Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(1,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, 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("731.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.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: | \(5.83706438776\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
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 | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 731.1 |
$q$-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 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | 2.56155 | 1.47891 | 0.739457 | − | 0.673204i | \(-0.235083\pi\) | ||||
0.739457 | + | 0.673204i | \(0.235083\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.56155 | −1.14556 | −0.572781 | − | 0.819709i | \(-0.694135\pi\) | ||||
−0.572781 | + | 0.819709i | \(0.694135\pi\) | |||||||
\(6\) | −2.56155 | −1.04575 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | 3.56155 | 1.18718 | ||||||||
\(10\) | 2.56155 | 0.810034 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | −2.56155 | −0.739457 | ||||||||
\(13\) | −4.56155 | −1.26515 | −0.632574 | − | 0.774500i | \(-0.718001\pi\) | ||||
−0.632574 | + | 0.774500i | \(0.718001\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.56155 | −1.69419 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −3.56155 | −0.839466 | ||||||||
\(19\) | −1.12311 | −0.257658 | −0.128829 | − | 0.991667i | \(-0.541122\pi\) | ||||
−0.128829 | + | 0.991667i | \(0.541122\pi\) | |||||||
\(20\) | 2.56155 | 0.572781 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | 2.00000 | 0.417029 | 0.208514 | − | 0.978019i | \(-0.433137\pi\) | ||||
0.208514 | + | 0.978019i | \(0.433137\pi\) | |||||||
\(24\) | 7.68466 | 1.56862 | ||||||||
\(25\) | 1.56155 | 0.312311 | ||||||||
\(26\) | 4.56155 | 0.894594 | ||||||||
\(27\) | 1.43845 | 0.276829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.12311 | −0.951337 | −0.475668 | − | 0.879625i | \(-0.657794\pi\) | ||||
−0.475668 | + | 0.879625i | \(0.657794\pi\) | |||||||
\(30\) | 6.56155 | 1.19797 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | −5.12311 | −0.891818 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.56155 | −0.593592 | ||||||||
\(37\) | −1.43845 | −0.236479 | −0.118240 | − | 0.992985i | \(-0.537725\pi\) | ||||
−0.118240 | + | 0.992985i | \(0.537725\pi\) | |||||||
\(38\) | 1.12311 | 0.182192 | ||||||||
\(39\) | −11.6847 | −1.87104 | ||||||||
\(40\) | −7.68466 | −1.21505 | ||||||||
\(41\) | 3.12311 | 0.487747 | 0.243874 | − | 0.969807i | \(-0.421582\pi\) | ||||
0.243874 | + | 0.969807i | \(0.421582\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | −9.12311 | −1.35999 | ||||||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | −5.43845 | −0.793279 | −0.396640 | − | 0.917974i | \(-0.629824\pi\) | ||||
−0.396640 | + | 0.917974i | \(0.629824\pi\) | |||||||
\(48\) | −2.56155 | −0.369728 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | −1.56155 | −0.220837 | ||||||||
\(51\) | −2.56155 | −0.358689 | ||||||||
\(52\) | 4.56155 | 0.632574 | ||||||||
\(53\) | 1.68466 | 0.231406 | 0.115703 | − | 0.993284i | \(-0.463088\pi\) | ||||
0.115703 | + | 0.993284i | \(0.463088\pi\) | |||||||
\(54\) | −1.43845 | −0.195748 | ||||||||
\(55\) | 5.12311 | 0.690799 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.87689 | −0.381054 | ||||||||
\(58\) | 5.12311 | 0.672697 | ||||||||
\(59\) | 8.80776 | 1.14667 | 0.573337 | − | 0.819320i | \(-0.305649\pi\) | ||||
0.573337 | + | 0.819320i | \(0.305649\pi\) | |||||||
\(60\) | 6.56155 | 0.847093 | ||||||||
\(61\) | −11.6847 | −1.49607 | −0.748034 | − | 0.663661i | \(-0.769002\pi\) | ||||
−0.748034 | + | 0.663661i | \(0.769002\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 11.6847 | 1.44930 | ||||||||
\(66\) | 5.12311 | 0.630611 | ||||||||
\(67\) | 1.43845 | 0.175734 | 0.0878671 | − | 0.996132i | \(-0.471995\pi\) | ||||
0.0878671 | + | 0.996132i | \(0.471995\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 5.12311 | 0.616749 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.43845 | 0.170712 | 0.0853561 | − | 0.996351i | \(-0.472797\pi\) | ||||
0.0853561 | + | 0.996351i | \(0.472797\pi\) | |||||||
\(72\) | 10.6847 | 1.25920 | ||||||||
\(73\) | 8.80776 | 1.03087 | 0.515435 | − | 0.856928i | \(-0.327630\pi\) | ||||
0.515435 | + | 0.856928i | \(0.327630\pi\) | |||||||
\(74\) | 1.43845 | 0.167216 | ||||||||
\(75\) | 4.00000 | 0.461880 | ||||||||
\(76\) | 1.12311 | 0.128829 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 11.6847 | 1.32303 | ||||||||
\(79\) | −0.876894 | −0.0986583 | −0.0493292 | − | 0.998783i | \(-0.515708\pi\) | ||||
−0.0493292 | + | 0.998783i | \(0.515708\pi\) | |||||||
\(80\) | 2.56155 | 0.286390 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | −3.12311 | −0.344889 | ||||||||
\(83\) | −4.80776 | −0.527721 | −0.263860 | − | 0.964561i | \(-0.584996\pi\) | ||||
−0.263860 | + | 0.964561i | \(0.584996\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.56155 | 0.277839 | ||||||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | −13.1231 | −1.40694 | ||||||||
\(88\) | −6.00000 | −0.639602 | ||||||||
\(89\) | 16.2462 | 1.72209 | 0.861047 | − | 0.508525i | \(-0.169809\pi\) | ||||
0.861047 | + | 0.508525i | \(0.169809\pi\) | |||||||
\(90\) | 9.12311 | 0.961660 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.00000 | −0.208514 | ||||||||
\(93\) | −15.3693 | −1.59372 | ||||||||
\(94\) | 5.43845 | 0.560933 | ||||||||
\(95\) | 2.87689 | 0.295163 | ||||||||
\(96\) | −12.8078 | −1.30719 | ||||||||
\(97\) | −0.246211 | −0.0249990 | −0.0124995 | − | 0.999922i | \(-0.503979\pi\) | ||||
−0.0124995 | + | 0.999922i | \(0.503979\pi\) | |||||||
\(98\) | 7.00000 | 0.707107 | ||||||||
\(99\) | −7.12311 | −0.715899 | ||||||||
\(100\) | −1.56155 | −0.156155 | ||||||||
\(101\) | −2.00000 | −0.199007 | −0.0995037 | − | 0.995037i | \(-0.531726\pi\) | ||||
−0.0995037 | + | 0.995037i | \(0.531726\pi\) | |||||||
\(102\) | 2.56155 | 0.253632 | ||||||||
\(103\) | −13.4384 | −1.32413 | −0.662065 | − | 0.749447i | \(-0.730320\pi\) | ||||
−0.662065 | + | 0.749447i | \(0.730320\pi\) | |||||||
\(104\) | −13.6847 | −1.34189 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.68466 | −0.163628 | ||||||||
\(107\) | 2.00000 | 0.193347 | 0.0966736 | − | 0.995316i | \(-0.469180\pi\) | ||||
0.0966736 | + | 0.995316i | \(0.469180\pi\) | |||||||
\(108\) | −1.43845 | −0.138415 | ||||||||
\(109\) | 12.2462 | 1.17297 | 0.586487 | − | 0.809959i | \(-0.300510\pi\) | ||||
0.586487 | + | 0.809959i | \(0.300510\pi\) | |||||||
\(110\) | −5.12311 | −0.488469 | ||||||||
\(111\) | −3.68466 | −0.349732 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.80776 | 0.828565 | 0.414282 | − | 0.910148i | \(-0.364033\pi\) | ||||
0.414282 | + | 0.910148i | \(0.364033\pi\) | |||||||
\(114\) | 2.87689 | 0.269446 | ||||||||
\(115\) | −5.12311 | −0.477732 | ||||||||
\(116\) | 5.12311 | 0.475668 | ||||||||
\(117\) | −16.2462 | −1.50196 | ||||||||
\(118\) | −8.80776 | −0.810820 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −19.6847 | −1.79696 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 11.6847 | 1.05788 | ||||||||
\(123\) | 8.00000 | 0.721336 | ||||||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | 8.80776 | 0.787790 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.0540 | −1.33582 | −0.667912 | − | 0.744240i | \(-0.732812\pi\) | ||||
−0.667912 | + | 0.744240i | \(0.732812\pi\) | |||||||
\(128\) | 3.00000 | 0.265165 | ||||||||
\(129\) | −2.56155 | −0.225532 | ||||||||
\(130\) | −11.6847 | −1.02481 | ||||||||
\(131\) | −8.80776 | −0.769538 | −0.384769 | − | 0.923013i | \(-0.625719\pi\) | ||||
−0.384769 | + | 0.923013i | \(0.625719\pi\) | |||||||
\(132\) | 5.12311 | 0.445909 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.43845 | −0.124263 | ||||||||
\(135\) | −3.68466 | −0.317125 | ||||||||
\(136\) | −3.00000 | −0.257248 | ||||||||
\(137\) | −4.24621 | −0.362778 | −0.181389 | − | 0.983411i | \(-0.558059\pi\) | ||||
−0.181389 | + | 0.983411i | \(0.558059\pi\) | |||||||
\(138\) | −5.12311 | −0.436108 | ||||||||
\(139\) | 5.36932 | 0.455420 | 0.227710 | − | 0.973729i | \(-0.426876\pi\) | ||||
0.227710 | + | 0.973729i | \(0.426876\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.9309 | −1.17319 | ||||||||
\(142\) | −1.43845 | −0.120712 | ||||||||
\(143\) | 9.12311 | 0.762912 | ||||||||
\(144\) | −3.56155 | −0.296796 | ||||||||
\(145\) | 13.1231 | 1.08981 | ||||||||
\(146\) | −8.80776 | −0.728936 | ||||||||
\(147\) | −17.9309 | −1.47891 | ||||||||
\(148\) | 1.43845 | 0.118240 | ||||||||
\(149\) | 8.24621 | 0.675556 | 0.337778 | − | 0.941226i | \(-0.390325\pi\) | ||||
0.337778 | + | 0.941226i | \(0.390325\pi\) | |||||||
\(150\) | −4.00000 | −0.326599 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | −3.36932 | −0.273288 | ||||||||
\(153\) | −3.56155 | −0.287934 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.3693 | 1.23449 | ||||||||
\(156\) | 11.6847 | 0.935521 | ||||||||
\(157\) | 10.4924 | 0.837386 | 0.418693 | − | 0.908128i | \(-0.362488\pi\) | ||||
0.418693 | + | 0.908128i | \(0.362488\pi\) | |||||||
\(158\) | 0.876894 | 0.0697620 | ||||||||
\(159\) | 4.31534 | 0.342229 | ||||||||
\(160\) | 12.8078 | 1.01254 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.00000 | 0.549972 | ||||||||
\(163\) | −17.4384 | −1.36588 | −0.682942 | − | 0.730472i | \(-0.739300\pi\) | ||||
−0.682942 | + | 0.730472i | \(0.739300\pi\) | |||||||
\(164\) | −3.12311 | −0.243874 | ||||||||
\(165\) | 13.1231 | 1.02163 | ||||||||
\(166\) | 4.80776 | 0.373155 | ||||||||
\(167\) | 22.0000 | 1.70241 | 0.851206 | − | 0.524832i | \(-0.175872\pi\) | ||||
0.851206 | + | 0.524832i | \(0.175872\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.80776 | 0.600597 | ||||||||
\(170\) | −2.56155 | −0.196462 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | 3.12311 | 0.237445 | 0.118723 | − | 0.992927i | \(-0.462120\pi\) | ||||
0.118723 | + | 0.992927i | \(0.462120\pi\) | |||||||
\(174\) | 13.1231 | 0.994860 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 22.5616 | 1.69583 | ||||||||
\(178\) | −16.2462 | −1.21771 | ||||||||
\(179\) | 17.1231 | 1.27984 | 0.639921 | − | 0.768441i | \(-0.278967\pi\) | ||||
0.639921 | + | 0.768441i | \(0.278967\pi\) | |||||||
\(180\) | 9.12311 | 0.679996 | ||||||||
\(181\) | 5.36932 | 0.399098 | 0.199549 | − | 0.979888i | \(-0.436052\pi\) | ||||
0.199549 | + | 0.979888i | \(0.436052\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −29.9309 | −2.21255 | ||||||||
\(184\) | 6.00000 | 0.442326 | ||||||||
\(185\) | 3.68466 | 0.270901 | ||||||||
\(186\) | 15.3693 | 1.12693 | ||||||||
\(187\) | 2.00000 | 0.146254 | ||||||||
\(188\) | 5.43845 | 0.396640 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.87689 | −0.208712 | ||||||||
\(191\) | 2.87689 | 0.208165 | 0.104082 | − | 0.994569i | \(-0.466809\pi\) | ||||
0.104082 | + | 0.994569i | \(0.466809\pi\) | |||||||
\(192\) | 17.9309 | 1.29405 | ||||||||
\(193\) | 2.00000 | 0.143963 | 0.0719816 | − | 0.997406i | \(-0.477068\pi\) | ||||
0.0719816 | + | 0.997406i | \(0.477068\pi\) | |||||||
\(194\) | 0.246211 | 0.0176769 | ||||||||
\(195\) | 29.9309 | 2.14339 | ||||||||
\(196\) | 7.00000 | 0.500000 | ||||||||
\(197\) | −23.6155 | −1.68254 | −0.841268 | − | 0.540618i | \(-0.818191\pi\) | ||||
−0.841268 | + | 0.540618i | \(0.818191\pi\) | |||||||
\(198\) | 7.12311 | 0.506217 | ||||||||
\(199\) | 25.9309 | 1.83819 | 0.919095 | − | 0.394035i | \(-0.128921\pi\) | ||||
0.919095 | + | 0.394035i | \(0.128921\pi\) | |||||||
\(200\) | 4.68466 | 0.331255 | ||||||||
\(201\) | 3.68466 | 0.259896 | ||||||||
\(202\) | 2.00000 | 0.140720 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.56155 | 0.179345 | ||||||||
\(205\) | −8.00000 | −0.558744 | ||||||||
\(206\) | 13.4384 | 0.936301 | ||||||||
\(207\) | 7.12311 | 0.495090 | ||||||||
\(208\) | 4.56155 | 0.316287 | ||||||||
\(209\) | 2.24621 | 0.155374 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.8078 | −1.70784 | −0.853918 | − | 0.520407i | \(-0.825780\pi\) | ||||
−0.853918 | + | 0.520407i | \(0.825780\pi\) | |||||||
\(212\) | −1.68466 | −0.115703 | ||||||||
\(213\) | 3.68466 | 0.252469 | ||||||||
\(214\) | −2.00000 | −0.136717 | ||||||||
\(215\) | 2.56155 | 0.174696 | ||||||||
\(216\) | 4.31534 | 0.293622 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −12.2462 | −0.829418 | ||||||||
\(219\) | 22.5616 | 1.52457 | ||||||||
\(220\) | −5.12311 | −0.345400 | ||||||||
\(221\) | 4.56155 | 0.306843 | ||||||||
\(222\) | 3.68466 | 0.247298 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.56155 | 0.370770 | ||||||||
\(226\) | −8.80776 | −0.585884 | ||||||||
\(227\) | −12.4924 | −0.829151 | −0.414576 | − | 0.910015i | \(-0.636070\pi\) | ||||
−0.414576 | + | 0.910015i | \(0.636070\pi\) | |||||||
\(228\) | 2.87689 | 0.190527 | ||||||||
\(229\) | −14.8078 | −0.978525 | −0.489262 | − | 0.872137i | \(-0.662734\pi\) | ||||
−0.489262 | + | 0.872137i | \(0.662734\pi\) | |||||||
\(230\) | 5.12311 | 0.337808 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15.3693 | −1.00905 | ||||||||
\(233\) | 10.8769 | 0.712569 | 0.356285 | − | 0.934378i | \(-0.384043\pi\) | ||||
0.356285 | + | 0.934378i | \(0.384043\pi\) | |||||||
\(234\) | 16.2462 | 1.06205 | ||||||||
\(235\) | 13.9309 | 0.908750 | ||||||||
\(236\) | −8.80776 | −0.573337 | ||||||||
\(237\) | −2.24621 | −0.145907 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 6.56155 | 0.423546 | ||||||||
\(241\) | 19.3693 | 1.24769 | 0.623844 | − | 0.781549i | \(-0.285570\pi\) | ||||
0.623844 | + | 0.781549i | \(0.285570\pi\) | |||||||
\(242\) | 7.00000 | 0.449977 | ||||||||
\(243\) | −22.2462 | −1.42710 | ||||||||
\(244\) | 11.6847 | 0.748034 | ||||||||
\(245\) | 17.9309 | 1.14556 | ||||||||
\(246\) | −8.00000 | −0.510061 | ||||||||
\(247\) | 5.12311 | 0.325975 | ||||||||
\(248\) | −18.0000 | −1.14300 | ||||||||
\(249\) | −12.3153 | −0.780453 | ||||||||
\(250\) | −8.80776 | −0.557052 | ||||||||
\(251\) | −10.5616 | −0.666639 | −0.333320 | − | 0.942814i | \(-0.608169\pi\) | ||||
−0.333320 | + | 0.942814i | \(0.608169\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 15.0540 | 0.944570 | ||||||||
\(255\) | 6.56155 | 0.410900 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 26.0000 | 1.62184 | 0.810918 | − | 0.585160i | \(-0.198968\pi\) | ||||
0.810918 | + | 0.585160i | \(0.198968\pi\) | |||||||
\(258\) | 2.56155 | 0.159475 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −11.6847 | −0.724652 | ||||||||
\(261\) | −18.2462 | −1.12941 | ||||||||
\(262\) | 8.80776 | 0.544145 | ||||||||
\(263\) | −20.4924 | −1.26362 | −0.631808 | − | 0.775125i | \(-0.717687\pi\) | ||||
−0.631808 | + | 0.775125i | \(0.717687\pi\) | |||||||
\(264\) | −15.3693 | −0.945916 | ||||||||
\(265\) | −4.31534 | −0.265089 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 41.6155 | 2.54683 | ||||||||
\(268\) | −1.43845 | −0.0878671 | ||||||||
\(269\) | −8.24621 | −0.502780 | −0.251390 | − | 0.967886i | \(-0.580888\pi\) | ||||
−0.251390 | + | 0.967886i | \(0.580888\pi\) | |||||||
\(270\) | 3.68466 | 0.224241 | ||||||||
\(271\) | 9.93087 | 0.603257 | 0.301629 | − | 0.953425i | \(-0.402470\pi\) | ||||
0.301629 | + | 0.953425i | \(0.402470\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.24621 | 0.256523 | ||||||||
\(275\) | −3.12311 | −0.188330 | ||||||||
\(276\) | −5.12311 | −0.308375 | ||||||||
\(277\) | 2.06913 | 0.124322 | 0.0621610 | − | 0.998066i | \(-0.480201\pi\) | ||||
0.0621610 | + | 0.998066i | \(0.480201\pi\) | |||||||
\(278\) | −5.36932 | −0.322030 | ||||||||
\(279\) | −21.3693 | −1.27935 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.93087 | 0.473116 | 0.236558 | − | 0.971617i | \(-0.423981\pi\) | ||||
0.236558 | + | 0.971617i | \(0.423981\pi\) | |||||||
\(282\) | 13.9309 | 0.829571 | ||||||||
\(283\) | −4.24621 | −0.252411 | −0.126206 | − | 0.992004i | \(-0.540280\pi\) | ||||
−0.126206 | + | 0.992004i | \(0.540280\pi\) | |||||||
\(284\) | −1.43845 | −0.0853561 | ||||||||
\(285\) | 7.36932 | 0.436521 | ||||||||
\(286\) | −9.12311 | −0.539461 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −17.8078 | −1.04933 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −13.1231 | −0.770615 | ||||||||
\(291\) | −0.630683 | −0.0369713 | ||||||||
\(292\) | −8.80776 | −0.515435 | ||||||||
\(293\) | 16.2462 | 0.949114 | 0.474557 | − | 0.880225i | \(-0.342608\pi\) | ||||
0.474557 | + | 0.880225i | \(0.342608\pi\) | |||||||
\(294\) | 17.9309 | 1.04575 | ||||||||
\(295\) | −22.5616 | −1.31358 | ||||||||
\(296\) | −4.31534 | −0.250824 | ||||||||
\(297\) | −2.87689 | −0.166934 | ||||||||
\(298\) | −8.24621 | −0.477690 | ||||||||
\(299\) | −9.12311 | −0.527603 | ||||||||
\(300\) | −4.00000 | −0.230940 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −8.00000 | −0.460348 | ||||||||
\(303\) | −5.12311 | −0.294315 | ||||||||
\(304\) | 1.12311 | 0.0644145 | ||||||||
\(305\) | 29.9309 | 1.71384 | ||||||||
\(306\) | 3.56155 | 0.203600 | ||||||||
\(307\) | 2.24621 | 0.128198 | 0.0640990 | − | 0.997944i | \(-0.479583\pi\) | ||||
0.0640990 | + | 0.997944i | \(0.479583\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −34.4233 | −1.95827 | ||||||||
\(310\) | −15.3693 | −0.872919 | ||||||||
\(311\) | −9.36932 | −0.531285 | −0.265643 | − | 0.964072i | \(-0.585584\pi\) | ||||
−0.265643 | + | 0.964072i | \(0.585584\pi\) | |||||||
\(312\) | −35.0540 | −1.98454 | ||||||||
\(313\) | −4.80776 | −0.271751 | −0.135875 | − | 0.990726i | \(-0.543385\pi\) | ||||
−0.135875 | + | 0.990726i | \(0.543385\pi\) | |||||||
\(314\) | −10.4924 | −0.592122 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.876894 | 0.0493292 | ||||||||
\(317\) | 5.36932 | 0.301571 | 0.150785 | − | 0.988567i | \(-0.451820\pi\) | ||||
0.150785 | + | 0.988567i | \(0.451820\pi\) | |||||||
\(318\) | −4.31534 | −0.241992 | ||||||||
\(319\) | 10.2462 | 0.573678 | ||||||||
\(320\) | −17.9309 | −1.00237 | ||||||||
\(321\) | 5.12311 | 0.285944 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.12311 | 0.0624913 | ||||||||
\(324\) | 7.00000 | 0.388889 | ||||||||
\(325\) | −7.12311 | −0.395119 | ||||||||
\(326\) | 17.4384 | 0.965826 | ||||||||
\(327\) | 31.3693 | 1.73473 | ||||||||
\(328\) | 9.36932 | 0.517334 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −13.1231 | −0.722403 | ||||||||
\(331\) | 12.0000 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(332\) | 4.80776 | 0.263860 | ||||||||
\(333\) | −5.12311 | −0.280744 | ||||||||
\(334\) | −22.0000 | −1.20379 | ||||||||
\(335\) | −3.68466 | −0.201314 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.2462 | −1.10288 | −0.551441 | − | 0.834214i | \(-0.685922\pi\) | ||||
−0.551441 | + | 0.834214i | \(0.685922\pi\) | |||||||
\(338\) | −7.80776 | −0.424686 | ||||||||
\(339\) | 22.5616 | 1.22538 | ||||||||
\(340\) | −2.56155 | −0.138920 | ||||||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | 4.00000 | 0.216295 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.00000 | −0.161749 | ||||||||
\(345\) | −13.1231 | −0.706524 | ||||||||
\(346\) | −3.12311 | −0.167899 | ||||||||
\(347\) | −22.5616 | −1.21117 | −0.605584 | − | 0.795782i | \(-0.707060\pi\) | ||||
−0.605584 | + | 0.795782i | \(0.707060\pi\) | |||||||
\(348\) | 13.1231 | 0.703472 | ||||||||
\(349\) | −19.1231 | −1.02364 | −0.511818 | − | 0.859094i | \(-0.671028\pi\) | ||||
−0.511818 | + | 0.859094i | \(0.671028\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.56155 | −0.350230 | ||||||||
\(352\) | 10.0000 | 0.533002 | ||||||||
\(353\) | 26.1771 | 1.39327 | 0.696633 | − | 0.717428i | \(-0.254681\pi\) | ||||
0.696633 | + | 0.717428i | \(0.254681\pi\) | |||||||
\(354\) | −22.5616 | −1.19913 | ||||||||
\(355\) | −3.68466 | −0.195561 | ||||||||
\(356\) | −16.2462 | −0.861047 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −17.1231 | −0.904984 | ||||||||
\(359\) | 16.8078 | 0.887080 | 0.443540 | − | 0.896255i | \(-0.353722\pi\) | ||||
0.443540 | + | 0.896255i | \(0.353722\pi\) | |||||||
\(360\) | −27.3693 | −1.44249 | ||||||||
\(361\) | −17.7386 | −0.933612 | ||||||||
\(362\) | −5.36932 | −0.282205 | ||||||||
\(363\) | −17.9309 | −0.941127 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.5616 | −1.18093 | ||||||||
\(366\) | 29.9309 | 1.56451 | ||||||||
\(367\) | −14.4924 | −0.756498 | −0.378249 | − | 0.925704i | \(-0.623474\pi\) | ||||
−0.378249 | + | 0.925704i | \(0.623474\pi\) | |||||||
\(368\) | −2.00000 | −0.104257 | ||||||||
\(369\) | 11.1231 | 0.579046 | ||||||||
\(370\) | −3.68466 | −0.191556 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 15.3693 | 0.796862 | ||||||||
\(373\) | −37.3693 | −1.93491 | −0.967455 | − | 0.253043i | \(-0.918568\pi\) | ||||
−0.967455 | + | 0.253043i | \(0.918568\pi\) | |||||||
\(374\) | −2.00000 | −0.103418 | ||||||||
\(375\) | 22.5616 | 1.16507 | ||||||||
\(376\) | −16.3153 | −0.841399 | ||||||||
\(377\) | 23.3693 | 1.20358 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.876894 | −0.0450430 | −0.0225215 | − | 0.999746i | \(-0.507169\pi\) | ||||
−0.0225215 | + | 0.999746i | \(0.507169\pi\) | |||||||
\(380\) | −2.87689 | −0.147582 | ||||||||
\(381\) | −38.5616 | −1.97557 | ||||||||
\(382\) | −2.87689 | −0.147195 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 7.68466 | 0.392156 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.00000 | −0.101797 | ||||||||
\(387\) | −3.56155 | −0.181044 | ||||||||
\(388\) | 0.246211 | 0.0124995 | ||||||||
\(389\) | −30.4924 | −1.54603 | −0.773014 | − | 0.634389i | \(-0.781252\pi\) | ||||
−0.773014 | + | 0.634389i | \(0.781252\pi\) | |||||||
\(390\) | −29.9309 | −1.51561 | ||||||||
\(391\) | −2.00000 | −0.101144 | ||||||||
\(392\) | −21.0000 | −1.06066 | ||||||||
\(393\) | −22.5616 | −1.13808 | ||||||||
\(394\) | 23.6155 | 1.18973 | ||||||||
\(395\) | 2.24621 | 0.113019 | ||||||||
\(396\) | 7.12311 | 0.357950 | ||||||||
\(397\) | 15.1231 | 0.759007 | 0.379503 | − | 0.925190i | \(-0.376095\pi\) | ||||
0.379503 | + | 0.925190i | \(0.376095\pi\) | |||||||
\(398\) | −25.9309 | −1.29980 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.56155 | −0.0780776 | ||||||||
\(401\) | −20.2462 | −1.01105 | −0.505524 | − | 0.862813i | \(-0.668701\pi\) | ||||
−0.505524 | + | 0.862813i | \(0.668701\pi\) | |||||||
\(402\) | −3.68466 | −0.183774 | ||||||||
\(403\) | 27.3693 | 1.36336 | ||||||||
\(404\) | 2.00000 | 0.0995037 | ||||||||
\(405\) | 17.9309 | 0.890992 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.87689 | 0.142602 | ||||||||
\(408\) | −7.68466 | −0.380447 | ||||||||
\(409\) | 21.8617 | 1.08099 | 0.540497 | − | 0.841346i | \(-0.318236\pi\) | ||||
0.540497 | + | 0.841346i | \(0.318236\pi\) | |||||||
\(410\) | 8.00000 | 0.395092 | ||||||||
\(411\) | −10.8769 | −0.536518 | ||||||||
\(412\) | 13.4384 | 0.662065 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −7.12311 | −0.350082 | ||||||||
\(415\) | 12.3153 | 0.604536 | ||||||||
\(416\) | 22.8078 | 1.11824 | ||||||||
\(417\) | 13.7538 | 0.673526 | ||||||||
\(418\) | −2.24621 | −0.109866 | ||||||||
\(419\) | −20.0000 | −0.977064 | −0.488532 | − | 0.872546i | \(-0.662467\pi\) | ||||
−0.488532 | + | 0.872546i | \(0.662467\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.7386 | −1.79053 | −0.895266 | − | 0.445533i | \(-0.853014\pi\) | ||||
−0.895266 | + | 0.445533i | \(0.853014\pi\) | |||||||
\(422\) | 24.8078 | 1.20762 | ||||||||
\(423\) | −19.3693 | −0.941768 | ||||||||
\(424\) | 5.05398 | 0.245443 | ||||||||
\(425\) | −1.56155 | −0.0757464 | ||||||||
\(426\) | −3.68466 | −0.178522 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.00000 | −0.0966736 | ||||||||
\(429\) | 23.3693 | 1.12828 | ||||||||
\(430\) | −2.56155 | −0.123529 | ||||||||
\(431\) | −4.87689 | −0.234912 | −0.117456 | − | 0.993078i | \(-0.537474\pi\) | ||||
−0.117456 | + | 0.993078i | \(0.537474\pi\) | |||||||
\(432\) | −1.43845 | −0.0692073 | ||||||||
\(433\) | −13.3693 | −0.642488 | −0.321244 | − | 0.946996i | \(-0.604101\pi\) | ||||
−0.321244 | + | 0.946996i | \(0.604101\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 33.6155 | 1.61174 | ||||||||
\(436\) | −12.2462 | −0.586487 | ||||||||
\(437\) | −2.24621 | −0.107451 | ||||||||
\(438\) | −22.5616 | −1.07803 | ||||||||
\(439\) | −9.36932 | −0.447173 | −0.223587 | − | 0.974684i | \(-0.571777\pi\) | ||||
−0.223587 | + | 0.974684i | \(0.571777\pi\) | |||||||
\(440\) | 15.3693 | 0.732703 | ||||||||
\(441\) | −24.9309 | −1.18718 | ||||||||
\(442\) | −4.56155 | −0.216971 | ||||||||
\(443\) | 30.4233 | 1.44545 | 0.722727 | − | 0.691133i | \(-0.242888\pi\) | ||||
0.722727 | + | 0.691133i | \(0.242888\pi\) | |||||||
\(444\) | 3.68466 | 0.174866 | ||||||||
\(445\) | −41.6155 | −1.97277 | ||||||||
\(446\) | 16.0000 | 0.757622 | ||||||||
\(447\) | 21.1231 | 0.999089 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.5616 | −1.63106 | −0.815530 | − | 0.578714i | \(-0.803555\pi\) | ||||
−0.815530 | + | 0.578714i | \(0.803555\pi\) | |||||||
\(450\) | −5.56155 | −0.262174 | ||||||||
\(451\) | −6.24621 | −0.294123 | ||||||||
\(452\) | −8.80776 | −0.414282 | ||||||||
\(453\) | 20.4924 | 0.962818 | ||||||||
\(454\) | 12.4924 | 0.586298 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.63068 | −0.404169 | ||||||||
\(457\) | −29.3693 | −1.37384 | −0.686919 | − | 0.726734i | \(-0.741037\pi\) | ||||
−0.686919 | + | 0.726734i | \(0.741037\pi\) | |||||||
\(458\) | 14.8078 | 0.691921 | ||||||||
\(459\) | −1.43845 | −0.0671410 | ||||||||
\(460\) | 5.12311 | 0.238866 | ||||||||
\(461\) | 2.80776 | 0.130771 | 0.0653853 | − | 0.997860i | \(-0.479172\pi\) | ||||
0.0653853 | + | 0.997860i | \(0.479172\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 5.12311 | 0.237834 | ||||||||
\(465\) | 39.3693 | 1.82571 | ||||||||
\(466\) | −10.8769 | −0.503862 | ||||||||
\(467\) | 0.492423 | 0.0227866 | 0.0113933 | − | 0.999935i | \(-0.496373\pi\) | ||||
0.0113933 | + | 0.999935i | \(0.496373\pi\) | |||||||
\(468\) | 16.2462 | 0.750981 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −13.9309 | −0.642583 | ||||||||
\(471\) | 26.8769 | 1.23842 | ||||||||
\(472\) | 26.4233 | 1.21623 | ||||||||
\(473\) | 2.00000 | 0.0919601 | ||||||||
\(474\) | 2.24621 | 0.103172 | ||||||||
\(475\) | −1.75379 | −0.0804693 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 8.00000 | 0.365911 | ||||||||
\(479\) | 6.63068 | 0.302964 | 0.151482 | − | 0.988460i | \(-0.451595\pi\) | ||||
0.151482 | + | 0.988460i | \(0.451595\pi\) | |||||||
\(480\) | 32.8078 | 1.49746 | ||||||||
\(481\) | 6.56155 | 0.299181 | ||||||||
\(482\) | −19.3693 | −0.882248 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 0.630683 | 0.0286378 | ||||||||
\(486\) | 22.2462 | 1.00911 | ||||||||
\(487\) | 6.49242 | 0.294200 | 0.147100 | − | 0.989122i | \(-0.453006\pi\) | ||||
0.147100 | + | 0.989122i | \(0.453006\pi\) | |||||||
\(488\) | −35.0540 | −1.58682 | ||||||||
\(489\) | −44.6695 | −2.02002 | ||||||||
\(490\) | −17.9309 | −0.810034 | ||||||||
\(491\) | 19.3693 | 0.874125 | 0.437063 | − | 0.899431i | \(-0.356019\pi\) | ||||
0.437063 | + | 0.899431i | \(0.356019\pi\) | |||||||
\(492\) | −8.00000 | −0.360668 | ||||||||
\(493\) | 5.12311 | 0.230733 | ||||||||
\(494\) | −5.12311 | −0.230499 | ||||||||
\(495\) | 18.2462 | 0.820106 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 12.3153 | 0.551864 | ||||||||
\(499\) | −7.68466 | −0.344013 | −0.172006 | − | 0.985096i | \(-0.555025\pi\) | ||||
−0.172006 | + | 0.985096i | \(0.555025\pi\) | |||||||
\(500\) | −8.80776 | −0.393895 | ||||||||
\(501\) | 56.3542 | 2.51772 | ||||||||
\(502\) | 10.5616 | 0.471385 | ||||||||
\(503\) | −22.4233 | −0.999805 | −0.499903 | − | 0.866082i | \(-0.666631\pi\) | ||||
−0.499903 | + | 0.866082i | \(0.666631\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.12311 | 0.227975 | ||||||||
\(506\) | 4.00000 | 0.177822 | ||||||||
\(507\) | 20.0000 | 0.888231 | ||||||||
\(508\) | 15.0540 | 0.667912 | ||||||||
\(509\) | −33.0540 | −1.46509 | −0.732546 | − | 0.680718i | \(-0.761668\pi\) | ||||
−0.732546 | + | 0.680718i | \(0.761668\pi\) | |||||||
\(510\) | −6.56155 | −0.290550 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | −1.61553 | −0.0713273 | ||||||||
\(514\) | −26.0000 | −1.14681 | ||||||||
\(515\) | 34.4233 | 1.51687 | ||||||||
\(516\) | 2.56155 | 0.112766 | ||||||||
\(517\) | 10.8769 | 0.478365 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.00000 | 0.351161 | ||||||||
\(520\) | 35.0540 | 1.53722 | ||||||||
\(521\) | −27.3693 | −1.19907 | −0.599536 | − | 0.800348i | \(-0.704648\pi\) | ||||
−0.599536 | + | 0.800348i | \(0.704648\pi\) | |||||||
\(522\) | 18.2462 | 0.798615 | ||||||||
\(523\) | 30.8769 | 1.35015 | 0.675076 | − | 0.737748i | \(-0.264111\pi\) | ||||
0.675076 | + | 0.737748i | \(0.264111\pi\) | |||||||
\(524\) | 8.80776 | 0.384769 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.4924 | 0.893512 | ||||||||
\(527\) | 6.00000 | 0.261364 | ||||||||
\(528\) | 5.12311 | 0.222955 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 4.31534 | 0.187446 | ||||||||
\(531\) | 31.3693 | 1.36131 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.2462 | −0.617072 | ||||||||
\(534\) | −41.6155 | −1.80088 | ||||||||
\(535\) | −5.12311 | −0.221491 | ||||||||
\(536\) | 4.31534 | 0.186394 | ||||||||
\(537\) | 43.8617 | 1.89277 | ||||||||
\(538\) | 8.24621 | 0.355519 | ||||||||
\(539\) | 14.0000 | 0.603023 | ||||||||
\(540\) | 3.68466 | 0.158562 | ||||||||
\(541\) | −19.6155 | −0.843337 | −0.421669 | − | 0.906750i | \(-0.638555\pi\) | ||||
−0.421669 | + | 0.906750i | \(0.638555\pi\) | |||||||
\(542\) | −9.93087 | −0.426567 | ||||||||
\(543\) | 13.7538 | 0.590232 | ||||||||
\(544\) | 5.00000 | 0.214373 | ||||||||
\(545\) | −31.3693 | −1.34371 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.50758 | 0.0644594 | 0.0322297 | − | 0.999480i | \(-0.489739\pi\) | ||||
0.0322297 | + | 0.999480i | \(0.489739\pi\) | |||||||
\(548\) | 4.24621 | 0.181389 | ||||||||
\(549\) | −41.6155 | −1.77611 | ||||||||
\(550\) | 3.12311 | 0.133170 | ||||||||
\(551\) | 5.75379 | 0.245120 | ||||||||
\(552\) | 15.3693 | 0.654162 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.06913 | −0.0879089 | ||||||||
\(555\) | 9.43845 | 0.400640 | ||||||||
\(556\) | −5.36932 | −0.227710 | ||||||||
\(557\) | −26.1771 | −1.10916 | −0.554579 | − | 0.832131i | \(-0.687121\pi\) | ||||
−0.554579 | + | 0.832131i | \(0.687121\pi\) | |||||||
\(558\) | 21.3693 | 0.904635 | ||||||||
\(559\) | 4.56155 | 0.192933 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.12311 | 0.216298 | ||||||||
\(562\) | −7.93087 | −0.334544 | ||||||||
\(563\) | −18.2462 | −0.768986 | −0.384493 | − | 0.923128i | \(-0.625624\pi\) | ||||
−0.384493 | + | 0.923128i | \(0.625624\pi\) | |||||||
\(564\) | 13.9309 | 0.586595 | ||||||||
\(565\) | −22.5616 | −0.949172 | ||||||||
\(566\) | 4.24621 | 0.178482 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.31534 | 0.181068 | ||||||||
\(569\) | −0.561553 | −0.0235415 | −0.0117708 | − | 0.999931i | \(-0.503747\pi\) | ||||
−0.0117708 | + | 0.999931i | \(0.503747\pi\) | |||||||
\(570\) | −7.36932 | −0.308667 | ||||||||
\(571\) | −13.7538 | −0.575578 | −0.287789 | − | 0.957694i | \(-0.592920\pi\) | ||||
−0.287789 | + | 0.957694i | \(0.592920\pi\) | |||||||
\(572\) | −9.12311 | −0.381456 | ||||||||
\(573\) | 7.36932 | 0.307858 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.12311 | 0.130243 | ||||||||
\(576\) | 24.9309 | 1.03879 | ||||||||
\(577\) | 44.7386 | 1.86249 | 0.931247 | − | 0.364389i | \(-0.118722\pi\) | ||||
0.931247 | + | 0.364389i | \(0.118722\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 5.12311 | 0.212909 | ||||||||
\(580\) | −13.1231 | −0.544907 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.630683 | 0.0261427 | ||||||||
\(583\) | −3.36932 | −0.139543 | ||||||||
\(584\) | 26.4233 | 1.09340 | ||||||||
\(585\) | 41.6155 | 1.72059 | ||||||||
\(586\) | −16.2462 | −0.671125 | ||||||||
\(587\) | −27.3693 | −1.12965 | −0.564826 | − | 0.825210i | \(-0.691057\pi\) | ||||
−0.564826 | + | 0.825210i | \(0.691057\pi\) | |||||||
\(588\) | 17.9309 | 0.739457 | ||||||||
\(589\) | 6.73863 | 0.277661 | ||||||||
\(590\) | 22.5616 | 0.928844 | ||||||||
\(591\) | −60.4924 | −2.48833 | ||||||||
\(592\) | 1.43845 | 0.0591198 | ||||||||
\(593\) | −4.24621 | −0.174371 | −0.0871855 | − | 0.996192i | \(-0.527787\pi\) | ||||
−0.0871855 | + | 0.996192i | \(0.527787\pi\) | |||||||
\(594\) | 2.87689 | 0.118040 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.24621 | −0.337778 | ||||||||
\(597\) | 66.4233 | 2.71852 | ||||||||
\(598\) | 9.12311 | 0.373072 | ||||||||
\(599\) | 12.3153 | 0.503191 | 0.251596 | − | 0.967832i | \(-0.419045\pi\) | ||||
0.251596 | + | 0.967832i | \(0.419045\pi\) | |||||||
\(600\) | 12.0000 | 0.489898 | ||||||||
\(601\) | 6.56155 | 0.267651 | 0.133826 | − | 0.991005i | \(-0.457274\pi\) | ||||
0.133826 | + | 0.991005i | \(0.457274\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.12311 | 0.208629 | ||||||||
\(604\) | −8.00000 | −0.325515 | ||||||||
\(605\) | 17.9309 | 0.728994 | ||||||||
\(606\) | 5.12311 | 0.208112 | ||||||||
\(607\) | 31.6847 | 1.28604 | 0.643020 | − | 0.765849i | \(-0.277681\pi\) | ||||
0.643020 | + | 0.765849i | \(0.277681\pi\) | |||||||
\(608\) | 5.61553 | 0.227740 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −29.9309 | −1.21187 | ||||||||
\(611\) | 24.8078 | 1.00361 | ||||||||
\(612\) | 3.56155 | 0.143967 | ||||||||
\(613\) | −34.4924 | −1.39314 | −0.696568 | − | 0.717491i | \(-0.745291\pi\) | ||||
−0.696568 | + | 0.717491i | \(0.745291\pi\) | |||||||
\(614\) | −2.24621 | −0.0906497 | ||||||||
\(615\) | −20.4924 | −0.826334 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.7538 | 0.956292 | 0.478146 | − | 0.878280i | \(-0.341309\pi\) | ||||
0.478146 | + | 0.878280i | \(0.341309\pi\) | |||||||
\(618\) | 34.4233 | 1.38471 | ||||||||
\(619\) | −0.738634 | −0.0296882 | −0.0148441 | − | 0.999890i | \(-0.504725\pi\) | ||||
−0.0148441 | + | 0.999890i | \(0.504725\pi\) | |||||||
\(620\) | −15.3693 | −0.617247 | ||||||||
\(621\) | 2.87689 | 0.115446 | ||||||||
\(622\) | 9.36932 | 0.375675 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 11.6847 | 0.467761 | ||||||||
\(625\) | −30.3693 | −1.21477 | ||||||||
\(626\) | 4.80776 | 0.192157 | ||||||||
\(627\) | 5.75379 | 0.229784 | ||||||||
\(628\) | −10.4924 | −0.418693 | ||||||||
\(629\) | 1.43845 | 0.0573546 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.6155 | −1.65669 | −0.828344 | − | 0.560220i | \(-0.810717\pi\) | ||||
−0.828344 | + | 0.560220i | \(0.810717\pi\) | |||||||
\(632\) | −2.63068 | −0.104643 | ||||||||
\(633\) | −63.5464 | −2.52574 | ||||||||
\(634\) | −5.36932 | −0.213243 | ||||||||
\(635\) | 38.5616 | 1.53027 | ||||||||
\(636\) | −4.31534 | −0.171114 | ||||||||
\(637\) | 31.9309 | 1.26515 | ||||||||
\(638\) | −10.2462 | −0.405651 | ||||||||
\(639\) | 5.12311 | 0.202667 | ||||||||
\(640\) | −7.68466 | −0.303763 | ||||||||
\(641\) | 46.4233 | 1.83361 | 0.916805 | − | 0.399335i | \(-0.130759\pi\) | ||||
0.916805 | + | 0.399335i | \(0.130759\pi\) | |||||||
\(642\) | −5.12311 | −0.202193 | ||||||||
\(643\) | 27.7538 | 1.09450 | 0.547251 | − | 0.836968i | \(-0.315674\pi\) | ||||
0.547251 | + | 0.836968i | \(0.315674\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.56155 | 0.258361 | ||||||||
\(646\) | −1.12311 | −0.0441880 | ||||||||
\(647\) | 38.1080 | 1.49818 | 0.749089 | − | 0.662469i | \(-0.230491\pi\) | ||||
0.749089 | + | 0.662469i | \(0.230491\pi\) | |||||||
\(648\) | −21.0000 | −0.824958 | ||||||||
\(649\) | −17.6155 | −0.691470 | ||||||||
\(650\) | 7.12311 | 0.279391 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.4384 | 0.682942 | ||||||||
\(653\) | −2.87689 | −0.112582 | −0.0562908 | − | 0.998414i | \(-0.517927\pi\) | ||||
−0.0562908 | + | 0.998414i | \(0.517927\pi\) | |||||||
\(654\) | −31.3693 | −1.22664 | ||||||||
\(655\) | 22.5616 | 0.881553 | ||||||||
\(656\) | −3.12311 | −0.121937 | ||||||||
\(657\) | 31.3693 | 1.22383 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.7538 | −1.15904 | −0.579522 | − | 0.814957i | \(-0.696761\pi\) | ||||
−0.579522 | + | 0.814957i | \(0.696761\pi\) | |||||||
\(660\) | −13.1231 | −0.510816 | ||||||||
\(661\) | −44.5616 | −1.73324 | −0.866622 | − | 0.498966i | \(-0.833713\pi\) | ||||
−0.866622 | + | 0.498966i | \(0.833713\pi\) | |||||||
\(662\) | −12.0000 | −0.466393 | ||||||||
\(663\) | 11.6847 | 0.453795 | ||||||||
\(664\) | −14.4233 | −0.559732 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.12311 | 0.198516 | ||||||||
\(667\) | −10.2462 | −0.396735 | ||||||||
\(668\) | −22.0000 | −0.851206 | ||||||||
\(669\) | −40.9848 | −1.58457 | ||||||||
\(670\) | 3.68466 | 0.142351 | ||||||||
\(671\) | 23.3693 | 0.902162 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.8078 | 1.88140 | 0.940701 | − | 0.339238i | \(-0.110169\pi\) | ||||
0.940701 | + | 0.339238i | \(0.110169\pi\) | |||||||
\(674\) | 20.2462 | 0.779855 | ||||||||
\(675\) | 2.24621 | 0.0864567 | ||||||||
\(676\) | −7.80776 | −0.300299 | ||||||||
\(677\) | −41.6155 | −1.59941 | −0.799707 | − | 0.600390i | \(-0.795012\pi\) | ||||
−0.799707 | + | 0.600390i | \(0.795012\pi\) | |||||||
\(678\) | −22.5616 | −0.866471 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.68466 | 0.294693 | ||||||||
\(681\) | −32.0000 | −1.22624 | ||||||||
\(682\) | −12.0000 | −0.459504 | ||||||||
\(683\) | 18.6307 | 0.712883 | 0.356442 | − | 0.934318i | \(-0.383990\pi\) | ||||
0.356442 | + | 0.934318i | \(0.383990\pi\) | |||||||
\(684\) | 4.00000 | 0.152944 | ||||||||
\(685\) | 10.8769 | 0.415585 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −37.9309 | −1.44715 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | −7.68466 | −0.292762 | ||||||||
\(690\) | 13.1231 | 0.499588 | ||||||||
\(691\) | 32.4924 | 1.23607 | 0.618035 | − | 0.786151i | \(-0.287929\pi\) | ||||
0.618035 | + | 0.786151i | \(0.287929\pi\) | |||||||
\(692\) | −3.12311 | −0.118723 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.5616 | 0.856425 | ||||||||
\(695\) | −13.7538 | −0.521711 | ||||||||
\(696\) | −39.3693 | −1.49229 | ||||||||
\(697\) | −3.12311 | −0.118296 | ||||||||
\(698\) | 19.1231 | 0.723820 | ||||||||
\(699\) | 27.8617 | 1.05383 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.05398 | −0.341964 | −0.170982 | − | 0.985274i | \(-0.554694\pi\) | ||||
−0.170982 | + | 0.985274i | \(0.554694\pi\) | |||||||
\(702\) | 6.56155 | 0.247650 | ||||||||
\(703\) | 1.61553 | 0.0609308 | ||||||||
\(704\) | −14.0000 | −0.527645 | ||||||||
\(705\) | 35.6847 | 1.34396 | ||||||||
\(706\) | −26.1771 | −0.985187 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −22.5616 | −0.847915 | ||||||||
\(709\) | 38.4924 | 1.44561 | 0.722807 | − | 0.691050i | \(-0.242852\pi\) | ||||
0.722807 | + | 0.691050i | \(0.242852\pi\) | |||||||
\(710\) | 3.68466 | 0.138283 | ||||||||
\(711\) | −3.12311 | −0.117126 | ||||||||
\(712\) | 48.7386 | 1.82656 | ||||||||
\(713\) | −12.0000 | −0.449404 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.3693 | −0.873963 | ||||||||
\(716\) | −17.1231 | −0.639921 | ||||||||
\(717\) | −20.4924 | −0.765304 | ||||||||
\(718\) | −16.8078 | −0.627260 | ||||||||
\(719\) | −6.00000 | −0.223762 | −0.111881 | − | 0.993722i | \(-0.535688\pi\) | ||||
−0.111881 | + | 0.993722i | \(0.535688\pi\) | |||||||
\(720\) | 9.12311 | 0.339998 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 17.7386 | 0.660164 | ||||||||
\(723\) | 49.6155 | 1.84522 | ||||||||
\(724\) | −5.36932 | −0.199549 | ||||||||
\(725\) | −8.00000 | −0.297113 | ||||||||
\(726\) | 17.9309 | 0.665477 | ||||||||
\(727\) | −1.26137 | −0.0467815 | −0.0233907 | − | 0.999726i | \(-0.507446\pi\) | ||||
−0.0233907 | + | 0.999726i | \(0.507446\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 22.5616 | 0.835041 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 29.9309 | 1.10628 | ||||||||
\(733\) | −8.24621 | −0.304581 | −0.152290 | − | 0.988336i | \(-0.548665\pi\) | ||||
−0.152290 | + | 0.988336i | \(0.548665\pi\) | |||||||
\(734\) | 14.4924 | 0.534925 | ||||||||
\(735\) | 45.9309 | 1.69419 | ||||||||
\(736\) | −10.0000 | −0.368605 | ||||||||
\(737\) | −2.87689 | −0.105972 | ||||||||
\(738\) | −11.1231 | −0.409447 | ||||||||
\(739\) | 34.1080 | 1.25468 | 0.627341 | − | 0.778745i | \(-0.284143\pi\) | ||||
0.627341 | + | 0.778745i | \(0.284143\pi\) | |||||||
\(740\) | −3.68466 | −0.135451 | ||||||||
\(741\) | 13.1231 | 0.482089 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.5464 | −1.30407 | −0.652035 | − | 0.758188i | \(-0.726085\pi\) | ||||
−0.652035 | + | 0.758188i | \(0.726085\pi\) | |||||||
\(744\) | −46.1080 | −1.69040 | ||||||||
\(745\) | −21.1231 | −0.773891 | ||||||||
\(746\) | 37.3693 | 1.36819 | ||||||||
\(747\) | −17.1231 | −0.626502 | ||||||||
\(748\) | −2.00000 | −0.0731272 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −22.5616 | −0.823831 | ||||||||
\(751\) | 7.05398 | 0.257403 | 0.128702 | − | 0.991683i | \(-0.458919\pi\) | ||||
0.128702 | + | 0.991683i | \(0.458919\pi\) | |||||||
\(752\) | 5.43845 | 0.198320 | ||||||||
\(753\) | −27.0540 | −0.985902 | ||||||||
\(754\) | −23.3693 | −0.851060 | ||||||||
\(755\) | −20.4924 | −0.745796 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.49242 | −0.235971 | −0.117986 | − | 0.993015i | \(-0.537644\pi\) | ||||
−0.117986 | + | 0.993015i | \(0.537644\pi\) | |||||||
\(758\) | 0.876894 | 0.0318502 | ||||||||
\(759\) | −10.2462 | −0.371914 | ||||||||
\(760\) | 8.63068 | 0.313068 | ||||||||
\(761\) | −52.6004 | −1.90676 | −0.953381 | − | 0.301769i | \(-0.902423\pi\) | ||||
−0.953381 | + | 0.301769i | \(0.902423\pi\) | |||||||
\(762\) | 38.5616 | 1.39694 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.87689 | −0.104082 | ||||||||
\(765\) | 9.12311 | 0.329847 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −40.1771 | −1.45071 | ||||||||
\(768\) | −43.5464 | −1.57135 | ||||||||
\(769\) | −45.5464 | −1.64245 | −0.821223 | − | 0.570608i | \(-0.806708\pi\) | ||||
−0.821223 | + | 0.570608i | \(0.806708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 66.6004 | 2.39855 | ||||||||
\(772\) | −2.00000 | −0.0719816 | ||||||||
\(773\) | 10.4924 | 0.377386 | 0.188693 | − | 0.982036i | \(-0.439575\pi\) | ||||
0.188693 | + | 0.982036i | \(0.439575\pi\) | |||||||
\(774\) | 3.56155 | 0.128017 | ||||||||
\(775\) | −9.36932 | −0.336556 | ||||||||
\(776\) | −0.738634 | −0.0265154 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30.4924 | 1.09321 | ||||||||
\(779\) | −3.50758 | −0.125672 | ||||||||
\(780\) | −29.9309 | −1.07170 | ||||||||
\(781\) | −2.87689 | −0.102943 | ||||||||
\(782\) | 2.00000 | 0.0715199 | ||||||||
\(783\) | −7.36932 | −0.263358 | ||||||||
\(784\) | 7.00000 | 0.250000 | ||||||||
\(785\) | −26.8769 | −0.959277 | ||||||||
\(786\) | 22.5616 | 0.804744 | ||||||||
\(787\) | 30.9848 | 1.10449 | 0.552245 | − | 0.833682i | \(-0.313771\pi\) | ||||
0.552245 | + | 0.833682i | \(0.313771\pi\) | |||||||
\(788\) | 23.6155 | 0.841268 | ||||||||
\(789\) | −52.4924 | −1.86878 | ||||||||
\(790\) | −2.24621 | −0.0799166 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −21.3693 | −0.759326 | ||||||||
\(793\) | 53.3002 | 1.89275 | ||||||||
\(794\) | −15.1231 | −0.536699 | ||||||||
\(795\) | −11.0540 | −0.392044 | ||||||||
\(796\) | −25.9309 | −0.919095 | ||||||||
\(797\) | −15.9309 | −0.564300 | −0.282150 | − | 0.959370i | \(-0.591048\pi\) | ||||
−0.282150 | + | 0.959370i | \(0.591048\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.43845 | 0.192398 | ||||||||
\(800\) | −7.80776 | −0.276046 | ||||||||
\(801\) | 57.8617 | 2.04444 | ||||||||
\(802\) | 20.2462 | 0.714919 | ||||||||
\(803\) | −17.6155 | −0.621638 | ||||||||
\(804\) | −3.68466 | −0.129948 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −27.3693 | −0.964043 | ||||||||
\(807\) | −21.1231 | −0.743569 | ||||||||
\(808\) | −6.00000 | −0.211079 | ||||||||
\(809\) | 14.6307 | 0.514387 | 0.257194 | − | 0.966360i | \(-0.417202\pi\) | ||||
0.257194 | + | 0.966360i | \(0.417202\pi\) | |||||||
\(810\) | −17.9309 | −0.630027 | ||||||||
\(811\) | −40.4924 | −1.42188 | −0.710941 | − | 0.703252i | \(-0.751731\pi\) | ||||
−0.710941 | + | 0.703252i | \(0.751731\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.4384 | 0.892165 | ||||||||
\(814\) | −2.87689 | −0.100835 | ||||||||
\(815\) | 44.6695 | 1.56470 | ||||||||
\(816\) | 2.56155 | 0.0896723 | ||||||||
\(817\) | 1.12311 | 0.0392925 | ||||||||
\(818\) | −21.8617 | −0.764378 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.00000 | 0.279372 | ||||||||
\(821\) | 0.246211 | 0.00859283 | 0.00429642 | − | 0.999991i | \(-0.498632\pi\) | ||||
0.00429642 | + | 0.999991i | \(0.498632\pi\) | |||||||
\(822\) | 10.8769 | 0.379375 | ||||||||
\(823\) | 42.4924 | 1.48119 | 0.740596 | − | 0.671950i | \(-0.234543\pi\) | ||||
0.740596 | + | 0.671950i | \(0.234543\pi\) | |||||||
\(824\) | −40.3153 | −1.40445 | ||||||||
\(825\) | −8.00000 | −0.278524 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.7386 | 0.721153 | 0.360576 | − | 0.932730i | \(-0.382580\pi\) | ||||
0.360576 | + | 0.932730i | \(0.382580\pi\) | |||||||
\(828\) | −7.12311 | −0.247545 | ||||||||
\(829\) | 32.8769 | 1.14186 | 0.570931 | − | 0.820998i | \(-0.306582\pi\) | ||||
0.570931 | + | 0.820998i | \(0.306582\pi\) | |||||||
\(830\) | −12.3153 | −0.427472 | ||||||||
\(831\) | 5.30019 | 0.183861 | ||||||||
\(832\) | −31.9309 | −1.10700 | ||||||||
\(833\) | 7.00000 | 0.242536 | ||||||||
\(834\) | −13.7538 | −0.476255 | ||||||||
\(835\) | −56.3542 | −1.95022 | ||||||||
\(836\) | −2.24621 | −0.0776868 | ||||||||
\(837\) | −8.63068 | −0.298320 | ||||||||
\(838\) | 20.0000 | 0.690889 | ||||||||
\(839\) | −0.807764 | −0.0278871 | −0.0139436 | − | 0.999903i | \(-0.504439\pi\) | ||||
−0.0139436 | + | 0.999903i | \(0.504439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.75379 | −0.0949582 | ||||||||
\(842\) | 36.7386 | 1.26610 | ||||||||
\(843\) | 20.3153 | 0.699698 | ||||||||
\(844\) | 24.8078 | 0.853918 | ||||||||
\(845\) | −20.0000 | −0.688021 | ||||||||
\(846\) | 19.3693 | 0.665931 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.68466 | −0.0578514 | ||||||||
\(849\) | −10.8769 | −0.373294 | ||||||||
\(850\) | 1.56155 | 0.0535608 | ||||||||
\(851\) | −2.87689 | −0.0986187 | ||||||||
\(852\) | −3.68466 | −0.126234 | ||||||||
\(853\) | 10.9848 | 0.376114 | 0.188057 | − | 0.982158i | \(-0.439781\pi\) | ||||
0.188057 | + | 0.982158i | \(0.439781\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.2462 | 0.350413 | ||||||||
\(856\) | 6.00000 | 0.205076 | ||||||||
\(857\) | 28.8769 | 0.986416 | 0.493208 | − | 0.869911i | \(-0.335824\pi\) | ||||
0.493208 | + | 0.869911i | \(0.335824\pi\) | |||||||
\(858\) | −23.3693 | −0.797815 | ||||||||
\(859\) | 27.3693 | 0.933829 | 0.466915 | − | 0.884302i | \(-0.345366\pi\) | ||||
0.466915 | + | 0.884302i | \(0.345366\pi\) | |||||||
\(860\) | −2.56155 | −0.0873482 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.87689 | 0.166108 | ||||||||
\(863\) | 20.4924 | 0.697570 | 0.348785 | − | 0.937203i | \(-0.386594\pi\) | ||||
0.348785 | + | 0.937203i | \(0.386594\pi\) | |||||||
\(864\) | −7.19224 | −0.244685 | ||||||||
\(865\) | −8.00000 | −0.272008 | ||||||||
\(866\) | 13.3693 | 0.454308 | ||||||||
\(867\) | 2.56155 | 0.0869949 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.75379 | 0.0594932 | ||||||||
\(870\) | −33.6155 | −1.13967 | ||||||||
\(871\) | −6.56155 | −0.222330 | ||||||||
\(872\) | 36.7386 | 1.24413 | ||||||||
\(873\) | −0.876894 | −0.0296784 | ||||||||
\(874\) | 2.24621 | 0.0759792 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −22.5616 | −0.762284 | ||||||||
\(877\) | −12.8769 | −0.434822 | −0.217411 | − | 0.976080i | \(-0.569761\pi\) | ||||
−0.217411 | + | 0.976080i | \(0.569761\pi\) | |||||||
\(878\) | 9.36932 | 0.316199 | ||||||||
\(879\) | 41.6155 | 1.40366 | ||||||||
\(880\) | −5.12311 | −0.172700 | ||||||||
\(881\) | −26.0000 | −0.875962 | −0.437981 | − | 0.898984i | \(-0.644306\pi\) | ||||
−0.437981 | + | 0.898984i | \(0.644306\pi\) | |||||||
\(882\) | 24.9309 | 0.839466 | ||||||||
\(883\) | 42.9157 | 1.44423 | 0.722114 | − | 0.691774i | \(-0.243170\pi\) | ||||
0.722114 | + | 0.691774i | \(0.243170\pi\) | |||||||
\(884\) | −4.56155 | −0.153422 | ||||||||
\(885\) | −57.7926 | −1.94268 | ||||||||
\(886\) | −30.4233 | −1.02209 | ||||||||
\(887\) | 21.7538 | 0.730421 | 0.365210 | − | 0.930925i | \(-0.380997\pi\) | ||||
0.365210 | + | 0.930925i | \(0.380997\pi\) | |||||||
\(888\) | −11.0540 | −0.370947 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 41.6155 | 1.39496 | ||||||||
\(891\) | 14.0000 | 0.469018 | ||||||||
\(892\) | 16.0000 | 0.535720 | ||||||||
\(893\) | 6.10795 | 0.204395 | ||||||||
\(894\) | −21.1231 | −0.706462 | ||||||||
\(895\) | −43.8617 | −1.46614 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.3693 | −0.780279 | ||||||||
\(898\) | 34.5616 | 1.15333 | ||||||||
\(899\) | 30.7386 | 1.02519 | ||||||||
\(900\) | −5.56155 | −0.185385 | ||||||||
\(901\) | −1.68466 | −0.0561241 | ||||||||
\(902\) | 6.24621 | 0.207976 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26.4233 | 0.878826 | ||||||||
\(905\) | −13.7538 | −0.457191 | ||||||||
\(906\) | −20.4924 | −0.680815 | ||||||||
\(907\) | 22.0000 | 0.730498 | 0.365249 | − | 0.930910i | \(-0.380984\pi\) | ||||
0.365249 | + | 0.930910i | \(0.380984\pi\) | |||||||
\(908\) | 12.4924 | 0.414576 | ||||||||
\(909\) | −7.12311 | −0.236259 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.1922 | 0.370815 | 0.185408 | − | 0.982662i | \(-0.440639\pi\) | ||||
0.185408 | + | 0.982662i | \(0.440639\pi\) | |||||||
\(912\) | 2.87689 | 0.0952635 | ||||||||
\(913\) | 9.61553 | 0.318228 | ||||||||
\(914\) | 29.3693 | 0.971451 | ||||||||
\(915\) | 76.6695 | 2.53462 | ||||||||
\(916\) | 14.8078 | 0.489262 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.43845 | 0.0474758 | ||||||||
\(919\) | 8.80776 | 0.290541 | 0.145271 | − | 0.989392i | \(-0.453595\pi\) | ||||
0.145271 | + | 0.989392i | \(0.453595\pi\) | |||||||
\(920\) | −15.3693 | −0.506711 | ||||||||
\(921\) | 5.75379 | 0.189594 | ||||||||
\(922\) | −2.80776 | −0.0924688 | ||||||||
\(923\) | −6.56155 | −0.215976 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.24621 | −0.0738550 | ||||||||
\(926\) | 8.00000 | 0.262896 | ||||||||
\(927\) | −47.8617 | −1.57199 | ||||||||
\(928\) | 25.6155 | 0.840871 | ||||||||
\(929\) | 31.8617 | 1.04535 | 0.522675 | − | 0.852532i | \(-0.324934\pi\) | ||||
0.522675 | + | 0.852532i | \(0.324934\pi\) | |||||||
\(930\) | −39.3693 | −1.29097 | ||||||||
\(931\) | 7.86174 | 0.257658 | ||||||||
\(932\) | −10.8769 | −0.356285 | ||||||||
\(933\) | −24.0000 | −0.785725 | ||||||||
\(934\) | −0.492423 | −0.0161126 | ||||||||
\(935\) | −5.12311 | −0.167543 | ||||||||
\(936\) | −48.7386 | −1.59307 | ||||||||
\(937\) | −40.1080 | −1.31027 | −0.655135 | − | 0.755512i | \(-0.727388\pi\) | ||||
−0.655135 | + | 0.755512i | \(0.727388\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.3153 | −0.401896 | ||||||||
\(940\) | −13.9309 | −0.454375 | ||||||||
\(941\) | 53.3693 | 1.73979 | 0.869895 | − | 0.493237i | \(-0.164186\pi\) | ||||
0.869895 | + | 0.493237i | \(0.164186\pi\) | |||||||
\(942\) | −26.8769 | −0.875697 | ||||||||
\(943\) | 6.24621 | 0.203405 | ||||||||
\(944\) | −8.80776 | −0.286668 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.00000 | −0.0650256 | ||||||||
\(947\) | −16.2462 | −0.527931 | −0.263965 | − | 0.964532i | \(-0.585030\pi\) | ||||
−0.263965 | + | 0.964532i | \(0.585030\pi\) | |||||||
\(948\) | 2.24621 | 0.0729535 | ||||||||
\(949\) | −40.1771 | −1.30420 | ||||||||
\(950\) | 1.75379 | 0.0569004 | ||||||||
\(951\) | 13.7538 | 0.445997 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.8769 | −0.676269 | −0.338134 | − | 0.941098i | \(-0.609796\pi\) | ||||
−0.338134 | + | 0.941098i | \(0.609796\pi\) | |||||||
\(954\) | −6.00000 | −0.194257 | ||||||||
\(955\) | −7.36932 | −0.238465 | ||||||||
\(956\) | 8.00000 | 0.258738 | ||||||||
\(957\) | 26.2462 | 0.848420 | ||||||||
\(958\) | −6.63068 | −0.214228 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −45.9309 | −1.48241 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | −6.56155 | −0.211553 | ||||||||
\(963\) | 7.12311 | 0.229539 | ||||||||
\(964\) | −19.3693 | −0.623844 | ||||||||
\(965\) | −5.12311 | −0.164919 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.9848 | 1.31798 | 0.658992 | − | 0.752150i | \(-0.270983\pi\) | ||||
0.658992 | + | 0.752150i | \(0.270983\pi\) | |||||||
\(968\) | −21.0000 | −0.674966 | ||||||||
\(969\) | 2.87689 | 0.0924192 | ||||||||
\(970\) | −0.630683 | −0.0202500 | ||||||||
\(971\) | −28.1771 | −0.904246 | −0.452123 | − | 0.891956i | \(-0.649333\pi\) | ||||
−0.452123 | + | 0.891956i | \(0.649333\pi\) | |||||||
\(972\) | 22.2462 | 0.713548 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.49242 | −0.208031 | ||||||||
\(975\) | −18.2462 | −0.584346 | ||||||||
\(976\) | 11.6847 | 0.374017 | ||||||||
\(977\) | 40.2462 | 1.28759 | 0.643795 | − | 0.765198i | \(-0.277359\pi\) | ||||
0.643795 | + | 0.765198i | \(0.277359\pi\) | |||||||
\(978\) | 44.6695 | 1.42837 | ||||||||
\(979\) | −32.4924 | −1.03846 | ||||||||
\(980\) | −17.9309 | −0.572781 | ||||||||
\(981\) | 43.6155 | 1.39254 | ||||||||
\(982\) | −19.3693 | −0.618100 | ||||||||
\(983\) | 27.5464 | 0.878594 | 0.439297 | − | 0.898342i | \(-0.355228\pi\) | ||||
0.439297 | + | 0.898342i | \(0.355228\pi\) | |||||||
\(984\) | 24.0000 | 0.765092 | ||||||||
\(985\) | 60.4924 | 1.92745 | ||||||||
\(986\) | −5.12311 | −0.163153 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.12311 | −0.162988 | ||||||||
\(989\) | −2.00000 | −0.0635963 | ||||||||
\(990\) | −18.2462 | −0.579903 | ||||||||
\(991\) | 38.9157 | 1.23620 | 0.618099 | − | 0.786100i | \(-0.287903\pi\) | ||||
0.618099 | + | 0.786100i | \(0.287903\pi\) | |||||||
\(992\) | 30.0000 | 0.952501 | ||||||||
\(993\) | 30.7386 | 0.975461 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −66.4233 | −2.10576 | ||||||||
\(996\) | 12.3153 | 0.390227 | ||||||||
\(997\) | −9.12311 | −0.288932 | −0.144466 | − | 0.989510i | \(-0.546146\pi\) | ||||
−0.144466 | + | 0.989510i | \(0.546146\pi\) | |||||||
\(998\) | 7.68466 | 0.243254 | ||||||||
\(999\) | −2.06913 | −0.0654644 |
(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 | 731.2.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 6579.2.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
6579.2.a.f.1.2 | 2 | 3.2 | odd | 2 |