Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(451,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.451");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.c (of order \(2\), degree \(1\), 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.77720518656.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 121x^{4} + 14641 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 451.5 | ||
Root | \(-3.20361 - 0.858406i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.451 |
Dual form | 900.3.c.s.451.8 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | − | 1.00000i | 0.866025 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 9.38083i | − | 1.34012i | −0.742307 | − | 0.670059i | \(-0.766269\pi\) | ||
0.742307 | − | 0.670059i | \(-0.233731\pi\) | |||||||
\(8\) | − | 8.00000i | − | 1.00000i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.2481i | 1.47710i | 0.674200 | + | 0.738549i | \(0.264489\pi\) | ||||
−0.674200 | + | 0.738549i | \(0.735511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.2481 | 1.24985 | 0.624926 | − | 0.780684i | \(-0.285129\pi\) | ||||
0.624926 | + | 0.780684i | \(0.285129\pi\) | |||||||
\(14\) | −9.38083 | − | 16.2481i | −0.670059 | − | 1.16058i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(17\) | 10.3923 | 0.611312 | 0.305656 | − | 0.952142i | \(-0.401124\pi\) | ||||
0.305656 | + | 0.952142i | \(0.401124\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 20.7846i | − | 1.09393i | −0.837157 | − | 0.546963i | \(-0.815784\pi\) | ||
0.837157 | − | 0.546963i | \(-0.184216\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 16.2481 | + | 28.1425i | 0.738549 | + | 1.27920i | ||||
\(23\) | − | 28.0000i | − | 1.21739i | −0.793404 | − | 0.608696i | \(-0.791693\pi\) | ||
0.793404 | − | 0.608696i | \(-0.208307\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 28.1425 | − | 16.2481i | 1.08240 | − | 0.624926i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −32.4962 | − | 18.7617i | −1.16058 | − | 0.670059i | ||||
\(29\) | −9.38083 | −0.323477 | −0.161738 | − | 0.986834i | \(-0.551710\pi\) | ||||
−0.161738 | + | 0.986834i | \(0.551710\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 34.6410i | − | 1.11745i | −0.829352 | − | 0.558726i | \(-0.811290\pi\) | ||
0.829352 | − | 0.558726i | \(-0.188710\pi\) | |||||||
\(32\) | −27.7128 | − | 16.0000i | −0.866025 | − | 0.500000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 18.0000 | − | 10.3923i | 0.529412 | − | 0.305656i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −48.7442 | −1.31741 | −0.658706 | − | 0.752401i | \(-0.728896\pi\) | ||||
−0.658706 | + | 0.752401i | \(0.728896\pi\) | |||||||
\(38\) | −20.7846 | − | 36.0000i | −0.546963 | − | 0.947368i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18.7617 | −0.457602 | −0.228801 | − | 0.973473i | \(-0.573480\pi\) | ||||
−0.228801 | + | 0.973473i | \(0.573480\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 37.5233i | 0.872635i | 0.899793 | + | 0.436318i | \(0.143718\pi\) | ||||
−0.899793 | + | 0.436318i | \(0.856282\pi\) | |||||||
\(44\) | 56.2850 | + | 32.4962i | 1.27920 | + | 0.738549i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −28.0000 | − | 48.4974i | −0.608696 | − | 1.05429i | ||||
\(47\) | 4.00000i | 0.0851064i | 0.999094 | + | 0.0425532i | \(0.0135492\pi\) | ||||
−0.999094 | + | 0.0425532i | \(0.986451\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −39.0000 | −0.795918 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 32.4962 | − | 56.2850i | 0.624926 | − | 1.08240i | ||||
\(53\) | 31.1769 | 0.588244 | 0.294122 | − | 0.955768i | \(-0.404973\pi\) | ||||
0.294122 | + | 0.955768i | \(0.404973\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −75.0467 | −1.34012 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −16.2481 | + | 9.38083i | −0.280139 | + | 0.161738i | ||||
\(59\) | 16.2481i | 0.275391i | 0.990475 | + | 0.137696i | \(0.0439696\pi\) | ||||
−0.990475 | + | 0.137696i | \(0.956030\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −58.0000 | −0.950820 | −0.475410 | − | 0.879764i | \(-0.657700\pi\) | ||||
−0.475410 | + | 0.879764i | \(0.657700\pi\) | |||||||
\(62\) | −34.6410 | − | 60.0000i | −0.558726 | − | 0.967742i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 18.7617i | 0.280025i | 0.990150 | + | 0.140012i | \(0.0447142\pi\) | ||||
−0.990150 | + | 0.140012i | \(0.955286\pi\) | |||||||
\(68\) | 20.7846 | − | 36.0000i | 0.305656 | − | 0.529412i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 97.4885i | − | 1.37308i | −0.727093 | − | 0.686538i | \(-0.759129\pi\) | ||
0.727093 | − | 0.686538i | \(-0.240871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | −84.4275 | + | 48.7442i | −1.14091 | + | 0.658706i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −72.0000 | − | 41.5692i | −0.947368 | − | 0.546963i | ||||
\(77\) | 152.420 | 1.97949 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.92820i | 0.0876988i | 0.999038 | + | 0.0438494i | \(0.0139622\pi\) | ||||
−0.999038 | + | 0.0438494i | \(0.986038\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −32.4962 | + | 18.7617i | −0.396295 | + | 0.228801i | ||||
\(83\) | 32.0000i | 0.385542i | 0.981244 | + | 0.192771i | \(0.0617475\pi\) | ||||
−0.981244 | + | 0.192771i | \(0.938253\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 37.5233 | + | 64.9923i | 0.436318 | + | 0.755725i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 129.985 | 1.47710 | ||||||||
\(89\) | 75.0467 | 0.843221 | 0.421610 | − | 0.906777i | \(-0.361465\pi\) | ||||
0.421610 | + | 0.906777i | \(0.361465\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 152.420i | − | 1.67495i | ||||||
\(92\) | −96.9948 | − | 56.0000i | −1.05429 | − | 0.608696i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.00000 | + | 6.92820i | 0.0425532 | + | 0.0737043i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 162.481 | 1.67506 | 0.837530 | − | 0.546392i | \(-0.183999\pi\) | ||||
0.837530 | + | 0.546392i | \(0.183999\pi\) | |||||||
\(98\) | −67.5500 | + | 39.0000i | −0.689286 | + | 0.397959i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 121.951 | 1.20743 | 0.603717 | − | 0.797199i | \(-0.293686\pi\) | ||||
0.603717 | + | 0.797199i | \(0.293686\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 159.474i | − | 1.54829i | −0.633007 | − | 0.774146i | \(-0.718179\pi\) | ||
0.633007 | − | 0.774146i | \(-0.281821\pi\) | |||||||
\(104\) | − | 129.985i | − | 1.24985i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 54.0000 | − | 31.1769i | 0.509434 | − | 0.294122i | ||||
\(107\) | 184.000i | 1.71963i | 0.510609 | + | 0.859813i | \(0.329420\pi\) | ||||
−0.510609 | + | 0.859813i | \(0.670580\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 22.0000 | 0.201835 | 0.100917 | − | 0.994895i | \(-0.467822\pi\) | ||||
0.100917 | + | 0.994895i | \(0.467822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −129.985 | + | 75.0467i | −1.16058 | + | 0.670059i | ||||
\(113\) | 86.6025 | 0.766394 | 0.383197 | − | 0.923667i | \(-0.374823\pi\) | ||||
0.383197 | + | 0.923667i | \(0.374823\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −18.7617 | + | 32.4962i | −0.161738 | + | 0.280139i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 16.2481 | + | 28.1425i | 0.137696 | + | 0.238496i | ||||
\(119\) | − | 97.4885i | − | 0.819231i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −143.000 | −1.18182 | ||||||||
\(122\) | −100.459 | + | 58.0000i | −0.823434 | + | 0.475410i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −120.000 | − | 69.2820i | −0.967742 | − | 0.558726i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.38083i | − | 0.0738648i | −0.999318 | − | 0.0369324i | \(-0.988241\pi\) | ||
0.999318 | − | 0.0369324i | \(-0.0117586\pi\) | |||||||
\(128\) | −110.851 | + | 64.0000i | −0.866025 | + | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 178.729i | 1.36434i | 0.731193 | + | 0.682171i | \(0.238964\pi\) | ||||
−0.731193 | + | 0.682171i | \(0.761036\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −194.977 | −1.46599 | ||||||||
\(134\) | 18.7617 | + | 32.4962i | 0.140012 | + | 0.242509i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 83.1384i | − | 0.611312i | ||||||
\(137\) | 211.310 | 1.54241 | 0.771205 | − | 0.636587i | \(-0.219654\pi\) | ||||
0.771205 | + | 0.636587i | \(0.219654\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 90.0666i | − | 0.647961i | −0.946064 | − | 0.323981i | \(-0.894979\pi\) | ||
0.946064 | − | 0.323981i | \(-0.105021\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −97.4885 | − | 168.855i | −0.686538 | − | 1.18912i | ||||
\(143\) | 264.000i | 1.84615i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −97.4885 | + | 168.855i | −0.658706 | + | 1.14091i | ||||
\(149\) | −234.521 | −1.57397 | −0.786983 | − | 0.616975i | \(-0.788358\pi\) | ||||
−0.786983 | + | 0.616975i | \(0.788358\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 48.4974i | − | 0.321175i | −0.987022 | − | 0.160587i | \(-0.948661\pi\) | ||
0.987022 | − | 0.160587i | \(-0.0513389\pi\) | |||||||
\(152\) | −166.277 | −1.09393 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 264.000 | − | 152.420i | 1.71429 | − | 0.989743i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.2481 | −0.103491 | −0.0517455 | − | 0.998660i | \(-0.516478\pi\) | ||||
−0.0517455 | + | 0.998660i | \(0.516478\pi\) | |||||||
\(158\) | 6.92820 | + | 12.0000i | 0.0438494 | + | 0.0759494i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −262.663 | −1.63145 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 206.378i | 1.26612i | 0.774101 | + | 0.633062i | \(0.218202\pi\) | ||||
−0.774101 | + | 0.633062i | \(0.781798\pi\) | |||||||
\(164\) | −37.5233 | + | 64.9923i | −0.228801 | + | 0.396295i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 32.0000 | + | 55.4256i | 0.192771 | + | 0.333889i | ||||
\(167\) | 244.000i | 1.46108i | 0.682871 | + | 0.730539i | \(0.260731\pi\) | ||||
−0.682871 | + | 0.730539i | \(0.739269\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 95.0000 | 0.562130 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 129.985 | + | 75.0467i | 0.755725 | + | 0.436318i | ||||
\(173\) | 38.1051 | 0.220261 | 0.110130 | − | 0.993917i | \(-0.464873\pi\) | ||||
0.110130 | + | 0.993917i | \(0.464873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 225.140 | − | 129.985i | 1.27920 | − | 0.738549i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 129.985 | − | 75.0467i | 0.730251 | − | 0.421610i | ||||
\(179\) | 146.233i | 0.816942i | 0.912771 | + | 0.408471i | \(0.133938\pi\) | ||||
−0.912771 | + | 0.408471i | \(0.866062\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 230.000 | 1.27072 | 0.635359 | − | 0.772217i | \(-0.280852\pi\) | ||||
0.635359 | + | 0.772217i | \(0.280852\pi\) | |||||||
\(182\) | −152.420 | − | 264.000i | −0.837475 | − | 1.45055i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −224.000 | −1.21739 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 168.855i | 0.902968i | ||||||||
\(188\) | 13.8564 | + | 8.00000i | 0.0737043 | + | 0.0425532i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 32.4962i | − | 0.170137i | −0.996375 | − | 0.0850685i | \(-0.972889\pi\) | ||
0.996375 | − | 0.0850685i | \(-0.0271109\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 162.481 | 0.841869 | 0.420935 | − | 0.907091i | \(-0.361702\pi\) | ||||
0.420935 | + | 0.907091i | \(0.361702\pi\) | |||||||
\(194\) | 281.425 | − | 162.481i | 1.45064 | − | 0.837530i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −78.0000 | + | 135.100i | −0.397959 | + | 0.689286i | ||||
\(197\) | 342.946 | 1.74084 | 0.870421 | − | 0.492307i | \(-0.163846\pi\) | ||||
0.870421 | + | 0.492307i | \(0.163846\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 20.7846i | − | 0.104445i | −0.998635 | − | 0.0522226i | \(-0.983369\pi\) | ||
0.998635 | − | 0.0522226i | \(-0.0166305\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 211.225 | − | 121.951i | 1.04567 | − | 0.603717i | ||||
\(203\) | 88.0000i | 0.433498i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −159.474 | − | 276.217i | −0.774146 | − | 1.34086i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −129.985 | − | 225.140i | −0.624926 | − | 1.08240i | ||||
\(209\) | 337.710 | 1.61584 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 297.913i | 1.41191i | 0.708257 | + | 0.705954i | \(0.249482\pi\) | ||||
−0.708257 | + | 0.705954i | \(0.750518\pi\) | |||||||
\(212\) | 62.3538 | − | 108.000i | 0.294122 | − | 0.509434i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 184.000 | + | 318.697i | 0.859813 | + | 1.48924i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −324.962 | −1.49752 | ||||||||
\(218\) | 38.1051 | − | 22.0000i | 0.174794 | − | 0.100917i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 168.855 | 0.764050 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 159.474i | − | 0.715131i | −0.933888 | − | 0.357565i | \(-0.883607\pi\) | ||
0.933888 | − | 0.357565i | \(-0.116393\pi\) | |||||||
\(224\) | −150.093 | + | 259.969i | −0.670059 | + | 1.16058i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 150.000 | − | 86.6025i | 0.663717 | − | 0.383197i | ||||
\(227\) | − | 128.000i | − | 0.563877i | −0.959433 | − | 0.281938i | \(-0.909023\pi\) | ||
0.959433 | − | 0.281938i | \(-0.0909774\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −134.000 | −0.585153 | −0.292576 | − | 0.956242i | \(-0.594513\pi\) | ||||
−0.292576 | + | 0.956242i | \(0.594513\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 75.0467i | 0.323477i | ||||||||
\(233\) | 301.377 | 1.29346 | 0.646731 | − | 0.762718i | \(-0.276135\pi\) | ||||
0.646731 | + | 0.762718i | \(0.276135\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 56.2850 | + | 32.4962i | 0.238496 | + | 0.137696i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −97.4885 | − | 168.855i | −0.409615 | − | 0.709475i | ||||
\(239\) | 162.481i | 0.679836i | 0.940455 | + | 0.339918i | \(0.110399\pi\) | ||||
−0.940455 | + | 0.339918i | \(0.889601\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 50.0000 | 0.207469 | 0.103734 | − | 0.994605i | \(-0.466921\pi\) | ||||
0.103734 | + | 0.994605i | \(0.466921\pi\) | |||||||
\(242\) | −247.683 | + | 143.000i | −1.02348 | + | 0.590909i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −116.000 | + | 200.918i | −0.475410 | + | 0.823434i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 337.710i | − | 1.36725i | ||||||
\(248\) | −277.128 | −1.11745 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 146.233i | − | 0.582600i | −0.956632 | − | 0.291300i | \(-0.905912\pi\) | ||
0.956632 | − | 0.291300i | \(-0.0940878\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 454.946 | 1.79821 | ||||||||
\(254\) | −9.38083 | − | 16.2481i | −0.0369324 | − | 0.0639688i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.500000 | + | 0.866025i | ||||
\(257\) | −24.2487 | −0.0943530 | −0.0471765 | − | 0.998887i | \(-0.515022\pi\) | ||||
−0.0471765 | + | 0.998887i | \(0.515022\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 457.261i | 1.76549i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 178.729 | + | 309.567i | 0.682171 | + | 1.18156i | ||||
\(263\) | − | 340.000i | − | 1.29278i | −0.763009 | − | 0.646388i | \(-0.776279\pi\) | ||
0.763009 | − | 0.646388i | \(-0.223721\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −337.710 | + | 194.977i | −1.26959 | + | 0.732996i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 64.9923 | + | 37.5233i | 0.242509 | + | 0.140012i | ||||
\(269\) | −178.236 | −0.662587 | −0.331293 | − | 0.943528i | \(-0.607485\pi\) | ||||
−0.331293 | + | 0.943528i | \(0.607485\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 394.908i | 1.45722i | 0.684927 | + | 0.728612i | \(0.259834\pi\) | ||||
−0.684927 | + | 0.728612i | \(0.740166\pi\) | |||||||
\(272\) | −83.1384 | − | 144.000i | −0.305656 | − | 0.529412i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 366.000 | − | 211.310i | 1.33577 | − | 0.771205i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 113.737 | 0.410601 | 0.205301 | − | 0.978699i | \(-0.434183\pi\) | ||||
0.205301 | + | 0.978699i | \(0.434183\pi\) | |||||||
\(278\) | −90.0666 | − | 156.000i | −0.323981 | − | 0.561151i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −75.0467 | −0.267070 | −0.133535 | − | 0.991044i | \(-0.542633\pi\) | ||||
−0.133535 | + | 0.991044i | \(0.542633\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 318.948i | 1.12703i | 0.826107 | + | 0.563513i | \(0.190550\pi\) | ||||
−0.826107 | + | 0.563513i | \(0.809450\pi\) | |||||||
\(284\) | −337.710 | − | 194.977i | −1.18912 | − | 0.686538i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 264.000 | + | 457.261i | 0.923077 | + | 1.59882i | ||||
\(287\) | 176.000i | 0.613240i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −181.000 | −0.626298 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −349.874 | −1.19411 | −0.597055 | − | 0.802200i | \(-0.703663\pi\) | ||||
−0.597055 | + | 0.802200i | \(0.703663\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 389.954i | 1.31741i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −406.202 | + | 234.521i | −1.36309 | + | 0.786983i | ||||
\(299\) | − | 454.946i | − | 1.52156i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 352.000 | 1.16944 | ||||||||
\(302\) | −48.4974 | − | 84.0000i | −0.160587 | − | 0.278146i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −288.000 | + | 166.277i | −0.947368 | + | 0.546963i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 262.663i | − | 0.855581i | −0.903878 | − | 0.427790i | \(-0.859292\pi\) | ||
0.903878 | − | 0.427790i | \(-0.140708\pi\) | |||||||
\(308\) | 304.841 | − | 528.000i | 0.989743 | − | 1.71429i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.4962i | 0.104489i | 0.998634 | + | 0.0522446i | \(0.0166376\pi\) | ||||
−0.998634 | + | 0.0522446i | \(0.983362\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −357.458 | −1.14204 | −0.571019 | − | 0.820937i | \(-0.693452\pi\) | ||||
−0.571019 | + | 0.820937i | \(0.693452\pi\) | |||||||
\(314\) | −28.1425 | + | 16.2481i | −0.0896258 | + | 0.0517455i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.0000 | + | 13.8564i | 0.0759494 | + | 0.0438494i | ||||
\(317\) | 45.0333 | 0.142061 | 0.0710305 | − | 0.997474i | \(-0.477371\pi\) | ||||
0.0710305 | + | 0.997474i | \(0.477371\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 152.420i | − | 0.477807i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −454.946 | + | 262.663i | −1.41288 | + | 0.815724i | ||||
\(323\) | − | 216.000i | − | 0.668731i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 206.378 | + | 357.458i | 0.633062 | + | 1.09650i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 150.093i | 0.457602i | ||||||||
\(329\) | 37.5233 | 0.114053 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 325.626i | 0.983763i | 0.870662 | + | 0.491881i | \(0.163691\pi\) | ||||
−0.870662 | + | 0.491881i | \(0.836309\pi\) | |||||||
\(332\) | 110.851 | + | 64.0000i | 0.333889 | + | 0.192771i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 244.000 | + | 422.620i | 0.730539 | + | 1.26533i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −64.9923 | −0.192856 | −0.0964278 | − | 0.995340i | \(-0.530742\pi\) | ||||
−0.0964278 | + | 0.995340i | \(0.530742\pi\) | |||||||
\(338\) | 164.545 | − | 95.0000i | 0.486819 | − | 0.281065i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 562.850 | 1.65059 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 93.8083i | − | 0.273494i | ||||||
\(344\) | 300.187 | 0.872635 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 66.0000 | − | 38.1051i | 0.190751 | − | 0.110130i | ||||
\(347\) | − | 104.000i | − | 0.299712i | −0.988708 | − | 0.149856i | \(-0.952119\pi\) | ||
0.988708 | − | 0.149856i | \(-0.0478810\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 598.000 | 1.71347 | 0.856734 | − | 0.515759i | \(-0.172490\pi\) | ||||
0.856734 | + | 0.515759i | \(0.172490\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 259.969 | − | 450.280i | 0.738549 | − | 1.27920i | ||||
\(353\) | 79.6743 | 0.225706 | 0.112853 | − | 0.993612i | \(-0.464001\pi\) | ||||
0.112853 | + | 0.993612i | \(0.464001\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 150.093 | − | 259.969i | 0.421610 | − | 0.730251i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 146.233 | + | 253.282i | 0.408471 | + | 0.707493i | ||||
\(359\) | − | 194.977i | − | 0.543111i | −0.962423 | − | 0.271556i | \(-0.912462\pi\) | ||
0.962423 | − | 0.271556i | \(-0.0875381\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −71.0000 | −0.196676 | ||||||||
\(362\) | 398.372 | − | 230.000i | 1.10047 | − | 0.635359i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −528.000 | − | 304.841i | −1.45055 | − | 0.837475i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 553.469i | 1.50809i | 0.656823 | + | 0.754045i | \(0.271900\pi\) | ||||
−0.656823 | + | 0.754045i | \(0.728100\pi\) | |||||||
\(368\) | −387.979 | + | 224.000i | −1.05429 | + | 0.608696i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 292.465i | − | 0.788316i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −276.217 | −0.740529 | −0.370264 | − | 0.928926i | \(-0.620733\pi\) | ||||
−0.370264 | + | 0.928926i | \(0.620733\pi\) | |||||||
\(374\) | 168.855 | + | 292.465i | 0.451484 | + | 0.781993i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 32.0000 | 0.0851064 | ||||||||
\(377\) | −152.420 | −0.404298 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 103.923i | − | 0.274203i | −0.990557 | − | 0.137102i | \(-0.956221\pi\) | ||
0.990557 | − | 0.137102i | \(-0.0437787\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −32.4962 | − | 56.2850i | −0.0850685 | − | 0.147343i | ||||
\(383\) | − | 220.000i | − | 0.574413i | −0.957869 | − | 0.287206i | \(-0.907273\pi\) | ||
0.957869 | − | 0.287206i | \(-0.0927265\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 281.425 | − | 162.481i | 0.729080 | − | 0.420935i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 324.962 | − | 562.850i | 0.837530 | − | 1.45064i | ||||
\(389\) | −347.091 | −0.892264 | −0.446132 | − | 0.894967i | \(-0.647199\pi\) | ||||
−0.446132 | + | 0.894967i | \(0.647199\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 290.985i | − | 0.744206i | ||||||
\(392\) | 312.000i | 0.795918i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 594.000 | − | 342.946i | 1.50761 | − | 0.870421i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 341.210 | 0.859470 | 0.429735 | − | 0.902955i | \(-0.358607\pi\) | ||||
0.429735 | + | 0.902955i | \(0.358607\pi\) | |||||||
\(398\) | −20.7846 | − | 36.0000i | −0.0522226 | − | 0.0904523i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −581.612 | −1.45040 | −0.725201 | − | 0.688537i | \(-0.758253\pi\) | ||||
−0.725201 | + | 0.688537i | \(0.758253\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 562.850i | − | 1.39665i | ||||||
\(404\) | 243.902 | − | 422.450i | 0.603717 | − | 1.04567i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 88.0000 | + | 152.420i | 0.216749 | + | 0.375420i | ||||
\(407\) | − | 792.000i | − | 1.94595i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −122.000 | −0.298289 | −0.149144 | − | 0.988815i | \(-0.547652\pi\) | ||||
−0.149144 | + | 0.988815i | \(0.547652\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −552.435 | − | 318.948i | −1.34086 | − | 0.774146i | ||||
\(413\) | 152.420 | 0.369057 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −450.280 | − | 259.969i | −1.08240 | − | 0.624926i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 584.931 | − | 337.710i | 1.39936 | − | 0.807919i | ||||
\(419\) | 503.690i | 1.20213i | 0.799202 | + | 0.601063i | \(0.205256\pi\) | ||||
−0.799202 | + | 0.601063i | \(0.794744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 74.0000 | 0.175772 | 0.0878860 | − | 0.996131i | \(-0.471989\pi\) | ||||
0.0878860 | + | 0.996131i | \(0.471989\pi\) | |||||||
\(422\) | 297.913 | + | 516.000i | 0.705954 | + | 1.22275i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 249.415i | − | 0.588244i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 544.088i | 1.27421i | ||||||||
\(428\) | 637.395 | + | 368.000i | 1.48924 | + | 0.859813i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 779.908i | 1.80953i | 0.425911 | + | 0.904765i | \(0.359954\pi\) | ||||
−0.425911 | + | 0.904765i | \(0.640046\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −97.4885 | −0.225147 | −0.112573 | − | 0.993643i | \(-0.535909\pi\) | ||||
−0.112573 | + | 0.993643i | \(0.535909\pi\) | |||||||
\(434\) | −562.850 | + | 324.962i | −1.29689 | + | 0.748759i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 44.0000 | − | 76.2102i | 0.100917 | − | 0.174794i | ||||
\(437\) | −581.969 | −1.33174 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 339.482i | 0.773307i | 0.922225 | + | 0.386654i | \(0.126369\pi\) | ||||
−0.922225 | + | 0.386654i | \(0.873631\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 292.465 | − | 168.855i | 0.661686 | − | 0.382025i | ||||
\(443\) | 176.000i | 0.397291i | 0.980071 | + | 0.198646i | \(0.0636543\pi\) | ||||
−0.980071 | + | 0.198646i | \(0.936346\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −159.474 | − | 276.217i | −0.357565 | − | 0.619321i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 600.373i | 1.34012i | ||||||||
\(449\) | 469.042 | 1.04464 | 0.522318 | − | 0.852751i | \(-0.325067\pi\) | ||||
0.522318 | + | 0.852751i | \(0.325067\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 304.841i | − | 0.675922i | ||||||
\(452\) | 173.205 | − | 300.000i | 0.383197 | − | 0.663717i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −128.000 | − | 221.703i | −0.281938 | − | 0.488332i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 357.458 | 0.782183 | 0.391092 | − | 0.920352i | \(-0.372098\pi\) | ||||
0.391092 | + | 0.920352i | \(0.372098\pi\) | |||||||
\(458\) | −232.095 | + | 134.000i | −0.506757 | + | 0.292576i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −497.184 | −1.07849 | −0.539245 | − | 0.842149i | \(-0.681290\pi\) | ||||
−0.539245 | + | 0.842149i | \(0.681290\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 347.091i | 0.749656i | 0.927094 | + | 0.374828i | \(0.122298\pi\) | ||||
−0.927094 | + | 0.374828i | \(0.877702\pi\) | |||||||
\(464\) | 75.0467 | + | 129.985i | 0.161738 | + | 0.280139i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 522.000 | − | 301.377i | 1.12017 | − | 0.646731i | ||||
\(467\) | 520.000i | 1.11349i | 0.830683 | + | 0.556745i | \(0.187950\pi\) | ||||
−0.830683 | + | 0.556745i | \(0.812050\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 176.000 | 0.375267 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 129.985 | 0.275391 | ||||||||
\(473\) | −609.682 | −1.28897 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −337.710 | − | 194.977i | −0.709475 | − | 0.409615i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 162.481 | + | 281.425i | 0.339918 | + | 0.588755i | ||||
\(479\) | 812.404i | 1.69604i | 0.529963 | + | 0.848021i | \(0.322206\pi\) | ||||
−0.529963 | + | 0.848021i | \(0.677794\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −792.000 | −1.64657 | ||||||||
\(482\) | 86.6025 | − | 50.0000i | 0.179673 | − | 0.103734i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −286.000 | + | 495.367i | −0.590909 | + | 1.02348i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 290.806i | − | 0.597137i | −0.954388 | − | 0.298569i | \(-0.903491\pi\) | ||
0.954388 | − | 0.298569i | \(-0.0965092\pi\) | |||||||
\(488\) | 464.000i | 0.950820i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 406.202i | − | 0.827295i | −0.910437 | − | 0.413648i | \(-0.864255\pi\) | ||
0.910437 | − | 0.413648i | \(-0.135745\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −97.4885 | −0.197745 | ||||||||
\(494\) | −337.710 | − | 584.931i | −0.683623 | − | 1.18407i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −480.000 | + | 277.128i | −0.967742 | + | 0.558726i | ||||
\(497\) | −914.523 | −1.84009 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 838.313i | − | 1.67999i | −0.542598 | − | 0.839993i | \(-0.682559\pi\) | ||
0.542598 | − | 0.839993i | \(-0.317441\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −146.233 | − | 253.282i | −0.291300 | − | 0.504547i | ||||
\(503\) | 932.000i | 1.85288i | 0.376439 | + | 0.926441i | \(0.377148\pi\) | ||||
−0.376439 | + | 0.926441i | \(0.622852\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 787.990 | − | 454.946i | 1.55729 | − | 0.899103i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −32.4962 | − | 18.7617i | −0.0639688 | − | 0.0369324i | ||||
\(509\) | 440.899 | 0.866206 | 0.433103 | − | 0.901344i | \(-0.357419\pi\) | ||||
0.433103 | + | 0.901344i | \(0.357419\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000i | 1.00000i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −42.0000 | + | 24.2487i | −0.0817121 | + | 0.0471765i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −64.9923 | −0.125710 | ||||||||
\(518\) | 457.261 | + | 792.000i | 0.882744 | + | 1.52896i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 431.518 | 0.828250 | 0.414125 | − | 0.910220i | \(-0.364088\pi\) | ||||
0.414125 | + | 0.910220i | \(0.364088\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 243.902i | − | 0.466351i | −0.972435 | − | 0.233176i | \(-0.925088\pi\) | ||
0.972435 | − | 0.233176i | \(-0.0749117\pi\) | |||||||
\(524\) | 619.135 | + | 357.458i | 1.18156 | + | 0.682171i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −340.000 | − | 588.897i | −0.646388 | − | 1.11958i | ||||
\(527\) | − | 360.000i | − | 0.683112i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −255.000 | −0.482042 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −389.954 | + | 675.420i | −0.732996 | + | 1.26959i | ||||
\(533\) | −304.841 | −0.571934 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 150.093 | 0.280025 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −308.713 | + | 178.236i | −0.573817 | + | 0.331293i | ||||
\(539\) | − | 633.675i | − | 1.17565i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 374.000 | 0.691312 | 0.345656 | − | 0.938361i | \(-0.387656\pi\) | ||||
0.345656 | + | 0.938361i | \(0.387656\pi\) | |||||||
\(542\) | 394.908 | + | 684.000i | 0.728612 | + | 1.26199i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −288.000 | − | 166.277i | −0.529412 | − | 0.305656i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 938.083i | − | 1.71496i | −0.514517 | − | 0.857480i | \(-0.672029\pi\) | ||
0.514517 | − | 0.857480i | \(-0.327971\pi\) | |||||||
\(548\) | 422.620 | − | 732.000i | 0.771205 | − | 1.33577i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 194.977i | 0.353860i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 64.9923 | 0.117527 | ||||||||
\(554\) | 196.997 | − | 113.737i | 0.355591 | − | 0.205301i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −312.000 | − | 180.133i | −0.561151 | − | 0.323981i | ||||
\(557\) | −426.084 | −0.764963 | −0.382482 | − | 0.923963i | \(-0.624930\pi\) | ||||
−0.382482 | + | 0.923963i | \(0.624930\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 609.682i | 1.09067i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −129.985 | + | 75.0467i | −0.231289 | + | 0.133535i | ||||
\(563\) | − | 136.000i | − | 0.241563i | −0.992679 | − | 0.120782i | \(-0.961460\pi\) | ||
0.992679 | − | 0.120782i | \(-0.0385400\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 318.948 | + | 552.435i | 0.563513 | + | 0.976033i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −779.908 | −1.37308 | ||||||||
\(569\) | −881.798 | −1.54973 | −0.774867 | − | 0.632125i | \(-0.782183\pi\) | ||||
−0.774867 | + | 0.632125i | \(0.782183\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 949.164i | − | 1.66228i | −0.556061 | − | 0.831142i | \(-0.687688\pi\) | ||
0.556061 | − | 0.831142i | \(-0.312312\pi\) | |||||||
\(572\) | 914.523 | + | 528.000i | 1.59882 | + | 0.923077i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 176.000 | + | 304.841i | 0.306620 | + | 0.531082i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −389.954 | −0.675830 | −0.337915 | − | 0.941177i | \(-0.609722\pi\) | ||||
−0.337915 | + | 0.941177i | \(0.609722\pi\) | |||||||
\(578\) | −313.501 | + | 181.000i | −0.542390 | + | 0.313149i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 300.187 | 0.516672 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 506.565i | 0.868893i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −606.000 | + | 349.874i | −1.03413 | + | 0.597055i | ||||
\(587\) | − | 680.000i | − | 1.15843i | −0.815174 | − | 0.579216i | \(-0.803359\pi\) | ||
0.815174 | − | 0.579216i | \(-0.196641\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −720.000 | −1.22241 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 389.954 | + | 675.420i | 0.658706 | + | 1.14091i | ||||
\(593\) | 114.315 | 0.192775 | 0.0963873 | − | 0.995344i | \(-0.469271\pi\) | ||||
0.0963873 | + | 0.995344i | \(0.469271\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −469.042 | + | 812.404i | −0.786983 | + | 1.36309i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −454.946 | − | 787.990i | −0.760780 | − | 1.31771i | ||||
\(599\) | − | 1104.87i | − | 1.84452i | −0.386567 | − | 0.922261i | \(-0.626339\pi\) | ||
0.386567 | − | 0.922261i | \(-0.373661\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −682.000 | −1.13478 | −0.567388 | − | 0.823451i | \(-0.692046\pi\) | ||||
−0.567388 | + | 0.823451i | \(0.692046\pi\) | |||||||
\(602\) | 609.682 | − | 352.000i | 1.01276 | − | 0.584718i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −168.000 | − | 96.9948i | −0.278146 | − | 0.160587i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 272.044i | 0.448178i | 0.974569 | + | 0.224089i | \(0.0719407\pi\) | ||||
−0.974569 | + | 0.224089i | \(0.928059\pi\) | |||||||
\(608\) | −332.554 | + | 576.000i | −0.546963 | + | 0.947368i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 64.9923i | 0.106370i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 341.210 | 0.556623 | 0.278311 | − | 0.960491i | \(-0.410225\pi\) | ||||
0.278311 | + | 0.960491i | \(0.410225\pi\) | |||||||
\(614\) | −262.663 | − | 454.946i | −0.427790 | − | 0.740955i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 1219.36i | − | 1.97949i | ||||||
\(617\) | −336.018 | −0.544599 | −0.272300 | − | 0.962212i | \(-0.587784\pi\) | ||||
−0.272300 | + | 0.962212i | \(0.587784\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 381.051i | 0.615592i | 0.951452 | + | 0.307796i | \(0.0995914\pi\) | ||||
−0.951452 | + | 0.307796i | \(0.900409\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 32.4962 | + | 56.2850i | 0.0522446 | + | 0.0904903i | ||||
\(623\) | − | 704.000i | − | 1.13002i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −619.135 | + | 357.458i | −0.989033 | + | 0.571019i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −32.4962 | + | 56.2850i | −0.0517455 | + | 0.0896258i | ||||
\(629\) | −506.565 | −0.805350 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 145.492i | 0.230574i | 0.993332 | + | 0.115287i | \(0.0367788\pi\) | ||||
−0.993332 | + | 0.115287i | \(0.963221\pi\) | |||||||
\(632\) | 55.4256 | 0.0876988 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 78.0000 | − | 45.0333i | 0.123028 | − | 0.0710305i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −633.675 | −0.994780 | ||||||||
\(638\) | −152.420 | − | 264.000i | −0.238904 | − | 0.413793i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 431.518 | 0.673195 | 0.336598 | − | 0.941649i | \(-0.390724\pi\) | ||||
0.336598 | + | 0.941649i | \(0.390724\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 356.472i | − | 0.554388i | −0.960814 | − | 0.277194i | \(-0.910595\pi\) | ||
0.960814 | − | 0.277194i | \(-0.0894045\pi\) | |||||||
\(644\) | −525.327 | + | 909.892i | −0.815724 | + | 1.41288i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −216.000 | − | 374.123i | −0.334365 | − | 0.579138i | ||||
\(647\) | 364.000i | 0.562597i | 0.959620 | + | 0.281298i | \(0.0907650\pi\) | ||||
−0.959620 | + | 0.281298i | \(0.909235\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −264.000 | −0.406780 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 714.915 | + | 412.757i | 1.09650 | + | 0.633062i | ||||
\(653\) | −162.813 | −0.249330 | −0.124665 | − | 0.992199i | \(-0.539786\pi\) | ||||
−0.124665 | + | 0.992199i | \(0.539786\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 150.093 | + | 259.969i | 0.228801 | + | 0.396295i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 64.9923 | − | 37.5233i | 0.0987725 | − | 0.0570263i | ||||
\(659\) | 178.729i | 0.271212i | 0.990763 | + | 0.135606i | \(0.0432982\pi\) | ||||
−0.990763 | + | 0.135606i | \(0.956702\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 662.000 | 1.00151 | 0.500756 | − | 0.865588i | \(-0.333055\pi\) | ||||
0.500756 | + | 0.865588i | \(0.333055\pi\) | |||||||
\(662\) | 325.626 | + | 564.000i | 0.491881 | + | 0.851964i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 256.000 | 0.385542 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 262.663i | 0.393798i | ||||||||
\(668\) | 845.241 | + | 488.000i | 1.26533 | + | 0.730539i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 942.388i | − | 1.40445i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1202.36 | 1.78656 | 0.893282 | − | 0.449497i | \(-0.148397\pi\) | ||||
0.893282 | + | 0.449497i | \(0.148397\pi\) | |||||||
\(674\) | −112.570 | + | 64.9923i | −0.167018 | + | 0.0964278i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 190.000 | − | 329.090i | 0.281065 | − | 0.486819i | ||||
\(677\) | −495.367 | −0.731708 | −0.365854 | − | 0.930672i | \(-0.619223\pi\) | ||||
−0.365854 | + | 0.930672i | \(0.619223\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1524.20i | − | 2.24478i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 974.885 | − | 562.850i | 1.42945 | − | 0.825293i | ||||
\(683\) | − | 88.0000i | − | 0.128843i | −0.997923 | − | 0.0644217i | \(-0.979480\pi\) | ||
0.997923 | − | 0.0644217i | \(-0.0205203\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −93.8083 | − | 162.481i | −0.136747 | − | 0.236852i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 519.938 | − | 300.187i | 0.755725 | − | 0.436318i | ||||
\(689\) | 506.565 | 0.735218 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 339.482i | − | 0.491291i | −0.969360 | − | 0.245645i | \(-0.921000\pi\) | ||
0.969360 | − | 0.245645i | \(-0.0789999\pi\) | |||||||
\(692\) | 76.2102 | − | 132.000i | 0.110130 | − | 0.190751i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −104.000 | − | 180.133i | −0.149856 | − | 0.259558i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −194.977 | −0.279737 | ||||||||
\(698\) | 1035.77 | − | 598.000i | 1.48391 | − | 0.856734i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −834.894 | −1.19100 | −0.595502 | − | 0.803354i | \(-0.703047\pi\) | ||||
−0.595502 | + | 0.803354i | \(0.703047\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1013.13i | 1.44115i | ||||||||
\(704\) | − | 1039.88i | − | 1.47710i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 138.000 | − | 79.6743i | 0.195467 | − | 0.112853i | ||||
\(707\) | − | 1144.00i | − | 1.61810i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 490.000 | 0.691114 | 0.345557 | − | 0.938398i | \(-0.387690\pi\) | ||||
0.345557 | + | 0.938398i | \(0.387690\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 600.373i | − | 0.843221i | ||||||
\(713\) | −969.948 | −1.36038 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 506.565 | + | 292.465i | 0.707493 | + | 0.408471i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −194.977 | − | 337.710i | −0.271556 | − | 0.470348i | ||||
\(719\) | 584.931i | 0.813534i | 0.913532 | + | 0.406767i | \(0.133344\pi\) | ||||
−0.913532 | + | 0.406767i | \(0.866656\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1496.00 | −2.07490 | ||||||||
\(722\) | −122.976 | + | 71.0000i | −0.170326 | + | 0.0983380i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 460.000 | − | 796.743i | 0.635359 | − | 1.10047i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 178.236i | − | 0.245166i | −0.992458 | − | 0.122583i | \(-0.960882\pi\) | ||
0.992458 | − | 0.122583i | \(-0.0391178\pi\) | |||||||
\(728\) | −1219.36 | −1.67495 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 389.954i | 0.533453i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −81.2404 | −0.110833 | −0.0554164 | − | 0.998463i | \(-0.517649\pi\) | ||||
−0.0554164 | + | 0.998463i | \(0.517649\pi\) | |||||||
\(734\) | 553.469 | + | 958.637i | 0.754045 | + | 1.30604i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −448.000 | + | 775.959i | −0.608696 | + | 1.05429i | ||||
\(737\) | −304.841 | −0.413624 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 311.769i | − | 0.421880i | −0.977499 | − | 0.210940i | \(-0.932348\pi\) | ||
0.977499 | − | 0.210940i | \(-0.0676524\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −292.465 | − | 506.565i | −0.394158 | − | 0.682702i | ||||
\(743\) | − | 676.000i | − | 0.909825i | −0.890536 | − | 0.454913i | \(-0.849671\pi\) | ||
0.890536 | − | 0.454913i | \(-0.150329\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −478.422 | + | 276.217i | −0.641317 | + | 0.370264i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 584.931 | + | 337.710i | 0.781993 | + | 0.451484i | ||||
\(749\) | 1726.07 | 2.30450 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1281.72i | − | 1.70668i | −0.521354 | − | 0.853341i | \(-0.674573\pi\) | ||
0.521354 | − | 0.853341i | \(-0.325427\pi\) | |||||||
\(752\) | 55.4256 | − | 32.0000i | 0.0737043 | − | 0.0425532i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −264.000 | + | 152.420i | −0.350133 | + | 0.202149i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −341.210 | −0.450739 | −0.225370 | − | 0.974273i | \(-0.572359\pi\) | ||||
−0.225370 | + | 0.974273i | \(0.572359\pi\) | |||||||
\(758\) | −103.923 | − | 180.000i | −0.137102 | − | 0.237467i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 994.368 | 1.30666 | 0.653330 | − | 0.757073i | \(-0.273371\pi\) | ||||
0.653330 | + | 0.757073i | \(0.273371\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 206.378i | − | 0.270483i | ||||||
\(764\) | −112.570 | − | 64.9923i | −0.147343 | − | 0.0850685i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −220.000 | − | 381.051i | −0.287206 | − | 0.497456i | ||||
\(767\) | 264.000i | 0.344198i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −314.000 | −0.408322 | −0.204161 | − | 0.978937i | \(-0.565447\pi\) | ||||
−0.204161 | + | 0.978937i | \(0.565447\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 324.962 | − | 562.850i | 0.420935 | − | 0.729080i | ||||
\(773\) | 904.131 | 1.16964 | 0.584819 | − | 0.811164i | \(-0.301165\pi\) | ||||
0.584819 | + | 0.811164i | \(0.301165\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 1299.85i | − | 1.67506i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −601.179 | + | 347.091i | −0.772723 | + | 0.446132i | ||||
\(779\) | 389.954i | 0.500583i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1584.00 | 2.02817 | ||||||||
\(782\) | −290.985 | − | 504.000i | −0.372103 | − | 0.644501i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 312.000 | + | 540.400i | 0.397959 | + | 0.689286i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 431.518i | − | 0.548308i | −0.961686 | − | 0.274154i | \(-0.911602\pi\) | ||
0.961686 | − | 0.274154i | \(-0.0883978\pi\) | |||||||
\(788\) | 685.892 | − | 1188.00i | 0.870421 | − | 1.50761i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 812.404i | − | 1.02706i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −942.388 | −1.18838 | ||||||||
\(794\) | 590.992 | − | 341.210i | 0.744323 | − | 0.429735i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −72.0000 | − | 41.5692i | −0.0904523 | − | 0.0522226i | ||||
\(797\) | −1292.11 | −1.62122 | −0.810608 | − | 0.585589i | \(-0.800863\pi\) | ||||
−0.810608 | + | 0.585589i | \(0.800863\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.5692i | 0.0520266i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1007.38 | + | 581.612i | −1.25609 | + | 0.725201i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −562.850 | − | 974.885i | −0.698325 | − | 1.20953i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 975.606i | − | 1.20743i | ||||||
\(809\) | −1219.51 | −1.50743 | −0.753713 | − | 0.657203i | \(-0.771739\pi\) | ||||
−0.753713 | + | 0.657203i | \(0.771739\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1018.45i | 1.25579i | 0.778298 | + | 0.627895i | \(0.216083\pi\) | ||||
−0.778298 | + | 0.627895i | \(0.783917\pi\) | |||||||
\(812\) | 304.841 | + | 176.000i | 0.375420 | + | 0.216749i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −792.000 | − | 1371.78i | −0.972973 | − | 1.68524i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 779.908 | 0.954599 | ||||||||
\(818\) | −211.310 | + | 122.000i | −0.258325 | + | 0.149144i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −497.184 | −0.605584 | −0.302792 | − | 0.953057i | \(-0.597919\pi\) | ||||
−0.302792 | + | 0.953057i | \(0.597919\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 440.899i | − | 0.535722i | −0.963458 | − | 0.267861i | \(-0.913683\pi\) | ||
0.963458 | − | 0.267861i | \(-0.0863168\pi\) | |||||||
\(824\) | −1275.79 | −1.54829 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 264.000 | − | 152.420i | 0.319613 | − | 0.184528i | ||||
\(827\) | − | 752.000i | − | 0.909311i | −0.890667 | − | 0.454655i | \(-0.849762\pi\) | ||
0.890667 | − | 0.454655i | \(-0.150238\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1030.00 | 1.24246 | 0.621230 | − | 0.783628i | \(-0.286633\pi\) | ||||
0.621230 | + | 0.783628i | \(0.286633\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1039.88 | −1.24985 | ||||||||
\(833\) | −405.300 | −0.486554 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 675.420 | − | 1169.86i | 0.807919 | − | 1.39936i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 503.690 | + | 872.417i | 0.601063 | + | 1.04107i | ||||
\(839\) | 519.938i | 0.619712i | 0.950783 | + | 0.309856i | \(0.100281\pi\) | ||||
−0.950783 | + | 0.309856i | \(0.899719\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −753.000 | −0.895363 | ||||||||
\(842\) | 128.172 | − | 74.0000i | 0.152223 | − | 0.0878860i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1032.00 | + | 595.825i | 1.22275 | + | 0.705954i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1341.46i | 1.58378i | ||||||||
\(848\) | −249.415 | − | 432.000i | −0.294122 | − | 0.509434i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1364.84i | 1.60381i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −698.667 | −0.819071 | −0.409535 | − | 0.912294i | \(-0.634309\pi\) | ||||
−0.409535 | + | 0.912294i | \(0.634309\pi\) | |||||||
\(854\) | 544.088 | + | 942.388i | 0.637106 | + | 1.10350i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1472.00 | 1.71963 | ||||||||
\(857\) | 897.202 | 1.04691 | 0.523455 | − | 0.852053i | \(-0.324643\pi\) | ||||
0.523455 | + | 0.852053i | \(0.324643\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 533.472i | 0.621038i | 0.950567 | + | 0.310519i | \(0.100503\pi\) | ||||
−0.950567 | + | 0.310519i | \(0.899497\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 779.908 | + | 1350.84i | 0.904765 | + | 1.56710i | ||||
\(863\) | − | 220.000i | − | 0.254925i | −0.991843 | − | 0.127462i | \(-0.959317\pi\) | ||
0.991843 | − | 0.127462i | \(-0.0406832\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −168.855 | + | 97.4885i | −0.194983 | + | 0.112573i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −649.923 | + | 1125.70i | −0.748759 | + | 1.29689i | ||||
\(869\) | −112.570 | −0.129540 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 304.841i | 0.349990i | ||||||||
\(872\) | − | 176.000i | − | 0.201835i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1008.00 | + | 581.969i | −1.15332 | + | 0.665869i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 763.660 | 0.870764 | 0.435382 | − | 0.900246i | \(-0.356613\pi\) | ||||
0.435382 | + | 0.900246i | \(0.356613\pi\) | |||||||
\(878\) | 339.482 | + | 588.000i | 0.386654 | + | 0.669704i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1088.18 | −1.23516 | −0.617580 | − | 0.786508i | \(-0.711887\pi\) | ||||
−0.617580 | + | 0.786508i | \(0.711887\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1257.03i | − | 1.42359i | −0.702386 | − | 0.711796i | \(-0.747882\pi\) | ||
0.702386 | − | 0.711796i | \(-0.252118\pi\) | |||||||
\(884\) | 337.710 | − | 584.931i | 0.382025 | − | 0.661686i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 176.000 | + | 304.841i | 0.198646 | + | 0.344064i | ||||
\(887\) | − | 140.000i | − | 0.157835i | −0.996881 | − | 0.0789177i | \(-0.974854\pi\) | ||
0.996881 | − | 0.0789177i | \(-0.0251464\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −88.0000 | −0.0989876 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −552.435 | − | 318.948i | −0.619321 | − | 0.357565i | ||||
\(893\) | 83.1384 | 0.0931002 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 600.373 | + | 1039.88i | 0.670059 | + | 1.16058i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 812.404 | − | 469.042i | 0.904681 | − | 0.522318i | ||||
\(899\) | 324.962i | 0.361470i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 324.000 | 0.359600 | ||||||||
\(902\) | −304.841 | − | 528.000i | −0.337961 | − | 0.585366i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 692.820i | − | 0.766394i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 75.0467i | 0.0827416i | 0.999144 | + | 0.0413708i | \(0.0131725\pi\) | ||||
−0.999144 | + | 0.0413708i | \(0.986828\pi\) | |||||||
\(908\) | −443.405 | − | 256.000i | −0.488332 | − | 0.281938i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 649.923i | 0.713417i | 0.934216 | + | 0.356709i | \(0.116101\pi\) | ||||
−0.934216 | + | 0.356709i | \(0.883899\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −519.938 | −0.569484 | ||||||||
\(914\) | 619.135 | − | 357.458i | 0.677390 | − | 0.391092i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −268.000 | + | 464.190i | −0.292576 | + | 0.506757i | ||||
\(917\) | 1676.63 | 1.82838 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1101.58i | 1.19868i | 0.800496 | + | 0.599339i | \(0.204570\pi\) | ||||
−0.800496 | + | 0.599339i | \(0.795430\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −861.148 | + | 497.184i | −0.934000 | + | 0.539245i | ||||
\(923\) | − | 1584.00i | − | 1.71614i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 347.091 | + | 601.179i | 0.374828 | + | 0.649221i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 259.969 | + | 150.093i | 0.280139 | + | 0.161738i | ||||
\(929\) | −1219.51 | −1.31271 | −0.656355 | − | 0.754452i | \(-0.727903\pi\) | ||||
−0.656355 | + | 0.754452i | \(0.727903\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 810.600i | 0.870676i | ||||||||
\(932\) | 602.754 | − | 1044.00i | 0.646731 | − | 1.12017i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 520.000 | + | 900.666i | 0.556745 | + | 0.964311i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1754.79 | 1.87278 | 0.936389 | − | 0.350965i | \(-0.114146\pi\) | ||||
0.936389 | + | 0.350965i | \(0.114146\pi\) | |||||||
\(938\) | 304.841 | − | 176.000i | 0.324990 | − | 0.187633i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1285.17 | −1.36575 | −0.682877 | − | 0.730534i | \(-0.739271\pi\) | ||||
−0.682877 | + | 0.730534i | \(0.739271\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 525.327i | 0.557080i | ||||||||
\(944\) | 225.140 | − | 129.985i | 0.238496 | − | 0.137696i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1056.00 | + | 609.682i | −1.11628 | + | 0.644484i | ||||
\(947\) | 1480.00i | 1.56283i | 0.624012 | + | 0.781415i | \(0.285502\pi\) | ||||
−0.624012 | + | 0.781415i | \(0.714498\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −779.908 | −0.819231 | ||||||||
\(953\) | 1486.10 | 1.55939 | 0.779695 | − | 0.626159i | \(-0.215374\pi\) | ||||
0.779695 | + | 0.626159i | \(0.215374\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 562.850 | + | 324.962i | 0.588755 | + | 0.339918i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 812.404 | + | 1407.12i | 0.848021 | + | 1.46881i | ||||
\(959\) | − | 1982.27i | − | 2.06701i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −239.000 | −0.248699 | ||||||||
\(962\) | −1371.78 | + | 792.000i | −1.42597 | + | 0.823285i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 100.000 | − | 173.205i | 0.103734 | − | 0.179673i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1247.65i | − | 1.29023i | −0.764086 | − | 0.645114i | \(-0.776810\pi\) | ||
0.764086 | − | 0.645114i | \(-0.223190\pi\) | |||||||
\(968\) | 1144.00i | 1.18182i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 438.698i | 0.451800i | 0.974150 | + | 0.225900i | \(0.0725323\pi\) | ||||
−0.974150 | + | 0.225900i | \(0.927468\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −844.900 | −0.868345 | ||||||||
\(974\) | −290.806 | − | 503.690i | −0.298569 | − | 0.517136i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 464.000 | + | 803.672i | 0.475410 | + | 0.823434i | ||||
\(977\) | 869.490 | 0.889959 | 0.444979 | − | 0.895541i | \(-0.353211\pi\) | ||||
0.444979 | + | 0.895541i | \(0.353211\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1219.36i | 1.24552i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −406.202 | − | 703.562i | −0.413648 | − | 0.716459i | ||||
\(983\) | 860.000i | 0.874873i | 0.899249 | + | 0.437436i | \(0.144113\pi\) | ||||
−0.899249 | + | 0.437436i | \(0.855887\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −168.855 | + | 97.4885i | −0.171253 | + | 0.0988727i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1169.86 | − | 675.420i | −1.18407 | − | 0.683623i | ||||
\(989\) | 1050.65 | 1.06234 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 436.477i | 0.440441i | 0.975450 | + | 0.220220i | \(0.0706777\pi\) | ||||
−0.975450 | + | 0.220220i | \(0.929322\pi\) | |||||||
\(992\) | −554.256 | + | 960.000i | −0.558726 | + | 0.967742i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1584.00 | + | 914.523i | −1.59356 | + | 0.920043i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1056.12 | −1.05930 | −0.529651 | − | 0.848215i | \(-0.677677\pi\) | ||||
−0.529651 | + | 0.848215i | \(0.677677\pi\) | |||||||
\(998\) | −838.313 | − | 1452.00i | −0.839993 | − | 1.45491i | ||||
\(999\) | 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 | 900.3.c.s.451.5 | 8 | ||
3.2 | odd | 2 | inner | 900.3.c.s.451.3 | 8 | ||
4.3 | odd | 2 | inner | 900.3.c.s.451.8 | 8 | ||
5.2 | odd | 4 | 180.3.f.g.19.4 | yes | 4 | ||
5.3 | odd | 4 | 180.3.f.d.19.2 | yes | 4 | ||
5.4 | even | 2 | inner | 900.3.c.s.451.4 | 8 | ||
12.11 | even | 2 | inner | 900.3.c.s.451.2 | 8 | ||
15.2 | even | 4 | 180.3.f.d.19.1 | ✓ | 4 | ||
15.8 | even | 4 | 180.3.f.g.19.3 | yes | 4 | ||
15.14 | odd | 2 | inner | 900.3.c.s.451.6 | 8 | ||
20.3 | even | 4 | 180.3.f.g.19.2 | yes | 4 | ||
20.7 | even | 4 | 180.3.f.d.19.4 | yes | 4 | ||
20.19 | odd | 2 | inner | 900.3.c.s.451.1 | 8 | ||
60.23 | odd | 4 | 180.3.f.d.19.3 | yes | 4 | ||
60.47 | odd | 4 | 180.3.f.g.19.1 | yes | 4 | ||
60.59 | even | 2 | inner | 900.3.c.s.451.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.f.d.19.1 | ✓ | 4 | 15.2 | even | 4 | ||
180.3.f.d.19.2 | yes | 4 | 5.3 | odd | 4 | ||
180.3.f.d.19.3 | yes | 4 | 60.23 | odd | 4 | ||
180.3.f.d.19.4 | yes | 4 | 20.7 | even | 4 | ||
180.3.f.g.19.1 | yes | 4 | 60.47 | odd | 4 | ||
180.3.f.g.19.2 | yes | 4 | 20.3 | even | 4 | ||
180.3.f.g.19.3 | yes | 4 | 15.8 | even | 4 | ||
180.3.f.g.19.4 | yes | 4 | 5.2 | odd | 4 | ||
900.3.c.s.451.1 | 8 | 20.19 | odd | 2 | inner | ||
900.3.c.s.451.2 | 8 | 12.11 | even | 2 | inner | ||
900.3.c.s.451.3 | 8 | 3.2 | odd | 2 | inner | ||
900.3.c.s.451.4 | 8 | 5.4 | even | 2 | inner | ||
900.3.c.s.451.5 | 8 | 1.1 | even | 1 | trivial | ||
900.3.c.s.451.6 | 8 | 15.14 | odd | 2 | inner | ||
900.3.c.s.451.7 | 8 | 60.59 | even | 2 | inner | ||
900.3.c.s.451.8 | 8 | 4.3 | odd | 2 | inner |