Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(449,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.dc (of order \(6\), degree \(2\), not 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} - 18 x^{18} + 232 x^{17} + 208 x^{16} - 3152 x^{15} - 2732 x^{14} + 24552 x^{13} + \cdots + 414864 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 1368) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 449.6 | ||
Root | \(1.85589 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.449 |
Dual form | 2736.2.dc.f.1889.6 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.0242659 | − | 0.0140099i | 0.0108520 | − | 0.00626542i | −0.494564 | − | 0.869141i | \(-0.664672\pi\) |
0.505416 | + | 0.862876i | \(0.331339\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.95697 | 0.739664 | 0.369832 | − | 0.929099i | \(-0.379415\pi\) | ||||
0.369832 | + | 0.929099i | \(0.379415\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.26548i | 0.683067i | 0.939870 | + | 0.341534i | \(0.110946\pi\) | ||||
−0.939870 | + | 0.341534i | \(0.889054\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.04824 | − | 0.605203i | −0.290730 | − | 0.167853i | 0.347541 | − | 0.937665i | \(-0.387017\pi\) |
−0.638271 | + | 0.769812i | \(0.720350\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.68055 | + | 3.27967i | −1.37774 | + | 0.795436i | −0.991887 | − | 0.127126i | \(-0.959425\pi\) |
−0.385849 | + | 0.922562i | \(0.626091\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.90798 | − | 1.93073i | −0.896551 | − | 0.442940i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.86319 | − | 1.65306i | −0.597015 | − | 0.344687i | 0.170851 | − | 0.985297i | \(-0.445348\pi\) |
−0.767867 | + | 0.640610i | \(0.778682\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.49961 | + | 4.32945i | −0.499921 | + | 0.865889i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.972667 | + | 1.68471i | −0.180620 | + | 0.312843i | −0.942092 | − | 0.335355i | \(-0.891144\pi\) |
0.761472 | + | 0.648198i | \(0.224477\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.53692i | − | 1.35367i | −0.736134 | − | 0.676836i | \(-0.763351\pi\) | ||
0.736134 | − | 0.676836i | \(-0.236649\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0474875 | − | 0.0274169i | 0.00802685 | − | 0.00463431i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.60246i | 0.263444i | 0.991287 | + | 0.131722i | \(0.0420505\pi\) | ||||
−0.991287 | + | 0.131722i | \(0.957949\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.51426 | − | 9.55099i | −0.861183 | − | 1.49161i | −0.870788 | − | 0.491659i | \(-0.836391\pi\) |
0.00960424 | − | 0.999954i | \(-0.496943\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.35764 | − | 11.0117i | −0.969531 | − | 1.67928i | −0.696916 | − | 0.717153i | \(-0.745445\pi\) |
−0.272615 | − | 0.962123i | \(-0.587888\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.51811 | + | 3.18588i | 0.804899 | + | 0.464708i | 0.845181 | − | 0.534480i | \(-0.179492\pi\) |
−0.0402825 | + | 0.999188i | \(0.512826\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.17028 | −0.452898 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.92934 | + | 10.2699i | −0.814457 | + | 1.41068i | 0.0952593 | + | 0.995452i | \(0.469632\pi\) |
−0.909717 | + | 0.415229i | \(0.863701\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0317391 | + | 0.0549738i | 0.00427970 | + | 0.00741266i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.67047 | + | 4.62540i | 0.347666 | + | 0.602175i | 0.985834 | − | 0.167721i | \(-0.0536409\pi\) |
−0.638168 | + | 0.769897i | \(0.720308\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.233163 | + | 0.403850i | −0.0298534 | + | 0.0517077i | −0.880566 | − | 0.473923i | \(-0.842837\pi\) |
0.850713 | + | 0.525631i | \(0.176171\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0339154 | −0.00420669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.18806 | + | 2.41798i | 0.511652 | + | 0.295403i | 0.733513 | − | 0.679676i | \(-0.237880\pi\) |
−0.221860 | + | 0.975078i | \(0.571213\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.11337 | − | 1.92842i | −0.132133 | − | 0.228861i | 0.792366 | − | 0.610047i | \(-0.208849\pi\) |
−0.924499 | + | 0.381185i | \(0.875516\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.85674 | + | 3.21597i | 0.217315 | + | 0.376401i | 0.953986 | − | 0.299850i | \(-0.0969367\pi\) |
−0.736671 | + | 0.676251i | \(0.763603\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.43346i | 0.505240i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.79782 | − | 2.77002i | 0.539796 | − | 0.311652i | −0.205200 | − | 0.978720i | \(-0.565784\pi\) |
0.744996 | + | 0.667068i | \(0.232451\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.64123i | − | 0.289913i | −0.989438 | − | 0.144956i | \(-0.953696\pi\) | ||
0.989438 | − | 0.144956i | \(-0.0463041\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0918956 | + | 0.159168i | −0.00996748 | + | 0.0172642i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.78874 | + | 3.09818i | −0.189606 | + | 0.328406i | −0.945119 | − | 0.326727i | \(-0.894054\pi\) |
0.755513 | + | 0.655133i | \(0.227388\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.05138 | − | 1.18436i | −0.215043 | − | 0.124155i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.121880 | + | 0.00789951i | −0.0125046 | + | 0.000810473i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.80237 | − | 5.65940i | 0.995279 | − | 0.574625i | 0.0884312 | − | 0.996082i | \(-0.471815\pi\) |
0.906848 | + | 0.421457i | \(0.138481\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.1242 | − | 5.84519i | −1.00739 | − | 0.581618i | −0.0969652 | − | 0.995288i | \(-0.530914\pi\) |
−0.910427 | + | 0.413670i | \(0.864247\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.3345i | − | 1.01829i | −0.860682 | − | 0.509144i | \(-0.829962\pi\) | ||
0.860682 | − | 0.509144i | \(-0.170038\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.30575 | 0.222905 | 0.111453 | − | 0.993770i | \(-0.464450\pi\) | ||||
0.111453 | + | 0.993770i | \(0.464450\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.9111 | + | 6.87687i | −1.14088 | + | 0.658684i | −0.946647 | − | 0.322272i | \(-0.895553\pi\) |
−0.194228 | + | 0.980956i | \(0.562220\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.919294 | 0.0864799 | 0.0432400 | − | 0.999065i | \(-0.486232\pi\) | ||||
0.0432400 | + | 0.999065i | \(0.486232\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0926369 | −0.00863844 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.1166 | + | 6.41819i | −1.01906 | + | 0.588355i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.86761 | 0.533419 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.280176i | 0.0250597i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9970 | − | 7.50381i | −1.15330 | − | 0.665856i | −0.203607 | − | 0.979053i | \(-0.565267\pi\) |
−0.949688 | + | 0.313197i | \(0.898600\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.4272 | + | 10.6389i | −1.60999 | + | 0.929529i | −0.620620 | + | 0.784111i | \(0.713119\pi\) |
−0.989370 | + | 0.145417i | \(0.953547\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.64778 | − | 3.77838i | −0.663146 | − | 0.327627i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.71514 | + | 0.990237i | 0.146534 | + | 0.0846017i | 0.571475 | − | 0.820620i | \(-0.306372\pi\) |
−0.424940 | + | 0.905221i | \(0.639705\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.31672 | + | 2.28063i | −0.111683 | + | 0.193441i | −0.916449 | − | 0.400152i | \(-0.868957\pi\) |
0.804766 | + | 0.593592i | \(0.202291\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.37107 | − | 2.37477i | 0.114655 | − | 0.198588i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.0545079i | 0.00452664i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.5891 | + | 9.57774i | −1.35903 | + | 0.784639i | −0.989494 | − | 0.144576i | \(-0.953818\pi\) |
−0.369540 | + | 0.929215i | \(0.620485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5023i | 0.936041i | 0.883718 | + | 0.468021i | \(0.155033\pi\) | ||||
−0.883718 | + | 0.468021i | \(0.844967\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.105592 | − | 0.182890i | −0.00848132 | − | 0.0146901i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.536899 | + | 0.929936i | 0.0428492 | + | 0.0742169i | 0.886655 | − | 0.462432i | \(-0.153023\pi\) |
−0.843805 | + | 0.536649i | \(0.819690\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.60316 | − | 3.23498i | −0.441591 | − | 0.254952i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.23141 | 0.488082 | 0.244041 | − | 0.969765i | \(-0.421527\pi\) | ||||
0.244041 | + | 0.969765i | \(0.421527\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.41891 | − | 2.45762i | 0.109798 | − | 0.190176i | −0.805890 | − | 0.592065i | \(-0.798313\pi\) |
0.915688 | + | 0.401889i | \(0.131646\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.76746 | − | 9.98953i | −0.443651 | − | 0.768425i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.22395 | + | 10.7802i | 0.473198 | + | 0.819603i | 0.999529 | − | 0.0306763i | \(-0.00976610\pi\) |
−0.526331 | + | 0.850280i | \(0.676433\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.89165 | + | 8.47258i | −0.369774 | + | 0.640467i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.78997 | 0.208532 | 0.104266 | − | 0.994549i | \(-0.466751\pi\) | ||||
0.104266 | + | 0.994549i | \(0.466751\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.8842 | − | 10.9028i | −1.40365 | − | 0.810401i | −0.408889 | − | 0.912584i | \(-0.634084\pi\) |
−0.994766 | + | 0.102183i | \(0.967417\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.0224504 | + | 0.0388852i | 0.00165059 | + | 0.00285890i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.43001 | − | 12.8691i | −0.543336 | − | 0.941085i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.08745i | − | 0.0786848i | −0.999226 | − | 0.0393424i | \(-0.987474\pi\) | ||
0.999226 | − | 0.0393424i | \(-0.0125263\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.15756 | − | 2.97772i | 0.371249 | − | 0.214341i | −0.302755 | − | 0.953069i | \(-0.597906\pi\) |
0.674004 | + | 0.738728i | \(0.264573\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.52729i | 0.180062i | 0.995939 | + | 0.0900312i | \(0.0286967\pi\) | ||||
−0.995939 | + | 0.0900312i | \(0.971303\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.26276 | − | 14.3115i | 0.585731 | − | 1.01452i | −0.409053 | − | 0.912511i | \(-0.634141\pi\) |
0.994784 | − | 0.102006i | \(-0.0325259\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.90348 | + | 3.29692i | −0.133598 | + | 0.231398i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.267617 | − | 0.154509i | −0.0186912 | − | 0.0107914i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.37403 | − | 8.85343i | 0.302558 | − | 0.612405i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.08255 | − | 3.51176i | 0.418740 | − | 0.241760i | −0.275798 | − | 0.961216i | \(-0.588942\pi\) |
0.694538 | + | 0.719456i | \(0.255609\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.308547 | − | 0.178140i | −0.0210427 | − | 0.0121490i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 14.7495i | − | 1.00126i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.93946 | 0.534066 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.7211 | + | 10.8086i | −1.25366 | + | 0.723799i | −0.971834 | − | 0.235668i | \(-0.924272\pi\) |
−0.281822 | + | 0.959467i | \(0.590939\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.5102 | −0.697587 | −0.348794 | − | 0.937200i | \(-0.613409\pi\) | ||||
−0.348794 | + | 0.937200i | \(0.613409\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.4754 | 1.48522 | 0.742609 | − | 0.669726i | \(-0.233588\pi\) | ||||
0.742609 | + | 0.669726i | \(0.233588\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.2218 | + | 11.0977i | −1.25926 | + | 0.727036i | −0.972931 | − | 0.231094i | \(-0.925769\pi\) |
−0.286332 | + | 0.958130i | \(0.592436\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.178536 | 0.0116464 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.6897i | 1.27362i | 0.771019 | + | 0.636812i | \(0.219747\pi\) | ||||
−0.771019 | + | 0.636812i | \(0.780253\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.25313 | + | 0.723492i | 0.0807209 | + | 0.0466042i | 0.539817 | − | 0.841782i | \(-0.318493\pi\) |
−0.459096 | + | 0.888387i | \(0.651827\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.0769297 | + | 0.0444154i | −0.00491486 | + | 0.00283759i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.92802 | + | 4.38900i | 0.186306 | + | 0.279265i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.4324 | − | 6.02313i | −0.658486 | − | 0.380177i | 0.133214 | − | 0.991087i | \(-0.457470\pi\) |
−0.791700 | + | 0.610910i | \(0.790804\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.74497 | − | 6.48648i | 0.235444 | − | 0.407802i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.6723 | − | 20.2169i | 0.728095 | − | 1.26110i | −0.229592 | − | 0.973287i | \(-0.573739\pi\) |
0.957687 | − | 0.287811i | \(-0.0929276\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.13597i | 0.194860i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.1039 | + | 11.6070i | −1.23966 | + | 0.715717i | −0.969024 | − | 0.246965i | \(-0.920567\pi\) |
−0.270634 | + | 0.962682i | \(0.587233\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.332278i | 0.0204117i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.5865 | + | 23.5324i | 0.828381 | + | 1.43480i | 0.899307 | + | 0.437317i | \(0.144071\pi\) |
−0.0709262 | + | 0.997482i | \(0.522595\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.5687 | + | 23.5017i | 0.824241 | + | 1.42763i | 0.902498 | + | 0.430693i | \(0.141731\pi\) |
−0.0782578 | + | 0.996933i | \(0.524936\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.80826 | − | 5.66280i | −0.591461 | − | 0.341480i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.2717 | −1.21801 | −0.609003 | − | 0.793168i | \(-0.708430\pi\) | ||||
−0.609003 | + | 0.793168i | \(0.708430\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.8887 | − | 18.8598i | 0.649564 | − | 1.12508i | −0.333662 | − | 0.942693i | \(-0.608285\pi\) |
0.983227 | − | 0.182386i | \(-0.0583821\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.51299 | + | 14.7449i | 0.506045 | + | 0.876495i | 0.999976 | + | 0.00699380i | \(0.00222622\pi\) |
−0.493931 | + | 0.869501i | \(0.664440\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.7912 | − | 18.6910i | −0.636986 | − | 1.10329i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0124 | − | 22.5382i | 0.765436 | − | 1.32577i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.4499 | 0.668911 | 0.334456 | − | 0.942411i | \(-0.391448\pi\) | ||||
0.334456 | + | 0.942411i | \(0.391448\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.129603 | + | 0.0748262i | 0.00754577 | + | 0.00435655i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.00088 | + | 3.46562i | 0.115714 | + | 0.200422i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.4417 | − | 21.5496i | −0.717127 | − | 1.24210i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.0130664i | 0.000748178i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.02178 | + | 1.16727i | −0.115389 | + | 0.0666198i | −0.556584 | − | 0.830792i | \(-0.687888\pi\) |
0.441195 | + | 0.897411i | \(0.354555\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 10.3009i | − | 0.584112i | −0.956401 | − | 0.292056i | \(-0.905661\pi\) | ||
0.956401 | − | 0.292056i | \(-0.0943393\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.62720 | + | 13.2107i | −0.431115 | + | 0.746713i | −0.996970 | − | 0.0777919i | \(-0.975213\pi\) |
0.565855 | + | 0.824505i | \(0.308546\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.14205 | + | 10.6384i | −0.344972 | + | 0.597509i | −0.985349 | − | 0.170552i | \(-0.945445\pi\) |
0.640377 | + | 0.768061i | \(0.278778\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.81667 | − | 2.20355i | −0.213692 | − | 0.123375i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.5316 | − | 1.84925i | 1.58754 | − | 0.102895i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.24039 | − | 3.02554i | 0.290685 | − | 0.167827i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.7987 | + | 6.23466i | 0.595354 | + | 0.343728i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.8419i | 1.53033i | 0.643833 | + | 0.765166i | \(0.277343\pi\) | ||||
−0.643833 | + | 0.765166i | \(0.722657\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.135502 | 0.00740329 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.04577 | + | 1.18113i | −0.111440 | + | 0.0643401i | −0.554684 | − | 0.832061i | \(-0.687161\pi\) |
0.443244 | + | 0.896401i | \(0.353828\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.0747 | 0.924648 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9029 | −1.07466 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.6674 | − | 9.62291i | 0.894751 | − | 0.516585i | 0.0192576 | − | 0.999815i | \(-0.493870\pi\) |
0.875494 | + | 0.483230i | \(0.160536\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.64786 | −0.248794 | −0.124397 | − | 0.992232i | \(-0.539700\pi\) | ||||
−0.124397 | + | 0.992232i | \(0.539700\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 26.0686i | − | 1.38749i | −0.720220 | − | 0.693746i | \(-0.755959\pi\) | ||
0.720220 | − | 0.693746i | \(-0.244041\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.0540339 | − | 0.0311965i | −0.00286782 | − | 0.00165574i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.70064 | − | 0.981864i | 0.0897563 | − | 0.0518208i | −0.454450 | − | 0.890772i | \(-0.650164\pi\) |
0.544206 | + | 0.838951i | \(0.316831\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.5446 | + | 15.0905i | 0.607608 | + | 0.794237i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.0901109 | + | 0.0520256i | 0.00471662 | + | 0.00272314i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.75091 | − | 11.6929i | 0.352395 | − | 0.610365i | −0.634274 | − | 0.773108i | \(-0.718701\pi\) |
0.986668 | + | 0.162743i | \(0.0520342\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.6035 | + | 20.0979i | −0.602425 | + | 1.04343i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 7.71743i | − | 0.399593i | −0.979837 | − | 0.199797i | \(-0.935972\pi\) | ||
0.979837 | − | 0.199797i | \(-0.0640281\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.03918 | − | 1.17732i | 0.105023 | − | 0.0606352i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.4327i | 1.25503i | 0.778606 | + | 0.627513i | \(0.215927\pi\) | ||||
−0.778606 | + | 0.627513i | \(0.784073\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.25602 | + | 7.37165i | 0.217473 | + | 0.376674i | 0.954035 | − | 0.299696i | \(-0.0968854\pi\) |
−0.736562 | + | 0.676370i | \(0.763552\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0621124 | + | 0.107582i | 0.00316554 | + | 0.00548288i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.86282 | + | 1.65285i | 0.145151 | + | 0.0838030i | 0.570817 | − | 0.821078i | \(-0.306627\pi\) |
−0.425666 | + | 0.904881i | \(0.639960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.6859 | 1.09671 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.0776155 | − | 0.134434i | 0.00390526 | − | 0.00676411i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.136363 | + | 0.236188i | 0.00684388 | + | 0.0118540i | 0.869427 | − | 0.494061i | \(-0.164488\pi\) |
−0.862583 | + | 0.505915i | \(0.831155\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.81087 | − | 4.86857i | −0.140368 | − | 0.243125i | 0.787267 | − | 0.616612i | \(-0.211495\pi\) |
−0.927635 | + | 0.373487i | \(0.878162\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.56137 | + | 7.90053i | −0.227218 | + | 0.393553i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.63035 | −0.179950 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.1399 | + | 13.9372i | 1.19364 | + | 0.689148i | 0.959130 | − | 0.282966i | \(-0.0913182\pi\) |
0.234510 | + | 0.972114i | \(0.424652\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.22603 | + | 9.05175i | 0.257156 | + | 0.445407i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0370034 | − | 0.0640917i | −0.00181642 | − | 0.00314614i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 20.9837i | − | 1.02512i | −0.858651 | − | 0.512560i | \(-0.828697\pi\) | ||
0.858651 | − | 0.512560i | \(-0.171303\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.5540 | + | 10.1348i | −0.855530 | + | 0.493941i | −0.862513 | − | 0.506035i | \(-0.831111\pi\) |
0.00698280 | + | 0.999976i | \(0.497777\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 32.7915i | − | 1.59062i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.456292 | + | 0.790321i | −0.0220815 | + | 0.0382463i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.56201 | − | 16.5619i | 0.460586 | − | 0.797758i | −0.538404 | − | 0.842687i | \(-0.680973\pi\) |
0.998990 | + | 0.0449285i | \(0.0143060\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.4861 | + | 14.1371i | 1.17673 | + | 0.679383i | 0.955255 | − | 0.295783i | \(-0.0955806\pi\) |
0.221472 | + | 0.975167i | \(0.428914\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.99764 | + | 11.9882i | 0.382579 | + | 0.573472i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.0618 | + | 12.7374i | −1.05295 | + | 0.607923i | −0.923475 | − | 0.383659i | \(-0.874664\pi\) |
−0.129479 | + | 0.991582i | \(0.541330\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.423087 | + | 0.244269i | 0.0201015 | + | 0.0116056i | 0.510017 | − | 0.860164i | \(-0.329639\pi\) |
−0.489916 | + | 0.871770i | \(0.662972\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.100240i | 0.00475184i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.5253 | −0.874263 | −0.437131 | − | 0.899398i | \(-0.644006\pi\) | ||||
−0.437131 | + | 0.899398i | \(0.644006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.6375 | − | 12.4924i | 1.01887 | − | 0.588246i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0663713 | −0.00311153 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.784145 | 0.0366808 | 0.0183404 | − | 0.999832i | \(-0.494162\pi\) | ||||
0.0183404 | + | 0.999832i | \(0.494162\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.52710 | − | 4.34578i | 0.350572 | − | 0.202403i | −0.314365 | − | 0.949302i | \(-0.601792\pi\) |
0.664937 | + | 0.746899i | \(0.268458\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.9548 | 1.20622 | 0.603112 | − | 0.797656i | \(-0.293927\pi\) | ||||
0.603112 | + | 0.797656i | \(0.293927\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 29.2996i | − | 1.35583i | −0.735143 | − | 0.677913i | \(-0.762885\pi\) | ||
0.735143 | − | 0.677913i | \(-0.237115\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.19588 | + | 4.73190i | 0.378451 | + | 0.218499i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.9469 | − | 14.4031i | 1.14706 | − | 0.662254i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.1274 | − | 12.0933i | 0.831742 | − | 0.554879i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.5829 | + | 6.68741i | 0.529237 | + | 0.305555i | 0.740706 | − | 0.671829i | \(-0.234491\pi\) |
−0.211468 | + | 0.977385i | \(0.567825\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.969817 | − | 1.67977i | 0.0442198 | − | 0.0765910i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.158575 | − | 0.274661i | 0.00720053 | − | 0.0124717i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.50566i | 0.340114i | 0.985434 | + | 0.170057i | \(0.0543952\pi\) | ||||
−0.985434 | + | 0.170057i | \(0.945605\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.62320 | + | 0.937156i | −0.0732540 | + | 0.0422932i | −0.536180 | − | 0.844104i | \(-0.680133\pi\) |
0.462926 | + | 0.886397i | \(0.346800\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 12.7601i | − | 0.574686i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.17883 | − | 3.77385i | −0.0977340 | − | 0.169280i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.6861 | − | 21.9729i | −0.567907 | − | 0.983643i | −0.996773 | − | 0.0802750i | \(-0.974420\pi\) |
0.428866 | − | 0.903368i | \(-0.358913\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.1031 | + | 8.71977i | 0.673413 | + | 0.388795i | 0.797369 | − | 0.603492i | \(-0.206225\pi\) |
−0.123955 | + | 0.992288i | \(0.539558\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.327562 | −0.0145763 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.8213 | + | 30.8674i | −0.789916 | + | 1.36817i | 0.136102 | + | 0.990695i | \(0.456542\pi\) |
−0.926018 | + | 0.377479i | \(0.876791\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.63358 | + | 6.29355i | 0.160740 | + | 0.278410i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.144785 | − | 0.250775i | −0.00638000 | − | 0.0110505i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.21754 | + | 12.5011i | −0.317427 | + | 0.549800i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.1812 | 0.927965 | 0.463982 | − | 0.885844i | \(-0.346420\pi\) | ||||
0.463982 | + | 0.885844i | \(0.346420\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.7491 | + | 11.4022i | 0.863568 | + | 0.498581i | 0.865206 | − | 0.501417i | \(-0.167188\pi\) |
−0.00163745 | + | 0.999999i | \(0.500521\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.7186 | + | 42.8138i | 1.07676 | + | 1.86500i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.03478 | − | 10.4525i | −0.262382 | − | 0.454458i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.3490i | 0.578210i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0559510 | − | 0.0323033i | 0.00241897 | − | 0.00139659i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 7.18220i | − | 0.309359i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.5455 | + | 35.5858i | −0.883318 | + | 1.52995i | −0.0356895 | + | 0.999363i | \(0.511363\pi\) |
−0.847629 | + | 0.530589i | \(0.821971\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.192689 | + | 0.333746i | −0.00825387 | + | 0.0142961i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.0347 | − | 21.3820i | −1.58349 | − | 0.914229i | −0.994345 | − | 0.106203i | \(-0.966131\pi\) |
−0.589146 | − | 0.808026i | \(-0.700536\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.05388 | − | 4.70584i | 0.300505 | − | 0.200476i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.38916 | − | 5.42084i | 0.399268 | − | 0.230517i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.40605 | − | 3.12119i | −0.229062 | − | 0.132249i | 0.381077 | − | 0.924543i | \(-0.375553\pi\) |
−0.610139 | + | 0.792294i | \(0.708886\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.3907i | 0.650955i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.28035 | 0.264685 | 0.132343 | − | 0.991204i | \(-0.457750\pi\) | ||||
0.132343 | + | 0.991204i | \(0.457750\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.0223075 | − | 0.0128792i | 0.000938483 | − | 0.000541833i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 40.8651 | 1.71315 | 0.856576 | − | 0.516021i | \(-0.172587\pi\) | ||||
0.856576 | + | 0.516021i | \(0.172587\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.7423 | −0.449551 | −0.224775 | − | 0.974411i | \(-0.572165\pi\) | ||||
−0.224775 | + | 0.974411i | \(0.572165\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.3137 | − | 8.26401i | 0.596922 | − | 0.344633i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.6355 | 1.02559 | 0.512795 | − | 0.858511i | \(-0.328610\pi\) | ||||
0.512795 | + | 0.858511i | \(0.328610\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 5.16880i | − | 0.214438i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.2663 | − | 13.4328i | −0.963590 | − | 0.556329i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.64931 | + | 3.26163i | −0.233172 | + | 0.134622i | −0.612034 | − | 0.790831i | \(-0.709649\pi\) |
0.378863 | + | 0.925453i | \(0.376315\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.5518 | + | 29.4541i | −0.599595 | + | 1.21364i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.6643 | − | 8.46645i | −0.602192 | − | 0.347676i | 0.167712 | − | 0.985836i | \(-0.446362\pi\) |
−0.769903 | + | 0.638161i | \(0.779696\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.179837 | + | 0.311486i | −0.00737258 | + | 0.0127697i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.07972 | − | 13.9945i | 0.330128 | − | 0.571799i | −0.652408 | − | 0.757868i | \(-0.726241\pi\) |
0.982537 | + | 0.186069i | \(0.0595747\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 16.6915i | − | 0.680861i | −0.940270 | − | 0.340430i | \(-0.889427\pi\) | ||
0.940270 | − | 0.340430i | \(-0.110573\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.142383 | − | 0.0822047i | 0.00578868 | − | 0.00334210i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.6154i | 0.958521i | 0.877673 | + | 0.479261i | \(0.159095\pi\) | ||||
−0.877673 | + | 0.479261i | \(0.840905\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.85621 | − | 6.67915i | −0.156006 | − | 0.270210i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.5746 | + | 18.3158i | 0.427106 | + | 0.739769i | 0.996615 | − | 0.0822162i | \(-0.0261998\pi\) |
−0.569509 | + | 0.821985i | \(0.692866\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.0334 | − | 19.6492i | −1.37013 | − | 0.791046i | −0.379188 | − | 0.925320i | \(-0.623797\pi\) |
−0.990944 | + | 0.134273i | \(0.957130\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.65391 | −0.227250 | −0.113625 | − | 0.993524i | \(-0.536246\pi\) | ||||
−0.113625 | + | 0.993524i | \(0.536246\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.50049 | + | 6.06303i | −0.140244 | + | 0.242910i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4941 | − | 21.6404i | −0.499764 | − | 0.865617i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.25555 | − | 9.10288i | −0.209552 | − | 0.362955i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.9285 | − | 36.2492i | 0.833151 | − | 1.44306i | −0.0623768 | − | 0.998053i | \(-0.519868\pi\) |
0.895527 | − | 0.445006i | \(-0.146799\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.420511 | −0.0166875 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.32323 | + | 1.91867i | 0.131671 | + | 0.0760203i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.91177 | − | 10.2395i | −0.233501 | − | 0.404435i | 0.725335 | − | 0.688396i | \(-0.241685\pi\) |
−0.958836 | + | 0.283961i | \(0.908351\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.55537 | + | 6.15808i | 0.140210 | + | 0.242851i | 0.927576 | − | 0.373635i | \(-0.121889\pi\) |
−0.787366 | + | 0.616486i | \(0.788556\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 35.9205i | − | 1.41218i | −0.708121 | − | 0.706091i | \(-0.750457\pi\) | ||
0.708121 | − | 0.706091i | \(-0.249543\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.4787 | + | 6.04990i | −0.411326 | + | 0.237479i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 35.4760i | − | 1.38828i | −0.719839 | − | 0.694141i | \(-0.755784\pi\) | ||
0.719839 | − | 0.694141i | \(-0.244216\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.298101 | + | 0.516326i | −0.0116478 | + | 0.0201745i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.3388 | − | 17.9073i | 0.402741 | − | 0.697568i | −0.591314 | − | 0.806441i | \(-0.701391\pi\) |
0.994056 | + | 0.108873i | \(0.0347241\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.99396 | − | 2.88326i | −0.194242 | − | 0.112146i | 0.399725 | − | 0.916635i | \(-0.369106\pi\) |
−0.593967 | + | 0.804489i | \(0.702439\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.238515 | + | 0.0154591i | −0.00924920 | + | 0.000599477i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.56985 | − | 3.21576i | 0.215666 | − | 0.124515i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.914913 | − | 0.528225i | −0.0353198 | − | 0.0203919i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.9658i | 1.54057i | 0.637702 | + | 0.770284i | \(0.279885\pi\) | ||||
−0.637702 | + | 0.770284i | \(0.720115\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.9424 | 0.881747 | 0.440874 | − | 0.897569i | \(-0.354669\pi\) | ||||
0.440874 | + | 0.897569i | \(0.354669\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.1829 | − | 11.0753i | 0.736172 | − | 0.425029i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 45.4321 | 1.73841 | 0.869206 | − | 0.494449i | \(-0.164630\pi\) | ||||
0.869206 | + | 0.494449i | \(0.164630\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.0554925 | 0.00212026 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.4308 | − | 7.17691i | 0.473575 | − | 0.273419i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.0596 | 1.33373 | 0.666865 | − | 0.745178i | \(-0.267636\pi\) | ||||
0.666865 | + | 0.745178i | \(0.267636\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.0737887i | 0.00279897i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 62.6481 | + | 36.1699i | 2.37296 | + | 1.37003i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.0720 | + | 15.0527i | −0.984725 | + | 0.568531i | −0.903693 | − | 0.428180i | \(-0.859155\pi\) |
−0.0810317 | + | 0.996712i | \(0.525822\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.09393 | − | 6.26239i | 0.116690 | − | 0.236191i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.8127 | − | 11.4388i | −0.745132 | − | 0.430202i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.9216 | + | 29.3091i | −0.635505 | + | 1.10073i | 0.350903 | + | 0.936412i | \(0.385875\pi\) |
−0.986408 | + | 0.164315i | \(0.947459\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.4590 | + | 21.5796i | −0.466593 | + | 0.808163i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 0.0768345i | − | 0.00287345i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.3342 | − | 7.69852i | 0.497283 | − | 0.287106i | −0.230308 | − | 0.973118i | \(-0.573973\pi\) |
0.727591 | + | 0.686011i | \(0.240640\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 20.2242i | − | 0.753190i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.86257 | − | 8.42222i | −0.180591 | − | 0.312793i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.9650 | − | 24.1881i | −0.517934 | − | 0.897088i | −0.999783 | − | 0.0208336i | \(-0.993368\pi\) |
0.481849 | − | 0.876254i | \(-0.339965\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 72.2297 | + | 41.7018i | 2.67151 | + | 1.54240i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.0809344 | −0.00298938 | −0.00149469 | − | 0.999999i | \(-0.500476\pi\) | ||||
−0.00149469 | + | 0.999999i | \(0.500476\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.47787 | + | 9.48794i | −0.201780 | + | 0.349493i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.5420 | − | 26.9195i | −0.571720 | − | 0.990249i | −0.996389 | − | 0.0849002i | \(-0.972943\pi\) |
0.424669 | − | 0.905349i | \(-0.360390\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.5752 | − | 32.1732i | −0.681458 | − | 1.18032i | −0.974536 | − | 0.224232i | \(-0.928013\pi\) |
0.293078 | − | 0.956089i | \(-0.405321\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.268366 | + | 0.464824i | −0.00983219 | + | 0.0170298i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.51227 | 0.164875 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.7892 | + | 10.2706i | 0.649136 | + | 0.374779i | 0.788125 | − | 0.615515i | \(-0.211052\pi\) |
−0.138989 | + | 0.990294i | \(0.544385\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.161146 | + | 0.279113i | 0.00586469 | + | 0.0101579i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.1466 | + | 29.6987i | 0.623202 | + | 1.07942i | 0.988886 | + | 0.148679i | \(0.0475021\pi\) |
−0.365683 | + | 0.930739i | \(0.619165\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.14685i | − | 0.0415734i | −0.999784 | − | 0.0207867i | \(-0.993383\pi\) | ||
0.999784 | − | 0.0207867i | \(-0.00661709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.3096 | + | 13.4578i | −0.843864 | + | 0.487205i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.46472i | − | 0.233428i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.3092 | + | 23.0522i | −0.479942 | + | 0.831285i | −0.999735 | − | 0.0230077i | \(-0.992676\pi\) |
0.519793 | + | 0.854292i | \(0.326009\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.8406 | + | 39.5611i | −0.821519 | + | 1.42291i | 0.0830322 | + | 0.996547i | \(0.473540\pi\) |
−0.904551 | + | 0.426365i | \(0.859794\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.6307 | + | 18.8393i | 1.17213 | + | 0.676729i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.10923 | + | 47.9716i | 0.111400 | + | 1.71876i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.36879 | − | 2.52232i | 0.156327 | − | 0.0902557i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0260566 | + | 0.0150438i | 0.000930001 | + | 0.000536936i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.1982i | 1.14774i | 0.818946 | + | 0.573871i | \(0.194559\pi\) | ||||
−0.818946 | + | 0.573871i | \(0.805441\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.79903 | 0.0639661 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.488823 | − | 0.282222i | 0.0173586 | − | 0.0100220i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.6289 | 0.836980 | 0.418490 | − | 0.908221i | \(-0.362559\pi\) | ||||
0.418490 | + | 0.908221i | \(0.362559\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.7945 | −1.47858 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.28571 | + | 4.20641i | −0.257107 | + | 0.148441i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.181287 | −0.00638954 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 24.8880i | − | 0.875015i | −0.899215 | − | 0.437508i | \(-0.855861\pi\) | ||
0.899215 | − | 0.437508i | \(-0.144139\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.88792 | − | 3.39939i | −0.206753 | − | 0.119369i | 0.393049 | − | 0.919518i | \(-0.371420\pi\) |
−0.599801 | + | 0.800149i | \(0.704754\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.151211 | − | 0.0873015i | 0.00529668 | − | 0.00305804i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.58477 | + | 55.3085i | 0.125415 | + | 1.93500i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.9682 | + | 19.0342i | 1.15060 | + | 0.664299i | 0.949033 | − | 0.315176i | \(-0.102064\pi\) |
0.201566 | + | 0.979475i | \(0.435397\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.1459 | − | 41.8219i | 0.841673 | − | 1.45782i | −0.0468069 | − | 0.998904i | \(-0.514905\pi\) |
0.888480 | − | 0.458916i | \(-0.151762\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.50746 | − | 16.4674i | 0.330607 | − | 0.572628i | −0.652024 | − | 0.758198i | \(-0.726080\pi\) |
0.982631 | + | 0.185570i | \(0.0594133\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.6461i | 1.34223i | 0.741351 | + | 0.671117i | \(0.234185\pi\) | ||||
−0.741351 | + | 0.671117i | \(0.765815\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0089 | − | 10.3975i | 0.623973 | − | 0.360251i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 0.0795149i | − | 0.00275173i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.9272 | + | 24.1226i | 0.480819 | + | 0.832803i | 0.999758 | − | 0.0220085i | \(-0.00700608\pi\) |
−0.518939 | + | 0.854811i | \(0.673673\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.6078 | + | 21.8374i | 0.434753 | + | 0.753014i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.279905 | − | 0.161603i | −0.00962902 | − | 0.00555932i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.4827 | 0.394551 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.64897 | − | 4.58815i | 0.0908056 | − | 0.157280i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.6282 | − | 39.1933i | −0.774777 | − | 1.34195i | −0.934920 | − | 0.354859i | \(-0.884529\pi\) |
0.160143 | − | 0.987094i | \(-0.448804\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.9079 | − | 32.7495i | −0.645883 | − | 1.11870i | −0.984097 | − | 0.177632i | \(-0.943156\pi\) |
0.338214 | − | 0.941069i | \(-0.390177\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.59497 | + | 16.6190i | −0.327376 | + | 0.567032i | −0.981990 | − | 0.188931i | \(-0.939498\pi\) |
0.654614 | + | 0.755963i | \(0.272831\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.6978 | −1.28325 | −0.641624 | − | 0.767019i | \(-0.721739\pi\) | ||||
−0.641624 | + | 0.767019i | \(0.721739\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.302059 | + | 0.174394i | 0.0102703 | + | 0.00592957i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.27542 | + | 10.8693i | 0.212879 | + | 0.368717i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.92673 | − | 5.06925i | −0.0991686 | − | 0.171765i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.548295i | 0.0185358i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.4147 | − | 18.7146i | 1.09457 | − | 0.631948i | 0.159778 | − | 0.987153i | \(-0.448922\pi\) |
0.934789 | + | 0.355205i | \(0.115589\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 0.698543i | − | 0.0235345i | −0.999931 | − | 0.0117673i | \(-0.996254\pi\) | ||
0.999931 | − | 0.0117673i | \(-0.00374572\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.0805 | − | 50.3689i | 0.978636 | − | 1.69505i | 0.311264 | − | 0.950323i | \(-0.399248\pi\) |
0.667372 | − | 0.744724i | \(-0.267419\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.5940 | − | 21.8134i | 0.422865 | − | 0.732423i | −0.573354 | − | 0.819308i | \(-0.694358\pi\) |
0.996218 | + | 0.0868850i | \(0.0276913\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.4347 | − | 14.6847i | −0.853051 | − | 0.492509i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.4136 | − | 23.1043i | −0.515795 | − | 0.773157i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.0677010 | − | 0.0390872i | 0.00226300 | − | 0.00130654i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.6975 | + | 7.33092i | 0.423486 | + | 0.244500i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 77.7850i | − | 2.59139i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.610990 | −0.0203100 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.37701 | + | 3.68177i | −0.211745 | + | 0.122251i | −0.602122 | − | 0.798404i | \(-0.705678\pi\) |
0.390377 | + | 0.920655i | \(0.372345\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.0294 | 1.06118 | 0.530590 | − | 0.847629i | \(-0.321970\pi\) | ||||
0.530590 | + | 0.847629i | \(0.321970\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.98364 | 0.198030 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.0614 | + | 20.8200i | −1.19085 | + | 0.687539i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.20294 | −0.204616 | −0.102308 | − | 0.994753i | \(-0.532623\pi\) | ||||
−0.102308 | + | 0.994753i | \(0.532623\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.69527i | 0.0887158i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.93779 | − | 4.00553i | −0.228113 | − | 0.131701i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.902179 | + | 0.520873i | −0.0295995 | + | 0.0170893i | −0.514727 | − | 0.857354i | \(-0.672107\pi\) |
0.485127 | + | 0.874444i | \(0.338773\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.3894 | + | 6.12096i | 0.406046 | + | 0.200606i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.360591 | − | 0.208187i | −0.0117926 | − | 0.00680846i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.1422 | − | 24.4950i | 0.462006 | − | 0.800217i | −0.537055 | − | 0.843547i | \(-0.680463\pi\) |
0.999061 | + | 0.0433298i | \(0.0137966\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.5894 | − | 33.9298i | 0.638595 | − | 1.10608i | −0.347147 | − | 0.937811i | \(-0.612849\pi\) |
0.985741 | − | 0.168268i | \(-0.0538173\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.4617i | 1.18735i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.8474 | + | 8.57215i | −0.482475 | + | 0.278557i | −0.721448 | − | 0.692469i | \(-0.756523\pi\) |
0.238972 | + | 0.971026i | \(0.423190\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4.49482i | − | 0.145908i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.08753 | + | 14.0080i | 0.261981 | + | 0.453764i | 0.966768 | − | 0.255654i | \(-0.0822909\pi\) |
−0.704787 | + | 0.709419i | \(0.748958\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.0152350 | − | 0.0263878i | −0.000492994 | − | 0.000853890i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.35647 | + | 1.93786i | 0.108386 | + | 0.0625768i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.8052 | −0.832426 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.0834352 | − | 0.144514i | 0.00268587 | − | 0.00465207i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.0997161 | + | 0.172713i | 0.00320665 | + | 0.00555409i | 0.867624 | − | 0.497220i | \(-0.165646\pi\) |
−0.864418 | + | 0.502774i | \(0.832313\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.4475 | − | 19.8276i | −0.367368 | − | 0.636299i | 0.621785 | − | 0.783188i | \(-0.286408\pi\) |
−0.989153 | + | 0.146888i | \(0.953074\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.57678 | + | 4.46312i | −0.0826079 | + | 0.143081i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.3775 | −0.843891 | −0.421945 | − | 0.906621i | \(-0.638653\pi\) | ||||
−0.421945 | + | 0.906621i | \(0.638653\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.01886 | − | 4.05234i | −0.224324 | − | 0.129513i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.0334 | − | 48.5553i | −0.894128 | − | 1.54867i | −0.834880 | − | 0.550431i | \(-0.814463\pi\) |
−0.0592474 | − | 0.998243i | \(-0.518870\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.0354072 | + | 0.0613270i | 0.00112817 | + | 0.00195404i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.0382i | 1.33674i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.3299 | + | 15.2016i | −0.836398 | + | 0.482895i | −0.856038 | − | 0.516913i | \(-0.827081\pi\) |
0.0196403 | + | 0.999807i | \(0.493748\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 0.463042i | − | 0.0146794i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.0115 | + | 20.8046i | −0.380409 | + | 0.658888i | −0.991121 | − | 0.132965i | \(-0.957550\pi\) |
0.610712 | + | 0.791853i | \(0.290884\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2736.2.dc.f.449.6 | 20 | ||
3.2 | odd | 2 | 2736.2.dc.e.449.5 | 20 | |||
4.3 | odd | 2 | 1368.2.cu.b.449.6 | yes | 20 | ||
12.11 | even | 2 | 1368.2.cu.a.449.5 | ✓ | 20 | ||
19.8 | odd | 6 | 2736.2.dc.e.1889.5 | 20 | |||
57.8 | even | 6 | inner | 2736.2.dc.f.1889.6 | 20 | ||
76.27 | even | 6 | 1368.2.cu.a.521.5 | yes | 20 | ||
228.179 | odd | 6 | 1368.2.cu.b.521.6 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1368.2.cu.a.449.5 | ✓ | 20 | 12.11 | even | 2 | ||
1368.2.cu.a.521.5 | yes | 20 | 76.27 | even | 6 | ||
1368.2.cu.b.449.6 | yes | 20 | 4.3 | odd | 2 | ||
1368.2.cu.b.521.6 | yes | 20 | 228.179 | odd | 6 | ||
2736.2.dc.e.449.5 | 20 | 3.2 | odd | 2 | |||
2736.2.dc.e.1889.5 | 20 | 19.8 | odd | 6 | |||
2736.2.dc.f.449.6 | 20 | 1.1 | even | 1 | trivial | ||
2736.2.dc.f.1889.6 | 20 | 57.8 | even | 6 | inner |