Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6525,2,Mod(1,6525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6525, 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("6525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6525 = 3^{2} \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6525.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: | \(52.1023873189\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 12x^{6} + 23x^{5} + 36x^{4} - 62x^{3} - 15x^{2} + 14x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2175) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.59587\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59587 | −1.83556 | −0.917779 | − | 0.397090i | \(-0.870020\pi\) | ||||
−0.917779 | + | 0.397090i | \(0.870020\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.73855 | 2.36928 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.93826 | −1.48852 | −0.744262 | − | 0.667888i | \(-0.767198\pi\) | ||||
−0.744262 | + | 0.667888i | \(0.767198\pi\) | |||||||
\(8\) | −7.10893 | −2.51339 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.24645 | −0.677329 | −0.338665 | − | 0.940907i | \(-0.609975\pi\) | ||||
−0.338665 | + | 0.940907i | \(0.609975\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.09464 | 0.580950 | 0.290475 | − | 0.956883i | \(-0.406187\pi\) | ||||
0.290475 | + | 0.956883i | \(0.406187\pi\) | |||||||
\(14\) | 10.2232 | 2.73227 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.97678 | 2.24420 | ||||||||
\(17\) | −6.95310 | −1.68637 | −0.843187 | − | 0.537620i | \(-0.819324\pi\) | ||||
−0.843187 | + | 0.537620i | \(0.819324\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.29591 | 0.985549 | 0.492774 | − | 0.870157i | \(-0.335983\pi\) | ||||
0.492774 | + | 0.870157i | \(0.335983\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.83149 | 1.24328 | ||||||||
\(23\) | 5.19955 | 1.08418 | 0.542090 | − | 0.840320i | \(-0.317633\pi\) | ||||
0.542090 | + | 0.840320i | \(0.317633\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.43743 | −1.06637 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −18.6617 | −3.52672 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.25035 | 0.404175 | 0.202087 | − | 0.979367i | \(-0.435227\pi\) | ||||
0.202087 | + | 0.979367i | \(0.435227\pi\) | |||||||
\(32\) | −9.08471 | −1.60596 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 18.0494 | 3.09544 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.5280 | −1.73079 | −0.865397 | − | 0.501086i | \(-0.832934\pi\) | ||||
−0.865397 | + | 0.501086i | \(0.832934\pi\) | |||||||
\(38\) | −11.1516 | −1.80903 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.66629 | 0.416405 | 0.208202 | − | 0.978086i | \(-0.433239\pi\) | ||||
0.208202 | + | 0.978086i | \(0.433239\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.03681 | 0.920605 | 0.460302 | − | 0.887762i | \(-0.347741\pi\) | ||||
0.460302 | + | 0.887762i | \(0.347741\pi\) | |||||||
\(44\) | −10.6449 | −1.60478 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −13.4974 | −1.99008 | ||||||||
\(47\) | 7.74829 | 1.13020 | 0.565102 | − | 0.825021i | \(-0.308837\pi\) | ||||
0.565102 | + | 0.825021i | \(0.308837\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.50991 | 1.21570 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.92559 | 1.37643 | ||||||||
\(53\) | 1.41309 | 0.194103 | 0.0970513 | − | 0.995279i | \(-0.469059\pi\) | ||||
0.0970513 | + | 0.995279i | \(0.469059\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 27.9968 | 3.74124 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.59587 | 0.340855 | ||||||||
\(59\) | −5.76800 | −0.750929 | −0.375465 | − | 0.926837i | \(-0.622517\pi\) | ||||
−0.375465 | + | 0.926837i | \(0.622517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.9192 | −1.39806 | −0.699030 | − | 0.715092i | \(-0.746385\pi\) | ||||
−0.699030 | + | 0.715092i | \(0.746385\pi\) | |||||||
\(62\) | −5.84162 | −0.741887 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.62918 | 0.703647 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.7471 | −1.43514 | −0.717569 | − | 0.696487i | \(-0.754745\pi\) | ||||
−0.717569 | + | 0.696487i | \(0.754745\pi\) | |||||||
\(68\) | −32.9476 | −3.99549 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.55691 | 0.540806 | 0.270403 | − | 0.962747i | \(-0.412843\pi\) | ||||
0.270403 | + | 0.962747i | \(0.412843\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.3564 | 1.44621 | 0.723103 | − | 0.690740i | \(-0.242715\pi\) | ||||
0.723103 | + | 0.690740i | \(0.242715\pi\) | |||||||
\(74\) | 27.3294 | 3.17698 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.3564 | 2.33504 | ||||||||
\(77\) | 8.84710 | 1.00822 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.4098 | 1.62122 | 0.810612 | − | 0.585584i | \(-0.199135\pi\) | ||||
0.810612 | + | 0.585584i | \(0.199135\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.92135 | −0.764335 | ||||||||
\(83\) | 3.81272 | 0.418501 | 0.209250 | − | 0.977862i | \(-0.432898\pi\) | ||||
0.209250 | + | 0.977862i | \(0.432898\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −15.6708 | −1.68982 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 15.9699 | 1.70239 | ||||||||
\(89\) | 2.07340 | 0.219780 | 0.109890 | − | 0.993944i | \(-0.464950\pi\) | ||||
0.109890 | + | 0.993944i | \(0.464950\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.24926 | −0.864757 | ||||||||
\(92\) | 24.6383 | 2.56872 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −20.1136 | −2.07456 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0068 | 1.21911 | 0.609553 | − | 0.792745i | \(-0.291349\pi\) | ||||
0.609553 | + | 0.792745i | \(0.291349\pi\) | |||||||
\(98\) | −22.0906 | −2.23149 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.8642 | 1.57855 | 0.789276 | − | 0.614039i | \(-0.210456\pi\) | ||||
0.789276 | + | 0.614039i | \(0.210456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.3119 | −1.01606 | −0.508031 | − | 0.861339i | \(-0.669627\pi\) | ||||
−0.508031 | + | 0.861339i | \(0.669627\pi\) | |||||||
\(104\) | −14.8907 | −1.46015 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.66820 | −0.356287 | ||||||||
\(107\) | −4.47645 | −0.432755 | −0.216378 | − | 0.976310i | \(-0.569424\pi\) | ||||
−0.216378 | + | 0.976310i | \(0.569424\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.4783 | 1.29098 | 0.645492 | − | 0.763767i | \(-0.276652\pi\) | ||||
0.645492 | + | 0.763767i | \(0.276652\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −35.3529 | −3.34054 | ||||||||
\(113\) | 11.4525 | 1.07736 | 0.538679 | − | 0.842511i | \(-0.318923\pi\) | ||||
0.538679 | + | 0.842511i | \(0.318923\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.73855 | −0.439964 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.9730 | 1.37838 | ||||||||
\(119\) | 27.3831 | 2.51021 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.95347 | −0.541225 | ||||||||
\(122\) | 28.3449 | 2.56622 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.6634 | 0.957602 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.23499 | −0.287059 | −0.143529 | − | 0.989646i | \(-0.545845\pi\) | ||||
−0.143529 | + | 0.989646i | \(0.545845\pi\) | |||||||
\(128\) | 3.55679 | 0.314378 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3567 | 1.16698 | 0.583489 | − | 0.812121i | \(-0.301687\pi\) | ||||
0.583489 | + | 0.812121i | \(0.301687\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.9184 | −1.46701 | ||||||||
\(134\) | 30.4940 | 2.63428 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 49.4291 | 4.23851 | ||||||||
\(137\) | −4.35642 | −0.372194 | −0.186097 | − | 0.982531i | \(-0.559584\pi\) | ||||
−0.186097 | + | 0.982531i | \(0.559584\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.4171 | −1.56212 | −0.781061 | − | 0.624455i | \(-0.785321\pi\) | ||||
−0.781061 | + | 0.624455i | \(0.785321\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.8292 | −0.992681 | ||||||||
\(143\) | −4.70551 | −0.393495 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −32.0756 | −2.65460 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −49.8876 | −4.10073 | ||||||||
\(149\) | −17.6427 | −1.44535 | −0.722674 | − | 0.691189i | \(-0.757087\pi\) | ||||
−0.722674 | + | 0.691189i | \(0.757087\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.02381 | 0.327453 | 0.163726 | − | 0.986506i | \(-0.447649\pi\) | ||||
0.163726 | + | 0.986506i | \(0.447649\pi\) | |||||||
\(152\) | −30.5393 | −2.47707 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −22.9659 | −1.85065 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.70119 | −0.614622 | −0.307311 | − | 0.951609i | \(-0.599429\pi\) | ||||
−0.307311 | + | 0.951609i | \(0.599429\pi\) | |||||||
\(158\) | −37.4059 | −2.97585 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.4772 | −1.61383 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.6829 | −1.07173 | −0.535866 | − | 0.844303i | \(-0.680015\pi\) | ||||
−0.535866 | + | 0.844303i | \(0.680015\pi\) | |||||||
\(164\) | 12.6344 | 0.986578 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.89734 | −0.768183 | ||||||||
\(167\) | 24.9607 | 1.93151 | 0.965757 | − | 0.259449i | \(-0.0835408\pi\) | ||||
0.965757 | + | 0.259449i | \(0.0835408\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.61246 | −0.662497 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 28.6057 | 2.18117 | ||||||||
\(173\) | −19.9187 | −1.51439 | −0.757194 | − | 0.653191i | \(-0.773430\pi\) | ||||
−0.757194 | + | 0.653191i | \(0.773430\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −20.1659 | −1.52006 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.38227 | −0.403418 | ||||||||
\(179\) | −10.8816 | −0.813329 | −0.406664 | − | 0.913578i | \(-0.633308\pi\) | ||||
−0.406664 | + | 0.913578i | \(0.633308\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.9372 | −1.03594 | −0.517972 | − | 0.855398i | \(-0.673313\pi\) | ||||
−0.517972 | + | 0.855398i | \(0.673313\pi\) | |||||||
\(182\) | 21.4140 | 1.58731 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −36.9632 | −2.72497 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.6198 | 1.14223 | ||||||||
\(188\) | 36.7157 | 2.67777 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.3458 | −0.965670 | −0.482835 | − | 0.875711i | \(-0.660393\pi\) | ||||
−0.482835 | + | 0.875711i | \(0.660393\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.6337 | 1.12534 | 0.562668 | − | 0.826683i | \(-0.309775\pi\) | ||||
0.562668 | + | 0.826683i | \(0.309775\pi\) | |||||||
\(194\) | −31.1681 | −2.23774 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 40.3247 | 2.88033 | ||||||||
\(197\) | 20.1140 | 1.43306 | 0.716530 | − | 0.697556i | \(-0.245729\pi\) | ||||
0.716530 | + | 0.697556i | \(0.245729\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.27232 | −0.657297 | −0.328649 | − | 0.944452i | \(-0.606593\pi\) | ||||
−0.328649 | + | 0.944452i | \(0.606593\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −41.1816 | −2.89752 | ||||||||
\(203\) | 3.93826 | 0.276412 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 26.7684 | 1.86504 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 18.8032 | 1.30376 | ||||||||
\(209\) | −9.65053 | −0.667541 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.228998 | −0.0157649 | −0.00788245 | − | 0.999969i | \(-0.502509\pi\) | ||||
−0.00788245 | + | 0.999969i | \(0.502509\pi\) | |||||||
\(212\) | 6.69600 | 0.459883 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.6203 | 0.794348 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.86247 | −0.601624 | ||||||||
\(218\) | −34.9879 | −2.36968 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.5643 | −0.979699 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.1117 | −1.68160 | −0.840802 | − | 0.541342i | \(-0.817916\pi\) | ||||
−0.840802 | + | 0.541342i | \(0.817916\pi\) | |||||||
\(224\) | 35.7780 | 2.39052 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −29.7292 | −1.97756 | ||||||||
\(227\) | 4.98706 | 0.331003 | 0.165501 | − | 0.986210i | \(-0.447076\pi\) | ||||
0.165501 | + | 0.986210i | \(0.447076\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.60591 | 0.106122 | 0.0530608 | − | 0.998591i | \(-0.483102\pi\) | ||||
0.0530608 | + | 0.998591i | \(0.483102\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.10893 | 0.466724 | ||||||||
\(233\) | −6.65588 | −0.436041 | −0.218021 | − | 0.975944i | \(-0.569960\pi\) | ||||
−0.218021 | + | 0.975944i | \(0.569960\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −27.3320 | −1.77916 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −71.0831 | −4.60763 | ||||||||
\(239\) | −2.87227 | −0.185792 | −0.0928959 | − | 0.995676i | \(-0.529612\pi\) | ||||
−0.0928959 | + | 0.995676i | \(0.529612\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.2768 | 0.984068 | 0.492034 | − | 0.870576i | \(-0.336254\pi\) | ||||
0.492034 | + | 0.870576i | \(0.336254\pi\) | |||||||
\(242\) | 15.4545 | 0.993450 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −51.7412 | −3.31239 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.99840 | 0.572554 | ||||||||
\(248\) | −15.9976 | −1.01585 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.8782 | −0.686627 | −0.343314 | − | 0.939221i | \(-0.611549\pi\) | ||||
−0.343314 | + | 0.939221i | \(0.611549\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.6805 | −0.734348 | ||||||||
\(254\) | 8.39761 | 0.526913 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −20.4913 | −1.28071 | ||||||||
\(257\) | 18.0748 | 1.12748 | 0.563739 | − | 0.825953i | \(-0.309363\pi\) | ||||
0.563739 | + | 0.825953i | \(0.309363\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 41.4621 | 2.57633 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −34.6722 | −2.14206 | ||||||||
\(263\) | 18.4454 | 1.13739 | 0.568697 | − | 0.822547i | \(-0.307448\pi\) | ||||
0.568697 | + | 0.822547i | \(0.307448\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 43.9180 | 2.69279 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −55.6643 | −3.40024 | ||||||||
\(269\) | −11.6702 | −0.711544 | −0.355772 | − | 0.934573i | \(-0.615782\pi\) | ||||
−0.355772 | + | 0.934573i | \(0.615782\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.2501 | 1.23011 | 0.615054 | − | 0.788485i | \(-0.289134\pi\) | ||||
0.615054 | + | 0.788485i | \(0.289134\pi\) | |||||||
\(272\) | −62.4165 | −3.78455 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.3087 | 0.683184 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.66952 | 0.220480 | 0.110240 | − | 0.993905i | \(-0.464838\pi\) | ||||
0.110240 | + | 0.993905i | \(0.464838\pi\) | |||||||
\(278\) | 47.8085 | 2.86737 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.8056 | −1.36047 | −0.680233 | − | 0.732996i | \(-0.738121\pi\) | ||||
−0.680233 | + | 0.732996i | \(0.738121\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.38657 | −0.141867 | −0.0709335 | − | 0.997481i | \(-0.522598\pi\) | ||||
−0.0709335 | + | 0.997481i | \(0.522598\pi\) | |||||||
\(284\) | 21.5932 | 1.28132 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.2149 | 0.722282 | ||||||||
\(287\) | −10.5006 | −0.619828 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.3456 | 1.84386 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 58.5514 | 3.42646 | ||||||||
\(293\) | −19.4843 | −1.13828 | −0.569142 | − | 0.822239i | \(-0.692725\pi\) | ||||
−0.569142 | + | 0.822239i | \(0.692725\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 74.8430 | 4.35016 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 45.7982 | 2.65302 | ||||||||
\(299\) | 10.8912 | 0.629855 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.7745 | −1.37034 | ||||||||
\(302\) | −10.4453 | −0.601059 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 38.5634 | 2.21176 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.527333 | −0.0300965 | −0.0150482 | − | 0.999887i | \(-0.504790\pi\) | ||||
−0.0150482 | + | 0.999887i | \(0.504790\pi\) | |||||||
\(308\) | 41.9225 | 2.38875 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.89624 | 0.447755 | 0.223877 | − | 0.974617i | \(-0.428129\pi\) | ||||
0.223877 | + | 0.974617i | \(0.428129\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0064 | 0.565597 | 0.282799 | − | 0.959179i | \(-0.408737\pi\) | ||||
0.282799 | + | 0.959179i | \(0.408737\pi\) | |||||||
\(314\) | 19.9913 | 1.12818 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 68.2814 | 3.84113 | ||||||||
\(317\) | −32.5401 | −1.82763 | −0.913817 | − | 0.406125i | \(-0.866880\pi\) | ||||
−0.913817 | + | 0.406125i | \(0.866880\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.24645 | 0.125777 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 53.1562 | 2.96228 | ||||||||
\(323\) | −29.8699 | −1.66200 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 35.5192 | 1.96723 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −18.9545 | −1.04659 | ||||||||
\(329\) | −30.5148 | −1.68233 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.9411 | 1.26096 | 0.630480 | − | 0.776206i | \(-0.282858\pi\) | ||||
0.630480 | + | 0.776206i | \(0.282858\pi\) | |||||||
\(332\) | 18.0668 | 0.991544 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −64.7947 | −3.54541 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0039 | 0.871789 | 0.435894 | − | 0.899998i | \(-0.356432\pi\) | ||||
0.435894 | + | 0.899998i | \(0.356432\pi\) | |||||||
\(338\) | 22.3569 | 1.21605 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.05529 | −0.273760 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.94642 | −0.321076 | ||||||||
\(344\) | −42.9153 | −2.31384 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 51.7063 | 2.77975 | ||||||||
\(347\) | −22.9990 | −1.23465 | −0.617326 | − | 0.786707i | \(-0.711784\pi\) | ||||
−0.617326 | + | 0.786707i | \(0.711784\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.3108 | 1.30133 | 0.650664 | − | 0.759366i | \(-0.274491\pi\) | ||||
0.650664 | + | 0.759366i | \(0.274491\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.4083 | 1.08777 | ||||||||
\(353\) | 29.2685 | 1.55780 | 0.778902 | − | 0.627146i | \(-0.215777\pi\) | ||||
0.778902 | + | 0.627146i | \(0.215777\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.82490 | 0.520719 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 28.2472 | 1.49291 | ||||||||
\(359\) | −18.5090 | −0.976868 | −0.488434 | − | 0.872601i | \(-0.662432\pi\) | ||||
−0.488434 | + | 0.872601i | \(0.662432\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.545179 | −0.0286936 | ||||||||
\(362\) | 36.1792 | 1.90154 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −39.0896 | −2.04885 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.896398 | 0.0467916 | 0.0233958 | − | 0.999726i | \(-0.492552\pi\) | ||||
0.0233958 | + | 0.999726i | \(0.492552\pi\) | |||||||
\(368\) | 46.6752 | 2.43311 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.56511 | −0.288926 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.64559 | 0.240540 | 0.120270 | − | 0.992741i | \(-0.461624\pi\) | ||||
0.120270 | + | 0.992741i | \(0.461624\pi\) | |||||||
\(374\) | −40.5469 | −2.09663 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −55.0821 | −2.84064 | ||||||||
\(377\) | −2.09464 | −0.107880 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.4863 | −1.66871 | −0.834356 | − | 0.551226i | \(-0.814160\pi\) | ||||
−0.834356 | + | 0.551226i | \(0.814160\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 34.6441 | 1.77254 | ||||||||
\(383\) | −9.48311 | −0.484564 | −0.242282 | − | 0.970206i | \(-0.577896\pi\) | ||||
−0.242282 | + | 0.970206i | \(0.577896\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −40.5830 | −2.06562 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 56.8949 | 2.88840 | ||||||||
\(389\) | −33.9509 | −1.72138 | −0.860689 | − | 0.509132i | \(-0.829967\pi\) | ||||
−0.860689 | + | 0.509132i | \(0.829967\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.1530 | −1.82833 | ||||||||
\(392\) | −60.4964 | −3.05553 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −52.2132 | −2.63047 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.0892 | −1.25919 | −0.629596 | − | 0.776923i | \(-0.716780\pi\) | ||||
−0.629596 | + | 0.776923i | \(0.716780\pi\) | |||||||
\(398\) | 24.0698 | 1.20651 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.85814 | 0.242604 | 0.121302 | − | 0.992616i | \(-0.461293\pi\) | ||||
0.121302 | + | 0.992616i | \(0.461293\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.71368 | 0.234805 | ||||||||
\(404\) | 75.1736 | 3.74003 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.2232 | −0.507370 | ||||||||
\(407\) | 23.6506 | 1.17232 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.6604 | 0.724911 | 0.362456 | − | 0.932001i | \(-0.381938\pi\) | ||||
0.362456 | + | 0.932001i | \(0.381938\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −48.8635 | −2.40733 | ||||||||
\(413\) | 22.7159 | 1.11778 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −19.0292 | −0.932985 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 25.0515 | 1.22531 | ||||||||
\(419\) | 18.4123 | 0.899502 | 0.449751 | − | 0.893154i | \(-0.351513\pi\) | ||||
0.449751 | + | 0.893154i | \(0.351513\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.1489 | 1.42063 | 0.710316 | − | 0.703883i | \(-0.248552\pi\) | ||||
0.710316 | + | 0.703883i | \(0.248552\pi\) | |||||||
\(422\) | 0.594451 | 0.0289374 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.0456 | −0.487855 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 43.0027 | 2.08105 | ||||||||
\(428\) | −21.2119 | −1.02532 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.05315 | 0.0988966 | 0.0494483 | − | 0.998777i | \(-0.484254\pi\) | ||||
0.0494483 | + | 0.998777i | \(0.484254\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.7820 | −0.902603 | −0.451302 | − | 0.892371i | \(-0.649040\pi\) | ||||
−0.451302 | + | 0.892371i | \(0.649040\pi\) | |||||||
\(434\) | 23.0058 | 1.10432 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 63.8675 | 3.05870 | ||||||||
\(437\) | 22.3368 | 1.06851 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.7889 | −1.61266 | −0.806329 | − | 0.591467i | \(-0.798549\pi\) | ||||
−0.806329 | + | 0.591467i | \(0.798549\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 37.8070 | 1.79830 | ||||||||
\(443\) | −24.2962 | −1.15435 | −0.577173 | − | 0.816622i | \(-0.695844\pi\) | ||||
−0.577173 | + | 0.816622i | \(0.695844\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 65.1868 | 3.08668 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −22.1692 | −1.04740 | ||||||||
\(449\) | 21.0976 | 0.995656 | 0.497828 | − | 0.867276i | \(-0.334131\pi\) | ||||
0.497828 | + | 0.867276i | \(0.334131\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.98968 | −0.282043 | ||||||||
\(452\) | 54.2682 | 2.55256 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.9458 | −0.607575 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.70983 | 0.407429 | 0.203714 | − | 0.979030i | \(-0.434699\pi\) | ||||
0.203714 | + | 0.979030i | \(0.434699\pi\) | |||||||
\(458\) | −4.16874 | −0.194793 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.5424 | −1.37592 | −0.687962 | − | 0.725746i | \(-0.741495\pi\) | ||||
−0.687962 | + | 0.725746i | \(0.741495\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.3067 | 1.73379 | 0.866894 | − | 0.498493i | \(-0.166113\pi\) | ||||
0.866894 | + | 0.498493i | \(0.166113\pi\) | |||||||
\(464\) | −8.97678 | −0.416737 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.2778 | 0.800379 | ||||||||
\(467\) | −30.2144 | −1.39816 | −0.699079 | − | 0.715045i | \(-0.746406\pi\) | ||||
−0.699079 | + | 0.715045i | \(0.746406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 46.2632 | 2.13624 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 41.0043 | 1.88738 | ||||||||
\(473\) | −13.5614 | −0.623553 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 129.756 | 5.94738 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.45605 | 0.341032 | ||||||||
\(479\) | −39.1511 | −1.78886 | −0.894430 | − | 0.447209i | \(-0.852418\pi\) | ||||
−0.894430 | + | 0.447209i | \(0.852418\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.0524 | −1.00551 | ||||||||
\(482\) | −39.6567 | −1.80632 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −28.2108 | −1.28231 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.9182 | −1.08384 | −0.541919 | − | 0.840430i | \(-0.682302\pi\) | ||||
−0.541919 | + | 0.840430i | \(0.682302\pi\) | |||||||
\(488\) | 77.6239 | 3.51387 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.40974 | −0.199009 | −0.0995044 | − | 0.995037i | \(-0.531726\pi\) | ||||
−0.0995044 | + | 0.995037i | \(0.531726\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.95310 | 0.313152 | ||||||||
\(494\) | −23.3587 | −1.05096 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.2009 | 0.907047 | ||||||||
\(497\) | −17.9463 | −0.805002 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −37.0446 | −1.65834 | −0.829171 | − | 0.558995i | \(-0.811187\pi\) | ||||
−0.829171 | + | 0.558995i | \(0.811187\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.2385 | 1.26034 | ||||||||
\(503\) | 12.6691 | 0.564886 | 0.282443 | − | 0.959284i | \(-0.408855\pi\) | ||||
0.282443 | + | 0.959284i | \(0.408855\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 30.3211 | 1.34794 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.3292 | −0.680121 | ||||||||
\(509\) | 11.7078 | 0.518939 | 0.259469 | − | 0.965751i | \(-0.416452\pi\) | ||||
0.259469 | + | 0.965751i | \(0.416452\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −48.6627 | −2.15271 | ||||||||
\(512\) | 46.0793 | 2.03644 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −46.9200 | −2.06955 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.4061 | −0.765520 | ||||||||
\(518\) | −107.630 | −4.72900 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.0559550 | −0.00245143 | −0.00122572 | − | 0.999999i | \(-0.500390\pi\) | ||||
−0.00122572 | + | 0.999999i | \(0.500390\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.256669 | −0.0112234 | −0.00561168 | − | 0.999984i | \(-0.501786\pi\) | ||||
−0.00561168 | + | 0.999984i | \(0.501786\pi\) | |||||||
\(524\) | 63.2913 | 2.76489 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −47.8819 | −2.08775 | ||||||||
\(527\) | −15.6469 | −0.681590 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.03530 | 0.175448 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −80.1688 | −3.47576 | ||||||||
\(533\) | 5.58493 | 0.241910 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 83.5095 | 3.60706 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 30.2943 | 1.30608 | ||||||||
\(539\) | −19.1171 | −0.823430 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.88887 | 0.0812090 | 0.0406045 | − | 0.999175i | \(-0.487072\pi\) | ||||
0.0406045 | + | 0.999175i | \(0.487072\pi\) | |||||||
\(542\) | −52.5668 | −2.25794 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 63.1669 | 2.70826 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.193341 | −0.00826668 | −0.00413334 | − | 0.999991i | \(-0.501316\pi\) | ||||
−0.00413334 | + | 0.999991i | \(0.501316\pi\) | |||||||
\(548\) | −20.6431 | −0.881831 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.29591 | −0.183012 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −56.7494 | −2.41323 | ||||||||
\(554\) | −9.52561 | −0.404704 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −87.2706 | −3.70110 | ||||||||
\(557\) | 26.4282 | 1.11980 | 0.559899 | − | 0.828561i | \(-0.310840\pi\) | ||||
0.559899 | + | 0.828561i | \(0.310840\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.6450 | 0.534825 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 59.2003 | 2.49722 | ||||||||
\(563\) | 6.18961 | 0.260861 | 0.130430 | − | 0.991457i | \(-0.458364\pi\) | ||||
0.130430 | + | 0.991457i | \(0.458364\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.19523 | 0.260405 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −32.3948 | −1.35926 | ||||||||
\(569\) | 15.9034 | 0.666705 | 0.333353 | − | 0.942802i | \(-0.391820\pi\) | ||||
0.333353 | + | 0.942802i | \(0.391820\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.8555 | −0.705380 | −0.352690 | − | 0.935740i | \(-0.614733\pi\) | ||||
−0.352690 | + | 0.935740i | \(0.614733\pi\) | |||||||
\(572\) | −22.2973 | −0.932297 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 27.2581 | 1.13773 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.1237 | −0.962650 | −0.481325 | − | 0.876542i | \(-0.659844\pi\) | ||||
−0.481325 | + | 0.876542i | \(0.659844\pi\) | |||||||
\(578\) | −81.3692 | −3.38451 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.0155 | −0.622948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.17443 | −0.131471 | ||||||||
\(584\) | −87.8408 | −3.63488 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 50.5787 | 2.08939 | ||||||||
\(587\) | 7.80902 | 0.322313 | 0.161156 | − | 0.986929i | \(-0.448478\pi\) | ||||
0.161156 | + | 0.986929i | \(0.448478\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.66730 | 0.398334 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −94.5077 | −3.88424 | ||||||||
\(593\) | −19.5804 | −0.804069 | −0.402034 | − | 0.915625i | \(-0.631697\pi\) | ||||
−0.402034 | + | 0.915625i | \(0.631697\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −83.6009 | −3.42443 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −28.2722 | −1.15614 | ||||||||
\(599\) | −30.2322 | −1.23525 | −0.617627 | − | 0.786471i | \(-0.711906\pi\) | ||||
−0.617627 | + | 0.786471i | \(0.711906\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.1180 | 1.35091 | 0.675457 | − | 0.737400i | \(-0.263947\pi\) | ||||
0.675457 | + | 0.737400i | \(0.263947\pi\) | |||||||
\(602\) | 61.7157 | 2.51534 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19.0670 | 0.775826 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.4711 | −0.952661 | −0.476330 | − | 0.879266i | \(-0.658033\pi\) | ||||
−0.476330 | + | 0.879266i | \(0.658033\pi\) | |||||||
\(608\) | −39.0271 | −1.58276 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.2299 | 0.656592 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.1560 | 0.975650 | 0.487825 | − | 0.872941i | \(-0.337790\pi\) | ||||
0.487825 | + | 0.872941i | \(0.337790\pi\) | |||||||
\(614\) | 1.36889 | 0.0552439 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −62.8935 | −2.53405 | ||||||||
\(617\) | 47.7509 | 1.92238 | 0.961189 | − | 0.275890i | \(-0.0889725\pi\) | ||||
0.961189 | + | 0.275890i | \(0.0889725\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.779735 | 0.0313402 | 0.0156701 | − | 0.999877i | \(-0.495012\pi\) | ||||
0.0156701 | + | 0.999877i | \(0.495012\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20.4976 | −0.821880 | ||||||||
\(623\) | −8.16558 | −0.327147 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −25.9754 | −1.03819 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −36.4925 | −1.45621 | ||||||||
\(629\) | 73.2023 | 2.91877 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.8120 | 0.709083 | 0.354542 | − | 0.935040i | \(-0.384637\pi\) | ||||
0.354542 | + | 0.935040i | \(0.384637\pi\) | |||||||
\(632\) | −102.438 | −4.07476 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 84.4700 | 3.35473 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.8252 | 0.706262 | ||||||||
\(638\) | −5.83149 | −0.230871 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.7647 | −1.17563 | −0.587817 | − | 0.808994i | \(-0.700013\pi\) | ||||
−0.587817 | + | 0.808994i | \(0.700013\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.4049 | −1.63285 | −0.816426 | − | 0.577451i | \(-0.804048\pi\) | ||||
−0.816426 | + | 0.577451i | \(0.804048\pi\) | |||||||
\(644\) | −97.0322 | −3.82361 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 77.5384 | 3.05071 | ||||||||
\(647\) | −14.6074 | −0.574275 | −0.287137 | − | 0.957889i | \(-0.592704\pi\) | ||||
−0.287137 | + | 0.957889i | \(0.592704\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.9575 | 0.508627 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −64.8374 | −2.53923 | ||||||||
\(653\) | −30.5647 | −1.19609 | −0.598045 | − | 0.801462i | \(-0.704056\pi\) | ||||
−0.598045 | + | 0.801462i | \(0.704056\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 23.9347 | 0.934493 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 79.2125 | 3.08802 | ||||||||
\(659\) | −22.1893 | −0.864371 | −0.432186 | − | 0.901785i | \(-0.642257\pi\) | ||||
−0.432186 | + | 0.901785i | \(0.642257\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.85731 | −0.383405 | −0.191702 | − | 0.981453i | \(-0.561401\pi\) | ||||
−0.191702 | + | 0.981453i | \(0.561401\pi\) | |||||||
\(662\) | −59.5523 | −2.31457 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −27.1044 | −1.05185 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.19955 | −0.201327 | ||||||||
\(668\) | 118.277 | 4.57629 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.5294 | 0.946948 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.3057 | −0.975463 | −0.487732 | − | 0.872994i | \(-0.662176\pi\) | ||||
−0.487732 | + | 0.872994i | \(0.662176\pi\) | |||||||
\(674\) | −41.5441 | −1.60022 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −40.8106 | −1.56964 | ||||||||
\(677\) | 3.67306 | 0.141167 | 0.0705836 | − | 0.997506i | \(-0.477514\pi\) | ||||
0.0705836 | + | 0.997506i | \(0.477514\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −47.2860 | −1.81467 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 13.1229 | 0.502502 | ||||||||
\(683\) | −17.3807 | −0.665053 | −0.332527 | − | 0.943094i | \(-0.607901\pi\) | ||||
−0.332527 | + | 0.943094i | \(0.607901\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15.4361 | 0.589354 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 54.1911 | 2.06602 | ||||||||
\(689\) | 2.95992 | 0.112764 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.5585 | −1.08642 | −0.543209 | − | 0.839598i | \(-0.682791\pi\) | ||||
−0.543209 | + | 0.839598i | \(0.682791\pi\) | |||||||
\(692\) | −94.3856 | −3.58800 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 59.7025 | 2.26628 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.5390 | −0.702214 | ||||||||
\(698\) | −63.1078 | −2.38866 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.5401 | −0.813557 | −0.406779 | − | 0.913527i | \(-0.633348\pi\) | ||||
−0.406779 | + | 0.913527i | \(0.633348\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −45.2274 | −1.70578 | ||||||||
\(704\) | −12.6457 | −0.476601 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −75.9772 | −2.85944 | ||||||||
\(707\) | −62.4776 | −2.34971 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.29948 | −0.0863587 | −0.0431793 | − | 0.999067i | \(-0.513749\pi\) | ||||
−0.0431793 | + | 0.999067i | \(0.513749\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.7396 | −0.552391 | ||||||||
\(713\) | 11.7008 | 0.438199 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −51.5630 | −1.92700 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 48.0470 | 1.79310 | ||||||||
\(719\) | −13.6814 | −0.510232 | −0.255116 | − | 0.966910i | \(-0.582114\pi\) | ||||
−0.255116 | + | 0.966910i | \(0.582114\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.6110 | 1.51243 | ||||||||
\(722\) | 1.41521 | 0.0526688 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −66.0422 | −2.45444 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.0451 | 1.85607 | 0.928035 | − | 0.372492i | \(-0.121497\pi\) | ||||
0.928035 | + | 0.372492i | \(0.121497\pi\) | |||||||
\(728\) | 58.6435 | 2.17347 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41.9745 | −1.55248 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.7734 | 1.43213 | 0.716065 | − | 0.698034i | \(-0.245942\pi\) | ||||
0.716065 | + | 0.698034i | \(0.245942\pi\) | |||||||
\(734\) | −2.32694 | −0.0858887 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −47.2364 | −1.74116 | ||||||||
\(737\) | 26.3893 | 0.972062 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.0707 | −0.664742 | −0.332371 | − | 0.943149i | \(-0.607849\pi\) | ||||
−0.332371 | + | 0.943149i | \(0.607849\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.4463 | 0.530341 | ||||||||
\(743\) | 20.9864 | 0.769917 | 0.384959 | − | 0.922934i | \(-0.374216\pi\) | ||||
0.384959 | + | 0.922934i | \(0.374216\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12.0594 | −0.441525 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 74.0151 | 2.70626 | ||||||||
\(749\) | 17.6294 | 0.644166 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.3274 | −0.741758 | −0.370879 | − | 0.928681i | \(-0.620944\pi\) | ||||
−0.370879 | + | 0.928681i | \(0.620944\pi\) | |||||||
\(752\) | 69.5547 | 2.53640 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.43743 | 0.198020 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.0654846 | 0.00238008 | 0.00119004 | − | 0.999999i | \(-0.499621\pi\) | ||||
0.00119004 | + | 0.999999i | \(0.499621\pi\) | |||||||
\(758\) | 84.3304 | 3.06302 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.8872 | 1.04716 | 0.523580 | − | 0.851976i | \(-0.324596\pi\) | ||||
0.523580 | + | 0.851976i | \(0.324596\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −53.0810 | −1.92166 | ||||||||
\(764\) | −63.2399 | −2.28794 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.6169 | 0.889446 | ||||||||
\(767\) | −12.0819 | −0.436252 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.0813 | −0.363541 | −0.181771 | − | 0.983341i | \(-0.558183\pi\) | ||||
−0.181771 | + | 0.983341i | \(0.558183\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 74.0809 | 2.66623 | ||||||||
\(773\) | 20.5353 | 0.738602 | 0.369301 | − | 0.929310i | \(-0.379597\pi\) | ||||
0.369301 | + | 0.929310i | \(0.379597\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −85.3556 | −3.06409 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 88.1321 | 3.15969 | ||||||||
\(779\) | 11.4541 | 0.410387 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.2369 | −0.366304 | ||||||||
\(782\) | 93.8485 | 3.35602 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 76.3916 | 2.72827 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.0601 | −1.64186 | −0.820932 | − | 0.571026i | \(-0.806545\pi\) | ||||
−0.820932 | + | 0.571026i | \(0.806545\pi\) | |||||||
\(788\) | 95.3110 | 3.39531 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −45.1029 | −1.60367 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.8718 | −0.812203 | ||||||||
\(794\) | 65.1284 | 2.31132 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −43.9374 | −1.55732 | ||||||||
\(797\) | −37.4745 | −1.32742 | −0.663708 | − | 0.747992i | \(-0.731018\pi\) | ||||
−0.663708 | + | 0.747992i | \(0.731018\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −53.8746 | −1.90595 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12.6111 | −0.445314 | ||||||||
\(803\) | −27.7580 | −0.979558 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.2361 | −0.430999 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −112.778 | −3.96751 | ||||||||
\(809\) | −29.9284 | −1.05223 | −0.526113 | − | 0.850414i | \(-0.676351\pi\) | ||||
−0.526113 | + | 0.850414i | \(0.676351\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.1738 | −1.72673 | −0.863363 | − | 0.504583i | \(-0.831646\pi\) | ||||
−0.863363 | + | 0.504583i | \(0.831646\pi\) | |||||||
\(812\) | 18.6617 | 0.654896 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −61.3940 | −2.15186 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.9336 | 0.907301 | ||||||||
\(818\) | −38.0566 | −1.33062 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.9715 | −1.18561 | −0.592807 | − | 0.805345i | \(-0.701980\pi\) | ||||
−0.592807 | + | 0.805345i | \(0.701980\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.8272 | 1.17914 | 0.589572 | − | 0.807716i | \(-0.299297\pi\) | ||||
0.589572 | + | 0.807716i | \(0.299297\pi\) | |||||||
\(824\) | 73.3067 | 2.55376 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −58.9676 | −2.05174 | ||||||||
\(827\) | −35.1083 | −1.22083 | −0.610417 | − | 0.792080i | \(-0.708998\pi\) | ||||
−0.610417 | + | 0.792080i | \(0.708998\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.6701 | 0.544245 | 0.272122 | − | 0.962263i | \(-0.412274\pi\) | ||||
0.272122 | + | 0.962263i | \(0.412274\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.7911 | 0.408784 | ||||||||
\(833\) | −59.1702 | −2.05013 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −45.7296 | −1.58159 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −47.7961 | −1.65109 | ||||||||
\(839\) | 16.5131 | 0.570095 | 0.285047 | − | 0.958513i | \(-0.407991\pi\) | ||||
0.285047 | + | 0.958513i | \(0.407991\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −75.6669 | −2.60765 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.08512 | −0.0373514 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.4463 | 0.805626 | ||||||||
\(848\) | 12.6850 | 0.435604 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −54.7409 | −1.87649 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.3926 | −0.561271 | −0.280636 | − | 0.959814i | \(-0.590545\pi\) | ||||
−0.280636 | + | 0.959814i | \(0.590545\pi\) | |||||||
\(854\) | −111.629 | −3.81988 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 31.8228 | 1.08768 | ||||||||
\(857\) | −9.83745 | −0.336041 | −0.168020 | − | 0.985784i | \(-0.553737\pi\) | ||||
−0.168020 | + | 0.985784i | \(0.553737\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.8257 | 1.35883 | 0.679417 | − | 0.733752i | \(-0.262233\pi\) | ||||
0.679417 | + | 0.733752i | \(0.262233\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.32971 | −0.181530 | ||||||||
\(863\) | −15.6707 | −0.533438 | −0.266719 | − | 0.963774i | \(-0.585940\pi\) | ||||
−0.266719 | + | 0.963774i | \(0.585940\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 48.7556 | 1.65678 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −41.9953 | −1.42541 | ||||||||
\(869\) | −32.3708 | −1.09810 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.6060 | −0.833744 | ||||||||
\(872\) | −95.8162 | −3.24474 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −57.9834 | −1.96132 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.2819 | −0.718640 | −0.359320 | − | 0.933214i | \(-0.616991\pi\) | ||||
−0.359320 | + | 0.933214i | \(0.616991\pi\) | |||||||
\(878\) | 87.7118 | 2.96013 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.1037 | −0.980529 | −0.490265 | − | 0.871574i | \(-0.663100\pi\) | ||||
−0.490265 | + | 0.871574i | \(0.663100\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.03715 | −0.135861 | −0.0679305 | − | 0.997690i | \(-0.521640\pi\) | ||||
−0.0679305 | + | 0.997690i | \(0.521640\pi\) | |||||||
\(884\) | −69.0136 | −2.32118 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 63.0698 | 2.11887 | ||||||||
\(887\) | 2.85498 | 0.0958608 | 0.0479304 | − | 0.998851i | \(-0.484737\pi\) | ||||
0.0479304 | + | 0.998851i | \(0.484737\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.7402 | 0.427293 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −118.993 | −3.98419 | ||||||||
\(893\) | 33.2859 | 1.11387 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −14.0076 | −0.467960 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −54.7666 | −1.82758 | ||||||||
\(899\) | −2.25035 | −0.0750534 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.82535 | −0.327330 | ||||||||
\(902\) | 15.5485 | 0.517707 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −81.4150 | −2.70782 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.08757 | −0.102521 | −0.0512605 | − | 0.998685i | \(-0.516324\pi\) | ||||
−0.0512605 | + | 0.998685i | \(0.516324\pi\) | |||||||
\(908\) | 23.6314 | 0.784237 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.1306 | −1.13080 | −0.565398 | − | 0.824818i | \(-0.691277\pi\) | ||||
−0.565398 | + | 0.824818i | \(0.691277\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.56508 | −0.283463 | ||||||||
\(914\) | −22.6096 | −0.747860 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.60970 | 0.251432 | ||||||||
\(917\) | −52.6021 | −1.73707 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.9603 | 0.559468 | 0.279734 | − | 0.960078i | \(-0.409754\pi\) | ||||
0.279734 | + | 0.960078i | \(0.409754\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 76.6882 | 2.52559 | ||||||||
\(923\) | 9.54511 | 0.314181 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −96.8433 | −3.18247 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.08471 | 0.298220 | ||||||||
\(929\) | −5.63831 | −0.184987 | −0.0924935 | − | 0.995713i | \(-0.529484\pi\) | ||||
−0.0924935 | + | 0.995713i | \(0.529484\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.5578 | 1.19813 | ||||||||
\(932\) | −31.5392 | −1.03310 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 78.4328 | 2.56640 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.0790 | 1.04798 | 0.523988 | − | 0.851726i | \(-0.324444\pi\) | ||||
0.523988 | + | 0.851726i | \(0.324444\pi\) | |||||||
\(938\) | −120.093 | −3.92119 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.2028 | −1.01718 | −0.508592 | − | 0.861008i | \(-0.669834\pi\) | ||||
−0.508592 | + | 0.861008i | \(0.669834\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.8635 | 0.451458 | ||||||||
\(944\) | −51.7781 | −1.68523 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35.2036 | 1.14457 | ||||||||
\(947\) | 27.7302 | 0.901110 | 0.450555 | − | 0.892749i | \(-0.351226\pi\) | ||||
0.450555 | + | 0.892749i | \(0.351226\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.8822 | 0.840173 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −194.665 | −6.30913 | ||||||||
\(953\) | −23.9481 | −0.775755 | −0.387877 | − | 0.921711i | \(-0.626792\pi\) | ||||
−0.387877 | + | 0.921711i | \(0.626792\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.6104 | −0.440192 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 101.631 | 3.28356 | ||||||||
\(959\) | 17.1567 | 0.554020 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.9359 | −0.836643 | ||||||||
\(962\) | 57.2453 | 1.84566 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 72.3902 | 2.33153 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.6821 | −1.40472 | −0.702361 | − | 0.711821i | \(-0.747871\pi\) | ||||
−0.702361 | + | 0.711821i | \(0.747871\pi\) | |||||||
\(968\) | 42.3228 | 1.36031 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.12406 | −0.0360729 | −0.0180365 | − | 0.999837i | \(-0.505741\pi\) | ||||
−0.0180365 | + | 0.999837i | \(0.505741\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 72.5315 | 2.32525 | ||||||||
\(974\) | 62.0887 | 1.98945 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −98.0193 | −3.13752 | ||||||||
\(977\) | 18.8819 | 0.604086 | 0.302043 | − | 0.953294i | \(-0.402331\pi\) | ||||
0.302043 | + | 0.953294i | \(0.402331\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.65778 | −0.148863 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.4471 | 0.365292 | ||||||||
\(983\) | 23.5807 | 0.752109 | 0.376054 | − | 0.926598i | \(-0.377281\pi\) | ||||
0.376054 | + | 0.926598i | \(0.377281\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −18.0494 | −0.574809 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 42.6394 | 1.35654 | ||||||||
\(989\) | 31.3887 | 0.998102 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.3818 | −0.996877 | −0.498438 | − | 0.866925i | \(-0.666093\pi\) | ||||
−0.498438 | + | 0.866925i | \(0.666093\pi\) | |||||||
\(992\) | −20.4438 | −0.649090 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 46.5864 | 1.47763 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.3442 | 1.43606 | 0.718032 | − | 0.696010i | \(-0.245043\pi\) | ||||
0.718032 | + | 0.696010i | \(0.245043\pi\) | |||||||
\(998\) | 96.1629 | 3.04398 | ||||||||
\(999\) | 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 | 6525.2.a.by.1.1 | 8 | ||
3.2 | odd | 2 | 2175.2.a.bd.1.8 | yes | 8 | ||
5.4 | even | 2 | 6525.2.a.bz.1.8 | 8 | |||
15.2 | even | 4 | 2175.2.c.p.349.15 | 16 | |||
15.8 | even | 4 | 2175.2.c.p.349.2 | 16 | |||
15.14 | odd | 2 | 2175.2.a.bc.1.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2175.2.a.bc.1.1 | ✓ | 8 | 15.14 | odd | 2 | ||
2175.2.a.bd.1.8 | yes | 8 | 3.2 | odd | 2 | ||
2175.2.c.p.349.2 | 16 | 15.8 | even | 4 | |||
2175.2.c.p.349.15 | 16 | 15.2 | even | 4 | |||
6525.2.a.by.1.1 | 8 | 1.1 | even | 1 | trivial | ||
6525.2.a.bz.1.8 | 8 | 5.4 | even | 2 |