Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.b (of order \(2\), degree \(1\), 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: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 54x^{6} + 889x^{4} + 4584x^{2} + 5776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 13^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.4 | ||
Root | \(-2.46610i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.4.b.h.337.5 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.46610i | − 0.518345i | −0.965831 | − | 0.259173i | \(-0.916550\pi\) | ||||
0.965831 | − | 0.259173i | \(-0.0834498\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 5.85055 | 0.731318 | ||||||||
\(5\) | 9.85055i | 0.881060i | 0.897738 | + | 0.440530i | \(0.145209\pi\) | ||||
−0.897738 | + | 0.440530i | \(0.854791\pi\) | |||||||
\(6\) | 4.39830i | 0.299267i | ||||||||
\(7\) | − 29.9396i | − 1.61659i | −0.588780 | − | 0.808293i | \(-0.700392\pi\) | ||||
0.588780 | − | 0.808293i | \(-0.299608\pi\) | |||||||
\(8\) | − 20.3063i | − 0.897421i | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 14.4419 | 0.456693 | ||||||||
\(11\) | − 46.9257i | − 1.28624i | −0.765765 | − | 0.643120i | \(-0.777640\pi\) | ||||
0.765765 | − | 0.643120i | \(-0.222360\pi\) | |||||||
\(12\) | −17.5516 | −0.422227 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −43.8945 | −0.837950 | ||||||||
\(15\) | − 29.5516i | − 0.508680i | ||||||||
\(16\) | 17.0333 | 0.266145 | ||||||||
\(17\) | 48.2616 | 0.688539 | 0.344270 | − | 0.938871i | \(-0.388127\pi\) | ||||
0.344270 | + | 0.938871i | \(0.388127\pi\) | |||||||
\(18\) | − 13.1949i | − 0.172782i | ||||||||
\(19\) | 120.300i | 1.45257i | 0.687396 | + | 0.726283i | \(0.258754\pi\) | ||||
−0.687396 | + | 0.726283i | \(0.741246\pi\) | |||||||
\(20\) | 57.6311i | 0.644335i | ||||||||
\(21\) | 89.8188i | 0.933337i | ||||||||
\(22\) | −68.7979 | −0.666717 | ||||||||
\(23\) | −130.697 | −1.18488 | −0.592440 | − | 0.805615i | \(-0.701835\pi\) | ||||
−0.592440 | + | 0.805615i | \(0.701835\pi\) | |||||||
\(24\) | 60.9189i | 0.518126i | ||||||||
\(25\) | 27.9667 | 0.223734 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | − 175.163i | − 1.18224i | ||||||||
\(29\) | −194.946 | −1.24829 | −0.624147 | − | 0.781307i | \(-0.714553\pi\) | ||||
−0.624147 | + | 0.781307i | \(0.714553\pi\) | |||||||
\(30\) | −43.3257 | −0.263672 | ||||||||
\(31\) | − 32.0123i | − 0.185470i | −0.995691 | − | 0.0927351i | \(-0.970439\pi\) | ||||
0.995691 | − | 0.0927351i | \(-0.0295610\pi\) | |||||||
\(32\) | − 187.423i | − 1.03538i | ||||||||
\(33\) | 140.777i | 0.742611i | ||||||||
\(34\) | − 70.7565i | − 0.356901i | ||||||||
\(35\) | 294.921 | 1.42431 | ||||||||
\(36\) | 52.6549 | 0.243773 | ||||||||
\(37\) | 32.4250i | 0.144071i | 0.997402 | + | 0.0720355i | \(0.0229495\pi\) | ||||
−0.997402 | + | 0.0720355i | \(0.977051\pi\) | |||||||
\(38\) | 176.372 | 0.752931 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 200.028 | 0.790681 | ||||||||
\(41\) | − 241.825i | − 0.921140i | −0.887623 | − | 0.460570i | \(-0.847645\pi\) | ||||
0.887623 | − | 0.460570i | \(-0.152355\pi\) | |||||||
\(42\) | 131.684 | 0.483791 | ||||||||
\(43\) | −96.4087 | −0.341911 | −0.170956 | − | 0.985279i | \(-0.554686\pi\) | ||||
−0.170956 | + | 0.985279i | \(0.554686\pi\) | |||||||
\(44\) | − 274.541i | − 0.940651i | ||||||||
\(45\) | 88.6549i | 0.293687i | ||||||||
\(46\) | 191.615i | 0.614177i | ||||||||
\(47\) | − 539.015i | − 1.67284i | −0.548090 | − | 0.836419i | \(-0.684645\pi\) | ||||
0.548090 | − | 0.836419i | \(-0.315355\pi\) | |||||||
\(48\) | −51.0998 | −0.153659 | ||||||||
\(49\) | −553.380 | −1.61335 | ||||||||
\(50\) | − 41.0021i | − 0.115971i | ||||||||
\(51\) | −144.785 | −0.397528 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −152.277 | −0.394657 | −0.197328 | − | 0.980337i | \(-0.563226\pi\) | ||||
−0.197328 | + | 0.980337i | \(0.563226\pi\) | |||||||
\(54\) | 39.5847i | 0.0997556i | ||||||||
\(55\) | 462.244 | 1.13325 | ||||||||
\(56\) | −607.963 | −1.45076 | ||||||||
\(57\) | − 360.901i | − 0.838640i | ||||||||
\(58\) | 285.810i | 0.647047i | ||||||||
\(59\) | − 327.792i | − 0.723304i | −0.932313 | − | 0.361652i | \(-0.882213\pi\) | ||||
0.932313 | − | 0.361652i | \(-0.117787\pi\) | |||||||
\(60\) | − 172.893i | − 0.372007i | ||||||||
\(61\) | −98.4180 | −0.206576 | −0.103288 | − | 0.994651i | \(-0.532936\pi\) | ||||
−0.103288 | + | 0.994651i | \(0.532936\pi\) | |||||||
\(62\) | −46.9332 | −0.0961376 | ||||||||
\(63\) | − 269.456i | − 0.538862i | ||||||||
\(64\) | −138.515 | −0.270537 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 206.394 | 0.384929 | ||||||||
\(67\) | − 441.151i | − 0.804405i | −0.915551 | − | 0.402202i | \(-0.868245\pi\) | ||||
0.915551 | − | 0.402202i | \(-0.131755\pi\) | |||||||
\(68\) | 282.357 | 0.503541 | ||||||||
\(69\) | 392.091 | 0.684090 | ||||||||
\(70\) | − 432.385i | − 0.738284i | ||||||||
\(71\) | 345.049i | 0.576757i | 0.957516 | + | 0.288379i | \(0.0931161\pi\) | ||||
−0.957516 | + | 0.288379i | \(0.906884\pi\) | |||||||
\(72\) | − 182.757i | − 0.299140i | ||||||||
\(73\) | − 773.839i | − 1.24070i | −0.784326 | − | 0.620349i | \(-0.786991\pi\) | ||||
0.784326 | − | 0.620349i | \(-0.213009\pi\) | |||||||
\(74\) | 47.5383 | 0.0746785 | ||||||||
\(75\) | −83.9002 | −0.129173 | ||||||||
\(76\) | 703.822i | 1.06229i | ||||||||
\(77\) | −1404.94 | −2.07932 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −150.332 | −0.214097 | −0.107049 | − | 0.994254i | \(-0.534140\pi\) | ||||
−0.107049 | + | 0.994254i | \(0.534140\pi\) | |||||||
\(80\) | 167.787i | 0.234489i | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −354.540 | −0.477469 | ||||||||
\(83\) | 337.966i | 0.446947i | 0.974710 | + | 0.223473i | \(0.0717396\pi\) | ||||
−0.974710 | + | 0.223473i | \(0.928260\pi\) | |||||||
\(84\) | 525.489i | 0.682566i | ||||||||
\(85\) | 475.403i | 0.606644i | ||||||||
\(86\) | 141.345i | 0.177228i | ||||||||
\(87\) | 584.837 | 0.720703 | ||||||||
\(88\) | −952.889 | −1.15430 | ||||||||
\(89\) | − 169.913i | − 0.202368i | −0.994868 | − | 0.101184i | \(-0.967737\pi\) | ||||
0.994868 | − | 0.101184i | \(-0.0322631\pi\) | |||||||
\(90\) | 129.977 | 0.152231 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −764.649 | −0.866524 | ||||||||
\(93\) | 96.0368i | 0.107081i | ||||||||
\(94\) | −790.250 | −0.867108 | ||||||||
\(95\) | −1185.02 | −1.27980 | ||||||||
\(96\) | 562.269i | 0.597774i | ||||||||
\(97\) | 214.201i | 0.224215i | 0.993696 | + | 0.112107i | \(0.0357601\pi\) | ||||
−0.993696 | + | 0.112107i | \(0.964240\pi\) | |||||||
\(98\) | 811.311i | 0.836273i | ||||||||
\(99\) | − 422.332i | − 0.428747i | ||||||||
\(100\) | 163.621 | 0.163621 | ||||||||
\(101\) | −1595.11 | −1.57148 | −0.785741 | − | 0.618556i | \(-0.787718\pi\) | ||||
−0.785741 | + | 0.618556i | \(0.787718\pi\) | |||||||
\(102\) | 212.269i | 0.206057i | ||||||||
\(103\) | 1570.30 | 1.50219 | 0.751096 | − | 0.660193i | \(-0.229525\pi\) | ||||
0.751096 | + | 0.660193i | \(0.229525\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −884.764 | −0.822325 | ||||||||
\(106\) | 223.253i | 0.204568i | ||||||||
\(107\) | −6.73302 | −0.00608323 | −0.00304161 | − | 0.999995i | \(-0.500968\pi\) | ||||
−0.00304161 | + | 0.999995i | \(0.500968\pi\) | |||||||
\(108\) | −157.965 | −0.140742 | ||||||||
\(109\) | − 542.422i | − 0.476648i | −0.971186 | − | 0.238324i | \(-0.923402\pi\) | ||||
0.971186 | − | 0.238324i | \(-0.0765979\pi\) | |||||||
\(110\) | − 677.697i | − 0.587417i | ||||||||
\(111\) | − 97.2749i | − 0.0831795i | ||||||||
\(112\) | − 509.969i | − 0.430246i | ||||||||
\(113\) | −1442.82 | −1.20114 | −0.600572 | − | 0.799571i | \(-0.705060\pi\) | ||||
−0.600572 | + | 0.799571i | \(0.705060\pi\) | |||||||
\(114\) | −529.117 | −0.434705 | ||||||||
\(115\) | − 1287.44i | − 1.04395i | ||||||||
\(116\) | −1140.54 | −0.912900 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −480.577 | −0.374921 | ||||||||
\(119\) | − 1444.93i | − 1.11308i | ||||||||
\(120\) | −600.085 | −0.456500 | ||||||||
\(121\) | −871.025 | −0.654414 | ||||||||
\(122\) | 144.291i | 0.107078i | ||||||||
\(123\) | 725.476i | 0.531821i | ||||||||
\(124\) | − 187.289i | − 0.135638i | ||||||||
\(125\) | 1506.81i | 1.07818i | ||||||||
\(126\) | −395.051 | −0.279317 | ||||||||
\(127\) | 2492.84 | 1.74176 | 0.870881 | − | 0.491494i | \(-0.163549\pi\) | ||||
0.870881 | + | 0.491494i | \(0.163549\pi\) | |||||||
\(128\) | − 1296.31i | − 0.895144i | ||||||||
\(129\) | 289.226 | 0.197403 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 744.561 | 0.496585 | 0.248292 | − | 0.968685i | \(-0.420131\pi\) | ||||
0.248292 | + | 0.968685i | \(0.420131\pi\) | |||||||
\(132\) | 823.624i | 0.543085i | ||||||||
\(133\) | 3601.74 | 2.34820 | ||||||||
\(134\) | −646.772 | −0.416959 | ||||||||
\(135\) | − 265.965i | − 0.169560i | ||||||||
\(136\) | − 980.016i | − 0.617909i | ||||||||
\(137\) | 222.167i | 0.138547i | 0.997598 | + | 0.0692736i | \(0.0220682\pi\) | ||||
−0.997598 | + | 0.0692736i | \(0.977932\pi\) | |||||||
\(138\) | − 574.846i | − 0.354595i | ||||||||
\(139\) | −777.145 | −0.474220 | −0.237110 | − | 0.971483i | \(-0.576200\pi\) | ||||
−0.237110 | + | 0.971483i | \(0.576200\pi\) | |||||||
\(140\) | 1725.45 | 1.04162 | ||||||||
\(141\) | 1617.04i | 0.965814i | ||||||||
\(142\) | 505.876 | 0.298959 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 153.299 | 0.0887149 | ||||||||
\(145\) | − 1920.32i | − 1.09982i | ||||||||
\(146\) | −1134.53 | −0.643110 | ||||||||
\(147\) | 1660.14 | 0.931469 | ||||||||
\(148\) | 189.704i | 0.105362i | ||||||||
\(149\) | 1778.29i | 0.977742i | 0.872356 | + | 0.488871i | \(0.162591\pi\) | ||||
−0.872356 | + | 0.488871i | \(0.837409\pi\) | |||||||
\(150\) | 123.006i | 0.0669561i | ||||||||
\(151\) | − 1166.00i | − 0.628394i | −0.949358 | − | 0.314197i | \(-0.898265\pi\) | ||||
0.949358 | − | 0.314197i | \(-0.101735\pi\) | |||||||
\(152\) | 2442.85 | 1.30356 | ||||||||
\(153\) | 434.355 | 0.229513 | ||||||||
\(154\) | 2059.78i | 1.07780i | ||||||||
\(155\) | 315.338 | 0.163410 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 517.628 | 0.263129 | 0.131564 | − | 0.991308i | \(-0.458000\pi\) | ||||
0.131564 | + | 0.991308i | \(0.458000\pi\) | |||||||
\(158\) | 220.402i | 0.110976i | ||||||||
\(159\) | 456.830 | 0.227855 | ||||||||
\(160\) | 1846.22 | 0.912227 | ||||||||
\(161\) | 3913.02i | 1.91546i | ||||||||
\(162\) | − 118.754i | − 0.0575939i | ||||||||
\(163\) | − 610.188i | − 0.293212i | −0.989195 | − | 0.146606i | \(-0.953165\pi\) | ||||
0.989195 | − | 0.146606i | \(-0.0468350\pi\) | |||||||
\(164\) | − 1414.81i | − 0.673647i | ||||||||
\(165\) | −1386.73 | −0.654285 | ||||||||
\(166\) | 495.493 | 0.231673 | ||||||||
\(167\) | − 2983.01i | − 1.38223i | −0.722745 | − | 0.691115i | \(-0.757120\pi\) | ||||
0.722745 | − | 0.691115i | \(-0.242880\pi\) | |||||||
\(168\) | 1823.89 | 0.837596 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 696.990 | 0.314451 | ||||||||
\(171\) | 1082.70i | 0.484189i | ||||||||
\(172\) | −564.044 | −0.250046 | ||||||||
\(173\) | −978.212 | −0.429896 | −0.214948 | − | 0.976625i | \(-0.568958\pi\) | ||||
−0.214948 | + | 0.976625i | \(0.568958\pi\) | |||||||
\(174\) | − 857.431i | − 0.373573i | ||||||||
\(175\) | − 837.313i | − 0.361685i | ||||||||
\(176\) | − 799.298i | − 0.342326i | ||||||||
\(177\) | 983.377i | 0.417599i | ||||||||
\(178\) | −249.110 | −0.104897 | ||||||||
\(179\) | −1852.94 | −0.773717 | −0.386858 | − | 0.922139i | \(-0.626440\pi\) | ||||
−0.386858 | + | 0.922139i | \(0.626440\pi\) | |||||||
\(180\) | 518.680i | 0.214778i | ||||||||
\(181\) | −852.777 | −0.350201 | −0.175101 | − | 0.984551i | \(-0.556025\pi\) | ||||
−0.175101 | + | 0.984551i | \(0.556025\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 295.254 | 0.119267 | ||||||||
\(184\) | 2653.98i | 1.06334i | ||||||||
\(185\) | −319.403 | −0.126935 | ||||||||
\(186\) | 140.800 | 0.0555050 | ||||||||
\(187\) | − 2264.71i | − 0.885627i | ||||||||
\(188\) | − 3153.53i | − 1.22338i | ||||||||
\(189\) | 808.369i | 0.311112i | ||||||||
\(190\) | 1737.36i | 0.663377i | ||||||||
\(191\) | 4441.29 | 1.68252 | 0.841258 | − | 0.540633i | \(-0.181815\pi\) | ||||
0.841258 | + | 0.540633i | \(0.181815\pi\) | |||||||
\(192\) | 415.545 | 0.156195 | ||||||||
\(193\) | 2482.43i | 0.925851i | 0.886397 | + | 0.462925i | \(0.153200\pi\) | ||||
−0.886397 | + | 0.462925i | \(0.846800\pi\) | |||||||
\(194\) | 314.041 | 0.116221 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3237.57 | −1.17987 | ||||||||
\(197\) | 1260.23i | 0.455775i | 0.973687 | + | 0.227888i | \(0.0731819\pi\) | ||||
−0.973687 | + | 0.227888i | \(0.926818\pi\) | |||||||
\(198\) | −619.181 | −0.222239 | ||||||||
\(199\) | 5520.96 | 1.96669 | 0.983344 | − | 0.181756i | \(-0.0581782\pi\) | ||||
0.983344 | + | 0.181756i | \(0.0581782\pi\) | |||||||
\(200\) | − 567.901i | − 0.200783i | ||||||||
\(201\) | 1323.45i | 0.464423i | ||||||||
\(202\) | 2338.60i | 0.814570i | ||||||||
\(203\) | 5836.60i | 2.01798i | ||||||||
\(204\) | −847.071 | −0.290720 | ||||||||
\(205\) | 2382.11 | 0.811580 | ||||||||
\(206\) | − 2302.21i | − 0.778654i | ||||||||
\(207\) | −1176.27 | −0.394960 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5645.18 | 1.86835 | ||||||||
\(210\) | 1297.15i | 0.426248i | ||||||||
\(211\) | −4527.79 | −1.47728 | −0.738640 | − | 0.674100i | \(-0.764532\pi\) | ||||
−0.738640 | + | 0.674100i | \(0.764532\pi\) | |||||||
\(212\) | −890.901 | −0.288620 | ||||||||
\(213\) | − 1035.15i | − 0.332991i | ||||||||
\(214\) | 9.87129i | 0.00315321i | ||||||||
\(215\) | − 949.679i | − 0.301244i | ||||||||
\(216\) | 548.270i | 0.172709i | ||||||||
\(217\) | −958.435 | −0.299829 | ||||||||
\(218\) | −795.245 | −0.247068 | ||||||||
\(219\) | 2321.52i | 0.716318i | ||||||||
\(220\) | 2704.38 | 0.828770 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −142.615 | −0.0431157 | ||||||||
\(223\) | 4481.17i | 1.34566i | 0.739798 | + | 0.672829i | \(0.234921\pi\) | ||||
−0.739798 | + | 0.672829i | \(0.765079\pi\) | |||||||
\(224\) | −5611.37 | −1.67377 | ||||||||
\(225\) | 251.701 | 0.0745780 | ||||||||
\(226\) | 2115.32i | 0.622607i | ||||||||
\(227\) | − 5759.75i | − 1.68409i | −0.539408 | − | 0.842044i | \(-0.681352\pi\) | ||||
0.539408 | − | 0.842044i | \(-0.318648\pi\) | |||||||
\(228\) | − 2111.47i | − 0.613312i | ||||||||
\(229\) | 4635.08i | 1.33753i | 0.743473 | + | 0.668766i | \(0.233177\pi\) | ||||
−0.743473 | + | 0.668766i | \(0.766823\pi\) | |||||||
\(230\) | −1887.51 | −0.541126 | ||||||||
\(231\) | 4214.81 | 1.20050 | ||||||||
\(232\) | 3958.63i | 1.12024i | ||||||||
\(233\) | −5886.33 | −1.65505 | −0.827524 | − | 0.561431i | \(-0.810251\pi\) | ||||
−0.827524 | + | 0.561431i | \(0.810251\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5309.59 | 1.47387 | ||||||||
\(236\) | − 1917.76i | − 0.528965i | ||||||||
\(237\) | 450.996 | 0.123609 | ||||||||
\(238\) | −2118.42 | −0.576961 | ||||||||
\(239\) | 2135.84i | 0.578060i | 0.957320 | + | 0.289030i | \(0.0933327\pi\) | ||||
−0.957320 | + | 0.289030i | \(0.906667\pi\) | |||||||
\(240\) | − 503.361i | − 0.135382i | ||||||||
\(241\) | − 4692.92i | − 1.25435i | −0.778880 | − | 0.627173i | \(-0.784212\pi\) | ||||
0.778880 | − | 0.627173i | \(-0.215788\pi\) | |||||||
\(242\) | 1277.01i | 0.339212i | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −575.799 | −0.151073 | ||||||||
\(245\) | − 5451.09i | − 1.42146i | ||||||||
\(246\) | 1063.62 | 0.275667 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −650.051 | −0.166445 | ||||||||
\(249\) | − 1013.90i | − 0.258045i | ||||||||
\(250\) | 2209.13 | 0.558871 | ||||||||
\(251\) | 3902.88 | 0.981464 | 0.490732 | − | 0.871310i | \(-0.336729\pi\) | ||||
0.490732 | + | 0.871310i | \(0.336729\pi\) | |||||||
\(252\) | − 1576.47i | − 0.394080i | ||||||||
\(253\) | 6133.06i | 1.52404i | ||||||||
\(254\) | − 3654.76i | − 0.902834i | ||||||||
\(255\) | − 1426.21i | − 0.350246i | ||||||||
\(256\) | −3008.64 | −0.734531 | ||||||||
\(257\) | 4130.83 | 1.00262 | 0.501312 | − | 0.865267i | \(-0.332851\pi\) | ||||
0.501312 | + | 0.865267i | \(0.332851\pi\) | |||||||
\(258\) | − 424.035i | − 0.102323i | ||||||||
\(259\) | 970.790 | 0.232903 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1754.51 | −0.416098 | ||||||||
\(262\) | − 1091.60i | − 0.257402i | ||||||||
\(263\) | 6352.17 | 1.48932 | 0.744661 | − | 0.667443i | \(-0.232611\pi\) | ||||
0.744661 | + | 0.667443i | \(0.232611\pi\) | |||||||
\(264\) | 2858.67 | 0.666435 | ||||||||
\(265\) | − 1500.01i | − 0.347716i | ||||||||
\(266\) | − 5280.52i | − 1.21718i | ||||||||
\(267\) | 509.740i | 0.116837i | ||||||||
\(268\) | − 2580.97i | − 0.588276i | ||||||||
\(269\) | 181.524 | 0.0411439 | 0.0205719 | − | 0.999788i | \(-0.493451\pi\) | ||||
0.0205719 | + | 0.999788i | \(0.493451\pi\) | |||||||
\(270\) | −389.931 | −0.0878906 | ||||||||
\(271\) | − 3460.35i | − 0.775651i | −0.921733 | − | 0.387825i | \(-0.873226\pi\) | ||||
0.921733 | − | 0.387825i | \(-0.126774\pi\) | |||||||
\(272\) | 822.053 | 0.183251 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 325.719 | 0.0718153 | ||||||||
\(275\) | − 1312.36i | − 0.287776i | ||||||||
\(276\) | 2293.95 | 0.500288 | ||||||||
\(277\) | 6437.94 | 1.39646 | 0.698228 | − | 0.715876i | \(-0.253972\pi\) | ||||
0.698228 | + | 0.715876i | \(0.253972\pi\) | |||||||
\(278\) | 1139.37i | 0.245810i | ||||||||
\(279\) | − 288.110i | − 0.0618234i | ||||||||
\(280\) | − 5988.77i | − 1.27820i | ||||||||
\(281\) | 2974.26i | 0.631421i | 0.948855 | + | 0.315711i | \(0.102243\pi\) | ||||
−0.948855 | + | 0.315711i | \(0.897757\pi\) | |||||||
\(282\) | 2370.75 | 0.500625 | ||||||||
\(283\) | −3035.72 | −0.637649 | −0.318825 | − | 0.947814i | \(-0.603288\pi\) | ||||
−0.318825 | + | 0.947814i | \(0.603288\pi\) | |||||||
\(284\) | 2018.72i | 0.421793i | ||||||||
\(285\) | 3555.07 | 0.738891 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7240.15 | −1.48910 | ||||||||
\(288\) | − 1686.81i | − 0.345125i | ||||||||
\(289\) | −2583.81 | −0.525914 | ||||||||
\(290\) | −2815.39 | −0.570087 | ||||||||
\(291\) | − 642.604i | − 0.129451i | ||||||||
\(292\) | − 4527.38i | − 0.907346i | ||||||||
\(293\) | 1955.74i | 0.389952i | 0.980808 | + | 0.194976i | \(0.0624628\pi\) | ||||
−0.980808 | + | 0.194976i | \(0.937537\pi\) | |||||||
\(294\) | − 2433.93i | − 0.482823i | ||||||||
\(295\) | 3228.93 | 0.637274 | ||||||||
\(296\) | 658.431 | 0.129292 | ||||||||
\(297\) | 1267.00i | 0.247537i | ||||||||
\(298\) | 2607.16 | 0.506808 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −490.862 | −0.0944665 | ||||||||
\(301\) | 2886.44i | 0.552729i | ||||||||
\(302\) | −1709.47 | −0.325725 | ||||||||
\(303\) | 4785.34 | 0.907295 | ||||||||
\(304\) | 2049.10i | 0.386593i | ||||||||
\(305\) | − 969.471i | − 0.182006i | ||||||||
\(306\) | − 636.808i | − 0.118967i | ||||||||
\(307\) | 1027.56i | 0.191029i | 0.995428 | + | 0.0955147i | \(0.0304497\pi\) | ||||
−0.995428 | + | 0.0955147i | \(0.969550\pi\) | |||||||
\(308\) | −8219.66 | −1.52064 | ||||||||
\(309\) | −4710.89 | −0.867291 | ||||||||
\(310\) | − 462.318i | − 0.0847029i | ||||||||
\(311\) | −3405.61 | −0.620947 | −0.310474 | − | 0.950582i | \(-0.600488\pi\) | ||||
−0.310474 | + | 0.950582i | \(0.600488\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4813.20 | 0.869196 | 0.434598 | − | 0.900625i | \(-0.356890\pi\) | ||||
0.434598 | + | 0.900625i | \(0.356890\pi\) | |||||||
\(314\) | − 758.895i | − 0.136391i | ||||||||
\(315\) | 2654.29 | 0.474770 | ||||||||
\(316\) | −879.525 | −0.156573 | ||||||||
\(317\) | 1141.33i | 0.202219i | 0.994875 | + | 0.101110i | \(0.0322393\pi\) | ||||
−0.994875 | + | 0.101110i | \(0.967761\pi\) | |||||||
\(318\) | − 669.759i | − 0.118108i | ||||||||
\(319\) | 9147.98i | 1.60561i | ||||||||
\(320\) | − 1364.45i | − 0.238359i | ||||||||
\(321\) | 20.1991 | 0.00351215 | ||||||||
\(322\) | 5736.88 | 0.992870 | ||||||||
\(323\) | 5805.88i | 1.00015i | ||||||||
\(324\) | 473.894 | 0.0812576 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −894.597 | −0.151985 | ||||||||
\(327\) | 1627.27i | 0.275193i | ||||||||
\(328\) | −4910.58 | −0.826650 | ||||||||
\(329\) | −16137.9 | −2.70429 | ||||||||
\(330\) | 2033.09i | 0.339145i | ||||||||
\(331\) | 7652.57i | 1.27076i | 0.772198 | + | 0.635382i | \(0.219157\pi\) | ||||
−0.772198 | + | 0.635382i | \(0.780843\pi\) | |||||||
\(332\) | 1977.29i | 0.326860i | ||||||||
\(333\) | 291.825i | 0.0480237i | ||||||||
\(334\) | −4373.40 | −0.716472 | ||||||||
\(335\) | 4345.57 | 0.708729 | ||||||||
\(336\) | 1529.91i | 0.248403i | ||||||||
\(337\) | 2503.69 | 0.404702 | 0.202351 | − | 0.979313i | \(-0.435142\pi\) | ||||
0.202351 | + | 0.979313i | \(0.435142\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4328.47 | 0.693481 | ||||||||
\(340\) | 2781.37i | 0.443650i | ||||||||
\(341\) | −1502.20 | −0.238559 | ||||||||
\(342\) | 1587.35 | 0.250977 | ||||||||
\(343\) | 6298.69i | 0.991537i | ||||||||
\(344\) | 1957.71i | 0.306838i | ||||||||
\(345\) | 3862.31i | 0.602724i | ||||||||
\(346\) | 1434.16i | 0.222835i | ||||||||
\(347\) | 4496.12 | 0.695574 | 0.347787 | − | 0.937574i | \(-0.386933\pi\) | ||||
0.347787 | + | 0.937574i | \(0.386933\pi\) | |||||||
\(348\) | 3421.62 | 0.527063 | ||||||||
\(349\) | − 3577.61i | − 0.548726i | −0.961626 | − | 0.274363i | \(-0.911533\pi\) | ||||
0.961626 | − | 0.274363i | \(-0.0884670\pi\) | |||||||
\(350\) | −1227.59 | −0.187478 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8794.96 | −1.33174 | ||||||||
\(353\) | − 8045.17i | − 1.21303i | −0.795070 | − | 0.606517i | \(-0.792566\pi\) | ||||
0.795070 | − | 0.606517i | \(-0.207434\pi\) | |||||||
\(354\) | 1441.73 | 0.216461 | ||||||||
\(355\) | −3398.92 | −0.508157 | ||||||||
\(356\) | − 994.086i | − 0.147996i | ||||||||
\(357\) | 4334.80i | 0.642639i | ||||||||
\(358\) | 2716.60i | 0.401052i | ||||||||
\(359\) | 2172.90i | 0.319447i | 0.987162 | + | 0.159724i | \(0.0510603\pi\) | ||||
−0.987162 | + | 0.159724i | \(0.948940\pi\) | |||||||
\(360\) | 1800.25 | 0.263560 | ||||||||
\(361\) | −7613.14 | −1.10995 | ||||||||
\(362\) | 1250.26i | 0.181525i | ||||||||
\(363\) | 2613.08 | 0.377826 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7622.74 | 1.09313 | ||||||||
\(366\) | − 432.872i | − 0.0618213i | ||||||||
\(367\) | 7662.76 | 1.08990 | 0.544949 | − | 0.838469i | \(-0.316549\pi\) | ||||
0.544949 | + | 0.838469i | \(0.316549\pi\) | |||||||
\(368\) | −2226.20 | −0.315349 | ||||||||
\(369\) | − 2176.43i | − 0.307047i | ||||||||
\(370\) | 468.278i | 0.0657962i | ||||||||
\(371\) | 4559.10i | 0.637996i | ||||||||
\(372\) | 561.868i | 0.0783105i | ||||||||
\(373\) | 10542.5 | 1.46346 | 0.731732 | − | 0.681593i | \(-0.238712\pi\) | ||||
0.731732 | + | 0.681593i | \(0.238712\pi\) | |||||||
\(374\) | −3320.30 | −0.459060 | ||||||||
\(375\) | − 4520.42i | − 0.622489i | ||||||||
\(376\) | −10945.4 | −1.50124 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1185.15 | 0.161264 | ||||||||
\(379\) | 5475.54i | 0.742110i | 0.928611 | + | 0.371055i | \(0.121004\pi\) | ||||
−0.928611 | + | 0.371055i | \(0.878996\pi\) | |||||||
\(380\) | −6933.03 | −0.935939 | ||||||||
\(381\) | −7478.52 | −1.00561 | ||||||||
\(382\) | − 6511.39i | − 0.872124i | ||||||||
\(383\) | 808.085i | 0.107810i | 0.998546 | + | 0.0539050i | \(0.0171668\pi\) | ||||
−0.998546 | + | 0.0539050i | \(0.982833\pi\) | |||||||
\(384\) | 3888.92i | 0.516811i | ||||||||
\(385\) | − 13839.4i | − 1.83200i | ||||||||
\(386\) | 3639.49 | 0.479910 | ||||||||
\(387\) | −867.679 | −0.113970 | ||||||||
\(388\) | 1253.19i | 0.163972i | ||||||||
\(389\) | 7060.26 | 0.920230 | 0.460115 | − | 0.887859i | \(-0.347808\pi\) | ||||
0.460115 | + | 0.887859i | \(0.347808\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6307.65 | −0.815836 | ||||||||
\(392\) | 11237.1i | 1.44786i | ||||||||
\(393\) | −2233.68 | −0.286703 | ||||||||
\(394\) | 1847.63 | 0.236249 | ||||||||
\(395\) | − 1480.85i | − 0.188633i | ||||||||
\(396\) | − 2470.87i | − 0.313550i | ||||||||
\(397\) | 1419.89i | 0.179502i | 0.995964 | + | 0.0897511i | \(0.0286072\pi\) | ||||
−0.995964 | + | 0.0897511i | \(0.971393\pi\) | |||||||
\(398\) | − 8094.29i | − 1.01942i | ||||||||
\(399\) | −10805.2 | −1.35573 | ||||||||
\(400\) | 476.365 | 0.0595456 | ||||||||
\(401\) | − 10670.7i | − 1.32886i | −0.747353 | − | 0.664428i | \(-0.768675\pi\) | ||||
0.747353 | − | 0.664428i | \(-0.231325\pi\) | |||||||
\(402\) | 1940.31 | 0.240732 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −9332.28 | −1.14925 | ||||||||
\(405\) | 797.894i | 0.0978955i | ||||||||
\(406\) | 8557.05 | 1.04601 | ||||||||
\(407\) | 1521.56 | 0.185310 | ||||||||
\(408\) | 2940.05i | 0.356750i | ||||||||
\(409\) | 6351.56i | 0.767883i | 0.923357 | + | 0.383942i | \(0.125434\pi\) | ||||
−0.923357 | + | 0.383942i | \(0.874566\pi\) | |||||||
\(410\) | − 3492.42i | − 0.420678i | ||||||||
\(411\) | − 666.500i | − 0.0799903i | ||||||||
\(412\) | 9187.09 | 1.09858 | ||||||||
\(413\) | −9813.97 | −1.16928 | ||||||||
\(414\) | 1724.54i | 0.204726i | ||||||||
\(415\) | −3329.15 | −0.393787 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2331.44 | 0.273791 | ||||||||
\(418\) | − 8276.40i | − 0.968450i | ||||||||
\(419\) | 5617.87 | 0.655015 | 0.327507 | − | 0.944849i | \(-0.393791\pi\) | ||||
0.327507 | + | 0.944849i | \(0.393791\pi\) | |||||||
\(420\) | −5176.35 | −0.601382 | ||||||||
\(421\) | − 1518.29i | − 0.175765i | −0.996131 | − | 0.0878825i | \(-0.971990\pi\) | ||||
0.996131 | − | 0.0878825i | \(-0.0280100\pi\) | |||||||
\(422\) | 6638.20i | 0.765741i | ||||||||
\(423\) | − 4851.13i | − 0.557613i | ||||||||
\(424\) | 3092.17i | 0.354173i | ||||||||
\(425\) | 1349.72 | 0.154050 | ||||||||
\(426\) | −1517.63 | −0.172604 | ||||||||
\(427\) | 2946.60i | 0.333948i | ||||||||
\(428\) | −39.3918 | −0.00444878 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1392.33 | −0.156149 | ||||||||
\(431\) | − 4970.13i | − 0.555459i | −0.960659 | − | 0.277730i | \(-0.910418\pi\) | ||||
0.960659 | − | 0.277730i | \(-0.0895819\pi\) | |||||||
\(432\) | −459.898 | −0.0512196 | ||||||||
\(433\) | 3298.71 | 0.366111 | 0.183055 | − | 0.983103i | \(-0.441401\pi\) | ||||
0.183055 | + | 0.983103i | \(0.441401\pi\) | |||||||
\(434\) | 1405.16i | 0.155415i | ||||||||
\(435\) | 5760.97i | 0.634982i | ||||||||
\(436\) | − 3173.46i | − 0.348581i | ||||||||
\(437\) | − 15722.9i | − 1.72112i | ||||||||
\(438\) | 3403.58 | 0.371300 | ||||||||
\(439\) | 6048.47 | 0.657581 | 0.328790 | − | 0.944403i | \(-0.393359\pi\) | ||||
0.328790 | + | 0.944403i | \(0.393359\pi\) | |||||||
\(440\) | − 9386.47i | − 1.01701i | ||||||||
\(441\) | −4980.42 | −0.537784 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6822.62 | 0.731722 | 0.365861 | − | 0.930670i | \(-0.380775\pi\) | ||||
0.365861 | + | 0.930670i | \(0.380775\pi\) | |||||||
\(444\) | − 569.111i | − 0.0608307i | ||||||||
\(445\) | 1673.74 | 0.178299 | ||||||||
\(446\) | 6569.86 | 0.697515 | ||||||||
\(447\) | − 5334.88i | − 0.564500i | ||||||||
\(448\) | 4147.09i | 0.437347i | ||||||||
\(449\) | − 410.410i | − 0.0431369i | −0.999767 | − | 0.0215684i | \(-0.993134\pi\) | ||||
0.999767 | − | 0.0215684i | \(-0.00686598\pi\) | |||||||
\(450\) | − 369.019i | − 0.0386571i | ||||||||
\(451\) | −11347.8 | −1.18481 | ||||||||
\(452\) | −8441.30 | −0.878419 | ||||||||
\(453\) | 3497.99i | 0.362804i | ||||||||
\(454\) | −8444.38 | −0.872939 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7328.56 | −0.752612 | ||||||||
\(457\) | − 16642.8i | − 1.70354i | −0.523915 | − | 0.851771i | \(-0.675529\pi\) | ||||
0.523915 | − | 0.851771i | \(-0.324471\pi\) | |||||||
\(458\) | 6795.50 | 0.693303 | ||||||||
\(459\) | −1303.06 | −0.132509 | ||||||||
\(460\) | − 7532.21i | − 0.763459i | ||||||||
\(461\) | − 11729.7i | − 1.18505i | −0.805553 | − | 0.592523i | \(-0.798132\pi\) | ||||
0.805553 | − | 0.592523i | \(-0.201868\pi\) | |||||||
\(462\) | − 6179.35i | − 0.622271i | ||||||||
\(463\) | 3564.93i | 0.357832i | 0.983864 | + | 0.178916i | \(0.0572591\pi\) | ||||
−0.983864 | + | 0.178916i | \(0.942741\pi\) | |||||||
\(464\) | −3320.56 | −0.332227 | ||||||||
\(465\) | −946.015 | −0.0943450 | ||||||||
\(466\) | 8629.95i | 0.857886i | ||||||||
\(467\) | −1134.81 | −0.112447 | −0.0562233 | − | 0.998418i | \(-0.517906\pi\) | ||||
−0.0562233 | + | 0.998418i | \(0.517906\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13207.9 | −1.30039 | ||||||||
\(470\) | − 7784.40i | − 0.763974i | ||||||||
\(471\) | −1552.88 | −0.151917 | ||||||||
\(472\) | −6656.25 | −0.649107 | ||||||||
\(473\) | 4524.05i | 0.439780i | ||||||||
\(474\) | − 661.207i | − 0.0640722i | ||||||||
\(475\) | 3364.40i | 0.324988i | ||||||||
\(476\) | − 8453.65i | − 0.814018i | ||||||||
\(477\) | −1370.49 | −0.131552 | ||||||||
\(478\) | 3131.36 | 0.299635 | ||||||||
\(479\) | 19372.6i | 1.84793i | 0.382481 | + | 0.923963i | \(0.375070\pi\) | ||||
−0.382481 | + | 0.923963i | \(0.624930\pi\) | |||||||
\(480\) | −5538.66 | −0.526675 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −6880.29 | −0.650184 | ||||||||
\(483\) | − 11739.1i | − 1.10589i | ||||||||
\(484\) | −5095.97 | −0.478585 | ||||||||
\(485\) | −2110.00 | −0.197547 | ||||||||
\(486\) | 356.263i | 0.0332519i | ||||||||
\(487\) | − 9045.95i | − 0.841707i | −0.907129 | − | 0.420853i | \(-0.861731\pi\) | ||||
0.907129 | − | 0.420853i | \(-0.138269\pi\) | |||||||
\(488\) | 1998.51i | 0.185385i | ||||||||
\(489\) | 1830.56i | 0.169286i | ||||||||
\(490\) | −7991.86 | −0.736807 | ||||||||
\(491\) | −14403.3 | −1.32385 | −0.661927 | − | 0.749568i | \(-0.730261\pi\) | ||||
−0.661927 | + | 0.749568i | \(0.730261\pi\) | |||||||
\(492\) | 4244.43i | 0.388930i | ||||||||
\(493\) | −9408.40 | −0.859499 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4160.20 | 0.377751 | ||||||||
\(496\) | − 545.273i | − 0.0493619i | ||||||||
\(497\) | 10330.6 | 0.932378 | ||||||||
\(498\) | −1486.48 | −0.133756 | ||||||||
\(499\) | − 9319.75i | − 0.836091i | −0.908426 | − | 0.418045i | \(-0.862715\pi\) | ||||
0.908426 | − | 0.418045i | \(-0.137285\pi\) | |||||||
\(500\) | 8815.64i | 0.788495i | ||||||||
\(501\) | 8949.03i | 0.798030i | ||||||||
\(502\) | − 5722.02i | − 0.508737i | ||||||||
\(503\) | 2745.98 | 0.243414 | 0.121707 | − | 0.992566i | \(-0.461163\pi\) | ||||
0.121707 | + | 0.992566i | \(0.461163\pi\) | |||||||
\(504\) | −5471.67 | −0.483586 | ||||||||
\(505\) | − 15712.7i | − 1.38457i | ||||||||
\(506\) | 8991.69 | 0.789979 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14584.5 | 1.27378 | ||||||||
\(509\) | − 1182.11i | − 0.102939i | −0.998675 | − | 0.0514697i | \(-0.983609\pi\) | ||||
0.998675 | − | 0.0514697i | \(-0.0163905\pi\) | |||||||
\(510\) | −2090.97 | −0.181548 | ||||||||
\(511\) | −23168.4 | −2.00570 | ||||||||
\(512\) | − 5959.48i | − 0.514403i | ||||||||
\(513\) | − 3248.11i | − 0.279547i | ||||||||
\(514\) | − 6056.22i | − 0.519705i | ||||||||
\(515\) | 15468.3i | 1.32352i | ||||||||
\(516\) | 1692.13 | 0.144364 | ||||||||
\(517\) | −25293.7 | −2.15167 | ||||||||
\(518\) | − 1423.28i | − 0.120724i | ||||||||
\(519\) | 2934.64 | 0.248201 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10858.8 | 0.913115 | 0.456558 | − | 0.889694i | \(-0.349082\pi\) | ||||
0.456558 | + | 0.889694i | \(0.349082\pi\) | |||||||
\(522\) | 2572.29i | 0.215682i | ||||||||
\(523\) | −10161.7 | −0.849602 | −0.424801 | − | 0.905287i | \(-0.639656\pi\) | ||||
−0.424801 | + | 0.905287i | \(0.639656\pi\) | |||||||
\(524\) | 4356.09 | 0.363162 | ||||||||
\(525\) | 2511.94i | 0.208819i | ||||||||
\(526\) | − 9312.93i | − 0.771983i | ||||||||
\(527\) | − 1544.96i | − 0.127703i | ||||||||
\(528\) | 2397.89i | 0.197642i | ||||||||
\(529\) | 4914.73 | 0.403939 | ||||||||
\(530\) | −2199.16 | −0.180237 | ||||||||
\(531\) | − 2950.13i | − 0.241101i | ||||||||
\(532\) | 21072.1 | 1.71728 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 747.331 | 0.0605621 | ||||||||
\(535\) | − 66.3239i | − 0.00535969i | ||||||||
\(536\) | −8958.14 | −0.721889 | ||||||||
\(537\) | 5558.82 | 0.446706 | ||||||||
\(538\) | − 266.132i | − 0.0213267i | ||||||||
\(539\) | 25967.8i | 2.07516i | ||||||||
\(540\) | − 1556.04i | − 0.124002i | ||||||||
\(541\) | 9573.04i | 0.760771i | 0.924828 | + | 0.380386i | \(0.124209\pi\) | ||||
−0.924828 | + | 0.380386i | \(0.875791\pi\) | |||||||
\(542\) | −5073.23 | −0.402055 | ||||||||
\(543\) | 2558.33 | 0.202189 | ||||||||
\(544\) | − 9045.34i | − 0.712896i | ||||||||
\(545\) | 5343.15 | 0.419955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15958.9 | 1.24745 | 0.623724 | − | 0.781645i | \(-0.285619\pi\) | ||||
0.623724 | + | 0.781645i | \(0.285619\pi\) | |||||||
\(548\) | 1299.80i | 0.101322i | ||||||||
\(549\) | −885.762 | −0.0688586 | ||||||||
\(550\) | −1924.05 | −0.149167 | ||||||||
\(551\) | − 23452.0i | − 1.81323i | ||||||||
\(552\) | − 7961.93i | − 0.613917i | ||||||||
\(553\) | 4500.89i | 0.346107i | ||||||||
\(554\) | − 9438.67i | − 0.723846i | ||||||||
\(555\) | 958.210 | 0.0732861 | ||||||||
\(556\) | −4546.72 | −0.346806 | ||||||||
\(557\) | 2145.09i | 0.163178i | 0.996666 | + | 0.0815892i | \(0.0259996\pi\) | ||||
−0.996666 | + | 0.0815892i | \(0.974000\pi\) | |||||||
\(558\) | −422.399 | −0.0320459 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 5023.47 | 0.379072 | ||||||||
\(561\) | 6794.14i | 0.511317i | ||||||||
\(562\) | 4360.57 | 0.327294 | ||||||||
\(563\) | 22318.6 | 1.67072 | 0.835362 | − | 0.549701i | \(-0.185258\pi\) | ||||
0.835362 | + | 0.549701i | \(0.185258\pi\) | |||||||
\(564\) | 9460.59i | 0.706317i | ||||||||
\(565\) | − 14212.6i | − 1.05828i | ||||||||
\(566\) | 4450.67i | 0.330523i | ||||||||
\(567\) | − 2425.11i | − 0.179621i | ||||||||
\(568\) | 7006.67 | 0.517594 | ||||||||
\(569\) | 19753.0 | 1.45534 | 0.727671 | − | 0.685927i | \(-0.240603\pi\) | ||||
0.727671 | + | 0.685927i | \(0.240603\pi\) | |||||||
\(570\) | − 5212.09i | − 0.383001i | ||||||||
\(571\) | 10640.6 | 0.779850 | 0.389925 | − | 0.920847i | \(-0.372501\pi\) | ||||
0.389925 | + | 0.920847i | \(0.372501\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13323.9 | −0.971401 | ||||||||
\(574\) | 10614.8i | 0.771870i | ||||||||
\(575\) | −3655.17 | −0.265098 | ||||||||
\(576\) | −1246.64 | −0.0901791 | ||||||||
\(577\) | 6547.89i | 0.472430i | 0.971701 | + | 0.236215i | \(0.0759070\pi\) | ||||
−0.971701 | + | 0.236215i | \(0.924093\pi\) | |||||||
\(578\) | 3788.13i | 0.272605i | ||||||||
\(579\) | − 7447.29i | − 0.534540i | ||||||||
\(580\) | − 11234.9i | − 0.804319i | ||||||||
\(581\) | 10118.6 | 0.722529 | ||||||||
\(582\) | −942.123 | −0.0671001 | ||||||||
\(583\) | 7145.69i | 0.507623i | ||||||||
\(584\) | −15713.8 | −1.11343 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2867.32 | 0.202130 | ||||||||
\(587\) | 5900.33i | 0.414877i | 0.978248 | + | 0.207439i | \(0.0665127\pi\) | ||||
−0.978248 | + | 0.207439i | \(0.933487\pi\) | |||||||
\(588\) | 9712.72 | 0.681201 | ||||||||
\(589\) | 3851.08 | 0.269408 | ||||||||
\(590\) | − 4733.94i | − 0.330328i | ||||||||
\(591\) | − 3780.69i | − 0.263142i | ||||||||
\(592\) | 552.303i | 0.0383437i | ||||||||
\(593\) | 15261.5i | 1.05686i | 0.848978 | + | 0.528428i | \(0.177218\pi\) | ||||
−0.848978 | + | 0.528428i | \(0.822782\pi\) | |||||||
\(594\) | 1857.54 | 0.128310 | ||||||||
\(595\) | 14233.4 | 0.980693 | ||||||||
\(596\) | 10404.0i | 0.715041i | ||||||||
\(597\) | −16562.9 | −1.13547 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18900.6 | −1.28925 | −0.644623 | − | 0.764501i | \(-0.722986\pi\) | ||||
−0.644623 | + | 0.764501i | \(0.722986\pi\) | |||||||
\(600\) | 1703.70i | 0.115922i | ||||||||
\(601\) | −18507.0 | −1.25610 | −0.628049 | − | 0.778174i | \(-0.716146\pi\) | ||||
−0.628049 | + | 0.778174i | \(0.716146\pi\) | |||||||
\(602\) | 4231.81 | 0.286505 | ||||||||
\(603\) | − 3970.36i | − 0.268135i | ||||||||
\(604\) | − 6821.72i | − 0.459556i | ||||||||
\(605\) | − 8580.08i | − 0.576578i | ||||||||
\(606\) | − 7015.79i | − 0.470292i | ||||||||
\(607\) | −6408.50 | −0.428522 | −0.214261 | − | 0.976776i | \(-0.568734\pi\) | ||||
−0.214261 | + | 0.976776i | \(0.568734\pi\) | |||||||
\(608\) | 22547.0 | 1.50395 | ||||||||
\(609\) | − 17509.8i | − 1.16508i | ||||||||
\(610\) | −1421.34 | −0.0943418 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2541.21 | 0.167847 | ||||||||
\(613\) | − 3507.26i | − 0.231088i | −0.993302 | − | 0.115544i | \(-0.963139\pi\) | ||||
0.993302 | − | 0.115544i | \(-0.0368612\pi\) | |||||||
\(614\) | 1506.51 | 0.0990192 | ||||||||
\(615\) | −7146.33 | −0.468566 | ||||||||
\(616\) | 28529.1i | 1.86602i | ||||||||
\(617\) | 14507.8i | 0.946614i | 0.880897 | + | 0.473307i | \(0.156940\pi\) | ||||
−0.880897 | + | 0.473307i | \(0.843060\pi\) | |||||||
\(618\) | 6906.64i | 0.449556i | ||||||||
\(619\) | − 4750.85i | − 0.308486i | −0.988033 | − | 0.154243i | \(-0.950706\pi\) | ||||
0.988033 | − | 0.154243i | \(-0.0492939\pi\) | |||||||
\(620\) | 1844.90 | 0.119505 | ||||||||
\(621\) | 3528.82 | 0.228030 | ||||||||
\(622\) | 4992.98i | 0.321865i | ||||||||
\(623\) | −5087.14 | −0.327146 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11347.0 | −0.726209 | ||||||||
\(626\) | − 7056.65i | − 0.450544i | ||||||||
\(627\) | −16935.5 | −1.07869 | ||||||||
\(628\) | 3028.40 | 0.192431 | ||||||||
\(629\) | 1564.88i | 0.0991986i | ||||||||
\(630\) | − 3891.46i | − 0.246095i | ||||||||
\(631\) | − 4825.19i | − 0.304418i | −0.988348 | − | 0.152209i | \(-0.951361\pi\) | ||||
0.988348 | − | 0.152209i | \(-0.0486387\pi\) | |||||||
\(632\) | 3052.69i | 0.192135i | ||||||||
\(633\) | 13583.4 | 0.852908 | ||||||||
\(634\) | 1673.30 | 0.104819 | ||||||||
\(635\) | 24555.8i | 1.53460i | ||||||||
\(636\) | 2672.70 | 0.166635 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13411.9 | 0.832258 | ||||||||
\(639\) | 3105.44i | 0.192252i | ||||||||
\(640\) | 12769.3 | 0.788675 | ||||||||
\(641\) | 5911.89 | 0.364284 | 0.182142 | − | 0.983272i | \(-0.441697\pi\) | ||||
0.182142 | + | 0.983272i | \(0.441697\pi\) | |||||||
\(642\) | − 29.6139i | − 0.00182051i | ||||||||
\(643\) | 23408.3i | 1.43567i | 0.696216 | + | 0.717833i | \(0.254866\pi\) | ||||
−0.696216 | + | 0.717833i | \(0.745134\pi\) | |||||||
\(644\) | 22893.3i | 1.40081i | ||||||||
\(645\) | 2849.04i | 0.173924i | ||||||||
\(646\) | 8512.02 | 0.518422 | ||||||||
\(647\) | 16398.7 | 0.996442 | 0.498221 | − | 0.867050i | \(-0.333987\pi\) | ||||
0.498221 | + | 0.867050i | \(0.333987\pi\) | |||||||
\(648\) | − 1644.81i | − 0.0997134i | ||||||||
\(649\) | −15381.9 | −0.930342 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2875.30 | 0.173106 | ||||||||
\(652\) | − 3569.93i | − 0.214431i | ||||||||
\(653\) | 27529.6 | 1.64979 | 0.824897 | − | 0.565283i | \(-0.191233\pi\) | ||||
0.824897 | + | 0.565283i | \(0.191233\pi\) | |||||||
\(654\) | 2385.74 | 0.142645 | ||||||||
\(655\) | 7334.34i | 0.437521i | ||||||||
\(656\) | − 4119.07i | − 0.245157i | ||||||||
\(657\) | − 6964.55i | − 0.413566i | ||||||||
\(658\) | 23659.8i | 1.40175i | ||||||||
\(659\) | −24179.7 | −1.42930 | −0.714650 | − | 0.699482i | \(-0.753414\pi\) | ||||
−0.714650 | + | 0.699482i | \(0.753414\pi\) | |||||||
\(660\) | −8113.14 | −0.478490 | ||||||||
\(661\) | − 4525.04i | − 0.266269i | −0.991098 | − | 0.133134i | \(-0.957496\pi\) | ||||
0.991098 | − | 0.133134i | \(-0.0425042\pi\) | |||||||
\(662\) | 11219.4 | 0.658695 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6862.84 | 0.401099 | ||||||||
\(665\) | 35479.1i | 2.06890i | ||||||||
\(666\) | 427.844 | 0.0248928 | ||||||||
\(667\) | 25478.8 | 1.47908 | ||||||||
\(668\) | − 17452.2i | − 1.01085i | ||||||||
\(669\) | − 13443.5i | − 0.776916i | ||||||||
\(670\) | − 6371.05i | − 0.367366i | ||||||||
\(671\) | 4618.34i | 0.265706i | ||||||||
\(672\) | 16834.1 | 0.966354 | ||||||||
\(673\) | −3287.18 | −0.188279 | −0.0941393 | − | 0.995559i | \(-0.530010\pi\) | ||||
−0.0941393 | + | 0.995559i | \(0.530010\pi\) | |||||||
\(674\) | − 3670.66i | − 0.209775i | ||||||||
\(675\) | −755.102 | −0.0430576 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9724.21 | −0.552041 | −0.276020 | − | 0.961152i | \(-0.589016\pi\) | ||||
−0.276020 | + | 0.961152i | \(0.589016\pi\) | |||||||
\(678\) | − 6345.97i | − 0.359462i | ||||||||
\(679\) | 6413.10 | 0.362463 | ||||||||
\(680\) | 9653.69 | 0.544415 | ||||||||
\(681\) | 17279.3i | 0.972309i | ||||||||
\(682\) | 2202.38i | 0.123656i | ||||||||
\(683\) | − 14548.7i | − 0.815065i | −0.913191 | − | 0.407532i | \(-0.866389\pi\) | ||||
0.913191 | − | 0.407532i | \(-0.133611\pi\) | |||||||
\(684\) | 6334.40i | 0.354096i | ||||||||
\(685\) | −2188.46 | −0.122068 | ||||||||
\(686\) | 9234.52 | 0.513959 | ||||||||
\(687\) | − 13905.2i | − 0.772224i | ||||||||
\(688\) | −1642.15 | −0.0909979 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 5662.54 | 0.312419 | ||||||||
\(691\) | 6728.96i | 0.370451i | 0.982696 | + | 0.185226i | \(0.0593016\pi\) | ||||
−0.982696 | + | 0.185226i | \(0.940698\pi\) | |||||||
\(692\) | −5723.07 | −0.314391 | ||||||||
\(693\) | −12644.4 | −0.693106 | ||||||||
\(694\) | − 6591.76i | − 0.360548i | ||||||||
\(695\) | − 7655.31i | − 0.417816i | ||||||||
\(696\) | − 11875.9i | − 0.646774i | ||||||||
\(697\) | − 11670.9i | − 0.634241i | ||||||||
\(698\) | −5245.15 | −0.284429 | ||||||||
\(699\) | 17659.0 | 0.955542 | ||||||||
\(700\) | − 4898.74i | − 0.264507i | ||||||||
\(701\) | 29159.8 | 1.57111 | 0.785557 | − | 0.618789i | \(-0.212376\pi\) | ||||
0.785557 | + | 0.618789i | \(0.212376\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3900.73 | −0.209273 | ||||||||
\(704\) | 6499.92i | 0.347976i | ||||||||
\(705\) | −15928.8 | −0.850939 | ||||||||
\(706\) | −11795.0 | −0.628770 | ||||||||
\(707\) | 47757.0i | 2.54044i | ||||||||
\(708\) | 5753.29i | 0.305398i | ||||||||
\(709\) | 20489.0i | 1.08531i | 0.839957 | + | 0.542653i | \(0.182580\pi\) | ||||
−0.839957 | + | 0.542653i | \(0.817420\pi\) | |||||||
\(710\) | 4983.16i | 0.263401i | ||||||||
\(711\) | −1352.99 | −0.0713658 | ||||||||
\(712\) | −3450.31 | −0.181609 | ||||||||
\(713\) | 4183.91i | 0.219760i | ||||||||
\(714\) | 6355.26 | 0.333109 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10840.7 | −0.565833 | ||||||||
\(717\) | − 6407.53i | − 0.333743i | ||||||||
\(718\) | 3185.70 | 0.165584 | ||||||||
\(719\) | 17990.1 | 0.933127 | 0.466563 | − | 0.884488i | \(-0.345492\pi\) | ||||
0.466563 | + | 0.884488i | \(0.345492\pi\) | |||||||
\(720\) | 1510.08i | 0.0781631i | ||||||||
\(721\) | − 47014.0i | − 2.42842i | ||||||||
\(722\) | 11161.6i | 0.575337i | ||||||||
\(723\) | 14078.8i | 0.724197i | ||||||||
\(724\) | −4989.21 | −0.256108 | ||||||||
\(725\) | −5452.00 | −0.279286 | ||||||||
\(726\) | − 3831.04i | − 0.195844i | ||||||||
\(727\) | 37652.7 | 1.92086 | 0.960428 | − | 0.278528i | \(-0.0898465\pi\) | ||||
0.960428 | + | 0.278528i | \(0.0898465\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | − 11175.7i | − 0.566618i | ||||||||
\(731\) | −4652.84 | −0.235419 | ||||||||
\(732\) | 1727.40 | 0.0872219 | ||||||||
\(733\) | 4524.26i | 0.227977i | 0.993482 | + | 0.113989i | \(0.0363627\pi\) | ||||
−0.993482 | + | 0.113989i | \(0.963637\pi\) | |||||||
\(734\) | − 11234.4i | − 0.564944i | ||||||||
\(735\) | 16353.3i | 0.820680i | ||||||||
\(736\) | 24495.6i | 1.22679i | ||||||||
\(737\) | −20701.3 | −1.03466 | ||||||||
\(738\) | −3190.86 | −0.159156 | ||||||||
\(739\) | − 818.302i | − 0.0407331i | −0.999793 | − | 0.0203665i | \(-0.993517\pi\) | ||||
0.999793 | − | 0.0203665i | \(-0.00648332\pi\) | |||||||
\(740\) | −1868.68 | −0.0928300 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6684.10 | 0.330702 | ||||||||
\(743\) | 39002.2i | 1.92578i | 0.269901 | + | 0.962888i | \(0.413009\pi\) | ||||
−0.269901 | + | 0.962888i | \(0.586991\pi\) | |||||||
\(744\) | 1950.15 | 0.0960969 | ||||||||
\(745\) | −17517.2 | −0.861449 | ||||||||
\(746\) | − 15456.4i | − 0.758579i | ||||||||
\(747\) | 3041.69i | 0.148982i | ||||||||
\(748\) | − 13249.8i | − 0.647675i | ||||||||
\(749\) | 201.584i | 0.00983407i | ||||||||
\(750\) | −6627.39 | −0.322664 | ||||||||
\(751\) | 22377.7 | 1.08732 | 0.543658 | − | 0.839307i | \(-0.317039\pi\) | ||||
0.543658 | + | 0.839307i | \(0.317039\pi\) | |||||||
\(752\) | − 9181.18i | − 0.445217i | ||||||||
\(753\) | −11708.6 | −0.566649 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11485.7 | 0.553653 | ||||||||
\(756\) | 4729.40i | 0.227522i | ||||||||
\(757\) | −34512.6 | −1.65704 | −0.828521 | − | 0.559958i | \(-0.810817\pi\) | ||||
−0.828521 | + | 0.559958i | \(0.810817\pi\) | |||||||
\(758\) | 8027.70 | 0.384669 | ||||||||
\(759\) | − 18399.2i | − 0.879905i | ||||||||
\(760\) | 24063.4i | 1.14852i | ||||||||
\(761\) | − 19975.6i | − 0.951529i | −0.879573 | − | 0.475764i | \(-0.842172\pi\) | ||||
0.879573 | − | 0.475764i | \(-0.157828\pi\) | |||||||
\(762\) | 10964.3i | 0.521251i | ||||||||
\(763\) | −16239.9 | −0.770542 | ||||||||
\(764\) | 25984.0 | 1.23046 | ||||||||
\(765\) | 4278.63i | 0.202215i | ||||||||
\(766\) | 1184.73 | 0.0558827 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 9025.91 | 0.424081 | ||||||||
\(769\) | − 33064.9i | − 1.55052i | −0.631642 | − | 0.775260i | \(-0.717619\pi\) | ||||
0.631642 | − | 0.775260i | \(-0.282381\pi\) | |||||||
\(770\) | −20290.0 | −0.949610 | ||||||||
\(771\) | −12392.5 | −0.578865 | ||||||||
\(772\) | 14523.6i | 0.677091i | ||||||||
\(773\) | − 18564.0i | − 0.863779i | −0.901927 | − | 0.431890i | \(-0.857847\pi\) | ||||
0.901927 | − | 0.431890i | \(-0.142153\pi\) | |||||||
\(774\) | 1272.10i | 0.0590761i | ||||||||
\(775\) | − 895.279i | − 0.0414960i | ||||||||
\(776\) | 4349.64 | 0.201215 | ||||||||
\(777\) | −2912.37 | −0.134467 | ||||||||
\(778\) | − 10351.1i | − 0.476997i | ||||||||
\(779\) | 29091.6 | 1.33802 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16191.7 | 0.741848 | ||||||||
\(782\) | 9247.66i | 0.422885i | ||||||||
\(783\) | 5263.54 | 0.240234 | ||||||||
\(784\) | −9425.86 | −0.429385 | ||||||||
\(785\) | 5098.91i | 0.231832i | ||||||||
\(786\) | 3274.81i | 0.148611i | ||||||||
\(787\) | − 36436.8i | − 1.65036i | −0.564871 | − | 0.825179i | \(-0.691074\pi\) | ||||
0.564871 | − | 0.825179i | \(-0.308926\pi\) | |||||||
\(788\) | 7373.04i | 0.333317i | ||||||||
\(789\) | −19056.5 | −0.859861 | ||||||||
\(790\) | −2171.08 | −0.0977768 | ||||||||
\(791\) | 43197.5i | 1.94175i | ||||||||
\(792\) | −8576.00 | −0.384766 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 2081.71 | 0.0930441 | ||||||||
\(795\) | 4500.02i | 0.200754i | ||||||||
\(796\) | 32300.7 | 1.43827 | ||||||||
\(797\) | −12365.6 | −0.549576 | −0.274788 | − | 0.961505i | \(-0.588608\pi\) | ||||
−0.274788 | + | 0.961505i | \(0.588608\pi\) | |||||||
\(798\) | 15841.6i | 0.702738i | ||||||||
\(799\) | − 26013.7i | − 1.15181i | ||||||||
\(800\) | − 5241.61i | − 0.231649i | ||||||||
\(801\) | − 1529.22i | − 0.0674561i | ||||||||
\(802\) | −15644.4 | −0.688806 | ||||||||
\(803\) | −36313.0 | −1.59584 | ||||||||
\(804\) | 7742.92i | 0.339641i | ||||||||
\(805\) | −38545.4 | −1.68763 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −544.571 | −0.0237544 | ||||||||
\(808\) | 32390.9i | 1.41028i | ||||||||
\(809\) | −8093.75 | −0.351744 | −0.175872 | − | 0.984413i | \(-0.556274\pi\) | ||||
−0.175872 | + | 0.984413i | \(0.556274\pi\) | |||||||
\(810\) | 1169.79 | 0.0507437 | ||||||||
\(811\) | 15984.7i | 0.692105i | 0.938215 | + | 0.346052i | \(0.112478\pi\) | ||||
−0.938215 | + | 0.346052i | \(0.887522\pi\) | |||||||
\(812\) | 34147.3i | 1.47578i | ||||||||
\(813\) | 10381.1i | 0.447822i | ||||||||
\(814\) | − 2230.77i | − 0.0960546i | ||||||||
\(815\) | 6010.68 | 0.258337 | ||||||||
\(816\) | −2466.16 | −0.105800 | ||||||||
\(817\) | − 11598.0i | − 0.496649i | ||||||||
\(818\) | 9312.03 | 0.398029 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13936.6 | 0.593523 | ||||||||
\(821\) | − 26861.9i | − 1.14188i | −0.820990 | − | 0.570942i | \(-0.806578\pi\) | ||||
0.820990 | − | 0.570942i | \(-0.193422\pi\) | |||||||
\(822\) | −977.156 | −0.0414626 | ||||||||
\(823\) | 5205.94 | 0.220495 | 0.110248 | − | 0.993904i | \(-0.464836\pi\) | ||||
0.110248 | + | 0.993904i | \(0.464836\pi\) | |||||||
\(824\) | − 31886.9i | − 1.34810i | ||||||||
\(825\) | 3937.08i | 0.166147i | ||||||||
\(826\) | 14388.3i | 0.606092i | ||||||||
\(827\) | − 46621.5i | − 1.96032i | −0.198200 | − | 0.980162i | \(-0.563509\pi\) | ||||
0.198200 | − | 0.980162i | \(-0.436491\pi\) | |||||||
\(828\) | −6881.84 | −0.288841 | ||||||||
\(829\) | 41829.7 | 1.75248 | 0.876241 | − | 0.481874i | \(-0.160044\pi\) | ||||
0.876241 | + | 0.481874i | \(0.160044\pi\) | |||||||
\(830\) | 4880.87i | 0.204118i | ||||||||
\(831\) | −19313.8 | −0.806244 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26707.0 | −1.11086 | ||||||||
\(834\) | − 3418.12i | − 0.141918i | ||||||||
\(835\) | 29384.3 | 1.21783 | ||||||||
\(836\) | 33027.4 | 1.36636 | ||||||||
\(837\) | 864.331i | 0.0356937i | ||||||||
\(838\) | − 8236.37i | − 0.339524i | ||||||||
\(839\) | − 12685.1i | − 0.521975i | −0.965342 | − | 0.260988i | \(-0.915952\pi\) | ||||
0.965342 | − | 0.260988i | \(-0.0840482\pi\) | |||||||
\(840\) | 17966.3i | 0.737972i | ||||||||
\(841\) | 13614.9 | 0.558238 | ||||||||
\(842\) | −2225.97 | −0.0911069 | ||||||||
\(843\) | − 8922.78i | − 0.364551i | ||||||||
\(844\) | −26490.1 | −1.08036 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7112.25 | −0.289036 | ||||||||
\(847\) | 26078.2i | 1.05792i | ||||||||
\(848\) | −2593.77 | −0.105036 | ||||||||
\(849\) | 9107.16 | 0.368147 | ||||||||
\(850\) | − 1978.83i | − 0.0798509i | ||||||||
\(851\) | − 4237.85i | − 0.170707i | ||||||||
\(852\) | − 6056.17i | − 0.243522i | ||||||||
\(853\) | 37493.3i | 1.50498i | 0.658606 | + | 0.752488i | \(0.271146\pi\) | ||||
−0.658606 | + | 0.752488i | \(0.728854\pi\) | |||||||
\(854\) | 4320.01 | 0.173100 | ||||||||
\(855\) | −10665.2 | −0.426599 | ||||||||
\(856\) | 136.723i | 0.00545921i | ||||||||
\(857\) | 11826.3 | 0.471386 | 0.235693 | − | 0.971828i | \(-0.424264\pi\) | ||||
0.235693 | + | 0.971828i | \(0.424264\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36498.7 | −1.44973 | −0.724866 | − | 0.688890i | \(-0.758099\pi\) | ||||
−0.724866 | + | 0.688890i | \(0.758099\pi\) | |||||||
\(860\) | − 5556.14i | − 0.220306i | ||||||||
\(861\) | 21720.5 | 0.859734 | ||||||||
\(862\) | −7286.72 | −0.287920 | ||||||||
\(863\) | 2292.79i | 0.0904372i | 0.998977 | + | 0.0452186i | \(0.0143984\pi\) | ||||
−0.998977 | + | 0.0452186i | \(0.985602\pi\) | |||||||
\(864\) | 5060.42i | 0.199258i | ||||||||
\(865\) | − 9635.92i | − 0.378764i | ||||||||
\(866\) | − 4836.24i | − 0.189772i | ||||||||
\(867\) | 7751.44 | 0.303636 | ||||||||
\(868\) | −5607.37 | −0.219270 | ||||||||
\(869\) | 7054.45i | 0.275381i | ||||||||
\(870\) | 8446.16 | 0.329140 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −11014.6 | −0.427753 | ||||||||
\(873\) | 1927.81i | 0.0747383i | ||||||||
\(874\) | −23051.3 | −0.892132 | ||||||||
\(875\) | 45113.2 | 1.74298 | ||||||||
\(876\) | 13582.1i | 0.523856i | ||||||||
\(877\) | − 20800.3i | − 0.800885i | −0.916322 | − | 0.400442i | \(-0.868856\pi\) | ||||
0.916322 | − | 0.400442i | \(-0.131144\pi\) | |||||||
\(878\) | − 8867.68i | − 0.340854i | ||||||||
\(879\) | − 5867.23i | − 0.225139i | ||||||||
\(880\) | 7873.52 | 0.301610 | ||||||||
\(881\) | 19255.9 | 0.736377 | 0.368188 | − | 0.929751i | \(-0.379978\pi\) | ||||
0.368188 | + | 0.929751i | \(0.379978\pi\) | |||||||
\(882\) | 7301.80i | 0.278758i | ||||||||
\(883\) | −1744.49 | −0.0664857 | −0.0332429 | − | 0.999447i | \(-0.510583\pi\) | ||||
−0.0332429 | + | 0.999447i | \(0.510583\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9686.80 | −0.367930 | ||||||||
\(886\) | − 10002.7i | − 0.379284i | ||||||||
\(887\) | 2970.70 | 0.112454 | 0.0562268 | − | 0.998418i | \(-0.482093\pi\) | ||||
0.0562268 | + | 0.998418i | \(0.482093\pi\) | |||||||
\(888\) | −1975.29 | −0.0746470 | ||||||||
\(889\) | − 74634.6i | − 2.81571i | ||||||||
\(890\) | − 2453.87i | − 0.0924202i | ||||||||
\(891\) | − 3800.99i | − 0.142916i | ||||||||
\(892\) | 26217.3i | 0.984104i | ||||||||
\(893\) | 64843.6 | 2.42991 | ||||||||
\(894\) | −7821.48 | −0.292606 | ||||||||
\(895\) | − 18252.5i | − 0.681691i | ||||||||
\(896\) | −38810.9 | −1.44708 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −601.703 | −0.0223598 | ||||||||
\(899\) | 6240.66i | 0.231521i | ||||||||
\(900\) | 1472.59 | 0.0545402 | ||||||||
\(901\) | −7349.12 | −0.271736 | ||||||||
\(902\) | 16637.1i | 0.614140i | ||||||||
\(903\) | − 8659.32i | − 0.319119i | ||||||||
\(904\) | 29298.4i | 1.07793i | ||||||||
\(905\) | − 8400.32i | − 0.308548i | ||||||||
\(906\) | 5128.41 | 0.188058 | ||||||||
\(907\) | −33003.3 | −1.20822 | −0.604111 | − | 0.796900i | \(-0.706472\pi\) | ||||
−0.604111 | + | 0.796900i | \(0.706472\pi\) | |||||||
\(908\) | − 33697.7i | − 1.23160i | ||||||||
\(909\) | −14356.0 | −0.523827 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14977.0 | 0.544686 | 0.272343 | − | 0.962200i | \(-0.412201\pi\) | ||||
0.272343 | + | 0.962200i | \(0.412201\pi\) | |||||||
\(912\) | − 6147.31i | − 0.223199i | ||||||||
\(913\) | 15859.3 | 0.574881 | ||||||||
\(914\) | −24400.1 | −0.883022 | ||||||||
\(915\) | 2908.41i | 0.105081i | ||||||||
\(916\) | 27117.7i | 0.978161i | ||||||||
\(917\) | − 22291.9i | − 0.802773i | ||||||||
\(918\) | 1910.42i | 0.0686856i | ||||||||
\(919\) | 11425.4 | 0.410107 | 0.205054 | − | 0.978751i | \(-0.434263\pi\) | ||||
0.205054 | + | 0.978751i | \(0.434263\pi\) | |||||||
\(920\) | −26143.1 | −0.936862 | ||||||||
\(921\) | − 3082.69i | − 0.110291i | ||||||||
\(922\) | −17196.9 | −0.614263 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 24659.0 | 0.877944 | ||||||||
\(925\) | 906.820i | 0.0322336i | ||||||||
\(926\) | 5226.55 | 0.185481 | ||||||||
\(927\) | 14132.7 | 0.500731 | ||||||||
\(928\) | 36537.3i | 1.29245i | ||||||||
\(929\) | 11954.2i | 0.422179i | 0.977467 | + | 0.211090i | \(0.0677012\pi\) | ||||
−0.977467 | + | 0.211090i | \(0.932299\pi\) | |||||||
\(930\) | 1386.95i | 0.0489033i | ||||||||
\(931\) | − 66571.7i | − 2.34350i | ||||||||
\(932\) | −34438.2 | −1.21037 | ||||||||
\(933\) | 10216.8 | 0.358504 | ||||||||
\(934\) | 1663.74i | 0.0582861i | ||||||||
\(935\) | 22308.7 | 0.780290 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42546.4 | 1.48338 | 0.741692 | − | 0.670740i | \(-0.234024\pi\) | ||||
0.741692 | + | 0.670740i | \(0.234024\pi\) | |||||||
\(938\) | 19364.1i | 0.674051i | ||||||||
\(939\) | −14439.6 | −0.501831 | ||||||||
\(940\) | 31064.0 | 1.07787 | ||||||||
\(941\) | 20665.1i | 0.715903i | 0.933740 | + | 0.357951i | \(0.116525\pi\) | ||||
−0.933740 | + | 0.357951i | \(0.883475\pi\) | |||||||
\(942\) | 2276.68i | 0.0787456i | ||||||||
\(943\) | 31605.9i | 1.09144i | ||||||||
\(944\) | − 5583.37i | − 0.192503i | ||||||||
\(945\) | −7962.88 | −0.274108 | ||||||||
\(946\) | 6632.72 | 0.227958 | ||||||||
\(947\) | 9493.73i | 0.325771i | 0.986645 | + | 0.162885i | \(0.0520801\pi\) | ||||
−0.986645 | + | 0.162885i | \(0.947920\pi\) | |||||||
\(948\) | 2638.58 | 0.0903976 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4932.56 | 0.168456 | ||||||||
\(951\) | − 3423.99i | − 0.116751i | ||||||||
\(952\) | −29341.3 | −0.998904 | ||||||||
\(953\) | −53334.1 | −1.81287 | −0.906433 | − | 0.422349i | \(-0.861206\pi\) | ||||
−0.906433 | + | 0.422349i | \(0.861206\pi\) | |||||||
\(954\) | 2009.28i | 0.0681894i | ||||||||
\(955\) | 43749.2i | 1.48240i | ||||||||
\(956\) | 12495.9i | 0.422746i | ||||||||
\(957\) | − 27443.9i | − 0.926997i | ||||||||
\(958\) | 28402.2 | 0.957864 | ||||||||
\(959\) | 6651.58 | 0.223974 | ||||||||
\(960\) | 4093.35i | 0.137617i | ||||||||
\(961\) | 28766.2 | 0.965601 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −60.5972 | −0.00202774 | ||||||||
\(964\) | − 27456.1i | − 0.917326i | ||||||||
\(965\) | −24453.3 | −0.815730 | ||||||||
\(966\) | −17210.6 | −0.573233 | ||||||||
\(967\) | − 42110.1i | − 1.40038i | −0.713956 | − | 0.700191i | \(-0.753098\pi\) | ||||
0.713956 | − | 0.700191i | \(-0.246902\pi\) | |||||||
\(968\) | 17687.3i | 0.587285i | ||||||||
\(969\) | − 17417.7i | − 0.577436i | ||||||||
\(970\) | 3093.47i | 0.102397i | ||||||||
\(971\) | −13827.7 | −0.457006 | −0.228503 | − | 0.973543i | \(-0.573383\pi\) | ||||
−0.228503 | + | 0.973543i | \(0.573383\pi\) | |||||||
\(972\) | −1421.68 | −0.0469141 | ||||||||
\(973\) | 23267.4i | 0.766618i | ||||||||
\(974\) | −13262.3 | −0.436295 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1676.38 | −0.0549791 | ||||||||
\(977\) | 1133.89i | 0.0371302i | 0.999828 | + | 0.0185651i | \(0.00590979\pi\) | ||||
−0.999828 | + | 0.0185651i | \(0.994090\pi\) | |||||||
\(978\) | 2683.79 | 0.0877487 | ||||||||
\(979\) | −7973.31 | −0.260294 | ||||||||
\(980\) | − 31891.9i | − 1.03954i | ||||||||
\(981\) | − 4881.80i | − 0.158883i | ||||||||
\(982\) | 21116.7i | 0.686214i | ||||||||
\(983\) | − 26250.2i | − 0.851729i | −0.904787 | − | 0.425865i | \(-0.859970\pi\) | ||||
0.904787 | − | 0.425865i | \(-0.140030\pi\) | |||||||
\(984\) | 14731.7 | 0.477267 | ||||||||
\(985\) | −12414.0 | −0.401565 | ||||||||
\(986\) | 13793.7i | 0.445517i | ||||||||
\(987\) | 48413.7 | 1.56132 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12600.3 | 0.405124 | ||||||||
\(990\) | − 6099.27i | − 0.195806i | ||||||||
\(991\) | −29360.4 | −0.941133 | −0.470566 | − | 0.882365i | \(-0.655950\pi\) | ||||
−0.470566 | + | 0.882365i | \(0.655950\pi\) | |||||||
\(992\) | −5999.84 | −0.192031 | ||||||||
\(993\) | − 22957.7i | − 0.733676i | ||||||||
\(994\) | − 15145.7i | − 0.483293i | ||||||||
\(995\) | 54384.5i | 1.73277i | ||||||||
\(996\) | − 5931.86i | − 0.188713i | ||||||||
\(997\) | 16835.9 | 0.534803 | 0.267401 | − | 0.963585i | \(-0.413835\pi\) | ||||
0.267401 | + | 0.963585i | \(0.413835\pi\) | |||||||
\(998\) | −13663.7 | −0.433384 | ||||||||
\(999\) | − 875.474i | − 0.0277265i |
(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 | 507.4.b.h.337.4 | 8 | ||
13.2 | odd | 12 | 39.4.e.c.22.3 | yes | 8 | ||
13.5 | odd | 4 | 507.4.a.m.1.2 | 4 | |||
13.6 | odd | 12 | 39.4.e.c.16.3 | ✓ | 8 | ||
13.8 | odd | 4 | 507.4.a.i.1.3 | 4 | |||
13.12 | even | 2 | inner | 507.4.b.h.337.5 | 8 | ||
39.2 | even | 12 | 117.4.g.e.100.2 | 8 | |||
39.5 | even | 4 | 1521.4.a.v.1.3 | 4 | |||
39.8 | even | 4 | 1521.4.a.bb.1.2 | 4 | |||
39.32 | even | 12 | 117.4.g.e.55.2 | 8 | |||
52.15 | even | 12 | 624.4.q.i.529.4 | 8 | |||
52.19 | even | 12 | 624.4.q.i.289.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.c.16.3 | ✓ | 8 | 13.6 | odd | 12 | ||
39.4.e.c.22.3 | yes | 8 | 13.2 | odd | 12 | ||
117.4.g.e.55.2 | 8 | 39.32 | even | 12 | |||
117.4.g.e.100.2 | 8 | 39.2 | even | 12 | |||
507.4.a.i.1.3 | 4 | 13.8 | odd | 4 | |||
507.4.a.m.1.2 | 4 | 13.5 | odd | 4 | |||
507.4.b.h.337.4 | 8 | 1.1 | even | 1 | trivial | ||
507.4.b.h.337.5 | 8 | 13.12 | even | 2 | inner | ||
624.4.q.i.289.4 | 8 | 52.19 | even | 12 | |||
624.4.q.i.529.4 | 8 | 52.15 | even | 12 | |||
1521.4.a.v.1.3 | 4 | 39.5 | even | 4 | |||
1521.4.a.bb.1.2 | 4 | 39.8 | even | 4 |