Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(1999,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3330.1999");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3330.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.5901838731\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 51x^{6} - 124x^{5} + 154x^{4} - 46x^{3} + x^{2} + 4x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 370) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1999.1 | ||
Root | \(1.24331 + 1.24331i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.1999 |
Dual form | 3330.2.d.p.1999.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.07757 | + | 0.826871i | −0.929116 | + | 0.369788i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.67211i | 1.76589i | 0.469475 | + | 0.882946i | \(0.344443\pi\) | ||||
−0.469475 | + | 0.882946i | \(0.655557\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.826871 | + | 2.07757i | 0.261480 | + | 0.656984i | ||||
\(11\) | −0.0451320 | −0.0136078 | −0.00680390 | − | 0.999977i | \(-0.502166\pi\) | ||||
−0.00680390 | + | 0.999977i | \(0.502166\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.26514i | − | 1.46029i | −0.683294 | − | 0.730143i | \(-0.739453\pi\) | ||
0.683294 | − | 0.730143i | \(-0.260547\pi\) | |||||||
\(14\) | 4.67211 | 1.24867 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.60861i | − | 0.875217i | −0.899166 | − | 0.437608i | \(-0.855826\pi\) | ||
0.899166 | − | 0.437608i | \(-0.144174\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.22000 | 1.42697 | 0.713483 | − | 0.700672i | \(-0.247116\pi\) | ||||
0.713483 | + | 0.700672i | \(0.247116\pi\) | |||||||
\(20\) | 2.07757 | − | 0.826871i | 0.464558 | − | 0.184894i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0451320i | 0.00962217i | ||||||||
\(23\) | − | 2.20164i | − | 0.459073i | −0.973300 | − | 0.229536i | \(-0.926279\pi\) | ||
0.973300 | − | 0.229536i | \(-0.0737210\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.63257 | − | 3.43576i | 0.726514 | − | 0.687152i | ||||
\(26\) | −5.26514 | −1.03258 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 4.67211i | − | 0.882946i | ||||||
\(29\) | −4.20386 | −0.780637 | −0.390319 | − | 0.920680i | \(-0.627635\pi\) | ||||
−0.390319 | + | 0.920680i | \(0.627635\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.01051 | −0.540704 | −0.270352 | − | 0.962762i | \(-0.587140\pi\) | ||||
−0.270352 | + | 0.962762i | \(0.587140\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.60861 | −0.618872 | ||||||||
\(35\) | −3.86323 | − | 9.70662i | −0.653006 | − | 1.64072i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000i | 0.164399i | ||||||||
\(38\) | − | 6.22000i | − | 1.00902i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.826871 | − | 2.07757i | −0.130740 | − | 0.328492i | ||||
\(41\) | 7.38299 | 1.15303 | 0.576515 | − | 0.817087i | \(-0.304412\pi\) | ||||
0.576515 | + | 0.817087i | \(0.304412\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.54789i | 0.846046i | 0.906119 | + | 0.423023i | \(0.139031\pi\) | ||||
−0.906119 | + | 0.423023i | \(0.860969\pi\) | |||||||
\(44\) | 0.0451320 | 0.00680390 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.20164 | −0.324613 | ||||||||
\(47\) | 4.28072i | 0.624407i | 0.950015 | + | 0.312204i | \(0.101067\pi\) | ||||
−0.950015 | + | 0.312204i | \(0.898933\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.8286 | −2.11837 | ||||||||
\(50\) | −3.43576 | − | 3.63257i | −0.485890 | − | 0.513723i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.26514i | 0.730143i | ||||||||
\(53\) | 6.10215i | 0.838194i | 0.907941 | + | 0.419097i | \(0.137653\pi\) | ||||
−0.907941 | + | 0.419097i | \(0.862347\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0937647 | − | 0.0373183i | 0.0126432 | − | 0.00503200i | ||||
\(56\) | −4.67211 | −0.624337 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.20386i | 0.551994i | ||||||||
\(59\) | 13.5275 | 1.76113 | 0.880565 | − | 0.473926i | \(-0.157164\pi\) | ||||
0.880565 | + | 0.473926i | \(0.157164\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.27299 | −0.547100 | −0.273550 | − | 0.961858i | \(-0.588198\pi\) | ||||
−0.273550 | + | 0.961858i | \(0.588198\pi\) | |||||||
\(62\) | 3.01051i | 0.382335i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 4.35359 | + | 10.9387i | 0.539996 | + | 1.35678i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.3751i | 1.51186i | 0.654650 | + | 0.755932i | \(0.272816\pi\) | ||||
−0.654650 | + | 0.755932i | \(0.727184\pi\) | |||||||
\(68\) | 3.60861i | 0.437608i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.70662 | + | 3.86323i | −1.16016 | + | 0.461745i | ||||
\(71\) | 4.49354 | 0.533285 | 0.266642 | − | 0.963796i | \(-0.414086\pi\) | ||||
0.266642 | + | 0.963796i | \(0.414086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.03811i | − | 0.823748i | −0.911241 | − | 0.411874i | \(-0.864874\pi\) | ||
0.911241 | − | 0.411874i | \(-0.135126\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.22000 | −0.713483 | ||||||||
\(77\) | − | 0.210861i | − | 0.0240299i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.72499 | 0.981638 | 0.490819 | − | 0.871262i | \(-0.336698\pi\) | ||||
0.490819 | + | 0.871262i | \(0.336698\pi\) | |||||||
\(80\) | −2.07757 | + | 0.826871i | −0.232279 | + | 0.0924470i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 7.38299i | − | 0.815315i | ||||||
\(83\) | − | 0.880231i | − | 0.0966179i | −0.998832 | − | 0.0483090i | \(-0.984617\pi\) | ||
0.998832 | − | 0.0483090i | \(-0.0153832\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.98386 | + | 7.49713i | 0.323645 | + | 0.813178i | ||||
\(86\) | 5.54789 | 0.598245 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 0.0451320i | − | 0.00481108i | ||||||
\(89\) | 9.97602 | 1.05746 | 0.528728 | − | 0.848791i | \(-0.322669\pi\) | ||||
0.528728 | + | 0.848791i | \(0.322669\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 24.5993 | 2.57871 | ||||||||
\(92\) | 2.20164i | 0.229536i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.28072 | 0.441523 | ||||||||
\(95\) | −12.9225 | + | 5.14314i | −1.32582 | + | 0.527675i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.240408i | 0.0244097i | 0.999926 | + | 0.0122049i | \(0.00388502\pi\) | ||||
−0.999926 | + | 0.0122049i | \(0.996115\pi\) | |||||||
\(98\) | 14.8286i | 1.49792i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.63257 | + | 3.43576i | −0.363257 | + | 0.343576i | ||||
\(101\) | 5.61775 | 0.558987 | 0.279494 | − | 0.960148i | \(-0.409833\pi\) | ||||
0.279494 | + | 0.960148i | \(0.409833\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.5663i | 1.23819i | 0.785316 | + | 0.619095i | \(0.212501\pi\) | ||||
−0.785316 | + | 0.619095i | \(0.787499\pi\) | |||||||
\(104\) | 5.26514 | 0.516289 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.10215 | 0.592693 | ||||||||
\(107\) | 17.9395i | 1.73427i | 0.498070 | + | 0.867137i | \(0.334042\pi\) | ||||
−0.498070 | + | 0.867137i | \(0.665958\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.09936 | −0.296865 | −0.148433 | − | 0.988923i | \(-0.547423\pi\) | ||||
−0.148433 | + | 0.988923i | \(0.547423\pi\) | |||||||
\(110\) | −0.0373183 | − | 0.0937647i | −0.00355816 | − | 0.00894011i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.67211i | 0.441473i | ||||||||
\(113\) | 4.36184i | 0.410328i | 0.978728 | + | 0.205164i | \(0.0657727\pi\) | ||||
−0.978728 | + | 0.205164i | \(0.934227\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.82047 | + | 4.57405i | 0.169760 | + | 0.426532i | ||||
\(116\) | 4.20386 | 0.390319 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 13.5275i | − | 1.24531i | ||||||
\(119\) | 16.8598 | 1.54554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9980 | −0.999815 | ||||||||
\(122\) | 4.27299i | 0.386858i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.01051 | 0.270352 | ||||||||
\(125\) | −4.70597 | + | 10.1417i | −0.420915 | + | 0.907100i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.6572i | 1.56683i | 0.621502 | + | 0.783413i | \(0.286523\pi\) | ||||
−0.621502 | + | 0.783413i | \(0.713477\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.9387 | − | 4.35359i | 0.959385 | − | 0.381835i | ||||
\(131\) | 10.3103 | 0.900812 | 0.450406 | − | 0.892824i | \(-0.351279\pi\) | ||||
0.450406 | + | 0.892824i | \(0.351279\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 29.0605i | 2.51987i | ||||||||
\(134\) | 12.3751 | 1.06905 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.60861 | 0.309436 | ||||||||
\(137\) | − | 3.21863i | − | 0.274986i | −0.990503 | − | 0.137493i | \(-0.956095\pi\) | ||
0.990503 | − | 0.137493i | \(-0.0439045\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.9400 | −1.77611 | −0.888055 | − | 0.459737i | \(-0.847944\pi\) | ||||
−0.888055 | + | 0.459737i | \(0.847944\pi\) | |||||||
\(140\) | 3.86323 | + | 9.70662i | 0.326503 | + | 0.820359i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 4.49354i | − | 0.377089i | ||||||
\(143\) | 0.237626i | 0.0198713i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.73380 | − | 3.47605i | 0.725303 | − | 0.288670i | ||||
\(146\) | −7.03811 | −0.582478 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | −21.9832 | −1.80093 | −0.900467 | − | 0.434924i | \(-0.856775\pi\) | ||||
−0.900467 | + | 0.434924i | \(0.856775\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1877 | 1.15458 | 0.577290 | − | 0.816539i | \(-0.304110\pi\) | ||||
0.577290 | + | 0.816539i | \(0.304110\pi\) | |||||||
\(152\) | 6.22000i | 0.504509i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.210861 | −0.0169917 | ||||||||
\(155\) | 6.25454 | − | 2.48931i | 0.502377 | − | 0.199946i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 19.9316i | − | 1.59072i | −0.606139 | − | 0.795359i | \(-0.707283\pi\) | ||
0.606139 | − | 0.795359i | \(-0.292717\pi\) | |||||||
\(158\) | − | 8.72499i | − | 0.694123i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.826871 | + | 2.07757i | 0.0653699 | + | 0.164246i | ||||
\(161\) | 10.2863 | 0.810673 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.65087i | − | 0.677588i | −0.940861 | − | 0.338794i | \(-0.889981\pi\) | ||
0.940861 | − | 0.338794i | \(-0.110019\pi\) | |||||||
\(164\) | −7.38299 | −0.576515 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.880231 | −0.0683192 | ||||||||
\(167\) | 11.9640i | 0.925803i | 0.886410 | + | 0.462901i | \(0.153192\pi\) | ||||
−0.886410 | + | 0.462901i | \(0.846808\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.7216 | −1.13243 | ||||||||
\(170\) | 7.49713 | − | 2.98386i | 0.575004 | − | 0.228851i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 5.54789i | − | 0.423023i | ||||||
\(173\) | − | 5.33508i | − | 0.405619i | −0.979218 | − | 0.202809i | \(-0.934993\pi\) | ||
0.979218 | − | 0.202809i | \(-0.0650071\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.0523 | + | 16.9718i | 1.21344 | + | 1.28294i | ||||
\(176\) | −0.0451320 | −0.00340195 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 9.97602i | − | 0.747734i | ||||||
\(179\) | −5.27905 | −0.394575 | −0.197288 | − | 0.980346i | \(-0.563213\pi\) | ||||
−0.197288 | + | 0.980346i | \(0.563213\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.7448 | 1.31896 | 0.659478 | − | 0.751723i | \(-0.270777\pi\) | ||||
0.659478 | + | 0.751723i | \(0.270777\pi\) | |||||||
\(182\) | − | 24.5993i | − | 1.82342i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.20164 | 0.162307 | ||||||||
\(185\) | −0.826871 | − | 2.07757i | −0.0607928 | − | 0.152746i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.162864i | 0.0119098i | ||||||||
\(188\) | − | 4.28072i | − | 0.312204i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.14314 | + | 12.9225i | 0.373123 | + | 0.937495i | ||||
\(191\) | 3.11649 | 0.225501 | 0.112751 | − | 0.993623i | \(-0.464034\pi\) | ||||
0.112751 | + | 0.993623i | \(0.464034\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.78278i | 0.632198i | 0.948726 | + | 0.316099i | \(0.102373\pi\) | ||||
−0.948726 | + | 0.316099i | \(0.897627\pi\) | |||||||
\(194\) | 0.240408 | 0.0172603 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.8286 | 1.05919 | ||||||||
\(197\) | − | 7.00278i | − | 0.498928i | −0.968384 | − | 0.249464i | \(-0.919746\pi\) | ||
0.968384 | − | 0.249464i | \(-0.0802544\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.3202 | −1.22780 | −0.613900 | − | 0.789384i | \(-0.710400\pi\) | ||||
−0.613900 | + | 0.789384i | \(0.710400\pi\) | |||||||
\(200\) | 3.43576 | + | 3.63257i | 0.242945 | + | 0.256861i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 5.61775i | − | 0.395264i | ||||||
\(203\) | − | 19.6409i | − | 1.37852i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.3387 | + | 6.10478i | −1.07130 | + | 0.426377i | ||||
\(206\) | 12.5663 | 0.875533 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 5.26514i | − | 0.365071i | ||||||
\(209\) | −0.280721 | −0.0194179 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.77438 | 0.466368 | 0.233184 | − | 0.972433i | \(-0.425086\pi\) | ||||
0.233184 | + | 0.972433i | \(0.425086\pi\) | |||||||
\(212\) | − | 6.10215i | − | 0.419097i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17.9395 | 1.22632 | ||||||||
\(215\) | −4.58739 | − | 11.5261i | −0.312858 | − | 0.786075i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 14.0654i | − | 0.954825i | ||||||
\(218\) | 3.09936i | 0.209915i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.0937647 | + | 0.0373183i | −0.00632161 | + | 0.00251600i | ||||
\(221\) | −18.9998 | −1.27807 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.2559i | 0.686784i | 0.939192 | + | 0.343392i | \(0.111576\pi\) | ||||
−0.939192 | + | 0.343392i | \(0.888424\pi\) | |||||||
\(224\) | 4.67211 | 0.312168 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.36184 | 0.290145 | ||||||||
\(227\) | 11.2744i | 0.748306i | 0.927367 | + | 0.374153i | \(0.122066\pi\) | ||||
−0.927367 | + | 0.374153i | \(0.877934\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.40494 | 0.621496 | 0.310748 | − | 0.950492i | \(-0.399421\pi\) | ||||
0.310748 | + | 0.950492i | \(0.399421\pi\) | |||||||
\(230\) | 4.57405 | − | 1.82047i | 0.301604 | − | 0.120038i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 4.20386i | − | 0.275997i | ||||||
\(233\) | − | 3.22867i | − | 0.211517i | −0.994392 | − | 0.105759i | \(-0.966273\pi\) | ||
0.994392 | − | 0.105759i | \(-0.0337271\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.53961 | − | 8.89348i | −0.230898 | − | 0.580147i | ||||
\(236\) | −13.5275 | −0.880565 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 16.8598i | − | 1.09286i | ||||||
\(239\) | −17.8612 | −1.15534 | −0.577672 | − | 0.816269i | \(-0.696039\pi\) | ||||
−0.577672 | + | 0.816269i | \(0.696039\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.6840 | 1.71887 | 0.859434 | − | 0.511248i | \(-0.170816\pi\) | ||||
0.859434 | + | 0.511248i | \(0.170816\pi\) | |||||||
\(242\) | 10.9980i | 0.706976i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.27299 | 0.273550 | ||||||||
\(245\) | 30.8074 | − | 12.2614i | 1.96821 | − | 0.783349i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 32.7492i | − | 2.08378i | ||||||
\(248\) | − | 3.01051i | − | 0.191168i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.1417 | + | 4.70597i | 0.641417 | + | 0.297632i | ||||
\(251\) | 30.1552 | 1.90338 | 0.951690 | − | 0.307060i | \(-0.0993453\pi\) | ||||
0.951690 | + | 0.307060i | \(0.0993453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0993641i | 0.00624697i | ||||||||
\(254\) | 17.6572 | 1.10791 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.15376i | 0.196726i | 0.995151 | + | 0.0983632i | \(0.0313607\pi\) | ||||
−0.995151 | + | 0.0983632i | \(0.968639\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.67211 | −0.290311 | ||||||||
\(260\) | −4.35359 | − | 10.9387i | −0.269998 | − | 0.678388i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 10.3103i | − | 0.636970i | ||||||
\(263\) | 14.0332i | 0.865322i | 0.901557 | + | 0.432661i | \(0.142425\pi\) | ||||
−0.901557 | + | 0.432661i | \(0.857575\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.04569 | − | 12.6776i | −0.309954 | − | 0.778780i | ||||
\(266\) | 29.0605 | 1.78182 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 12.3751i | − | 0.755932i | ||||||
\(269\) | −30.1257 | −1.83679 | −0.918397 | − | 0.395660i | \(-0.870516\pi\) | ||||
−0.918397 | + | 0.395660i | \(0.870516\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.8802 | 0.903910 | 0.451955 | − | 0.892041i | \(-0.350727\pi\) | ||||
0.451955 | + | 0.892041i | \(0.350727\pi\) | |||||||
\(272\) | − | 3.60861i | − | 0.218804i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.21863 | −0.194445 | ||||||||
\(275\) | −0.163945 | + | 0.155063i | −0.00988625 | + | 0.00935063i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.147278i | 0.00884908i | 0.999990 | + | 0.00442454i | \(0.00140838\pi\) | ||||
−0.999990 | + | 0.00442454i | \(0.998592\pi\) | |||||||
\(278\) | 20.9400i | 1.25590i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9.70662 | − | 3.86323i | 0.580082 | − | 0.230872i | ||||
\(281\) | 25.5247 | 1.52268 | 0.761339 | − | 0.648354i | \(-0.224542\pi\) | ||||
0.761339 | + | 0.648354i | \(0.224542\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 0.0562691i | − | 0.00334485i | −0.999999 | − | 0.00167242i | \(-0.999468\pi\) | ||
0.999999 | − | 0.00167242i | \(-0.000532349\pi\) | |||||||
\(284\) | −4.49354 | −0.266642 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.237626 | 0.0140511 | ||||||||
\(287\) | 34.4942i | 2.03613i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.97793 | 0.233996 | ||||||||
\(290\) | −3.47605 | − | 8.73380i | −0.204121 | − | 0.512866i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.03811i | 0.411874i | ||||||||
\(293\) | 13.7033i | 0.800557i | 0.916394 | + | 0.400278i | \(0.131087\pi\) | ||||
−0.916394 | + | 0.400278i | \(0.868913\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.1043 | + | 11.1855i | −1.63629 | + | 0.651245i | ||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 21.9832i | 1.27345i | ||||||||
\(299\) | −11.5919 | −0.670377 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.9204 | −1.49403 | ||||||||
\(302\) | − | 14.1877i | − | 0.816411i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.22000 | 0.356742 | ||||||||
\(305\) | 8.87742 | − | 3.53321i | 0.508320 | − | 0.202311i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 17.5823i | − | 1.00348i | −0.865020 | − | 0.501738i | \(-0.832694\pi\) | ||
0.865020 | − | 0.501738i | \(-0.167306\pi\) | |||||||
\(308\) | 0.210861i | 0.0120149i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.48931 | − | 6.25454i | −0.141383 | − | 0.355234i | ||||
\(311\) | −0.353133 | −0.0200244 | −0.0100122 | − | 0.999950i | \(-0.503187\pi\) | ||||
−0.0100122 | + | 0.999950i | \(0.503187\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.8717i | 1.06669i | 0.845897 | + | 0.533346i | \(0.179066\pi\) | ||||
−0.845897 | + | 0.533346i | \(0.820934\pi\) | |||||||
\(314\) | −19.9316 | −1.12481 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.72499 | −0.490819 | ||||||||
\(317\) | − | 15.1979i | − | 0.853601i | −0.904346 | − | 0.426800i | \(-0.859641\pi\) | ||
0.904346 | − | 0.426800i | \(-0.140359\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.189728 | 0.0106228 | ||||||||
\(320\) | 2.07757 | − | 0.826871i | 0.116140 | − | 0.0462235i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 10.2863i | − | 0.573232i | ||||||
\(323\) | − | 22.4456i | − | 1.24890i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.0897 | − | 19.1260i | −1.00344 | − | 1.06092i | ||||
\(326\) | −8.65087 | −0.479127 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.38299i | 0.407658i | ||||||||
\(329\) | −20.0000 | −1.10264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.0210 | −1.26535 | −0.632674 | − | 0.774418i | \(-0.718043\pi\) | ||||
−0.632674 | + | 0.774418i | \(0.718043\pi\) | |||||||
\(332\) | 0.880231i | 0.0483090i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.9640 | 0.654641 | ||||||||
\(335\) | −10.2326 | − | 25.7102i | −0.559069 | − | 1.40470i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.0776i | 1.85633i | 0.372173 | + | 0.928163i | \(0.378613\pi\) | ||||
−0.372173 | + | 0.928163i | \(0.621387\pi\) | |||||||
\(338\) | 14.7216i | 0.800752i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.98386 | − | 7.49713i | −0.161822 | − | 0.406589i | ||||
\(341\) | 0.135870 | 0.00735779 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 36.5761i | − | 1.97493i | ||||||
\(344\) | −5.54789 | −0.299122 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.33508 | −0.286816 | ||||||||
\(347\) | − | 13.8449i | − | 0.743236i | −0.928386 | − | 0.371618i | \(-0.878803\pi\) | ||
0.928386 | − | 0.371618i | \(-0.121197\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.3765 | −0.608970 | −0.304485 | − | 0.952517i | \(-0.598484\pi\) | ||||
−0.304485 | + | 0.952517i | \(0.598484\pi\) | |||||||
\(350\) | 16.9718 | − | 16.0523i | 0.907179 | − | 0.858029i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.0451320i | 0.00240554i | ||||||||
\(353\) | 19.2631i | 1.02527i | 0.858606 | + | 0.512636i | \(0.171331\pi\) | ||||
−0.858606 | + | 0.512636i | \(0.828669\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.33562 | + | 3.71558i | −0.495483 | + | 0.197202i | ||||
\(356\) | −9.97602 | −0.528728 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.27905i | 0.279007i | ||||||||
\(359\) | 14.6645 | 0.773961 | 0.386980 | − | 0.922088i | \(-0.373518\pi\) | ||||
0.386980 | + | 0.922088i | \(0.373518\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.6884 | 1.03623 | ||||||||
\(362\) | − | 17.7448i | − | 0.932643i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −24.5993 | −1.28935 | ||||||||
\(365\) | 5.81961 | + | 14.6221i | 0.304612 | + | 0.765357i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.868349i | 0.0453275i | 0.999743 | + | 0.0226637i | \(0.00721471\pi\) | ||||
−0.999743 | + | 0.0226637i | \(0.992785\pi\) | |||||||
\(368\) | − | 2.20164i | − | 0.114768i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.07757 | + | 0.826871i | −0.108008 | + | 0.0429870i | ||||
\(371\) | −28.5099 | −1.48016 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 32.4555i | − | 1.68048i | −0.542214 | − | 0.840240i | \(-0.682414\pi\) | ||
0.542214 | − | 0.840240i | \(-0.317586\pi\) | |||||||
\(374\) | 0.162864 | 0.00842148 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.28072 | −0.220761 | ||||||||
\(377\) | 22.1339i | 1.13995i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.2511 | 1.55389 | 0.776947 | − | 0.629566i | \(-0.216767\pi\) | ||||
0.776947 | + | 0.629566i | \(0.216767\pi\) | |||||||
\(380\) | 12.9225 | − | 5.14314i | 0.662909 | − | 0.263838i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 3.11649i | − | 0.159453i | ||||||
\(383\) | 14.4935i | 0.740585i | 0.928915 | + | 0.370293i | \(0.120743\pi\) | ||||
−0.928915 | + | 0.370293i | \(0.879257\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.174355 | + | 0.438079i | 0.00888597 | + | 0.0223266i | ||||
\(386\) | 8.78278 | 0.447032 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 0.240408i | − | 0.0122049i | ||||||
\(389\) | 36.9033 | 1.87107 | 0.935537 | − | 0.353229i | \(-0.114916\pi\) | ||||
0.935537 | + | 0.353229i | \(0.114916\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.94485 | −0.401788 | ||||||||
\(392\) | − | 14.8286i | − | 0.748958i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.00278 | −0.352795 | ||||||||
\(395\) | −18.1267 | + | 7.21444i | −0.912056 | + | 0.362998i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.9365i | 1.15115i | 0.817749 | + | 0.575575i | \(0.195222\pi\) | ||||
−0.817749 | + | 0.575575i | \(0.804778\pi\) | |||||||
\(398\) | 17.3202i | 0.868185i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.63257 | − | 3.43576i | 0.181628 | − | 0.171788i | ||||
\(401\) | −27.4332 | −1.36995 | −0.684973 | − | 0.728568i | \(-0.740186\pi\) | ||||
−0.684973 | + | 0.728568i | \(0.740186\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.8508i | 0.789582i | ||||||||
\(404\) | −5.61775 | −0.279494 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −19.6409 | −0.974761 | ||||||||
\(407\) | − | 0.0451320i | − | 0.00223711i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.3920 | 1.05777 | 0.528883 | − | 0.848695i | \(-0.322611\pi\) | ||||
0.528883 | + | 0.848695i | \(0.322611\pi\) | |||||||
\(410\) | 6.10478 | + | 15.3387i | 0.301494 | + | 0.757522i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 12.5663i | − | 0.619095i | ||||||
\(413\) | 63.2019i | 3.10996i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.727838 | + | 1.82874i | 0.0357282 | + | 0.0897693i | ||||
\(416\) | −5.26514 | −0.258144 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.280721i | 0.0137305i | ||||||||
\(419\) | 23.0891 | 1.12797 | 0.563987 | − | 0.825784i | \(-0.309267\pi\) | ||||
0.563987 | + | 0.825784i | \(0.309267\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.83757 | −0.0895576 | −0.0447788 | − | 0.998997i | \(-0.514258\pi\) | ||||
−0.0447788 | + | 0.998997i | \(0.514258\pi\) | |||||||
\(422\) | − | 6.77438i | − | 0.329772i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.10215 | −0.296346 | ||||||||
\(425\) | −12.3983 | − | 13.1085i | −0.601407 | − | 0.635857i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 19.9639i | − | 0.966120i | ||||||
\(428\) | − | 17.9395i | − | 0.867137i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.5261 | + | 4.58739i | −0.555839 | + | 0.221224i | ||||
\(431\) | 15.9796 | 0.769710 | 0.384855 | − | 0.922977i | \(-0.374251\pi\) | ||||
0.384855 | + | 0.922977i | \(0.374251\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.2525i | 1.21356i | 0.794870 | + | 0.606779i | \(0.207539\pi\) | ||||
−0.794870 | + | 0.606779i | \(0.792461\pi\) | |||||||
\(434\) | −14.0654 | −0.675163 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.09936 | 0.148433 | ||||||||
\(437\) | − | 13.6942i | − | 0.655082i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.30792 | 0.444243 | 0.222121 | − | 0.975019i | \(-0.428702\pi\) | ||||
0.222121 | + | 0.975019i | \(0.428702\pi\) | |||||||
\(440\) | 0.0373183 | + | 0.0937647i | 0.00177908 | + | 0.00447005i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 18.9998i | 0.903729i | ||||||||
\(443\) | − | 9.52445i | − | 0.452520i | −0.974067 | − | 0.226260i | \(-0.927350\pi\) | ||
0.974067 | − | 0.226260i | \(-0.0726500\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.7258 | + | 8.24888i | −0.982499 | + | 0.391035i | ||||
\(446\) | 10.2559 | 0.485629 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 4.67211i | − | 0.220736i | ||||||
\(449\) | 5.43278 | 0.256389 | 0.128194 | − | 0.991749i | \(-0.459082\pi\) | ||||
0.128194 | + | 0.991749i | \(0.459082\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.333209 | −0.0156902 | ||||||||
\(452\) | − | 4.36184i | − | 0.205164i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.2744 | 0.529132 | ||||||||
\(455\) | −51.1067 | + | 20.3404i | −2.39592 | + | 0.953575i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.54789i | 0.353076i | 0.984294 | + | 0.176538i | \(0.0564898\pi\) | ||||
−0.984294 | + | 0.176538i | \(0.943510\pi\) | |||||||
\(458\) | − | 9.40494i | − | 0.439464i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.82047 | − | 4.57405i | −0.0848798 | − | 0.213266i | ||||
\(461\) | 35.4323 | 1.65025 | 0.825124 | − | 0.564952i | \(-0.191105\pi\) | ||||
0.825124 | + | 0.564952i | \(0.191105\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 20.9124i | − | 0.971883i | −0.873991 | − | 0.485942i | \(-0.838477\pi\) | ||
0.873991 | − | 0.485942i | \(-0.161523\pi\) | |||||||
\(464\) | −4.20386 | −0.195159 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.22867 | −0.149565 | ||||||||
\(467\) | − | 6.62523i | − | 0.306579i | −0.988181 | − | 0.153289i | \(-0.951013\pi\) | ||
0.988181 | − | 0.153289i | \(-0.0489867\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −57.8180 | −2.66979 | ||||||||
\(470\) | −8.89348 | + | 3.53961i | −0.410226 | + | 0.163270i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.5275i | 0.622653i | ||||||||
\(473\) | − | 0.250387i | − | 0.0115128i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.5946 | − | 21.3704i | 1.03671 | − | 0.980543i | ||||
\(476\) | −16.8598 | −0.772769 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 17.8612i | 0.816952i | ||||||||
\(479\) | −29.4581 | −1.34597 | −0.672987 | − | 0.739655i | \(-0.734989\pi\) | ||||
−0.672987 | + | 0.739655i | \(0.734989\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.26514 | 0.240070 | ||||||||
\(482\) | − | 26.6840i | − | 1.21542i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.9980 | 0.499907 | ||||||||
\(485\) | −0.198786 | − | 0.499463i | −0.00902642 | − | 0.0226795i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.80654i | 0.399063i | 0.979891 | + | 0.199531i | \(0.0639419\pi\) | ||||
−0.979891 | + | 0.199531i | \(0.936058\pi\) | |||||||
\(488\) | − | 4.27299i | − | 0.193429i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −12.2614 | − | 30.8074i | −0.553912 | − | 1.39174i | ||||
\(491\) | −5.14258 | −0.232082 | −0.116041 | − | 0.993244i | \(-0.537020\pi\) | ||||
−0.116041 | + | 0.993244i | \(0.537020\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.1701i | 0.683227i | ||||||||
\(494\) | −32.7492 | −1.47345 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.01051 | −0.135176 | ||||||||
\(497\) | 20.9943i | 0.941723i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.9692 | 0.580579 | 0.290290 | − | 0.956939i | \(-0.406248\pi\) | ||||
0.290290 | + | 0.956939i | \(0.406248\pi\) | |||||||
\(500\) | 4.70597 | − | 10.1417i | 0.210457 | − | 0.453550i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 30.1552i | − | 1.34589i | ||||||
\(503\) | 17.2091i | 0.767314i | 0.923476 | + | 0.383657i | \(0.125336\pi\) | ||||
−0.923476 | + | 0.383657i | \(0.874664\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.6713 | + | 4.64516i | −0.519364 | + | 0.206707i | ||||
\(506\) | 0.0993641 | 0.00441727 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 17.6572i | − | 0.783413i | ||||||
\(509\) | −12.1085 | −0.536698 | −0.268349 | − | 0.963322i | \(-0.586478\pi\) | ||||
−0.268349 | + | 0.963322i | \(0.586478\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.8828 | 1.45465 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.15376 | 0.139107 | ||||||||
\(515\) | −10.3907 | − | 26.1072i | −0.457868 | − | 1.15042i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.193197i | − | 0.00849681i | ||||||
\(518\) | 4.67211i | 0.205281i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.9387 | + | 4.35359i | −0.479692 | + | 0.190918i | ||||
\(521\) | 18.7936 | 0.823362 | 0.411681 | − | 0.911328i | \(-0.364942\pi\) | ||||
0.411681 | + | 0.911328i | \(0.364942\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.9985i | 1.88019i | 0.340909 | + | 0.940096i | \(0.389265\pi\) | ||||
−0.340909 | + | 0.940096i | \(0.610735\pi\) | |||||||
\(524\) | −10.3103 | −0.450406 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.0332 | 0.611875 | ||||||||
\(527\) | 10.8638i | 0.473233i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.1528 | 0.789252 | ||||||||
\(530\) | −12.6776 | + | 5.04569i | −0.550680 | + | 0.219171i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 29.0605i | − | 1.25993i | ||||||
\(533\) | − | 38.8725i | − | 1.68375i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.8336 | − | 37.2704i | −0.641314 | − | 1.61134i | ||||
\(536\) | −12.3751 | −0.534525 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 30.1257i | 1.29881i | ||||||||
\(539\) | 0.669244 | 0.0288264 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.1751 | 1.29733 | 0.648664 | − | 0.761075i | \(-0.275328\pi\) | ||||
0.648664 | + | 0.761075i | \(0.275328\pi\) | |||||||
\(542\) | − | 14.8802i | − | 0.639161i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.60861 | −0.154718 | ||||||||
\(545\) | 6.43914 | − | 2.56278i | 0.275822 | − | 0.109777i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 31.6736i | − | 1.35426i | −0.735862 | − | 0.677132i | \(-0.763223\pi\) | ||
0.735862 | − | 0.677132i | \(-0.236777\pi\) | |||||||
\(548\) | 3.21863i | 0.137493i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.155063 | + | 0.163945i | 0.00661189 | + | 0.00699063i | ||||
\(551\) | −26.1480 | −1.11394 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 40.7641i | 1.73347i | ||||||||
\(554\) | 0.147278 | 0.00625724 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.9400 | 0.888055 | ||||||||
\(557\) | 0.708971i | 0.0300401i | 0.999887 | + | 0.0150200i | \(0.00478120\pi\) | ||||
−0.999887 | + | 0.0150200i | \(0.995219\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.2104 | 1.23547 | ||||||||
\(560\) | −3.86323 | − | 9.70662i | −0.163251 | − | 0.410180i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 25.5247i | − | 1.07670i | ||||||
\(563\) | − | 29.9399i | − | 1.26182i | −0.775857 | − | 0.630908i | \(-0.782682\pi\) | ||
0.775857 | − | 0.630908i | \(-0.217318\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.60668 | − | 9.06202i | −0.151734 | − | 0.381242i | ||||
\(566\) | −0.0562691 | −0.00236517 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.49354i | 0.188545i | ||||||||
\(569\) | 21.1453 | 0.886456 | 0.443228 | − | 0.896409i | \(-0.353833\pi\) | ||||
0.443228 | + | 0.896409i | \(0.353833\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.5326 | −0.817416 | −0.408708 | − | 0.912665i | \(-0.634020\pi\) | ||||
−0.408708 | + | 0.912665i | \(0.634020\pi\) | |||||||
\(572\) | − | 0.237626i | − | 0.00993564i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 34.4942 | 1.43976 | ||||||||
\(575\) | −7.56429 | − | 7.99759i | −0.315453 | − | 0.333523i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.08303i | 0.0450873i | 0.999746 | + | 0.0225436i | \(0.00717647\pi\) | ||||
−0.999746 | + | 0.0225436i | \(0.992824\pi\) | |||||||
\(578\) | − | 3.97793i | − | 0.165460i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.73380 | + | 3.47605i | −0.362651 | + | 0.144335i | ||||
\(581\) | 4.11254 | 0.170617 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 0.275402i | − | 0.0114060i | ||||||
\(584\) | 7.03811 | 0.291239 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.7033 | 0.566079 | ||||||||
\(587\) | − | 1.16839i | − | 0.0482244i | −0.999709 | − | 0.0241122i | \(-0.992324\pi\) | ||
0.999709 | − | 0.0241122i | \(-0.00767590\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.7254 | −0.771566 | ||||||||
\(590\) | 11.1855 | + | 28.1043i | 0.460499 | + | 1.15703i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000i | 0.0410997i | ||||||||
\(593\) | − | 6.01305i | − | 0.246926i | −0.992349 | − | 0.123463i | \(-0.960600\pi\) | ||
0.992349 | − | 0.123463i | \(-0.0394001\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −35.0274 | + | 13.9409i | −1.43598 | + | 0.571521i | ||||
\(596\) | 21.9832 | 0.900467 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.5919i | 0.474028i | ||||||||
\(599\) | −11.9208 | −0.487072 | −0.243536 | − | 0.969892i | \(-0.578307\pi\) | ||||
−0.243536 | + | 0.969892i | \(0.578307\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.7772 | 0.888309 | 0.444155 | − | 0.895950i | \(-0.353504\pi\) | ||||
0.444155 | + | 0.895950i | \(0.353504\pi\) | |||||||
\(602\) | 25.9204i | 1.05644i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.1877 | −0.577290 | ||||||||
\(605\) | 22.8490 | − | 9.09390i | 0.928944 | − | 0.369720i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.16486i | 0.209635i | 0.994491 | + | 0.104818i | \(0.0334259\pi\) | ||||
−0.994491 | + | 0.104818i | \(0.966574\pi\) | |||||||
\(608\) | − | 6.22000i | − | 0.252254i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.53321 | − | 8.87742i | −0.143056 | − | 0.359436i | ||||
\(611\) | 22.5386 | 0.911813 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.5817i | 1.59869i | 0.600873 | + | 0.799344i | \(0.294820\pi\) | ||||
−0.600873 | + | 0.799344i | \(0.705180\pi\) | |||||||
\(614\) | −17.5823 | −0.709565 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.210861 | 0.00849585 | ||||||||
\(617\) | − | 44.9917i | − | 1.81130i | −0.424027 | − | 0.905650i | \(-0.639384\pi\) | ||
0.424027 | − | 0.905650i | \(-0.360616\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.0465 | −1.20767 | −0.603836 | − | 0.797108i | \(-0.706362\pi\) | ||||
−0.603836 | + | 0.797108i | \(0.706362\pi\) | |||||||
\(620\) | −6.25454 | + | 2.48931i | −0.251188 | + | 0.0999729i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.353133i | 0.0141594i | ||||||||
\(623\) | 46.6091i | 1.86735i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.39110 | − | 24.9613i | 0.0556438 | − | 0.998451i | ||||
\(626\) | 18.8717 | 0.754265 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.9316i | 0.795359i | ||||||||
\(629\) | 3.60861 | 0.143885 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.01448 | 0.199623 | 0.0998116 | − | 0.995006i | \(-0.468176\pi\) | ||||
0.0998116 | + | 0.995006i | \(0.468176\pi\) | |||||||
\(632\) | 8.72499i | 0.347061i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.1979 | −0.603587 | ||||||||
\(635\) | −14.6003 | − | 36.6841i | −0.579393 | − | 1.45576i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 78.0747i | 3.09343i | ||||||||
\(638\) | − | 0.189728i | − | 0.00751142i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.826871 | − | 2.07757i | −0.0326850 | − | 0.0821230i | ||||
\(641\) | −18.9133 | −0.747031 | −0.373515 | − | 0.927624i | \(-0.621848\pi\) | ||||
−0.373515 | + | 0.927624i | \(0.621848\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 22.9344i | − | 0.904444i | −0.891906 | − | 0.452222i | \(-0.850632\pi\) | ||
0.891906 | − | 0.452222i | \(-0.149368\pi\) | |||||||
\(644\) | −10.2863 | −0.405336 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −22.4456 | −0.883109 | ||||||||
\(647\) | − | 10.4741i | − | 0.411779i | −0.978575 | − | 0.205889i | \(-0.933991\pi\) | ||
0.978575 | − | 0.205889i | \(-0.0660087\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.610522 | −0.0239651 | ||||||||
\(650\) | −19.1260 | + | 18.0897i | −0.750182 | + | 0.709538i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.65087i | 0.338794i | ||||||||
\(653\) | − | 44.7251i | − | 1.75023i | −0.483916 | − | 0.875115i | \(-0.660786\pi\) | ||
0.483916 | − | 0.875115i | \(-0.339214\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.4203 | + | 8.52526i | −0.836959 | + | 0.333110i | ||||
\(656\) | 7.38299 | 0.288257 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 20.0000i | 0.779681i | ||||||||
\(659\) | 15.1056 | 0.588431 | 0.294215 | − | 0.955739i | \(-0.404942\pi\) | ||||
0.294215 | + | 0.955739i | \(0.404942\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.9654 | 1.36000 | 0.679998 | − | 0.733214i | \(-0.261981\pi\) | ||||
0.679998 | + | 0.733214i | \(0.261981\pi\) | |||||||
\(662\) | 23.0210i | 0.894736i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.880231 | 0.0341596 | ||||||||
\(665\) | −24.0293 | − | 60.3752i | −0.931817 | − | 2.34125i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.25537i | 0.358369i | ||||||||
\(668\) | − | 11.9640i | − | 0.462901i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −25.7102 | + | 10.2326i | −0.993271 | + | 0.395322i | ||||
\(671\) | 0.192848 | 0.00744483 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 35.2496i | − | 1.35877i | −0.733782 | − | 0.679385i | \(-0.762246\pi\) | ||
0.733782 | − | 0.679385i | \(-0.237754\pi\) | |||||||
\(674\) | 34.0776 | 1.31262 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.7216 | 0.566217 | ||||||||
\(677\) | 23.2835i | 0.894858i | 0.894320 | + | 0.447429i | \(0.147660\pi\) | ||||
−0.894320 | + | 0.447429i | \(0.852340\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.12321 | −0.0431049 | ||||||||
\(680\) | −7.49713 | + | 2.98386i | −0.287502 | + | 0.114426i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 0.135870i | − | 0.00520274i | ||||||
\(683\) | − | 11.8131i | − | 0.452017i | −0.974125 | − | 0.226008i | \(-0.927432\pi\) | ||
0.974125 | − | 0.226008i | \(-0.0725676\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.66140 | + | 6.68693i | 0.101687 | + | 0.255494i | ||||
\(686\) | −36.5761 | −1.39648 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.54789i | 0.211511i | ||||||||
\(689\) | 32.1286 | 1.22400 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.1858 | 0.539652 | 0.269826 | − | 0.962909i | \(-0.413034\pi\) | ||||
0.269826 | + | 0.962909i | \(0.413034\pi\) | |||||||
\(692\) | 5.33508i | 0.202809i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.8449 | −0.525547 | ||||||||
\(695\) | 43.5043 | − | 17.3147i | 1.65021 | − | 0.656784i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 26.6423i | − | 1.00915i | ||||||
\(698\) | 11.3765i | 0.430607i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −16.0523 | − | 16.9718i | −0.606718 | − | 0.641472i | ||||
\(701\) | −19.2184 | −0.725870 | −0.362935 | − | 0.931815i | \(-0.618225\pi\) | ||||
−0.362935 | + | 0.931815i | \(0.618225\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.22000i | 0.234592i | ||||||||
\(704\) | 0.0451320 | 0.00170097 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.2631 | 0.724976 | ||||||||
\(707\) | 26.2468i | 0.987111i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.52525 | −0.169949 | −0.0849746 | − | 0.996383i | \(-0.527081\pi\) | ||||
−0.0849746 | + | 0.996383i | \(0.527081\pi\) | |||||||
\(710\) | 3.71558 | + | 9.33562i | 0.139443 | + | 0.350360i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.97602i | 0.373867i | ||||||||
\(713\) | 6.62805i | 0.248222i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.196486 | − | 0.493684i | −0.00734816 | − | 0.0184627i | ||||
\(716\) | 5.27905 | 0.197288 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 14.6645i | − | 0.547273i | ||||||
\(719\) | 0.915477 | 0.0341415 | 0.0170708 | − | 0.999854i | \(-0.494566\pi\) | ||||
0.0170708 | + | 0.999854i | \(0.494566\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −58.7110 | −2.18651 | ||||||||
\(722\) | − | 19.6884i | − | 0.732728i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17.7448 | −0.659478 | ||||||||
\(725\) | −15.2708 | + | 14.4435i | −0.567143 | + | 0.536417i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 11.7429i | − | 0.435521i | −0.976002 | − | 0.217760i | \(-0.930125\pi\) | ||
0.976002 | − | 0.217760i | \(-0.0698752\pi\) | |||||||
\(728\) | 24.5993i | 0.911710i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.6221 | − | 5.81961i | 0.541189 | − | 0.215393i | ||||
\(731\) | 20.0202 | 0.740473 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 27.6776i | − | 1.02230i | −0.859493 | − | 0.511148i | \(-0.829220\pi\) | ||
0.859493 | − | 0.511148i | \(-0.170780\pi\) | |||||||
\(734\) | 0.868349 | 0.0320514 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.20164 | −0.0811534 | ||||||||
\(737\) | − | 0.558514i | − | 0.0205731i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.52187 | 0.239911 | 0.119956 | − | 0.992779i | \(-0.461725\pi\) | ||||
0.119956 | + | 0.992779i | \(0.461725\pi\) | |||||||
\(740\) | 0.826871 | + | 2.07757i | 0.0303964 | + | 0.0763729i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 28.5099i | 1.04663i | ||||||||
\(743\) | 43.0091i | 1.57785i | 0.614489 | + | 0.788925i | \(0.289362\pi\) | ||||
−0.614489 | + | 0.788925i | \(0.710638\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 45.6716 | − | 18.1773i | 1.67328 | − | 0.665964i | ||||
\(746\) | −32.4555 | −1.18828 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 0.162864i | − | 0.00595489i | ||||||
\(749\) | −83.8152 | −3.06254 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.7068 | −1.08402 | −0.542008 | − | 0.840373i | \(-0.682336\pi\) | ||||
−0.542008 | + | 0.840373i | \(0.682336\pi\) | |||||||
\(752\) | 4.28072i | 0.156102i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 22.1339 | 0.806069 | ||||||||
\(755\) | −29.4759 | + | 11.7314i | −1.07274 | + | 0.426950i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.7918i | 1.19184i | 0.803044 | + | 0.595920i | \(0.203212\pi\) | ||||
−0.803044 | + | 0.595920i | \(0.796788\pi\) | |||||||
\(758\) | − | 30.2511i | − | 1.09877i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.14314 | − | 12.9225i | −0.186561 | − | 0.468747i | ||||
\(761\) | −22.9411 | −0.831616 | −0.415808 | − | 0.909452i | \(-0.636501\pi\) | ||||
−0.415808 | + | 0.909452i | \(0.636501\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 14.4806i | − | 0.524232i | ||||||
\(764\) | −3.11649 | −0.112751 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14.4935 | 0.523673 | ||||||||
\(767\) | − | 71.2241i | − | 2.57175i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.8123 | −0.389902 | −0.194951 | − | 0.980813i | \(-0.562455\pi\) | ||||
−0.194951 | + | 0.980813i | \(0.562455\pi\) | |||||||
\(770\) | 0.438079 | − | 0.174355i | 0.0157873 | − | 0.00628333i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 8.78278i | − | 0.316099i | ||||||
\(773\) | − | 37.9989i | − | 1.36673i | −0.730079 | − | 0.683363i | \(-0.760517\pi\) | ||
0.730079 | − | 0.683363i | \(-0.239483\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.9359 | + | 10.3434i | −0.392829 | + | 0.371546i | ||||
\(776\) | −0.240408 | −0.00863014 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 36.9033i | − | 1.32305i | ||||||
\(779\) | 45.9222 | 1.64533 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.202802 | −0.00725683 | ||||||||
\(782\) | 7.94485i | 0.284107i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −14.8286 | −0.529593 | ||||||||
\(785\) | 16.4809 | + | 41.4093i | 0.588228 | + | 1.47796i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.7730i | 1.13258i | 0.824205 | + | 0.566292i | \(0.191623\pi\) | ||||
−0.824205 | + | 0.566292i | \(0.808377\pi\) | |||||||
\(788\) | 7.00278i | 0.249464i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.21444 | + | 18.1267i | 0.256678 | + | 0.644921i | ||||
\(791\) | −20.3790 | −0.724594 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.4979i | 0.798923i | ||||||||
\(794\) | 22.9365 | 0.813986 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.3202 | 0.613900 | ||||||||
\(797\) | − | 9.02551i | − | 0.319700i | −0.987141 | − | 0.159850i | \(-0.948899\pi\) | ||
0.987141 | − | 0.159850i | \(-0.0511011\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.4475 | 0.546492 | ||||||||
\(800\) | −3.43576 | − | 3.63257i | −0.121472 | − | 0.128431i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 27.4332i | 0.968698i | ||||||||
\(803\) | 0.317643i | 0.0112094i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.3704 | + | 8.50543i | −0.753209 | + | 0.299777i | ||||
\(806\) | 15.8508 | 0.558319 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.61775i | 0.197632i | ||||||||
\(809\) | 29.7376 | 1.04552 | 0.522759 | − | 0.852481i | \(-0.324903\pi\) | ||||
0.522759 | + | 0.852481i | \(0.324903\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.7650 | 0.553585 | 0.276793 | − | 0.960930i | \(-0.410729\pi\) | ||||
0.276793 | + | 0.960930i | \(0.410729\pi\) | |||||||
\(812\) | 19.6409i | 0.689260i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.0451320 | −0.00158187 | ||||||||
\(815\) | 7.15315 | + | 17.9728i | 0.250564 | + | 0.629558i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.5079i | 1.20728i | ||||||||
\(818\) | − | 21.3920i | − | 0.747954i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.3387 | − | 6.10478i | 0.535649 | − | 0.213188i | ||||
\(821\) | 4.27798 | 0.149303 | 0.0746513 | − | 0.997210i | \(-0.476216\pi\) | ||||
0.0746513 | + | 0.997210i | \(0.476216\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.8985i | 0.484471i | 0.970217 | + | 0.242236i | \(0.0778807\pi\) | ||||
−0.970217 | + | 0.242236i | \(0.922119\pi\) | |||||||
\(824\) | −12.5663 | −0.437766 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 63.2019 | 2.19908 | ||||||||
\(827\) | 30.4944i | 1.06039i | 0.847875 | + | 0.530197i | \(0.177882\pi\) | ||||
−0.847875 | + | 0.530197i | \(0.822118\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.493020 | −0.0171233 | −0.00856165 | − | 0.999963i | \(-0.502725\pi\) | ||||
−0.00856165 | + | 0.999963i | \(0.502725\pi\) | |||||||
\(830\) | 1.82874 | − | 0.727838i | 0.0634765 | − | 0.0252636i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.26514i | 0.182536i | ||||||||
\(833\) | 53.5107i | 1.85404i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.89270 | − | 24.8560i | −0.342351 | − | 0.860178i | ||||
\(836\) | 0.280721 | 0.00970894 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 23.0891i | − | 0.797598i | ||||||
\(839\) | −27.9308 | −0.964278 | −0.482139 | − | 0.876095i | \(-0.660140\pi\) | ||||
−0.482139 | + | 0.876095i | \(0.660140\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.3276 | −0.390606 | ||||||||
\(842\) | 1.83757i | 0.0633268i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.77438 | −0.233184 | ||||||||
\(845\) | 30.5852 | − | 12.1729i | 1.05216 | − | 0.418761i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 51.3837i | − | 1.76556i | ||||||
\(848\) | 6.10215i | 0.209549i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.1085 | + | 12.3983i | −0.449619 | + | 0.425259i | ||||
\(851\) | 2.20164 | 0.0754711 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 31.4029i | − | 1.07521i | −0.843195 | − | 0.537607i | \(-0.819328\pi\) | ||
0.843195 | − | 0.537607i | \(-0.180672\pi\) | |||||||
\(854\) | −19.9639 | −0.683150 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.9395 | −0.613158 | ||||||||
\(857\) | − | 39.7806i | − | 1.35888i | −0.733731 | − | 0.679441i | \(-0.762223\pi\) | ||
0.733731 | − | 0.679441i | \(-0.237777\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.8673 | −1.42849 | −0.714247 | − | 0.699894i | \(-0.753231\pi\) | ||||
−0.714247 | + | 0.699894i | \(0.753231\pi\) | |||||||
\(860\) | 4.58739 | + | 11.5261i | 0.156429 | + | 0.393037i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 15.9796i | − | 0.544267i | ||||||
\(863\) | − | 8.52387i | − | 0.290156i | −0.989420 | − | 0.145078i | \(-0.953657\pi\) | ||
0.989420 | − | 0.145078i | \(-0.0463433\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.41142 | + | 11.0840i | 0.149993 | + | 0.376867i | ||||
\(866\) | 25.2525 | 0.858116 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.0654i | 0.477412i | ||||||||
\(869\) | −0.393776 | −0.0133579 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 65.1568 | 2.20775 | ||||||||
\(872\) | − | 3.09936i | − | 0.104958i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.6942 | −0.463213 | ||||||||
\(875\) | −47.3831 | − | 21.9868i | −1.60184 | − | 0.743290i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 37.1163i | − | 1.25333i | −0.779289 | − | 0.626664i | \(-0.784420\pi\) | ||
0.779289 | − | 0.626664i | \(-0.215580\pi\) | |||||||
\(878\) | − | 9.30792i | − | 0.314127i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.0937647 | − | 0.0373183i | 0.00316081 | − | 0.00125800i | ||||
\(881\) | −29.8633 | −1.00612 | −0.503060 | − | 0.864252i | \(-0.667792\pi\) | ||||
−0.503060 | + | 0.864252i | \(0.667792\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.98952i | 0.336174i | 0.985772 | + | 0.168087i | \(0.0537590\pi\) | ||||
−0.985772 | + | 0.168087i | \(0.946241\pi\) | |||||||
\(884\) | 18.9998 | 0.639033 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.52445 | −0.319980 | ||||||||
\(887\) | − | 23.2703i | − | 0.781340i | −0.920531 | − | 0.390670i | \(-0.872243\pi\) | ||
0.920531 | − | 0.390670i | \(-0.127757\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −82.4965 | −2.76684 | ||||||||
\(890\) | 8.24888 | + | 20.7258i | 0.276503 | + | 0.694732i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 10.2559i | − | 0.343392i | ||||||
\(893\) | 26.6261i | 0.891008i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.9676 | − | 4.36510i | 0.366606 | − | 0.145909i | ||||
\(896\) | −4.67211 | −0.156084 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 5.43278i | − | 0.181294i | ||||||
\(899\) | 12.6558 | 0.422094 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.0203 | 0.733602 | ||||||||
\(902\) | 0.333209i | 0.0110946i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.36184 | −0.145073 | ||||||||
\(905\) | −36.8659 | + | 14.6726i | −1.22546 | + | 0.487735i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 34.0053i | − | 1.12913i | −0.825389 | − | 0.564564i | \(-0.809044\pi\) | ||
0.825389 | − | 0.564564i | \(-0.190956\pi\) | |||||||
\(908\) | − | 11.2744i | − | 0.374153i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 20.3404 | + | 51.1067i | 0.674279 | + | 1.69417i | ||||
\(911\) | 29.2297 | 0.968424 | 0.484212 | − | 0.874951i | \(-0.339106\pi\) | ||||
0.484212 | + | 0.874951i | \(0.339106\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.0397266i | 0.00131476i | ||||||||
\(914\) | 7.54789 | 0.249662 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.40494 | −0.310748 | ||||||||
\(917\) | 48.1707i | 1.59074i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.0238 | −1.41923 | −0.709613 | − | 0.704592i | \(-0.751130\pi\) | ||||
−0.709613 | + | 0.704592i | \(0.751130\pi\) | |||||||
\(920\) | −4.57405 | + | 1.82047i | −0.150802 | + | 0.0600191i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 35.4323i | − | 1.16690i | ||||||
\(923\) | − | 23.6591i | − | 0.778748i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.43576 | + | 3.63257i | 0.112967 | + | 0.119438i | ||||
\(926\) | −20.9124 | −0.687225 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.20386i | 0.137998i | ||||||||
\(929\) | 10.7786 | 0.353635 | 0.176817 | − | 0.984244i | \(-0.443420\pi\) | ||||
0.176817 | + | 0.984244i | \(0.443420\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −92.2340 | −3.02285 | ||||||||
\(932\) | 3.22867i | 0.105759i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.62523 | −0.216784 | ||||||||
\(935\) | −0.134667 | − | 0.338360i | −0.00440409 | − | 0.0110656i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.5755i | 1.19487i | 0.801918 | + | 0.597435i | \(0.203813\pi\) | ||||
−0.801918 | + | 0.597435i | \(0.796187\pi\) | |||||||
\(938\) | 57.8180i | 1.88782i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.53961 | + | 8.89348i | 0.115449 | + | 0.290073i | ||||
\(941\) | −58.9579 | −1.92197 | −0.960986 | − | 0.276596i | \(-0.910794\pi\) | ||||
−0.960986 | + | 0.276596i | \(0.910794\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 16.2547i | − | 0.529325i | ||||||
\(944\) | 13.5275 | 0.440282 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.250387 | −0.00814079 | ||||||||
\(947\) | − | 9.63990i | − | 0.313255i | −0.987658 | − | 0.156627i | \(-0.949938\pi\) | ||
0.987658 | − | 0.156627i | \(-0.0500621\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37.0566 | −1.20291 | ||||||||
\(950\) | −21.3704 | − | 22.5946i | −0.693349 | − | 0.733065i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 16.8598i | 0.546430i | ||||||||
\(953\) | 31.4809i | 1.01977i | 0.860243 | + | 0.509884i | \(0.170312\pi\) | ||||
−0.860243 | + | 0.509884i | \(0.829688\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.47471 | + | 2.57693i | −0.209517 | + | 0.0833876i | ||||
\(956\) | 17.8612 | 0.577672 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 29.4581i | 0.951747i | ||||||||
\(959\) | 15.0378 | 0.485596 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.9368 | −0.707639 | ||||||||
\(962\) | − | 5.26514i | − | 0.169755i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −26.6840 | −0.859434 | ||||||||
\(965\) | −7.26223 | − | 18.2468i | −0.233779 | − | 0.587386i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.5439i | 0.821438i | 0.911762 | + | 0.410719i | \(0.134722\pi\) | ||||
−0.911762 | + | 0.410719i | \(0.865278\pi\) | |||||||
\(968\) | − | 10.9980i | − | 0.353488i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.499463 | + | 0.198786i | −0.0160368 | + | 0.00638264i | ||||
\(971\) | −43.7224 | −1.40312 | −0.701559 | − | 0.712611i | \(-0.747512\pi\) | ||||
−0.701559 | + | 0.712611i | \(0.747512\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 97.8341i | − | 3.13642i | ||||||
\(974\) | 8.80654 | 0.282180 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.27299 | −0.136775 | ||||||||
\(977\) | 44.6598i | 1.42879i | 0.699741 | + | 0.714396i | \(0.253299\pi\) | ||||
−0.699741 | + | 0.714396i | \(0.746701\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.450237 | −0.0143896 | ||||||||
\(980\) | −30.8074 | + | 12.2614i | −0.984107 | + | 0.391675i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.14258i | 0.164106i | ||||||||
\(983\) | 9.17840i | 0.292745i | 0.989230 | + | 0.146373i | \(0.0467599\pi\) | ||||
−0.989230 | + | 0.146373i | \(0.953240\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.79040 | + | 14.5487i | 0.184497 | + | 0.463562i | ||||
\(986\) | 15.1701 | 0.483114 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 32.7492i | 1.04189i | ||||||||
\(989\) | 12.2144 | 0.388397 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.1246 | 0.512216 | 0.256108 | − | 0.966648i | \(-0.417560\pi\) | ||||
0.256108 | + | 0.966648i | \(0.417560\pi\) | |||||||
\(992\) | 3.01051i | 0.0955839i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 20.9943 | 0.665899 | ||||||||
\(995\) | 35.9840 | − | 14.3216i | 1.14077 | − | 0.454026i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.99979i | 0.285026i | 0.989793 | + | 0.142513i | \(0.0455183\pi\) | ||||
−0.989793 | + | 0.142513i | \(0.954482\pi\) | |||||||
\(998\) | − | 12.9692i | − | 0.410532i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3330.2.d.p.1999.1 | 10 | ||
3.2 | odd | 2 | 370.2.b.d.149.7 | yes | 10 | ||
5.4 | even | 2 | inner | 3330.2.d.p.1999.6 | 10 | ||
15.2 | even | 4 | 1850.2.a.bd.1.2 | 5 | |||
15.8 | even | 4 | 1850.2.a.be.1.4 | 5 | |||
15.14 | odd | 2 | 370.2.b.d.149.4 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.b.d.149.4 | ✓ | 10 | 15.14 | odd | 2 | ||
370.2.b.d.149.7 | yes | 10 | 3.2 | odd | 2 | ||
1850.2.a.bd.1.2 | 5 | 15.2 | even | 4 | |||
1850.2.a.be.1.4 | 5 | 15.8 | even | 4 | |||
3330.2.d.p.1999.1 | 10 | 1.1 | even | 1 | trivial | ||
3330.2.d.p.1999.6 | 10 | 5.4 | even | 2 | inner |