Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, 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("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{10} + 88x^{8} - 197x^{6} + 172x^{4} - 36x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(2.58860\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.58860 | 1.83042 | 0.915209 | − | 0.402981i | \(-0.132026\pi\) | ||||
0.915209 | + | 0.402981i | \(0.132026\pi\) | |||||||
\(3\) | −0.518466 | −0.299336 | −0.149668 | − | 0.988736i | \(-0.547821\pi\) | ||||
−0.149668 | + | 0.988736i | \(0.547821\pi\) | |||||||
\(4\) | 4.70085 | 2.35043 | ||||||||
\(5\) | −1.61205 | −0.720932 | −0.360466 | − | 0.932772i | \(-0.617382\pi\) | ||||
−0.360466 | + | 0.932772i | \(0.617382\pi\) | |||||||
\(6\) | −1.34210 | −0.547910 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 6.99143 | 2.47184 | ||||||||
\(9\) | −2.73119 | −0.910398 | ||||||||
\(10\) | −4.17296 | −1.31961 | ||||||||
\(11\) | 2.70496 | 0.815575 | 0.407788 | − | 0.913077i | \(-0.366300\pi\) | ||||
0.407788 | + | 0.913077i | \(0.366300\pi\) | |||||||
\(12\) | −2.43723 | −0.703568 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.835795 | 0.215801 | ||||||||
\(16\) | 8.69632 | 2.17408 | ||||||||
\(17\) | −3.12661 | −0.758314 | −0.379157 | − | 0.925332i | \(-0.623786\pi\) | ||||
−0.379157 | + | 0.925332i | \(0.623786\pi\) | |||||||
\(18\) | −7.06997 | −1.66641 | ||||||||
\(19\) | −3.68150 | −0.844595 | −0.422297 | − | 0.906457i | \(-0.638776\pi\) | ||||
−0.422297 | + | 0.906457i | \(0.638776\pi\) | |||||||
\(20\) | −7.57803 | −1.69450 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.00205 | 1.49284 | ||||||||
\(23\) | 1.98604 | 0.414117 | 0.207059 | − | 0.978329i | \(-0.433611\pi\) | ||||
0.207059 | + | 0.978329i | \(0.433611\pi\) | |||||||
\(24\) | −3.62482 | −0.739913 | ||||||||
\(25\) | −2.40128 | −0.480257 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.97143 | 0.571852 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.37271 | −0.997687 | −0.498844 | − | 0.866692i | \(-0.666242\pi\) | ||||
−0.498844 | + | 0.866692i | \(0.666242\pi\) | |||||||
\(30\) | 2.16354 | 0.395006 | ||||||||
\(31\) | −10.4780 | −1.88191 | −0.940956 | − | 0.338529i | \(-0.890071\pi\) | ||||
−0.940956 | + | 0.338529i | \(0.890071\pi\) | |||||||
\(32\) | 8.52843 | 1.50763 | ||||||||
\(33\) | −1.40243 | −0.244131 | ||||||||
\(34\) | −8.09354 | −1.38803 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −12.8389 | −2.13982 | ||||||||
\(37\) | 5.95346 | 0.978743 | 0.489371 | − | 0.872075i | \(-0.337226\pi\) | ||||
0.489371 | + | 0.872075i | \(0.337226\pi\) | |||||||
\(38\) | −9.52994 | −1.54596 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −11.2706 | −1.78203 | ||||||||
\(41\) | 7.70150 | 1.20277 | 0.601386 | − | 0.798958i | \(-0.294615\pi\) | ||||
0.601386 | + | 0.798958i | \(0.294615\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.35600 | −0.511785 | −0.255892 | − | 0.966705i | \(-0.582369\pi\) | ||||
−0.255892 | + | 0.966705i | \(0.582369\pi\) | |||||||
\(44\) | 12.7156 | 1.91695 | ||||||||
\(45\) | 4.40283 | 0.656335 | ||||||||
\(46\) | 5.14106 | 0.758008 | ||||||||
\(47\) | −1.05508 | −0.153900 | −0.0769500 | − | 0.997035i | \(-0.524518\pi\) | ||||
−0.0769500 | + | 0.997035i | \(0.524518\pi\) | |||||||
\(48\) | −4.50874 | −0.650781 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.21596 | −0.879070 | ||||||||
\(51\) | 1.62104 | 0.226991 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.26568 | 0.998017 | 0.499009 | − | 0.866597i | \(-0.333698\pi\) | ||||
0.499009 | + | 0.866597i | \(0.333698\pi\) | |||||||
\(54\) | 7.69184 | 1.04673 | ||||||||
\(55\) | −4.36054 | −0.587975 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.90873 | 0.252818 | ||||||||
\(58\) | −13.9078 | −1.82618 | ||||||||
\(59\) | −11.4241 | −1.48729 | −0.743643 | − | 0.668577i | \(-0.766904\pi\) | ||||
−0.743643 | + | 0.668577i | \(0.766904\pi\) | |||||||
\(60\) | 3.92895 | 0.507225 | ||||||||
\(61\) | 2.92507 | 0.374517 | 0.187259 | − | 0.982311i | \(-0.440040\pi\) | ||||
0.187259 | + | 0.982311i | \(0.440040\pi\) | |||||||
\(62\) | −27.1235 | −3.44468 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.68406 | 0.585507 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.63033 | −0.446862 | ||||||||
\(67\) | −13.5818 | −1.65928 | −0.829642 | − | 0.558296i | \(-0.811455\pi\) | ||||
−0.829642 | + | 0.558296i | \(0.811455\pi\) | |||||||
\(68\) | −14.6977 | −1.78236 | ||||||||
\(69\) | −1.02969 | −0.123960 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.35111 | −0.160347 | −0.0801736 | − | 0.996781i | \(-0.525547\pi\) | ||||
−0.0801736 | + | 0.996781i | \(0.525547\pi\) | |||||||
\(72\) | −19.0949 | −2.25036 | ||||||||
\(73\) | −9.10335 | −1.06547 | −0.532733 | − | 0.846283i | \(-0.678835\pi\) | ||||
−0.532733 | + | 0.846283i | \(0.678835\pi\) | |||||||
\(74\) | 15.4111 | 1.79151 | ||||||||
\(75\) | 1.24498 | 0.143758 | ||||||||
\(76\) | −17.3062 | −1.98516 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.20578 | −0.698205 | −0.349102 | − | 0.937085i | \(-0.613513\pi\) | ||||
−0.349102 | + | 0.937085i | \(0.613513\pi\) | |||||||
\(80\) | −14.0189 | −1.56736 | ||||||||
\(81\) | 6.65300 | 0.739222 | ||||||||
\(82\) | 19.9361 | 2.20158 | ||||||||
\(83\) | 2.69672 | 0.296003 | 0.148002 | − | 0.988987i | \(-0.452716\pi\) | ||||
0.148002 | + | 0.988987i | \(0.452716\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.04026 | 0.546693 | ||||||||
\(86\) | −8.68734 | −0.936780 | ||||||||
\(87\) | 2.78557 | 0.298644 | ||||||||
\(88\) | 18.9115 | 2.01597 | ||||||||
\(89\) | −1.75988 | −0.186546 | −0.0932732 | − | 0.995641i | \(-0.529733\pi\) | ||||
−0.0932732 | + | 0.995641i | \(0.529733\pi\) | |||||||
\(90\) | 11.3972 | 1.20137 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.33607 | 0.973353 | ||||||||
\(93\) | 5.43251 | 0.563325 | ||||||||
\(94\) | −2.73119 | −0.281701 | ||||||||
\(95\) | 5.93478 | 0.608896 | ||||||||
\(96\) | −4.42170 | −0.451288 | ||||||||
\(97\) | −15.4820 | −1.57196 | −0.785981 | − | 0.618250i | \(-0.787842\pi\) | ||||
−0.785981 | + | 0.618250i | \(0.787842\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.38776 | −0.742498 | ||||||||
\(100\) | −11.2881 | −1.12881 | ||||||||
\(101\) | 1.27930 | 0.127295 | 0.0636477 | − | 0.997972i | \(-0.479727\pi\) | ||||
0.0636477 | + | 0.997972i | \(0.479727\pi\) | |||||||
\(102\) | 4.19622 | 0.415488 | ||||||||
\(103\) | 11.4673 | 1.12991 | 0.564956 | − | 0.825121i | \(-0.308893\pi\) | ||||
0.564956 | + | 0.825121i | \(0.308893\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 18.8079 | 1.82679 | ||||||||
\(107\) | −5.13525 | −0.496444 | −0.248222 | − | 0.968703i | \(-0.579846\pi\) | ||||
−0.248222 | + | 0.968703i | \(0.579846\pi\) | |||||||
\(108\) | 13.9682 | 1.34410 | ||||||||
\(109\) | 1.72783 | 0.165496 | 0.0827481 | − | 0.996570i | \(-0.473630\pi\) | ||||
0.0827481 | + | 0.996570i | \(0.473630\pi\) | |||||||
\(110\) | −11.2877 | −1.07624 | ||||||||
\(111\) | −3.08667 | −0.292973 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.59113 | −0.808185 | −0.404093 | − | 0.914718i | \(-0.632413\pi\) | ||||
−0.404093 | + | 0.914718i | \(0.632413\pi\) | |||||||
\(114\) | 4.94095 | 0.462762 | ||||||||
\(115\) | −3.20160 | −0.298551 | ||||||||
\(116\) | −25.2563 | −2.34499 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −29.5723 | −2.72235 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.84340 | 0.533427 | ||||||||
\(121\) | −3.68321 | −0.334837 | ||||||||
\(122\) | 7.57184 | 0.685522 | ||||||||
\(123\) | −3.99297 | −0.360034 | ||||||||
\(124\) | −49.2557 | −4.42330 | ||||||||
\(125\) | 11.9313 | 1.06716 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.12412 | −0.277221 | −0.138610 | − | 0.990347i | \(-0.544264\pi\) | ||||
−0.138610 | + | 0.990347i | \(0.544264\pi\) | |||||||
\(128\) | −4.93170 | −0.435904 | ||||||||
\(129\) | 1.73997 | 0.153196 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.2092 | −0.891982 | −0.445991 | − | 0.895038i | \(-0.647149\pi\) | ||||
−0.445991 | + | 0.895038i | \(0.647149\pi\) | |||||||
\(132\) | −6.59261 | −0.573813 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −35.1579 | −3.03718 | ||||||||
\(135\) | −4.79010 | −0.412266 | ||||||||
\(136\) | −21.8595 | −1.87443 | ||||||||
\(137\) | −9.99261 | −0.853726 | −0.426863 | − | 0.904316i | \(-0.640381\pi\) | ||||
−0.426863 | + | 0.904316i | \(0.640381\pi\) | |||||||
\(138\) | −2.66546 | −0.226899 | ||||||||
\(139\) | 1.66420 | 0.141156 | 0.0705778 | − | 0.997506i | \(-0.477516\pi\) | ||||
0.0705778 | + | 0.997506i | \(0.477516\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.547025 | 0.0460679 | ||||||||
\(142\) | −3.49748 | −0.293502 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −23.7513 | −1.97928 | ||||||||
\(145\) | 8.66110 | 0.719265 | ||||||||
\(146\) | −23.5649 | −1.95025 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 27.9863 | 2.30046 | ||||||||
\(149\) | 19.7980 | 1.62192 | 0.810959 | − | 0.585103i | \(-0.198946\pi\) | ||||
0.810959 | + | 0.585103i | \(0.198946\pi\) | |||||||
\(150\) | 3.22276 | 0.263138 | ||||||||
\(151\) | 7.53493 | 0.613184 | 0.306592 | − | 0.951841i | \(-0.400811\pi\) | ||||
0.306592 | + | 0.951841i | \(0.400811\pi\) | |||||||
\(152\) | −25.7390 | −2.08771 | ||||||||
\(153\) | 8.53937 | 0.690367 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.8912 | 1.35673 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0045 | −1.11768 | −0.558839 | − | 0.829276i | \(-0.688753\pi\) | ||||
−0.558839 | + | 0.829276i | \(0.688753\pi\) | |||||||
\(158\) | −16.0643 | −1.27801 | ||||||||
\(159\) | −3.76700 | −0.298743 | ||||||||
\(160\) | −13.7483 | −1.08690 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 17.2219 | 1.35308 | ||||||||
\(163\) | −7.16995 | −0.561594 | −0.280797 | − | 0.959767i | \(-0.590599\pi\) | ||||
−0.280797 | + | 0.959767i | \(0.590599\pi\) | |||||||
\(164\) | 36.2036 | 2.82703 | ||||||||
\(165\) | 2.26079 | 0.176002 | ||||||||
\(166\) | 6.98072 | 0.541809 | ||||||||
\(167\) | 17.9805 | 1.39138 | 0.695688 | − | 0.718344i | \(-0.255099\pi\) | ||||
0.695688 | + | 0.718344i | \(0.255099\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 13.0472 | 1.00068 | ||||||||
\(171\) | 10.0549 | 0.768917 | ||||||||
\(172\) | −15.7761 | −1.20291 | ||||||||
\(173\) | 12.8116 | 0.974047 | 0.487023 | − | 0.873389i | \(-0.338083\pi\) | ||||
0.487023 | + | 0.873389i | \(0.338083\pi\) | |||||||
\(174\) | 7.21072 | 0.546643 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 23.5232 | 1.77312 | ||||||||
\(177\) | 5.92298 | 0.445199 | ||||||||
\(178\) | −4.55561 | −0.341458 | ||||||||
\(179\) | 1.84022 | 0.137545 | 0.0687723 | − | 0.997632i | \(-0.478092\pi\) | ||||
0.0687723 | + | 0.997632i | \(0.478092\pi\) | |||||||
\(180\) | 20.6971 | 1.54267 | ||||||||
\(181\) | −3.29928 | −0.245234 | −0.122617 | − | 0.992454i | \(-0.539129\pi\) | ||||
−0.122617 | + | 0.992454i | \(0.539129\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.51655 | −0.112107 | ||||||||
\(184\) | 13.8852 | 1.02363 | ||||||||
\(185\) | −9.59730 | −0.705607 | ||||||||
\(186\) | 14.0626 | 1.03112 | ||||||||
\(187\) | −8.45734 | −0.618462 | ||||||||
\(188\) | −4.95980 | −0.361731 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15.3628 | 1.11453 | ||||||||
\(191\) | 4.89614 | 0.354272 | 0.177136 | − | 0.984186i | \(-0.443317\pi\) | ||||
0.177136 | + | 0.984186i | \(0.443317\pi\) | |||||||
\(192\) | −2.42852 | −0.175264 | ||||||||
\(193\) | 3.01910 | 0.217320 | 0.108660 | − | 0.994079i | \(-0.465344\pi\) | ||||
0.108660 | + | 0.994079i | \(0.465344\pi\) | |||||||
\(194\) | −40.0768 | −2.87735 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.64991 | 0.331292 | 0.165646 | − | 0.986185i | \(-0.447029\pi\) | ||||
0.165646 | + | 0.986185i | \(0.447029\pi\) | |||||||
\(198\) | −19.1240 | −1.35908 | ||||||||
\(199\) | −0.410721 | −0.0291152 | −0.0145576 | − | 0.999894i | \(-0.504634\pi\) | ||||
−0.0145576 | + | 0.999894i | \(0.504634\pi\) | |||||||
\(200\) | −16.7884 | −1.18712 | ||||||||
\(201\) | 7.04171 | 0.496684 | ||||||||
\(202\) | 3.31160 | 0.233004 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.62027 | 0.533525 | ||||||||
\(205\) | −12.4152 | −0.867118 | ||||||||
\(206\) | 29.6844 | 2.06821 | ||||||||
\(207\) | −5.42425 | −0.377012 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.95831 | −0.688831 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.51600 | −0.517423 | −0.258711 | − | 0.965955i | \(-0.583298\pi\) | ||||
−0.258711 | + | 0.965955i | \(0.583298\pi\) | |||||||
\(212\) | 34.1549 | 2.34577 | ||||||||
\(213\) | 0.700504 | 0.0479977 | ||||||||
\(214\) | −13.2931 | −0.908699 | ||||||||
\(215\) | 5.41005 | 0.368962 | ||||||||
\(216\) | 20.7745 | 1.41353 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.47267 | 0.302927 | ||||||||
\(219\) | 4.71978 | 0.318933 | ||||||||
\(220\) | −20.4982 | −1.38199 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −7.99014 | −0.536263 | ||||||||
\(223\) | 22.5794 | 1.51203 | 0.756016 | − | 0.654553i | \(-0.227143\pi\) | ||||
0.756016 | + | 0.654553i | \(0.227143\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.55837 | 0.437225 | ||||||||
\(226\) | −22.2390 | −1.47932 | ||||||||
\(227\) | −13.6717 | −0.907424 | −0.453712 | − | 0.891148i | \(-0.649901\pi\) | ||||
−0.453712 | + | 0.891148i | \(0.649901\pi\) | |||||||
\(228\) | 8.97268 | 0.594230 | ||||||||
\(229\) | −7.93086 | −0.524086 | −0.262043 | − | 0.965056i | \(-0.584396\pi\) | ||||
−0.262043 | + | 0.965056i | \(0.584396\pi\) | |||||||
\(230\) | −8.28766 | −0.546472 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −37.5629 | −2.46613 | ||||||||
\(233\) | −6.57171 | −0.430527 | −0.215263 | − | 0.976556i | \(-0.569061\pi\) | ||||
−0.215263 | + | 0.976556i | \(0.569061\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.70085 | 0.110951 | ||||||||
\(236\) | −53.7028 | −3.49576 | ||||||||
\(237\) | 3.21749 | 0.208998 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.39284 | −0.607572 | −0.303786 | − | 0.952740i | \(-0.598251\pi\) | ||||
−0.303786 | + | 0.952740i | \(0.598251\pi\) | |||||||
\(240\) | 7.26833 | 0.469169 | ||||||||
\(241\) | 10.0858 | 0.649686 | 0.324843 | − | 0.945768i | \(-0.394689\pi\) | ||||
0.324843 | + | 0.945768i | \(0.394689\pi\) | |||||||
\(242\) | −9.53435 | −0.612891 | ||||||||
\(243\) | −12.3636 | −0.793128 | ||||||||
\(244\) | 13.7503 | 0.880275 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10.3362 | −0.659012 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −73.2565 | −4.65179 | ||||||||
\(249\) | −1.39816 | −0.0886045 | ||||||||
\(250\) | 30.8853 | 1.95336 | ||||||||
\(251\) | 10.3485 | 0.653194 | 0.326597 | − | 0.945164i | \(-0.394098\pi\) | ||||
0.326597 | + | 0.945164i | \(0.394098\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.37215 | 0.337744 | ||||||||
\(254\) | −8.08709 | −0.507429 | ||||||||
\(255\) | −2.61320 | −0.163645 | ||||||||
\(256\) | −22.1343 | −1.38339 | ||||||||
\(257\) | −7.98658 | −0.498189 | −0.249095 | − | 0.968479i | \(-0.580133\pi\) | ||||
−0.249095 | + | 0.968479i | \(0.580133\pi\) | |||||||
\(258\) | 4.50409 | 0.280412 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.6739 | 0.908292 | ||||||||
\(262\) | −26.4275 | −1.63270 | ||||||||
\(263\) | 5.05934 | 0.311972 | 0.155986 | − | 0.987759i | \(-0.450144\pi\) | ||||
0.155986 | + | 0.987759i | \(0.450144\pi\) | |||||||
\(264\) | −9.80498 | −0.603455 | ||||||||
\(265\) | −11.7127 | −0.719503 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.912435 | 0.0558401 | ||||||||
\(268\) | −63.8461 | −3.90002 | ||||||||
\(269\) | −13.8902 | −0.846902 | −0.423451 | − | 0.905919i | \(-0.639181\pi\) | ||||
−0.423451 | + | 0.905919i | \(0.639181\pi\) | |||||||
\(270\) | −12.3997 | −0.754619 | ||||||||
\(271\) | 8.32721 | 0.505842 | 0.252921 | − | 0.967487i | \(-0.418609\pi\) | ||||
0.252921 | + | 0.967487i | \(0.418609\pi\) | |||||||
\(272\) | −27.1900 | −1.64863 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −25.8669 | −1.56267 | ||||||||
\(275\) | −6.49537 | −0.391685 | ||||||||
\(276\) | −4.84043 | −0.291360 | ||||||||
\(277\) | −23.2116 | −1.39465 | −0.697325 | − | 0.716755i | \(-0.745626\pi\) | ||||
−0.697325 | + | 0.716755i | \(0.745626\pi\) | |||||||
\(278\) | 4.30795 | 0.258374 | ||||||||
\(279\) | 28.6176 | 1.71329 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.1595 | 1.62020 | 0.810100 | − | 0.586292i | \(-0.199413\pi\) | ||||
0.810100 | + | 0.586292i | \(0.199413\pi\) | |||||||
\(282\) | 1.41603 | 0.0843234 | ||||||||
\(283\) | 16.1513 | 0.960092 | 0.480046 | − | 0.877243i | \(-0.340620\pi\) | ||||
0.480046 | + | 0.877243i | \(0.340620\pi\) | |||||||
\(284\) | −6.35136 | −0.376884 | ||||||||
\(285\) | −3.07698 | −0.182265 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −23.2928 | −1.37254 | ||||||||
\(289\) | −7.22433 | −0.424960 | ||||||||
\(290\) | 22.4201 | 1.31656 | ||||||||
\(291\) | 8.02691 | 0.470546 | ||||||||
\(292\) | −42.7935 | −2.50430 | ||||||||
\(293\) | 14.6452 | 0.855582 | 0.427791 | − | 0.903878i | \(-0.359292\pi\) | ||||
0.427791 | + | 0.903878i | \(0.359292\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.4162 | 1.07223 | ||||||||
\(296\) | 41.6232 | 2.41930 | ||||||||
\(297\) | 8.03758 | 0.466388 | ||||||||
\(298\) | 51.2492 | 2.96879 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5.85248 | 0.337893 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 19.5049 | 1.12238 | ||||||||
\(303\) | −0.663274 | −0.0381041 | ||||||||
\(304\) | −32.0155 | −1.83622 | ||||||||
\(305\) | −4.71537 | −0.270001 | ||||||||
\(306\) | 22.1050 | 1.26366 | ||||||||
\(307\) | 8.97844 | 0.512427 | 0.256213 | − | 0.966620i | \(-0.417525\pi\) | ||||
0.256213 | + | 0.966620i | \(0.417525\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.94543 | −0.338224 | ||||||||
\(310\) | 43.7245 | 2.48338 | ||||||||
\(311\) | −12.1816 | −0.690755 | −0.345378 | − | 0.938464i | \(-0.612249\pi\) | ||||
−0.345378 | + | 0.938464i | \(0.612249\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.1240 | −0.741810 | −0.370905 | − | 0.928671i | \(-0.620953\pi\) | ||||
−0.370905 | + | 0.928671i | \(0.620953\pi\) | |||||||
\(314\) | −36.2520 | −2.04582 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −29.1725 | −1.64108 | ||||||||
\(317\) | −16.7155 | −0.938836 | −0.469418 | − | 0.882976i | \(-0.655536\pi\) | ||||
−0.469418 | + | 0.882976i | \(0.655536\pi\) | |||||||
\(318\) | −9.75127 | −0.546824 | ||||||||
\(319\) | −14.5330 | −0.813689 | ||||||||
\(320\) | −7.55095 | −0.422111 | ||||||||
\(321\) | 2.66245 | 0.148604 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.5106 | 0.640468 | ||||||||
\(324\) | 31.2748 | 1.73749 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.5601 | −1.02795 | ||||||||
\(327\) | −0.895821 | −0.0495390 | ||||||||
\(328\) | 53.8445 | 2.97307 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.85228 | 0.322157 | ||||||||
\(331\) | −3.96665 | −0.218027 | −0.109013 | − | 0.994040i | \(-0.534769\pi\) | ||||
−0.109013 | + | 0.994040i | \(0.534769\pi\) | |||||||
\(332\) | 12.6769 | 0.695733 | ||||||||
\(333\) | −16.2600 | −0.891045 | ||||||||
\(334\) | 46.5445 | 2.54680 | ||||||||
\(335\) | 21.8946 | 1.19623 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.7032 | 0.746461 | 0.373230 | − | 0.927739i | \(-0.378250\pi\) | ||||
0.373230 | + | 0.927739i | \(0.378250\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.45421 | 0.241919 | ||||||||
\(340\) | 23.6935 | 1.28496 | ||||||||
\(341\) | −28.3426 | −1.53484 | ||||||||
\(342\) | 26.0281 | 1.40744 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −23.4632 | −1.26505 | ||||||||
\(345\) | 1.65992 | 0.0893671 | ||||||||
\(346\) | 33.1641 | 1.78291 | ||||||||
\(347\) | −26.3979 | −1.41711 | −0.708556 | − | 0.705655i | \(-0.750653\pi\) | ||||
−0.708556 | + | 0.705655i | \(0.750653\pi\) | |||||||
\(348\) | 13.0945 | 0.701941 | ||||||||
\(349\) | −4.89024 | −0.261769 | −0.130884 | − | 0.991398i | \(-0.541782\pi\) | ||||
−0.130884 | + | 0.991398i | \(0.541782\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 23.0690 | 1.22958 | ||||||||
\(353\) | −13.5577 | −0.721605 | −0.360802 | − | 0.932642i | \(-0.617497\pi\) | ||||
−0.360802 | + | 0.932642i | \(0.617497\pi\) | |||||||
\(354\) | 15.3322 | 0.814899 | ||||||||
\(355\) | 2.17806 | 0.115599 | ||||||||
\(356\) | −8.27291 | −0.438464 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.76360 | 0.251764 | ||||||||
\(359\) | 8.58568 | 0.453135 | 0.226567 | − | 0.973996i | \(-0.427250\pi\) | ||||
0.226567 | + | 0.973996i | \(0.427250\pi\) | |||||||
\(360\) | 30.7821 | 1.62236 | ||||||||
\(361\) | −5.44653 | −0.286659 | ||||||||
\(362\) | −8.54053 | −0.448880 | ||||||||
\(363\) | 1.90962 | 0.100229 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.6751 | 0.768130 | ||||||||
\(366\) | −3.92574 | −0.205202 | ||||||||
\(367\) | 1.66322 | 0.0868196 | 0.0434098 | − | 0.999057i | \(-0.486178\pi\) | ||||
0.0434098 | + | 0.999057i | \(0.486178\pi\) | |||||||
\(368\) | 17.2712 | 0.900324 | ||||||||
\(369\) | −21.0343 | −1.09500 | ||||||||
\(370\) | −24.8436 | −1.29156 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 25.5374 | 1.32405 | ||||||||
\(373\) | 13.9635 | 0.723002 | 0.361501 | − | 0.932372i | \(-0.382264\pi\) | ||||
0.361501 | + | 0.932372i | \(0.382264\pi\) | |||||||
\(374\) | −21.8927 | −1.13204 | ||||||||
\(375\) | −6.18595 | −0.319441 | ||||||||
\(376\) | −7.37655 | −0.380417 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.5758 | −1.62194 | −0.810969 | − | 0.585089i | \(-0.801059\pi\) | ||||
−0.810969 | + | 0.585089i | \(0.801059\pi\) | |||||||
\(380\) | 27.8985 | 1.43116 | ||||||||
\(381\) | 1.61975 | 0.0829822 | ||||||||
\(382\) | 12.6741 | 0.648466 | ||||||||
\(383\) | 31.9082 | 1.63043 | 0.815217 | − | 0.579156i | \(-0.196618\pi\) | ||||
0.815217 | + | 0.579156i | \(0.196618\pi\) | |||||||
\(384\) | 2.55692 | 0.130482 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.81525 | 0.397786 | ||||||||
\(387\) | 9.16588 | 0.465928 | ||||||||
\(388\) | −72.7788 | −3.69478 | ||||||||
\(389\) | −25.4150 | −1.28859 | −0.644296 | − | 0.764776i | \(-0.722850\pi\) | ||||
−0.644296 | + | 0.764776i | \(0.722850\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.20956 | −0.314031 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.29312 | 0.267003 | ||||||||
\(394\) | 12.0368 | 0.606403 | ||||||||
\(395\) | 10.0041 | 0.503358 | ||||||||
\(396\) | −34.7288 | −1.74519 | ||||||||
\(397\) | −4.15897 | −0.208733 | −0.104366 | − | 0.994539i | \(-0.533281\pi\) | ||||
−0.104366 | + | 0.994539i | \(0.533281\pi\) | |||||||
\(398\) | −1.06319 | −0.0532930 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.8823 | −1.04412 | ||||||||
\(401\) | −19.6013 | −0.978844 | −0.489422 | − | 0.872047i | \(-0.662792\pi\) | ||||
−0.489422 | + | 0.872047i | \(0.662792\pi\) | |||||||
\(402\) | 18.2282 | 0.909139 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6.01381 | 0.299198 | ||||||||
\(405\) | −10.7250 | −0.532929 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.1039 | 0.798238 | ||||||||
\(408\) | 11.3334 | 0.561086 | ||||||||
\(409\) | 17.6337 | 0.871930 | 0.435965 | − | 0.899964i | \(-0.356407\pi\) | ||||
0.435965 | + | 0.899964i | \(0.356407\pi\) | |||||||
\(410\) | −32.1381 | −1.58719 | ||||||||
\(411\) | 5.18083 | 0.255551 | ||||||||
\(412\) | 53.9063 | 2.65577 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −14.0412 | −0.690088 | ||||||||
\(415\) | −4.34725 | −0.213398 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.862831 | −0.0422530 | ||||||||
\(418\) | −25.7781 | −1.26085 | ||||||||
\(419\) | −29.8911 | −1.46027 | −0.730137 | − | 0.683301i | \(-0.760544\pi\) | ||||
−0.730137 | + | 0.683301i | \(0.760544\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.8528 | −0.626407 | −0.313203 | − | 0.949686i | \(-0.601402\pi\) | ||||
−0.313203 | + | 0.949686i | \(0.601402\pi\) | |||||||
\(422\) | −19.4559 | −0.947100 | ||||||||
\(423\) | 2.88164 | 0.140110 | ||||||||
\(424\) | 50.7975 | 2.46694 | ||||||||
\(425\) | 7.50787 | 0.364185 | ||||||||
\(426\) | 1.81332 | 0.0878559 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −24.1401 | −1.16685 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.0045 | 0.675355 | ||||||||
\(431\) | −8.97060 | −0.432098 | −0.216049 | − | 0.976382i | \(-0.569317\pi\) | ||||
−0.216049 | + | 0.976382i | \(0.569317\pi\) | |||||||
\(432\) | 25.8405 | 1.24325 | ||||||||
\(433\) | 3.45062 | 0.165826 | 0.0829132 | − | 0.996557i | \(-0.473578\pi\) | ||||
0.0829132 | + | 0.996557i | \(0.473578\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.49048 | −0.215302 | ||||||||
\(436\) | 8.12228 | 0.388987 | ||||||||
\(437\) | −7.31161 | −0.349762 | ||||||||
\(438\) | 12.2176 | 0.583780 | ||||||||
\(439\) | 38.5144 | 1.83819 | 0.919096 | − | 0.394034i | \(-0.128921\pi\) | ||||
0.919096 | + | 0.394034i | \(0.128921\pi\) | |||||||
\(440\) | −30.4864 | −1.45338 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.0399 | −0.714569 | −0.357284 | − | 0.933996i | \(-0.616297\pi\) | ||||
−0.357284 | + | 0.933996i | \(0.616297\pi\) | |||||||
\(444\) | −14.5100 | −0.688612 | ||||||||
\(445\) | 2.83701 | 0.134487 | ||||||||
\(446\) | 58.4492 | 2.76765 | ||||||||
\(447\) | −10.2646 | −0.485499 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.9235 | 1.83691 | 0.918456 | − | 0.395522i | \(-0.129436\pi\) | ||||
0.918456 | + | 0.395522i | \(0.129436\pi\) | |||||||
\(450\) | 16.9770 | 0.800303 | ||||||||
\(451\) | 20.8322 | 0.980952 | ||||||||
\(452\) | −40.3856 | −1.89958 | ||||||||
\(453\) | −3.90660 | −0.183548 | ||||||||
\(454\) | −35.3906 | −1.66097 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.3448 | 0.624927 | ||||||||
\(457\) | 13.9396 | 0.652069 | 0.326034 | − | 0.945358i | \(-0.394287\pi\) | ||||
0.326034 | + | 0.945358i | \(0.394287\pi\) | |||||||
\(458\) | −20.5298 | −0.959295 | ||||||||
\(459\) | −9.29049 | −0.433643 | ||||||||
\(460\) | −15.0502 | −0.701721 | ||||||||
\(461\) | 37.4635 | 1.74485 | 0.872424 | − | 0.488749i | \(-0.162547\pi\) | ||||
0.872424 | + | 0.488749i | \(0.162547\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.75275 | −0.313827 | −0.156913 | − | 0.987612i | \(-0.550154\pi\) | ||||
−0.156913 | + | 0.987612i | \(0.550154\pi\) | |||||||
\(464\) | −46.7228 | −2.16905 | ||||||||
\(465\) | −8.75749 | −0.406119 | ||||||||
\(466\) | −17.0115 | −0.788044 | ||||||||
\(467\) | −5.05032 | −0.233701 | −0.116851 | − | 0.993150i | \(-0.537280\pi\) | ||||
−0.116851 | + | 0.993150i | \(0.537280\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.40283 | 0.203087 | ||||||||
\(471\) | 7.26084 | 0.334562 | ||||||||
\(472\) | −79.8705 | −3.67634 | ||||||||
\(473\) | −9.07783 | −0.417399 | ||||||||
\(474\) | 8.32878 | 0.382554 | ||||||||
\(475\) | 8.84033 | 0.405622 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.8440 | −0.908593 | ||||||||
\(478\) | −24.3143 | −1.11211 | ||||||||
\(479\) | −9.45319 | −0.431927 | −0.215964 | − | 0.976401i | \(-0.569289\pi\) | ||||
−0.215964 | + | 0.976401i | \(0.569289\pi\) | |||||||
\(480\) | 7.12801 | 0.325348 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 26.1082 | 1.18920 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.3142 | −0.787010 | ||||||||
\(485\) | 24.9579 | 1.13328 | ||||||||
\(486\) | −32.0045 | −1.45175 | ||||||||
\(487\) | 39.9996 | 1.81255 | 0.906277 | − | 0.422684i | \(-0.138912\pi\) | ||||
0.906277 | + | 0.422684i | \(0.138912\pi\) | |||||||
\(488\) | 20.4504 | 0.925748 | ||||||||
\(489\) | 3.71737 | 0.168105 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.76097 | −0.305118 | −0.152559 | − | 0.988294i | \(-0.548751\pi\) | ||||
−0.152559 | + | 0.988294i | \(0.548751\pi\) | |||||||
\(492\) | −18.7704 | −0.846233 | ||||||||
\(493\) | 16.7984 | 0.756560 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.9095 | 0.535291 | ||||||||
\(496\) | −91.1203 | −4.09142 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.61927 | −0.162183 | ||||||||
\(499\) | 11.3575 | 0.508433 | 0.254217 | − | 0.967147i | \(-0.418182\pi\) | ||||
0.254217 | + | 0.967147i | \(0.418182\pi\) | |||||||
\(500\) | 56.0871 | 2.50829 | ||||||||
\(501\) | −9.32230 | −0.416490 | ||||||||
\(502\) | 26.7882 | 1.19562 | ||||||||
\(503\) | 13.9285 | 0.621040 | 0.310520 | − | 0.950567i | \(-0.399497\pi\) | ||||
0.310520 | + | 0.950567i | \(0.399497\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.06230 | −0.0917713 | ||||||||
\(506\) | 13.9063 | 0.618212 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.6860 | −0.651587 | ||||||||
\(509\) | 19.8149 | 0.878281 | 0.439141 | − | 0.898418i | \(-0.355283\pi\) | ||||
0.439141 | + | 0.898418i | \(0.355283\pi\) | |||||||
\(510\) | −6.76454 | −0.299539 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −47.4335 | −2.09628 | ||||||||
\(513\) | −10.9393 | −0.482983 | ||||||||
\(514\) | −20.6741 | −0.911894 | ||||||||
\(515\) | −18.4860 | −0.814590 | ||||||||
\(516\) | 8.17934 | 0.360076 | ||||||||
\(517\) | −2.85396 | −0.125517 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.64237 | −0.291568 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.0951 | 1.36230 | 0.681151 | − | 0.732143i | \(-0.261480\pi\) | ||||
0.681151 | + | 0.732143i | \(0.261480\pi\) | |||||||
\(522\) | 37.9849 | 1.66255 | ||||||||
\(523\) | −22.7202 | −0.993485 | −0.496742 | − | 0.867898i | \(-0.665471\pi\) | ||||
−0.496742 | + | 0.867898i | \(0.665471\pi\) | |||||||
\(524\) | −47.9919 | −2.09654 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.0966 | 0.571040 | ||||||||
\(527\) | 32.7607 | 1.42708 | ||||||||
\(528\) | −12.1960 | −0.530761 | ||||||||
\(529\) | −19.0557 | −0.828507 | ||||||||
\(530\) | −30.3194 | −1.31699 | ||||||||
\(531\) | 31.2013 | 1.35402 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2.36193 | 0.102211 | ||||||||
\(535\) | 8.27830 | 0.357902 | ||||||||
\(536\) | −94.9564 | −4.10149 | ||||||||
\(537\) | −0.954091 | −0.0411721 | ||||||||
\(538\) | −35.9563 | −1.55018 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −22.5176 | −0.969002 | ||||||||
\(541\) | 2.09872 | 0.0902310 | 0.0451155 | − | 0.998982i | \(-0.485634\pi\) | ||||
0.0451155 | + | 0.998982i | \(0.485634\pi\) | |||||||
\(542\) | 21.5558 | 0.925902 | ||||||||
\(543\) | 1.71057 | 0.0734074 | ||||||||
\(544\) | −26.6650 | −1.14325 | ||||||||
\(545\) | −2.78536 | −0.119312 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.3770 | 1.08504 | 0.542521 | − | 0.840042i | \(-0.317470\pi\) | ||||
0.542521 | + | 0.840042i | \(0.317470\pi\) | |||||||
\(548\) | −46.9738 | −2.00662 | ||||||||
\(549\) | −7.98894 | −0.340959 | ||||||||
\(550\) | −16.8139 | −0.716948 | ||||||||
\(551\) | 19.7797 | 0.842642 | ||||||||
\(552\) | −7.19902 | −0.306411 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −60.0855 | −2.55279 | ||||||||
\(555\) | 4.97587 | 0.211214 | ||||||||
\(556\) | 7.82316 | 0.331776 | ||||||||
\(557\) | −44.2503 | −1.87495 | −0.937473 | − | 0.348058i | \(-0.886841\pi\) | ||||
−0.937473 | + | 0.348058i | \(0.886841\pi\) | |||||||
\(558\) | 74.0794 | 3.13603 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.38484 | 0.185128 | ||||||||
\(562\) | 70.3051 | 2.96564 | ||||||||
\(563\) | 38.8907 | 1.63905 | 0.819523 | − | 0.573046i | \(-0.194238\pi\) | ||||
0.819523 | + | 0.573046i | \(0.194238\pi\) | |||||||
\(564\) | 2.57149 | 0.108279 | ||||||||
\(565\) | 13.8494 | 0.582647 | ||||||||
\(566\) | 41.8092 | 1.75737 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.44618 | −0.396353 | ||||||||
\(569\) | 46.1579 | 1.93504 | 0.967520 | − | 0.252796i | \(-0.0813500\pi\) | ||||
0.967520 | + | 0.252796i | \(0.0813500\pi\) | |||||||
\(570\) | −7.96508 | −0.333620 | ||||||||
\(571\) | 21.1368 | 0.884548 | 0.442274 | − | 0.896880i | \(-0.354172\pi\) | ||||
0.442274 | + | 0.896880i | \(0.354172\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.53848 | −0.106047 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.76904 | −0.198883 | ||||||||
\(576\) | −12.7931 | −0.533045 | ||||||||
\(577\) | −25.3304 | −1.05452 | −0.527259 | − | 0.849705i | \(-0.676780\pi\) | ||||
−0.527259 | + | 0.849705i | \(0.676780\pi\) | |||||||
\(578\) | −18.7009 | −0.777855 | ||||||||
\(579\) | −1.56530 | −0.0650517 | ||||||||
\(580\) | 40.7146 | 1.69058 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 20.7785 | 0.861295 | ||||||||
\(583\) | 19.6533 | 0.813958 | ||||||||
\(584\) | −63.6455 | −2.63367 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 37.9106 | 1.56607 | ||||||||
\(587\) | −3.56287 | −0.147056 | −0.0735278 | − | 0.997293i | \(-0.523426\pi\) | ||||
−0.0735278 | + | 0.997293i | \(0.523426\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 38.5749 | 1.58945 | ||||||||
\(590\) | 47.6722 | 1.96263 | ||||||||
\(591\) | −2.41082 | −0.0991679 | ||||||||
\(592\) | 51.7732 | 2.12786 | ||||||||
\(593\) | −25.3536 | −1.04115 | −0.520573 | − | 0.853817i | \(-0.674282\pi\) | ||||
−0.520573 | + | 0.853817i | \(0.674282\pi\) | |||||||
\(594\) | 20.8061 | 0.853685 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 93.0677 | 3.81220 | ||||||||
\(597\) | 0.212945 | 0.00871524 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.9216 | 0.446243 | 0.223122 | − | 0.974791i | \(-0.428375\pi\) | ||||
0.223122 | + | 0.974791i | \(0.428375\pi\) | |||||||
\(600\) | 8.70421 | 0.355348 | ||||||||
\(601\) | −24.2564 | −0.989439 | −0.494720 | − | 0.869053i | \(-0.664729\pi\) | ||||
−0.494720 | + | 0.869053i | \(0.664729\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 37.0946 | 1.51061 | ||||||||
\(604\) | 35.4206 | 1.44124 | ||||||||
\(605\) | 5.93753 | 0.241395 | ||||||||
\(606\) | −1.71695 | −0.0697464 | ||||||||
\(607\) | 9.85447 | 0.399981 | 0.199990 | − | 0.979798i | \(-0.435909\pi\) | ||||
0.199990 | + | 0.979798i | \(0.435909\pi\) | |||||||
\(608\) | −31.3974 | −1.27333 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.2062 | −0.494215 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 40.1423 | 1.62266 | ||||||||
\(613\) | 3.67688 | 0.148508 | 0.0742540 | − | 0.997239i | \(-0.476342\pi\) | ||||
0.0742540 | + | 0.997239i | \(0.476342\pi\) | |||||||
\(614\) | 23.2416 | 0.937955 | ||||||||
\(615\) | 6.43688 | 0.259560 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.7468 | −0.754718 | −0.377359 | − | 0.926067i | \(-0.623168\pi\) | ||||
−0.377359 | + | 0.926067i | \(0.623168\pi\) | |||||||
\(618\) | −15.3903 | −0.619090 | ||||||||
\(619\) | 15.8945 | 0.638854 | 0.319427 | − | 0.947611i | \(-0.396510\pi\) | ||||
0.319427 | + | 0.947611i | \(0.396510\pi\) | |||||||
\(620\) | 79.4029 | 3.18890 | ||||||||
\(621\) | 5.90137 | 0.236814 | ||||||||
\(622\) | −31.5333 | −1.26437 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.22743 | −0.289097 | ||||||||
\(626\) | −33.9727 | −1.35782 | ||||||||
\(627\) | 5.16304 | 0.206192 | ||||||||
\(628\) | −65.8330 | −2.62702 | ||||||||
\(629\) | −18.6141 | −0.742194 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.7451 | −0.786040 | −0.393020 | − | 0.919530i | \(-0.628570\pi\) | ||||
−0.393020 | + | 0.919530i | \(0.628570\pi\) | |||||||
\(632\) | −43.3873 | −1.72585 | ||||||||
\(633\) | 3.89679 | 0.154883 | ||||||||
\(634\) | −43.2698 | −1.71846 | ||||||||
\(635\) | 5.03624 | 0.199857 | ||||||||
\(636\) | −17.7081 | −0.702173 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −37.6200 | −1.48939 | ||||||||
\(639\) | 3.69014 | 0.145980 | ||||||||
\(640\) | 7.95016 | 0.314258 | ||||||||
\(641\) | −29.7786 | −1.17618 | −0.588092 | − | 0.808794i | \(-0.700121\pi\) | ||||
−0.588092 | + | 0.808794i | \(0.700121\pi\) | |||||||
\(642\) | 6.89203 | 0.272007 | ||||||||
\(643\) | 11.5725 | 0.456373 | 0.228187 | − | 0.973617i | \(-0.426720\pi\) | ||||
0.228187 | + | 0.973617i | \(0.426720\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.80493 | −0.110444 | ||||||||
\(646\) | 29.7964 | 1.17232 | ||||||||
\(647\) | −25.5065 | −1.00276 | −0.501382 | − | 0.865226i | \(-0.667175\pi\) | ||||
−0.501382 | + | 0.865226i | \(0.667175\pi\) | |||||||
\(648\) | 46.5140 | 1.82724 | ||||||||
\(649\) | −30.9016 | −1.21299 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −33.7049 | −1.31999 | ||||||||
\(653\) | −44.8293 | −1.75430 | −0.877152 | − | 0.480212i | \(-0.840560\pi\) | ||||
−0.877152 | + | 0.480212i | \(0.840560\pi\) | |||||||
\(654\) | −2.31892 | −0.0906771 | ||||||||
\(655\) | 16.4578 | 0.643058 | ||||||||
\(656\) | 66.9747 | 2.61492 | ||||||||
\(657\) | 24.8630 | 0.969999 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.1734 | 1.60389 | 0.801944 | − | 0.597399i | \(-0.203799\pi\) | ||||
0.801944 | + | 0.597399i | \(0.203799\pi\) | |||||||
\(660\) | 10.6276 | 0.413680 | ||||||||
\(661\) | 21.8938 | 0.851569 | 0.425785 | − | 0.904825i | \(-0.359998\pi\) | ||||
0.425785 | + | 0.904825i | \(0.359998\pi\) | |||||||
\(662\) | −10.2681 | −0.399080 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.8539 | 0.731673 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −42.0908 | −1.63098 | ||||||||
\(667\) | −10.6704 | −0.413160 | ||||||||
\(668\) | 84.5239 | 3.27033 | ||||||||
\(669\) | −11.7067 | −0.452606 | ||||||||
\(670\) | 56.6764 | 2.18960 | ||||||||
\(671\) | 7.91219 | 0.305447 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.6688 | 1.37493 | 0.687466 | − | 0.726217i | \(-0.258723\pi\) | ||||
0.687466 | + | 0.726217i | \(0.258723\pi\) | |||||||
\(674\) | 35.4721 | 1.36633 | ||||||||
\(675\) | −7.13524 | −0.274635 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.55532 | −0.0982089 | −0.0491044 | − | 0.998794i | \(-0.515637\pi\) | ||||
−0.0491044 | + | 0.998794i | \(0.515637\pi\) | |||||||
\(678\) | 11.5302 | 0.442813 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 35.2386 | 1.35134 | ||||||||
\(681\) | 7.08832 | 0.271625 | ||||||||
\(682\) | −73.3678 | −2.80940 | ||||||||
\(683\) | 35.7399 | 1.36755 | 0.683775 | − | 0.729693i | \(-0.260337\pi\) | ||||
0.683775 | + | 0.729693i | \(0.260337\pi\) | |||||||
\(684\) | 47.2666 | 1.80728 | ||||||||
\(685\) | 16.1086 | 0.615479 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.11188 | 0.156878 | ||||||||
\(688\) | −29.1848 | −1.11266 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.29687 | 0.163579 | ||||||||
\(691\) | 26.0292 | 0.990197 | 0.495099 | − | 0.868837i | \(-0.335132\pi\) | ||||
0.495099 | + | 0.868837i | \(0.335132\pi\) | |||||||
\(692\) | 60.2254 | 2.28943 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −68.3335 | −2.59391 | ||||||||
\(695\) | −2.68278 | −0.101764 | ||||||||
\(696\) | 19.4751 | 0.738202 | ||||||||
\(697\) | −24.0796 | −0.912079 | ||||||||
\(698\) | −12.6589 | −0.479146 | ||||||||
\(699\) | 3.40721 | 0.128872 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.12731 | 0.0425779 | 0.0212890 | − | 0.999773i | \(-0.493223\pi\) | ||||
0.0212890 | + | 0.999773i | \(0.493223\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.9177 | −0.826641 | ||||||||
\(704\) | 12.6702 | 0.477525 | ||||||||
\(705\) | −0.881834 | −0.0332118 | ||||||||
\(706\) | −35.0955 | −1.32084 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 27.8431 | 1.04641 | ||||||||
\(709\) | 6.05031 | 0.227224 | 0.113612 | − | 0.993525i | \(-0.463758\pi\) | ||||
0.113612 | + | 0.993525i | \(0.463758\pi\) | |||||||
\(710\) | 5.63813 | 0.211595 | ||||||||
\(711\) | 16.9492 | 0.635644 | ||||||||
\(712\) | −12.3040 | −0.461114 | ||||||||
\(713\) | −20.8098 | −0.779332 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.65061 | 0.323288 | ||||||||
\(717\) | 4.86986 | 0.181868 | ||||||||
\(718\) | 22.2249 | 0.829425 | ||||||||
\(719\) | −47.1177 | −1.75719 | −0.878597 | − | 0.477563i | \(-0.841520\pi\) | ||||
−0.878597 | + | 0.477563i | \(0.841520\pi\) | |||||||
\(720\) | 38.2884 | 1.42692 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −14.0989 | −0.524706 | ||||||||
\(723\) | −5.22916 | −0.194475 | ||||||||
\(724\) | −15.5095 | −0.576404 | ||||||||
\(725\) | 12.9014 | 0.479146 | ||||||||
\(726\) | 4.94324 | 0.183461 | ||||||||
\(727\) | 17.9215 | 0.664671 | 0.332335 | − | 0.943161i | \(-0.392163\pi\) | ||||
0.332335 | + | 0.943161i | \(0.392163\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.5489 | −0.501810 | ||||||||
\(730\) | 37.9880 | 1.40600 | ||||||||
\(731\) | 10.4929 | 0.388093 | ||||||||
\(732\) | −7.12908 | −0.263498 | ||||||||
\(733\) | −45.2685 | −1.67203 | −0.836016 | − | 0.548705i | \(-0.815121\pi\) | ||||
−0.836016 | + | 0.548705i | \(0.815121\pi\) | |||||||
\(734\) | 4.30542 | 0.158916 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.9378 | 0.624335 | ||||||||
\(737\) | −36.7382 | −1.35327 | ||||||||
\(738\) | −54.4494 | −2.00431 | ||||||||
\(739\) | 19.2613 | 0.708539 | 0.354270 | − | 0.935143i | \(-0.384730\pi\) | ||||
0.354270 | + | 0.935143i | \(0.384730\pi\) | |||||||
\(740\) | −45.1155 | −1.65848 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.8853 | 1.27982 | 0.639908 | − | 0.768452i | \(-0.278972\pi\) | ||||
0.639908 | + | 0.768452i | \(0.278972\pi\) | |||||||
\(744\) | 37.9810 | 1.39245 | ||||||||
\(745\) | −31.9155 | −1.16929 | ||||||||
\(746\) | 36.1459 | 1.32339 | ||||||||
\(747\) | −7.36525 | −0.269480 | ||||||||
\(748\) | −39.7567 | −1.45365 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −16.0130 | −0.584711 | ||||||||
\(751\) | −24.9668 | −0.911051 | −0.455526 | − | 0.890223i | \(-0.650549\pi\) | ||||
−0.455526 | + | 0.890223i | \(0.650549\pi\) | |||||||
\(752\) | −9.17535 | −0.334591 | ||||||||
\(753\) | −5.36536 | −0.195525 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.1467 | −0.442064 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.6049 | −0.385440 | −0.192720 | − | 0.981254i | \(-0.561731\pi\) | ||||
−0.192720 | + | 0.981254i | \(0.561731\pi\) | |||||||
\(758\) | −81.7370 | −2.96882 | ||||||||
\(759\) | −2.78527 | −0.101099 | ||||||||
\(760\) | 41.4926 | 1.50510 | ||||||||
\(761\) | 32.6388 | 1.18316 | 0.591578 | − | 0.806248i | \(-0.298505\pi\) | ||||
0.591578 | + | 0.806248i | \(0.298505\pi\) | |||||||
\(762\) | 4.19288 | 0.151892 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 23.0160 | 0.832691 | ||||||||
\(765\) | −13.7659 | −0.497708 | ||||||||
\(766\) | 82.5976 | 2.98437 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 11.4759 | 0.414100 | ||||||||
\(769\) | 52.1752 | 1.88149 | 0.940744 | − | 0.339119i | \(-0.110129\pi\) | ||||
0.940744 | + | 0.339119i | \(0.110129\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.14077 | 0.149126 | ||||||||
\(772\) | 14.1924 | 0.510794 | ||||||||
\(773\) | 35.7057 | 1.28425 | 0.642123 | − | 0.766602i | \(-0.278054\pi\) | ||||
0.642123 | + | 0.766602i | \(0.278054\pi\) | |||||||
\(774\) | 23.7268 | 0.852842 | ||||||||
\(775\) | 25.1607 | 0.903800 | ||||||||
\(776\) | −108.242 | −3.88565 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −65.7893 | −2.35866 | ||||||||
\(779\) | −28.3531 | −1.01586 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.65469 | −0.130775 | ||||||||
\(782\) | −16.0741 | −0.574808 | ||||||||
\(783\) | −15.9646 | −0.570529 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.5760 | 0.805770 | ||||||||
\(786\) | 13.7018 | 0.488726 | ||||||||
\(787\) | 6.10621 | 0.217663 | 0.108831 | − | 0.994060i | \(-0.465289\pi\) | ||||
0.108831 | + | 0.994060i | \(0.465289\pi\) | |||||||
\(788\) | 21.8586 | 0.778679 | ||||||||
\(789\) | −2.62310 | −0.0933847 | ||||||||
\(790\) | 25.8965 | 0.921356 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −51.6510 | −1.83534 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −10.7659 | −0.382068 | ||||||||
\(795\) | 6.07261 | 0.215373 | ||||||||
\(796\) | −1.93074 | −0.0684332 | ||||||||
\(797\) | 46.2299 | 1.63755 | 0.818773 | − | 0.574117i | \(-0.194654\pi\) | ||||
0.818773 | + | 0.574117i | \(0.194654\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.29884 | 0.116704 | ||||||||
\(800\) | −20.4792 | −0.724048 | ||||||||
\(801\) | 4.80656 | 0.169831 | ||||||||
\(802\) | −50.7400 | −1.79169 | ||||||||
\(803\) | −24.6242 | −0.868968 | ||||||||
\(804\) | 33.1020 | 1.16742 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.20161 | 0.253509 | ||||||||
\(808\) | 8.94415 | 0.314654 | ||||||||
\(809\) | 39.2879 | 1.38129 | 0.690644 | − | 0.723195i | \(-0.257327\pi\) | ||||
0.690644 | + | 0.723195i | \(0.257327\pi\) | |||||||
\(810\) | −27.7627 | −0.975482 | ||||||||
\(811\) | 6.90664 | 0.242525 | 0.121262 | − | 0.992620i | \(-0.461306\pi\) | ||||
0.121262 | + | 0.992620i | \(0.461306\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.31738 | −0.151417 | ||||||||
\(814\) | 41.6864 | 1.46111 | ||||||||
\(815\) | 11.5583 | 0.404871 | ||||||||
\(816\) | 14.0971 | 0.493496 | ||||||||
\(817\) | 12.3551 | 0.432251 | ||||||||
\(818\) | 45.6466 | 1.59600 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −58.3622 | −2.03810 | ||||||||
\(821\) | 1.91049 | 0.0666765 | 0.0333382 | − | 0.999444i | \(-0.489386\pi\) | ||||
0.0333382 | + | 0.999444i | \(0.489386\pi\) | |||||||
\(822\) | 13.4111 | 0.467765 | ||||||||
\(823\) | 1.57969 | 0.0550645 | 0.0275322 | − | 0.999621i | \(-0.491235\pi\) | ||||
0.0275322 | + | 0.999621i | \(0.491235\pi\) | |||||||
\(824\) | 80.1732 | 2.79296 | ||||||||
\(825\) | 3.36763 | 0.117246 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.5050 | 1.13031 | 0.565155 | − | 0.824985i | \(-0.308816\pi\) | ||||
0.565155 | + | 0.824985i | \(0.308816\pi\) | |||||||
\(828\) | −25.4986 | −0.886138 | ||||||||
\(829\) | 35.0538 | 1.21747 | 0.608735 | − | 0.793373i | \(-0.291677\pi\) | ||||
0.608735 | + | 0.793373i | \(0.291677\pi\) | |||||||
\(830\) | −11.2533 | −0.390608 | ||||||||
\(831\) | 12.0344 | 0.417469 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.23353 | −0.0773407 | ||||||||
\(835\) | −28.9856 | −1.00309 | ||||||||
\(836\) | −46.8126 | −1.61905 | ||||||||
\(837\) | −31.1347 | −1.07617 | ||||||||
\(838\) | −77.3760 | −2.67291 | ||||||||
\(839\) | −5.35487 | −0.184871 | −0.0924354 | − | 0.995719i | \(-0.529465\pi\) | ||||
−0.0924354 | + | 0.995719i | \(0.529465\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.133978 | −0.00461993 | ||||||||
\(842\) | −33.2708 | −1.14659 | ||||||||
\(843\) | −14.0813 | −0.484985 | ||||||||
\(844\) | −35.3316 | −1.21616 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.45942 | 0.256460 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 63.1846 | 2.16977 | ||||||||
\(849\) | −8.37387 | −0.287391 | ||||||||
\(850\) | 19.4349 | 0.666611 | ||||||||
\(851\) | 11.8238 | 0.405314 | ||||||||
\(852\) | 3.29297 | 0.112815 | ||||||||
\(853\) | −49.6270 | −1.69920 | −0.849598 | − | 0.527431i | \(-0.823155\pi\) | ||||
−0.849598 | + | 0.527431i | \(0.823155\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.2090 | −0.554337 | ||||||||
\(856\) | −35.9028 | −1.22713 | ||||||||
\(857\) | −5.88392 | −0.200991 | −0.100496 | − | 0.994938i | \(-0.532043\pi\) | ||||
−0.100496 | + | 0.994938i | \(0.532043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.3862 | −1.48032 | −0.740159 | − | 0.672432i | \(-0.765250\pi\) | ||||
−0.740159 | + | 0.672432i | \(0.765250\pi\) | |||||||
\(860\) | 25.4318 | 0.867219 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.2213 | −0.790920 | ||||||||
\(863\) | −31.1272 | −1.05958 | −0.529792 | − | 0.848128i | \(-0.677730\pi\) | ||||
−0.529792 | + | 0.848128i | \(0.677730\pi\) | |||||||
\(864\) | 25.3416 | 0.862139 | ||||||||
\(865\) | −20.6530 | −0.702222 | ||||||||
\(866\) | 8.93228 | 0.303531 | ||||||||
\(867\) | 3.74557 | 0.127206 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.7864 | −0.569439 | ||||||||
\(870\) | −11.6241 | −0.394093 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 12.0800 | 0.409081 | ||||||||
\(873\) | 42.2844 | 1.43111 | ||||||||
\(874\) | −18.9268 | −0.640209 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 22.1870 | 0.749629 | ||||||||
\(877\) | 29.9106 | 1.01001 | 0.505004 | − | 0.863117i | \(-0.331491\pi\) | ||||
0.505004 | + | 0.863117i | \(0.331491\pi\) | |||||||
\(878\) | 99.6984 | 3.36466 | ||||||||
\(879\) | −7.59304 | −0.256107 | ||||||||
\(880\) | −37.9206 | −1.27830 | ||||||||
\(881\) | −14.5695 | −0.490860 | −0.245430 | − | 0.969414i | \(-0.578929\pi\) | ||||
−0.245430 | + | 0.969414i | \(0.578929\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.9296 | −1.64661 | −0.823307 | − | 0.567597i | \(-0.807873\pi\) | ||||
−0.823307 | + | 0.567597i | \(0.807873\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.54817 | −0.320958 | ||||||||
\(886\) | −38.9324 | −1.30796 | ||||||||
\(887\) | −54.5902 | −1.83296 | −0.916480 | − | 0.400080i | \(-0.868982\pi\) | ||||
−0.916480 | + | 0.400080i | \(0.868982\pi\) | |||||||
\(888\) | −21.5802 | −0.724184 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.34389 | 0.246168 | ||||||||
\(891\) | 17.9961 | 0.602891 | ||||||||
\(892\) | 106.143 | 3.55392 | ||||||||
\(893\) | 3.88430 | 0.129983 | ||||||||
\(894\) | −26.5710 | −0.888666 | ||||||||
\(895\) | −2.96653 | −0.0991603 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 100.757 | 3.36232 | ||||||||
\(899\) | 56.2955 | 1.87756 | ||||||||
\(900\) | 30.8299 | 1.02766 | ||||||||
\(901\) | −22.7169 | −0.756810 | ||||||||
\(902\) | 53.9263 | 1.79555 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −60.0643 | −1.99771 | ||||||||
\(905\) | 5.31862 | 0.176797 | ||||||||
\(906\) | −10.1126 | −0.335970 | ||||||||
\(907\) | 22.7255 | 0.754589 | 0.377295 | − | 0.926093i | \(-0.376854\pi\) | ||||
0.377295 | + | 0.926093i | \(0.376854\pi\) | |||||||
\(908\) | −64.2688 | −2.13283 | ||||||||
\(909\) | −3.49402 | −0.115889 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.2359 | −1.39934 | −0.699669 | − | 0.714467i | \(-0.746669\pi\) | ||||
−0.699669 | + | 0.714467i | \(0.746669\pi\) | |||||||
\(912\) | 16.5990 | 0.549646 | ||||||||
\(913\) | 7.29450 | 0.241413 | ||||||||
\(914\) | 36.0842 | 1.19356 | ||||||||
\(915\) | 2.44476 | 0.0808213 | ||||||||
\(916\) | −37.2818 | −1.23182 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −24.0494 | −0.793747 | ||||||||
\(919\) | 30.6940 | 1.01250 | 0.506251 | − | 0.862386i | \(-0.331031\pi\) | ||||
0.506251 | + | 0.862386i | \(0.331031\pi\) | |||||||
\(920\) | −22.3838 | −0.737971 | ||||||||
\(921\) | −4.65502 | −0.153388 | ||||||||
\(922\) | 96.9780 | 3.19380 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.2959 | −0.470048 | ||||||||
\(926\) | −17.4802 | −0.574434 | ||||||||
\(927\) | −31.3195 | −1.02867 | ||||||||
\(928\) | −45.8208 | −1.50414 | ||||||||
\(929\) | 37.4250 | 1.22787 | 0.613936 | − | 0.789355i | \(-0.289585\pi\) | ||||
0.613936 | + | 0.789355i | \(0.289585\pi\) | |||||||
\(930\) | −22.6696 | −0.743367 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −30.8926 | −1.01192 | ||||||||
\(933\) | 6.31574 | 0.206768 | ||||||||
\(934\) | −13.0733 | −0.427770 | ||||||||
\(935\) | 13.6337 | 0.445869 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.3386 | −1.44848 | −0.724239 | − | 0.689549i | \(-0.757809\pi\) | ||||
−0.724239 | + | 0.689549i | \(0.757809\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.80433 | 0.222051 | ||||||||
\(940\) | 7.99546 | 0.260783 | ||||||||
\(941\) | 27.5052 | 0.896646 | 0.448323 | − | 0.893872i | \(-0.352022\pi\) | ||||
0.448323 | + | 0.893872i | \(0.352022\pi\) | |||||||
\(942\) | 18.7954 | 0.612388 | ||||||||
\(943\) | 15.2955 | 0.498089 | ||||||||
\(944\) | −99.3472 | −3.23348 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −23.4989 | −0.764014 | ||||||||
\(947\) | 5.08330 | 0.165185 | 0.0825925 | − | 0.996583i | \(-0.473680\pi\) | ||||
0.0825925 | + | 0.996583i | \(0.473680\pi\) | |||||||
\(948\) | 15.1249 | 0.491235 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 22.8841 | 0.742458 | ||||||||
\(951\) | 8.66642 | 0.281028 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.81437 | 0.317919 | 0.158959 | − | 0.987285i | \(-0.449186\pi\) | ||||
0.158959 | + | 0.987285i | \(0.449186\pi\) | |||||||
\(954\) | −51.3681 | −1.66310 | ||||||||
\(955\) | −7.89284 | −0.255406 | ||||||||
\(956\) | −44.1543 | −1.42805 | ||||||||
\(957\) | 7.53484 | 0.243567 | ||||||||
\(958\) | −24.4705 | −0.790607 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.91491 | 0.126353 | ||||||||
\(961\) | 78.7893 | 2.54159 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.0254 | 0.451961 | ||||||||
\(964\) | 47.4121 | 1.52704 | ||||||||
\(965\) | −4.86695 | −0.156673 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.69619 | −0.0867036 | −0.0433518 | − | 0.999060i | \(-0.513804\pi\) | ||||
−0.0433518 | + | 0.999060i | \(0.513804\pi\) | |||||||
\(968\) | −25.7509 | −0.827665 | ||||||||
\(969\) | −5.96786 | −0.191715 | ||||||||
\(970\) | 64.6060 | 2.07437 | ||||||||
\(971\) | −24.9240 | −0.799850 | −0.399925 | − | 0.916548i | \(-0.630964\pi\) | ||||
−0.399925 | + | 0.916548i | \(0.630964\pi\) | |||||||
\(972\) | −58.1196 | −1.86419 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 103.543 | 3.31773 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 25.4373 | 0.814230 | ||||||||
\(977\) | −28.3129 | −0.905811 | −0.452906 | − | 0.891558i | \(-0.649613\pi\) | ||||
−0.452906 | + | 0.891558i | \(0.649613\pi\) | |||||||
\(978\) | 9.62280 | 0.307703 | ||||||||
\(979\) | −4.76039 | −0.152143 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.71904 | −0.150667 | ||||||||
\(982\) | −17.5015 | −0.558494 | ||||||||
\(983\) | −37.8517 | −1.20728 | −0.603641 | − | 0.797256i | \(-0.706284\pi\) | ||||
−0.603641 | + | 0.797256i | \(0.706284\pi\) | |||||||
\(984\) | −27.9166 | −0.889947 | ||||||||
\(985\) | −7.49591 | −0.238839 | ||||||||
\(986\) | 43.4842 | 1.38482 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.66514 | −0.211939 | ||||||||
\(990\) | 30.8289 | 0.979805 | ||||||||
\(991\) | 58.4158 | 1.85564 | 0.927820 | − | 0.373028i | \(-0.121681\pi\) | ||||
0.927820 | + | 0.373028i | \(0.121681\pi\) | |||||||
\(992\) | −89.3612 | −2.83722 | ||||||||
\(993\) | 2.05657 | 0.0652633 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.662104 | 0.0209901 | ||||||||
\(996\) | −6.57252 | −0.208258 | ||||||||
\(997\) | −28.0588 | −0.888632 | −0.444316 | − | 0.895870i | \(-0.646553\pi\) | ||||
−0.444316 | + | 0.895870i | \(0.646553\pi\) | |||||||
\(998\) | 29.4001 | 0.930645 | ||||||||
\(999\) | 17.6903 | 0.559696 |
(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 | 8281.2.a.co.1.12 | 12 | ||
7.3 | odd | 6 | 1183.2.e.j.170.1 | 24 | |||
7.5 | odd | 6 | 1183.2.e.j.508.1 | 24 | |||
7.6 | odd | 2 | 8281.2.a.cp.1.12 | 12 | |||
13.2 | odd | 12 | 637.2.q.i.589.6 | 12 | |||
13.7 | odd | 12 | 637.2.q.i.491.6 | 12 | |||
13.12 | even | 2 | inner | 8281.2.a.co.1.1 | 12 | ||
91.2 | odd | 12 | 637.2.k.i.459.1 | 12 | |||
91.12 | odd | 6 | 1183.2.e.j.508.12 | 24 | |||
91.20 | even | 12 | 637.2.q.g.491.6 | 12 | |||
91.33 | even | 12 | 91.2.u.b.88.1 | yes | 12 | ||
91.38 | odd | 6 | 1183.2.e.j.170.12 | 24 | |||
91.41 | even | 12 | 637.2.q.g.589.6 | 12 | |||
91.46 | odd | 12 | 637.2.k.i.569.6 | 12 | |||
91.54 | even | 12 | 91.2.k.b.4.1 | ✓ | 12 | ||
91.59 | even | 12 | 91.2.k.b.23.6 | yes | 12 | ||
91.67 | odd | 12 | 637.2.u.g.30.1 | 12 | |||
91.72 | odd | 12 | 637.2.u.g.361.1 | 12 | |||
91.80 | even | 12 | 91.2.u.b.30.1 | yes | 12 | ||
91.90 | odd | 2 | 8281.2.a.cp.1.1 | 12 | |||
273.59 | odd | 12 | 819.2.bm.f.478.1 | 12 | |||
273.80 | odd | 12 | 819.2.do.e.667.6 | 12 | |||
273.215 | odd | 12 | 819.2.do.e.361.6 | 12 | |||
273.236 | odd | 12 | 819.2.bm.f.550.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.1 | ✓ | 12 | 91.54 | even | 12 | ||
91.2.k.b.23.6 | yes | 12 | 91.59 | even | 12 | ||
91.2.u.b.30.1 | yes | 12 | 91.80 | even | 12 | ||
91.2.u.b.88.1 | yes | 12 | 91.33 | even | 12 | ||
637.2.k.i.459.1 | 12 | 91.2 | odd | 12 | |||
637.2.k.i.569.6 | 12 | 91.46 | odd | 12 | |||
637.2.q.g.491.6 | 12 | 91.20 | even | 12 | |||
637.2.q.g.589.6 | 12 | 91.41 | even | 12 | |||
637.2.q.i.491.6 | 12 | 13.7 | odd | 12 | |||
637.2.q.i.589.6 | 12 | 13.2 | odd | 12 | |||
637.2.u.g.30.1 | 12 | 91.67 | odd | 12 | |||
637.2.u.g.361.1 | 12 | 91.72 | odd | 12 | |||
819.2.bm.f.478.1 | 12 | 273.59 | odd | 12 | |||
819.2.bm.f.550.6 | 12 | 273.236 | odd | 12 | |||
819.2.do.e.361.6 | 12 | 273.215 | odd | 12 | |||
819.2.do.e.667.6 | 12 | 273.80 | odd | 12 | |||
1183.2.e.j.170.1 | 24 | 7.3 | odd | 6 | |||
1183.2.e.j.170.12 | 24 | 91.38 | odd | 6 | |||
1183.2.e.j.508.1 | 24 | 7.5 | odd | 6 | |||
1183.2.e.j.508.12 | 24 | 91.12 | odd | 6 | |||
8281.2.a.co.1.1 | 12 | 13.12 | even | 2 | inner | ||
8281.2.a.co.1.12 | 12 | 1.1 | even | 1 | trivial | ||
8281.2.a.cp.1.1 | 12 | 91.90 | odd | 2 | |||
8281.2.a.cp.1.12 | 12 | 7.6 | odd | 2 |