Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [744,2,Mod(25,744)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(744, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("744.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 744 = 2^{3} \cdot 3 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 744.q (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: | \(5.94086991038\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 25.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 744.25 |
Dual form | 744.2.q.c.625.1 |
$q$-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 \(\left(\mathbb{Z}/744\mathbb{Z}\right)^\times\).
\(n\) | \(313\) | \(373\) | \(497\) | \(559\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | + | 1.73205i | −0.447214 | + | 0.774597i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | + | 4.33013i | 0.944911 | + | 1.63663i | 0.755929 | + | 0.654654i | \(0.227186\pi\) |
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | − | 5.19615i | −0.727607 | − | 1.26025i | −0.957892 | − | 0.287129i | \(-0.907299\pi\) |
0.230285 | − | 0.973123i | \(-0.426034\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | − | 5.19615i | −0.688247 | − | 1.19208i | −0.972404 | − | 0.233301i | \(-0.925047\pi\) |
0.284157 | − | 0.958778i | \(-0.408286\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.50000 | + | 4.33013i | −0.545545 | + | 0.944911i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.50000 | − | 4.33013i | 0.628619 | − | 0.777714i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.00000 | −0.522233 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.0000 | −1.69031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | + | 6.92820i | 0.657596 | + | 1.13899i | 0.981236 | + | 0.192809i | \(0.0617599\pi\) |
−0.323640 | + | 0.946180i | \(0.604907\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | + | 3.46410i | −0.312348 | + | 0.541002i | −0.978870 | − | 0.204483i | \(-0.934449\pi\) |
0.666523 | + | 0.745485i | \(0.267782\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | + | 6.92820i | 0.609994 | + | 1.05654i | 0.991241 | + | 0.132068i | \(0.0421616\pi\) |
−0.381246 | + | 0.924473i | \(0.624505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | − | 1.73205i | −0.149071 | − | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.00000 | 0.875190 | 0.437595 | − | 0.899172i | \(-0.355830\pi\) | ||||
0.437595 | + | 0.899172i | \(0.355830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.00000 | + | 15.5885i | −1.28571 | + | 2.22692i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.00000 | − | 5.19615i | 0.420084 | − | 0.727607i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.500000 | + | 0.866025i | −0.0686803 | + | 0.118958i | −0.898321 | − | 0.439340i | \(-0.855212\pi\) |
0.829640 | + | 0.558298i | \(0.188546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | − | 5.19615i | −0.404520 | − | 0.700649i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | − | 5.19615i | 0.397360 | − | 0.688247i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.50000 | + | 9.52628i | 0.716039 | + | 1.24022i | 0.962557 | + | 0.271078i | \(0.0873801\pi\) |
−0.246518 | + | 0.969138i | \(0.579287\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.00000 | −1.02430 | −0.512148 | − | 0.858898i | \(-0.671150\pi\) | ||||
−0.512148 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.00000 | −0.629941 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.00000 | − | 10.3923i | 0.733017 | − | 1.26962i | −0.222571 | − | 0.974916i | \(-0.571445\pi\) |
0.955588 | − | 0.294706i | \(-0.0952216\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | − | 13.8564i | 0.949425 | − | 1.64445i | 0.202787 | − | 0.979223i | \(-0.435000\pi\) |
0.746639 | − | 0.665230i | \(-0.231667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | + | 1.73205i | −0.117041 | + | 0.202721i | −0.918594 | − | 0.395203i | \(-0.870674\pi\) |
0.801553 | + | 0.597924i | \(0.204008\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.0000 | −1.70941 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | + | 6.92820i | 0.450035 | + | 0.779484i | 0.998388 | − | 0.0567635i | \(-0.0180781\pi\) |
−0.548352 | + | 0.836247i | \(0.684745\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.50000 | + | 9.52628i | −0.603703 | + | 1.04565i | 0.388552 | + | 0.921427i | \(0.372976\pi\) |
−0.992255 | + | 0.124218i | \(0.960358\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0000 | 1.30158 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.50000 | − | 2.59808i | −0.160817 | − | 0.278543i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.50000 | + | 0.866025i | 0.570323 | + | 0.0898027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.0000 | 1.23117 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 19.0000 | 1.92916 | 0.964579 | − | 0.263795i | \(-0.0849741\pi\) | ||||
0.964579 | + | 0.263795i | \(0.0849741\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.50000 | − | 2.59808i | −0.150756 | − | 0.261116i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.00000 | −0.298511 | −0.149256 | − | 0.988799i | \(-0.547688\pi\) | ||||
−0.149256 | + | 0.988799i | \(0.547688\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.500000 | − | 0.866025i | 0.0492665 | − | 0.0853320i | −0.840341 | − | 0.542059i | \(-0.817645\pi\) |
0.889607 | + | 0.456727i | \(0.150978\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.00000 | − | 8.66025i | −0.487950 | − | 0.845154i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.50000 | − | 9.52628i | −0.531705 | − | 0.920940i | −0.999315 | − | 0.0370053i | \(-0.988218\pi\) |
0.467610 | − | 0.883935i | \(-0.345115\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | + | 6.92820i | −0.379663 | + | 0.657596i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | − | 3.46410i | 0.188144 | − | 0.325875i | −0.756487 | − | 0.654008i | \(-0.773086\pi\) |
0.944632 | + | 0.328133i | \(0.106419\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.0000 | − | 25.9808i | 1.37505 | − | 2.38165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.00000 | −0.360668 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.50000 | + | 2.59808i | 0.133103 | + | 0.230542i | 0.924871 | − | 0.380280i | \(-0.124172\pi\) |
−0.791768 | + | 0.610822i | \(0.790839\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.00000 | + | 6.92820i | −0.352180 | + | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | + | 10.3923i | 0.524222 | + | 0.907980i | 0.999602 | + | 0.0281993i | \(0.00897729\pi\) |
−0.475380 | + | 0.879781i | \(0.657689\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.0000 | − | 25.9808i | 1.30066 | − | 2.25282i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | − | 1.73205i | 0.0860663 | − | 0.149071i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.00000 | + | 15.5885i | −0.768922 | + | 1.33181i | 0.169226 | + | 0.985577i | \(0.445873\pi\) |
−0.938148 | + | 0.346235i | \(0.887460\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.0000 | −1.18746 | −0.593732 | − | 0.804663i | \(-0.702346\pi\) | ||||
−0.593732 | + | 0.804663i | \(0.702346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | + | 5.19615i | 0.252646 | + | 0.437595i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.00000 | − | 5.19615i | 0.249136 | − | 0.431517i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −18.0000 | −1.48461 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.50000 | + | 4.33013i | 0.204808 | + | 0.354738i | 0.950072 | − | 0.312032i | \(-0.101010\pi\) |
−0.745264 | + | 0.666770i | \(0.767676\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0000 | 0.895167 | 0.447584 | − | 0.894242i | \(-0.352285\pi\) | ||||
0.447584 | + | 0.894242i | \(0.352285\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.00000 | 0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | + | 10.3923i | 0.321288 | + | 0.834730i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.0000 | 1.27694 | 0.638470 | − | 0.769647i | \(-0.279568\pi\) | ||||
0.638470 | + | 0.769647i | \(0.279568\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.00000 | −0.0793052 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.00000 | − | 5.19615i | 0.233550 | − | 0.404520i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.00000 | + | 6.92820i | 0.309529 | + | 0.536120i | 0.978259 | − | 0.207385i | \(-0.0664952\pi\) |
−0.668730 | + | 0.743505i | \(0.733162\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.50000 | + | 11.2583i | 0.500000 | + | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.00000 | 0.458831 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.50000 | − | 7.79423i | 0.342129 | − | 0.592584i | −0.642699 | − | 0.766119i | \(-0.722185\pi\) |
0.984828 | + | 0.173534i | \(0.0555188\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.50000 | + | 4.33013i | −0.188982 | + | 0.327327i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.50000 | + | 9.52628i | −0.413405 | + | 0.716039i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.50000 | − | 7.79423i | −0.336346 | − | 0.582568i | 0.647397 | − | 0.762153i | \(-0.275858\pi\) |
−0.983742 | + | 0.179585i | \(0.942524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.00000 | + | 1.73205i | −0.0743294 | + | 0.128742i | −0.900794 | − | 0.434246i | \(-0.857015\pi\) |
0.826465 | + | 0.562988i | \(0.190348\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.00000 | − | 6.92820i | −0.295689 | − | 0.512148i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.0000 | −1.17634 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.0000 | 1.31629 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.50000 | − | 4.33013i | −0.181848 | − | 0.314970i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00000 | − | 10.3923i | 0.434145 | − | 0.751961i | −0.563081 | − | 0.826402i | \(-0.690384\pi\) |
0.997225 | + | 0.0744412i | \(0.0237173\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.50000 | − | 11.2583i | −0.467880 | − | 0.810392i | 0.531446 | − | 0.847092i | \(-0.321649\pi\) |
−0.999326 | + | 0.0366998i | \(0.988315\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.00000 | + | 5.19615i | −0.213741 | + | 0.370211i | −0.952882 | − | 0.303340i | \(-0.901898\pi\) |
0.739141 | + | 0.673550i | \(0.235232\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.50000 | − | 11.2583i | 0.460773 | − | 0.798082i | −0.538227 | − | 0.842800i | \(-0.680906\pi\) |
0.999000 | + | 0.0447181i | \(0.0142390\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.0000 | 0.846415 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.50000 | − | 12.9904i | −0.526397 | − | 0.911746i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | − | 6.92820i | −0.279372 | − | 0.483887i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.0000 | 1.24509 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.00000 | − | 1.73205i | −0.0688428 | − | 0.119239i | 0.829549 | − | 0.558433i | \(-0.188597\pi\) |
−0.898392 | + | 0.439194i | \(0.855264\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.0000 | 1.09630 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.0000 | −1.09119 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.5000 | + | 4.33013i | 1.86682 | + | 0.293948i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.00000 | −0.135147 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.50000 | − | 12.9904i | −0.502237 | − | 0.869900i | −0.999997 | − | 0.00258516i | \(-0.999177\pi\) |
0.497760 | − | 0.867315i | \(-0.334156\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.5000 | − | 21.6506i | 0.829654 | − | 1.43700i | −0.0686556 | − | 0.997640i | \(-0.521871\pi\) |
0.898310 | − | 0.439363i | \(-0.144796\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.00000 | − | 13.8564i | −0.528655 | − | 0.915657i | −0.999442 | − | 0.0334101i | \(-0.989363\pi\) |
0.470787 | − | 0.882247i | \(-0.343970\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.50000 | − | 12.9904i | −0.493464 | − | 0.854704i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.0000 | 0.786146 | 0.393073 | − | 0.919507i | \(-0.371412\pi\) | ||||
0.393073 | + | 0.919507i | \(0.371412\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | + | 10.3923i | −0.391397 | + | 0.677919i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.00000 | + | 6.92820i | −0.259828 | + | 0.450035i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0000 | + | 20.7846i | −0.776215 | + | 1.34444i | 0.157893 | + | 0.987456i | \(0.449530\pi\) |
−0.934109 | + | 0.356988i | \(0.883804\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.50000 | − | 12.9904i | −0.483117 | − | 0.836784i | 0.516695 | − | 0.856170i | \(-0.327162\pi\) |
−0.999812 | + | 0.0193858i | \(0.993829\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.0000 | − | 31.1769i | −1.14998 | − | 1.99182i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.0000 | −0.697097 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.0000 | + | 24.2487i | 0.883672 | + | 1.53057i | 0.847228 | + | 0.531229i | \(0.178270\pi\) |
0.0364441 | + | 0.999336i | \(0.488397\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.00000 | + | 10.3923i | 0.375735 | + | 0.650791i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.00000 | − | 13.8564i | 0.499026 | − | 0.864339i | −0.500973 | − | 0.865463i | \(-0.667024\pi\) |
0.999999 | + | 0.00112398i | \(0.000357774\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.0000 | + | 34.6410i | −1.24274 | + | 2.15249i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.50000 | − | 2.59808i | 0.0928477 | − | 0.160817i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.0000 | 1.35658 | 0.678289 | − | 0.734795i | \(-0.262722\pi\) | ||||
0.678289 | + | 0.734795i | \(0.262722\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.00000 | − | 1.73205i | −0.0614295 | − | 0.106399i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.00000 | − | 1.73205i | −0.0611990 | − | 0.106000i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.00000 | − | 15.5885i | 0.548740 | − | 0.950445i | −0.449622 | − | 0.893219i | \(-0.648441\pi\) |
0.998361 | − | 0.0572259i | \(-0.0182255\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.0000 | 1.88312 | 0.941558 | − | 0.336851i | \(-0.109362\pi\) | ||||
0.941558 | + | 0.336851i | \(0.109362\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.00000 | −0.180907 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.00000 | −0.360505 | −0.180253 | − | 0.983620i | \(-0.557691\pi\) | ||||
−0.180253 | + | 0.983620i | \(0.557691\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.00000 | + | 5.19615i | 0.119737 | + | 0.311086i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.0000 | −1.42665 | −0.713326 | − | 0.700832i | \(-0.752812\pi\) | ||||
−0.713326 | + | 0.700832i | \(0.752812\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.00000 | + | 10.3923i | 0.355409 | + | 0.615587i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.0000 | −1.18056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.50000 | + | 16.4545i | 0.556900 | + | 0.964579i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.50000 | − | 7.79423i | −0.262893 | − | 0.455344i | 0.704117 | − | 0.710084i | \(-0.251343\pi\) |
−0.967009 | + | 0.254741i | \(0.918010\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.0000 | −1.28089 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.50000 | − | 2.59808i | 0.0870388 | − | 0.150756i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.0000 | + | 34.6410i | −1.15278 | + | 1.99667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.50000 | − | 2.59808i | −0.0861727 | − | 0.149256i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.00000 | − | 13.8564i | 0.458079 | − | 0.793416i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.00000 | + | 8.66025i | 0.285365 | + | 0.494267i | 0.972698 | − | 0.232076i | \(-0.0745518\pi\) |
−0.687333 | + | 0.726343i | \(0.741218\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.50000 | − | 7.79423i | −0.254355 | − | 0.440556i | 0.710365 | − | 0.703833i | \(-0.248530\pi\) |
−0.964720 | + | 0.263278i | \(0.915197\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.00000 | − | 8.66025i | 0.281718 | − | 0.487950i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.5000 | − | 18.1865i | −0.589739 | − | 1.02146i | −0.994266 | − | 0.106932i | \(-0.965897\pi\) |
0.404528 | − | 0.914526i | \(-0.367436\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.50000 | − | 7.79423i | 0.251952 | − | 0.436393i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.50000 | − | 9.52628i | 0.306980 | − | 0.531705i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.0000 | + | 31.1769i | −1.00155 | + | 1.73473i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.00000 | − | 1.73205i | −0.0553001 | − | 0.0957826i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.0000 | + | 25.9808i | 0.826977 | + | 1.43237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0000 | + | 17.3205i | −0.549650 | + | 0.952021i | 0.448649 | + | 0.893708i | \(0.351905\pi\) |
−0.998298 | + | 0.0583130i | \(0.981428\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.00000 | −0.438397 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.0000 | + | 20.7846i | 0.655630 | + | 1.13558i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.00000 | −0.381314 | −0.190657 | − | 0.981657i | \(-0.561062\pi\) | ||||
−0.190657 | + | 0.981657i | \(0.561062\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.00000 | 0.217250 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | + | 15.5885i | 0.324918 | + | 0.844162i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −55.0000 | −2.96972 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.5000 | + | 30.3109i | 0.939449 | + | 1.62717i | 0.766501 | + | 0.642243i | \(0.221996\pi\) |
0.172948 | + | 0.984931i | \(0.444671\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.0000 | − | 22.5167i | −0.691920 | − | 1.19844i | −0.971208 | − | 0.238233i | \(-0.923432\pi\) |
0.279288 | − | 0.960207i | \(-0.409902\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.0000 | + | 27.7128i | 0.849192 | + | 1.47084i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 30.0000 | 1.58777 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.50000 | + | 14.7224i | −0.447368 | + | 0.774865i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.00000 | + | 1.73205i | −0.0524864 | + | 0.0909091i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.00000 | − | 3.46410i | −0.104685 | − | 0.181319i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.00000 | + | 6.92820i | −0.208798 | + | 0.361649i | −0.951336 | − | 0.308155i | \(-0.900289\pi\) |
0.742538 | + | 0.669804i | \(0.233622\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.00000 | − | 3.46410i | −0.104116 | − | 0.180334i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.00000 | −0.259587 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.00000 | −0.310668 | −0.155334 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155334 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.00000 | − | 10.3923i | −0.309839 | − | 0.536656i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.00000 | − | 15.5885i | −0.462299 | − | 0.800725i | 0.536776 | − | 0.843725i | \(-0.319642\pi\) |
−0.999075 | + | 0.0429994i | \(0.986309\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.50000 | + | 2.59808i | −0.0768473 | + | 0.133103i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.0000 | − | 24.2487i | 0.715367 | − | 1.23905i | −0.247451 | − | 0.968900i | \(-0.579593\pi\) |
0.962818 | − | 0.270151i | \(-0.0870736\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.0000 | − | 25.9808i | 0.764471 | − | 1.32410i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.0000 | + | 25.9808i | 0.760530 | + | 1.31728i | 0.942578 | + | 0.333987i | \(0.108394\pi\) |
−0.182047 | + | 0.983290i | \(0.558272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.00000 | + | 10.3923i | −0.302660 | + | 0.524222i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.0000 | −0.805047 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.0000 | + | 22.5167i | 0.652451 | + | 1.13008i | 0.982526 | + | 0.186124i | \(0.0595926\pi\) |
−0.330075 | + | 0.943955i | \(0.607074\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 30.0000 | 1.50188 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.0000 | 0.799002 | 0.399501 | − | 0.916733i | \(-0.369183\pi\) | ||||
0.399501 | + | 0.916733i | \(0.369183\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.00000 | 0.0993808 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.0000 | −1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.5000 | − | 19.9186i | −0.568638 | − | 0.984911i | −0.996701 | − | 0.0811615i | \(-0.974137\pi\) |
0.428063 | − | 0.903749i | \(-0.359196\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.0000 | −0.887875 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.5000 | + | 47.6314i | −1.35319 | + | 2.34379i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.0000 | − | 19.0526i | −0.539969 | − | 0.935253i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.00000 | − | 12.1244i | −0.342791 | − | 0.593732i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.00000 | −0.439679 | −0.219839 | − | 0.975536i | \(-0.570553\pi\) | ||||
−0.219839 | + | 0.975536i | \(0.570553\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.00000 | − | 6.92820i | 0.194948 | − | 0.337660i | −0.751935 | − | 0.659237i | \(-0.770879\pi\) |
0.946883 | + | 0.321577i | \(0.104213\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00000 | + | 5.19615i | −0.145865 | + | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.00000 | − | 5.19615i | 0.145521 | − | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.0000 | − | 34.6410i | −0.967868 | − | 1.67640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.0000 | + | 32.9090i | 0.915198 | + | 1.58517i | 0.806611 | + | 0.591082i | \(0.201299\pi\) |
0.108586 | + | 0.994087i | \(0.465368\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.0000 | −1.44171 | −0.720854 | − | 0.693087i | \(-0.756250\pi\) | ||||
−0.720854 | + | 0.693087i | \(0.756250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.00000 | 0.287678 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.50000 | − | 14.7224i | 0.405683 | − | 0.702663i | −0.588718 | − | 0.808339i | \(-0.700367\pi\) |
0.994401 | + | 0.105675i | \(0.0337004\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.00000 | − | 15.5885i | −0.428571 | − | 0.742307i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.00000 | + | 10.3923i | −0.285069 | + | 0.493753i | −0.972626 | − | 0.232377i | \(-0.925350\pi\) |
0.687557 | + | 0.726130i | \(0.258683\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.00000 | − | 3.46410i | 0.0948091 | − | 0.164214i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.50000 | + | 4.33013i | −0.118246 | + | 0.204808i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | − | 10.3923i | −0.282529 | − | 0.489355i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.50000 | + | 9.52628i | 0.258413 | + | 0.447584i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0000 | −0.467780 | −0.233890 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.00000 | + | 5.19615i | 0.140028 | + | 0.242536i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.0000 | 0.512321 | 0.256161 | − | 0.966634i | \(-0.417542\pi\) | ||||
0.256161 | + | 0.966634i | \(0.417542\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.00000 | 0.0464739 | 0.0232370 | − | 0.999730i | \(-0.492603\pi\) | ||||
0.0232370 | + | 0.999730i | \(0.492603\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.00000 | + | 8.66025i | −0.324617 | + | 0.401610i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.00000 | 0.138823 | 0.0694117 | − | 0.997588i | \(-0.477888\pi\) | ||||
0.0694117 | + | 0.997588i | \(0.477888\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 60.0000 | 2.77054 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.00000 | + | 13.8564i | 0.368621 | + | 0.638470i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.0000 | −1.10352 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.00000 | − | 5.19615i | 0.137649 | − | 0.238416i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.500000 | − | 0.866025i | −0.0228934 | − | 0.0396526i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.00000 | − | 8.66025i | −0.228456 | − | 0.395697i | 0.728895 | − | 0.684626i | \(-0.240034\pi\) |
−0.957351 | + | 0.288929i | \(0.906701\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.0000 | + | 32.9090i | −0.862746 | + | 1.49432i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.50000 | − | 14.7224i | 0.385172 | − | 0.667137i | −0.606621 | − | 0.794991i | \(-0.707476\pi\) |
0.991793 | + | 0.127854i | \(0.0408089\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.00000 | + | 3.46410i | 0.0904431 | + | 0.156652i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.50000 | − | 14.7224i | 0.383600 | − | 0.664414i | −0.607974 | − | 0.793957i | \(-0.708018\pi\) |
0.991574 | + | 0.129543i | \(0.0413509\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | + | 15.5885i | 0.405340 | + | 0.702069i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.00000 | 0.269680 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 80.0000 | 3.58849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.0000 | − | 20.7846i | −0.537194 | − | 0.930447i | −0.999054 | − | 0.0434940i | \(-0.986151\pi\) |
0.461860 | − | 0.886953i | \(-0.347182\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.00000 | + | 6.92820i | −0.178707 | + | 0.309529i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.0000 | + | 34.6410i | 0.891756 | + | 1.54457i | 0.837769 | + | 0.546025i | \(0.183860\pi\) |
0.0539870 | + | 0.998542i | \(0.482807\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.00000 | − | 5.19615i | 0.133498 | − | 0.231226i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.50000 | + | 11.2583i | −0.288675 | + | 0.500000i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.50000 | − | 6.06218i | 0.155135 | − | 0.268701i | −0.777973 | − | 0.628297i | \(-0.783752\pi\) |
0.933108 | + | 0.359596i | \(0.117085\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0000 | −0.442374 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.00000 | + | 5.19615i | 0.132453 | + | 0.229416i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.00000 | + | 1.73205i | 0.0440653 | + | 0.0763233i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.00000 | + | 15.5885i | −0.395820 | + | 0.685580i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.00000 | 0.395056 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.00000 | − | 3.46410i | −0.0876216 | − | 0.151765i | 0.818884 | − | 0.573959i | \(-0.194593\pi\) |
−0.906505 | + | 0.422194i | \(0.861260\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.0000 | −1.57417 | −0.787085 | − | 0.616844i | \(-0.788411\pi\) | ||||
−0.787085 | + | 0.616844i | \(0.788411\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.00000 | −0.218218 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −33.0000 | − | 5.19615i | −1.43750 | − | 0.226348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.0000 | −0.477359 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.0000 | 0.951143 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.50000 | − | 7.79423i | 0.194189 | − | 0.336346i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27.0000 | − | 46.7654i | −1.16297 | − | 2.01433i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.00000 | + | 10.3923i | 0.257960 | + | 0.446800i | 0.965695 | − | 0.259678i | \(-0.0836163\pi\) |
−0.707735 | + | 0.706478i | \(0.750283\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.00000 | −0.0858282 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.00000 | − | 3.46410i | 0.0856706 | − | 0.148386i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.0000 | + | 29.4449i | −0.726868 | + | 1.25897i | 0.231333 | + | 0.972875i | \(0.425691\pi\) |
−0.958201 | + | 0.286097i | \(0.907642\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.00000 | − | 6.92820i | 0.170716 | − | 0.295689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.00000 | + | 15.5885i | 0.383413 | + | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.0000 | + | 34.6410i | −0.850487 | + | 1.47309i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.00000 | − | 13.8564i | −0.339581 | − | 0.588172i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.0000 | 0.974541 | 0.487271 | − | 0.873251i | \(-0.337993\pi\) | ||||
0.487271 | + | 0.873251i | \(0.337993\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.00000 | + | 15.5885i | 0.379980 | + | 0.658145i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.5000 | − | 30.3109i | 0.737537 | − | 1.27745i | −0.216064 | − | 0.976379i | \(-0.569322\pi\) |
0.953601 | − | 0.301073i | \(-0.0973446\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00000 | + | 6.92820i | 0.168281 | + | 0.291472i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.50000 | − | 4.33013i | 0.104990 | − | 0.181848i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.0000 | − | 20.7846i | 0.503066 | − | 0.871336i | −0.496928 | − | 0.867792i | \(-0.665539\pi\) |
0.999994 | − | 0.00354413i | \(-0.00112814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.0000 | − | 22.5167i | 0.544033 | − | 0.942293i | −0.454634 | − | 0.890678i | \(-0.650230\pi\) |
0.998667 | − | 0.0516146i | \(-0.0164367\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.0000 | − | 32.9090i | −0.790980 | − | 1.37002i | −0.925361 | − | 0.379088i | \(-0.876238\pi\) |
0.134380 | − | 0.990930i | \(-0.457096\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.50000 | − | 11.2583i | 0.270131 | − | 0.467880i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −55.0000 | −2.28178 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.50000 | − | 2.59808i | −0.0621237 | − | 0.107601i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.0000 | 1.69225 | 0.846126 | − | 0.532984i | \(-0.178929\pi\) | ||||
0.846126 | + | 0.532984i | \(0.178929\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.0000 | − | 5.19615i | −1.35974 | − | 0.214104i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.00000 | −0.246807 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −42.0000 | −1.72473 | −0.862367 | − | 0.506284i | \(-0.831019\pi\) | ||||
−0.862367 | + | 0.506284i | \(0.831019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.0000 | + | 51.9615i | 1.22988 | + | 2.13021i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.0000 | 0.532055 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.0000 | − | 34.6410i | 0.817178 | − | 1.41539i | −0.0905757 | − | 0.995890i | \(-0.528871\pi\) |
0.907754 | − | 0.419504i | \(-0.137796\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.0000 | − | 19.0526i | −0.448699 | − | 0.777170i | 0.549602 | − | 0.835426i | \(-0.314779\pi\) |
−0.998302 | + | 0.0582563i | \(0.981446\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.00000 | + | 10.3923i | 0.244339 | + | 0.423207i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.00000 | −0.162623 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.0000 | − | 20.7846i | 0.487065 | − | 0.843621i | −0.512824 | − | 0.858494i | \(-0.671401\pi\) |
0.999889 | + | 0.0148722i | \(0.00473415\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.50000 | − | 12.9904i | 0.303915 | − | 0.526397i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.0000 | − | 24.2487i | −0.565455 | − | 0.979396i | −0.997007 | − | 0.0773084i | \(-0.975367\pi\) |
0.431553 | − | 0.902088i | \(-0.357966\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.00000 | − | 6.92820i | 0.161296 | − | 0.279372i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.00000 | − | 10.3923i | −0.241551 | − | 0.418378i | 0.719605 | − | 0.694383i | \(-0.244323\pi\) |
−0.961156 | + | 0.276005i | \(0.910989\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0000 | 0.401934 | 0.200967 | − | 0.979598i | \(-0.435592\pi\) | ||||
0.200967 | + | 0.979598i | \(0.435592\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.00000 | − | 8.66025i | −0.200321 | − | 0.346966i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.00000 | + | 15.5885i | 0.359425 | + | 0.622543i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.0000 | − | 41.5692i | 0.956943 | − | 1.65747i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.50000 | − | 4.33013i | 0.0995234 | − | 0.172380i | −0.811964 | − | 0.583707i | \(-0.801602\pi\) |
0.911487 | + | 0.411328i | \(0.134935\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.00000 | − | 1.73205i | 0.0397464 | − | 0.0688428i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.00000 | −0.238103 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.00000 | + | 13.8564i | 0.316475 | + | 0.548151i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.00000 | + | 10.3923i | −0.236986 | + | 0.410471i | −0.959848 | − | 0.280521i | \(-0.909493\pi\) |
0.722862 | + | 0.690992i | \(0.242826\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.0000 | −0.630978 | −0.315489 | − | 0.948929i | \(-0.602169\pi\) | ||||
−0.315489 | + | 0.948929i | \(0.602169\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.00000 | − | 13.8564i | −0.315000 | − | 0.545595i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.00000 | −0.235884 | −0.117942 | − | 0.993020i | \(-0.537630\pi\) | ||||
−0.117942 | + | 0.993020i | \(0.537630\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.0000 | −1.29536 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.0000 | + | 25.9808i | 0.391931 | + | 1.01827i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −41.0000 | −1.60445 | −0.802227 | − | 0.597019i | \(-0.796352\pi\) | ||||
−0.802227 | + | 0.597019i | \(0.796352\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.0000 | −0.937758 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.00000 | − | 1.73205i | −0.0390137 | − | 0.0675737i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.0000 | 1.28550 | 0.642749 | − | 0.766077i | \(-0.277794\pi\) | ||||
0.642749 | + | 0.766077i | \(0.277794\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.0000 | − | 34.6410i | 0.777910 | − | 1.34738i | −0.155235 | − | 0.987878i | \(-0.549613\pi\) |
0.933144 | − | 0.359502i | \(-0.117053\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30.0000 | + | 51.9615i | 1.16335 | + | 2.01498i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.50000 | − | 12.9904i | 0.289967 | − | 0.502237i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | − | 20.7846i | 0.463255 | − | 0.802381i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.50000 | + | 11.2583i | −0.250557 | + | 0.433977i | −0.963679 | − | 0.267063i | \(-0.913947\pi\) |
0.713123 | + | 0.701039i | \(0.247280\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.500000 | − | 0.866025i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.5000 | − | 32.0429i | 0.711013 | − | 1.23151i | −0.253465 | − | 0.967345i | \(-0.581570\pi\) |
0.964477 | − | 0.264166i | \(-0.0850965\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 47.5000 | + | 82.2724i | 1.82288 | + | 3.15733i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.0000 | 0.958002 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.00000 | 0.191320 | 0.0956598 | − | 0.995414i | \(-0.469504\pi\) | ||||
0.0956598 | + | 0.995414i | \(0.469504\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0000 | − | 31.1769i | −0.687745 | − | 1.19121i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.00000 | − | 13.8564i | 0.305219 | − | 0.528655i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.0000 | − | 19.0526i | 0.418460 | − | 0.724793i | −0.577325 | − | 0.816514i | \(-0.695903\pi\) |
0.995785 | + | 0.0917209i | \(0.0292368\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.50000 | − | 12.9904i | 0.284901 | − | 0.493464i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.0000 | − | 24.2487i | 0.531050 | − | 0.919806i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0000 | 0.909065 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.00000 | + | 10.3923i | 0.226941 | + | 0.393073i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.50000 | + | 12.9904i | 0.283271 | + | 0.490640i | 0.972188 | − | 0.234200i | \(-0.0752470\pi\) |
−0.688917 | + | 0.724840i | \(0.741914\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.0000 | − | 41.5692i | 0.905177 | − | 1.56781i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.0000 | −0.451946 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.50000 | − | 12.9904i | −0.282067 | − | 0.488554i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.00000 | −0.150223 | −0.0751116 | − | 0.997175i | \(-0.523931\pi\) | ||||
−0.0751116 | + | 0.997175i | \(0.523931\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.00000 | −0.300023 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.0000 | −0.896296 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.00000 | + | 1.73205i | 0.0372937 | + | 0.0645946i | 0.884070 | − | 0.467355i | \(-0.154793\pi\) |
−0.846776 | + | 0.531949i | \(0.821460\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.00000 | 0.186210 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.50000 | − | 12.9904i | 0.278928 | − | 0.483117i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.50000 | − | 2.59808i | −0.0557086 | − | 0.0964901i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.5000 | + | 40.7032i | 0.871567 | + | 1.50960i | 0.860376 | + | 0.509661i | \(0.170229\pi\) |
0.0111912 | + | 0.999937i | \(0.496438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0000 | − | 41.5692i | 0.887672 | − | 1.53749i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.0000 | + | 29.4449i | −0.627909 | + | 1.08757i | 0.360061 | + | 0.932929i | \(0.382756\pi\) |
−0.987971 | + | 0.154642i | \(0.950578\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.0000 | − | 31.1769i | 0.663940 | − | 1.14998i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.0000 | + | 31.1769i | 0.663039 | + | 1.14842i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.00000 | + | 12.1244i | −0.257499 | + | 0.446002i | −0.965571 | − | 0.260138i | \(-0.916232\pi\) |
0.708072 | + | 0.706140i | \(0.249565\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.0000 | −1.10059 | −0.550297 | − | 0.834969i | \(-0.685485\pi\) | ||||
−0.550297 | + | 0.834969i | \(0.685485\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.0000 | −0.366372 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.50000 | − | 9.52628i | −0.201234 | − | 0.348548i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27.5000 | − | 47.6314i | 1.00483 | − | 1.74041i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.5000 | + | 28.5788i | 0.602094 | + | 1.04286i | 0.992504 | + | 0.122216i | \(0.0389999\pi\) |
−0.390410 | + | 0.920641i | \(0.627667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.0000 | + | 24.2487i | −0.510188 | + | 0.883672i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.0000 | + | 19.0526i | −0.400331 | + | 0.693394i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0000 | + | 36.3731i | 0.761249 | + | 1.31852i | 0.942207 | + | 0.335032i | \(0.108747\pi\) |
−0.180957 | + | 0.983491i | \(0.557920\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.00000 | − | 8.66025i | −0.181012 | − | 0.313522i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.00000 | + | 10.3923i | −0.216930 | + | 0.375735i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.5000 | + | 47.6314i | 0.991675 | + | 1.71763i | 0.607350 | + | 0.794434i | \(0.292233\pi\) |
0.384325 | + | 0.923198i | \(0.374434\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.0000 | 0.576226 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.0000 | −0.935155 | −0.467578 | − | 0.883952i | \(-0.654873\pi\) | ||||
−0.467578 | + | 0.883952i | \(0.654873\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.50000 | + | 0.866025i | 0.197566 | + | 0.0311086i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −40.0000 | −1.43499 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.0000 | 0.859889 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | + | 41.5692i | 0.858788 | + | 1.48746i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.00000 | 0.107211 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.0000 | + | 27.7128i | −0.571064 | + | 0.989113i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.0000 | − | 24.2487i | −0.499046 | − | 0.864373i | 0.500953 | − | 0.865474i | \(-0.332983\pi\) |
−0.999999 | + | 0.00110111i | \(0.999650\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.0000 | + | 19.0526i | 0.391610 | + | 0.678289i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.0000 | 0.711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.00000 | − | 1.73205i | 0.0354663 | − | 0.0614295i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.50000 | − | 7.79423i | 0.159398 | − | 0.276086i | −0.775254 | − | 0.631650i | \(-0.782378\pi\) |
0.934652 | + | 0.355564i | \(0.115711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.0000 | − | 31.1769i | −0.636794 | − | 1.10296i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.00000 | − | 1.73205i | 0.0353333 | − | 0.0611990i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.00000 | − | 5.19615i | −0.105868 | − | 0.183368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.0000 | 0.633630 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.0000 | + | 25.9808i | 0.527372 | + | 0.913435i | 0.999491 | + | 0.0319002i | \(0.0101559\pi\) |
−0.472119 | + | 0.881535i | \(0.656511\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.00000 | + | 1.73205i | −0.0351147 | + | 0.0608205i | −0.883049 | − | 0.469281i | \(-0.844513\pi\) |
0.847934 | + | 0.530102i | \(0.177846\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.5000 | + | 26.8468i | 0.543609 | + | 0.941558i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.00000 | + | 6.92820i | −0.140114 | + | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.0000 | − | 41.5692i | 0.839654 | − | 1.45432i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.00000 | −0.104701 | −0.0523504 | − | 0.998629i | \(-0.516671\pi\) | ||||
−0.0523504 | + | 0.998629i | \(0.516671\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.5000 | − | 42.4352i | −0.854016 | − | 1.47920i | −0.877555 | − | 0.479477i | \(-0.840826\pi\) |
0.0235383 | − | 0.999723i | \(-0.492507\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.50000 | − | 2.59808i | −0.0522233 | − | 0.0904534i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | + | 20.7846i | −0.417281 | + | 0.722752i | −0.995665 | − | 0.0930129i | \(-0.970350\pi\) |
0.578384 | + | 0.815765i | \(0.303684\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.00000 | −0.208389 | −0.104194 | − | 0.994557i | \(-0.533226\pi\) | ||||
−0.104194 | + | 0.994557i | \(0.533226\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.00000 | − | 5.19615i | −0.104069 | − | 0.180253i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 108.000 | 3.74198 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.0000 | −0.553703 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.50000 | + | 4.33013i | −0.120978 | + | 0.149671i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.0000 | −1.58810 | −0.794048 | − | 0.607855i | \(-0.792030\pi\) | ||||
−0.794048 | + | 0.607855i | \(0.792030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.00000 | − | 8.66025i | −0.172209 | − | 0.298275i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −26.0000 | −0.894427 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | + | 8.66025i | −0.171802 | + | 0.297570i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.0000 | − | 20.7846i | −0.411839 | − | 0.713326i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.0000 | 0.547830 | 0.273915 | − | 0.961754i | \(-0.411681\pi\) | ||||
0.273915 | + | 0.961754i | \(0.411681\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.00000 | + | 10.3923i | −0.205196 | + | 0.355409i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.0000 | − | 41.5692i | 0.818869 | − | 1.41832i | −0.0876464 | − | 0.996152i | \(-0.527935\pi\) |
0.906516 | − | 0.422172i | \(-0.138732\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.0000 | − | 17.3205i | −0.340799 | − | 0.590281i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.0000 | + | 20.7846i | −0.408485 | + | 0.707516i | −0.994720 | − | 0.102624i | \(-0.967276\pi\) |
0.586235 | + | 0.810141i | \(0.300609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | + | 15.5885i | 0.306009 | + | 0.530023i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.0000 | −0.645274 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.0000 | −0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.50000 | + | 16.4545i | −0.321526 | + | 0.556900i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.0000 | − | 51.9615i | −1.01419 | − | 1.75662i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.0000 | + | 20.7846i | −0.405211 | + | 0.701846i | −0.994346 | − | 0.106188i | \(-0.966135\pi\) |
0.589135 | + | 0.808035i | \(0.299469\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.50000 | − | 7.79423i | 0.151781 | − | 0.262893i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.00000 | − | 13.8564i | 0.269527 | − | 0.466834i | −0.699213 | − | 0.714914i | \(-0.746466\pi\) |
0.968740 | + | 0.248079i | \(0.0797994\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.0000 | 1.21150 | 0.605748 | − | 0.795656i | \(-0.292874\pi\) | ||||
0.605748 | + | 0.795656i | \(0.292874\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.0000 | − | 19.0526i | −0.369761 | − | 0.640445i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.0000 | + | 22.5167i | 0.436497 | + | 0.756035i | 0.997417 | − | 0.0718351i | \(-0.0228855\pi\) |
−0.560919 | + | 0.827871i | \(0.689552\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.50000 | + | 12.9904i | −0.251542 | + | 0.435683i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.00000 | 0.100504 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.0000 | − | 31.1769i | −0.602347 | − | 1.04330i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0000 | 0.601674 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.5000 | + | 12.9904i | −0.350195 | + | 0.433253i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.00000 | 0.199889 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −40.0000 | −1.33112 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.00000 | − | 3.46410i | −0.0664822 | − | 0.115151i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0000 | −0.531271 | −0.265636 | − | 0.964073i | \(-0.585582\pi\) | ||||
−0.265636 | + | 0.964073i | \(0.585582\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.50000 | − | 2.59808i | 0.0497519 | − | 0.0861727i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.0000 | − | 25.9808i | −0.496972 | − | 0.860781i | 0.503022 | − | 0.864274i | \(-0.332222\pi\) |
−0.999994 | + | 0.00349271i | \(0.998888\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.5000 | − | 28.5788i | −0.546070 | − | 0.945822i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.0000 | 0.528944 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.0000 | + | 51.9615i | −0.990687 | + | 1.71592i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.50000 | − | 9.52628i | 0.181428 | − | 0.314243i | −0.760939 | − | 0.648824i | \(-0.775261\pi\) |
0.942367 | + | 0.334581i | \(0.108595\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.00000 | + | 8.66025i | −0.164756 | + | 0.285365i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | + | 6.92820i | −0.131519 | + | 0.227798i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.500000 | + | 0.866025i | 0.0164222 | + | 0.0284440i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.0000 | 0.590561 | 0.295280 | − | 0.955411i | \(-0.404587\pi\) | ||||
0.295280 | + | 0.955411i | \(0.404587\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 108.000 | 3.53956 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.0000 | + | 31.1769i | −0.588663 | + | 1.01959i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.0000 | − | 25.9808i | −0.490029 | − | 0.848755i | 0.509906 | − | 0.860230i | \(-0.329680\pi\) |
−0.999934 | + | 0.0114759i | \(0.996347\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.50000 | − | 7.79423i | 0.146852 | − | 0.254355i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.5000 | − | 18.1865i | 0.342290 | − | 0.592864i | −0.642567 | − | 0.766229i | \(-0.722131\pi\) |
0.984858 | + | 0.173365i | \(0.0554641\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.0000 | 0.325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.0000 | − | 45.0333i | −0.844886 | − | 1.46339i | −0.885720 | − | 0.464220i | \(-0.846335\pi\) |
0.0408333 | − | 0.999166i | \(-0.486999\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.5000 | − | 18.1865i | 0.340486 | − | 0.589739i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.0000 | −1.29573 | −0.647864 | − | 0.761756i | \(-0.724337\pi\) | ||||
−0.647864 | + | 0.761756i | \(0.724337\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.0000 | + | 20.7846i | 0.388311 | + | 0.672574i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.00000 | 0.290929 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −90.0000 | −2.90625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.50000 | − | 30.3109i | −0.209677 | − | 0.977771i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.0000 | 0.354470 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.0000 | 0.836970 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.0000 | + | 20.7846i | 0.385894 | + | 0.668388i | 0.991893 | − | 0.127078i | \(-0.0405597\pi\) |
−0.605999 | + | 0.795466i | \(0.707226\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −36.0000 | −1.15649 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.5000 | + | 18.1865i | −0.336961 | + | 0.583634i | −0.983860 | − | 0.178942i | \(-0.942732\pi\) |
0.646899 | + | 0.762576i | \(0.276066\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.0000 | − | 60.6218i | −1.12205 | − | 1.94344i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.0000 | 0.767828 | 0.383914 | − | 0.923369i | \(-0.374576\pi\) | ||||
0.383914 | + | 0.923369i | \(0.374576\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.00000 | − | 5.19615i | 0.0958804 | − | 0.166070i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.00000 | − | 1.73205i | 0.0319275 | − | 0.0553001i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.0000 | + | 29.4449i | −0.542216 | + | 0.939145i | 0.456561 | + | 0.889692i | \(0.349081\pi\) |
−0.998776 | + | 0.0494530i | \(0.984252\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | − | 10.3923i | −0.191176 | − | 0.331126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.0000 | + | 25.9808i | −0.477455 | + | 0.826977i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.0000 | −1.39771 | −0.698853 | − | 0.715265i | \(-0.746306\pi\) | ||||
−0.698853 | + | 0.715265i | \(0.746306\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.0000 | −0.634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.0000 | + | 22.5167i | 0.412128 | + | 0.713826i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.00000 | + | 10.3923i | −0.190022 | + | 0.329128i | −0.945257 | − | 0.326326i | \(-0.894189\pi\) |
0.755235 | + | 0.655454i | \(0.227523\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.00000 | − | 6.92820i | −0.126554 | − | 0.219199i |
(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 | 744.2.q.c.25.1 | ✓ | 2 | |
3.2 | odd | 2 | 2232.2.q.e.1513.1 | 2 | |||
4.3 | odd | 2 | 1488.2.q.a.769.1 | 2 | |||
31.5 | even | 3 | inner | 744.2.q.c.625.1 | yes | 2 | |
93.5 | odd | 6 | 2232.2.q.e.1369.1 | 2 | |||
124.67 | odd | 6 | 1488.2.q.a.625.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
744.2.q.c.25.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
744.2.q.c.625.1 | yes | 2 | 31.5 | even | 3 | inner | |
1488.2.q.a.625.1 | 2 | 124.67 | odd | 6 | |||
1488.2.q.a.769.1 | 2 | 4.3 | odd | 2 | |||
2232.2.q.e.1369.1 | 2 | 93.5 | odd | 6 | |||
2232.2.q.e.1513.1 | 2 | 3.2 | odd | 2 |