Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5577,2,Mod(1,5577)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5577, 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("5577.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5577 = 3 \cdot 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5577.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: | \(44.5325692073\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.233489.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + x^{2} + 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 429) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.881963\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5577.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.118037 | −0.0834650 | −0.0417325 | − | 0.999129i | \(-0.513288\pi\) | ||||
−0.0417325 | + | 0.999129i | \(0.513288\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.98607 | −0.993034 | ||||||||
\(5\) | −2.39753 | −1.07221 | −0.536103 | − | 0.844153i | \(-0.680104\pi\) | ||||
−0.536103 | + | 0.844153i | \(0.680104\pi\) | |||||||
\(6\) | −0.118037 | −0.0481885 | ||||||||
\(7\) | −2.97027 | −1.12266 | −0.561328 | − | 0.827593i | \(-0.689709\pi\) | ||||
−0.561328 | + | 0.827593i | \(0.689709\pi\) | |||||||
\(8\) | 0.470505 | 0.166348 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.282997 | 0.0894916 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.98607 | −0.573328 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.350603 | 0.0937025 | ||||||||
\(15\) | −2.39753 | −0.619038 | ||||||||
\(16\) | 3.91660 | 0.979149 | ||||||||
\(17\) | 4.58456 | 1.11192 | 0.555960 | − | 0.831209i | \(-0.312351\pi\) | ||||
0.555960 | + | 0.831209i | \(0.312351\pi\) | |||||||
\(18\) | −0.118037 | −0.0278217 | ||||||||
\(19\) | −4.85223 | −1.11318 | −0.556589 | − | 0.830788i | \(-0.687890\pi\) | ||||
−0.556589 | + | 0.830788i | \(0.687890\pi\) | |||||||
\(20\) | 4.76165 | 1.06474 | ||||||||
\(21\) | −2.97027 | −0.648166 | ||||||||
\(22\) | −0.118037 | −0.0251656 | ||||||||
\(23\) | 1.75350 | 0.365630 | 0.182815 | − | 0.983147i | \(-0.441479\pi\) | ||||
0.182815 | + | 0.983147i | \(0.441479\pi\) | |||||||
\(24\) | 0.470505 | 0.0960413 | ||||||||
\(25\) | 0.748128 | 0.149626 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 5.89916 | 1.11484 | ||||||||
\(29\) | 5.42498 | 1.00739 | 0.503696 | − | 0.863881i | \(-0.331973\pi\) | ||||
0.503696 | + | 0.863881i | \(0.331973\pi\) | |||||||
\(30\) | 0.282997 | 0.0516680 | ||||||||
\(31\) | −1.91984 | −0.344813 | −0.172407 | − | 0.985026i | \(-0.555154\pi\) | ||||
−0.172407 | + | 0.985026i | \(0.555154\pi\) | |||||||
\(32\) | −1.40331 | −0.248073 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | −0.541149 | −0.0928063 | ||||||||
\(35\) | 7.12130 | 1.20372 | ||||||||
\(36\) | −1.98607 | −0.331011 | ||||||||
\(37\) | −3.76743 | −0.619362 | −0.309681 | − | 0.950840i | \(-0.600222\pi\) | ||||
−0.309681 | + | 0.950840i | \(0.600222\pi\) | |||||||
\(38\) | 0.572744 | 0.0929114 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.12805 | −0.178360 | ||||||||
\(41\) | 5.41472 | 0.845637 | 0.422818 | − | 0.906214i | \(-0.361041\pi\) | ||||
0.422818 | + | 0.906214i | \(0.361041\pi\) | |||||||
\(42\) | 0.350603 | 0.0540992 | ||||||||
\(43\) | −7.01491 | −1.06976 | −0.534882 | − | 0.844927i | \(-0.679644\pi\) | ||||
−0.534882 | + | 0.844927i | \(0.679644\pi\) | |||||||
\(44\) | −1.98607 | −0.299411 | ||||||||
\(45\) | −2.39753 | −0.357402 | ||||||||
\(46\) | −0.206979 | −0.0305173 | ||||||||
\(47\) | 12.3378 | 1.79966 | 0.899828 | − | 0.436246i | \(-0.143692\pi\) | ||||
0.899828 | + | 0.436246i | \(0.143692\pi\) | |||||||
\(48\) | 3.91660 | 0.565312 | ||||||||
\(49\) | 1.82250 | 0.260357 | ||||||||
\(50\) | −0.0883070 | −0.0124885 | ||||||||
\(51\) | 4.58456 | 0.641967 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.41104 | 0.605903 | 0.302952 | − | 0.953006i | \(-0.402028\pi\) | ||||
0.302952 | + | 0.953006i | \(0.402028\pi\) | |||||||
\(54\) | −0.118037 | −0.0160628 | ||||||||
\(55\) | −2.39753 | −0.323282 | ||||||||
\(56\) | −1.39753 | −0.186752 | ||||||||
\(57\) | −4.85223 | −0.642694 | ||||||||
\(58\) | −0.640350 | −0.0840820 | ||||||||
\(59\) | 2.76930 | 0.360532 | 0.180266 | − | 0.983618i | \(-0.442304\pi\) | ||||
0.180266 | + | 0.983618i | \(0.442304\pi\) | |||||||
\(60\) | 4.76165 | 0.614726 | ||||||||
\(61\) | 5.44077 | 0.696620 | 0.348310 | − | 0.937379i | \(-0.386756\pi\) | ||||
0.348310 | + | 0.937379i | \(0.386756\pi\) | |||||||
\(62\) | 0.226612 | 0.0287798 | ||||||||
\(63\) | −2.97027 | −0.374219 | ||||||||
\(64\) | −7.66755 | −0.958444 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.118037 | −0.0145294 | ||||||||
\(67\) | 5.70032 | 0.696405 | 0.348203 | − | 0.937419i | \(-0.386792\pi\) | ||||
0.348203 | + | 0.937419i | \(0.386792\pi\) | |||||||
\(68\) | −9.10525 | −1.10417 | ||||||||
\(69\) | 1.75350 | 0.211097 | ||||||||
\(70\) | −0.840579 | −0.100468 | ||||||||
\(71\) | −14.9505 | −1.77430 | −0.887152 | − | 0.461478i | \(-0.847319\pi\) | ||||
−0.887152 | + | 0.461478i | \(0.847319\pi\) | |||||||
\(72\) | 0.470505 | 0.0554495 | ||||||||
\(73\) | 10.5499 | 1.23478 | 0.617389 | − | 0.786658i | \(-0.288190\pi\) | ||||
0.617389 | + | 0.786658i | \(0.288190\pi\) | |||||||
\(74\) | 0.444698 | 0.0516951 | ||||||||
\(75\) | 0.748128 | 0.0863864 | ||||||||
\(76\) | 9.63686 | 1.10542 | ||||||||
\(77\) | −2.97027 | −0.338494 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.55834 | 0.287836 | 0.143918 | − | 0.989590i | \(-0.454030\pi\) | ||||
0.143918 | + | 0.989590i | \(0.454030\pi\) | |||||||
\(80\) | −9.39014 | −1.04985 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.639139 | −0.0705810 | ||||||||
\(83\) | −9.41168 | −1.03307 | −0.516533 | − | 0.856267i | \(-0.672778\pi\) | ||||
−0.516533 | + | 0.856267i | \(0.672778\pi\) | |||||||
\(84\) | 5.89916 | 0.643651 | ||||||||
\(85\) | −10.9916 | −1.19221 | ||||||||
\(86\) | 0.828021 | 0.0892878 | ||||||||
\(87\) | 5.42498 | 0.581619 | ||||||||
\(88\) | 0.470505 | 0.0501560 | ||||||||
\(89\) | 0.0288464 | 0.00305771 | 0.00152886 | − | 0.999999i | \(-0.499513\pi\) | ||||
0.00152886 | + | 0.999999i | \(0.499513\pi\) | |||||||
\(90\) | 0.282997 | 0.0298305 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.48257 | −0.363083 | ||||||||
\(93\) | −1.91984 | −0.199078 | ||||||||
\(94\) | −1.45632 | −0.150208 | ||||||||
\(95\) | 11.6334 | 1.19356 | ||||||||
\(96\) | −1.40331 | −0.143225 | ||||||||
\(97\) | −11.0811 | −1.12512 | −0.562560 | − | 0.826757i | \(-0.690183\pi\) | ||||
−0.562560 | + | 0.826757i | \(0.690183\pi\) | |||||||
\(98\) | −0.215123 | −0.0217307 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −1.48583 | −0.148583 | ||||||||
\(101\) | −12.8478 | −1.27841 | −0.639204 | − | 0.769037i | \(-0.720736\pi\) | ||||
−0.639204 | + | 0.769037i | \(0.720736\pi\) | |||||||
\(102\) | −0.541149 | −0.0535818 | ||||||||
\(103\) | 16.2544 | 1.60159 | 0.800797 | − | 0.598935i | \(-0.204409\pi\) | ||||
0.800797 | + | 0.598935i | \(0.204409\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.12130 | 0.694967 | ||||||||
\(106\) | −0.520668 | −0.0505717 | ||||||||
\(107\) | −0.848723 | −0.0820492 | −0.0410246 | − | 0.999158i | \(-0.513062\pi\) | ||||
−0.0410246 | + | 0.999158i | \(0.513062\pi\) | |||||||
\(108\) | −1.98607 | −0.191109 | ||||||||
\(109\) | 13.4908 | 1.29218 | 0.646092 | − | 0.763260i | \(-0.276402\pi\) | ||||
0.646092 | + | 0.763260i | \(0.276402\pi\) | |||||||
\(110\) | 0.282997 | 0.0269827 | ||||||||
\(111\) | −3.76743 | −0.357589 | ||||||||
\(112\) | −11.6334 | −1.09925 | ||||||||
\(113\) | 8.63196 | 0.812026 | 0.406013 | − | 0.913867i | \(-0.366919\pi\) | ||||
0.406013 | + | 0.913867i | \(0.366919\pi\) | |||||||
\(114\) | 0.572744 | 0.0536424 | ||||||||
\(115\) | −4.20407 | −0.392031 | ||||||||
\(116\) | −10.7744 | −1.00037 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.326881 | −0.0300918 | ||||||||
\(119\) | −13.6174 | −1.24830 | ||||||||
\(120\) | −1.12805 | −0.102976 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.642214 | −0.0581433 | ||||||||
\(123\) | 5.41472 | 0.488229 | ||||||||
\(124\) | 3.81293 | 0.342411 | ||||||||
\(125\) | 10.1940 | 0.911776 | ||||||||
\(126\) | 0.350603 | 0.0312342 | ||||||||
\(127\) | −17.0045 | −1.50890 | −0.754452 | − | 0.656355i | \(-0.772097\pi\) | ||||
−0.754452 | + | 0.656355i | \(0.772097\pi\) | |||||||
\(128\) | 3.71168 | 0.328070 | ||||||||
\(129\) | −7.01491 | −0.617629 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.4417 | −1.26178 | −0.630889 | − | 0.775873i | \(-0.717310\pi\) | ||||
−0.630889 | + | 0.775873i | \(0.717310\pi\) | |||||||
\(132\) | −1.98607 | −0.172865 | ||||||||
\(133\) | 14.4124 | 1.24972 | ||||||||
\(134\) | −0.672850 | −0.0581254 | ||||||||
\(135\) | −2.39753 | −0.206346 | ||||||||
\(136\) | 2.15706 | 0.184966 | ||||||||
\(137\) | −14.1069 | −1.20523 | −0.602617 | − | 0.798031i | \(-0.705875\pi\) | ||||
−0.602617 | + | 0.798031i | \(0.705875\pi\) | |||||||
\(138\) | −0.206979 | −0.0176192 | ||||||||
\(139\) | 4.87137 | 0.413185 | 0.206592 | − | 0.978427i | \(-0.433763\pi\) | ||||
0.206592 | + | 0.978427i | \(0.433763\pi\) | |||||||
\(140\) | −14.1434 | −1.19533 | ||||||||
\(141\) | 12.3378 | 1.03903 | ||||||||
\(142\) | 1.76472 | 0.148092 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.91660 | 0.326383 | ||||||||
\(145\) | −13.0065 | −1.08013 | ||||||||
\(146\) | −1.24529 | −0.103061 | ||||||||
\(147\) | 1.82250 | 0.150317 | ||||||||
\(148\) | 7.48238 | 0.615048 | ||||||||
\(149\) | −8.78924 | −0.720043 | −0.360021 | − | 0.932944i | \(-0.617231\pi\) | ||||
−0.360021 | + | 0.932944i | \(0.617231\pi\) | |||||||
\(150\) | −0.0883070 | −0.00721024 | ||||||||
\(151\) | −21.4502 | −1.74559 | −0.872797 | − | 0.488083i | \(-0.837696\pi\) | ||||
−0.872797 | + | 0.488083i | \(0.837696\pi\) | |||||||
\(152\) | −2.28300 | −0.185176 | ||||||||
\(153\) | 4.58456 | 0.370640 | ||||||||
\(154\) | 0.350603 | 0.0282524 | ||||||||
\(155\) | 4.60286 | 0.369711 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.3349 | −1.78252 | −0.891259 | − | 0.453495i | \(-0.850177\pi\) | ||||
−0.891259 | + | 0.453495i | \(0.850177\pi\) | |||||||
\(158\) | −0.301980 | −0.0240242 | ||||||||
\(159\) | 4.41104 | 0.349819 | ||||||||
\(160\) | 3.36448 | 0.265985 | ||||||||
\(161\) | −5.20837 | −0.410477 | ||||||||
\(162\) | −0.118037 | −0.00927388 | ||||||||
\(163\) | −18.7766 | −1.47069 | −0.735347 | − | 0.677691i | \(-0.762981\pi\) | ||||
−0.735347 | + | 0.677691i | \(0.762981\pi\) | |||||||
\(164\) | −10.7540 | −0.839746 | ||||||||
\(165\) | −2.39753 | −0.186647 | ||||||||
\(166\) | 1.11093 | 0.0862248 | ||||||||
\(167\) | −2.35518 | −0.182249 | −0.0911247 | − | 0.995839i | \(-0.529046\pi\) | ||||
−0.0911247 | + | 0.995839i | \(0.529046\pi\) | |||||||
\(168\) | −1.39753 | −0.107821 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.29742 | 0.0995075 | ||||||||
\(171\) | −4.85223 | −0.371059 | ||||||||
\(172\) | 13.9321 | 1.06231 | ||||||||
\(173\) | −1.46817 | −0.111623 | −0.0558115 | − | 0.998441i | \(-0.517775\pi\) | ||||
−0.0558115 | + | 0.998441i | \(0.517775\pi\) | |||||||
\(174\) | −0.640350 | −0.0485448 | ||||||||
\(175\) | −2.22214 | −0.167978 | ||||||||
\(176\) | 3.91660 | 0.295225 | ||||||||
\(177\) | 2.76930 | 0.208153 | ||||||||
\(178\) | −0.00340495 | −0.000255212 0 | ||||||||
\(179\) | 8.61218 | 0.643704 | 0.321852 | − | 0.946790i | \(-0.395695\pi\) | ||||
0.321852 | + | 0.946790i | \(0.395695\pi\) | |||||||
\(180\) | 4.76165 | 0.354912 | ||||||||
\(181\) | −16.8486 | −1.25235 | −0.626173 | − | 0.779684i | \(-0.715380\pi\) | ||||
−0.626173 | + | 0.779684i | \(0.715380\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.44077 | 0.402194 | ||||||||
\(184\) | 0.825031 | 0.0608221 | ||||||||
\(185\) | 9.03252 | 0.664084 | ||||||||
\(186\) | 0.226612 | 0.0166160 | ||||||||
\(187\) | 4.58456 | 0.335256 | ||||||||
\(188\) | −24.5037 | −1.78712 | ||||||||
\(189\) | −2.97027 | −0.216055 | ||||||||
\(190\) | −1.37317 | −0.0996202 | ||||||||
\(191\) | −3.66308 | −0.265051 | −0.132526 | − | 0.991180i | \(-0.542309\pi\) | ||||
−0.132526 | + | 0.991180i | \(0.542309\pi\) | |||||||
\(192\) | −7.66755 | −0.553358 | ||||||||
\(193\) | −3.93409 | −0.283182 | −0.141591 | − | 0.989925i | \(-0.545222\pi\) | ||||
−0.141591 | + | 0.989925i | \(0.545222\pi\) | |||||||
\(194\) | 1.30799 | 0.0939081 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.61961 | −0.258544 | ||||||||
\(197\) | 17.1892 | 1.22468 | 0.612339 | − | 0.790596i | \(-0.290229\pi\) | ||||
0.612339 | + | 0.790596i | \(0.290229\pi\) | |||||||
\(198\) | −0.118037 | −0.00838854 | ||||||||
\(199\) | −7.87050 | −0.557925 | −0.278962 | − | 0.960302i | \(-0.589990\pi\) | ||||
−0.278962 | + | 0.960302i | \(0.589990\pi\) | |||||||
\(200\) | 0.351998 | 0.0248900 | ||||||||
\(201\) | 5.70032 | 0.402070 | ||||||||
\(202\) | 1.51652 | 0.106702 | ||||||||
\(203\) | −16.1136 | −1.13096 | ||||||||
\(204\) | −9.10525 | −0.637495 | ||||||||
\(205\) | −12.9819 | −0.906697 | ||||||||
\(206\) | −1.91863 | −0.133677 | ||||||||
\(207\) | 1.75350 | 0.121877 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.85223 | −0.335636 | ||||||||
\(210\) | −0.840579 | −0.0580054 | ||||||||
\(211\) | 11.7612 | 0.809671 | 0.404836 | − | 0.914389i | \(-0.367329\pi\) | ||||
0.404836 | + | 0.914389i | \(0.367329\pi\) | |||||||
\(212\) | −8.76063 | −0.601683 | ||||||||
\(213\) | −14.9505 | −1.02439 | ||||||||
\(214\) | 0.100181 | 0.00684823 | ||||||||
\(215\) | 16.8184 | 1.14701 | ||||||||
\(216\) | 0.470505 | 0.0320138 | ||||||||
\(217\) | 5.70244 | 0.387107 | ||||||||
\(218\) | −1.59242 | −0.107852 | ||||||||
\(219\) | 10.5499 | 0.712899 | ||||||||
\(220\) | 4.76165 | 0.321030 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.444698 | 0.0298462 | ||||||||
\(223\) | −25.2830 | −1.69307 | −0.846536 | − | 0.532332i | \(-0.821316\pi\) | ||||
−0.846536 | + | 0.532332i | \(0.821316\pi\) | |||||||
\(224\) | 4.16822 | 0.278501 | ||||||||
\(225\) | 0.748128 | 0.0498752 | ||||||||
\(226\) | −1.01889 | −0.0677757 | ||||||||
\(227\) | 11.7460 | 0.779612 | 0.389806 | − | 0.920897i | \(-0.372542\pi\) | ||||
0.389806 | + | 0.920897i | \(0.372542\pi\) | |||||||
\(228\) | 9.63686 | 0.638217 | ||||||||
\(229\) | 9.52159 | 0.629205 | 0.314602 | − | 0.949224i | \(-0.398129\pi\) | ||||
0.314602 | + | 0.949224i | \(0.398129\pi\) | |||||||
\(230\) | 0.496236 | 0.0327209 | ||||||||
\(231\) | −2.97027 | −0.195429 | ||||||||
\(232\) | 2.55248 | 0.167578 | ||||||||
\(233\) | 3.30327 | 0.216404 | 0.108202 | − | 0.994129i | \(-0.465491\pi\) | ||||
0.108202 | + | 0.994129i | \(0.465491\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.5802 | −1.92960 | ||||||||
\(236\) | −5.50001 | −0.358020 | ||||||||
\(237\) | 2.55834 | 0.166182 | ||||||||
\(238\) | 1.60736 | 0.104190 | ||||||||
\(239\) | −9.99602 | −0.646589 | −0.323294 | − | 0.946298i | \(-0.604790\pi\) | ||||
−0.323294 | + | 0.946298i | \(0.604790\pi\) | |||||||
\(240\) | −9.39014 | −0.606131 | ||||||||
\(241\) | 1.26482 | 0.0814740 | 0.0407370 | − | 0.999170i | \(-0.487029\pi\) | ||||
0.0407370 | + | 0.999170i | \(0.487029\pi\) | |||||||
\(242\) | −0.118037 | −0.00758772 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −10.8057 | −0.691767 | ||||||||
\(245\) | −4.36950 | −0.279157 | ||||||||
\(246\) | −0.639139 | −0.0407500 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.903292 | −0.0573591 | ||||||||
\(249\) | −9.41168 | −0.596441 | ||||||||
\(250\) | −1.20327 | −0.0761014 | ||||||||
\(251\) | −12.4728 | −0.787279 | −0.393639 | − | 0.919265i | \(-0.628784\pi\) | ||||
−0.393639 | + | 0.919265i | \(0.628784\pi\) | |||||||
\(252\) | 5.89916 | 0.371612 | ||||||||
\(253\) | 1.75350 | 0.110242 | ||||||||
\(254\) | 2.00716 | 0.125941 | ||||||||
\(255\) | −10.9916 | −0.688321 | ||||||||
\(256\) | 14.8970 | 0.931062 | ||||||||
\(257\) | 3.42223 | 0.213473 | 0.106736 | − | 0.994287i | \(-0.465960\pi\) | ||||
0.106736 | + | 0.994287i | \(0.465960\pi\) | |||||||
\(258\) | 0.828021 | 0.0515504 | ||||||||
\(259\) | 11.1903 | 0.695331 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.42498 | 0.335798 | ||||||||
\(262\) | 1.70466 | 0.105314 | ||||||||
\(263\) | −20.2069 | −1.24601 | −0.623004 | − | 0.782219i | \(-0.714088\pi\) | ||||
−0.623004 | + | 0.782219i | \(0.714088\pi\) | |||||||
\(264\) | 0.470505 | 0.0289576 | ||||||||
\(265\) | −10.5756 | −0.649653 | ||||||||
\(266\) | −1.70121 | −0.104308 | ||||||||
\(267\) | 0.0288464 | 0.00176537 | ||||||||
\(268\) | −11.3212 | −0.691554 | ||||||||
\(269\) | −24.7199 | −1.50720 | −0.753598 | − | 0.657335i | \(-0.771684\pi\) | ||||
−0.753598 | + | 0.657335i | \(0.771684\pi\) | |||||||
\(270\) | 0.282997 | 0.0172227 | ||||||||
\(271\) | −8.10763 | −0.492504 | −0.246252 | − | 0.969206i | \(-0.579199\pi\) | ||||
−0.246252 | + | 0.969206i | \(0.579199\pi\) | |||||||
\(272\) | 17.9559 | 1.08874 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.66514 | 0.100595 | ||||||||
\(275\) | 0.748128 | 0.0451138 | ||||||||
\(276\) | −3.48257 | −0.209626 | ||||||||
\(277\) | 25.7639 | 1.54800 | 0.774001 | − | 0.633185i | \(-0.218253\pi\) | ||||
0.774001 | + | 0.633185i | \(0.218253\pi\) | |||||||
\(278\) | −0.575004 | −0.0344864 | ||||||||
\(279\) | −1.91984 | −0.114938 | ||||||||
\(280\) | 3.35060 | 0.200237 | ||||||||
\(281\) | −8.10067 | −0.483245 | −0.241623 | − | 0.970370i | \(-0.577680\pi\) | ||||
−0.241623 | + | 0.970370i | \(0.577680\pi\) | |||||||
\(282\) | −1.45632 | −0.0867227 | ||||||||
\(283\) | −16.8117 | −0.999350 | −0.499675 | − | 0.866213i | \(-0.666547\pi\) | ||||
−0.499675 | + | 0.866213i | \(0.666547\pi\) | |||||||
\(284\) | 29.6928 | 1.76194 | ||||||||
\(285\) | 11.6334 | 0.689100 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.0832 | −0.949360 | ||||||||
\(288\) | −1.40331 | −0.0826910 | ||||||||
\(289\) | 4.01822 | 0.236366 | ||||||||
\(290\) | 1.53525 | 0.0901532 | ||||||||
\(291\) | −11.0811 | −0.649588 | ||||||||
\(292\) | −20.9529 | −1.22618 | ||||||||
\(293\) | −16.2136 | −0.947208 | −0.473604 | − | 0.880738i | \(-0.657047\pi\) | ||||
−0.473604 | + | 0.880738i | \(0.657047\pi\) | |||||||
\(294\) | −0.215123 | −0.0125462 | ||||||||
\(295\) | −6.63947 | −0.386565 | ||||||||
\(296\) | −1.77260 | −0.103030 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 1.03746 | 0.0600983 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.48583 | −0.0857846 | ||||||||
\(301\) | 20.8362 | 1.20098 | ||||||||
\(302\) | 2.53193 | 0.145696 | ||||||||
\(303\) | −12.8478 | −0.738089 | ||||||||
\(304\) | −19.0042 | −1.08997 | ||||||||
\(305\) | −13.0444 | −0.746920 | ||||||||
\(306\) | −0.541149 | −0.0309354 | ||||||||
\(307\) | −3.19713 | −0.182470 | −0.0912349 | − | 0.995829i | \(-0.529081\pi\) | ||||
−0.0912349 | + | 0.995829i | \(0.529081\pi\) | |||||||
\(308\) | 5.89916 | 0.336136 | ||||||||
\(309\) | 16.2544 | 0.924681 | ||||||||
\(310\) | −0.543309 | −0.0308579 | ||||||||
\(311\) | −19.9402 | −1.13071 | −0.565353 | − | 0.824849i | \(-0.691260\pi\) | ||||
−0.565353 | + | 0.824849i | \(0.691260\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.3968 | −1.20942 | −0.604709 | − | 0.796447i | \(-0.706711\pi\) | ||||
−0.604709 | + | 0.796447i | \(0.706711\pi\) | |||||||
\(314\) | 2.63635 | 0.148778 | ||||||||
\(315\) | 7.12130 | 0.401240 | ||||||||
\(316\) | −5.08104 | −0.285831 | ||||||||
\(317\) | −13.6654 | −0.767526 | −0.383763 | − | 0.923432i | \(-0.625372\pi\) | ||||
−0.383763 | + | 0.923432i | \(0.625372\pi\) | |||||||
\(318\) | −0.520668 | −0.0291976 | ||||||||
\(319\) | 5.42498 | 0.303740 | ||||||||
\(320\) | 18.3831 | 1.02765 | ||||||||
\(321\) | −0.848723 | −0.0473711 | ||||||||
\(322\) | 0.614782 | 0.0342605 | ||||||||
\(323\) | −22.2454 | −1.23777 | ||||||||
\(324\) | −1.98607 | −0.110337 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.21633 | 0.122751 | ||||||||
\(327\) | 13.4908 | 0.746043 | ||||||||
\(328\) | 2.54765 | 0.140670 | ||||||||
\(329\) | −36.6466 | −2.02039 | ||||||||
\(330\) | 0.282997 | 0.0155785 | ||||||||
\(331\) | 9.56314 | 0.525638 | 0.262819 | − | 0.964845i | \(-0.415348\pi\) | ||||
0.262819 | + | 0.964845i | \(0.415348\pi\) | |||||||
\(332\) | 18.6922 | 1.02587 | ||||||||
\(333\) | −3.76743 | −0.206454 | ||||||||
\(334\) | 0.277999 | 0.0152114 | ||||||||
\(335\) | −13.6667 | −0.746690 | ||||||||
\(336\) | −11.6334 | −0.634651 | ||||||||
\(337\) | 30.5568 | 1.66453 | 0.832266 | − | 0.554376i | \(-0.187043\pi\) | ||||
0.832266 | + | 0.554376i | \(0.187043\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.63196 | 0.468823 | ||||||||
\(340\) | 21.8301 | 1.18390 | ||||||||
\(341\) | −1.91984 | −0.103965 | ||||||||
\(342\) | 0.572744 | 0.0309705 | ||||||||
\(343\) | 15.3786 | 0.830364 | ||||||||
\(344\) | −3.30055 | −0.177954 | ||||||||
\(345\) | −4.20407 | −0.226339 | ||||||||
\(346\) | 0.173299 | 0.00931660 | ||||||||
\(347\) | 7.61080 | 0.408569 | 0.204285 | − | 0.978912i | \(-0.434513\pi\) | ||||
0.204285 | + | 0.978912i | \(0.434513\pi\) | |||||||
\(348\) | −10.7744 | −0.577567 | ||||||||
\(349\) | −14.4841 | −0.775316 | −0.387658 | − | 0.921803i | \(-0.626716\pi\) | ||||
−0.387658 | + | 0.921803i | \(0.626716\pi\) | |||||||
\(350\) | 0.262296 | 0.0140203 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.40331 | −0.0747969 | ||||||||
\(353\) | −26.6472 | −1.41829 | −0.709144 | − | 0.705064i | \(-0.750918\pi\) | ||||
−0.709144 | + | 0.705064i | \(0.750918\pi\) | |||||||
\(354\) | −0.326881 | −0.0173735 | ||||||||
\(355\) | 35.8443 | 1.90242 | ||||||||
\(356\) | −0.0572909 | −0.00303641 | ||||||||
\(357\) | −13.6174 | −0.720709 | ||||||||
\(358\) | −1.01656 | −0.0537268 | ||||||||
\(359\) | −26.4230 | −1.39455 | −0.697277 | − | 0.716802i | \(-0.745605\pi\) | ||||
−0.697277 | + | 0.716802i | \(0.745605\pi\) | |||||||
\(360\) | −1.12805 | −0.0594533 | ||||||||
\(361\) | 4.54416 | 0.239166 | ||||||||
\(362\) | 1.98876 | 0.104527 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −25.2938 | −1.32394 | ||||||||
\(366\) | −0.642214 | −0.0335691 | ||||||||
\(367\) | −18.7868 | −0.980662 | −0.490331 | − | 0.871536i | \(-0.663124\pi\) | ||||
−0.490331 | + | 0.871536i | \(0.663124\pi\) | |||||||
\(368\) | 6.86776 | 0.358007 | ||||||||
\(369\) | 5.41472 | 0.281879 | ||||||||
\(370\) | −1.06617 | −0.0554278 | ||||||||
\(371\) | −13.1020 | −0.680221 | ||||||||
\(372\) | 3.81293 | 0.197691 | ||||||||
\(373\) | 22.6389 | 1.17220 | 0.586099 | − | 0.810240i | \(-0.300663\pi\) | ||||
0.586099 | + | 0.810240i | \(0.300663\pi\) | |||||||
\(374\) | −0.541149 | −0.0279822 | ||||||||
\(375\) | 10.1940 | 0.526414 | ||||||||
\(376\) | 5.80500 | 0.299370 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.350603 | 0.0180331 | ||||||||
\(379\) | −1.22574 | −0.0629621 | −0.0314810 | − | 0.999504i | \(-0.510022\pi\) | ||||
−0.0314810 | + | 0.999504i | \(0.510022\pi\) | |||||||
\(380\) | −23.1046 | −1.18524 | ||||||||
\(381\) | −17.0045 | −0.871166 | ||||||||
\(382\) | 0.432380 | 0.0221225 | ||||||||
\(383\) | 32.1997 | 1.64533 | 0.822664 | − | 0.568528i | \(-0.192487\pi\) | ||||
0.822664 | + | 0.568528i | \(0.192487\pi\) | |||||||
\(384\) | 3.71168 | 0.189411 | ||||||||
\(385\) | 7.12130 | 0.362935 | ||||||||
\(386\) | 0.464370 | 0.0236358 | ||||||||
\(387\) | −7.01491 | −0.356588 | ||||||||
\(388\) | 22.0079 | 1.11728 | ||||||||
\(389\) | 37.4190 | 1.89722 | 0.948609 | − | 0.316451i | \(-0.102491\pi\) | ||||
0.948609 | + | 0.316451i | \(0.102491\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.03904 | 0.406552 | ||||||||
\(392\) | 0.857496 | 0.0433101 | ||||||||
\(393\) | −14.4417 | −0.728487 | ||||||||
\(394\) | −2.02896 | −0.102218 | ||||||||
\(395\) | −6.13369 | −0.308619 | ||||||||
\(396\) | −1.98607 | −0.0998036 | ||||||||
\(397\) | −11.1588 | −0.560046 | −0.280023 | − | 0.959993i | \(-0.590342\pi\) | ||||
−0.280023 | + | 0.959993i | \(0.590342\pi\) | |||||||
\(398\) | 0.929012 | 0.0465672 | ||||||||
\(399\) | 14.4124 | 0.721524 | ||||||||
\(400\) | 2.93012 | 0.146506 | ||||||||
\(401\) | 9.92369 | 0.495566 | 0.247783 | − | 0.968816i | \(-0.420298\pi\) | ||||
0.247783 | + | 0.968816i | \(0.420298\pi\) | |||||||
\(402\) | −0.672850 | −0.0335587 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 25.5167 | 1.26950 | ||||||||
\(405\) | −2.39753 | −0.119134 | ||||||||
\(406\) | 1.90201 | 0.0943952 | ||||||||
\(407\) | −3.76743 | −0.186745 | ||||||||
\(408\) | 2.15706 | 0.106790 | ||||||||
\(409\) | 30.8931 | 1.52756 | 0.763782 | − | 0.645475i | \(-0.223340\pi\) | ||||
0.763782 | + | 0.645475i | \(0.223340\pi\) | |||||||
\(410\) | 1.53235 | 0.0756774 | ||||||||
\(411\) | −14.1069 | −0.695842 | ||||||||
\(412\) | −32.2824 | −1.59044 | ||||||||
\(413\) | −8.22557 | −0.404754 | ||||||||
\(414\) | −0.206979 | −0.0101724 | ||||||||
\(415\) | 22.5647 | 1.10766 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.87137 | 0.238552 | ||||||||
\(418\) | 0.572744 | 0.0280138 | ||||||||
\(419\) | 24.2611 | 1.18523 | 0.592616 | − | 0.805485i | \(-0.298095\pi\) | ||||
0.592616 | + | 0.805485i | \(0.298095\pi\) | |||||||
\(420\) | −14.1434 | −0.690126 | ||||||||
\(421\) | 1.39751 | 0.0681103 | 0.0340551 | − | 0.999420i | \(-0.489158\pi\) | ||||
0.0340551 | + | 0.999420i | \(0.489158\pi\) | |||||||
\(422\) | −1.38825 | −0.0675792 | ||||||||
\(423\) | 12.3378 | 0.599885 | ||||||||
\(424\) | 2.07542 | 0.100791 | ||||||||
\(425\) | 3.42984 | 0.166372 | ||||||||
\(426\) | 1.76472 | 0.0855011 | ||||||||
\(427\) | −16.1606 | −0.782065 | ||||||||
\(428\) | 1.68562 | 0.0814776 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.98520 | −0.0957349 | ||||||||
\(431\) | −25.2996 | −1.21864 | −0.609320 | − | 0.792925i | \(-0.708557\pi\) | ||||
−0.609320 | + | 0.792925i | \(0.708557\pi\) | |||||||
\(432\) | 3.91660 | 0.188437 | ||||||||
\(433\) | 33.9631 | 1.63216 | 0.816081 | − | 0.577938i | \(-0.196142\pi\) | ||||
0.816081 | + | 0.577938i | \(0.196142\pi\) | |||||||
\(434\) | −0.673100 | −0.0323098 | ||||||||
\(435\) | −13.0065 | −0.623615 | ||||||||
\(436\) | −26.7936 | −1.28318 | ||||||||
\(437\) | −8.50840 | −0.407012 | ||||||||
\(438\) | −1.24529 | −0.0595021 | ||||||||
\(439\) | −11.5414 | −0.550840 | −0.275420 | − | 0.961324i | \(-0.588817\pi\) | ||||
−0.275420 | + | 0.961324i | \(0.588817\pi\) | |||||||
\(440\) | −1.12805 | −0.0537775 | ||||||||
\(441\) | 1.82250 | 0.0867858 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 41.2202 | 1.95843 | 0.979216 | − | 0.202823i | \(-0.0650115\pi\) | ||||
0.979216 | + | 0.202823i | \(0.0650115\pi\) | |||||||
\(444\) | 7.48238 | 0.355098 | ||||||||
\(445\) | −0.0691600 | −0.00327850 | ||||||||
\(446\) | 2.98433 | 0.141312 | ||||||||
\(447\) | −8.78924 | −0.415717 | ||||||||
\(448\) | 22.7747 | 1.07600 | ||||||||
\(449\) | 11.3930 | 0.537671 | 0.268836 | − | 0.963186i | \(-0.413361\pi\) | ||||
0.268836 | + | 0.963186i | \(0.413361\pi\) | |||||||
\(450\) | −0.0883070 | −0.00416283 | ||||||||
\(451\) | 5.41472 | 0.254969 | ||||||||
\(452\) | −17.1436 | −0.806369 | ||||||||
\(453\) | −21.4502 | −1.00782 | ||||||||
\(454\) | −1.38647 | −0.0650703 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.28300 | −0.106911 | ||||||||
\(457\) | 9.69328 | 0.453433 | 0.226716 | − | 0.973961i | \(-0.427201\pi\) | ||||
0.226716 | + | 0.973961i | \(0.427201\pi\) | |||||||
\(458\) | −1.12390 | −0.0525165 | ||||||||
\(459\) | 4.58456 | 0.213989 | ||||||||
\(460\) | 8.34956 | 0.389300 | ||||||||
\(461\) | −11.5806 | −0.539362 | −0.269681 | − | 0.962950i | \(-0.586918\pi\) | ||||
−0.269681 | + | 0.962950i | \(0.586918\pi\) | |||||||
\(462\) | 0.350603 | 0.0163115 | ||||||||
\(463\) | 34.5395 | 1.60519 | 0.802593 | − | 0.596527i | \(-0.203453\pi\) | ||||
0.802593 | + | 0.596527i | \(0.203453\pi\) | |||||||
\(464\) | 21.2474 | 0.986388 | ||||||||
\(465\) | 4.60286 | 0.213452 | ||||||||
\(466\) | −0.389908 | −0.0180622 | ||||||||
\(467\) | 3.73036 | 0.172621 | 0.0863103 | − | 0.996268i | \(-0.472492\pi\) | ||||
0.0863103 | + | 0.996268i | \(0.472492\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.9315 | −0.781824 | ||||||||
\(470\) | 3.49157 | 0.161054 | ||||||||
\(471\) | −22.3349 | −1.02914 | ||||||||
\(472\) | 1.30297 | 0.0599740 | ||||||||
\(473\) | −7.01491 | −0.322546 | ||||||||
\(474\) | −0.301980 | −0.0138704 | ||||||||
\(475\) | −3.63009 | −0.166560 | ||||||||
\(476\) | 27.0450 | 1.23961 | ||||||||
\(477\) | 4.41104 | 0.201968 | ||||||||
\(478\) | 1.17990 | 0.0539675 | ||||||||
\(479\) | −14.1843 | −0.648099 | −0.324050 | − | 0.946040i | \(-0.605044\pi\) | ||||
−0.324050 | + | 0.946040i | \(0.605044\pi\) | |||||||
\(480\) | 3.36448 | 0.153567 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.149296 | −0.00680022 | ||||||||
\(483\) | −5.20837 | −0.236989 | ||||||||
\(484\) | −1.98607 | −0.0902758 | ||||||||
\(485\) | 26.5673 | 1.20636 | ||||||||
\(486\) | −0.118037 | −0.00535428 | ||||||||
\(487\) | −26.8742 | −1.21778 | −0.608892 | − | 0.793253i | \(-0.708386\pi\) | ||||
−0.608892 | + | 0.793253i | \(0.708386\pi\) | |||||||
\(488\) | 2.55991 | 0.115882 | ||||||||
\(489\) | −18.7766 | −0.849105 | ||||||||
\(490\) | 0.515763 | 0.0232998 | ||||||||
\(491\) | 34.0614 | 1.53717 | 0.768585 | − | 0.639747i | \(-0.220961\pi\) | ||||
0.768585 | + | 0.639747i | \(0.220961\pi\) | |||||||
\(492\) | −10.7540 | −0.484827 | ||||||||
\(493\) | 24.8711 | 1.12014 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.39753 | −0.107761 | ||||||||
\(496\) | −7.51923 | −0.337623 | ||||||||
\(497\) | 44.4072 | 1.99193 | ||||||||
\(498\) | 1.11093 | 0.0497819 | ||||||||
\(499\) | −0.146884 | −0.00657542 | −0.00328771 | − | 0.999995i | \(-0.501047\pi\) | ||||
−0.00328771 | + | 0.999995i | \(0.501047\pi\) | |||||||
\(500\) | −20.2459 | −0.905425 | ||||||||
\(501\) | −2.35518 | −0.105222 | ||||||||
\(502\) | 1.47226 | 0.0657102 | ||||||||
\(503\) | 7.30757 | 0.325829 | 0.162914 | − | 0.986640i | \(-0.447911\pi\) | ||||
0.162914 | + | 0.986640i | \(0.447911\pi\) | |||||||
\(504\) | −1.39753 | −0.0622507 | ||||||||
\(505\) | 30.8030 | 1.37072 | ||||||||
\(506\) | −0.206979 | −0.00920132 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 33.7721 | 1.49839 | ||||||||
\(509\) | 22.1135 | 0.980163 | 0.490081 | − | 0.871677i | \(-0.336967\pi\) | ||||
0.490081 | + | 0.871677i | \(0.336967\pi\) | |||||||
\(510\) | 1.29742 | 0.0574507 | ||||||||
\(511\) | −31.3362 | −1.38623 | ||||||||
\(512\) | −9.18177 | −0.405781 | ||||||||
\(513\) | −4.85223 | −0.214231 | ||||||||
\(514\) | −0.403951 | −0.0178175 | ||||||||
\(515\) | −38.9704 | −1.71724 | ||||||||
\(516\) | 13.9321 | 0.613326 | ||||||||
\(517\) | 12.3378 | 0.542616 | ||||||||
\(518\) | −1.32087 | −0.0580358 | ||||||||
\(519\) | −1.46817 | −0.0644455 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.57882 | −0.156791 | −0.0783954 | − | 0.996922i | \(-0.524980\pi\) | ||||
−0.0783954 | + | 0.996922i | \(0.524980\pi\) | |||||||
\(522\) | −0.640350 | −0.0280273 | ||||||||
\(523\) | 19.2320 | 0.840955 | 0.420478 | − | 0.907303i | \(-0.361862\pi\) | ||||
0.420478 | + | 0.907303i | \(0.361862\pi\) | |||||||
\(524\) | 28.6822 | 1.25299 | ||||||||
\(525\) | −2.22214 | −0.0969822 | ||||||||
\(526\) | 2.38516 | 0.103998 | ||||||||
\(527\) | −8.80162 | −0.383404 | ||||||||
\(528\) | 3.91660 | 0.170448 | ||||||||
\(529\) | −19.9252 | −0.866314 | ||||||||
\(530\) | 1.24831 | 0.0542233 | ||||||||
\(531\) | 2.76930 | 0.120177 | ||||||||
\(532\) | −28.6241 | −1.24101 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.00340495 | −0.000147347 0 | ||||||||
\(535\) | 2.03484 | 0.0879736 | ||||||||
\(536\) | 2.68203 | 0.115846 | ||||||||
\(537\) | 8.61218 | 0.371643 | ||||||||
\(538\) | 2.91787 | 0.125798 | ||||||||
\(539\) | 1.82250 | 0.0785007 | ||||||||
\(540\) | 4.76165 | 0.204909 | ||||||||
\(541\) | −13.5069 | −0.580705 | −0.290353 | − | 0.956920i | \(-0.593773\pi\) | ||||
−0.290353 | + | 0.956920i | \(0.593773\pi\) | |||||||
\(542\) | 0.957003 | 0.0411068 | ||||||||
\(543\) | −16.8486 | −0.723043 | ||||||||
\(544\) | −6.43358 | −0.275837 | ||||||||
\(545\) | −32.3445 | −1.38549 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.5839 | −1.90627 | −0.953134 | − | 0.302548i | \(-0.902163\pi\) | ||||
−0.953134 | + | 0.302548i | \(0.902163\pi\) | |||||||
\(548\) | 28.0172 | 1.19684 | ||||||||
\(549\) | 5.44077 | 0.232207 | ||||||||
\(550\) | −0.0883070 | −0.00376542 | ||||||||
\(551\) | −26.3232 | −1.12141 | ||||||||
\(552\) | 0.825031 | 0.0351156 | ||||||||
\(553\) | −7.59897 | −0.323141 | ||||||||
\(554\) | −3.04110 | −0.129204 | ||||||||
\(555\) | 9.03252 | 0.383409 | ||||||||
\(556\) | −9.67488 | −0.410306 | ||||||||
\(557\) | −18.0166 | −0.763389 | −0.381694 | − | 0.924289i | \(-0.624659\pi\) | ||||
−0.381694 | + | 0.924289i | \(0.624659\pi\) | |||||||
\(558\) | 0.226612 | 0.00959327 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 27.8913 | 1.17862 | ||||||||
\(561\) | 4.58456 | 0.193560 | ||||||||
\(562\) | 0.956181 | 0.0403341 | ||||||||
\(563\) | −23.2744 | −0.980901 | −0.490450 | − | 0.871469i | \(-0.663168\pi\) | ||||
−0.490450 | + | 0.871469i | \(0.663168\pi\) | |||||||
\(564\) | −24.5037 | −1.03179 | ||||||||
\(565\) | −20.6953 | −0.870659 | ||||||||
\(566\) | 1.98440 | 0.0834107 | ||||||||
\(567\) | −2.97027 | −0.124740 | ||||||||
\(568\) | −7.03430 | −0.295153 | ||||||||
\(569\) | −32.8125 | −1.37557 | −0.687785 | − | 0.725914i | \(-0.741417\pi\) | ||||
−0.687785 | + | 0.725914i | \(0.741417\pi\) | |||||||
\(570\) | −1.37317 | −0.0575157 | ||||||||
\(571\) | −22.2440 | −0.930883 | −0.465441 | − | 0.885079i | \(-0.654104\pi\) | ||||
−0.465441 | + | 0.885079i | \(0.654104\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.66308 | −0.153027 | ||||||||
\(574\) | 1.89841 | 0.0792383 | ||||||||
\(575\) | 1.31184 | 0.0547077 | ||||||||
\(576\) | −7.66755 | −0.319481 | ||||||||
\(577\) | 15.5700 | 0.648188 | 0.324094 | − | 0.946025i | \(-0.394941\pi\) | ||||
0.324094 | + | 0.946025i | \(0.394941\pi\) | |||||||
\(578\) | −0.474299 | −0.0197283 | ||||||||
\(579\) | −3.93409 | −0.163495 | ||||||||
\(580\) | 25.8318 | 1.07261 | ||||||||
\(581\) | 27.9552 | 1.15978 | ||||||||
\(582\) | 1.30799 | 0.0542178 | ||||||||
\(583\) | 4.41104 | 0.182687 | ||||||||
\(584\) | 4.96380 | 0.205403 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.91381 | 0.0790586 | ||||||||
\(587\) | 8.16350 | 0.336944 | 0.168472 | − | 0.985706i | \(-0.446117\pi\) | ||||
0.168472 | + | 0.985706i | \(0.446117\pi\) | |||||||
\(588\) | −3.61961 | −0.149270 | ||||||||
\(589\) | 9.31550 | 0.383838 | ||||||||
\(590\) | 0.783704 | 0.0322646 | ||||||||
\(591\) | 17.1892 | 0.707068 | ||||||||
\(592\) | −14.7555 | −0.606448 | ||||||||
\(593\) | 19.9116 | 0.817673 | 0.408837 | − | 0.912608i | \(-0.365935\pi\) | ||||
0.408837 | + | 0.912608i | \(0.365935\pi\) | |||||||
\(594\) | −0.118037 | −0.00484313 | ||||||||
\(595\) | 32.6480 | 1.33844 | ||||||||
\(596\) | 17.4560 | 0.715027 | ||||||||
\(597\) | −7.87050 | −0.322118 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.4044 | 1.20143 | 0.600716 | − | 0.799463i | \(-0.294882\pi\) | ||||
0.600716 | + | 0.799463i | \(0.294882\pi\) | |||||||
\(600\) | 0.351998 | 0.0143702 | ||||||||
\(601\) | 18.9161 | 0.771604 | 0.385802 | − | 0.922582i | \(-0.373925\pi\) | ||||
0.385802 | + | 0.922582i | \(0.373925\pi\) | |||||||
\(602\) | −2.45945 | −0.100240 | ||||||||
\(603\) | 5.70032 | 0.232135 | ||||||||
\(604\) | 42.6016 | 1.73343 | ||||||||
\(605\) | −2.39753 | −0.0974733 | ||||||||
\(606\) | 1.51652 | 0.0616046 | ||||||||
\(607\) | −46.9451 | −1.90544 | −0.952722 | − | 0.303845i | \(-0.901730\pi\) | ||||
−0.952722 | + | 0.303845i | \(0.901730\pi\) | |||||||
\(608\) | 6.80920 | 0.276150 | ||||||||
\(609\) | −16.1136 | −0.652958 | ||||||||
\(610\) | 1.53972 | 0.0623416 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −9.10525 | −0.368058 | ||||||||
\(613\) | 36.4861 | 1.47366 | 0.736830 | − | 0.676078i | \(-0.236322\pi\) | ||||
0.736830 | + | 0.676078i | \(0.236322\pi\) | |||||||
\(614\) | 0.377380 | 0.0152298 | ||||||||
\(615\) | −12.9819 | −0.523482 | ||||||||
\(616\) | −1.39753 | −0.0563079 | ||||||||
\(617\) | −3.43595 | −0.138326 | −0.0691632 | − | 0.997605i | \(-0.522033\pi\) | ||||
−0.0691632 | + | 0.997605i | \(0.522033\pi\) | |||||||
\(618\) | −1.91863 | −0.0771785 | ||||||||
\(619\) | 39.5437 | 1.58939 | 0.794697 | − | 0.607006i | \(-0.207630\pi\) | ||||
0.794697 | + | 0.607006i | \(0.207630\pi\) | |||||||
\(620\) | −9.14159 | −0.367135 | ||||||||
\(621\) | 1.75350 | 0.0703656 | ||||||||
\(622\) | 2.35369 | 0.0943743 | ||||||||
\(623\) | −0.0856816 | −0.00343276 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.1809 | −1.12724 | ||||||||
\(626\) | 2.52562 | 0.100944 | ||||||||
\(627\) | −4.85223 | −0.193779 | ||||||||
\(628\) | 44.3586 | 1.77010 | ||||||||
\(629\) | −17.2720 | −0.688681 | ||||||||
\(630\) | −0.840579 | −0.0334895 | ||||||||
\(631\) | 10.4143 | 0.414586 | 0.207293 | − | 0.978279i | \(-0.433535\pi\) | ||||
0.207293 | + | 0.978279i | \(0.433535\pi\) | |||||||
\(632\) | 1.20371 | 0.0478811 | ||||||||
\(633\) | 11.7612 | 0.467464 | ||||||||
\(634\) | 1.61303 | 0.0640615 | ||||||||
\(635\) | 40.7687 | 1.61786 | ||||||||
\(636\) | −8.76063 | −0.347382 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −0.640350 | −0.0253517 | ||||||||
\(639\) | −14.9505 | −0.591435 | ||||||||
\(640\) | −8.89886 | −0.351758 | ||||||||
\(641\) | −49.1700 | −1.94210 | −0.971049 | − | 0.238882i | \(-0.923219\pi\) | ||||
−0.971049 | + | 0.238882i | \(0.923219\pi\) | |||||||
\(642\) | 0.100181 | 0.00395383 | ||||||||
\(643\) | −3.00230 | −0.118399 | −0.0591995 | − | 0.998246i | \(-0.518855\pi\) | ||||
−0.0591995 | + | 0.998246i | \(0.518855\pi\) | |||||||
\(644\) | 10.3442 | 0.407618 | ||||||||
\(645\) | 16.8184 | 0.662225 | ||||||||
\(646\) | 2.62578 | 0.103310 | ||||||||
\(647\) | 0.306983 | 0.0120687 | 0.00603437 | − | 0.999982i | \(-0.498079\pi\) | ||||
0.00603437 | + | 0.999982i | \(0.498079\pi\) | |||||||
\(648\) | 0.470505 | 0.0184832 | ||||||||
\(649\) | 2.76930 | 0.108705 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.70244 | 0.223496 | ||||||||
\(652\) | 37.2915 | 1.46045 | ||||||||
\(653\) | −50.4557 | −1.97449 | −0.987243 | − | 0.159223i | \(-0.949101\pi\) | ||||
−0.987243 | + | 0.159223i | \(0.949101\pi\) | |||||||
\(654\) | −1.59242 | −0.0622684 | ||||||||
\(655\) | 34.6243 | 1.35288 | ||||||||
\(656\) | 21.2073 | 0.828005 | ||||||||
\(657\) | 10.5499 | 0.411593 | ||||||||
\(658\) | 4.32567 | 0.168632 | ||||||||
\(659\) | 37.7604 | 1.47094 | 0.735468 | − | 0.677560i | \(-0.236963\pi\) | ||||
0.735468 | + | 0.677560i | \(0.236963\pi\) | |||||||
\(660\) | 4.76165 | 0.185347 | ||||||||
\(661\) | −3.39981 | −0.132237 | −0.0661186 | − | 0.997812i | \(-0.521062\pi\) | ||||
−0.0661186 | + | 0.997812i | \(0.521062\pi\) | |||||||
\(662\) | −1.12881 | −0.0438723 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.42824 | −0.171849 | ||||||||
\(665\) | −34.5542 | −1.33995 | ||||||||
\(666\) | 0.444698 | 0.0172317 | ||||||||
\(667\) | 9.51271 | 0.368333 | ||||||||
\(668\) | 4.67755 | 0.180980 | ||||||||
\(669\) | −25.2830 | −0.977495 | ||||||||
\(670\) | 1.61318 | 0.0623224 | ||||||||
\(671\) | 5.44077 | 0.210039 | ||||||||
\(672\) | 4.16822 | 0.160793 | ||||||||
\(673\) | 23.7851 | 0.916846 | 0.458423 | − | 0.888734i | \(-0.348414\pi\) | ||||
0.458423 | + | 0.888734i | \(0.348414\pi\) | |||||||
\(674\) | −3.60684 | −0.138930 | ||||||||
\(675\) | 0.748128 | 0.0287955 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −50.2857 | −1.93264 | −0.966319 | − | 0.257349i | \(-0.917151\pi\) | ||||
−0.966319 | + | 0.257349i | \(0.917151\pi\) | |||||||
\(678\) | −1.01889 | −0.0391303 | ||||||||
\(679\) | 32.9140 | 1.26312 | ||||||||
\(680\) | −5.17160 | −0.198322 | ||||||||
\(681\) | 11.7460 | 0.450109 | ||||||||
\(682\) | 0.226612 | 0.00867744 | ||||||||
\(683\) | −9.68266 | −0.370497 | −0.185248 | − | 0.982692i | \(-0.559309\pi\) | ||||
−0.185248 | + | 0.982692i | \(0.559309\pi\) | |||||||
\(684\) | 9.63686 | 0.368475 | ||||||||
\(685\) | 33.8216 | 1.29226 | ||||||||
\(686\) | −1.81524 | −0.0693063 | ||||||||
\(687\) | 9.52159 | 0.363271 | ||||||||
\(688\) | −27.4746 | −1.04746 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.496236 | 0.0188914 | ||||||||
\(691\) | 7.44899 | 0.283373 | 0.141686 | − | 0.989912i | \(-0.454748\pi\) | ||||
0.141686 | + | 0.989912i | \(0.454748\pi\) | |||||||
\(692\) | 2.91588 | 0.110845 | ||||||||
\(693\) | −2.97027 | −0.112831 | ||||||||
\(694\) | −0.898359 | −0.0341012 | ||||||||
\(695\) | −11.6792 | −0.443019 | ||||||||
\(696\) | 2.55248 | 0.0967514 | ||||||||
\(697\) | 24.8241 | 0.940280 | ||||||||
\(698\) | 1.70966 | 0.0647117 | ||||||||
\(699\) | 3.30327 | 0.124941 | ||||||||
\(700\) | 4.41332 | 0.166808 | ||||||||
\(701\) | 33.0152 | 1.24697 | 0.623483 | − | 0.781837i | \(-0.285717\pi\) | ||||
0.623483 | + | 0.781837i | \(0.285717\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.2805 | 0.689461 | ||||||||
\(704\) | −7.66755 | −0.288982 | ||||||||
\(705\) | −29.5802 | −1.11406 | ||||||||
\(706\) | 3.14536 | 0.118377 | ||||||||
\(707\) | 38.1615 | 1.43521 | ||||||||
\(708\) | −5.50001 | −0.206703 | ||||||||
\(709\) | 30.1377 | 1.13185 | 0.565923 | − | 0.824458i | \(-0.308520\pi\) | ||||
0.565923 | + | 0.824458i | \(0.308520\pi\) | |||||||
\(710\) | −4.23097 | −0.158785 | ||||||||
\(711\) | 2.55834 | 0.0959453 | ||||||||
\(712\) | 0.0135724 | 0.000508646 0 | ||||||||
\(713\) | −3.36644 | −0.126074 | ||||||||
\(714\) | 1.60736 | 0.0601539 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.1044 | −0.639220 | ||||||||
\(717\) | −9.99602 | −0.373308 | ||||||||
\(718\) | 3.11890 | 0.116396 | ||||||||
\(719\) | −15.5594 | −0.580268 | −0.290134 | − | 0.956986i | \(-0.593700\pi\) | ||||
−0.290134 | + | 0.956986i | \(0.593700\pi\) | |||||||
\(720\) | −9.39014 | −0.349950 | ||||||||
\(721\) | −48.2800 | −1.79804 | ||||||||
\(722\) | −0.536380 | −0.0199620 | ||||||||
\(723\) | 1.26482 | 0.0470390 | ||||||||
\(724\) | 33.4625 | 1.24362 | ||||||||
\(725\) | 4.05858 | 0.150732 | ||||||||
\(726\) | −0.118037 | −0.00438077 | ||||||||
\(727\) | −41.0629 | −1.52294 | −0.761469 | − | 0.648201i | \(-0.775522\pi\) | ||||
−0.761469 | + | 0.648201i | \(0.775522\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.98561 | 0.110502 | ||||||||
\(731\) | −32.1603 | −1.18949 | ||||||||
\(732\) | −10.8057 | −0.399392 | ||||||||
\(733\) | −2.28843 | −0.0845251 | −0.0422625 | − | 0.999107i | \(-0.513457\pi\) | ||||
−0.0422625 | + | 0.999107i | \(0.513457\pi\) | |||||||
\(734\) | 2.21754 | 0.0818509 | ||||||||
\(735\) | −4.36950 | −0.161171 | ||||||||
\(736\) | −2.46071 | −0.0907031 | ||||||||
\(737\) | 5.70032 | 0.209974 | ||||||||
\(738\) | −0.639139 | −0.0235270 | ||||||||
\(739\) | 44.6950 | 1.64413 | 0.822066 | − | 0.569393i | \(-0.192822\pi\) | ||||
0.822066 | + | 0.569393i | \(0.192822\pi\) | |||||||
\(740\) | −17.9392 | −0.659458 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.54652 | 0.0567747 | ||||||||
\(743\) | 20.9315 | 0.767902 | 0.383951 | − | 0.923354i | \(-0.374563\pi\) | ||||
0.383951 | + | 0.923354i | \(0.374563\pi\) | |||||||
\(744\) | −0.903292 | −0.0331163 | ||||||||
\(745\) | 21.0724 | 0.772034 | ||||||||
\(746\) | −2.67223 | −0.0978374 | ||||||||
\(747\) | −9.41168 | −0.344355 | ||||||||
\(748\) | −9.10525 | −0.332921 | ||||||||
\(749\) | 2.52094 | 0.0921130 | ||||||||
\(750\) | −1.20327 | −0.0439372 | ||||||||
\(751\) | −1.37108 | −0.0500316 | −0.0250158 | − | 0.999687i | \(-0.507964\pi\) | ||||
−0.0250158 | + | 0.999687i | \(0.507964\pi\) | |||||||
\(752\) | 48.3223 | 1.76213 | ||||||||
\(753\) | −12.4728 | −0.454536 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 51.4275 | 1.87164 | ||||||||
\(756\) | 5.89916 | 0.214550 | ||||||||
\(757\) | −9.16942 | −0.333268 | −0.166634 | − | 0.986019i | \(-0.553290\pi\) | ||||
−0.166634 | + | 0.986019i | \(0.553290\pi\) | |||||||
\(758\) | 0.144683 | 0.00525513 | ||||||||
\(759\) | 1.75350 | 0.0636481 | ||||||||
\(760\) | 5.47354 | 0.198546 | ||||||||
\(761\) | −29.5359 | −1.07067 | −0.535337 | − | 0.844638i | \(-0.679815\pi\) | ||||
−0.535337 | + | 0.844638i | \(0.679815\pi\) | |||||||
\(762\) | 2.00716 | 0.0727119 | ||||||||
\(763\) | −40.0713 | −1.45068 | ||||||||
\(764\) | 7.27512 | 0.263205 | ||||||||
\(765\) | −10.9916 | −0.397402 | ||||||||
\(766\) | −3.80076 | −0.137327 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 14.8970 | 0.537549 | ||||||||
\(769\) | 21.1718 | 0.763475 | 0.381737 | − | 0.924271i | \(-0.375326\pi\) | ||||
0.381737 | + | 0.924271i | \(0.375326\pi\) | |||||||
\(770\) | −0.840579 | −0.0302923 | ||||||||
\(771\) | 3.42223 | 0.123249 | ||||||||
\(772\) | 7.81338 | 0.281210 | ||||||||
\(773\) | 46.3060 | 1.66551 | 0.832755 | − | 0.553641i | \(-0.186762\pi\) | ||||
0.832755 | + | 0.553641i | \(0.186762\pi\) | |||||||
\(774\) | 0.828021 | 0.0297626 | ||||||||
\(775\) | −1.43628 | −0.0515929 | ||||||||
\(776\) | −5.21373 | −0.187162 | ||||||||
\(777\) | 11.1903 | 0.401450 | ||||||||
\(778\) | −4.41683 | −0.158351 | ||||||||
\(779\) | −26.2735 | −0.941345 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.9505 | −0.534973 | ||||||||
\(782\) | −0.948906 | −0.0339328 | ||||||||
\(783\) | 5.42498 | 0.193873 | ||||||||
\(784\) | 7.13801 | 0.254929 | ||||||||
\(785\) | 53.5484 | 1.91123 | ||||||||
\(786\) | 1.70466 | 0.0608032 | ||||||||
\(787\) | −9.12758 | −0.325363 | −0.162681 | − | 0.986679i | \(-0.552014\pi\) | ||||
−0.162681 | + | 0.986679i | \(0.552014\pi\) | |||||||
\(788\) | −34.1388 | −1.21615 | ||||||||
\(789\) | −20.2069 | −0.719383 | ||||||||
\(790\) | 0.724004 | 0.0257589 | ||||||||
\(791\) | −25.6392 | −0.911626 | ||||||||
\(792\) | 0.470505 | 0.0167187 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 1.31716 | 0.0467442 | ||||||||
\(795\) | −10.5756 | −0.375078 | ||||||||
\(796\) | 15.6313 | 0.554038 | ||||||||
\(797\) | −26.9051 | −0.953028 | −0.476514 | − | 0.879167i | \(-0.658100\pi\) | ||||
−0.476514 | + | 0.879167i | \(0.658100\pi\) | |||||||
\(798\) | −1.70121 | −0.0602220 | ||||||||
\(799\) | 56.5635 | 2.00107 | ||||||||
\(800\) | −1.04986 | −0.0371181 | ||||||||
\(801\) | 0.0288464 | 0.00101924 | ||||||||
\(802\) | −1.17137 | −0.0413624 | ||||||||
\(803\) | 10.5499 | 0.372300 | ||||||||
\(804\) | −11.3212 | −0.399269 | ||||||||
\(805\) | 12.4872 | 0.440116 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.7199 | −0.870181 | ||||||||
\(808\) | −6.04497 | −0.212661 | ||||||||
\(809\) | −15.6777 | −0.551199 | −0.275599 | − | 0.961273i | \(-0.588876\pi\) | ||||
−0.275599 | + | 0.961273i | \(0.588876\pi\) | |||||||
\(810\) | 0.282997 | 0.00994351 | ||||||||
\(811\) | 21.5800 | 0.757775 | 0.378888 | − | 0.925443i | \(-0.376307\pi\) | ||||
0.378888 | + | 0.925443i | \(0.376307\pi\) | |||||||
\(812\) | 32.0028 | 1.12308 | ||||||||
\(813\) | −8.10763 | −0.284347 | ||||||||
\(814\) | 0.444698 | 0.0155866 | ||||||||
\(815\) | 45.0173 | 1.57689 | ||||||||
\(816\) | 17.9559 | 0.628582 | ||||||||
\(817\) | 34.0380 | 1.19084 | ||||||||
\(818\) | −3.64653 | −0.127498 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 25.7830 | 0.900380 | ||||||||
\(821\) | −51.1405 | −1.78482 | −0.892408 | − | 0.451229i | \(-0.850986\pi\) | ||||
−0.892408 | + | 0.451229i | \(0.850986\pi\) | |||||||
\(822\) | 1.66514 | 0.0580784 | ||||||||
\(823\) | −46.5261 | −1.62180 | −0.810900 | − | 0.585185i | \(-0.801022\pi\) | ||||
−0.810900 | + | 0.585185i | \(0.801022\pi\) | |||||||
\(824\) | 7.64777 | 0.266423 | ||||||||
\(825\) | 0.748128 | 0.0260465 | ||||||||
\(826\) | 0.970923 | 0.0337827 | ||||||||
\(827\) | −47.1916 | −1.64101 | −0.820506 | − | 0.571637i | \(-0.806308\pi\) | ||||
−0.820506 | + | 0.571637i | \(0.806308\pi\) | |||||||
\(828\) | −3.48257 | −0.121028 | ||||||||
\(829\) | −51.5875 | −1.79171 | −0.895855 | − | 0.444347i | \(-0.853436\pi\) | ||||
−0.895855 | + | 0.444347i | \(0.853436\pi\) | |||||||
\(830\) | −2.66348 | −0.0924508 | ||||||||
\(831\) | 25.7639 | 0.893739 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.35538 | 0.289497 | ||||||||
\(834\) | −0.575004 | −0.0199108 | ||||||||
\(835\) | 5.64661 | 0.195409 | ||||||||
\(836\) | 9.63686 | 0.333298 | ||||||||
\(837\) | −1.91984 | −0.0663593 | ||||||||
\(838\) | −2.86371 | −0.0989253 | ||||||||
\(839\) | −38.3814 | −1.32507 | −0.662536 | − | 0.749030i | \(-0.730520\pi\) | ||||
−0.662536 | + | 0.749030i | \(0.730520\pi\) | |||||||
\(840\) | 3.35060 | 0.115607 | ||||||||
\(841\) | 0.430373 | 0.0148404 | ||||||||
\(842\) | −0.164958 | −0.00568482 | ||||||||
\(843\) | −8.10067 | −0.279002 | ||||||||
\(844\) | −23.3584 | −0.804031 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.45632 | −0.0500694 | ||||||||
\(847\) | −2.97027 | −0.102060 | ||||||||
\(848\) | 17.2763 | 0.593270 | ||||||||
\(849\) | −16.8117 | −0.576975 | ||||||||
\(850\) | −0.404849 | −0.0138862 | ||||||||
\(851\) | −6.60620 | −0.226458 | ||||||||
\(852\) | 29.6928 | 1.01726 | ||||||||
\(853\) | 17.7010 | 0.606070 | 0.303035 | − | 0.952979i | \(-0.402000\pi\) | ||||
0.303035 | + | 0.952979i | \(0.402000\pi\) | |||||||
\(854\) | 1.90755 | 0.0652750 | ||||||||
\(855\) | 11.6334 | 0.397852 | ||||||||
\(856\) | −0.399328 | −0.0136488 | ||||||||
\(857\) | −4.15263 | −0.141851 | −0.0709256 | − | 0.997482i | \(-0.522595\pi\) | ||||
−0.0709256 | + | 0.997482i | \(0.522595\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.5684 | 0.633547 | 0.316773 | − | 0.948501i | \(-0.397401\pi\) | ||||
0.316773 | + | 0.948501i | \(0.397401\pi\) | |||||||
\(860\) | −33.4025 | −1.13902 | ||||||||
\(861\) | −16.0832 | −0.548113 | ||||||||
\(862\) | 2.98630 | 0.101714 | ||||||||
\(863\) | −2.09641 | −0.0713626 | −0.0356813 | − | 0.999363i | \(-0.511360\pi\) | ||||
−0.0356813 | + | 0.999363i | \(0.511360\pi\) | |||||||
\(864\) | −1.40331 | −0.0477417 | ||||||||
\(865\) | 3.51998 | 0.119683 | ||||||||
\(866\) | −4.00891 | −0.136228 | ||||||||
\(867\) | 4.01822 | 0.136466 | ||||||||
\(868\) | −11.3254 | −0.384410 | ||||||||
\(869\) | 2.55834 | 0.0867858 | ||||||||
\(870\) | 1.53525 | 0.0520500 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.34748 | 0.214953 | ||||||||
\(873\) | −11.0811 | −0.375040 | ||||||||
\(874\) | 1.00431 | 0.0339712 | ||||||||
\(875\) | −30.2788 | −1.02361 | ||||||||
\(876\) | −20.9529 | −0.707933 | ||||||||
\(877\) | −7.78390 | −0.262843 | −0.131422 | − | 0.991327i | \(-0.541954\pi\) | ||||
−0.131422 | + | 0.991327i | \(0.541954\pi\) | |||||||
\(878\) | 1.36231 | 0.0459759 | ||||||||
\(879\) | −16.2136 | −0.546871 | ||||||||
\(880\) | −9.39014 | −0.316542 | ||||||||
\(881\) | 54.9122 | 1.85004 | 0.925019 | − | 0.379922i | \(-0.124049\pi\) | ||||
0.925019 | + | 0.379922i | \(0.124049\pi\) | |||||||
\(882\) | −0.215123 | −0.00724357 | ||||||||
\(883\) | 12.5693 | 0.422990 | 0.211495 | − | 0.977379i | \(-0.432167\pi\) | ||||
0.211495 | + | 0.977379i | \(0.432167\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.63947 | −0.223183 | ||||||||
\(886\) | −4.86552 | −0.163460 | ||||||||
\(887\) | −31.9437 | −1.07256 | −0.536282 | − | 0.844039i | \(-0.680172\pi\) | ||||
−0.536282 | + | 0.844039i | \(0.680172\pi\) | |||||||
\(888\) | −1.77260 | −0.0594844 | ||||||||
\(889\) | 50.5079 | 1.69398 | ||||||||
\(890\) | 0.00816346 | 0.000273640 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 50.2136 | 1.68128 | ||||||||
\(893\) | −59.8659 | −2.00334 | ||||||||
\(894\) | 1.03746 | 0.0346978 | ||||||||
\(895\) | −20.6479 | −0.690184 | ||||||||
\(896\) | −11.0247 | −0.368309 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.34480 | −0.0448767 | ||||||||
\(899\) | −10.4151 | −0.347362 | ||||||||
\(900\) | −1.48583 | −0.0495277 | ||||||||
\(901\) | 20.2227 | 0.673716 | ||||||||
\(902\) | −0.639139 | −0.0212810 | ||||||||
\(903\) | 20.8362 | 0.693385 | ||||||||
\(904\) | 4.06137 | 0.135079 | ||||||||
\(905\) | 40.3949 | 1.34277 | ||||||||
\(906\) | 2.53193 | 0.0841176 | ||||||||
\(907\) | −15.1727 | −0.503802 | −0.251901 | − | 0.967753i | \(-0.581056\pi\) | ||||
−0.251901 | + | 0.967753i | \(0.581056\pi\) | |||||||
\(908\) | −23.3284 | −0.774181 | ||||||||
\(909\) | −12.8478 | −0.426136 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.7790 | 1.31794 | 0.658969 | − | 0.752170i | \(-0.270993\pi\) | ||||
0.658969 | + | 0.752170i | \(0.270993\pi\) | |||||||
\(912\) | −19.0042 | −0.629293 | ||||||||
\(913\) | −9.41168 | −0.311481 | ||||||||
\(914\) | −1.14417 | −0.0378457 | ||||||||
\(915\) | −13.0444 | −0.431234 | ||||||||
\(916\) | −18.9105 | −0.624821 | ||||||||
\(917\) | 42.8957 | 1.41654 | ||||||||
\(918\) | −0.541149 | −0.0178606 | ||||||||
\(919\) | −29.8226 | −0.983757 | −0.491878 | − | 0.870664i | \(-0.663690\pi\) | ||||
−0.491878 | + | 0.870664i | \(0.663690\pi\) | |||||||
\(920\) | −1.97803 | −0.0652138 | ||||||||
\(921\) | −3.19713 | −0.105349 | ||||||||
\(922\) | 1.36694 | 0.0450179 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 5.89916 | 0.194068 | ||||||||
\(925\) | −2.81852 | −0.0926725 | ||||||||
\(926\) | −4.07695 | −0.133977 | ||||||||
\(927\) | 16.2544 | 0.533865 | ||||||||
\(928\) | −7.61294 | −0.249907 | ||||||||
\(929\) | 25.2173 | 0.827353 | 0.413676 | − | 0.910424i | \(-0.364244\pi\) | ||||
0.413676 | + | 0.910424i | \(0.364244\pi\) | |||||||
\(930\) | −0.543309 | −0.0178158 | ||||||||
\(931\) | −8.84320 | −0.289824 | ||||||||
\(932\) | −6.56051 | −0.214897 | ||||||||
\(933\) | −19.9402 | −0.652813 | ||||||||
\(934\) | −0.440322 | −0.0144078 | ||||||||
\(935\) | −10.9916 | −0.359464 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.42706 | −0.177294 | −0.0886471 | − | 0.996063i | \(-0.528254\pi\) | ||||
−0.0886471 | + | 0.996063i | \(0.528254\pi\) | |||||||
\(938\) | 1.99855 | 0.0652549 | ||||||||
\(939\) | −21.3968 | −0.698258 | ||||||||
\(940\) | 58.7483 | 1.91616 | ||||||||
\(941\) | −25.3338 | −0.825859 | −0.412929 | − | 0.910763i | \(-0.635494\pi\) | ||||
−0.412929 | + | 0.910763i | \(0.635494\pi\) | |||||||
\(942\) | 2.63635 | 0.0858969 | ||||||||
\(943\) | 9.49472 | 0.309191 | ||||||||
\(944\) | 10.8462 | 0.353015 | ||||||||
\(945\) | 7.12130 | 0.231656 | ||||||||
\(946\) | 0.828021 | 0.0269213 | ||||||||
\(947\) | −57.5038 | −1.86862 | −0.934312 | − | 0.356457i | \(-0.883985\pi\) | ||||
−0.934312 | + | 0.356457i | \(0.883985\pi\) | |||||||
\(948\) | −5.08104 | −0.165024 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.428486 | 0.0139019 | ||||||||
\(951\) | −13.6654 | −0.443131 | ||||||||
\(952\) | −6.40704 | −0.207653 | ||||||||
\(953\) | 12.5498 | 0.406529 | 0.203265 | − | 0.979124i | \(-0.434845\pi\) | ||||
0.203265 | + | 0.979124i | \(0.434845\pi\) | |||||||
\(954\) | −0.520668 | −0.0168572 | ||||||||
\(955\) | 8.78233 | 0.284189 | ||||||||
\(956\) | 19.8528 | 0.642084 | ||||||||
\(957\) | 5.42498 | 0.175365 | ||||||||
\(958\) | 1.67428 | 0.0540936 | ||||||||
\(959\) | 41.9013 | 1.35306 | ||||||||
\(960\) | 18.3831 | 0.593314 | ||||||||
\(961\) | −27.3142 | −0.881104 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.848723 | −0.0273497 | ||||||||
\(964\) | −2.51201 | −0.0809064 | ||||||||
\(965\) | 9.43209 | 0.303630 | ||||||||
\(966\) | 0.614782 | 0.0197803 | ||||||||
\(967\) | −1.49036 | −0.0479266 | −0.0239633 | − | 0.999713i | \(-0.507628\pi\) | ||||
−0.0239633 | + | 0.999713i | \(0.507628\pi\) | |||||||
\(968\) | 0.470505 | 0.0151226 | ||||||||
\(969\) | −22.2454 | −0.714624 | ||||||||
\(970\) | −3.13593 | −0.100689 | ||||||||
\(971\) | −39.4787 | −1.26693 | −0.633466 | − | 0.773771i | \(-0.718368\pi\) | ||||
−0.633466 | + | 0.773771i | \(0.718368\pi\) | |||||||
\(972\) | −1.98607 | −0.0637031 | ||||||||
\(973\) | −14.4693 | −0.463864 | ||||||||
\(974\) | 3.17215 | 0.101642 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 21.3093 | 0.682095 | ||||||||
\(977\) | −18.7508 | −0.599891 | −0.299945 | − | 0.953956i | \(-0.596968\pi\) | ||||
−0.299945 | + | 0.953956i | \(0.596968\pi\) | |||||||
\(978\) | 2.21633 | 0.0708706 | ||||||||
\(979\) | 0.0288464 | 0.000921935 0 | ||||||||
\(980\) | 8.67811 | 0.277212 | ||||||||
\(981\) | 13.4908 | 0.430728 | ||||||||
\(982\) | −4.02052 | −0.128300 | ||||||||
\(983\) | −23.9822 | −0.764914 | −0.382457 | − | 0.923973i | \(-0.624922\pi\) | ||||
−0.382457 | + | 0.923973i | \(0.624922\pi\) | |||||||
\(984\) | 2.54765 | 0.0812161 | ||||||||
\(985\) | −41.2115 | −1.31311 | ||||||||
\(986\) | −2.93572 | −0.0934925 | ||||||||
\(987\) | −36.6466 | −1.16648 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.3007 | −0.391138 | ||||||||
\(990\) | 0.282997 | 0.00899425 | ||||||||
\(991\) | −21.7643 | −0.691365 | −0.345683 | − | 0.938351i | \(-0.612353\pi\) | ||||
−0.345683 | + | 0.938351i | \(0.612353\pi\) | |||||||
\(992\) | 2.69413 | 0.0855388 | ||||||||
\(993\) | 9.56314 | 0.303477 | ||||||||
\(994\) | −5.24170 | −0.166257 | ||||||||
\(995\) | 18.8697 | 0.598210 | ||||||||
\(996\) | 18.6922 | 0.592286 | ||||||||
\(997\) | −34.5397 | −1.09388 | −0.546941 | − | 0.837171i | \(-0.684208\pi\) | ||||
−0.546941 | + | 0.837171i | \(0.684208\pi\) | |||||||
\(998\) | 0.0173378 | 0.000548817 0 | ||||||||
\(999\) | −3.76743 | −0.119196 |
(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 | 5577.2.a.n.1.4 | 5 | ||
13.3 | even | 3 | 429.2.i.f.100.2 | ✓ | 10 | ||
13.9 | even | 3 | 429.2.i.f.133.2 | yes | 10 | ||
13.12 | even | 2 | 5577.2.a.w.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.i.f.100.2 | ✓ | 10 | 13.3 | even | 3 | ||
429.2.i.f.133.2 | yes | 10 | 13.9 | even | 3 | ||
5577.2.a.n.1.4 | 5 | 1.1 | even | 1 | trivial | ||
5577.2.a.w.1.2 | 5 | 13.12 | even | 2 |