Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8030,2,Mod(1,8030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8030, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8030.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: | \(64.1198728231\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.216637.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 4x^{3} + 7x^{2} + x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.581553\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8030.1 |
$q$-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 | ||||||||
\(3\) | −3.38979 | −1.95709 | −0.978547 | − | 0.206023i | \(-0.933948\pi\) | ||||
−0.978547 | + | 0.206023i | \(0.933948\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −3.38979 | −1.38387 | ||||||||
\(7\) | 1.27596 | 0.482269 | 0.241135 | − | 0.970492i | \(-0.422480\pi\) | ||||
0.241135 | + | 0.970492i | \(0.422480\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 8.49065 | 2.83022 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −3.38979 | −0.978547 | ||||||||
\(13\) | −6.37288 | −1.76752 | −0.883759 | − | 0.467942i | \(-0.844995\pi\) | ||||
−0.883759 | + | 0.467942i | \(0.844995\pi\) | |||||||
\(14\) | 1.27596 | 0.341016 | ||||||||
\(15\) | −3.38979 | −0.875239 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.31350 | −1.04618 | −0.523088 | − | 0.852278i | \(-0.675220\pi\) | ||||
−0.523088 | + | 0.852278i | \(0.675220\pi\) | |||||||
\(18\) | 8.49065 | 2.00127 | ||||||||
\(19\) | 2.03588 | 0.467062 | 0.233531 | − | 0.972349i | \(-0.424972\pi\) | ||||
0.233531 | + | 0.972349i | \(0.424972\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −4.32525 | −0.943846 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 5.87814 | 1.22568 | 0.612838 | − | 0.790208i | \(-0.290028\pi\) | ||||
0.612838 | + | 0.790208i | \(0.290028\pi\) | |||||||
\(24\) | −3.38979 | −0.691937 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −6.37288 | −1.24982 | ||||||||
\(27\) | −18.6121 | −3.58191 | ||||||||
\(28\) | 1.27596 | 0.241135 | ||||||||
\(29\) | −1.36916 | −0.254247 | −0.127124 | − | 0.991887i | \(-0.540575\pi\) | ||||
−0.127124 | + | 0.991887i | \(0.540575\pi\) | |||||||
\(30\) | −3.38979 | −0.618888 | ||||||||
\(31\) | 8.83773 | 1.58730 | 0.793651 | − | 0.608373i | \(-0.208177\pi\) | ||||
0.793651 | + | 0.608373i | \(0.208177\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.38979 | −0.590086 | ||||||||
\(34\) | −4.31350 | −0.739759 | ||||||||
\(35\) | 1.27596 | 0.215677 | ||||||||
\(36\) | 8.49065 | 1.41511 | ||||||||
\(37\) | −1.21239 | −0.199315 | −0.0996577 | − | 0.995022i | \(-0.531775\pi\) | ||||
−0.0996577 | + | 0.995022i | \(0.531775\pi\) | |||||||
\(38\) | 2.03588 | 0.330263 | ||||||||
\(39\) | 21.6027 | 3.45920 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 3.71434 | 0.580083 | 0.290041 | − | 0.957014i | \(-0.406331\pi\) | ||||
0.290041 | + | 0.957014i | \(0.406331\pi\) | |||||||
\(42\) | −4.32525 | −0.667400 | ||||||||
\(43\) | −6.71830 | −1.02453 | −0.512265 | − | 0.858827i | \(-0.671194\pi\) | ||||
−0.512265 | + | 0.858827i | \(0.671194\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 8.49065 | 1.26571 | ||||||||
\(46\) | 5.87814 | 0.866684 | ||||||||
\(47\) | −10.0246 | −1.46223 | −0.731117 | − | 0.682252i | \(-0.761001\pi\) | ||||
−0.731117 | + | 0.682252i | \(0.761001\pi\) | |||||||
\(48\) | −3.38979 | −0.489274 | ||||||||
\(49\) | −5.37191 | −0.767416 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 14.6218 | 2.04747 | ||||||||
\(52\) | −6.37288 | −0.883759 | ||||||||
\(53\) | −8.27201 | −1.13625 | −0.568124 | − | 0.822943i | \(-0.692331\pi\) | ||||
−0.568124 | + | 0.822943i | \(0.692331\pi\) | |||||||
\(54\) | −18.6121 | −2.53279 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 1.27596 | 0.170508 | ||||||||
\(57\) | −6.90119 | −0.914085 | ||||||||
\(58\) | −1.36916 | −0.179780 | ||||||||
\(59\) | −13.9774 | −1.81970 | −0.909848 | − | 0.414942i | \(-0.863802\pi\) | ||||
−0.909848 | + | 0.414942i | \(0.863802\pi\) | |||||||
\(60\) | −3.38979 | −0.437620 | ||||||||
\(61\) | −0.979378 | −0.125396 | −0.0626982 | − | 0.998033i | \(-0.519971\pi\) | ||||
−0.0626982 | + | 0.998033i | \(0.519971\pi\) | |||||||
\(62\) | 8.83773 | 1.12239 | ||||||||
\(63\) | 10.8338 | 1.36493 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.37288 | −0.790458 | ||||||||
\(66\) | −3.38979 | −0.417254 | ||||||||
\(67\) | 0.367267 | 0.0448688 | 0.0224344 | − | 0.999748i | \(-0.492858\pi\) | ||||
0.0224344 | + | 0.999748i | \(0.492858\pi\) | |||||||
\(68\) | −4.31350 | −0.523088 | ||||||||
\(69\) | −19.9256 | −2.39877 | ||||||||
\(70\) | 1.27596 | 0.152507 | ||||||||
\(71\) | −4.19342 | −0.497667 | −0.248834 | − | 0.968546i | \(-0.580047\pi\) | ||||
−0.248834 | + | 0.968546i | \(0.580047\pi\) | |||||||
\(72\) | 8.49065 | 1.00063 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | −1.21239 | −0.140937 | ||||||||
\(75\) | −3.38979 | −0.391419 | ||||||||
\(76\) | 2.03588 | 0.233531 | ||||||||
\(77\) | 1.27596 | 0.145410 | ||||||||
\(78\) | 21.6027 | 2.44602 | ||||||||
\(79\) | −7.97460 | −0.897213 | −0.448606 | − | 0.893729i | \(-0.648079\pi\) | ||||
−0.448606 | + | 0.893729i | \(0.648079\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 37.6192 | 4.17991 | ||||||||
\(82\) | 3.71434 | 0.410180 | ||||||||
\(83\) | −9.52819 | −1.04585 | −0.522927 | − | 0.852377i | \(-0.675160\pi\) | ||||
−0.522927 | + | 0.852377i | \(0.675160\pi\) | |||||||
\(84\) | −4.32525 | −0.471923 | ||||||||
\(85\) | −4.31350 | −0.467864 | ||||||||
\(86\) | −6.71830 | −0.724453 | ||||||||
\(87\) | 4.64117 | 0.497586 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 18.4531 | 1.95603 | 0.978013 | − | 0.208542i | \(-0.0668718\pi\) | ||||
0.978013 | + | 0.208542i | \(0.0668718\pi\) | |||||||
\(90\) | 8.49065 | 0.894993 | ||||||||
\(91\) | −8.13157 | −0.852420 | ||||||||
\(92\) | 5.87814 | 0.612838 | ||||||||
\(93\) | −29.9580 | −3.10650 | ||||||||
\(94\) | −10.0246 | −1.03396 | ||||||||
\(95\) | 2.03588 | 0.208877 | ||||||||
\(96\) | −3.38979 | −0.345969 | ||||||||
\(97\) | 15.7497 | 1.59914 | 0.799570 | − | 0.600573i | \(-0.205061\pi\) | ||||
0.799570 | + | 0.600573i | \(0.205061\pi\) | |||||||
\(98\) | −5.37191 | −0.542645 | ||||||||
\(99\) | 8.49065 | 0.853343 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 13.7088 | 1.36408 | 0.682041 | − | 0.731314i | \(-0.261093\pi\) | ||||
0.682041 | + | 0.731314i | \(0.261093\pi\) | |||||||
\(102\) | 14.6218 | 1.44778 | ||||||||
\(103\) | −9.11681 | −0.898306 | −0.449153 | − | 0.893455i | \(-0.648274\pi\) | ||||
−0.449153 | + | 0.893455i | \(0.648274\pi\) | |||||||
\(104\) | −6.37288 | −0.624912 | ||||||||
\(105\) | −4.32525 | −0.422101 | ||||||||
\(106\) | −8.27201 | −0.803449 | ||||||||
\(107\) | 14.3074 | 1.38315 | 0.691573 | − | 0.722306i | \(-0.256918\pi\) | ||||
0.691573 | + | 0.722306i | \(0.256918\pi\) | |||||||
\(108\) | −18.6121 | −1.79095 | ||||||||
\(109\) | −0.438667 | −0.0420167 | −0.0210083 | − | 0.999779i | \(-0.506688\pi\) | ||||
−0.0210083 | + | 0.999779i | \(0.506688\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | 4.10974 | 0.390079 | ||||||||
\(112\) | 1.27596 | 0.120567 | ||||||||
\(113\) | 16.5312 | 1.55512 | 0.777561 | − | 0.628807i | \(-0.216457\pi\) | ||||
0.777561 | + | 0.628807i | \(0.216457\pi\) | |||||||
\(114\) | −6.90119 | −0.646356 | ||||||||
\(115\) | 5.87814 | 0.548139 | ||||||||
\(116\) | −1.36916 | −0.127124 | ||||||||
\(117\) | −54.1099 | −5.00246 | ||||||||
\(118\) | −13.9774 | −1.28672 | ||||||||
\(119\) | −5.50387 | −0.504539 | ||||||||
\(120\) | −3.38979 | −0.309444 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.979378 | −0.0886687 | ||||||||
\(123\) | −12.5908 | −1.13528 | ||||||||
\(124\) | 8.83773 | 0.793651 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 10.8338 | 0.965149 | ||||||||
\(127\) | 4.98622 | 0.442456 | 0.221228 | − | 0.975222i | \(-0.428994\pi\) | ||||
0.221228 | + | 0.975222i | \(0.428994\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 22.7736 | 2.00510 | ||||||||
\(130\) | −6.37288 | −0.558938 | ||||||||
\(131\) | −3.68306 | −0.321791 | −0.160895 | − | 0.986971i | \(-0.551438\pi\) | ||||
−0.160895 | + | 0.986971i | \(0.551438\pi\) | |||||||
\(132\) | −3.38979 | −0.295043 | ||||||||
\(133\) | 2.59771 | 0.225250 | ||||||||
\(134\) | 0.367267 | 0.0317270 | ||||||||
\(135\) | −18.6121 | −1.60188 | ||||||||
\(136\) | −4.31350 | −0.369879 | ||||||||
\(137\) | −11.4421 | −0.977564 | −0.488782 | − | 0.872406i | \(-0.662559\pi\) | ||||
−0.488782 | + | 0.872406i | \(0.662559\pi\) | |||||||
\(138\) | −19.9256 | −1.69618 | ||||||||
\(139\) | −9.29033 | −0.787996 | −0.393998 | − | 0.919111i | \(-0.628908\pi\) | ||||
−0.393998 | + | 0.919111i | \(0.628908\pi\) | |||||||
\(140\) | 1.27596 | 0.107839 | ||||||||
\(141\) | 33.9812 | 2.86173 | ||||||||
\(142\) | −4.19342 | −0.351904 | ||||||||
\(143\) | −6.37288 | −0.532927 | ||||||||
\(144\) | 8.49065 | 0.707554 | ||||||||
\(145\) | −1.36916 | −0.113703 | ||||||||
\(146\) | 1.00000 | 0.0827606 | ||||||||
\(147\) | 18.2096 | 1.50191 | ||||||||
\(148\) | −1.21239 | −0.0996577 | ||||||||
\(149\) | −8.20032 | −0.671796 | −0.335898 | − | 0.941898i | \(-0.609040\pi\) | ||||
−0.335898 | + | 0.941898i | \(0.609040\pi\) | |||||||
\(150\) | −3.38979 | −0.276775 | ||||||||
\(151\) | −19.4245 | −1.58074 | −0.790370 | − | 0.612630i | \(-0.790112\pi\) | ||||
−0.790370 | + | 0.612630i | \(0.790112\pi\) | |||||||
\(152\) | 2.03588 | 0.165131 | ||||||||
\(153\) | −36.6244 | −2.96091 | ||||||||
\(154\) | 1.27596 | 0.102820 | ||||||||
\(155\) | 8.83773 | 0.709863 | ||||||||
\(156\) | 21.6027 | 1.72960 | ||||||||
\(157\) | −19.3921 | −1.54766 | −0.773828 | − | 0.633395i | \(-0.781661\pi\) | ||||
−0.773828 | + | 0.633395i | \(0.781661\pi\) | |||||||
\(158\) | −7.97460 | −0.634425 | ||||||||
\(159\) | 28.0403 | 2.22374 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 7.50030 | 0.591106 | ||||||||
\(162\) | 37.6192 | 2.95565 | ||||||||
\(163\) | −6.99055 | −0.547542 | −0.273771 | − | 0.961795i | \(-0.588271\pi\) | ||||
−0.273771 | + | 0.961795i | \(0.588271\pi\) | |||||||
\(164\) | 3.71434 | 0.290041 | ||||||||
\(165\) | −3.38979 | −0.263895 | ||||||||
\(166\) | −9.52819 | −0.739531 | ||||||||
\(167\) | 10.9337 | 0.846073 | 0.423037 | − | 0.906113i | \(-0.360964\pi\) | ||||
0.423037 | + | 0.906113i | \(0.360964\pi\) | |||||||
\(168\) | −4.32525 | −0.333700 | ||||||||
\(169\) | 27.6136 | 2.12412 | ||||||||
\(170\) | −4.31350 | −0.330830 | ||||||||
\(171\) | 17.2859 | 1.32189 | ||||||||
\(172\) | −6.71830 | −0.512265 | ||||||||
\(173\) | −14.2779 | −1.08553 | −0.542764 | − | 0.839885i | \(-0.682622\pi\) | ||||
−0.542764 | + | 0.839885i | \(0.682622\pi\) | |||||||
\(174\) | 4.64117 | 0.351847 | ||||||||
\(175\) | 1.27596 | 0.0964539 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 47.3802 | 3.56132 | ||||||||
\(178\) | 18.4531 | 1.38312 | ||||||||
\(179\) | −11.7461 | −0.877947 | −0.438974 | − | 0.898500i | \(-0.644658\pi\) | ||||
−0.438974 | + | 0.898500i | \(0.644658\pi\) | |||||||
\(180\) | 8.49065 | 0.632856 | ||||||||
\(181\) | 4.67451 | 0.347454 | 0.173727 | − | 0.984794i | \(-0.444419\pi\) | ||||
0.173727 | + | 0.984794i | \(0.444419\pi\) | |||||||
\(182\) | −8.13157 | −0.602752 | ||||||||
\(183\) | 3.31988 | 0.245413 | ||||||||
\(184\) | 5.87814 | 0.433342 | ||||||||
\(185\) | −1.21239 | −0.0891366 | ||||||||
\(186\) | −29.9580 | −2.19663 | ||||||||
\(187\) | −4.31350 | −0.315434 | ||||||||
\(188\) | −10.0246 | −0.731117 | ||||||||
\(189\) | −23.7484 | −1.72744 | ||||||||
\(190\) | 2.03588 | 0.147698 | ||||||||
\(191\) | 8.41189 | 0.608663 | 0.304331 | − | 0.952566i | \(-0.401567\pi\) | ||||
0.304331 | + | 0.952566i | \(0.401567\pi\) | |||||||
\(192\) | −3.38979 | −0.244637 | ||||||||
\(193\) | −3.85445 | −0.277449 | −0.138725 | − | 0.990331i | \(-0.544300\pi\) | ||||
−0.138725 | + | 0.990331i | \(0.544300\pi\) | |||||||
\(194\) | 15.7497 | 1.13076 | ||||||||
\(195\) | 21.6027 | 1.54700 | ||||||||
\(196\) | −5.37191 | −0.383708 | ||||||||
\(197\) | 4.87162 | 0.347088 | 0.173544 | − | 0.984826i | \(-0.444478\pi\) | ||||
0.173544 | + | 0.984826i | \(0.444478\pi\) | |||||||
\(198\) | 8.49065 | 0.603404 | ||||||||
\(199\) | −17.6913 | −1.25410 | −0.627051 | − | 0.778978i | \(-0.715738\pi\) | ||||
−0.627051 | + | 0.778978i | \(0.715738\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −1.24496 | −0.0878125 | ||||||||
\(202\) | 13.7088 | 0.964551 | ||||||||
\(203\) | −1.74701 | −0.122616 | ||||||||
\(204\) | 14.6218 | 1.02373 | ||||||||
\(205\) | 3.71434 | 0.259421 | ||||||||
\(206\) | −9.11681 | −0.635199 | ||||||||
\(207\) | 49.9092 | 3.46893 | ||||||||
\(208\) | −6.37288 | −0.441879 | ||||||||
\(209\) | 2.03588 | 0.140825 | ||||||||
\(210\) | −4.32525 | −0.298470 | ||||||||
\(211\) | 20.6081 | 1.41872 | 0.709360 | − | 0.704846i | \(-0.248984\pi\) | ||||
0.709360 | + | 0.704846i | \(0.248984\pi\) | |||||||
\(212\) | −8.27201 | −0.568124 | ||||||||
\(213\) | 14.2148 | 0.973982 | ||||||||
\(214\) | 14.3074 | 0.978032 | ||||||||
\(215\) | −6.71830 | −0.458184 | ||||||||
\(216\) | −18.6121 | −1.26640 | ||||||||
\(217\) | 11.2766 | 0.765507 | ||||||||
\(218\) | −0.438667 | −0.0297103 | ||||||||
\(219\) | −3.38979 | −0.229061 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | 27.4894 | 1.84914 | ||||||||
\(222\) | 4.10974 | 0.275828 | ||||||||
\(223\) | 17.7959 | 1.19170 | 0.595850 | − | 0.803096i | \(-0.296815\pi\) | ||||
0.595850 | + | 0.803096i | \(0.296815\pi\) | |||||||
\(224\) | 1.27596 | 0.0852540 | ||||||||
\(225\) | 8.49065 | 0.566044 | ||||||||
\(226\) | 16.5312 | 1.09964 | ||||||||
\(227\) | 24.0405 | 1.59563 | 0.797813 | − | 0.602905i | \(-0.205990\pi\) | ||||
0.797813 | + | 0.602905i | \(0.205990\pi\) | |||||||
\(228\) | −6.90119 | −0.457043 | ||||||||
\(229\) | −10.3646 | −0.684910 | −0.342455 | − | 0.939534i | \(-0.611259\pi\) | ||||
−0.342455 | + | 0.939534i | \(0.611259\pi\) | |||||||
\(230\) | 5.87814 | 0.387593 | ||||||||
\(231\) | −4.32525 | −0.284580 | ||||||||
\(232\) | −1.36916 | −0.0898900 | ||||||||
\(233\) | 9.05203 | 0.593018 | 0.296509 | − | 0.955030i | \(-0.404177\pi\) | ||||
0.296509 | + | 0.955030i | \(0.404177\pi\) | |||||||
\(234\) | −54.1099 | −3.53727 | ||||||||
\(235\) | −10.0246 | −0.653931 | ||||||||
\(236\) | −13.9774 | −0.909848 | ||||||||
\(237\) | 27.0322 | 1.75593 | ||||||||
\(238\) | −5.50387 | −0.356763 | ||||||||
\(239\) | −10.4398 | −0.675294 | −0.337647 | − | 0.941273i | \(-0.609631\pi\) | ||||
−0.337647 | + | 0.941273i | \(0.609631\pi\) | |||||||
\(240\) | −3.38979 | −0.218810 | ||||||||
\(241\) | −20.1320 | −1.29682 | −0.648409 | − | 0.761293i | \(-0.724565\pi\) | ||||
−0.648409 | + | 0.761293i | \(0.724565\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −71.6847 | −4.59858 | ||||||||
\(244\) | −0.979378 | −0.0626982 | ||||||||
\(245\) | −5.37191 | −0.343199 | ||||||||
\(246\) | −12.5908 | −0.802762 | ||||||||
\(247\) | −12.9744 | −0.825541 | ||||||||
\(248\) | 8.83773 | 0.561196 | ||||||||
\(249\) | 32.2985 | 2.04684 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −8.61093 | −0.543517 | −0.271759 | − | 0.962365i | \(-0.587605\pi\) | ||||
−0.271759 | + | 0.962365i | \(0.587605\pi\) | |||||||
\(252\) | 10.8338 | 0.682464 | ||||||||
\(253\) | 5.87814 | 0.369555 | ||||||||
\(254\) | 4.98622 | 0.312863 | ||||||||
\(255\) | 14.6218 | 0.915655 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.2178 | −1.26115 | −0.630577 | − | 0.776127i | \(-0.717182\pi\) | ||||
−0.630577 | + | 0.776127i | \(0.717182\pi\) | |||||||
\(258\) | 22.7736 | 1.41782 | ||||||||
\(259\) | −1.54696 | −0.0961237 | ||||||||
\(260\) | −6.37288 | −0.395229 | ||||||||
\(261\) | −11.6251 | −0.719575 | ||||||||
\(262\) | −3.68306 | −0.227540 | ||||||||
\(263\) | −16.3950 | −1.01096 | −0.505478 | − | 0.862839i | \(-0.668684\pi\) | ||||
−0.505478 | + | 0.862839i | \(0.668684\pi\) | |||||||
\(264\) | −3.38979 | −0.208627 | ||||||||
\(265\) | −8.27201 | −0.508146 | ||||||||
\(266\) | 2.59771 | 0.159276 | ||||||||
\(267\) | −62.5521 | −3.82813 | ||||||||
\(268\) | 0.367267 | 0.0224344 | ||||||||
\(269\) | 2.88126 | 0.175674 | 0.0878368 | − | 0.996135i | \(-0.472005\pi\) | ||||
0.0878368 | + | 0.996135i | \(0.472005\pi\) | |||||||
\(270\) | −18.6121 | −1.13270 | ||||||||
\(271\) | −25.8594 | −1.57084 | −0.785422 | − | 0.618960i | \(-0.787554\pi\) | ||||
−0.785422 | + | 0.618960i | \(0.787554\pi\) | |||||||
\(272\) | −4.31350 | −0.261544 | ||||||||
\(273\) | 27.5643 | 1.66827 | ||||||||
\(274\) | −11.4421 | −0.691242 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −19.9256 | −1.19938 | ||||||||
\(277\) | 11.5823 | 0.695914 | 0.347957 | − | 0.937511i | \(-0.386876\pi\) | ||||
0.347957 | + | 0.937511i | \(0.386876\pi\) | |||||||
\(278\) | −9.29033 | −0.557197 | ||||||||
\(279\) | 75.0381 | 4.49241 | ||||||||
\(280\) | 1.27596 | 0.0762535 | ||||||||
\(281\) | −7.14607 | −0.426299 | −0.213149 | − | 0.977020i | \(-0.568372\pi\) | ||||
−0.213149 | + | 0.977020i | \(0.568372\pi\) | |||||||
\(282\) | 33.9812 | 2.02355 | ||||||||
\(283\) | 27.5523 | 1.63781 | 0.818906 | − | 0.573927i | \(-0.194581\pi\) | ||||
0.818906 | + | 0.573927i | \(0.194581\pi\) | |||||||
\(284\) | −4.19342 | −0.248834 | ||||||||
\(285\) | −6.90119 | −0.408791 | ||||||||
\(286\) | −6.37288 | −0.376836 | ||||||||
\(287\) | 4.73937 | 0.279756 | ||||||||
\(288\) | 8.49065 | 0.500317 | ||||||||
\(289\) | 1.60626 | 0.0944858 | ||||||||
\(290\) | −1.36916 | −0.0804001 | ||||||||
\(291\) | −53.3881 | −3.12967 | ||||||||
\(292\) | 1.00000 | 0.0585206 | ||||||||
\(293\) | −16.0728 | −0.938984 | −0.469492 | − | 0.882937i | \(-0.655563\pi\) | ||||
−0.469492 | + | 0.882937i | \(0.655563\pi\) | |||||||
\(294\) | 18.2096 | 1.06201 | ||||||||
\(295\) | −13.9774 | −0.813793 | ||||||||
\(296\) | −1.21239 | −0.0704686 | ||||||||
\(297\) | −18.6121 | −1.07999 | ||||||||
\(298\) | −8.20032 | −0.475032 | ||||||||
\(299\) | −37.4607 | −2.16641 | ||||||||
\(300\) | −3.38979 | −0.195709 | ||||||||
\(301\) | −8.57231 | −0.494100 | ||||||||
\(302\) | −19.4245 | −1.11775 | ||||||||
\(303\) | −46.4701 | −2.66964 | ||||||||
\(304\) | 2.03588 | 0.116766 | ||||||||
\(305\) | −0.979378 | −0.0560790 | ||||||||
\(306\) | −36.6244 | −2.09368 | ||||||||
\(307\) | 7.46421 | 0.426005 | 0.213002 | − | 0.977052i | \(-0.431676\pi\) | ||||
0.213002 | + | 0.977052i | \(0.431676\pi\) | |||||||
\(308\) | 1.27596 | 0.0727048 | ||||||||
\(309\) | 30.9041 | 1.75807 | ||||||||
\(310\) | 8.83773 | 0.501949 | ||||||||
\(311\) | −33.0919 | −1.87647 | −0.938236 | − | 0.345997i | \(-0.887541\pi\) | ||||
−0.938236 | + | 0.345997i | \(0.887541\pi\) | |||||||
\(312\) | 21.6027 | 1.22301 | ||||||||
\(313\) | 10.5337 | 0.595403 | 0.297701 | − | 0.954659i | \(-0.403780\pi\) | ||||
0.297701 | + | 0.954659i | \(0.403780\pi\) | |||||||
\(314\) | −19.3921 | −1.09436 | ||||||||
\(315\) | 10.8338 | 0.610414 | ||||||||
\(316\) | −7.97460 | −0.448606 | ||||||||
\(317\) | −24.9034 | −1.39872 | −0.699358 | − | 0.714771i | \(-0.746531\pi\) | ||||
−0.699358 | + | 0.714771i | \(0.746531\pi\) | |||||||
\(318\) | 28.0403 | 1.57242 | ||||||||
\(319\) | −1.36916 | −0.0766585 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −48.4989 | −2.70695 | ||||||||
\(322\) | 7.50030 | 0.417975 | ||||||||
\(323\) | −8.78175 | −0.488630 | ||||||||
\(324\) | 37.6192 | 2.08996 | ||||||||
\(325\) | −6.37288 | −0.353504 | ||||||||
\(326\) | −6.99055 | −0.387171 | ||||||||
\(327\) | 1.48699 | 0.0822306 | ||||||||
\(328\) | 3.71434 | 0.205090 | ||||||||
\(329\) | −12.7910 | −0.705191 | ||||||||
\(330\) | −3.38979 | −0.186602 | ||||||||
\(331\) | −20.7557 | −1.14083 | −0.570417 | − | 0.821355i | \(-0.693218\pi\) | ||||
−0.570417 | + | 0.821355i | \(0.693218\pi\) | |||||||
\(332\) | −9.52819 | −0.522927 | ||||||||
\(333\) | −10.2940 | −0.564106 | ||||||||
\(334\) | 10.9337 | 0.598264 | ||||||||
\(335\) | 0.367267 | 0.0200659 | ||||||||
\(336\) | −4.32525 | −0.235962 | ||||||||
\(337\) | 20.6643 | 1.12566 | 0.562828 | − | 0.826574i | \(-0.309713\pi\) | ||||
0.562828 | + | 0.826574i | \(0.309713\pi\) | |||||||
\(338\) | 27.6136 | 1.50198 | ||||||||
\(339\) | −56.0372 | −3.04352 | ||||||||
\(340\) | −4.31350 | −0.233932 | ||||||||
\(341\) | 8.83773 | 0.478590 | ||||||||
\(342\) | 17.2859 | 0.934716 | ||||||||
\(343\) | −15.7861 | −0.852371 | ||||||||
\(344\) | −6.71830 | −0.362226 | ||||||||
\(345\) | −19.9256 | −1.07276 | ||||||||
\(346\) | −14.2779 | −0.767584 | ||||||||
\(347\) | −6.77594 | −0.363751 | −0.181876 | − | 0.983322i | \(-0.558217\pi\) | ||||
−0.181876 | + | 0.983322i | \(0.558217\pi\) | |||||||
\(348\) | 4.64117 | 0.248793 | ||||||||
\(349\) | 8.50296 | 0.455153 | 0.227577 | − | 0.973760i | \(-0.426920\pi\) | ||||
0.227577 | + | 0.973760i | \(0.426920\pi\) | |||||||
\(350\) | 1.27596 | 0.0682032 | ||||||||
\(351\) | 118.613 | 6.33109 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −31.1164 | −1.65616 | −0.828081 | − | 0.560609i | \(-0.810567\pi\) | ||||
−0.828081 | + | 0.560609i | \(0.810567\pi\) | |||||||
\(354\) | 47.3802 | 2.51823 | ||||||||
\(355\) | −4.19342 | −0.222564 | ||||||||
\(356\) | 18.4531 | 0.978013 | ||||||||
\(357\) | 18.6569 | 0.987430 | ||||||||
\(358\) | −11.7461 | −0.620803 | ||||||||
\(359\) | 26.0884 | 1.37689 | 0.688446 | − | 0.725288i | \(-0.258293\pi\) | ||||
0.688446 | + | 0.725288i | \(0.258293\pi\) | |||||||
\(360\) | 8.49065 | 0.447497 | ||||||||
\(361\) | −14.8552 | −0.781853 | ||||||||
\(362\) | 4.67451 | 0.245687 | ||||||||
\(363\) | −3.38979 | −0.177918 | ||||||||
\(364\) | −8.13157 | −0.426210 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | 3.31988 | 0.173533 | ||||||||
\(367\) | −21.7528 | −1.13549 | −0.567744 | − | 0.823205i | \(-0.692184\pi\) | ||||
−0.567744 | + | 0.823205i | \(0.692184\pi\) | |||||||
\(368\) | 5.87814 | 0.306419 | ||||||||
\(369\) | 31.5372 | 1.64176 | ||||||||
\(370\) | −1.21239 | −0.0630291 | ||||||||
\(371\) | −10.5548 | −0.547978 | ||||||||
\(372\) | −29.9580 | −1.55325 | ||||||||
\(373\) | 29.9923 | 1.55294 | 0.776471 | − | 0.630153i | \(-0.217008\pi\) | ||||
0.776471 | + | 0.630153i | \(0.217008\pi\) | |||||||
\(374\) | −4.31350 | −0.223046 | ||||||||
\(375\) | −3.38979 | −0.175048 | ||||||||
\(376\) | −10.0246 | −0.516978 | ||||||||
\(377\) | 8.72551 | 0.449387 | ||||||||
\(378\) | −23.7484 | −1.22149 | ||||||||
\(379\) | −17.9651 | −0.922807 | −0.461404 | − | 0.887190i | \(-0.652654\pi\) | ||||
−0.461404 | + | 0.887190i | \(0.652654\pi\) | |||||||
\(380\) | 2.03588 | 0.104438 | ||||||||
\(381\) | −16.9022 | −0.865928 | ||||||||
\(382\) | 8.41189 | 0.430390 | ||||||||
\(383\) | −28.3772 | −1.45001 | −0.725004 | − | 0.688745i | \(-0.758162\pi\) | ||||
−0.725004 | + | 0.688745i | \(0.758162\pi\) | |||||||
\(384\) | −3.38979 | −0.172984 | ||||||||
\(385\) | 1.27596 | 0.0650292 | ||||||||
\(386\) | −3.85445 | −0.196186 | ||||||||
\(387\) | −57.0427 | −2.89964 | ||||||||
\(388\) | 15.7497 | 0.799570 | ||||||||
\(389\) | −4.69308 | −0.237949 | −0.118974 | − | 0.992897i | \(-0.537961\pi\) | ||||
−0.118974 | + | 0.992897i | \(0.537961\pi\) | |||||||
\(390\) | 21.6027 | 1.09389 | ||||||||
\(391\) | −25.3553 | −1.28227 | ||||||||
\(392\) | −5.37191 | −0.271323 | ||||||||
\(393\) | 12.4848 | 0.629775 | ||||||||
\(394\) | 4.87162 | 0.245428 | ||||||||
\(395\) | −7.97460 | −0.401246 | ||||||||
\(396\) | 8.49065 | 0.426671 | ||||||||
\(397\) | −5.85893 | −0.294051 | −0.147026 | − | 0.989133i | \(-0.546970\pi\) | ||||
−0.147026 | + | 0.989133i | \(0.546970\pi\) | |||||||
\(398\) | −17.6913 | −0.886784 | ||||||||
\(399\) | −8.80568 | −0.440835 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 23.4591 | 1.17149 | 0.585745 | − | 0.810495i | \(-0.300802\pi\) | ||||
0.585745 | + | 0.810495i | \(0.300802\pi\) | |||||||
\(402\) | −1.24496 | −0.0620928 | ||||||||
\(403\) | −56.3218 | −2.80559 | ||||||||
\(404\) | 13.7088 | 0.682041 | ||||||||
\(405\) | 37.6192 | 1.86931 | ||||||||
\(406\) | −1.74701 | −0.0867024 | ||||||||
\(407\) | −1.21239 | −0.0600959 | ||||||||
\(408\) | 14.6218 | 0.723889 | ||||||||
\(409\) | −8.00003 | −0.395576 | −0.197788 | − | 0.980245i | \(-0.563376\pi\) | ||||
−0.197788 | + | 0.980245i | \(0.563376\pi\) | |||||||
\(410\) | 3.71434 | 0.183438 | ||||||||
\(411\) | 38.7862 | 1.91318 | ||||||||
\(412\) | −9.11681 | −0.449153 | ||||||||
\(413\) | −17.8346 | −0.877584 | ||||||||
\(414\) | 49.9092 | 2.45291 | ||||||||
\(415\) | −9.52819 | −0.467720 | ||||||||
\(416\) | −6.37288 | −0.312456 | ||||||||
\(417\) | 31.4922 | 1.54218 | ||||||||
\(418\) | 2.03588 | 0.0995780 | ||||||||
\(419\) | −38.0151 | −1.85716 | −0.928579 | − | 0.371136i | \(-0.878969\pi\) | ||||
−0.928579 | + | 0.371136i | \(0.878969\pi\) | |||||||
\(420\) | −4.32525 | −0.211050 | ||||||||
\(421\) | 20.9173 | 1.01945 | 0.509724 | − | 0.860338i | \(-0.329748\pi\) | ||||
0.509724 | + | 0.860338i | \(0.329748\pi\) | |||||||
\(422\) | 20.6081 | 1.00319 | ||||||||
\(423\) | −85.1152 | −4.13844 | ||||||||
\(424\) | −8.27201 | −0.401724 | ||||||||
\(425\) | −4.31350 | −0.209235 | ||||||||
\(426\) | 14.2148 | 0.688709 | ||||||||
\(427\) | −1.24965 | −0.0604749 | ||||||||
\(428\) | 14.3074 | 0.691573 | ||||||||
\(429\) | 21.6027 | 1.04299 | ||||||||
\(430\) | −6.71830 | −0.323985 | ||||||||
\(431\) | 18.8663 | 0.908758 | 0.454379 | − | 0.890808i | \(-0.349861\pi\) | ||||
0.454379 | + | 0.890808i | \(0.349861\pi\) | |||||||
\(432\) | −18.6121 | −0.895477 | ||||||||
\(433\) | 11.4356 | 0.549561 | 0.274781 | − | 0.961507i | \(-0.411395\pi\) | ||||
0.274781 | + | 0.961507i | \(0.411395\pi\) | |||||||
\(434\) | 11.2766 | 0.541296 | ||||||||
\(435\) | 4.64117 | 0.222527 | ||||||||
\(436\) | −0.438667 | −0.0210083 | ||||||||
\(437\) | 11.9672 | 0.572468 | ||||||||
\(438\) | −3.38979 | −0.161970 | ||||||||
\(439\) | −10.7841 | −0.514697 | −0.257348 | − | 0.966319i | \(-0.582849\pi\) | ||||
−0.257348 | + | 0.966319i | \(0.582849\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | −45.6111 | −2.17196 | ||||||||
\(442\) | 27.4894 | 1.30754 | ||||||||
\(443\) | 8.47840 | 0.402821 | 0.201410 | − | 0.979507i | \(-0.435448\pi\) | ||||
0.201410 | + | 0.979507i | \(0.435448\pi\) | |||||||
\(444\) | 4.10974 | 0.195040 | ||||||||
\(445\) | 18.4531 | 0.874762 | ||||||||
\(446\) | 17.7959 | 0.842659 | ||||||||
\(447\) | 27.7973 | 1.31477 | ||||||||
\(448\) | 1.27596 | 0.0602837 | ||||||||
\(449\) | 0.252706 | 0.0119259 | 0.00596296 | − | 0.999982i | \(-0.498102\pi\) | ||||
0.00596296 | + | 0.999982i | \(0.498102\pi\) | |||||||
\(450\) | 8.49065 | 0.400253 | ||||||||
\(451\) | 3.71434 | 0.174902 | ||||||||
\(452\) | 16.5312 | 0.777561 | ||||||||
\(453\) | 65.8448 | 3.09366 | ||||||||
\(454\) | 24.0405 | 1.12828 | ||||||||
\(455\) | −8.13157 | −0.381214 | ||||||||
\(456\) | −6.90119 | −0.323178 | ||||||||
\(457\) | −25.2732 | −1.18223 | −0.591116 | − | 0.806587i | \(-0.701312\pi\) | ||||
−0.591116 | + | 0.806587i | \(0.701312\pi\) | |||||||
\(458\) | −10.3646 | −0.484305 | ||||||||
\(459\) | 80.2834 | 3.74731 | ||||||||
\(460\) | 5.87814 | 0.274070 | ||||||||
\(461\) | −5.64748 | −0.263029 | −0.131515 | − | 0.991314i | \(-0.541984\pi\) | ||||
−0.131515 | + | 0.991314i | \(0.541984\pi\) | |||||||
\(462\) | −4.32525 | −0.201229 | ||||||||
\(463\) | −21.8640 | −1.01611 | −0.508053 | − | 0.861326i | \(-0.669635\pi\) | ||||
−0.508053 | + | 0.861326i | \(0.669635\pi\) | |||||||
\(464\) | −1.36916 | −0.0635618 | ||||||||
\(465\) | −29.9580 | −1.38927 | ||||||||
\(466\) | 9.05203 | 0.419327 | ||||||||
\(467\) | −21.0845 | −0.975674 | −0.487837 | − | 0.872935i | \(-0.662214\pi\) | ||||
−0.487837 | + | 0.872935i | \(0.662214\pi\) | |||||||
\(468\) | −54.1099 | −2.50123 | ||||||||
\(469\) | 0.468620 | 0.0216388 | ||||||||
\(470\) | −10.0246 | −0.462399 | ||||||||
\(471\) | 65.7350 | 3.02891 | ||||||||
\(472\) | −13.9774 | −0.643360 | ||||||||
\(473\) | −6.71830 | −0.308908 | ||||||||
\(474\) | 27.0322 | 1.24163 | ||||||||
\(475\) | 2.03588 | 0.0934125 | ||||||||
\(476\) | −5.50387 | −0.252269 | ||||||||
\(477\) | −70.2348 | −3.21583 | ||||||||
\(478\) | −10.4398 | −0.477505 | ||||||||
\(479\) | −21.3653 | −0.976207 | −0.488103 | − | 0.872786i | \(-0.662311\pi\) | ||||
−0.488103 | + | 0.872786i | \(0.662311\pi\) | |||||||
\(480\) | −3.38979 | −0.154722 | ||||||||
\(481\) | 7.72640 | 0.352294 | ||||||||
\(482\) | −20.1320 | −0.916988 | ||||||||
\(483\) | −25.4244 | −1.15685 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 15.7497 | 0.715157 | ||||||||
\(486\) | −71.6847 | −3.25169 | ||||||||
\(487\) | 0.110895 | 0.00502515 | 0.00251258 | − | 0.999997i | \(-0.499200\pi\) | ||||
0.00251258 | + | 0.999997i | \(0.499200\pi\) | |||||||
\(488\) | −0.979378 | −0.0443343 | ||||||||
\(489\) | 23.6965 | 1.07159 | ||||||||
\(490\) | −5.37191 | −0.242678 | ||||||||
\(491\) | 17.4258 | 0.786415 | 0.393208 | − | 0.919450i | \(-0.371365\pi\) | ||||
0.393208 | + | 0.919450i | \(0.371365\pi\) | |||||||
\(492\) | −12.5908 | −0.567638 | ||||||||
\(493\) | 5.90589 | 0.265988 | ||||||||
\(494\) | −12.9744 | −0.583746 | ||||||||
\(495\) | 8.49065 | 0.381626 | ||||||||
\(496\) | 8.83773 | 0.396826 | ||||||||
\(497\) | −5.35066 | −0.240010 | ||||||||
\(498\) | 32.2985 | 1.44733 | ||||||||
\(499\) | 9.08271 | 0.406598 | 0.203299 | − | 0.979117i | \(-0.434834\pi\) | ||||
0.203299 | + | 0.979117i | \(0.434834\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −37.0628 | −1.65585 | ||||||||
\(502\) | −8.61093 | −0.384325 | ||||||||
\(503\) | −11.2180 | −0.500186 | −0.250093 | − | 0.968222i | \(-0.580461\pi\) | ||||
−0.250093 | + | 0.968222i | \(0.580461\pi\) | |||||||
\(504\) | 10.8338 | 0.482575 | ||||||||
\(505\) | 13.7088 | 0.610036 | ||||||||
\(506\) | 5.87814 | 0.261315 | ||||||||
\(507\) | −93.6041 | −4.15710 | ||||||||
\(508\) | 4.98622 | 0.221228 | ||||||||
\(509\) | −17.4712 | −0.774395 | −0.387198 | − | 0.921997i | \(-0.626557\pi\) | ||||
−0.387198 | + | 0.921997i | \(0.626557\pi\) | |||||||
\(510\) | 14.6218 | 0.647466 | ||||||||
\(511\) | 1.27596 | 0.0564454 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −37.8920 | −1.67297 | ||||||||
\(514\) | −20.2178 | −0.891771 | ||||||||
\(515\) | −9.11681 | −0.401735 | ||||||||
\(516\) | 22.7736 | 1.00255 | ||||||||
\(517\) | −10.0246 | −0.440880 | ||||||||
\(518\) | −1.54696 | −0.0679697 | ||||||||
\(519\) | 48.3990 | 2.12448 | ||||||||
\(520\) | −6.37288 | −0.279469 | ||||||||
\(521\) | −10.5796 | −0.463500 | −0.231750 | − | 0.972775i | \(-0.574445\pi\) | ||||
−0.231750 | + | 0.972775i | \(0.574445\pi\) | |||||||
\(522\) | −11.6251 | −0.508817 | ||||||||
\(523\) | −26.3499 | −1.15220 | −0.576099 | − | 0.817380i | \(-0.695426\pi\) | ||||
−0.576099 | + | 0.817380i | \(0.695426\pi\) | |||||||
\(524\) | −3.68306 | −0.160895 | ||||||||
\(525\) | −4.32525 | −0.188769 | ||||||||
\(526\) | −16.3950 | −0.714854 | ||||||||
\(527\) | −38.1215 | −1.66060 | ||||||||
\(528\) | −3.38979 | −0.147522 | ||||||||
\(529\) | 11.5525 | 0.502284 | ||||||||
\(530\) | −8.27201 | −0.359313 | ||||||||
\(531\) | −118.677 | −5.15014 | ||||||||
\(532\) | 2.59771 | 0.112625 | ||||||||
\(533\) | −23.6710 | −1.02531 | ||||||||
\(534\) | −62.5521 | −2.70690 | ||||||||
\(535\) | 14.3074 | 0.618562 | ||||||||
\(536\) | 0.367267 | 0.0158635 | ||||||||
\(537\) | 39.8169 | 1.71823 | ||||||||
\(538\) | 2.88126 | 0.124220 | ||||||||
\(539\) | −5.37191 | −0.231385 | ||||||||
\(540\) | −18.6121 | −0.800939 | ||||||||
\(541\) | −16.0995 | −0.692173 | −0.346087 | − | 0.938203i | \(-0.612490\pi\) | ||||
−0.346087 | + | 0.938203i | \(0.612490\pi\) | |||||||
\(542\) | −25.8594 | −1.11076 | ||||||||
\(543\) | −15.8456 | −0.679999 | ||||||||
\(544\) | −4.31350 | −0.184940 | ||||||||
\(545\) | −0.438667 | −0.0187904 | ||||||||
\(546\) | 27.5643 | 1.17964 | ||||||||
\(547\) | −13.2619 | −0.567039 | −0.283520 | − | 0.958966i | \(-0.591502\pi\) | ||||
−0.283520 | + | 0.958966i | \(0.591502\pi\) | |||||||
\(548\) | −11.4421 | −0.488782 | ||||||||
\(549\) | −8.31555 | −0.354899 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | −2.78745 | −0.118749 | ||||||||
\(552\) | −19.9256 | −0.848092 | ||||||||
\(553\) | −10.1753 | −0.432698 | ||||||||
\(554\) | 11.5823 | 0.492085 | ||||||||
\(555\) | 4.10974 | 0.174449 | ||||||||
\(556\) | −9.29033 | −0.393998 | ||||||||
\(557\) | 41.2407 | 1.74743 | 0.873713 | − | 0.486442i | \(-0.161706\pi\) | ||||
0.873713 | + | 0.486442i | \(0.161706\pi\) | |||||||
\(558\) | 75.0381 | 3.17662 | ||||||||
\(559\) | 42.8149 | 1.81088 | ||||||||
\(560\) | 1.27596 | 0.0539193 | ||||||||
\(561\) | 14.6218 | 0.617334 | ||||||||
\(562\) | −7.14607 | −0.301439 | ||||||||
\(563\) | −23.0088 | −0.969707 | −0.484853 | − | 0.874595i | \(-0.661127\pi\) | ||||
−0.484853 | + | 0.874595i | \(0.661127\pi\) | |||||||
\(564\) | 33.9812 | 1.43087 | ||||||||
\(565\) | 16.5312 | 0.695472 | ||||||||
\(566\) | 27.5523 | 1.15811 | ||||||||
\(567\) | 48.0008 | 2.01584 | ||||||||
\(568\) | −4.19342 | −0.175952 | ||||||||
\(569\) | 1.16222 | 0.0487227 | 0.0243614 | − | 0.999703i | \(-0.492245\pi\) | ||||
0.0243614 | + | 0.999703i | \(0.492245\pi\) | |||||||
\(570\) | −6.90119 | −0.289059 | ||||||||
\(571\) | −24.0024 | −1.00447 | −0.502234 | − | 0.864732i | \(-0.667488\pi\) | ||||
−0.502234 | + | 0.864732i | \(0.667488\pi\) | |||||||
\(572\) | −6.37288 | −0.266463 | ||||||||
\(573\) | −28.5145 | −1.19121 | ||||||||
\(574\) | 4.73937 | 0.197817 | ||||||||
\(575\) | 5.87814 | 0.245135 | ||||||||
\(576\) | 8.49065 | 0.353777 | ||||||||
\(577\) | 2.81263 | 0.117092 | 0.0585458 | − | 0.998285i | \(-0.481354\pi\) | ||||
0.0585458 | + | 0.998285i | \(0.481354\pi\) | |||||||
\(578\) | 1.60626 | 0.0668116 | ||||||||
\(579\) | 13.0658 | 0.542995 | ||||||||
\(580\) | −1.36916 | −0.0568514 | ||||||||
\(581\) | −12.1576 | −0.504383 | ||||||||
\(582\) | −53.3881 | −2.21301 | ||||||||
\(583\) | −8.27201 | −0.342592 | ||||||||
\(584\) | 1.00000 | 0.0413803 | ||||||||
\(585\) | −54.1099 | −2.23717 | ||||||||
\(586\) | −16.0728 | −0.663962 | ||||||||
\(587\) | 41.0009 | 1.69229 | 0.846144 | − | 0.532954i | \(-0.178918\pi\) | ||||
0.846144 | + | 0.532954i | \(0.178918\pi\) | |||||||
\(588\) | 18.2096 | 0.750953 | ||||||||
\(589\) | 17.9925 | 0.741369 | ||||||||
\(590\) | −13.9774 | −0.575438 | ||||||||
\(591\) | −16.5137 | −0.679284 | ||||||||
\(592\) | −1.21239 | −0.0498289 | ||||||||
\(593\) | −11.5317 | −0.473549 | −0.236775 | − | 0.971565i | \(-0.576090\pi\) | ||||
−0.236775 | + | 0.971565i | \(0.576090\pi\) | |||||||
\(594\) | −18.6121 | −0.763665 | ||||||||
\(595\) | −5.50387 | −0.225637 | ||||||||
\(596\) | −8.20032 | −0.335898 | ||||||||
\(597\) | 59.9697 | 2.45440 | ||||||||
\(598\) | −37.4607 | −1.53188 | ||||||||
\(599\) | −46.0055 | −1.87974 | −0.939868 | − | 0.341539i | \(-0.889052\pi\) | ||||
−0.939868 | + | 0.341539i | \(0.889052\pi\) | |||||||
\(600\) | −3.38979 | −0.138387 | ||||||||
\(601\) | −25.2379 | −1.02947 | −0.514737 | − | 0.857348i | \(-0.672110\pi\) | ||||
−0.514737 | + | 0.857348i | \(0.672110\pi\) | |||||||
\(602\) | −8.57231 | −0.349381 | ||||||||
\(603\) | 3.11834 | 0.126988 | ||||||||
\(604\) | −19.4245 | −0.790370 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −46.4701 | −1.88772 | ||||||||
\(607\) | 36.6941 | 1.48937 | 0.744684 | − | 0.667417i | \(-0.232600\pi\) | ||||
0.744684 | + | 0.667417i | \(0.232600\pi\) | |||||||
\(608\) | 2.03588 | 0.0825657 | ||||||||
\(609\) | 5.92197 | 0.239971 | ||||||||
\(610\) | −0.979378 | −0.0396538 | ||||||||
\(611\) | 63.8854 | 2.58453 | ||||||||
\(612\) | −36.6244 | −1.48045 | ||||||||
\(613\) | −2.42111 | −0.0977878 | −0.0488939 | − | 0.998804i | \(-0.515570\pi\) | ||||
−0.0488939 | + | 0.998804i | \(0.515570\pi\) | |||||||
\(614\) | 7.46421 | 0.301231 | ||||||||
\(615\) | −12.5908 | −0.507711 | ||||||||
\(616\) | 1.27596 | 0.0514101 | ||||||||
\(617\) | −16.2627 | −0.654710 | −0.327355 | − | 0.944901i | \(-0.606157\pi\) | ||||
−0.327355 | + | 0.944901i | \(0.606157\pi\) | |||||||
\(618\) | 30.9041 | 1.24314 | ||||||||
\(619\) | −39.7723 | −1.59858 | −0.799292 | − | 0.600943i | \(-0.794792\pi\) | ||||
−0.799292 | + | 0.600943i | \(0.794792\pi\) | |||||||
\(620\) | 8.83773 | 0.354932 | ||||||||
\(621\) | −109.405 | −4.39026 | ||||||||
\(622\) | −33.0919 | −1.32687 | ||||||||
\(623\) | 23.5455 | 0.943332 | ||||||||
\(624\) | 21.6027 | 0.864800 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 10.5337 | 0.421013 | ||||||||
\(627\) | −6.90119 | −0.275607 | ||||||||
\(628\) | −19.3921 | −0.773828 | ||||||||
\(629\) | 5.22963 | 0.208519 | ||||||||
\(630\) | 10.8338 | 0.431628 | ||||||||
\(631\) | 27.8864 | 1.11014 | 0.555070 | − | 0.831804i | \(-0.312691\pi\) | ||||
0.555070 | + | 0.831804i | \(0.312691\pi\) | |||||||
\(632\) | −7.97460 | −0.317213 | ||||||||
\(633\) | −69.8571 | −2.77657 | ||||||||
\(634\) | −24.9034 | −0.989042 | ||||||||
\(635\) | 4.98622 | 0.197872 | ||||||||
\(636\) | 28.0403 | 1.11187 | ||||||||
\(637\) | 34.2345 | 1.35642 | ||||||||
\(638\) | −1.36916 | −0.0542057 | ||||||||
\(639\) | −35.6049 | −1.40851 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 21.0769 | 0.832486 | 0.416243 | − | 0.909253i | \(-0.363347\pi\) | ||||
0.416243 | + | 0.909253i | \(0.363347\pi\) | |||||||
\(642\) | −48.4989 | −1.91410 | ||||||||
\(643\) | 3.03460 | 0.119673 | 0.0598364 | − | 0.998208i | \(-0.480942\pi\) | ||||
0.0598364 | + | 0.998208i | \(0.480942\pi\) | |||||||
\(644\) | 7.50030 | 0.295553 | ||||||||
\(645\) | 22.7736 | 0.896709 | ||||||||
\(646\) | −8.78175 | −0.345513 | ||||||||
\(647\) | 1.92977 | 0.0758671 | 0.0379336 | − | 0.999280i | \(-0.487922\pi\) | ||||
0.0379336 | + | 0.999280i | \(0.487922\pi\) | |||||||
\(648\) | 37.6192 | 1.47782 | ||||||||
\(649\) | −13.9774 | −0.548659 | ||||||||
\(650\) | −6.37288 | −0.249965 | ||||||||
\(651\) | −38.2254 | −1.49817 | ||||||||
\(652\) | −6.99055 | −0.273771 | ||||||||
\(653\) | −40.7993 | −1.59660 | −0.798300 | − | 0.602261i | \(-0.794267\pi\) | ||||
−0.798300 | + | 0.602261i | \(0.794267\pi\) | |||||||
\(654\) | 1.48699 | 0.0581458 | ||||||||
\(655\) | −3.68306 | −0.143909 | ||||||||
\(656\) | 3.71434 | 0.145021 | ||||||||
\(657\) | 8.49065 | 0.331252 | ||||||||
\(658\) | −12.7910 | −0.498645 | ||||||||
\(659\) | 29.0631 | 1.13214 | 0.566068 | − | 0.824359i | \(-0.308464\pi\) | ||||
0.566068 | + | 0.824359i | \(0.308464\pi\) | |||||||
\(660\) | −3.38979 | −0.131947 | ||||||||
\(661\) | 17.2958 | 0.672728 | 0.336364 | − | 0.941732i | \(-0.390803\pi\) | ||||
0.336364 | + | 0.941732i | \(0.390803\pi\) | |||||||
\(662\) | −20.7557 | −0.806691 | ||||||||
\(663\) | −93.1831 | −3.61893 | ||||||||
\(664\) | −9.52819 | −0.369765 | ||||||||
\(665\) | 2.59771 | 0.100735 | ||||||||
\(666\) | −10.2940 | −0.398883 | ||||||||
\(667\) | −8.04814 | −0.311625 | ||||||||
\(668\) | 10.9337 | 0.423037 | ||||||||
\(669\) | −60.3242 | −2.33227 | ||||||||
\(670\) | 0.367267 | 0.0141888 | ||||||||
\(671\) | −0.979378 | −0.0378085 | ||||||||
\(672\) | −4.32525 | −0.166850 | ||||||||
\(673\) | 30.3727 | 1.17078 | 0.585391 | − | 0.810751i | \(-0.300941\pi\) | ||||
0.585391 | + | 0.810751i | \(0.300941\pi\) | |||||||
\(674\) | 20.6643 | 0.795959 | ||||||||
\(675\) | −18.6121 | −0.716382 | ||||||||
\(676\) | 27.6136 | 1.06206 | ||||||||
\(677\) | 47.9364 | 1.84234 | 0.921172 | − | 0.389156i | \(-0.127233\pi\) | ||||
0.921172 | + | 0.389156i | \(0.127233\pi\) | |||||||
\(678\) | −56.0372 | −2.15209 | ||||||||
\(679\) | 20.0961 | 0.771216 | ||||||||
\(680\) | −4.31350 | −0.165415 | ||||||||
\(681\) | −81.4923 | −3.12279 | ||||||||
\(682\) | 8.83773 | 0.338414 | ||||||||
\(683\) | −28.9872 | −1.10916 | −0.554581 | − | 0.832129i | \(-0.687122\pi\) | ||||
−0.554581 | + | 0.832129i | \(0.687122\pi\) | |||||||
\(684\) | 17.2859 | 0.660944 | ||||||||
\(685\) | −11.4421 | −0.437180 | ||||||||
\(686\) | −15.7861 | −0.602717 | ||||||||
\(687\) | 35.1337 | 1.34043 | ||||||||
\(688\) | −6.71830 | −0.256133 | ||||||||
\(689\) | 52.7165 | 2.00834 | ||||||||
\(690\) | −19.9256 | −0.758556 | ||||||||
\(691\) | 22.9624 | 0.873531 | 0.436766 | − | 0.899575i | \(-0.356124\pi\) | ||||
0.436766 | + | 0.899575i | \(0.356124\pi\) | |||||||
\(692\) | −14.2779 | −0.542764 | ||||||||
\(693\) | 10.8338 | 0.411541 | ||||||||
\(694\) | −6.77594 | −0.257211 | ||||||||
\(695\) | −9.29033 | −0.352402 | ||||||||
\(696\) | 4.64117 | 0.175923 | ||||||||
\(697\) | −16.0218 | −0.606869 | ||||||||
\(698\) | 8.50296 | 0.321842 | ||||||||
\(699\) | −30.6845 | −1.16059 | ||||||||
\(700\) | 1.27596 | 0.0482269 | ||||||||
\(701\) | −8.23029 | −0.310854 | −0.155427 | − | 0.987847i | \(-0.549675\pi\) | ||||
−0.155427 | + | 0.987847i | \(0.549675\pi\) | |||||||
\(702\) | 118.613 | 4.47675 | ||||||||
\(703\) | −2.46827 | −0.0930927 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 33.9812 | 1.27981 | ||||||||
\(706\) | −31.1164 | −1.17108 | ||||||||
\(707\) | 17.4920 | 0.657854 | ||||||||
\(708\) | 47.3802 | 1.78066 | ||||||||
\(709\) | 19.3126 | 0.725299 | 0.362649 | − | 0.931926i | \(-0.381872\pi\) | ||||
0.362649 | + | 0.931926i | \(0.381872\pi\) | |||||||
\(710\) | −4.19342 | −0.157376 | ||||||||
\(711\) | −67.7096 | −2.53931 | ||||||||
\(712\) | 18.4531 | 0.691560 | ||||||||
\(713\) | 51.9494 | 1.94552 | ||||||||
\(714\) | 18.6569 | 0.698219 | ||||||||
\(715\) | −6.37288 | −0.238332 | ||||||||
\(716\) | −11.7461 | −0.438974 | ||||||||
\(717\) | 35.3887 | 1.32161 | ||||||||
\(718\) | 26.0884 | 0.973609 | ||||||||
\(719\) | −26.3634 | −0.983189 | −0.491594 | − | 0.870824i | \(-0.663586\pi\) | ||||
−0.491594 | + | 0.870824i | \(0.663586\pi\) | |||||||
\(720\) | 8.49065 | 0.316428 | ||||||||
\(721\) | −11.6327 | −0.433226 | ||||||||
\(722\) | −14.8552 | −0.552853 | ||||||||
\(723\) | 68.2432 | 2.53799 | ||||||||
\(724\) | 4.67451 | 0.173727 | ||||||||
\(725\) | −1.36916 | −0.0508495 | ||||||||
\(726\) | −3.38979 | −0.125807 | ||||||||
\(727\) | −13.4850 | −0.500130 | −0.250065 | − | 0.968229i | \(-0.580452\pi\) | ||||
−0.250065 | + | 0.968229i | \(0.580452\pi\) | |||||||
\(728\) | −8.13157 | −0.301376 | ||||||||
\(729\) | 130.138 | 4.81994 | ||||||||
\(730\) | 1.00000 | 0.0370117 | ||||||||
\(731\) | 28.9794 | 1.07184 | ||||||||
\(732\) | 3.31988 | 0.122706 | ||||||||
\(733\) | −9.52840 | −0.351939 | −0.175970 | − | 0.984396i | \(-0.556306\pi\) | ||||
−0.175970 | + | 0.984396i | \(0.556306\pi\) | |||||||
\(734\) | −21.7528 | −0.802912 | ||||||||
\(735\) | 18.2096 | 0.671673 | ||||||||
\(736\) | 5.87814 | 0.216671 | ||||||||
\(737\) | 0.367267 | 0.0135285 | ||||||||
\(738\) | 31.5372 | 1.16090 | ||||||||
\(739\) | −20.6913 | −0.761143 | −0.380571 | − | 0.924752i | \(-0.624273\pi\) | ||||
−0.380571 | + | 0.924752i | \(0.624273\pi\) | |||||||
\(740\) | −1.21239 | −0.0445683 | ||||||||
\(741\) | 43.9804 | 1.61566 | ||||||||
\(742\) | −10.5548 | −0.387479 | ||||||||
\(743\) | 4.55144 | 0.166976 | 0.0834882 | − | 0.996509i | \(-0.473394\pi\) | ||||
0.0834882 | + | 0.996509i | \(0.473394\pi\) | |||||||
\(744\) | −29.9580 | −1.09831 | ||||||||
\(745\) | −8.20032 | −0.300436 | ||||||||
\(746\) | 29.9923 | 1.09810 | ||||||||
\(747\) | −80.9005 | −2.96000 | ||||||||
\(748\) | −4.31350 | −0.157717 | ||||||||
\(749\) | 18.2557 | 0.667049 | ||||||||
\(750\) | −3.38979 | −0.123778 | ||||||||
\(751\) | −24.0964 | −0.879290 | −0.439645 | − | 0.898172i | \(-0.644896\pi\) | ||||
−0.439645 | + | 0.898172i | \(0.644896\pi\) | |||||||
\(752\) | −10.0246 | −0.365559 | ||||||||
\(753\) | 29.1892 | 1.06371 | ||||||||
\(754\) | 8.72551 | 0.317764 | ||||||||
\(755\) | −19.4245 | −0.706928 | ||||||||
\(756\) | −23.7484 | −0.863722 | ||||||||
\(757\) | 1.78991 | 0.0650554 | 0.0325277 | − | 0.999471i | \(-0.489644\pi\) | ||||
0.0325277 | + | 0.999471i | \(0.489644\pi\) | |||||||
\(758\) | −17.9651 | −0.652523 | ||||||||
\(759\) | −19.9256 | −0.723255 | ||||||||
\(760\) | 2.03588 | 0.0738490 | ||||||||
\(761\) | 23.6257 | 0.856430 | 0.428215 | − | 0.903677i | \(-0.359143\pi\) | ||||
0.428215 | + | 0.903677i | \(0.359143\pi\) | |||||||
\(762\) | −16.9022 | −0.612303 | ||||||||
\(763\) | −0.559724 | −0.0202634 | ||||||||
\(764\) | 8.41189 | 0.304331 | ||||||||
\(765\) | −36.6244 | −1.32416 | ||||||||
\(766\) | −28.3772 | −1.02531 | ||||||||
\(767\) | 89.0759 | 3.21635 | ||||||||
\(768\) | −3.38979 | −0.122318 | ||||||||
\(769\) | 19.4885 | 0.702772 | 0.351386 | − | 0.936231i | \(-0.385710\pi\) | ||||
0.351386 | + | 0.936231i | \(0.385710\pi\) | |||||||
\(770\) | 1.27596 | 0.0459826 | ||||||||
\(771\) | 68.5342 | 2.46820 | ||||||||
\(772\) | −3.85445 | −0.138725 | ||||||||
\(773\) | −1.46336 | −0.0526333 | −0.0263167 | − | 0.999654i | \(-0.508378\pi\) | ||||
−0.0263167 | + | 0.999654i | \(0.508378\pi\) | |||||||
\(774\) | −57.0427 | −2.05036 | ||||||||
\(775\) | 8.83773 | 0.317461 | ||||||||
\(776\) | 15.7497 | 0.565382 | ||||||||
\(777\) | 5.24388 | 0.188123 | ||||||||
\(778\) | −4.69308 | −0.168255 | ||||||||
\(779\) | 7.56195 | 0.270935 | ||||||||
\(780\) | 21.6027 | 0.773500 | ||||||||
\(781\) | −4.19342 | −0.150052 | ||||||||
\(782\) | −25.3553 | −0.906705 | ||||||||
\(783\) | 25.4831 | 0.910691 | ||||||||
\(784\) | −5.37191 | −0.191854 | ||||||||
\(785\) | −19.3921 | −0.692133 | ||||||||
\(786\) | 12.4848 | 0.445318 | ||||||||
\(787\) | 30.4362 | 1.08493 | 0.542466 | − | 0.840078i | \(-0.317491\pi\) | ||||
0.542466 | + | 0.840078i | \(0.317491\pi\) | |||||||
\(788\) | 4.87162 | 0.173544 | ||||||||
\(789\) | 55.5754 | 1.97854 | ||||||||
\(790\) | −7.97460 | −0.283724 | ||||||||
\(791\) | 21.0932 | 0.749988 | ||||||||
\(792\) | 8.49065 | 0.301702 | ||||||||
\(793\) | 6.24145 | 0.221640 | ||||||||
\(794\) | −5.85893 | −0.207926 | ||||||||
\(795\) | 28.0403 | 0.994489 | ||||||||
\(796\) | −17.6913 | −0.627051 | ||||||||
\(797\) | −32.4395 | −1.14906 | −0.574532 | − | 0.818482i | \(-0.694816\pi\) | ||||
−0.574532 | + | 0.818482i | \(0.694816\pi\) | |||||||
\(798\) | −8.80568 | −0.311718 | ||||||||
\(799\) | 43.2410 | 1.52976 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 156.679 | 5.53598 | ||||||||
\(802\) | 23.4591 | 0.828369 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | −1.24496 | −0.0439062 | ||||||||
\(805\) | 7.50030 | 0.264351 | ||||||||
\(806\) | −56.3218 | −1.98385 | ||||||||
\(807\) | −9.76686 | −0.343810 | ||||||||
\(808\) | 13.7088 | 0.482276 | ||||||||
\(809\) | 18.6206 | 0.654666 | 0.327333 | − | 0.944909i | \(-0.393850\pi\) | ||||
0.327333 | + | 0.944909i | \(0.393850\pi\) | |||||||
\(810\) | 37.6192 | 1.32181 | ||||||||
\(811\) | 7.42173 | 0.260612 | 0.130306 | − | 0.991474i | \(-0.458404\pi\) | ||||
0.130306 | + | 0.991474i | \(0.458404\pi\) | |||||||
\(812\) | −1.74701 | −0.0613079 | ||||||||
\(813\) | 87.6577 | 3.07429 | ||||||||
\(814\) | −1.21239 | −0.0424942 | ||||||||
\(815\) | −6.99055 | −0.244868 | ||||||||
\(816\) | 14.6218 | 0.511867 | ||||||||
\(817\) | −13.6776 | −0.478520 | ||||||||
\(818\) | −8.00003 | −0.279714 | ||||||||
\(819\) | −69.0423 | −2.41253 | ||||||||
\(820\) | 3.71434 | 0.129710 | ||||||||
\(821\) | 19.6264 | 0.684964 | 0.342482 | − | 0.939524i | \(-0.388732\pi\) | ||||
0.342482 | + | 0.939524i | \(0.388732\pi\) | |||||||
\(822\) | 38.7862 | 1.35283 | ||||||||
\(823\) | 16.9073 | 0.589353 | 0.294676 | − | 0.955597i | \(-0.404788\pi\) | ||||
0.294676 | + | 0.955597i | \(0.404788\pi\) | |||||||
\(824\) | −9.11681 | −0.317599 | ||||||||
\(825\) | −3.38979 | −0.118017 | ||||||||
\(826\) | −17.8346 | −0.620545 | ||||||||
\(827\) | 40.0169 | 1.39152 | 0.695762 | − | 0.718273i | \(-0.255067\pi\) | ||||
0.695762 | + | 0.718273i | \(0.255067\pi\) | |||||||
\(828\) | 49.9092 | 1.73447 | ||||||||
\(829\) | 2.53035 | 0.0878828 | 0.0439414 | − | 0.999034i | \(-0.486009\pi\) | ||||
0.0439414 | + | 0.999034i | \(0.486009\pi\) | |||||||
\(830\) | −9.52819 | −0.330728 | ||||||||
\(831\) | −39.2616 | −1.36197 | ||||||||
\(832\) | −6.37288 | −0.220940 | ||||||||
\(833\) | 23.1717 | 0.802853 | ||||||||
\(834\) | 31.4922 | 1.09049 | ||||||||
\(835\) | 10.9337 | 0.378376 | ||||||||
\(836\) | 2.03588 | 0.0704123 | ||||||||
\(837\) | −164.489 | −5.68557 | ||||||||
\(838\) | −38.0151 | −1.31321 | ||||||||
\(839\) | −0.203583 | −0.00702845 | −0.00351423 | − | 0.999994i | \(-0.501119\pi\) | ||||
−0.00351423 | + | 0.999994i | \(0.501119\pi\) | |||||||
\(840\) | −4.32525 | −0.149235 | ||||||||
\(841\) | −27.1254 | −0.935358 | ||||||||
\(842\) | 20.9173 | 0.720858 | ||||||||
\(843\) | 24.2236 | 0.834306 | ||||||||
\(844\) | 20.6081 | 0.709360 | ||||||||
\(845\) | 27.6136 | 0.949935 | ||||||||
\(846\) | −85.1152 | −2.92632 | ||||||||
\(847\) | 1.27596 | 0.0438427 | ||||||||
\(848\) | −8.27201 | −0.284062 | ||||||||
\(849\) | −93.3963 | −3.20535 | ||||||||
\(850\) | −4.31350 | −0.147952 | ||||||||
\(851\) | −7.12659 | −0.244296 | ||||||||
\(852\) | 14.2148 | 0.486991 | ||||||||
\(853\) | 48.7852 | 1.67037 | 0.835187 | − | 0.549966i | \(-0.185359\pi\) | ||||
0.835187 | + | 0.549966i | \(0.185359\pi\) | |||||||
\(854\) | −1.24965 | −0.0427622 | ||||||||
\(855\) | 17.2859 | 0.591166 | ||||||||
\(856\) | 14.3074 | 0.489016 | ||||||||
\(857\) | −26.7364 | −0.913299 | −0.456650 | − | 0.889647i | \(-0.650951\pi\) | ||||
−0.456650 | + | 0.889647i | \(0.650951\pi\) | |||||||
\(858\) | 21.6027 | 0.737504 | ||||||||
\(859\) | 26.7839 | 0.913855 | 0.456928 | − | 0.889504i | \(-0.348950\pi\) | ||||
0.456928 | + | 0.889504i | \(0.348950\pi\) | |||||||
\(860\) | −6.71830 | −0.229092 | ||||||||
\(861\) | −16.0655 | −0.547509 | ||||||||
\(862\) | 18.8663 | 0.642589 | ||||||||
\(863\) | −27.7878 | −0.945907 | −0.472954 | − | 0.881087i | \(-0.656812\pi\) | ||||
−0.472954 | + | 0.881087i | \(0.656812\pi\) | |||||||
\(864\) | −18.6121 | −0.633198 | ||||||||
\(865\) | −14.2779 | −0.485463 | ||||||||
\(866\) | 11.4356 | 0.388599 | ||||||||
\(867\) | −5.44487 | −0.184918 | ||||||||
\(868\) | 11.2766 | 0.382754 | ||||||||
\(869\) | −7.97460 | −0.270520 | ||||||||
\(870\) | 4.64117 | 0.157351 | ||||||||
\(871\) | −2.34055 | −0.0793064 | ||||||||
\(872\) | −0.438667 | −0.0148551 | ||||||||
\(873\) | 133.725 | 4.52592 | ||||||||
\(874\) | 11.9672 | 0.404796 | ||||||||
\(875\) | 1.27596 | 0.0431355 | ||||||||
\(876\) | −3.38979 | −0.114530 | ||||||||
\(877\) | 27.7794 | 0.938043 | 0.469021 | − | 0.883187i | \(-0.344607\pi\) | ||||
0.469021 | + | 0.883187i | \(0.344607\pi\) | |||||||
\(878\) | −10.7841 | −0.363946 | ||||||||
\(879\) | 54.4834 | 1.83768 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | −10.1732 | −0.342744 | −0.171372 | − | 0.985206i | \(-0.554820\pi\) | ||||
−0.171372 | + | 0.985206i | \(0.554820\pi\) | |||||||
\(882\) | −45.6111 | −1.53580 | ||||||||
\(883\) | 13.6724 | 0.460112 | 0.230056 | − | 0.973177i | \(-0.426109\pi\) | ||||
0.230056 | + | 0.973177i | \(0.426109\pi\) | |||||||
\(884\) | 27.4894 | 0.924568 | ||||||||
\(885\) | 47.3802 | 1.59267 | ||||||||
\(886\) | 8.47840 | 0.284837 | ||||||||
\(887\) | −47.6510 | −1.59996 | −0.799982 | − | 0.600024i | \(-0.795158\pi\) | ||||
−0.799982 | + | 0.600024i | \(0.795158\pi\) | |||||||
\(888\) | 4.10974 | 0.137914 | ||||||||
\(889\) | 6.36224 | 0.213383 | ||||||||
\(890\) | 18.4531 | 0.618550 | ||||||||
\(891\) | 37.6192 | 1.26029 | ||||||||
\(892\) | 17.7959 | 0.595850 | ||||||||
\(893\) | −20.4088 | −0.682955 | ||||||||
\(894\) | 27.7973 | 0.929682 | ||||||||
\(895\) | −11.7461 | −0.392630 | ||||||||
\(896\) | 1.27596 | 0.0426270 | ||||||||
\(897\) | 126.984 | 4.23986 | ||||||||
\(898\) | 0.252706 | 0.00843289 | ||||||||
\(899\) | −12.1003 | −0.403568 | ||||||||
\(900\) | 8.49065 | 0.283022 | ||||||||
\(901\) | 35.6813 | 1.18872 | ||||||||
\(902\) | 3.71434 | 0.123674 | ||||||||
\(903\) | 29.0583 | 0.967000 | ||||||||
\(904\) | 16.5312 | 0.549819 | ||||||||
\(905\) | 4.67451 | 0.155386 | ||||||||
\(906\) | 65.8448 | 2.18755 | ||||||||
\(907\) | −10.5984 | −0.351914 | −0.175957 | − | 0.984398i | \(-0.556302\pi\) | ||||
−0.175957 | + | 0.984398i | \(0.556302\pi\) | |||||||
\(908\) | 24.0405 | 0.797813 | ||||||||
\(909\) | 116.397 | 3.86065 | ||||||||
\(910\) | −8.13157 | −0.269559 | ||||||||
\(911\) | 21.3971 | 0.708918 | 0.354459 | − | 0.935072i | \(-0.384665\pi\) | ||||
0.354459 | + | 0.935072i | \(0.384665\pi\) | |||||||
\(912\) | −6.90119 | −0.228521 | ||||||||
\(913\) | −9.52819 | −0.315337 | ||||||||
\(914\) | −25.2732 | −0.835964 | ||||||||
\(915\) | 3.31988 | 0.109752 | ||||||||
\(916\) | −10.3646 | −0.342455 | ||||||||
\(917\) | −4.69946 | −0.155190 | ||||||||
\(918\) | 80.2834 | 2.64975 | ||||||||
\(919\) | 26.2661 | 0.866439 | 0.433220 | − | 0.901288i | \(-0.357377\pi\) | ||||
0.433220 | + | 0.901288i | \(0.357377\pi\) | |||||||
\(920\) | 5.87814 | 0.193797 | ||||||||
\(921\) | −25.3021 | −0.833731 | ||||||||
\(922\) | −5.64748 | −0.185990 | ||||||||
\(923\) | 26.7242 | 0.879636 | ||||||||
\(924\) | −4.32525 | −0.142290 | ||||||||
\(925\) | −1.21239 | −0.0398631 | ||||||||
\(926\) | −21.8640 | −0.718496 | ||||||||
\(927\) | −77.4077 | −2.54240 | ||||||||
\(928\) | −1.36916 | −0.0449450 | ||||||||
\(929\) | −29.8500 | −0.979347 | −0.489673 | − | 0.871906i | \(-0.662884\pi\) | ||||
−0.489673 | + | 0.871906i | \(0.662884\pi\) | |||||||
\(930\) | −29.9580 | −0.982362 | ||||||||
\(931\) | −10.9366 | −0.358431 | ||||||||
\(932\) | 9.05203 | 0.296509 | ||||||||
\(933\) | 112.175 | 3.67243 | ||||||||
\(934\) | −21.0845 | −0.689906 | ||||||||
\(935\) | −4.31350 | −0.141066 | ||||||||
\(936\) | −54.1099 | −1.76864 | ||||||||
\(937\) | 31.8793 | 1.04145 | 0.520726 | − | 0.853724i | \(-0.325661\pi\) | ||||
0.520726 | + | 0.853724i | \(0.325661\pi\) | |||||||
\(938\) | 0.468620 | 0.0153010 | ||||||||
\(939\) | −35.7072 | −1.16526 | ||||||||
\(940\) | −10.0246 | −0.326966 | ||||||||
\(941\) | −40.1454 | −1.30870 | −0.654352 | − | 0.756190i | \(-0.727058\pi\) | ||||
−0.654352 | + | 0.756190i | \(0.727058\pi\) | |||||||
\(942\) | 65.7350 | 2.14176 | ||||||||
\(943\) | 21.8334 | 0.710994 | ||||||||
\(944\) | −13.9774 | −0.454924 | ||||||||
\(945\) | −23.7484 | −0.772537 | ||||||||
\(946\) | −6.71830 | −0.218431 | ||||||||
\(947\) | 22.4925 | 0.730909 | 0.365454 | − | 0.930829i | \(-0.380914\pi\) | ||||
0.365454 | + | 0.930829i | \(0.380914\pi\) | |||||||
\(948\) | 27.0322 | 0.877965 | ||||||||
\(949\) | −6.37288 | −0.206872 | ||||||||
\(950\) | 2.03588 | 0.0660526 | ||||||||
\(951\) | 84.4173 | 2.73742 | ||||||||
\(952\) | −5.50387 | −0.178381 | ||||||||
\(953\) | 8.80007 | 0.285062 | 0.142531 | − | 0.989790i | \(-0.454476\pi\) | ||||
0.142531 | + | 0.989790i | \(0.454476\pi\) | |||||||
\(954\) | −70.2348 | −2.27393 | ||||||||
\(955\) | 8.41189 | 0.272202 | ||||||||
\(956\) | −10.4398 | −0.337647 | ||||||||
\(957\) | 4.64117 | 0.150028 | ||||||||
\(958\) | −21.3653 | −0.690282 | ||||||||
\(959\) | −14.5997 | −0.471449 | ||||||||
\(960\) | −3.38979 | −0.109405 | ||||||||
\(961\) | 47.1054 | 1.51953 | ||||||||
\(962\) | 7.72640 | 0.249109 | ||||||||
\(963\) | 121.479 | 3.91460 | ||||||||
\(964\) | −20.1320 | −0.648409 | ||||||||
\(965\) | −3.85445 | −0.124079 | ||||||||
\(966\) | −25.4244 | −0.818017 | ||||||||
\(967\) | −23.4336 | −0.753574 | −0.376787 | − | 0.926300i | \(-0.622971\pi\) | ||||
−0.376787 | + | 0.926300i | \(0.622971\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 29.7683 | 0.956295 | ||||||||
\(970\) | 15.7497 | 0.505693 | ||||||||
\(971\) | −0.800642 | −0.0256938 | −0.0128469 | − | 0.999917i | \(-0.504089\pi\) | ||||
−0.0128469 | + | 0.999917i | \(0.504089\pi\) | |||||||
\(972\) | −71.6847 | −2.29929 | ||||||||
\(973\) | −11.8541 | −0.380026 | ||||||||
\(974\) | 0.110895 | 0.00355332 | ||||||||
\(975\) | 21.6027 | 0.691840 | ||||||||
\(976\) | −0.979378 | −0.0313491 | ||||||||
\(977\) | −4.12175 | −0.131867 | −0.0659333 | − | 0.997824i | \(-0.521002\pi\) | ||||
−0.0659333 | + | 0.997824i | \(0.521002\pi\) | |||||||
\(978\) | 23.6965 | 0.757730 | ||||||||
\(979\) | 18.4531 | 0.589764 | ||||||||
\(980\) | −5.37191 | −0.171600 | ||||||||
\(981\) | −3.72457 | −0.118916 | ||||||||
\(982\) | 17.4258 | 0.556080 | ||||||||
\(983\) | −38.1352 | −1.21632 | −0.608162 | − | 0.793813i | \(-0.708093\pi\) | ||||
−0.608162 | + | 0.793813i | \(0.708093\pi\) | |||||||
\(984\) | −12.5908 | −0.401381 | ||||||||
\(985\) | 4.87162 | 0.155223 | ||||||||
\(986\) | 5.90589 | 0.188082 | ||||||||
\(987\) | 43.3588 | 1.38013 | ||||||||
\(988\) | −12.9744 | −0.412771 | ||||||||
\(989\) | −39.4911 | −1.25574 | ||||||||
\(990\) | 8.49065 | 0.269851 | ||||||||
\(991\) | −5.10825 | −0.162269 | −0.0811344 | − | 0.996703i | \(-0.525854\pi\) | ||||
−0.0811344 | + | 0.996703i | \(0.525854\pi\) | |||||||
\(992\) | 8.83773 | 0.280598 | ||||||||
\(993\) | 70.3572 | 2.23272 | ||||||||
\(994\) | −5.35066 | −0.169713 | ||||||||
\(995\) | −17.6913 | −0.560852 | ||||||||
\(996\) | 32.2985 | 1.02342 | ||||||||
\(997\) | 29.8704 | 0.946005 | 0.473003 | − | 0.881061i | \(-0.343170\pi\) | ||||
0.473003 | + | 0.881061i | \(0.343170\pi\) | |||||||
\(998\) | 9.08271 | 0.287508 | ||||||||
\(999\) | 22.5651 | 0.713930 |
(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 | 8030.2.a.v.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8030.2.a.v.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial |