Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2052,3,Mod(881,2052)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2052, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2052.881");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2052 = 2^{2} \cdot 3^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2052.m (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: | \(55.9129502467\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 684) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 881.7 | ||
Character | \(\chi\) | \(=\) | 2052.881 |
Dual form | 2052.3.m.a.1493.34 |
$q$-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 \(\left(\mathbb{Z}/2052\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1027\) | \(1217\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 6.32167i | − | 1.26433i | −0.774832 | − | 0.632167i | \(-0.782165\pi\) | ||
0.774832 | − | 0.632167i | \(-0.217835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00114 | + | 3.46607i | 0.285877 | + | 0.495153i | 0.972821 | − | 0.231557i | \(-0.0743819\pi\) |
−0.686945 | + | 0.726710i | \(0.741049\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.04816 | − | 3.49191i | 0.549833 | − | 0.317446i | −0.199222 | − | 0.979954i | \(-0.563841\pi\) |
0.749055 | + | 0.662508i | \(0.230508\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.14076 | + | 7.17201i | 0.318520 | + | 0.551693i | 0.980180 | − | 0.198111i | \(-0.0634807\pi\) |
−0.661659 | + | 0.749805i | \(0.730147\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −23.9657 | + | 13.8366i | −1.40975 | + | 0.813918i | −0.995364 | − | 0.0961842i | \(-0.969336\pi\) |
−0.414384 | + | 0.910102i | \(0.636003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.9139 | − | 6.33195i | −0.942835 | − | 0.333261i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 27.0361 | − | 15.6093i | 1.17548 | − | 0.678665i | 0.220517 | − | 0.975383i | \(-0.429225\pi\) |
0.954965 | + | 0.296718i | \(0.0958921\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.9636 | −0.598543 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 18.4925i | − | 0.637671i | −0.947810 | − | 0.318835i | \(-0.896708\pi\) | ||
0.947810 | − | 0.318835i | \(-0.103292\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.7611 | − | 39.4233i | 0.734227 | − | 1.27172i | −0.220834 | − | 0.975311i | \(-0.570878\pi\) |
0.955061 | − | 0.296408i | \(-0.0957888\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 21.9114 | − | 12.6505i | 0.626039 | − | 0.361444i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −40.3326 | −1.09007 | −0.545035 | − | 0.838413i | \(-0.683484\pi\) | ||||
−0.545035 | + | 0.838413i | \(0.683484\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.03661i | 0.220405i | 0.993909 | + | 0.110203i | \(0.0351499\pi\) | ||||
−0.993909 | + | 0.110203i | \(0.964850\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.29062 | + | 14.3598i | −0.192805 | + | 0.333948i | −0.946179 | − | 0.323644i | \(-0.895092\pi\) |
0.753374 | + | 0.657593i | \(0.228425\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 54.4672i | − | 1.15888i | −0.815016 | − | 0.579438i | \(-0.803272\pi\) | ||
0.815016 | − | 0.579438i | \(-0.196728\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.4909 | − | 28.5631i | 0.336549 | − | 0.582920i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 26.2519 | + | 15.1566i | 0.495320 | + | 0.285973i | 0.726779 | − | 0.686872i | \(-0.241017\pi\) |
−0.231459 | + | 0.972845i | \(0.574350\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −22.0747 | − | 38.2345i | −0.401358 | − | 0.695173i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 40.5469i | − | 0.687236i | −0.939110 | − | 0.343618i | \(-0.888347\pi\) | ||
0.939110 | − | 0.343618i | \(-0.111653\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 37.9214 | 0.621661 | 0.310831 | − | 0.950465i | \(-0.399393\pi\) | ||||
0.310831 | + | 0.950465i | \(0.399393\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 45.3391 | − | 26.1766i | 0.697525 | − | 0.402716i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.6512 | + | 23.6445i | 0.203749 | + | 0.352904i | 0.949733 | − | 0.313060i | \(-0.101354\pi\) |
−0.745984 | + | 0.665963i | \(0.768021\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.8327 | + | 9.71834i | −0.237080 | + | 0.136878i | −0.613834 | − | 0.789435i | \(-0.710374\pi\) |
0.376754 | + | 0.926313i | \(0.377040\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −32.2512 | − | 55.8608i | −0.441798 | − | 0.765216i | 0.556025 | − | 0.831165i | \(-0.312326\pi\) |
−0.997823 | + | 0.0659493i | \(0.978992\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 24.2064 | + | 13.9756i | 0.314369 | + | 0.181501i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −43.0462 | + | 74.5583i | −0.544889 | + | 0.943776i | 0.453725 | + | 0.891142i | \(0.350095\pi\) |
−0.998614 | + | 0.0526337i | \(0.983238\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −122.748 | + | 70.8687i | −1.47889 | + | 0.853840i | −0.999715 | − | 0.0238776i | \(-0.992399\pi\) |
−0.479179 | + | 0.877717i | \(0.659065\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 87.4705 | + | 151.503i | 1.02906 | + | 1.78239i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −72.8836 | − | 42.0794i | −0.818917 | − | 0.472802i | 0.0311261 | − | 0.999515i | \(-0.490091\pi\) |
−0.850043 | + | 0.526714i | \(0.823424\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.5725 | + | 28.7044i | −0.182115 | + | 0.315433i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −40.0285 | + | 113.246i | −0.421353 | + | 1.19206i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 73.5940 | − | 127.469i | 0.758701 | − | 1.31411i | −0.184813 | − | 0.982774i | \(-0.559168\pi\) |
0.943513 | − | 0.331335i | \(-0.107499\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 13.4881i | − | 0.133545i | −0.997768 | − | 0.0667726i | \(-0.978730\pi\) | ||
0.997768 | − | 0.0667726i | \(-0.0212702\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.7030 | − | 34.1266i | 0.191292 | − | 0.331327i | −0.754387 | − | 0.656430i | \(-0.772066\pi\) |
0.945679 | + | 0.325103i | \(0.105399\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 38.1059i | − | 0.356130i | −0.984019 | − | 0.178065i | \(-0.943016\pi\) | ||
0.984019 | − | 0.178065i | \(-0.0569837\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.3506 | − | 23.1239i | −0.122483 | − | 0.212146i | 0.798263 | − | 0.602308i | \(-0.205752\pi\) |
−0.920746 | + | 0.390162i | \(0.872419\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −161.778 | − | 93.4027i | −1.43167 | − | 0.826573i | −0.434418 | − | 0.900712i | \(-0.643046\pi\) |
−0.997248 | + | 0.0741390i | \(0.976379\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −98.6769 | − | 170.913i | −0.858060 | − | 1.48620i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −95.9173 | − | 55.3779i | −0.806028 | − | 0.465360i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −36.1131 | + | 62.5498i | −0.298456 | + | 0.516941i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 63.4471i | − | 0.507577i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −59.6131 | + | 103.253i | −0.469394 | + | 0.813015i | −0.999388 | − | 0.0349868i | \(-0.988861\pi\) |
0.529993 | + | 0.848002i | \(0.322194\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 148.423i | − | 1.13300i | −0.824063 | − | 0.566498i | \(-0.808298\pi\) | ||
0.824063 | − | 0.566498i | \(-0.191702\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.9011 | − | 74.7618i | −0.104520 | − | 0.562119i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 211.149i | 1.54124i | 0.637298 | + | 0.770618i | \(0.280052\pi\) | ||||
−0.637298 | + | 0.770618i | \(0.719948\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −108.298 | − | 187.578i | −0.779124 | − | 1.34948i | −0.932447 | − | 0.361307i | \(-0.882331\pi\) |
0.153322 | − | 0.988176i | \(-0.451003\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 50.0880 | + | 28.9183i | 0.350266 | + | 0.202226i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −116.903 | −0.806230 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 228.955i | − | 1.53661i | −0.640084 | − | 0.768305i | \(-0.721100\pi\) | ||
0.640084 | − | 0.768305i | \(-0.278900\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 51.3731 | + | 88.9809i | 0.340219 | + | 0.589277i | 0.984473 | − | 0.175534i | \(-0.0561653\pi\) |
−0.644254 | + | 0.764812i | \(0.722832\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −249.221 | − | 143.888i | −1.60788 | − | 0.928309i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 182.678 | 1.16355 | 0.581777 | − | 0.813348i | \(-0.302357\pi\) | ||||
0.581777 | + | 0.813348i | \(0.302357\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 108.206 | + | 62.4727i | 0.672086 | + | 0.388029i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −279.869 | −1.71699 | −0.858495 | − | 0.512822i | \(-0.828600\pi\) | ||||
−0.858495 | + | 0.512822i | \(0.828600\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −152.723 | + | 88.1747i | −0.914510 | + | 0.527992i | −0.881879 | − | 0.471475i | \(-0.843722\pi\) |
−0.0326302 | + | 0.999467i | \(0.510388\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 50.2081 | − | 86.9630i | 0.297090 | − | 0.514574i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −66.4404 | − | 38.3594i | −0.384049 | − | 0.221731i | 0.295530 | − | 0.955334i | \(-0.404504\pi\) |
−0.679578 | + | 0.733603i | \(0.737837\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −29.9441 | − | 51.8648i | −0.171109 | − | 0.296370i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 42.0832i | − | 0.235102i | −0.993067 | − | 0.117551i | \(-0.962496\pi\) | ||
0.993067 | − | 0.117551i | \(-0.0375043\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 70.5353 | − | 122.171i | 0.389698 | − | 0.674977i | −0.602711 | − | 0.797960i | \(-0.705913\pi\) |
0.992409 | + | 0.122983i | \(0.0392461\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 254.970i | 1.37821i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −96.6323 | + | 167.372i | −0.516750 | + | 0.895038i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −96.4688 | + | 55.6963i | −0.505072 | + | 0.291604i | −0.730806 | − | 0.682585i | \(-0.760856\pi\) |
0.225733 | + | 0.974189i | \(0.427522\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −35.8077 | −0.185532 | −0.0927661 | − | 0.995688i | \(-0.529571\pi\) | ||||
−0.0927661 | + | 0.995688i | \(0.529571\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 201.997i | 1.02537i | 0.858578 | + | 0.512683i | \(0.171348\pi\) | ||||
−0.858578 | + | 0.512683i | \(0.828652\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 68.6408 | − | 118.889i | 0.344929 | − | 0.597434i | −0.640412 | − | 0.768032i | \(-0.721236\pi\) |
0.985341 | + | 0.170597i | \(0.0545697\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 64.0962 | − | 37.0059i | 0.315745 | − | 0.182295i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 57.1265 | 0.278666 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −130.457 | + | 24.2569i | −0.624194 | + | 0.116062i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 148.420 | 0.703413 | 0.351706 | − | 0.936110i | \(-0.385602\pi\) | ||||
0.351706 | + | 0.936110i | \(0.385602\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 90.7778 | + | 52.4106i | 0.422222 | + | 0.243770i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 182.192 | 0.839594 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −198.473 | − | 114.588i | −0.898066 | − | 0.518499i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 183.175 | − | 317.269i | 0.821414 | − | 1.42273i | −0.0832152 | − | 0.996532i | \(-0.526519\pi\) |
0.904629 | − | 0.426199i | \(-0.140148\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −229.354 | + | 132.417i | −1.01037 | + | 0.583336i | −0.911299 | − | 0.411744i | \(-0.864920\pi\) |
−0.0990686 | + | 0.995081i | \(0.531586\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 176.804 | − | 306.233i | 0.772068 | − | 1.33726i | −0.164360 | − | 0.986400i | \(-0.552556\pi\) |
0.936428 | − | 0.350860i | \(-0.114111\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −65.2399 | + | 37.6663i | −0.280000 | + | 0.161658i | −0.633423 | − | 0.773805i | \(-0.718351\pi\) |
0.353424 | + | 0.935463i | \(0.385017\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −344.324 | −1.46521 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.42144 | − | 2.55272i | −0.0184998 | − | 0.0106808i | 0.490722 | − | 0.871316i | \(-0.336733\pi\) |
−0.509221 | + | 0.860636i | \(0.670067\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 175.057 | 0.726378 | 0.363189 | − | 0.931716i | \(-0.381688\pi\) | ||||
0.363189 | + | 0.931716i | \(0.381688\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −180.567 | − | 104.250i | −0.737006 | − | 0.425511i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.7642 | − | 154.698i | −0.116454 | − | 0.626306i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 416.120 | + | 240.247i | 1.65785 | + | 0.957160i | 0.973704 | + | 0.227816i | \(0.0731584\pi\) |
0.684146 | + | 0.729345i | \(0.260175\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 109.012 | − | 188.815i | 0.430879 | − | 0.746305i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −269.498 | + | 155.595i | −1.04863 | + | 0.605426i | −0.922265 | − | 0.386558i | \(-0.873664\pi\) |
−0.126364 | + | 0.991984i | \(0.540331\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −80.7111 | − | 139.796i | −0.311626 | − | 0.539752i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −48.0406 | − | 27.7362i | −0.182664 | − | 0.105461i | 0.405880 | − | 0.913926i | \(-0.366965\pi\) |
−0.588544 | + | 0.808465i | \(0.700298\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 95.8148 | − | 165.956i | 0.361565 | − | 0.626250i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −179.719 | + | 103.761i | −0.668102 | + | 0.385729i | −0.795357 | − | 0.606141i | \(-0.792717\pi\) |
0.127255 | + | 0.991870i | \(0.459383\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 108.517 | + | 187.957i | 0.400433 | + | 0.693570i | 0.993778 | − | 0.111378i | \(-0.0355265\pi\) |
−0.593345 | + | 0.804948i | \(0.702193\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −90.5021 | + | 52.2514i | −0.329098 | + | 0.190005i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −66.9535 | − | 115.967i | −0.241709 | − | 0.418653i | 0.719492 | − | 0.694501i | \(-0.244375\pi\) |
−0.961201 | + | 0.275848i | \(0.911041\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 325.724i | − | 1.15916i | −0.814915 | − | 0.579580i | \(-0.803216\pi\) | ||
0.814915 | − | 0.579580i | \(-0.196784\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −406.710 | −1.43714 | −0.718570 | − | 0.695455i | \(-0.755203\pi\) | ||||
−0.718570 | + | 0.695455i | \(0.755203\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −31.3215 | + | 18.0835i | −0.109134 | + | 0.0630087i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 238.403 | − | 412.927i | 0.824925 | − | 1.42881i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 218.194 | + | 125.974i | 0.744688 | + | 0.429946i | 0.823771 | − | 0.566922i | \(-0.191866\pi\) |
−0.0790834 | + | 0.996868i | \(0.525199\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −256.324 | −0.868896 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 223.900 | + | 129.269i | 0.748830 | + | 0.432337i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −66.3626 | −0.220474 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 239.726i | − | 0.785988i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −58.6501 | − | 101.585i | −0.191043 | − | 0.330896i | 0.754553 | − | 0.656239i | \(-0.227854\pi\) |
−0.945596 | + | 0.325343i | \(0.894520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 75.4767 | + | 43.5765i | 0.242690 | + | 0.140117i | 0.616413 | − | 0.787423i | \(-0.288585\pi\) |
−0.373722 | + | 0.927541i | \(0.621919\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −321.081 | −1.02582 | −0.512909 | − | 0.858443i | \(-0.671432\pi\) | ||||
−0.512909 | + | 0.858443i | \(0.671432\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 461.392i | − | 1.45550i | −0.685845 | − | 0.727748i | \(-0.740567\pi\) | ||
0.685845 | − | 0.727748i | \(-0.259433\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −64.5740 | − | 111.845i | −0.202426 | − | 0.350613i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 516.931 | − | 96.1174i | 1.60041 | − | 0.297577i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −61.9606 | − | 107.319i | −0.190648 | − | 0.330212i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 188.787 | − | 108.996i | 0.573821 | − | 0.331296i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −106.818 | − | 185.014i | −0.322712 | − | 0.558954i | 0.658334 | − | 0.752726i | \(-0.271261\pi\) |
−0.981047 | + | 0.193771i | \(0.937928\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 149.473 | − | 86.2983i | 0.446188 | − | 0.257607i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 182.989 | 0.542995 | 0.271497 | − | 0.962439i | \(-0.412481\pi\) | ||||
0.271497 | + | 0.962439i | \(0.412481\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 317.918i | − | 0.932311i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 328.114 | 0.956599 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 110.589i | 0.318700i | 0.987222 | + | 0.159350i | \(0.0509399\pi\) | ||||
−0.987222 | + | 0.159350i | \(0.949060\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −110.819 | − | 191.944i | −0.317532 | − | 0.549982i | 0.662440 | − | 0.749115i | \(-0.269521\pi\) |
−0.979972 | + | 0.199133i | \(0.936187\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −322.547 | + | 186.223i | −0.913732 | + | 0.527543i | −0.881630 | − | 0.471941i | \(-0.843553\pi\) |
−0.0321020 | + | 0.999485i | \(0.510220\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 61.4362 | + | 106.411i | 0.173060 | + | 0.299748i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 64.0955 | − | 37.0056i | 0.178539 | − | 0.103080i | −0.408067 | − | 0.912952i | \(-0.633797\pi\) |
0.586606 | + | 0.809872i | \(0.300464\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 280.813 | + | 226.859i | 0.777875 | + | 0.628419i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −353.134 | + | 203.882i | −0.967489 | + | 0.558580i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 377.052 | 1.02739 | 0.513695 | − | 0.857973i | \(-0.328276\pi\) | ||||
0.513695 | + | 0.857973i | \(0.328276\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 121.321i | 0.327012i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.67579 | + | 6.36666i | −0.00985467 | + | 0.0170688i | −0.870911 | − | 0.491441i | \(-0.836470\pi\) |
0.861056 | + | 0.508510i | \(0.169804\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 132.628 | − | 76.5729i | 0.351799 | − | 0.203111i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −366.651 | −0.967417 | −0.483709 | − | 0.875229i | \(-0.660711\pi\) | ||||
−0.483709 | + | 0.875229i | \(0.660711\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 274.610i | − | 0.716997i | −0.933530 | − | 0.358498i | \(-0.883289\pi\) | ||
0.933530 | − | 0.358498i | \(-0.116711\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 88.3490 | − | 153.025i | 0.229478 | − | 0.397467i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 664.121i | − | 1.70725i | −0.520887 | − | 0.853626i | \(-0.674399\pi\) | ||
0.520887 | − | 0.853626i | \(-0.325601\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −431.959 | + | 748.176i | −1.10476 | + | 1.91349i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 471.333 | + | 272.124i | 1.19325 | + | 0.688922i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 156.466 | + | 271.007i | 0.394120 | + | 0.682636i | 0.992988 | − | 0.118211i | \(-0.0377160\pi\) |
−0.598868 | + | 0.800848i | \(0.704383\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 473.726i | 1.18136i | 0.806906 | + | 0.590680i | \(0.201141\pi\) | ||||
−0.806906 | + | 0.590680i | \(0.798859\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 376.993 | 0.935466 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −243.938 | + | 140.838i | −0.599357 | + | 0.346039i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 276.393 | + | 478.727i | 0.675777 | + | 1.17048i | 0.976241 | + | 0.216688i | \(0.0695253\pi\) |
−0.300464 | + | 0.953793i | \(0.597141\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 140.538 | − | 81.1399i | 0.340287 | − | 0.196465i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 448.009 | + | 775.974i | 1.07954 | + | 1.86982i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.32796 | + | 0.766697i | 0.00316935 | + | 0.00182983i | 0.501584 | − | 0.865109i | \(-0.332751\pi\) |
−0.498414 | + | 0.866939i | \(0.666084\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −97.1313 | + | 168.236i | −0.230716 | + | 0.399611i | −0.958019 | − | 0.286705i | \(-0.907440\pi\) |
0.727303 | + | 0.686316i | \(0.240773\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 358.612 | − | 207.045i | 0.843794 | − | 0.487165i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 75.8858 | + | 131.438i | 0.177719 | + | 0.307817i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 60.2968 | + | 34.8124i | 0.139900 | + | 0.0807711i | 0.568316 | − | 0.822810i | \(-0.307595\pi\) |
−0.428416 | + | 0.903581i | \(0.640928\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −125.295 | + | 217.018i | −0.289365 | + | 0.501196i | −0.973658 | − | 0.228012i | \(-0.926778\pi\) |
0.684293 | + | 0.729207i | \(0.260111\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −583.158 | + | 108.432i | −1.33446 | + | 0.248127i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −359.264 | + | 622.264i | −0.818369 | + | 1.41746i | 0.0885135 | + | 0.996075i | \(0.471788\pi\) |
−0.906883 | + | 0.421383i | \(0.861545\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 595.462i | − | 1.34416i | −0.740479 | − | 0.672079i | \(-0.765402\pi\) | ||
0.740479 | − | 0.672079i | \(-0.234598\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −266.012 | + | 460.746i | −0.597780 | + | 1.03538i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 649.900i | 1.44744i | 0.690094 | + | 0.723720i | \(0.257569\pi\) | ||||
−0.690094 | + | 0.723720i | \(0.742431\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.5550 | + | 54.6549i | 0.0699668 | + | 0.121186i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 181.460 | + | 104.766i | 0.398812 | + | 0.230254i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −386.945 | − | 670.209i | −0.846707 | − | 1.46654i | −0.884130 | − | 0.467241i | \(-0.845248\pi\) |
0.0374227 | − | 0.999300i | \(-0.488085\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −108.581 | − | 62.6890i | −0.235533 | − | 0.135985i | 0.377589 | − | 0.925973i | \(-0.376753\pi\) |
−0.613122 | + | 0.789988i | \(0.710087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −295.738 | + | 512.234i | −0.638744 | + | 1.10634i | 0.346965 | + | 0.937878i | \(0.387212\pi\) |
−0.985709 | + | 0.168459i | \(0.946121\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 411.110i | − | 0.880320i | −0.897919 | − | 0.440160i | \(-0.854922\pi\) | ||
0.897919 | − | 0.440160i | \(-0.145078\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −54.6357 | + | 94.6319i | −0.116494 | + | 0.201774i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 115.800i | 0.244821i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 268.055 | + | 94.7485i | 0.564327 | + | 0.199471i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 123.171i | − | 0.257141i | −0.991700 | − | 0.128571i | \(-0.958961\pi\) | ||
0.991700 | − | 0.128571i | \(-0.0410389\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −167.008 | − | 289.266i | −0.347210 | − | 0.601385i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −805.814 | − | 465.237i | −1.66147 | − | 0.959252i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −682.651 | −1.40175 | −0.700874 | − | 0.713285i | \(-0.747207\pi\) | ||||
−0.700874 | + | 0.713285i | \(0.747207\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 198.231i | 0.403729i | 0.979413 | + | 0.201865i | \(0.0647001\pi\) | ||||
−0.979413 | + | 0.201865i | \(0.935300\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 255.873 | + | 443.185i | 0.519012 | + | 0.898955i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −67.3689 | − | 38.8954i | −0.135551 | − | 0.0782605i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 543.154 | 1.08849 | 0.544243 | − | 0.838928i | \(-0.316817\pi\) | ||||
0.544243 | + | 0.838928i | \(0.316817\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 344.739 | + | 199.035i | 0.685365 | + | 0.395696i | 0.801873 | − | 0.597494i | \(-0.203837\pi\) |
−0.116508 | + | 0.993190i | \(0.537170\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −85.2672 | −0.168846 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 296.983 | − | 171.463i | 0.583463 | − | 0.336863i | −0.179045 | − | 0.983841i | \(-0.557301\pi\) |
0.762509 | + | 0.646978i | \(0.223968\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 129.078 | − | 223.570i | 0.252599 | − | 0.437515i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −215.738 | − | 124.556i | −0.418908 | − | 0.241857i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −190.194 | − | 329.427i | −0.367881 | − | 0.637189i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 664.298i | − | 1.27504i | −0.770432 | − | 0.637522i | \(-0.779960\pi\) | ||
0.770432 | − | 0.637522i | \(-0.220040\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −259.118 | + | 448.806i | −0.495446 | + | 0.858138i | −0.999986 | − | 0.00525011i | \(-0.998329\pi\) |
0.504540 | + | 0.863388i | \(0.331662\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1259.74i | 2.39040i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 222.800 | − | 385.902i | 0.421173 | − | 0.729493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −64.8107 | + | 37.4185i | −0.121596 | + | 0.0702035i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −240.893 | −0.450267 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 230.339i | − | 0.427345i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 430.351 | − | 745.389i | 0.795472 | − | 1.37780i | −0.127066 | − | 0.991894i | \(-0.540556\pi\) |
0.922539 | − | 0.385905i | \(-0.126111\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −146.182 | + | 84.3982i | −0.268224 | + | 0.154859i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 117.128 | 0.214127 | 0.107064 | − | 0.994252i | \(-0.465855\pi\) | ||||
0.107064 | + | 0.994252i | \(0.465855\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −117.093 | + | 331.271i | −0.212511 | + | 0.601218i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −344.566 | −0.623084 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 200.752 | + | 115.904i | 0.360416 | + | 0.208086i | 0.669263 | − | 0.743025i | \(-0.266610\pi\) |
−0.308847 | + | 0.951112i | \(0.599943\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −137.318 | −0.245649 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 465.717 | + | 268.882i | 0.827205 | + | 0.477587i | 0.852895 | − | 0.522083i | \(-0.174845\pi\) |
−0.0256895 | + | 0.999670i | \(0.508178\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −590.461 | + | 1022.71i | −1.04506 | + | 1.81010i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 880.392 | − | 508.295i | 1.54726 | − | 0.893312i | 0.548912 | − | 0.835880i | \(-0.315042\pi\) |
0.998349 | − | 0.0574321i | \(-0.0182913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −58.4285 | + | 101.201i | −0.102327 | + | 0.177235i | −0.912643 | − | 0.408758i | \(-0.865962\pi\) |
0.810316 | + | 0.585993i | \(0.199295\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −404.556 | + | 233.571i | −0.703576 | + | 0.406210i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 115.022 | 0.199345 | 0.0996724 | − | 0.995020i | \(-0.468221\pi\) | ||||
0.0996724 | + | 0.995020i | \(0.468221\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −491.272 | − | 283.636i | −0.845562 | − | 0.488186i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 211.701 | 0.363124 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 862.770 | + | 498.120i | 1.46980 | + | 0.848587i | 0.999426 | − | 0.0338825i | \(-0.0107872\pi\) |
0.470370 | + | 0.882469i | \(0.344121\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −657.365 | + | 562.102i | −1.11607 | + | 0.954332i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −109.232 | − | 63.0651i | −0.184202 | − | 0.106349i | 0.405063 | − | 0.914289i | \(-0.367249\pi\) |
−0.589266 | + | 0.807939i | \(0.700583\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −350.081 | + | 606.358i | −0.588371 | + | 1.01909i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −740.979 | + | 427.804i | −1.23703 | + | 0.714197i | −0.968485 | − | 0.249071i | \(-0.919875\pi\) |
−0.268541 | + | 0.963268i | \(0.586541\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 527.598 | + | 913.826i | 0.877866 | + | 1.52051i | 0.853678 | + | 0.520801i | \(0.174367\pi\) |
0.0241883 | + | 0.999707i | \(0.492300\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 395.419 | + | 228.296i | 0.653586 | + | 0.377348i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 330.385 | − | 572.243i | 0.544291 | − | 0.942740i | −0.454360 | − | 0.890818i | \(-0.650132\pi\) |
0.998651 | − | 0.0519218i | \(-0.0165347\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 390.640 | − | 225.536i | 0.639345 | − | 0.369126i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 303.879 | + | 526.335i | 0.495725 | + | 0.858621i | 0.999988 | − | 0.00492941i | \(-0.00156909\pi\) |
−0.504263 | + | 0.863550i | \(0.668236\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 801.853 | − | 462.950i | 1.29960 | − | 0.750324i | 0.319265 | − | 0.947666i | \(-0.396564\pi\) |
0.980335 | + | 0.197342i | \(0.0632308\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 62.0433 | + | 107.462i | 0.100231 | + | 0.173606i | 0.911780 | − | 0.410679i | \(-0.134708\pi\) |
−0.811549 | + | 0.584285i | \(0.801375\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 336.826i | − | 0.540652i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −775.181 | −1.24029 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 966.600 | − | 558.067i | 1.53672 | − | 0.887228i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 464.866 | − | 805.172i | 0.736713 | − | 1.27603i | −0.217254 | − | 0.976115i | \(-0.569710\pi\) |
0.953967 | − | 0.299910i | \(-0.0969567\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 652.731 | + | 376.855i | 1.02792 | + | 0.593472i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 273.140 | 0.428791 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 830.818 | + | 479.673i | 1.29613 | + | 0.748320i | 0.979733 | − | 0.200307i | \(-0.0641941\pi\) |
0.316395 | + | 0.948627i | \(0.397527\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1034.89 | 1.60947 | 0.804736 | − | 0.593633i | \(-0.202307\pi\) | ||||
0.804736 | + | 0.593633i | \(0.202307\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1029.68i | 1.59147i | 0.605647 | + | 0.795733i | \(0.292914\pi\) | ||||
−0.605647 | + | 0.795733i | \(0.707086\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −141.586 | − | 245.234i | −0.218160 | − | 0.377865i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 193.285 | + | 111.593i | 0.295996 | + | 0.170893i | 0.640643 | − | 0.767839i | \(-0.278668\pi\) |
−0.344647 | + | 0.938732i | \(0.612001\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −938.279 | −1.43249 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 470.828i | 0.714458i | 0.934017 | + | 0.357229i | \(0.116278\pi\) | ||||
−0.934017 | + | 0.357229i | \(0.883722\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −184.554 | − | 319.657i | −0.279204 | − | 0.483596i | 0.691983 | − | 0.721914i | \(-0.256737\pi\) |
−0.971187 | + | 0.238318i | \(0.923404\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −472.620 | + | 87.8782i | −0.710706 | + | 0.132148i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −288.654 | − | 499.964i | −0.432765 | − | 0.749571i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 229.355 | − | 132.418i | 0.341810 | − | 0.197344i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 556.859 | + | 964.509i | 0.827429 | + | 1.43315i | 0.900049 | + | 0.435789i | \(0.143531\pi\) |
−0.0726204 | + | 0.997360i | \(0.523136\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −83.3953 | + | 48.1483i | −0.123184 | + | 0.0711201i | −0.560326 | − | 0.828272i | \(-0.689324\pi\) |
0.437142 | + | 0.899392i | \(0.355991\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 589.086 | 0.867579 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 56.7307i | 0.0830611i | 0.999137 | + | 0.0415305i | \(0.0132234\pi\) | ||||
−0.999137 | + | 0.0415305i | \(0.986777\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1334.82 | 1.94864 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 251.039i | 0.364353i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −199.549 | − | 345.629i | −0.288783 | − | 0.500187i | 0.684736 | − | 0.728791i | \(-0.259917\pi\) |
−0.973520 | + | 0.228604i | \(0.926584\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1185.81 | + | 684.627i | −1.70620 | + | 0.985074i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −125.036 | − | 216.569i | −0.179392 | − | 0.310715i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 401.210 | − | 231.639i | 0.572339 | − | 0.330440i | −0.185744 | − | 0.982598i | \(-0.559469\pi\) |
0.758083 | + | 0.652158i | \(0.226136\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 722.513 | + | 255.384i | 1.02776 | + | 0.363278i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 46.7506 | − | 26.9915i | 0.0661253 | − | 0.0381775i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 254.458 | 0.358898 | 0.179449 | − | 0.983767i | \(-0.442569\pi\) | ||||
0.179449 | + | 0.983767i | \(0.442569\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1421.14i | − | 1.99318i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 182.812 | − | 316.640i | 0.255682 | − | 0.442854i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.1832 | − | 18.5810i | 0.0447610 | − | 0.0258428i | −0.477453 | − | 0.878658i | \(-0.658440\pi\) |
0.522214 | + | 0.852815i | \(0.325106\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 157.714 | 0.218743 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 276.713i | 0.381673i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −125.786 | + | 217.868i | −0.173021 | + | 0.299681i | −0.939475 | − | 0.342619i | \(-0.888686\pi\) |
0.766454 | + | 0.642299i | \(0.222019\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 458.856i | − | 0.627710i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 424.518 | − | 735.287i | 0.579151 | − | 1.00312i | −0.416426 | − | 0.909170i | \(-0.636717\pi\) |
0.995577 | − | 0.0939498i | \(-0.0299493\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 165.129 | + | 95.3373i | 0.224056 | + | 0.129359i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −222.140 | − | 384.757i | −0.300595 | − | 0.520646i | 0.675676 | − | 0.737199i | \(-0.263852\pi\) |
−0.976271 | + | 0.216553i | \(0.930519\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 294.169i | − | 0.395921i | −0.980210 | − | 0.197960i | \(-0.936568\pi\) | ||
0.980210 | − | 0.197960i | \(-0.0634317\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1447.38 | −1.94279 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 132.078 | − | 76.2551i | 0.176339 | − | 0.101809i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 748.371 | + | 1296.22i | 0.996499 | + | 1.72599i | 0.570654 | + | 0.821191i | \(0.306690\pi\) |
0.425845 | + | 0.904796i | \(0.359977\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 562.508 | − | 324.764i | 0.745044 | − | 0.430151i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.2134 | + | 19.4222i | 0.0148130 | + | 0.0256568i | 0.873337 | − | 0.487117i | \(-0.161951\pi\) |
−0.858524 | + | 0.512774i | \(0.828618\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 410.105 | + | 236.774i | 0.538903 | + | 0.311136i | 0.744634 | − | 0.667473i | \(-0.232624\pi\) |
−0.205731 | + | 0.978608i | \(0.565957\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 53.4328 | − | 92.5483i | 0.0700299 | − | 0.121295i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 290.803 | − | 167.895i | 0.379144 | − | 0.218899i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −476.791 | − | 825.826i | −0.620014 | − | 1.07390i | −0.989483 | − | 0.144652i | \(-0.953794\pi\) |
0.369469 | − | 0.929243i | \(-0.379540\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 776.662 | + | 448.406i | 1.00474 | + | 0.580085i | 0.909647 | − | 0.415383i | \(-0.136352\pi\) |
0.0950909 | + | 0.995469i | \(0.469686\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −340.586 | + | 589.913i | −0.439466 | + | 0.761178i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 57.2193 | − | 161.881i | 0.0734523 | − | 0.207806i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −67.8711 | + | 117.556i | −0.0869028 | + | 0.150520i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1154.83i | − | 1.47112i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 200.246 | − | 346.836i | 0.254442 | − | 0.440706i | −0.710302 | − | 0.703897i | \(-0.751442\pi\) |
0.964744 | + | 0.263191i | \(0.0847750\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 747.646i | − | 0.945191i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 157.023 | + | 271.972i | 0.198012 | + | 0.342967i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −537.021 | − | 310.049i | −0.673803 | − | 0.389020i | 0.123713 | − | 0.992318i | \(-0.460520\pi\) |
−0.797516 | + | 0.603298i | \(0.793853\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 753.641 | + | 1305.34i | 0.943230 | + | 1.63372i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −390.121 | − | 225.237i | −0.485830 | − | 0.280494i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 394.932 | − | 684.042i | 0.490599 | − | 0.849742i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 365.081i | 0.451275i | 0.974211 | + | 0.225637i | \(0.0724465\pi\) | ||||
−0.974211 | + | 0.225637i | \(0.927554\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 452.295 | − | 783.397i | 0.557700 | − | 0.965965i | −0.439988 | − | 0.898004i | \(-0.645017\pi\) |
0.997688 | − | 0.0679610i | \(-0.0216493\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1769.24i | 2.17085i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 239.442 | − | 204.743i | 0.293075 | − | 0.250604i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1249.88i | − | 1.52239i | −0.648522 | − | 0.761196i | \(-0.724613\pi\) | ||
0.648522 | − | 0.761196i | \(-0.275387\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −720.887 | − | 1248.61i | −0.875926 | − | 1.51715i | −0.855773 | − | 0.517352i | \(-0.826918\pi\) |
−0.0201535 | − | 0.999797i | \(-0.506415\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1076.73 | + | 621.651i | 1.30197 | + | 0.751694i | 0.980742 | − | 0.195307i | \(-0.0625704\pi\) |
0.321230 | + | 0.947001i | \(0.395904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1617.54 | 1.95119 | 0.975594 | − | 0.219581i | \(-0.0704691\pi\) | ||||
0.975594 | + | 0.219581i | \(0.0704691\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 912.713i | 1.09569i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 557.412 | + | 965.466i | 0.667559 | + | 1.15625i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 441.625 | + | 254.973i | 0.526371 | + | 0.303901i | 0.739538 | − | 0.673115i | \(-0.235044\pi\) |
−0.213166 | + | 0.977016i | \(0.568378\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 499.029 | 0.593376 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −549.752 | − | 317.399i | −0.650594 | − | 0.375621i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −289.069 | −0.341286 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1090.44 | + | 629.564i | −1.28136 | + | 0.739793i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −545.610 | + | 945.024i | −0.639636 | + | 1.10788i | 0.345876 | + | 0.938280i | \(0.387582\pi\) |
−0.985513 | + | 0.169602i | \(0.945752\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 896.786 | + | 517.760i | 1.04642 | + | 0.604154i | 0.921646 | − | 0.388031i | \(-0.126845\pi\) |
0.124779 | + | 0.992185i | \(0.460178\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −263.394 | − | 456.211i | −0.306628 | − | 0.531096i | 0.670994 | − | 0.741462i | \(-0.265867\pi\) |
−0.977623 | + | 0.210367i | \(0.932534\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 717.519i | 0.831424i | 0.909496 | + | 0.415712i | \(0.136468\pi\) | ||||
−0.909496 | + | 0.415712i | \(0.863532\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −242.496 | + | 420.015i | −0.280342 | + | 0.485566i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 601.254i | 0.691892i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −113.053 | + | 195.813i | −0.129796 | + | 0.224814i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 219.912 | − | 126.966i | 0.251328 | − | 0.145104i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −88.2260 | −0.100600 | −0.0502999 | − | 0.998734i | \(-0.516018\pi\) | ||||
−0.0502999 | + | 0.998734i | \(0.516018\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 439.288i | 0.498625i | 0.968423 | + | 0.249312i | \(0.0802046\pi\) | ||||
−0.968423 | + | 0.249312i | \(0.919795\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −482.731 | + | 836.115i | −0.546695 | + | 0.946903i | 0.451804 | + | 0.892117i | \(0.350781\pi\) |
−0.998498 | + | 0.0547853i | \(0.982553\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1154.40 | − | 666.494i | 1.30147 | − | 0.751403i | 0.320812 | − | 0.947143i | \(-0.396044\pi\) |
0.980656 | + | 0.195740i | \(0.0627108\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −477.176 | −0.536756 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −344.884 | + | 975.718i | −0.386208 | + | 1.09263i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −266.036 | −0.297247 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −729.034 | − | 420.908i | −0.810938 | − | 0.468196i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −838.861 | −0.931034 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −772.324 | − | 445.901i | −0.853397 | − | 0.492709i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 431.199 | − | 746.858i | 0.475412 | − | 0.823438i | −0.524191 | − | 0.851601i | \(-0.675632\pi\) |
0.999603 | + | 0.0281627i | \(0.00896566\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1310.94 | + | 756.870i | −1.43901 | + | 0.830813i | −0.997781 | − | 0.0665817i | \(-0.978791\pi\) |
−0.441229 | + | 0.897395i | \(0.645457\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −494.934 | + | 857.251i | −0.542096 | + | 0.938939i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 514.443 | − | 297.014i | 0.561006 | − | 0.323897i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −863.054 | −0.939123 | −0.469561 | − | 0.882900i | \(-0.655588\pi\) | ||||
−0.469561 | + | 0.882900i | \(0.655588\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −139.400 | − | 80.4827i | −0.151029 | − | 0.0871969i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 603.520 | 0.652454 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1065.48 | + | 615.154i | 1.14691 | + | 0.662167i | 0.948132 | − | 0.317878i | \(-0.102970\pi\) |
0.198776 | + | 0.980045i | \(0.436303\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −476.276 | + | 407.256i | −0.511574 | + | 0.437439i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1058.07 | + | 610.878i | 1.13163 | + | 0.653346i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 562.399 | − | 974.104i | 0.600212 | − | 1.03960i | −0.392576 | − | 0.919719i | \(-0.628416\pi\) |
0.992789 | − | 0.119879i | \(-0.0382506\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −670.472 | + | 387.097i | −0.712511 | + | 0.411368i | −0.811990 | − | 0.583671i | \(-0.801616\pi\) |
0.0994794 | + | 0.995040i | \(0.468282\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 141.055 | + | 244.315i | 0.149581 | + | 0.259082i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1025.04 | − | 591.807i | −1.08241 | − | 0.624929i | −0.150863 | − | 0.988555i | \(-0.548205\pi\) |
−0.931545 | + | 0.363626i | \(0.881539\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 267.090 | − | 462.613i | 0.281443 | − | 0.487474i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 563.432 | − | 325.298i | 0.591219 | − | 0.341341i | −0.174360 | − | 0.984682i | \(-0.555786\pi\) |
0.765579 | + | 0.643341i | \(0.222452\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 352.094 | + | 609.845i | 0.368685 | + | 0.638581i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −731.858 | + | 422.538i | −0.763147 | + | 0.440603i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −555.631 | − | 962.381i | −0.578180 | − | 1.00144i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 226.365i | 0.234575i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1473.44 | −1.52373 | −0.761863 | − | 0.647738i | \(-0.775715\pi\) | ||||
−0.761863 | + | 0.647738i | \(0.775715\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −168.684 | + | 97.3900i | −0.173722 | + | 0.100299i | −0.584340 | − | 0.811509i | \(-0.698646\pi\) |
0.410618 | + | 0.911808i | \(0.365313\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 433.439 | − | 750.739i | 0.445467 | − | 0.771571i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −203.255 | − | 117.349i | −0.208040 | − | 0.120112i | 0.392360 | − | 0.919812i | \(-0.371659\pi\) |
−0.600400 | + | 0.799700i | \(0.704992\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −587.749 | −0.600357 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 270.658 | + | 156.265i | 0.275339 | + | 0.158967i | 0.631312 | − | 0.775529i | \(-0.282517\pi\) |
−0.355972 | + | 0.934496i | \(0.615850\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1276.96 | 1.29641 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 517.643i | 0.523400i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −327.808 | − | 567.781i | −0.330786 | − | 0.572937i | 0.651881 | − | 0.758322i | \(-0.273980\pi\) |
−0.982666 | + | 0.185384i | \(0.940647\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −751.580 | − | 433.925i | −0.755357 | − | 0.436106i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1365.95 | 1.37006 | 0.685029 | − | 0.728516i | \(-0.259790\pi\) | ||||
0.685029 | + | 0.728516i | \(0.259790\pi\) | |||||||
\(998\) | 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 | 2052.3.m.a.881.7 | 80 | ||
3.2 | odd | 2 | 684.3.m.a.653.36 | yes | 80 | ||
9.2 | odd | 6 | 2052.3.be.a.197.7 | 80 | |||
9.7 | even | 3 | 684.3.be.a.425.18 | yes | 80 | ||
19.11 | even | 3 | 2052.3.be.a.125.7 | 80 | |||
57.11 | odd | 6 | 684.3.be.a.581.18 | yes | 80 | ||
171.11 | odd | 6 | inner | 2052.3.m.a.1493.34 | 80 | ||
171.106 | even | 3 | 684.3.m.a.353.36 | ✓ | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.m.a.353.36 | ✓ | 80 | 171.106 | even | 3 | ||
684.3.m.a.653.36 | yes | 80 | 3.2 | odd | 2 | ||
684.3.be.a.425.18 | yes | 80 | 9.7 | even | 3 | ||
684.3.be.a.581.18 | yes | 80 | 57.11 | odd | 6 | ||
2052.3.m.a.881.7 | 80 | 1.1 | even | 1 | trivial | ||
2052.3.m.a.1493.34 | 80 | 171.11 | odd | 6 | inner | ||
2052.3.be.a.125.7 | 80 | 19.11 | even | 3 | |||
2052.3.be.a.197.7 | 80 | 9.2 | odd | 6 |