Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.24483 | −1.58734 | −0.793669 | − | 0.608350i | \(-0.791832\pi\) | ||||
−0.793669 | + | 0.608350i | \(0.791832\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.03928 | 1.51964 | ||||||||
\(5\) | 2.70888 | 1.21145 | 0.605724 | − | 0.795675i | \(-0.292883\pi\) | ||||
0.605724 | + | 0.795675i | \(0.292883\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.81542 | −0.686163 | −0.343081 | − | 0.939306i | \(-0.611471\pi\) | ||||
−0.343081 | + | 0.939306i | \(0.611471\pi\) | |||||||
\(8\) | −2.33301 | −0.824843 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.08099 | −1.92298 | ||||||||
\(11\) | 1.28860 | 0.388528 | 0.194264 | − | 0.980949i | \(-0.437768\pi\) | ||||
0.194264 | + | 0.980949i | \(0.437768\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.53826 | 1.25869 | 0.629343 | − | 0.777127i | \(-0.283324\pi\) | ||||
0.629343 | + | 0.777127i | \(0.283324\pi\) | |||||||
\(14\) | 4.07531 | 1.08917 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.841340 | −0.210335 | ||||||||
\(17\) | −4.48595 | −1.08800 | −0.544001 | − | 0.839085i | \(-0.683091\pi\) | ||||
−0.544001 | + | 0.839085i | \(0.683091\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.67238 | 0.613087 | 0.306543 | − | 0.951857i | \(-0.400828\pi\) | ||||
0.306543 | + | 0.951857i | \(0.400828\pi\) | |||||||
\(20\) | 8.23305 | 1.84097 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.89270 | −0.616725 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.33804 | 0.467607 | ||||||||
\(26\) | −10.1876 | −1.99796 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.51756 | −1.04272 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.79860 | −1.04146 | −0.520730 | − | 0.853722i | \(-0.674340\pi\) | ||||
−0.520730 | + | 0.853722i | \(0.674340\pi\) | |||||||
\(32\) | 6.55469 | 1.15872 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.0702 | 1.72703 | ||||||||
\(35\) | −4.91775 | −0.831251 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.91943 | −0.973147 | −0.486574 | − | 0.873640i | \(-0.661754\pi\) | ||||
−0.486574 | + | 0.873640i | \(0.661754\pi\) | |||||||
\(38\) | −5.99906 | −0.973175 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.31985 | −0.999255 | ||||||||
\(41\) | −7.82902 | −1.22269 | −0.611344 | − | 0.791365i | \(-0.709371\pi\) | ||||
−0.611344 | + | 0.791365i | \(0.709371\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.28362 | −0.805744 | −0.402872 | − | 0.915256i | \(-0.631988\pi\) | ||||
−0.402872 | + | 0.915256i | \(0.631988\pi\) | |||||||
\(44\) | 3.91642 | 0.590423 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.24483 | −0.330983 | ||||||||
\(47\) | 2.52885 | 0.368871 | 0.184436 | − | 0.982845i | \(-0.440954\pi\) | ||||
0.184436 | + | 0.982845i | \(0.440954\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.70427 | −0.529181 | ||||||||
\(50\) | −5.24851 | −0.742251 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 13.7930 | 1.91275 | ||||||||
\(53\) | 7.14230 | 0.981070 | 0.490535 | − | 0.871421i | \(-0.336801\pi\) | ||||
0.490535 | + | 0.871421i | \(0.336801\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.49067 | 0.470682 | ||||||||
\(56\) | 4.23538 | 0.565977 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.24483 | −0.294761 | ||||||||
\(59\) | −7.87478 | −1.02521 | −0.512605 | − | 0.858625i | \(-0.671319\pi\) | ||||
−0.512605 | + | 0.858625i | \(0.671319\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.0192849 | 0.00246918 | 0.00123459 | − | 0.999999i | \(-0.499607\pi\) | ||||
0.00123459 | + | 0.999999i | \(0.499607\pi\) | |||||||
\(62\) | 13.0169 | 1.65315 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0315 | −1.62894 | ||||||||
\(65\) | 12.2936 | 1.52483 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.5222 | −1.89634 | −0.948170 | − | 0.317764i | \(-0.897068\pi\) | ||||
−0.948170 | + | 0.317764i | \(0.897068\pi\) | |||||||
\(68\) | −13.6340 | −1.65337 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.0395 | 1.31948 | ||||||||
\(71\) | 8.18804 | 0.971742 | 0.485871 | − | 0.874031i | \(-0.338502\pi\) | ||||
0.485871 | + | 0.874031i | \(0.338502\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.8537 | −1.97258 | −0.986288 | − | 0.165035i | \(-0.947226\pi\) | ||||
−0.986288 | + | 0.165035i | \(0.947226\pi\) | |||||||
\(74\) | 13.2881 | 1.54471 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.12212 | 0.931671 | ||||||||
\(77\) | −2.33935 | −0.266593 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.32730 | 0.261842 | 0.130921 | − | 0.991393i | \(-0.458207\pi\) | ||||
0.130921 | + | 0.991393i | \(0.458207\pi\) | |||||||
\(80\) | −2.27909 | −0.254810 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 17.5749 | 1.94082 | ||||||||
\(83\) | 8.65460 | 0.949966 | 0.474983 | − | 0.879995i | \(-0.342454\pi\) | ||||
0.474983 | + | 0.879995i | \(0.342454\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.1519 | −1.31806 | ||||||||
\(86\) | 11.8608 | 1.27899 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.00632 | −0.320475 | ||||||||
\(89\) | 17.6714 | 1.87316 | 0.936581 | − | 0.350451i | \(-0.113972\pi\) | ||||
0.936581 | + | 0.350451i | \(0.113972\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.23883 | −0.863664 | ||||||||
\(92\) | 3.03928 | 0.316867 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.67686 | −0.585523 | ||||||||
\(95\) | 7.23917 | 0.742723 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.50809 | −0.762331 | −0.381166 | − | 0.924507i | \(-0.624477\pi\) | ||||
−0.381166 | + | 0.924507i | \(0.624477\pi\) | |||||||
\(98\) | 8.31546 | 0.839989 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.10595 | 0.710595 | ||||||||
\(101\) | −12.9202 | −1.28561 | −0.642804 | − | 0.766031i | \(-0.722229\pi\) | ||||
−0.642804 | + | 0.766031i | \(0.722229\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.730126 | 0.0719415 | 0.0359707 | − | 0.999353i | \(-0.488548\pi\) | ||||
0.0359707 | + | 0.999353i | \(0.488548\pi\) | |||||||
\(104\) | −10.5878 | −1.03822 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.0333 | −1.55729 | ||||||||
\(107\) | −2.51770 | −0.243395 | −0.121697 | − | 0.992567i | \(-0.538834\pi\) | ||||
−0.121697 | + | 0.992567i | \(0.538834\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.164640 | 0.0157696 | 0.00788481 | − | 0.999969i | \(-0.497490\pi\) | ||||
0.00788481 | + | 0.999969i | \(0.497490\pi\) | |||||||
\(110\) | −7.83597 | −0.747131 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.52738 | 0.144324 | ||||||||
\(113\) | −12.0351 | −1.13216 | −0.566082 | − | 0.824349i | \(-0.691541\pi\) | ||||
−0.566082 | + | 0.824349i | \(0.691541\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.70888 | 0.252604 | ||||||||
\(116\) | 3.03928 | 0.282190 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.6776 | 1.62735 | ||||||||
\(119\) | 8.14386 | 0.746546 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.33951 | −0.849046 | ||||||||
\(122\) | −0.0432915 | −0.00391942 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −17.6236 | −1.58264 | ||||||||
\(125\) | −7.21094 | −0.644966 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.8939 | −1.14415 | −0.572076 | − | 0.820201i | \(-0.693862\pi\) | ||||
−0.572076 | + | 0.820201i | \(0.693862\pi\) | |||||||
\(128\) | 16.1442 | 1.42696 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −27.5971 | −2.42043 | ||||||||
\(131\) | −15.3953 | −1.34510 | −0.672549 | − | 0.740053i | \(-0.734800\pi\) | ||||
−0.672549 | + | 0.740053i | \(0.734800\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.85149 | −0.420677 | ||||||||
\(134\) | 34.8448 | 3.01013 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.4658 | 0.897431 | ||||||||
\(137\) | −4.85694 | −0.414956 | −0.207478 | − | 0.978240i | \(-0.566526\pi\) | ||||
−0.207478 | + | 0.978240i | \(0.566526\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.76830 | 0.743718 | 0.371859 | − | 0.928289i | \(-0.378721\pi\) | ||||
0.371859 | + | 0.928289i | \(0.378721\pi\) | |||||||
\(140\) | −14.9464 | −1.26320 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −18.3808 | −1.54248 | ||||||||
\(143\) | 5.84801 | 0.489035 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.70888 | 0.224960 | ||||||||
\(146\) | 37.8337 | 3.13114 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −17.9908 | −1.47883 | ||||||||
\(149\) | −1.66660 | −0.136534 | −0.0682668 | − | 0.997667i | \(-0.521747\pi\) | ||||
−0.0682668 | + | 0.997667i | \(0.521747\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.6639 | 1.27471 | 0.637357 | − | 0.770569i | \(-0.280028\pi\) | ||||
0.637357 | + | 0.770569i | \(0.280028\pi\) | |||||||
\(152\) | −6.23469 | −0.505701 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.25145 | 0.423174 | ||||||||
\(155\) | −15.7077 | −1.26167 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.5561 | −1.40113 | −0.700563 | − | 0.713591i | \(-0.747068\pi\) | ||||
−0.700563 | + | 0.713591i | \(0.747068\pi\) | |||||||
\(158\) | −5.22441 | −0.415632 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 17.7559 | 1.40372 | ||||||||
\(161\) | −1.81542 | −0.143075 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.2450 | 1.74236 | 0.871180 | − | 0.490964i | \(-0.163355\pi\) | ||||
0.871180 | + | 0.490964i | \(0.163355\pi\) | |||||||
\(164\) | −23.7946 | −1.85805 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.4281 | −1.50792 | ||||||||
\(167\) | −20.9725 | −1.62290 | −0.811449 | − | 0.584423i | \(-0.801321\pi\) | ||||
−0.811449 | + | 0.584423i | \(0.801321\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.59580 | 0.584292 | ||||||||
\(170\) | 27.2790 | 2.09220 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −16.0584 | −1.22444 | ||||||||
\(173\) | 19.8975 | 1.51278 | 0.756389 | − | 0.654122i | \(-0.226962\pi\) | ||||
0.756389 | + | 0.654122i | \(0.226962\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.24451 | −0.320855 | ||||||||
\(176\) | −1.08415 | −0.0817210 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −39.6693 | −2.97334 | ||||||||
\(179\) | 0.697223 | 0.0521129 | 0.0260564 | − | 0.999660i | \(-0.491705\pi\) | ||||
0.0260564 | + | 0.999660i | \(0.491705\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.7053 | −1.61334 | −0.806670 | − | 0.591001i | \(-0.798733\pi\) | ||||
−0.806670 | + | 0.591001i | \(0.798733\pi\) | |||||||
\(182\) | 18.4948 | 1.37093 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.33301 | −0.171992 | ||||||||
\(185\) | −16.0350 | −1.17892 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.78060 | −0.422719 | ||||||||
\(188\) | 7.68589 | 0.560551 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −16.2507 | −1.17895 | ||||||||
\(191\) | 14.0930 | 1.01974 | 0.509869 | − | 0.860252i | \(-0.329694\pi\) | ||||
0.509869 | + | 0.860252i | \(0.329694\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.1691 | 0.803973 | 0.401986 | − | 0.915646i | \(-0.368320\pi\) | ||||
0.401986 | + | 0.915646i | \(0.368320\pi\) | |||||||
\(194\) | 16.8544 | 1.21008 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.2583 | −0.804164 | ||||||||
\(197\) | 11.8308 | 0.842910 | 0.421455 | − | 0.906849i | \(-0.361520\pi\) | ||||
0.421455 | + | 0.906849i | \(0.361520\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.23419 | 0.512818 | 0.256409 | − | 0.966568i | \(-0.417461\pi\) | ||||
0.256409 | + | 0.966568i | \(0.417461\pi\) | |||||||
\(200\) | −5.45466 | −0.385703 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 29.0037 | 2.04069 | ||||||||
\(203\) | −1.81542 | −0.127417 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.2079 | −1.48122 | ||||||||
\(206\) | −1.63901 | −0.114195 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.81822 | −0.264746 | ||||||||
\(209\) | 3.44364 | 0.238201 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.94613 | −0.340506 | −0.170253 | − | 0.985400i | \(-0.554458\pi\) | ||||
−0.170253 | + | 0.985400i | \(0.554458\pi\) | |||||||
\(212\) | 21.7074 | 1.49087 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.65181 | 0.386350 | ||||||||
\(215\) | −14.3127 | −0.976117 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.5269 | 0.714610 | ||||||||
\(218\) | −0.369589 | −0.0250317 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.6091 | 0.715267 | ||||||||
\(221\) | −20.3584 | −1.36945 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.4975 | −0.836891 | −0.418446 | − | 0.908242i | \(-0.637425\pi\) | ||||
−0.418446 | + | 0.908242i | \(0.637425\pi\) | |||||||
\(224\) | −11.8995 | −0.795068 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 27.0167 | 1.79712 | ||||||||
\(227\) | −14.7488 | −0.978911 | −0.489456 | − | 0.872028i | \(-0.662804\pi\) | ||||
−0.489456 | + | 0.872028i | \(0.662804\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.4103 | −0.754016 | −0.377008 | − | 0.926210i | \(-0.623047\pi\) | ||||
−0.377008 | + | 0.926210i | \(0.623047\pi\) | |||||||
\(230\) | −6.08099 | −0.400969 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.33301 | −0.153170 | ||||||||
\(233\) | −10.5481 | −0.691029 | −0.345514 | − | 0.938413i | \(-0.612296\pi\) | ||||
−0.345514 | + | 0.938413i | \(0.612296\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.85036 | 0.446868 | ||||||||
\(236\) | −23.9337 | −1.55795 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −18.2816 | −1.18502 | ||||||||
\(239\) | −3.76141 | −0.243306 | −0.121653 | − | 0.992573i | \(-0.538819\pi\) | ||||
−0.121653 | + | 0.992573i | \(0.538819\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.4984 | −0.740677 | −0.370339 | − | 0.928897i | \(-0.620758\pi\) | ||||
−0.370339 | + | 0.928897i | \(0.620758\pi\) | |||||||
\(242\) | 20.9656 | 1.34772 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.0586123 | 0.00375227 | ||||||||
\(245\) | −10.0344 | −0.641075 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.1280 | 0.771684 | ||||||||
\(248\) | 13.5282 | 0.859041 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 16.1874 | 1.02378 | ||||||||
\(251\) | 1.24214 | 0.0784034 | 0.0392017 | − | 0.999231i | \(-0.487519\pi\) | ||||
0.0392017 | + | 0.999231i | \(0.487519\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.28860 | 0.0810137 | ||||||||
\(254\) | 28.9447 | 1.81615 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.1780 | −0.636126 | ||||||||
\(257\) | 11.4715 | 0.715575 | 0.357788 | − | 0.933803i | \(-0.383531\pi\) | ||||
0.357788 | + | 0.933803i | \(0.383531\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.7462 | 0.667737 | ||||||||
\(260\) | 37.3637 | 2.31720 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 34.5600 | 2.13512 | ||||||||
\(263\) | 31.2502 | 1.92697 | 0.963486 | − | 0.267760i | \(-0.0862836\pi\) | ||||
0.963486 | + | 0.267760i | \(0.0862836\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.3476 | 1.18852 | ||||||||
\(266\) | 10.8908 | 0.667757 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −47.1763 | −2.88175 | ||||||||
\(269\) | 24.6573 | 1.50338 | 0.751691 | − | 0.659516i | \(-0.229239\pi\) | ||||
0.751691 | + | 0.659516i | \(0.229239\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.4463 | 1.60650 | 0.803248 | − | 0.595644i | \(-0.203103\pi\) | ||||
0.803248 | + | 0.595644i | \(0.203103\pi\) | |||||||
\(272\) | 3.77421 | 0.228845 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.9030 | 0.658675 | ||||||||
\(275\) | 3.01280 | 0.181679 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.9981 | 1.08140 | 0.540702 | − | 0.841214i | \(-0.318159\pi\) | ||||
0.540702 | + | 0.841214i | \(0.318159\pi\) | |||||||
\(278\) | −19.6834 | −1.18053 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11.4731 | 0.685652 | ||||||||
\(281\) | −19.6129 | −1.17001 | −0.585004 | − | 0.811030i | \(-0.698907\pi\) | ||||
−0.585004 | + | 0.811030i | \(0.698907\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.74374 | 0.281986 | 0.140993 | − | 0.990011i | \(-0.454971\pi\) | ||||
0.140993 | + | 0.990011i | \(0.454971\pi\) | |||||||
\(284\) | 24.8858 | 1.47670 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −13.1278 | −0.776264 | ||||||||
\(287\) | 14.2129 | 0.838963 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.12372 | 0.183749 | ||||||||
\(290\) | −6.08099 | −0.357088 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −51.2231 | −2.99760 | ||||||||
\(293\) | 5.47082 | 0.319609 | 0.159804 | − | 0.987149i | \(-0.448914\pi\) | ||||
0.159804 | + | 0.987149i | \(0.448914\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.3319 | −1.24199 | ||||||||
\(296\) | 13.8101 | 0.802694 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.74125 | 0.216725 | ||||||||
\(299\) | 4.53826 | 0.262454 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.59196 | 0.552871 | ||||||||
\(302\) | −35.1629 | −2.02340 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.24838 | −0.128954 | ||||||||
\(305\) | 0.0522406 | 0.00299129 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.4112 | −1.67858 | −0.839292 | − | 0.543681i | \(-0.817030\pi\) | ||||
−0.839292 | + | 0.543681i | \(0.817030\pi\) | |||||||
\(308\) | −7.10993 | −0.405126 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 35.2612 | 2.00270 | ||||||||
\(311\) | 0.290134 | 0.0164520 | 0.00822598 | − | 0.999966i | \(-0.497382\pi\) | ||||
0.00822598 | + | 0.999966i | \(0.497382\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.75393 | 0.155661 | 0.0778306 | − | 0.996967i | \(-0.475201\pi\) | ||||
0.0778306 | + | 0.996967i | \(0.475201\pi\) | |||||||
\(314\) | 39.4104 | 2.22406 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.07332 | 0.397905 | ||||||||
\(317\) | −23.3102 | −1.30923 | −0.654617 | − | 0.755961i | \(-0.727170\pi\) | ||||
−0.654617 | + | 0.755961i | \(0.727170\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.28860 | 0.0721478 | ||||||||
\(320\) | −35.3008 | −1.97337 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.07531 | 0.227108 | ||||||||
\(323\) | −11.9882 | −0.667040 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.6106 | 0.588571 | ||||||||
\(326\) | −49.9363 | −2.76571 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 18.2652 | 1.00853 | ||||||||
\(329\) | −4.59092 | −0.253106 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.6297 | 1.57363 | 0.786816 | − | 0.617187i | \(-0.211728\pi\) | ||||
0.786816 | + | 0.617187i | \(0.211728\pi\) | |||||||
\(332\) | 26.3038 | 1.44361 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 47.0797 | 2.57609 | ||||||||
\(335\) | −42.0478 | −2.29732 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.8515 | −1.29927 | −0.649637 | − | 0.760245i | \(-0.725079\pi\) | ||||
−0.649637 | + | 0.760245i | \(0.725079\pi\) | |||||||
\(338\) | −17.0513 | −0.927469 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −36.9330 | −2.00297 | ||||||||
\(341\) | −7.47208 | −0.404636 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.4327 | 1.04927 | ||||||||
\(344\) | 12.3267 | 0.664613 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −44.6666 | −2.40129 | ||||||||
\(347\) | 12.6128 | 0.677093 | 0.338546 | − | 0.940950i | \(-0.390065\pi\) | ||||
0.338546 | + | 0.940950i | \(0.390065\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.6656 | 1.53443 | 0.767216 | − | 0.641389i | \(-0.221641\pi\) | ||||
0.767216 | + | 0.641389i | \(0.221641\pi\) | |||||||
\(350\) | 9.52822 | 0.509305 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.44638 | 0.450194 | ||||||||
\(353\) | 9.85003 | 0.524264 | 0.262132 | − | 0.965032i | \(-0.415574\pi\) | ||||
0.262132 | + | 0.965032i | \(0.415574\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.1804 | 1.17722 | ||||||||
\(356\) | 53.7082 | 2.84653 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.56515 | −0.0827207 | ||||||||
\(359\) | −6.28877 | −0.331909 | −0.165954 | − | 0.986133i | \(-0.553070\pi\) | ||||
−0.165954 | + | 0.986133i | \(0.553070\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.8584 | −0.624125 | ||||||||
\(362\) | 48.7248 | 2.56092 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −25.0401 | −1.31246 | ||||||||
\(365\) | −45.6546 | −2.38967 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.2153 | 1.78602 | 0.893011 | − | 0.450034i | \(-0.148588\pi\) | ||||
0.893011 | + | 0.450034i | \(0.148588\pi\) | |||||||
\(368\) | −0.841340 | −0.0438579 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 35.9960 | 1.87134 | ||||||||
\(371\) | −12.9662 | −0.673174 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.32053 | 0.327264 | 0.163632 | − | 0.986521i | \(-0.447679\pi\) | ||||
0.163632 | + | 0.986521i | \(0.447679\pi\) | |||||||
\(374\) | 12.9765 | 0.670998 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.89984 | −0.304261 | ||||||||
\(377\) | 4.53826 | 0.233732 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.3916 | 1.25291 | 0.626456 | − | 0.779457i | \(-0.284505\pi\) | ||||
0.626456 | + | 0.779457i | \(0.284505\pi\) | |||||||
\(380\) | 22.0019 | 1.12867 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −31.6366 | −1.61867 | ||||||||
\(383\) | 1.48836 | 0.0760516 | 0.0380258 | − | 0.999277i | \(-0.487893\pi\) | ||||
0.0380258 | + | 0.999277i | \(0.487893\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.33701 | −0.322964 | ||||||||
\(386\) | −25.0729 | −1.27618 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −22.8192 | −1.15847 | ||||||||
\(389\) | 32.8601 | 1.66607 | 0.833036 | − | 0.553219i | \(-0.186601\pi\) | ||||
0.833036 | + | 0.553219i | \(0.186601\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.48595 | −0.226864 | ||||||||
\(392\) | 8.64209 | 0.436491 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −26.5582 | −1.33798 | ||||||||
\(395\) | 6.30439 | 0.317208 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.95067 | 0.348844 | 0.174422 | − | 0.984671i | \(-0.444194\pi\) | ||||
0.174422 | + | 0.984671i | \(0.444194\pi\) | |||||||
\(398\) | −16.2396 | −0.814015 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.96708 | −0.0983542 | ||||||||
\(401\) | −2.64996 | −0.132333 | −0.0661664 | − | 0.997809i | \(-0.521077\pi\) | ||||
−0.0661664 | + | 0.997809i | \(0.521077\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.3155 | −1.31087 | ||||||||
\(404\) | −39.2681 | −1.95366 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.07531 | 0.202254 | ||||||||
\(407\) | −7.62778 | −0.378095 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.22912 | −0.406904 | −0.203452 | − | 0.979085i | \(-0.565216\pi\) | ||||
−0.203452 | + | 0.979085i | \(0.565216\pi\) | |||||||
\(410\) | 47.6082 | 2.35120 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.21906 | 0.109325 | ||||||||
\(413\) | 14.2960 | 0.703460 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.4443 | 1.15083 | ||||||||
\(416\) | 29.7469 | 1.45846 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.73039 | −0.378106 | ||||||||
\(419\) | −17.7332 | −0.866323 | −0.433161 | − | 0.901316i | \(-0.642602\pi\) | ||||
−0.433161 | + | 0.901316i | \(0.642602\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.8575 | 0.967795 | 0.483897 | − | 0.875125i | \(-0.339221\pi\) | ||||
0.483897 | + | 0.875125i | \(0.339221\pi\) | |||||||
\(422\) | 11.1032 | 0.540497 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −16.6631 | −0.809229 | ||||||||
\(425\) | −10.4883 | −0.508758 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0350102 | −0.00169426 | ||||||||
\(428\) | −7.65198 | −0.369873 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 32.1296 | 1.54943 | ||||||||
\(431\) | 16.6485 | 0.801930 | 0.400965 | − | 0.916093i | \(-0.368675\pi\) | ||||
0.400965 | + | 0.916093i | \(0.368675\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.5474 | −1.61219 | −0.806093 | − | 0.591789i | \(-0.798422\pi\) | ||||
−0.806093 | + | 0.591789i | \(0.798422\pi\) | |||||||
\(434\) | −23.6311 | −1.13433 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.500386 | 0.0239641 | ||||||||
\(437\) | 2.67238 | 0.127837 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.1685 | 0.867134 | 0.433567 | − | 0.901121i | \(-0.357255\pi\) | ||||
0.433567 | + | 0.901121i | \(0.357255\pi\) | |||||||
\(440\) | −8.14376 | −0.388239 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 45.7012 | 2.17379 | ||||||||
\(443\) | −26.5362 | −1.26077 | −0.630386 | − | 0.776282i | \(-0.717103\pi\) | ||||
−0.630386 | + | 0.776282i | \(0.717103\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 47.8697 | 2.26924 | ||||||||
\(446\) | 28.0547 | 1.32843 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 23.6576 | 1.11772 | ||||||||
\(449\) | −31.8845 | −1.50472 | −0.752362 | − | 0.658750i | \(-0.771085\pi\) | ||||
−0.752362 | + | 0.658750i | \(0.771085\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.0885 | −0.475049 | ||||||||
\(452\) | −36.5779 | −1.72048 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 33.1086 | 1.55386 | ||||||||
\(455\) | −22.3180 | −1.04628 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.81457 | −0.178438 | −0.0892190 | − | 0.996012i | \(-0.528437\pi\) | ||||
−0.0892190 | + | 0.996012i | \(0.528437\pi\) | |||||||
\(458\) | 25.6143 | 1.19688 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.23305 | 0.383868 | ||||||||
\(461\) | 15.5993 | 0.726532 | 0.363266 | − | 0.931685i | \(-0.381662\pi\) | ||||
0.363266 | + | 0.931685i | \(0.381662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.0523 | −1.48960 | −0.744799 | − | 0.667289i | \(-0.767455\pi\) | ||||
−0.744799 | + | 0.667289i | \(0.767455\pi\) | |||||||
\(464\) | −0.841340 | −0.0390582 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.6787 | 1.09690 | ||||||||
\(467\) | −27.7274 | −1.28307 | −0.641535 | − | 0.767094i | \(-0.721702\pi\) | ||||
−0.641535 | + | 0.767094i | \(0.721702\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.1793 | 1.30120 | ||||||||
\(470\) | −15.3779 | −0.709331 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18.3719 | 0.845637 | ||||||||
\(473\) | −6.80848 | −0.313054 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.24813 | 0.286684 | ||||||||
\(476\) | 24.7515 | 1.13448 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.44375 | 0.386208 | ||||||||
\(479\) | −28.8506 | −1.31822 | −0.659109 | − | 0.752048i | \(-0.729066\pi\) | ||||
−0.659109 | + | 0.752048i | \(0.729066\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.8639 | −1.22489 | ||||||||
\(482\) | 25.8120 | 1.17570 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −28.3854 | −1.29024 | ||||||||
\(485\) | −20.3385 | −0.923525 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.0525 | −0.591467 | −0.295734 | − | 0.955270i | \(-0.595564\pi\) | ||||
−0.295734 | + | 0.955270i | \(0.595564\pi\) | |||||||
\(488\) | −0.0449919 | −0.00203669 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 22.5256 | 1.01760 | ||||||||
\(491\) | 16.7180 | 0.754472 | 0.377236 | − | 0.926117i | \(-0.376875\pi\) | ||||
0.377236 | + | 0.926117i | \(0.376875\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.48595 | −0.202037 | ||||||||
\(494\) | −27.2253 | −1.22492 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.87859 | 0.219055 | ||||||||
\(497\) | −14.8647 | −0.666773 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.64497 | 0.252704 | 0.126352 | − | 0.991985i | \(-0.459673\pi\) | ||||
0.126352 | + | 0.991985i | \(0.459673\pi\) | |||||||
\(500\) | −21.9161 | −0.980116 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.78841 | −0.124453 | ||||||||
\(503\) | −18.7912 | −0.837858 | −0.418929 | − | 0.908019i | \(-0.637594\pi\) | ||||
−0.418929 | + | 0.908019i | \(0.637594\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.9993 | −1.55745 | ||||||||
\(506\) | −2.89270 | −0.128596 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −39.1883 | −1.73870 | ||||||||
\(509\) | 38.1542 | 1.69116 | 0.845579 | − | 0.533851i | \(-0.179256\pi\) | ||||
0.845579 | + | 0.533851i | \(0.179256\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.5965 | 1.35351 | ||||||||
\(512\) | −9.44042 | −0.417212 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25.7517 | −1.13586 | ||||||||
\(515\) | 1.97783 | 0.0871534 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.25868 | 0.143317 | ||||||||
\(518\) | −24.1235 | −1.05992 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −28.6811 | −1.25775 | ||||||||
\(521\) | 20.7383 | 0.908564 | 0.454282 | − | 0.890858i | \(-0.349896\pi\) | ||||
0.454282 | + | 0.890858i | \(0.349896\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.6601 | −1.55931 | −0.779654 | − | 0.626211i | \(-0.784605\pi\) | ||||
−0.779654 | + | 0.626211i | \(0.784605\pi\) | |||||||
\(524\) | −46.7907 | −2.04406 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −70.1516 | −3.05875 | ||||||||
\(527\) | 26.0122 | 1.13311 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −43.4322 | −1.88658 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.7450 | −0.639278 | ||||||||
\(533\) | −35.5301 | −1.53898 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.82014 | −0.294860 | ||||||||
\(536\) | 36.2135 | 1.56418 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −55.3515 | −2.38637 | ||||||||
\(539\) | −4.77332 | −0.205602 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.9936 | −0.558640 | −0.279320 | − | 0.960198i | \(-0.590109\pi\) | ||||
−0.279320 | + | 0.960198i | \(0.590109\pi\) | |||||||
\(542\) | −59.3675 | −2.55005 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −29.4040 | −1.26069 | ||||||||
\(545\) | 0.445989 | 0.0191041 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.0835 | 1.50006 | 0.750031 | − | 0.661403i | \(-0.230039\pi\) | ||||
0.750031 | + | 0.661403i | \(0.230039\pi\) | |||||||
\(548\) | −14.7616 | −0.630584 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.76323 | −0.288385 | ||||||||
\(551\) | 2.67238 | 0.113847 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.22502 | −0.179666 | ||||||||
\(554\) | −40.4028 | −1.71655 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 26.6493 | 1.13018 | ||||||||
\(557\) | 38.1951 | 1.61838 | 0.809190 | − | 0.587547i | \(-0.199906\pi\) | ||||
0.809190 | + | 0.587547i | \(0.199906\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.9784 | −1.01418 | ||||||||
\(560\) | 4.13749 | 0.174841 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 44.0277 | 1.85720 | ||||||||
\(563\) | 11.2679 | 0.474886 | 0.237443 | − | 0.971401i | \(-0.423691\pi\) | ||||
0.237443 | + | 0.971401i | \(0.423691\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.6015 | −1.37156 | ||||||||
\(566\) | −10.6489 | −0.447607 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19.1028 | −0.801535 | ||||||||
\(569\) | −21.5961 | −0.905356 | −0.452678 | − | 0.891674i | \(-0.649531\pi\) | ||||
−0.452678 | + | 0.891674i | \(0.649531\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.89694 | 0.372325 | 0.186163 | − | 0.982519i | \(-0.440395\pi\) | ||||
0.186163 | + | 0.982519i | \(0.440395\pi\) | |||||||
\(572\) | 17.7737 | 0.743157 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −31.9057 | −1.33172 | ||||||||
\(575\) | 2.33804 | 0.0975029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.9448 | −1.24662 | −0.623308 | − | 0.781976i | \(-0.714212\pi\) | ||||
−0.623308 | + | 0.781976i | \(0.714212\pi\) | |||||||
\(578\) | −7.01224 | −0.291671 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.23305 | 0.341859 | ||||||||
\(581\) | −15.7117 | −0.651831 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.20358 | 0.381173 | ||||||||
\(584\) | 39.3198 | 1.62707 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.2811 | −0.507327 | ||||||||
\(587\) | −23.3343 | −0.963109 | −0.481555 | − | 0.876416i | \(-0.659928\pi\) | ||||
−0.481555 | + | 0.876416i | \(0.659928\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.4961 | −0.638505 | ||||||||
\(590\) | 47.8865 | 1.97145 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.98025 | 0.204687 | ||||||||
\(593\) | −34.8623 | −1.43162 | −0.715811 | − | 0.698295i | \(-0.753943\pi\) | ||||
−0.715811 | + | 0.698295i | \(0.753943\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.0607 | 0.904402 | ||||||||
\(596\) | −5.06528 | −0.207482 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.1876 | −0.416604 | ||||||||
\(599\) | −13.7736 | −0.562775 | −0.281387 | − | 0.959594i | \(-0.590795\pi\) | ||||
−0.281387 | + | 0.959594i | \(0.590795\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.6882 | −0.476772 | −0.238386 | − | 0.971170i | \(-0.576618\pi\) | ||||
−0.238386 | + | 0.971170i | \(0.576618\pi\) | |||||||
\(602\) | −21.5324 | −0.877593 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 47.6071 | 1.93710 | ||||||||
\(605\) | −25.2996 | −1.02858 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.5491 | −0.915238 | −0.457619 | − | 0.889148i | \(-0.651298\pi\) | ||||
−0.457619 | + | 0.889148i | \(0.651298\pi\) | |||||||
\(608\) | 17.5166 | 0.710393 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.117271 | −0.00474818 | ||||||||
\(611\) | 11.4766 | 0.464293 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.0844 | −1.21510 | −0.607549 | − | 0.794282i | \(-0.707847\pi\) | ||||
−0.607549 | + | 0.794282i | \(0.707847\pi\) | |||||||
\(614\) | 66.0232 | 2.66448 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.45772 | 0.219898 | ||||||||
\(617\) | −3.34573 | −0.134694 | −0.0673471 | − | 0.997730i | \(-0.521453\pi\) | ||||
−0.0673471 | + | 0.997730i | \(0.521453\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.0042 | −1.08539 | −0.542694 | − | 0.839930i | \(-0.682596\pi\) | ||||
−0.542694 | + | 0.839930i | \(0.682596\pi\) | |||||||
\(620\) | −47.7401 | −1.91729 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.651302 | −0.0261148 | ||||||||
\(623\) | −32.0809 | −1.28529 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2238 | −1.24895 | ||||||||
\(626\) | −6.18211 | −0.247087 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −53.3578 | −2.12921 | ||||||||
\(629\) | 26.5542 | 1.05879 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.3154 | 0.689316 | 0.344658 | − | 0.938728i | \(-0.387995\pi\) | ||||
0.344658 | + | 0.938728i | \(0.387995\pi\) | |||||||
\(632\) | −5.42962 | −0.215979 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 52.3276 | 2.07819 | ||||||||
\(635\) | −34.9281 | −1.38608 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.8109 | −0.666073 | ||||||||
\(638\) | −2.89270 | −0.114523 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 43.7327 | 1.72869 | ||||||||
\(641\) | −48.1364 | −1.90128 | −0.950638 | − | 0.310304i | \(-0.899569\pi\) | ||||
−0.950638 | + | 0.310304i | \(0.899569\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.4951 | −1.32092 | −0.660460 | − | 0.750862i | \(-0.729639\pi\) | ||||
−0.660460 | + | 0.750862i | \(0.729639\pi\) | |||||||
\(644\) | −5.51756 | −0.217422 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26.9114 | 1.05882 | ||||||||
\(647\) | −15.8951 | −0.624900 | −0.312450 | − | 0.949934i | \(-0.601150\pi\) | ||||
−0.312450 | + | 0.949934i | \(0.601150\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.1475 | −0.398323 | ||||||||
\(650\) | −23.8191 | −0.934261 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 67.6087 | 2.64776 | ||||||||
\(653\) | −28.6078 | −1.11951 | −0.559754 | − | 0.828659i | \(-0.689104\pi\) | ||||
−0.559754 | + | 0.828659i | \(0.689104\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41.7041 | −1.62952 | ||||||||
\(656\) | 6.58687 | 0.257174 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10.3059 | 0.401764 | ||||||||
\(659\) | 32.2194 | 1.25509 | 0.627545 | − | 0.778580i | \(-0.284060\pi\) | ||||
0.627545 | + | 0.778580i | \(0.284060\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.50116 | −0.291761 | −0.145881 | − | 0.989302i | \(-0.546602\pi\) | ||||
−0.145881 | + | 0.989302i | \(0.546602\pi\) | |||||||
\(662\) | −64.2690 | −2.49789 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −20.1913 | −0.783573 | ||||||||
\(665\) | −13.1421 | −0.509629 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −63.7412 | −2.46622 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 94.3904 | 3.64662 | ||||||||
\(671\) | 0.0248506 | 0.000959346 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.3328 | 0.513941 | 0.256970 | − | 0.966419i | \(-0.417276\pi\) | ||||
0.256970 | + | 0.966419i | \(0.417276\pi\) | |||||||
\(674\) | 53.5426 | 2.06239 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.0858 | 0.887914 | ||||||||
\(677\) | 25.8323 | 0.992817 | 0.496408 | − | 0.868089i | \(-0.334652\pi\) | ||||
0.496408 | + | 0.868089i | \(0.334652\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.6303 | 0.523083 | ||||||||
\(680\) | 28.3505 | 1.08719 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16.7736 | 0.642294 | ||||||||
\(683\) | 2.67992 | 0.102544 | 0.0512722 | − | 0.998685i | \(-0.483672\pi\) | ||||
0.0512722 | + | 0.998685i | \(0.483672\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.1569 | −0.502698 | ||||||||
\(686\) | −43.6232 | −1.66554 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.44532 | 0.169476 | ||||||||
\(689\) | 32.4136 | 1.23486 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.5615 | −0.553945 | −0.276972 | − | 0.960878i | \(-0.589331\pi\) | ||||
−0.276972 | + | 0.960878i | \(0.589331\pi\) | |||||||
\(692\) | 60.4740 | 2.29888 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.3137 | −1.07477 | ||||||||
\(695\) | 23.7523 | 0.900976 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.1206 | 1.33029 | ||||||||
\(698\) | −64.3494 | −2.43566 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.9003 | −0.487584 | ||||||||
\(701\) | −12.8173 | −0.484103 | −0.242051 | − | 0.970263i | \(-0.577820\pi\) | ||||
−0.242051 | + | 0.970263i | \(0.577820\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.8190 | −0.596624 | ||||||||
\(704\) | −16.7924 | −0.632888 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.1117 | −0.832185 | ||||||||
\(707\) | 23.4555 | 0.882136 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.1202 | −0.380073 | −0.190036 | − | 0.981777i | \(-0.560861\pi\) | ||||
−0.190036 | + | 0.981777i | \(0.560861\pi\) | |||||||
\(710\) | −49.7914 | −1.86864 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −41.2275 | −1.54507 | ||||||||
\(713\) | −5.79860 | −0.217159 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.8416 | 0.592441 | ||||||||
\(716\) | 2.11905 | 0.0791928 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.1172 | 0.526851 | ||||||||
\(719\) | 50.2292 | 1.87323 | 0.936616 | − | 0.350357i | \(-0.113940\pi\) | ||||
0.936616 | + | 0.350357i | \(0.113940\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.32548 | −0.0493636 | ||||||||
\(722\) | 26.6201 | 0.990697 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −65.9684 | −2.45170 | ||||||||
\(725\) | 2.33804 | 0.0868325 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.3374 | −1.12515 | −0.562575 | − | 0.826746i | \(-0.690189\pi\) | ||||
−0.562575 | + | 0.826746i | \(0.690189\pi\) | |||||||
\(728\) | 19.2213 | 0.712387 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 102.487 | 3.79322 | ||||||||
\(731\) | 23.7020 | 0.876651 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.1824 | −1.07788 | −0.538939 | − | 0.842345i | \(-0.681175\pi\) | ||||
−0.538939 | + | 0.842345i | \(0.681175\pi\) | |||||||
\(734\) | −76.8076 | −2.83502 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.55469 | 0.241609 | ||||||||
\(737\) | −20.0019 | −0.736781 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.6927 | −0.650837 | −0.325419 | − | 0.945570i | \(-0.605505\pi\) | ||||
−0.325419 | + | 0.945570i | \(0.605505\pi\) | |||||||
\(740\) | −48.7349 | −1.79153 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 29.1071 | 1.06855 | ||||||||
\(743\) | −25.7647 | −0.945216 | −0.472608 | − | 0.881273i | \(-0.656687\pi\) | ||||
−0.472608 | + | 0.881273i | \(0.656687\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.51463 | −0.165403 | ||||||||
\(746\) | −14.1885 | −0.519479 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −17.5689 | −0.642381 | ||||||||
\(749\) | 4.57067 | 0.167008 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.702382 | 0.0256303 | 0.0128151 | − | 0.999918i | \(-0.495921\pi\) | ||||
0.0128151 | + | 0.999918i | \(0.495921\pi\) | |||||||
\(752\) | −2.12762 | −0.0775865 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.1876 | −0.371012 | ||||||||
\(755\) | 42.4318 | 1.54425 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.7740 | −1.22754 | −0.613768 | − | 0.789486i | \(-0.710347\pi\) | ||||
−0.613768 | + | 0.789486i | \(0.710347\pi\) | |||||||
\(758\) | −54.7551 | −1.98879 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.8890 | −0.612630 | ||||||||
\(761\) | −33.2497 | −1.20530 | −0.602651 | − | 0.798005i | \(-0.705889\pi\) | ||||
−0.602651 | + | 0.798005i | \(0.705889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.298889 | −0.0108205 | ||||||||
\(764\) | 42.8327 | 1.54963 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.34112 | −0.120720 | ||||||||
\(767\) | −35.7378 | −1.29042 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.8729 | 1.00512 | 0.502561 | − | 0.864542i | \(-0.332391\pi\) | ||||
0.502561 | + | 0.864542i | \(0.332391\pi\) | |||||||
\(770\) | 14.2255 | 0.512653 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 33.9462 | 1.22175 | ||||||||
\(773\) | −39.7315 | −1.42904 | −0.714522 | − | 0.699613i | \(-0.753356\pi\) | ||||
−0.714522 | + | 0.699613i | \(0.753356\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.5573 | −0.486994 | ||||||||
\(776\) | 17.5165 | 0.628804 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −73.7654 | −2.64462 | ||||||||
\(779\) | −20.9222 | −0.749614 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.5511 | 0.377549 | ||||||||
\(782\) | 10.0702 | 0.360110 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.11655 | 0.111305 | ||||||||
\(785\) | −47.5573 | −1.69739 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.77874 | 0.241636 | 0.120818 | − | 0.992675i | \(-0.461448\pi\) | ||||
0.120818 | + | 0.992675i | \(0.461448\pi\) | |||||||
\(788\) | 35.9571 | 1.28092 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.1523 | −0.503516 | ||||||||
\(791\) | 21.8486 | 0.776848 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0875200 | 0.00310793 | ||||||||
\(794\) | −15.6031 | −0.553734 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.9867 | 0.779299 | ||||||||
\(797\) | −45.6601 | −1.61737 | −0.808683 | − | 0.588245i | \(-0.799819\pi\) | ||||
−0.808683 | + | 0.588245i | \(0.799819\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.3443 | −0.401333 | ||||||||
\(800\) | 15.3251 | 0.541824 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.94872 | 0.210057 | ||||||||
\(803\) | −21.7177 | −0.766401 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.91775 | −0.173328 | ||||||||
\(806\) | 59.0740 | 2.08079 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 30.1429 | 1.06042 | ||||||||
\(809\) | 30.4752 | 1.07145 | 0.535725 | − | 0.844392i | \(-0.320038\pi\) | ||||
0.535725 | + | 0.844392i | \(0.320038\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.2770 | 1.73035 | 0.865174 | − | 0.501472i | \(-0.167208\pi\) | ||||
0.865174 | + | 0.501472i | \(0.167208\pi\) | |||||||
\(812\) | −5.51756 | −0.193628 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 17.1231 | 0.600164 | ||||||||
\(815\) | 60.2590 | 2.11078 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.1198 | −0.493991 | ||||||||
\(818\) | 18.4730 | 0.645893 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −64.4567 | −2.25093 | ||||||||
\(821\) | 11.2716 | 0.393382 | 0.196691 | − | 0.980466i | \(-0.436980\pi\) | ||||
0.196691 | + | 0.980466i | \(0.436980\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.9336 | −1.00856 | −0.504282 | − | 0.863539i | \(-0.668243\pi\) | ||||
−0.504282 | + | 0.863539i | \(0.668243\pi\) | |||||||
\(824\) | −1.70339 | −0.0593405 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −32.0922 | −1.11663 | ||||||||
\(827\) | 28.1166 | 0.977711 | 0.488855 | − | 0.872365i | \(-0.337415\pi\) | ||||
0.488855 | + | 0.872365i | \(0.337415\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.8841 | −0.864262 | −0.432131 | − | 0.901811i | \(-0.642238\pi\) | ||||
−0.432131 | + | 0.901811i | \(0.642238\pi\) | |||||||
\(830\) | −52.6285 | −1.82676 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −59.1404 | −2.05032 | ||||||||
\(833\) | 16.6171 | 0.575750 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −56.8119 | −1.96606 | ||||||||
\(836\) | 10.4662 | 0.361980 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 39.8080 | 1.37515 | ||||||||
\(839\) | 1.16783 | 0.0403180 | 0.0201590 | − | 0.999797i | \(-0.493583\pi\) | ||||
0.0201590 | + | 0.999797i | \(0.493583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −44.5768 | −1.53622 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15.0327 | −0.517446 | ||||||||
\(845\) | 20.5761 | 0.707840 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.9551 | 0.582584 | ||||||||
\(848\) | −6.00910 | −0.206353 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 23.5445 | 0.807570 | ||||||||
\(851\) | −5.91943 | −0.202915 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.52282 | 0.257577 | 0.128788 | − | 0.991672i | \(-0.458891\pi\) | ||||
0.128788 | + | 0.991672i | \(0.458891\pi\) | |||||||
\(854\) | 0.0785920 | 0.00268936 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.87381 | 0.200763 | ||||||||
\(857\) | −37.9847 | −1.29753 | −0.648766 | − | 0.760988i | \(-0.724715\pi\) | ||||
−0.648766 | + | 0.760988i | \(0.724715\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.5333 | −0.700588 | −0.350294 | − | 0.936640i | \(-0.613918\pi\) | ||||
−0.350294 | + | 0.936640i | \(0.613918\pi\) | |||||||
\(860\) | −43.5003 | −1.48335 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37.3731 | −1.27293 | ||||||||
\(863\) | 22.2904 | 0.758773 | 0.379386 | − | 0.925238i | \(-0.376135\pi\) | ||||
0.379386 | + | 0.925238i | \(0.376135\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 53.8999 | 1.83265 | ||||||||
\(866\) | 75.3084 | 2.55908 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 31.9941 | 1.08595 | ||||||||
\(869\) | 2.99897 | 0.101733 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −70.4438 | −2.38690 | ||||||||
\(872\) | −0.384106 | −0.0130075 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.99906 | −0.202921 | ||||||||
\(875\) | 13.0909 | 0.442552 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.67076 | −0.123953 | −0.0619763 | − | 0.998078i | \(-0.519740\pi\) | ||||
−0.0619763 | + | 0.998078i | \(0.519740\pi\) | |||||||
\(878\) | −40.7852 | −1.37643 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.93684 | −0.0990008 | ||||||||
\(881\) | 6.66693 | 0.224615 | 0.112307 | − | 0.993674i | \(-0.464176\pi\) | ||||
0.112307 | + | 0.993674i | \(0.464176\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.4496 | 0.654530 | 0.327265 | − | 0.944933i | \(-0.393873\pi\) | ||||
0.327265 | + | 0.944933i | \(0.393873\pi\) | |||||||
\(884\) | −61.8749 | −2.08108 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 59.5693 | 2.00127 | ||||||||
\(887\) | 6.36719 | 0.213789 | 0.106895 | − | 0.994270i | \(-0.465909\pi\) | ||||
0.106895 | + | 0.994270i | \(0.465909\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.4078 | 0.785074 | ||||||||
\(890\) | −107.459 | −3.60205 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −37.9833 | −1.27177 | ||||||||
\(893\) | 6.75806 | 0.226150 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.88869 | 0.0631320 | ||||||||
\(896\) | −29.3084 | −0.979125 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 71.5754 | 2.38850 | ||||||||
\(899\) | −5.79860 | −0.193394 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.0400 | −1.06741 | ||||||||
\(902\) | 22.6470 | 0.754062 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 28.0779 | 0.933857 | ||||||||
\(905\) | −58.7970 | −1.95448 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.3211 | 1.67089 | 0.835443 | − | 0.549578i | \(-0.185211\pi\) | ||||
0.835443 | + | 0.549578i | \(0.185211\pi\) | |||||||
\(908\) | −44.8257 | −1.48759 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 50.1002 | 1.66081 | ||||||||
\(911\) | −44.4615 | −1.47307 | −0.736537 | − | 0.676397i | \(-0.763541\pi\) | ||||
−0.736537 | + | 0.676397i | \(0.763541\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.1523 | 0.369088 | ||||||||
\(914\) | 8.56308 | 0.283241 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −34.6792 | −1.14583 | ||||||||
\(917\) | 27.9489 | 0.922955 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.7767 | 1.60899 | 0.804497 | − | 0.593957i | \(-0.202435\pi\) | ||||
0.804497 | + | 0.593957i | \(0.202435\pi\) | |||||||
\(920\) | −6.31985 | −0.208359 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −35.0179 | −1.15325 | ||||||||
\(923\) | 37.1595 | 1.22312 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.8398 | −0.455051 | ||||||||
\(926\) | 71.9522 | 2.36449 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.55469 | 0.215168 | ||||||||
\(929\) | −41.3850 | −1.35780 | −0.678898 | − | 0.734232i | \(-0.737542\pi\) | ||||
−0.678898 | + | 0.734232i | \(0.737542\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.89922 | −0.324434 | ||||||||
\(932\) | −32.0586 | −1.05011 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 62.2433 | 2.03666 | ||||||||
\(935\) | −15.6590 | −0.512103 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.0228 | 0.490774 | 0.245387 | − | 0.969425i | \(-0.421085\pi\) | ||||
0.245387 | + | 0.969425i | \(0.421085\pi\) | |||||||
\(938\) | −63.2578 | −2.06544 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 20.8202 | 0.679079 | ||||||||
\(941\) | 28.3415 | 0.923907 | 0.461954 | − | 0.886904i | \(-0.347149\pi\) | ||||
0.461954 | + | 0.886904i | \(0.347149\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.82902 | −0.254948 | ||||||||
\(944\) | 6.62537 | 0.215637 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.2839 | 0.496922 | ||||||||
\(947\) | −14.4377 | −0.469164 | −0.234582 | − | 0.972096i | \(-0.575372\pi\) | ||||
−0.234582 | + | 0.972096i | \(0.575372\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −76.4864 | −2.48285 | ||||||||
\(950\) | −14.0260 | −0.455064 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −18.9997 | −0.615784 | ||||||||
\(953\) | 13.5038 | 0.437431 | 0.218715 | − | 0.975789i | \(-0.429813\pi\) | ||||
0.218715 | + | 0.975789i | \(0.429813\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.1764 | 1.23536 | ||||||||
\(956\) | −11.4320 | −0.369737 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 64.7648 | 2.09246 | ||||||||
\(959\) | 8.81736 | 0.284727 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.62375 | 0.0846371 | ||||||||
\(962\) | 60.3050 | 1.94431 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −34.9469 | −1.12556 | ||||||||
\(965\) | 30.2559 | 0.973972 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.4673 | 0.818974 | 0.409487 | − | 0.912316i | \(-0.365708\pi\) | ||||
0.409487 | + | 0.912316i | \(0.365708\pi\) | |||||||
\(968\) | 21.7892 | 0.700330 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 45.6566 | 1.46595 | ||||||||
\(971\) | 13.8575 | 0.444708 | 0.222354 | − | 0.974966i | \(-0.428626\pi\) | ||||
0.222354 | + | 0.974966i | \(0.428626\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.9181 | −0.510311 | ||||||||
\(974\) | 29.3008 | 0.938858 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.0162252 | −0.000519355 0 | ||||||||
\(977\) | −10.0587 | −0.321805 | −0.160902 | − | 0.986970i | \(-0.551440\pi\) | ||||
−0.160902 | + | 0.986970i | \(0.551440\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.7714 | 0.727776 | ||||||||
\(980\) | −30.4974 | −0.974204 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −37.5291 | −1.19760 | ||||||||
\(983\) | 33.1846 | 1.05843 | 0.529213 | − | 0.848489i | \(-0.322487\pi\) | ||||
0.529213 | + | 0.848489i | \(0.322487\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32.0482 | 1.02114 | ||||||||
\(986\) | 10.0702 | 0.320701 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 36.8603 | 1.17268 | ||||||||
\(989\) | −5.28362 | −0.168009 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −60.1166 | −1.90967 | −0.954834 | − | 0.297141i | \(-0.903967\pi\) | ||||
−0.954834 | + | 0.297141i | \(0.903967\pi\) | |||||||
\(992\) | −38.0080 | −1.20676 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 33.3688 | 1.05839 | ||||||||
\(995\) | 19.5966 | 0.621253 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.86405 | −0.217387 | −0.108693 | − | 0.994075i | \(-0.534667\pi\) | ||||
−0.108693 | + | 0.994075i | \(0.534667\pi\) | |||||||
\(998\) | −12.6720 | −0.401126 | ||||||||
\(999\) | 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 | 6003.2.a.t.1.3 | ✓ | 22 | |
3.2 | odd | 2 | 6003.2.a.u.1.20 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.t.1.3 | ✓ | 22 | 1.1 | even | 1 | trivial | |
6003.2.a.u.1.20 | yes | 22 | 3.2 | odd | 2 |