362220 | ||||||||
\(557\) | −12.2016 | −0.516999 | −0.258500 | − | 0.966011i | \(-0.583228\pi\) | ||||
−0.258500 | + | 0.966011i | \(0.583228\pi\) | |||||||
\(558\) | −25.1591 | −1.06507 | ||||||||
\(559\) | −0.472136 | −0.0199692 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0902 | 0.510447 | ||||||||
\(562\) | 15.2705 | 0.644148 | ||||||||
\(563\) | −11.7639 | −0.495791 | −0.247895 | − | 0.968787i | \(-0.579739\pi\) | ||||
−0.247895 | + | 0.968787i | \(0.579739\pi\) | |||||||
\(564\) | 6.23607 | 0.262586 | ||||||||
\(565\) | −13.2705 | −0.558295 | ||||||||
\(566\) | 16.7426 | 0.703746 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.5279 | −0.441739 | ||||||||
\(569\) | 8.41641 | 0.352834 | 0.176417 | − | 0.984316i | \(-0.443549\pi\) | ||||
0.176417 | + | 0.984316i | \(0.443549\pi\) | |||||||
\(570\) | −1.61803 | −0.0677720 | ||||||||
\(571\) | −3.65248 | −0.152851 | −0.0764257 | − | 0.997075i | \(-0.524351\pi\) | ||||
−0.0764257 | + | 0.997075i | \(0.524351\pi\) | |||||||
\(572\) | 2.61803 | 0.109466 | ||||||||
\(573\) | −36.7426 | −1.53495 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.8885 | −0.579192 | ||||||||
\(576\) | −0.909830 | −0.0379096 | ||||||||
\(577\) | 12.7295 | 0.529936 | 0.264968 | − | 0.964257i | \(-0.414639\pi\) | ||||
0.264968 | + | 0.964257i | \(0.414639\pi\) | |||||||
\(578\) | 5.47214 | 0.227611 | ||||||||
\(579\) | −15.4721 | −0.643000 | ||||||||
\(580\) | 5.85410 | 0.243078 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.38197 | 0.0987357 | ||||||||
\(583\) | 3.00000 | 0.124247 | ||||||||
\(584\) | −9.67376 | −0.400303 | ||||||||
\(585\) | −3.85410 | −0.159348 | ||||||||
\(586\) | 13.4508 | 0.555649 | ||||||||
\(587\) | −38.0000 | −1.56843 | −0.784214 | − | 0.620491i | \(-0.786934\pi\) | ||||
−0.784214 | + | 0.620491i | \(0.786934\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.5623 | 0.435212 | ||||||||
\(590\) | −7.56231 | −0.311335 | ||||||||
\(591\) | 51.2148 | 2.10669 | ||||||||
\(592\) | −21.2705 | −0.874213 | ||||||||
\(593\) | 17.1803 | 0.705512 | 0.352756 | − | 0.935715i | \(-0.385245\pi\) | ||||
0.352756 | + | 0.935715i | \(0.385245\pi\) | |||||||
\(594\) | −2.23607 | −0.0917470 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 31.5066 | 1.29056 | ||||||||
\(597\) | 27.5623 | 1.12805 | ||||||||
\(598\) | −2.14590 | −0.0877523 | ||||||||
\(599\) | 10.9787 | 0.448578 | 0.224289 | − | 0.974523i | \(-0.427994\pi\) | ||||
0.224289 | + | 0.974523i | \(0.427994\pi\) | |||||||
\(600\) | 23.4164 | 0.955971 | ||||||||
\(601\) | −14.4377 | −0.588926 | −0.294463 | − | 0.955663i | \(-0.595141\pi\) | ||||
−0.294463 | + | 0.955663i | \(0.595141\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 51.3607 | 2.09157 | ||||||||
\(604\) | −30.7984 | −1.25317 | ||||||||
\(605\) | 8.38197 | 0.340775 | ||||||||
\(606\) | 31.0344 | 1.26069 | ||||||||
\(607\) | 14.2361 | 0.577824 | 0.288912 | − | 0.957356i | \(-0.406706\pi\) | ||||
0.288912 | + | 0.957356i | \(0.406706\pi\) | |||||||
\(608\) | −5.61803 | −0.227841 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.67376 | −0.148746 | ||||||||
\(611\) | 1.47214 | 0.0595562 | ||||||||
\(612\) | −17.7984 | −0.719457 | ||||||||
\(613\) | −0.798374 | −0.0322460 | −0.0161230 | − | 0.999870i | \(-0.505132\pi\) | ||||
−0.0161230 | + | 0.999870i | \(0.505132\pi\) | |||||||
\(614\) | −6.63932 | −0.267941 | ||||||||
\(615\) | −26.4164 | −1.06521 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.8541 | −1.72524 | −0.862621 | − | 0.505851i | \(-0.831178\pi\) | ||||
−0.862621 | + | 0.505851i | \(0.831178\pi\) | |||||||
\(618\) | −1.14590 | −0.0460948 | ||||||||
\(619\) | −1.38197 | −0.0555459 | −0.0277730 | − | 0.999614i | \(-0.508842\pi\) | ||||
−0.0277730 | + | 0.999614i | \(0.508842\pi\) | |||||||
\(620\) | 17.0902 | 0.686358 | ||||||||
\(621\) | −7.76393 | −0.311556 | ||||||||
\(622\) | 13.8754 | 0.556352 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.85410 | −0.194320 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | −15.8197 | −0.632281 | ||||||||
\(627\) | 4.23607 | 0.169172 | ||||||||
\(628\) | 5.38197 | 0.214764 | ||||||||
\(629\) | −32.7426 | −1.30553 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.1803 | 0.922795 | 0.461397 | − | 0.887194i | \(-0.347348\pi\) | ||||
0.461397 | + | 0.887194i | \(0.347348\pi\) | |||||||
\(632\) | 10.0000 | 0.397779 | ||||||||
\(633\) | −4.38197 | −0.174168 | ||||||||
\(634\) | 3.34752 | 0.132947 | ||||||||
\(635\) | −9.70820 | −0.385258 | ||||||||
\(636\) | −7.85410 | −0.311435 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.61803 | 0.143239 | ||||||||
\(639\) | −18.1459 | −0.717841 | ||||||||
\(640\) | −11.3820 | −0.449912 | ||||||||
\(641\) | 12.2016 | 0.481935 | 0.240968 | − | 0.970533i | \(-0.422535\pi\) | ||||
0.240968 | + | 0.970533i | \(0.422535\pi\) | |||||||
\(642\) | 16.5623 | 0.653662 | ||||||||
\(643\) | −19.6525 | −0.775018 | −0.387509 | − | 0.921866i | \(-0.626664\pi\) | ||||
−0.387509 | + | 0.921866i | \(0.626664\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.23607 | −0.0486701 | ||||||||
\(646\) | −1.76393 | −0.0694010 | ||||||||
\(647\) | 10.4164 | 0.409511 | 0.204756 | − | 0.978813i | \(-0.434360\pi\) | ||||
0.204756 | + | 0.978813i | \(0.434360\pi\) | |||||||
\(648\) | −12.7639 | −0.501415 | ||||||||
\(649\) | 19.7984 | 0.777154 | ||||||||
\(650\) | 2.47214 | 0.0969651 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 33.6525 | 1.31793 | ||||||||
\(653\) | 13.0689 | 0.511425 | 0.255712 | − | 0.966753i | \(-0.417690\pi\) | ||||
0.255712 | + | 0.966753i | \(0.417690\pi\) | |||||||
\(654\) | −12.5623 | −0.491225 | ||||||||
\(655\) | 14.5623 | 0.568996 | ||||||||
\(656\) | −18.7082 | −0.730433 | ||||||||
\(657\) | −16.6738 | −0.650505 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.32624 | −0.207481 | −0.103740 | − | 0.994604i | \(-0.533081\pi\) | ||||
−0.103740 | + | 0.994604i | \(0.533081\pi\) | |||||||
\(660\) | 6.85410 | 0.266796 | ||||||||
\(661\) | −2.00000 | −0.0777910 | −0.0388955 | − | 0.999243i | \(-0.512384\pi\) | ||||
−0.0388955 | + | 0.999243i | \(0.512384\pi\) | |||||||
\(662\) | −4.85410 | −0.188660 | ||||||||
\(663\) | −7.47214 | −0.290194 | ||||||||
\(664\) | −22.0344 | −0.855102 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 27.3262 | 1.05887 | ||||||||
\(667\) | 12.5623 | 0.486414 | ||||||||
\(668\) | −2.38197 | −0.0921610 | ||||||||
\(669\) | 6.32624 | 0.244586 | ||||||||
\(670\) | 8.23607 | 0.318187 | ||||||||
\(671\) | 9.61803 | 0.371300 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.5066 | −0.867565 | −0.433782 | − | 0.901018i | \(-0.642821\pi\) | ||||
−0.433782 | + | 0.901018i | \(0.642821\pi\) | |||||||
\(674\) | −11.0000 | −0.423704 | ||||||||
\(675\) | 8.94427 | 0.344265 | ||||||||
\(676\) | 19.4164 | 0.746785 | ||||||||
\(677\) | 39.1591 | 1.50500 | 0.752502 | − | 0.658590i | \(-0.228847\pi\) | ||||
0.752502 | + | 0.658590i | \(0.228847\pi\) | |||||||
\(678\) | 21.4721 | 0.824632 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.38197 | −0.244737 | ||||||||
\(681\) | 14.2361 | 0.545527 | ||||||||
\(682\) | 10.5623 | 0.404452 | ||||||||
\(683\) | 50.7082 | 1.94030 | 0.970148 | − | 0.242515i | \(-0.0779722\pi\) | ||||
0.970148 | + | 0.242515i | \(0.0779722\pi\) | |||||||
\(684\) | −6.23607 | −0.238442 | ||||||||
\(685\) | 10.9443 | 0.418159 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.1803 | 0.998842 | ||||||||
\(688\) | −0.875388 | −0.0333739 | ||||||||
\(689\) | −1.85410 | −0.0706357 | ||||||||
\(690\) | −5.61803 | −0.213875 | ||||||||
\(691\) | 46.5410 | 1.77050 | 0.885252 | − | 0.465112i | \(-0.153986\pi\) | ||||
0.885252 | + | 0.465112i | \(0.153986\pi\) | |||||||
\(692\) | 27.1246 | 1.03112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.0902 | −0.534856 | ||||||||
\(695\) | −0.527864 | −0.0200230 | ||||||||
\(696\) | −21.1803 | −0.802839 | ||||||||
\(697\) | −28.7984 | −1.09082 | ||||||||
\(698\) | −6.78522 | −0.256824 | ||||||||
\(699\) | −17.1803 | −0.649820 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.9443 | −0.639976 | −0.319988 | − | 0.947422i | \(-0.603679\pi\) | ||||
−0.319988 | + | 0.947422i | \(0.603679\pi\) | |||||||
\(702\) | 1.38197 | 0.0521589 | ||||||||
\(703\) | −11.4721 | −0.432680 | ||||||||
\(704\) | 0.381966 | 0.0143959 | ||||||||
\(705\) | 3.85410 | 0.145154 | ||||||||
\(706\) | −12.5279 | −0.471492 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −51.8328 | −1.94800 | ||||||||
\(709\) | 9.87539 | 0.370878 | 0.185439 | − | 0.982656i | \(-0.440629\pi\) | ||||
0.185439 | + | 0.982656i | \(0.440629\pi\) | |||||||
\(710\) | −2.90983 | −0.109204 | ||||||||
\(711\) | 17.2361 | 0.646403 | ||||||||
\(712\) | −16.1803 | −0.606384 | ||||||||
\(713\) | 36.6738 | 1.37344 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.61803 | 0.0605110 | ||||||||
\(716\) | 30.3262 | 1.13334 | ||||||||
\(717\) | 65.4508 | 2.44431 | ||||||||
\(718\) | 13.9443 | 0.520396 | ||||||||
\(719\) | 2.11146 | 0.0787440 | 0.0393720 | − | 0.999225i | \(-0.487464\pi\) | ||||
0.0393720 | + | 0.999225i | \(0.487464\pi\) | |||||||
\(720\) | −7.14590 | −0.266312 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.618034 | −0.0230008 | ||||||||
\(723\) | −22.6525 | −0.842455 | ||||||||
\(724\) | −26.0344 | −0.967562 | ||||||||
\(725\) | −14.4721 | −0.537482 | ||||||||
\(726\) | −13.5623 | −0.503344 | ||||||||
\(727\) | 26.5967 | 0.986419 | 0.493209 | − | 0.869911i | \(-0.335824\pi\) | ||||
0.493209 | + | 0.869911i | \(0.335824\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | −2.67376 | −0.0989604 | ||||||||
\(731\) | −1.34752 | −0.0498400 | ||||||||
\(732\) | −25.1803 | −0.930692 | ||||||||
\(733\) | −0.583592 | −0.0215555 | −0.0107777 | − | 0.999942i | \(-0.503431\pi\) | ||||
−0.0107777 | + | 0.999942i | \(0.503431\pi\) | |||||||
\(734\) | −8.79837 | −0.324754 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.5066 | −0.719022 | ||||||||
\(737\) | −21.5623 | −0.794258 | ||||||||
\(738\) | 24.0344 | 0.884720 | ||||||||
\(739\) | 29.4721 | 1.08415 | 0.542075 | − | 0.840330i | \(-0.317639\pi\) | ||||
0.542075 | + | 0.840330i | \(0.317639\pi\) | |||||||
\(740\) | −18.5623 | −0.682364 | ||||||||
\(741\) | −2.61803 | −0.0961759 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.6525 | 1.45471 | 0.727354 | − | 0.686262i | \(-0.240750\pi\) | ||||
0.727354 | + | 0.686262i | \(0.240750\pi\) | |||||||
\(744\) | −61.8328 | −2.26690 | ||||||||
\(745\) | 19.4721 | 0.713404 | ||||||||
\(746\) | −9.50658 | −0.348061 | ||||||||
\(747\) | −37.9787 | −1.38957 | ||||||||
\(748\) | 7.47214 | 0.273208 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 14.5623 | 0.531740 | ||||||||
\(751\) | 19.5623 | 0.713839 | 0.356919 | − | 0.934135i | \(-0.383827\pi\) | ||||
0.356919 | + | 0.934135i | \(0.383827\pi\) | |||||||
\(752\) | 2.72949 | 0.0995343 | ||||||||
\(753\) | 68.7771 | 2.50638 | ||||||||
\(754\) | −2.23607 | −0.0814328 | ||||||||
\(755\) | −19.0344 | −0.692734 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | 9.27051 | 0.336720 | ||||||||
\(759\) | 14.7082 | 0.533874 | ||||||||
\(760\) | −2.23607 | −0.0811107 | ||||||||
\(761\) | −22.5279 | −0.816634 | −0.408317 | − | 0.912840i | \(-0.633884\pi\) | ||||
−0.408317 | + | 0.912840i | \(0.633884\pi\) | |||||||
\(762\) | 15.7082 | 0.569048 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −22.7082 | −0.821554 | ||||||||
\(765\) | −11.0000 | −0.397706 | ||||||||
\(766\) | −7.85410 | −0.283780 | ||||||||
\(767\) | −12.2361 | −0.441819 | ||||||||
\(768\) | 17.1803 | 0.619942 | ||||||||
\(769\) | −3.41641 | −0.123199 | −0.0615994 | − | 0.998101i | \(-0.519620\pi\) | ||||
−0.0615994 | + | 0.998101i | \(0.519620\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.09017 | −0.219332 | ||||||||
\(772\) | −9.56231 | −0.344155 | ||||||||
\(773\) | −42.5410 | −1.53009 | −0.765047 | − | 0.643974i | \(-0.777284\pi\) | ||||
−0.765047 | + | 0.643974i | \(0.777284\pi\) | |||||||
\(774\) | 1.12461 | 0.0404233 | ||||||||
\(775\) | −42.2492 | −1.51764 | ||||||||
\(776\) | 3.29180 | 0.118169 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.7771 | 0.386377 | ||||||||
\(779\) | −10.0902 | −0.361518 | ||||||||
\(780\) | −4.23607 | −0.151676 | ||||||||
\(781\) | 7.61803 | 0.272595 | ||||||||
\(782\) | −6.12461 | −0.219016 | ||||||||
\(783\) | −8.09017 | −0.289119 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.32624 | 0.118719 | ||||||||
\(786\) | −23.5623 | −0.840440 | ||||||||
\(787\) | −23.7771 | −0.847562 | −0.423781 | − | 0.905765i | \(-0.639297\pi\) | ||||
−0.423781 | + | 0.905765i | \(0.639297\pi\) | |||||||
\(788\) | 31.6525 | 1.12757 | ||||||||
\(789\) | 9.32624 | 0.332023 | ||||||||
\(790\) | 2.76393 | 0.0983363 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −13.9443 | −0.495488 | ||||||||
\(793\) | −5.94427 | −0.211087 | ||||||||
\(794\) | −2.94427 | −0.104488 | ||||||||
\(795\) | −4.85410 | −0.172157 | ||||||||
\(796\) | 17.0344 | 0.603770 | ||||||||
\(797\) | −38.8541 | −1.37628 | −0.688141 | − | 0.725577i | \(-0.741573\pi\) | ||||
−0.688141 | + | 0.725577i | \(0.741573\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.20163 | 0.148643 | ||||||||
\(800\) | 22.4721 | 0.794510 | ||||||||
\(801\) | −27.8885 | −0.985393 | ||||||||
\(802\) | 14.8197 | 0.523300 | ||||||||
\(803\) | 7.00000 | 0.247025 | ||||||||
\(804\) | 56.4508 | 1.99087 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.52786 | −0.229934 | ||||||||
\(807\) | 54.9230 | 1.93338 | ||||||||
\(808\) | 42.8885 | 1.50881 | ||||||||
\(809\) | −12.2361 | −0.430197 | −0.215099 | − | 0.976592i | \(-0.569007\pi\) | ||||
−0.215099 | + | 0.976592i | \(0.569007\pi\) | |||||||
\(810\) | −3.52786 | −0.123957 | ||||||||
\(811\) | 38.0000 | 1.33436 | 0.667180 | − | 0.744896i | \(-0.267501\pi\) | ||||
0.667180 | + | 0.744896i | \(0.267501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.2361 | −0.499281 | ||||||||
\(814\) | −11.4721 | −0.402098 | ||||||||
\(815\) | 20.7984 | 0.728535 | ||||||||
\(816\) | −13.8541 | −0.484991 | ||||||||
\(817\) | −0.472136 | −0.0165179 | ||||||||
\(818\) | 17.4377 | 0.609695 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16.3262 | −0.570137 | ||||||||
\(821\) | 29.8885 | 1.04312 | 0.521559 | − | 0.853215i | \(-0.325351\pi\) | ||||
0.521559 | + | 0.853215i | \(0.325351\pi\) | |||||||
\(822\) | −17.7082 | −0.617645 | ||||||||
\(823\) | −11.1246 | −0.387780 | −0.193890 | − | 0.981023i | \(-0.562110\pi\) | ||||
−0.193890 | + | 0.981023i | \(0.562110\pi\) | |||||||
\(824\) | −1.58359 | −0.0551670 | ||||||||
\(825\) | −16.9443 | −0.589924 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.2361 | 1.39915 | 0.699573 | − | 0.714562i | \(-0.253374\pi\) | ||||
0.699573 | + | 0.714562i | \(0.253374\pi\) | |||||||
\(828\) | −21.6525 | −0.752476 | ||||||||
\(829\) | 8.94427 | 0.310647 | 0.155324 | − | 0.987864i | \(-0.450358\pi\) | ||||
0.155324 | + | 0.987864i | \(0.450358\pi\) | |||||||
\(830\) | −6.09017 | −0.211393 | ||||||||
\(831\) | −60.5410 | −2.10014 | ||||||||
\(832\) | −0.236068 | −0.00818418 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.854102 | 0.0295751 | ||||||||
\(835\) | −1.47214 | −0.0509454 | ||||||||
\(836\) | 2.61803 | 0.0905466 | ||||||||
\(837\) | −23.6180 | −0.816359 | ||||||||
\(838\) | 0.326238 | 0.0112697 | ||||||||
\(839\) | 52.3607 | 1.80769 | 0.903846 | − | 0.427859i | \(-0.140732\pi\) | ||||
0.903846 | + | 0.427859i | \(0.140732\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9098 | −0.548615 | ||||||||
\(842\) | −18.7984 | −0.647835 | ||||||||
\(843\) | 64.6869 | 2.22794 | ||||||||
\(844\) | −2.70820 | −0.0932202 | ||||||||
\(845\) | 12.0000 | 0.412813 | ||||||||
\(846\) | −3.50658 | −0.120559 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.43769 | −0.118051 | ||||||||
\(849\) | 70.9230 | 2.43407 | ||||||||
\(850\) | 7.05573 | 0.242009 | ||||||||
\(851\) | −39.8328 | −1.36545 | ||||||||
\(852\) | −19.9443 | −0.683279 | ||||||||
\(853\) | −41.5623 | −1.42307 | −0.711533 | − | 0.702653i | \(-0.751999\pi\) | ||||
−0.711533 | + | 0.702653i | \(0.751999\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.85410 | −0.131808 | ||||||||
\(856\) | 22.8885 | 0.782314 | ||||||||
\(857\) | 7.72949 | 0.264034 | 0.132017 | − | 0.991247i | \(-0.457855\pi\) | ||||
0.132017 | + | 0.991247i | \(0.457855\pi\) | |||||||
\(858\) | −2.61803 | −0.0893782 | ||||||||
\(859\) | 9.79837 | 0.334316 | 0.167158 | − | 0.985930i | \(-0.446541\pi\) | ||||
0.167158 | + | 0.985930i | \(0.446541\pi\) | |||||||
\(860\) | −0.763932 | −0.0260499 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.5410 | 0.495269 | ||||||||
\(863\) | 20.5066 | 0.698052 | 0.349026 | − | 0.937113i | \(-0.386512\pi\) | ||||
0.349026 | + | 0.937113i | \(0.386512\pi\) | |||||||
\(864\) | 12.5623 | 0.427378 | ||||||||
\(865\) | 16.7639 | 0.569991 | ||||||||
\(866\) | 14.9098 | 0.506657 | ||||||||
\(867\) | 23.1803 | 0.787246 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.23607 | −0.245467 | ||||||||
\(870\) | −5.85410 | −0.198473 | ||||||||
\(871\) | 13.3262 | 0.451542 | ||||||||
\(872\) | −17.3607 | −0.587907 | ||||||||
\(873\) | 5.67376 | 0.192028 | ||||||||
\(874\) | −2.14590 | −0.0725861 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −18.3262 | −0.619186 | ||||||||
\(877\) | −35.0132 | −1.18231 | −0.591155 | − | 0.806558i | \(-0.701328\pi\) | ||||
−0.591155 | + | 0.806558i | \(0.701328\pi\) | |||||||
\(878\) | −14.4721 | −0.488411 | ||||||||
\(879\) | 56.9787 | 1.92184 | ||||||||
\(880\) | 3.00000 | 0.101130 | ||||||||
\(881\) | 1.09017 | 0.0367288 | 0.0183644 | − | 0.999831i | \(-0.494154\pi\) | ||||
0.0183644 | + | 0.999831i | \(0.494154\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.52786 | 0.152375 | 0.0761874 | − | 0.997094i | \(-0.475725\pi\) | ||||
0.0761874 | + | 0.997094i | \(0.475725\pi\) | |||||||
\(884\) | −4.61803 | −0.155321 | ||||||||
\(885\) | −32.0344 | −1.07683 | ||||||||
\(886\) | −6.74265 | −0.226524 | ||||||||
\(887\) | 15.9443 | 0.535356 | 0.267678 | − | 0.963508i | \(-0.413744\pi\) | ||||
0.267678 | + | 0.963508i | \(0.413744\pi\) | |||||||
\(888\) | 67.1591 | 2.25371 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.47214 | −0.149906 | ||||||||
\(891\) | 9.23607 | 0.309420 | ||||||||
\(892\) | 3.90983 | 0.130911 | ||||||||
\(893\) | 1.47214 | 0.0492632 | ||||||||
\(894\) | −31.5066 | −1.05374 | ||||||||
\(895\) | 18.7426 | 0.626498 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.09017 | −0.303512 | ||||||||
\(898\) | 7.03444 | 0.234742 | ||||||||
\(899\) | 38.2148 | 1.27453 | ||||||||
\(900\) | 24.9443 | 0.831476 | ||||||||
\(901\) | −5.29180 | −0.176295 | ||||||||
\(902\) | −10.0902 | −0.335966 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 29.6738 | 0.986935 | ||||||||
\(905\) | −16.0902 | −0.534855 | ||||||||
\(906\) | 30.7984 | 1.02321 | ||||||||
\(907\) | 7.47214 | 0.248108 | 0.124054 | − | 0.992275i | \(-0.460410\pi\) | ||||
0.124054 | + | 0.992275i | \(0.460410\pi\) | |||||||
\(908\) | 8.79837 | 0.291984 | ||||||||
\(909\) | 73.9230 | 2.45187 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.0000 | 0.728893 | 0.364446 | − | 0.931224i | \(-0.381258\pi\) | ||||
0.364446 | + | 0.931224i | \(0.381258\pi\) | |||||||
\(912\) | −4.85410 | −0.160735 | ||||||||
\(913\) | 15.9443 | 0.527678 | ||||||||
\(914\) | −9.21478 | −0.304798 | ||||||||
\(915\) | −15.5623 | −0.514474 | ||||||||
\(916\) | 16.1803 | 0.534613 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.94427 | 0.130180 | ||||||||
\(919\) | −39.0689 | −1.28876 | −0.644382 | − | 0.764704i | \(-0.722885\pi\) | ||||
−0.644382 | + | 0.764704i | \(0.722885\pi\) | |||||||
\(920\) | −7.76393 | −0.255969 | ||||||||
\(921\) | −28.1246 | −0.926737 | ||||||||
\(922\) | 16.1591 | 0.532170 | ||||||||
\(923\) | −4.70820 | −0.154972 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45.8885 | 1.50881 | ||||||||
\(926\) | 21.6738 | 0.712244 | ||||||||
\(927\) | −2.72949 | −0.0896482 | ||||||||
\(928\) | −20.3262 | −0.667241 | ||||||||
\(929\) | 47.5623 | 1.56047 | 0.780234 | − | 0.625487i | \(-0.215100\pi\) | ||||
0.780234 | + | 0.625487i | \(0.215100\pi\) | |||||||
\(930\) | −17.0902 | −0.560409 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.6180 | −0.347805 | ||||||||
\(933\) | 58.7771 | 1.92428 | ||||||||
\(934\) | −5.50658 | −0.180181 | ||||||||
\(935\) | 4.61803 | 0.151026 | ||||||||
\(936\) | 8.61803 | 0.281689 | ||||||||
\(937\) | −12.9230 | −0.422176 | −0.211088 | − | 0.977467i | \(-0.567701\pi\) | ||||
−0.211088 | + | 0.977467i | \(0.567701\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −67.0132 | −2.18689 | ||||||||
\(940\) | 2.38197 | 0.0776912 | ||||||||
\(941\) | 39.3050 | 1.28130 | 0.640652 | − | 0.767831i | \(-0.278664\pi\) | ||||
0.640652 | + | 0.767831i | \(0.278664\pi\) | |||||||
\(942\) | −5.38197 | −0.175354 | ||||||||
\(943\) | −35.0344 | −1.14088 | ||||||||
\(944\) | −22.6869 | −0.738396 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.472136 | −0.0153505 | ||||||||
\(947\) | 36.6180 | 1.18993 | 0.594963 | − | 0.803753i | \(-0.297167\pi\) | ||||
0.594963 | + | 0.803753i | \(0.297167\pi\) | |||||||
\(948\) | 18.9443 | 0.615281 | ||||||||
\(949\) | −4.32624 | −0.140436 | ||||||||
\(950\) | 2.47214 | 0.0802067 | ||||||||
\(951\) | 14.1803 | 0.459829 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.7426 | −0.801493 | −0.400746 | − | 0.916189i | \(-0.631249\pi\) | ||||
−0.400746 | + | 0.916189i | \(0.631249\pi\) | |||||||
\(954\) | 4.41641 | 0.142986 | ||||||||
\(955\) | −14.0344 | −0.454144 | ||||||||
\(956\) | 40.4508 | 1.30827 | ||||||||
\(957\) | 15.3262 | 0.495427 | ||||||||
\(958\) | 6.05573 | 0.195652 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.618034 | −0.0199470 | ||||||||
\(961\) | 80.5623 | 2.59878 | ||||||||
\(962\) | 7.09017 | 0.228596 | ||||||||
\(963\) | 39.4508 | 1.27129 | ||||||||
\(964\) | −14.0000 | −0.450910 | ||||||||
\(965\) | −5.90983 | −0.190244 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.4508 | 0.593339 | 0.296670 | − | 0.954980i | \(-0.404124\pi\) | ||||
0.296670 | + | 0.954980i | \(0.404124\pi\) | |||||||
\(968\) | −18.7426 | −0.602411 | ||||||||
\(969\) | −7.47214 | −0.240040 | ||||||||
\(970\) | 0.909830 | 0.0292129 | ||||||||
\(971\) | −23.1803 | −0.743893 | −0.371946 | − | 0.928254i | \(-0.621309\pi\) | ||||
−0.371946 | + | 0.928254i | \(0.621309\pi\) | |||||||
\(972\) | −35.0344 | −1.12373 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.79837 | 0.281918 | ||||||||
\(975\) | 10.4721 | 0.335377 | ||||||||
\(976\) | −11.0213 | −0.352783 | ||||||||
\(977\) | 37.5967 | 1.20283 | 0.601413 | − | 0.798938i | \(-0.294605\pi\) | ||||
0.601413 | + | 0.798938i | \(0.294605\pi\) | |||||||
\(978\) | −33.6525 | −1.07609 | ||||||||
\(979\) | 11.7082 | 0.374196 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.9230 | −0.955367 | ||||||||
\(982\) | −10.8328 | −0.345689 | ||||||||
\(983\) | −47.5410 | −1.51632 | −0.758162 | − | 0.652067i | \(-0.773902\pi\) | ||||
−0.758162 | + | 0.652067i | \(0.773902\pi\) | |||||||
\(984\) | 59.0689 | 1.88305 | ||||||||
\(985\) | 19.5623 | 0.623307 | ||||||||
\(986\) | −6.38197 | −0.203243 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.61803 | −0.0514765 | ||||||||
\(989\) | −1.63932 | −0.0521274 | ||||||||
\(990\) | −3.85410 | −0.122491 | ||||||||
\(991\) | 5.81966 | 0.184868 | 0.0924338 | − | 0.995719i | \(-0.470535\pi\) | ||||
0.0924338 | + | 0.995719i | \(0.470535\pi\) | |||||||
\(992\) | −59.3394 | −1.88403 | ||||||||
\(993\) | −20.5623 | −0.652525 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.5279 | 0.333756 | ||||||||
\(996\) | −41.7426 | −1.32267 | ||||||||
\(997\) | −23.4508 | −0.742696 | −0.371348 | − | 0.928494i | \(-0.621104\pi\) | ||||
−0.371348 | + | 0.928494i | \(0.621104\pi\) | |||||||
\(998\) | 17.6869 | 0.559870 | ||||||||
\(999\) | 25.6525 | 0.811608 |
(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 | 931.2.a.j.1.1 | 2 | ||
3.2 | odd | 2 | 8379.2.a.w.1.2 | 2 | |||
7.2 | even | 3 | 931.2.f.e.704.2 | 4 | |||
7.3 | odd | 6 | 931.2.f.d.324.2 | 4 | |||
7.4 | even | 3 | 931.2.f.e.324.2 | 4 | |||
7.5 | odd | 6 | 931.2.f.d.704.2 | 4 | |||
7.6 | odd | 2 | 133.2.a.c.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 1197.2.a.g.1.2 | 2 | |||
28.27 | even | 2 | 2128.2.a.c.1.1 | 2 | |||
35.34 | odd | 2 | 3325.2.a.m.1.2 | 2 | |||
56.13 | odd | 2 | 8512.2.a.f.1.1 | 2 | |||
56.27 | even | 2 | 8512.2.a.bb.1.2 | 2 | |||
133.132 | even | 2 | 2527.2.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
133.2.a.c.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
931.2.a.j.1.1 | 2 | 1.1 | even | 1 | trivial | ||
931.2.f.d.324.2 | 4 | 7.3 | odd | 6 | |||
931.2.f.d.704.2 | 4 | 7.5 | odd | 6 | |||
931.2.f.e.324.2 | 4 | 7.4 | even | 3 | |||
931.2.f.e.704.2 | 4 | 7.2 | even | 3 | |||
1197.2.a.g.1.2 | 2 | 21.20 | even | 2 | |||
2128.2.a.c.1.1 | 2 | 28.27 | even | 2 | |||
2527.2.a.a.1.2 | 2 | 133.132 | even | 2 | |||
3325.2.a.m.1.2 | 2 | 35.34 | odd | 2 | |||
8379.2.a.w.1.2 | 2 | 3.2 | odd | 2 | |||
8512.2.a.f.1.1 | 2 | 56.13 | odd | 2 | |||
8512.2.a.bb.1.2 | 2 | 56.27 | even | 2 |