Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2394,2,Mod(505,2394)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2394, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2394.505");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2394.o (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.1161862439\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 798) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1261.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2394.1261 |
Dual form | 2394.2.o.a.505.1 |
$q$-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 \(\left(\mathbb{Z}/2394\mathbb{Z}\right)^\times\).
\(n\) | \(533\) | \(1009\) | \(1711\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.50000 | − | 2.59808i | −0.670820 | − | 1.16190i | −0.977672 | − | 0.210138i | \(-0.932609\pi\) |
0.306851 | − | 0.951757i | \(-0.400725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.50000 | + | 2.59808i | −0.474342 | + | 0.821584i | ||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50000 | + | 2.59808i | −0.416025 | + | 0.720577i | −0.995535 | − | 0.0943882i | \(-0.969911\pi\) |
0.579510 | + | 0.814965i | \(0.303244\pi\) | |||||||
\(14\) | 0.500000 | + | 0.866025i | 0.133631 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.00000 | − | 1.73205i | −0.242536 | − | 0.420084i | 0.718900 | − | 0.695113i | \(-0.244646\pi\) |
−0.961436 | + | 0.275029i | \(0.911312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.500000 | − | 4.33013i | −0.114708 | − | 0.993399i | ||||
\(20\) | 3.00000 | 0.670820 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | + | 3.46410i | 0.426401 | + | 0.738549i | ||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | −0.809177 | − | 0.587565i | \(-0.800087\pi\) |
0.913434 | + | 0.406986i | \(0.133420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 3.00000 | 0.588348 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.500000 | − | 0.866025i | 0.0944911 | − | 0.163663i | ||||
\(29\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.00000 | + | 1.73205i | −0.171499 | + | 0.297044i | ||||
\(35\) | 1.50000 | + | 2.59808i | 0.253546 | + | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | −3.50000 | + | 2.59808i | −0.567775 | + | 0.421464i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.50000 | − | 2.59808i | −0.237171 | − | 0.410792i | ||||
\(41\) | 2.00000 | + | 3.46410i | 0.312348 | + | 0.541002i | 0.978870 | − | 0.204483i | \(-0.0655513\pi\) |
−0.666523 | + | 0.745485i | \(0.732218\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.00000 | + | 5.19615i | 0.457496 | + | 0.792406i | 0.998828 | − | 0.0484030i | \(-0.0154132\pi\) |
−0.541332 | + | 0.840809i | \(0.682080\pi\) | |||||||
\(44\) | 2.00000 | − | 3.46410i | 0.301511 | − | 0.522233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −1.00000 | + | 1.73205i | −0.145865 | + | 0.252646i | −0.929695 | − | 0.368329i | \(-0.879930\pi\) |
0.783830 | + | 0.620975i | \(0.213263\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.00000 | 0.565685 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.50000 | − | 2.59808i | −0.208013 | − | 0.360288i | ||||
\(53\) | −2.00000 | + | 3.46410i | −0.274721 | + | 0.475831i | −0.970065 | − | 0.242846i | \(-0.921919\pi\) |
0.695344 | + | 0.718677i | \(0.255252\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | + | 10.3923i | 0.809040 | + | 1.40130i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.50000 | + | 11.2583i | 0.846228 | + | 1.46571i | 0.884551 | + | 0.466444i | \(0.154465\pi\) |
−0.0383226 | + | 0.999265i | \(0.512201\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.50000 | + | 4.33013i | −0.320092 | + | 0.554416i | −0.980507 | − | 0.196485i | \(-0.937047\pi\) |
0.660415 | + | 0.750901i | \(0.270381\pi\) | |||||||
\(62\) | 3.00000 | + | 5.19615i | 0.381000 | + | 0.659912i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.00000 | 1.11631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.00000 | − | 10.3923i | 0.733017 | − | 1.26962i | −0.222571 | − | 0.974916i | \(-0.571445\pi\) |
0.955588 | − | 0.294706i | \(-0.0952216\pi\) | |||||||
\(68\) | 2.00000 | 0.242536 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.50000 | − | 2.59808i | 0.179284 | − | 0.310530i | ||||
\(71\) | −3.50000 | − | 6.06218i | −0.415374 | − | 0.719448i | 0.580094 | − | 0.814550i | \(-0.303016\pi\) |
−0.995468 | + | 0.0951014i | \(0.969682\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000 | + | 1.73205i | 0.117041 | + | 0.202721i | 0.918594 | − | 0.395203i | \(-0.129326\pi\) |
−0.801553 | + | 0.597924i | \(0.795992\pi\) | |||||||
\(74\) | −2.00000 | − | 3.46410i | −0.232495 | − | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.00000 | + | 1.73205i | 0.458831 | + | 0.198680i | ||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | + | 6.92820i | 0.450035 | + | 0.779484i | 0.998388 | − | 0.0567635i | \(-0.0180781\pi\) |
−0.548352 | + | 0.836247i | \(0.684745\pi\) | |||||||
\(80\) | −1.50000 | + | 2.59808i | −0.167705 | + | 0.290474i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.00000 | − | 3.46410i | 0.220863 | − | 0.382546i | ||||
\(83\) | −17.0000 | −1.86599 | −0.932996 | − | 0.359886i | \(-0.882816\pi\) | ||||
−0.932996 | + | 0.359886i | \(0.882816\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | + | 5.19615i | −0.325396 | + | 0.563602i | ||||
\(86\) | 3.00000 | − | 5.19615i | 0.323498 | − | 0.560316i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.00000 | −0.426401 | ||||||||
\(89\) | 2.00000 | − | 3.46410i | 0.212000 | − | 0.367194i | −0.740341 | − | 0.672232i | \(-0.765336\pi\) |
0.952340 | + | 0.305038i | \(0.0986691\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.50000 | − | 2.59808i | 0.157243 | − | 0.272352i | ||||
\(92\) | 0.500000 | + | 0.866025i | 0.0521286 | + | 0.0902894i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.00000 | 0.206284 | ||||||||
\(95\) | −10.5000 | + | 7.79423i | −1.07728 | + | 0.799671i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00000 | + | 8.66025i | 0.507673 | + | 0.879316i | 0.999961 | + | 0.00888289i | \(0.00282755\pi\) |
−0.492287 | + | 0.870433i | \(0.663839\pi\) | |||||||
\(98\) | −0.500000 | − | 0.866025i | −0.0505076 | − | 0.0874818i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | − | 3.46410i | −0.200000 | − | 0.346410i | ||||
\(101\) | 7.00000 | − | 12.1244i | 0.696526 | − | 1.20642i | −0.273138 | − | 0.961975i | \(-0.588061\pi\) |
0.969664 | − | 0.244443i | \(-0.0786053\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | −1.50000 | + | 2.59808i | −0.147087 | + | 0.254762i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.00000 | 0.388514 | ||||||||
\(107\) | 10.0000 | 0.966736 | 0.483368 | − | 0.875417i | \(-0.339413\pi\) | ||||
0.483368 | + | 0.875417i | \(0.339413\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | + | 3.46410i | 0.191565 | + | 0.331801i | 0.945769 | − | 0.324840i | \(-0.105310\pi\) |
−0.754204 | + | 0.656640i | \(0.771977\pi\) | |||||||
\(110\) | 6.00000 | − | 10.3923i | 0.572078 | − | 0.990867i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | + | 0.866025i | 0.0472456 | + | 0.0818317i | ||||
\(113\) | 5.00000 | 0.470360 | 0.235180 | − | 0.971952i | \(-0.424432\pi\) | ||||
0.235180 | + | 0.971952i | \(0.424432\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | −0.279751 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.50000 | − | 11.2583i | 0.598374 | − | 1.03641i | ||||
\(119\) | 1.00000 | + | 1.73205i | 0.0916698 | + | 0.158777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 5.00000 | 0.452679 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.00000 | − | 5.19615i | 0.269408 | − | 0.466628i | ||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.50000 | − | 9.52628i | 0.488046 | − | 0.845321i | −0.511859 | − | 0.859069i | \(-0.671043\pi\) |
0.999905 | + | 0.0137486i | \(0.00437646\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.50000 | − | 7.79423i | −0.394676 | − | 0.683599i | ||||
\(131\) | −4.50000 | − | 7.79423i | −0.393167 | − | 0.680985i | 0.599699 | − | 0.800226i | \(-0.295287\pi\) |
−0.992865 | + | 0.119241i | \(0.961954\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.500000 | + | 4.33013i | 0.0433555 | + | 0.375470i | ||||
\(134\) | −12.0000 | −1.03664 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | − | 1.73205i | −0.0857493 | − | 0.148522i | ||||
\(137\) | −10.5000 | + | 18.1865i | −0.897076 | + | 1.55378i | −0.0658609 | + | 0.997829i | \(0.520979\pi\) |
−0.831215 | + | 0.555952i | \(0.812354\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | − | 13.8564i | 0.678551 | − | 1.17529i | −0.296866 | − | 0.954919i | \(-0.595942\pi\) |
0.975417 | − | 0.220366i | \(-0.0707252\pi\) | |||||||
\(140\) | −3.00000 | −0.253546 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.50000 | + | 6.06218i | −0.293713 | + | 0.508727i | ||||
\(143\) | 6.00000 | − | 10.3923i | 0.501745 | − | 0.869048i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.00000 | − | 1.73205i | 0.0827606 | − | 0.143346i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | + | 3.46410i | −0.164399 | + | 0.284747i | ||||
\(149\) | 10.0000 | + | 17.3205i | 0.819232 | + | 1.41895i | 0.906249 | + | 0.422744i | \(0.138933\pi\) |
−0.0870170 | + | 0.996207i | \(0.527733\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.0000 | 1.54620 | 0.773099 | − | 0.634285i | \(-0.218706\pi\) | ||||
0.773099 | + | 0.634285i | \(0.218706\pi\) | |||||||
\(152\) | −0.500000 | − | 4.33013i | −0.0405554 | − | 0.351220i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.00000 | − | 3.46410i | −0.161165 | − | 0.279145i | ||||
\(155\) | 9.00000 | + | 15.5885i | 0.722897 | + | 1.25210i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.50000 | + | 7.79423i | 0.359139 | + | 0.622047i | 0.987817 | − | 0.155618i | \(-0.0497370\pi\) |
−0.628678 | + | 0.777666i | \(0.716404\pi\) | |||||||
\(158\) | 4.00000 | − | 6.92820i | 0.318223 | − | 0.551178i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.00000 | 0.237171 | ||||||||
\(161\) | −0.500000 | + | 0.866025i | −0.0394055 | + | 0.0682524i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.0000 | 1.09656 | 0.548282 | − | 0.836293i | \(-0.315282\pi\) | ||||
0.548282 | + | 0.836293i | \(0.315282\pi\) | |||||||
\(164\) | −4.00000 | −0.312348 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.50000 | + | 14.7224i | 0.659728 | + | 1.14268i | ||||
\(167\) | −9.00000 | + | 15.5885i | −0.696441 | + | 1.20627i | 0.273252 | + | 0.961943i | \(0.411901\pi\) |
−0.969693 | + | 0.244328i | \(0.921432\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.00000 | + | 3.46410i | 0.153846 | + | 0.266469i | ||||
\(170\) | 6.00000 | 0.460179 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.00000 | −0.457496 | ||||||||
\(173\) | 7.50000 | + | 12.9904i | 0.570214 | + | 0.987640i | 0.996544 | + | 0.0830722i | \(0.0264732\pi\) |
−0.426329 | + | 0.904568i | \(0.640193\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | − | 3.46410i | 0.151186 | − | 0.261861i | ||||
\(176\) | 2.00000 | + | 3.46410i | 0.150756 | + | 0.261116i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.00000 | −0.299813 | ||||||||
\(179\) | −10.0000 | −0.747435 | −0.373718 | − | 0.927543i | \(-0.621917\pi\) | ||||
−0.373718 | + | 0.927543i | \(0.621917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.50000 | + | 2.59808i | −0.111494 | + | 0.193113i | −0.916373 | − | 0.400326i | \(-0.868897\pi\) |
0.804879 | + | 0.593439i | \(0.202230\pi\) | |||||||
\(182\) | −3.00000 | −0.222375 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.500000 | − | 0.866025i | 0.0368605 | − | 0.0638442i | ||||
\(185\) | −6.00000 | − | 10.3923i | −0.441129 | − | 0.764057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | + | 6.92820i | 0.292509 | + | 0.506640i | ||||
\(188\) | −1.00000 | − | 1.73205i | −0.0729325 | − | 0.126323i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.0000 | + | 5.19615i | 0.870572 | + | 0.376969i | ||||
\(191\) | 11.0000 | 0.795932 | 0.397966 | − | 0.917400i | \(-0.369716\pi\) | ||||
0.397966 | + | 0.917400i | \(0.369716\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.50000 | − | 4.33013i | −0.179954 | − | 0.311689i | 0.761911 | − | 0.647682i | \(-0.224262\pi\) |
−0.941865 | + | 0.335993i | \(0.890928\pi\) | |||||||
\(194\) | 5.00000 | − | 8.66025i | 0.358979 | − | 0.621770i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.500000 | + | 0.866025i | −0.0357143 | + | 0.0618590i | ||||
\(197\) | −4.00000 | −0.284988 | −0.142494 | − | 0.989796i | \(-0.545512\pi\) | ||||
−0.142494 | + | 0.989796i | \(0.545512\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.00000 | + | 12.1244i | −0.496217 | + | 0.859473i | −0.999990 | − | 0.00436292i | \(-0.998611\pi\) |
0.503774 | + | 0.863836i | \(0.331945\pi\) | |||||||
\(200\) | −2.00000 | + | 3.46410i | −0.141421 | + | 0.244949i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.0000 | −0.985037 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | − | 10.3923i | 0.419058 | − | 0.725830i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.00000 | 0.208013 | ||||||||
\(209\) | 2.00000 | + | 17.3205i | 0.138343 | + | 1.19808i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | + | 6.92820i | 0.275371 | + | 0.476957i | 0.970229 | − | 0.242190i | \(-0.0778659\pi\) |
−0.694857 | + | 0.719148i | \(0.744533\pi\) | |||||||
\(212\) | −2.00000 | − | 3.46410i | −0.137361 | − | 0.237915i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.00000 | − | 8.66025i | −0.341793 | − | 0.592003i | ||||
\(215\) | 9.00000 | − | 15.5885i | 0.613795 | − | 1.06312i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.00000 | 0.407307 | ||||||||
\(218\) | 2.00000 | − | 3.46410i | 0.135457 | − | 0.234619i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.0000 | −0.809040 | ||||||||
\(221\) | 6.00000 | 0.403604 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.00000 | + | 15.5885i | 0.602685 | + | 1.04388i | 0.992413 | + | 0.122950i | \(0.0392356\pi\) |
−0.389728 | + | 0.920930i | \(0.627431\pi\) | |||||||
\(224\) | 0.500000 | − | 0.866025i | 0.0334077 | − | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.50000 | − | 4.33013i | −0.166298 | − | 0.288036i | ||||
\(227\) | −5.00000 | −0.331862 | −0.165931 | − | 0.986137i | \(-0.553063\pi\) | ||||
−0.165931 | + | 0.986137i | \(0.553063\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.0000 | −1.12339 | −0.561696 | − | 0.827344i | \(-0.689851\pi\) | ||||
−0.561696 | + | 0.827344i | \(0.689851\pi\) | |||||||
\(230\) | 1.50000 | + | 2.59808i | 0.0989071 | + | 0.171312i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.50000 | + | 7.79423i | 0.294805 | + | 0.510617i | 0.974939 | − | 0.222470i | \(-0.0714120\pi\) |
−0.680135 | + | 0.733087i | \(0.738079\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.00000 | 0.391397 | ||||||||
\(236\) | −13.0000 | −0.846228 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.00000 | − | 1.73205i | 0.0648204 | − | 0.112272i | ||||
\(239\) | −27.0000 | −1.74648 | −0.873242 | − | 0.487286i | \(-0.837987\pi\) | ||||
−0.873242 | + | 0.487286i | \(0.837987\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.0000 | + | 19.0526i | −0.708572 | + | 1.22728i | 0.256814 | + | 0.966461i | \(0.417327\pi\) |
−0.965387 | + | 0.260822i | \(0.916006\pi\) | |||||||
\(242\) | −2.50000 | − | 4.33013i | −0.160706 | − | 0.278351i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.50000 | − | 4.33013i | −0.160046 | − | 0.277208i | ||||
\(245\) | −1.50000 | − | 2.59808i | −0.0958315 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | + | 5.19615i | 0.763542 | + | 0.330623i | ||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.50000 | + | 2.59808i | 0.0948683 | + | 0.164317i | ||||
\(251\) | 10.5000 | − | 18.1865i | 0.662754 | − | 1.14792i | −0.317135 | − | 0.948380i | \(-0.602721\pi\) |
0.979889 | − | 0.199543i | \(-0.0639459\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | + | 3.46410i | −0.125739 | + | 0.217786i | ||||
\(254\) | −11.0000 | −0.690201 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6.00000 | − | 10.3923i | 0.374270 | − | 0.648254i | −0.615948 | − | 0.787787i | \(-0.711227\pi\) |
0.990217 | + | 0.139533i | \(0.0445601\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | −0.248548 | ||||||||
\(260\) | −4.50000 | + | 7.79423i | −0.279078 | + | 0.483378i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.50000 | + | 7.79423i | −0.278011 | + | 0.481529i | ||||
\(263\) | −1.50000 | − | 2.59808i | −0.0924940 | − | 0.160204i | 0.816066 | − | 0.577959i | \(-0.196151\pi\) |
−0.908560 | + | 0.417755i | \(0.862817\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.0000 | 0.737154 | ||||||||
\(266\) | 3.50000 | − | 2.59808i | 0.214599 | − | 0.159298i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.00000 | + | 10.3923i | 0.366508 | + | 0.634811i | ||||
\(269\) | 7.00000 | + | 12.1244i | 0.426798 | + | 0.739235i | 0.996586 | − | 0.0825561i | \(-0.0263084\pi\) |
−0.569789 | + | 0.821791i | \(0.692975\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.0000 | − | 22.5167i | −0.789694 | − | 1.36779i | −0.926155 | − | 0.377144i | \(-0.876906\pi\) |
0.136461 | − | 0.990645i | \(-0.456427\pi\) | |||||||
\(272\) | −1.00000 | + | 1.73205i | −0.0606339 | + | 0.105021i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.0000 | 1.26866 | ||||||||
\(275\) | 8.00000 | − | 13.8564i | 0.482418 | − | 0.835573i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | −16.0000 | −0.959616 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.50000 | + | 2.59808i | 0.0896421 | + | 0.155265i | ||||
\(281\) | −13.0000 | + | 22.5167i | −0.775515 | + | 1.34323i | 0.158990 | + | 0.987280i | \(0.449176\pi\) |
−0.934505 | + | 0.355951i | \(0.884157\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.5000 | − | 21.6506i | −0.743048 | − | 1.28700i | −0.951101 | − | 0.308879i | \(-0.900046\pi\) |
0.208053 | − | 0.978117i | \(-0.433287\pi\) | |||||||
\(284\) | 7.00000 | 0.415374 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.0000 | −0.709575 | ||||||||
\(287\) | −2.00000 | − | 3.46410i | −0.118056 | − | 0.204479i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.00000 | −0.117041 | ||||||||
\(293\) | 19.0000 | 1.10999 | 0.554996 | − | 0.831853i | \(-0.312720\pi\) | ||||
0.554996 | + | 0.831853i | \(0.312720\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.5000 | − | 33.7750i | 1.13533 | − | 1.96646i | ||||
\(296\) | 4.00000 | 0.232495 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.0000 | − | 17.3205i | 0.579284 | − | 1.00335i | ||||
\(299\) | 1.50000 | + | 2.59808i | 0.0867472 | + | 0.150251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | − | 5.19615i | −0.172917 | − | 0.299501i | ||||
\(302\) | −9.50000 | − | 16.4545i | −0.546664 | − | 0.946849i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.50000 | + | 2.59808i | −0.200739 | + | 0.149010i | ||||
\(305\) | 15.0000 | 0.858898 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.50000 | − | 12.9904i | −0.428048 | − | 0.741400i | 0.568652 | − | 0.822578i | \(-0.307465\pi\) |
−0.996700 | + | 0.0811780i | \(0.974132\pi\) | |||||||
\(308\) | −2.00000 | + | 3.46410i | −0.113961 | + | 0.197386i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.00000 | − | 15.5885i | 0.511166 | − | 0.885365i | ||||
\(311\) | 2.00000 | 0.113410 | 0.0567048 | − | 0.998391i | \(-0.481941\pi\) | ||||
0.0567048 | + | 0.998391i | \(0.481941\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.0000 | + | 20.7846i | −0.678280 | + | 1.17482i | 0.297218 | + | 0.954810i | \(0.403941\pi\) |
−0.975499 | + | 0.220006i | \(0.929392\pi\) | |||||||
\(314\) | 4.50000 | − | 7.79423i | 0.253950 | − | 0.439854i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 3.00000 | − | 5.19615i | 0.168497 | − | 0.291845i | −0.769395 | − | 0.638774i | \(-0.779442\pi\) |
0.937892 | + | 0.346929i | \(0.112775\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.50000 | − | 2.59808i | −0.0838525 | − | 0.145237i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.00000 | 0.0557278 | ||||||||
\(323\) | −7.00000 | + | 5.19615i | −0.389490 | + | 0.289122i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.00000 | − | 10.3923i | −0.332820 | − | 0.576461i | ||||
\(326\) | −7.00000 | − | 12.1244i | −0.387694 | − | 0.671506i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.00000 | + | 3.46410i | 0.110432 | + | 0.191273i | ||||
\(329\) | 1.00000 | − | 1.73205i | 0.0551318 | − | 0.0954911i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.0000 | −1.31916 | −0.659580 | − | 0.751635i | \(-0.729266\pi\) | ||||
−0.659580 | + | 0.751635i | \(0.729266\pi\) | |||||||
\(332\) | 8.50000 | − | 14.7224i | 0.466498 | − | 0.807998i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 18.0000 | 0.984916 | ||||||||
\(335\) | −36.0000 | −1.96689 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.50000 | − | 14.7224i | −0.463025 | − | 0.801982i | 0.536085 | − | 0.844164i | \(-0.319902\pi\) |
−0.999110 | + | 0.0421818i | \(0.986569\pi\) | |||||||
\(338\) | 2.00000 | − | 3.46410i | 0.108786 | − | 0.188422i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.00000 | − | 5.19615i | −0.162698 | − | 0.281801i | ||||
\(341\) | 24.0000 | 1.29967 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 3.00000 | + | 5.19615i | 0.161749 | + | 0.280158i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.50000 | − | 12.9904i | 0.403202 | − | 0.698367i | ||||
\(347\) | 11.0000 | + | 19.0526i | 0.590511 | + | 1.02279i | 0.994164 | + | 0.107883i | \(0.0344071\pi\) |
−0.403653 | + | 0.914912i | \(0.632260\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | −4.00000 | −0.213809 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.00000 | − | 3.46410i | 0.106600 | − | 0.184637i | ||||
\(353\) | −12.0000 | −0.638696 | −0.319348 | − | 0.947638i | \(-0.603464\pi\) | ||||
−0.319348 | + | 0.947638i | \(0.603464\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.5000 | + | 18.1865i | −0.557282 | + | 0.965241i | ||||
\(356\) | 2.00000 | + | 3.46410i | 0.106000 | + | 0.183597i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.00000 | + | 8.66025i | 0.264258 | + | 0.457709i | ||||
\(359\) | 12.0000 | + | 20.7846i | 0.633336 | + | 1.09697i | 0.986865 | + | 0.161546i | \(0.0516481\pi\) |
−0.353529 | + | 0.935423i | \(0.615019\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5000 | + | 4.33013i | −0.973684 | + | 0.227901i | ||||
\(362\) | 3.00000 | 0.157676 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.50000 | + | 2.59808i | 0.0786214 | + | 0.136176i | ||||
\(365\) | 3.00000 | − | 5.19615i | 0.157027 | − | 0.271979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.0000 | + | 27.7128i | −0.835193 | + | 1.44660i | 0.0586798 | + | 0.998277i | \(0.481311\pi\) |
−0.893873 | + | 0.448320i | \(0.852022\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.00000 | + | 10.3923i | −0.311925 | + | 0.540270i | ||||
\(371\) | 2.00000 | − | 3.46410i | 0.103835 | − | 0.179847i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 4.00000 | − | 6.92820i | 0.206835 | − | 0.358249i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.00000 | + | 1.73205i | −0.0515711 | + | 0.0893237i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.0000 | −1.74646 | −0.873231 | − | 0.487306i | \(-0.837980\pi\) | ||||
−0.873231 | + | 0.487306i | \(0.837980\pi\) | |||||||
\(380\) | −1.50000 | − | 12.9904i | −0.0769484 | − | 0.666392i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.50000 | − | 9.52628i | −0.281404 | − | 0.487407i | ||||
\(383\) | −2.00000 | − | 3.46410i | −0.102195 | − | 0.177007i | 0.810394 | − | 0.585886i | \(-0.199253\pi\) |
−0.912589 | + | 0.408879i | \(0.865920\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.00000 | − | 10.3923i | −0.305788 | − | 0.529641i | ||||
\(386\) | −2.50000 | + | 4.33013i | −0.127247 | + | 0.220398i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.0000 | −0.507673 | ||||||||
\(389\) | 4.00000 | − | 6.92820i | 0.202808 | − | 0.351274i | −0.746624 | − | 0.665246i | \(-0.768327\pi\) |
0.949432 | + | 0.313972i | \(0.101660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.00000 | −0.101144 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.00000 | + | 3.46410i | 0.100759 | + | 0.174519i | ||||
\(395\) | 12.0000 | − | 20.7846i | 0.603786 | − | 1.04579i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.00000 | − | 15.5885i | −0.451697 | − | 0.782362i | 0.546795 | − | 0.837267i | \(-0.315848\pi\) |
−0.998492 | + | 0.0549046i | \(0.982515\pi\) | |||||||
\(398\) | 14.0000 | 0.701757 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | 1.50000 | + | 2.59808i | 0.0749064 | + | 0.129742i | 0.901046 | − | 0.433724i | \(-0.142801\pi\) |
−0.826139 | + | 0.563466i | \(0.809468\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.00000 | − | 15.5885i | 0.448322 | − | 0.776516i | ||||
\(404\) | 7.00000 | + | 12.1244i | 0.348263 | + | 0.603209i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.0000 | −0.793091 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.0000 | + | 20.7846i | −0.593362 | + | 1.02773i | 0.400414 | + | 0.916334i | \(0.368866\pi\) |
−0.993776 | + | 0.111398i | \(0.964467\pi\) | |||||||
\(410\) | −12.0000 | −0.592638 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.50000 | − | 11.2583i | −0.319844 | − | 0.553986i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.5000 | + | 44.1673i | 1.25175 | + | 2.16809i | ||||
\(416\) | −1.50000 | − | 2.59808i | −0.0735436 | − | 0.127381i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.0000 | − | 10.3923i | 0.684762 | − | 0.508304i | ||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.00000 | + | 6.92820i | 0.194948 | + | 0.337660i | 0.946883 | − | 0.321577i | \(-0.104213\pi\) |
−0.751935 | + | 0.659237i | \(0.770879\pi\) | |||||||
\(422\) | 4.00000 | − | 6.92820i | 0.194717 | − | 0.337260i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.00000 | + | 3.46410i | −0.0971286 | + | 0.168232i | ||||
\(425\) | 8.00000 | 0.388057 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.50000 | − | 4.33013i | 0.120983 | − | 0.209550i | ||||
\(428\) | −5.00000 | + | 8.66025i | −0.241684 | + | 0.418609i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.0000 | −0.868037 | ||||||||
\(431\) | −8.00000 | + | 13.8564i | −0.385346 | + | 0.667440i | −0.991817 | − | 0.127666i | \(-0.959251\pi\) |
0.606471 | + | 0.795106i | \(0.292585\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.0000 | − | 20.7846i | 0.576683 | − | 0.998845i | −0.419173 | − | 0.907906i | \(-0.637680\pi\) |
0.995857 | − | 0.0909384i | \(-0.0289866\pi\) | |||||||
\(434\) | −3.00000 | − | 5.19615i | −0.144005 | − | 0.249423i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.00000 | −0.191565 | ||||||||
\(437\) | −4.00000 | − | 1.73205i | −0.191346 | − | 0.0828552i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.00000 | − | 8.66025i | −0.238637 | − | 0.413331i | 0.721686 | − | 0.692220i | \(-0.243367\pi\) |
−0.960323 | + | 0.278889i | \(0.910034\pi\) | |||||||
\(440\) | 6.00000 | + | 10.3923i | 0.286039 | + | 0.495434i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.00000 | − | 5.19615i | −0.142695 | − | 0.247156i | ||||
\(443\) | 9.00000 | − | 15.5885i | 0.427603 | − | 0.740630i | −0.569057 | − | 0.822298i | \(-0.692691\pi\) |
0.996660 | + | 0.0816684i | \(0.0260248\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0000 | −0.568855 | ||||||||
\(446\) | 9.00000 | − | 15.5885i | 0.426162 | − | 0.738135i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 39.0000 | 1.84052 | 0.920262 | − | 0.391303i | \(-0.127976\pi\) | ||||
0.920262 | + | 0.391303i | \(0.127976\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.00000 | − | 13.8564i | −0.376705 | − | 0.652473i | ||||
\(452\) | −2.50000 | + | 4.33013i | −0.117590 | + | 0.203672i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.50000 | + | 4.33013i | 0.117331 | + | 0.203223i | ||||
\(455\) | −9.00000 | −0.421927 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.00000 | −0.327446 | −0.163723 | − | 0.986506i | \(-0.552350\pi\) | ||||
−0.163723 | + | 0.986506i | \(0.552350\pi\) | |||||||
\(458\) | 8.50000 | + | 14.7224i | 0.397179 | + | 0.687934i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.50000 | − | 2.59808i | 0.0699379 | − | 0.121136i | ||||
\(461\) | −16.5000 | − | 28.5788i | −0.768482 | − | 1.33105i | −0.938386 | − | 0.345589i | \(-0.887679\pi\) |
0.169904 | − | 0.985461i | \(-0.445654\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.00000 | −0.418265 | −0.209133 | − | 0.977887i | \(-0.567064\pi\) | ||||
−0.209133 | + | 0.977887i | \(0.567064\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.50000 | − | 7.79423i | 0.208458 | − | 0.361061i | ||||
\(467\) | 4.00000 | 0.185098 | 0.0925490 | − | 0.995708i | \(-0.470499\pi\) | ||||
0.0925490 | + | 0.995708i | \(0.470499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.00000 | + | 10.3923i | −0.277054 | + | 0.479872i | ||||
\(470\) | −3.00000 | − | 5.19615i | −0.138380 | − | 0.239681i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.50000 | + | 11.2583i | 0.299187 | + | 0.518207i | ||||
\(473\) | −12.0000 | − | 20.7846i | −0.551761 | − | 0.955677i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.0000 | + | 6.92820i | 0.734130 | + | 0.317888i | ||||
\(476\) | −2.00000 | −0.0916698 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.5000 | + | 23.3827i | 0.617476 | + | 1.06950i | ||||
\(479\) | −21.0000 | + | 36.3731i | −0.959514 | + | 1.66193i | −0.235833 | + | 0.971794i | \(0.575782\pi\) |
−0.723681 | + | 0.690134i | \(0.757551\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00000 | + | 10.3923i | −0.273576 | + | 0.473848i | ||||
\(482\) | 22.0000 | 1.00207 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.50000 | + | 4.33013i | −0.113636 | + | 0.196824i | ||||
\(485\) | 15.0000 | − | 25.9808i | 0.681115 | − | 1.17973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.0000 | −1.26880 | −0.634401 | − | 0.773004i | \(-0.718753\pi\) | ||||
−0.634401 | + | 0.773004i | \(0.718753\pi\) | |||||||
\(488\) | −2.50000 | + | 4.33013i | −0.113170 | + | 0.196016i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.50000 | + | 2.59808i | −0.0677631 | + | 0.117369i | ||||
\(491\) | 6.00000 | + | 10.3923i | 0.270776 | + | 0.468998i | 0.969061 | − | 0.246822i | \(-0.0793863\pi\) |
−0.698285 | + | 0.715820i | \(0.746053\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −1.50000 | − | 12.9904i | −0.0674882 | − | 0.584465i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.00000 | + | 5.19615i | 0.134704 | + | 0.233314i | ||||
\(497\) | 3.50000 | + | 6.06218i | 0.156996 | + | 0.271926i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.00000 | + | 8.66025i | 0.223831 | + | 0.387686i | 0.955968 | − | 0.293471i | \(-0.0948104\pi\) |
−0.732137 | + | 0.681157i | \(0.761477\pi\) | |||||||
\(500\) | 1.50000 | − | 2.59808i | 0.0670820 | − | 0.116190i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21.0000 | −0.937276 | ||||||||
\(503\) | 11.0000 | − | 19.0526i | 0.490466 | − | 0.849512i | −0.509474 | − | 0.860486i | \(-0.670160\pi\) |
0.999940 | + | 0.0109744i | \(0.00349334\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −42.0000 | −1.86898 | ||||||||
\(506\) | 4.00000 | 0.177822 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.50000 | + | 9.52628i | 0.244023 | + | 0.422660i | ||||
\(509\) | −6.50000 | + | 11.2583i | −0.288107 | + | 0.499017i | −0.973358 | − | 0.229291i | \(-0.926359\pi\) |
0.685251 | + | 0.728307i | \(0.259693\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.00000 | − | 1.73205i | −0.0442374 | − | 0.0766214i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.0000 | −0.529297 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.00000 | − | 6.92820i | 0.175920 | − | 0.304702i | ||||
\(518\) | 2.00000 | + | 3.46410i | 0.0878750 | + | 0.152204i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.00000 | 0.394676 | ||||||||
\(521\) | 14.0000 | 0.613351 | 0.306676 | − | 0.951814i | \(-0.400783\pi\) | ||||
0.306676 | + | 0.951814i | \(0.400783\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0000 | − | 27.7128i | 0.699631 | − | 1.21180i | −0.268963 | − | 0.963150i | \(-0.586681\pi\) |
0.968594 | − | 0.248646i | \(-0.0799857\pi\) | |||||||
\(524\) | 9.00000 | 0.393167 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.50000 | + | 2.59808i | −0.0654031 | + | 0.113282i | ||||
\(527\) | 6.00000 | + | 10.3923i | 0.261364 | + | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | + | 19.0526i | 0.478261 | + | 0.828372i | ||||
\(530\) | −6.00000 | − | 10.3923i | −0.260623 | − | 0.451413i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.00000 | − | 1.73205i | −0.173422 | − | 0.0750939i | ||||
\(533\) | −12.0000 | −0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.0000 | − | 25.9808i | −0.648507 | − | 1.12325i | ||||
\(536\) | 6.00000 | − | 10.3923i | 0.259161 | − | 0.448879i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.00000 | − | 12.1244i | 0.301791 | − | 0.522718i | ||||
\(539\) | −4.00000 | −0.172292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.0000 | + | 27.7128i | −0.687894 | + | 1.19147i | 0.284624 | + | 0.958639i | \(0.408131\pi\) |
−0.972518 | + | 0.232828i | \(0.925202\pi\) | |||||||
\(542\) | −13.0000 | + | 22.5167i | −0.558398 | + | 0.967173i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | 6.00000 | − | 10.3923i | 0.257012 | − | 0.445157i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.0000 | − | 39.8372i | 0.983409 | − | 1.70331i | 0.334606 | − | 0.942358i | \(-0.391397\pi\) |
0.648803 | − | 0.760956i | \(-0.275270\pi\) | |||||||
\(548\) | −10.5000 | − | 18.1865i | −0.448538 | − | 0.776890i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.0000 | −0.682242 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.00000 | − | 6.92820i | −0.170097 | − | 0.294617i | ||||
\(554\) | 1.00000 | + | 1.73205i | 0.0424859 | + | 0.0735878i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.00000 | + | 13.8564i | 0.339276 | + | 0.587643i | ||||
\(557\) | 11.0000 | − | 19.0526i | 0.466085 | − | 0.807283i | −0.533165 | − | 0.846011i | \(-0.678997\pi\) |
0.999250 | + | 0.0387286i | \(0.0123308\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.0000 | −0.761319 | ||||||||
\(560\) | 1.50000 | − | 2.59808i | 0.0633866 | − | 0.109789i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.0000 | 1.09674 | ||||||||
\(563\) | −33.0000 | −1.39078 | −0.695392 | − | 0.718631i | \(-0.744769\pi\) | ||||
−0.695392 | + | 0.718631i | \(0.744769\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.50000 | − | 12.9904i | −0.315527 | − | 0.546509i | ||||
\(566\) | −12.5000 | + | 21.6506i | −0.525414 | + | 0.910044i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.50000 | − | 6.06218i | −0.146857 | − | 0.254363i | ||||
\(569\) | 9.00000 | 0.377300 | 0.188650 | − | 0.982044i | \(-0.439589\pi\) | ||||
0.188650 | + | 0.982044i | \(0.439589\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | 0.0836974 | 0.0418487 | − | 0.999124i | \(-0.486675\pi\) | ||||
0.0418487 | + | 0.999124i | \(0.486675\pi\) | |||||||
\(572\) | 6.00000 | + | 10.3923i | 0.250873 | + | 0.434524i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.00000 | + | 3.46410i | −0.0834784 | + | 0.144589i | ||||
\(575\) | 2.00000 | + | 3.46410i | 0.0834058 | + | 0.144463i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.00000 | −0.333044 | −0.166522 | − | 0.986038i | \(-0.553254\pi\) | ||||
−0.166522 | + | 0.986038i | \(0.553254\pi\) | |||||||
\(578\) | −13.0000 | −0.540729 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.0000 | 0.705279 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.00000 | − | 13.8564i | 0.331326 | − | 0.573874i | ||||
\(584\) | 1.00000 | + | 1.73205i | 0.0413803 | + | 0.0716728i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.50000 | − | 16.4545i | −0.392441 | − | 0.679728i | ||||
\(587\) | −10.0000 | − | 17.3205i | −0.412744 | − | 0.714894i | 0.582445 | − | 0.812870i | \(-0.302096\pi\) |
−0.995189 | + | 0.0979766i | \(0.968763\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.00000 | + | 25.9808i | 0.123613 | + | 1.07052i | ||||
\(590\) | −39.0000 | −1.60560 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.00000 | − | 3.46410i | −0.0821995 | − | 0.142374i | ||||
\(593\) | −16.0000 | + | 27.7128i | −0.657041 | + | 1.13803i | 0.324337 | + | 0.945942i | \(0.394859\pi\) |
−0.981378 | + | 0.192087i | \(0.938474\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.00000 | − | 5.19615i | 0.122988 | − | 0.213021i | ||||
\(596\) | −20.0000 | −0.819232 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.50000 | − | 2.59808i | 0.0613396 | − | 0.106243i | ||||
\(599\) | −21.5000 | + | 37.2391i | −0.878466 | + | 1.52155i | −0.0254422 | + | 0.999676i | \(0.508099\pi\) |
−0.853024 | + | 0.521872i | \(0.825234\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.00000 | −0.244745 | −0.122373 | − | 0.992484i | \(-0.539050\pi\) | ||||
−0.122373 | + | 0.992484i | \(0.539050\pi\) | |||||||
\(602\) | −3.00000 | + | 5.19615i | −0.122271 | + | 0.211779i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.50000 | + | 16.4545i | −0.386550 | + | 0.669523i | ||||
\(605\) | −7.50000 | − | 12.9904i | −0.304918 | − | 0.528134i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0000 | −0.649420 | −0.324710 | − | 0.945814i | \(-0.605267\pi\) | ||||
−0.324710 | + | 0.945814i | \(0.605267\pi\) | |||||||
\(608\) | 4.00000 | + | 1.73205i | 0.162221 | + | 0.0702439i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.50000 | − | 12.9904i | −0.303666 | − | 0.525965i | ||||
\(611\) | −3.00000 | − | 5.19615i | −0.121367 | − | 0.210214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.00000 | + | 8.66025i | 0.201948 | + | 0.349784i | 0.949156 | − | 0.314806i | \(-0.101939\pi\) |
−0.747208 | + | 0.664590i | \(0.768606\pi\) | |||||||
\(614\) | −7.50000 | + | 12.9904i | −0.302675 | + | 0.524249i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.00000 | 0.161165 | ||||||||
\(617\) | −13.5000 | + | 23.3827i | −0.543490 | + | 0.941351i | 0.455211 | + | 0.890384i | \(0.349564\pi\) |
−0.998700 | + | 0.0509678i | \(0.983769\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.00000 | −0.200967 | −0.100483 | − | 0.994939i | \(-0.532039\pi\) | ||||
−0.100483 | + | 0.994939i | \(0.532039\pi\) | |||||||
\(620\) | −18.0000 | −0.722897 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.00000 | − | 1.73205i | −0.0400963 | − | 0.0694489i | ||||
\(623\) | −2.00000 | + | 3.46410i | −0.0801283 | + | 0.138786i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 24.0000 | 0.959233 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.00000 | −0.359139 | ||||||||
\(629\) | −4.00000 | − | 6.92820i | −0.159490 | − | 0.276246i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.00000 | + | 6.92820i | −0.159237 | + | 0.275807i | −0.934594 | − | 0.355716i | \(-0.884237\pi\) |
0.775356 | + | 0.631524i | \(0.217570\pi\) | |||||||
\(632\) | 4.00000 | + | 6.92820i | 0.159111 | + | 0.275589i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.00000 | −0.238290 | ||||||||
\(635\) | −33.0000 | −1.30957 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.50000 | + | 2.59808i | −0.0594322 | + | 0.102940i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.50000 | + | 2.59808i | −0.0592927 | + | 0.102698i | ||||
\(641\) | −8.50000 | − | 14.7224i | −0.335730 | − | 0.581501i | 0.647895 | − | 0.761730i | \(-0.275650\pi\) |
−0.983625 | + | 0.180229i | \(0.942316\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.5000 | + | 35.5070i | 0.808441 | + | 1.40026i | 0.913943 | + | 0.405842i | \(0.133022\pi\) |
−0.105502 | + | 0.994419i | \(0.533645\pi\) | |||||||
\(644\) | −0.500000 | − | 0.866025i | −0.0197028 | − | 0.0341262i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.00000 | + | 3.46410i | 0.314756 | + | 0.136293i | ||||
\(647\) | −30.0000 | −1.17942 | −0.589711 | − | 0.807614i | \(-0.700758\pi\) | ||||
−0.589711 | + | 0.807614i | \(0.700758\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.0000 | − | 45.0333i | −1.02059 | − | 1.76771i | ||||
\(650\) | −6.00000 | + | 10.3923i | −0.235339 | + | 0.407620i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.00000 | + | 12.1244i | −0.274141 | + | 0.474826i | ||||
\(653\) | −6.00000 | −0.234798 | −0.117399 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117399 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.5000 | + | 23.3827i | −0.527489 | + | 0.913637i | ||||
\(656\) | 2.00000 | − | 3.46410i | 0.0780869 | − | 0.135250i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.00000 | −0.0779681 | ||||||||
\(659\) | −13.0000 | + | 22.5167i | −0.506408 | + | 0.877125i | 0.493564 | + | 0.869709i | \(0.335694\pi\) |
−0.999973 | + | 0.00741531i | \(0.997640\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.50000 | − | 9.52628i | 0.213925 | − | 0.370529i | −0.739014 | − | 0.673690i | \(-0.764708\pi\) |
0.952940 | + | 0.303160i | \(0.0980418\pi\) | |||||||
\(662\) | 12.0000 | + | 20.7846i | 0.466393 | + | 0.807817i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17.0000 | −0.659728 | ||||||||
\(665\) | 10.5000 | − | 7.79423i | 0.407173 | − | 0.302247i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −9.00000 | − | 15.5885i | −0.348220 | − | 0.603136i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.0000 | + | 31.1769i | 0.695401 | + | 1.20447i | ||||
\(671\) | 10.0000 | − | 17.3205i | 0.386046 | − | 0.668651i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.0000 | 0.424019 | 0.212009 | − | 0.977268i | \(-0.431999\pi\) | ||||
0.212009 | + | 0.977268i | \(0.431999\pi\) | |||||||
\(674\) | −8.50000 | + | 14.7224i | −0.327408 | + | 0.567087i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.00000 | −0.153846 | ||||||||
\(677\) | −42.0000 | −1.61419 | −0.807096 | − | 0.590421i | \(-0.798962\pi\) | ||||
−0.807096 | + | 0.590421i | \(0.798962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.00000 | − | 8.66025i | −0.191882 | − | 0.332350i | ||||
\(680\) | −3.00000 | + | 5.19615i | −0.115045 | + | 0.199263i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.0000 | − | 20.7846i | −0.459504 | − | 0.795884i | ||||
\(683\) | 12.0000 | 0.459167 | 0.229584 | − | 0.973289i | \(-0.426264\pi\) | ||||
0.229584 | + | 0.973289i | \(0.426264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 63.0000 | 2.40711 | ||||||||
\(686\) | 0.500000 | + | 0.866025i | 0.0190901 | + | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.00000 | − | 5.19615i | 0.114374 | − | 0.198101i | ||||
\(689\) | −6.00000 | − | 10.3923i | −0.228582 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.0000 | −1.55971 | −0.779857 | − | 0.625958i | \(-0.784708\pi\) | ||||
−0.779857 | + | 0.625958i | \(0.784708\pi\) | |||||||
\(692\) | −15.0000 | −0.570214 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.0000 | − | 19.0526i | 0.417554 | − | 0.723225i | ||||
\(695\) | −48.0000 | −1.82074 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | − | 6.92820i | 0.151511 | − | 0.262424i | ||||
\(698\) | −5.00000 | − | 8.66025i | −0.189253 | − | 0.327795i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.00000 | + | 3.46410i | 0.0755929 | + | 0.130931i | ||||
\(701\) | −1.00000 | − | 1.73205i | −0.0377695 | − | 0.0654187i | 0.846523 | − | 0.532353i | \(-0.178692\pi\) |
−0.884292 | + | 0.466934i | \(0.845359\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.00000 | − | 17.3205i | −0.0754314 | − | 0.653255i | ||||
\(704\) | −4.00000 | −0.150756 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00000 | + | 10.3923i | 0.225813 | + | 0.391120i | ||||
\(707\) | −7.00000 | + | 12.1244i | −0.263262 | + | 0.455983i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.00000 | − | 3.46410i | 0.0751116 | − | 0.130097i | −0.826023 | − | 0.563636i | \(-0.809402\pi\) |
0.901135 | + | 0.433539i | \(0.142735\pi\) | |||||||
\(710\) | 21.0000 | 0.788116 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.00000 | − | 3.46410i | 0.0749532 | − | 0.129823i | ||||
\(713\) | −3.00000 | + | 5.19615i | −0.112351 | + | 0.194597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.0000 | −1.34632 | ||||||||
\(716\) | 5.00000 | − | 8.66025i | 0.186859 | − | 0.323649i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.0000 | − | 20.7846i | 0.447836 | − | 0.775675i | ||||
\(719\) | 11.0000 | + | 19.0526i | 0.410231 | + | 0.710541i | 0.994915 | − | 0.100721i | \(-0.0321148\pi\) |
−0.584684 | + | 0.811261i | \(0.698781\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.0000 | + | 13.8564i | 0.483810 | + | 0.515682i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.50000 | − | 2.59808i | −0.0557471 | − | 0.0965567i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.0000 | − | 38.1051i | −0.815935 | − | 1.41324i | −0.908655 | − | 0.417548i | \(-0.862889\pi\) |
0.0927199 | − | 0.995692i | \(-0.470444\pi\) | |||||||
\(728\) | 1.50000 | − | 2.59808i | 0.0555937 | − | 0.0962911i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.00000 | −0.222070 | ||||||||
\(731\) | 6.00000 | − | 10.3923i | 0.221918 | − | 0.384373i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.0000 | −0.406294 | −0.203147 | − | 0.979148i | \(-0.565117\pi\) | ||||
−0.203147 | + | 0.979148i | \(0.565117\pi\) | |||||||
\(734\) | 32.0000 | 1.18114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.500000 | + | 0.866025i | 0.0184302 | + | 0.0319221i | ||||
\(737\) | −24.0000 | + | 41.5692i | −0.884051 | + | 1.53122i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.0000 | + | 38.1051i | 0.809283 | + | 1.40172i | 0.913361 | + | 0.407150i | \(0.133477\pi\) |
−0.104078 | + | 0.994569i | \(0.533189\pi\) | |||||||
\(740\) | 12.0000 | 0.441129 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.00000 | −0.146845 | ||||||||
\(743\) | −1.50000 | − | 2.59808i | −0.0550297 | − | 0.0953142i | 0.837198 | − | 0.546899i | \(-0.184192\pi\) |
−0.892228 | + | 0.451585i | \(0.850859\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30.0000 | − | 51.9615i | 1.09911 | − | 1.90372i | ||||
\(746\) | 5.00000 | + | 8.66025i | 0.183063 | + | 0.317074i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.00000 | −0.292509 | ||||||||
\(749\) | −10.0000 | −0.365392 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.0000 | + | 34.6410i | −0.729810 | + | 1.26407i | 0.227153 | + | 0.973859i | \(0.427058\pi\) |
−0.956963 | + | 0.290209i | \(0.906275\pi\) | |||||||
\(752\) | 2.00000 | 0.0729325 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.5000 | − | 49.3634i | −1.03722 | − | 1.79652i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.0000 | + | 39.8372i | 0.835949 | + | 1.44791i | 0.893255 | + | 0.449550i | \(0.148416\pi\) |
−0.0573060 | + | 0.998357i | \(0.518251\pi\) | |||||||
\(758\) | 17.0000 | + | 29.4449i | 0.617468 | + | 1.06949i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10.5000 | + | 7.79423i | −0.380875 | + | 0.282726i | ||||
\(761\) | −8.00000 | −0.290000 | −0.145000 | − | 0.989432i | \(-0.546318\pi\) | ||||
−0.145000 | + | 0.989432i | \(0.546318\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00000 | − | 3.46410i | −0.0724049 | − | 0.125409i | ||||
\(764\) | −5.50000 | + | 9.52628i | −0.198983 | + | 0.344649i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.00000 | + | 3.46410i | −0.0722629 | + | 0.125163i | ||||
\(767\) | −39.0000 | −1.40821 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.0000 | − | 25.9808i | 0.540914 | − | 0.936890i | −0.457938 | − | 0.888984i | \(-0.651412\pi\) |
0.998852 | − | 0.0479061i | \(-0.0152548\pi\) | |||||||
\(770\) | −6.00000 | + | 10.3923i | −0.216225 | + | 0.374513i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.00000 | 0.179954 | ||||||||
\(773\) | 4.50000 | − | 7.79423i | 0.161854 | − | 0.280339i | −0.773680 | − | 0.633577i | \(-0.781586\pi\) |
0.935534 | + | 0.353238i | \(0.114919\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.0000 | − | 20.7846i | 0.431053 | − | 0.746605i | ||||
\(776\) | 5.00000 | + | 8.66025i | 0.179490 | + | 0.310885i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.00000 | −0.286814 | ||||||||
\(779\) | 14.0000 | − | 10.3923i | 0.501602 | − | 0.372343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.0000 | + | 24.2487i | 0.500959 | + | 0.867687i | ||||
\(782\) | 1.00000 | + | 1.73205i | 0.0357599 | + | 0.0619380i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.500000 | − | 0.866025i | −0.0178571 | − | 0.0309295i | ||||
\(785\) | 13.5000 | − | 23.3827i | 0.481836 | − | 0.834564i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −47.0000 | −1.67537 | −0.837685 | − | 0.546154i | \(-0.816091\pi\) | ||||
−0.837685 | + | 0.546154i | \(0.816091\pi\) | |||||||
\(788\) | 2.00000 | − | 3.46410i | 0.0712470 | − | 0.123404i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −24.0000 | −0.853882 | ||||||||
\(791\) | −5.00000 | −0.177780 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.50000 | − | 12.9904i | −0.266333 | − | 0.461302i | ||||
\(794\) | −9.00000 | + | 15.5885i | −0.319398 | + | 0.553214i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.00000 | − | 12.1244i | −0.248108 | − | 0.429736i | ||||
\(797\) | 49.0000 | 1.73567 | 0.867835 | − | 0.496853i | \(-0.165511\pi\) | ||||
0.867835 | + | 0.496853i | \(0.165511\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.00000 | 0.141510 | ||||||||
\(800\) | −2.00000 | − | 3.46410i | −0.0707107 | − | 0.122474i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.50000 | − | 2.59808i | 0.0529668 | − | 0.0917413i | ||||
\(803\) | −4.00000 | − | 6.92820i | −0.141157 | − | 0.244491i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.00000 | 0.105736 | ||||||||
\(806\) | −18.0000 | −0.634023 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.00000 | − | 12.1244i | 0.246259 | − | 0.426533i | ||||
\(809\) | −9.00000 | −0.316423 | −0.158212 | − | 0.987405i | \(-0.550573\pi\) | ||||
−0.158212 | + | 0.987405i | \(0.550573\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.0000 | − | 17.3205i | 0.351147 | − | 0.608205i | −0.635303 | − | 0.772263i | \(-0.719125\pi\) |
0.986451 | + | 0.164057i | \(0.0524582\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.00000 | + | 13.8564i | 0.280400 | + | 0.485667i | ||||
\(815\) | −21.0000 | − | 36.3731i | −0.735598 | − | 1.27409i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.0000 | − | 15.5885i | 0.734697 | − | 0.545371i | ||||
\(818\) | 24.0000 | 0.839140 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | + | 10.3923i | 0.209529 | + | 0.362915i | ||||
\(821\) | −24.0000 | + | 41.5692i | −0.837606 | + | 1.45078i | 0.0542853 | + | 0.998525i | \(0.482712\pi\) |
−0.891891 | + | 0.452250i | \(0.850621\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.5000 | + | 32.0429i | −0.644869 | + | 1.11695i | 0.339462 | + | 0.940620i | \(0.389755\pi\) |
−0.984332 | + | 0.176327i | \(0.943578\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.50000 | + | 11.2583i | −0.226164 | + | 0.391727i | ||||
\(827\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.0000 | 1.42399 | 0.711994 | − | 0.702185i | \(-0.247792\pi\) | ||||
0.711994 | + | 0.702185i | \(0.247792\pi\) | |||||||
\(830\) | 25.5000 | − | 44.1673i | 0.885118 | − | 1.53307i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.50000 | + | 2.59808i | −0.0520031 | + | 0.0900721i | ||||
\(833\) | −1.00000 | − | 1.73205i | −0.0346479 | − | 0.0600120i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 54.0000 | 1.86875 | ||||||||
\(836\) | −16.0000 | − | 6.92820i | −0.553372 | − | 0.239617i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.00000 | − | 10.3923i | −0.207267 | − | 0.358996i | ||||
\(839\) | 15.0000 | + | 25.9808i | 0.517858 | + | 0.896956i | 0.999785 | + | 0.0207443i | \(0.00660359\pi\) |
−0.481927 | + | 0.876211i | \(0.660063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.5000 | + | 25.1147i | 0.500000 | + | 0.866025i | ||||
\(842\) | 4.00000 | − | 6.92820i | 0.137849 | − | 0.238762i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.00000 | −0.275371 | ||||||||
\(845\) | 6.00000 | − | 10.3923i | 0.206406 | − | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | −0.171802 | ||||||||
\(848\) | 4.00000 | 0.137361 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.00000 | − | 6.92820i | −0.137199 | − | 0.237635i | ||||
\(851\) | 2.00000 | − | 3.46410i | 0.0685591 | − | 0.118748i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.0000 | + | 25.9808i | 0.513590 | + | 0.889564i | 0.999876 | + | 0.0157644i | \(0.00501816\pi\) |
−0.486286 | + | 0.873800i | \(0.661649\pi\) | |||||||
\(854\) | −5.00000 | −0.171096 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.0000 | 0.341793 | ||||||||
\(857\) | 21.0000 | + | 36.3731i | 0.717346 | + | 1.24248i | 0.962048 | + | 0.272882i | \(0.0879768\pi\) |
−0.244701 | + | 0.969599i | \(0.578690\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.0000 | − | 17.3205i | 0.341196 | − | 0.590968i | −0.643459 | − | 0.765480i | \(-0.722501\pi\) |
0.984655 | + | 0.174512i | \(0.0558348\pi\) | |||||||
\(860\) | 9.00000 | + | 15.5885i | 0.306897 | + | 0.531562i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.0000 | 0.544962 | ||||||||
\(863\) | 52.0000 | 1.77010 | 0.885050 | − | 0.465495i | \(-0.154124\pi\) | ||||
0.885050 | + | 0.465495i | \(0.154124\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.5000 | − | 38.9711i | 0.765023 | − | 1.32506i | ||||
\(866\) | −24.0000 | −0.815553 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.00000 | + | 5.19615i | −0.101827 | + | 0.176369i | ||||
\(869\) | −16.0000 | − | 27.7128i | −0.542763 | − | 0.940093i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.0000 | + | 31.1769i | 0.609907 | + | 1.05639i | ||||
\(872\) | 2.00000 | + | 3.46410i | 0.0677285 | + | 0.117309i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.500000 | + | 4.33013i | 0.0169128 | + | 0.146469i | ||||
\(875\) | 3.00000 | 0.101419 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.0000 | − | 17.3205i | −0.337676 | − | 0.584872i | 0.646319 | − | 0.763067i | \(-0.276307\pi\) |
−0.983995 | + | 0.178195i | \(0.942974\pi\) | |||||||
\(878\) | −5.00000 | + | 8.66025i | −0.168742 | + | 0.292269i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.00000 | − | 10.3923i | 0.202260 | − | 0.350325i | ||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.0000 | − | 25.9808i | 0.504790 | − | 0.874322i | −0.495194 | − | 0.868782i | \(-0.664903\pi\) |
0.999985 | − | 0.00554010i | \(-0.00176348\pi\) | |||||||
\(884\) | −3.00000 | + | 5.19615i | −0.100901 | + | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.0000 | −0.604722 | ||||||||
\(887\) | −21.0000 | + | 36.3731i | −0.705111 | + | 1.22129i | 0.261540 | + | 0.965193i | \(0.415770\pi\) |
−0.966651 | + | 0.256096i | \(0.917564\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.50000 | + | 9.52628i | −0.184464 | + | 0.319501i | ||||
\(890\) | 6.00000 | + | 10.3923i | 0.201120 | + | 0.348351i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.0000 | −0.602685 | ||||||||
\(893\) | 8.00000 | + | 3.46410i | 0.267710 | + | 0.115922i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.0000 | + | 25.9808i | 0.501395 | + | 0.868441i | ||||
\(896\) | 0.500000 | + | 0.866025i | 0.0167038 | + | 0.0289319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.5000 | − | 33.7750i | −0.650723 | − | 1.12709i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.00000 | 0.266519 | ||||||||
\(902\) | −8.00000 | + | 13.8564i | −0.266371 | + | 0.461368i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.00000 | 0.166298 | ||||||||
\(905\) | 9.00000 | 0.299170 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.0000 | − | 50.2295i | −0.962929 | − | 1.66784i | −0.715079 | − | 0.699044i | \(-0.753609\pi\) |
−0.247851 | − | 0.968798i | \(-0.579724\pi\) | |||||||
\(908\) | 2.50000 | − | 4.33013i | 0.0829654 | − | 0.143700i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.50000 | + | 7.79423i | 0.149174 | + | 0.258376i | ||||
\(911\) | −33.0000 | −1.09334 | −0.546669 | − | 0.837349i | \(-0.684105\pi\) | ||||
−0.546669 | + | 0.837349i | \(0.684105\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 68.0000 | 2.25047 | ||||||||
\(914\) | 3.50000 | + | 6.06218i | 0.115770 | + | 0.200519i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.50000 | − | 14.7224i | 0.280848 | − | 0.486443i | ||||
\(917\) | 4.50000 | + | 7.79423i | 0.148603 | + | 0.257388i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.0000 | −0.560778 | −0.280389 | − | 0.959886i | \(-0.590464\pi\) | ||||
−0.280389 | + | 0.959886i | \(0.590464\pi\) | |||||||
\(920\) | −3.00000 | −0.0989071 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.5000 | + | 28.5788i | −0.543399 | + | 0.941194i | ||||
\(923\) | 21.0000 | 0.691223 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.00000 | + | 13.8564i | −0.263038 | + | 0.455596i | ||||
\(926\) | 4.50000 | + | 7.79423i | 0.147879 | + | 0.256134i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.0000 | + | 41.5692i | 0.787414 | + | 1.36384i | 0.927546 | + | 0.373709i | \(0.121914\pi\) |
−0.140132 | + | 0.990133i | \(0.544753\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.500000 | − | 4.33013i | −0.0163868 | − | 0.141914i | ||||
\(932\) | −9.00000 | −0.294805 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.00000 | − | 3.46410i | −0.0654420 | − | 0.113349i | ||||
\(935\) | 12.0000 | − | 20.7846i | 0.392442 | − | 0.679729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.0000 | − | 39.8372i | 0.751377 | − | 1.30142i | −0.195778 | − | 0.980648i | \(-0.562723\pi\) |
0.947155 | − | 0.320775i | \(-0.103943\pi\) | |||||||
\(938\) | 12.0000 | 0.391814 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.00000 | + | 5.19615i | −0.0978492 | + | 0.169480i | ||||
\(941\) | 6.50000 | − | 11.2583i | 0.211894 | − | 0.367011i | −0.740413 | − | 0.672152i | \(-0.765370\pi\) |
0.952307 | + | 0.305141i | \(0.0987035\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.00000 | 0.130258 | ||||||||
\(944\) | 6.50000 | − | 11.2583i | 0.211557 | − | 0.366427i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0000 | + | 20.7846i | −0.390154 | + | 0.675766i | ||||
\(947\) | 11.0000 | + | 19.0526i | 0.357452 | + | 0.619125i | 0.987534 | − | 0.157403i | \(-0.0503122\pi\) |
−0.630082 | + | 0.776528i | \(0.716979\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | −0.194768 | ||||||||
\(950\) | −2.00000 | − | 17.3205i | −0.0648886 | − | 0.561951i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.00000 | + | 1.73205i | 0.0324102 | + | 0.0561361i | ||||
\(953\) | −3.00000 | − | 5.19615i | −0.0971795 | − | 0.168320i | 0.813337 | − | 0.581793i | \(-0.197649\pi\) |
−0.910516 | + | 0.413473i | \(0.864315\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.5000 | − | 28.5788i | −0.533927 | − | 0.924789i | ||||
\(956\) | 13.5000 | − | 23.3827i | 0.436621 | − | 0.756250i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 42.0000 | 1.35696 | ||||||||
\(959\) | 10.5000 | − | 18.1865i | 0.339063 | − | 0.587274i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 12.0000 | 0.386896 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.0000 | − | 19.0526i | −0.354286 | − | 0.613642i | ||||
\(965\) | −7.50000 | + | 12.9904i | −0.241434 | + | 0.418175i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.5000 | + | 38.9711i | 0.723551 | + | 1.25323i | 0.959568 | + | 0.281478i | \(0.0908248\pi\) |
−0.236016 | + | 0.971749i | \(0.575842\pi\) | |||||||
\(968\) | 5.00000 | 0.160706 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −30.0000 | −0.963242 | ||||||||
\(971\) | −16.5000 | − | 28.5788i | −0.529510 | − | 0.917139i | −0.999408 | − | 0.0344175i | \(-0.989042\pi\) |
0.469897 | − | 0.882721i | \(-0.344291\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.00000 | + | 13.8564i | −0.256468 | + | 0.444216i | ||||
\(974\) | 14.0000 | + | 24.2487i | 0.448589 | + | 0.776979i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.00000 | 0.160046 | ||||||||
\(977\) | 9.00000 | 0.287936 | 0.143968 | − | 0.989582i | \(-0.454014\pi\) | ||||
0.143968 | + | 0.989582i | \(0.454014\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.00000 | + | 13.8564i | −0.255681 | + | 0.442853i | ||||
\(980\) | 3.00000 | 0.0958315 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.00000 | − | 10.3923i | 0.191468 | − | 0.331632i | ||||
\(983\) | −21.0000 | − | 36.3731i | −0.669796 | − | 1.16012i | −0.977961 | − | 0.208788i | \(-0.933048\pi\) |
0.308165 | − | 0.951333i | \(-0.400285\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.00000 | + | 10.3923i | 0.191176 | + | 0.331126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.5000 | + | 7.79423i | −0.334050 | + | 0.247967i | ||||
\(989\) | 6.00000 | 0.190789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.5000 | + | 30.3109i | 0.555906 | + | 0.962857i | 0.997832 | + | 0.0658059i | \(0.0209618\pi\) |
−0.441927 | + | 0.897051i | \(0.645705\pi\) | |||||||
\(992\) | 3.00000 | − | 5.19615i | 0.0952501 | − | 0.164978i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.50000 | − | 6.06218i | 0.111013 | − | 0.192281i | ||||
\(995\) | 42.0000 | 1.33149 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.5000 | − | 37.2391i | 0.680912 | − | 1.17937i | −0.293791 | − | 0.955870i | \(-0.594917\pi\) |
0.974703 | − | 0.223504i | \(-0.0717497\pi\) | |||||||
\(998\) | 5.00000 | − | 8.66025i | 0.158272 | − | 0.274136i | ||||
\(999\) | 0 | 0 |
(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 | 2394.2.o.a.1261.1 | 2 | ||
3.2 | odd | 2 | 798.2.k.i.463.1 | ✓ | 2 | ||
19.11 | even | 3 | inner | 2394.2.o.a.505.1 | 2 | ||
57.11 | odd | 6 | 798.2.k.i.505.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.2.k.i.463.1 | ✓ | 2 | 3.2 | odd | 2 | ||
798.2.k.i.505.1 | yes | 2 | 57.11 | odd | 6 | ||
2394.2.o.a.505.1 | 2 | 19.11 | even | 3 | inner | ||
2394.2.o.a.1261.1 | 2 | 1.1 | even | 1 | trivial |