Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(518,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.518");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.k (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 782.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.782 |
Dual form | 825.2.k.b.518.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.70711 | + | 1.70711i | −1.20711 | + | 1.20711i | −0.235147 | + | 0.971960i | \(0.575557\pi\) |
−0.971960 | + | 0.235147i | \(0.924443\pi\) | |||||||
\(3\) | −1.70711 | − | 0.292893i | −0.985599 | − | 0.169102i | ||||
\(4\) | − | 3.82843i | − | 1.91421i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.41421 | − | 2.41421i | 1.39385 | − | 0.985599i | ||||
\(7\) | 3.41421 | + | 3.41421i | 1.29045 | + | 1.29045i | 0.934507 | + | 0.355944i | \(0.115841\pi\) |
0.355944 | + | 0.934507i | \(0.384159\pi\) | |||||||
\(8\) | 3.12132 | + | 3.12132i | 1.10355 | + | 1.10355i | ||||
\(9\) | 2.82843 | + | 1.00000i | 0.942809 | + | 0.333333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | −1.12132 | + | 6.53553i | −0.323697 | + | 1.88665i | ||||
\(13\) | 0.585786 | − | 0.585786i | 0.162468 | − | 0.162468i | −0.621191 | − | 0.783659i | \(-0.713351\pi\) |
0.783659 | + | 0.621191i | \(0.213351\pi\) | |||||||
\(14\) | −11.6569 | −3.11543 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.00000 | −0.750000 | ||||||||
\(17\) | 2.00000 | − | 2.00000i | 0.485071 | − | 0.485071i | −0.421676 | − | 0.906747i | \(-0.638558\pi\) |
0.906747 | + | 0.421676i | \(0.138558\pi\) | |||||||
\(18\) | −6.53553 | + | 3.12132i | −1.54044 | + | 0.735702i | ||||
\(19\) | − | 4.82843i | − | 1.10772i | −0.832611 | − | 0.553859i | \(-0.813155\pi\) | ||
0.832611 | − | 0.553859i | \(-0.186845\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.82843 | − | 6.82843i | −1.05365 | − | 1.49008i | ||||
\(22\) | 1.70711 | + | 1.70711i | 0.363956 | + | 0.363956i | ||||
\(23\) | −4.82843 | − | 4.82843i | −1.00680 | − | 1.00680i | −0.999977 | − | 0.00681991i | \(-0.997829\pi\) |
−0.00681991 | − | 0.999977i | \(-0.502171\pi\) | |||||||
\(24\) | −4.41421 | − | 6.24264i | −0.901048 | − | 1.27427i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000i | 0.392232i | ||||||||
\(27\) | −4.53553 | − | 2.53553i | −0.872864 | − | 0.487964i | ||||
\(28\) | 13.0711 | − | 13.0711i | 2.47020 | − | 2.47020i | ||||
\(29\) | 3.17157 | 0.588946 | 0.294473 | − | 0.955660i | \(-0.404856\pi\) | ||||
0.294473 | + | 0.955660i | \(0.404856\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −1.12132 | + | 1.12132i | −0.198223 | + | 0.198223i | ||||
\(33\) | −0.292893 | + | 1.70711i | −0.0509862 | + | 0.297169i | ||||
\(34\) | 6.82843i | 1.17107i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.82843 | − | 10.8284i | 0.638071 | − | 1.80474i | ||||
\(37\) | −5.65685 | − | 5.65685i | −0.929981 | − | 0.929981i | 0.0677230 | − | 0.997704i | \(-0.478427\pi\) |
−0.997704 | + | 0.0677230i | \(0.978427\pi\) | |||||||
\(38\) | 8.24264 | + | 8.24264i | 1.33713 | + | 1.33713i | ||||
\(39\) | −1.17157 | + | 0.828427i | −0.187602 | + | 0.132655i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.828427i | − | 0.129379i | −0.997905 | − | 0.0646893i | \(-0.979394\pi\) | ||
0.997905 | − | 0.0646893i | \(-0.0206056\pi\) | |||||||
\(42\) | 19.8995 | + | 3.41421i | 3.07056 | + | 0.526825i | ||||
\(43\) | 7.41421 | − | 7.41421i | 1.13066 | − | 1.13066i | 0.140589 | − | 0.990068i | \(-0.455100\pi\) |
0.990068 | − | 0.140589i | \(-0.0448996\pi\) | |||||||
\(44\) | −3.82843 | −0.577157 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 16.4853 | 2.43062 | ||||||||
\(47\) | −0.828427 | + | 0.828427i | −0.120839 | + | 0.120839i | −0.764940 | − | 0.644102i | \(-0.777231\pi\) |
0.644102 | + | 0.764940i | \(0.277231\pi\) | |||||||
\(48\) | 5.12132 | + | 0.878680i | 0.739199 | + | 0.126826i | ||||
\(49\) | 16.3137i | 2.33053i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | + | 2.82843i | −0.560112 | + | 0.396059i | ||||
\(52\) | −2.24264 | − | 2.24264i | −0.310998 | − | 0.310998i | ||||
\(53\) | 8.48528 | + | 8.48528i | 1.16554 | + | 1.16554i | 0.983243 | + | 0.182300i | \(0.0583542\pi\) |
0.182300 | + | 0.983243i | \(0.441646\pi\) | |||||||
\(54\) | 12.0711 | − | 3.41421i | 1.64266 | − | 0.464616i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 21.3137i | 2.84816i | ||||||||
\(57\) | −1.41421 | + | 8.24264i | −0.187317 | + | 1.09176i | ||||
\(58\) | −5.41421 | + | 5.41421i | −0.710921 | + | 0.710921i | ||||
\(59\) | 13.6569 | 1.77797 | 0.888985 | − | 0.457935i | \(-0.151411\pi\) | ||||
0.888985 | + | 0.457935i | \(0.151411\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | −6.82843 | + | 6.82843i | −0.867211 | + | 0.867211i | ||||
\(63\) | 6.24264 | + | 13.0711i | 0.786499 | + | 1.64680i | ||||
\(64\) | − | 9.82843i | − | 1.22855i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.41421 | − | 3.41421i | −0.297169 | − | 0.420261i | ||||
\(67\) | −5.41421 | − | 5.41421i | −0.661451 | − | 0.661451i | 0.294271 | − | 0.955722i | \(-0.404923\pi\) |
−0.955722 | + | 0.294271i | \(0.904923\pi\) | |||||||
\(68\) | −7.65685 | − | 7.65685i | −0.928530 | − | 0.928530i | ||||
\(69\) | 6.82843 | + | 9.65685i | 0.822046 | + | 1.16255i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.65685i | − | 0.196632i | −0.995155 | − | 0.0983162i | \(-0.968654\pi\) | ||
0.995155 | − | 0.0983162i | \(-0.0313457\pi\) | |||||||
\(72\) | 5.70711 | + | 11.9497i | 0.672589 | + | 1.40829i | ||||
\(73\) | 7.41421 | − | 7.41421i | 0.867768 | − | 0.867768i | −0.124457 | − | 0.992225i | \(-0.539719\pi\) |
0.992225 | + | 0.124457i | \(0.0397189\pi\) | |||||||
\(74\) | 19.3137 | 2.24517 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −18.4853 | −2.12041 | ||||||||
\(77\) | 3.41421 | − | 3.41421i | 0.389086 | − | 0.389086i | ||||
\(78\) | 0.585786 | − | 3.41421i | 0.0663273 | − | 0.386584i | ||||
\(79\) | 0.828427i | 0.0932053i | 0.998914 | + | 0.0466027i | \(0.0148395\pi\) | ||||
−0.998914 | + | 0.0466027i | \(0.985161\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.00000 | + | 5.65685i | 0.777778 | + | 0.628539i | ||||
\(82\) | 1.41421 | + | 1.41421i | 0.156174 | + | 0.156174i | ||||
\(83\) | −4.24264 | − | 4.24264i | −0.465690 | − | 0.465690i | 0.434825 | − | 0.900515i | \(-0.356810\pi\) |
−0.900515 | + | 0.434825i | \(0.856810\pi\) | |||||||
\(84\) | −26.1421 | + | 18.4853i | −2.85234 | + | 2.01691i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 25.3137i | 2.72965i | ||||||||
\(87\) | −5.41421 | − | 0.928932i | −0.580465 | − | 0.0995920i | ||||
\(88\) | 3.12132 | − | 3.12132i | 0.332734 | − | 0.332734i | ||||
\(89\) | −7.31371 | −0.775252 | −0.387626 | − | 0.921817i | \(-0.626705\pi\) | ||||
−0.387626 | + | 0.921817i | \(0.626705\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | −18.4853 | + | 18.4853i | −1.92722 | + | 1.92722i | ||||
\(93\) | −6.82843 | − | 1.17157i | −0.708075 | − | 0.121486i | ||||
\(94\) | − | 2.82843i | − | 0.291730i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.24264 | − | 1.58579i | 0.228889 | − | 0.161849i | ||||
\(97\) | 9.65685 | + | 9.65685i | 0.980505 | + | 0.980505i | 0.999814 | − | 0.0193086i | \(-0.00614649\pi\) |
−0.0193086 | + | 0.999814i | \(0.506146\pi\) | |||||||
\(98\) | −27.8492 | − | 27.8492i | −2.81320 | − | 2.81320i | ||||
\(99\) | 1.00000 | − | 2.82843i | 0.100504 | − | 0.284268i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 4.82843i | − | 0.480446i | −0.970718 | − | 0.240223i | \(-0.922779\pi\) | ||
0.970718 | − | 0.240223i | \(-0.0772206\pi\) | |||||||
\(102\) | 2.00000 | − | 11.6569i | 0.198030 | − | 1.15420i | ||||
\(103\) | −4.24264 | + | 4.24264i | −0.418040 | + | 0.418040i | −0.884528 | − | 0.466488i | \(-0.845519\pi\) |
0.466488 | + | 0.884528i | \(0.345519\pi\) | |||||||
\(104\) | 3.65685 | 0.358584 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −28.9706 | −2.81387 | ||||||||
\(107\) | 5.89949 | − | 5.89949i | 0.570326 | − | 0.570326i | −0.361894 | − | 0.932219i | \(-0.617870\pi\) |
0.932219 | + | 0.361894i | \(0.117870\pi\) | |||||||
\(108\) | −9.70711 | + | 17.3640i | −0.934067 | + | 1.67085i | ||||
\(109\) | 2.00000i | 0.191565i | 0.995402 | + | 0.0957826i | \(0.0305354\pi\) | ||||
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | + | 11.3137i | 0.759326 | + | 1.07385i | ||||
\(112\) | −10.2426 | − | 10.2426i | −0.967839 | − | 0.967839i | ||||
\(113\) | 8.48528 | + | 8.48528i | 0.798228 | + | 0.798228i | 0.982816 | − | 0.184588i | \(-0.0590950\pi\) |
−0.184588 | + | 0.982816i | \(0.559095\pi\) | |||||||
\(114\) | −11.6569 | − | 16.4853i | −1.09176 | − | 1.54399i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 12.1421i | − | 1.12737i | ||||||
\(117\) | 2.24264 | − | 1.07107i | 0.207332 | − | 0.0990203i | ||||
\(118\) | −23.3137 | + | 23.3137i | −2.14620 | + | 2.14620i | ||||
\(119\) | 13.6569 | 1.25192 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 10.2426 | − | 10.2426i | 0.927325 | − | 0.927325i | ||||
\(123\) | −0.242641 | + | 1.41421i | −0.0218782 | + | 0.127515i | ||||
\(124\) | − | 15.3137i | − | 1.37521i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −32.9706 | − | 11.6569i | −2.93725 | − | 1.03848i | ||||
\(127\) | −1.75736 | − | 1.75736i | −0.155940 | − | 0.155940i | 0.624825 | − | 0.780765i | \(-0.285170\pi\) |
−0.780765 | + | 0.624825i | \(0.785170\pi\) | |||||||
\(128\) | 14.5355 | + | 14.5355i | 1.28477 | + | 1.28477i | ||||
\(129\) | −14.8284 | + | 10.4853i | −1.30557 | + | 0.923178i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.34315i | 0.554203i | 0.960841 | + | 0.277102i | \(0.0893739\pi\) | ||||
−0.960841 | + | 0.277102i | \(0.910626\pi\) | |||||||
\(132\) | 6.53553 | + | 1.12132i | 0.568845 | + | 0.0975984i | ||||
\(133\) | 16.4853 | − | 16.4853i | 1.42946 | − | 1.42946i | ||||
\(134\) | 18.4853 | 1.59689 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.4853 | 1.07060 | ||||||||
\(137\) | 9.65685 | − | 9.65685i | 0.825041 | − | 0.825041i | −0.161785 | − | 0.986826i | \(-0.551725\pi\) |
0.986826 | + | 0.161785i | \(0.0517252\pi\) | |||||||
\(138\) | −28.1421 | − | 4.82843i | −2.39562 | − | 0.411023i | ||||
\(139\) | 11.1716i | 0.947560i | 0.880643 | + | 0.473780i | \(0.157111\pi\) | ||||
−0.880643 | + | 0.473780i | \(0.842889\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.65685 | − | 1.17157i | 0.139532 | − | 0.0986642i | ||||
\(142\) | 2.82843 | + | 2.82843i | 0.237356 | + | 0.237356i | ||||
\(143\) | −0.585786 | − | 0.585786i | −0.0489859 | − | 0.0489859i | ||||
\(144\) | −8.48528 | − | 3.00000i | −0.707107 | − | 0.250000i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 25.3137i | 2.09498i | ||||||||
\(147\) | 4.77817 | − | 27.8492i | 0.394097 | − | 2.29697i | ||||
\(148\) | −21.6569 | + | 21.6569i | −1.78018 | + | 1.78018i | ||||
\(149\) | 21.7990 | 1.78584 | 0.892921 | − | 0.450213i | \(-0.148652\pi\) | ||||
0.892921 | + | 0.450213i | \(0.148652\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.48528 | −0.202249 | −0.101125 | − | 0.994874i | \(-0.532244\pi\) | ||||
−0.101125 | + | 0.994874i | \(0.532244\pi\) | |||||||
\(152\) | 15.0711 | − | 15.0711i | 1.22243 | − | 1.22243i | ||||
\(153\) | 7.65685 | − | 3.65685i | 0.619020 | − | 0.295639i | ||||
\(154\) | 11.6569i | 0.939336i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.17157 | + | 4.48528i | 0.253929 | + | 0.359110i | ||||
\(157\) | 7.31371 | + | 7.31371i | 0.583697 | + | 0.583697i | 0.935917 | − | 0.352220i | \(-0.114573\pi\) |
−0.352220 | + | 0.935917i | \(0.614573\pi\) | |||||||
\(158\) | −1.41421 | − | 1.41421i | −0.112509 | − | 0.112509i | ||||
\(159\) | −12.0000 | − | 16.9706i | −0.951662 | − | 1.34585i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 32.9706i | − | 2.59844i | ||||||
\(162\) | −21.6066 | + | 2.29289i | −1.69757 | + | 0.180147i | ||||
\(163\) | 9.89949 | − | 9.89949i | 0.775388 | − | 0.775388i | −0.203655 | − | 0.979043i | \(-0.565282\pi\) |
0.979043 | + | 0.203655i | \(0.0652819\pi\) | |||||||
\(164\) | −3.17157 | −0.247658 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.4853 | 1.12428 | ||||||||
\(167\) | 0.242641 | − | 0.242641i | 0.0187761 | − | 0.0187761i | −0.697656 | − | 0.716433i | \(-0.745774\pi\) |
0.716433 | + | 0.697656i | \(0.245774\pi\) | |||||||
\(168\) | 6.24264 | − | 36.3848i | 0.481630 | − | 2.80715i | ||||
\(169\) | 12.3137i | 0.947208i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.82843 | − | 13.6569i | 0.369239 | − | 1.04437i | ||||
\(172\) | −28.3848 | − | 28.3848i | −2.16432 | − | 2.16432i | ||||
\(173\) | −0.828427 | − | 0.828427i | −0.0629841 | − | 0.0629841i | 0.674913 | − | 0.737897i | \(-0.264181\pi\) |
−0.737897 | + | 0.674913i | \(0.764181\pi\) | |||||||
\(174\) | 10.8284 | − | 7.65685i | 0.820901 | − | 0.580465i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000i | 0.226134i | ||||||||
\(177\) | −23.3137 | − | 4.00000i | −1.75237 | − | 0.300658i | ||||
\(178\) | 12.4853 | − | 12.4853i | 0.935811 | − | 0.935811i | ||||
\(179\) | −3.31371 | −0.247678 | −0.123839 | − | 0.992302i | \(-0.539521\pi\) | ||||
−0.123839 | + | 0.992302i | \(0.539521\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | −6.82843 | + | 6.82843i | −0.506157 | + | 0.506157i | ||||
\(183\) | 10.2426 | + | 1.75736i | 0.757158 | + | 0.129908i | ||||
\(184\) | − | 30.1421i | − | 2.22211i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 13.6569 | − | 9.65685i | 1.00137 | − | 0.708075i | ||||
\(187\) | −2.00000 | − | 2.00000i | −0.146254 | − | 0.146254i | ||||
\(188\) | 3.17157 | + | 3.17157i | 0.231311 | + | 0.231311i | ||||
\(189\) | −6.82843 | − | 24.1421i | −0.496695 | − | 1.75608i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.3137i | 0.818631i | 0.912393 | + | 0.409316i | \(0.134232\pi\) | ||||
−0.912393 | + | 0.409316i | \(0.865768\pi\) | |||||||
\(192\) | −2.87868 | + | 16.7782i | −0.207751 | + | 1.21086i | ||||
\(193\) | −5.07107 | + | 5.07107i | −0.365023 | + | 0.365023i | −0.865658 | − | 0.500635i | \(-0.833100\pi\) |
0.500635 | + | 0.865658i | \(0.333100\pi\) | |||||||
\(194\) | −32.9706 | −2.36715 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 62.4558 | 4.46113 | ||||||||
\(197\) | −2.48528 | + | 2.48528i | −0.177069 | + | 0.177069i | −0.790077 | − | 0.613008i | \(-0.789959\pi\) |
0.613008 | + | 0.790077i | \(0.289959\pi\) | |||||||
\(198\) | 3.12132 | + | 6.53553i | 0.221823 | + | 0.464460i | ||||
\(199\) | − | 20.9706i | − | 1.48656i | −0.668978 | − | 0.743282i | \(-0.733268\pi\) | ||
0.668978 | − | 0.743282i | \(-0.266732\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.65685 | + | 10.8284i | 0.540073 | + | 0.763778i | ||||
\(202\) | 8.24264 | + | 8.24264i | 0.579950 | + | 0.579950i | ||||
\(203\) | 10.8284 | + | 10.8284i | 0.760007 | + | 0.760007i | ||||
\(204\) | 10.8284 | + | 15.3137i | 0.758142 | + | 1.07217i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 14.4853i | − | 1.00924i | ||||||
\(207\) | −8.82843 | − | 18.4853i | −0.613618 | − | 1.28482i | ||||
\(208\) | −1.75736 | + | 1.75736i | −0.121851 | + | 0.121851i | ||||
\(209\) | −4.82843 | −0.333989 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.48528 | 0.446465 | 0.223233 | − | 0.974765i | \(-0.428339\pi\) | ||||
0.223233 | + | 0.974765i | \(0.428339\pi\) | |||||||
\(212\) | 32.4853 | − | 32.4853i | 2.23110 | − | 2.23110i | ||||
\(213\) | −0.485281 | + | 2.82843i | −0.0332509 | + | 0.193801i | ||||
\(214\) | 20.1421i | 1.37689i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.24264 | − | 22.0711i | −0.424758 | − | 1.50175i | ||||
\(217\) | 13.6569 | + | 13.6569i | 0.927088 | + | 0.927088i | ||||
\(218\) | −3.41421 | − | 3.41421i | −0.231240 | − | 0.231240i | ||||
\(219\) | −14.8284 | + | 10.4853i | −1.00201 | + | 0.708530i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.34315i | − | 0.157617i | ||||||
\(222\) | −32.9706 | − | 5.65685i | −2.21284 | − | 0.379663i | ||||
\(223\) | −7.75736 | + | 7.75736i | −0.519471 | + | 0.519471i | −0.917411 | − | 0.397940i | \(-0.869725\pi\) |
0.397940 | + | 0.917411i | \(0.369725\pi\) | |||||||
\(224\) | −7.65685 | −0.511595 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −28.9706 | −1.92709 | ||||||||
\(227\) | −11.7574 | + | 11.7574i | −0.780363 | + | 0.780363i | −0.979892 | − | 0.199529i | \(-0.936059\pi\) |
0.199529 | + | 0.979892i | \(0.436059\pi\) | |||||||
\(228\) | 31.5563 | + | 5.41421i | 2.08987 | + | 0.358565i | ||||
\(229\) | − | 18.0000i | − | 1.18947i | −0.803921 | − | 0.594737i | \(-0.797256\pi\) | ||
0.803921 | − | 0.594737i | \(-0.202744\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.82843 | + | 4.82843i | −0.449278 | + | 0.317687i | ||||
\(232\) | 9.89949 | + | 9.89949i | 0.649934 | + | 0.649934i | ||||
\(233\) | 10.0000 | + | 10.0000i | 0.655122 | + | 0.655122i | 0.954222 | − | 0.299100i | \(-0.0966864\pi\) |
−0.299100 | + | 0.954222i | \(0.596686\pi\) | |||||||
\(234\) | −2.00000 | + | 5.65685i | −0.130744 | + | 0.369800i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 52.2843i | − | 3.40342i | ||||||
\(237\) | 0.242641 | − | 1.41421i | 0.0157612 | − | 0.0918630i | ||||
\(238\) | −23.3137 | + | 23.3137i | −1.51120 | + | 1.51120i | ||||
\(239\) | −13.6569 | −0.883388 | −0.441694 | − | 0.897166i | \(-0.645622\pi\) | ||||
−0.441694 | + | 0.897166i | \(0.645622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.97056 | 0.449013 | 0.224507 | − | 0.974473i | \(-0.427923\pi\) | ||||
0.224507 | + | 0.974473i | \(0.427923\pi\) | |||||||
\(242\) | 1.70711 | − | 1.70711i | 0.109737 | − | 0.109737i | ||||
\(243\) | −10.2929 | − | 11.7071i | −0.660289 | − | 0.751011i | ||||
\(244\) | 22.9706i | 1.47054i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.00000 | − | 2.82843i | −0.127515 | − | 0.180334i | ||||
\(247\) | −2.82843 | − | 2.82843i | −0.179969 | − | 0.179969i | ||||
\(248\) | 12.4853 | + | 12.4853i | 0.792816 | + | 0.792816i | ||||
\(249\) | 6.00000 | + | 8.48528i | 0.380235 | + | 0.537733i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 9.65685i | − | 0.609535i | −0.952427 | − | 0.304768i | \(-0.901421\pi\) | ||
0.952427 | − | 0.304768i | \(-0.0985788\pi\) | |||||||
\(252\) | 50.0416 | − | 23.8995i | 3.15233 | − | 1.50553i | ||||
\(253\) | −4.82843 | + | 4.82843i | −0.303561 | + | 0.303561i | ||||
\(254\) | 6.00000 | 0.376473 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | −16.0000 | + | 16.0000i | −0.998053 | + | 0.998053i | −0.999998 | − | 0.00194553i | \(-0.999381\pi\) |
0.00194553 | + | 0.999998i | \(0.499381\pi\) | |||||||
\(258\) | 7.41421 | − | 43.2132i | 0.461589 | − | 2.69034i | ||||
\(259\) | − | 38.6274i | − | 2.40019i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.97056 | + | 3.17157i | 0.555264 | + | 0.196315i | ||||
\(262\) | −10.8284 | − | 10.8284i | −0.668982 | − | 0.668982i | ||||
\(263\) | −7.75736 | − | 7.75736i | −0.478339 | − | 0.478339i | 0.426261 | − | 0.904600i | \(-0.359831\pi\) |
−0.904600 | + | 0.426261i | \(0.859831\pi\) | |||||||
\(264\) | −6.24264 | + | 4.41421i | −0.384208 | + | 0.271676i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 56.2843i | 3.45101i | ||||||||
\(267\) | 12.4853 | + | 2.14214i | 0.764087 | + | 0.131097i | ||||
\(268\) | −20.7279 | + | 20.7279i | −1.26616 | + | 1.26616i | ||||
\(269\) | 2.34315 | 0.142864 | 0.0714321 | − | 0.997445i | \(-0.477243\pi\) | ||||
0.0714321 | + | 0.997445i | \(0.477243\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.4853 | −1.60887 | −0.804433 | − | 0.594043i | \(-0.797531\pi\) | ||||
−0.804433 | + | 0.594043i | \(0.797531\pi\) | |||||||
\(272\) | −6.00000 | + | 6.00000i | −0.363803 | + | 0.363803i | ||||
\(273\) | −6.82843 | − | 1.17157i | −0.413275 | − | 0.0709068i | ||||
\(274\) | 32.9706i | 1.99182i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 36.9706 | − | 26.1421i | 2.22537 | − | 1.57357i | ||||
\(277\) | 2.92893 | + | 2.92893i | 0.175982 | + | 0.175982i | 0.789602 | − | 0.613619i | \(-0.210287\pi\) |
−0.613619 | + | 0.789602i | \(0.710287\pi\) | |||||||
\(278\) | −19.0711 | − | 19.0711i | −1.14381 | − | 1.14381i | ||||
\(279\) | 11.3137 | + | 4.00000i | 0.677334 | + | 0.239474i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.1421i | 1.20158i | 0.799407 | + | 0.600790i | \(0.205147\pi\) | ||||
−0.799407 | + | 0.600790i | \(0.794853\pi\) | |||||||
\(282\) | −0.828427 | + | 4.82843i | −0.0493321 | + | 0.287529i | ||||
\(283\) | 7.41421 | − | 7.41421i | 0.440729 | − | 0.440729i | −0.451528 | − | 0.892257i | \(-0.649121\pi\) |
0.892257 | + | 0.451528i | \(0.149121\pi\) | |||||||
\(284\) | −6.34315 | −0.376396 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.00000 | 0.118262 | ||||||||
\(287\) | 2.82843 | − | 2.82843i | 0.166957 | − | 0.166957i | ||||
\(288\) | −4.29289 | + | 2.05025i | −0.252961 | + | 0.120812i | ||||
\(289\) | 9.00000i | 0.529412i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.6569 | − | 19.3137i | −0.800579 | − | 1.13219i | ||||
\(292\) | −28.3848 | − | 28.3848i | −1.66109 | − | 1.66109i | ||||
\(293\) | −14.4853 | − | 14.4853i | −0.846239 | − | 0.846239i | 0.143422 | − | 0.989662i | \(-0.454189\pi\) |
−0.989662 | + | 0.143422i | \(0.954189\pi\) | |||||||
\(294\) | 39.3848 | + | 55.6985i | 2.29697 | + | 3.24840i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 35.3137i | − | 2.05257i | ||||||
\(297\) | −2.53553 | + | 4.53553i | −0.147127 | + | 0.263178i | ||||
\(298\) | −37.2132 | + | 37.2132i | −2.15570 | + | 2.15570i | ||||
\(299\) | −5.65685 | −0.327144 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 50.6274 | 2.91812 | ||||||||
\(302\) | 4.24264 | − | 4.24264i | 0.244137 | − | 0.244137i | ||||
\(303\) | −1.41421 | + | 8.24264i | −0.0812444 | + | 0.473527i | ||||
\(304\) | 14.4853i | 0.830788i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.82843 | + | 19.3137i | −0.390355 | + | 1.10409i | ||||
\(307\) | 6.72792 | + | 6.72792i | 0.383983 | + | 0.383983i | 0.872535 | − | 0.488552i | \(-0.162475\pi\) |
−0.488552 | + | 0.872535i | \(0.662475\pi\) | |||||||
\(308\) | −13.0711 | − | 13.0711i | −0.744793 | − | 0.744793i | ||||
\(309\) | 8.48528 | − | 6.00000i | 0.482711 | − | 0.341328i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 21.6569i | − | 1.22805i | −0.789288 | − | 0.614024i | \(-0.789550\pi\) | ||
0.789288 | − | 0.614024i | \(-0.210450\pi\) | |||||||
\(312\) | −6.24264 | − | 1.07107i | −0.353420 | − | 0.0606373i | ||||
\(313\) | 13.1716 | − | 13.1716i | 0.744501 | − | 0.744501i | −0.228939 | − | 0.973441i | \(-0.573526\pi\) |
0.973441 | + | 0.228939i | \(0.0735258\pi\) | |||||||
\(314\) | −24.9706 | −1.40917 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.17157 | 0.178415 | ||||||||
\(317\) | −10.1421 | + | 10.1421i | −0.569639 | + | 0.569639i | −0.932027 | − | 0.362388i | \(-0.881961\pi\) |
0.362388 | + | 0.932027i | \(0.381961\pi\) | |||||||
\(318\) | 49.4558 | + | 8.48528i | 2.77335 | + | 0.475831i | ||||
\(319\) | − | 3.17157i | − | 0.177574i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.7990 | + | 8.34315i | −0.658555 | + | 0.465669i | ||||
\(322\) | 56.2843 | + | 56.2843i | 3.13660 | + | 3.13660i | ||||
\(323\) | −9.65685 | − | 9.65685i | −0.537322 | − | 0.537322i | ||||
\(324\) | 21.6569 | − | 26.7990i | 1.20316 | − | 1.48883i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 33.7990i | 1.87195i | ||||||||
\(327\) | 0.585786 | − | 3.41421i | 0.0323941 | − | 0.188806i | ||||
\(328\) | 2.58579 | − | 2.58579i | 0.142776 | − | 0.142776i | ||||
\(329\) | −5.65685 | −0.311872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.65685 | −0.530789 | −0.265394 | − | 0.964140i | \(-0.585502\pi\) | ||||
−0.265394 | + | 0.964140i | \(0.585502\pi\) | |||||||
\(332\) | −16.2426 | + | 16.2426i | −0.891431 | + | 0.891431i | ||||
\(333\) | −10.3431 | − | 21.6569i | −0.566801 | − | 1.18679i | ||||
\(334\) | 0.828427i | 0.0453295i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 14.4853 | + | 20.4853i | 0.790237 | + | 1.11756i | ||||
\(337\) | −3.89949 | − | 3.89949i | −0.212419 | − | 0.212419i | 0.592875 | − | 0.805294i | \(-0.297993\pi\) |
−0.805294 | + | 0.592875i | \(0.797993\pi\) | |||||||
\(338\) | −21.0208 | − | 21.0208i | −1.14338 | − | 1.14338i | ||||
\(339\) | −12.0000 | − | 16.9706i | −0.651751 | − | 0.921714i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4.00000i | − | 0.216612i | ||||||
\(342\) | 15.0711 | + | 31.5563i | 0.814950 | + | 1.70637i | ||||
\(343\) | −31.7990 | + | 31.7990i | −1.71698 | + | 1.71698i | ||||
\(344\) | 46.2843 | 2.49548 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.82843 | 0.152057 | ||||||||
\(347\) | 16.2426 | − | 16.2426i | 0.871951 | − | 0.871951i | −0.120734 | − | 0.992685i | \(-0.538525\pi\) |
0.992685 | + | 0.120734i | \(0.0385249\pi\) | |||||||
\(348\) | −3.55635 | + | 20.7279i | −0.190640 | + | 1.11113i | ||||
\(349\) | − | 22.9706i | − | 1.22959i | −0.788688 | − | 0.614793i | \(-0.789240\pi\) | ||
0.788688 | − | 0.614793i | \(-0.210760\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.14214 | + | 1.17157i | −0.221091 | + | 0.0625339i | ||||
\(352\) | 1.12132 | + | 1.12132i | 0.0597666 | + | 0.0597666i | ||||
\(353\) | 4.48528 | + | 4.48528i | 0.238727 | + | 0.238727i | 0.816323 | − | 0.577596i | \(-0.196009\pi\) |
−0.577596 | + | 0.816323i | \(0.696009\pi\) | |||||||
\(354\) | 46.6274 | − | 32.9706i | 2.47822 | − | 1.75237i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 28.0000i | 1.48400i | ||||||||
\(357\) | −23.3137 | − | 4.00000i | −1.23389 | − | 0.211702i | ||||
\(358\) | 5.65685 | − | 5.65685i | 0.298974 | − | 0.298974i | ||||
\(359\) | −16.9706 | −0.895672 | −0.447836 | − | 0.894116i | \(-0.647805\pi\) | ||||
−0.447836 | + | 0.894116i | \(0.647805\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.31371 | −0.227037 | ||||||||
\(362\) | 10.2426 | − | 10.2426i | 0.538341 | − | 0.538341i | ||||
\(363\) | 1.70711 | + | 0.292893i | 0.0895999 | + | 0.0153729i | ||||
\(364\) | − | 15.3137i | − | 0.802656i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −20.4853 | + | 14.4853i | −1.07078 | + | 0.757158i | ||||
\(367\) | 16.2426 | + | 16.2426i | 0.847859 | + | 0.847859i | 0.989866 | − | 0.142007i | \(-0.0453555\pi\) |
−0.142007 | + | 0.989866i | \(0.545355\pi\) | |||||||
\(368\) | 14.4853 | + | 14.4853i | 0.755097 | + | 0.755097i | ||||
\(369\) | 0.828427 | − | 2.34315i | 0.0431262 | − | 0.121979i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 57.9411i | 3.00815i | ||||||||
\(372\) | −4.48528 | + | 26.1421i | −0.232551 | + | 1.35541i | ||||
\(373\) | 3.89949 | − | 3.89949i | 0.201908 | − | 0.201908i | −0.598909 | − | 0.800817i | \(-0.704399\pi\) |
0.800817 | + | 0.598909i | \(0.204399\pi\) | |||||||
\(374\) | 6.82843 | 0.353090 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.17157 | −0.266704 | ||||||||
\(377\) | 1.85786 | − | 1.85786i | 0.0956849 | − | 0.0956849i | ||||
\(378\) | 52.8701 | + | 29.5563i | 2.71934 | + | 1.52021i | ||||
\(379\) | 26.6274i | 1.36776i | 0.729595 | + | 0.683879i | \(0.239709\pi\) | ||||
−0.729595 | + | 0.683879i | \(0.760291\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.48528 | + | 3.51472i | 0.127325 | + | 0.180064i | ||||
\(382\) | −19.3137 | − | 19.3137i | −0.988175 | − | 0.988175i | ||||
\(383\) | −13.3137 | − | 13.3137i | −0.680299 | − | 0.680299i | 0.279769 | − | 0.960067i | \(-0.409742\pi\) |
−0.960067 | + | 0.279769i | \(0.909742\pi\) | |||||||
\(384\) | −20.5563 | − | 29.0711i | −1.04901 | − | 1.48353i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 17.3137i | − | 0.881245i | ||||||
\(387\) | 28.3848 | − | 13.5563i | 1.44288 | − | 0.689108i | ||||
\(388\) | 36.9706 | − | 36.9706i | 1.87690 | − | 1.87690i | ||||
\(389\) | −12.0000 | −0.608424 | −0.304212 | − | 0.952604i | \(-0.598393\pi\) | ||||
−0.304212 | + | 0.952604i | \(0.598393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.3137 | −0.976736 | ||||||||
\(392\) | −50.9203 | + | 50.9203i | −2.57186 | + | 2.57186i | ||||
\(393\) | 1.85786 | − | 10.8284i | 0.0937169 | − | 0.546222i | ||||
\(394\) | − | 8.48528i | − | 0.427482i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −10.8284 | − | 3.82843i | −0.544149 | − | 0.192386i | ||||
\(397\) | 17.1716 | + | 17.1716i | 0.861817 | + | 0.861817i | 0.991549 | − | 0.129732i | \(-0.0414119\pi\) |
−0.129732 | + | 0.991549i | \(0.541412\pi\) | |||||||
\(398\) | 35.7990 | + | 35.7990i | 1.79444 | + | 1.79444i | ||||
\(399\) | −32.9706 | + | 23.3137i | −1.65059 | + | 1.16715i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.2843i | 1.81195i | 0.423331 | + | 0.905975i | \(0.360861\pi\) | ||||
−0.423331 | + | 0.905975i | \(0.639139\pi\) | |||||||
\(402\) | −31.5563 | − | 5.41421i | −1.57389 | − | 0.270036i | ||||
\(403\) | 2.34315 | − | 2.34315i | 0.116720 | − | 0.116720i | ||||
\(404\) | −18.4853 | −0.919677 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −36.9706 | −1.83482 | ||||||||
\(407\) | −5.65685 | + | 5.65685i | −0.280400 | + | 0.280400i | ||||
\(408\) | −21.3137 | − | 3.65685i | −1.05519 | − | 0.181041i | ||||
\(409\) | 27.6569i | 1.36754i | 0.729696 | + | 0.683772i | \(0.239662\pi\) | ||||
−0.729696 | + | 0.683772i | \(0.760338\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.3137 | + | 13.6569i | −0.952675 | + | 0.673643i | ||||
\(412\) | 16.2426 | + | 16.2426i | 0.800217 | + | 0.800217i | ||||
\(413\) | 46.6274 | + | 46.6274i | 2.29439 | + | 2.29439i | ||||
\(414\) | 46.6274 | + | 16.4853i | 2.29161 | + | 0.810207i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.31371i | 0.0644099i | ||||||||
\(417\) | 3.27208 | − | 19.0711i | 0.160234 | − | 0.933914i | ||||
\(418\) | 8.24264 | − | 8.24264i | 0.403161 | − | 0.403161i | ||||
\(419\) | −12.6863 | −0.619766 | −0.309883 | − | 0.950775i | \(-0.600290\pi\) | ||||
−0.309883 | + | 0.950775i | \(0.600290\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.31371 | −0.453922 | −0.226961 | − | 0.973904i | \(-0.572879\pi\) | ||||
−0.226961 | + | 0.973904i | \(0.572879\pi\) | |||||||
\(422\) | −11.0711 | + | 11.0711i | −0.538931 | + | 0.538931i | ||||
\(423\) | −3.17157 | + | 1.51472i | −0.154207 | + | 0.0736481i | ||||
\(424\) | 52.9706i | 2.57248i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.00000 | − | 5.65685i | −0.193801 | − | 0.274075i | ||||
\(427\) | −20.4853 | − | 20.4853i | −0.991352 | − | 0.991352i | ||||
\(428\) | −22.5858 | − | 22.5858i | −1.09173 | − | 1.09173i | ||||
\(429\) | 0.828427 | + | 1.17157i | 0.0399968 | + | 0.0565641i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 5.65685i | − | 0.272481i | −0.990676 | − | 0.136241i | \(-0.956498\pi\) | ||
0.990676 | − | 0.136241i | \(-0.0435020\pi\) | |||||||
\(432\) | 13.6066 | + | 7.60660i | 0.654648 | + | 0.365973i | ||||
\(433\) | 15.3137 | − | 15.3137i | 0.735930 | − | 0.735930i | −0.235858 | − | 0.971788i | \(-0.575790\pi\) |
0.971788 | + | 0.235858i | \(0.0757899\pi\) | |||||||
\(434\) | −46.6274 | −2.23819 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.65685 | 0.366697 | ||||||||
\(437\) | −23.3137 | + | 23.3137i | −1.11525 | + | 1.11525i | ||||
\(438\) | 7.41421 | − | 43.2132i | 0.354265 | − | 2.06481i | ||||
\(439\) | − | 4.14214i | − | 0.197693i | −0.995103 | − | 0.0988467i | \(-0.968485\pi\) | ||
0.995103 | − | 0.0988467i | \(-0.0315153\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.3137 | + | 46.1421i | −0.776843 | + | 2.19724i | ||||
\(442\) | 4.00000 | + | 4.00000i | 0.190261 | + | 0.190261i | ||||
\(443\) | 9.31371 | + | 9.31371i | 0.442508 | + | 0.442508i | 0.892854 | − | 0.450346i | \(-0.148699\pi\) |
−0.450346 | + | 0.892854i | \(0.648699\pi\) | |||||||
\(444\) | 43.3137 | − | 30.6274i | 2.05558 | − | 1.45351i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 26.4853i | − | 1.25411i | ||||||
\(447\) | −37.2132 | − | 6.38478i | −1.76012 | − | 0.301990i | ||||
\(448\) | 33.5563 | − | 33.5563i | 1.58539 | − | 1.58539i | ||||
\(449\) | 25.6569 | 1.21082 | 0.605411 | − | 0.795913i | \(-0.293009\pi\) | ||||
0.605411 | + | 0.795913i | \(0.293009\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.828427 | −0.0390091 | ||||||||
\(452\) | 32.4853 | − | 32.4853i | 1.52798 | − | 1.52798i | ||||
\(453\) | 4.24264 | + | 0.727922i | 0.199337 | + | 0.0342008i | ||||
\(454\) | − | 40.1421i | − | 1.88396i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −30.1421 | + | 21.3137i | −1.41153 | + | 0.998106i | ||||
\(457\) | 16.5858 | + | 16.5858i | 0.775850 | + | 0.775850i | 0.979122 | − | 0.203272i | \(-0.0651576\pi\) |
−0.203272 | + | 0.979122i | \(0.565158\pi\) | |||||||
\(458\) | 30.7279 | + | 30.7279i | 1.43582 | + | 1.43582i | ||||
\(459\) | −14.1421 | + | 4.00000i | −0.660098 | + | 0.186704i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 28.8284i | − | 1.34267i | −0.741152 | − | 0.671337i | \(-0.765720\pi\) | ||
0.741152 | − | 0.671337i | \(-0.234280\pi\) | |||||||
\(462\) | 3.41421 | − | 19.8995i | 0.158844 | − | 0.925808i | ||||
\(463\) | 14.3848 | − | 14.3848i | 0.668517 | − | 0.668517i | −0.288855 | − | 0.957373i | \(-0.593275\pi\) |
0.957373 | + | 0.288855i | \(0.0932747\pi\) | |||||||
\(464\) | −9.51472 | −0.441710 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −34.1421 | −1.58160 | ||||||||
\(467\) | 7.17157 | − | 7.17157i | 0.331861 | − | 0.331861i | −0.521432 | − | 0.853293i | \(-0.674602\pi\) |
0.853293 | + | 0.521432i | \(0.174602\pi\) | |||||||
\(468\) | −4.10051 | − | 8.58579i | −0.189546 | − | 0.396878i | ||||
\(469\) | − | 36.9706i | − | 1.70714i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.3431 | − | 14.6274i | −0.476587 | − | 0.673996i | ||||
\(472\) | 42.6274 | + | 42.6274i | 1.96209 | + | 1.96209i | ||||
\(473\) | −7.41421 | − | 7.41421i | −0.340906 | − | 0.340906i | ||||
\(474\) | 2.00000 | + | 2.82843i | 0.0918630 | + | 0.129914i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 52.2843i | − | 2.39645i | ||||||
\(477\) | 15.5147 | + | 32.4853i | 0.710370 | + | 1.48740i | ||||
\(478\) | 23.3137 | − | 23.3137i | 1.06634 | − | 1.06634i | ||||
\(479\) | 37.6569 | 1.72059 | 0.860293 | − | 0.509800i | \(-0.170281\pi\) | ||||
0.860293 | + | 0.509800i | \(0.170281\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.62742 | −0.302184 | ||||||||
\(482\) | −11.8995 | + | 11.8995i | −0.542007 | + | 0.542007i | ||||
\(483\) | −9.65685 | + | 56.2843i | −0.439402 | + | 2.56102i | ||||
\(484\) | 3.82843i | 0.174019i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 37.5563 | + | 2.41421i | 1.70359 | + | 0.109511i | ||||
\(487\) | −13.4142 | − | 13.4142i | −0.607856 | − | 0.607856i | 0.334529 | − | 0.942385i | \(-0.391423\pi\) |
−0.942385 | + | 0.334529i | \(0.891423\pi\) | |||||||
\(488\) | −18.7279 | − | 18.7279i | −0.847773 | − | 0.847773i | ||||
\(489\) | −19.7990 | + | 14.0000i | −0.895341 | + | 0.633102i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 26.6274i | − | 1.20168i | −0.799370 | − | 0.600839i | \(-0.794833\pi\) | ||
0.799370 | − | 0.600839i | \(-0.205167\pi\) | |||||||
\(492\) | 5.41421 | + | 0.928932i | 0.244092 | + | 0.0418795i | ||||
\(493\) | 6.34315 | − | 6.34315i | 0.285681 | − | 0.285681i | ||||
\(494\) | 9.65685 | 0.434482 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.0000 | −0.538816 | ||||||||
\(497\) | 5.65685 | − | 5.65685i | 0.253745 | − | 0.253745i | ||||
\(498\) | −24.7279 | − | 4.24264i | −1.10808 | − | 0.190117i | ||||
\(499\) | 13.6569i | 0.611365i | 0.952134 | + | 0.305682i | \(0.0988846\pi\) | ||||
−0.952134 | + | 0.305682i | \(0.901115\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.485281 | + | 0.343146i | −0.0216808 | + | 0.0153306i | ||||
\(502\) | 16.4853 | + | 16.4853i | 0.735774 | + | 0.735774i | ||||
\(503\) | −10.3848 | − | 10.3848i | −0.463034 | − | 0.463034i | 0.436614 | − | 0.899649i | \(-0.356177\pi\) |
−0.899649 | + | 0.436614i | \(0.856177\pi\) | |||||||
\(504\) | −21.3137 | + | 60.2843i | −0.949388 | + | 2.68527i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 16.4853i | − | 0.732860i | ||||||
\(507\) | 3.60660 | − | 21.0208i | 0.160175 | − | 0.933567i | ||||
\(508\) | −6.72792 | + | 6.72792i | −0.298503 | + | 0.298503i | ||||
\(509\) | −12.6863 | −0.562310 | −0.281155 | − | 0.959662i | \(-0.590718\pi\) | ||||
−0.281155 | + | 0.959662i | \(0.590718\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 50.6274 | 2.23963 | ||||||||
\(512\) | 22.0919 | − | 22.0919i | 0.976333 | − | 0.976333i | ||||
\(513\) | −12.2426 | + | 21.8995i | −0.540526 | + | 0.966886i | ||||
\(514\) | − | 54.6274i | − | 2.40951i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 40.1421 | + | 56.7696i | 1.76716 | + | 2.49914i | ||||
\(517\) | 0.828427 | + | 0.828427i | 0.0364342 | + | 0.0364342i | ||||
\(518\) | 65.9411 | + | 65.9411i | 2.89729 | + | 2.89729i | ||||
\(519\) | 1.17157 | + | 1.65685i | 0.0514263 | + | 0.0727278i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.02944i | − | 0.307965i | −0.988074 | − | 0.153983i | \(-0.950790\pi\) | ||
0.988074 | − | 0.153983i | \(-0.0492100\pi\) | |||||||
\(522\) | −20.7279 | + | 9.89949i | −0.907237 | + | 0.433289i | ||||
\(523\) | −17.0711 | + | 17.0711i | −0.746466 | + | 0.746466i | −0.973814 | − | 0.227348i | \(-0.926995\pi\) |
0.227348 | + | 0.973814i | \(0.426995\pi\) | |||||||
\(524\) | 24.2843 | 1.06086 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.4853 | 1.15481 | ||||||||
\(527\) | 8.00000 | − | 8.00000i | 0.348485 | − | 0.348485i | ||||
\(528\) | 0.878680 | − | 5.12132i | 0.0382396 | − | 0.222877i | ||||
\(529\) | 23.6274i | 1.02728i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 38.6274 | + | 13.6569i | 1.67629 | + | 0.592657i | ||||
\(532\) | −63.1127 | − | 63.1127i | −2.73628 | − | 2.73628i | ||||
\(533\) | −0.485281 | − | 0.485281i | −0.0210199 | − | 0.0210199i | ||||
\(534\) | −24.9706 | + | 17.6569i | −1.08058 | + | 0.764087i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 33.7990i | − | 1.45989i | ||||||
\(537\) | 5.65685 | + | 0.970563i | 0.244111 | + | 0.0418829i | ||||
\(538\) | −4.00000 | + | 4.00000i | −0.172452 | + | 0.172452i | ||||
\(539\) | 16.3137 | 0.702681 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.02944 | −0.0442590 | −0.0221295 | − | 0.999755i | \(-0.507045\pi\) | ||||
−0.0221295 | + | 0.999755i | \(0.507045\pi\) | |||||||
\(542\) | 45.2132 | − | 45.2132i | 1.94207 | − | 1.94207i | ||||
\(543\) | 10.2426 | + | 1.75736i | 0.439554 | + | 0.0754155i | ||||
\(544\) | 4.48528i | 0.192305i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 13.6569 | − | 9.65685i | 0.584459 | − | 0.413275i | ||||
\(547\) | −18.7279 | − | 18.7279i | −0.800748 | − | 0.800748i | 0.182464 | − | 0.983212i | \(-0.441593\pi\) |
−0.983212 | + | 0.182464i | \(0.941593\pi\) | |||||||
\(548\) | −36.9706 | − | 36.9706i | −1.57930 | − | 1.57930i | ||||
\(549\) | −16.9706 | − | 6.00000i | −0.724286 | − | 0.256074i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 15.3137i | − | 0.652386i | ||||||
\(552\) | −8.82843 | + | 51.4558i | −0.375763 | + | 2.19011i | ||||
\(553\) | −2.82843 | + | 2.82843i | −0.120277 | + | 0.120277i | ||||
\(554\) | −10.0000 | −0.424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 42.7696 | 1.81383 | ||||||||
\(557\) | 31.4558 | − | 31.4558i | 1.33283 | − | 1.33283i | 0.429996 | − | 0.902831i | \(-0.358515\pi\) |
0.902831 | − | 0.429996i | \(-0.141485\pi\) | |||||||
\(558\) | −26.1421 | + | 12.4853i | −1.10668 | + | 0.528544i | ||||
\(559\) | − | 8.68629i | − | 0.367391i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.82843 | + | 4.00000i | 0.119416 | + | 0.168880i | ||||
\(562\) | −34.3848 | − | 34.3848i | −1.45043 | − | 1.45043i | ||||
\(563\) | −8.24264 | − | 8.24264i | −0.347386 | − | 0.347386i | 0.511749 | − | 0.859135i | \(-0.328998\pi\) |
−0.859135 | + | 0.511749i | \(0.828998\pi\) | |||||||
\(564\) | −4.48528 | − | 6.34315i | −0.188864 | − | 0.267095i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 25.3137i | 1.06401i | ||||||||
\(567\) | 4.58579 | + | 43.2132i | 0.192585 | + | 1.81478i | ||||
\(568\) | 5.17157 | − | 5.17157i | 0.216994 | − | 0.216994i | ||||
\(569\) | 7.17157 | 0.300648 | 0.150324 | − | 0.988637i | \(-0.451968\pi\) | ||||
0.150324 | + | 0.988637i | \(0.451968\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.4853 | −1.61056 | −0.805279 | − | 0.592895i | \(-0.797985\pi\) | ||||
−0.805279 | + | 0.592895i | \(0.797985\pi\) | |||||||
\(572\) | −2.24264 | + | 2.24264i | −0.0937695 | + | 0.0937695i | ||||
\(573\) | 3.31371 | − | 19.3137i | 0.138432 | − | 0.806842i | ||||
\(574\) | 9.65685i | 0.403069i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 9.82843 | − | 27.7990i | 0.409518 | − | 1.15829i | ||||
\(577\) | 20.4853 | + | 20.4853i | 0.852813 | + | 0.852813i | 0.990479 | − | 0.137665i | \(-0.0439599\pi\) |
−0.137665 | + | 0.990479i | \(0.543960\pi\) | |||||||
\(578\) | −15.3640 | − | 15.3640i | −0.639057 | − | 0.639057i | ||||
\(579\) | 10.1421 | − | 7.17157i | 0.421493 | − | 0.298040i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 28.9706i | − | 1.20190i | ||||||
\(582\) | 56.2843 | + | 9.65685i | 2.33306 | + | 0.400289i | ||||
\(583\) | 8.48528 | − | 8.48528i | 0.351424 | − | 0.351424i | ||||
\(584\) | 46.2843 | 1.91526 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 49.4558 | 2.04300 | ||||||||
\(587\) | −5.51472 | + | 5.51472i | −0.227617 | + | 0.227617i | −0.811696 | − | 0.584080i | \(-0.801456\pi\) |
0.584080 | + | 0.811696i | \(0.301456\pi\) | |||||||
\(588\) | −106.619 | − | 18.2929i | −4.39689 | − | 0.754386i | ||||
\(589\) | − | 19.3137i | − | 0.795807i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.97056 | − | 3.51472i | 0.204462 | − | 0.144576i | ||||
\(592\) | 16.9706 | + | 16.9706i | 0.697486 | + | 0.697486i | ||||
\(593\) | −8.34315 | − | 8.34315i | −0.342612 | − | 0.342612i | 0.514737 | − | 0.857348i | \(-0.327890\pi\) |
−0.857348 | + | 0.514737i | \(0.827890\pi\) | |||||||
\(594\) | −3.41421 | − | 12.0711i | −0.140087 | − | 0.495282i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 83.4558i | − | 3.41848i | ||||||
\(597\) | −6.14214 | + | 35.7990i | −0.251381 | + | 1.46516i | ||||
\(598\) | 9.65685 | − | 9.65685i | 0.394898 | − | 0.394898i | ||||
\(599\) | −0.686292 | −0.0280411 | −0.0140206 | − | 0.999902i | \(-0.504463\pi\) | ||||
−0.0140206 | + | 0.999902i | \(0.504463\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.9706 | −0.447499 | −0.223749 | − | 0.974647i | \(-0.571830\pi\) | ||||
−0.223749 | + | 0.974647i | \(0.571830\pi\) | |||||||
\(602\) | −86.4264 | + | 86.4264i | −3.52248 | + | 3.52248i | ||||
\(603\) | −9.89949 | − | 20.7279i | −0.403139 | − | 0.844106i | ||||
\(604\) | 9.51472i | 0.387148i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.6569 | − | 16.4853i | −0.473527 | − | 0.669669i | ||||
\(607\) | −27.8995 | − | 27.8995i | −1.13241 | − | 1.13241i | −0.989776 | − | 0.142629i | \(-0.954444\pi\) |
−0.142629 | − | 0.989776i | \(-0.545556\pi\) | |||||||
\(608\) | 5.41421 | + | 5.41421i | 0.219575 | + | 0.219575i | ||||
\(609\) | −15.3137 | − | 21.6569i | −0.620543 | − | 0.877580i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.970563i | 0.0392648i | ||||||||
\(612\) | −14.0000 | − | 29.3137i | −0.565916 | − | 1.18494i | ||||
\(613\) | −30.0416 | + | 30.0416i | −1.21337 | + | 1.21337i | −0.243459 | + | 0.969911i | \(0.578282\pi\) |
−0.969911 | + | 0.243459i | \(0.921718\pi\) | |||||||
\(614\) | −22.9706 | −0.927016 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21.3137 | 0.858754 | ||||||||
\(617\) | −24.4853 | + | 24.4853i | −0.985740 | + | 0.985740i | −0.999900 | − | 0.0141594i | \(-0.995493\pi\) |
0.0141594 | + | 0.999900i | \(0.495493\pi\) | |||||||
\(618\) | −4.24264 | + | 24.7279i | −0.170664 | + | 0.994703i | ||||
\(619\) | 28.9706i | 1.16443i | 0.813037 | + | 0.582213i | \(0.197813\pi\) | ||||
−0.813037 | + | 0.582213i | \(0.802187\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.65685 | + | 34.1421i | 0.387516 | + | 1.37008i | ||||
\(622\) | 36.9706 | + | 36.9706i | 1.48238 | + | 1.48238i | ||||
\(623\) | −24.9706 | − | 24.9706i | −1.00042 | − | 1.00042i | ||||
\(624\) | 3.51472 | − | 2.48528i | 0.140701 | − | 0.0994909i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 44.9706i | 1.79739i | ||||||||
\(627\) | 8.24264 | + | 1.41421i | 0.329179 | + | 0.0564782i | ||||
\(628\) | 28.0000 | − | 28.0000i | 1.11732 | − | 1.11732i | ||||
\(629\) | −22.6274 | −0.902214 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.65685 | −0.384433 | −0.192217 | − | 0.981353i | \(-0.561568\pi\) | ||||
−0.192217 | + | 0.981353i | \(0.561568\pi\) | |||||||
\(632\) | −2.58579 | + | 2.58579i | −0.102857 | + | 0.102857i | ||||
\(633\) | −11.0711 | − | 1.89949i | −0.440035 | − | 0.0754981i | ||||
\(634\) | − | 34.6274i | − | 1.37523i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −64.9706 | + | 45.9411i | −2.57625 | + | 1.82168i | ||||
\(637\) | 9.55635 | + | 9.55635i | 0.378636 | + | 0.378636i | ||||
\(638\) | 5.41421 | + | 5.41421i | 0.214351 | + | 0.214351i | ||||
\(639\) | 1.65685 | − | 4.68629i | 0.0655441 | − | 0.185387i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.6569i | 0.697404i | 0.937234 | + | 0.348702i | \(0.113377\pi\) | ||||
−0.937234 | + | 0.348702i | \(0.886623\pi\) | |||||||
\(642\) | 5.89949 | − | 34.3848i | 0.232834 | − | 1.35706i | ||||
\(643\) | −1.41421 | + | 1.41421i | −0.0557711 | + | 0.0557711i | −0.734442 | − | 0.678671i | \(-0.762556\pi\) |
0.678671 | + | 0.734442i | \(0.262556\pi\) | |||||||
\(644\) | −126.225 | −4.97398 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 32.9706 | 1.29721 | ||||||||
\(647\) | 6.00000 | − | 6.00000i | 0.235884 | − | 0.235884i | −0.579259 | − | 0.815143i | \(-0.696658\pi\) |
0.815143 | + | 0.579259i | \(0.196658\pi\) | |||||||
\(648\) | 4.19239 | + | 39.5061i | 0.164693 | + | 1.55195i | ||||
\(649\) | − | 13.6569i | − | 0.536078i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.3137 | − | 27.3137i | −0.756964 | − | 1.07051i | ||||
\(652\) | −37.8995 | − | 37.8995i | −1.48426 | − | 1.48426i | ||||
\(653\) | 4.00000 | + | 4.00000i | 0.156532 | + | 0.156532i | 0.781028 | − | 0.624496i | \(-0.214696\pi\) |
−0.624496 | + | 0.781028i | \(0.714696\pi\) | |||||||
\(654\) | 4.82843 | + | 6.82843i | 0.188806 | + | 0.267013i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.48528i | 0.0970339i | ||||||||
\(657\) | 28.3848 | − | 13.5563i | 1.10740 | − | 0.528884i | ||||
\(658\) | 9.65685 | − | 9.65685i | 0.376463 | − | 0.376463i | ||||
\(659\) | 41.6569 | 1.62272 | 0.811360 | − | 0.584546i | \(-0.198727\pi\) | ||||
0.811360 | + | 0.584546i | \(0.198727\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.627417 | 0.0244037 | 0.0122018 | − | 0.999926i | \(-0.496116\pi\) | ||||
0.0122018 | + | 0.999926i | \(0.496116\pi\) | |||||||
\(662\) | 16.4853 | − | 16.4853i | 0.640719 | − | 0.640719i | ||||
\(663\) | −0.686292 | + | 4.00000i | −0.0266534 | + | 0.155347i | ||||
\(664\) | − | 26.4853i | − | 1.02783i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 54.6274 | + | 19.3137i | 2.11677 | + | 0.748391i | ||||
\(667\) | −15.3137 | − | 15.3137i | −0.592949 | − | 0.592949i | ||||
\(668\) | −0.928932 | − | 0.928932i | −0.0359415 | − | 0.0359415i | ||||
\(669\) | 15.5147 | − | 10.9706i | 0.599834 | − | 0.424146i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.00000i | 0.231627i | ||||||||
\(672\) | 13.0711 | + | 2.24264i | 0.504227 | + | 0.0865117i | ||||
\(673\) | −5.27208 | + | 5.27208i | −0.203224 | + | 0.203224i | −0.801380 | − | 0.598156i | \(-0.795900\pi\) |
0.598156 | + | 0.801380i | \(0.295900\pi\) | |||||||
\(674\) | 13.3137 | 0.512825 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 47.1421 | 1.81316 | ||||||||
\(677\) | −2.48528 | + | 2.48528i | −0.0955171 | + | 0.0955171i | −0.753251 | − | 0.657734i | \(-0.771515\pi\) |
0.657734 | + | 0.753251i | \(0.271515\pi\) | |||||||
\(678\) | 49.4558 | + | 8.48528i | 1.89934 | + | 0.325875i | ||||
\(679\) | 65.9411i | 2.53059i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.5147 | − | 16.6274i | 0.901086 | − | 0.637164i | ||||
\(682\) | 6.82843 | + | 6.82843i | 0.261474 | + | 0.261474i | ||||
\(683\) | 6.48528 | + | 6.48528i | 0.248152 | + | 0.248152i | 0.820212 | − | 0.572060i | \(-0.193855\pi\) |
−0.572060 | + | 0.820212i | \(0.693855\pi\) | |||||||
\(684\) | −52.2843 | − | 18.4853i | −1.99914 | − | 0.706802i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 108.569i | − | 4.14517i | ||||||
\(687\) | −5.27208 | + | 30.7279i | −0.201142 | + | 1.17234i | ||||
\(688\) | −22.2426 | + | 22.2426i | −0.847993 | + | 0.847993i | ||||
\(689\) | 9.94113 | 0.378727 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.9411 | −1.44335 | −0.721674 | − | 0.692233i | \(-0.756627\pi\) | ||||
−0.721674 | + | 0.692233i | \(0.756627\pi\) | |||||||
\(692\) | −3.17157 | + | 3.17157i | −0.120565 | + | 0.120565i | ||||
\(693\) | 13.0711 | − | 6.24264i | 0.496529 | − | 0.237138i | ||||
\(694\) | 55.4558i | 2.10508i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −14.0000 | − | 19.7990i | −0.530669 | − | 0.750479i | ||||
\(697\) | −1.65685 | − | 1.65685i | −0.0627578 | − | 0.0627578i | ||||
\(698\) | 39.2132 | + | 39.2132i | 1.48424 | + | 1.48424i | ||||
\(699\) | −14.1421 | − | 20.0000i | −0.534905 | − | 0.756469i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 50.4853i | − | 1.90680i | −0.301705 | − | 0.953401i | \(-0.597556\pi\) | ||
0.301705 | − | 0.953401i | \(-0.402444\pi\) | |||||||
\(702\) | 5.07107 | − | 9.07107i | 0.191395 | − | 0.342365i | ||||
\(703\) | −27.3137 | + | 27.3137i | −1.03016 | + | 1.03016i | ||||
\(704\) | −9.82843 | −0.370423 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.3137 | −0.576339 | ||||||||
\(707\) | 16.4853 | − | 16.4853i | 0.619993 | − | 0.619993i | ||||
\(708\) | −15.3137 | + | 89.2548i | −0.575524 | + | 3.35440i | ||||
\(709\) | 10.0000i | 0.375558i | 0.982211 | + | 0.187779i | \(0.0601289\pi\) | ||||
−0.982211 | + | 0.187779i | \(0.939871\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.828427 | + | 2.34315i | −0.0310684 | + | 0.0878748i | ||||
\(712\) | −22.8284 | − | 22.8284i | −0.855531 | − | 0.855531i | ||||
\(713\) | −19.3137 | − | 19.3137i | −0.723304 | − | 0.723304i | ||||
\(714\) | 46.6274 | − | 32.9706i | 1.74499 | − | 1.23389i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.6863i | 0.474109i | ||||||||
\(717\) | 23.3137 | + | 4.00000i | 0.870666 | + | 0.149383i | ||||
\(718\) | 28.9706 | − | 28.9706i | 1.08117 | − | 1.08117i | ||||
\(719\) | 27.3137 | 1.01863 | 0.509315 | − | 0.860580i | \(-0.329899\pi\) | ||||
0.509315 | + | 0.860580i | \(0.329899\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.9706 | −1.07892 | ||||||||
\(722\) | 7.36396 | − | 7.36396i | 0.274058 | − | 0.274058i | ||||
\(723\) | −11.8995 | − | 2.04163i | −0.442547 | − | 0.0759291i | ||||
\(724\) | 22.9706i | 0.853694i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.41421 | + | 2.41421i | −0.126713 | + | 0.0895999i | ||||
\(727\) | 9.89949 | + | 9.89949i | 0.367152 | + | 0.367152i | 0.866437 | − | 0.499286i | \(-0.166404\pi\) |
−0.499286 | + | 0.866437i | \(0.666404\pi\) | |||||||
\(728\) | 12.4853 | + | 12.4853i | 0.462735 | + | 0.462735i | ||||
\(729\) | 14.1421 | + | 23.0000i | 0.523783 | + | 0.851852i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 29.6569i | − | 1.09690i | ||||||
\(732\) | 6.72792 | − | 39.2132i | 0.248671 | − | 1.44936i | ||||
\(733\) | 11.8995 | − | 11.8995i | 0.439518 | − | 0.439518i | −0.452332 | − | 0.891850i | \(-0.649408\pi\) |
0.891850 | + | 0.452332i | \(0.149408\pi\) | |||||||
\(734\) | −55.4558 | −2.04691 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.8284 | 0.399141 | ||||||||
\(737\) | −5.41421 | + | 5.41421i | −0.199435 | + | 0.199435i | ||||
\(738\) | 2.58579 | + | 5.41421i | 0.0951841 | + | 0.199300i | ||||
\(739\) | − | 22.4853i | − | 0.827134i | −0.910474 | − | 0.413567i | \(-0.864283\pi\) | ||
0.910474 | − | 0.413567i | \(-0.135717\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.00000 | + | 5.65685i | 0.146944 | + | 0.207810i | ||||
\(742\) | −98.9117 | − | 98.9117i | −3.63116 | − | 3.63116i | ||||
\(743\) | −8.72792 | − | 8.72792i | −0.320196 | − | 0.320196i | 0.528646 | − | 0.848842i | \(-0.322700\pi\) |
−0.848842 | + | 0.528646i | \(0.822700\pi\) | |||||||
\(744\) | −17.6569 | − | 24.9706i | −0.647332 | − | 0.915465i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 13.3137i | 0.487450i | ||||||||
\(747\) | −7.75736 | − | 16.2426i | −0.283827 | − | 0.594287i | ||||
\(748\) | −7.65685 | + | 7.65685i | −0.279962 | + | 0.279962i | ||||
\(749\) | 40.2843 | 1.47196 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.2843 | 0.886146 | 0.443073 | − | 0.896486i | \(-0.353888\pi\) | ||||
0.443073 | + | 0.896486i | \(0.353888\pi\) | |||||||
\(752\) | 2.48528 | − | 2.48528i | 0.0906289 | − | 0.0906289i | ||||
\(753\) | −2.82843 | + | 16.4853i | −0.103074 | + | 0.600757i | ||||
\(754\) | 6.34315i | 0.231004i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −92.4264 | + | 26.1421i | −3.36152 | + | 0.950780i | ||||
\(757\) | 23.3137 | + | 23.3137i | 0.847351 | + | 0.847351i | 0.989802 | − | 0.142451i | \(-0.0454983\pi\) |
−0.142451 | + | 0.989802i | \(0.545498\pi\) | |||||||
\(758\) | −45.4558 | − | 45.4558i | −1.65103 | − | 1.65103i | ||||
\(759\) | 9.65685 | − | 6.82843i | 0.350522 | − | 0.247856i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 25.7990i | − | 0.935213i | −0.883937 | − | 0.467606i | \(-0.845117\pi\) | ||
0.883937 | − | 0.467606i | \(-0.154883\pi\) | |||||||
\(762\) | −10.2426 | − | 1.75736i | −0.371052 | − | 0.0636624i | ||||
\(763\) | −6.82843 | + | 6.82843i | −0.247206 | + | 0.247206i | ||||
\(764\) | 43.3137 | 1.56703 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 45.4558 | 1.64239 | ||||||||
\(767\) | 8.00000 | − | 8.00000i | 0.288863 | − | 0.288863i | ||||
\(768\) | 51.1630 | + | 8.77817i | 1.84618 | + | 0.316755i | ||||
\(769\) | − | 21.3137i | − | 0.768592i | −0.923210 | − | 0.384296i | \(-0.874444\pi\) | ||
0.923210 | − | 0.384296i | \(-0.125556\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.0000 | − | 22.6274i | 1.15245 | − | 0.814907i | ||||
\(772\) | 19.4142 | + | 19.4142i | 0.698733 | + | 0.698733i | ||||
\(773\) | −28.9706 | − | 28.9706i | −1.04200 | − | 1.04200i | −0.999079 | − | 0.0429202i | \(-0.986334\pi\) |
−0.0429202 | − | 0.999079i | \(-0.513666\pi\) | |||||||
\(774\) | −25.3137 | + | 71.5980i | −0.909882 | + | 2.57354i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 60.2843i | 2.16408i | ||||||||
\(777\) | −11.3137 | + | 65.9411i | −0.405877 | + | 2.36562i | ||||
\(778\) | 20.4853 | − | 20.4853i | 0.734433 | − | 0.734433i | ||||
\(779\) | −4.00000 | −0.143315 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.65685 | −0.0592869 | ||||||||
\(782\) | 32.9706 | − | 32.9706i | 1.17902 | − | 1.17902i | ||||
\(783\) | −14.3848 | − | 8.04163i | −0.514070 | − | 0.287384i | ||||
\(784\) | − | 48.9411i | − | 1.74790i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 15.3137 | + | 21.6569i | 0.546222 | + | 0.772474i | ||||
\(787\) | 3.21320 | + | 3.21320i | 0.114538 | + | 0.114538i | 0.762053 | − | 0.647515i | \(-0.224192\pi\) |
−0.647515 | + | 0.762053i | \(0.724192\pi\) | |||||||
\(788\) | 9.51472 | + | 9.51472i | 0.338948 | + | 0.338948i | ||||
\(789\) | 10.9706 | + | 15.5147i | 0.390562 | + | 0.552339i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 57.9411i | 2.06015i | ||||||||
\(792\) | 11.9497 | − | 5.70711i | 0.424616 | − | 0.202793i | ||||
\(793\) | −3.51472 | + | 3.51472i | −0.124811 | + | 0.124811i | ||||
\(794\) | −58.6274 | −2.08061 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −80.2843 | −2.84560 | ||||||||
\(797\) | 1.17157 | − | 1.17157i | 0.0414992 | − | 0.0414992i | −0.686053 | − | 0.727552i | \(-0.740658\pi\) |
0.727552 | + | 0.686053i | \(0.240658\pi\) | |||||||
\(798\) | 16.4853 | − | 96.0833i | 0.583573 | − | 3.40131i | ||||
\(799\) | 3.31371i | 0.117231i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.6863 | − | 7.31371i | −0.730914 | − | 0.258417i | ||||
\(802\) | −61.9411 | − | 61.9411i | −2.18722 | − | 2.18722i | ||||
\(803\) | −7.41421 | − | 7.41421i | −0.261642 | − | 0.261642i | ||||
\(804\) | 41.4558 | − | 29.3137i | 1.46203 | − | 1.03381i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.00000i | 0.281788i | ||||||||
\(807\) | −4.00000 | − | 0.686292i | −0.140807 | − | 0.0241586i | ||||
\(808\) | 15.0711 | − | 15.0711i | 0.530198 | − | 0.530198i | ||||
\(809\) | 41.7990 | 1.46957 | 0.734787 | − | 0.678298i | \(-0.237282\pi\) | ||||
0.734787 | + | 0.678298i | \(0.237282\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.8284 | 1.29322 | 0.646610 | − | 0.762820i | \(-0.276186\pi\) | ||||
0.646610 | + | 0.762820i | \(0.276186\pi\) | |||||||
\(812\) | 41.4558 | − | 41.4558i | 1.45481 | − | 1.45481i | ||||
\(813\) | 45.2132 | + | 7.75736i | 1.58570 | + | 0.272062i | ||||
\(814\) | − | 19.3137i | − | 0.676945i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.0000 | − | 8.48528i | 0.420084 | − | 0.297044i | ||||
\(817\) | −35.7990 | − | 35.7990i | −1.25245 | − | 1.25245i | ||||
\(818\) | −47.2132 | − | 47.2132i | −1.65077 | − | 1.65077i | ||||
\(819\) | 11.3137 | + | 4.00000i | 0.395333 | + | 0.139771i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.82843i | 0.308114i | 0.988062 | + | 0.154057i | \(0.0492340\pi\) | ||||
−0.988062 | + | 0.154057i | \(0.950766\pi\) | |||||||
\(822\) | 9.65685 | − | 56.2843i | 0.336821 | − | 1.96314i | ||||
\(823\) | −8.44365 | + | 8.44365i | −0.294327 | + | 0.294327i | −0.838787 | − | 0.544460i | \(-0.816735\pi\) |
0.544460 | + | 0.838787i | \(0.316735\pi\) | |||||||
\(824\) | −26.4853 | −0.922658 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −159.196 | −5.53914 | ||||||||
\(827\) | −32.2426 | + | 32.2426i | −1.12119 | + | 1.12119i | −0.129623 | + | 0.991563i | \(0.541377\pi\) |
−0.991563 | + | 0.129623i | \(0.958623\pi\) | |||||||
\(828\) | −70.7696 | + | 33.7990i | −2.45941 | + | 1.17460i | ||||
\(829\) | 22.6863i | 0.787927i | 0.919126 | + | 0.393964i | \(0.128896\pi\) | ||||
−0.919126 | + | 0.393964i | \(0.871104\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.14214 | − | 5.85786i | −0.143689 | − | 0.203207i | ||||
\(832\) | −5.75736 | − | 5.75736i | −0.199601 | − | 0.199601i | ||||
\(833\) | 32.6274 | + | 32.6274i | 1.13047 | + | 1.13047i | ||||
\(834\) | 26.9706 | + | 38.1421i | 0.933914 | + | 1.32075i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 18.4853i | 0.639327i | ||||||||
\(837\) | −18.1421 | − | 10.1421i | −0.627084 | − | 0.350563i | ||||
\(838\) | 21.6569 | − | 21.6569i | 0.748124 | − | 0.748124i | ||||
\(839\) | −39.5980 | −1.36707 | −0.683537 | − | 0.729916i | \(-0.739559\pi\) | ||||
−0.683537 | + | 0.729916i | \(0.739559\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9411 | −0.653142 | ||||||||
\(842\) | 15.8995 | − | 15.8995i | 0.547933 | − | 0.547933i | ||||
\(843\) | 5.89949 | − | 34.3848i | 0.203189 | − | 1.18427i | ||||
\(844\) | − | 24.8284i | − | 0.854630i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.82843 | − | 8.00000i | 0.0972433 | − | 0.275046i | ||||
\(847\) | −3.41421 | − | 3.41421i | −0.117314 | − | 0.117314i | ||||
\(848\) | −25.4558 | − | 25.4558i | −0.874157 | − | 0.874157i | ||||
\(849\) | −14.8284 | + | 10.4853i | −0.508910 | + | 0.359854i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 54.6274i | 1.87260i | ||||||||
\(852\) | 10.8284 | + | 1.85786i | 0.370976 | + | 0.0636494i | ||||
\(853\) | 7.41421 | − | 7.41421i | 0.253858 | − | 0.253858i | −0.568692 | − | 0.822550i | \(-0.692551\pi\) |
0.822550 | + | 0.568692i | \(0.192551\pi\) | |||||||
\(854\) | 69.9411 | 2.39334 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 36.8284 | 1.25877 | ||||||||
\(857\) | 8.34315 | − | 8.34315i | 0.284996 | − | 0.284996i | −0.550101 | − | 0.835098i | \(-0.685411\pi\) |
0.835098 | + | 0.550101i | \(0.185411\pi\) | |||||||
\(858\) | −3.41421 | − | 0.585786i | −0.116559 | − | 0.0199984i | ||||
\(859\) | − | 4.97056i | − | 0.169593i | −0.996398 | − | 0.0847967i | \(-0.972976\pi\) | ||
0.996398 | − | 0.0847967i | \(-0.0270241\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.65685 | + | 4.00000i | −0.192785 | + | 0.136320i | ||||
\(862\) | 9.65685 | + | 9.65685i | 0.328914 | + | 0.328914i | ||||
\(863\) | −2.97056 | − | 2.97056i | −0.101119 | − | 0.101119i | 0.654737 | − | 0.755856i | \(-0.272779\pi\) |
−0.755856 | + | 0.654737i | \(0.772779\pi\) | |||||||
\(864\) | 7.92893 | − | 2.24264i | 0.269748 | − | 0.0762962i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 52.2843i | 1.77669i | ||||||||
\(867\) | 2.63604 | − | 15.3640i | 0.0895246 | − | 0.521787i | ||||
\(868\) | 52.2843 | − | 52.2843i | 1.77464 | − | 1.77464i | ||||
\(869\) | 0.828427 | 0.0281025 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.34315 | −0.214929 | ||||||||
\(872\) | −6.24264 | + | 6.24264i | −0.211402 | + | 0.211402i | ||||
\(873\) | 17.6569 | + | 36.9706i | 0.597594 | + | 1.25126i | ||||
\(874\) | − | 79.5980i | − | 2.69244i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 40.1421 | + | 56.7696i | 1.35628 | + | 1.91807i | ||||
\(877\) | −5.07107 | − | 5.07107i | −0.171238 | − | 0.171238i | 0.616285 | − | 0.787523i | \(-0.288637\pi\) |
−0.787523 | + | 0.616285i | \(0.788637\pi\) | |||||||
\(878\) | 7.07107 | + | 7.07107i | 0.238637 | + | 0.238637i | ||||
\(879\) | 20.4853 | + | 28.9706i | 0.690951 | + | 0.977153i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 12.0000i | − | 0.404290i | −0.979356 | − | 0.202145i | \(-0.935209\pi\) | ||
0.979356 | − | 0.202145i | \(-0.0647913\pi\) | |||||||
\(882\) | −50.9203 | − | 106.619i | −1.71458 | − | 3.59004i | ||||
\(883\) | −9.41421 | + | 9.41421i | −0.316814 | + | 0.316814i | −0.847542 | − | 0.530728i | \(-0.821918\pi\) |
0.530728 | + | 0.847542i | \(0.321918\pi\) | |||||||
\(884\) | −8.97056 | −0.301713 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31.7990 | −1.06831 | ||||||||
\(887\) | 16.7279 | − | 16.7279i | 0.561669 | − | 0.561669i | −0.368113 | − | 0.929781i | \(-0.619996\pi\) |
0.929781 | + | 0.368113i | \(0.119996\pi\) | |||||||
\(888\) | −10.3431 | + | 60.2843i | −0.347093 | + | 2.02301i | ||||
\(889\) | − | 12.0000i | − | 0.402467i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.65685 | − | 7.00000i | 0.189512 | − | 0.234509i | ||||
\(892\) | 29.6985 | + | 29.6985i | 0.994379 | + | 0.994379i | ||||
\(893\) | 4.00000 | + | 4.00000i | 0.133855 | + | 0.133855i | ||||
\(894\) | 74.4264 | − | 52.6274i | 2.48919 | − | 1.76012i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 99.2548i | 3.31587i | ||||||||
\(897\) | 9.65685 | + | 1.65685i | 0.322433 | + | 0.0553208i | ||||
\(898\) | −43.7990 | + | 43.7990i | −1.46159 | + | 1.46159i | ||||
\(899\) | 12.6863 | 0.423112 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.9411 | 1.13074 | ||||||||
\(902\) | 1.41421 | − | 1.41421i | 0.0470882 | − | 0.0470882i | ||||
\(903\) | −86.4264 | − | 14.8284i | −2.87609 | − | 0.493459i | ||||
\(904\) | 52.9706i | 1.76177i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.48528 | + | 6.00000i | −0.281905 | + | 0.199337i | ||||
\(907\) | 0.727922 | + | 0.727922i | 0.0241703 | + | 0.0241703i | 0.719089 | − | 0.694918i | \(-0.244560\pi\) |
−0.694918 | + | 0.719089i | \(0.744560\pi\) | |||||||
\(908\) | 45.0122 | + | 45.0122i | 1.49378 | + | 1.49378i | ||||
\(909\) | 4.82843 | − | 13.6569i | 0.160149 | − | 0.452969i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 14.6274i | − | 0.484628i | −0.970198 | − | 0.242314i | \(-0.922094\pi\) | ||
0.970198 | − | 0.242314i | \(-0.0779064\pi\) | |||||||
\(912\) | 4.24264 | − | 24.7279i | 0.140488 | − | 0.818823i | ||||
\(913\) | −4.24264 | + | 4.24264i | −0.140411 | + | 0.140411i | ||||
\(914\) | −56.6274 | −1.87307 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −68.9117 | −2.27691 | ||||||||
\(917\) | −21.6569 | + | 21.6569i | −0.715172 | + | 0.715172i | ||||
\(918\) | 17.3137 | − | 30.9706i | 0.571438 | − | 1.02218i | ||||
\(919\) | − | 2.48528i | − | 0.0819819i | −0.999160 | − | 0.0409909i | \(-0.986949\pi\) | ||
0.999160 | − | 0.0409909i | \(-0.0130515\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.51472 | − | 13.4558i | −0.313521 | − | 0.443385i | ||||
\(922\) | 49.2132 | + | 49.2132i | 1.62075 | + | 1.62075i | ||||
\(923\) | −0.970563 | − | 0.970563i | −0.0319465 | − | 0.0319465i | ||||
\(924\) | 18.4853 | + | 26.1421i | 0.608121 | + | 0.860013i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 49.1127i | 1.61394i | ||||||||
\(927\) | −16.2426 | + | 7.75736i | −0.533478 | + | 0.254785i | ||||
\(928\) | −3.55635 | + | 3.55635i | −0.116743 | + | 0.116743i | ||||
\(929\) | −21.9411 | −0.719865 | −0.359932 | − | 0.932978i | \(-0.617200\pi\) | ||||
−0.359932 | + | 0.932978i | \(0.617200\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 78.7696 | 2.58157 | ||||||||
\(932\) | 38.2843 | − | 38.2843i | 1.25404 | − | 1.25404i | ||||
\(933\) | −6.34315 | + | 36.9706i | −0.207665 | + | 1.21036i | ||||
\(934\) | 24.4853i | 0.801183i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 10.3431 | + | 3.65685i | 0.338076 | + | 0.119528i | ||||
\(937\) | −1.75736 | − | 1.75736i | −0.0574104 | − | 0.0574104i | 0.677819 | − | 0.735229i | \(-0.262925\pi\) |
−0.735229 | + | 0.677819i | \(0.762925\pi\) | |||||||
\(938\) | 63.1127 | + | 63.1127i | 2.06070 | + | 2.06070i | ||||
\(939\) | −26.3431 | + | 18.6274i | −0.859676 | + | 0.607883i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 25.7990i | − | 0.841023i | −0.907287 | − | 0.420512i | \(-0.861851\pi\) | ||
0.907287 | − | 0.420512i | \(-0.138149\pi\) | |||||||
\(942\) | 42.6274 | + | 7.31371i | 1.38888 | + | 0.238293i | ||||
\(943\) | −4.00000 | + | 4.00000i | −0.130258 | + | 0.130258i | ||||
\(944\) | −40.9706 | −1.33348 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25.3137 | 0.823020 | ||||||||
\(947\) | −39.4558 | + | 39.4558i | −1.28214 | + | 1.28214i | −0.342696 | + | 0.939446i | \(0.611340\pi\) |
−0.939446 | + | 0.342696i | \(0.888660\pi\) | |||||||
\(948\) | −5.41421 | − | 0.928932i | −0.175845 | − | 0.0301703i | ||||
\(949\) | − | 8.68629i | − | 0.281969i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.2843 | − | 14.3431i | 0.657763 | − | 0.465108i | ||||
\(952\) | 42.6274 | + | 42.6274i | 1.38156 | + | 1.38156i | ||||
\(953\) | −26.0000 | − | 26.0000i | −0.842223 | − | 0.842223i | 0.146925 | − | 0.989148i | \(-0.453062\pi\) |
−0.989148 | + | 0.146925i | \(0.953062\pi\) | |||||||
\(954\) | −81.9411 | − | 28.9706i | −2.65294 | − | 0.937957i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 52.2843i | 1.69099i | ||||||||
\(957\) | −0.928932 | + | 5.41421i | −0.0300281 | + | 0.175017i | ||||
\(958\) | −64.2843 | + | 64.2843i | −2.07693 | + | 2.07693i | ||||
\(959\) | 65.9411 | 2.12935 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 11.3137 | − | 11.3137i | 0.364769 | − | 0.364769i | ||||
\(963\) | 22.5858 | − | 10.7868i | 0.727817 | − | 0.347600i | ||||
\(964\) | − | 26.6863i | − | 0.859508i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −79.5980 | − | 112.569i | −2.56102 | − | 3.62183i | ||||
\(967\) | 10.9289 | + | 10.9289i | 0.351451 | + | 0.351451i | 0.860649 | − | 0.509198i | \(-0.170058\pi\) |
−0.509198 | + | 0.860649i | \(0.670058\pi\) | |||||||
\(968\) | −3.12132 | − | 3.12132i | −0.100323 | − | 0.100323i | ||||
\(969\) | 13.6569 | + | 19.3137i | 0.438721 | + | 0.620446i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.6274i | 1.11125i | 0.831434 | + | 0.555623i | \(0.187520\pi\) | ||||
−0.831434 | + | 0.555623i | \(0.812480\pi\) | |||||||
\(972\) | −44.8198 | + | 39.4056i | −1.43760 | + | 1.26393i | ||||
\(973\) | −38.1421 | + | 38.1421i | −1.22278 | + | 1.22278i | ||||
\(974\) | 45.7990 | 1.46749 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18.0000 | 0.576166 | ||||||||
\(977\) | −20.0000 | + | 20.0000i | −0.639857 | + | 0.639857i | −0.950520 | − | 0.310663i | \(-0.899449\pi\) |
0.310663 | + | 0.950520i | \(0.399449\pi\) | |||||||
\(978\) | 9.89949 | − | 57.6985i | 0.316551 | − | 1.84499i | ||||
\(979\) | 7.31371i | 0.233747i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00000 | + | 5.65685i | −0.0638551 | + | 0.180609i | ||||
\(982\) | 45.4558 | + | 45.4558i | 1.45055 | + | 1.45055i | ||||
\(983\) | −19.6569 | − | 19.6569i | −0.626956 | − | 0.626956i | 0.320345 | − | 0.947301i | \(-0.396201\pi\) |
−0.947301 | + | 0.320345i | \(0.896201\pi\) | |||||||
\(984\) | −5.17157 | + | 3.65685i | −0.164864 | + | 0.116576i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 21.6569i | 0.689695i | ||||||||
\(987\) | 9.65685 | + | 1.65685i | 0.307381 | + | 0.0527383i | ||||
\(988\) | −10.8284 | + | 10.8284i | −0.344498 | + | 0.344498i | ||||
\(989\) | −71.5980 | −2.27668 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.9411 | 0.951111 | 0.475556 | − | 0.879686i | \(-0.342247\pi\) | ||||
0.475556 | + | 0.879686i | \(0.342247\pi\) | |||||||
\(992\) | −4.48528 | + | 4.48528i | −0.142408 | + | 0.142408i | ||||
\(993\) | 16.4853 | + | 2.82843i | 0.523145 | + | 0.0897574i | ||||
\(994\) | 19.3137i | 0.612594i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 32.4853 | − | 22.9706i | 1.02934 | − | 0.727850i | ||||
\(997\) | −9.55635 | − | 9.55635i | −0.302653 | − | 0.302653i | 0.539398 | − | 0.842051i | \(-0.318652\pi\) |
−0.842051 | + | 0.539398i | \(0.818652\pi\) | |||||||
\(998\) | −23.3137 | − | 23.3137i | −0.737983 | − | 0.737983i | ||||
\(999\) | 11.3137 | + | 40.0000i | 0.357950 | + | 1.26554i |
(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 | 825.2.k.b.782.1 | yes | 4 | |
3.2 | odd | 2 | 825.2.k.h.782.2 | yes | 4 | ||
5.2 | odd | 4 | 825.2.k.a.518.1 | ✓ | 4 | ||
5.3 | odd | 4 | 825.2.k.h.518.2 | yes | 4 | ||
5.4 | even | 2 | 825.2.k.g.782.2 | yes | 4 | ||
15.2 | even | 4 | 825.2.k.g.518.2 | yes | 4 | ||
15.8 | even | 4 | inner | 825.2.k.b.518.1 | yes | 4 | |
15.14 | odd | 2 | 825.2.k.a.782.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.k.a.518.1 | ✓ | 4 | 5.2 | odd | 4 | ||
825.2.k.a.782.1 | yes | 4 | 15.14 | odd | 2 | ||
825.2.k.b.518.1 | yes | 4 | 15.8 | even | 4 | inner | |
825.2.k.b.782.1 | yes | 4 | 1.1 | even | 1 | trivial | |
825.2.k.g.518.2 | yes | 4 | 15.2 | even | 4 | ||
825.2.k.g.782.2 | yes | 4 | 5.4 | even | 2 | ||
825.2.k.h.518.2 | yes | 4 | 5.3 | odd | 4 | ||
825.2.k.h.782.2 | yes | 4 | 3.2 | odd | 2 |