Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(121,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.i (of order \(3\), 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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 391.1 | ||
Root | \(1.32288 - 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.391 |
Dual form | 570.2.i.i.121.1 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | −2.64575 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | −6.29150 | −1.89696 | −0.948480 | − | 0.316838i | \(-0.897379\pi\) | ||||
−0.948480 | + | 0.316838i | \(0.897379\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(14\) | −1.32288 | + | 2.29129i | −0.353553 | + | 0.612372i | ||||
\(15\) | −0.500000 | − | 0.866025i | −0.129099 | − | 0.223607i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.82288 | − | 4.88936i | 0.684648 | − | 1.18584i | −0.288899 | − | 0.957359i | \(-0.593289\pi\) |
0.973547 | − | 0.228486i | \(-0.0733774\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.67712 | − | 4.02334i | −0.384759 | − | 0.923017i | ||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −1.32288 | + | 2.29129i | −0.288675 | + | 0.500000i | ||||
\(22\) | −3.14575 | + | 5.44860i | −0.670676 | + | 1.16165i | ||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | 0.809177 | − | 0.587565i | \(-0.199913\pi\) |
−0.913434 | + | 0.406986i | \(0.866580\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.32288 | + | 2.29129i | 0.250000 | + | 0.433013i | ||||
\(29\) | 1.82288 | + | 3.15731i | 0.338500 | + | 0.586298i | 0.984151 | − | 0.177334i | \(-0.0567473\pi\) |
−0.645651 | + | 0.763632i | \(0.723414\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 7.29150 | 1.30959 | 0.654796 | − | 0.755805i | \(-0.272754\pi\) | ||||
0.654796 | + | 0.755805i | \(0.272754\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −3.14575 | + | 5.44860i | −0.547605 | + | 0.948480i | ||||
\(34\) | −2.82288 | − | 4.88936i | −0.484119 | − | 0.838519i | ||||
\(35\) | −1.32288 | + | 2.29129i | −0.223607 | + | 0.387298i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 8.29150 | 1.36311 | 0.681557 | − | 0.731765i | \(-0.261303\pi\) | ||||
0.681557 | + | 0.731765i | \(0.261303\pi\) | |||||||
\(38\) | −4.32288 | − | 0.559237i | −0.701263 | − | 0.0907202i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | 4.32288 | − | 7.48744i | 0.675120 | − | 1.16934i | −0.301314 | − | 0.953525i | \(-0.597425\pi\) |
0.976434 | − | 0.215817i | \(-0.0692414\pi\) | |||||||
\(42\) | 1.32288 | + | 2.29129i | 0.204124 | + | 0.353553i | ||||
\(43\) | −3.00000 | + | 5.19615i | −0.457496 | + | 0.792406i | −0.998828 | − | 0.0484030i | \(-0.984587\pi\) |
0.541332 | + | 0.840809i | \(0.317920\pi\) | |||||||
\(44\) | 3.14575 | + | 5.44860i | 0.474240 | + | 0.821408i | ||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −6.29150 | − | 10.8972i | −0.917710 | − | 1.58952i | −0.802884 | − | 0.596135i | \(-0.796702\pi\) |
−0.114825 | − | 0.993386i | \(-0.536631\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −2.82288 | − | 4.88936i | −0.395282 | − | 0.684648i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.32288 | + | 4.02334i | 0.319072 | + | 0.552648i | 0.980295 | − | 0.197541i | \(-0.0632956\pi\) |
−0.661223 | + | 0.750189i | \(0.729962\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −3.14575 | + | 5.44860i | −0.424173 | + | 0.734689i | ||||
\(56\) | 2.64575 | 0.353553 | ||||||||
\(57\) | −4.32288 | − | 0.559237i | −0.572579 | − | 0.0740728i | ||||
\(58\) | 3.64575 | 0.478711 | ||||||||
\(59\) | −2.64575 | + | 4.58258i | −0.344447 | + | 0.596601i | −0.985253 | − | 0.171103i | \(-0.945267\pi\) |
0.640806 | + | 0.767703i | \(0.278600\pi\) | |||||||
\(60\) | −0.500000 | + | 0.866025i | −0.0645497 | + | 0.111803i | ||||
\(61\) | −3.46863 | − | 6.00784i | −0.444112 | − | 0.769225i | 0.553878 | − | 0.832598i | \(-0.313147\pi\) |
−0.997990 | + | 0.0633732i | \(0.979814\pi\) | |||||||
\(62\) | 3.64575 | − | 6.31463i | 0.463011 | − | 0.801958i | ||||
\(63\) | 1.32288 | + | 2.29129i | 0.166667 | + | 0.288675i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.14575 | + | 5.44860i | 0.387215 | + | 0.670676i | ||||
\(67\) | 4.82288 | + | 8.35347i | 0.589208 | + | 1.02054i | 0.994336 | + | 0.106278i | \(0.0338935\pi\) |
−0.405128 | + | 0.914260i | \(0.632773\pi\) | |||||||
\(68\) | −5.64575 | −0.684648 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 1.32288 | + | 2.29129i | 0.158114 | + | 0.273861i | ||||
\(71\) | 6.82288 | − | 11.8176i | 0.809726 | − | 1.40249i | −0.103327 | − | 0.994647i | \(-0.532949\pi\) |
0.913054 | − | 0.407840i | \(-0.133718\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −6.82288 | + | 11.8176i | −0.798557 | + | 1.38314i | 0.121998 | + | 0.992530i | \(0.461070\pi\) |
−0.920556 | + | 0.390611i | \(0.872264\pi\) | |||||||
\(74\) | 4.14575 | − | 7.18065i | 0.481934 | − | 0.834734i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −2.64575 | + | 3.46410i | −0.303488 | + | 0.397360i | ||||
\(77\) | 16.6458 | 1.89696 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.64575 | + | 4.58258i | −0.297670 | + | 0.515580i | −0.975603 | − | 0.219544i | \(-0.929543\pi\) |
0.677932 | + | 0.735124i | \(0.262876\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −4.32288 | − | 7.48744i | −0.477382 | − | 0.826849i | ||||
\(83\) | 16.5830 | 1.82022 | 0.910111 | − | 0.414365i | \(-0.135996\pi\) | ||||
0.910111 | + | 0.414365i | \(0.135996\pi\) | |||||||
\(84\) | 2.64575 | 0.288675 | ||||||||
\(85\) | −2.82288 | − | 4.88936i | −0.306184 | − | 0.530326i | ||||
\(86\) | 3.00000 | + | 5.19615i | 0.323498 | + | 0.560316i | ||||
\(87\) | 3.64575 | 0.390866 | ||||||||
\(88\) | 6.29150 | 0.670676 | ||||||||
\(89\) | −6.61438 | − | 11.4564i | −0.701123 | − | 1.21438i | −0.968073 | − | 0.250670i | \(-0.919349\pi\) |
0.266950 | − | 0.963710i | \(-0.413984\pi\) | |||||||
\(90\) | −0.500000 | + | 0.866025i | −0.0527046 | + | 0.0912871i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.500000 | + | 0.866025i | −0.0521286 | + | 0.0902894i | ||||
\(93\) | 3.64575 | − | 6.31463i | 0.378047 | − | 0.654796i | ||||
\(94\) | −12.5830 | −1.29784 | ||||||||
\(95\) | −4.32288 | − | 0.559237i | −0.443518 | − | 0.0573765i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 0.822876 | − | 1.42526i | 0.0835504 | − | 0.144713i | −0.821222 | − | 0.570609i | \(-0.806707\pi\) |
0.904773 | + | 0.425895i | \(0.140041\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.14575 | + | 5.44860i | 0.316160 | + | 0.547605i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −5.93725 | − | 10.2836i | −0.590779 | − | 1.02326i | −0.994128 | − | 0.108213i | \(-0.965487\pi\) |
0.403349 | − | 0.915046i | \(-0.367846\pi\) | |||||||
\(102\) | −5.64575 | −0.559013 | ||||||||
\(103\) | 1.93725 | 0.190883 | 0.0954417 | − | 0.995435i | \(-0.469574\pi\) | ||||
0.0954417 | + | 0.995435i | \(0.469574\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.32288 | + | 2.29129i | 0.129099 | + | 0.223607i | ||||
\(106\) | 4.64575 | 0.451235 | ||||||||
\(107\) | 4.35425 | 0.420941 | 0.210471 | − | 0.977600i | \(-0.432500\pi\) | ||||
0.210471 | + | 0.977600i | \(0.432500\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 0.177124 | − | 0.306788i | 0.0169654 | − | 0.0293850i | −0.857418 | − | 0.514621i | \(-0.827933\pi\) |
0.874383 | + | 0.485236i | \(0.161266\pi\) | |||||||
\(110\) | 3.14575 | + | 5.44860i | 0.299936 | + | 0.519504i | ||||
\(111\) | 4.14575 | − | 7.18065i | 0.393497 | − | 0.681557i | ||||
\(112\) | 1.32288 | − | 2.29129i | 0.125000 | − | 0.216506i | ||||
\(113\) | −5.64575 | −0.531108 | −0.265554 | − | 0.964096i | \(-0.585555\pi\) | ||||
−0.265554 | + | 0.964096i | \(0.585555\pi\) | |||||||
\(114\) | −2.64575 | + | 3.46410i | −0.247797 | + | 0.324443i | ||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 1.82288 | − | 3.15731i | 0.169250 | − | 0.293149i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.64575 | + | 4.58258i | 0.243561 | + | 0.421860i | ||||
\(119\) | −7.46863 | + | 12.9360i | −0.684648 | + | 1.18584i | ||||
\(120\) | 0.500000 | + | 0.866025i | 0.0456435 | + | 0.0790569i | ||||
\(121\) | 28.5830 | 2.59846 | ||||||||
\(122\) | −6.93725 | −0.628069 | ||||||||
\(123\) | −4.32288 | − | 7.48744i | −0.389781 | − | 0.675120i | ||||
\(124\) | −3.64575 | − | 6.31463i | −0.327398 | − | 0.567070i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.64575 | 0.235702 | ||||||||
\(127\) | 5.61438 | + | 9.72439i | 0.498196 | + | 0.862900i | 0.999998 | − | 0.00208239i | \(-0.000662847\pi\) |
−0.501802 | + | 0.864982i | \(0.667330\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 3.00000 | + | 5.19615i | 0.264135 | + | 0.457496i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.85425 | − | 6.67575i | 0.336747 | − | 0.583263i | −0.647072 | − | 0.762429i | \(-0.724007\pi\) |
0.983819 | + | 0.179166i | \(0.0573399\pi\) | |||||||
\(132\) | 6.29150 | 0.547605 | ||||||||
\(133\) | 4.43725 | + | 10.6448i | 0.384759 | + | 0.923017i | ||||
\(134\) | 9.64575 | 0.833266 | ||||||||
\(135\) | −0.500000 | + | 0.866025i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | −2.82288 | + | 4.88936i | −0.242060 | + | 0.419260i | ||||
\(137\) | 6.00000 | + | 10.3923i | 0.512615 | + | 0.887875i | 0.999893 | + | 0.0146279i | \(0.00465636\pi\) |
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(138\) | −0.500000 | + | 0.866025i | −0.0425628 | + | 0.0737210i | ||||
\(139\) | −1.64575 | − | 2.85052i | −0.139591 | − | 0.241778i | 0.787751 | − | 0.615994i | \(-0.211245\pi\) |
−0.927342 | + | 0.374215i | \(0.877912\pi\) | |||||||
\(140\) | 2.64575 | 0.223607 | ||||||||
\(141\) | −12.5830 | −1.05968 | ||||||||
\(142\) | −6.82288 | − | 11.8176i | −0.572563 | − | 0.991708i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.64575 | 0.302763 | ||||||||
\(146\) | 6.82288 | + | 11.8176i | 0.564665 | + | 0.978029i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.14575 | − | 7.18065i | −0.340779 | − | 0.590246i | ||||
\(149\) | 8.11438 | − | 14.0545i | 0.664756 | − | 1.15139i | −0.314596 | − | 0.949226i | \(-0.601869\pi\) |
0.979351 | − | 0.202165i | \(-0.0647977\pi\) | |||||||
\(150\) | −0.500000 | + | 0.866025i | −0.0408248 | + | 0.0707107i | ||||
\(151\) | −20.2288 | −1.64619 | −0.823096 | − | 0.567902i | \(-0.807755\pi\) | ||||
−0.823096 | + | 0.567902i | \(0.807755\pi\) | |||||||
\(152\) | 1.67712 | + | 4.02334i | 0.136033 | + | 0.326336i | ||||
\(153\) | −5.64575 | −0.456432 | ||||||||
\(154\) | 8.32288 | − | 14.4156i | 0.670676 | − | 1.16165i | ||||
\(155\) | 3.64575 | − | 6.31463i | 0.292834 | − | 0.507203i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.43725 | − | 11.1497i | 0.513749 | − | 0.889839i | −0.486124 | − | 0.873890i | \(-0.661590\pi\) |
0.999873 | − | 0.0159492i | \(-0.00507700\pi\) | |||||||
\(158\) | 2.64575 | + | 4.58258i | 0.210485 | + | 0.364570i | ||||
\(159\) | 4.64575 | 0.368432 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 1.32288 | + | 2.29129i | 0.104257 | + | 0.180579i | ||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | −2.70850 | −0.212146 | −0.106073 | − | 0.994358i | \(-0.533828\pi\) | ||||
−0.106073 | + | 0.994358i | \(0.533828\pi\) | |||||||
\(164\) | −8.64575 | −0.675120 | ||||||||
\(165\) | 3.14575 | + | 5.44860i | 0.244896 | + | 0.424173i | ||||
\(166\) | 8.29150 | − | 14.3613i | 0.643545 | − | 1.11465i | ||||
\(167\) | −8.79150 | − | 15.2273i | −0.680307 | − | 1.17833i | −0.974887 | − | 0.222699i | \(-0.928513\pi\) |
0.294580 | − | 0.955627i | \(-0.404820\pi\) | |||||||
\(168\) | 1.32288 | − | 2.29129i | 0.102062 | − | 0.176777i | ||||
\(169\) | 6.50000 | − | 11.2583i | 0.500000 | − | 0.866025i | ||||
\(170\) | −5.64575 | −0.433009 | ||||||||
\(171\) | −2.64575 | + | 3.46410i | −0.202326 | + | 0.264906i | ||||
\(172\) | 6.00000 | 0.457496 | ||||||||
\(173\) | −3.96863 | + | 6.87386i | −0.301729 | + | 0.522610i | −0.976528 | − | 0.215392i | \(-0.930897\pi\) |
0.674799 | + | 0.738002i | \(0.264230\pi\) | |||||||
\(174\) | 1.82288 | − | 3.15731i | 0.138192 | − | 0.239355i | ||||
\(175\) | 1.32288 | + | 2.29129i | 0.100000 | + | 0.173205i | ||||
\(176\) | 3.14575 | − | 5.44860i | 0.237120 | − | 0.410704i | ||||
\(177\) | 2.64575 | + | 4.58258i | 0.198867 | + | 0.344447i | ||||
\(178\) | −13.2288 | −0.991537 | ||||||||
\(179\) | 3.58301 | 0.267806 | 0.133903 | − | 0.990994i | \(-0.457249\pi\) | ||||
0.133903 | + | 0.990994i | \(0.457249\pi\) | |||||||
\(180\) | 0.500000 | + | 0.866025i | 0.0372678 | + | 0.0645497i | ||||
\(181\) | 7.17712 | + | 12.4311i | 0.533471 | + | 0.924000i | 0.999236 | + | 0.0390908i | \(0.0124462\pi\) |
−0.465764 | + | 0.884909i | \(0.654221\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.93725 | −0.512817 | ||||||||
\(184\) | 0.500000 | + | 0.866025i | 0.0368605 | + | 0.0638442i | ||||
\(185\) | 4.14575 | − | 7.18065i | 0.304802 | − | 0.527932i | ||||
\(186\) | −3.64575 | − | 6.31463i | −0.267319 | − | 0.463011i | ||||
\(187\) | −17.7601 | + | 30.7614i | −1.29875 | + | 2.24950i | ||||
\(188\) | −6.29150 | + | 10.8972i | −0.458855 | + | 0.794760i | ||||
\(189\) | 2.64575 | 0.192450 | ||||||||
\(190\) | −2.64575 | + | 3.46410i | −0.191943 | + | 0.251312i | ||||
\(191\) | −4.58301 | −0.331615 | −0.165807 | − | 0.986158i | \(-0.553023\pi\) | ||||
−0.165807 | + | 0.986158i | \(0.553023\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −5.82288 | + | 10.0855i | −0.419140 | + | 0.725971i | −0.995853 | − | 0.0909752i | \(-0.971002\pi\) |
0.576713 | + | 0.816947i | \(0.304335\pi\) | |||||||
\(194\) | −0.822876 | − | 1.42526i | −0.0590790 | − | 0.102328i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.64575 | −0.188502 | −0.0942510 | − | 0.995548i | \(-0.530046\pi\) | ||||
−0.0942510 | + | 0.995548i | \(0.530046\pi\) | |||||||
\(198\) | 6.29150 | 0.447118 | ||||||||
\(199\) | −1.53137 | − | 2.65242i | −0.108556 | − | 0.188025i | 0.806629 | − | 0.591058i | \(-0.201289\pi\) |
−0.915186 | + | 0.403033i | \(0.867956\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | 9.64575 | 0.680359 | ||||||||
\(202\) | −11.8745 | −0.835487 | ||||||||
\(203\) | −4.82288 | − | 8.35347i | −0.338500 | − | 0.586298i | ||||
\(204\) | −2.82288 | + | 4.88936i | −0.197641 | + | 0.342324i | ||||
\(205\) | −4.32288 | − | 7.48744i | −0.301923 | − | 0.522946i | ||||
\(206\) | 0.968627 | − | 1.67771i | 0.0674874 | − | 0.116892i | ||||
\(207\) | −0.500000 | + | 0.866025i | −0.0347524 | + | 0.0601929i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.5516 | + | 25.3128i | 0.729872 | + | 1.75093i | ||||
\(210\) | 2.64575 | 0.182574 | ||||||||
\(211\) | 9.26013 | − | 16.0390i | 0.637494 | − | 1.10417i | −0.348487 | − | 0.937313i | \(-0.613305\pi\) |
0.985981 | − | 0.166858i | \(-0.0533621\pi\) | |||||||
\(212\) | 2.32288 | − | 4.02334i | 0.159536 | − | 0.276324i | ||||
\(213\) | −6.82288 | − | 11.8176i | −0.467496 | − | 0.809726i | ||||
\(214\) | 2.17712 | − | 3.77089i | 0.148825 | − | 0.257773i | ||||
\(215\) | 3.00000 | + | 5.19615i | 0.204598 | + | 0.354375i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −19.2915 | −1.30959 | ||||||||
\(218\) | −0.177124 | − | 0.306788i | −0.0119964 | − | 0.0207783i | ||||
\(219\) | 6.82288 | + | 11.8176i | 0.461047 | + | 0.798557i | ||||
\(220\) | 6.29150 | 0.424173 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.14575 | − | 7.18065i | −0.278245 | − | 0.481934i | ||||
\(223\) | −3.32288 | + | 5.75539i | −0.222516 | + | 0.385409i | −0.955571 | − | 0.294760i | \(-0.904760\pi\) |
0.733055 | + | 0.680169i | \(0.238094\pi\) | |||||||
\(224\) | −1.32288 | − | 2.29129i | −0.0883883 | − | 0.153093i | ||||
\(225\) | −0.500000 | + | 0.866025i | −0.0333333 | + | 0.0577350i | ||||
\(226\) | −2.82288 | + | 4.88936i | −0.187775 | + | 0.325236i | ||||
\(227\) | 22.8118 | 1.51407 | 0.757035 | − | 0.653374i | \(-0.226647\pi\) | ||||
0.757035 | + | 0.653374i | \(0.226647\pi\) | |||||||
\(228\) | 1.67712 | + | 4.02334i | 0.111070 | + | 0.266452i | ||||
\(229\) | 14.7085 | 0.971965 | 0.485982 | − | 0.873969i | \(-0.338462\pi\) | ||||
0.485982 | + | 0.873969i | \(0.338462\pi\) | |||||||
\(230\) | −0.500000 | + | 0.866025i | −0.0329690 | + | 0.0571040i | ||||
\(231\) | 8.32288 | − | 14.4156i | 0.547605 | − | 0.948480i | ||||
\(232\) | −1.82288 | − | 3.15731i | −0.119678 | − | 0.207288i | ||||
\(233\) | −10.2915 | + | 17.8254i | −0.674219 | + | 1.16778i | 0.302478 | + | 0.953156i | \(0.402186\pi\) |
−0.976697 | + | 0.214625i | \(0.931147\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.5830 | −0.820825 | ||||||||
\(236\) | 5.29150 | 0.344447 | ||||||||
\(237\) | 2.64575 | + | 4.58258i | 0.171860 | + | 0.297670i | ||||
\(238\) | 7.46863 | + | 12.9360i | 0.484119 | + | 0.838519i | ||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −0.708497 | − | 1.22715i | −0.0456383 | − | 0.0790479i | 0.842304 | − | 0.539003i | \(-0.181199\pi\) |
−0.887942 | + | 0.459955i | \(0.847866\pi\) | |||||||
\(242\) | 14.2915 | − | 24.7536i | 0.918693 | − | 1.59122i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −3.46863 | + | 6.00784i | −0.222056 | + | 0.384612i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.64575 | −0.551233 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.29150 | −0.463011 | ||||||||
\(249\) | 8.29150 | − | 14.3613i | 0.525453 | − | 0.910111i | ||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | 1.29150 | + | 2.23695i | 0.0815189 | + | 0.141195i | 0.903903 | − | 0.427738i | \(-0.140690\pi\) |
−0.822384 | + | 0.568933i | \(0.807356\pi\) | |||||||
\(252\) | 1.32288 | − | 2.29129i | 0.0833333 | − | 0.144338i | ||||
\(253\) | 3.14575 | + | 5.44860i | 0.197772 | + | 0.342551i | ||||
\(254\) | 11.2288 | 0.704555 | ||||||||
\(255\) | −5.64575 | −0.353551 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −3.00000 | − | 5.19615i | −0.187135 | − | 0.324127i | 0.757159 | − | 0.653231i | \(-0.226587\pi\) |
−0.944294 | + | 0.329104i | \(0.893253\pi\) | |||||||
\(258\) | 6.00000 | 0.373544 | ||||||||
\(259\) | −21.9373 | −1.36311 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.82288 | − | 3.15731i | 0.112833 | − | 0.195433i | ||||
\(262\) | −3.85425 | − | 6.67575i | −0.238116 | − | 0.412429i | ||||
\(263\) | −2.14575 | + | 3.71655i | −0.132313 | + | 0.229172i | −0.924568 | − | 0.381018i | \(-0.875574\pi\) |
0.792255 | + | 0.610190i | \(0.208907\pi\) | |||||||
\(264\) | 3.14575 | − | 5.44860i | 0.193608 | − | 0.335338i | ||||
\(265\) | 4.64575 | 0.285386 | ||||||||
\(266\) | 11.4373 | + | 1.47960i | 0.701263 | + | 0.0907202i | ||||
\(267\) | −13.2288 | −0.809587 | ||||||||
\(268\) | 4.82288 | − | 8.35347i | 0.294604 | − | 0.510269i | ||||
\(269\) | −6.46863 | + | 11.2040i | −0.394399 | + | 0.683119i | −0.993024 | − | 0.117910i | \(-0.962381\pi\) |
0.598625 | + | 0.801029i | \(0.295714\pi\) | |||||||
\(270\) | 0.500000 | + | 0.866025i | 0.0304290 | + | 0.0527046i | ||||
\(271\) | −5.93725 | + | 10.2836i | −0.360662 | + | 0.624686i | −0.988070 | − | 0.154005i | \(-0.950783\pi\) |
0.627408 | + | 0.778691i | \(0.284116\pi\) | |||||||
\(272\) | 2.82288 | + | 4.88936i | 0.171162 | + | 0.296461i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.0000 | 0.724947 | ||||||||
\(275\) | 3.14575 | + | 5.44860i | 0.189696 | + | 0.328563i | ||||
\(276\) | 0.500000 | + | 0.866025i | 0.0300965 | + | 0.0521286i | ||||
\(277\) | −8.00000 | −0.480673 | −0.240337 | − | 0.970690i | \(-0.577258\pi\) | ||||
−0.240337 | + | 0.970690i | \(0.577258\pi\) | |||||||
\(278\) | −3.29150 | −0.197411 | ||||||||
\(279\) | −3.64575 | − | 6.31463i | −0.218265 | − | 0.378047i | ||||
\(280\) | 1.32288 | − | 2.29129i | 0.0790569 | − | 0.136931i | ||||
\(281\) | 9.90588 | + | 17.1575i | 0.590935 | + | 1.02353i | 0.994107 | + | 0.108406i | \(0.0345745\pi\) |
−0.403171 | + | 0.915124i | \(0.632092\pi\) | |||||||
\(282\) | −6.29150 | + | 10.8972i | −0.374654 | + | 0.648919i | ||||
\(283\) | −9.93725 | + | 17.2118i | −0.590708 | + | 1.02314i | 0.403429 | + | 0.915011i | \(0.367818\pi\) |
−0.994137 | + | 0.108126i | \(0.965515\pi\) | |||||||
\(284\) | −13.6458 | −0.809726 | ||||||||
\(285\) | −2.64575 | + | 3.46410i | −0.156721 | + | 0.205196i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.4373 | + | 19.8099i | −0.675120 | + | 1.16934i | ||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | −7.43725 | − | 12.8817i | −0.437486 | − | 0.757747i | ||||
\(290\) | 1.82288 | − | 3.15731i | 0.107043 | − | 0.185404i | ||||
\(291\) | −0.822876 | − | 1.42526i | −0.0482378 | − | 0.0835504i | ||||
\(292\) | 13.6458 | 0.798557 | ||||||||
\(293\) | −9.35425 | −0.546481 | −0.273241 | − | 0.961946i | \(-0.588095\pi\) | ||||
−0.273241 | + | 0.961946i | \(0.588095\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.64575 | + | 4.58258i | 0.154042 | + | 0.266808i | ||||
\(296\) | −8.29150 | −0.481934 | ||||||||
\(297\) | 6.29150 | 0.365070 | ||||||||
\(298\) | −8.11438 | − | 14.0545i | −0.470053 | − | 0.814156i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.500000 | + | 0.866025i | 0.0288675 | + | 0.0500000i | ||||
\(301\) | 7.93725 | − | 13.7477i | 0.457496 | − | 0.792406i | ||||
\(302\) | −10.1144 | + | 17.5186i | −0.582017 | + | 1.00808i | ||||
\(303\) | −11.8745 | −0.682173 | ||||||||
\(304\) | 4.32288 | + | 0.559237i | 0.247934 | + | 0.0320744i | ||||
\(305\) | −6.93725 | −0.397226 | ||||||||
\(306\) | −2.82288 | + | 4.88936i | −0.161373 | + | 0.279506i | ||||
\(307\) | 12.7601 | − | 22.1012i | 0.728259 | − | 1.26138i | −0.229359 | − | 0.973342i | \(-0.573663\pi\) |
0.957618 | − | 0.288040i | \(-0.0930036\pi\) | |||||||
\(308\) | −8.32288 | − | 14.4156i | −0.474240 | − | 0.821408i | ||||
\(309\) | 0.968627 | − | 1.67771i | 0.0551033 | − | 0.0954417i | ||||
\(310\) | −3.64575 | − | 6.31463i | −0.207065 | − | 0.358647i | ||||
\(311\) | −25.1660 | −1.42703 | −0.713517 | − | 0.700638i | \(-0.752899\pi\) | ||||
−0.713517 | + | 0.700638i | \(0.752899\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.29150 | + | 2.23695i | 0.0730000 | + | 0.126440i | 0.900215 | − | 0.435446i | \(-0.143409\pi\) |
−0.827215 | + | 0.561886i | \(0.810076\pi\) | |||||||
\(314\) | −6.43725 | − | 11.1497i | −0.363275 | − | 0.629211i | ||||
\(315\) | 2.64575 | 0.149071 | ||||||||
\(316\) | 5.29150 | 0.297670 | ||||||||
\(317\) | −2.03137 | − | 3.51844i | −0.114093 | − | 0.197615i | 0.803324 | − | 0.595543i | \(-0.203063\pi\) |
−0.917417 | + | 0.397927i | \(0.869730\pi\) | |||||||
\(318\) | 2.32288 | − | 4.02334i | 0.130260 | − | 0.225618i | ||||
\(319\) | −11.4686 | − | 19.8642i | −0.642120 | − | 1.11218i | ||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | 2.17712 | − | 3.77089i | 0.121515 | − | 0.210471i | ||||
\(322\) | 2.64575 | 0.147442 | ||||||||
\(323\) | −24.4059 | − | 3.15731i | −1.35798 | − | 0.175678i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.35425 | + | 2.34563i | −0.0750049 | + | 0.129912i | ||||
\(327\) | −0.177124 | − | 0.306788i | −0.00979500 | − | 0.0169654i | ||||
\(328\) | −4.32288 | + | 7.48744i | −0.238691 | + | 0.413425i | ||||
\(329\) | 16.6458 | + | 28.8313i | 0.917710 | + | 1.58952i | ||||
\(330\) | 6.29150 | 0.346336 | ||||||||
\(331\) | −18.6458 | −1.02486 | −0.512432 | − | 0.858728i | \(-0.671255\pi\) | ||||
−0.512432 | + | 0.858728i | \(0.671255\pi\) | |||||||
\(332\) | −8.29150 | − | 14.3613i | −0.455055 | − | 0.788179i | ||||
\(333\) | −4.14575 | − | 7.18065i | −0.227186 | − | 0.393497i | ||||
\(334\) | −17.5830 | −0.962099 | ||||||||
\(335\) | 9.64575 | 0.527004 | ||||||||
\(336\) | −1.32288 | − | 2.29129i | −0.0721688 | − | 0.125000i | ||||
\(337\) | −3.35425 | + | 5.80973i | −0.182718 | + | 0.316476i | −0.942805 | − | 0.333345i | \(-0.891823\pi\) |
0.760087 | + | 0.649821i | \(0.225156\pi\) | |||||||
\(338\) | −6.50000 | − | 11.2583i | −0.353553 | − | 0.612372i | ||||
\(339\) | −2.82288 | + | 4.88936i | −0.153318 | + | 0.265554i | ||||
\(340\) | −2.82288 | + | 4.88936i | −0.153092 | + | 0.265163i | ||||
\(341\) | −45.8745 | −2.48424 | ||||||||
\(342\) | 1.67712 | + | 4.02334i | 0.0906885 | + | 0.217557i | ||||
\(343\) | 18.5203 | 1.00000 | ||||||||
\(344\) | 3.00000 | − | 5.19615i | 0.161749 | − | 0.280158i | ||||
\(345\) | −0.500000 | + | 0.866025i | −0.0269191 | + | 0.0466252i | ||||
\(346\) | 3.96863 | + | 6.87386i | 0.213355 | + | 0.369541i | ||||
\(347\) | −6.29150 | + | 10.8972i | −0.337746 | + | 0.584992i | −0.984008 | − | 0.178122i | \(-0.942998\pi\) |
0.646263 | + | 0.763115i | \(0.276331\pi\) | |||||||
\(348\) | −1.82288 | − | 3.15731i | −0.0977164 | − | 0.169250i | ||||
\(349\) | 17.0627 | 0.913348 | 0.456674 | − | 0.889634i | \(-0.349041\pi\) | ||||
0.456674 | + | 0.889634i | \(0.349041\pi\) | |||||||
\(350\) | 2.64575 | 0.141421 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.14575 | − | 5.44860i | −0.167669 | − | 0.290411i | ||||
\(353\) | −7.06275 | −0.375912 | −0.187956 | − | 0.982177i | \(-0.560186\pi\) | ||||
−0.187956 | + | 0.982177i | \(0.560186\pi\) | |||||||
\(354\) | 5.29150 | 0.281240 | ||||||||
\(355\) | −6.82288 | − | 11.8176i | −0.362121 | − | 0.627211i | ||||
\(356\) | −6.61438 | + | 11.4564i | −0.350561 | + | 0.607190i | ||||
\(357\) | 7.46863 | + | 12.9360i | 0.395282 | + | 0.684648i | ||||
\(358\) | 1.79150 | − | 3.10297i | 0.0946839 | − | 0.163997i | ||||
\(359\) | −2.46863 | + | 4.27579i | −0.130289 | + | 0.225667i | −0.923788 | − | 0.382904i | \(-0.874924\pi\) |
0.793499 | + | 0.608572i | \(0.208257\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −13.3745 | + | 13.4953i | −0.703921 | + | 0.710278i | ||||
\(362\) | 14.3542 | 0.754443 | ||||||||
\(363\) | 14.2915 | − | 24.7536i | 0.750109 | − | 1.29923i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.82288 | + | 11.8176i | 0.357126 | + | 0.618560i | ||||
\(366\) | −3.46863 | + | 6.00784i | −0.181308 | + | 0.314035i | ||||
\(367\) | 0.937254 | + | 1.62337i | 0.0489243 | + | 0.0847393i | 0.889450 | − | 0.457032i | \(-0.151087\pi\) |
−0.840526 | + | 0.541771i | \(0.817754\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −8.64575 | −0.450080 | ||||||||
\(370\) | −4.14575 | − | 7.18065i | −0.215527 | − | 0.373304i | ||||
\(371\) | −6.14575 | − | 10.6448i | −0.319072 | − | 0.552648i | ||||
\(372\) | −7.29150 | −0.378047 | ||||||||
\(373\) | 18.2915 | 0.947098 | 0.473549 | − | 0.880767i | \(-0.342973\pi\) | ||||
0.473549 | + | 0.880767i | \(0.342973\pi\) | |||||||
\(374\) | 17.7601 | + | 30.7614i | 0.918354 | + | 1.59064i | ||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | 6.29150 | + | 10.8972i | 0.324459 | + | 0.561980i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.32288 | − | 2.29129i | 0.0680414 | − | 0.117851i | ||||
\(379\) | 17.8745 | 0.918152 | 0.459076 | − | 0.888397i | \(-0.348181\pi\) | ||||
0.459076 | + | 0.888397i | \(0.348181\pi\) | |||||||
\(380\) | 1.67712 | + | 4.02334i | 0.0860347 | + | 0.206393i | ||||
\(381\) | 11.2288 | 0.575267 | ||||||||
\(382\) | −2.29150 | + | 3.96900i | −0.117243 | + | 0.203072i | ||||
\(383\) | 18.2915 | − | 31.6818i | 0.934652 | − | 1.61886i | 0.159399 | − | 0.987214i | \(-0.449044\pi\) |
0.775253 | − | 0.631651i | \(-0.217622\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | 8.32288 | − | 14.4156i | 0.424173 | − | 0.734689i | ||||
\(386\) | 5.82288 | + | 10.0855i | 0.296377 | + | 0.513339i | ||||
\(387\) | 6.00000 | 0.304997 | ||||||||
\(388\) | −1.64575 | −0.0835504 | ||||||||
\(389\) | 8.76013 | + | 15.1730i | 0.444156 | + | 0.769301i | 0.997993 | − | 0.0633241i | \(-0.0201702\pi\) |
−0.553837 | + | 0.832625i | \(0.686837\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.64575 | −0.285518 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.85425 | − | 6.67575i | −0.194421 | − | 0.336747i | ||||
\(394\) | −1.32288 | + | 2.29129i | −0.0666455 | + | 0.115433i | ||||
\(395\) | 2.64575 | + | 4.58258i | 0.133122 | + | 0.230574i | ||||
\(396\) | 3.14575 | − | 5.44860i | 0.158080 | − | 0.273803i | ||||
\(397\) | 13.7288 | − | 23.7789i | 0.689027 | − | 1.19343i | −0.283127 | − | 0.959083i | \(-0.591372\pi\) |
0.972153 | − | 0.234346i | \(-0.0752950\pi\) | |||||||
\(398\) | −3.06275 | −0.153522 | ||||||||
\(399\) | 11.4373 | + | 1.47960i | 0.572579 | + | 0.0740728i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −3.00000 | + | 5.19615i | −0.149813 | + | 0.259483i | −0.931158 | − | 0.364615i | \(-0.881200\pi\) |
0.781345 | + | 0.624099i | \(0.214534\pi\) | |||||||
\(402\) | 4.82288 | − | 8.35347i | 0.240543 | − | 0.416633i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5.93725 | + | 10.2836i | −0.295389 | + | 0.511629i | ||||
\(405\) | 0.500000 | + | 0.866025i | 0.0248452 | + | 0.0430331i | ||||
\(406\) | −9.64575 | −0.478711 | ||||||||
\(407\) | −52.1660 | −2.58577 | ||||||||
\(408\) | 2.82288 | + | 4.88936i | 0.139753 | + | 0.242060i | ||||
\(409\) | 9.20850 | + | 15.9496i | 0.455331 | + | 0.788656i | 0.998707 | − | 0.0508330i | \(-0.0161876\pi\) |
−0.543376 | + | 0.839489i | \(0.682854\pi\) | |||||||
\(410\) | −8.64575 | −0.426983 | ||||||||
\(411\) | 12.0000 | 0.591916 | ||||||||
\(412\) | −0.968627 | − | 1.67771i | −0.0477208 | − | 0.0826549i | ||||
\(413\) | 7.00000 | − | 12.1244i | 0.344447 | − | 0.596601i | ||||
\(414\) | 0.500000 | + | 0.866025i | 0.0245737 | + | 0.0425628i | ||||
\(415\) | 8.29150 | − | 14.3613i | 0.407014 | − | 0.704969i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.29150 | −0.161186 | ||||||||
\(418\) | 27.1974 | + | 3.51844i | 1.33027 | + | 0.172093i | ||||
\(419\) | 38.1660 | 1.86453 | 0.932266 | − | 0.361774i | \(-0.117829\pi\) | ||||
0.932266 | + | 0.361774i | \(0.117829\pi\) | |||||||
\(420\) | 1.32288 | − | 2.29129i | 0.0645497 | − | 0.111803i | ||||
\(421\) | 9.46863 | − | 16.4001i | 0.461473 | − | 0.799294i | −0.537562 | − | 0.843224i | \(-0.680655\pi\) |
0.999035 | + | 0.0439302i | \(0.0139879\pi\) | |||||||
\(422\) | −9.26013 | − | 16.0390i | −0.450776 | − | 0.780767i | ||||
\(423\) | −6.29150 | + | 10.8972i | −0.305903 | + | 0.529840i | ||||
\(424\) | −2.32288 | − | 4.02334i | −0.112809 | − | 0.195391i | ||||
\(425\) | −5.64575 | −0.273859 | ||||||||
\(426\) | −13.6458 | −0.661139 | ||||||||
\(427\) | 9.17712 | + | 15.8952i | 0.444112 | + | 0.769225i | ||||
\(428\) | −2.17712 | − | 3.77089i | −0.105235 | − | 0.182273i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.00000 | 0.289346 | ||||||||
\(431\) | −14.1771 | − | 24.5555i | −0.682888 | − | 1.18280i | −0.974096 | − | 0.226137i | \(-0.927390\pi\) |
0.291207 | − | 0.956660i | \(-0.405943\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −2.46863 | − | 4.27579i | −0.118635 | − | 0.205481i | 0.800592 | − | 0.599210i | \(-0.204518\pi\) |
−0.919227 | + | 0.393728i | \(0.871185\pi\) | |||||||
\(434\) | −9.64575 | + | 16.7069i | −0.463011 | + | 0.801958i | ||||
\(435\) | 1.82288 | − | 3.15731i | 0.0874002 | − | 0.151382i | ||||
\(436\) | −0.354249 | −0.0169654 | ||||||||
\(437\) | −2.64575 | + | 3.46410i | −0.126563 | + | 0.165710i | ||||
\(438\) | 13.6458 | 0.652019 | ||||||||
\(439\) | 1.53137 | − | 2.65242i | 0.0730884 | − | 0.126593i | −0.827165 | − | 0.561959i | \(-0.810048\pi\) |
0.900253 | + | 0.435366i | \(0.143381\pi\) | |||||||
\(440\) | 3.14575 | − | 5.44860i | 0.149968 | − | 0.259752i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.5314 | + | 21.7050i | 0.595384 | + | 1.03123i | 0.993493 | + | 0.113896i | \(0.0363332\pi\) |
−0.398109 | + | 0.917338i | \(0.630333\pi\) | |||||||
\(444\) | −8.29150 | −0.393497 | ||||||||
\(445\) | −13.2288 | −0.627103 | ||||||||
\(446\) | 3.32288 | + | 5.75539i | 0.157343 | + | 0.272526i | ||||
\(447\) | −8.11438 | − | 14.0545i | −0.383797 | − | 0.664756i | ||||
\(448\) | −2.64575 | −0.125000 | ||||||||
\(449\) | −17.3542 | −0.818998 | −0.409499 | − | 0.912311i | \(-0.634296\pi\) | ||||
−0.409499 | + | 0.912311i | \(0.634296\pi\) | |||||||
\(450\) | 0.500000 | + | 0.866025i | 0.0235702 | + | 0.0408248i | ||||
\(451\) | −27.1974 | + | 47.1073i | −1.28067 | + | 2.21819i | ||||
\(452\) | 2.82288 | + | 4.88936i | 0.132777 | + | 0.229976i | ||||
\(453\) | −10.1144 | + | 17.5186i | −0.475215 | + | 0.823096i | ||||
\(454\) | 11.4059 | − | 19.7556i | 0.535305 | − | 0.927175i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.32288 | + | 0.559237i | 0.202437 | + | 0.0261887i | ||||
\(457\) | 1.77124 | 0.0828553 | 0.0414276 | − | 0.999142i | \(-0.486809\pi\) | ||||
0.0414276 | + | 0.999142i | \(0.486809\pi\) | |||||||
\(458\) | 7.35425 | − | 12.7379i | 0.343641 | − | 0.595204i | ||||
\(459\) | −2.82288 | + | 4.88936i | −0.131761 | + | 0.228216i | ||||
\(460\) | 0.500000 | + | 0.866025i | 0.0233126 | + | 0.0403786i | ||||
\(461\) | 17.5830 | − | 30.4547i | 0.818922 | − | 1.41841i | −0.0875548 | − | 0.996160i | \(-0.527905\pi\) |
0.906477 | − | 0.422255i | \(-0.138761\pi\) | |||||||
\(462\) | −8.32288 | − | 14.4156i | −0.387215 | − | 0.670676i | ||||
\(463\) | 29.3542 | 1.36421 | 0.682104 | − | 0.731255i | \(-0.261065\pi\) | ||||
0.682104 | + | 0.731255i | \(0.261065\pi\) | |||||||
\(464\) | −3.64575 | −0.169250 | ||||||||
\(465\) | −3.64575 | − | 6.31463i | −0.169068 | − | 0.292834i | ||||
\(466\) | 10.2915 | + | 17.8254i | 0.476745 | + | 0.825746i | ||||
\(467\) | 15.5203 | 0.718192 | 0.359096 | − | 0.933301i | \(-0.383085\pi\) | ||||
0.359096 | + | 0.933301i | \(0.383085\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.7601 | − | 22.1012i | −0.589208 | − | 1.02054i | ||||
\(470\) | −6.29150 | + | 10.8972i | −0.290205 | + | 0.502650i | ||||
\(471\) | −6.43725 | − | 11.1497i | −0.296613 | − | 0.513749i | ||||
\(472\) | 2.64575 | − | 4.58258i | 0.121781 | − | 0.210930i | ||||
\(473\) | 18.8745 | − | 32.6916i | 0.867851 | − | 1.50316i | ||||
\(474\) | 5.29150 | 0.243047 | ||||||||
\(475\) | −2.64575 | + | 3.46410i | −0.121395 | + | 0.158944i | ||||
\(476\) | 14.9373 | 0.684648 | ||||||||
\(477\) | 2.32288 | − | 4.02334i | 0.106357 | − | 0.184216i | ||||
\(478\) | −12.0000 | + | 20.7846i | −0.548867 | + | 0.950666i | ||||
\(479\) | −2.46863 | − | 4.27579i | −0.112794 | − | 0.195366i | 0.804102 | − | 0.594492i | \(-0.202647\pi\) |
−0.916896 | + | 0.399126i | \(0.869313\pi\) | |||||||
\(480\) | 0.500000 | − | 0.866025i | 0.0228218 | − | 0.0395285i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.41699 | −0.0645423 | ||||||||
\(483\) | 2.64575 | 0.120386 | ||||||||
\(484\) | −14.2915 | − | 24.7536i | −0.649614 | − | 1.12516i | ||||
\(485\) | −0.822876 | − | 1.42526i | −0.0373649 | − | 0.0647178i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 20.6458 | 0.935548 | 0.467774 | − | 0.883848i | \(-0.345056\pi\) | ||||
0.467774 | + | 0.883848i | \(0.345056\pi\) | |||||||
\(488\) | 3.46863 | + | 6.00784i | 0.157017 | + | 0.271962i | ||||
\(489\) | −1.35425 | + | 2.34563i | −0.0612412 | + | 0.106073i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.7288 | + | 34.1712i | −0.890346 | + | 1.54213i | −0.0508857 | + | 0.998704i | \(0.516204\pi\) |
−0.839461 | + | 0.543421i | \(0.817129\pi\) | |||||||
\(492\) | −4.32288 | + | 7.48744i | −0.194890 | + | 0.337560i | ||||
\(493\) | 20.5830 | 0.927012 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.29150 | 0.282782 | ||||||||
\(496\) | −3.64575 | + | 6.31463i | −0.163699 | + | 0.283535i | ||||
\(497\) | −18.0516 | + | 31.2663i | −0.809726 | + | 1.40249i | ||||
\(498\) | −8.29150 | − | 14.3613i | −0.371551 | − | 0.643545i | ||||
\(499\) | −3.67712 | + | 6.36897i | −0.164611 | + | 0.285114i | −0.936517 | − | 0.350622i | \(-0.885970\pi\) |
0.771906 | + | 0.635736i | \(0.219303\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | −17.5830 | −0.785551 | ||||||||
\(502\) | 2.58301 | 0.115285 | ||||||||
\(503\) | −13.3745 | − | 23.1653i | −0.596340 | − | 1.03289i | −0.993356 | − | 0.115079i | \(-0.963288\pi\) |
0.397016 | − | 0.917811i | \(-0.370046\pi\) | |||||||
\(504\) | −1.32288 | − | 2.29129i | −0.0589256 | − | 0.102062i | ||||
\(505\) | −11.8745 | −0.528409 | ||||||||
\(506\) | 6.29150 | 0.279691 | ||||||||
\(507\) | −6.50000 | − | 11.2583i | −0.288675 | − | 0.500000i | ||||
\(508\) | 5.61438 | − | 9.72439i | 0.249098 | − | 0.431450i | ||||
\(509\) | 1.35425 | + | 2.34563i | 0.0600260 | + | 0.103968i | 0.894477 | − | 0.447114i | \(-0.147548\pi\) |
−0.834451 | + | 0.551082i | \(0.814215\pi\) | |||||||
\(510\) | −2.82288 | + | 4.88936i | −0.124999 | + | 0.216505i | ||||
\(511\) | 18.0516 | − | 31.2663i | 0.798557 | − | 1.38314i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.67712 | + | 4.02334i | 0.0740468 | + | 0.177635i | ||||
\(514\) | −6.00000 | −0.264649 | ||||||||
\(515\) | 0.968627 | − | 1.67771i | 0.0426828 | − | 0.0739288i | ||||
\(516\) | 3.00000 | − | 5.19615i | 0.132068 | − | 0.228748i | ||||
\(517\) | 39.5830 | + | 68.5598i | 1.74086 | + | 3.01526i | ||||
\(518\) | −10.9686 | + | 18.9982i | −0.481934 | + | 0.834734i | ||||
\(519\) | 3.96863 | + | 6.87386i | 0.174203 | + | 0.301729i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.4575 | 0.983882 | 0.491941 | − | 0.870629i | \(-0.336288\pi\) | ||||
0.491941 | + | 0.870629i | \(0.336288\pi\) | |||||||
\(522\) | −1.82288 | − | 3.15731i | −0.0797851 | − | 0.138192i | ||||
\(523\) | 6.88562 | + | 11.9262i | 0.301087 | + | 0.521498i | 0.976382 | − | 0.216049i | \(-0.0693171\pi\) |
−0.675295 | + | 0.737547i | \(0.735984\pi\) | |||||||
\(524\) | −7.70850 | −0.336747 | ||||||||
\(525\) | 2.64575 | 0.115470 | ||||||||
\(526\) | 2.14575 | + | 3.71655i | 0.0935592 | + | 0.162049i | ||||
\(527\) | 20.5830 | − | 35.6508i | 0.896610 | − | 1.55297i | ||||
\(528\) | −3.14575 | − | 5.44860i | −0.136901 | − | 0.237120i | ||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | 2.32288 | − | 4.02334i | 0.100899 | − | 0.174763i | ||||
\(531\) | 5.29150 | 0.229632 | ||||||||
\(532\) | 7.00000 | − | 9.16515i | 0.303488 | − | 0.397360i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −6.61438 | + | 11.4564i | −0.286232 | + | 0.495769i | ||||
\(535\) | 2.17712 | − | 3.77089i | 0.0941253 | − | 0.163030i | ||||
\(536\) | −4.82288 | − | 8.35347i | −0.208316 | − | 0.360815i | ||||
\(537\) | 1.79150 | − | 3.10297i | 0.0773090 | − | 0.133903i | ||||
\(538\) | 6.46863 | + | 11.2040i | 0.278882 | + | 0.483038i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −8.93725 | − | 15.4798i | −0.384243 | − | 0.665528i | 0.607421 | − | 0.794380i | \(-0.292204\pi\) |
−0.991664 | + | 0.128852i | \(0.958871\pi\) | |||||||
\(542\) | 5.93725 | + | 10.2836i | 0.255027 | + | 0.441720i | ||||
\(543\) | 14.3542 | 0.616000 | ||||||||
\(544\) | 5.64575 | 0.242060 | ||||||||
\(545\) | −0.177124 | − | 0.306788i | −0.00758717 | − | 0.0131414i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.35425 | − | 16.2020i | −0.399959 | − | 0.692749i | 0.593762 | − | 0.804641i | \(-0.297642\pi\) |
−0.993720 | + | 0.111892i | \(0.964309\pi\) | |||||||
\(548\) | 6.00000 | − | 10.3923i | 0.256307 | − | 0.443937i | ||||
\(549\) | −3.46863 | + | 6.00784i | −0.148037 | + | 0.256408i | ||||
\(550\) | 6.29150 | 0.268271 | ||||||||
\(551\) | 9.64575 | − | 12.6293i | 0.410923 | − | 0.538024i | ||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 7.00000 | − | 12.1244i | 0.297670 | − | 0.515580i | ||||
\(554\) | −4.00000 | + | 6.92820i | −0.169944 | + | 0.294351i | ||||
\(555\) | −4.14575 | − | 7.18065i | −0.175977 | − | 0.304802i | ||||
\(556\) | −1.64575 | + | 2.85052i | −0.0697954 | + | 0.120889i | ||||
\(557\) | 12.2601 | + | 21.2352i | 0.519478 | + | 0.899763i | 0.999744 | + | 0.0226397i | \(0.00720704\pi\) |
−0.480265 | + | 0.877123i | \(0.659460\pi\) | |||||||
\(558\) | −7.29150 | −0.308674 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.32288 | − | 2.29129i | −0.0559017 | − | 0.0968246i | ||||
\(561\) | 17.7601 | + | 30.7614i | 0.749833 | + | 1.29875i | ||||
\(562\) | 19.8118 | 0.835709 | ||||||||
\(563\) | 21.4170 | 0.902619 | 0.451309 | − | 0.892368i | \(-0.350957\pi\) | ||||
0.451309 | + | 0.892368i | \(0.350957\pi\) | |||||||
\(564\) | 6.29150 | + | 10.8972i | 0.264920 | + | 0.458855i | ||||
\(565\) | −2.82288 | + | 4.88936i | −0.118759 | + | 0.205697i | ||||
\(566\) | 9.93725 | + | 17.2118i | 0.417694 | + | 0.723467i | ||||
\(567\) | 1.32288 | − | 2.29129i | 0.0555556 | − | 0.0962250i | ||||
\(568\) | −6.82288 | + | 11.8176i | −0.286282 | + | 0.495854i | ||||
\(569\) | 5.35425 | 0.224462 | 0.112231 | − | 0.993682i | \(-0.464200\pi\) | ||||
0.112231 | + | 0.993682i | \(0.464200\pi\) | |||||||
\(570\) | 1.67712 | + | 4.02334i | 0.0702470 | + | 0.168519i | ||||
\(571\) | 26.4575 | 1.10721 | 0.553606 | − | 0.832779i | \(-0.313251\pi\) | ||||
0.553606 | + | 0.832779i | \(0.313251\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.29150 | + | 3.96900i | −0.0957289 | + | 0.165807i | ||||
\(574\) | 11.4373 | + | 19.8099i | 0.477382 | + | 0.826849i | ||||
\(575\) | −0.500000 | + | 0.866025i | −0.0208514 | + | 0.0361158i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 2.93725 | 0.122279 | 0.0611397 | − | 0.998129i | \(-0.480526\pi\) | ||||
0.0611397 | + | 0.998129i | \(0.480526\pi\) | |||||||
\(578\) | −14.8745 | −0.618698 | ||||||||
\(579\) | 5.82288 | + | 10.0855i | 0.241990 | + | 0.419140i | ||||
\(580\) | −1.82288 | − | 3.15731i | −0.0756908 | − | 0.131100i | ||||
\(581\) | −43.8745 | −1.82022 | ||||||||
\(582\) | −1.64575 | −0.0682186 | ||||||||
\(583\) | −14.6144 | − | 25.3128i | −0.605266 | − | 1.04835i | ||||
\(584\) | 6.82288 | − | 11.8176i | 0.282333 | − | 0.489014i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.67712 | + | 8.10102i | −0.193210 | + | 0.334650i | ||||
\(587\) | −16.3542 | + | 28.3264i | −0.675012 | + | 1.16916i | 0.301453 | + | 0.953481i | \(0.402528\pi\) |
−0.976465 | + | 0.215674i | \(0.930805\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.2288 | − | 29.3362i | −0.503877 | − | 1.20878i | ||||
\(590\) | 5.29150 | 0.217848 | ||||||||
\(591\) | −1.32288 | + | 2.29129i | −0.0544158 | + | 0.0942510i | ||||
\(592\) | −4.14575 | + | 7.18065i | −0.170389 | + | 0.295123i | ||||
\(593\) | 17.8229 | + | 30.8701i | 0.731898 | + | 1.26768i | 0.956071 | + | 0.293135i | \(0.0946985\pi\) |
−0.224173 | + | 0.974549i | \(0.571968\pi\) | |||||||
\(594\) | 3.14575 | − | 5.44860i | 0.129072 | − | 0.223559i | ||||
\(595\) | 7.46863 | + | 12.9360i | 0.306184 | + | 0.530326i | ||||
\(596\) | −16.2288 | −0.664756 | ||||||||
\(597\) | −3.06275 | −0.125350 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.76013 | + | 15.1730i | 0.357929 | + | 0.619952i | 0.987615 | − | 0.156899i | \(-0.0501496\pi\) |
−0.629686 | + | 0.776850i | \(0.716816\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −16.2915 | −0.664544 | −0.332272 | − | 0.943184i | \(-0.607815\pi\) | ||||
−0.332272 | + | 0.943184i | \(0.607815\pi\) | |||||||
\(602\) | −7.93725 | − | 13.7477i | −0.323498 | − | 0.560316i | ||||
\(603\) | 4.82288 | − | 8.35347i | 0.196403 | − | 0.340179i | ||||
\(604\) | 10.1144 | + | 17.5186i | 0.411548 | + | 0.712822i | ||||
\(605\) | 14.2915 | − | 24.7536i | 0.581032 | − | 1.00638i | ||||
\(606\) | −5.93725 | + | 10.2836i | −0.241184 | + | 0.417744i | ||||
\(607\) | −7.22876 | −0.293406 | −0.146703 | − | 0.989181i | \(-0.546866\pi\) | ||||
−0.146703 | + | 0.989181i | \(0.546866\pi\) | |||||||
\(608\) | 2.64575 | − | 3.46410i | 0.107299 | − | 0.140488i | ||||
\(609\) | −9.64575 | −0.390866 | ||||||||
\(610\) | −3.46863 | + | 6.00784i | −0.140441 | + | 0.243250i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.82288 | + | 4.88936i | 0.114108 | + | 0.197641i | ||||
\(613\) | 14.4373 | − | 25.0061i | 0.583115 | − | 1.00999i | −0.411992 | − | 0.911187i | \(-0.635167\pi\) |
0.995108 | − | 0.0987978i | \(-0.0314997\pi\) | |||||||
\(614\) | −12.7601 | − | 22.1012i | −0.514957 | − | 0.891932i | ||||
\(615\) | −8.64575 | −0.348630 | ||||||||
\(616\) | −16.6458 | −0.670676 | ||||||||
\(617\) | 1.29150 | + | 2.23695i | 0.0519939 | + | 0.0900561i | 0.890851 | − | 0.454296i | \(-0.150109\pi\) |
−0.838857 | + | 0.544352i | \(0.816776\pi\) | |||||||
\(618\) | −0.968627 | − | 1.67771i | −0.0389639 | − | 0.0674874i | ||||
\(619\) | −18.0627 | −0.726003 | −0.363002 | − | 0.931789i | \(-0.618248\pi\) | ||||
−0.363002 | + | 0.931789i | \(0.618248\pi\) | |||||||
\(620\) | −7.29150 | −0.292834 | ||||||||
\(621\) | 0.500000 | + | 0.866025i | 0.0200643 | + | 0.0347524i | ||||
\(622\) | −12.5830 | + | 21.7944i | −0.504533 | + | 0.873876i | ||||
\(623\) | 17.5000 | + | 30.3109i | 0.701123 | + | 1.21438i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 2.58301 | 0.103238 | ||||||||
\(627\) | 27.1974 | + | 3.51844i | 1.08616 | + | 0.140513i | ||||
\(628\) | −12.8745 | −0.513749 | ||||||||
\(629\) | 23.4059 | − | 40.5402i | 0.933254 | − | 1.61644i | ||||
\(630\) | 1.32288 | − | 2.29129i | 0.0527046 | − | 0.0912871i | ||||
\(631\) | −8.17712 | − | 14.1632i | −0.325526 | − | 0.563828i | 0.656093 | − | 0.754680i | \(-0.272208\pi\) |
−0.981619 | + | 0.190853i | \(0.938875\pi\) | |||||||
\(632\) | 2.64575 | − | 4.58258i | 0.105242 | − | 0.182285i | ||||
\(633\) | −9.26013 | − | 16.0390i | −0.368057 | − | 0.637494i | ||||
\(634\) | −4.06275 | −0.161352 | ||||||||
\(635\) | 11.2288 | 0.445600 | ||||||||
\(636\) | −2.32288 | − | 4.02334i | −0.0921080 | − | 0.159536i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −22.9373 | −0.908095 | ||||||||
\(639\) | −13.6458 | −0.539818 | ||||||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 10.6458 | − | 18.4390i | 0.420482 | − | 0.728296i | −0.575505 | − | 0.817798i | \(-0.695194\pi\) |
0.995987 | + | 0.0895025i | \(0.0285277\pi\) | |||||||
\(642\) | −2.17712 | − | 3.77089i | −0.0859242 | − | 0.148825i | ||||
\(643\) | −0.594119 | + | 1.02904i | −0.0234298 | + | 0.0405816i | −0.877503 | − | 0.479572i | \(-0.840792\pi\) |
0.854073 | + | 0.520154i | \(0.174125\pi\) | |||||||
\(644\) | 1.32288 | − | 2.29129i | 0.0521286 | − | 0.0902894i | ||||
\(645\) | 6.00000 | 0.236250 | ||||||||
\(646\) | −14.9373 | + | 19.5575i | −0.587698 | + | 0.769478i | ||||
\(647\) | 36.8745 | 1.44969 | 0.724843 | − | 0.688914i | \(-0.241912\pi\) | ||||
0.724843 | + | 0.688914i | \(0.241912\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 16.6458 | − | 28.8313i | 0.653403 | − | 1.13173i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.64575 | + | 16.7069i | −0.378047 | + | 0.654796i | ||||
\(652\) | 1.35425 | + | 2.34563i | 0.0530365 | + | 0.0918619i | ||||
\(653\) | 25.9373 | 1.01500 | 0.507502 | − | 0.861651i | \(-0.330569\pi\) | ||||
0.507502 | + | 0.861651i | \(0.330569\pi\) | |||||||
\(654\) | −0.354249 | −0.0138522 | ||||||||
\(655\) | −3.85425 | − | 6.67575i | −0.150598 | − | 0.260843i | ||||
\(656\) | 4.32288 | + | 7.48744i | 0.168780 | + | 0.292335i | ||||
\(657\) | 13.6458 | 0.532371 | ||||||||
\(658\) | 33.2915 | 1.29784 | ||||||||
\(659\) | −4.79150 | − | 8.29913i | −0.186650 | − | 0.323288i | 0.757481 | − | 0.652857i | \(-0.226430\pi\) |
−0.944131 | + | 0.329569i | \(0.893097\pi\) | |||||||
\(660\) | 3.14575 | − | 5.44860i | 0.122448 | − | 0.212087i | ||||
\(661\) | 17.2915 | + | 29.9498i | 0.672562 | + | 1.16491i | 0.977175 | + | 0.212435i | \(0.0681393\pi\) |
−0.304614 | + | 0.952476i | \(0.598527\pi\) | |||||||
\(662\) | −9.32288 | + | 16.1477i | −0.362344 | + | 0.627598i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.5830 | −0.643545 | ||||||||
\(665\) | 11.4373 | + | 1.47960i | 0.443518 | + | 0.0573765i | ||||
\(666\) | −8.29150 | −0.321289 | ||||||||
\(667\) | 1.82288 | − | 3.15731i | 0.0705820 | − | 0.122252i | ||||
\(668\) | −8.79150 | + | 15.2273i | −0.340153 | + | 0.589163i | ||||
\(669\) | 3.32288 | + | 5.75539i | 0.128470 | + | 0.222516i | ||||
\(670\) | 4.82288 | − | 8.35347i | 0.186324 | − | 0.322723i | ||||
\(671\) | 21.8229 | + | 37.7983i | 0.842463 | + | 1.45919i | ||||
\(672\) | −2.64575 | −0.102062 | ||||||||
\(673\) | −37.8745 | −1.45995 | −0.729977 | − | 0.683471i | \(-0.760469\pi\) | ||||
−0.729977 | + | 0.683471i | \(0.760469\pi\) | |||||||
\(674\) | 3.35425 | + | 5.80973i | 0.129201 | + | 0.223782i | ||||
\(675\) | 0.500000 | + | 0.866025i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | −14.7712 | −0.567705 | −0.283853 | − | 0.958868i | \(-0.591613\pi\) | ||||
−0.283853 | + | 0.958868i | \(0.591613\pi\) | |||||||
\(678\) | 2.82288 | + | 4.88936i | 0.108412 | + | 0.187775i | ||||
\(679\) | −2.17712 | + | 3.77089i | −0.0835504 | + | 0.144713i | ||||
\(680\) | 2.82288 | + | 4.88936i | 0.108252 | + | 0.187499i | ||||
\(681\) | 11.4059 | − | 19.7556i | 0.437074 | − | 0.757035i | ||||
\(682\) | −22.9373 | + | 39.7285i | −0.878313 | + | 1.52128i | ||||
\(683\) | 13.0627 | 0.499832 | 0.249916 | − | 0.968268i | \(-0.419597\pi\) | ||||
0.249916 | + | 0.968268i | \(0.419597\pi\) | |||||||
\(684\) | 4.32288 | + | 0.559237i | 0.165289 | + | 0.0213830i | ||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | 9.26013 | − | 16.0390i | 0.353553 | − | 0.612372i | ||||
\(687\) | 7.35425 | − | 12.7379i | 0.280582 | − | 0.485982i | ||||
\(688\) | −3.00000 | − | 5.19615i | −0.114374 | − | 0.198101i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.500000 | + | 0.866025i | 0.0190347 | + | 0.0329690i | ||||
\(691\) | 33.8118 | 1.28626 | 0.643130 | − | 0.765757i | \(-0.277635\pi\) | ||||
0.643130 | + | 0.765757i | \(0.277635\pi\) | |||||||
\(692\) | 7.93725 | 0.301729 | ||||||||
\(693\) | −8.32288 | − | 14.4156i | −0.316160 | − | 0.547605i | ||||
\(694\) | 6.29150 | + | 10.8972i | 0.238822 | + | 0.413652i | ||||
\(695\) | −3.29150 | −0.124854 | ||||||||
\(696\) | −3.64575 | −0.138192 | ||||||||
\(697\) | −24.4059 | − | 42.2722i | −0.924439 | − | 1.60117i | ||||
\(698\) | 8.53137 | − | 14.7768i | 0.322917 | − | 0.559309i | ||||
\(699\) | 10.2915 | + | 17.8254i | 0.389260 | + | 0.674219i | ||||
\(700\) | 1.32288 | − | 2.29129i | 0.0500000 | − | 0.0866025i | ||||
\(701\) | −22.1660 | + | 38.3927i | −0.837199 | + | 1.45007i | 0.0550290 | + | 0.998485i | \(0.482475\pi\) |
−0.892228 | + | 0.451586i | \(0.850858\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.9059 | − | 33.3595i | −0.524470 | − | 1.25818i | ||||
\(704\) | −6.29150 | −0.237120 | ||||||||
\(705\) | −6.29150 | + | 10.8972i | −0.236952 | + | 0.410412i | ||||
\(706\) | −3.53137 | + | 6.11652i | −0.132905 | + | 0.230198i | ||||
\(707\) | 15.7085 | + | 27.2079i | 0.590779 | + | 1.02326i | ||||
\(708\) | 2.64575 | − | 4.58258i | 0.0994334 | − | 0.172224i | ||||
\(709\) | −4.53137 | − | 7.84857i | −0.170179 | − | 0.294759i | 0.768303 | − | 0.640086i | \(-0.221101\pi\) |
−0.938482 | + | 0.345327i | \(0.887768\pi\) | |||||||
\(710\) | −13.6458 | −0.512116 | ||||||||
\(711\) | 5.29150 | 0.198447 | ||||||||
\(712\) | 6.61438 | + | 11.4564i | 0.247884 | + | 0.429348i | ||||
\(713\) | −3.64575 | − | 6.31463i | −0.136534 | − | 0.236485i | ||||
\(714\) | 14.9373 | 0.559013 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.79150 | − | 3.10297i | −0.0669516 | − | 0.115964i | ||||
\(717\) | −12.0000 | + | 20.7846i | −0.448148 | + | 0.776215i | ||||
\(718\) | 2.46863 | + | 4.27579i | 0.0921283 | + | 0.159571i | ||||
\(719\) | 6.35425 | − | 11.0059i | 0.236973 | − | 0.410450i | −0.722871 | − | 0.690983i | \(-0.757178\pi\) |
0.959844 | + | 0.280533i | \(0.0905112\pi\) | |||||||
\(720\) | 0.500000 | − | 0.866025i | 0.0186339 | − | 0.0322749i | ||||
\(721\) | −5.12549 | −0.190883 | ||||||||
\(722\) | 5.00000 | + | 18.3303i | 0.186081 | + | 0.682183i | ||||
\(723\) | −1.41699 | −0.0526986 | ||||||||
\(724\) | 7.17712 | − | 12.4311i | 0.266736 | − | 0.462000i | ||||
\(725\) | 1.82288 | − | 3.15731i | 0.0676999 | − | 0.117260i | ||||
\(726\) | −14.2915 | − | 24.7536i | −0.530407 | − | 0.918693i | ||||
\(727\) | −5.93725 | + | 10.2836i | −0.220201 | + | 0.381399i | −0.954869 | − | 0.297028i | \(-0.904005\pi\) |
0.734668 | + | 0.678427i | \(0.237338\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 13.6458 | 0.505052 | ||||||||
\(731\) | 16.9373 | + | 29.3362i | 0.626447 | + | 1.08504i | ||||
\(732\) | 3.46863 | + | 6.00784i | 0.128204 | + | 0.222056i | ||||
\(733\) | −12.2915 | −0.453997 | −0.226999 | − | 0.973895i | \(-0.572891\pi\) | ||||
−0.226999 | + | 0.973895i | \(0.572891\pi\) | |||||||
\(734\) | 1.87451 | 0.0691893 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.500000 | − | 0.866025i | 0.0184302 | − | 0.0319221i | ||||
\(737\) | −30.3431 | − | 52.5559i | −1.11770 | − | 1.93592i | ||||
\(738\) | −4.32288 | + | 7.48744i | −0.159127 | + | 0.275616i | ||||
\(739\) | −19.4889 | + | 33.7557i | −0.716910 | + | 1.24173i | 0.245308 | + | 0.969445i | \(0.421111\pi\) |
−0.962218 | + | 0.272280i | \(0.912222\pi\) | |||||||
\(740\) | −8.29150 | −0.304802 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.2915 | −0.451235 | ||||||||
\(743\) | 20.7915 | − | 36.0119i | 0.762766 | − | 1.32115i | −0.178653 | − | 0.983912i | \(-0.557174\pi\) |
0.941419 | − | 0.337238i | \(-0.109493\pi\) | |||||||
\(744\) | −3.64575 | + | 6.31463i | −0.133660 | + | 0.231505i | ||||
\(745\) | −8.11438 | − | 14.0545i | −0.297288 | − | 0.514918i | ||||
\(746\) | 9.14575 | − | 15.8409i | 0.334850 | − | 0.579977i | ||||
\(747\) | −8.29150 | − | 14.3613i | −0.303370 | − | 0.525453i | ||||
\(748\) | 35.5203 | 1.29875 | ||||||||
\(749\) | −11.5203 | −0.420941 | ||||||||
\(750\) | 0.500000 | + | 0.866025i | 0.0182574 | + | 0.0316228i | ||||
\(751\) | 22.0000 | + | 38.1051i | 0.802791 | + | 1.39048i | 0.917772 | + | 0.397108i | \(0.129986\pi\) |
−0.114981 | + | 0.993368i | \(0.536681\pi\) | |||||||
\(752\) | 12.5830 | 0.458855 | ||||||||
\(753\) | 2.58301 | 0.0941299 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.1144 | + | 17.5186i | −0.368100 | + | 0.637568i | ||||
\(756\) | −1.32288 | − | 2.29129i | −0.0481125 | − | 0.0833333i | ||||
\(757\) | −11.7288 | + | 20.3148i | −0.426289 | + | 0.738354i | −0.996540 | − | 0.0831165i | \(-0.973513\pi\) |
0.570251 | + | 0.821471i | \(0.306846\pi\) | |||||||
\(758\) | 8.93725 | − | 15.4798i | 0.324616 | − | 0.562251i | ||||
\(759\) | 6.29150 | 0.228367 | ||||||||
\(760\) | 4.32288 | + | 0.559237i | 0.156807 | + | 0.0202857i | ||||
\(761\) | −20.5203 | −0.743859 | −0.371929 | − | 0.928261i | \(-0.621304\pi\) | ||||
−0.371929 | + | 0.928261i | \(0.621304\pi\) | |||||||
\(762\) | 5.61438 | − | 9.72439i | 0.203387 | − | 0.352277i | ||||
\(763\) | −0.468627 | + | 0.811686i | −0.0169654 | + | 0.0293850i | ||||
\(764\) | 2.29150 | + | 3.96900i | 0.0829037 | + | 0.143593i | ||||
\(765\) | −2.82288 | + | 4.88936i | −0.102061 | + | 0.176775i | ||||
\(766\) | −18.2915 | − | 31.6818i | −0.660899 | − | 1.14471i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −9.64575 | − | 16.7069i | −0.347835 | − | 0.602467i | 0.638030 | − | 0.770012i | \(-0.279750\pi\) |
−0.985865 | + | 0.167544i | \(0.946416\pi\) | |||||||
\(770\) | −8.32288 | − | 14.4156i | −0.299936 | − | 0.519504i | ||||
\(771\) | −6.00000 | −0.216085 | ||||||||
\(772\) | 11.6458 | 0.419140 | ||||||||
\(773\) | 0.968627 | + | 1.67771i | 0.0348391 | + | 0.0603431i | 0.882919 | − | 0.469525i | \(-0.155575\pi\) |
−0.848080 | + | 0.529868i | \(0.822241\pi\) | |||||||
\(774\) | 3.00000 | − | 5.19615i | 0.107833 | − | 0.186772i | ||||
\(775\) | −3.64575 | − | 6.31463i | −0.130959 | − | 0.226828i | ||||
\(776\) | −0.822876 | + | 1.42526i | −0.0295395 | + | 0.0511639i | ||||
\(777\) | −10.9686 | + | 18.9982i | −0.393497 | + | 0.681557i | ||||
\(778\) | 17.5203 | 0.628132 | ||||||||
\(779\) | −37.3745 | − | 4.83502i | −1.33908 | − | 0.173233i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.9261 | + | 74.3503i | −1.53602 | + | 2.66046i | ||||
\(782\) | −2.82288 | + | 4.88936i | −0.100946 | + | 0.174843i | ||||
\(783\) | −1.82288 | − | 3.15731i | −0.0651443 | − | 0.112833i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.43725 | − | 11.1497i | −0.229755 | − | 0.397948i | ||||
\(786\) | −7.70850 | −0.274953 | ||||||||
\(787\) | 8.10326 | 0.288850 | 0.144425 | − | 0.989516i | \(-0.453867\pi\) | ||||
0.144425 | + | 0.989516i | \(0.453867\pi\) | |||||||
\(788\) | 1.32288 | + | 2.29129i | 0.0471255 | + | 0.0816237i | ||||
\(789\) | 2.14575 | + | 3.71655i | 0.0763908 | + | 0.132313i | ||||
\(790\) | 5.29150 | 0.188263 | ||||||||
\(791\) | 14.9373 | 0.531108 | ||||||||
\(792\) | −3.14575 | − | 5.44860i | −0.111779 | − | 0.193608i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −13.7288 | − | 23.7789i | −0.487215 | − | 0.843882i | ||||
\(795\) | 2.32288 | − | 4.02334i | 0.0823839 | − | 0.142693i | ||||
\(796\) | −1.53137 | + | 2.65242i | −0.0542781 | + | 0.0940124i | ||||
\(797\) | −37.6863 | −1.33492 | −0.667458 | − | 0.744647i | \(-0.732618\pi\) | ||||
−0.667458 | + | 0.744647i | \(0.732618\pi\) | |||||||
\(798\) | 7.00000 | − | 9.16515i | 0.247797 | − | 0.324443i | ||||
\(799\) | −71.0405 | −2.51323 | ||||||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | −6.61438 | + | 11.4564i | −0.233708 | + | 0.404793i | ||||
\(802\) | 3.00000 | + | 5.19615i | 0.105934 | + | 0.183483i | ||||
\(803\) | 42.9261 | − | 74.3503i | 1.51483 | − | 2.62376i | ||||
\(804\) | −4.82288 | − | 8.35347i | −0.170090 | − | 0.294604i | ||||
\(805\) | 2.64575 | 0.0932505 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.46863 | + | 11.2040i | 0.227706 | + | 0.394399i | ||||
\(808\) | 5.93725 | + | 10.2836i | 0.208872 | + | 0.361777i | ||||
\(809\) | −24.0000 | −0.843795 | −0.421898 | − | 0.906644i | \(-0.638636\pi\) | ||||
−0.421898 | + | 0.906644i | \(0.638636\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −13.6771 | − | 23.6895i | −0.480269 | − | 0.831850i | 0.519475 | − | 0.854486i | \(-0.326128\pi\) |
−0.999744 | + | 0.0226357i | \(0.992794\pi\) | |||||||
\(812\) | −4.82288 | + | 8.35347i | −0.169250 | + | 0.293149i | ||||
\(813\) | 5.93725 | + | 10.2836i | 0.208229 | + | 0.360662i | ||||
\(814\) | −26.0830 | + | 45.1771i | −0.914209 | + | 1.58346i | ||||
\(815\) | −1.35425 | + | 2.34563i | −0.0474373 | + | 0.0821637i | ||||
\(816\) | 5.64575 | 0.197641 | ||||||||
\(817\) | 25.9373 | + | 3.35542i | 0.907430 | + | 0.117391i | ||||
\(818\) | 18.4170 | 0.643935 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.32288 | + | 7.48744i | −0.150961 | + | 0.261473i | ||||
\(821\) | 10.2915 | + | 17.8254i | 0.359176 | + | 0.622111i | 0.987823 | − | 0.155579i | \(-0.0497245\pi\) |
−0.628647 | + | 0.777690i | \(0.716391\pi\) | |||||||
\(822\) | 6.00000 | − | 10.3923i | 0.209274 | − | 0.362473i | ||||
\(823\) | −15.6144 | − | 27.0449i | −0.544283 | − | 0.942726i | −0.998652 | − | 0.0519121i | \(-0.983468\pi\) |
0.454369 | − | 0.890814i | \(-0.349865\pi\) | |||||||
\(824\) | −1.93725 | −0.0674874 | ||||||||
\(825\) | 6.29150 | 0.219042 | ||||||||
\(826\) | −7.00000 | − | 12.1244i | −0.243561 | − | 0.421860i | ||||
\(827\) | −15.5314 | − | 26.9011i | −0.540079 | − | 0.935444i | −0.998899 | − | 0.0469147i | \(-0.985061\pi\) |
0.458820 | − | 0.888529i | \(-0.348272\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −52.4575 | −1.82192 | −0.910962 | − | 0.412489i | \(-0.864659\pi\) | ||||
−0.910962 | + | 0.412489i | \(0.864659\pi\) | |||||||
\(830\) | −8.29150 | − | 14.3613i | −0.287802 | − | 0.498488i | ||||
\(831\) | −4.00000 | + | 6.92820i | −0.138758 | + | 0.240337i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.64575 | + | 2.85052i | −0.0569877 | + | 0.0987056i | ||||
\(835\) | −17.5830 | −0.608485 | ||||||||
\(836\) | 16.6458 | − | 21.7944i | 0.575705 | − | 0.753775i | ||||
\(837\) | −7.29150 | −0.252031 | ||||||||
\(838\) | 19.0830 | − | 33.0527i | 0.659211 | − | 1.14179i | ||||
\(839\) | −7.93725 | + | 13.7477i | −0.274024 | + | 0.474624i | −0.969889 | − | 0.243549i | \(-0.921688\pi\) |
0.695864 | + | 0.718173i | \(0.255022\pi\) | |||||||
\(840\) | −1.32288 | − | 2.29129i | −0.0456435 | − | 0.0790569i | ||||
\(841\) | 7.85425 | − | 13.6040i | 0.270836 | − | 0.469102i | ||||
\(842\) | −9.46863 | − | 16.4001i | −0.326310 | − | 0.565186i | ||||
\(843\) | 19.8118 | 0.682353 | ||||||||
\(844\) | −18.5203 | −0.637494 | ||||||||
\(845\) | −6.50000 | − | 11.2583i | −0.223607 | − | 0.387298i | ||||
\(846\) | 6.29150 | + | 10.8972i | 0.216306 | + | 0.374654i | ||||
\(847\) | −75.6235 | −2.59846 | ||||||||
\(848\) | −4.64575 | −0.159536 | ||||||||
\(849\) | 9.93725 | + | 17.2118i | 0.341046 | + | 0.590708i | ||||
\(850\) | −2.82288 | + | 4.88936i | −0.0968238 | + | 0.167704i | ||||
\(851\) | −4.14575 | − | 7.18065i | −0.142115 | − | 0.246150i | ||||
\(852\) | −6.82288 | + | 11.8176i | −0.233748 | + | 0.404863i | ||||
\(853\) | 7.70850 | − | 13.3515i | 0.263934 | − | 0.457147i | −0.703350 | − | 0.710844i | \(-0.748313\pi\) |
0.967284 | + | 0.253697i | \(0.0816466\pi\) | |||||||
\(854\) | 18.3542 | 0.628069 | ||||||||
\(855\) | 1.67712 | + | 4.02334i | 0.0573564 | + | 0.137595i | ||||
\(856\) | −4.35425 | −0.148825 | ||||||||
\(857\) | 6.00000 | − | 10.3923i | 0.204956 | − | 0.354994i | −0.745163 | − | 0.666883i | \(-0.767628\pi\) |
0.950119 | + | 0.311888i | \(0.100962\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.26013 | + | 10.8429i | 0.213593 | + | 0.369954i | 0.952836 | − | 0.303485i | \(-0.0981501\pi\) |
−0.739243 | + | 0.673438i | \(0.764817\pi\) | |||||||
\(860\) | 3.00000 | − | 5.19615i | 0.102299 | − | 0.177187i | ||||
\(861\) | 11.4373 | + | 19.8099i | 0.389781 | + | 0.675120i | ||||
\(862\) | −28.3542 | −0.965750 | ||||||||
\(863\) | 20.4170 | 0.695003 | 0.347501 | − | 0.937680i | \(-0.387030\pi\) | ||||
0.347501 | + | 0.937680i | \(0.387030\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 3.96863 | + | 6.87386i | 0.134937 | + | 0.233718i | ||||
\(866\) | −4.93725 | −0.167775 | ||||||||
\(867\) | −14.8745 | −0.505165 | ||||||||
\(868\) | 9.64575 | + | 16.7069i | 0.327398 | + | 0.567070i | ||||
\(869\) | 16.6458 | − | 28.8313i | 0.564668 | − | 0.978034i | ||||
\(870\) | −1.82288 | − | 3.15731i | −0.0618013 | − | 0.107043i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.177124 | + | 0.306788i | −0.00599819 | + | 0.0103892i | ||||
\(873\) | −1.64575 | −0.0557002 | ||||||||
\(874\) | 1.67712 | + | 4.02334i | 0.0567296 | + | 0.136091i | ||||
\(875\) | 2.64575 | 0.0894427 | ||||||||
\(876\) | 6.82288 | − | 11.8176i | 0.230524 | − | 0.399279i | ||||
\(877\) | 22.1458 | − | 38.3576i | 0.747809 | − | 1.29524i | −0.201062 | − | 0.979579i | \(-0.564439\pi\) |
0.948871 | − | 0.315664i | \(-0.102227\pi\) | |||||||
\(878\) | −1.53137 | − | 2.65242i | −0.0516813 | − | 0.0895147i | ||||
\(879\) | −4.67712 | + | 8.10102i | −0.157755 | + | 0.273241i | ||||
\(880\) | −3.14575 | − | 5.44860i | −0.106043 | − | 0.183672i | ||||
\(881\) | −35.3542 | −1.19111 | −0.595557 | − | 0.803313i | \(-0.703069\pi\) | ||||
−0.595557 | + | 0.803313i | \(0.703069\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.0516 | + | 39.9266i | 0.775749 | + | 1.34364i | 0.934372 | + | 0.356298i | \(0.115961\pi\) |
−0.158623 | + | 0.987339i | \(0.550706\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.29150 | 0.177872 | ||||||||
\(886\) | 25.0627 | 0.841999 | ||||||||
\(887\) | 3.22876 | + | 5.59237i | 0.108411 | + | 0.187773i | 0.915127 | − | 0.403166i | \(-0.132090\pi\) |
−0.806716 | + | 0.590940i | \(0.798757\pi\) | |||||||
\(888\) | −4.14575 | + | 7.18065i | −0.139122 | + | 0.240967i | ||||
\(889\) | −14.8542 | − | 25.7283i | −0.498196 | − | 0.862900i | ||||
\(890\) | −6.61438 | + | 11.4564i | −0.221714 | + | 0.384021i | ||||
\(891\) | 3.14575 | − | 5.44860i | 0.105387 | − | 0.182535i | ||||
\(892\) | 6.64575 | 0.222516 | ||||||||
\(893\) | −33.2915 | + | 43.5888i | −1.11406 | + | 1.45864i | ||||
\(894\) | −16.2288 | −0.542771 | ||||||||
\(895\) | 1.79150 | − | 3.10297i | 0.0598833 | − | 0.103721i | ||||
\(896\) | −1.32288 | + | 2.29129i | −0.0441942 | + | 0.0765466i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.67712 | + | 15.0292i | −0.289559 | + | 0.501532i | ||||
\(899\) | 13.2915 | + | 23.0216i | 0.443296 | + | 0.767812i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 26.2288 | 0.873807 | ||||||||
\(902\) | 27.1974 | + | 47.1073i | 0.905574 | + | 1.56850i | ||||
\(903\) | −7.93725 | − | 13.7477i | −0.264135 | − | 0.457496i | ||||
\(904\) | 5.64575 | 0.187775 | ||||||||
\(905\) | 14.3542 | 0.477151 | ||||||||
\(906\) | 10.1144 | + | 17.5186i | 0.336028 | + | 0.582017i | ||||
\(907\) | 8.29150 | − | 14.3613i | 0.275315 | − | 0.476859i | −0.694900 | − | 0.719107i | \(-0.744551\pi\) |
0.970215 | + | 0.242247i | \(0.0778846\pi\) | |||||||
\(908\) | −11.4059 | − | 19.7556i | −0.378517 | − | 0.655611i | ||||
\(909\) | −5.93725 | + | 10.2836i | −0.196926 | + | 0.341086i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.2915 | 0.440367 | 0.220184 | − | 0.975458i | \(-0.429334\pi\) | ||||
0.220184 | + | 0.975458i | \(0.429334\pi\) | |||||||
\(912\) | 2.64575 | − | 3.46410i | 0.0876096 | − | 0.114708i | ||||
\(913\) | −104.332 | −3.45289 | ||||||||
\(914\) | 0.885622 | − | 1.53394i | 0.0292938 | − | 0.0507383i | ||||
\(915\) | −3.46863 | + | 6.00784i | −0.114669 | + | 0.198613i | ||||
\(916\) | −7.35425 | − | 12.7379i | −0.242991 | − | 0.420873i | ||||
\(917\) | −10.1974 | + | 17.6624i | −0.336747 | + | 0.583263i | ||||
\(918\) | 2.82288 | + | 4.88936i | 0.0931688 | + | 0.161373i | ||||
\(919\) | 10.2288 | 0.337416 | 0.168708 | − | 0.985666i | \(-0.446041\pi\) | ||||
0.168708 | + | 0.985666i | \(0.446041\pi\) | |||||||
\(920\) | 1.00000 | 0.0329690 | ||||||||
\(921\) | −12.7601 | − | 22.1012i | −0.420461 | − | 0.728259i | ||||
\(922\) | −17.5830 | − | 30.4547i | −0.579065 | − | 1.00297i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −16.6458 | −0.547605 | ||||||||
\(925\) | −4.14575 | − | 7.18065i | −0.136311 | − | 0.236098i | ||||
\(926\) | 14.6771 | − | 25.4215i | 0.482320 | − | 0.835403i | ||||
\(927\) | −0.968627 | − | 1.67771i | −0.0318139 | − | 0.0551033i | ||||
\(928\) | −1.82288 | + | 3.15731i | −0.0598388 | + | 0.103644i | ||||
\(929\) | 15.9686 | − | 27.6585i | 0.523914 | − | 0.907445i | −0.475699 | − | 0.879608i | \(-0.657805\pi\) |
0.999612 | − | 0.0278368i | \(-0.00886189\pi\) | |||||||
\(930\) | −7.29150 | −0.239098 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20.5830 | 0.674219 | ||||||||
\(933\) | −12.5830 | + | 21.7944i | −0.411949 | + | 0.713517i | ||||
\(934\) | 7.76013 | − | 13.4409i | 0.253919 | − | 0.439801i | ||||
\(935\) | 17.7601 | + | 30.7614i | 0.580818 | + | 1.00601i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.4686 | − | 31.9886i | −0.603344 | − | 1.04502i | −0.992311 | − | 0.123770i | \(-0.960501\pi\) |
0.388967 | − | 0.921252i | \(-0.372832\pi\) | |||||||
\(938\) | −25.5203 | −0.833266 | ||||||||
\(939\) | 2.58301 | 0.0842932 | ||||||||
\(940\) | 6.29150 | + | 10.8972i | 0.205206 | + | 0.355428i | ||||
\(941\) | −23.1144 | − | 40.0353i | −0.753507 | − | 1.30511i | −0.946113 | − | 0.323837i | \(-0.895027\pi\) |
0.192606 | − | 0.981276i | \(-0.438306\pi\) | |||||||
\(942\) | −12.8745 | −0.419474 | ||||||||
\(943\) | −8.64575 | −0.281544 | ||||||||
\(944\) | −2.64575 | − | 4.58258i | −0.0861119 | − | 0.149150i | ||||
\(945\) | 1.32288 | − | 2.29129i | 0.0430331 | − | 0.0745356i | ||||
\(946\) | −18.8745 | − | 32.6916i | −0.613663 | − | 1.06290i | ||||
\(947\) | 21.6974 | − | 37.5810i | 0.705070 | − | 1.22122i | −0.261596 | − | 0.965177i | \(-0.584249\pi\) |
0.966666 | − | 0.256040i | \(-0.0824179\pi\) | |||||||
\(948\) | 2.64575 | − | 4.58258i | 0.0859300 | − | 0.148835i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.67712 | + | 4.02334i | 0.0544131 | + | 0.130534i | ||||
\(951\) | −4.06275 | −0.131744 | ||||||||
\(952\) | 7.46863 | − | 12.9360i | 0.242060 | − | 0.419260i | ||||
\(953\) | 14.5830 | − | 25.2585i | 0.472390 | − | 0.818203i | −0.527111 | − | 0.849796i | \(-0.676725\pi\) |
0.999501 | + | 0.0315932i | \(0.0100581\pi\) | |||||||
\(954\) | −2.32288 | − | 4.02334i | −0.0752059 | − | 0.130260i | ||||
\(955\) | −2.29150 | + | 3.96900i | −0.0741513 | + | 0.128434i | ||||
\(956\) | 12.0000 | + | 20.7846i | 0.388108 | + | 0.672222i | ||||
\(957\) | −22.9373 | −0.741456 | ||||||||
\(958\) | −4.93725 | −0.159515 | ||||||||
\(959\) | −15.8745 | − | 27.4955i | −0.512615 | − | 0.887875i | ||||
\(960\) | −0.500000 | − | 0.866025i | −0.0161374 | − | 0.0279508i | ||||
\(961\) | 22.1660 | 0.715033 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.17712 | − | 3.77089i | −0.0701569 | − | 0.121515i | ||||
\(964\) | −0.708497 | + | 1.22715i | −0.0228192 | + | 0.0395240i | ||||
\(965\) | 5.82288 | + | 10.0855i | 0.187445 | + | 0.324664i | ||||
\(966\) | 1.32288 | − | 2.29129i | 0.0425628 | − | 0.0737210i | ||||
\(967\) | −16.9373 | + | 29.3362i | −0.544665 | + | 0.943388i | 0.453963 | + | 0.891021i | \(0.350010\pi\) |
−0.998628 | + | 0.0523673i | \(0.983323\pi\) | |||||||
\(968\) | −28.5830 | −0.918693 | ||||||||
\(969\) | −14.9373 | + | 19.5575i | −0.479854 | + | 0.628276i | ||||
\(970\) | −1.64575 | −0.0528419 | ||||||||
\(971\) | 0.874508 | − | 1.51469i | 0.0280643 | − | 0.0486088i | −0.851652 | − | 0.524107i | \(-0.824399\pi\) |
0.879716 | + | 0.475499i | \(0.157732\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | 4.35425 | + | 7.54178i | 0.139591 | + | 0.241778i | ||||
\(974\) | 10.3229 | − | 17.8797i | 0.330766 | − | 0.572904i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.93725 | 0.222056 | ||||||||
\(977\) | −1.06275 | −0.0340003 | −0.0170001 | − | 0.999855i | \(-0.505412\pi\) | ||||
−0.0170001 | + | 0.999855i | \(0.505412\pi\) | |||||||
\(978\) | 1.35425 | + | 2.34563i | 0.0433041 | + | 0.0750049i | ||||
\(979\) | 41.6144 | + | 72.0782i | 1.33000 | + | 2.30363i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.354249 | −0.0113103 | ||||||||
\(982\) | 19.7288 | + | 34.1712i | 0.629570 | + | 1.09045i | ||||
\(983\) | 24.4373 | − | 42.3266i | 0.779427 | − | 1.35001i | −0.152845 | − | 0.988250i | \(-0.548843\pi\) |
0.932272 | − | 0.361758i | \(-0.117823\pi\) | |||||||
\(984\) | 4.32288 | + | 7.48744i | 0.137808 | + | 0.238691i | ||||
\(985\) | −1.32288 | + | 2.29129i | −0.0421503 | + | 0.0730065i | ||||
\(986\) | 10.2915 | − | 17.8254i | 0.327748 | − | 0.567677i | ||||
\(987\) | 33.2915 | 1.05968 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.00000 | 0.190789 | ||||||||
\(990\) | 3.14575 | − | 5.44860i | 0.0999785 | − | 0.173168i | ||||
\(991\) | 5.82288 | − | 10.0855i | 0.184970 | − | 0.320377i | −0.758597 | − | 0.651561i | \(-0.774115\pi\) |
0.943566 | + | 0.331184i | \(0.107448\pi\) | |||||||
\(992\) | 3.64575 | + | 6.31463i | 0.115753 | + | 0.200490i | ||||
\(993\) | −9.32288 | + | 16.1477i | −0.295853 | + | 0.512432i | ||||
\(994\) | 18.0516 | + | 31.2663i | 0.572563 | + | 0.991708i | ||||
\(995\) | −3.06275 | −0.0970956 | ||||||||
\(996\) | −16.5830 | −0.525453 | ||||||||
\(997\) | −5.50000 | − | 9.52628i | −0.174187 | − | 0.301700i | 0.765693 | − | 0.643206i | \(-0.222396\pi\) |
−0.939880 | + | 0.341506i | \(0.889063\pi\) | |||||||
\(998\) | 3.67712 | + | 6.36897i | 0.116397 | + | 0.201606i | ||||
\(999\) | −8.29150 | −0.262332 |
(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 | 570.2.i.i.391.1 | yes | 4 | |
3.2 | odd | 2 | 1710.2.l.j.1531.1 | 4 | |||
19.7 | even | 3 | inner | 570.2.i.i.121.1 | ✓ | 4 | |
57.26 | odd | 6 | 1710.2.l.j.1261.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.i.i.121.1 | ✓ | 4 | 19.7 | even | 3 | inner | |
570.2.i.i.391.1 | yes | 4 | 1.1 | even | 1 | trivial | |
1710.2.l.j.1261.1 | 4 | 57.26 | odd | 6 | |||
1710.2.l.j.1531.1 | 4 | 3.2 | odd | 2 |