Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [833,2,Mod(344,833)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(833, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("833.344");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 833 = 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 833.g (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.65153848837\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 119) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 540.1 | ||
Root | \(1.65831 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 833.540 |
Dual form | 833.2.g.c.344.1 |
$q$-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 \(\left(\mathbb{Z}/833\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | 0.935414 | + | 0.353553i | \(0.115027\pi\) | ||||
−0.935414 | + | 0.353553i | \(0.884973\pi\) | |||||||
\(3\) | −2.15831 | − | 2.15831i | −1.24610 | − | 1.24610i | −0.957427 | − | 0.288675i | \(-0.906785\pi\) |
−0.288675 | − | 0.957427i | \(-0.593215\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | + | 1.00000i | 0.447214 | + | 0.447214i | 0.894427 | − | 0.447214i | \(-0.147584\pi\) |
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 2.15831 | − | 2.15831i | 0.881127 | − | 0.881127i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.00000i | 1.06066i | ||||||||
\(9\) | 6.31662i | 2.10554i | ||||||||
\(10\) | −1.00000 | + | 1.00000i | −0.316228 | + | 0.316228i | ||||
\(11\) | −0.841688 | + | 0.841688i | −0.253778 | + | 0.253778i | −0.822518 | − | 0.568739i | \(-0.807431\pi\) |
0.568739 | + | 0.822518i | \(0.307431\pi\) | |||||||
\(12\) | −2.15831 | − | 2.15831i | −0.623051 | − | 0.623051i | ||||
\(13\) | −3.31662 | −0.919866 | −0.459933 | − | 0.887954i | \(-0.652127\pi\) | ||||
−0.459933 | + | 0.887954i | \(0.652127\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 4.31662i | − | 1.11455i | ||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.00000 | − | 1.00000i | −0.970143 | − | 0.242536i | ||||
\(18\) | −6.31662 | −1.48884 | ||||||||
\(19\) | 4.31662i | 0.990302i | 0.868807 | + | 0.495151i | \(0.164887\pi\) | ||||
−0.868807 | + | 0.495151i | \(0.835113\pi\) | |||||||
\(20\) | 1.00000 | + | 1.00000i | 0.223607 | + | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.841688 | − | 0.841688i | −0.179448 | − | 0.179448i | ||||
\(23\) | −3.00000 | + | 3.00000i | −0.625543 | + | 0.625543i | −0.946943 | − | 0.321400i | \(-0.895847\pi\) |
0.321400 | + | 0.946943i | \(0.395847\pi\) | |||||||
\(24\) | 6.47494 | − | 6.47494i | 1.32169 | − | 1.32169i | ||||
\(25\) | − | 3.00000i | − | 0.600000i | ||||||
\(26\) | − | 3.31662i | − | 0.650444i | ||||||
\(27\) | 7.15831 | − | 7.15831i | 1.37762 | − | 1.37762i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.31662 | − | 1.31662i | −0.244491 | − | 0.244491i | 0.574214 | − | 0.818705i | \(-0.305308\pi\) |
−0.818705 | + | 0.574214i | \(0.805308\pi\) | |||||||
\(30\) | 4.31662 | 0.788104 | ||||||||
\(31\) | 5.31662 | + | 5.31662i | 0.954894 | + | 0.954894i | 0.999026 | − | 0.0441317i | \(-0.0140521\pi\) |
−0.0441317 | + | 0.999026i | \(0.514052\pi\) | |||||||
\(32\) | 5.00000i | 0.883883i | ||||||||
\(33\) | 3.63325 | 0.632468 | ||||||||
\(34\) | 1.00000 | − | 4.00000i | 0.171499 | − | 0.685994i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.31662i | 1.05277i | ||||||||
\(37\) | −6.63325 | − | 6.63325i | −1.09050 | − | 1.09050i | −0.995475 | − | 0.0950246i | \(-0.969707\pi\) |
−0.0950246 | − | 0.995475i | \(-0.530293\pi\) | |||||||
\(38\) | −4.31662 | −0.700249 | ||||||||
\(39\) | 7.15831 | + | 7.15831i | 1.14625 | + | 1.14625i | ||||
\(40\) | −3.00000 | + | 3.00000i | −0.474342 | + | 0.474342i | ||||
\(41\) | −1.31662 | + | 1.31662i | −0.205622 | + | 0.205622i | −0.802404 | − | 0.596782i | \(-0.796446\pi\) |
0.596782 | + | 0.802404i | \(0.296446\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.63325i | 1.31656i | 0.752774 | + | 0.658279i | \(0.228715\pi\) | ||||
−0.752774 | + | 0.658279i | \(0.771285\pi\) | |||||||
\(44\) | −0.841688 | + | 0.841688i | −0.126889 | + | 0.126889i | ||||
\(45\) | −6.31662 | + | 6.31662i | −0.941627 | + | 0.941627i | ||||
\(46\) | −3.00000 | − | 3.00000i | −0.442326 | − | 0.442326i | ||||
\(47\) | −4.31662 | −0.629644 | −0.314822 | − | 0.949151i | \(-0.601945\pi\) | ||||
−0.314822 | + | 0.949151i | \(0.601945\pi\) | |||||||
\(48\) | 2.15831 | + | 2.15831i | 0.311526 | + | 0.311526i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.00000 | 0.424264 | ||||||||
\(51\) | 6.47494 | + | 10.7916i | 0.906673 | + | 1.51112i | ||||
\(52\) | −3.31662 | −0.459933 | ||||||||
\(53\) | 9.63325i | 1.32323i | 0.749844 | + | 0.661614i | \(0.230128\pi\) | ||||
−0.749844 | + | 0.661614i | \(0.769872\pi\) | |||||||
\(54\) | 7.15831 | + | 7.15831i | 0.974123 | + | 0.974123i | ||||
\(55\) | −1.68338 | −0.226986 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.31662 | − | 9.31662i | 1.23402 | − | 1.23402i | ||||
\(58\) | 1.31662 | − | 1.31662i | 0.172881 | − | 0.172881i | ||||
\(59\) | 10.6332i | 1.38433i | 0.721739 | + | 0.692166i | \(0.243343\pi\) | ||||
−0.721739 | + | 0.692166i | \(0.756657\pi\) | |||||||
\(60\) | − | 4.31662i | − | 0.557274i | ||||||
\(61\) | 1.68338 | − | 1.68338i | 0.215534 | − | 0.215534i | −0.591079 | − | 0.806613i | \(-0.701298\pi\) |
0.806613 | + | 0.591079i | \(0.201298\pi\) | |||||||
\(62\) | −5.31662 | + | 5.31662i | −0.675212 | + | 0.675212i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | −3.31662 | − | 3.31662i | −0.411377 | − | 0.411377i | ||||
\(66\) | 3.63325i | 0.447222i | ||||||||
\(67\) | 2.31662 | 0.283021 | 0.141510 | − | 0.989937i | \(-0.454804\pi\) | ||||
0.141510 | + | 0.989937i | \(0.454804\pi\) | |||||||
\(68\) | −4.00000 | − | 1.00000i | −0.485071 | − | 0.121268i | ||||
\(69\) | 12.9499 | 1.55898 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.158312 | + | 0.158312i | 0.0187882 | + | 0.0187882i | 0.716438 | − | 0.697650i | \(-0.245771\pi\) |
−0.697650 | + | 0.716438i | \(0.745771\pi\) | |||||||
\(72\) | −18.9499 | −2.23326 | ||||||||
\(73\) | 5.00000 | + | 5.00000i | 0.585206 | + | 0.585206i | 0.936329 | − | 0.351123i | \(-0.114200\pi\) |
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 6.63325 | − | 6.63325i | 0.771100 | − | 0.771100i | ||||
\(75\) | −6.47494 | + | 6.47494i | −0.747661 | + | 0.747661i | ||||
\(76\) | 4.31662i | 0.495151i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.15831 | + | 7.15831i | −0.810519 | + | 0.810519i | ||||
\(79\) | 5.47494 | − | 5.47494i | 0.615979 | − | 0.615979i | −0.328519 | − | 0.944497i | \(-0.606549\pi\) |
0.944497 | + | 0.328519i | \(0.106549\pi\) | |||||||
\(80\) | −1.00000 | − | 1.00000i | −0.111803 | − | 0.111803i | ||||
\(81\) | −11.9499 | −1.32776 | ||||||||
\(82\) | −1.31662 | − | 1.31662i | −0.145397 | − | 0.145397i | ||||
\(83\) | 4.63325i | 0.508565i | 0.967130 | + | 0.254283i | \(0.0818393\pi\) | ||||
−0.967130 | + | 0.254283i | \(0.918161\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | − | 5.00000i | −0.325396 | − | 0.542326i | ||||
\(86\) | −8.63325 | −0.930947 | ||||||||
\(87\) | 5.68338i | 0.609322i | ||||||||
\(88\) | −2.52506 | − | 2.52506i | −0.269173 | − | 0.269173i | ||||
\(89\) | −17.3166 | −1.83556 | −0.917779 | − | 0.397091i | \(-0.870020\pi\) | ||||
−0.917779 | + | 0.397091i | \(0.870020\pi\) | |||||||
\(90\) | −6.31662 | − | 6.31662i | −0.665831 | − | 0.665831i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.00000 | + | 3.00000i | −0.312772 | + | 0.312772i | ||||
\(93\) | − | 22.9499i | − | 2.37979i | ||||||
\(94\) | − | 4.31662i | − | 0.445226i | ||||||
\(95\) | −4.31662 | + | 4.31662i | −0.442876 | + | 0.442876i | ||||
\(96\) | 10.7916 | − | 10.7916i | 1.10141 | − | 1.10141i | ||||
\(97\) | −8.94987 | − | 8.94987i | −0.908722 | − | 0.908722i | 0.0874471 | − | 0.996169i | \(-0.472129\pi\) |
−0.996169 | + | 0.0874471i | \(0.972129\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.31662 | − | 5.31662i | −0.534341 | − | 0.534341i | ||||
\(100\) | − | 3.00000i | − | 0.300000i | ||||||
\(101\) | 6.63325 | 0.660033 | 0.330017 | − | 0.943975i | \(-0.392946\pi\) | ||||
0.330017 | + | 0.943975i | \(0.392946\pi\) | |||||||
\(102\) | −10.7916 | + | 6.47494i | −1.06852 | + | 0.641114i | ||||
\(103\) | 6.31662 | 0.622396 | 0.311198 | − | 0.950345i | \(-0.399270\pi\) | ||||
0.311198 | + | 0.950345i | \(0.399270\pi\) | |||||||
\(104\) | − | 9.94987i | − | 0.975665i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.63325 | −0.935664 | ||||||||
\(107\) | 8.79156 | + | 8.79156i | 0.849912 | + | 0.849912i | 0.990122 | − | 0.140209i | \(-0.0447776\pi\) |
−0.140209 | + | 0.990122i | \(0.544778\pi\) | |||||||
\(108\) | 7.15831 | − | 7.15831i | 0.688809 | − | 0.688809i | ||||
\(109\) | 6.31662 | − | 6.31662i | 0.605023 | − | 0.605023i | −0.336618 | − | 0.941641i | \(-0.609283\pi\) |
0.941641 | + | 0.336618i | \(0.109283\pi\) | |||||||
\(110\) | − | 1.68338i | − | 0.160504i | ||||||
\(111\) | 28.6332i | 2.71775i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.31662 | − | 6.31662i | 0.594218 | − | 0.594218i | −0.344550 | − | 0.938768i | \(-0.611968\pi\) |
0.938768 | + | 0.344550i | \(0.111968\pi\) | |||||||
\(114\) | 9.31662 | + | 9.31662i | 0.872582 | + | 0.872582i | ||||
\(115\) | −6.00000 | −0.559503 | ||||||||
\(116\) | −1.31662 | − | 1.31662i | −0.122246 | − | 0.122246i | ||||
\(117\) | − | 20.9499i | − | 1.93682i | ||||||
\(118\) | −10.6332 | −0.978870 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 12.9499 | 1.18216 | ||||||||
\(121\) | 9.58312i | 0.871193i | ||||||||
\(122\) | 1.68338 | + | 1.68338i | 0.152406 | + | 0.152406i | ||||
\(123\) | 5.68338 | 0.512453 | ||||||||
\(124\) | 5.31662 | + | 5.31662i | 0.477447 | + | 0.477447i | ||||
\(125\) | 8.00000 | − | 8.00000i | 0.715542 | − | 0.715542i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.3166i | − | 0.915452i | −0.889093 | − | 0.457726i | \(-0.848664\pi\) | ||
0.889093 | − | 0.457726i | \(-0.151336\pi\) | |||||||
\(128\) | 3.00000i | 0.265165i | ||||||||
\(129\) | 18.6332 | − | 18.6332i | 1.64057 | − | 1.64057i | ||||
\(130\) | 3.31662 | − | 3.31662i | 0.290887 | − | 0.290887i | ||||
\(131\) | 9.63325 | + | 9.63325i | 0.841661 | + | 0.841661i | 0.989075 | − | 0.147414i | \(-0.0470950\pi\) |
−0.147414 | + | 0.989075i | \(0.547095\pi\) | |||||||
\(132\) | 3.63325 | 0.316234 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.31662i | 0.200126i | ||||||||
\(135\) | 14.3166 | 1.23218 | ||||||||
\(136\) | 3.00000 | − | 12.0000i | 0.257248 | − | 1.02899i | ||||
\(137\) | 9.31662 | 0.795973 | 0.397986 | − | 0.917391i | \(-0.369709\pi\) | ||||
0.397986 | + | 0.917391i | \(0.369709\pi\) | |||||||
\(138\) | 12.9499i | 1.10237i | ||||||||
\(139\) | −0.525063 | − | 0.525063i | −0.0445352 | − | 0.0445352i | 0.684488 | − | 0.729024i | \(-0.260026\pi\) |
−0.729024 | + | 0.684488i | \(0.760026\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.31662 | + | 9.31662i | 0.784601 | + | 0.784601i | ||||
\(142\) | −0.158312 | + | 0.158312i | −0.0132853 | + | 0.0132853i | ||||
\(143\) | 2.79156 | − | 2.79156i | 0.233442 | − | 0.233442i | ||||
\(144\) | − | 6.31662i | − | 0.526385i | ||||||
\(145\) | − | 2.63325i | − | 0.218679i | ||||||
\(146\) | −5.00000 | + | 5.00000i | −0.413803 | + | 0.413803i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.63325 | − | 6.63325i | −0.545250 | − | 0.545250i | ||||
\(149\) | −1.00000 | −0.0819232 | −0.0409616 | − | 0.999161i | \(-0.513042\pi\) | ||||
−0.0409616 | + | 0.999161i | \(0.513042\pi\) | |||||||
\(150\) | −6.47494 | − | 6.47494i | −0.528676 | − | 0.528676i | ||||
\(151\) | − | 19.5831i | − | 1.59365i | −0.604209 | − | 0.796826i | \(-0.706511\pi\) | ||
0.604209 | − | 0.796826i | \(-0.293489\pi\) | |||||||
\(152\) | −12.9499 | −1.05037 | ||||||||
\(153\) | 6.31662 | − | 25.2665i | 0.510669 | − | 2.04268i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.6332i | 0.854083i | ||||||||
\(156\) | 7.15831 | + | 7.15831i | 0.573124 | + | 0.573124i | ||||
\(157\) | −16.2665 | −1.29821 | −0.649104 | − | 0.760700i | \(-0.724856\pi\) | ||||
−0.649104 | + | 0.760700i | \(0.724856\pi\) | |||||||
\(158\) | 5.47494 | + | 5.47494i | 0.435563 | + | 0.435563i | ||||
\(159\) | 20.7916 | − | 20.7916i | 1.64888 | − | 1.64888i | ||||
\(160\) | −5.00000 | + | 5.00000i | −0.395285 | + | 0.395285i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 11.9499i | − | 0.938871i | ||||||
\(163\) | −3.63325 | + | 3.63325i | −0.284578 | + | 0.284578i | −0.834932 | − | 0.550354i | \(-0.814493\pi\) |
0.550354 | + | 0.834932i | \(0.314493\pi\) | |||||||
\(164\) | −1.31662 | + | 1.31662i | −0.102811 | + | 0.102811i | ||||
\(165\) | 3.63325 | + | 3.63325i | 0.282848 | + | 0.282848i | ||||
\(166\) | −4.63325 | −0.359610 | ||||||||
\(167\) | −3.15831 | − | 3.15831i | −0.244398 | − | 0.244398i | 0.574269 | − | 0.818667i | \(-0.305286\pi\) |
−0.818667 | + | 0.574269i | \(0.805286\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.00000 | −0.153846 | ||||||||
\(170\) | 5.00000 | − | 3.00000i | 0.383482 | − | 0.230089i | ||||
\(171\) | −27.2665 | −2.08512 | ||||||||
\(172\) | 8.63325i | 0.658279i | ||||||||
\(173\) | 4.00000 | + | 4.00000i | 0.304114 | + | 0.304114i | 0.842621 | − | 0.538507i | \(-0.181011\pi\) |
−0.538507 | + | 0.842621i | \(0.681011\pi\) | |||||||
\(174\) | −5.68338 | −0.430856 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.841688 | − | 0.841688i | 0.0634446 | − | 0.0634446i | ||||
\(177\) | 22.9499 | − | 22.9499i | 1.72502 | − | 1.72502i | ||||
\(178\) | − | 17.3166i | − | 1.29794i | ||||||
\(179\) | − | 12.6332i | − | 0.944253i | −0.881531 | − | 0.472127i | \(-0.843486\pi\) | ||
0.881531 | − | 0.472127i | \(-0.156514\pi\) | |||||||
\(180\) | −6.31662 | + | 6.31662i | −0.470813 | + | 0.470813i | ||||
\(181\) | −5.68338 | + | 5.68338i | −0.422442 | + | 0.422442i | −0.886044 | − | 0.463602i | \(-0.846557\pi\) |
0.463602 | + | 0.886044i | \(0.346557\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.26650 | −0.537155 | ||||||||
\(184\) | −9.00000 | − | 9.00000i | −0.663489 | − | 0.663489i | ||||
\(185\) | − | 13.2665i | − | 0.975372i | ||||||
\(186\) | 22.9499 | 1.68277 | ||||||||
\(187\) | 4.20844 | − | 2.52506i | 0.307751 | − | 0.184651i | ||||
\(188\) | −4.31662 | −0.314822 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.31662 | − | 4.31662i | −0.313161 | − | 0.313161i | ||||
\(191\) | −19.2665 | −1.39407 | −0.697037 | − | 0.717035i | \(-0.745499\pi\) | ||||
−0.697037 | + | 0.717035i | \(0.745499\pi\) | |||||||
\(192\) | 15.1082 | + | 15.1082i | 1.09034 | + | 1.09034i | ||||
\(193\) | −8.94987 | + | 8.94987i | −0.644226 | + | 0.644226i | −0.951592 | − | 0.307365i | \(-0.900553\pi\) |
0.307365 | + | 0.951592i | \(0.400553\pi\) | |||||||
\(194\) | 8.94987 | − | 8.94987i | 0.642564 | − | 0.642564i | ||||
\(195\) | 14.3166i | 1.02523i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.68338 | − | 2.68338i | 0.191183 | − | 0.191183i | −0.605024 | − | 0.796207i | \(-0.706837\pi\) |
0.796207 | + | 0.605024i | \(0.206837\pi\) | |||||||
\(198\) | 5.31662 | − | 5.31662i | 0.377836 | − | 0.377836i | ||||
\(199\) | 11.4749 | + | 11.4749i | 0.813437 | + | 0.813437i | 0.985147 | − | 0.171711i | \(-0.0549294\pi\) |
−0.171711 | + | 0.985147i | \(0.554929\pi\) | |||||||
\(200\) | 9.00000 | 0.636396 | ||||||||
\(201\) | −5.00000 | − | 5.00000i | −0.352673 | − | 0.352673i | ||||
\(202\) | 6.63325i | 0.466714i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.47494 | + | 10.7916i | 0.453336 | + | 0.755560i | ||||
\(205\) | −2.63325 | −0.183914 | ||||||||
\(206\) | 6.31662i | 0.440100i | ||||||||
\(207\) | −18.9499 | − | 18.9499i | −1.31711 | − | 1.31711i | ||||
\(208\) | 3.31662 | 0.229967 | ||||||||
\(209\) | −3.63325 | − | 3.63325i | −0.251317 | − | 0.251317i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.63325 | − | 9.63325i | 0.663180 | − | 0.663180i | −0.292948 | − | 0.956128i | \(-0.594636\pi\) |
0.956128 | + | 0.292948i | \(0.0946363\pi\) | |||||||
\(212\) | 9.63325i | 0.661614i | ||||||||
\(213\) | − | 0.683375i | − | 0.0468241i | ||||||
\(214\) | −8.79156 | + | 8.79156i | −0.600979 | + | 0.600979i | ||||
\(215\) | −8.63325 | + | 8.63325i | −0.588783 | + | 0.588783i | ||||
\(216\) | 21.4749 | + | 21.4749i | 1.46118 | + | 1.46118i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.31662 | + | 6.31662i | 0.427816 | + | 0.427816i | ||||
\(219\) | − | 21.5831i | − | 1.45845i | ||||||
\(220\) | −1.68338 | −0.113493 | ||||||||
\(221\) | 13.2665 | + | 3.31662i | 0.892401 | + | 0.223100i | ||||
\(222\) | −28.6332 | −1.92174 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 18.9499 | 1.26332 | ||||||||
\(226\) | 6.31662 | + | 6.31662i | 0.420176 | + | 0.420176i | ||||
\(227\) | 2.20844 | − | 2.20844i | 0.146579 | − | 0.146579i | −0.630009 | − | 0.776588i | \(-0.716949\pi\) |
0.776588 | + | 0.630009i | \(0.216949\pi\) | |||||||
\(228\) | 9.31662 | − | 9.31662i | 0.617009 | − | 0.617009i | ||||
\(229\) | 0.733501i | 0.0484711i | 0.999706 | + | 0.0242355i | \(0.00771517\pi\) | ||||
−0.999706 | + | 0.0242355i | \(0.992285\pi\) | |||||||
\(230\) | − | 6.00000i | − | 0.395628i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.94987 | − | 3.94987i | 0.259322 | − | 0.259322i | ||||
\(233\) | −2.31662 | − | 2.31662i | −0.151767 | − | 0.151767i | 0.627140 | − | 0.778907i | \(-0.284226\pi\) |
−0.778907 | + | 0.627140i | \(0.784226\pi\) | |||||||
\(234\) | 20.9499 | 1.36954 | ||||||||
\(235\) | −4.31662 | − | 4.31662i | −0.281586 | − | 0.281586i | ||||
\(236\) | 10.6332i | 0.692166i | ||||||||
\(237\) | −23.6332 | −1.53514 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.2665 | −0.858138 | −0.429069 | − | 0.903272i | \(-0.641158\pi\) | ||||
−0.429069 | + | 0.903272i | \(0.641158\pi\) | |||||||
\(240\) | 4.31662i | 0.278637i | ||||||||
\(241\) | −12.6834 | − | 12.6834i | −0.817008 | − | 0.817008i | 0.168665 | − | 0.985673i | \(-0.446054\pi\) |
−0.985673 | + | 0.168665i | \(0.946054\pi\) | |||||||
\(242\) | −9.58312 | −0.616027 | ||||||||
\(243\) | 4.31662 | + | 4.31662i | 0.276912 | + | 0.276912i | ||||
\(244\) | 1.68338 | − | 1.68338i | 0.107767 | − | 0.107767i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.68338i | 0.362359i | ||||||||
\(247\) | − | 14.3166i | − | 0.910945i | ||||||
\(248\) | −15.9499 | + | 15.9499i | −1.01282 | + | 1.01282i | ||||
\(249\) | 10.0000 | − | 10.0000i | 0.633724 | − | 0.633724i | ||||
\(250\) | 8.00000 | + | 8.00000i | 0.505964 | + | 0.505964i | ||||
\(251\) | 17.6834 | 1.11616 | 0.558082 | − | 0.829786i | \(-0.311537\pi\) | ||||
0.558082 | + | 0.829786i | \(0.311537\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 5.05013i | − | 0.317499i | ||||||
\(254\) | 10.3166 | 0.647323 | ||||||||
\(255\) | −4.31662 | + | 17.2665i | −0.270318 | + | 1.08127i | ||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | − | 9.31662i | − | 0.581155i | −0.956851 | − | 0.290578i | \(-0.906153\pi\) | ||
0.956851 | − | 0.290578i | \(-0.0938474\pi\) | |||||||
\(258\) | 18.6332 | + | 18.6332i | 1.16006 | + | 1.16006i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.31662 | − | 3.31662i | −0.205688 | − | 0.205688i | ||||
\(261\) | 8.31662 | − | 8.31662i | 0.514786 | − | 0.514786i | ||||
\(262\) | −9.63325 | + | 9.63325i | −0.595144 | + | 0.595144i | ||||
\(263\) | − | 1.68338i | − | 0.103801i | −0.998652 | − | 0.0519007i | \(-0.983472\pi\) | ||
0.998652 | − | 0.0519007i | \(-0.0165279\pi\) | |||||||
\(264\) | 10.8997i | 0.670833i | ||||||||
\(265\) | −9.63325 | + | 9.63325i | −0.591766 | + | 0.591766i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 37.3747 | + | 37.3747i | 2.28729 | + | 2.28729i | ||||
\(268\) | 2.31662 | 0.141510 | ||||||||
\(269\) | 3.00000 | + | 3.00000i | 0.182913 | + | 0.182913i | 0.792624 | − | 0.609711i | \(-0.208714\pi\) |
−0.609711 | + | 0.792624i | \(0.708714\pi\) | |||||||
\(270\) | 14.3166i | 0.871282i | ||||||||
\(271\) | 2.00000 | 0.121491 | 0.0607457 | − | 0.998153i | \(-0.480652\pi\) | ||||
0.0607457 | + | 0.998153i | \(0.480652\pi\) | |||||||
\(272\) | 4.00000 | + | 1.00000i | 0.242536 | + | 0.0606339i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.31662i | 0.562838i | ||||||||
\(275\) | 2.52506 | + | 2.52506i | 0.152267 | + | 0.152267i | ||||
\(276\) | 12.9499 | 0.779491 | ||||||||
\(277\) | 0.633250 | + | 0.633250i | 0.0380483 | + | 0.0380483i | 0.725875 | − | 0.687827i | \(-0.241435\pi\) |
−0.687827 | + | 0.725875i | \(0.741435\pi\) | |||||||
\(278\) | 0.525063 | − | 0.525063i | 0.0314912 | − | 0.0314912i | ||||
\(279\) | −33.5831 | + | 33.5831i | −2.01057 | + | 2.01057i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.0000i | 0.894825i | 0.894328 | + | 0.447412i | \(0.147654\pi\) | ||||
−0.894328 | + | 0.447412i | \(0.852346\pi\) | |||||||
\(282\) | −9.31662 | + | 9.31662i | −0.554797 | + | 0.554797i | ||||
\(283\) | 15.4248 | − | 15.4248i | 0.916910 | − | 0.916910i | −0.0798935 | − | 0.996803i | \(-0.525458\pi\) |
0.996803 | + | 0.0798935i | \(0.0254580\pi\) | |||||||
\(284\) | 0.158312 | + | 0.158312i | 0.00939411 | + | 0.00939411i | ||||
\(285\) | 18.6332 | 1.10374 | ||||||||
\(286\) | 2.79156 | + | 2.79156i | 0.165069 | + | 0.165069i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −31.5831 | −1.86105 | ||||||||
\(289\) | 15.0000 | + | 8.00000i | 0.882353 | + | 0.470588i | ||||
\(290\) | 2.63325 | 0.154630 | ||||||||
\(291\) | 38.6332i | 2.26472i | ||||||||
\(292\) | 5.00000 | + | 5.00000i | 0.292603 | + | 0.292603i | ||||
\(293\) | 27.5330 | 1.60849 | 0.804247 | − | 0.594295i | \(-0.202569\pi\) | ||||
0.804247 | + | 0.594295i | \(0.202569\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.6332 | + | 10.6332i | −0.619092 | + | 0.619092i | ||||
\(296\) | 19.8997 | − | 19.8997i | 1.15665 | − | 1.15665i | ||||
\(297\) | 12.0501i | 0.699219i | ||||||||
\(298\) | − | 1.00000i | − | 0.0579284i | ||||||
\(299\) | 9.94987 | − | 9.94987i | 0.575416 | − | 0.575416i | ||||
\(300\) | −6.47494 | + | 6.47494i | −0.373831 | + | 0.373831i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 19.5831 | 1.12688 | ||||||||
\(303\) | −14.3166 | − | 14.3166i | −0.822469 | − | 0.822469i | ||||
\(304\) | − | 4.31662i | − | 0.247575i | ||||||
\(305\) | 3.36675 | 0.192780 | ||||||||
\(306\) | 25.2665 | + | 6.31662i | 1.44439 | + | 0.361097i | ||||
\(307\) | −7.05013 | −0.402372 | −0.201186 | − | 0.979553i | \(-0.564480\pi\) | ||||
−0.201186 | + | 0.979553i | \(0.564480\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.6332 | − | 13.6332i | −0.775568 | − | 0.775568i | ||||
\(310\) | −10.6332 | −0.603928 | ||||||||
\(311\) | −10.4749 | − | 10.4749i | −0.593979 | − | 0.593979i | 0.344725 | − | 0.938704i | \(-0.387972\pi\) |
−0.938704 | + | 0.344725i | \(0.887972\pi\) | |||||||
\(312\) | −21.4749 | + | 21.4749i | −1.21578 | + | 1.21578i | ||||
\(313\) | 5.94987 | − | 5.94987i | 0.336307 | − | 0.336307i | −0.518669 | − | 0.854975i | \(-0.673572\pi\) |
0.854975 | + | 0.518669i | \(0.173572\pi\) | |||||||
\(314\) | − | 16.2665i | − | 0.917972i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.47494 | − | 5.47494i | 0.307989 | − | 0.307989i | ||||
\(317\) | −16.3166 | + | 16.3166i | −0.916433 | + | 0.916433i | −0.996768 | − | 0.0803350i | \(-0.974401\pi\) |
0.0803350 | + | 0.996768i | \(0.474401\pi\) | |||||||
\(318\) | 20.7916 | + | 20.7916i | 1.16593 | + | 1.16593i | ||||
\(319\) | 2.21637 | 0.124093 | ||||||||
\(320\) | −7.00000 | − | 7.00000i | −0.391312 | − | 0.391312i | ||||
\(321\) | − | 37.9499i | − | 2.11816i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.31662 | − | 17.2665i | 0.240183 | − | 0.960734i | ||||
\(324\) | −11.9499 | −0.663882 | ||||||||
\(325\) | 9.94987i | 0.551920i | ||||||||
\(326\) | −3.63325 | − | 3.63325i | −0.201227 | − | 0.201227i | ||||
\(327\) | −27.2665 | −1.50784 | ||||||||
\(328\) | −3.94987 | − | 3.94987i | −0.218095 | − | 0.218095i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.63325 | + | 3.63325i | −0.200004 | + | 0.200004i | ||||
\(331\) | 20.0000i | 1.09930i | 0.835395 | + | 0.549650i | \(0.185239\pi\) | ||||
−0.835395 | + | 0.549650i | \(0.814761\pi\) | |||||||
\(332\) | 4.63325i | 0.254283i | ||||||||
\(333\) | 41.8997 | − | 41.8997i | 2.29609 | − | 2.29609i | ||||
\(334\) | 3.15831 | − | 3.15831i | 0.172815 | − | 0.172815i | ||||
\(335\) | 2.31662 | + | 2.31662i | 0.126571 | + | 0.126571i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.6332 | − | 22.6332i | −1.23291 | − | 1.23291i | −0.962840 | − | 0.270071i | \(-0.912953\pi\) |
−0.270071 | − | 0.962840i | \(-0.587047\pi\) | |||||||
\(338\) | − | 2.00000i | − | 0.108786i | ||||||
\(339\) | −27.2665 | −1.48091 | ||||||||
\(340\) | −3.00000 | − | 5.00000i | −0.162698 | − | 0.271163i | ||||
\(341\) | −8.94987 | −0.484663 | ||||||||
\(342\) | − | 27.2665i | − | 1.47440i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −25.8997 | −1.39642 | ||||||||
\(345\) | 12.9499 | + | 12.9499i | 0.697198 | + | 0.697198i | ||||
\(346\) | −4.00000 | + | 4.00000i | −0.215041 | + | 0.215041i | ||||
\(347\) | −8.36675 | + | 8.36675i | −0.449151 | + | 0.449151i | −0.895072 | − | 0.445921i | \(-0.852876\pi\) |
0.445921 | + | 0.895072i | \(0.352876\pi\) | |||||||
\(348\) | 5.68338i | 0.304661i | ||||||||
\(349\) | − | 16.0000i | − | 0.856460i | −0.903670 | − | 0.428230i | \(-0.859137\pi\) | ||
0.903670 | − | 0.428230i | \(-0.140863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23.7414 | + | 23.7414i | −1.26722 | + | 1.26722i | ||||
\(352\) | −4.20844 | − | 4.20844i | −0.224311 | − | 0.224311i | ||||
\(353\) | 25.0000 | 1.33062 | 0.665308 | − | 0.746569i | \(-0.268300\pi\) | ||||
0.665308 | + | 0.746569i | \(0.268300\pi\) | |||||||
\(354\) | 22.9499 | + | 22.9499i | 1.21977 | + | 1.21977i | ||||
\(355\) | 0.316625i | 0.0168047i | ||||||||
\(356\) | −17.3166 | −0.917779 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.6332 | 0.667688 | ||||||||
\(359\) | 7.89975i | 0.416933i | 0.978030 | + | 0.208466i | \(0.0668472\pi\) | ||||
−0.978030 | + | 0.208466i | \(0.933153\pi\) | |||||||
\(360\) | −18.9499 | − | 18.9499i | −0.998746 | − | 0.998746i | ||||
\(361\) | 0.366750 | 0.0193027 | ||||||||
\(362\) | −5.68338 | − | 5.68338i | −0.298712 | − | 0.298712i | ||||
\(363\) | 20.6834 | − | 20.6834i | 1.08560 | − | 1.08560i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0000i | 0.523424i | ||||||||
\(366\) | − | 7.26650i | − | 0.379826i | ||||||
\(367\) | 5.15831 | − | 5.15831i | 0.269262 | − | 0.269262i | −0.559541 | − | 0.828803i | \(-0.689023\pi\) |
0.828803 | + | 0.559541i | \(0.189023\pi\) | |||||||
\(368\) | 3.00000 | − | 3.00000i | 0.156386 | − | 0.156386i | ||||
\(369\) | −8.31662 | − | 8.31662i | −0.432946 | − | 0.432946i | ||||
\(370\) | 13.2665 | 0.689692 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 22.9499i | − | 1.18990i | ||||||
\(373\) | 2.58312 | 0.133749 | 0.0668745 | − | 0.997761i | \(-0.478697\pi\) | ||||
0.0668745 | + | 0.997761i | \(0.478697\pi\) | |||||||
\(374\) | 2.52506 | + | 4.20844i | 0.130568 | + | 0.217613i | ||||
\(375\) | −34.5330 | −1.78328 | ||||||||
\(376\) | − | 12.9499i | − | 0.667839i | ||||||
\(377\) | 4.36675 | + | 4.36675i | 0.224899 | + | 0.224899i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.4749 | − | 10.4749i | −0.538061 | − | 0.538061i | 0.384898 | − | 0.922959i | \(-0.374237\pi\) |
−0.922959 | + | 0.384898i | \(0.874237\pi\) | |||||||
\(380\) | −4.31662 | + | 4.31662i | −0.221438 | + | 0.221438i | ||||
\(381\) | −22.2665 | + | 22.2665i | −1.14075 | + | 1.14075i | ||||
\(382\) | − | 19.2665i | − | 0.985760i | ||||||
\(383\) | − | 10.6332i | − | 0.543334i | −0.962391 | − | 0.271667i | \(-0.912425\pi\) | ||
0.962391 | − | 0.271667i | \(-0.0875749\pi\) | |||||||
\(384\) | 6.47494 | − | 6.47494i | 0.330423 | − | 0.330423i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.94987 | − | 8.94987i | −0.455537 | − | 0.455537i | ||||
\(387\) | −54.5330 | −2.77207 | ||||||||
\(388\) | −8.94987 | − | 8.94987i | −0.454361 | − | 0.454361i | ||||
\(389\) | 38.5831i | 1.95624i | 0.208037 | + | 0.978121i | \(0.433293\pi\) | ||||
−0.208037 | + | 0.978121i | \(0.566707\pi\) | |||||||
\(390\) | −14.3166 | −0.724950 | ||||||||
\(391\) | 15.0000 | − | 9.00000i | 0.758583 | − | 0.455150i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 41.5831i | − | 2.09759i | ||||||
\(394\) | 2.68338 | + | 2.68338i | 0.135186 | + | 0.135186i | ||||
\(395\) | 10.9499 | 0.550948 | ||||||||
\(396\) | −5.31662 | − | 5.31662i | −0.267170 | − | 0.267170i | ||||
\(397\) | −17.8997 | + | 17.8997i | −0.898363 | + | 0.898363i | −0.995291 | − | 0.0969287i | \(-0.969098\pi\) |
0.0969287 | + | 0.995291i | \(0.469098\pi\) | |||||||
\(398\) | −11.4749 | + | 11.4749i | −0.575187 | + | 0.575187i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000i | 0.150000i | ||||||||
\(401\) | −18.0000 | + | 18.0000i | −0.898877 | + | 0.898877i | −0.995337 | − | 0.0964598i | \(-0.969248\pi\) |
0.0964598 | + | 0.995337i | \(0.469248\pi\) | |||||||
\(402\) | 5.00000 | − | 5.00000i | 0.249377 | − | 0.249377i | ||||
\(403\) | −17.6332 | − | 17.6332i | −0.878375 | − | 0.878375i | ||||
\(404\) | 6.63325 | 0.330017 | ||||||||
\(405\) | −11.9499 | − | 11.9499i | −0.593794 | − | 0.593794i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.1662 | 0.553490 | ||||||||
\(408\) | −32.3747 | + | 19.4248i | −1.60279 | + | 0.961671i | ||||
\(409\) | 6.26650 | 0.309858 | 0.154929 | − | 0.987926i | \(-0.450485\pi\) | ||||
0.154929 | + | 0.987926i | \(0.450485\pi\) | |||||||
\(410\) | − | 2.63325i | − | 0.130047i | ||||||
\(411\) | −20.1082 | − | 20.1082i | −0.991864 | − | 0.991864i | ||||
\(412\) | 6.31662 | 0.311198 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 18.9499 | − | 18.9499i | 0.931336 | − | 0.931336i | ||||
\(415\) | −4.63325 | + | 4.63325i | −0.227437 | + | 0.227437i | ||||
\(416\) | − | 16.5831i | − | 0.813055i | ||||||
\(417\) | 2.26650i | 0.110991i | ||||||||
\(418\) | 3.63325 | − | 3.63325i | 0.177708 | − | 0.177708i | ||||
\(419\) | −5.15831 | + | 5.15831i | −0.252000 | + | 0.252000i | −0.821790 | − | 0.569790i | \(-0.807024\pi\) |
0.569790 | + | 0.821790i | \(0.307024\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.6332 | 1.49297 | 0.746487 | − | 0.665400i | \(-0.231739\pi\) | ||||
0.746487 | + | 0.665400i | \(0.231739\pi\) | |||||||
\(422\) | 9.63325 | + | 9.63325i | 0.468939 | + | 0.468939i | ||||
\(423\) | − | 27.2665i | − | 1.32574i | ||||||
\(424\) | −28.8997 | −1.40350 | ||||||||
\(425\) | −3.00000 | + | 12.0000i | −0.145521 | + | 0.582086i | ||||
\(426\) | 0.683375 | 0.0331096 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.79156 | + | 8.79156i | 0.424956 | + | 0.424956i | ||||
\(429\) | −12.0501 | −0.581786 | ||||||||
\(430\) | −8.63325 | − | 8.63325i | −0.416332 | − | 0.416332i | ||||
\(431\) | −5.52506 | + | 5.52506i | −0.266133 | + | 0.266133i | −0.827540 | − | 0.561407i | \(-0.810260\pi\) |
0.561407 | + | 0.827540i | \(0.310260\pi\) | |||||||
\(432\) | −7.15831 | + | 7.15831i | −0.344404 | + | 0.344404i | ||||
\(433\) | − | 2.00000i | − | 0.0961139i | −0.998845 | − | 0.0480569i | \(-0.984697\pi\) | ||
0.998845 | − | 0.0480569i | \(-0.0153029\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.68338 | + | 5.68338i | −0.272497 | + | 0.272497i | ||||
\(436\) | 6.31662 | − | 6.31662i | 0.302511 | − | 0.302511i | ||||
\(437\) | −12.9499 | − | 12.9499i | −0.619477 | − | 0.619477i | ||||
\(438\) | 21.5831 | 1.03128 | ||||||||
\(439\) | 25.4248 | + | 25.4248i | 1.21346 | + | 1.21346i | 0.969881 | + | 0.243579i | \(0.0783215\pi\) |
0.243579 | + | 0.969881i | \(0.421678\pi\) | |||||||
\(440\) | − | 5.05013i | − | 0.240755i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.31662 | + | 13.2665i | −0.157756 | + | 0.631023i | ||||
\(443\) | 25.8997 | 1.23053 | 0.615267 | − | 0.788319i | \(-0.289048\pi\) | ||||
0.615267 | + | 0.788319i | \(0.289048\pi\) | |||||||
\(444\) | 28.6332i | 1.35887i | ||||||||
\(445\) | −17.3166 | − | 17.3166i | −0.820887 | − | 0.820887i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.15831 | + | 2.15831i | 0.102085 | + | 0.102085i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.00000 | + | 9.00000i | −0.424736 | + | 0.424736i | −0.886831 | − | 0.462094i | \(-0.847098\pi\) |
0.462094 | + | 0.886831i | \(0.347098\pi\) | |||||||
\(450\) | 18.9499i | 0.893306i | ||||||||
\(451\) | − | 2.21637i | − | 0.104365i | ||||||
\(452\) | 6.31662 | − | 6.31662i | 0.297109 | − | 0.297109i | ||||
\(453\) | −42.2665 | + | 42.2665i | −1.98585 | + | 1.98585i | ||||
\(454\) | 2.20844 | + | 2.20844i | 0.103647 | + | 0.103647i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 27.9499 | + | 27.9499i | 1.30887 | + | 1.30887i | ||||
\(457\) | 10.6332i | 0.497402i | 0.968580 | + | 0.248701i | \(0.0800037\pi\) | ||||
−0.968580 | + | 0.248701i | \(0.919996\pi\) | |||||||
\(458\) | −0.733501 | −0.0342742 | ||||||||
\(459\) | −35.7916 | + | 21.4749i | −1.67061 | + | 1.00236i | ||||
\(460\) | −6.00000 | −0.279751 | ||||||||
\(461\) | − | 6.36675i | − | 0.296529i | −0.988948 | − | 0.148265i | \(-0.952631\pi\) | ||
0.988948 | − | 0.148265i | \(-0.0473687\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.58312 | 0.166522 | 0.0832609 | − | 0.996528i | \(-0.473467\pi\) | ||||
0.0832609 | + | 0.996528i | \(0.473467\pi\) | |||||||
\(464\) | 1.31662 | + | 1.31662i | 0.0611228 | + | 0.0611228i | ||||
\(465\) | 22.9499 | − | 22.9499i | 1.06427 | − | 1.06427i | ||||
\(466\) | 2.31662 | − | 2.31662i | 0.107316 | − | 0.107316i | ||||
\(467\) | − | 13.6834i | − | 0.633191i | −0.948561 | − | 0.316596i | \(-0.897460\pi\) | ||
0.948561 | − | 0.316596i | \(-0.102540\pi\) | |||||||
\(468\) | − | 20.9499i | − | 0.968408i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.31662 | − | 4.31662i | 0.199111 | − | 0.199111i | ||||
\(471\) | 35.1082 | + | 35.1082i | 1.61770 | + | 1.61770i | ||||
\(472\) | −31.8997 | −1.46830 | ||||||||
\(473\) | −7.26650 | − | 7.26650i | −0.334114 | − | 0.334114i | ||||
\(474\) | − | 23.6332i | − | 1.08551i | ||||||
\(475\) | 12.9499 | 0.594181 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −60.8496 | −2.78611 | ||||||||
\(478\) | − | 13.2665i | − | 0.606796i | ||||||
\(479\) | 16.2665 | + | 16.2665i | 0.743235 | + | 0.743235i | 0.973199 | − | 0.229964i | \(-0.0738608\pi\) |
−0.229964 | + | 0.973199i | \(0.573861\pi\) | |||||||
\(480\) | 21.5831 | 0.985130 | ||||||||
\(481\) | 22.0000 | + | 22.0000i | 1.00311 | + | 1.00311i | ||||
\(482\) | 12.6834 | − | 12.6834i | 0.577712 | − | 0.577712i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.58312i | 0.435597i | ||||||||
\(485\) | − | 17.8997i | − | 0.812786i | ||||||
\(486\) | −4.31662 | + | 4.31662i | −0.195806 | + | 0.195806i | ||||
\(487\) | 12.5251 | − | 12.5251i | 0.567565 | − | 0.567565i | −0.363881 | − | 0.931446i | \(-0.618548\pi\) |
0.931446 | + | 0.363881i | \(0.118548\pi\) | |||||||
\(488\) | 5.05013 | + | 5.05013i | 0.228608 | + | 0.228608i | ||||
\(489\) | 15.6834 | 0.709227 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.58312i | − | 0.161704i | −0.996726 | − | 0.0808521i | \(-0.974236\pi\) | ||
0.996726 | − | 0.0808521i | \(-0.0257641\pi\) | |||||||
\(492\) | 5.68338 | 0.256226 | ||||||||
\(493\) | 3.94987 | + | 6.58312i | 0.177893 | + | 0.296489i | ||||
\(494\) | 14.3166 | 0.644135 | ||||||||
\(495\) | − | 10.6332i | − | 0.477929i | ||||||
\(496\) | −5.31662 | − | 5.31662i | −0.238724 | − | 0.238724i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 10.0000 | + | 10.0000i | 0.448111 | + | 0.448111i | ||||
\(499\) | 2.79156 | − | 2.79156i | 0.124967 | − | 0.124967i | −0.641857 | − | 0.766824i | \(-0.721836\pi\) |
0.766824 | + | 0.641857i | \(0.221836\pi\) | |||||||
\(500\) | 8.00000 | − | 8.00000i | 0.357771 | − | 0.357771i | ||||
\(501\) | 13.6332i | 0.609089i | ||||||||
\(502\) | 17.6834i | 0.789248i | ||||||||
\(503\) | 3.42481 | − | 3.42481i | 0.152705 | − | 0.152705i | −0.626620 | − | 0.779325i | \(-0.715562\pi\) |
0.779325 | + | 0.626620i | \(0.215562\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.63325 | + | 6.63325i | 0.295176 | + | 0.295176i | ||||
\(506\) | 5.05013 | 0.224505 | ||||||||
\(507\) | 4.31662 | + | 4.31662i | 0.191708 | + | 0.191708i | ||||
\(508\) | − | 10.3166i | − | 0.457726i | ||||||
\(509\) | 31.1662 | 1.38142 | 0.690710 | − | 0.723132i | \(-0.257298\pi\) | ||||
0.690710 | + | 0.723132i | \(0.257298\pi\) | |||||||
\(510\) | −17.2665 | − | 4.31662i | −0.764573 | − | 0.191143i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 11.0000i | − | 0.486136i | ||||||
\(513\) | 30.8997 | + | 30.8997i | 1.36426 | + | 1.36426i | ||||
\(514\) | 9.31662 | 0.410939 | ||||||||
\(515\) | 6.31662 | + | 6.31662i | 0.278344 | + | 0.278344i | ||||
\(516\) | 18.6332 | − | 18.6332i | 0.820283 | − | 0.820283i | ||||
\(517\) | 3.63325 | − | 3.63325i | 0.159790 | − | 0.159790i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 17.2665i | − | 0.757915i | ||||||
\(520\) | 9.94987 | − | 9.94987i | 0.436331 | − | 0.436331i | ||||
\(521\) | 6.26650 | − | 6.26650i | 0.274540 | − | 0.274540i | −0.556385 | − | 0.830925i | \(-0.687812\pi\) |
0.830925 | + | 0.556385i | \(0.187812\pi\) | |||||||
\(522\) | 8.31662 | + | 8.31662i | 0.364009 | + | 0.364009i | ||||
\(523\) | 7.89975 | 0.345432 | 0.172716 | − | 0.984972i | \(-0.444746\pi\) | ||||
0.172716 | + | 0.984972i | \(0.444746\pi\) | |||||||
\(524\) | 9.63325 | + | 9.63325i | 0.420830 | + | 0.420830i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.68338 | 0.0733986 | ||||||||
\(527\) | −15.9499 | − | 26.5831i | −0.694787 | − | 1.15798i | ||||
\(528\) | −3.63325 | −0.158117 | ||||||||
\(529\) | 5.00000i | 0.217391i | ||||||||
\(530\) | −9.63325 | − | 9.63325i | −0.418442 | − | 0.418442i | ||||
\(531\) | −67.1662 | −2.91477 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.36675 | − | 4.36675i | 0.189145 | − | 0.189145i | ||||
\(534\) | −37.3747 | + | 37.3747i | −1.61736 | + | 1.61736i | ||||
\(535\) | 17.5831i | 0.760185i | ||||||||
\(536\) | 6.94987i | 0.300189i | ||||||||
\(537\) | −27.2665 | + | 27.2665i | −1.17664 | + | 1.17664i | ||||
\(538\) | −3.00000 | + | 3.00000i | −0.129339 | + | 0.129339i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 14.3166 | 0.616089 | ||||||||
\(541\) | −4.94987 | − | 4.94987i | −0.212812 | − | 0.212812i | 0.592649 | − | 0.805461i | \(-0.298082\pi\) |
−0.805461 | + | 0.592649i | \(0.798082\pi\) | |||||||
\(542\) | 2.00000i | 0.0859074i | ||||||||
\(543\) | 24.5330 | 1.05281 | ||||||||
\(544\) | 5.00000 | − | 20.0000i | 0.214373 | − | 0.857493i | ||||
\(545\) | 12.6332 | 0.541149 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.79156 | − | 3.79156i | −0.162115 | − | 0.162115i | 0.621388 | − | 0.783503i | \(-0.286569\pi\) |
−0.783503 | + | 0.621388i | \(0.786569\pi\) | |||||||
\(548\) | 9.31662 | 0.397986 | ||||||||
\(549\) | 10.6332 | + | 10.6332i | 0.453816 | + | 0.453816i | ||||
\(550\) | −2.52506 | + | 2.52506i | −0.107669 | + | 0.107669i | ||||
\(551\) | 5.68338 | − | 5.68338i | 0.242120 | − | 0.242120i | ||||
\(552\) | 38.8496i | 1.65355i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.633250 | + | 0.633250i | −0.0269042 | + | 0.0269042i | ||||
\(555\) | −28.6332 | + | 28.6332i | −1.21541 | + | 1.21541i | ||||
\(556\) | −0.525063 | − | 0.525063i | −0.0222676 | − | 0.0222676i | ||||
\(557\) | −42.4829 | −1.80006 | −0.900029 | − | 0.435831i | \(-0.856455\pi\) | ||||
−0.900029 | + | 0.435831i | \(0.856455\pi\) | |||||||
\(558\) | −33.5831 | − | 33.5831i | −1.42169 | − | 1.42169i | ||||
\(559\) | − | 28.6332i | − | 1.21106i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.5330 | − | 3.63325i | −0.613584 | − | 0.153396i | ||||
\(562\) | −15.0000 | −0.632737 | ||||||||
\(563\) | 37.1662i | 1.56637i | 0.621788 | + | 0.783185i | \(0.286406\pi\) | ||||
−0.621788 | + | 0.783185i | \(0.713594\pi\) | |||||||
\(564\) | 9.31662 | + | 9.31662i | 0.392301 | + | 0.392301i | ||||
\(565\) | 12.6332 | 0.531485 | ||||||||
\(566\) | 15.4248 | + | 15.4248i | 0.648353 | + | 0.648353i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.474937 | + | 0.474937i | −0.0199279 | + | 0.0199279i | ||||
\(569\) | − | 19.0000i | − | 0.796521i | −0.917272 | − | 0.398261i | \(-0.869614\pi\) | ||
0.917272 | − | 0.398261i | \(-0.130386\pi\) | |||||||
\(570\) | 18.6332i | 0.780461i | ||||||||
\(571\) | −26.5831 | + | 26.5831i | −1.11247 | + | 1.11247i | −0.119653 | + | 0.992816i | \(0.538178\pi\) |
−0.992816 | + | 0.119653i | \(0.961822\pi\) | |||||||
\(572\) | 2.79156 | − | 2.79156i | 0.116721 | − | 0.116721i | ||||
\(573\) | 41.5831 | + | 41.5831i | 1.73716 | + | 1.73716i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.00000 | + | 9.00000i | 0.375326 | + | 0.375326i | ||||
\(576\) | − | 44.2164i | − | 1.84235i | ||||||
\(577\) | −10.5831 | −0.440581 | −0.220291 | − | 0.975434i | \(-0.570701\pi\) | ||||
−0.220291 | + | 0.975434i | \(0.570701\pi\) | |||||||
\(578\) | −8.00000 | + | 15.0000i | −0.332756 | + | 0.623918i | ||||
\(579\) | 38.6332 | 1.60554 | ||||||||
\(580\) | − | 2.63325i | − | 0.109340i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −38.6332 | −1.60140 | ||||||||
\(583\) | −8.10819 | − | 8.10819i | −0.335807 | − | 0.335807i | ||||
\(584\) | −15.0000 | + | 15.0000i | −0.620704 | + | 0.620704i | ||||
\(585\) | 20.9499 | − | 20.9499i | 0.866171 | − | 0.866171i | ||||
\(586\) | 27.5330i | 1.13738i | ||||||||
\(587\) | 40.9499i | 1.69018i | 0.534622 | + | 0.845091i | \(0.320454\pi\) | ||||
−0.534622 | + | 0.845091i | \(0.679546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.9499 | + | 22.9499i | −0.945633 | + | 0.945633i | ||||
\(590\) | −10.6332 | − | 10.6332i | −0.437764 | − | 0.437764i | ||||
\(591\) | −11.5831 | −0.476466 | ||||||||
\(592\) | 6.63325 | + | 6.63325i | 0.272625 | + | 0.272625i | ||||
\(593\) | 16.2665i | 0.667985i | 0.942576 | + | 0.333993i | \(0.108396\pi\) | ||||
−0.942576 | + | 0.333993i | \(0.891604\pi\) | |||||||
\(594\) | −12.0501 | −0.494423 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | − | 49.5330i | − | 2.02725i | ||||||
\(598\) | 9.94987 | + | 9.94987i | 0.406881 | + | 0.406881i | ||||
\(599\) | 22.6332 | 0.924770 | 0.462385 | − | 0.886679i | \(-0.346994\pi\) | ||||
0.462385 | + | 0.886679i | \(0.346994\pi\) | |||||||
\(600\) | −19.4248 | − | 19.4248i | −0.793015 | − | 0.793015i | ||||
\(601\) | 23.9499 | − | 23.9499i | 0.976936 | − | 0.976936i | −0.0228042 | − | 0.999740i | \(-0.507259\pi\) |
0.999740 | + | 0.0228042i | \(0.00725943\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.6332i | 0.595912i | ||||||||
\(604\) | − | 19.5831i | − | 0.796826i | ||||||
\(605\) | −9.58312 | + | 9.58312i | −0.389609 | + | 0.389609i | ||||
\(606\) | 14.3166 | − | 14.3166i | 0.581573 | − | 0.581573i | ||||
\(607\) | 28.4248 | + | 28.4248i | 1.15373 | + | 1.15373i | 0.985799 | + | 0.167928i | \(0.0537077\pi\) |
0.167928 | + | 0.985799i | \(0.446292\pi\) | |||||||
\(608\) | −21.5831 | −0.875311 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.36675i | 0.136316i | ||||||||
\(611\) | 14.3166 | 0.579189 | ||||||||
\(612\) | 6.31662 | − | 25.2665i | 0.255334 | − | 1.02134i | ||||
\(613\) | 32.2665 | 1.30323 | 0.651616 | − | 0.758549i | \(-0.274091\pi\) | ||||
0.651616 | + | 0.758549i | \(0.274091\pi\) | |||||||
\(614\) | − | 7.05013i | − | 0.284520i | ||||||
\(615\) | 5.68338 | + | 5.68338i | 0.229176 | + | 0.229176i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.9499 | + | 15.9499i | 0.642118 | + | 0.642118i | 0.951076 | − | 0.308958i | \(-0.0999802\pi\) |
−0.308958 | + | 0.951076i | \(0.599980\pi\) | |||||||
\(618\) | 13.6332 | − | 13.6332i | 0.548410 | − | 0.548410i | ||||
\(619\) | −5.84169 | + | 5.84169i | −0.234797 | + | 0.234797i | −0.814692 | − | 0.579894i | \(-0.803094\pi\) |
0.579894 | + | 0.814692i | \(0.303094\pi\) | |||||||
\(620\) | 10.6332i | 0.427042i | ||||||||
\(621\) | 42.9499i | 1.72352i | ||||||||
\(622\) | 10.4749 | − | 10.4749i | 0.420007 | − | 0.420007i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.15831 | − | 7.15831i | −0.286562 | − | 0.286562i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 5.94987 | + | 5.94987i | 0.237805 | + | 0.237805i | ||||
\(627\) | 15.6834i | 0.626334i | ||||||||
\(628\) | −16.2665 | −0.649104 | ||||||||
\(629\) | 19.8997 | + | 33.1662i | 0.793455 | + | 1.32242i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.3668i | 1.08945i | 0.838614 | + | 0.544727i | \(0.183367\pi\) | ||||
−0.838614 | + | 0.544727i | \(0.816633\pi\) | |||||||
\(632\) | 16.4248 | + | 16.4248i | 0.653344 | + | 0.653344i | ||||
\(633\) | −41.5831 | −1.65278 | ||||||||
\(634\) | −16.3166 | − | 16.3166i | −0.648016 | − | 0.648016i | ||||
\(635\) | 10.3166 | − | 10.3166i | 0.409403 | − | 0.409403i | ||||
\(636\) | 20.7916 | − | 20.7916i | 0.824439 | − | 0.824439i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.21637i | 0.0877471i | ||||||||
\(639\) | −1.00000 | + | 1.00000i | −0.0395594 | + | 0.0395594i | ||||
\(640\) | −3.00000 | + | 3.00000i | −0.118585 | + | 0.118585i | ||||
\(641\) | −16.6834 | − | 16.6834i | −0.658954 | − | 0.658954i | 0.296179 | − | 0.955133i | \(-0.404288\pi\) |
−0.955133 | + | 0.296179i | \(0.904288\pi\) | |||||||
\(642\) | 37.9499 | 1.49776 | ||||||||
\(643\) | −9.89181 | − | 9.89181i | −0.390095 | − | 0.390095i | 0.484626 | − | 0.874721i | \(-0.338956\pi\) |
−0.874721 | + | 0.484626i | \(0.838956\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 37.2665 | 1.46737 | ||||||||
\(646\) | 17.2665 | + | 4.31662i | 0.679341 | + | 0.169835i | ||||
\(647\) | 18.6332 | 0.732549 | 0.366274 | − | 0.930507i | \(-0.380633\pi\) | ||||
0.366274 | + | 0.930507i | \(0.380633\pi\) | |||||||
\(648\) | − | 35.8496i | − | 1.40831i | ||||||
\(649\) | −8.94987 | − | 8.94987i | −0.351313 | − | 0.351313i | ||||
\(650\) | −9.94987 | −0.390266 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.63325 | + | 3.63325i | −0.142289 | + | 0.142289i | ||||
\(653\) | −11.5831 | + | 11.5831i | −0.453283 | + | 0.453283i | −0.896443 | − | 0.443160i | \(-0.853857\pi\) |
0.443160 | + | 0.896443i | \(0.353857\pi\) | |||||||
\(654\) | − | 27.2665i | − | 1.06620i | ||||||
\(655\) | 19.2665i | 0.752804i | ||||||||
\(656\) | 1.31662 | − | 1.31662i | 0.0514056 | − | 0.0514056i | ||||
\(657\) | −31.5831 | + | 31.5831i | −1.23218 | + | 1.23218i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.00000 | −0.233727 | −0.116863 | − | 0.993148i | \(-0.537284\pi\) | ||||
−0.116863 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(660\) | 3.63325 | + | 3.63325i | 0.141424 | + | 0.141424i | ||||
\(661\) | 14.5330i | 0.565268i | 0.959228 | + | 0.282634i | \(0.0912082\pi\) | ||||
−0.959228 | + | 0.282634i | \(0.908792\pi\) | |||||||
\(662\) | −20.0000 | −0.777322 | ||||||||
\(663\) | −21.4749 | − | 35.7916i | −0.834017 | − | 1.39003i | ||||
\(664\) | −13.8997 | −0.539415 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 41.8997 | + | 41.8997i | 1.62358 | + | 1.62358i | ||||
\(667\) | 7.89975 | 0.305879 | ||||||||
\(668\) | −3.15831 | − | 3.15831i | −0.122199 | − | 0.122199i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.31662 | + | 2.31662i | −0.0894990 | + | 0.0894990i | ||||
\(671\) | 2.83375i | 0.109396i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.9499 | − | 27.9499i | 1.07739 | − | 1.07739i | 0.0806456 | − | 0.996743i | \(-0.474302\pi\) |
0.996743 | − | 0.0806456i | \(-0.0256982\pi\) | |||||||
\(674\) | 22.6332 | − | 22.6332i | 0.871800 | − | 0.871800i | ||||
\(675\) | −21.4749 | − | 21.4749i | −0.826571 | − | 0.826571i | ||||
\(676\) | −2.00000 | −0.0769231 | ||||||||
\(677\) | −8.36675 | − | 8.36675i | −0.321560 | − | 0.321560i | 0.527805 | − | 0.849365i | \(-0.323015\pi\) |
−0.849365 | + | 0.527805i | \(0.823015\pi\) | |||||||
\(678\) | − | 27.2665i | − | 1.04716i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 15.0000 | − | 9.00000i | 0.575224 | − | 0.345134i | ||||
\(681\) | −9.53300 | −0.365305 | ||||||||
\(682\) | − | 8.94987i | − | 0.342708i | ||||||
\(683\) | 7.47494 | + | 7.47494i | 0.286021 | + | 0.286021i | 0.835504 | − | 0.549484i | \(-0.185176\pi\) |
−0.549484 | + | 0.835504i | \(0.685176\pi\) | |||||||
\(684\) | −27.2665 | −1.04256 | ||||||||
\(685\) | 9.31662 | + | 9.31662i | 0.355970 | + | 0.355970i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.58312 | − | 1.58312i | 0.0603999 | − | 0.0603999i | ||||
\(688\) | − | 8.63325i | − | 0.329140i | ||||||
\(689\) | − | 31.9499i | − | 1.21719i | ||||||
\(690\) | −12.9499 | + | 12.9499i | −0.492993 | + | 0.492993i | ||||
\(691\) | 0.366750 | − | 0.366750i | 0.0139518 | − | 0.0139518i | −0.700096 | − | 0.714048i | \(-0.746860\pi\) |
0.714048 | + | 0.700096i | \(0.246860\pi\) | |||||||
\(692\) | 4.00000 | + | 4.00000i | 0.152057 | + | 0.152057i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.36675 | − | 8.36675i | −0.317598 | − | 0.317598i | ||||
\(695\) | − | 1.05013i | − | 0.0398335i | ||||||
\(696\) | −17.0501 | −0.646283 | ||||||||
\(697\) | 6.58312 | − | 3.94987i | 0.249354 | − | 0.149612i | ||||
\(698\) | 16.0000 | 0.605609 | ||||||||
\(699\) | 10.0000i | 0.378235i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.2164 | 1.33010 | 0.665052 | − | 0.746797i | \(-0.268409\pi\) | ||||
0.665052 | + | 0.746797i | \(0.268409\pi\) | |||||||
\(702\) | −23.7414 | − | 23.7414i | −0.896063 | − | 0.896063i | ||||
\(703\) | 28.6332 | − | 28.6332i | 1.07992 | − | 1.07992i | ||||
\(704\) | 5.89181 | − | 5.89181i | 0.222056 | − | 0.222056i | ||||
\(705\) | 18.6332i | 0.701769i | ||||||||
\(706\) | 25.0000i | 0.940887i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 22.9499 | − | 22.9499i | 0.862509 | − | 0.862509i | ||||
\(709\) | 23.3166 | + | 23.3166i | 0.875674 | + | 0.875674i | 0.993084 | − | 0.117409i | \(-0.0374590\pi\) |
−0.117409 | + | 0.993084i | \(0.537459\pi\) | |||||||
\(710\) | −0.316625 | −0.0118827 | ||||||||
\(711\) | 34.5831 | + | 34.5831i | 1.29697 | + | 1.29697i | ||||
\(712\) | − | 51.9499i | − | 1.94690i | ||||||
\(713\) | −31.8997 | −1.19465 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.58312 | 0.208797 | ||||||||
\(716\) | − | 12.6332i | − | 0.472127i | ||||||
\(717\) | 28.6332 | + | 28.6332i | 1.06933 | + | 1.06933i | ||||
\(718\) | −7.89975 | −0.294816 | ||||||||
\(719\) | −5.79156 | − | 5.79156i | −0.215989 | − | 0.215989i | 0.590817 | − | 0.806806i | \(-0.298806\pi\) |
−0.806806 | + | 0.590817i | \(0.798806\pi\) | |||||||
\(720\) | 6.31662 | − | 6.31662i | 0.235407 | − | 0.235407i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.366750i | 0.0136490i | ||||||||
\(723\) | 54.7494i | 2.03615i | ||||||||
\(724\) | −5.68338 | + | 5.68338i | −0.211221 | + | 0.211221i | ||||
\(725\) | −3.94987 | + | 3.94987i | −0.146695 | + | 0.146695i | ||||
\(726\) | 20.6834 | + | 20.6834i | 0.767632 | + | 0.767632i | ||||
\(727\) | −40.6332 | −1.50700 | −0.753502 | − | 0.657446i | \(-0.771637\pi\) | ||||
−0.753502 | + | 0.657446i | \(0.771637\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.2164i | 0.637643i | ||||||||
\(730\) | −10.0000 | −0.370117 | ||||||||
\(731\) | 8.63325 | − | 34.5330i | 0.319312 | − | 1.27725i | ||||
\(732\) | −7.26650 | −0.268578 | ||||||||
\(733\) | − | 10.2665i | − | 0.379202i | −0.981861 | − | 0.189601i | \(-0.939281\pi\) | ||
0.981861 | − | 0.189601i | \(-0.0607194\pi\) | |||||||
\(734\) | 5.15831 | + | 5.15831i | 0.190397 | + | 0.190397i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.0000 | − | 15.0000i | −0.552907 | − | 0.552907i | ||||
\(737\) | −1.94987 | + | 1.94987i | −0.0718245 | + | 0.0718245i | ||||
\(738\) | 8.31662 | − | 8.31662i | 0.306139 | − | 0.306139i | ||||
\(739\) | 37.2665i | 1.37087i | 0.728134 | + | 0.685435i | \(0.240388\pi\) | ||||
−0.728134 | + | 0.685435i | \(0.759612\pi\) | |||||||
\(740\) | − | 13.2665i | − | 0.487686i | ||||||
\(741\) | −30.8997 | + | 30.8997i | −1.13513 | + | 1.13513i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.0581 | − | 15.0581i | −0.552427 | − | 0.552427i | 0.374714 | − | 0.927141i | \(-0.377741\pi\) |
−0.927141 | + | 0.374714i | \(0.877741\pi\) | |||||||
\(744\) | 68.8496 | 2.52415 | ||||||||
\(745\) | −1.00000 | − | 1.00000i | −0.0366372 | − | 0.0366372i | ||||
\(746\) | 2.58312i | 0.0945749i | ||||||||
\(747\) | −29.2665 | −1.07081 | ||||||||
\(748\) | 4.20844 | − | 2.52506i | 0.153876 | − | 0.0923254i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 34.5330i | − | 1.26097i | ||||||
\(751\) | −9.74144 | − | 9.74144i | −0.355470 | − | 0.355470i | 0.506670 | − | 0.862140i | \(-0.330876\pi\) |
−0.862140 | + | 0.506670i | \(0.830876\pi\) | |||||||
\(752\) | 4.31662 | 0.157411 | ||||||||
\(753\) | −38.1662 | − | 38.1662i | −1.39086 | − | 1.39086i | ||||
\(754\) | −4.36675 | + | 4.36675i | −0.159028 | + | 0.159028i | ||||
\(755\) | 19.5831 | − | 19.5831i | 0.712703 | − | 0.712703i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.3166i | 0.411310i | 0.978625 | + | 0.205655i | \(0.0659324\pi\) | ||||
−0.978625 | + | 0.205655i | \(0.934068\pi\) | |||||||
\(758\) | 10.4749 | − | 10.4749i | 0.380467 | − | 0.380467i | ||||
\(759\) | −10.8997 | + | 10.8997i | −0.395636 | + | 0.395636i | ||||
\(760\) | −12.9499 | − | 12.9499i | −0.469741 | − | 0.469741i | ||||
\(761\) | −34.5831 | −1.25364 | −0.626819 | − | 0.779165i | \(-0.715643\pi\) | ||||
−0.626819 | + | 0.779165i | \(0.715643\pi\) | |||||||
\(762\) | −22.2665 | − | 22.2665i | −0.806630 | − | 0.806630i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −19.2665 | −0.697037 | ||||||||
\(765\) | 31.5831 | − | 18.9499i | 1.14189 | − | 0.685134i | ||||
\(766\) | 10.6332 | 0.384195 | ||||||||
\(767\) | − | 35.2665i | − | 1.27340i | ||||||
\(768\) | 36.6913 | + | 36.6913i | 1.32398 | + | 1.32398i | ||||
\(769\) | −9.41688 | −0.339581 | −0.169791 | − | 0.985480i | \(-0.554309\pi\) | ||||
−0.169791 | + | 0.985480i | \(0.554309\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.1082 | + | 20.1082i | −0.724179 | + | 0.724179i | ||||
\(772\) | −8.94987 | + | 8.94987i | −0.322113 | + | 0.322113i | ||||
\(773\) | 38.5831i | 1.38774i | 0.720101 | + | 0.693869i | \(0.244095\pi\) | ||||
−0.720101 | + | 0.693869i | \(0.755905\pi\) | |||||||
\(774\) | − | 54.5330i | − | 1.96015i | ||||||
\(775\) | 15.9499 | − | 15.9499i | 0.572936 | − | 0.572936i | ||||
\(776\) | 26.8496 | − | 26.8496i | 0.963845 | − | 0.963845i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −38.5831 | −1.38327 | ||||||||
\(779\) | −5.68338 | − | 5.68338i | −0.203628 | − | 0.203628i | ||||
\(780\) | 14.3166i | 0.512617i | ||||||||
\(781\) | −0.266499 | −0.00953609 | ||||||||
\(782\) | 9.00000 | + | 15.0000i | 0.321839 | + | 0.536399i | ||||
\(783\) | −18.8496 | −0.673631 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.2665 | − | 16.2665i | −0.580576 | − | 0.580576i | ||||
\(786\) | 41.5831 | 1.48322 | ||||||||
\(787\) | 24.3668 | + | 24.3668i | 0.868581 | + | 0.868581i | 0.992315 | − | 0.123735i | \(-0.0394871\pi\) |
−0.123735 | + | 0.992315i | \(0.539487\pi\) | |||||||
\(788\) | 2.68338 | − | 2.68338i | 0.0955913 | − | 0.0955913i | ||||
\(789\) | −3.63325 | + | 3.63325i | −0.129347 | + | 0.129347i | ||||
\(790\) | 10.9499i | 0.389579i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 15.9499 | − | 15.9499i | 0.566754 | − | 0.566754i | ||||
\(793\) | −5.58312 | + | 5.58312i | −0.198263 | + | 0.198263i | ||||
\(794\) | −17.8997 | − | 17.8997i | −0.635238 | − | 0.635238i | ||||
\(795\) | 41.5831 | 1.47480 | ||||||||
\(796\) | 11.4749 | + | 11.4749i | 0.406718 | + | 0.406718i | ||||
\(797\) | 6.89975i | 0.244402i | 0.992505 | + | 0.122201i | \(0.0389952\pi\) | ||||
−0.992505 | + | 0.122201i | \(0.961005\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.2665 | + | 4.31662i | 0.610845 | + | 0.152711i | ||||
\(800\) | 15.0000 | 0.530330 | ||||||||
\(801\) | − | 109.383i | − | 3.86484i | ||||||
\(802\) | −18.0000 | − | 18.0000i | −0.635602 | − | 0.635602i | ||||
\(803\) | −8.41688 | −0.297025 | ||||||||
\(804\) | −5.00000 | − | 5.00000i | −0.176336 | − | 0.176336i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.6332 | − | 17.6332i | 0.621105 | − | 0.621105i | ||||
\(807\) | − | 12.9499i | − | 0.455857i | ||||||
\(808\) | 19.8997i | 0.700071i | ||||||||
\(809\) | 36.8997 | − | 36.8997i | 1.29733 | − | 1.29733i | 0.367174 | − | 0.930152i | \(-0.380325\pi\) |
0.930152 | − | 0.367174i | \(-0.119675\pi\) | |||||||
\(810\) | 11.9499 | − | 11.9499i | 0.419876 | − | 0.419876i | ||||
\(811\) | −5.10819 | − | 5.10819i | −0.179373 | − | 0.179373i | 0.611710 | − | 0.791082i | \(-0.290482\pi\) |
−0.791082 | + | 0.611710i | \(0.790482\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.31662 | − | 4.31662i | −0.151391 | − | 0.151391i | ||||
\(814\) | 11.1662i | 0.391377i | ||||||||
\(815\) | −7.26650 | −0.254534 | ||||||||
\(816\) | −6.47494 | − | 10.7916i | −0.226668 | − | 0.377780i | ||||
\(817\) | −37.2665 | −1.30379 | ||||||||
\(818\) | 6.26650i | 0.219103i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.63325 | −0.0919571 | ||||||||
\(821\) | −20.6332 | − | 20.6332i | −0.720105 | − | 0.720105i | 0.248521 | − | 0.968626i | \(-0.420055\pi\) |
−0.968626 | + | 0.248521i | \(0.920055\pi\) | |||||||
\(822\) | 20.1082 | − | 20.1082i | 0.701354 | − | 0.701354i | ||||
\(823\) | −18.0581 | + | 18.0581i | −0.629464 | + | 0.629464i | −0.947933 | − | 0.318469i | \(-0.896831\pi\) |
0.318469 | + | 0.947933i | \(0.396831\pi\) | |||||||
\(824\) | 18.9499i | 0.660150i | ||||||||
\(825\) | − | 10.8997i | − | 0.379481i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.0581 | + | 15.0581i | −0.523620 | + | 0.523620i | −0.918663 | − | 0.395043i | \(-0.870730\pi\) |
0.395043 | + | 0.918663i | \(0.370730\pi\) | |||||||
\(828\) | −18.9499 | − | 18.9499i | −0.658554 | − | 0.658554i | ||||
\(829\) | 16.8997 | 0.586953 | 0.293476 | − | 0.955966i | \(-0.405188\pi\) | ||||
0.293476 | + | 0.955966i | \(0.405188\pi\) | |||||||
\(830\) | −4.63325 | − | 4.63325i | −0.160822 | − | 0.160822i | ||||
\(831\) | − | 2.73350i | − | 0.0948241i | ||||||
\(832\) | 23.2164 | 0.804883 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.26650 | −0.0784824 | ||||||||
\(835\) | − | 6.31662i | − | 0.218596i | ||||||
\(836\) | −3.63325 | − | 3.63325i | −0.125659 | − | 0.125659i | ||||
\(837\) | 76.1161 | 2.63096 | ||||||||
\(838\) | −5.15831 | − | 5.15831i | −0.178191 | − | 0.178191i | ||||
\(839\) | −10.0501 | + | 10.0501i | −0.346969 | + | 0.346969i | −0.858979 | − | 0.512010i | \(-0.828901\pi\) |
0.512010 | + | 0.858979i | \(0.328901\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 25.5330i | − | 0.880448i | ||||||
\(842\) | 30.6332i | 1.05569i | ||||||||
\(843\) | 32.3747 | − | 32.3747i | 1.11504 | − | 1.11504i | ||||
\(844\) | 9.63325 | − | 9.63325i | 0.331590 | − | 0.331590i | ||||
\(845\) | −2.00000 | − | 2.00000i | −0.0688021 | − | 0.0688021i | ||||
\(846\) | 27.2665 | 0.937442 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 9.63325i | − | 0.330807i | ||||||
\(849\) | −66.5831 | −2.28513 | ||||||||
\(850\) | −12.0000 | − | 3.00000i | −0.411597 | − | 0.102899i | ||||
\(851\) | 39.7995 | 1.36431 | ||||||||
\(852\) | − | 0.683375i | − | 0.0234120i | ||||||
\(853\) | 29.6332 | + | 29.6332i | 1.01462 | + | 1.01462i | 0.999891 | + | 0.0147317i | \(0.00468940\pi\) |
0.0147317 | + | 0.999891i | \(0.495311\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −27.2665 | − | 27.2665i | −0.932495 | − | 0.932495i | ||||
\(856\) | −26.3747 | + | 26.3747i | −0.901468 | + | 0.901468i | ||||
\(857\) | 22.0000 | − | 22.0000i | 0.751506 | − | 0.751506i | −0.223255 | − | 0.974760i | \(-0.571668\pi\) |
0.974760 | + | 0.223255i | \(0.0716681\pi\) | |||||||
\(858\) | − | 12.0501i | − | 0.411385i | ||||||
\(859\) | − | 1.68338i | − | 0.0574360i | −0.999588 | − | 0.0287180i | \(-0.990858\pi\) | ||
0.999588 | − | 0.0287180i | \(-0.00914248\pi\) | |||||||
\(860\) | −8.63325 | + | 8.63325i | −0.294391 | + | 0.294391i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.52506 | − | 5.52506i | −0.188184 | − | 0.188184i | ||||
\(863\) | 39.1662 | 1.33323 | 0.666617 | − | 0.745400i | \(-0.267742\pi\) | ||||
0.666617 | + | 0.745400i | \(0.267742\pi\) | |||||||
\(864\) | 35.7916 | + | 35.7916i | 1.21765 | + | 1.21765i | ||||
\(865\) | 8.00000i | 0.272008i | ||||||||
\(866\) | 2.00000 | 0.0679628 | ||||||||
\(867\) | −15.1082 | − | 49.6412i | −0.513101 | − | 1.68590i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.21637i | 0.312644i | ||||||||
\(870\) | −5.68338 | − | 5.68338i | −0.192684 | − | 0.192684i | ||||
\(871\) | −7.68338 | −0.260341 | ||||||||
\(872\) | 18.9499 | + | 18.9499i | 0.641724 | + | 0.641724i | ||||
\(873\) | 56.5330 | − | 56.5330i | 1.91335 | − | 1.91335i | ||||
\(874\) | 12.9499 | − | 12.9499i | 0.438036 | − | 0.438036i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 21.5831i | − | 0.729226i | ||||||
\(877\) | 6.68338 | − | 6.68338i | 0.225682 | − | 0.225682i | −0.585204 | − | 0.810886i | \(-0.698986\pi\) |
0.810886 | + | 0.585204i | \(0.198986\pi\) | |||||||
\(878\) | −25.4248 | + | 25.4248i | −0.858046 | + | 0.858046i | ||||
\(879\) | −59.4248 | − | 59.4248i | −2.00435 | − | 2.00435i | ||||
\(880\) | 1.68338 | 0.0567466 | ||||||||
\(881\) | −19.8997 | − | 19.8997i | −0.670440 | − | 0.670440i | 0.287378 | − | 0.957817i | \(-0.407216\pi\) |
−0.957817 | + | 0.287378i | \(0.907216\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.8997 | −0.467764 | −0.233882 | − | 0.972265i | \(-0.575143\pi\) | ||||
−0.233882 | + | 0.972265i | \(0.575143\pi\) | |||||||
\(884\) | 13.2665 | + | 3.31662i | 0.446201 | + | 0.111550i | ||||
\(885\) | 45.8997 | 1.54290 | ||||||||
\(886\) | 25.8997i | 0.870119i | ||||||||
\(887\) | 12.8417 | + | 12.8417i | 0.431182 | + | 0.431182i | 0.889030 | − | 0.457849i | \(-0.151380\pi\) |
−0.457849 | + | 0.889030i | \(0.651380\pi\) | |||||||
\(888\) | −85.8997 | −2.88261 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 17.3166 | − | 17.3166i | 0.580455 | − | 0.580455i | ||||
\(891\) | 10.0581 | − | 10.0581i | 0.336958 | − | 0.336958i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 18.6332i | − | 0.623538i | ||||||
\(894\) | −2.15831 | + | 2.15831i | −0.0721848 | + | 0.0721848i | ||||
\(895\) | 12.6332 | − | 12.6332i | 0.422283 | − | 0.422283i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.9499 | −1.43405 | ||||||||
\(898\) | −9.00000 | − | 9.00000i | −0.300334 | − | 0.300334i | ||||
\(899\) | − | 14.0000i | − | 0.466926i | ||||||
\(900\) | 18.9499 | 0.631662 | ||||||||
\(901\) | 9.63325 | − | 38.5330i | 0.320930 | − | 1.28372i | ||||
\(902\) | 2.21637 | 0.0737972 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.9499 | + | 18.9499i | 0.630263 | + | 0.630263i | ||||
\(905\) | −11.3668 | −0.377844 | ||||||||
\(906\) | −42.2665 | − | 42.2665i | −1.40421 | − | 1.40421i | ||||
\(907\) | 4.58312 | − | 4.58312i | 0.152180 | − | 0.152180i | −0.626911 | − | 0.779091i | \(-0.715681\pi\) |
0.779091 | + | 0.626911i | \(0.215681\pi\) | |||||||
\(908\) | 2.20844 | − | 2.20844i | 0.0732896 | − | 0.0732896i | ||||
\(909\) | 41.8997i | 1.38973i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.9499 | + | 21.9499i | −0.727232 | + | 0.727232i | −0.970067 | − | 0.242836i | \(-0.921922\pi\) |
0.242836 | + | 0.970067i | \(0.421922\pi\) | |||||||
\(912\) | −9.31662 | + | 9.31662i | −0.308504 | + | 0.308504i | ||||
\(913\) | −3.89975 | − | 3.89975i | −0.129063 | − | 0.129063i | ||||
\(914\) | −10.6332 | −0.351717 | ||||||||
\(915\) | −7.26650 | − | 7.26650i | −0.240223 | − | 0.240223i | ||||
\(916\) | 0.733501i | 0.0242355i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −21.4749 | − | 35.7916i | −0.708779 | − | 1.18130i | ||||
\(919\) | 33.4829 | 1.10450 | 0.552249 | − | 0.833679i | \(-0.313770\pi\) | ||||
0.552249 | + | 0.833679i | \(0.313770\pi\) | |||||||
\(920\) | − | 18.0000i | − | 0.593442i | ||||||
\(921\) | 15.2164 | + | 15.2164i | 0.501397 | + | 0.501397i | ||||
\(922\) | 6.36675 | 0.209678 | ||||||||
\(923\) | −0.525063 | − | 0.525063i | −0.0172827 | − | 0.0172827i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.8997 | + | 19.8997i | −0.654300 | + | 0.654300i | ||||
\(926\) | 3.58312i | 0.117749i | ||||||||
\(927\) | 39.8997i | 1.31048i | ||||||||
\(928\) | 6.58312 | − | 6.58312i | 0.216102 | − | 0.216102i | ||||
\(929\) | −17.3166 | + | 17.3166i | −0.568140 | + | 0.568140i | −0.931607 | − | 0.363467i | \(-0.881593\pi\) |
0.363467 | + | 0.931607i | \(0.381593\pi\) | |||||||
\(930\) | 22.9499 | + | 22.9499i | 0.752556 | + | 0.752556i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.31662 | − | 2.31662i | −0.0758836 | − | 0.0758836i | ||||
\(933\) | 45.2164i | 1.48032i | ||||||||
\(934\) | 13.6834 | 0.447734 | ||||||||
\(935\) | 6.73350 | + | 1.68338i | 0.220209 | + | 0.0550523i | ||||
\(936\) | 62.8496 | 2.05430 | ||||||||
\(937\) | 27.7995i | 0.908170i | 0.890958 | + | 0.454085i | \(0.150034\pi\) | ||||
−0.890958 | + | 0.454085i | \(0.849966\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.6834 | −0.838145 | ||||||||
\(940\) | −4.31662 | − | 4.31662i | −0.140793 | − | 0.140793i | ||||
\(941\) | −9.63325 | + | 9.63325i | −0.314035 | + | 0.314035i | −0.846471 | − | 0.532436i | \(-0.821277\pi\) |
0.532436 | + | 0.846471i | \(0.321277\pi\) | |||||||
\(942\) | −35.1082 | + | 35.1082i | −1.14389 | + | 1.14389i | ||||
\(943\) | − | 7.89975i | − | 0.257251i | ||||||
\(944\) | − | 10.6332i | − | 0.346083i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.26650 | − | 7.26650i | 0.236254 | − | 0.236254i | ||||
\(947\) | −5.42481 | − | 5.42481i | −0.176283 | − | 0.176283i | 0.613450 | − | 0.789733i | \(-0.289781\pi\) |
−0.789733 | + | 0.613450i | \(0.789781\pi\) | |||||||
\(948\) | −23.6332 | −0.767572 | ||||||||
\(949\) | −16.5831 | − | 16.5831i | −0.538311 | − | 0.538311i | ||||
\(950\) | 12.9499i | 0.420149i | ||||||||
\(951\) | 70.4327 | 2.28394 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.7494 | 1.74111 | 0.870556 | − | 0.492069i | \(-0.163759\pi\) | ||||
0.870556 | + | 0.492069i | \(0.163759\pi\) | |||||||
\(954\) | − | 60.8496i | − | 1.97008i | ||||||
\(955\) | −19.2665 | − | 19.2665i | −0.623449 | − | 0.623449i | ||||
\(956\) | −13.2665 | −0.429069 | ||||||||
\(957\) | −4.78363 | − | 4.78363i | −0.154633 | − | 0.154633i | ||||
\(958\) | −16.2665 | + | 16.2665i | −0.525547 | + | 0.525547i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 30.2164i | 0.975229i | ||||||||
\(961\) | 25.5330i | 0.823645i | ||||||||
\(962\) | −22.0000 | + | 22.0000i | −0.709308 | + | 0.709308i | ||||
\(963\) | −55.5330 | + | 55.5330i | −1.78953 | + | 1.78953i | ||||
\(964\) | −12.6834 | − | 12.6834i | −0.408504 | − | 0.408504i | ||||
\(965\) | −17.8997 | −0.576213 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.58312i | 0.243857i | 0.992539 | + | 0.121928i | \(0.0389078\pi\) | ||||
−0.992539 | + | 0.121928i | \(0.961092\pi\) | |||||||
\(968\) | −28.7494 | −0.924040 | ||||||||
\(969\) | −46.5831 | + | 27.9499i | −1.49647 | + | 0.897879i | ||||
\(970\) | 17.8997 | 0.574726 | ||||||||
\(971\) | − | 50.2164i | − | 1.61152i | −0.592242 | − | 0.805760i | \(-0.701757\pi\) | ||
0.592242 | − | 0.805760i | \(-0.298243\pi\) | |||||||
\(972\) | 4.31662 | + | 4.31662i | 0.138456 | + | 0.138456i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12.5251 | + | 12.5251i | 0.401329 | + | 0.401329i | ||||
\(975\) | 21.4749 | − | 21.4749i | 0.687748 | − | 0.687748i | ||||
\(976\) | −1.68338 | + | 1.68338i | −0.0538835 | + | 0.0538835i | ||||
\(977\) | − | 55.1662i | − | 1.76492i | −0.470383 | − | 0.882462i | \(-0.655884\pi\) | ||
0.470383 | − | 0.882462i | \(-0.344116\pi\) | |||||||
\(978\) | 15.6834i | 0.501499i | ||||||||
\(979\) | 14.5752 | − | 14.5752i | 0.465825 | − | 0.465825i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39.8997 | + | 39.8997i | 1.27390 | + | 1.27390i | ||||
\(982\) | 3.58312 | 0.114342 | ||||||||
\(983\) | −43.4248 | − | 43.4248i | −1.38504 | − | 1.38504i | −0.835412 | − | 0.549625i | \(-0.814771\pi\) |
−0.549625 | − | 0.835412i | \(-0.685229\pi\) | |||||||
\(984\) | 17.0501i | 0.543538i | ||||||||
\(985\) | 5.36675 | 0.170999 | ||||||||
\(986\) | −6.58312 | + | 3.94987i | −0.209649 | + | 0.125790i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 14.3166i | − | 0.455473i | ||||||
\(989\) | −25.8997 | − | 25.8997i | −0.823564 | − | 0.823564i | ||||
\(990\) | 10.6332 | 0.337947 | ||||||||
\(991\) | 37.1583 | + | 37.1583i | 1.18037 | + | 1.18037i | 0.979648 | + | 0.200725i | \(0.0643298\pi\) |
0.200725 | + | 0.979648i | \(0.435670\pi\) | |||||||
\(992\) | −26.5831 | + | 26.5831i | −0.844015 | + | 0.844015i | ||||
\(993\) | 43.1662 | − | 43.1662i | 1.36984 | − | 1.36984i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.9499i | 0.727560i | ||||||||
\(996\) | 10.0000 | − | 10.0000i | 0.316862 | − | 0.316862i | ||||
\(997\) | 9.31662 | − | 9.31662i | 0.295060 | − | 0.295060i | −0.544015 | − | 0.839075i | \(-0.683097\pi\) |
0.839075 | + | 0.544015i | \(0.183097\pi\) | |||||||
\(998\) | 2.79156 | + | 2.79156i | 0.0883654 | + | 0.0883654i | ||||
\(999\) | −94.9657 | −3.00458 |
(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 | 833.2.g.c.540.1 | 4 | ||
7.2 | even | 3 | 833.2.o.c.557.2 | 8 | |||
7.3 | odd | 6 | 119.2.n.a.30.2 | yes | 8 | ||
7.4 | even | 3 | 833.2.o.c.30.1 | 8 | |||
7.5 | odd | 6 | 119.2.n.a.81.1 | yes | 8 | ||
7.6 | odd | 2 | 833.2.g.d.540.2 | 4 | |||
17.4 | even | 4 | inner | 833.2.g.c.344.1 | 4 | ||
119.4 | even | 12 | 833.2.o.c.667.2 | 8 | |||
119.38 | odd | 12 | 119.2.n.a.72.1 | yes | 8 | ||
119.55 | odd | 4 | 833.2.g.d.344.2 | 4 | |||
119.72 | even | 12 | 833.2.o.c.361.1 | 8 | |||
119.89 | odd | 12 | 119.2.n.a.4.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
119.2.n.a.4.2 | ✓ | 8 | 119.89 | odd | 12 | ||
119.2.n.a.30.2 | yes | 8 | 7.3 | odd | 6 | ||
119.2.n.a.72.1 | yes | 8 | 119.38 | odd | 12 | ||
119.2.n.a.81.1 | yes | 8 | 7.5 | odd | 6 | ||
833.2.g.c.344.1 | 4 | 17.4 | even | 4 | inner | ||
833.2.g.c.540.1 | 4 | 1.1 | even | 1 | trivial | ||
833.2.g.d.344.2 | 4 | 119.55 | odd | 4 | |||
833.2.g.d.540.2 | 4 | 7.6 | odd | 2 | |||
833.2.o.c.30.1 | 8 | 7.4 | even | 3 | |||
833.2.o.c.361.1 | 8 | 119.72 | even | 12 | |||
833.2.o.c.557.2 | 8 | 7.2 | even | 3 | |||
833.2.o.c.667.2 | 8 | 119.4 | even | 12 |