Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.316645497.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 12x^{4} + 24x^{3} + 13x^{2} - 24x + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.19765\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.19765 | 1.26881 | 0.634406 | − | 0.773000i | \(-0.281245\pi\) | ||||
0.634406 | + | 0.773000i | \(0.281245\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.12703 | 1.39845 | 0.699225 | − | 0.714901i | \(-0.253528\pi\) | ||||
0.699225 | + | 0.714901i | \(0.253528\pi\) | |||||||
\(6\) | 2.19765 | 0.897186 | ||||||||
\(7\) | 2.17944 | 0.823750 | 0.411875 | − | 0.911240i | \(-0.364874\pi\) | ||||
0.411875 | + | 0.911240i | \(0.364874\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.82965 | 0.609884 | ||||||||
\(10\) | 3.12703 | 0.988854 | ||||||||
\(11\) | 3.12703 | 0.942835 | 0.471418 | − | 0.881910i | \(-0.343742\pi\) | ||||
0.471418 | + | 0.881910i | \(0.343742\pi\) | |||||||
\(12\) | 2.19765 | 0.634406 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.17944 | 0.582479 | ||||||||
\(15\) | 6.87211 | 1.77437 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.10300 | −1.72273 | −0.861365 | − | 0.507986i | \(-0.830390\pi\) | ||||
−0.861365 | + | 0.507986i | \(0.830390\pi\) | |||||||
\(18\) | 1.82965 | 0.431253 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 3.12703 | 0.699225 | ||||||||
\(21\) | 4.78963 | 1.04518 | ||||||||
\(22\) | 3.12703 | 0.666685 | ||||||||
\(23\) | −0.644393 | −0.134365 | −0.0671826 | − | 0.997741i | \(-0.521401\pi\) | ||||
−0.0671826 | + | 0.997741i | \(0.521401\pi\) | |||||||
\(24\) | 2.19765 | 0.448593 | ||||||||
\(25\) | 4.77832 | 0.955664 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.57201 | −0.494984 | ||||||||
\(28\) | 2.17944 | 0.411875 | ||||||||
\(29\) | 0.426223 | 0.0791477 | 0.0395738 | − | 0.999217i | \(-0.487400\pi\) | ||||
0.0395738 | + | 0.999217i | \(0.487400\pi\) | |||||||
\(30\) | 6.87211 | 1.25467 | ||||||||
\(31\) | −4.85159 | −0.871371 | −0.435685 | − | 0.900099i | \(-0.643494\pi\) | ||||
−0.435685 | + | 0.900099i | \(0.643494\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.87211 | 1.19628 | ||||||||
\(34\) | −7.10300 | −1.21815 | ||||||||
\(35\) | 6.81517 | 1.15197 | ||||||||
\(36\) | 1.82965 | 0.304942 | ||||||||
\(37\) | 7.52510 | 1.23712 | 0.618559 | − | 0.785738i | \(-0.287717\pi\) | ||||
0.618559 | + | 0.785738i | \(0.287717\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.12703 | 0.494427 | ||||||||
\(41\) | −0.117941 | −0.0184193 | −0.00920967 | − | 0.999958i | \(-0.502932\pi\) | ||||
−0.00920967 | + | 0.999958i | \(0.502932\pi\) | |||||||
\(42\) | 4.78963 | 0.739057 | ||||||||
\(43\) | 2.42854 | 0.370348 | 0.185174 | − | 0.982706i | \(-0.440715\pi\) | ||||
0.185174 | + | 0.982706i | \(0.440715\pi\) | |||||||
\(44\) | 3.12703 | 0.471418 | ||||||||
\(45\) | 5.72138 | 0.852893 | ||||||||
\(46\) | −0.644393 | −0.0950106 | ||||||||
\(47\) | 6.12703 | 0.893719 | 0.446860 | − | 0.894604i | \(-0.352542\pi\) | ||||
0.446860 | + | 0.894604i | \(0.352542\pi\) | |||||||
\(48\) | 2.19765 | 0.317203 | ||||||||
\(49\) | −2.25005 | −0.321436 | ||||||||
\(50\) | 4.77832 | 0.675757 | ||||||||
\(51\) | −15.6099 | −2.18582 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.11436 | 0.565151 | 0.282575 | − | 0.959245i | \(-0.408811\pi\) | ||||
0.282575 | + | 0.959245i | \(0.408811\pi\) | |||||||
\(54\) | −2.57201 | −0.350006 | ||||||||
\(55\) | 9.77832 | 1.31851 | ||||||||
\(56\) | 2.17944 | 0.291240 | ||||||||
\(57\) | −2.19765 | −0.291085 | ||||||||
\(58\) | 0.426223 | 0.0559658 | ||||||||
\(59\) | −10.6322 | −1.38420 | −0.692099 | − | 0.721803i | \(-0.743314\pi\) | ||||
−0.692099 | + | 0.721803i | \(0.743314\pi\) | |||||||
\(60\) | 6.87211 | 0.887186 | ||||||||
\(61\) | 8.65802 | 1.10855 | 0.554273 | − | 0.832335i | \(-0.312996\pi\) | ||||
0.554273 | + | 0.832335i | \(0.312996\pi\) | |||||||
\(62\) | −4.85159 | −0.616152 | ||||||||
\(63\) | 3.98761 | 0.502392 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.87211 | 0.845898 | ||||||||
\(67\) | 1.75463 | 0.214362 | 0.107181 | − | 0.994240i | \(-0.465818\pi\) | ||||
0.107181 | + | 0.994240i | \(0.465818\pi\) | |||||||
\(68\) | −7.10300 | −0.861365 | ||||||||
\(69\) | −1.41615 | −0.170484 | ||||||||
\(70\) | 6.81517 | 0.814568 | ||||||||
\(71\) | 10.2346 | 1.21463 | 0.607313 | − | 0.794463i | \(-0.292248\pi\) | ||||
0.607313 | + | 0.794463i | \(0.292248\pi\) | |||||||
\(72\) | 1.82965 | 0.215627 | ||||||||
\(73\) | 13.3753 | 1.56546 | 0.782728 | − | 0.622363i | \(-0.213827\pi\) | ||||
0.782728 | + | 0.622363i | \(0.213827\pi\) | |||||||
\(74\) | 7.52510 | 0.874775 | ||||||||
\(75\) | 10.5011 | 1.21256 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 6.81517 | 0.776660 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3371 | 1.27552 | 0.637760 | − | 0.770235i | \(-0.279861\pi\) | ||||
0.637760 | + | 0.770235i | \(0.279861\pi\) | |||||||
\(80\) | 3.12703 | 0.349613 | ||||||||
\(81\) | −11.1413 | −1.23793 | ||||||||
\(82\) | −0.117941 | −0.0130244 | ||||||||
\(83\) | −12.5884 | −1.38175 | −0.690876 | − | 0.722973i | \(-0.742775\pi\) | ||||
−0.690876 | + | 0.722973i | \(0.742775\pi\) | |||||||
\(84\) | 4.78963 | 0.522592 | ||||||||
\(85\) | −22.2113 | −2.40915 | ||||||||
\(86\) | 2.42854 | 0.261876 | ||||||||
\(87\) | 0.936688 | 0.100423 | ||||||||
\(88\) | 3.12703 | 0.333343 | ||||||||
\(89\) | 1.43889 | 0.152522 | 0.0762612 | − | 0.997088i | \(-0.475702\pi\) | ||||
0.0762612 | + | 0.997088i | \(0.475702\pi\) | |||||||
\(90\) | 5.72138 | 0.603086 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.644393 | −0.0671826 | ||||||||
\(93\) | −10.6621 | −1.10561 | ||||||||
\(94\) | 6.12703 | 0.631955 | ||||||||
\(95\) | −3.12703 | −0.320827 | ||||||||
\(96\) | 2.19765 | 0.224296 | ||||||||
\(97\) | −11.9346 | −1.21178 | −0.605888 | − | 0.795550i | \(-0.707182\pi\) | ||||
−0.605888 | + | 0.795550i | \(0.707182\pi\) | |||||||
\(98\) | −2.25005 | −0.227290 | ||||||||
\(99\) | 5.72138 | 0.575020 | ||||||||
\(100\) | 4.77832 | 0.477832 | ||||||||
\(101\) | −12.1844 | −1.21239 | −0.606197 | − | 0.795315i | \(-0.707306\pi\) | ||||
−0.606197 | + | 0.795315i | \(0.707306\pi\) | |||||||
\(102\) | −15.6099 | −1.54561 | ||||||||
\(103\) | 10.5338 | 1.03792 | 0.518961 | − | 0.854798i | \(-0.326319\pi\) | ||||
0.518961 | + | 0.854798i | \(0.326319\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.9773 | 1.46164 | ||||||||
\(106\) | 4.11436 | 0.399622 | ||||||||
\(107\) | 5.67809 | 0.548922 | 0.274461 | − | 0.961598i | \(-0.411501\pi\) | ||||
0.274461 | + | 0.961598i | \(0.411501\pi\) | |||||||
\(108\) | −2.57201 | −0.247492 | ||||||||
\(109\) | −11.7186 | −1.12243 | −0.561217 | − | 0.827669i | \(-0.689667\pi\) | ||||
−0.561217 | + | 0.827669i | \(0.689667\pi\) | |||||||
\(110\) | 9.77832 | 0.932326 | ||||||||
\(111\) | 16.5375 | 1.56967 | ||||||||
\(112\) | 2.17944 | 0.205937 | ||||||||
\(113\) | −0.945828 | −0.0889760 | −0.0444880 | − | 0.999010i | \(-0.514166\pi\) | ||||
−0.0444880 | + | 0.999010i | \(0.514166\pi\) | |||||||
\(114\) | −2.19765 | −0.205828 | ||||||||
\(115\) | −2.01504 | −0.187903 | ||||||||
\(116\) | 0.426223 | 0.0395738 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.6322 | −0.978775 | ||||||||
\(119\) | −15.4805 | −1.41910 | ||||||||
\(120\) | 6.87211 | 0.627335 | ||||||||
\(121\) | −1.22168 | −0.111062 | ||||||||
\(122\) | 8.65802 | 0.783860 | ||||||||
\(123\) | −0.259193 | −0.0233707 | ||||||||
\(124\) | −4.85159 | −0.435685 | ||||||||
\(125\) | −0.693196 | −0.0620013 | ||||||||
\(126\) | 3.98761 | 0.355245 | ||||||||
\(127\) | 9.51474 | 0.844296 | 0.422148 | − | 0.906527i | \(-0.361276\pi\) | ||||
0.422148 | + | 0.906527i | \(0.361276\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.33707 | 0.469902 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.94454 | 0.257266 | 0.128633 | − | 0.991692i | \(-0.458941\pi\) | ||||
0.128633 | + | 0.991692i | \(0.458941\pi\) | |||||||
\(132\) | 6.87211 | 0.598140 | ||||||||
\(133\) | −2.17944 | −0.188981 | ||||||||
\(134\) | 1.75463 | 0.151577 | ||||||||
\(135\) | −8.04276 | −0.692210 | ||||||||
\(136\) | −7.10300 | −0.609077 | ||||||||
\(137\) | −4.54962 | −0.388701 | −0.194350 | − | 0.980932i | \(-0.562260\pi\) | ||||
−0.194350 | + | 0.980932i | \(0.562260\pi\) | |||||||
\(138\) | −1.41615 | −0.120551 | ||||||||
\(139\) | −14.9108 | −1.26472 | −0.632359 | − | 0.774675i | \(-0.717913\pi\) | ||||
−0.632359 | + | 0.774675i | \(0.717913\pi\) | |||||||
\(140\) | 6.81517 | 0.575987 | ||||||||
\(141\) | 13.4651 | 1.13396 | ||||||||
\(142\) | 10.2346 | 0.858870 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.82965 | 0.152471 | ||||||||
\(145\) | 1.33281 | 0.110684 | ||||||||
\(146\) | 13.3753 | 1.10695 | ||||||||
\(147\) | −4.94482 | −0.407842 | ||||||||
\(148\) | 7.52510 | 0.618559 | ||||||||
\(149\) | 22.5037 | 1.84358 | 0.921788 | − | 0.387694i | \(-0.126728\pi\) | ||||
0.921788 | + | 0.387694i | \(0.126728\pi\) | |||||||
\(150\) | 10.5011 | 0.857408 | ||||||||
\(151\) | 9.30065 | 0.756876 | 0.378438 | − | 0.925627i | \(-0.376461\pi\) | ||||
0.378438 | + | 0.925627i | \(0.376461\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −12.9960 | −1.05067 | ||||||||
\(154\) | 6.81517 | 0.549182 | ||||||||
\(155\) | −15.1711 | −1.21857 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.58803 | 0.206547 | 0.103274 | − | 0.994653i | \(-0.467068\pi\) | ||||
0.103274 | + | 0.994653i | \(0.467068\pi\) | |||||||
\(158\) | 11.3371 | 0.901929 | ||||||||
\(159\) | 9.04191 | 0.717070 | ||||||||
\(160\) | 3.12703 | 0.247213 | ||||||||
\(161\) | −1.40441 | −0.110683 | ||||||||
\(162\) | −11.1413 | −0.875346 | ||||||||
\(163\) | −22.3172 | −1.74802 | −0.874008 | − | 0.485911i | \(-0.838488\pi\) | ||||
−0.874008 | + | 0.485911i | \(0.838488\pi\) | |||||||
\(164\) | −0.117941 | −0.00920967 | ||||||||
\(165\) | 21.4893 | 1.67294 | ||||||||
\(166\) | −12.5884 | −0.977046 | ||||||||
\(167\) | −23.2517 | −1.79927 | −0.899636 | − | 0.436640i | \(-0.856168\pi\) | ||||
−0.899636 | + | 0.436640i | \(0.856168\pi\) | |||||||
\(168\) | 4.78963 | 0.369528 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −22.2113 | −1.70353 | ||||||||
\(171\) | −1.82965 | −0.139917 | ||||||||
\(172\) | 2.42854 | 0.185174 | ||||||||
\(173\) | −21.7696 | −1.65511 | −0.827557 | − | 0.561381i | \(-0.810270\pi\) | ||||
−0.827557 | + | 0.561381i | \(0.810270\pi\) | |||||||
\(174\) | 0.936688 | 0.0710101 | ||||||||
\(175\) | 10.4141 | 0.787228 | ||||||||
\(176\) | 3.12703 | 0.235709 | ||||||||
\(177\) | −23.3659 | −1.75629 | ||||||||
\(178\) | 1.43889 | 0.107850 | ||||||||
\(179\) | −24.6147 | −1.83979 | −0.919893 | − | 0.392170i | \(-0.871725\pi\) | ||||
−0.919893 | + | 0.392170i | \(0.871725\pi\) | |||||||
\(180\) | 5.72138 | 0.426446 | ||||||||
\(181\) | −3.87802 | −0.288251 | −0.144126 | − | 0.989559i | \(-0.546037\pi\) | ||||
−0.144126 | + | 0.989559i | \(0.546037\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.0273 | 1.40654 | ||||||||
\(184\) | −0.644393 | −0.0475053 | ||||||||
\(185\) | 23.5312 | 1.73005 | ||||||||
\(186\) | −10.6621 | −0.781781 | ||||||||
\(187\) | −22.2113 | −1.62425 | ||||||||
\(188\) | 6.12703 | 0.446860 | ||||||||
\(189\) | −5.60554 | −0.407743 | ||||||||
\(190\) | −3.12703 | −0.226859 | ||||||||
\(191\) | 14.5288 | 1.05127 | 0.525634 | − | 0.850711i | \(-0.323828\pi\) | ||||
0.525634 | + | 0.850711i | \(0.323828\pi\) | |||||||
\(192\) | 2.19765 | 0.158602 | ||||||||
\(193\) | −25.5087 | −1.83616 | −0.918080 | − | 0.396396i | \(-0.870261\pi\) | ||||
−0.918080 | + | 0.396396i | \(0.870261\pi\) | |||||||
\(194\) | −11.9346 | −0.856855 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.25005 | −0.160718 | ||||||||
\(197\) | −5.12980 | −0.365483 | −0.182742 | − | 0.983161i | \(-0.558497\pi\) | ||||
−0.182742 | + | 0.983161i | \(0.558497\pi\) | |||||||
\(198\) | 5.72138 | 0.406601 | ||||||||
\(199\) | −6.58770 | −0.466989 | −0.233495 | − | 0.972358i | \(-0.575016\pi\) | ||||
−0.233495 | + | 0.972358i | \(0.575016\pi\) | |||||||
\(200\) | 4.77832 | 0.337878 | ||||||||
\(201\) | 3.85605 | 0.271985 | ||||||||
\(202\) | −12.1844 | −0.857291 | ||||||||
\(203\) | 0.928927 | 0.0651979 | ||||||||
\(204\) | −15.6099 | −1.09291 | ||||||||
\(205\) | −0.368806 | −0.0257585 | ||||||||
\(206\) | 10.5338 | 0.733922 | ||||||||
\(207\) | −1.17902 | −0.0819472 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.12703 | −0.216301 | ||||||||
\(210\) | 14.9773 | 1.03353 | ||||||||
\(211\) | −4.98682 | −0.343307 | −0.171654 | − | 0.985157i | \(-0.554911\pi\) | ||||
−0.171654 | + | 0.985157i | \(0.554911\pi\) | |||||||
\(212\) | 4.11436 | 0.282575 | ||||||||
\(213\) | 22.4921 | 1.54113 | ||||||||
\(214\) | 5.67809 | 0.388146 | ||||||||
\(215\) | 7.59411 | 0.517914 | ||||||||
\(216\) | −2.57201 | −0.175003 | ||||||||
\(217\) | −10.5737 | −0.717791 | ||||||||
\(218\) | −11.7186 | −0.793681 | ||||||||
\(219\) | 29.3941 | 1.98627 | ||||||||
\(220\) | 9.77832 | 0.659254 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 16.5375 | 1.10992 | ||||||||
\(223\) | −22.9805 | −1.53889 | −0.769445 | − | 0.638713i | \(-0.779467\pi\) | ||||
−0.769445 | + | 0.638713i | \(0.779467\pi\) | |||||||
\(224\) | 2.17944 | 0.145620 | ||||||||
\(225\) | 8.74267 | 0.582844 | ||||||||
\(226\) | −0.945828 | −0.0629155 | ||||||||
\(227\) | 5.49722 | 0.364863 | 0.182432 | − | 0.983219i | \(-0.441603\pi\) | ||||
0.182432 | + | 0.983219i | \(0.441603\pi\) | |||||||
\(228\) | −2.19765 | −0.145543 | ||||||||
\(229\) | −1.52318 | −0.100655 | −0.0503274 | − | 0.998733i | \(-0.516026\pi\) | ||||
−0.0503274 | + | 0.998733i | \(0.516026\pi\) | |||||||
\(230\) | −2.01504 | −0.132868 | ||||||||
\(231\) | 14.9773 | 0.985436 | ||||||||
\(232\) | 0.426223 | 0.0279829 | ||||||||
\(233\) | 25.9377 | 1.69924 | 0.849618 | − | 0.527399i | \(-0.176833\pi\) | ||||
0.849618 | + | 0.527399i | \(0.176833\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.1594 | 1.24982 | ||||||||
\(236\) | −10.6322 | −0.692099 | ||||||||
\(237\) | 24.9149 | 1.61839 | ||||||||
\(238\) | −15.4805 | −1.00345 | ||||||||
\(239\) | −5.55924 | −0.359597 | −0.179799 | − | 0.983703i | \(-0.557545\pi\) | ||||
−0.179799 | + | 0.983703i | \(0.557545\pi\) | |||||||
\(240\) | 6.87211 | 0.443593 | ||||||||
\(241\) | 11.9583 | 0.770302 | 0.385151 | − | 0.922853i | \(-0.374149\pi\) | ||||
0.385151 | + | 0.922853i | \(0.374149\pi\) | |||||||
\(242\) | −1.22168 | −0.0785325 | ||||||||
\(243\) | −16.7687 | −1.07571 | ||||||||
\(244\) | 8.65802 | 0.554273 | ||||||||
\(245\) | −7.03599 | −0.449513 | ||||||||
\(246\) | −0.259193 | −0.0165256 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4.85159 | −0.308076 | ||||||||
\(249\) | −27.6648 | −1.75318 | ||||||||
\(250\) | −0.693196 | −0.0438416 | ||||||||
\(251\) | −22.4814 | −1.41902 | −0.709508 | − | 0.704697i | \(-0.751083\pi\) | ||||
−0.709508 | + | 0.704697i | \(0.751083\pi\) | |||||||
\(252\) | 3.98761 | 0.251196 | ||||||||
\(253\) | −2.01504 | −0.126684 | ||||||||
\(254\) | 9.51474 | 0.597008 | ||||||||
\(255\) | −48.8126 | −3.05676 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.85032 | 0.302555 | 0.151277 | − | 0.988491i | \(-0.451661\pi\) | ||||
0.151277 | + | 0.988491i | \(0.451661\pi\) | |||||||
\(258\) | 5.33707 | 0.332271 | ||||||||
\(259\) | 16.4005 | 1.01908 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.779840 | 0.0482709 | ||||||||
\(262\) | 2.94454 | 0.181914 | ||||||||
\(263\) | −10.1214 | −0.624109 | −0.312055 | − | 0.950064i | \(-0.601017\pi\) | ||||
−0.312055 | + | 0.950064i | \(0.601017\pi\) | |||||||
\(264\) | 6.87211 | 0.422949 | ||||||||
\(265\) | 12.8657 | 0.790335 | ||||||||
\(266\) | −2.17944 | −0.133630 | ||||||||
\(267\) | 3.16218 | 0.193522 | ||||||||
\(268\) | 1.75463 | 0.107181 | ||||||||
\(269\) | 7.99747 | 0.487614 | 0.243807 | − | 0.969824i | \(-0.421604\pi\) | ||||
0.243807 | + | 0.969824i | \(0.421604\pi\) | |||||||
\(270\) | −8.04276 | −0.489467 | ||||||||
\(271\) | 9.26475 | 0.562794 | 0.281397 | − | 0.959591i | \(-0.409202\pi\) | ||||
0.281397 | + | 0.959591i | \(0.409202\pi\) | |||||||
\(272\) | −7.10300 | −0.430683 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.54962 | −0.274853 | ||||||||
\(275\) | 14.9420 | 0.901034 | ||||||||
\(276\) | −1.41615 | −0.0852421 | ||||||||
\(277\) | 14.1772 | 0.851823 | 0.425912 | − | 0.904765i | \(-0.359953\pi\) | ||||
0.425912 | + | 0.904765i | \(0.359953\pi\) | |||||||
\(278\) | −14.9108 | −0.894291 | ||||||||
\(279\) | −8.87672 | −0.531435 | ||||||||
\(280\) | 6.81517 | 0.407284 | ||||||||
\(281\) | −27.3738 | −1.63299 | −0.816493 | − | 0.577355i | \(-0.804085\pi\) | ||||
−0.816493 | + | 0.577355i | \(0.804085\pi\) | |||||||
\(282\) | 13.4651 | 0.801832 | ||||||||
\(283\) | 23.5136 | 1.39774 | 0.698868 | − | 0.715250i | \(-0.253687\pi\) | ||||
0.698868 | + | 0.715250i | \(0.253687\pi\) | |||||||
\(284\) | 10.2346 | 0.607313 | ||||||||
\(285\) | −6.87211 | −0.407069 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.257046 | −0.0151729 | ||||||||
\(288\) | 1.82965 | 0.107813 | ||||||||
\(289\) | 33.4526 | 1.96780 | ||||||||
\(290\) | 1.33281 | 0.0782655 | ||||||||
\(291\) | −26.2281 | −1.53752 | ||||||||
\(292\) | 13.3753 | 0.782728 | ||||||||
\(293\) | 11.1201 | 0.649645 | 0.324823 | − | 0.945775i | \(-0.394695\pi\) | ||||
0.324823 | + | 0.945775i | \(0.394695\pi\) | |||||||
\(294\) | −4.94482 | −0.288388 | ||||||||
\(295\) | −33.2473 | −1.93573 | ||||||||
\(296\) | 7.52510 | 0.437387 | ||||||||
\(297\) | −8.04276 | −0.466688 | ||||||||
\(298\) | 22.5037 | 1.30361 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 10.5011 | 0.606279 | ||||||||
\(301\) | 5.29284 | 0.305074 | ||||||||
\(302\) | 9.30065 | 0.535192 | ||||||||
\(303\) | −26.7770 | −1.53830 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 27.0739 | 1.55025 | ||||||||
\(306\) | −12.9960 | −0.742933 | ||||||||
\(307\) | −10.2579 | −0.585450 | −0.292725 | − | 0.956197i | \(-0.594562\pi\) | ||||
−0.292725 | + | 0.956197i | \(0.594562\pi\) | |||||||
\(308\) | 6.81517 | 0.388330 | ||||||||
\(309\) | 23.1495 | 1.31693 | ||||||||
\(310\) | −15.1711 | −0.861658 | ||||||||
\(311\) | 13.8693 | 0.786455 | 0.393228 | − | 0.919441i | \(-0.371358\pi\) | ||||
0.393228 | + | 0.919441i | \(0.371358\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.37717 | −0.190889 | −0.0954446 | − | 0.995435i | \(-0.530427\pi\) | ||||
−0.0954446 | + | 0.995435i | \(0.530427\pi\) | |||||||
\(314\) | 2.58803 | 0.146051 | ||||||||
\(315\) | 12.4694 | 0.702570 | ||||||||
\(316\) | 11.3371 | 0.637760 | ||||||||
\(317\) | 6.12834 | 0.344202 | 0.172101 | − | 0.985079i | \(-0.444944\pi\) | ||||
0.172101 | + | 0.985079i | \(0.444944\pi\) | |||||||
\(318\) | 9.04191 | 0.507045 | ||||||||
\(319\) | 1.33281 | 0.0746232 | ||||||||
\(320\) | 3.12703 | 0.174806 | ||||||||
\(321\) | 12.4784 | 0.696479 | ||||||||
\(322\) | −1.40441 | −0.0782649 | ||||||||
\(323\) | 7.10300 | 0.395221 | ||||||||
\(324\) | −11.1413 | −0.618963 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −22.3172 | −1.23603 | ||||||||
\(327\) | −25.7533 | −1.42416 | ||||||||
\(328\) | −0.117941 | −0.00651222 | ||||||||
\(329\) | 13.3535 | 0.736201 | ||||||||
\(330\) | 21.4893 | 1.18295 | ||||||||
\(331\) | 0.0943337 | 0.00518505 | 0.00259253 | − | 0.999997i | \(-0.499175\pi\) | ||||
0.00259253 | + | 0.999997i | \(0.499175\pi\) | |||||||
\(332\) | −12.5884 | −0.690876 | ||||||||
\(333\) | 13.7683 | 0.754499 | ||||||||
\(334\) | −23.2517 | −1.27228 | ||||||||
\(335\) | 5.48677 | 0.299774 | ||||||||
\(336\) | 4.78963 | 0.261296 | ||||||||
\(337\) | −9.25406 | −0.504101 | −0.252050 | − | 0.967714i | \(-0.581105\pi\) | ||||
−0.252050 | + | 0.967714i | \(0.581105\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.07860 | −0.112894 | ||||||||
\(340\) | −22.2113 | −1.20458 | ||||||||
\(341\) | −15.1711 | −0.821559 | ||||||||
\(342\) | −1.82965 | −0.0989363 | ||||||||
\(343\) | −20.1599 | −1.08853 | ||||||||
\(344\) | 2.42854 | 0.130938 | ||||||||
\(345\) | −4.42834 | −0.238414 | ||||||||
\(346\) | −21.7696 | −1.17034 | ||||||||
\(347\) | −29.1677 | −1.56580 | −0.782902 | − | 0.622145i | \(-0.786261\pi\) | ||||
−0.782902 | + | 0.622145i | \(0.786261\pi\) | |||||||
\(348\) | 0.936688 | 0.0502117 | ||||||||
\(349\) | −29.5303 | −1.58072 | −0.790361 | − | 0.612641i | \(-0.790107\pi\) | ||||
−0.790361 | + | 0.612641i | \(0.790107\pi\) | |||||||
\(350\) | 10.4141 | 0.556654 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.12703 | 0.166671 | ||||||||
\(353\) | −29.0884 | −1.54822 | −0.774110 | − | 0.633052i | \(-0.781802\pi\) | ||||
−0.774110 | + | 0.633052i | \(0.781802\pi\) | |||||||
\(354\) | −23.3659 | −1.24188 | ||||||||
\(355\) | 32.0040 | 1.69859 | ||||||||
\(356\) | 1.43889 | 0.0762612 | ||||||||
\(357\) | −34.0208 | −1.80057 | ||||||||
\(358\) | −24.6147 | −1.30092 | ||||||||
\(359\) | −19.0423 | −1.00502 | −0.502508 | − | 0.864573i | \(-0.667589\pi\) | ||||
−0.502508 | + | 0.864573i | \(0.667589\pi\) | |||||||
\(360\) | 5.72138 | 0.301543 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −3.87802 | −0.203824 | ||||||||
\(363\) | −2.68482 | −0.140916 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 41.8249 | 2.18921 | ||||||||
\(366\) | 19.0273 | 0.994571 | ||||||||
\(367\) | 1.02770 | 0.0536456 | 0.0268228 | − | 0.999640i | \(-0.491461\pi\) | ||||
0.0268228 | + | 0.999640i | \(0.491461\pi\) | |||||||
\(368\) | −0.644393 | −0.0335913 | ||||||||
\(369\) | −0.215792 | −0.0112337 | ||||||||
\(370\) | 23.5312 | 1.22333 | ||||||||
\(371\) | 8.96699 | 0.465543 | ||||||||
\(372\) | −10.6621 | −0.552803 | ||||||||
\(373\) | 15.9433 | 0.825512 | 0.412756 | − | 0.910842i | \(-0.364566\pi\) | ||||
0.412756 | + | 0.910842i | \(0.364566\pi\) | |||||||
\(374\) | −22.2113 | −1.14852 | ||||||||
\(375\) | −1.52340 | −0.0786681 | ||||||||
\(376\) | 6.12703 | 0.315977 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −5.60554 | −0.288318 | ||||||||
\(379\) | 4.79302 | 0.246201 | 0.123100 | − | 0.992394i | \(-0.460716\pi\) | ||||
0.123100 | + | 0.992394i | \(0.460716\pi\) | |||||||
\(380\) | −3.12703 | −0.160413 | ||||||||
\(381\) | 20.9100 | 1.07125 | ||||||||
\(382\) | 14.5288 | 0.743359 | ||||||||
\(383\) | −21.8340 | −1.11567 | −0.557833 | − | 0.829953i | \(-0.688367\pi\) | ||||
−0.557833 | + | 0.829953i | \(0.688367\pi\) | |||||||
\(384\) | 2.19765 | 0.112148 | ||||||||
\(385\) | 21.3112 | 1.08612 | ||||||||
\(386\) | −25.5087 | −1.29836 | ||||||||
\(387\) | 4.44338 | 0.225870 | ||||||||
\(388\) | −11.9346 | −0.605888 | ||||||||
\(389\) | 16.3944 | 0.831231 | 0.415615 | − | 0.909540i | \(-0.363566\pi\) | ||||
0.415615 | + | 0.909540i | \(0.363566\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.57712 | 0.231475 | ||||||||
\(392\) | −2.25005 | −0.113645 | ||||||||
\(393\) | 6.47106 | 0.326422 | ||||||||
\(394\) | −5.12980 | −0.258436 | ||||||||
\(395\) | 35.4514 | 1.78375 | ||||||||
\(396\) | 5.72138 | 0.287510 | ||||||||
\(397\) | 8.32544 | 0.417842 | 0.208921 | − | 0.977933i | \(-0.433005\pi\) | ||||
0.208921 | + | 0.977933i | \(0.433005\pi\) | |||||||
\(398\) | −6.58770 | −0.330211 | ||||||||
\(399\) | −4.78963 | −0.239782 | ||||||||
\(400\) | 4.77832 | 0.238916 | ||||||||
\(401\) | 35.8203 | 1.78878 | 0.894390 | − | 0.447289i | \(-0.147610\pi\) | ||||
0.894390 | + | 0.447289i | \(0.147610\pi\) | |||||||
\(402\) | 3.85605 | 0.192322 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −12.1844 | −0.606197 | ||||||||
\(405\) | −34.8393 | −1.73118 | ||||||||
\(406\) | 0.928927 | 0.0461019 | ||||||||
\(407\) | 23.5312 | 1.16640 | ||||||||
\(408\) | −15.6099 | −0.772804 | ||||||||
\(409\) | 28.5608 | 1.41224 | 0.706121 | − | 0.708091i | \(-0.250444\pi\) | ||||
0.706121 | + | 0.708091i | \(0.250444\pi\) | |||||||
\(410\) | −0.368806 | −0.0182140 | ||||||||
\(411\) | −9.99847 | −0.493188 | ||||||||
\(412\) | 10.5338 | 0.518961 | ||||||||
\(413\) | −23.1723 | −1.14023 | ||||||||
\(414\) | −1.17902 | −0.0579454 | ||||||||
\(415\) | −39.3642 | −1.93231 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −32.7687 | −1.60469 | ||||||||
\(418\) | −3.12703 | −0.152948 | ||||||||
\(419\) | −39.0336 | −1.90692 | −0.953459 | − | 0.301522i | \(-0.902505\pi\) | ||||
−0.953459 | + | 0.301522i | \(0.902505\pi\) | |||||||
\(420\) | 14.9773 | 0.730819 | ||||||||
\(421\) | 35.6361 | 1.73680 | 0.868398 | − | 0.495867i | \(-0.165150\pi\) | ||||
0.868398 | + | 0.495867i | \(0.165150\pi\) | |||||||
\(422\) | −4.98682 | −0.242755 | ||||||||
\(423\) | 11.2103 | 0.545065 | ||||||||
\(424\) | 4.11436 | 0.199811 | ||||||||
\(425\) | −33.9404 | −1.64635 | ||||||||
\(426\) | 22.4921 | 1.08974 | ||||||||
\(427\) | 18.8696 | 0.913164 | ||||||||
\(428\) | 5.67809 | 0.274461 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.59411 | 0.366220 | ||||||||
\(431\) | 28.5835 | 1.37682 | 0.688408 | − | 0.725323i | \(-0.258310\pi\) | ||||
0.688408 | + | 0.725323i | \(0.258310\pi\) | |||||||
\(432\) | −2.57201 | −0.123746 | ||||||||
\(433\) | −24.3228 | −1.16888 | −0.584440 | − | 0.811437i | \(-0.698686\pi\) | ||||
−0.584440 | + | 0.811437i | \(0.698686\pi\) | |||||||
\(434\) | −10.5737 | −0.507555 | ||||||||
\(435\) | 2.92905 | 0.140437 | ||||||||
\(436\) | −11.7186 | −0.561217 | ||||||||
\(437\) | 0.644393 | 0.0308255 | ||||||||
\(438\) | 29.3941 | 1.40451 | ||||||||
\(439\) | −3.40022 | −0.162283 | −0.0811417 | − | 0.996703i | \(-0.525857\pi\) | ||||
−0.0811417 | + | 0.996703i | \(0.525857\pi\) | |||||||
\(440\) | 9.77832 | 0.466163 | ||||||||
\(441\) | −4.11682 | −0.196039 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.5029 | 0.784075 | 0.392038 | − | 0.919949i | \(-0.371770\pi\) | ||||
0.392038 | + | 0.919949i | \(0.371770\pi\) | |||||||
\(444\) | 16.5375 | 0.784835 | ||||||||
\(445\) | 4.49947 | 0.213295 | ||||||||
\(446\) | −22.9805 | −1.08816 | ||||||||
\(447\) | 49.4552 | 2.33915 | ||||||||
\(448\) | 2.17944 | 0.102969 | ||||||||
\(449\) | 7.72011 | 0.364335 | 0.182167 | − | 0.983268i | \(-0.441689\pi\) | ||||
0.182167 | + | 0.983268i | \(0.441689\pi\) | |||||||
\(450\) | 8.74267 | 0.412133 | ||||||||
\(451\) | −0.368806 | −0.0173664 | ||||||||
\(452\) | −0.945828 | −0.0444880 | ||||||||
\(453\) | 20.4395 | 0.960333 | ||||||||
\(454\) | 5.49722 | 0.257997 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.19765 | −0.102914 | ||||||||
\(457\) | 35.4938 | 1.66033 | 0.830165 | − | 0.557518i | \(-0.188246\pi\) | ||||
0.830165 | + | 0.557518i | \(0.188246\pi\) | |||||||
\(458\) | −1.52318 | −0.0711737 | ||||||||
\(459\) | 18.2690 | 0.852724 | ||||||||
\(460\) | −2.01504 | −0.0939516 | ||||||||
\(461\) | −14.3955 | −0.670467 | −0.335233 | − | 0.942135i | \(-0.608815\pi\) | ||||
−0.335233 | + | 0.942135i | \(0.608815\pi\) | |||||||
\(462\) | 14.9773 | 0.696809 | ||||||||
\(463\) | 2.13703 | 0.0993164 | 0.0496582 | − | 0.998766i | \(-0.484187\pi\) | ||||
0.0496582 | + | 0.998766i | \(0.484187\pi\) | |||||||
\(464\) | 0.426223 | 0.0197869 | ||||||||
\(465\) | −33.3406 | −1.54613 | ||||||||
\(466\) | 25.9377 | 1.20154 | ||||||||
\(467\) | 22.3298 | 1.03330 | 0.516651 | − | 0.856196i | \(-0.327179\pi\) | ||||
0.516651 | + | 0.856196i | \(0.327179\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.82410 | 0.176580 | ||||||||
\(470\) | 19.1594 | 0.883758 | ||||||||
\(471\) | 5.68757 | 0.262070 | ||||||||
\(472\) | −10.6322 | −0.489388 | ||||||||
\(473\) | 7.59411 | 0.349177 | ||||||||
\(474\) | 24.9149 | 1.14438 | ||||||||
\(475\) | −4.77832 | −0.219244 | ||||||||
\(476\) | −15.4805 | −0.709549 | ||||||||
\(477\) | 7.52785 | 0.344676 | ||||||||
\(478\) | −5.55924 | −0.254274 | ||||||||
\(479\) | 6.43997 | 0.294250 | 0.147125 | − | 0.989118i | \(-0.452998\pi\) | ||||
0.147125 | + | 0.989118i | \(0.452998\pi\) | |||||||
\(480\) | 6.87211 | 0.313667 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 11.9583 | 0.544686 | ||||||||
\(483\) | −3.08641 | −0.140436 | ||||||||
\(484\) | −1.22168 | −0.0555308 | ||||||||
\(485\) | −37.3199 | −1.69461 | ||||||||
\(486\) | −16.7687 | −0.760643 | ||||||||
\(487\) | −34.7098 | −1.57285 | −0.786427 | − | 0.617684i | \(-0.788071\pi\) | ||||
−0.786427 | + | 0.617684i | \(0.788071\pi\) | |||||||
\(488\) | 8.65802 | 0.391930 | ||||||||
\(489\) | −49.0453 | −2.21790 | ||||||||
\(490\) | −7.03599 | −0.317853 | ||||||||
\(491\) | 27.6996 | 1.25006 | 0.625032 | − | 0.780599i | \(-0.285086\pi\) | ||||
0.625032 | + | 0.780599i | \(0.285086\pi\) | |||||||
\(492\) | −0.259193 | −0.0116853 | ||||||||
\(493\) | −3.02746 | −0.136350 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.8909 | 0.804137 | ||||||||
\(496\) | −4.85159 | −0.217843 | ||||||||
\(497\) | 22.3057 | 1.00055 | ||||||||
\(498\) | −27.6648 | −1.23969 | ||||||||
\(499\) | −10.0199 | −0.448551 | −0.224276 | − | 0.974526i | \(-0.572002\pi\) | ||||
−0.224276 | + | 0.974526i | \(0.572002\pi\) | |||||||
\(500\) | −0.693196 | −0.0310007 | ||||||||
\(501\) | −51.0991 | −2.28294 | ||||||||
\(502\) | −22.4814 | −1.00340 | ||||||||
\(503\) | −0.0625293 | −0.00278804 | −0.00139402 | − | 0.999999i | \(-0.500444\pi\) | ||||
−0.00139402 | + | 0.999999i | \(0.500444\pi\) | |||||||
\(504\) | 3.98761 | 0.177622 | ||||||||
\(505\) | −38.1010 | −1.69547 | ||||||||
\(506\) | −2.01504 | −0.0895793 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.51474 | 0.422148 | ||||||||
\(509\) | −26.8041 | −1.18807 | −0.594035 | − | 0.804439i | \(-0.702466\pi\) | ||||
−0.594035 | + | 0.804439i | \(0.702466\pi\) | |||||||
\(510\) | −48.8126 | −2.16146 | ||||||||
\(511\) | 29.1506 | 1.28954 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.57201 | 0.113557 | ||||||||
\(514\) | 4.85032 | 0.213938 | ||||||||
\(515\) | 32.9394 | 1.45148 | ||||||||
\(516\) | 5.33707 | 0.234951 | ||||||||
\(517\) | 19.1594 | 0.842630 | ||||||||
\(518\) | 16.4005 | 0.720595 | ||||||||
\(519\) | −47.8420 | −2.10003 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.2646 | −0.931619 | −0.465810 | − | 0.884885i | \(-0.654237\pi\) | ||||
−0.465810 | + | 0.884885i | \(0.654237\pi\) | |||||||
\(522\) | 0.779840 | 0.0341327 | ||||||||
\(523\) | −11.6367 | −0.508838 | −0.254419 | − | 0.967094i | \(-0.581884\pi\) | ||||
−0.254419 | + | 0.967094i | \(0.581884\pi\) | |||||||
\(524\) | 2.94454 | 0.128633 | ||||||||
\(525\) | 22.8864 | 0.998845 | ||||||||
\(526\) | −10.1214 | −0.441312 | ||||||||
\(527\) | 34.4608 | 1.50114 | ||||||||
\(528\) | 6.87211 | 0.299070 | ||||||||
\(529\) | −22.5848 | −0.981946 | ||||||||
\(530\) | 12.8657 | 0.558852 | ||||||||
\(531\) | −19.4533 | −0.844200 | ||||||||
\(532\) | −2.17944 | −0.0944906 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.16218 | 0.136841 | ||||||||
\(535\) | 17.7556 | 0.767640 | ||||||||
\(536\) | 1.75463 | 0.0757883 | ||||||||
\(537\) | −54.0943 | −2.33434 | ||||||||
\(538\) | 7.99747 | 0.344795 | ||||||||
\(539\) | −7.03599 | −0.303061 | ||||||||
\(540\) | −8.04276 | −0.346105 | ||||||||
\(541\) | 11.0025 | 0.473033 | 0.236517 | − | 0.971627i | \(-0.423994\pi\) | ||||
0.236517 | + | 0.971627i | \(0.423994\pi\) | |||||||
\(542\) | 9.26475 | 0.397955 | ||||||||
\(543\) | −8.52252 | −0.365736 | ||||||||
\(544\) | −7.10300 | −0.304539 | ||||||||
\(545\) | −36.6443 | −1.56967 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −42.3946 | −1.81266 | −0.906332 | − | 0.422566i | \(-0.861129\pi\) | ||||
−0.906332 | + | 0.422566i | \(0.861129\pi\) | |||||||
\(548\) | −4.54962 | −0.194350 | ||||||||
\(549\) | 15.8412 | 0.676084 | ||||||||
\(550\) | 14.9420 | 0.637127 | ||||||||
\(551\) | −0.426223 | −0.0181577 | ||||||||
\(552\) | −1.41615 | −0.0602753 | ||||||||
\(553\) | 24.7084 | 1.05071 | ||||||||
\(554\) | 14.1772 | 0.602330 | ||||||||
\(555\) | 51.7133 | 2.19511 | ||||||||
\(556\) | −14.9108 | −0.632359 | ||||||||
\(557\) | 21.7486 | 0.921519 | 0.460760 | − | 0.887525i | \(-0.347577\pi\) | ||||
0.460760 | + | 0.887525i | \(0.347577\pi\) | |||||||
\(558\) | −8.87672 | −0.375781 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 6.81517 | 0.287993 | ||||||||
\(561\) | −48.8126 | −2.06087 | ||||||||
\(562\) | −27.3738 | −1.15470 | ||||||||
\(563\) | −6.23601 | −0.262817 | −0.131408 | − | 0.991328i | \(-0.541950\pi\) | ||||
−0.131408 | + | 0.991328i | \(0.541950\pi\) | |||||||
\(564\) | 13.4651 | 0.566981 | ||||||||
\(565\) | −2.95763 | −0.124429 | ||||||||
\(566\) | 23.5136 | 0.988349 | ||||||||
\(567\) | −24.2818 | −1.01974 | ||||||||
\(568\) | 10.2346 | 0.429435 | ||||||||
\(569\) | −24.7089 | −1.03585 | −0.517925 | − | 0.855426i | \(-0.673295\pi\) | ||||
−0.517925 | + | 0.855426i | \(0.673295\pi\) | |||||||
\(570\) | −6.87211 | −0.287841 | ||||||||
\(571\) | 12.5056 | 0.523342 | 0.261671 | − | 0.965157i | \(-0.415727\pi\) | ||||
0.261671 | + | 0.965157i | \(0.415727\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 31.9292 | 1.33386 | ||||||||
\(574\) | −0.257046 | −0.0107289 | ||||||||
\(575\) | −3.07912 | −0.128408 | ||||||||
\(576\) | 1.82965 | 0.0762355 | ||||||||
\(577\) | −23.2185 | −0.966599 | −0.483300 | − | 0.875455i | \(-0.660562\pi\) | ||||
−0.483300 | + | 0.875455i | \(0.660562\pi\) | |||||||
\(578\) | 33.4526 | 1.39144 | ||||||||
\(579\) | −56.0592 | −2.32974 | ||||||||
\(580\) | 1.33281 | 0.0553420 | ||||||||
\(581\) | −27.4355 | −1.13822 | ||||||||
\(582\) | −26.2281 | −1.08719 | ||||||||
\(583\) | 12.8657 | 0.532844 | ||||||||
\(584\) | 13.3753 | 0.553473 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.1201 | 0.459368 | ||||||||
\(587\) | −32.3213 | −1.33404 | −0.667022 | − | 0.745038i | \(-0.732431\pi\) | ||||
−0.667022 | + | 0.745038i | \(0.732431\pi\) | |||||||
\(588\) | −4.94482 | −0.203921 | ||||||||
\(589\) | 4.85159 | 0.199906 | ||||||||
\(590\) | −33.2473 | −1.36877 | ||||||||
\(591\) | −11.2735 | −0.463729 | ||||||||
\(592\) | 7.52510 | 0.309280 | ||||||||
\(593\) | −19.5435 | −0.802556 | −0.401278 | − | 0.915956i | \(-0.631434\pi\) | ||||
−0.401278 | + | 0.915956i | \(0.631434\pi\) | |||||||
\(594\) | −8.04276 | −0.329998 | ||||||||
\(595\) | −48.4081 | −1.98454 | ||||||||
\(596\) | 22.5037 | 0.921788 | ||||||||
\(597\) | −14.4774 | −0.592522 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.8796 | 0.975692 | 0.487846 | − | 0.872930i | \(-0.337783\pi\) | ||||
0.487846 | + | 0.872930i | \(0.337783\pi\) | |||||||
\(600\) | 10.5011 | 0.428704 | ||||||||
\(601\) | −1.52829 | −0.0623402 | −0.0311701 | − | 0.999514i | \(-0.509923\pi\) | ||||
−0.0311701 | + | 0.999514i | \(0.509923\pi\) | |||||||
\(602\) | 5.29284 | 0.215720 | ||||||||
\(603\) | 3.21035 | 0.130736 | ||||||||
\(604\) | 9.30065 | 0.378438 | ||||||||
\(605\) | −3.82023 | −0.155314 | ||||||||
\(606\) | −26.7770 | −1.08774 | ||||||||
\(607\) | 43.4059 | 1.76179 | 0.880896 | − | 0.473309i | \(-0.156941\pi\) | ||||
0.880896 | + | 0.473309i | \(0.156941\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 2.04145 | 0.0827238 | ||||||||
\(610\) | 27.0739 | 1.09619 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −12.9960 | −0.525333 | ||||||||
\(613\) | 36.6253 | 1.47928 | 0.739641 | − | 0.673001i | \(-0.234995\pi\) | ||||
0.739641 | + | 0.673001i | \(0.234995\pi\) | |||||||
\(614\) | −10.2579 | −0.413975 | ||||||||
\(615\) | −0.810506 | −0.0326827 | ||||||||
\(616\) | 6.81517 | 0.274591 | ||||||||
\(617\) | 37.2515 | 1.49969 | 0.749844 | − | 0.661614i | \(-0.230128\pi\) | ||||
0.749844 | + | 0.661614i | \(0.230128\pi\) | |||||||
\(618\) | 23.1495 | 0.931209 | ||||||||
\(619\) | 16.3273 | 0.656249 | 0.328124 | − | 0.944635i | \(-0.393584\pi\) | ||||
0.328124 | + | 0.944635i | \(0.393584\pi\) | |||||||
\(620\) | −15.1711 | −0.609284 | ||||||||
\(621\) | 1.65739 | 0.0665086 | ||||||||
\(622\) | 13.8693 | 0.556108 | ||||||||
\(623\) | 3.13598 | 0.125640 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.0593 | −1.04237 | ||||||||
\(626\) | −3.37717 | −0.134979 | ||||||||
\(627\) | −6.87211 | −0.274446 | ||||||||
\(628\) | 2.58803 | 0.103274 | ||||||||
\(629\) | −53.4507 | −2.13122 | ||||||||
\(630\) | 12.4694 | 0.496792 | ||||||||
\(631\) | −6.00903 | −0.239216 | −0.119608 | − | 0.992821i | \(-0.538164\pi\) | ||||
−0.119608 | + | 0.992821i | \(0.538164\pi\) | |||||||
\(632\) | 11.3371 | 0.450964 | ||||||||
\(633\) | −10.9593 | −0.435592 | ||||||||
\(634\) | 6.12834 | 0.243387 | ||||||||
\(635\) | 29.7529 | 1.18071 | ||||||||
\(636\) | 9.04191 | 0.358535 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.33281 | 0.0527666 | ||||||||
\(639\) | 18.7258 | 0.740781 | ||||||||
\(640\) | 3.12703 | 0.123607 | ||||||||
\(641\) | −14.9927 | −0.592178 | −0.296089 | − | 0.955160i | \(-0.595682\pi\) | ||||
−0.296089 | + | 0.955160i | \(0.595682\pi\) | |||||||
\(642\) | 12.4784 | 0.492485 | ||||||||
\(643\) | 48.0012 | 1.89298 | 0.946492 | − | 0.322727i | \(-0.104600\pi\) | ||||
0.946492 | + | 0.322727i | \(0.104600\pi\) | |||||||
\(644\) | −1.40441 | −0.0553417 | ||||||||
\(645\) | 16.6892 | 0.657135 | ||||||||
\(646\) | 7.10300 | 0.279464 | ||||||||
\(647\) | 37.2312 | 1.46371 | 0.731855 | − | 0.681460i | \(-0.238655\pi\) | ||||
0.731855 | + | 0.681460i | \(0.238655\pi\) | |||||||
\(648\) | −11.1413 | −0.437673 | ||||||||
\(649\) | −33.2473 | −1.30507 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.2373 | −0.910742 | ||||||||
\(652\) | −22.3172 | −0.874008 | ||||||||
\(653\) | 36.6613 | 1.43467 | 0.717334 | − | 0.696730i | \(-0.245362\pi\) | ||||
0.717334 | + | 0.696730i | \(0.245362\pi\) | |||||||
\(654\) | −25.7533 | −1.00703 | ||||||||
\(655\) | 9.20767 | 0.359773 | ||||||||
\(656\) | −0.117941 | −0.00460483 | ||||||||
\(657\) | 24.4721 | 0.954747 | ||||||||
\(658\) | 13.3535 | 0.520573 | ||||||||
\(659\) | 22.8356 | 0.889550 | 0.444775 | − | 0.895642i | \(-0.353284\pi\) | ||||
0.444775 | + | 0.895642i | \(0.353284\pi\) | |||||||
\(660\) | 21.4893 | 0.836470 | ||||||||
\(661\) | 44.8720 | 1.74532 | 0.872660 | − | 0.488329i | \(-0.162393\pi\) | ||||
0.872660 | + | 0.488329i | \(0.162393\pi\) | |||||||
\(662\) | 0.0943337 | 0.00366638 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.5884 | −0.488523 | ||||||||
\(665\) | −6.81517 | −0.264281 | ||||||||
\(666\) | 13.7683 | 0.533511 | ||||||||
\(667\) | −0.274655 | −0.0106347 | ||||||||
\(668\) | −23.2517 | −0.899636 | ||||||||
\(669\) | −50.5031 | −1.95256 | ||||||||
\(670\) | 5.48677 | 0.211972 | ||||||||
\(671\) | 27.0739 | 1.04518 | ||||||||
\(672\) | 4.78963 | 0.184764 | ||||||||
\(673\) | −7.38846 | −0.284804 | −0.142402 | − | 0.989809i | \(-0.545483\pi\) | ||||
−0.142402 | + | 0.989809i | \(0.545483\pi\) | |||||||
\(674\) | −9.25406 | −0.356453 | ||||||||
\(675\) | −12.2899 | −0.473038 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.5549 | 0.482526 | 0.241263 | − | 0.970460i | \(-0.422438\pi\) | ||||
0.241263 | + | 0.970460i | \(0.422438\pi\) | |||||||
\(678\) | −2.07860 | −0.0798280 | ||||||||
\(679\) | −26.0107 | −0.998200 | ||||||||
\(680\) | −22.2113 | −0.851764 | ||||||||
\(681\) | 12.0809 | 0.462943 | ||||||||
\(682\) | −15.1711 | −0.580930 | ||||||||
\(683\) | 30.5047 | 1.16723 | 0.583616 | − | 0.812030i | \(-0.301637\pi\) | ||||
0.583616 | + | 0.812030i | \(0.301637\pi\) | |||||||
\(684\) | −1.82965 | −0.0699585 | ||||||||
\(685\) | −14.2268 | −0.543579 | ||||||||
\(686\) | −20.1599 | −0.769709 | ||||||||
\(687\) | −3.34742 | −0.127712 | ||||||||
\(688\) | 2.42854 | 0.0925871 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −4.42834 | −0.168584 | ||||||||
\(691\) | −4.48550 | −0.170637 | −0.0853183 | − | 0.996354i | \(-0.527191\pi\) | ||||
−0.0853183 | + | 0.996354i | \(0.527191\pi\) | |||||||
\(692\) | −21.7696 | −0.827557 | ||||||||
\(693\) | 12.4694 | 0.473673 | ||||||||
\(694\) | −29.1677 | −1.10719 | ||||||||
\(695\) | −46.6266 | −1.76865 | ||||||||
\(696\) | 0.936688 | 0.0355051 | ||||||||
\(697\) | 0.837737 | 0.0317315 | ||||||||
\(698\) | −29.5303 | −1.11774 | ||||||||
\(699\) | 57.0019 | 2.15601 | ||||||||
\(700\) | 10.4141 | 0.393614 | ||||||||
\(701\) | −6.07918 | −0.229607 | −0.114804 | − | 0.993388i | \(-0.536624\pi\) | ||||
−0.114804 | + | 0.993388i | \(0.536624\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.52510 | −0.283814 | ||||||||
\(704\) | 3.12703 | 0.117854 | ||||||||
\(705\) | 42.1056 | 1.58579 | ||||||||
\(706\) | −29.0884 | −1.09476 | ||||||||
\(707\) | −26.5551 | −0.998709 | ||||||||
\(708\) | −23.3659 | −0.878143 | ||||||||
\(709\) | −45.0758 | −1.69286 | −0.846429 | − | 0.532502i | \(-0.821252\pi\) | ||||
−0.846429 | + | 0.532502i | \(0.821252\pi\) | |||||||
\(710\) | 32.0040 | 1.20109 | ||||||||
\(711\) | 20.7429 | 0.777919 | ||||||||
\(712\) | 1.43889 | 0.0539248 | ||||||||
\(713\) | 3.12633 | 0.117082 | ||||||||
\(714\) | −34.0208 | −1.27320 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.6147 | −0.919893 | ||||||||
\(717\) | −12.2172 | −0.456262 | ||||||||
\(718\) | −19.0423 | −0.710654 | ||||||||
\(719\) | 24.2298 | 0.903621 | 0.451810 | − | 0.892114i | \(-0.350778\pi\) | ||||
0.451810 | + | 0.892114i | \(0.350778\pi\) | |||||||
\(720\) | 5.72138 | 0.213223 | ||||||||
\(721\) | 22.9577 | 0.854988 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 26.2801 | 0.977369 | ||||||||
\(724\) | −3.87802 | −0.144126 | ||||||||
\(725\) | 2.03663 | 0.0756386 | ||||||||
\(726\) | −2.68482 | −0.0996430 | ||||||||
\(727\) | −10.3596 | −0.384218 | −0.192109 | − | 0.981374i | \(-0.561533\pi\) | ||||
−0.192109 | + | 0.981374i | \(0.561533\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.42764 | −0.126950 | ||||||||
\(730\) | 41.8249 | 1.54801 | ||||||||
\(731\) | −17.2499 | −0.638010 | ||||||||
\(732\) | 19.0273 | 0.703268 | ||||||||
\(733\) | −24.3843 | −0.900654 | −0.450327 | − | 0.892864i | \(-0.648693\pi\) | ||||
−0.450327 | + | 0.892864i | \(0.648693\pi\) | |||||||
\(734\) | 1.02770 | 0.0379332 | ||||||||
\(735\) | −15.4626 | −0.570347 | ||||||||
\(736\) | −0.644393 | −0.0237526 | ||||||||
\(737\) | 5.48677 | 0.202108 | ||||||||
\(738\) | −0.215792 | −0.00794340 | ||||||||
\(739\) | −1.07875 | −0.0396825 | −0.0198413 | − | 0.999803i | \(-0.506316\pi\) | ||||
−0.0198413 | + | 0.999803i | \(0.506316\pi\) | |||||||
\(740\) | 23.5312 | 0.865024 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.96699 | 0.329188 | ||||||||
\(743\) | −3.38672 | −0.124247 | −0.0621233 | − | 0.998068i | \(-0.519787\pi\) | ||||
−0.0621233 | + | 0.998068i | \(0.519787\pi\) | |||||||
\(744\) | −10.6621 | −0.390891 | ||||||||
\(745\) | 70.3698 | 2.57815 | ||||||||
\(746\) | 15.9433 | 0.583725 | ||||||||
\(747\) | −23.0323 | −0.842708 | ||||||||
\(748\) | −22.2113 | −0.812125 | ||||||||
\(749\) | 12.3750 | 0.452174 | ||||||||
\(750\) | −1.52340 | −0.0556267 | ||||||||
\(751\) | 25.1897 | 0.919186 | 0.459593 | − | 0.888130i | \(-0.347995\pi\) | ||||
0.459593 | + | 0.888130i | \(0.347995\pi\) | |||||||
\(752\) | 6.12703 | 0.223430 | ||||||||
\(753\) | −49.4063 | −1.80046 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29.0834 | 1.05845 | ||||||||
\(756\) | −5.60554 | −0.203871 | ||||||||
\(757\) | 42.8857 | 1.55871 | 0.779353 | − | 0.626585i | \(-0.215548\pi\) | ||||
0.779353 | + | 0.626585i | \(0.215548\pi\) | |||||||
\(758\) | 4.79302 | 0.174090 | ||||||||
\(759\) | −4.42834 | −0.160739 | ||||||||
\(760\) | −3.12703 | −0.113429 | ||||||||
\(761\) | 22.8112 | 0.826906 | 0.413453 | − | 0.910525i | \(-0.364323\pi\) | ||||
0.413453 | + | 0.910525i | \(0.364323\pi\) | |||||||
\(762\) | 20.9100 | 0.757491 | ||||||||
\(763\) | −25.5399 | −0.924605 | ||||||||
\(764\) | 14.5288 | 0.525634 | ||||||||
\(765\) | −40.6389 | −1.46930 | ||||||||
\(766\) | −21.8340 | −0.788895 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.19765 | 0.0793008 | ||||||||
\(769\) | 16.1128 | 0.581042 | 0.290521 | − | 0.956869i | \(-0.406171\pi\) | ||||
0.290521 | + | 0.956869i | \(0.406171\pi\) | |||||||
\(770\) | 21.3112 | 0.768004 | ||||||||
\(771\) | 10.6593 | 0.383885 | ||||||||
\(772\) | −25.5087 | −0.918080 | ||||||||
\(773\) | 33.3582 | 1.19981 | 0.599905 | − | 0.800071i | \(-0.295205\pi\) | ||||
0.599905 | + | 0.800071i | \(0.295205\pi\) | |||||||
\(774\) | 4.44338 | 0.159714 | ||||||||
\(775\) | −23.1824 | −0.832738 | ||||||||
\(776\) | −11.9346 | −0.428428 | ||||||||
\(777\) | 36.0424 | 1.29302 | ||||||||
\(778\) | 16.3944 | 0.587769 | ||||||||
\(779\) | 0.117941 | 0.00422569 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.0040 | 1.14519 | ||||||||
\(782\) | 4.57712 | 0.163678 | ||||||||
\(783\) | −1.09625 | −0.0391768 | ||||||||
\(784\) | −2.25005 | −0.0803591 | ||||||||
\(785\) | 8.09285 | 0.288846 | ||||||||
\(786\) | 6.47106 | 0.230815 | ||||||||
\(787\) | −14.1846 | −0.505628 | −0.252814 | − | 0.967515i | \(-0.581356\pi\) | ||||
−0.252814 | + | 0.967515i | \(0.581356\pi\) | |||||||
\(788\) | −5.12980 | −0.182742 | ||||||||
\(789\) | −22.2432 | −0.791877 | ||||||||
\(790\) | 35.4514 | 1.26130 | ||||||||
\(791\) | −2.06137 | −0.0732940 | ||||||||
\(792\) | 5.72138 | 0.203300 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 8.32544 | 0.295459 | ||||||||
\(795\) | 28.2743 | 1.00279 | ||||||||
\(796\) | −6.58770 | −0.233495 | ||||||||
\(797\) | −16.5599 | −0.586581 | −0.293291 | − | 0.956023i | \(-0.594750\pi\) | ||||
−0.293291 | + | 0.956023i | \(0.594750\pi\) | |||||||
\(798\) | −4.78963 | −0.169551 | ||||||||
\(799\) | −43.5203 | −1.53964 | ||||||||
\(800\) | 4.77832 | 0.168939 | ||||||||
\(801\) | 2.63268 | 0.0930210 | ||||||||
\(802\) | 35.8203 | 1.26486 | ||||||||
\(803\) | 41.8249 | 1.47597 | ||||||||
\(804\) | 3.85605 | 0.135992 | ||||||||
\(805\) | −4.39165 | −0.154785 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.5756 | 0.618691 | ||||||||
\(808\) | −12.1844 | −0.428646 | ||||||||
\(809\) | 22.3953 | 0.787378 | 0.393689 | − | 0.919244i | \(-0.371199\pi\) | ||||
0.393689 | + | 0.919244i | \(0.371199\pi\) | |||||||
\(810\) | −34.8393 | −1.22413 | ||||||||
\(811\) | −28.1667 | −0.989066 | −0.494533 | − | 0.869159i | \(-0.664661\pi\) | ||||
−0.494533 | + | 0.869159i | \(0.664661\pi\) | |||||||
\(812\) | 0.928927 | 0.0325989 | ||||||||
\(813\) | 20.3607 | 0.714080 | ||||||||
\(814\) | 23.5312 | 0.824768 | ||||||||
\(815\) | −69.7865 | −2.44452 | ||||||||
\(816\) | −15.6099 | −0.546455 | ||||||||
\(817\) | −2.42854 | −0.0849637 | ||||||||
\(818\) | 28.5608 | 0.998606 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.368806 | −0.0128793 | ||||||||
\(821\) | −10.2960 | −0.359334 | −0.179667 | − | 0.983727i | \(-0.557502\pi\) | ||||
−0.179667 | + | 0.983727i | \(0.557502\pi\) | |||||||
\(822\) | −9.99847 | −0.348737 | ||||||||
\(823\) | 18.1042 | 0.631074 | 0.315537 | − | 0.948913i | \(-0.397815\pi\) | ||||
0.315537 | + | 0.948913i | \(0.397815\pi\) | |||||||
\(824\) | 10.5338 | 0.366961 | ||||||||
\(825\) | 32.8371 | 1.14324 | ||||||||
\(826\) | −23.1723 | −0.806266 | ||||||||
\(827\) | −0.466529 | −0.0162228 | −0.00811139 | − | 0.999967i | \(-0.502582\pi\) | ||||
−0.00811139 | + | 0.999967i | \(0.502582\pi\) | |||||||
\(828\) | −1.17902 | −0.0409736 | ||||||||
\(829\) | −14.4832 | −0.503023 | −0.251511 | − | 0.967854i | \(-0.580928\pi\) | ||||
−0.251511 | + | 0.967854i | \(0.580928\pi\) | |||||||
\(830\) | −39.3642 | −1.36635 | ||||||||
\(831\) | 31.1564 | 1.08080 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.9821 | 0.553748 | ||||||||
\(834\) | −32.7687 | −1.13469 | ||||||||
\(835\) | −72.7089 | −2.51619 | ||||||||
\(836\) | −3.12703 | −0.108151 | ||||||||
\(837\) | 12.4783 | 0.431314 | ||||||||
\(838\) | −39.0336 | −1.34839 | ||||||||
\(839\) | −0.938352 | −0.0323955 | −0.0161978 | − | 0.999869i | \(-0.505156\pi\) | ||||
−0.0161978 | + | 0.999869i | \(0.505156\pi\) | |||||||
\(840\) | 14.9773 | 0.516767 | ||||||||
\(841\) | −28.8183 | −0.993736 | ||||||||
\(842\) | 35.6361 | 1.22810 | ||||||||
\(843\) | −60.1580 | −2.07195 | ||||||||
\(844\) | −4.98682 | −0.171654 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11.2103 | 0.385419 | ||||||||
\(847\) | −2.66257 | −0.0914871 | ||||||||
\(848\) | 4.11436 | 0.141288 | ||||||||
\(849\) | 51.6745 | 1.77346 | ||||||||
\(850\) | −33.9404 | −1.16415 | ||||||||
\(851\) | −4.84912 | −0.166226 | ||||||||
\(852\) | 22.4921 | 0.770566 | ||||||||
\(853\) | −16.5020 | −0.565018 | −0.282509 | − | 0.959265i | \(-0.591167\pi\) | ||||
−0.282509 | + | 0.959265i | \(0.591167\pi\) | |||||||
\(854\) | 18.8696 | 0.645705 | ||||||||
\(855\) | −5.72138 | −0.195667 | ||||||||
\(856\) | 5.67809 | 0.194073 | ||||||||
\(857\) | −1.55202 | −0.0530159 | −0.0265079 | − | 0.999649i | \(-0.508439\pi\) | ||||
−0.0265079 | + | 0.999649i | \(0.508439\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.1217 | 0.618306 | 0.309153 | − | 0.951012i | \(-0.399955\pi\) | ||||
0.309153 | + | 0.951012i | \(0.399955\pi\) | |||||||
\(860\) | 7.59411 | 0.258957 | ||||||||
\(861\) | −0.564896 | −0.0192516 | ||||||||
\(862\) | 28.5835 | 0.973557 | ||||||||
\(863\) | 47.5374 | 1.61819 | 0.809096 | − | 0.587676i | \(-0.199957\pi\) | ||||
0.809096 | + | 0.587676i | \(0.199957\pi\) | |||||||
\(864\) | −2.57201 | −0.0875016 | ||||||||
\(865\) | −68.0743 | −2.31460 | ||||||||
\(866\) | −24.3228 | −0.826524 | ||||||||
\(867\) | 73.5170 | 2.49677 | ||||||||
\(868\) | −10.5737 | −0.358896 | ||||||||
\(869\) | 35.4514 | 1.20260 | ||||||||
\(870\) | 2.92905 | 0.0993042 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −11.7186 | −0.396841 | ||||||||
\(873\) | −21.8362 | −0.739043 | ||||||||
\(874\) | 0.644393 | 0.0217969 | ||||||||
\(875\) | −1.51078 | −0.0510736 | ||||||||
\(876\) | 29.3941 | 0.993135 | ||||||||
\(877\) | −53.0121 | −1.79009 | −0.895046 | − | 0.445973i | \(-0.852858\pi\) | ||||
−0.895046 | + | 0.445973i | \(0.852858\pi\) | |||||||
\(878\) | −3.40022 | −0.114752 | ||||||||
\(879\) | 24.4381 | 0.824278 | ||||||||
\(880\) | 9.77832 | 0.329627 | ||||||||
\(881\) | −26.0499 | −0.877645 | −0.438822 | − | 0.898574i | \(-0.644604\pi\) | ||||
−0.438822 | + | 0.898574i | \(0.644604\pi\) | |||||||
\(882\) | −4.11682 | −0.138620 | ||||||||
\(883\) | 36.9504 | 1.24348 | 0.621740 | − | 0.783224i | \(-0.286426\pi\) | ||||
0.621740 | + | 0.783224i | \(0.286426\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −73.0658 | −2.45608 | ||||||||
\(886\) | 16.5029 | 0.554425 | ||||||||
\(887\) | 42.5093 | 1.42732 | 0.713661 | − | 0.700491i | \(-0.247036\pi\) | ||||
0.713661 | + | 0.700491i | \(0.247036\pi\) | |||||||
\(888\) | 16.5375 | 0.554962 | ||||||||
\(889\) | 20.7368 | 0.695489 | ||||||||
\(890\) | 4.49947 | 0.150822 | ||||||||
\(891\) | −34.8393 | −1.16716 | ||||||||
\(892\) | −22.9805 | −0.769445 | ||||||||
\(893\) | −6.12703 | −0.205033 | ||||||||
\(894\) | 49.4552 | 1.65403 | ||||||||
\(895\) | −76.9708 | −2.57285 | ||||||||
\(896\) | 2.17944 | 0.0728099 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.72011 | 0.257623 | ||||||||
\(899\) | −2.06786 | −0.0689669 | ||||||||
\(900\) | 8.74267 | 0.291422 | ||||||||
\(901\) | −29.2243 | −0.973602 | ||||||||
\(902\) | −0.368806 | −0.0122799 | ||||||||
\(903\) | 11.6318 | 0.387082 | ||||||||
\(904\) | −0.945828 | −0.0314578 | ||||||||
\(905\) | −12.1267 | −0.403105 | ||||||||
\(906\) | 20.4395 | 0.679058 | ||||||||
\(907\) | 4.12649 | 0.137018 | 0.0685090 | − | 0.997651i | \(-0.478176\pi\) | ||||
0.0685090 | + | 0.997651i | \(0.478176\pi\) | |||||||
\(908\) | 5.49722 | 0.182432 | ||||||||
\(909\) | −22.2932 | −0.739419 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.4605 | 0.479097 | 0.239549 | − | 0.970884i | \(-0.423001\pi\) | ||||
0.239549 | + | 0.970884i | \(0.423001\pi\) | |||||||
\(912\) | −2.19765 | −0.0727714 | ||||||||
\(913\) | −39.3642 | −1.30276 | ||||||||
\(914\) | 35.4938 | 1.17403 | ||||||||
\(915\) | 59.4989 | 1.96697 | ||||||||
\(916\) | −1.52318 | −0.0503274 | ||||||||
\(917\) | 6.41744 | 0.211923 | ||||||||
\(918\) | 18.2690 | 0.602967 | ||||||||
\(919\) | 59.7790 | 1.97193 | 0.985963 | − | 0.166965i | \(-0.0533967\pi\) | ||||
0.985963 | + | 0.166965i | \(0.0533967\pi\) | |||||||
\(920\) | −2.01504 | −0.0664338 | ||||||||
\(921\) | −22.5433 | −0.742826 | ||||||||
\(922\) | −14.3955 | −0.474092 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 14.9773 | 0.492718 | ||||||||
\(925\) | 35.9573 | 1.18227 | ||||||||
\(926\) | 2.13703 | 0.0702273 | ||||||||
\(927\) | 19.2731 | 0.633012 | ||||||||
\(928\) | 0.426223 | 0.0139915 | ||||||||
\(929\) | 5.85030 | 0.191942 | 0.0959711 | − | 0.995384i | \(-0.469404\pi\) | ||||
0.0959711 | + | 0.995384i | \(0.469404\pi\) | |||||||
\(930\) | −33.3406 | −1.09328 | ||||||||
\(931\) | 2.25005 | 0.0737425 | ||||||||
\(932\) | 25.9377 | 0.849618 | ||||||||
\(933\) | 30.4798 | 0.997864 | ||||||||
\(934\) | 22.3298 | 0.730654 | ||||||||
\(935\) | −69.4554 | −2.27143 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.4140 | −0.928243 | −0.464122 | − | 0.885771i | \(-0.653630\pi\) | ||||
−0.464122 | + | 0.885771i | \(0.653630\pi\) | |||||||
\(938\) | 3.82410 | 0.124861 | ||||||||
\(939\) | −7.42184 | −0.242203 | ||||||||
\(940\) | 19.1594 | 0.624911 | ||||||||
\(941\) | 5.81060 | 0.189420 | 0.0947101 | − | 0.995505i | \(-0.469808\pi\) | ||||
0.0947101 | + | 0.995505i | \(0.469808\pi\) | |||||||
\(942\) | 5.68757 | 0.185311 | ||||||||
\(943\) | 0.0760006 | 0.00247492 | ||||||||
\(944\) | −10.6322 | −0.346049 | ||||||||
\(945\) | −17.5287 | −0.570208 | ||||||||
\(946\) | 7.59411 | 0.246906 | ||||||||
\(947\) | 8.52929 | 0.277165 | 0.138582 | − | 0.990351i | \(-0.455745\pi\) | ||||
0.138582 | + | 0.990351i | \(0.455745\pi\) | |||||||
\(948\) | 24.9149 | 0.809197 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4.77832 | −0.155029 | ||||||||
\(951\) | 13.4679 | 0.436727 | ||||||||
\(952\) | −15.4805 | −0.501727 | ||||||||
\(953\) | 37.1660 | 1.20392 | 0.601962 | − | 0.798525i | \(-0.294386\pi\) | ||||
0.601962 | + | 0.798525i | \(0.294386\pi\) | |||||||
\(954\) | 7.52785 | 0.243723 | ||||||||
\(955\) | 45.4321 | 1.47015 | ||||||||
\(956\) | −5.55924 | −0.179799 | ||||||||
\(957\) | 2.92905 | 0.0946828 | ||||||||
\(958\) | 6.43997 | 0.208066 | ||||||||
\(959\) | −9.91562 | −0.320192 | ||||||||
\(960\) | 6.87211 | 0.221796 | ||||||||
\(961\) | −7.46211 | −0.240713 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.3889 | 0.334779 | ||||||||
\(964\) | 11.9583 | 0.385151 | ||||||||
\(965\) | −79.7666 | −2.56778 | ||||||||
\(966\) | −3.08641 | −0.0993035 | ||||||||
\(967\) | −38.7782 | −1.24702 | −0.623511 | − | 0.781815i | \(-0.714294\pi\) | ||||
−0.623511 | + | 0.781815i | \(0.714294\pi\) | |||||||
\(968\) | −1.22168 | −0.0392662 | ||||||||
\(969\) | 15.6099 | 0.501462 | ||||||||
\(970\) | −37.3199 | −1.19827 | ||||||||
\(971\) | 4.84313 | 0.155424 | 0.0777118 | − | 0.996976i | \(-0.475239\pi\) | ||||
0.0777118 | + | 0.996976i | \(0.475239\pi\) | |||||||
\(972\) | −16.7687 | −0.537856 | ||||||||
\(973\) | −32.4972 | −1.04181 | ||||||||
\(974\) | −34.7098 | −1.11218 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.65802 | 0.277136 | ||||||||
\(977\) | −20.1405 | −0.644352 | −0.322176 | − | 0.946680i | \(-0.604414\pi\) | ||||
−0.322176 | + | 0.946680i | \(0.604414\pi\) | |||||||
\(978\) | −49.0453 | −1.56830 | ||||||||
\(979\) | 4.49947 | 0.143804 | ||||||||
\(980\) | −7.03599 | −0.224756 | ||||||||
\(981\) | −21.4409 | −0.684555 | ||||||||
\(982\) | 27.6996 | 0.883929 | ||||||||
\(983\) | 11.3342 | 0.361506 | 0.180753 | − | 0.983529i | \(-0.442147\pi\) | ||||
0.180753 | + | 0.983529i | \(0.442147\pi\) | |||||||
\(984\) | −0.259193 | −0.00826278 | ||||||||
\(985\) | −16.0410 | −0.511110 | ||||||||
\(986\) | −3.02746 | −0.0964140 | ||||||||
\(987\) | 29.3462 | 0.934101 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.56493 | −0.0497619 | ||||||||
\(990\) | 17.8909 | 0.568611 | ||||||||
\(991\) | −52.9777 | −1.68289 | −0.841447 | − | 0.540340i | \(-0.818296\pi\) | ||||
−0.841447 | + | 0.540340i | \(0.818296\pi\) | |||||||
\(992\) | −4.85159 | −0.154038 | ||||||||
\(993\) | 0.207312 | 0.00657885 | ||||||||
\(994\) | 22.3057 | 0.707494 | ||||||||
\(995\) | −20.5999 | −0.653062 | ||||||||
\(996\) | −27.6648 | −0.876592 | ||||||||
\(997\) | 54.6400 | 1.73047 | 0.865233 | − | 0.501369i | \(-0.167170\pi\) | ||||
0.865233 | + | 0.501369i | \(0.167170\pi\) | |||||||
\(998\) | −10.0199 | −0.317174 | ||||||||
\(999\) | −19.3546 | −0.612353 |
(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 | 6422.2.a.bd.1.5 | 6 | ||
13.3 | even | 3 | 494.2.g.f.191.2 | ✓ | 12 | ||
13.9 | even | 3 | 494.2.g.f.419.2 | yes | 12 | ||
13.12 | even | 2 | 6422.2.a.bc.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.g.f.191.2 | ✓ | 12 | 13.3 | even | 3 | ||
494.2.g.f.419.2 | yes | 12 | 13.9 | even | 3 | ||
6422.2.a.bc.1.5 | 6 | 13.12 | even | 2 | |||
6422.2.a.bd.1.5 | 6 | 1.1 | even | 1 | trivial |