Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(274,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.274");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.d (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: | \(30.9760027530\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.4 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.274 |
Dual form | 525.4.d.l.274.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.82843i | 1.35355i | 0.736188 | + | 0.676777i | \(0.236624\pi\) | ||||
−0.736188 | + | 0.676777i | \(0.763376\pi\) | |||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | −6.65685 | −0.832107 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 11.4853 | 0.781474 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | 5.14214i | 0.227252i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 48.5685 | 1.33127 | 0.665635 | − | 0.746278i | \(-0.268161\pi\) | ||||
0.665635 | + | 0.746278i | \(0.268161\pi\) | |||||||
\(12\) | 19.9706i | 0.480417i | ||||||||
\(13\) | − 43.6569i | − 0.931403i | −0.884942 | − | 0.465701i | \(-0.845802\pi\) | ||||
0.884942 | − | 0.465701i | \(-0.154198\pi\) | |||||||
\(14\) | −26.7990 | −0.511595 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −72.9411 | −1.13971 | ||||||||
\(17\) | 67.6569i | 0.965247i | 0.875828 | + | 0.482623i | \(0.160316\pi\) | ||||
−0.875828 | + | 0.482623i | \(0.839684\pi\) | |||||||
\(18\) | − 34.4558i | − 0.451184i | ||||||||
\(19\) | 93.2548 | 1.12601 | 0.563003 | − | 0.826455i | \(-0.309646\pi\) | ||||
0.563003 | + | 0.826455i | \(0.309646\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 185.941i | 1.80194i | ||||||||
\(23\) | − 104.167i | − 0.944357i | −0.881503 | − | 0.472179i | \(-0.843468\pi\) | ||||
0.881503 | − | 0.472179i | \(-0.156532\pi\) | |||||||
\(24\) | 15.4264 | 0.131204 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 167.137 | 1.26070 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | − 46.5980i | − 0.314507i | ||||||||
\(29\) | 58.7351 | 0.376098 | 0.188049 | − | 0.982160i | \(-0.439784\pi\) | ||||
0.188049 | + | 0.982160i | \(0.439784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.08831 | −0.0526551 | −0.0263276 | − | 0.999653i | \(-0.508381\pi\) | ||||
−0.0263276 | + | 0.999653i | \(0.508381\pi\) | |||||||
\(32\) | − 238.113i | − 1.31540i | ||||||||
\(33\) | − 145.706i | − 0.768609i | ||||||||
\(34\) | −259.019 | −1.30651 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 59.9117 | 0.277369 | ||||||||
\(37\) | 252.676i | 1.12269i | 0.827580 | + | 0.561347i | \(0.189717\pi\) | ||||
−0.827580 | + | 0.561347i | \(0.810283\pi\) | |||||||
\(38\) | 357.019i | 1.52411i | ||||||||
\(39\) | −130.971 | −0.537745 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 276.274 | 1.05236 | 0.526180 | − | 0.850373i | \(-0.323624\pi\) | ||||
0.526180 | + | 0.850373i | \(0.323624\pi\) | |||||||
\(42\) | 80.3970i | 0.295370i | ||||||||
\(43\) | − 92.6375i | − 0.328537i | −0.986416 | − | 0.164268i | \(-0.947474\pi\) | ||||
0.986416 | − | 0.164268i | \(-0.0525263\pi\) | |||||||
\(44\) | −323.314 | −1.10776 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 398.794 | 1.27824 | ||||||||
\(47\) | 582.794i | 1.80871i | 0.426784 | + | 0.904354i | \(0.359646\pi\) | ||||
−0.426784 | + | 0.904354i | \(0.640354\pi\) | |||||||
\(48\) | 218.823i | 0.658009i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 202.971 | 0.557286 | ||||||||
\(52\) | 290.617i | 0.775026i | ||||||||
\(53\) | 623.019i | 1.61468i | 0.590083 | + | 0.807342i | \(0.299095\pi\) | ||||
−0.590083 | + | 0.807342i | \(0.700905\pi\) | |||||||
\(54\) | −103.368 | −0.260491 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −35.9949 | −0.0858933 | ||||||||
\(57\) | − 279.765i | − 0.650100i | ||||||||
\(58\) | 224.863i | 0.509068i | ||||||||
\(59\) | 524.999 | 1.15846 | 0.579229 | − | 0.815165i | \(-0.303354\pi\) | ||||
0.579229 | + | 0.815165i | \(0.303354\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −352.794 | −0.740502 | −0.370251 | − | 0.928932i | \(-0.620728\pi\) | ||||
−0.370251 | + | 0.928932i | \(0.620728\pi\) | |||||||
\(62\) | − 34.7939i | − 0.0712715i | ||||||||
\(63\) | − 63.0000i | − 0.125988i | ||||||||
\(64\) | 328.068 | 0.640758 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 557.823 | 1.04035 | ||||||||
\(67\) | 736.520i | 1.34299i | 0.741010 | + | 0.671494i | \(0.234347\pi\) | ||||
−0.741010 | + | 0.671494i | \(0.765653\pi\) | |||||||
\(68\) | − 450.382i | − 0.803188i | ||||||||
\(69\) | −312.500 | −0.545225 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −492.264 | −0.822831 | −0.411415 | − | 0.911448i | \(-0.634965\pi\) | ||||
−0.411415 | + | 0.911448i | \(0.634965\pi\) | |||||||
\(72\) | − 46.2792i | − 0.0757508i | ||||||||
\(73\) | 1164.75i | 1.86745i | 0.357987 | + | 0.933727i | \(0.383463\pi\) | ||||
−0.357987 | + | 0.933727i | \(0.616537\pi\) | |||||||
\(74\) | −967.352 | −1.51963 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −620.784 | −0.936958 | ||||||||
\(77\) | 339.980i | 0.503173i | ||||||||
\(78\) | − 501.411i | − 0.727867i | ||||||||
\(79\) | 872.195 | 1.24215 | 0.621074 | − | 0.783752i | \(-0.286697\pi\) | ||||
0.621074 | + | 0.783752i | \(0.286697\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1057.70i | 1.42443i | ||||||||
\(83\) | − 529.588i | − 0.700359i | −0.936683 | − | 0.350180i | \(-0.886121\pi\) | ||||
0.936683 | − | 0.350180i | \(-0.113879\pi\) | |||||||
\(84\) | −139.794 | −0.181581 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 354.656 | 0.444692 | ||||||||
\(87\) | − 176.205i | − 0.217140i | ||||||||
\(88\) | 249.746i | 0.302534i | ||||||||
\(89\) | 385.216 | 0.458796 | 0.229398 | − | 0.973333i | \(-0.426324\pi\) | ||||
0.229398 | + | 0.973333i | \(0.426324\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 305.598 | 0.352037 | ||||||||
\(92\) | 693.421i | 0.785806i | ||||||||
\(93\) | 27.2649i | 0.0304005i | ||||||||
\(94\) | −2231.18 | −2.44818 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −714.338 | −0.759446 | ||||||||
\(97\) | 463.892i | 0.485579i | 0.970079 | + | 0.242789i | \(0.0780624\pi\) | ||||
−0.970079 | + | 0.242789i | \(0.921938\pi\) | |||||||
\(98\) | − 187.593i | − 0.193365i | ||||||||
\(99\) | −437.117 | −0.443757 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −432.725 | −0.426314 | −0.213157 | − | 0.977018i | \(-0.568375\pi\) | ||||
−0.213157 | + | 0.977018i | \(0.568375\pi\) | |||||||
\(102\) | 777.058i | 0.754316i | ||||||||
\(103\) | 512.626i | 0.490393i | 0.969473 | + | 0.245197i | \(0.0788525\pi\) | ||||
−0.969473 | + | 0.245197i | \(0.921147\pi\) | |||||||
\(104\) | 224.489 | 0.211663 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2385.18 | −2.18556 | ||||||||
\(107\) | − 1963.09i | − 1.77363i | −0.462122 | − | 0.886817i | \(-0.652912\pi\) | ||||
0.462122 | − | 0.886817i | \(-0.347088\pi\) | |||||||
\(108\) | − 179.735i | − 0.160139i | ||||||||
\(109\) | −545.176 | −0.479068 | −0.239534 | − | 0.970888i | \(-0.576995\pi\) | ||||
−0.239534 | + | 0.970888i | \(0.576995\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 758.029 | 0.648188 | ||||||||
\(112\) | − 510.588i | − 0.430768i | ||||||||
\(113\) | − 231.823i | − 0.192992i | −0.995333 | − | 0.0964961i | \(-0.969236\pi\) | ||||
0.995333 | − | 0.0964961i | \(-0.0307635\pi\) | |||||||
\(114\) | 1071.06 | 0.879945 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −390.991 | −0.312953 | ||||||||
\(117\) | 392.912i | 0.310468i | ||||||||
\(118\) | 2009.92i | 1.56804i | ||||||||
\(119\) | −473.598 | −0.364829 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1027.90 | 0.772279 | ||||||||
\(122\) | − 1350.65i | − 1.00231i | ||||||||
\(123\) | − 828.823i | − 0.607581i | ||||||||
\(124\) | 60.4996 | 0.0438147 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 241.191 | 0.170532 | ||||||||
\(127\) | − 2372.90i | − 1.65796i | −0.559280 | − | 0.828979i | \(-0.688922\pi\) | ||||
0.559280 | − | 0.828979i | \(-0.311078\pi\) | |||||||
\(128\) | − 648.917i | − 0.448099i | ||||||||
\(129\) | −277.913 | −0.189681 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1200.04 | 0.800364 | 0.400182 | − | 0.916436i | \(-0.368947\pi\) | ||||
0.400182 | + | 0.916436i | \(0.368947\pi\) | |||||||
\(132\) | 969.941i | 0.639565i | ||||||||
\(133\) | 652.784i | 0.425591i | ||||||||
\(134\) | −2819.71 | −1.81781 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −347.901 | −0.219355 | ||||||||
\(137\) | − 2781.25i | − 1.73444i | −0.497924 | − | 0.867221i | \(-0.665904\pi\) | ||||
0.497924 | − | 0.867221i | \(-0.334096\pi\) | |||||||
\(138\) | − 1196.38i | − 0.737991i | ||||||||
\(139\) | 1245.60 | 0.760078 | 0.380039 | − | 0.924971i | \(-0.375911\pi\) | ||||
0.380039 | + | 0.924971i | \(0.375911\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1748.38 | 1.04426 | ||||||||
\(142\) | − 1884.60i | − 1.11375i | ||||||||
\(143\) | − 2120.35i | − 1.23995i | ||||||||
\(144\) | 656.470 | 0.379902 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4459.17 | −2.52770 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | − 1682.03i | − 0.934202i | ||||||||
\(149\) | −19.4046 | −0.0106690 | −0.00533452 | − | 0.999986i | \(-0.501698\pi\) | ||||
−0.00533452 | + | 0.999986i | \(0.501698\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2349.80 | −1.26638 | −0.633192 | − | 0.773995i | \(-0.718256\pi\) | ||||
−0.633192 | + | 0.773995i | \(0.718256\pi\) | |||||||
\(152\) | 479.529i | 0.255888i | ||||||||
\(153\) | − 608.912i | − 0.321749i | ||||||||
\(154\) | −1301.59 | −0.681071 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 871.852 | 0.447462 | ||||||||
\(157\) | 3898.46i | 1.98172i | 0.134880 | + | 0.990862i | \(0.456935\pi\) | ||||
−0.134880 | + | 0.990862i | \(0.543065\pi\) | |||||||
\(158\) | 3339.14i | 1.68131i | ||||||||
\(159\) | 1869.06 | 0.932239 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 729.166 | 0.356934 | ||||||||
\(162\) | 310.103i | 0.150395i | ||||||||
\(163\) | 1527.54i | 0.734024i | 0.930216 | + | 0.367012i | \(0.119619\pi\) | ||||
−0.930216 | + | 0.367012i | \(0.880381\pi\) | |||||||
\(164\) | −1839.12 | −0.875676 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2027.49 | 0.947974 | ||||||||
\(167\) | 998.518i | 0.462681i | 0.972873 | + | 0.231340i | \(0.0743111\pi\) | ||||
−0.972873 | + | 0.231340i | \(0.925689\pi\) | |||||||
\(168\) | 107.985i | 0.0495905i | ||||||||
\(169\) | 291.079 | 0.132489 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −839.294 | −0.375336 | ||||||||
\(172\) | 616.674i | 0.273378i | ||||||||
\(173\) | 685.253i | 0.301149i | 0.988599 | + | 0.150575i | \(0.0481124\pi\) | ||||
−0.988599 | + | 0.150575i | \(0.951888\pi\) | |||||||
\(174\) | 674.589 | 0.293911 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3542.64 | −1.51725 | ||||||||
\(177\) | − 1575.00i | − 0.668836i | ||||||||
\(178\) | 1474.77i | 0.621005i | ||||||||
\(179\) | −1025.58 | −0.428245 | −0.214122 | − | 0.976807i | \(-0.568689\pi\) | ||||
−0.214122 | + | 0.976807i | \(0.568689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2899.40 | 1.19067 | 0.595333 | − | 0.803479i | \(-0.297020\pi\) | ||||
0.595333 | + | 0.803479i | \(0.297020\pi\) | |||||||
\(182\) | 1169.96i | 0.476501i | ||||||||
\(183\) | 1058.38i | 0.427529i | ||||||||
\(184\) | 535.638 | 0.214608 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −104.382 | −0.0411486 | ||||||||
\(187\) | 3285.99i | 1.28500i | ||||||||
\(188\) | − 3879.57i | − 1.50504i | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1074.18 | 0.406939 | 0.203469 | − | 0.979081i | \(-0.434778\pi\) | ||||
0.203469 | + | 0.979081i | \(0.434778\pi\) | |||||||
\(192\) | − 984.204i | − 0.369942i | ||||||||
\(193\) | 898.999i | 0.335292i | 0.985847 | + | 0.167646i | \(0.0536166\pi\) | ||||
−0.985847 | + | 0.167646i | \(0.946383\pi\) | |||||||
\(194\) | −1775.98 | −0.657257 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 326.186 | 0.118872 | ||||||||
\(197\) | − 3063.63i | − 1.10799i | −0.832519 | − | 0.553996i | \(-0.813102\pi\) | ||||
0.832519 | − | 0.553996i | \(-0.186898\pi\) | |||||||
\(198\) | − 1673.47i | − 0.600648i | ||||||||
\(199\) | 949.522 | 0.338240 | 0.169120 | − | 0.985595i | \(-0.445907\pi\) | ||||
0.169120 | + | 0.985595i | \(0.445907\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2209.56 | 0.775375 | ||||||||
\(202\) | − 1656.66i | − 0.577039i | ||||||||
\(203\) | 411.145i | 0.142151i | ||||||||
\(204\) | −1351.15 | −0.463721 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1962.55 | −0.663774 | ||||||||
\(207\) | 937.499i | 0.314786i | ||||||||
\(208\) | 3184.38i | 1.06152i | ||||||||
\(209\) | 4529.25 | 1.49902 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2306.64 | 0.752587 | 0.376294 | − | 0.926500i | \(-0.377198\pi\) | ||||
0.376294 | + | 0.926500i | \(0.377198\pi\) | |||||||
\(212\) | − 4147.35i | − 1.34359i | ||||||||
\(213\) | 1476.79i | 0.475062i | ||||||||
\(214\) | 7515.53 | 2.40071 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −138.838 | −0.0437348 | ||||||||
\(217\) | − 63.6182i | − 0.0199018i | ||||||||
\(218\) | − 2087.17i | − 0.648444i | ||||||||
\(219\) | 3494.26 | 1.07817 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2953.69 | 0.899033 | ||||||||
\(222\) | 2902.06i | 0.877357i | ||||||||
\(223\) | − 3227.61i | − 0.969222i | −0.874730 | − | 0.484611i | \(-0.838961\pi\) | ||||
0.874730 | − | 0.484611i | \(-0.161039\pi\) | |||||||
\(224\) | 1666.79 | 0.497174 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 887.519 | 0.261225 | ||||||||
\(227\) | 637.820i | 0.186492i | 0.995643 | + | 0.0932458i | \(0.0297242\pi\) | ||||
−0.995643 | + | 0.0932458i | \(0.970276\pi\) | |||||||
\(228\) | 1862.35i | 0.540953i | ||||||||
\(229\) | −544.774 | −0.157204 | −0.0786019 | − | 0.996906i | \(-0.525046\pi\) | ||||
−0.0786019 | + | 0.996906i | \(0.525046\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1019.94 | 0.290507 | ||||||||
\(232\) | 302.024i | 0.0854691i | ||||||||
\(233\) | − 5748.54i | − 1.61631i | −0.588972 | − | 0.808154i | \(-0.700467\pi\) | ||||
0.588972 | − | 0.808154i | \(-0.299533\pi\) | |||||||
\(234\) | −1504.23 | −0.420234 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3494.84 | −0.963961 | ||||||||
\(237\) | − 2616.59i | − 0.717154i | ||||||||
\(238\) | − 1813.14i | − 0.493816i | ||||||||
\(239\) | 2678.10 | 0.724820 | 0.362410 | − | 0.932019i | \(-0.381954\pi\) | ||||
0.362410 | + | 0.932019i | \(0.381954\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2202.16 | −0.588604 | −0.294302 | − | 0.955713i | \(-0.595087\pi\) | ||||
−0.294302 | + | 0.955713i | \(0.595087\pi\) | |||||||
\(242\) | 3935.25i | 1.04532i | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 2348.50 | 0.616177 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3173.09 | 0.822393 | ||||||||
\(247\) | − 4071.21i | − 1.04877i | ||||||||
\(248\) | − 46.7333i | − 0.0119660i | ||||||||
\(249\) | −1588.76 | −0.404353 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5716.90 | −1.43764 | −0.718820 | − | 0.695196i | \(-0.755317\pi\) | ||||
−0.718820 | + | 0.695196i | \(0.755317\pi\) | |||||||
\(252\) | 419.382i | 0.104836i | ||||||||
\(253\) | − 5059.22i | − 1.25719i | ||||||||
\(254\) | 9084.47 | 2.24413 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5108.88 | 1.24728 | ||||||||
\(257\) | − 4724.29i | − 1.14666i | −0.819323 | − | 0.573332i | \(-0.805650\pi\) | ||||
0.819323 | − | 0.573332i | \(-0.194350\pi\) | |||||||
\(258\) | − 1063.97i | − 0.256743i | ||||||||
\(259\) | −1768.73 | −0.424339 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −528.616 | −0.125366 | ||||||||
\(262\) | 4594.25i | 1.08334i | ||||||||
\(263\) | 5975.36i | 1.40097i | 0.713665 | + | 0.700487i | \(0.247034\pi\) | ||||
−0.713665 | + | 0.700487i | \(0.752966\pi\) | |||||||
\(264\) | 749.238 | 0.174668 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2499.14 | −0.576059 | ||||||||
\(267\) | − 1155.65i | − 0.264886i | ||||||||
\(268\) | − 4902.90i | − 1.11751i | ||||||||
\(269\) | −4486.11 | −1.01681 | −0.508407 | − | 0.861117i | \(-0.669766\pi\) | ||||
−0.508407 | + | 0.861117i | \(0.669766\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3827.68 | 0.857989 | 0.428994 | − | 0.903307i | \(-0.358868\pi\) | ||||
0.428994 | + | 0.903307i | \(0.358868\pi\) | |||||||
\(272\) | − 4934.97i | − 1.10010i | ||||||||
\(273\) | − 916.794i | − 0.203249i | ||||||||
\(274\) | 10647.8 | 2.34766 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2080.26 | 0.453685 | ||||||||
\(277\) | 3420.54i | 0.741950i | 0.928643 | + | 0.370975i | \(0.120976\pi\) | ||||
−0.928643 | + | 0.370975i | \(0.879024\pi\) | |||||||
\(278\) | 4768.71i | 1.02881i | ||||||||
\(279\) | 81.7948 | 0.0175517 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5235.92 | 1.11156 | 0.555781 | − | 0.831329i | \(-0.312419\pi\) | ||||
0.555781 | + | 0.831329i | \(0.312419\pi\) | |||||||
\(282\) | 6693.55i | 1.41346i | ||||||||
\(283\) | − 6985.88i | − 1.46738i | −0.679486 | − | 0.733688i | \(-0.737797\pi\) | ||||
0.679486 | − | 0.733688i | \(-0.262203\pi\) | |||||||
\(284\) | 3276.93 | 0.684683 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8117.60 | 1.67834 | ||||||||
\(287\) | 1933.92i | 0.397755i | ||||||||
\(288\) | 2143.01i | 0.438466i | ||||||||
\(289\) | 335.550 | 0.0682984 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1391.68 | 0.280349 | ||||||||
\(292\) | − 7753.59i | − 1.55392i | ||||||||
\(293\) | 7399.70i | 1.47541i | 0.675123 | + | 0.737705i | \(0.264090\pi\) | ||||
−0.675123 | + | 0.737705i | \(0.735910\pi\) | |||||||
\(294\) | −562.779 | −0.111639 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1299.30 | −0.255135 | ||||||||
\(297\) | 1311.35i | 0.256203i | ||||||||
\(298\) | − 74.2892i | − 0.0144411i | ||||||||
\(299\) | −4547.58 | −0.879577 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 648.463 | 0.124175 | ||||||||
\(302\) | − 8996.04i | − 1.71412i | ||||||||
\(303\) | 1298.17i | 0.246133i | ||||||||
\(304\) | −6802.11 | −1.28332 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2331.17 | 0.435504 | ||||||||
\(307\) | − 2668.64i | − 0.496116i | −0.968745 | − | 0.248058i | \(-0.920208\pi\) | ||||
0.968745 | − | 0.248058i | \(-0.0797923\pi\) | |||||||
\(308\) | − 2263.20i | − 0.418693i | ||||||||
\(309\) | 1537.88 | 0.283129 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6189.25 | 1.12849 | 0.564244 | − | 0.825608i | \(-0.309168\pi\) | ||||
0.564244 | + | 0.825608i | \(0.309168\pi\) | |||||||
\(312\) | − 673.468i | − 0.122204i | ||||||||
\(313\) | − 2921.59i | − 0.527598i | −0.964578 | − | 0.263799i | \(-0.915024\pi\) | ||||
0.964578 | − | 0.263799i | \(-0.0849755\pi\) | |||||||
\(314\) | −14925.0 | −2.68237 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5806.08 | −1.03360 | ||||||||
\(317\) | − 9825.56i | − 1.74088i | −0.492276 | − | 0.870439i | \(-0.663835\pi\) | ||||
0.492276 | − | 0.870439i | \(-0.336165\pi\) | |||||||
\(318\) | 7155.55i | 1.26183i | ||||||||
\(319\) | 2852.68 | 0.500687 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5889.26 | −1.02401 | ||||||||
\(322\) | 2791.56i | 0.483129i | ||||||||
\(323\) | 6309.33i | 1.08687i | ||||||||
\(324\) | −539.205 | −0.0924563 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5848.07 | −0.993541 | ||||||||
\(327\) | 1635.53i | 0.276590i | ||||||||
\(328\) | 1420.64i | 0.239151i | ||||||||
\(329\) | −4079.56 | −0.683627 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9258.17 | −1.53739 | −0.768693 | − | 0.639618i | \(-0.779093\pi\) | ||||
−0.768693 | + | 0.639618i | \(0.779093\pi\) | |||||||
\(332\) | 3525.39i | 0.582774i | ||||||||
\(333\) | − 2274.09i | − 0.374232i | ||||||||
\(334\) | −3822.75 | −0.626263 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1531.76 | −0.248704 | ||||||||
\(337\) | 3693.98i | 0.597103i | 0.954394 | + | 0.298552i | \(0.0965035\pi\) | ||||
−0.954394 | + | 0.298552i | \(0.903497\pi\) | |||||||
\(338\) | 1114.38i | 0.179331i | ||||||||
\(339\) | −695.470 | −0.111424 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −441.406 | −0.0700982 | ||||||||
\(342\) | − 3213.17i | − 0.508037i | ||||||||
\(343\) | − 343.000i | − 0.0539949i | ||||||||
\(344\) | 476.355 | 0.0746608 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2623.44 | −0.407622 | ||||||||
\(347\) | − 3832.83i | − 0.592960i | −0.955039 | − | 0.296480i | \(-0.904187\pi\) | ||||
0.955039 | − | 0.296480i | \(-0.0958128\pi\) | |||||||
\(348\) | 1172.97i | 0.180684i | ||||||||
\(349\) | −8325.22 | −1.27690 | −0.638451 | − | 0.769662i | \(-0.720425\pi\) | ||||
−0.638451 | + | 0.769662i | \(0.720425\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1178.74 | 0.179248 | ||||||||
\(352\) | − 11564.8i | − 1.75115i | ||||||||
\(353\) | − 8991.52i | − 1.35572i | −0.735189 | − | 0.677862i | \(-0.762907\pi\) | ||||
0.735189 | − | 0.677862i | \(-0.237093\pi\) | |||||||
\(354\) | 6029.76 | 0.905306 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2564.33 | −0.381767 | ||||||||
\(357\) | 1420.79i | 0.210634i | ||||||||
\(358\) | − 3926.38i | − 0.579652i | ||||||||
\(359\) | 12893.8 | 1.89557 | 0.947783 | − | 0.318917i | \(-0.103319\pi\) | ||||
0.947783 | + | 0.318917i | \(0.103319\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1837.46 | 0.267891 | ||||||||
\(362\) | 11100.1i | 1.61163i | ||||||||
\(363\) | − 3083.71i | − 0.445875i | ||||||||
\(364\) | −2034.32 | −0.292932 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4051.94 | −0.578684 | ||||||||
\(367\) | 7480.17i | 1.06393i | 0.846767 | + | 0.531964i | \(0.178546\pi\) | ||||
−0.846767 | + | 0.531964i | \(0.821454\pi\) | |||||||
\(368\) | 7598.02i | 1.07629i | ||||||||
\(369\) | −2486.47 | −0.350787 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4361.14 | −0.610293 | ||||||||
\(372\) | − 181.499i | − 0.0252964i | ||||||||
\(373\) | − 3523.32i | − 0.489090i | −0.969638 | − | 0.244545i | \(-0.921361\pi\) | ||||
0.969638 | − | 0.244545i | \(-0.0786386\pi\) | |||||||
\(374\) | −12580.2 | −1.73932 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2996.81 | −0.411033 | ||||||||
\(377\) | − 2564.19i | − 0.350298i | ||||||||
\(378\) | − 723.573i | − 0.0984565i | ||||||||
\(379\) | −13515.4 | −1.83177 | −0.915886 | − | 0.401438i | \(-0.868510\pi\) | ||||
−0.915886 | + | 0.401438i | \(0.868510\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7118.69 | −0.957222 | ||||||||
\(382\) | 4112.44i | 0.550813i | ||||||||
\(383\) | − 657.182i | − 0.0876774i | −0.999039 | − | 0.0438387i | \(-0.986041\pi\) | ||||
0.999039 | − | 0.0438387i | \(-0.0139588\pi\) | |||||||
\(384\) | −1946.75 | −0.258710 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3441.75 | −0.453836 | ||||||||
\(387\) | 833.738i | 0.109512i | ||||||||
\(388\) | − 3088.06i | − 0.404053i | ||||||||
\(389\) | 9741.87 | 1.26975 | 0.634875 | − | 0.772615i | \(-0.281052\pi\) | ||||
0.634875 | + | 0.772615i | \(0.281052\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7047.58 | 0.911538 | ||||||||
\(392\) | − 251.965i | − 0.0324646i | ||||||||
\(393\) | − 3600.11i | − 0.462091i | ||||||||
\(394\) | 11728.9 | 1.49973 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2909.82 | 0.369253 | ||||||||
\(397\) | − 4407.42i | − 0.557184i | −0.960410 | − | 0.278592i | \(-0.910132\pi\) | ||||
0.960410 | − | 0.278592i | \(-0.0898678\pi\) | |||||||
\(398\) | 3635.18i | 0.457827i | ||||||||
\(399\) | 1958.35 | 0.245715 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11569.5 | −1.44078 | −0.720391 | − | 0.693568i | \(-0.756037\pi\) | ||||
−0.720391 | + | 0.693568i | \(0.756037\pi\) | |||||||
\(402\) | 8459.14i | 1.04951i | ||||||||
\(403\) | 396.767i | 0.0490431i | ||||||||
\(404\) | 2880.59 | 0.354739 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1574.04 | −0.192410 | ||||||||
\(407\) | 12272.1i | 1.49461i | ||||||||
\(408\) | 1043.70i | 0.126645i | ||||||||
\(409\) | 3083.03 | 0.372729 | 0.186364 | − | 0.982481i | \(-0.440330\pi\) | ||||
0.186364 | + | 0.982481i | \(0.440330\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8343.76 | −1.00138 | ||||||||
\(412\) | − 3412.47i | − 0.408060i | ||||||||
\(413\) | 3674.99i | 0.437856i | ||||||||
\(414\) | −3589.15 | −0.426079 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −10395.3 | −1.22517 | ||||||||
\(417\) | − 3736.81i | − 0.438831i | ||||||||
\(418\) | 17339.9i | 2.02900i | ||||||||
\(419\) | 5415.21 | 0.631385 | 0.315692 | − | 0.948862i | \(-0.397763\pi\) | ||||
0.315692 | + | 0.948862i | \(0.397763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4188.34 | 0.484863 | 0.242432 | − | 0.970168i | \(-0.422055\pi\) | ||||
0.242432 | + | 0.970168i | \(0.422055\pi\) | |||||||
\(422\) | 8830.82i | 1.01867i | ||||||||
\(423\) | − 5245.15i | − 0.602902i | ||||||||
\(424\) | −3203.65 | −0.366941 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5653.79 | −0.643021 | ||||||||
\(427\) | − 2469.56i | − 0.279884i | ||||||||
\(428\) | 13068.0i | 1.47585i | ||||||||
\(429\) | −6361.05 | −0.715884 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9108.41 | −1.01795 | −0.508975 | − | 0.860781i | \(-0.669976\pi\) | ||||
−0.508975 | + | 0.860781i | \(0.669976\pi\) | |||||||
\(432\) | − 1969.41i | − 0.219336i | ||||||||
\(433\) | − 16847.0i | − 1.86979i | −0.354930 | − | 0.934893i | \(-0.615495\pi\) | ||||
0.354930 | − | 0.934893i | \(-0.384505\pi\) | |||||||
\(434\) | 243.558 | 0.0269381 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3629.16 | 0.398635 | ||||||||
\(437\) | − 9714.03i | − 1.06335i | ||||||||
\(438\) | 13377.5i | 1.45937i | ||||||||
\(439\) | −8434.14 | −0.916946 | −0.458473 | − | 0.888708i | \(-0.651603\pi\) | ||||
−0.458473 | + | 0.888708i | \(0.651603\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 11308.0i | 1.21689i | ||||||||
\(443\) | − 4298.49i | − 0.461010i | −0.973071 | − | 0.230505i | \(-0.925962\pi\) | ||||
0.973071 | − | 0.230505i | \(-0.0740378\pi\) | |||||||
\(444\) | −5046.09 | −0.539362 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12356.7 | 1.31189 | ||||||||
\(447\) | 58.2139i | 0.00615978i | ||||||||
\(448\) | 2296.48i | 0.242184i | ||||||||
\(449\) | −10545.0 | −1.10835 | −0.554173 | − | 0.832402i | \(-0.686965\pi\) | ||||
−0.554173 | + | 0.832402i | \(0.686965\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13418.2 | 1.40098 | ||||||||
\(452\) | 1543.21i | 0.160590i | ||||||||
\(453\) | 7049.40i | 0.731147i | ||||||||
\(454\) | −2441.85 | −0.252426 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1438.59 | 0.147737 | ||||||||
\(457\) | − 11952.4i | − 1.22344i | −0.791075 | − | 0.611719i | \(-0.790478\pi\) | ||||
0.791075 | − | 0.611719i | \(-0.209522\pi\) | |||||||
\(458\) | − 2085.63i | − 0.212784i | ||||||||
\(459\) | −1826.74 | −0.185762 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17200.9 | −1.73780 | −0.868900 | − | 0.494988i | \(-0.835173\pi\) | ||||
−0.868900 | + | 0.494988i | \(0.835173\pi\) | |||||||
\(462\) | 3904.76i | 0.393217i | ||||||||
\(463\) | − 10368.7i | − 1.04076i | −0.853934 | − | 0.520381i | \(-0.825790\pi\) | ||||
0.853934 | − | 0.520381i | \(-0.174210\pi\) | |||||||
\(464\) | −4284.20 | −0.428640 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22007.9 | 2.18776 | ||||||||
\(467\) | 16879.5i | 1.67257i | 0.548296 | + | 0.836284i | \(0.315277\pi\) | ||||
−0.548296 | + | 0.836284i | \(0.684723\pi\) | |||||||
\(468\) | − 2615.56i | − 0.258342i | ||||||||
\(469\) | −5155.64 | −0.507602 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11695.4 | 1.14415 | ||||||||
\(472\) | 2699.62i | 0.263263i | ||||||||
\(473\) | − 4499.27i | − 0.437371i | ||||||||
\(474\) | 10017.4 | 0.970706 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3152.67 | 0.303577 | ||||||||
\(477\) | − 5607.17i | − 0.538228i | ||||||||
\(478\) | 10252.9i | 0.981082i | ||||||||
\(479\) | −7329.12 | −0.699115 | −0.349558 | − | 0.936915i | \(-0.613668\pi\) | ||||
−0.349558 | + | 0.936915i | \(0.613668\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11031.0 | 1.04568 | ||||||||
\(482\) | − 8430.80i | − 0.796706i | ||||||||
\(483\) | − 2187.50i | − 0.206076i | ||||||||
\(484\) | −6842.60 | −0.642619 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 930.308 | 0.0868305 | ||||||||
\(487\) | 17209.5i | 1.60131i | 0.599125 | + | 0.800655i | \(0.295515\pi\) | ||||
−0.599125 | + | 0.800655i | \(0.704485\pi\) | |||||||
\(488\) | − 1814.11i | − 0.168281i | ||||||||
\(489\) | 4582.61 | 0.423789 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11392.5 | 1.04712 | 0.523560 | − | 0.851989i | \(-0.324604\pi\) | ||||
0.523560 | + | 0.851989i | \(0.324604\pi\) | |||||||
\(492\) | 5517.35i | 0.505572i | ||||||||
\(493\) | 3973.83i | 0.363027i | ||||||||
\(494\) | 15586.3 | 1.41956 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 662.912 | 0.0600113 | ||||||||
\(497\) | − 3445.85i | − 0.311001i | ||||||||
\(498\) | − 6082.47i | − 0.547313i | ||||||||
\(499\) | −19079.4 | −1.71164 | −0.855822 | − | 0.517271i | \(-0.826948\pi\) | ||||
−0.855822 | + | 0.517271i | \(0.826948\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2995.55 | 0.267129 | ||||||||
\(502\) | − 21886.7i | − 1.94592i | ||||||||
\(503\) | − 13499.4i | − 1.19663i | −0.801259 | − | 0.598317i | \(-0.795836\pi\) | ||||
0.801259 | − | 0.598317i | \(-0.204164\pi\) | |||||||
\(504\) | 323.955 | 0.0286311 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 19368.8 | 1.70168 | ||||||||
\(507\) | − 873.237i | − 0.0764928i | ||||||||
\(508\) | 15796.0i | 1.37960i | ||||||||
\(509\) | 4328.85 | 0.376960 | 0.188480 | − | 0.982077i | \(-0.439644\pi\) | ||||
0.188480 | + | 0.982077i | \(0.439644\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8153.27 | −0.705831 | ||||||||
\(512\) | 14367.6i | 1.24017i | ||||||||
\(513\) | 2517.88i | 0.216700i | ||||||||
\(514\) | 18086.6 | 1.55207 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1850.02 | 0.157835 | ||||||||
\(517\) | 28305.5i | 2.40788i | ||||||||
\(518\) | − 6771.47i | − 0.574365i | ||||||||
\(519\) | 2055.76 | 0.173869 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19395.7 | 1.63098 | 0.815490 | − | 0.578771i | \(-0.196468\pi\) | ||||
0.815490 | + | 0.578771i | \(0.196468\pi\) | |||||||
\(522\) | − 2023.77i | − 0.169689i | ||||||||
\(523\) | 20413.8i | 1.70675i | 0.521294 | + | 0.853377i | \(0.325450\pi\) | ||||
−0.521294 | + | 0.853377i | \(0.674550\pi\) | |||||||
\(524\) | −7988.47 | −0.665989 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22876.2 | −1.89629 | ||||||||
\(527\) | − 614.887i | − 0.0508252i | ||||||||
\(528\) | 10627.9i | 0.875987i | ||||||||
\(529\) | 1316.34 | 0.108189 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4724.99 | −0.386153 | ||||||||
\(532\) | − 4345.49i | − 0.354137i | ||||||||
\(533\) | − 12061.3i | − 0.980171i | ||||||||
\(534\) | 4424.32 | 0.358537 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3787.28 | −0.305197 | ||||||||
\(537\) | 3076.75i | 0.247247i | ||||||||
\(538\) | − 17174.8i | − 1.37631i | ||||||||
\(539\) | −2379.86 | −0.190181 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4919.18 | −0.390928 | −0.195464 | − | 0.980711i | \(-0.562621\pi\) | ||||
−0.195464 | + | 0.980711i | \(0.562621\pi\) | |||||||
\(542\) | 14654.0i | 1.16133i | ||||||||
\(543\) | − 8698.19i | − 0.687431i | ||||||||
\(544\) | 16110.0 | 1.26969 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3509.88 | 0.275108 | ||||||||
\(547\) | − 15334.2i | − 1.19862i | −0.800518 | − | 0.599308i | \(-0.795442\pi\) | ||||
0.800518 | − | 0.599308i | \(-0.204558\pi\) | |||||||
\(548\) | 18514.4i | 1.44324i | ||||||||
\(549\) | 3175.15 | 0.246834 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5477.33 | 0.423488 | ||||||||
\(552\) | − 1606.92i | − 0.123904i | ||||||||
\(553\) | 6105.37i | 0.469487i | ||||||||
\(554\) | −13095.3 | −1.00427 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8291.81 | −0.632466 | ||||||||
\(557\) | 8613.78i | 0.655256i | 0.944807 | + | 0.327628i | \(0.106249\pi\) | ||||
−0.944807 | + | 0.327628i | \(0.893751\pi\) | |||||||
\(558\) | 313.145i | 0.0237572i | ||||||||
\(559\) | −4044.26 | −0.306000 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9857.98 | 0.741897 | ||||||||
\(562\) | 20045.3i | 1.50456i | ||||||||
\(563\) | − 2320.81i | − 0.173731i | −0.996220 | − | 0.0868654i | \(-0.972315\pi\) | ||||
0.996220 | − | 0.0868654i | \(-0.0276850\pi\) | |||||||
\(564\) | −11638.7 | −0.868934 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 26744.9 | 1.98617 | ||||||||
\(567\) | 567.000i | 0.0419961i | ||||||||
\(568\) | − 2531.29i | − 0.186990i | ||||||||
\(569\) | 1736.04 | 0.127906 | 0.0639529 | − | 0.997953i | \(-0.479629\pi\) | ||||
0.0639529 | + | 0.997953i | \(0.479629\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23897.8 | 1.75148 | 0.875738 | − | 0.482786i | \(-0.160375\pi\) | ||||
0.875738 | + | 0.482786i | \(0.160375\pi\) | |||||||
\(572\) | 14114.9i | 1.03177i | ||||||||
\(573\) | − 3222.55i | − 0.234946i | ||||||||
\(574\) | −7403.87 | −0.538382 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2952.61 | −0.213586 | ||||||||
\(577\) | − 8029.26i | − 0.579311i | −0.957131 | − | 0.289655i | \(-0.906459\pi\) | ||||
0.957131 | − | 0.289655i | \(-0.0935407\pi\) | |||||||
\(578\) | 1284.63i | 0.0924455i | ||||||||
\(579\) | 2697.00 | 0.193581 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3707.12 | 0.264711 | ||||||||
\(582\) | 5327.93i | 0.379467i | ||||||||
\(583\) | 30259.1i | 2.14958i | ||||||||
\(584\) | −5989.32 | −0.424383 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28329.2 | −1.99705 | ||||||||
\(587\) | 8015.14i | 0.563578i | 0.959476 | + | 0.281789i | \(0.0909278\pi\) | ||||
−0.959476 | + | 0.281789i | \(0.909072\pi\) | |||||||
\(588\) | − 978.558i | − 0.0686310i | ||||||||
\(589\) | −847.529 | −0.0592900 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9190.88 | −0.639700 | ||||||||
\(592\) | − 18430.5i | − 1.27954i | ||||||||
\(593\) | 12820.3i | 0.887801i | 0.896076 | + | 0.443901i | \(0.146406\pi\) | ||||
−0.896076 | + | 0.443901i | \(0.853594\pi\) | |||||||
\(594\) | −5020.41 | −0.346784 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 129.174 | 0.00887779 | ||||||||
\(597\) | − 2848.57i | − 0.195283i | ||||||||
\(598\) | − 17410.1i | − 1.19055i | ||||||||
\(599\) | 15330.5 | 1.04572 | 0.522860 | − | 0.852418i | \(-0.324865\pi\) | ||||
0.522860 | + | 0.852418i | \(0.324865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 107.658 | 0.00730694 | 0.00365347 | − | 0.999993i | \(-0.498837\pi\) | ||||
0.00365347 | + | 0.999993i | \(0.498837\pi\) | |||||||
\(602\) | 2482.59i | 0.168078i | ||||||||
\(603\) | − 6628.68i | − 0.447663i | ||||||||
\(604\) | 15642.3 | 1.05377 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4969.97 | −0.333154 | ||||||||
\(607\) | 8213.06i | 0.549189i | 0.961560 | + | 0.274595i | \(0.0885436\pi\) | ||||
−0.961560 | + | 0.274595i | \(0.911456\pi\) | |||||||
\(608\) | − 22205.2i | − 1.48115i | ||||||||
\(609\) | 1233.44 | 0.0820712 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25443.0 | 1.68463 | ||||||||
\(612\) | 4053.44i | 0.267729i | ||||||||
\(613\) | 1242.60i | 0.0818732i | 0.999162 | + | 0.0409366i | \(0.0130342\pi\) | ||||
−0.999162 | + | 0.0409366i | \(0.986966\pi\) | |||||||
\(614\) | 10216.7 | 0.671519 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1748.22 | −0.114347 | ||||||||
\(617\) | 13170.6i | 0.859367i | 0.902980 | + | 0.429683i | \(0.141375\pi\) | ||||
−0.902980 | + | 0.429683i | \(0.858625\pi\) | |||||||
\(618\) | 5887.65i | 0.383230i | ||||||||
\(619\) | −19774.1 | −1.28399 | −0.641993 | − | 0.766711i | \(-0.721892\pi\) | ||||
−0.641993 | + | 0.766711i | \(0.721892\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2812.50 | 0.181742 | ||||||||
\(622\) | 23695.1i | 1.52747i | ||||||||
\(623\) | 2696.51i | 0.173409i | ||||||||
\(624\) | 9553.14 | 0.612871 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11185.1 | 0.714132 | ||||||||
\(627\) | − 13587.8i | − 0.865459i | ||||||||
\(628\) | − 25951.5i | − 1.64901i | ||||||||
\(629\) | −17095.3 | −1.08368 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14308.8 | −0.902735 | −0.451367 | − | 0.892338i | \(-0.649064\pi\) | ||||
−0.451367 | + | 0.892338i | \(0.649064\pi\) | |||||||
\(632\) | 4484.95i | 0.282281i | ||||||||
\(633\) | − 6919.93i | − 0.434507i | ||||||||
\(634\) | 37616.4 | 2.35637 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12442.0 | −0.775722 | ||||||||
\(637\) | 2139.19i | 0.133058i | ||||||||
\(638\) | 10921.3i | 0.677707i | ||||||||
\(639\) | 4430.38 | 0.274277 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11537.5 | 0.710925 | 0.355463 | − | 0.934691i | \(-0.384323\pi\) | ||||
0.355463 | + | 0.934691i | \(0.384323\pi\) | |||||||
\(642\) | − 22546.6i | − 1.38605i | ||||||||
\(643\) | 19603.0i | 1.20228i | 0.799144 | + | 0.601139i | \(0.205286\pi\) | ||||
−0.799144 | + | 0.601139i | \(0.794714\pi\) | |||||||
\(644\) | −4853.95 | −0.297007 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24154.8 | −1.47114 | ||||||||
\(647\) | − 21650.0i | − 1.31553i | −0.753223 | − | 0.657765i | \(-0.771502\pi\) | ||||
0.753223 | − | 0.657765i | \(-0.228498\pi\) | |||||||
\(648\) | 416.513i | 0.0252503i | ||||||||
\(649\) | 25498.4 | 1.54222 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −190.855 | −0.0114903 | ||||||||
\(652\) | − 10168.6i | − 0.610787i | ||||||||
\(653\) | − 2927.33i | − 0.175429i | −0.996146 | − | 0.0877145i | \(-0.972044\pi\) | ||||
0.996146 | − | 0.0877145i | \(-0.0279563\pi\) | |||||||
\(654\) | −6261.50 | −0.374379 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −20151.7 | −1.19938 | ||||||||
\(657\) | − 10482.8i | − 0.622484i | ||||||||
\(658\) | − 15618.3i | − 0.925326i | ||||||||
\(659\) | 4778.76 | 0.282480 | 0.141240 | − | 0.989975i | \(-0.454891\pi\) | ||||
0.141240 | + | 0.989975i | \(0.454891\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31510.3 | −1.85417 | −0.927086 | − | 0.374849i | \(-0.877695\pi\) | ||||
−0.927086 | + | 0.374849i | \(0.877695\pi\) | |||||||
\(662\) | − 35444.2i | − 2.08093i | ||||||||
\(663\) | − 8861.06i | − 0.519057i | ||||||||
\(664\) | 2723.21 | 0.159158 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8706.17 | 0.506542 | ||||||||
\(667\) | − 6118.23i | − 0.355170i | ||||||||
\(668\) | − 6646.99i | − 0.385000i | ||||||||
\(669\) | −9682.82 | −0.559581 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17134.7 | −0.985808 | ||||||||
\(672\) | − 5000.37i | − 0.287044i | ||||||||
\(673\) | − 8992.15i | − 0.515040i | −0.966273 | − | 0.257520i | \(-0.917095\pi\) | ||||
0.966273 | − | 0.257520i | \(-0.0829054\pi\) | |||||||
\(674\) | −14142.1 | −0.808211 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1937.67 | −0.110245 | ||||||||
\(677\) | − 19340.8i | − 1.09797i | −0.835832 | − | 0.548985i | \(-0.815014\pi\) | ||||
0.835832 | − | 0.548985i | \(-0.184986\pi\) | |||||||
\(678\) | − 2662.56i | − 0.150818i | ||||||||
\(679\) | −3247.25 | −0.183531 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1913.46 | 0.107671 | ||||||||
\(682\) | − 1689.89i | − 0.0948816i | ||||||||
\(683\) | − 4255.14i | − 0.238387i | −0.992871 | − | 0.119194i | \(-0.961969\pi\) | ||||
0.992871 | − | 0.119194i | \(-0.0380309\pi\) | |||||||
\(684\) | 5587.05 | 0.312319 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1313.15 | 0.0730850 | ||||||||
\(687\) | 1634.32i | 0.0907616i | ||||||||
\(688\) | 6757.08i | 0.374435i | ||||||||
\(689\) | 27199.1 | 1.50392 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17505.5 | −0.963733 | −0.481867 | − | 0.876245i | \(-0.660041\pi\) | ||||
−0.481867 | + | 0.876245i | \(0.660041\pi\) | |||||||
\(692\) | − 4561.63i | − 0.250588i | ||||||||
\(693\) | − 3059.82i | − 0.167724i | ||||||||
\(694\) | 14673.7 | 0.802603 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 906.071 | 0.0493456 | ||||||||
\(697\) | 18691.8i | 1.01579i | ||||||||
\(698\) | − 31872.5i | − 1.72836i | ||||||||
\(699\) | −17245.6 | −0.933175 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3240.77 | −0.174611 | −0.0873054 | − | 0.996182i | \(-0.527826\pi\) | ||||
−0.0873054 | + | 0.996182i | \(0.527826\pi\) | |||||||
\(702\) | 4512.70i | 0.242622i | ||||||||
\(703\) | 23563.3i | 1.26416i | ||||||||
\(704\) | 15933.8 | 0.853022 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 34423.4 | 1.83504 | ||||||||
\(707\) | − 3029.07i | − 0.161132i | ||||||||
\(708\) | 10484.5i | 0.556543i | ||||||||
\(709\) | −19949.3 | −1.05672 | −0.528358 | − | 0.849022i | \(-0.677192\pi\) | ||||
−0.528358 | + | 0.849022i | \(0.677192\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7849.76 | −0.414049 | ||||||||
\(712\) | 1980.83i | 0.104262i | ||||||||
\(713\) | 946.698i | 0.0497253i | ||||||||
\(714\) | −5439.41 | −0.285105 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6827.17 | 0.356345 | ||||||||
\(717\) | − 8034.30i | − 0.418475i | ||||||||
\(718\) | 49362.9i | 2.56575i | ||||||||
\(719\) | 11259.4 | 0.584011 | 0.292006 | − | 0.956417i | \(-0.405677\pi\) | ||||
0.292006 | + | 0.956417i | \(0.405677\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3588.38 | −0.185351 | ||||||||
\(722\) | 7034.60i | 0.362605i | ||||||||
\(723\) | 6606.47i | 0.339830i | ||||||||
\(724\) | −19300.9 | −0.990761 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 11805.8 | 0.603516 | ||||||||
\(727\) | 12228.5i | 0.623840i | 0.950108 | + | 0.311920i | \(0.100972\pi\) | ||||
−0.950108 | + | 0.311920i | \(0.899028\pi\) | |||||||
\(728\) | 1571.43i | 0.0800013i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6267.56 | 0.317119 | ||||||||
\(732\) | − 7045.49i | − 0.355750i | ||||||||
\(733\) | − 26635.1i | − 1.34214i | −0.741392 | − | 0.671072i | \(-0.765834\pi\) | ||||
0.741392 | − | 0.671072i | \(-0.234166\pi\) | |||||||
\(734\) | −28637.3 | −1.44008 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24803.4 | −1.24221 | ||||||||
\(737\) | 35771.7i | 1.78788i | ||||||||
\(738\) | − 9519.26i | − 0.474809i | ||||||||
\(739\) | 6074.00 | 0.302349 | 0.151174 | − | 0.988507i | \(-0.451694\pi\) | ||||
0.151174 | + | 0.988507i | \(0.451694\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12213.6 | −0.605505 | ||||||||
\(742\) | − 16696.3i | − 0.826065i | ||||||||
\(743\) | − 4016.87i | − 0.198337i | −0.995071 | − | 0.0991686i | \(-0.968382\pi\) | ||||
0.995071 | − | 0.0991686i | \(-0.0316183\pi\) | |||||||
\(744\) | −140.200 | −0.00690858 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 13488.8 | 0.662010 | ||||||||
\(747\) | 4766.29i | 0.233453i | ||||||||
\(748\) | − 21874.4i | − 1.06926i | ||||||||
\(749\) | 13741.6 | 0.670370 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23913.2 | −1.16192 | −0.580962 | − | 0.813931i | \(-0.697324\pi\) | ||||
−0.580962 | + | 0.813931i | \(0.697324\pi\) | |||||||
\(752\) | − 42509.6i | − 2.06139i | ||||||||
\(753\) | 17150.7i | 0.830022i | ||||||||
\(754\) | 9816.81 | 0.474147 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1258.15 | 0.0605269 | ||||||||
\(757\) | − 31044.9i | − 1.49055i | −0.666758 | − | 0.745275i | \(-0.732318\pi\) | ||||
0.666758 | − | 0.745275i | \(-0.267682\pi\) | |||||||
\(758\) | − 51742.9i | − 2.47940i | ||||||||
\(759\) | −15177.6 | −0.725842 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14011.8 | 0.667446 | 0.333723 | − | 0.942671i | \(-0.391695\pi\) | ||||
0.333723 | + | 0.942671i | \(0.391695\pi\) | |||||||
\(762\) | − 27253.4i | − 1.29565i | ||||||||
\(763\) | − 3816.23i | − 0.181071i | ||||||||
\(764\) | −7150.69 | −0.338616 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2515.97 | 0.118676 | ||||||||
\(767\) | − 22919.8i | − 1.07899i | ||||||||
\(768\) | − 15326.6i | − 0.720120i | ||||||||
\(769\) | −3342.49 | −0.156740 | −0.0783701 | − | 0.996924i | \(-0.524972\pi\) | ||||
−0.0783701 | + | 0.996924i | \(0.524972\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14172.9 | −0.662027 | ||||||||
\(772\) | − 5984.51i | − 0.278999i | ||||||||
\(773\) | − 21074.6i | − 0.980594i | −0.871555 | − | 0.490297i | \(-0.836888\pi\) | ||||
0.871555 | − | 0.490297i | \(-0.163112\pi\) | |||||||
\(774\) | −3191.90 | −0.148231 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2385.40 | −0.110349 | ||||||||
\(777\) | 5306.20i | 0.244992i | ||||||||
\(778\) | 37296.0i | 1.71867i | ||||||||
\(779\) | 25763.9 | 1.18496 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23908.5 | −1.09541 | ||||||||
\(782\) | 26981.1i | 1.23382i | ||||||||
\(783\) | 1585.85i | 0.0723800i | ||||||||
\(784\) | 3574.12 | 0.162815 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13782.8 | 0.625464 | ||||||||
\(787\) | − 21394.8i | − 0.969048i | −0.874778 | − | 0.484524i | \(-0.838993\pi\) | ||||
0.874778 | − | 0.484524i | \(-0.161007\pi\) | |||||||
\(788\) | 20394.1i | 0.921968i | ||||||||
\(789\) | 17926.1 | 0.808853 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1622.76 | 0.0729442 | ||||||||
\(792\) | − 2247.71i | − 0.100845i | ||||||||
\(793\) | 15401.9i | 0.689706i | ||||||||
\(794\) | 16873.5 | 0.754179 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6320.83 | −0.281452 | ||||||||
\(797\) | − 20645.0i | − 0.917547i | −0.888553 | − | 0.458773i | \(-0.848289\pi\) | ||||
0.888553 | − | 0.458773i | \(-0.151711\pi\) | |||||||
\(798\) | 7497.41i | 0.332588i | ||||||||
\(799\) | −39430.0 | −1.74585 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3466.95 | −0.152932 | ||||||||
\(802\) | − 44293.0i | − 1.95017i | ||||||||
\(803\) | 56570.4i | 2.48608i | ||||||||
\(804\) | −14708.7 | −0.645194 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1518.99 | −0.0663825 | ||||||||
\(807\) | 13458.3i | 0.587058i | ||||||||
\(808\) | − 2225.13i | − 0.0968810i | ||||||||
\(809\) | 15939.0 | 0.692688 | 0.346344 | − | 0.938108i | \(-0.387423\pi\) | ||||
0.346344 | + | 0.938108i | \(0.387423\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22829.2 | 0.988460 | 0.494230 | − | 0.869331i | \(-0.335450\pi\) | ||||
0.494230 | + | 0.869331i | \(0.335450\pi\) | |||||||
\(812\) | − 2736.94i | − 0.118285i | ||||||||
\(813\) | − 11483.0i | − 0.495360i | ||||||||
\(814\) | −46982.9 | −2.02303 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −14804.9 | −0.635141 | ||||||||
\(817\) | − 8638.90i | − 0.369935i | ||||||||
\(818\) | 11803.2i | 0.504508i | ||||||||
\(819\) | −2750.38 | −0.117346 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5700.22 | −0.242313 | −0.121157 | − | 0.992633i | \(-0.538660\pi\) | ||||
−0.121157 | + | 0.992633i | \(0.538660\pi\) | |||||||
\(822\) | − 31943.5i | − 1.35542i | ||||||||
\(823\) | − 32438.0i | − 1.37390i | −0.726707 | − | 0.686948i | \(-0.758950\pi\) | ||||
0.726707 | − | 0.686948i | \(-0.241050\pi\) | |||||||
\(824\) | −2635.99 | −0.111443 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14069.4 | −0.592662 | ||||||||
\(827\) | 12762.6i | 0.536638i | 0.963330 | + | 0.268319i | \(0.0864681\pi\) | ||||
−0.963330 | + | 0.268319i | \(0.913532\pi\) | |||||||
\(828\) | − 6240.79i | − 0.261935i | ||||||||
\(829\) | 30766.7 | 1.28899 | 0.644494 | − | 0.764609i | \(-0.277068\pi\) | ||||
0.644494 | + | 0.764609i | \(0.277068\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10261.6 | 0.428365 | ||||||||
\(832\) | − 14322.4i | − 0.596804i | ||||||||
\(833\) | − 3315.19i | − 0.137892i | ||||||||
\(834\) | 14306.1 | 0.593981 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −30150.6 | −1.24734 | ||||||||
\(837\) | − 245.384i | − 0.0101335i | ||||||||
\(838\) | 20731.7i | 0.854613i | ||||||||
\(839\) | 9779.71 | 0.402423 | 0.201212 | − | 0.979548i | \(-0.435512\pi\) | ||||
0.201212 | + | 0.979548i | \(0.435512\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20939.2 | −0.858551 | ||||||||
\(842\) | 16034.8i | 0.656288i | ||||||||
\(843\) | − 15707.8i | − 0.641760i | ||||||||
\(844\) | −15355.0 | −0.626233 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 20080.7 | 0.816061 | ||||||||
\(847\) | 7195.32i | 0.291894i | ||||||||
\(848\) | − 45443.7i | − 1.84026i | ||||||||
\(849\) | −20957.6 | −0.847190 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26320.4 | 1.06023 | ||||||||
\(852\) | − 9830.79i | − 0.395302i | ||||||||
\(853\) | 24201.5i | 0.971445i | 0.874113 | + | 0.485723i | \(0.161444\pi\) | ||||
−0.874113 | + | 0.485723i | \(0.838556\pi\) | |||||||
\(854\) | 9454.52 | 0.378837 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10094.5 | 0.403062 | ||||||||
\(857\) | − 21036.7i | − 0.838507i | −0.907869 | − | 0.419254i | \(-0.862292\pi\) | ||||
0.907869 | − | 0.419254i | \(-0.137708\pi\) | |||||||
\(858\) | − 24352.8i | − 0.968988i | ||||||||
\(859\) | 6179.19 | 0.245438 | 0.122719 | − | 0.992441i | \(-0.460839\pi\) | ||||
0.122719 | + | 0.992441i | \(0.460839\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5801.76 | 0.229644 | ||||||||
\(862\) | − 34870.9i | − 1.37785i | ||||||||
\(863\) | 50256.2i | 1.98232i | 0.132671 | + | 0.991160i | \(0.457644\pi\) | ||||
−0.132671 | + | 0.991160i | \(0.542356\pi\) | |||||||
\(864\) | 6429.04 | 0.253149 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 64497.7 | 2.53085 | ||||||||
\(867\) | − 1006.65i | − 0.0394321i | ||||||||
\(868\) | 423.497i | 0.0165604i | ||||||||
\(869\) | 42361.2 | 1.65363 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32154.1 | 1.25086 | ||||||||
\(872\) | − 2803.37i | − 0.108869i | ||||||||
\(873\) | − 4175.03i | − 0.161860i | ||||||||
\(874\) | 37189.5 | 1.43930 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −23260.8 | −0.897156 | ||||||||
\(877\) | 9175.95i | 0.353306i | 0.984273 | + | 0.176653i | \(0.0565271\pi\) | ||||
−0.984273 | + | 0.176653i | \(0.943473\pi\) | |||||||
\(878\) | − 32289.5i | − 1.24114i | ||||||||
\(879\) | 22199.1 | 0.851828 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26172.7 | −1.00089 | −0.500444 | − | 0.865769i | \(-0.666830\pi\) | ||||
−0.500444 | + | 0.865769i | \(0.666830\pi\) | |||||||
\(882\) | 1688.34i | 0.0644549i | ||||||||
\(883\) | 18615.5i | 0.709471i | 0.934967 | + | 0.354736i | \(0.115429\pi\) | ||||
−0.934967 | + | 0.354736i | \(0.884571\pi\) | |||||||
\(884\) | −19662.3 | −0.748092 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16456.4 | 0.624001 | ||||||||
\(887\) | 12837.8i | 0.485964i | 0.970031 | + | 0.242982i | \(0.0781256\pi\) | ||||
−0.970031 | + | 0.242982i | \(0.921874\pi\) | |||||||
\(888\) | 3897.89i | 0.147302i | ||||||||
\(889\) | 16610.3 | 0.626649 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3934.05 | 0.147919 | ||||||||
\(892\) | 21485.7i | 0.806496i | ||||||||
\(893\) | 54348.4i | 2.03662i | ||||||||
\(894\) | −222.868 | −0.00833759 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4542.42 | 0.169366 | ||||||||
\(897\) | 13642.7i | 0.507824i | ||||||||
\(898\) | − 40370.6i | − 1.50020i | ||||||||
\(899\) | −533.803 | −0.0198035 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42151.5 | −1.55857 | ||||||||
\(902\) | 51370.7i | 1.89630i | ||||||||
\(903\) | − 1945.39i | − 0.0716926i | ||||||||
\(904\) | 1192.07 | 0.0438579 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −26988.1 | −0.989647 | ||||||||
\(907\) | 26766.1i | 0.979885i | 0.871755 | + | 0.489942i | \(0.162982\pi\) | ||||
−0.871755 | + | 0.489942i | \(0.837018\pi\) | |||||||
\(908\) | − 4245.87i | − 0.155181i | ||||||||
\(909\) | 3894.52 | 0.142105 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5022.67 | 0.182666 | 0.0913328 | − | 0.995820i | \(-0.470887\pi\) | ||||
0.0913328 | + | 0.995820i | \(0.470887\pi\) | |||||||
\(912\) | 20406.3i | 0.740923i | ||||||||
\(913\) | − 25721.3i | − 0.932367i | ||||||||
\(914\) | 45759.0 | 1.65599 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3626.48 | 0.130810 | ||||||||
\(917\) | 8400.26i | 0.302509i | ||||||||
\(918\) | − 6993.52i | − 0.251439i | ||||||||
\(919\) | −9541.79 | −0.342497 | −0.171248 | − | 0.985228i | \(-0.554780\pi\) | ||||
−0.171248 | + | 0.985228i | \(0.554780\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8005.93 | −0.286432 | ||||||||
\(922\) | − 65852.4i | − 2.35220i | ||||||||
\(923\) | 21490.7i | 0.766387i | ||||||||
\(924\) | −6789.59 | −0.241733 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 39695.7 | 1.40873 | ||||||||
\(927\) | − 4613.63i | − 0.163464i | ||||||||
\(928\) | − 13985.6i | − 0.494718i | ||||||||
\(929\) | 25479.6 | 0.899846 | 0.449923 | − | 0.893067i | \(-0.351451\pi\) | ||||
0.449923 | + | 0.893067i | \(0.351451\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4569.49 | −0.160858 | ||||||||
\(932\) | 38267.2i | 1.34494i | ||||||||
\(933\) | − 18567.7i | − 0.651533i | ||||||||
\(934\) | −64621.9 | −2.26391 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2020.41 | −0.0705545 | ||||||||
\(937\) | 33608.3i | 1.17176i | 0.810399 | + | 0.585878i | \(0.199250\pi\) | ||||
−0.810399 | + | 0.585878i | \(0.800750\pi\) | |||||||
\(938\) | − 19738.0i | − 0.687066i | ||||||||
\(939\) | −8764.77 | −0.304609 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19173.6 | −0.664232 | −0.332116 | − | 0.943239i | \(-0.607762\pi\) | ||||
−0.332116 | + | 0.943239i | \(0.607762\pi\) | |||||||
\(942\) | 44774.9i | 1.54867i | ||||||||
\(943\) | − 28778.5i | − 0.993804i | ||||||||
\(944\) | −38294.0 | −1.32030 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17225.1 | 0.592005 | ||||||||
\(947\) | 979.315i | 0.0336045i | 0.999859 | + | 0.0168023i | \(0.00534857\pi\) | ||||
−0.999859 | + | 0.0168023i | \(0.994651\pi\) | |||||||
\(948\) | 17418.2i | 0.596749i | ||||||||
\(949\) | 50849.5 | 1.73935 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29476.7 | −1.00510 | ||||||||
\(952\) | − 2435.31i | − 0.0829083i | ||||||||
\(953\) | 3048.61i | 0.103624i | 0.998657 | + | 0.0518122i | \(0.0164997\pi\) | ||||
−0.998657 | + | 0.0518122i | \(0.983500\pi\) | |||||||
\(954\) | 21466.7 | 0.728521 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −17827.7 | −0.603127 | ||||||||
\(957\) | − 8558.03i | − 0.289072i | ||||||||
\(958\) | − 28059.0i | − 0.946290i | ||||||||
\(959\) | 19468.8 | 0.655557 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29708.4 | −0.997227 | ||||||||
\(962\) | 42231.6i | 1.41538i | ||||||||
\(963\) | 17667.8i | 0.591211i | ||||||||
\(964\) | 14659.4 | 0.489781 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8374.67 | 0.278934 | ||||||||
\(967\) | 14467.9i | 0.481133i | 0.970633 | + | 0.240567i | \(0.0773332\pi\) | ||||
−0.970633 | + | 0.240567i | \(0.922667\pi\) | |||||||
\(968\) | 5285.62i | 0.175502i | ||||||||
\(969\) | 18928.0 | 0.627507 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12952.8 | 0.428090 | 0.214045 | − | 0.976824i | \(-0.431336\pi\) | ||||
0.214045 | + | 0.976824i | \(0.431336\pi\) | |||||||
\(972\) | 1617.62i | 0.0533797i | ||||||||
\(973\) | 8719.23i | 0.287282i | ||||||||
\(974\) | −65885.4 | −2.16746 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 25733.2 | 0.843954 | ||||||||
\(977\) | − 47244.2i | − 1.54706i | −0.633760 | − | 0.773529i | \(-0.718489\pi\) | ||||
0.633760 | − | 0.773529i | \(-0.281511\pi\) | |||||||
\(978\) | 17544.2i | 0.573621i | ||||||||
\(979\) | 18709.4 | 0.610781 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4906.58 | 0.159689 | ||||||||
\(982\) | 43615.3i | 1.41733i | ||||||||
\(983\) | − 1536.84i | − 0.0498651i | −0.999689 | − | 0.0249326i | \(-0.992063\pi\) | ||||
0.999689 | − | 0.0249326i | \(-0.00793711\pi\) | |||||||
\(984\) | 4261.92 | 0.138074 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −15213.5 | −0.491376 | ||||||||
\(987\) | 12238.7i | 0.394692i | ||||||||
\(988\) | 27101.5i | 0.872685i | ||||||||
\(989\) | −9649.73 | −0.310256 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3785.22 | 0.121334 | 0.0606668 | − | 0.998158i | \(-0.480677\pi\) | ||||
0.0606668 | + | 0.998158i | \(0.480677\pi\) | |||||||
\(992\) | 2164.04i | 0.0692625i | ||||||||
\(993\) | 27774.5i | 0.887610i | ||||||||
\(994\) | 13192.2 | 0.420956 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 10576.2 | 0.336465 | ||||||||
\(997\) | 25894.9i | 0.822566i | 0.911508 | + | 0.411283i | \(0.134919\pi\) | ||||
−0.911508 | + | 0.411283i | \(0.865081\pi\) | |||||||
\(998\) | − 73044.0i | − 2.31680i | ||||||||
\(999\) | −6822.26 | −0.216063 |
(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 | 525.4.d.l.274.4 | 4 | ||
5.2 | odd | 4 | 105.4.a.e.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 525.4.a.l.1.2 | 2 | |||
5.4 | even | 2 | inner | 525.4.d.l.274.1 | 4 | ||
15.2 | even | 4 | 315.4.a.k.1.2 | 2 | |||
15.8 | even | 4 | 1575.4.a.q.1.1 | 2 | |||
20.7 | even | 4 | 1680.4.a.bo.1.1 | 2 | |||
35.27 | even | 4 | 735.4.a.o.1.1 | 2 | |||
105.62 | odd | 4 | 2205.4.a.bb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.e.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
315.4.a.k.1.2 | 2 | 15.2 | even | 4 | |||
525.4.a.l.1.2 | 2 | 5.3 | odd | 4 | |||
525.4.d.l.274.1 | 4 | 5.4 | even | 2 | inner | ||
525.4.d.l.274.4 | 4 | 1.1 | even | 1 | trivial | ||
735.4.a.o.1.1 | 2 | 35.27 | even | 4 | |||
1575.4.a.q.1.1 | 2 | 15.8 | even | 4 | |||
1680.4.a.bo.1.1 | 2 | 20.7 | even | 4 | |||
2205.4.a.bb.1.2 | 2 | 105.62 | odd | 4 |