Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, 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("1575.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(12.5764383184\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.174928.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} + 13 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.68190\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.68190 | −1.89639 | −0.948194 | − | 0.317690i | \(-0.897093\pi\) | ||||
−0.948194 | + | 0.317690i | \(0.897093\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.19258 | 2.59629 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −8.56218 | −3.02719 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.19839 | −0.964350 | −0.482175 | − | 0.876075i | \(-0.660153\pi\) | ||||
−0.482175 | + | 0.876075i | \(0.660153\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.38516 | −1.77093 | −0.885463 | − | 0.464710i | \(-0.846159\pi\) | ||||
−0.885463 | + | 0.464710i | \(0.846159\pi\) | |||||||
\(14\) | −2.68190 | −0.716768 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.5777 | 3.14444 | ||||||||
\(17\) | −5.36380 | −1.30091 | −0.650456 | − | 0.759544i | \(-0.725422\pi\) | ||||
−0.650456 | + | 0.759544i | \(0.725422\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.38516 | −0.547194 | −0.273597 | − | 0.961844i | \(-0.588214\pi\) | ||||
−0.273597 | + | 0.961844i | \(0.588214\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.57775 | 1.82878 | ||||||||
\(23\) | 3.19839 | 0.666909 | 0.333455 | − | 0.942766i | \(-0.391786\pi\) | ||||
0.333455 | + | 0.942766i | \(0.391786\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 17.1244 | 3.35836 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.19258 | 0.981306 | ||||||||
\(29\) | −2.16541 | −0.402107 | −0.201054 | − | 0.979580i | \(-0.564437\pi\) | ||||
−0.201054 | + | 0.979580i | \(0.564437\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | −16.6079 | −2.93589 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 14.3852 | 2.46704 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | −0.493197 | −0.246598 | − | 0.969118i | \(-0.579313\pi\) | ||||
−0.246598 | + | 0.969118i | \(0.579313\pi\) | |||||||
\(38\) | 6.39677 | 1.03769 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.7276 | 1.67537 | 0.837685 | − | 0.546154i | \(-0.183909\pi\) | ||||
0.837685 | + | 0.546154i | \(0.183909\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.38516 | 1.43122 | 0.715612 | − | 0.698498i | \(-0.246148\pi\) | ||||
0.715612 | + | 0.698498i | \(0.246148\pi\) | |||||||
\(44\) | −16.6079 | −2.50373 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.57775 | −1.26472 | ||||||||
\(47\) | 11.7606 | 1.71546 | 0.857728 | − | 0.514104i | \(-0.171876\pi\) | ||||
0.857728 | + | 0.514104i | \(0.171876\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −33.1555 | −4.59784 | ||||||||
\(53\) | 10.7276 | 1.47355 | 0.736774 | − | 0.676139i | \(-0.236348\pi\) | ||||
0.736774 | + | 0.676139i | \(0.236348\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.56218 | −1.14417 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.80742 | 0.762551 | ||||||||
\(59\) | −11.7606 | −1.53110 | −0.765548 | − | 0.643379i | \(-0.777532\pi\) | ||||
−0.765548 | + | 0.643379i | \(0.777532\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | −16.0914 | −2.04361 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 19.3852 | 2.42315 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.38516 | 1.14658 | 0.573290 | − | 0.819352i | \(-0.305667\pi\) | ||||
0.573290 | + | 0.819352i | \(0.305667\pi\) | |||||||
\(68\) | −27.8520 | −3.37755 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9260 | 1.65271 | 0.826355 | − | 0.563150i | \(-0.190411\pi\) | ||||
0.826355 | + | 0.563150i | \(0.190411\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.38516 | −0.513245 | −0.256622 | − | 0.966512i | \(-0.582610\pi\) | ||||
−0.256622 | + | 0.966512i | \(0.582610\pi\) | |||||||
\(74\) | 8.04570 | 0.935293 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.3852 | −1.42068 | ||||||||
\(77\) | −3.19839 | −0.364490 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.38516 | −0.605878 | −0.302939 | − | 0.953010i | \(-0.597968\pi\) | ||||
−0.302939 | + | 0.953010i | \(0.597968\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −28.7703 | −3.17715 | ||||||||
\(83\) | 4.33082 | 0.475370 | 0.237685 | − | 0.971342i | \(-0.423611\pi\) | ||||
0.237685 | + | 0.971342i | \(0.423611\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −25.1701 | −2.71416 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 27.3852 | 2.91927 | ||||||||
\(89\) | 1.03297 | 0.109495 | 0.0547475 | − | 0.998500i | \(-0.482565\pi\) | ||||
0.0547475 | + | 0.998500i | \(0.482565\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.38516 | −0.669347 | ||||||||
\(92\) | 16.6079 | 1.73149 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −31.5407 | −3.25317 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7703 | 1.09356 | 0.546781 | − | 0.837276i | \(-0.315853\pi\) | ||||
0.546781 | + | 0.837276i | \(0.315853\pi\) | |||||||
\(98\) | −2.68190 | −0.270913 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.36380 | −0.533718 | −0.266859 | − | 0.963736i | \(-0.585986\pi\) | ||||
−0.266859 | + | 0.963736i | \(0.585986\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.61484 | −0.553246 | −0.276623 | − | 0.960978i | \(-0.589215\pi\) | ||||
−0.276623 | + | 0.960978i | \(0.589215\pi\) | |||||||
\(104\) | 54.6710 | 5.36093 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −28.7703 | −2.79442 | ||||||||
\(107\) | 4.33082 | 0.418677 | 0.209338 | − | 0.977843i | \(-0.432869\pi\) | ||||
0.209338 | + | 0.977843i | \(0.432869\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | 0.670478 | 0.335239 | − | 0.942133i | \(-0.391183\pi\) | ||||
0.335239 | + | 0.942133i | \(0.391183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.5777 | 1.18849 | ||||||||
\(113\) | −2.16541 | −0.203705 | −0.101852 | − | 0.994800i | \(-0.532477\pi\) | ||||
−0.101852 | + | 0.994800i | \(0.532477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −11.2441 | −1.04399 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 31.5407 | 2.90355 | ||||||||
\(119\) | −5.36380 | −0.491699 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.770330 | −0.0700300 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 31.1555 | 2.79785 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.61484 | 0.409500 | 0.204750 | − | 0.978814i | \(-0.434362\pi\) | ||||
0.204750 | + | 0.978814i | \(0.434362\pi\) | |||||||
\(128\) | −18.7733 | −1.65934 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.36380 | −0.468637 | −0.234319 | − | 0.972160i | \(-0.575286\pi\) | ||||
−0.234319 | + | 0.972160i | \(0.575286\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.38516 | −0.206820 | ||||||||
\(134\) | −25.1701 | −2.17436 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 45.9258 | 3.93811 | ||||||||
\(137\) | 10.7276 | 0.916520 | 0.458260 | − | 0.888818i | \(-0.348473\pi\) | ||||
0.458260 | + | 0.888818i | \(0.348473\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.38516 | −0.371945 | −0.185972 | − | 0.982555i | \(-0.559544\pi\) | ||||
−0.185972 | + | 0.982555i | \(0.559544\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −37.3481 | −3.13418 | ||||||||
\(143\) | 20.4222 | 1.70779 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.7606 | 0.973312 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −15.5777 | −1.28048 | ||||||||
\(149\) | −12.8930 | −1.05624 | −0.528118 | − | 0.849171i | \(-0.677102\pi\) | ||||
−0.528118 | + | 0.849171i | \(0.677102\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3852 | 0.926512 | 0.463256 | − | 0.886225i | \(-0.346681\pi\) | ||||
0.463256 | + | 0.886225i | \(0.346681\pi\) | |||||||
\(152\) | 20.4222 | 1.65646 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.57775 | 0.691215 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.7703 | −1.33842 | −0.669209 | − | 0.743074i | \(-0.733367\pi\) | ||||
−0.669209 | + | 0.743074i | \(0.733367\pi\) | |||||||
\(158\) | 14.4425 | 1.14898 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.19839 | 0.252068 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.7703 | −1.31355 | −0.656777 | − | 0.754085i | \(-0.728081\pi\) | ||||
−0.656777 | + | 0.754085i | \(0.728081\pi\) | |||||||
\(164\) | 55.7039 | 4.34975 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.6148 | −0.901486 | ||||||||
\(167\) | 1.03297 | 0.0799339 | 0.0399669 | − | 0.999201i | \(-0.487275\pi\) | ||||
0.0399669 | + | 0.999201i | \(0.487275\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.7703 | 2.13618 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 48.7332 | 3.71587 | ||||||||
\(173\) | 22.4882 | 1.70974 | 0.854872 | − | 0.518839i | \(-0.173636\pi\) | ||||
0.854872 | + | 0.518839i | \(0.173636\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −40.2285 | −3.03234 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.77033 | −0.207645 | ||||||||
\(179\) | 4.33082 | 0.323701 | 0.161851 | − | 0.986815i | \(-0.448254\pi\) | ||||
0.161851 | + | 0.986815i | \(0.448254\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.3852 | 1.51522 | 0.757609 | − | 0.652709i | \(-0.226368\pi\) | ||||
0.757609 | + | 0.652709i | \(0.226368\pi\) | |||||||
\(182\) | 17.1244 | 1.26934 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −27.3852 | −2.01886 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.1555 | 1.25453 | ||||||||
\(188\) | 61.0677 | 4.45382 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.39677 | 0.462854 | 0.231427 | − | 0.972852i | \(-0.425661\pi\) | ||||
0.231427 | + | 0.972852i | \(0.425661\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | −0.0719816 | −0.0359908 | − | 0.999352i | \(-0.511459\pi\) | ||||
−0.0359908 | + | 0.999352i | \(0.511459\pi\) | |||||||
\(194\) | −28.8849 | −2.07382 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.19258 | 0.370899 | ||||||||
\(197\) | 23.6206 | 1.68290 | 0.841449 | − | 0.540336i | \(-0.181703\pi\) | ||||
0.841449 | + | 0.540336i | \(0.181703\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.770330 | 0.0546072 | 0.0273036 | − | 0.999627i | \(-0.491308\pi\) | ||||
0.0273036 | + | 0.999627i | \(0.491308\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.3852 | 1.01214 | ||||||||
\(203\) | −2.16541 | −0.151982 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.0584 | 1.04917 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −80.3110 | −5.56857 | ||||||||
\(209\) | 7.62868 | 0.527687 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | 55.7039 | 3.82576 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.6148 | −0.793974 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.00000 | 0.407307 | ||||||||
\(218\) | −18.7733 | −1.27149 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 34.2487 | 2.30382 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.61484 | −0.242067 | −0.121034 | − | 0.992648i | \(-0.538621\pi\) | ||||
−0.121034 | + | 0.992648i | \(0.538621\pi\) | |||||||
\(224\) | −16.6079 | −1.10966 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.80742 | 0.386304 | ||||||||
\(227\) | −11.7606 | −0.780576 | −0.390288 | − | 0.920693i | \(-0.627625\pi\) | ||||
−0.390288 | + | 0.920693i | \(0.627625\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.5407 | −1.02696 | −0.513478 | − | 0.858103i | \(-0.671643\pi\) | ||||
−0.513478 | + | 0.858103i | \(0.671643\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.5407 | 1.21725 | ||||||||
\(233\) | −4.23136 | −0.277206 | −0.138603 | − | 0.990348i | \(-0.544261\pi\) | ||||
−0.138603 | + | 0.990348i | \(0.544261\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −61.0677 | −3.97517 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 14.3852 | 0.932452 | ||||||||
\(239\) | 6.39677 | 0.413773 | 0.206886 | − | 0.978365i | \(-0.433667\pi\) | ||||
0.206886 | + | 0.978365i | \(0.433667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.3852 | 1.18429 | 0.592146 | − | 0.805830i | \(-0.298281\pi\) | ||||
0.592146 | + | 0.805830i | \(0.298281\pi\) | |||||||
\(242\) | 2.06595 | 0.132804 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.2297 | 0.969041 | ||||||||
\(248\) | −51.3731 | −3.26220 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.29785 | 0.208159 | 0.104079 | − | 0.994569i | \(-0.466810\pi\) | ||||
0.104079 | + | 0.994569i | \(0.466810\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.2297 | −0.643134 | ||||||||
\(254\) | −12.3765 | −0.776572 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.5777 | 0.723609 | ||||||||
\(257\) | −17.1244 | −1.06819 | −0.534094 | − | 0.845425i | \(-0.679347\pi\) | ||||
−0.534094 | + | 0.845425i | \(0.679347\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.00000 | −0.186411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.3852 | 0.888718 | ||||||||
\(263\) | −20.3228 | −1.25315 | −0.626577 | − | 0.779359i | \(-0.715545\pi\) | ||||
−0.626577 | + | 0.779359i | \(0.715545\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.39677 | 0.392211 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 48.7332 | 2.97686 | ||||||||
\(269\) | −4.33082 | −0.264055 | −0.132028 | − | 0.991246i | \(-0.542149\pi\) | ||||
−0.132028 | + | 0.991246i | \(0.542149\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1555 | 0.920631 | 0.460315 | − | 0.887755i | \(-0.347736\pi\) | ||||
0.460315 | + | 0.887755i | \(0.347736\pi\) | |||||||
\(272\) | −67.4645 | −4.09064 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −28.7703 | −1.73808 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.5407 | −1.41442 | −0.707211 | − | 0.707003i | \(-0.750047\pi\) | ||||
−0.707211 | + | 0.707003i | \(0.750047\pi\) | |||||||
\(278\) | 11.7606 | 0.705352 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.9590 | −0.892376 | −0.446188 | − | 0.894939i | \(-0.647219\pi\) | ||||
−0.446188 | + | 0.894939i | \(0.647219\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.0000 | −0.832214 | −0.416107 | − | 0.909316i | \(-0.636606\pi\) | ||||
−0.416107 | + | 0.909316i | \(0.636606\pi\) | |||||||
\(284\) | 72.3118 | 4.29092 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −54.7703 | −3.23864 | ||||||||
\(287\) | 10.7276 | 0.633230 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.7703 | 0.692372 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −22.7703 | −1.33253 | ||||||||
\(293\) | 11.7606 | 0.687060 | 0.343530 | − | 0.939142i | \(-0.388377\pi\) | ||||
0.343530 | + | 0.939142i | \(0.388377\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 25.6866 | 1.49300 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 34.5777 | 2.00304 | ||||||||
\(299\) | −20.4222 | −1.18105 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.38516 | 0.540952 | ||||||||
\(302\) | −30.5339 | −1.75703 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −30.0000 | −1.72062 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.1555 | −0.750824 | −0.375412 | − | 0.926858i | \(-0.622499\pi\) | ||||
−0.375412 | + | 0.926858i | \(0.622499\pi\) | |||||||
\(308\) | −16.6079 | −0.946322 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.8190 | −1.52077 | −0.760383 | − | 0.649475i | \(-0.774989\pi\) | ||||
−0.760383 | + | 0.649475i | \(0.774989\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.9258 | 1.35237 | 0.676184 | − | 0.736733i | \(-0.263633\pi\) | ||||
0.676184 | + | 0.736733i | \(0.263633\pi\) | |||||||
\(314\) | 44.9763 | 2.53816 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −27.9629 | −1.57304 | ||||||||
\(317\) | −8.56218 | −0.480900 | −0.240450 | − | 0.970662i | \(-0.577295\pi\) | ||||
−0.240450 | + | 0.970662i | \(0.577295\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.92582 | 0.387772 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.57775 | −0.478019 | ||||||||
\(323\) | 12.7935 | 0.711852 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 44.9763 | 2.49101 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −91.8516 | −5.07166 | ||||||||
\(329\) | 11.7606 | 0.648381 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.1555 | 0.558196 | 0.279098 | − | 0.960263i | \(-0.409964\pi\) | ||||
0.279098 | + | 0.960263i | \(0.409964\pi\) | |||||||
\(332\) | 22.4882 | 1.23420 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.77033 | −0.151586 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.7703 | 0.586697 | 0.293349 | − | 0.956006i | \(-0.405230\pi\) | ||||
0.293349 | + | 0.956006i | \(0.405230\pi\) | |||||||
\(338\) | −74.4772 | −4.05103 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.1903 | −1.03921 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −80.3575 | −4.33259 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −60.3110 | −3.24234 | ||||||||
\(347\) | −24.6536 | −1.32347 | −0.661737 | − | 0.749736i | \(-0.730180\pi\) | ||||
−0.661737 | + | 0.749736i | \(0.730180\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.38516 | 0.127675 | 0.0638375 | − | 0.997960i | \(-0.479666\pi\) | ||||
0.0638375 | + | 0.997960i | \(0.479666\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 53.1184 | 2.83122 | ||||||||
\(353\) | 17.1244 | 0.911438 | 0.455719 | − | 0.890124i | \(-0.349382\pi\) | ||||
0.455719 | + | 0.890124i | \(0.349382\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.36380 | 0.284281 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.6148 | −0.613863 | ||||||||
\(359\) | −18.2568 | −0.963557 | −0.481779 | − | 0.876293i | \(-0.660009\pi\) | ||||
−0.481779 | + | 0.876293i | \(0.660009\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.3110 | −0.700578 | ||||||||
\(362\) | −54.6710 | −2.87344 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −33.1555 | −1.73782 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.00000 | 0.208798 | 0.104399 | − | 0.994535i | \(-0.466708\pi\) | ||||
0.104399 | + | 0.994535i | \(0.466708\pi\) | |||||||
\(368\) | 40.2285 | 2.09705 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.7276 | 0.556949 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.0000 | 1.29445 | 0.647225 | − | 0.762299i | \(-0.275929\pi\) | ||||
0.647225 | + | 0.762299i | \(0.275929\pi\) | |||||||
\(374\) | −46.0093 | −2.37908 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −100.696 | −5.19301 | ||||||||
\(377\) | 13.8265 | 0.712102 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.3852 | −0.584817 | −0.292408 | − | 0.956294i | \(-0.594457\pi\) | ||||
−0.292408 | + | 0.956294i | \(0.594457\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.1555 | −0.877751 | ||||||||
\(383\) | −9.69462 | −0.495372 | −0.247686 | − | 0.968840i | \(-0.579670\pi\) | ||||
−0.247686 | + | 0.968840i | \(0.579670\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.68190 | 0.136505 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 55.9258 | 2.83920 | ||||||||
\(389\) | −10.6281 | −0.538868 | −0.269434 | − | 0.963019i | \(-0.586837\pi\) | ||||
−0.269434 | + | 0.963019i | \(0.586837\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.1555 | −0.867591 | ||||||||
\(392\) | −8.56218 | −0.432456 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −63.3481 | −3.19143 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.22967 | 0.0617154 | 0.0308577 | − | 0.999524i | \(-0.490176\pi\) | ||||
0.0308577 | + | 0.999524i | \(0.490176\pi\) | |||||||
\(398\) | −2.06595 | −0.103557 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.8930 | −0.643846 | −0.321923 | − | 0.946766i | \(-0.604329\pi\) | ||||
−0.321923 | + | 0.946766i | \(0.604329\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38.3110 | −1.90841 | ||||||||
\(404\) | −27.8520 | −1.38569 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.80742 | 0.288217 | ||||||||
\(407\) | 9.59516 | 0.475614 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.3852 | 1.10688 | 0.553438 | − | 0.832891i | \(-0.313316\pi\) | ||||
0.553438 | + | 0.832891i | \(0.313316\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −29.1555 | −1.43639 | ||||||||
\(413\) | −11.7606 | −0.578700 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 106.044 | 5.19924 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −20.4593 | −1.00070 | ||||||||
\(419\) | 17.1244 | 0.836580 | 0.418290 | − | 0.908314i | \(-0.362630\pi\) | ||||
0.418290 | + | 0.908314i | \(0.362630\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.3110 | 1.23358 | 0.616791 | − | 0.787127i | \(-0.288432\pi\) | ||||
0.616791 | + | 0.787127i | \(0.288432\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −91.8516 | −4.46071 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 22.4882 | 1.08701 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.7860 | 1.24207 | 0.621034 | − | 0.783783i | \(-0.286713\pi\) | ||||
0.621034 | + | 0.783783i | \(0.286713\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.54066 | 0.458495 | 0.229247 | − | 0.973368i | \(-0.426374\pi\) | ||||
0.229247 | + | 0.973368i | \(0.426374\pi\) | |||||||
\(434\) | −16.0914 | −0.772412 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 36.3481 | 1.74076 | ||||||||
\(437\) | −7.62868 | −0.364929 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.1555 | 0.914242 | 0.457121 | − | 0.889405i | \(-0.348881\pi\) | ||||
0.457121 | + | 0.889405i | \(0.348881\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −91.8516 | −4.36894 | ||||||||
\(443\) | 19.1903 | 0.911759 | 0.455880 | − | 0.890041i | \(-0.349325\pi\) | ||||
0.455880 | + | 0.890041i | \(0.349325\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.69462 | 0.459054 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 19.3852 | 0.915863 | ||||||||
\(449\) | −12.8930 | −0.608459 | −0.304229 | − | 0.952599i | \(-0.598399\pi\) | ||||
−0.304229 | + | 0.952599i | \(0.598399\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −34.3110 | −1.61564 | ||||||||
\(452\) | −11.2441 | −0.528877 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 31.5407 | 1.48028 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.5407 | 1.33508 | 0.667538 | − | 0.744576i | \(-0.267348\pi\) | ||||
0.667538 | + | 0.744576i | \(0.267348\pi\) | |||||||
\(458\) | 41.6785 | 1.94751 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.03297 | 0.0481104 | 0.0240552 | − | 0.999711i | \(-0.492342\pi\) | ||||
0.0240552 | + | 0.999711i | \(0.492342\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.77033 | 0.407592 | 0.203796 | − | 0.979013i | \(-0.434672\pi\) | ||||
0.203796 | + | 0.979013i | \(0.434672\pi\) | |||||||
\(464\) | −27.2360 | −1.26440 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.3481 | 0.525690 | ||||||||
\(467\) | −6.39677 | −0.296007 | −0.148004 | − | 0.988987i | \(-0.547285\pi\) | ||||
−0.148004 | + | 0.988987i | \(0.547285\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.38516 | 0.433367 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 100.696 | 4.63492 | ||||||||
\(473\) | −30.0174 | −1.38020 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −27.8520 | −1.27659 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.1555 | −0.784674 | ||||||||
\(479\) | 33.2158 | 1.51767 | 0.758833 | − | 0.651285i | \(-0.225770\pi\) | ||||
0.758833 | + | 0.651285i | \(0.225770\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.1555 | 0.873415 | ||||||||
\(482\) | −49.3072 | −2.24588 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.00000 | −0.181818 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.3852 | 0.606540 | 0.303270 | − | 0.952905i | \(-0.401922\pi\) | ||||
0.303270 | + | 0.952905i | \(0.401922\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.3812 | 1.59673 | 0.798365 | − | 0.602174i | \(-0.205699\pi\) | ||||
0.798365 | + | 0.602174i | \(0.205699\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.6148 | 0.523106 | ||||||||
\(494\) | −40.8444 | −1.83768 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 75.4665 | 3.38855 | ||||||||
\(497\) | 13.9260 | 0.624666 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.5407 | 1.32242 | 0.661211 | − | 0.750200i | \(-0.270043\pi\) | ||||
0.661211 | + | 0.750200i | \(0.270043\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.84451 | −0.394750 | ||||||||
\(503\) | −40.6455 | −1.81229 | −0.906147 | − | 0.422963i | \(-0.860990\pi\) | ||||
−0.906147 | + | 0.422963i | \(0.860990\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 27.4349 | 1.21963 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 23.9629 | 1.06318 | ||||||||
\(509\) | 9.69462 | 0.429707 | 0.214853 | − | 0.976646i | \(-0.431073\pi\) | ||||
0.214853 | + | 0.976646i | \(0.431073\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.38516 | −0.193988 | ||||||||
\(512\) | 6.49624 | 0.287096 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 45.9258 | 2.02570 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −37.6148 | −1.65430 | ||||||||
\(518\) | 8.04570 | 0.353508 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.5136 | −1.59969 | −0.799845 | − | 0.600206i | \(-0.795085\pi\) | ||||
−0.799845 | + | 0.600206i | \(0.795085\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.2297 | −0.840855 | −0.420427 | − | 0.907326i | \(-0.638120\pi\) | ||||
−0.420427 | + | 0.907326i | \(0.638120\pi\) | |||||||
\(524\) | −27.8520 | −1.21672 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 54.5036 | 2.37647 | ||||||||
\(527\) | −32.1828 | −1.40190 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.7703 | −0.555232 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.3852 | −0.536965 | ||||||||
\(533\) | −68.4975 | −2.96695 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −80.3575 | −3.47092 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11.6148 | 0.500751 | ||||||||
\(539\) | −3.19839 | −0.137764 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.5407 | −0.625152 | −0.312576 | − | 0.949893i | \(-0.601192\pi\) | ||||
−0.312576 | + | 0.949893i | \(0.601192\pi\) | |||||||
\(542\) | −40.6455 | −1.74587 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 89.0813 | 3.81933 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.6148 | 0.539371 | 0.269686 | − | 0.962948i | \(-0.413080\pi\) | ||||
0.269686 | + | 0.962948i | \(0.413080\pi\) | |||||||
\(548\) | 55.7039 | 2.37955 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.16487 | 0.220031 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.38516 | −0.229001 | ||||||||
\(554\) | 63.1337 | 2.68229 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22.7703 | −0.965677 | ||||||||
\(557\) | 8.56218 | 0.362791 | 0.181396 | − | 0.983410i | \(-0.441939\pi\) | ||||
0.181396 | + | 0.983410i | \(0.441939\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −59.9258 | −2.53459 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 40.1184 | 1.69229 | ||||||||
\(563\) | −4.33082 | −0.182523 | −0.0912613 | − | 0.995827i | \(-0.529090\pi\) | ||||
−0.0912613 | + | 0.995827i | \(0.529090\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 37.5466 | 1.57820 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −119.237 | −5.00307 | ||||||||
\(569\) | 32.0833 | 1.34500 | 0.672501 | − | 0.740096i | \(-0.265220\pi\) | ||||
0.672501 | + | 0.740096i | \(0.265220\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.3852 | 1.48082 | 0.740412 | − | 0.672154i | \(-0.234631\pi\) | ||||
0.740412 | + | 0.672154i | \(0.234631\pi\) | |||||||
\(572\) | 106.044 | 4.43392 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −28.7703 | −1.20085 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 47.1555 | 1.96311 | 0.981554 | − | 0.191183i | \(-0.0612323\pi\) | ||||
0.981554 | + | 0.191183i | \(0.0612323\pi\) | |||||||
\(578\) | −31.5668 | −1.31301 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.33082 | 0.179673 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.3110 | −1.42102 | ||||||||
\(584\) | 37.5466 | 1.55369 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −31.5407 | −1.30293 | ||||||||
\(587\) | 14.0254 | 0.578892 | 0.289446 | − | 0.957194i | \(-0.406529\pi\) | ||||
0.289446 | + | 0.957194i | \(0.406529\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.3110 | −0.589674 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −37.7332 | −1.55083 | ||||||||
\(593\) | −34.2487 | −1.40643 | −0.703213 | − | 0.710979i | \(-0.748252\pi\) | ||||
−0.703213 | + | 0.710979i | \(0.748252\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −66.9480 | −2.74230 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 54.7703 | 2.23973 | ||||||||
\(599\) | 26.7195 | 1.09173 | 0.545865 | − | 0.837873i | \(-0.316201\pi\) | ||||
0.545865 | + | 0.837873i | \(0.316201\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.5407 | 1.69448 | 0.847239 | − | 0.531211i | \(-0.178263\pi\) | ||||
0.847239 | + | 0.531211i | \(0.178263\pi\) | |||||||
\(602\) | −25.1701 | −1.02586 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 59.1184 | 2.40549 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.1555 | 0.939853 | 0.469926 | − | 0.882706i | \(-0.344280\pi\) | ||||
0.469926 | + | 0.882706i | \(0.344280\pi\) | |||||||
\(608\) | 39.6125 | 1.60650 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −75.0932 | −3.03794 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.0000 | 0.928961 | 0.464481 | − | 0.885583i | \(-0.346241\pi\) | ||||
0.464481 | + | 0.885583i | \(0.346241\pi\) | |||||||
\(614\) | 35.2817 | 1.42385 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 27.3852 | 1.10338 | ||||||||
\(617\) | −10.6281 | −0.427872 | −0.213936 | − | 0.976848i | \(-0.568628\pi\) | ||||
−0.213936 | + | 0.976848i | \(0.568628\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.1555 | −1.09147 | −0.545736 | − | 0.837957i | \(-0.683750\pi\) | ||||
−0.545736 | + | 0.837957i | \(0.683750\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 71.9258 | 2.88396 | ||||||||
\(623\) | 1.03297 | 0.0413852 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −64.1666 | −2.56461 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −87.0813 | −3.47492 | ||||||||
\(629\) | 16.0914 | 0.641606 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.38516 | −0.214380 | −0.107190 | − | 0.994239i | \(-0.534185\pi\) | ||||
−0.107190 | + | 0.994239i | \(0.534185\pi\) | |||||||
\(632\) | 46.1088 | 1.83411 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22.9629 | 0.911974 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.38516 | −0.252989 | ||||||||
\(638\) | −18.5744 | −0.735366 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.3557 | −0.843500 | −0.421750 | − | 0.906712i | \(-0.638584\pi\) | ||||
−0.421750 | + | 0.906712i | \(0.638584\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.45934 | −0.254732 | −0.127366 | − | 0.991856i | \(-0.540652\pi\) | ||||
−0.127366 | + | 0.991856i | \(0.540652\pi\) | |||||||
\(644\) | 16.6079 | 0.654442 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −34.3110 | −1.34995 | ||||||||
\(647\) | −38.5796 | −1.51672 | −0.758359 | − | 0.651837i | \(-0.773999\pi\) | ||||
−0.758359 | + | 0.651837i | \(0.773999\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 37.6148 | 1.47651 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −87.0813 | −3.41037 | ||||||||
\(653\) | 10.7276 | 0.419803 | 0.209902 | − | 0.977723i | \(-0.432686\pi\) | ||||
0.209902 | + | 0.977723i | \(0.432686\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 134.929 | 5.26809 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −31.5407 | −1.22958 | ||||||||
\(659\) | 47.2412 | 1.84026 | 0.920128 | − | 0.391617i | \(-0.128084\pi\) | ||||
0.920128 | + | 0.391617i | \(0.128084\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.9258 | 1.24177 | 0.620885 | − | 0.783901i | \(-0.286773\pi\) | ||||
0.620885 | + | 0.783901i | \(0.286773\pi\) | |||||||
\(662\) | −27.2360 | −1.05856 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −37.0813 | −1.43903 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.92582 | −0.268169 | ||||||||
\(668\) | 5.36380 | 0.207532 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.54066 | −0.136482 | −0.0682412 | − | 0.997669i | \(-0.521739\pi\) | ||||
−0.0682412 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(674\) | −28.8849 | −1.11261 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 144.200 | 5.54614 | ||||||||
\(677\) | 6.39677 | 0.245848 | 0.122924 | − | 0.992416i | \(-0.460773\pi\) | ||||
0.122924 | + | 0.992416i | \(0.460773\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.7703 | 0.413327 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 51.4665 | 1.97075 | ||||||||
\(683\) | 9.59516 | 0.367148 | 0.183574 | − | 0.983006i | \(-0.441233\pi\) | ||||
0.183574 | + | 0.983006i | \(0.441233\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.68190 | −0.102395 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 118.044 | 4.50039 | ||||||||
\(689\) | −68.4975 | −2.60955 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.2297 | −0.579364 | −0.289682 | − | 0.957123i | \(-0.593550\pi\) | ||||
−0.289682 | + | 0.957123i | \(0.593550\pi\) | |||||||
\(692\) | 116.772 | 4.43899 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 66.1184 | 2.50982 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −57.5407 | −2.17951 | ||||||||
\(698\) | −6.39677 | −0.242121 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.9763 | 1.69873 | 0.849366 | − | 0.527804i | \(-0.176984\pi\) | ||||
0.849366 | + | 0.527804i | \(0.176984\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.15549 | 0.269875 | ||||||||
\(704\) | −62.0012 | −2.33676 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −45.9258 | −1.72844 | ||||||||
\(707\) | −5.36380 | −0.201726 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.5407 | 1.48498 | 0.742490 | − | 0.669857i | \(-0.233645\pi\) | ||||
0.742490 | + | 0.669857i | \(0.233645\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.84451 | −0.331462 | ||||||||
\(713\) | 19.1903 | 0.718683 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.4882 | 0.840422 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 48.9629 | 1.82728 | ||||||||
\(719\) | 19.3892 | 0.723097 | 0.361548 | − | 0.932353i | \(-0.382248\pi\) | ||||
0.361548 | + | 0.932353i | \(0.382248\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.61484 | −0.209107 | ||||||||
\(722\) | 35.6987 | 1.32857 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 105.852 | 3.93395 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.3852 | −1.20110 | −0.600550 | − | 0.799587i | \(-0.705052\pi\) | ||||
−0.600550 | + | 0.799587i | \(0.705052\pi\) | |||||||
\(728\) | 54.6710 | 2.02624 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −50.3401 | −1.86190 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.0000 | 1.03420 | 0.517102 | − | 0.855924i | \(-0.327011\pi\) | ||||
0.517102 | + | 0.855924i | \(0.327011\pi\) | |||||||
\(734\) | −10.7276 | −0.395963 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −53.1184 | −1.95797 | ||||||||
\(737\) | −30.0174 | −1.10570 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.3852 | −1.59595 | −0.797975 | − | 0.602691i | \(-0.794095\pi\) | ||||
−0.797975 | + | 0.602691i | \(0.794095\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28.7703 | −1.05619 | ||||||||
\(743\) | −15.0584 | −0.552440 | −0.276220 | − | 0.961094i | \(-0.589082\pi\) | ||||
−0.276220 | + | 0.961094i | \(0.589082\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −67.0475 | −2.45478 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 89.0813 | 3.25714 | ||||||||
\(749\) | 4.33082 | 0.158245 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.7703 | −1.04984 | −0.524922 | − | 0.851150i | \(-0.675906\pi\) | ||||
−0.524922 | + | 0.851150i | \(0.675906\pi\) | |||||||
\(752\) | 147.921 | 5.39414 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −37.0813 | −1.35042 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.3110 | 0.411105 | 0.205552 | − | 0.978646i | \(-0.434101\pi\) | ||||
0.205552 | + | 0.978646i | \(0.434101\pi\) | |||||||
\(758\) | 30.5339 | 1.10904 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.7935 | 0.463766 | 0.231883 | − | 0.972744i | \(-0.425511\pi\) | ||||
0.231883 | + | 0.972744i | \(0.425511\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.00000 | 0.253417 | ||||||||
\(764\) | 33.2158 | 1.20170 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.0000 | 0.939418 | ||||||||
\(767\) | 75.0932 | 2.71146 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.7703 | 1.61446 | 0.807230 | − | 0.590237i | \(-0.200966\pi\) | ||||
0.807230 | + | 0.590237i | \(0.200966\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.19258 | −0.186885 | ||||||||
\(773\) | 15.0584 | 0.541614 | 0.270807 | − | 0.962634i | \(-0.412710\pi\) | ||||
0.270807 | + | 0.962634i | \(0.412710\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −92.2175 | −3.31042 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.5036 | 1.02190 | ||||||||
\(779\) | −25.5871 | −0.916752 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −44.5407 | −1.59379 | ||||||||
\(782\) | 46.0093 | 1.64529 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.5777 | 0.449205 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.385165 | 0.0137296 | 0.00686482 | − | 0.999976i | \(-0.497815\pi\) | ||||
0.00686482 | + | 0.999976i | \(0.497815\pi\) | |||||||
\(788\) | 122.652 | 4.36929 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.16541 | −0.0769932 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −3.29785 | −0.117036 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.00000 | 0.141776 | ||||||||
\(797\) | −30.9509 | −1.09634 | −0.548168 | − | 0.836368i | \(-0.684675\pi\) | ||||
−0.548168 | + | 0.836368i | \(0.684675\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −63.0813 | −2.23166 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 34.5777 | 1.22098 | ||||||||
\(803\) | 14.0254 | 0.494947 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 102.746 | 3.61908 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 45.9258 | 1.61566 | ||||||||
\(809\) | 36.4141 | 1.28025 | 0.640127 | − | 0.768269i | \(-0.278882\pi\) | ||||
0.640127 | + | 0.768269i | \(0.278882\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.7703 | 1.08049 | 0.540246 | − | 0.841507i | \(-0.318331\pi\) | ||||
0.540246 | + | 0.841507i | \(0.318331\pi\) | |||||||
\(812\) | −11.2441 | −0.394590 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −25.7332 | −0.901950 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.3852 | −0.783158 | ||||||||
\(818\) | −60.0348 | −2.09907 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.0423 | −1.64179 | −0.820893 | − | 0.571081i | \(-0.806524\pi\) | ||||
−0.820893 | + | 0.571081i | \(0.806524\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.9258 | −0.868860 | −0.434430 | − | 0.900706i | \(-0.643050\pi\) | ||||
−0.434430 | + | 0.900706i | \(0.643050\pi\) | |||||||
\(824\) | 48.0753 | 1.67478 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 31.5407 | 1.09744 | ||||||||
\(827\) | 13.9260 | 0.484254 | 0.242127 | − | 0.970245i | \(-0.422155\pi\) | ||||
0.242127 | + | 0.970245i | \(0.422155\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.38516 | −0.291229 | −0.145614 | − | 0.989341i | \(-0.546516\pi\) | ||||
−0.145614 | + | 0.989341i | \(0.546516\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −123.777 | −4.29121 | ||||||||
\(833\) | −5.36380 | −0.185845 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 39.6125 | 1.37003 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −45.9258 | −1.58648 | ||||||||
\(839\) | −14.0254 | −0.484212 | −0.242106 | − | 0.970250i | \(-0.577838\pi\) | ||||
−0.242106 | + | 0.970250i | \(0.577838\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.3110 | −0.838310 | ||||||||
\(842\) | −67.8815 | −2.33935 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.770330 | −0.0264688 | ||||||||
\(848\) | 134.929 | 4.63348 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.59516 | −0.328918 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.3110 | −1.03783 | −0.518914 | − | 0.854826i | \(-0.673664\pi\) | ||||
−0.518914 | + | 0.854826i | \(0.673664\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −37.0813 | −1.26741 | ||||||||
\(857\) | −36.3147 | −1.24049 | −0.620243 | − | 0.784410i | \(-0.712966\pi\) | ||||
−0.620243 | + | 0.784410i | \(0.712966\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.5407 | −0.939675 | −0.469838 | − | 0.882753i | \(-0.655688\pi\) | ||||
−0.469838 | + | 0.882753i | \(0.655688\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −69.1555 | −2.35545 | ||||||||
\(863\) | 1.13244 | 0.0385487 | 0.0192743 | − | 0.999814i | \(-0.493864\pi\) | ||||
0.0192743 | + | 0.999814i | \(0.493864\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −25.5871 | −0.869485 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 31.1555 | 1.05749 | ||||||||
\(869\) | 17.2238 | 0.584279 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −59.9258 | −2.03051 | ||||||||
\(872\) | −59.9353 | −2.02966 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 20.4593 | 0.692048 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.5407 | −0.659841 | −0.329921 | − | 0.944009i | \(-0.607022\pi\) | ||||
−0.329921 | + | 0.944009i | \(0.607022\pi\) | |||||||
\(878\) | −51.3731 | −1.73376 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.6455 | 1.36938 | 0.684691 | − | 0.728834i | \(-0.259937\pi\) | ||||
0.684691 | + | 0.728834i | \(0.259937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.61484 | −0.289912 | −0.144956 | − | 0.989438i | \(-0.546304\pi\) | ||||
−0.144956 | + | 0.989438i | \(0.546304\pi\) | |||||||
\(884\) | 177.839 | 5.98139 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −51.4665 | −1.72905 | ||||||||
\(887\) | −10.7276 | −0.360197 | −0.180099 | − | 0.983649i | \(-0.557642\pi\) | ||||
−0.180099 | + | 0.983649i | \(0.557642\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.61484 | 0.154777 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.7703 | −0.628477 | ||||||||
\(893\) | −28.0509 | −0.938687 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −18.7733 | −0.627172 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 34.5777 | 1.15387 | ||||||||
\(899\) | −12.9925 | −0.433323 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −57.5407 | −1.91696 | ||||||||
\(902\) | 92.0186 | 3.06388 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.5407 | 0.616653 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.3110 | 0.740824 | 0.370412 | − | 0.928868i | \(-0.379216\pi\) | ||||
0.370412 | + | 0.928868i | \(0.379216\pi\) | |||||||
\(908\) | −61.0677 | −2.02660 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.46326 | −0.181006 | −0.0905030 | − | 0.995896i | \(-0.528847\pi\) | ||||
−0.0905030 | + | 0.995896i | \(0.528847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.8516 | −0.458423 | ||||||||
\(914\) | −76.5432 | −2.53182 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −80.6962 | −2.66628 | ||||||||
\(917\) | −5.36380 | −0.177128 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.6962 | −1.63932 | −0.819662 | − | 0.572847i | \(-0.805839\pi\) | ||||
−0.819662 | + | 0.572847i | \(0.805839\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.77033 | −0.0912359 | ||||||||
\(923\) | −88.9197 | −2.92683 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −23.5211 | −0.772953 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 35.9629 | 1.18054 | ||||||||
\(929\) | 16.0914 | 0.527942 | 0.263971 | − | 0.964531i | \(-0.414968\pi\) | ||||
0.263971 | + | 0.964531i | \(0.414968\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.38516 | −0.0781706 | ||||||||
\(932\) | −21.9717 | −0.719706 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.1555 | 0.561345 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.2297 | −0.628206 | −0.314103 | − | 0.949389i | \(-0.601704\pi\) | ||||
−0.314103 | + | 0.949389i | \(0.601704\pi\) | |||||||
\(938\) | −25.1701 | −0.821832 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.3072 | −1.60737 | −0.803684 | − | 0.595057i | \(-0.797130\pi\) | ||||
−0.803684 | + | 0.595057i | \(0.797130\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.3110 | 1.11732 | ||||||||
\(944\) | −147.921 | −4.81443 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 80.5036 | 2.61740 | ||||||||
\(947\) | 42.7115 | 1.38794 | 0.693968 | − | 0.720006i | \(-0.255861\pi\) | ||||
0.693968 | + | 0.720006i | \(0.255861\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.0000 | 0.908918 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 45.9258 | 1.48846 | ||||||||
\(953\) | −0.0994662 | −0.00322203 | −0.00161101 | − | 0.999999i | \(-0.500513\pi\) | ||||
−0.00161101 | + | 0.999999i | \(0.500513\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 33.2158 | 1.07427 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −89.0813 | −2.87809 | ||||||||
\(959\) | 10.7276 | 0.346412 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | −51.3731 | −1.65634 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 95.4665 | 3.07477 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.5407 | 1.20723 | 0.603613 | − | 0.797277i | \(-0.293727\pi\) | ||||
0.603613 | + | 0.797277i | \(0.293727\pi\) | |||||||
\(968\) | 6.59570 | 0.211994 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.09892 | −0.0994491 | −0.0497245 | − | 0.998763i | \(-0.515834\pi\) | ||||
−0.0497245 | + | 0.998763i | \(0.515834\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.38516 | −0.140582 | ||||||||
\(974\) | −35.8977 | −1.15024 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.1493 | 1.09253 | 0.546266 | − | 0.837612i | \(-0.316049\pi\) | ||||
0.546266 | + | 0.837612i | \(0.316049\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.30385 | −0.105591 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −94.8887 | −3.02802 | ||||||||
\(983\) | 36.5136 | 1.16460 | 0.582302 | − | 0.812973i | \(-0.302152\pi\) | ||||
0.582302 | + | 0.812973i | \(0.302152\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −31.1498 | −0.992012 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 79.0813 | 2.51591 | ||||||||
\(989\) | 30.0174 | 0.954497 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.6962 | 1.26099 | 0.630495 | − | 0.776193i | \(-0.282852\pi\) | ||||
0.630495 | + | 0.776193i | \(0.282852\pi\) | |||||||
\(992\) | −99.6473 | −3.16380 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −37.3481 | −1.18461 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.8445 | −0.786833 | −0.393417 | − | 0.919360i | \(-0.628707\pi\) | ||||
−0.393417 | + | 0.919360i | \(0.628707\pi\) | |||||||
\(998\) | −79.2251 | −2.50783 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1575.2.a.z.1.1 | yes | 4 | |
3.2 | odd | 2 | inner | 1575.2.a.z.1.4 | yes | 4 | |
5.2 | odd | 4 | 1575.2.d.l.1324.2 | 8 | |||
5.3 | odd | 4 | 1575.2.d.l.1324.7 | 8 | |||
5.4 | even | 2 | 1575.2.a.y.1.4 | yes | 4 | ||
15.2 | even | 4 | 1575.2.d.l.1324.8 | 8 | |||
15.8 | even | 4 | 1575.2.d.l.1324.1 | 8 | |||
15.14 | odd | 2 | 1575.2.a.y.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1575.2.a.y.1.1 | ✓ | 4 | 15.14 | odd | 2 | ||
1575.2.a.y.1.4 | yes | 4 | 5.4 | even | 2 | ||
1575.2.a.z.1.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1575.2.a.z.1.4 | yes | 4 | 3.2 | odd | 2 | inner | |
1575.2.d.l.1324.1 | 8 | 15.8 | even | 4 | |||
1575.2.d.l.1324.2 | 8 | 5.2 | odd | 4 | |||
1575.2.d.l.1324.7 | 8 | 5.3 | odd | 4 | |||
1575.2.d.l.1324.8 | 8 | 15.2 | even | 4 |