Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [152,2,Mod(27,152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(152, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("152.27");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 152 = 2^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 152.o (of order \(6\), 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: | \(1.21372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 152.107 |
Dual form | 152.2.o.a.27.1 |
$q$-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 \(\left(\mathbb{Z}/152\mathbb{Z}\right)^\times\).
\(n\) | \(39\) | \(77\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 1.22474i | −0.500000 | − | 0.866025i | ||||
\(3\) | −1.50000 | + | 0.866025i | −0.866025 | + | 0.500000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||||
\(5\) | 2.12132 | − | 1.22474i | 0.948683 | − | 0.547723i | 0.0560116 | − | 0.998430i | \(-0.482162\pi\) |
0.892672 | + | 0.450708i | \(0.148828\pi\) | |||||||
\(6\) | 2.12132 | + | 1.22474i | 0.866025 | + | 0.500000i | ||||
\(7\) | 2.44949i | 0.925820i | 0.886405 | + | 0.462910i | \(0.153195\pi\) | ||||
−0.886405 | + | 0.462910i | \(0.846805\pi\) | |||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.00000 | − | 1.73205i | −0.948683 | − | 0.547723i | ||||
\(11\) | 5.00000 | 1.50756 | 0.753778 | − | 0.657129i | \(-0.228229\pi\) | ||||
0.753778 | + | 0.657129i | \(0.228229\pi\) | |||||||
\(12\) | − | 3.46410i | − | 1.00000i | ||||||
\(13\) | 2.82843 | − | 4.89898i | 0.784465 | − | 1.35873i | −0.144854 | − | 0.989453i | \(-0.546271\pi\) |
0.929318 | − | 0.369279i | \(-0.120395\pi\) | |||||||
\(14\) | 3.00000 | − | 1.73205i | 0.801784 | − | 0.462910i | ||||
\(15\) | −2.12132 | + | 3.67423i | −0.547723 | + | 0.948683i | ||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | 2.00000 | + | 3.46410i | 0.485071 | + | 0.840168i | 0.999853 | − | 0.0171533i | \(-0.00546033\pi\) |
−0.514782 | + | 0.857321i | \(0.672127\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | + | 4.33013i | −0.114708 | + | 0.993399i | ||||
\(20\) | 4.89898i | 1.09545i | ||||||||
\(21\) | −2.12132 | − | 3.67423i | −0.462910 | − | 0.801784i | ||||
\(22\) | −3.53553 | − | 6.12372i | −0.753778 | − | 1.30558i | ||||
\(23\) | −2.12132 | − | 1.22474i | −0.442326 | − | 0.255377i | 0.262258 | − | 0.964998i | \(-0.415533\pi\) |
−0.704584 | + | 0.709621i | \(0.748866\pi\) | |||||||
\(24\) | −4.24264 | + | 2.44949i | −0.866025 | + | 0.500000i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −8.00000 | −1.56893 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | −4.24264 | − | 2.44949i | −0.801784 | − | 0.462910i | ||||
\(29\) | −3.53553 | + | 6.12372i | −0.656532 | + | 1.13715i | 0.324975 | + | 0.945723i | \(0.394644\pi\) |
−0.981507 | + | 0.191425i | \(0.938689\pi\) | |||||||
\(30\) | 6.00000 | 1.09545 | ||||||||
\(31\) | 1.41421 | 0.254000 | 0.127000 | − | 0.991903i | \(-0.459465\pi\) | ||||
0.127000 | + | 0.991903i | \(0.459465\pi\) | |||||||
\(32\) | −2.82843 | + | 4.89898i | −0.500000 | + | 0.866025i | ||||
\(33\) | −7.50000 | + | 4.33013i | −1.30558 | + | 0.753778i | ||||
\(34\) | 2.82843 | − | 4.89898i | 0.485071 | − | 0.840168i | ||||
\(35\) | 3.00000 | + | 5.19615i | 0.507093 | + | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.41421 | −0.232495 | −0.116248 | − | 0.993220i | \(-0.537087\pi\) | ||||
−0.116248 | + | 0.993220i | \(0.537087\pi\) | |||||||
\(38\) | 5.65685 | − | 2.44949i | 0.917663 | − | 0.397360i | ||||
\(39\) | 9.79796i | 1.56893i | ||||||||
\(40\) | 6.00000 | − | 3.46410i | 0.948683 | − | 0.547723i | ||||
\(41\) | 4.50000 | − | 2.59808i | 0.702782 | − | 0.405751i | −0.105601 | − | 0.994409i | \(-0.533677\pi\) |
0.808383 | + | 0.588657i | \(0.200343\pi\) | |||||||
\(42\) | −3.00000 | + | 5.19615i | −0.462910 | + | 0.801784i | ||||
\(43\) | −3.00000 | − | 5.19615i | −0.457496 | − | 0.792406i | 0.541332 | − | 0.840809i | \(-0.317920\pi\) |
−0.998828 | + | 0.0484030i | \(0.984587\pi\) | |||||||
\(44\) | −5.00000 | + | 8.66025i | −0.753778 | + | 1.30558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.46410i | 0.510754i | ||||||||
\(47\) | −6.36396 | − | 3.67423i | −0.928279 | − | 0.535942i | −0.0420122 | − | 0.999117i | \(-0.513377\pi\) |
−0.886267 | + | 0.463175i | \(0.846710\pi\) | |||||||
\(48\) | 6.00000 | + | 3.46410i | 0.866025 | + | 0.500000i | ||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.41421 | −0.200000 | ||||||||
\(51\) | −6.00000 | − | 3.46410i | −0.840168 | − | 0.485071i | ||||
\(52\) | 5.65685 | + | 9.79796i | 0.784465 | + | 1.35873i | ||||
\(53\) | 4.24264 | − | 7.34847i | 0.582772 | − | 1.00939i | −0.412378 | − | 0.911013i | \(-0.635302\pi\) |
0.995149 | − | 0.0983769i | \(-0.0313651\pi\) | |||||||
\(54\) | −6.36396 | + | 3.67423i | −0.866025 | + | 0.500000i | ||||
\(55\) | 10.6066 | − | 6.12372i | 1.43019 | − | 0.825723i | ||||
\(56\) | 6.92820i | 0.925820i | ||||||||
\(57\) | −3.00000 | − | 6.92820i | −0.397360 | − | 0.917663i | ||||
\(58\) | 10.0000 | 1.31306 | ||||||||
\(59\) | −1.50000 | + | 0.866025i | −0.195283 | + | 0.112747i | −0.594454 | − | 0.804130i | \(-0.702632\pi\) |
0.399170 | + | 0.916877i | \(0.369298\pi\) | |||||||
\(60\) | −4.24264 | − | 7.34847i | −0.547723 | − | 0.948683i | ||||
\(61\) | −6.36396 | − | 3.67423i | −0.814822 | − | 0.470438i | 0.0338058 | − | 0.999428i | \(-0.489237\pi\) |
−0.848628 | + | 0.528991i | \(0.822571\pi\) | |||||||
\(62\) | −1.00000 | − | 1.73205i | −0.127000 | − | 0.219971i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | − | 13.8564i | − | 1.71868i | ||||||
\(66\) | 10.6066 | + | 6.12372i | 1.30558 | + | 0.753778i | ||||
\(67\) | −10.5000 | − | 6.06218i | −1.28278 | − | 0.740613i | −0.305424 | − | 0.952217i | \(-0.598798\pi\) |
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | −8.00000 | −0.970143 | ||||||||
\(69\) | 4.24264 | 0.510754 | ||||||||
\(70\) | 4.24264 | − | 7.34847i | 0.507093 | − | 0.878310i | ||||
\(71\) | 1.41421 | + | 2.44949i | 0.167836 | + | 0.290701i | 0.937659 | − | 0.347557i | \(-0.112989\pi\) |
−0.769823 | + | 0.638258i | \(0.779655\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.50000 | − | 2.59808i | −0.175562 | − | 0.304082i | 0.764794 | − | 0.644275i | \(-0.222841\pi\) |
−0.940356 | + | 0.340193i | \(0.889507\pi\) | |||||||
\(74\) | 1.00000 | + | 1.73205i | 0.116248 | + | 0.201347i | ||||
\(75\) | 1.73205i | 0.200000i | ||||||||
\(76\) | −7.00000 | − | 5.19615i | −0.802955 | − | 0.596040i | ||||
\(77\) | 12.2474i | 1.39573i | ||||||||
\(78\) | 12.0000 | − | 6.92820i | 1.35873 | − | 0.784465i | ||||
\(79\) | −1.41421 | − | 2.44949i | −0.159111 | − | 0.275589i | 0.775437 | − | 0.631425i | \(-0.217530\pi\) |
−0.934549 | + | 0.355836i | \(0.884196\pi\) | |||||||
\(80\) | −8.48528 | − | 4.89898i | −0.948683 | − | 0.547723i | ||||
\(81\) | 4.50000 | + | 7.79423i | 0.500000 | + | 0.866025i | ||||
\(82\) | −6.36396 | − | 3.67423i | −0.702782 | − | 0.405751i | ||||
\(83\) | 7.00000 | 0.768350 | 0.384175 | − | 0.923260i | \(-0.374486\pi\) | ||||
0.384175 | + | 0.923260i | \(0.374486\pi\) | |||||||
\(84\) | 8.48528 | 0.925820 | ||||||||
\(85\) | 8.48528 | + | 4.89898i | 0.920358 | + | 0.531369i | ||||
\(86\) | −4.24264 | + | 7.34847i | −0.457496 | + | 0.792406i | ||||
\(87\) | − | 12.2474i | − | 1.31306i | ||||||
\(88\) | 14.1421 | 1.50756 | ||||||||
\(89\) | 3.00000 | + | 1.73205i | 0.317999 | + | 0.183597i | 0.650500 | − | 0.759506i | \(-0.274559\pi\) |
−0.332501 | + | 0.943103i | \(0.607893\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | + | 6.92820i | 1.25794 | + | 0.726273i | ||||
\(92\) | 4.24264 | − | 2.44949i | 0.442326 | − | 0.255377i | ||||
\(93\) | −2.12132 | + | 1.22474i | −0.219971 | + | 0.127000i | ||||
\(94\) | 10.3923i | 1.07188i | ||||||||
\(95\) | 4.24264 | + | 9.79796i | 0.435286 | + | 1.00525i | ||||
\(96\) | − | 9.79796i | − | 1.00000i | ||||||
\(97\) | −16.5000 | + | 9.52628i | −1.67532 | + | 0.967247i | −0.710742 | + | 0.703452i | \(0.751641\pi\) |
−0.964579 | + | 0.263795i | \(0.915026\pi\) | |||||||
\(98\) | −0.707107 | − | 1.22474i | −0.0714286 | − | 0.123718i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | + | 1.73205i | 0.100000 | + | 0.173205i | ||||
\(101\) | 6.36396 | + | 3.67423i | 0.633238 | + | 0.365600i | 0.782005 | − | 0.623272i | \(-0.214197\pi\) |
−0.148767 | + | 0.988872i | \(0.547530\pi\) | |||||||
\(102\) | 9.79796i | 0.970143i | ||||||||
\(103\) | −2.82843 | −0.278693 | −0.139347 | − | 0.990244i | \(-0.544500\pi\) | ||||
−0.139347 | + | 0.990244i | \(0.544500\pi\) | |||||||
\(104\) | 8.00000 | − | 13.8564i | 0.784465 | − | 1.35873i | ||||
\(105\) | −9.00000 | − | 5.19615i | −0.878310 | − | 0.507093i | ||||
\(106\) | −12.0000 | −1.16554 | ||||||||
\(107\) | − | 6.92820i | − | 0.669775i | −0.942258 | − | 0.334887i | \(-0.891302\pi\) | ||
0.942258 | − | 0.334887i | \(-0.108698\pi\) | |||||||
\(108\) | 9.00000 | + | 5.19615i | 0.866025 | + | 0.500000i | ||||
\(109\) | −7.07107 | − | 12.2474i | −0.677285 | − | 1.17309i | −0.975795 | − | 0.218686i | \(-0.929823\pi\) |
0.298510 | − | 0.954407i | \(-0.403510\pi\) | |||||||
\(110\) | −15.0000 | − | 8.66025i | −1.43019 | − | 0.825723i | ||||
\(111\) | 2.12132 | − | 1.22474i | 0.201347 | − | 0.116248i | ||||
\(112\) | 8.48528 | − | 4.89898i | 0.801784 | − | 0.462910i | ||||
\(113\) | 12.1244i | 1.14056i | 0.821449 | + | 0.570282i | \(0.193166\pi\) | ||||
−0.821449 | + | 0.570282i | \(0.806834\pi\) | |||||||
\(114\) | −6.36396 | + | 8.57321i | −0.596040 | + | 0.802955i | ||||
\(115\) | −6.00000 | −0.559503 | ||||||||
\(116\) | −7.07107 | − | 12.2474i | −0.656532 | − | 1.13715i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.12132 | + | 1.22474i | 0.195283 | + | 0.112747i | ||||
\(119\) | −8.48528 | + | 4.89898i | −0.777844 | + | 0.449089i | ||||
\(120\) | −6.00000 | + | 10.3923i | −0.547723 | + | 0.948683i | ||||
\(121\) | 14.0000 | 1.27273 | ||||||||
\(122\) | 10.3923i | 0.940875i | ||||||||
\(123\) | −4.50000 | + | 7.79423i | −0.405751 | + | 0.702782i | ||||
\(124\) | −1.41421 | + | 2.44949i | −0.127000 | + | 0.219971i | ||||
\(125\) | 9.79796i | 0.876356i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.41421 | − | 2.44949i | 0.125491 | − | 0.217357i | −0.796434 | − | 0.604726i | \(-0.793283\pi\) |
0.921925 | + | 0.387369i | \(0.126616\pi\) | |||||||
\(128\) | −5.65685 | − | 9.79796i | −0.500000 | − | 0.866025i | ||||
\(129\) | 9.00000 | + | 5.19615i | 0.792406 | + | 0.457496i | ||||
\(130\) | −16.9706 | + | 9.79796i | −1.48842 | + | 0.859338i | ||||
\(131\) | 3.50000 | + | 6.06218i | 0.305796 | + | 0.529655i | 0.977438 | − | 0.211221i | \(-0.0677440\pi\) |
−0.671642 | + | 0.740876i | \(0.734411\pi\) | |||||||
\(132\) | − | 17.3205i | − | 1.50756i | ||||||
\(133\) | −10.6066 | − | 1.22474i | −0.919709 | − | 0.106199i | ||||
\(134\) | 17.1464i | 1.48123i | ||||||||
\(135\) | −6.36396 | − | 11.0227i | −0.547723 | − | 0.948683i | ||||
\(136\) | 5.65685 | + | 9.79796i | 0.485071 | + | 0.840168i | ||||
\(137\) | 8.50000 | − | 14.7224i | 0.726204 | − | 1.25782i | −0.232273 | − | 0.972651i | \(-0.574616\pi\) |
0.958477 | − | 0.285171i | \(-0.0920506\pi\) | |||||||
\(138\) | −3.00000 | − | 5.19615i | −0.255377 | − | 0.442326i | ||||
\(139\) | 4.50000 | − | 7.79423i | 0.381685 | − | 0.661098i | −0.609618 | − | 0.792695i | \(-0.708677\pi\) |
0.991303 | + | 0.131597i | \(0.0420106\pi\) | |||||||
\(140\) | −12.0000 | −1.01419 | ||||||||
\(141\) | 12.7279 | 1.07188 | ||||||||
\(142\) | 2.00000 | − | 3.46410i | 0.167836 | − | 0.290701i | ||||
\(143\) | 14.1421 | − | 24.4949i | 1.18262 | − | 2.04837i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.3205i | 1.43839i | ||||||||
\(146\) | −2.12132 | + | 3.67423i | −0.175562 | + | 0.304082i | ||||
\(147\) | −1.50000 | + | 0.866025i | −0.123718 | + | 0.0714286i | ||||
\(148\) | 1.41421 | − | 2.44949i | 0.116248 | − | 0.201347i | ||||
\(149\) | −14.8492 | + | 8.57321i | −1.21650 | + | 0.702345i | −0.964167 | − | 0.265296i | \(-0.914530\pi\) |
−0.252330 | + | 0.967641i | \(0.581197\pi\) | |||||||
\(150\) | 2.12132 | − | 1.22474i | 0.173205 | − | 0.100000i | ||||
\(151\) | −15.5563 | −1.26596 | −0.632979 | − | 0.774169i | \(-0.718168\pi\) | ||||
−0.632979 | + | 0.774169i | \(0.718168\pi\) | |||||||
\(152\) | −1.41421 | + | 12.2474i | −0.114708 | + | 0.993399i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 15.0000 | − | 8.66025i | 1.20873 | − | 0.697863i | ||||
\(155\) | 3.00000 | − | 1.73205i | 0.240966 | − | 0.139122i | ||||
\(156\) | −16.9706 | − | 9.79796i | −1.35873 | − | 0.784465i | ||||
\(157\) | −4.24264 | + | 2.44949i | −0.338600 | + | 0.195491i | −0.659653 | − | 0.751571i | \(-0.729297\pi\) |
0.321053 | + | 0.947061i | \(0.395963\pi\) | |||||||
\(158\) | −2.00000 | + | 3.46410i | −0.159111 | + | 0.275589i | ||||
\(159\) | 14.6969i | 1.16554i | ||||||||
\(160\) | 13.8564i | 1.09545i | ||||||||
\(161\) | 3.00000 | − | 5.19615i | 0.236433 | − | 0.409514i | ||||
\(162\) | 6.36396 | − | 11.0227i | 0.500000 | − | 0.866025i | ||||
\(163\) | 3.00000 | 0.234978 | 0.117489 | − | 0.993074i | \(-0.462515\pi\) | ||||
0.117489 | + | 0.993074i | \(0.462515\pi\) | |||||||
\(164\) | 10.3923i | 0.811503i | ||||||||
\(165\) | −10.6066 | + | 18.3712i | −0.825723 | + | 1.43019i | ||||
\(166\) | −4.94975 | − | 8.57321i | −0.384175 | − | 0.665410i | ||||
\(167\) | 2.82843 | − | 4.89898i | 0.218870 | − | 0.379094i | −0.735593 | − | 0.677424i | \(-0.763096\pi\) |
0.954463 | + | 0.298330i | \(0.0964295\pi\) | |||||||
\(168\) | −6.00000 | − | 10.3923i | −0.462910 | − | 0.801784i | ||||
\(169\) | −9.50000 | − | 16.4545i | −0.730769 | − | 1.26573i | ||||
\(170\) | − | 13.8564i | − | 1.06274i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.0000 | 0.914991 | ||||||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | −15.0000 | + | 8.66025i | −1.13715 | + | 0.656532i | ||||
\(175\) | 2.12132 | + | 1.22474i | 0.160357 | + | 0.0925820i | ||||
\(176\) | −10.0000 | − | 17.3205i | −0.753778 | − | 1.30558i | ||||
\(177\) | 1.50000 | − | 2.59808i | 0.112747 | − | 0.195283i | ||||
\(178\) | − | 4.89898i | − | 0.367194i | ||||||
\(179\) | − | 8.66025i | − | 0.647298i | −0.946177 | − | 0.323649i | \(-0.895090\pi\) | ||
0.946177 | − | 0.323649i | \(-0.104910\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.0208 | + | 20.8207i | −0.893500 | + | 1.54759i | −0.0578502 | + | 0.998325i | \(0.518425\pi\) |
−0.835650 | + | 0.549262i | \(0.814909\pi\) | |||||||
\(182\) | − | 19.5959i | − | 1.45255i | ||||||
\(183\) | 12.7279 | 0.940875 | ||||||||
\(184\) | −6.00000 | − | 3.46410i | −0.442326 | − | 0.255377i | ||||
\(185\) | −3.00000 | + | 1.73205i | −0.220564 | + | 0.127343i | ||||
\(186\) | 3.00000 | + | 1.73205i | 0.219971 | + | 0.127000i | ||||
\(187\) | 10.0000 | + | 17.3205i | 0.731272 | + | 1.26660i | ||||
\(188\) | 12.7279 | − | 7.34847i | 0.928279 | − | 0.535942i | ||||
\(189\) | 12.7279 | 0.925820 | ||||||||
\(190\) | 9.00000 | − | 12.1244i | 0.652929 | − | 0.879593i | ||||
\(191\) | − | 19.5959i | − | 1.41791i | −0.705253 | − | 0.708955i | \(-0.749167\pi\) | ||
0.705253 | − | 0.708955i | \(-0.250833\pi\) | |||||||
\(192\) | −12.0000 | + | 6.92820i | −0.866025 | + | 0.500000i | ||||
\(193\) | −3.00000 | + | 1.73205i | −0.215945 | + | 0.124676i | −0.604071 | − | 0.796930i | \(-0.706456\pi\) |
0.388126 | + | 0.921606i | \(0.373122\pi\) | |||||||
\(194\) | 23.3345 | + | 13.4722i | 1.67532 | + | 0.967247i | ||||
\(195\) | 12.0000 | + | 20.7846i | 0.859338 | + | 1.48842i | ||||
\(196\) | −1.00000 | + | 1.73205i | −0.0714286 | + | 0.123718i | ||||
\(197\) | − | 17.1464i | − | 1.22163i | −0.791772 | − | 0.610816i | \(-0.790841\pi\) | ||
0.791772 | − | 0.610816i | \(-0.209159\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.2132 | + | 12.2474i | 1.50376 | + | 0.868199i | 0.999990 | + | 0.00436292i | \(0.00138876\pi\) |
0.503774 | + | 0.863836i | \(0.331945\pi\) | |||||||
\(200\) | 1.41421 | − | 2.44949i | 0.100000 | − | 0.173205i | ||||
\(201\) | 21.0000 | 1.48123 | ||||||||
\(202\) | − | 10.3923i | − | 0.731200i | ||||||
\(203\) | −15.0000 | − | 8.66025i | −1.05279 | − | 0.607831i | ||||
\(204\) | 12.0000 | − | 6.92820i | 0.840168 | − | 0.485071i | ||||
\(205\) | 6.36396 | − | 11.0227i | 0.444478 | − | 0.769859i | ||||
\(206\) | 2.00000 | + | 3.46410i | 0.139347 | + | 0.241355i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −22.6274 | −1.56893 | ||||||||
\(209\) | −2.50000 | + | 21.6506i | −0.172929 | + | 1.49761i | ||||
\(210\) | 14.6969i | 1.01419i | ||||||||
\(211\) | −9.00000 | + | 5.19615i | −0.619586 | + | 0.357718i | −0.776708 | − | 0.629861i | \(-0.783112\pi\) |
0.157122 | + | 0.987579i | \(0.449778\pi\) | |||||||
\(212\) | 8.48528 | + | 14.6969i | 0.582772 | + | 1.00939i | ||||
\(213\) | −4.24264 | − | 2.44949i | −0.290701 | − | 0.167836i | ||||
\(214\) | −8.48528 | + | 4.89898i | −0.580042 | + | 0.334887i | ||||
\(215\) | −12.7279 | − | 7.34847i | −0.868037 | − | 0.501161i | ||||
\(216\) | − | 14.6969i | − | 1.00000i | ||||||
\(217\) | 3.46410i | 0.235159i | ||||||||
\(218\) | −10.0000 | + | 17.3205i | −0.677285 | + | 1.17309i | ||||
\(219\) | 4.50000 | + | 2.59808i | 0.304082 | + | 0.175562i | ||||
\(220\) | 24.4949i | 1.65145i | ||||||||
\(221\) | 22.6274 | 1.52208 | ||||||||
\(222\) | −3.00000 | − | 1.73205i | −0.201347 | − | 0.116248i | ||||
\(223\) | 12.0208 | + | 20.8207i | 0.804973 | + | 1.39425i | 0.916309 | + | 0.400472i | \(0.131154\pi\) |
−0.111336 | + | 0.993783i | \(0.535513\pi\) | |||||||
\(224\) | −12.0000 | − | 6.92820i | −0.801784 | − | 0.462910i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.8492 | − | 8.57321i | 0.987757 | − | 0.570282i | ||||
\(227\) | − | 1.73205i | − | 0.114960i | −0.998347 | − | 0.0574801i | \(-0.981693\pi\) | ||
0.998347 | − | 0.0574801i | \(-0.0183066\pi\) | |||||||
\(228\) | 15.0000 | + | 1.73205i | 0.993399 | + | 0.114708i | ||||
\(229\) | − | 9.79796i | − | 0.647467i | −0.946148 | − | 0.323734i | \(-0.895062\pi\) | ||
0.946148 | − | 0.323734i | \(-0.104938\pi\) | |||||||
\(230\) | 4.24264 | + | 7.34847i | 0.279751 | + | 0.484544i | ||||
\(231\) | −10.6066 | − | 18.3712i | −0.697863 | − | 1.20873i | ||||
\(232\) | −10.0000 | + | 17.3205i | −0.656532 | + | 1.13715i | ||||
\(233\) | −0.500000 | − | 0.866025i | −0.0327561 | − | 0.0567352i | 0.849183 | − | 0.528099i | \(-0.177095\pi\) |
−0.881939 | + | 0.471364i | \(0.843762\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.0000 | −1.17419 | ||||||||
\(236\) | − | 3.46410i | − | 0.225494i | ||||||
\(237\) | 4.24264 | + | 2.44949i | 0.275589 | + | 0.159111i | ||||
\(238\) | 12.0000 | + | 6.92820i | 0.777844 | + | 0.449089i | ||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 16.9706 | 1.09545 | ||||||||
\(241\) | −13.5000 | − | 7.79423i | −0.869611 | − | 0.502070i | −0.00239235 | − | 0.999997i | \(-0.500762\pi\) |
−0.867219 | + | 0.497927i | \(0.834095\pi\) | |||||||
\(242\) | −9.89949 | − | 17.1464i | −0.636364 | − | 1.10221i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.7279 | − | 7.34847i | 0.814822 | − | 0.470438i | ||||
\(245\) | 2.12132 | − | 1.22474i | 0.135526 | − | 0.0782461i | ||||
\(246\) | 12.7279 | 0.811503 | ||||||||
\(247\) | 19.7990 | + | 14.6969i | 1.25978 | + | 0.935144i | ||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | −10.5000 | + | 6.06218i | −0.665410 | + | 0.384175i | ||||
\(250\) | 12.0000 | − | 6.92820i | 0.758947 | − | 0.438178i | ||||
\(251\) | 11.5000 | − | 19.9186i | 0.725874 | − | 1.25725i | −0.232740 | − | 0.972539i | \(-0.574769\pi\) |
0.958613 | − | 0.284711i | \(-0.0918976\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.6066 | − | 6.12372i | −0.666831 | − | 0.384995i | ||||
\(254\) | −4.00000 | −0.250982 | ||||||||
\(255\) | −16.9706 | −1.06274 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 13.5000 | + | 7.79423i | 0.842107 | + | 0.486191i | 0.857980 | − | 0.513683i | \(-0.171719\pi\) |
−0.0158730 | + | 0.999874i | \(0.505053\pi\) | |||||||
\(258\) | − | 14.6969i | − | 0.914991i | ||||||
\(259\) | − | 3.46410i | − | 0.215249i | ||||||
\(260\) | 24.0000 | + | 13.8564i | 1.48842 | + | 0.859338i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.94975 | − | 8.57321i | 0.305796 | − | 0.529655i | ||||
\(263\) | −23.3345 | + | 13.4722i | −1.43887 | + | 0.830731i | −0.997771 | − | 0.0667283i | \(-0.978744\pi\) |
−0.441097 | + | 0.897459i | \(0.645411\pi\) | |||||||
\(264\) | −21.2132 | + | 12.2474i | −1.30558 | + | 0.753778i | ||||
\(265\) | − | 20.7846i | − | 1.27679i | ||||||
\(266\) | 6.00000 | + | 13.8564i | 0.367884 | + | 0.849591i | ||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 21.0000 | − | 12.1244i | 1.28278 | − | 0.740613i | ||||
\(269\) | −4.24264 | − | 7.34847i | −0.258678 | − | 0.448044i | 0.707210 | − | 0.707004i | \(-0.249954\pi\) |
−0.965888 | + | 0.258960i | \(0.916620\pi\) | |||||||
\(270\) | −9.00000 | + | 15.5885i | −0.547723 | + | 0.948683i | ||||
\(271\) | 2.12132 | − | 1.22474i | 0.128861 | − | 0.0743980i | −0.434184 | − | 0.900824i | \(-0.642963\pi\) |
0.563045 | + | 0.826426i | \(0.309630\pi\) | |||||||
\(272\) | 8.00000 | − | 13.8564i | 0.485071 | − | 0.840168i | ||||
\(273\) | −24.0000 | −1.45255 | ||||||||
\(274\) | −24.0416 | −1.45241 | ||||||||
\(275\) | 2.50000 | − | 4.33013i | 0.150756 | − | 0.261116i | ||||
\(276\) | −4.24264 | + | 7.34847i | −0.255377 | + | 0.442326i | ||||
\(277\) | − | 7.34847i | − | 0.441527i | −0.975327 | − | 0.220763i | \(-0.929145\pi\) | ||
0.975327 | − | 0.220763i | \(-0.0708548\pi\) | |||||||
\(278\) | −12.7279 | −0.763370 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.48528 | + | 14.6969i | 0.507093 | + | 0.878310i | ||||
\(281\) | 1.50000 | + | 0.866025i | 0.0894825 | + | 0.0516627i | 0.544074 | − | 0.839038i | \(-0.316881\pi\) |
−0.454591 | + | 0.890700i | \(0.650215\pi\) | |||||||
\(282\) | −9.00000 | − | 15.5885i | −0.535942 | − | 0.928279i | ||||
\(283\) | −8.50000 | − | 14.7224i | −0.505273 | − | 0.875158i | −0.999981 | − | 0.00609896i | \(-0.998059\pi\) |
0.494709 | − | 0.869059i | \(-0.335275\pi\) | |||||||
\(284\) | −5.65685 | −0.335673 | ||||||||
\(285\) | −14.8492 | − | 11.0227i | −0.879593 | − | 0.652929i | ||||
\(286\) | −40.0000 | −2.36525 | ||||||||
\(287\) | 6.36396 | + | 11.0227i | 0.375653 | + | 0.650650i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | 21.2132 | − | 12.2474i | 1.24568 | − | 0.719195i | ||||
\(291\) | 16.5000 | − | 28.5788i | 0.967247 | − | 1.67532i | ||||
\(292\) | 6.00000 | 0.351123 | ||||||||
\(293\) | 29.6985 | 1.73500 | 0.867502 | − | 0.497434i | \(-0.165724\pi\) | ||||
0.867502 | + | 0.497434i | \(0.165724\pi\) | |||||||
\(294\) | 2.12132 | + | 1.22474i | 0.123718 | + | 0.0714286i | ||||
\(295\) | −2.12132 | + | 3.67423i | −0.123508 | + | 0.213922i | ||||
\(296\) | −4.00000 | −0.232495 | ||||||||
\(297\) | − | 25.9808i | − | 1.50756i | ||||||
\(298\) | 21.0000 | + | 12.1244i | 1.21650 | + | 0.702345i | ||||
\(299\) | −12.0000 | + | 6.92820i | −0.693978 | + | 0.400668i | ||||
\(300\) | −3.00000 | − | 1.73205i | −0.173205 | − | 0.100000i | ||||
\(301\) | 12.7279 | − | 7.34847i | 0.733625 | − | 0.423559i | ||||
\(302\) | 11.0000 | + | 19.0526i | 0.632979 | + | 1.09635i | ||||
\(303\) | −12.7279 | −0.731200 | ||||||||
\(304\) | 16.0000 | − | 6.92820i | 0.917663 | − | 0.397360i | ||||
\(305\) | −18.0000 | −1.03068 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.50000 | − | 2.59808i | 0.256829 | − | 0.148280i | −0.366058 | − | 0.930592i | \(-0.619293\pi\) |
0.622887 | + | 0.782312i | \(0.285960\pi\) | |||||||
\(308\) | −21.2132 | − | 12.2474i | −1.20873 | − | 0.697863i | ||||
\(309\) | 4.24264 | − | 2.44949i | 0.241355 | − | 0.139347i | ||||
\(310\) | −4.24264 | − | 2.44949i | −0.240966 | − | 0.139122i | ||||
\(311\) | 12.2474i | 0.694489i | 0.937775 | + | 0.347245i | \(0.112883\pi\) | ||||
−0.937775 | + | 0.347245i | \(0.887117\pi\) | |||||||
\(312\) | 27.7128i | 1.56893i | ||||||||
\(313\) | −0.500000 | + | 0.866025i | −0.0282617 | + | 0.0489506i | −0.879810 | − | 0.475325i | \(-0.842331\pi\) |
0.851549 | + | 0.524276i | \(0.175664\pi\) | |||||||
\(314\) | 6.00000 | + | 3.46410i | 0.338600 | + | 0.195491i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.65685 | 0.318223 | ||||||||
\(317\) | −4.24264 | + | 7.34847i | −0.238290 | + | 0.412731i | −0.960224 | − | 0.279231i | \(-0.909920\pi\) |
0.721933 | + | 0.691963i | \(0.243254\pi\) | |||||||
\(318\) | 18.0000 | − | 10.3923i | 1.00939 | − | 0.582772i | ||||
\(319\) | −17.6777 | + | 30.6186i | −0.989759 | + | 1.71431i | ||||
\(320\) | 16.9706 | − | 9.79796i | 0.948683 | − | 0.547723i | ||||
\(321\) | 6.00000 | + | 10.3923i | 0.334887 | + | 0.580042i | ||||
\(322\) | −8.48528 | −0.472866 | ||||||||
\(323\) | −16.0000 | + | 6.92820i | −0.890264 | + | 0.385496i | ||||
\(324\) | −18.0000 | −1.00000 | ||||||||
\(325\) | −2.82843 | − | 4.89898i | −0.156893 | − | 0.271746i | ||||
\(326\) | −2.12132 | − | 3.67423i | −0.117489 | − | 0.203497i | ||||
\(327\) | 21.2132 | + | 12.2474i | 1.17309 | + | 0.677285i | ||||
\(328\) | 12.7279 | − | 7.34847i | 0.702782 | − | 0.405751i | ||||
\(329\) | 9.00000 | − | 15.5885i | 0.496186 | − | 0.859419i | ||||
\(330\) | 30.0000 | 1.65145 | ||||||||
\(331\) | 5.19615i | 0.285606i | 0.989751 | + | 0.142803i | \(0.0456116\pi\) | ||||
−0.989751 | + | 0.142803i | \(0.954388\pi\) | |||||||
\(332\) | −7.00000 | + | 12.1244i | −0.384175 | + | 0.665410i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | −29.6985 | −1.62260 | ||||||||
\(336\) | −8.48528 | + | 14.6969i | −0.462910 | + | 0.801784i | ||||
\(337\) | 22.5000 | − | 12.9904i | 1.22565 | − | 0.707631i | 0.259536 | − | 0.965734i | \(-0.416431\pi\) |
0.966118 | + | 0.258102i | \(0.0830972\pi\) | |||||||
\(338\) | −13.4350 | + | 23.2702i | −0.730769 | + | 1.26573i | ||||
\(339\) | −10.5000 | − | 18.1865i | −0.570282 | − | 0.987757i | ||||
\(340\) | −16.9706 | + | 9.79796i | −0.920358 | + | 0.531369i | ||||
\(341\) | 7.07107 | 0.382920 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5959i | 1.05808i | ||||||||
\(344\) | −8.48528 | − | 14.6969i | −0.457496 | − | 0.792406i | ||||
\(345\) | 9.00000 | − | 5.19615i | 0.484544 | − | 0.279751i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.5000 | + | 19.9186i | 0.617352 | + | 1.06929i | 0.989967 | + | 0.141299i | \(0.0451280\pi\) |
−0.372615 | + | 0.927986i | \(0.621539\pi\) | |||||||
\(348\) | 21.2132 | + | 12.2474i | 1.13715 | + | 0.656532i | ||||
\(349\) | − | 29.3939i | − | 1.57342i | −0.617324 | − | 0.786709i | \(-0.711783\pi\) | ||
0.617324 | − | 0.786709i | \(-0.288217\pi\) | |||||||
\(350\) | − | 3.46410i | − | 0.185164i | ||||||
\(351\) | −25.4558 | − | 14.6969i | −1.35873 | − | 0.784465i | ||||
\(352\) | −14.1421 | + | 24.4949i | −0.753778 | + | 1.30558i | ||||
\(353\) | −31.0000 | −1.64996 | −0.824982 | − | 0.565159i | \(-0.808815\pi\) | ||||
−0.824982 | + | 0.565159i | \(0.808815\pi\) | |||||||
\(354\) | −4.24264 | −0.225494 | ||||||||
\(355\) | 6.00000 | + | 3.46410i | 0.318447 | + | 0.183855i | ||||
\(356\) | −6.00000 | + | 3.46410i | −0.317999 | + | 0.183597i | ||||
\(357\) | 8.48528 | − | 14.6969i | 0.449089 | − | 0.777844i | ||||
\(358\) | −10.6066 | + | 6.12372i | −0.560576 | + | 0.323649i | ||||
\(359\) | 14.8492 | − | 8.57321i | 0.783713 | − | 0.452477i | −0.0540315 | − | 0.998539i | \(-0.517207\pi\) |
0.837745 | + | 0.546062i | \(0.183874\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5000 | − | 4.33013i | −0.973684 | − | 0.227901i | ||||
\(362\) | 34.0000 | 1.78700 | ||||||||
\(363\) | −21.0000 | + | 12.1244i | −1.10221 | + | 0.636364i | ||||
\(364\) | −24.0000 | + | 13.8564i | −1.25794 | + | 0.726273i | ||||
\(365\) | −6.36396 | − | 3.67423i | −0.333105 | − | 0.192318i | ||||
\(366\) | −9.00000 | − | 15.5885i | −0.470438 | − | 0.814822i | ||||
\(367\) | 6.36396 | + | 3.67423i | 0.332196 | + | 0.191793i | 0.656816 | − | 0.754051i | \(-0.271903\pi\) |
−0.324620 | + | 0.945845i | \(0.605236\pi\) | |||||||
\(368\) | 9.79796i | 0.510754i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.24264 | + | 2.44949i | 0.220564 | + | 0.127343i | ||||
\(371\) | 18.0000 | + | 10.3923i | 0.934513 | + | 0.539542i | ||||
\(372\) | − | 4.89898i | − | 0.254000i | ||||||
\(373\) | −11.3137 | −0.585802 | −0.292901 | − | 0.956143i | \(-0.594621\pi\) | ||||
−0.292901 | + | 0.956143i | \(0.594621\pi\) | |||||||
\(374\) | 14.1421 | − | 24.4949i | 0.731272 | − | 1.26660i | ||||
\(375\) | −8.48528 | − | 14.6969i | −0.438178 | − | 0.758947i | ||||
\(376\) | −18.0000 | − | 10.3923i | −0.928279 | − | 0.535942i | ||||
\(377\) | 20.0000 | + | 34.6410i | 1.03005 | + | 1.78410i | ||||
\(378\) | −9.00000 | − | 15.5885i | −0.462910 | − | 0.801784i | ||||
\(379\) | 24.2487i | 1.24557i | 0.782392 | + | 0.622786i | \(0.213999\pi\) | ||||
−0.782392 | + | 0.622786i | \(0.786001\pi\) | |||||||
\(380\) | −21.2132 | − | 2.44949i | −1.08821 | − | 0.125656i | ||||
\(381\) | 4.89898i | 0.250982i | ||||||||
\(382\) | −24.0000 | + | 13.8564i | −1.22795 | + | 0.708955i | ||||
\(383\) | 4.94975 | + | 8.57321i | 0.252920 | + | 0.438071i | 0.964329 | − | 0.264708i | \(-0.0852756\pi\) |
−0.711408 | + | 0.702779i | \(0.751942\pi\) | |||||||
\(384\) | 16.9706 | + | 9.79796i | 0.866025 | + | 0.500000i | ||||
\(385\) | 15.0000 | + | 25.9808i | 0.764471 | + | 1.32410i | ||||
\(386\) | 4.24264 | + | 2.44949i | 0.215945 | + | 0.124676i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 38.1051i | − | 1.93449i | ||||||
\(389\) | −29.6985 | − | 17.1464i | −1.50577 | − | 0.869358i | −0.999978 | − | 0.00670497i | \(-0.997866\pi\) |
−0.505795 | − | 0.862653i | \(-0.668801\pi\) | |||||||
\(390\) | 16.9706 | − | 29.3939i | 0.859338 | − | 1.48842i | ||||
\(391\) | − | 9.79796i | − | 0.495504i | ||||||
\(392\) | 2.82843 | 0.142857 | ||||||||
\(393\) | −10.5000 | − | 6.06218i | −0.529655 | − | 0.305796i | ||||
\(394\) | −21.0000 | + | 12.1244i | −1.05796 | + | 0.610816i | ||||
\(395\) | −6.00000 | − | 3.46410i | −0.301893 | − | 0.174298i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.5772 | + | 15.9217i | −1.38406 | + | 0.799086i | −0.992637 | − | 0.121125i | \(-0.961350\pi\) |
−0.391421 | + | 0.920212i | \(0.628016\pi\) | |||||||
\(398\) | − | 34.6410i | − | 1.73640i | ||||||
\(399\) | 16.9706 | − | 7.34847i | 0.849591 | − | 0.367884i | ||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | 10.5000 | − | 6.06218i | 0.524345 | − | 0.302731i | −0.214366 | − | 0.976753i | \(-0.568768\pi\) |
0.738711 | + | 0.674023i | \(0.235435\pi\) | |||||||
\(402\) | −14.8492 | − | 25.7196i | −0.740613 | − | 1.28278i | ||||
\(403\) | 4.00000 | − | 6.92820i | 0.199254 | − | 0.345118i | ||||
\(404\) | −12.7279 | + | 7.34847i | −0.633238 | + | 0.365600i | ||||
\(405\) | 19.0919 | + | 11.0227i | 0.948683 | + | 0.547723i | ||||
\(406\) | 24.4949i | 1.21566i | ||||||||
\(407\) | −7.07107 | −0.350500 | ||||||||
\(408\) | −16.9706 | − | 9.79796i | −0.840168 | − | 0.485071i | ||||
\(409\) | 7.50000 | + | 4.33013i | 0.370851 | + | 0.214111i | 0.673830 | − | 0.738886i | \(-0.264648\pi\) |
−0.302979 | + | 0.952997i | \(0.597981\pi\) | |||||||
\(410\) | −18.0000 | −0.888957 | ||||||||
\(411\) | 29.4449i | 1.45241i | ||||||||
\(412\) | 2.82843 | − | 4.89898i | 0.139347 | − | 0.241355i | ||||
\(413\) | −2.12132 | − | 3.67423i | −0.104383 | − | 0.180797i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.8492 | − | 8.57321i | 0.728921 | − | 0.420843i | ||||
\(416\) | 16.0000 | + | 27.7128i | 0.784465 | + | 1.35873i | ||||
\(417\) | 15.5885i | 0.763370i | ||||||||
\(418\) | 28.2843 | − | 12.2474i | 1.38343 | − | 0.599042i | ||||
\(419\) | 14.0000 | 0.683945 | 0.341972 | − | 0.939710i | \(-0.388905\pi\) | ||||
0.341972 | + | 0.939710i | \(0.388905\pi\) | |||||||
\(420\) | 18.0000 | − | 10.3923i | 0.878310 | − | 0.507093i | ||||
\(421\) | 16.2635 | + | 28.1691i | 0.792632 | + | 1.37288i | 0.924332 | + | 0.381590i | \(0.124623\pi\) |
−0.131699 | + | 0.991290i | \(0.542043\pi\) | |||||||
\(422\) | 12.7279 | + | 7.34847i | 0.619586 | + | 0.357718i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.0000 | − | 20.7846i | 0.582772 | − | 1.00939i | ||||
\(425\) | 4.00000 | 0.194029 | ||||||||
\(426\) | 6.92820i | 0.335673i | ||||||||
\(427\) | 9.00000 | − | 15.5885i | 0.435541 | − | 0.754378i | ||||
\(428\) | 12.0000 | + | 6.92820i | 0.580042 | + | 0.334887i | ||||
\(429\) | 48.9898i | 2.36525i | ||||||||
\(430\) | 20.7846i | 1.00232i | ||||||||
\(431\) | 4.24264 | − | 7.34847i | 0.204361 | − | 0.353963i | −0.745568 | − | 0.666429i | \(-0.767822\pi\) |
0.949929 | + | 0.312466i | \(0.101155\pi\) | |||||||
\(432\) | −18.0000 | + | 10.3923i | −0.866025 | + | 0.500000i | ||||
\(433\) | 27.0000 | + | 15.5885i | 1.29754 | + | 0.749133i | 0.979978 | − | 0.199105i | \(-0.0638035\pi\) |
0.317559 | + | 0.948239i | \(0.397137\pi\) | |||||||
\(434\) | 4.24264 | − | 2.44949i | 0.203653 | − | 0.117579i | ||||
\(435\) | −15.0000 | − | 25.9808i | −0.719195 | − | 1.24568i | ||||
\(436\) | 28.2843 | 1.35457 | ||||||||
\(437\) | 6.36396 | − | 8.57321i | 0.304430 | − | 0.410112i | ||||
\(438\) | − | 7.34847i | − | 0.351123i | ||||||
\(439\) | 4.94975 | + | 8.57321i | 0.236239 | + | 0.409177i | 0.959632 | − | 0.281259i | \(-0.0907520\pi\) |
−0.723393 | + | 0.690436i | \(0.757419\pi\) | |||||||
\(440\) | 30.0000 | − | 17.3205i | 1.43019 | − | 0.825723i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16.0000 | − | 27.7128i | −0.761042 | − | 1.31816i | ||||
\(443\) | −15.5000 | + | 26.8468i | −0.736427 | + | 1.27553i | 0.217667 | + | 0.976023i | \(0.430155\pi\) |
−0.954094 | + | 0.299506i | \(0.903178\pi\) | |||||||
\(444\) | 4.89898i | 0.232495i | ||||||||
\(445\) | 8.48528 | 0.402241 | ||||||||
\(446\) | 17.0000 | − | 29.4449i | 0.804973 | − | 1.39425i | ||||
\(447\) | 14.8492 | − | 25.7196i | 0.702345 | − | 1.21650i | ||||
\(448\) | 19.5959i | 0.925820i | ||||||||
\(449\) | − | 12.1244i | − | 0.572184i | −0.958202 | − | 0.286092i | \(-0.907644\pi\) | ||
0.958202 | − | 0.286092i | \(-0.0923563\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.5000 | − | 12.9904i | 1.05948 | − | 0.611693i | ||||
\(452\) | −21.0000 | − | 12.1244i | −0.987757 | − | 0.570282i | ||||
\(453\) | 23.3345 | − | 13.4722i | 1.09635 | − | 0.632979i | ||||
\(454\) | −2.12132 | + | 1.22474i | −0.0995585 | + | 0.0574801i | ||||
\(455\) | 33.9411 | 1.59118 | ||||||||
\(456\) | −8.48528 | − | 19.5959i | −0.397360 | − | 0.917663i | ||||
\(457\) | −11.0000 | −0.514558 | −0.257279 | − | 0.966337i | \(-0.582826\pi\) | ||||
−0.257279 | + | 0.966337i | \(0.582826\pi\) | |||||||
\(458\) | −12.0000 | + | 6.92820i | −0.560723 | + | 0.323734i | ||||
\(459\) | 18.0000 | − | 10.3923i | 0.840168 | − | 0.485071i | ||||
\(460\) | 6.00000 | − | 10.3923i | 0.279751 | − | 0.484544i | ||||
\(461\) | 12.7279 | − | 7.34847i | 0.592798 | − | 0.342252i | −0.173405 | − | 0.984851i | \(-0.555477\pi\) |
0.766203 | + | 0.642598i | \(0.222144\pi\) | |||||||
\(462\) | −15.0000 | + | 25.9808i | −0.697863 | + | 1.20873i | ||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 28.2843 | 1.31306 | ||||||||
\(465\) | −3.00000 | + | 5.19615i | −0.139122 | + | 0.240966i | ||||
\(466\) | −0.707107 | + | 1.22474i | −0.0327561 | + | 0.0567352i | ||||
\(467\) | 13.0000 | 0.601568 | 0.300784 | − | 0.953692i | \(-0.402752\pi\) | ||||
0.300784 | + | 0.953692i | \(0.402752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.8492 | − | 25.7196i | 0.685674 | − | 1.18762i | ||||
\(470\) | 12.7279 | + | 22.0454i | 0.587095 | + | 1.01688i | ||||
\(471\) | 4.24264 | − | 7.34847i | 0.195491 | − | 0.338600i | ||||
\(472\) | −4.24264 | + | 2.44949i | −0.195283 | + | 0.112747i | ||||
\(473\) | −15.0000 | − | 25.9808i | −0.689701 | − | 1.19460i | ||||
\(474\) | − | 6.92820i | − | 0.318223i | ||||||
\(475\) | 3.50000 | + | 2.59808i | 0.160591 | + | 0.119208i | ||||
\(476\) | − | 19.5959i | − | 0.898177i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.2132 | + | 12.2474i | 0.969256 | + | 0.559600i | 0.899009 | − | 0.437929i | \(-0.144288\pi\) |
0.0702467 | + | 0.997530i | \(0.477621\pi\) | |||||||
\(480\) | −12.0000 | − | 20.7846i | −0.547723 | − | 0.948683i | ||||
\(481\) | −4.00000 | + | 6.92820i | −0.182384 | + | 0.315899i | ||||
\(482\) | 22.0454i | 1.00414i | ||||||||
\(483\) | 10.3923i | 0.472866i | ||||||||
\(484\) | −14.0000 | + | 24.2487i | −0.636364 | + | 1.10221i | ||||
\(485\) | −23.3345 | + | 40.4166i | −1.05957 | + | 1.83522i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.3553 | −1.60210 | −0.801052 | − | 0.598595i | \(-0.795726\pi\) | ||||
−0.801052 | + | 0.598595i | \(0.795726\pi\) | |||||||
\(488\) | −18.0000 | − | 10.3923i | −0.814822 | − | 0.470438i | ||||
\(489\) | −4.50000 | + | 2.59808i | −0.203497 | + | 0.117489i | ||||
\(490\) | −3.00000 | − | 1.73205i | −0.135526 | − | 0.0782461i | ||||
\(491\) | −17.0000 | − | 29.4449i | −0.767199 | − | 1.32883i | −0.939076 | − | 0.343710i | \(-0.888316\pi\) |
0.171877 | − | 0.985118i | \(-0.445017\pi\) | |||||||
\(492\) | −9.00000 | − | 15.5885i | −0.405751 | − | 0.702782i | ||||
\(493\) | −28.2843 | −1.27386 | ||||||||
\(494\) | 4.00000 | − | 34.6410i | 0.179969 | − | 1.55857i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.82843 | − | 4.89898i | −0.127000 | − | 0.219971i | ||||
\(497\) | −6.00000 | + | 3.46410i | −0.269137 | + | 0.155386i | ||||
\(498\) | 14.8492 | + | 8.57321i | 0.665410 | + | 0.384175i | ||||
\(499\) | −0.500000 | − | 0.866025i | −0.0223831 | − | 0.0387686i | 0.854617 | − | 0.519259i | \(-0.173792\pi\) |
−0.877000 | + | 0.480490i | \(0.840459\pi\) | |||||||
\(500\) | −16.9706 | − | 9.79796i | −0.758947 | − | 0.438178i | ||||
\(501\) | 9.79796i | 0.437741i | ||||||||
\(502\) | −32.5269 | −1.45175 | ||||||||
\(503\) | 2.12132 | + | 1.22474i | 0.0945850 | + | 0.0546087i | 0.546546 | − | 0.837429i | \(-0.315942\pi\) |
−0.451961 | + | 0.892037i | \(0.649276\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | 17.3205i | 0.769991i | ||||||||
\(507\) | 28.5000 | + | 16.4545i | 1.26573 | + | 0.730769i | ||||
\(508\) | 2.82843 | + | 4.89898i | 0.125491 | + | 0.217357i | ||||
\(509\) | −11.3137 | + | 19.5959i | −0.501471 | + | 0.868574i | 0.498527 | + | 0.866874i | \(0.333874\pi\) |
−0.999999 | + | 0.00169976i | \(0.999459\pi\) | |||||||
\(510\) | 12.0000 | + | 20.7846i | 0.531369 | + | 0.920358i | ||||
\(511\) | 6.36396 | − | 3.67423i | 0.281525 | − | 0.162539i | ||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | 22.5000 | + | 2.59808i | 0.993399 | + | 0.114708i | ||||
\(514\) | − | 22.0454i | − | 0.972381i | ||||||
\(515\) | −6.00000 | + | 3.46410i | −0.264392 | + | 0.152647i | ||||
\(516\) | −18.0000 | + | 10.3923i | −0.792406 | + | 0.457496i | ||||
\(517\) | −31.8198 | − | 18.3712i | −1.39943 | − | 0.807963i | ||||
\(518\) | −4.24264 | + | 2.44949i | −0.186411 | + | 0.107624i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | − | 39.1918i | − | 1.71868i | ||||||
\(521\) | 22.5167i | 0.986473i | 0.869895 | + | 0.493236i | \(0.164186\pi\) | ||||
−0.869895 | + | 0.493236i | \(0.835814\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.0000 | − | 10.3923i | −0.787085 | − | 0.454424i | 0.0518503 | − | 0.998655i | \(-0.483488\pi\) |
−0.838935 | + | 0.544231i | \(0.816821\pi\) | |||||||
\(524\) | −14.0000 | −0.611593 | ||||||||
\(525\) | −4.24264 | −0.185164 | ||||||||
\(526\) | 33.0000 | + | 19.0526i | 1.43887 | + | 0.830731i | ||||
\(527\) | 2.82843 | + | 4.89898i | 0.123208 | + | 0.213403i | ||||
\(528\) | 30.0000 | + | 17.3205i | 1.30558 | + | 0.753778i | ||||
\(529\) | −8.50000 | − | 14.7224i | −0.369565 | − | 0.640106i | ||||
\(530\) | −25.4558 | + | 14.6969i | −1.10573 | + | 0.638394i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.7279 | − | 17.1464i | 0.551825 | − | 0.743392i | ||||
\(533\) | − | 29.3939i | − | 1.27319i | ||||||
\(534\) | 4.24264 | + | 7.34847i | 0.183597 | + | 0.317999i | ||||
\(535\) | −8.48528 | − | 14.6969i | −0.366851 | − | 0.635404i | ||||
\(536\) | −29.6985 | − | 17.1464i | −1.28278 | − | 0.740613i | ||||
\(537\) | 7.50000 | + | 12.9904i | 0.323649 | + | 0.560576i | ||||
\(538\) | −6.00000 | + | 10.3923i | −0.258678 | + | 0.448044i | ||||
\(539\) | 5.00000 | 0.215365 | ||||||||
\(540\) | 25.4558 | 1.09545 | ||||||||
\(541\) | 12.7279 | + | 7.34847i | 0.547216 | + | 0.315935i | 0.747998 | − | 0.663701i | \(-0.231015\pi\) |
−0.200782 | + | 0.979636i | \(0.564348\pi\) | |||||||
\(542\) | −3.00000 | − | 1.73205i | −0.128861 | − | 0.0743980i | ||||
\(543\) | − | 41.6413i | − | 1.78700i | ||||||
\(544\) | −22.6274 | −0.970143 | ||||||||
\(545\) | −30.0000 | − | 17.3205i | −1.28506 | − | 0.741929i | ||||
\(546\) | 16.9706 | + | 29.3939i | 0.726273 | + | 1.25794i | ||||
\(547\) | 12.0000 | + | 6.92820i | 0.513083 | + | 0.296229i | 0.734100 | − | 0.679041i | \(-0.237604\pi\) |
−0.221017 | + | 0.975270i | \(0.570938\pi\) | |||||||
\(548\) | 17.0000 | + | 29.4449i | 0.726204 | + | 1.25782i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.07107 | −0.301511 | ||||||||
\(551\) | −24.7487 | − | 18.3712i | −1.05433 | − | 0.782638i | ||||
\(552\) | 12.0000 | 0.510754 | ||||||||
\(553\) | 6.00000 | − | 3.46410i | 0.255146 | − | 0.147309i | ||||
\(554\) | −9.00000 | + | 5.19615i | −0.382373 | + | 0.220763i | ||||
\(555\) | 3.00000 | − | 5.19615i | 0.127343 | − | 0.220564i | ||||
\(556\) | 9.00000 | + | 15.5885i | 0.381685 | + | 0.661098i | ||||
\(557\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.9411 | −1.43556 | ||||||||
\(560\) | 12.0000 | − | 20.7846i | 0.507093 | − | 0.878310i | ||||
\(561\) | −30.0000 | − | 17.3205i | −1.26660 | − | 0.731272i | ||||
\(562\) | − | 2.44949i | − | 0.103325i | ||||||
\(563\) | 22.5167i | 0.948964i | 0.880265 | + | 0.474482i | \(0.157365\pi\) | ||||
−0.880265 | + | 0.474482i | \(0.842635\pi\) | |||||||
\(564\) | −12.7279 | + | 22.0454i | −0.535942 | + | 0.928279i | ||||
\(565\) | 14.8492 | + | 25.7196i | 0.624712 | + | 1.08203i | ||||
\(566\) | −12.0208 | + | 20.8207i | −0.505273 | + | 0.875158i | ||||
\(567\) | −19.0919 | + | 11.0227i | −0.801784 | + | 0.462910i | ||||
\(568\) | 4.00000 | + | 6.92820i | 0.167836 | + | 0.290701i | ||||
\(569\) | 17.3205i | 0.726113i | 0.931767 | + | 0.363057i | \(0.118267\pi\) | ||||
−0.931767 | + | 0.363057i | \(0.881733\pi\) | |||||||
\(570\) | −3.00000 | + | 25.9808i | −0.125656 | + | 1.08821i | ||||
\(571\) | −9.00000 | −0.376638 | −0.188319 | − | 0.982108i | \(-0.560304\pi\) | ||||
−0.188319 | + | 0.982108i | \(0.560304\pi\) | |||||||
\(572\) | 28.2843 | + | 48.9898i | 1.18262 | + | 2.04837i | ||||
\(573\) | 16.9706 | + | 29.3939i | 0.708955 | + | 1.22795i | ||||
\(574\) | 9.00000 | − | 15.5885i | 0.375653 | − | 0.650650i | ||||
\(575\) | −2.12132 | + | 1.22474i | −0.0884652 | + | 0.0510754i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.00000 | −0.124892 | −0.0624458 | − | 0.998048i | \(-0.519890\pi\) | ||||
−0.0624458 | + | 0.998048i | \(0.519890\pi\) | |||||||
\(578\) | −1.41421 | −0.0588235 | ||||||||
\(579\) | 3.00000 | − | 5.19615i | 0.124676 | − | 0.215945i | ||||
\(580\) | −30.0000 | − | 17.3205i | −1.24568 | − | 0.719195i | ||||
\(581\) | 17.1464i | 0.711354i | ||||||||
\(582\) | −46.6690 | −1.93449 | ||||||||
\(583\) | 21.2132 | − | 36.7423i | 0.878561 | − | 1.52171i | ||||
\(584\) | −4.24264 | − | 7.34847i | −0.175562 | − | 0.304082i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.0000 | − | 36.3731i | −0.867502 | − | 1.50256i | ||||
\(587\) | −1.00000 | − | 1.73205i | −0.0412744 | − | 0.0714894i | 0.844650 | − | 0.535319i | \(-0.179808\pi\) |
−0.885925 | + | 0.463829i | \(0.846475\pi\) | |||||||
\(588\) | − | 3.46410i | − | 0.142857i | ||||||
\(589\) | −0.707107 | + | 6.12372i | −0.0291358 | + | 0.252324i | ||||
\(590\) | 6.00000 | 0.247016 | ||||||||
\(591\) | 14.8492 | + | 25.7196i | 0.610816 | + | 1.05796i | ||||
\(592\) | 2.82843 | + | 4.89898i | 0.116248 | + | 0.201347i | ||||
\(593\) | 6.50000 | − | 11.2583i | 0.266923 | − | 0.462324i | −0.701143 | − | 0.713021i | \(-0.747326\pi\) |
0.968066 | + | 0.250697i | \(0.0806597\pi\) | |||||||
\(594\) | −31.8198 | + | 18.3712i | −1.30558 | + | 0.753778i | ||||
\(595\) | −12.0000 | + | 20.7846i | −0.491952 | + | 0.852086i | ||||
\(596\) | − | 34.2929i | − | 1.40469i | ||||||
\(597\) | −42.4264 | −1.73640 | ||||||||
\(598\) | 16.9706 | + | 9.79796i | 0.693978 | + | 0.400668i | ||||
\(599\) | 9.19239 | − | 15.9217i | 0.375591 | − | 0.650542i | −0.614824 | − | 0.788664i | \(-0.710773\pi\) |
0.990415 | + | 0.138122i | \(0.0441065\pi\) | |||||||
\(600\) | 4.89898i | 0.200000i | ||||||||
\(601\) | − | 22.5167i | − | 0.918474i | −0.888314 | − | 0.459237i | \(-0.848123\pi\) | ||
0.888314 | − | 0.459237i | \(-0.151877\pi\) | |||||||
\(602\) | −18.0000 | − | 10.3923i | −0.733625 | − | 0.423559i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 15.5563 | − | 26.9444i | 0.632979 | − | 1.09635i | ||||
\(605\) | 29.6985 | − | 17.1464i | 1.20742 | − | 0.697101i | ||||
\(606\) | 9.00000 | + | 15.5885i | 0.365600 | + | 0.633238i | ||||
\(607\) | 7.07107 | 0.287006 | 0.143503 | − | 0.989650i | \(-0.454163\pi\) | ||||
0.143503 | + | 0.989650i | \(0.454163\pi\) | |||||||
\(608\) | −19.7990 | − | 14.6969i | −0.802955 | − | 0.596040i | ||||
\(609\) | 30.0000 | 1.21566 | ||||||||
\(610\) | 12.7279 | + | 22.0454i | 0.515339 | + | 0.892592i | ||||
\(611\) | −36.0000 | + | 20.7846i | −1.45640 | + | 0.840855i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.48528 | + | 4.89898i | −0.342717 | + | 0.197868i | −0.661473 | − | 0.749969i | \(-0.730068\pi\) |
0.318756 | + | 0.947837i | \(0.396735\pi\) | |||||||
\(614\) | −6.36396 | − | 3.67423i | −0.256829 | − | 0.148280i | ||||
\(615\) | 22.0454i | 0.888957i | ||||||||
\(616\) | 34.6410i | 1.39573i | ||||||||
\(617\) | −6.50000 | + | 11.2583i | −0.261680 | + | 0.453243i | −0.966689 | − | 0.255956i | \(-0.917610\pi\) |
0.705008 | + | 0.709199i | \(0.250943\pi\) | |||||||
\(618\) | −6.00000 | − | 3.46410i | −0.241355 | − | 0.139347i | ||||
\(619\) | −10.0000 | −0.401934 | −0.200967 | − | 0.979598i | \(-0.564408\pi\) | ||||
−0.200967 | + | 0.979598i | \(0.564408\pi\) | |||||||
\(620\) | 6.92820i | 0.278243i | ||||||||
\(621\) | −6.36396 | + | 11.0227i | −0.255377 | + | 0.442326i | ||||
\(622\) | 15.0000 | − | 8.66025i | 0.601445 | − | 0.347245i | ||||
\(623\) | −4.24264 | + | 7.34847i | −0.169978 | + | 0.294410i | ||||
\(624\) | 33.9411 | − | 19.5959i | 1.35873 | − | 0.784465i | ||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 1.41421 | 0.0565233 | ||||||||
\(627\) | −15.0000 | − | 34.6410i | −0.599042 | − | 1.38343i | ||||
\(628\) | − | 9.79796i | − | 0.390981i | ||||||
\(629\) | −2.82843 | − | 4.89898i | −0.112777 | − | 0.195335i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.0919 | + | 11.0227i | 0.760036 | + | 0.438807i | 0.829309 | − | 0.558791i | \(-0.188735\pi\) |
−0.0692728 | + | 0.997598i | \(0.522068\pi\) | |||||||
\(632\) | −4.00000 | − | 6.92820i | −0.159111 | − | 0.275589i | ||||
\(633\) | 9.00000 | − | 15.5885i | 0.357718 | − | 0.619586i | ||||
\(634\) | 12.0000 | 0.476581 | ||||||||
\(635\) | − | 6.92820i | − | 0.274937i | ||||||
\(636\) | −25.4558 | − | 14.6969i | −1.00939 | − | 0.582772i | ||||
\(637\) | 2.82843 | − | 4.89898i | 0.112066 | − | 0.194105i | ||||
\(638\) | 50.0000 | 1.97952 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24.0000 | − | 13.8564i | −0.948683 | − | 0.547723i | ||||
\(641\) | 7.50000 | − | 4.33013i | 0.296232 | − | 0.171030i | −0.344517 | − | 0.938780i | \(-0.611957\pi\) |
0.640749 | + | 0.767750i | \(0.278624\pi\) | |||||||
\(642\) | 8.48528 | − | 14.6969i | 0.334887 | − | 0.580042i | ||||
\(643\) | 9.50000 | + | 16.4545i | 0.374643 | + | 0.648901i | 0.990274 | − | 0.139134i | \(-0.0444318\pi\) |
−0.615630 | + | 0.788035i | \(0.711098\pi\) | |||||||
\(644\) | 6.00000 | + | 10.3923i | 0.236433 | + | 0.409514i | ||||
\(645\) | 25.4558 | 1.00232 | ||||||||
\(646\) | 19.7990 | + | 14.6969i | 0.778981 | + | 0.578243i | ||||
\(647\) | 29.3939i | 1.15559i | 0.816181 | + | 0.577796i | \(0.196087\pi\) | ||||
−0.816181 | + | 0.577796i | \(0.803913\pi\) | |||||||
\(648\) | 12.7279 | + | 22.0454i | 0.500000 | + | 0.866025i | ||||
\(649\) | −7.50000 | + | 4.33013i | −0.294401 | + | 0.169972i | ||||
\(650\) | −4.00000 | + | 6.92820i | −0.156893 | + | 0.271746i | ||||
\(651\) | −3.00000 | − | 5.19615i | −0.117579 | − | 0.203653i | ||||
\(652\) | −3.00000 | + | 5.19615i | −0.117489 | + | 0.203497i | ||||
\(653\) | 14.6969i | 0.575136i | 0.957760 | + | 0.287568i | \(0.0928467\pi\) | ||||
−0.957760 | + | 0.287568i | \(0.907153\pi\) | |||||||
\(654\) | − | 34.6410i | − | 1.35457i | ||||||
\(655\) | 14.8492 | + | 8.57321i | 0.580208 | + | 0.334983i | ||||
\(656\) | −18.0000 | − | 10.3923i | −0.702782 | − | 0.405751i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −25.4558 | −0.992372 | ||||||||
\(659\) | −30.0000 | − | 17.3205i | −1.16863 | − | 0.674711i | −0.215276 | − | 0.976553i | \(-0.569065\pi\) |
−0.953358 | + | 0.301842i | \(0.902398\pi\) | |||||||
\(660\) | −21.2132 | − | 36.7423i | −0.825723 | − | 1.43019i | ||||
\(661\) | −4.94975 | + | 8.57321i | −0.192523 | + | 0.333459i | −0.946086 | − | 0.323917i | \(-0.895000\pi\) |
0.753563 | + | 0.657376i | \(0.228334\pi\) | |||||||
\(662\) | 6.36396 | − | 3.67423i | 0.247342 | − | 0.142803i | ||||
\(663\) | −33.9411 | + | 19.5959i | −1.31816 | + | 0.761042i | ||||
\(664\) | 19.7990 | 0.768350 | ||||||||
\(665\) | −24.0000 | + | 10.3923i | −0.930680 | + | 0.402996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.0000 | − | 8.66025i | 0.580802 | − | 0.335326i | ||||
\(668\) | 5.65685 | + | 9.79796i | 0.218870 | + | 0.379094i | ||||
\(669\) | −36.0624 | − | 20.8207i | −1.39425 | − | 0.804973i | ||||
\(670\) | 21.0000 | + | 36.3731i | 0.811301 | + | 1.40521i | ||||
\(671\) | −31.8198 | − | 18.3712i | −1.22839 | − | 0.709211i | ||||
\(672\) | 24.0000 | 0.925820 | ||||||||
\(673\) | − | 24.2487i | − | 0.934719i | −0.884067 | − | 0.467360i | \(-0.845205\pi\) | ||
0.884067 | − | 0.467360i | \(-0.154795\pi\) | |||||||
\(674\) | −31.8198 | − | 18.3712i | −1.22565 | − | 0.707631i | ||||
\(675\) | −4.50000 | − | 2.59808i | −0.173205 | − | 0.100000i | ||||
\(676\) | 38.0000 | 1.46154 | ||||||||
\(677\) | 16.9706 | 0.652232 | 0.326116 | − | 0.945330i | \(-0.394260\pi\) | ||||
0.326116 | + | 0.945330i | \(0.394260\pi\) | |||||||
\(678\) | −14.8492 | + | 25.7196i | −0.570282 | + | 0.987757i | ||||
\(679\) | −23.3345 | − | 40.4166i | −0.895497 | − | 1.55105i | ||||
\(680\) | 24.0000 | + | 13.8564i | 0.920358 | + | 0.531369i | ||||
\(681\) | 1.50000 | + | 2.59808i | 0.0574801 | + | 0.0995585i | ||||
\(682\) | −5.00000 | − | 8.66025i | −0.191460 | − | 0.331618i | ||||
\(683\) | − | 20.7846i | − | 0.795301i | −0.917537 | − | 0.397650i | \(-0.869826\pi\) | ||
0.917537 | − | 0.397650i | \(-0.130174\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 41.6413i | − | 1.59103i | ||||||
\(686\) | 24.0000 | − | 13.8564i | 0.916324 | − | 0.529040i | ||||
\(687\) | 8.48528 | + | 14.6969i | 0.323734 | + | 0.560723i | ||||
\(688\) | −12.0000 | + | 20.7846i | −0.457496 | + | 0.792406i | ||||
\(689\) | −24.0000 | − | 41.5692i | −0.914327 | − | 1.58366i | ||||
\(690\) | −12.7279 | − | 7.34847i | −0.484544 | − | 0.279751i | ||||
\(691\) | 6.00000 | 0.228251 | 0.114125 | − | 0.993466i | \(-0.463593\pi\) | ||||
0.114125 | + | 0.993466i | \(0.463593\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.2635 | − | 28.1691i | 0.617352 | − | 1.06929i | ||||
\(695\) | − | 22.0454i | − | 0.836230i | ||||||
\(696\) | − | 34.6410i | − | 1.31306i | ||||||
\(697\) | 18.0000 | + | 10.3923i | 0.681799 | + | 0.393637i | ||||
\(698\) | −36.0000 | + | 20.7846i | −1.36262 | + | 0.786709i | ||||
\(699\) | 1.50000 | + | 0.866025i | 0.0567352 | + | 0.0327561i | ||||
\(700\) | −4.24264 | + | 2.44949i | −0.160357 | + | 0.0925820i | ||||
\(701\) | −10.6066 | + | 6.12372i | −0.400606 | + | 0.231290i | −0.686745 | − | 0.726898i | \(-0.740961\pi\) |
0.286140 | + | 0.958188i | \(0.407628\pi\) | |||||||
\(702\) | 41.5692i | 1.56893i | ||||||||
\(703\) | 0.707107 | − | 6.12372i | 0.0266690 | − | 0.230961i | ||||
\(704\) | 40.0000 | 1.50756 | ||||||||
\(705\) | 27.0000 | − | 15.5885i | 1.01688 | − | 0.587095i | ||||
\(706\) | 21.9203 | + | 37.9671i | 0.824982 | + | 1.42891i | ||||
\(707\) | −9.00000 | + | 15.5885i | −0.338480 | + | 0.586264i | ||||
\(708\) | 3.00000 | + | 5.19615i | 0.112747 | + | 0.195283i | ||||
\(709\) | 27.5772 | + | 15.9217i | 1.03568 | + | 0.597951i | 0.918607 | − | 0.395172i | \(-0.129315\pi\) |
0.117075 | + | 0.993123i | \(0.462648\pi\) | |||||||
\(710\) | − | 9.79796i | − | 0.367711i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.48528 | + | 4.89898i | 0.317999 | + | 0.183597i | ||||
\(713\) | −3.00000 | − | 1.73205i | −0.112351 | − | 0.0648658i | ||||
\(714\) | −24.0000 | −0.898177 | ||||||||
\(715\) | − | 69.2820i | − | 2.59100i | ||||||
\(716\) | 15.0000 | + | 8.66025i | 0.560576 | + | 0.323649i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −21.0000 | − | 12.1244i | −0.783713 | − | 0.452477i | ||||
\(719\) | 16.9706 | − | 9.79796i | 0.632895 | − | 0.365402i | −0.148977 | − | 0.988841i | \(-0.547598\pi\) |
0.781872 | + | 0.623438i | \(0.214265\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 6.92820i | − | 0.258020i | ||||||
\(722\) | 7.77817 | + | 25.7196i | 0.289474 | + | 0.957186i | ||||
\(723\) | 27.0000 | 1.00414 | ||||||||
\(724\) | −24.0416 | − | 41.6413i | −0.893500 | − | 1.54759i | ||||
\(725\) | 3.53553 | + | 6.12372i | 0.131306 | + | 0.227429i | ||||
\(726\) | 29.6985 | + | 17.1464i | 1.10221 | + | 0.636364i | ||||
\(727\) | 42.4264 | − | 24.4949i | 1.57351 | − | 0.908465i | 0.577774 | − | 0.816197i | \(-0.303921\pi\) |
0.995734 | − | 0.0922688i | \(-0.0294119\pi\) | |||||||
\(728\) | 33.9411 | + | 19.5959i | 1.25794 | + | 0.726273i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 10.3923i | 0.384636i | ||||||||
\(731\) | 12.0000 | − | 20.7846i | 0.443836 | − | 0.768747i | ||||
\(732\) | −12.7279 | + | 22.0454i | −0.470438 | + | 0.814822i | ||||
\(733\) | 7.34847i | 0.271422i | 0.990748 | + | 0.135711i | \(0.0433318\pi\) | ||||
−0.990748 | + | 0.135711i | \(0.956668\pi\) | |||||||
\(734\) | − | 10.3923i | − | 0.383587i | ||||||
\(735\) | −2.12132 | + | 3.67423i | −0.0782461 | + | 0.135526i | ||||
\(736\) | 12.0000 | − | 6.92820i | 0.442326 | − | 0.255377i | ||||
\(737\) | −52.5000 | − | 30.3109i | −1.93386 | − | 1.11652i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.5000 | + | 44.1673i | 0.938033 | + | 1.62472i | 0.769135 | + | 0.639087i | \(0.220687\pi\) |
0.168898 | + | 0.985634i | \(0.445979\pi\) | |||||||
\(740\) | − | 6.92820i | − | 0.254686i | ||||||
\(741\) | −42.4264 | − | 4.89898i | −1.55857 | − | 0.179969i | ||||
\(742\) | − | 29.3939i | − | 1.07908i | ||||||
\(743\) | 6.36396 | + | 11.0227i | 0.233471 | + | 0.404384i | 0.958827 | − | 0.283990i | \(-0.0916582\pi\) |
−0.725356 | + | 0.688374i | \(0.758325\pi\) | |||||||
\(744\) | −6.00000 | + | 3.46410i | −0.219971 | + | 0.127000i | ||||
\(745\) | −21.0000 | + | 36.3731i | −0.769380 | + | 1.33261i | ||||
\(746\) | 8.00000 | + | 13.8564i | 0.292901 | + | 0.507319i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −40.0000 | −1.46254 | ||||||||
\(749\) | 16.9706 | 0.620091 | ||||||||
\(750\) | −12.0000 | + | 20.7846i | −0.438178 | + | 0.758947i | ||||
\(751\) | 5.65685 | − | 9.79796i | 0.206422 | − | 0.357533i | −0.744163 | − | 0.667998i | \(-0.767152\pi\) |
0.950585 | + | 0.310465i | \(0.100485\pi\) | |||||||
\(752\) | 29.3939i | 1.07188i | ||||||||
\(753\) | 39.8372i | 1.45175i | ||||||||
\(754\) | 28.2843 | − | 48.9898i | 1.03005 | − | 1.78410i | ||||
\(755\) | −33.0000 | + | 19.0526i | −1.20099 | + | 0.693394i | ||||
\(756\) | −12.7279 | + | 22.0454i | −0.462910 | + | 0.801784i | ||||
\(757\) | 33.9411 | − | 19.5959i | 1.23361 | − | 0.712226i | 0.265830 | − | 0.964020i | \(-0.414354\pi\) |
0.967781 | + | 0.251794i | \(0.0810206\pi\) | |||||||
\(758\) | 29.6985 | − | 17.1464i | 1.07870 | − | 0.622786i | ||||
\(759\) | 21.2132 | 0.769991 | ||||||||
\(760\) | 12.0000 | + | 27.7128i | 0.435286 | + | 1.00525i | ||||
\(761\) | −1.00000 | −0.0362500 | −0.0181250 | − | 0.999836i | \(-0.505770\pi\) | ||||
−0.0181250 | + | 0.999836i | \(0.505770\pi\) | |||||||
\(762\) | 6.00000 | − | 3.46410i | 0.217357 | − | 0.125491i | ||||
\(763\) | 30.0000 | − | 17.3205i | 1.08607 | − | 0.627044i | ||||
\(764\) | 33.9411 | + | 19.5959i | 1.22795 | + | 0.708955i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.00000 | − | 12.1244i | 0.252920 | − | 0.438071i | ||||
\(767\) | 9.79796i | 0.353784i | ||||||||
\(768\) | − | 27.7128i | − | 1.00000i | ||||||
\(769\) | 8.00000 | − | 13.8564i | 0.288487 | − | 0.499675i | −0.684962 | − | 0.728579i | \(-0.740181\pi\) |
0.973449 | + | 0.228904i | \(0.0735143\pi\) | |||||||
\(770\) | 21.2132 | − | 36.7423i | 0.764471 | − | 1.32410i | ||||
\(771\) | −27.0000 | −0.972381 | ||||||||
\(772\) | − | 6.92820i | − | 0.249351i | ||||||
\(773\) | −24.7487 | + | 42.8661i | −0.890150 | + | 1.54179i | −0.0504557 | + | 0.998726i | \(0.516067\pi\) |
−0.839694 | + | 0.543059i | \(0.817266\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.707107 | − | 1.22474i | 0.0254000 | − | 0.0439941i | ||||
\(776\) | −46.6690 | + | 26.9444i | −1.67532 | + | 0.967247i | ||||
\(777\) | 3.00000 | + | 5.19615i | 0.107624 | + | 0.186411i | ||||
\(778\) | 48.4974i | 1.73872i | ||||||||
\(779\) | 9.00000 | + | 20.7846i | 0.322458 | + | 0.744686i | ||||
\(780\) | −48.0000 | −1.71868 | ||||||||
\(781\) | 7.07107 | + | 12.2474i | 0.253023 | + | 0.438248i | ||||
\(782\) | −12.0000 | + | 6.92820i | −0.429119 | + | 0.247752i | ||||
\(783\) | 31.8198 | + | 18.3712i | 1.13715 | + | 0.656532i | ||||
\(784\) | −2.00000 | − | 3.46410i | −0.0714286 | − | 0.123718i | ||||
\(785\) | −6.00000 | + | 10.3923i | −0.214149 | + | 0.370917i | ||||
\(786\) | 17.1464i | 0.611593i | ||||||||
\(787\) | − | 25.9808i | − | 0.926114i | −0.886328 | − | 0.463057i | \(-0.846752\pi\) | ||
0.886328 | − | 0.463057i | \(-0.153248\pi\) | |||||||
\(788\) | 29.6985 | + | 17.1464i | 1.05796 | + | 0.610816i | ||||
\(789\) | 23.3345 | − | 40.4166i | 0.830731 | − | 1.43887i | ||||
\(790\) | 9.79796i | 0.348596i | ||||||||
\(791\) | −29.6985 | −1.05596 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.0000 | + | 20.7846i | −1.27840 | + | 0.738083i | ||||
\(794\) | 39.0000 | + | 22.5167i | 1.38406 | + | 0.799086i | ||||
\(795\) | 18.0000 | + | 31.1769i | 0.638394 | + | 1.10573i | ||||
\(796\) | −42.4264 | + | 24.4949i | −1.50376 | + | 0.868199i | ||||
\(797\) | −9.89949 | −0.350658 | −0.175329 | − | 0.984510i | \(-0.556099\pi\) | ||||
−0.175329 | + | 0.984510i | \(0.556099\pi\) | |||||||
\(798\) | −21.0000 | − | 15.5885i | −0.743392 | − | 0.551825i | ||||
\(799\) | − | 29.3939i | − | 1.03988i | ||||||
\(800\) | 2.82843 | + | 4.89898i | 0.100000 | + | 0.173205i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.8492 | − | 8.57321i | −0.524345 | − | 0.302731i | ||||
\(803\) | −7.50000 | − | 12.9904i | −0.264669 | − | 0.458421i | ||||
\(804\) | −21.0000 | + | 36.3731i | −0.740613 | + | 1.28278i | ||||
\(805\) | − | 14.6969i | − | 0.517999i | ||||||
\(806\) | −11.3137 | −0.398508 | ||||||||
\(807\) | 12.7279 | + | 7.34847i | 0.448044 | + | 0.258678i | ||||
\(808\) | 18.0000 | + | 10.3923i | 0.633238 | + | 0.365600i | ||||
\(809\) | 47.0000 | 1.65243 | 0.826216 | − | 0.563353i | \(-0.190489\pi\) | ||||
0.826216 | + | 0.563353i | \(0.190489\pi\) | |||||||
\(810\) | − | 31.1769i | − | 1.09545i | ||||||
\(811\) | 6.00000 | + | 3.46410i | 0.210688 | + | 0.121641i | 0.601631 | − | 0.798774i | \(-0.294518\pi\) |
−0.390943 | + | 0.920415i | \(0.627851\pi\) | |||||||
\(812\) | 30.0000 | − | 17.3205i | 1.05279 | − | 0.607831i | ||||
\(813\) | −2.12132 | + | 3.67423i | −0.0743980 | + | 0.128861i | ||||
\(814\) | 5.00000 | + | 8.66025i | 0.175250 | + | 0.303542i | ||||
\(815\) | 6.36396 | − | 3.67423i | 0.222920 | − | 0.128703i | ||||
\(816\) | 27.7128i | 0.970143i | ||||||||
\(817\) | 24.0000 | − | 10.3923i | 0.839654 | − | 0.363581i | ||||
\(818\) | − | 12.2474i | − | 0.428222i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.7279 | + | 22.0454i | 0.444478 | + | 0.769859i | ||||
\(821\) | 12.7279 | + | 7.34847i | 0.444208 | + | 0.256463i | 0.705381 | − | 0.708829i | \(-0.250776\pi\) |
−0.261173 | + | 0.965292i | \(0.584109\pi\) | |||||||
\(822\) | 36.0624 | − | 20.8207i | 1.25782 | − | 0.726204i | ||||
\(823\) | 29.6985 | + | 17.1464i | 1.03522 | + | 0.597687i | 0.918477 | − | 0.395475i | \(-0.129420\pi\) |
0.116747 | + | 0.993162i | \(0.462753\pi\) | |||||||
\(824\) | −8.00000 | −0.278693 | ||||||||
\(825\) | 8.66025i | 0.301511i | ||||||||
\(826\) | −3.00000 | + | 5.19615i | −0.104383 | + | 0.180797i | ||||
\(827\) | 22.5000 | + | 12.9904i | 0.782402 | + | 0.451720i | 0.837281 | − | 0.546773i | \(-0.184144\pi\) |
−0.0548791 | + | 0.998493i | \(0.517477\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.1127 | 1.08059 | 0.540294 | − | 0.841476i | \(-0.318313\pi\) | ||||
0.540294 | + | 0.841476i | \(0.318313\pi\) | |||||||
\(830\) | −21.0000 | − | 12.1244i | −0.728921 | − | 0.420843i | ||||
\(831\) | 6.36396 | + | 11.0227i | 0.220763 | + | 0.382373i | ||||
\(832\) | 22.6274 | − | 39.1918i | 0.784465 | − | 1.35873i | ||||
\(833\) | 2.00000 | + | 3.46410i | 0.0692959 | + | 0.120024i | ||||
\(834\) | 19.0919 | − | 11.0227i | 0.661098 | − | 0.381685i | ||||
\(835\) | − | 13.8564i | − | 0.479521i | ||||||
\(836\) | −35.0000 | − | 25.9808i | −1.21050 | − | 0.898563i | ||||
\(837\) | − | 7.34847i | − | 0.254000i | ||||||
\(838\) | −9.89949 | − | 17.1464i | −0.341972 | − | 0.592314i | ||||
\(839\) | 2.12132 | + | 3.67423i | 0.0732361 | + | 0.126849i | 0.900318 | − | 0.435233i | \(-0.143334\pi\) |
−0.827082 | + | 0.562082i | \(0.810001\pi\) | |||||||
\(840\) | −25.4558 | − | 14.6969i | −0.878310 | − | 0.507093i | ||||
\(841\) | −10.5000 | − | 18.1865i | −0.362069 | − | 0.627122i | ||||
\(842\) | 23.0000 | − | 39.8372i | 0.792632 | − | 1.37288i | ||||
\(843\) | −3.00000 | −0.103325 | ||||||||
\(844\) | − | 20.7846i | − | 0.715436i | ||||||
\(845\) | −40.3051 | − | 23.2702i | −1.38654 | − | 0.800518i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34.2929i | 1.17832i | ||||||||
\(848\) | −33.9411 | −1.16554 | ||||||||
\(849\) | 25.5000 | + | 14.7224i | 0.875158 | + | 0.505273i | ||||
\(850\) | −2.82843 | − | 4.89898i | −0.0970143 | − | 0.168034i | ||||
\(851\) | 3.00000 | + | 1.73205i | 0.102839 | + | 0.0593739i | ||||
\(852\) | 8.48528 | − | 4.89898i | 0.290701 | − | 0.167836i | ||||
\(853\) | −16.9706 | + | 9.79796i | −0.581061 | + | 0.335476i | −0.761555 | − | 0.648100i | \(-0.775564\pi\) |
0.180494 | + | 0.983576i | \(0.442230\pi\) | |||||||
\(854\) | −25.4558 | −0.871081 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 19.5959i | − | 0.669775i | ||||||
\(857\) | 19.5000 | − | 11.2583i | 0.666107 | − | 0.384577i | −0.128493 | − | 0.991710i | \(-0.541014\pi\) |
0.794600 | + | 0.607133i | \(0.207681\pi\) | |||||||
\(858\) | 60.0000 | − | 34.6410i | 2.04837 | − | 1.18262i | ||||
\(859\) | −14.5000 | + | 25.1147i | −0.494734 | + | 0.856904i | −0.999982 | − | 0.00607046i | \(-0.998068\pi\) |
0.505248 | + | 0.862974i | \(0.331401\pi\) | |||||||
\(860\) | 25.4558 | − | 14.6969i | 0.868037 | − | 0.501161i | ||||
\(861\) | −19.0919 | − | 11.0227i | −0.650650 | − | 0.375653i | ||||
\(862\) | −12.0000 | −0.408722 | ||||||||
\(863\) | −21.2132 | −0.722106 | −0.361053 | − | 0.932545i | \(-0.617583\pi\) | ||||
−0.361053 | + | 0.932545i | \(0.617583\pi\) | |||||||
\(864\) | 25.4558 | + | 14.6969i | 0.866025 | + | 0.500000i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 44.0908i | − | 1.49827i | ||||||
\(867\) | 1.73205i | 0.0588235i | ||||||||
\(868\) | −6.00000 | − | 3.46410i | −0.203653 | − | 0.117579i | ||||
\(869\) | −7.07107 | − | 12.2474i | −0.239870 | − | 0.415466i | ||||
\(870\) | −21.2132 | + | 36.7423i | −0.719195 | + | 1.24568i | ||||
\(871\) | −59.3970 | + | 34.2929i | −2.01259 | + | 1.16197i | ||||
\(872\) | −20.0000 | − | 34.6410i | −0.677285 | − | 1.17309i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15.0000 | − | 1.73205i | −0.507383 | − | 0.0585875i | ||||
\(875\) | −24.0000 | −0.811348 | ||||||||
\(876\) | −9.00000 | + | 5.19615i | −0.304082 | + | 0.175562i | ||||
\(877\) | 3.53553 | + | 6.12372i | 0.119386 | + | 0.206783i | 0.919525 | − | 0.393032i | \(-0.128574\pi\) |
−0.800138 | + | 0.599816i | \(0.795241\pi\) | |||||||
\(878\) | 7.00000 | − | 12.1244i | 0.236239 | − | 0.409177i | ||||
\(879\) | −44.5477 | + | 25.7196i | −1.50256 | + | 0.867502i | ||||
\(880\) | −42.4264 | − | 24.4949i | −1.43019 | − | 0.825723i | ||||
\(881\) | 35.0000 | 1.17918 | 0.589590 | − | 0.807703i | \(-0.299289\pi\) | ||||
0.589590 | + | 0.807703i | \(0.299289\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.5000 | + | 47.6314i | −0.925449 | + | 1.60292i | −0.134611 | + | 0.990899i | \(0.542978\pi\) |
−0.790838 | + | 0.612026i | \(0.790355\pi\) | |||||||
\(884\) | −22.6274 | + | 39.1918i | −0.761042 | + | 1.31816i | ||||
\(885\) | − | 7.34847i | − | 0.247016i | ||||||
\(886\) | 43.8406 | 1.47285 | ||||||||
\(887\) | −11.3137 | + | 19.5959i | −0.379877 | + | 0.657967i | −0.991044 | − | 0.133535i | \(-0.957367\pi\) |
0.611167 | + | 0.791502i | \(0.290700\pi\) | |||||||
\(888\) | 6.00000 | − | 3.46410i | 0.201347 | − | 0.116248i | ||||
\(889\) | 6.00000 | + | 3.46410i | 0.201234 | + | 0.116182i | ||||
\(890\) | −6.00000 | − | 10.3923i | −0.201120 | − | 0.348351i | ||||
\(891\) | 22.5000 | + | 38.9711i | 0.753778 | + | 1.30558i | ||||
\(892\) | −48.0833 | −1.60995 | ||||||||
\(893\) | 19.0919 | − | 25.7196i | 0.638886 | − | 0.860675i | ||||
\(894\) | −42.0000 | −1.40469 | ||||||||
\(895\) | −10.6066 | − | 18.3712i | −0.354540 | − | 0.614081i | ||||
\(896\) | 24.0000 | − | 13.8564i | 0.801784 | − | 0.462910i | ||||
\(897\) | 12.0000 | − | 20.7846i | 0.400668 | − | 0.693978i | ||||
\(898\) | −14.8492 | + | 8.57321i | −0.495526 | + | 0.286092i | ||||
\(899\) | −5.00000 | + | 8.66025i | −0.166759 | + | 0.288836i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.9411 | 1.13074 | ||||||||
\(902\) | −31.8198 | − | 18.3712i | −1.05948 | − | 0.611693i | ||||
\(903\) | −12.7279 | + | 22.0454i | −0.423559 | + | 0.733625i | ||||
\(904\) | 34.2929i | 1.14056i | ||||||||
\(905\) | 58.8897i | 1.95756i | ||||||||
\(906\) | −33.0000 | − | 19.0526i | −1.09635 | − | 0.632979i | ||||
\(907\) | −13.5000 | + | 7.79423i | −0.448260 | + | 0.258803i | −0.707095 | − | 0.707118i | \(-0.749995\pi\) |
0.258835 | + | 0.965922i | \(0.416661\pi\) | |||||||
\(908\) | 3.00000 | + | 1.73205i | 0.0995585 | + | 0.0574801i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −24.0000 | − | 41.5692i | −0.795592 | − | 1.37801i | ||||
\(911\) | −24.0416 | −0.796535 | −0.398267 | − | 0.917269i | \(-0.630388\pi\) | ||||
−0.398267 | + | 0.917269i | \(0.630388\pi\) | |||||||
\(912\) | −18.0000 | + | 24.2487i | −0.596040 | + | 0.802955i | ||||
\(913\) | 35.0000 | 1.15833 | ||||||||
\(914\) | 7.77817 | + | 13.4722i | 0.257279 | + | 0.445621i | ||||
\(915\) | 27.0000 | − | 15.5885i | 0.892592 | − | 0.515339i | ||||
\(916\) | 16.9706 | + | 9.79796i | 0.560723 | + | 0.323734i | ||||
\(917\) | −14.8492 | + | 8.57321i | −0.490365 | + | 0.283112i | ||||
\(918\) | −25.4558 | − | 14.6969i | −0.840168 | − | 0.485071i | ||||
\(919\) | − | 19.5959i | − | 0.646410i | −0.946329 | − | 0.323205i | \(-0.895240\pi\) | ||
0.946329 | − | 0.323205i | \(-0.104760\pi\) | |||||||
\(920\) | −16.9706 | −0.559503 | ||||||||
\(921\) | −4.50000 | + | 7.79423i | −0.148280 | + | 0.256829i | ||||
\(922\) | −18.0000 | − | 10.3923i | −0.592798 | − | 0.342252i | ||||
\(923\) | 16.0000 | 0.526646 | ||||||||
\(924\) | 42.4264 | 1.39573 | ||||||||
\(925\) | −0.707107 | + | 1.22474i | −0.0232495 | + | 0.0402694i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20.0000 | − | 34.6410i | −0.656532 | − | 1.13715i | ||||
\(929\) | 3.50000 | + | 6.06218i | 0.114831 | + | 0.198894i | 0.917712 | − | 0.397246i | \(-0.130034\pi\) |
−0.802881 | + | 0.596139i | \(0.796701\pi\) | |||||||
\(930\) | 8.48528 | 0.278243 | ||||||||
\(931\) | −0.500000 | + | 4.33013i | −0.0163868 | + | 0.141914i | ||||
\(932\) | 2.00000 | 0.0655122 | ||||||||
\(933\) | −10.6066 | − | 18.3712i | −0.347245 | − | 0.601445i | ||||
\(934\) | −9.19239 | − | 15.9217i | −0.300784 | − | 0.520973i | ||||
\(935\) | 42.4264 | + | 24.4949i | 1.38749 | + | 0.801069i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.5000 | + | 28.5788i | −0.539032 | + | 0.933630i | 0.459925 | + | 0.887958i | \(0.347876\pi\) |
−0.998956 | + | 0.0456722i | \(0.985457\pi\) | |||||||
\(938\) | −42.0000 | −1.37135 | ||||||||
\(939\) | − | 1.73205i | − | 0.0565233i | ||||||
\(940\) | 18.0000 | − | 31.1769i | 0.587095 | − | 1.01688i | ||||
\(941\) | 9.89949 | − | 17.1464i | 0.322714 | − | 0.558958i | −0.658333 | − | 0.752727i | \(-0.728738\pi\) |
0.981047 | + | 0.193769i | \(0.0620714\pi\) | |||||||
\(942\) | −12.0000 | −0.390981 | ||||||||
\(943\) | −12.7279 | −0.414478 | ||||||||
\(944\) | 6.00000 | + | 3.46410i | 0.195283 | + | 0.112747i | ||||
\(945\) | 27.0000 | − | 15.5885i | 0.878310 | − | 0.507093i | ||||
\(946\) | −21.2132 | + | 36.7423i | −0.689701 | + | 1.19460i | ||||
\(947\) | −11.0000 | − | 19.0526i | −0.357452 | − | 0.619125i | 0.630082 | − | 0.776528i | \(-0.283021\pi\) |
−0.987534 | + | 0.157403i | \(0.949688\pi\) | |||||||
\(948\) | −8.48528 | + | 4.89898i | −0.275589 | + | 0.159111i | ||||
\(949\) | −16.9706 | −0.550888 | ||||||||
\(950\) | 0.707107 | − | 6.12372i | 0.0229416 | − | 0.198680i | ||||
\(951\) | − | 14.6969i | − | 0.476581i | ||||||
\(952\) | −24.0000 | + | 13.8564i | −0.777844 | + | 0.449089i | ||||
\(953\) | −19.5000 | + | 11.2583i | −0.631667 | + | 0.364693i | −0.781397 | − | 0.624034i | \(-0.785493\pi\) |
0.149730 | + | 0.988727i | \(0.452159\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.0000 | − | 41.5692i | −0.776622 | − | 1.34515i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 61.2372i | − | 1.97952i | ||||||
\(958\) | − | 34.6410i | − | 1.11920i | ||||||
\(959\) | 36.0624 | + | 20.8207i | 1.16452 | + | 0.672334i | ||||
\(960\) | −16.9706 | + | 29.3939i | −0.547723 | + | 0.948683i | ||||
\(961\) | −29.0000 | −0.935484 | ||||||||
\(962\) | 11.3137 | 0.364769 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 27.0000 | − | 15.5885i | 0.869611 | − | 0.502070i | ||||
\(965\) | −4.24264 | + | 7.34847i | −0.136575 | + | 0.236556i | ||||
\(966\) | 12.7279 | − | 7.34847i | 0.409514 | − | 0.236433i | ||||
\(967\) | −25.4558 | + | 14.6969i | −0.818605 | + | 0.472622i | −0.849935 | − | 0.526887i | \(-0.823359\pi\) |
0.0313303 | + | 0.999509i | \(0.490026\pi\) | |||||||
\(968\) | 39.5980 | 1.27273 | ||||||||
\(969\) | 18.0000 | − | 24.2487i | 0.578243 | − | 0.778981i | ||||
\(970\) | 66.0000 | 2.11913 | ||||||||
\(971\) | 37.5000 | − | 21.6506i | 1.20343 | − | 0.694802i | 0.242116 | − | 0.970247i | \(-0.422159\pi\) |
0.961317 | + | 0.275445i | \(0.0888254\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.0919 | + | 11.0227i | 0.612058 | + | 0.353372i | ||||
\(974\) | 25.0000 | + | 43.3013i | 0.801052 | + | 1.38746i | ||||
\(975\) | 8.48528 | + | 4.89898i | 0.271746 | + | 0.156893i | ||||
\(976\) | 29.3939i | 0.940875i | ||||||||
\(977\) | − | 32.9090i | − | 1.05285i | −0.850221 | − | 0.526426i | \(-0.823532\pi\) | ||
0.850221 | − | 0.526426i | \(-0.176468\pi\) | |||||||
\(978\) | 6.36396 | + | 3.67423i | 0.203497 | + | 0.117489i | ||||
\(979\) | 15.0000 | + | 8.66025i | 0.479402 | + | 0.276783i | ||||
\(980\) | 4.89898i | 0.156492i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −24.0416 | + | 41.6413i | −0.767199 | + | 1.32883i | ||||
\(983\) | −4.24264 | − | 7.34847i | −0.135319 | − | 0.234380i | 0.790400 | − | 0.612591i | \(-0.209873\pi\) |
−0.925719 | + | 0.378211i | \(0.876539\pi\) | |||||||
\(984\) | −12.7279 | + | 22.0454i | −0.405751 | + | 0.702782i | ||||
\(985\) | −21.0000 | − | 36.3731i | −0.669116 | − | 1.15894i | ||||
\(986\) | 20.0000 | + | 34.6410i | 0.636930 | + | 1.10319i | ||||
\(987\) | 31.1769i | 0.992372i | ||||||||
\(988\) | −45.2548 | + | 19.5959i | −1.43975 | + | 0.623429i | ||||
\(989\) | 14.6969i | 0.467335i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.8701 | − | 46.5403i | −0.853556 | − | 1.47840i | −0.877979 | − | 0.478700i | \(-0.841108\pi\) |
0.0244231 | − | 0.999702i | \(-0.492225\pi\) | |||||||
\(992\) | −4.00000 | + | 6.92820i | −0.127000 | + | 0.219971i | ||||
\(993\) | −4.50000 | − | 7.79423i | −0.142803 | − | 0.247342i | ||||
\(994\) | 8.48528 | + | 4.89898i | 0.269137 | + | 0.155386i | ||||
\(995\) | 60.0000 | 1.90213 | ||||||||
\(996\) | − | 24.2487i | − | 0.768350i | ||||||
\(997\) | −23.3345 | − | 13.4722i | −0.739012 | − | 0.426669i | 0.0826981 | − | 0.996575i | \(-0.473646\pi\) |
−0.821710 | + | 0.569906i | \(0.806980\pi\) | |||||||
\(998\) | −0.707107 | + | 1.22474i | −0.0223831 | + | 0.0387686i | ||||
\(999\) | 7.34847i | 0.232495i |
(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 | 152.2.o.a.107.1 | yes | 4 | |
4.3 | odd | 2 | 608.2.s.b.335.2 | 4 | |||
8.3 | odd | 2 | inner | 152.2.o.a.107.2 | yes | 4 | |
8.5 | even | 2 | 608.2.s.b.335.1 | 4 | |||
19.8 | odd | 6 | inner | 152.2.o.a.27.2 | yes | 4 | |
76.27 | even | 6 | 608.2.s.b.559.1 | 4 | |||
152.27 | even | 6 | inner | 152.2.o.a.27.1 | ✓ | 4 | |
152.141 | odd | 6 | 608.2.s.b.559.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.o.a.27.1 | ✓ | 4 | 152.27 | even | 6 | inner | |
152.2.o.a.27.2 | yes | 4 | 19.8 | odd | 6 | inner | |
152.2.o.a.107.1 | yes | 4 | 1.1 | even | 1 | trivial | |
152.2.o.a.107.2 | yes | 4 | 8.3 | odd | 2 | inner | |
608.2.s.b.335.1 | 4 | 8.5 | even | 2 | |||
608.2.s.b.335.2 | 4 | 4.3 | odd | 2 | |||
608.2.s.b.559.1 | 4 | 76.27 | even | 6 | |||
608.2.s.b.559.2 | 4 | 152.141 | odd | 6 |