Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(2155,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3234.2155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.e (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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2155.13 | ||
Character | \(\chi\) | \(=\) | 3234.2155 |
Dual form | 3234.2.e.c.2155.12 |
$q$-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 \(\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(1079\) | \(2059\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 4.05345i | − | 1.81276i | −0.422466 | − | 0.906379i | \(-0.638836\pi\) | ||
0.422466 | − | 0.906379i | \(-0.361164\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 4.05345 | 1.28181 | ||||||||
\(11\) | −1.17914 | + | 3.09994i | −0.355523 | + | 0.934668i | ||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | −3.91265 | −1.08517 | −0.542587 | − | 0.840000i | \(-0.682555\pi\) | ||||
−0.542587 | + | 0.840000i | \(0.682555\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.05345 | 1.04660 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.188398 | 0.0456933 | 0.0228466 | − | 0.999739i | \(-0.492727\pi\) | ||||
0.0228466 | + | 0.999739i | \(0.492727\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 4.37877 | 1.00456 | 0.502279 | − | 0.864706i | \(-0.332495\pi\) | ||||
0.502279 | + | 0.864706i | \(0.332495\pi\) | |||||||
\(20\) | 4.05345i | 0.906379i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.09994 | − | 1.17914i | −0.660910 | − | 0.251393i | ||||
\(23\) | −3.58348 | −0.747208 | −0.373604 | − | 0.927588i | \(-0.621878\pi\) | ||||
−0.373604 | + | 0.927588i | \(0.621878\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −11.4304 | −2.28609 | ||||||||
\(26\) | − | 3.91265i | − | 0.767334i | ||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.75703i | 1.06905i | 0.845152 | + | 0.534527i | \(0.179510\pi\) | ||||
−0.845152 | + | 0.534527i | \(0.820490\pi\) | |||||||
\(30\) | 4.05345i | 0.740055i | ||||||||
\(31\) | 3.21035i | 0.576596i | 0.957541 | + | 0.288298i | \(0.0930893\pi\) | ||||
−0.957541 | + | 0.288298i | \(0.906911\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −3.09994 | − | 1.17914i | −0.539631 | − | 0.205261i | ||||
\(34\) | 0.188398i | 0.0323100i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.09649 | 0.837859 | 0.418929 | − | 0.908019i | \(-0.362406\pi\) | ||||
0.418929 | + | 0.908019i | \(0.362406\pi\) | |||||||
\(38\) | 4.37877i | 0.710330i | ||||||||
\(39\) | − | 3.91265i | − | 0.626526i | ||||||
\(40\) | −4.05345 | −0.640906 | ||||||||
\(41\) | 8.14212 | 1.27159 | 0.635793 | − | 0.771860i | \(-0.280673\pi\) | ||||
0.635793 | + | 0.771860i | \(0.280673\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.21078i | 0.489639i | 0.969569 | + | 0.244819i | \(0.0787287\pi\) | ||||
−0.969569 | + | 0.244819i | \(0.921271\pi\) | |||||||
\(44\) | 1.17914 | − | 3.09994i | 0.177761 | − | 0.467334i | ||||
\(45\) | 4.05345i | 0.604252i | ||||||||
\(46\) | − | 3.58348i | − | 0.528356i | ||||||
\(47\) | − | 4.37618i | − | 0.638331i | −0.947699 | − | 0.319165i | \(-0.896597\pi\) | ||
0.947699 | − | 0.319165i | \(-0.103403\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 11.4304i | − | 1.61651i | ||||||
\(51\) | 0.188398i | 0.0263810i | ||||||||
\(52\) | 3.91265 | 0.542587 | ||||||||
\(53\) | 2.83716 | 0.389714 | 0.194857 | − | 0.980832i | \(-0.437576\pi\) | ||||
0.194857 | + | 0.980832i | \(0.437576\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 12.5655 | + | 4.77956i | 1.69433 | + | 0.644476i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.37877i | 0.579982i | ||||||||
\(58\) | −5.75703 | −0.755935 | ||||||||
\(59\) | − | 4.99905i | − | 0.650822i | −0.945573 | − | 0.325411i | \(-0.894497\pi\) | ||
0.945573 | − | 0.325411i | \(-0.105503\pi\) | |||||||
\(60\) | −4.05345 | −0.523298 | ||||||||
\(61\) | −7.95115 | −1.01804 | −0.509020 | − | 0.860755i | \(-0.669992\pi\) | ||||
−0.509020 | + | 0.860755i | \(0.669992\pi\) | |||||||
\(62\) | −3.21035 | −0.407715 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 15.8597i | 1.96716i | ||||||||
\(66\) | 1.17914 | − | 3.09994i | 0.145142 | − | 0.381576i | ||||
\(67\) | −6.50120 | −0.794248 | −0.397124 | − | 0.917765i | \(-0.629992\pi\) | ||||
−0.397124 | + | 0.917765i | \(0.629992\pi\) | |||||||
\(68\) | −0.188398 | −0.0228466 | ||||||||
\(69\) | − | 3.58348i | − | 0.431401i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.2739 | 1.93136 | 0.965681 | − | 0.259732i | \(-0.0836341\pi\) | ||||
0.965681 | + | 0.259732i | \(0.0836341\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 12.3419 | 1.44451 | 0.722253 | − | 0.691629i | \(-0.243107\pi\) | ||||
0.722253 | + | 0.691629i | \(0.243107\pi\) | |||||||
\(74\) | 5.09649i | 0.592455i | ||||||||
\(75\) | − | 11.4304i | − | 1.31987i | ||||||
\(76\) | −4.37877 | −0.502279 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.91265 | 0.443021 | ||||||||
\(79\) | − | 8.55410i | − | 0.962411i | −0.876608 | − | 0.481206i | \(-0.840199\pi\) | ||
0.876608 | − | 0.481206i | \(-0.159801\pi\) | |||||||
\(80\) | − | 4.05345i | − | 0.453189i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.14212i | 0.899147i | ||||||||
\(83\) | 12.5690 | 1.37962 | 0.689811 | − | 0.723989i | \(-0.257694\pi\) | ||||
0.689811 | + | 0.723989i | \(0.257694\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 0.763662i | − | 0.0828308i | ||||||
\(86\) | −3.21078 | −0.346227 | ||||||||
\(87\) | −5.75703 | −0.617218 | ||||||||
\(88\) | 3.09994 | + | 1.17914i | 0.330455 | + | 0.125696i | ||||
\(89\) | 14.2616i | 1.51172i | 0.654732 | + | 0.755861i | \(0.272781\pi\) | ||||
−0.654732 | + | 0.755861i | \(0.727219\pi\) | |||||||
\(90\) | −4.05345 | −0.427271 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.58348 | 0.373604 | ||||||||
\(93\) | −3.21035 | −0.332898 | ||||||||
\(94\) | 4.37618 | 0.451368 | ||||||||
\(95\) | − | 17.7491i | − | 1.82102i | ||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 17.4901i | 1.77585i | 0.459986 | + | 0.887926i | \(0.347854\pi\) | ||||
−0.459986 | + | 0.887926i | \(0.652146\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.17914 | − | 3.09994i | 0.118508 | − | 0.311556i | ||||
\(100\) | 11.4304 | 1.14304 | ||||||||
\(101\) | −2.87801 | −0.286373 | −0.143186 | − | 0.989696i | \(-0.545735\pi\) | ||||
−0.143186 | + | 0.989696i | \(0.545735\pi\) | |||||||
\(102\) | −0.188398 | −0.0186542 | ||||||||
\(103\) | 17.7997i | 1.75385i | 0.480624 | + | 0.876927i | \(0.340410\pi\) | ||||
−0.480624 | + | 0.876927i | \(0.659590\pi\) | |||||||
\(104\) | 3.91265i | 0.383667i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.83716i | 0.275569i | ||||||||
\(107\) | 6.46948i | 0.625429i | 0.949847 | + | 0.312714i | \(0.101238\pi\) | ||||
−0.949847 | + | 0.312714i | \(0.898762\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | 17.4531i | 1.67171i | 0.548953 | + | 0.835853i | \(0.315026\pi\) | ||||
−0.548953 | + | 0.835853i | \(0.684974\pi\) | |||||||
\(110\) | −4.77956 | + | 12.5655i | −0.455714 | + | 1.19807i | ||||
\(111\) | 5.09649i | 0.483738i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.749179 | 0.0704768 | 0.0352384 | − | 0.999379i | \(-0.488781\pi\) | ||||
0.0352384 | + | 0.999379i | \(0.488781\pi\) | |||||||
\(114\) | −4.37877 | −0.410109 | ||||||||
\(115\) | 14.5255i | 1.35451i | ||||||||
\(116\) | − | 5.75703i | − | 0.534527i | ||||||
\(117\) | 3.91265 | 0.361725 | ||||||||
\(118\) | 4.99905 | 0.460200 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 4.05345i | − | 0.370028i | ||||||
\(121\) | −8.21928 | − | 7.31050i | −0.747207 | − | 0.664591i | ||||
\(122\) | − | 7.95115i | − | 0.719863i | ||||||
\(123\) | 8.14212i | 0.734150i | ||||||||
\(124\) | − | 3.21035i | − | 0.288298i | ||||||
\(125\) | 26.0655i | 2.33137i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.79955i | 0.603363i | 0.953409 | + | 0.301681i | \(0.0975479\pi\) | ||||
−0.953409 | + | 0.301681i | \(0.902452\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −3.21078 | −0.282693 | ||||||||
\(130\) | −15.8597 | −1.39099 | ||||||||
\(131\) | 21.7846 | 1.90333 | 0.951663 | − | 0.307145i | \(-0.0993738\pi\) | ||||
0.951663 | + | 0.307145i | \(0.0993738\pi\) | |||||||
\(132\) | 3.09994 | + | 1.17914i | 0.269815 | + | 0.102631i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 6.50120i | − | 0.561618i | ||||||
\(135\) | −4.05345 | −0.348865 | ||||||||
\(136\) | − | 0.188398i | − | 0.0161550i | ||||||
\(137\) | 7.02179 | 0.599912 | 0.299956 | − | 0.953953i | \(-0.403028\pi\) | ||||
0.299956 | + | 0.953953i | \(0.403028\pi\) | |||||||
\(138\) | 3.58348 | 0.305046 | ||||||||
\(139\) | 15.5729 | 1.32088 | 0.660438 | − | 0.750881i | \(-0.270371\pi\) | ||||
0.660438 | + | 0.750881i | \(0.270371\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.37618 | 0.368541 | ||||||||
\(142\) | 16.2739i | 1.36568i | ||||||||
\(143\) | 4.61355 | − | 12.1290i | 0.385804 | − | 1.01428i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 23.3358 | 1.93793 | ||||||||
\(146\) | 12.3419i | 1.02142i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.09649 | −0.418929 | ||||||||
\(149\) | 0.875307i | 0.0717079i | 0.999357 | + | 0.0358540i | \(0.0114151\pi\) | ||||
−0.999357 | + | 0.0358540i | \(0.988585\pi\) | |||||||
\(150\) | 11.4304 | 0.933292 | ||||||||
\(151\) | − | 18.1267i | − | 1.47513i | −0.675275 | − | 0.737566i | \(-0.735975\pi\) | ||
0.675275 | − | 0.737566i | \(-0.264025\pi\) | |||||||
\(152\) | − | 4.37877i | − | 0.355165i | ||||||
\(153\) | −0.188398 | −0.0152311 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.0130 | 1.04523 | ||||||||
\(156\) | 3.91265i | 0.313263i | ||||||||
\(157\) | − | 8.01869i | − | 0.639961i | −0.947424 | − | 0.319981i | \(-0.896324\pi\) | ||
0.947424 | − | 0.319981i | \(-0.103676\pi\) | |||||||
\(158\) | 8.55410 | 0.680528 | ||||||||
\(159\) | 2.83716i | 0.225001i | ||||||||
\(160\) | 4.05345 | 0.320453 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | −3.40939 | −0.267044 | −0.133522 | − | 0.991046i | \(-0.542629\pi\) | ||||
−0.133522 | + | 0.991046i | \(0.542629\pi\) | |||||||
\(164\) | −8.14212 | −0.635793 | ||||||||
\(165\) | −4.77956 | + | 12.5655i | −0.372089 | + | 0.978219i | ||||
\(166\) | 12.5690i | 0.975540i | ||||||||
\(167\) | −11.1360 | −0.861727 | −0.430863 | − | 0.902417i | \(-0.641791\pi\) | ||||
−0.430863 | + | 0.902417i | \(0.641791\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.30884 | 0.177603 | ||||||||
\(170\) | 0.763662 | 0.0585702 | ||||||||
\(171\) | −4.37877 | −0.334853 | ||||||||
\(172\) | − | 3.21078i | − | 0.244819i | ||||||
\(173\) | 5.89901 | 0.448494 | 0.224247 | − | 0.974532i | \(-0.428008\pi\) | ||||
0.224247 | + | 0.974532i | \(0.428008\pi\) | |||||||
\(174\) | − | 5.75703i | − | 0.436439i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.17914 | + | 3.09994i | −0.0888807 | + | 0.233667i | ||||
\(177\) | 4.99905 | 0.375752 | ||||||||
\(178\) | −14.2616 | −1.06895 | ||||||||
\(179\) | −3.92282 | −0.293205 | −0.146603 | − | 0.989195i | \(-0.546834\pi\) | ||||
−0.146603 | + | 0.989195i | \(0.546834\pi\) | |||||||
\(180\) | − | 4.05345i | − | 0.302126i | ||||||
\(181\) | − | 13.8033i | − | 1.02599i | −0.858392 | − | 0.512994i | \(-0.828536\pi\) | ||
0.858392 | − | 0.512994i | \(-0.171464\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 7.95115i | − | 0.587766i | ||||||
\(184\) | 3.58348i | 0.264178i | ||||||||
\(185\) | − | 20.6584i | − | 1.51883i | ||||||
\(186\) | − | 3.21035i | − | 0.235394i | ||||||
\(187\) | −0.222147 | + | 0.584023i | −0.0162450 | + | 0.0427080i | ||||
\(188\) | 4.37618i | 0.319165i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 17.7491 | 1.28766 | ||||||||
\(191\) | −9.49736 | −0.687205 | −0.343602 | − | 0.939115i | \(-0.611647\pi\) | ||||
−0.343602 | + | 0.939115i | \(0.611647\pi\) | |||||||
\(192\) | − | 1.00000i | − | 0.0721688i | ||||||
\(193\) | 13.5397i | 0.974612i | 0.873231 | + | 0.487306i | \(0.162020\pi\) | ||||
−0.873231 | + | 0.487306i | \(0.837980\pi\) | |||||||
\(194\) | −17.4901 | −1.25572 | ||||||||
\(195\) | −15.8597 | −1.13574 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.1952i | 1.86633i | 0.359447 | + | 0.933165i | \(0.382965\pi\) | ||||
−0.359447 | + | 0.933165i | \(0.617035\pi\) | |||||||
\(198\) | 3.09994 | + | 1.17914i | 0.220303 | + | 0.0837975i | ||||
\(199\) | 6.10803i | 0.432987i | 0.976284 | + | 0.216493i | \(0.0694619\pi\) | ||||
−0.976284 | + | 0.216493i | \(0.930538\pi\) | |||||||
\(200\) | 11.4304i | 0.808254i | ||||||||
\(201\) | − | 6.50120i | − | 0.458559i | ||||||
\(202\) | − | 2.87801i | − | 0.202496i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 0.188398i | − | 0.0131905i | ||||||
\(205\) | − | 33.0037i | − | 2.30508i | ||||||
\(206\) | −17.7997 | −1.24016 | ||||||||
\(207\) | 3.58348 | 0.249069 | ||||||||
\(208\) | −3.91265 | −0.271294 | ||||||||
\(209\) | −5.16316 | + | 13.5739i | −0.357143 | + | 0.938928i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 19.8676i | − | 1.36774i | −0.729604 | − | 0.683870i | \(-0.760296\pi\) | ||
0.729604 | − | 0.683870i | \(-0.239704\pi\) | |||||||
\(212\) | −2.83716 | −0.194857 | ||||||||
\(213\) | 16.2739i | 1.11507i | ||||||||
\(214\) | −6.46948 | −0.442245 | ||||||||
\(215\) | 13.0147 | 0.887597 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −17.4531 | −1.18207 | ||||||||
\(219\) | 12.3419i | 0.833986i | ||||||||
\(220\) | −12.5655 | − | 4.77956i | −0.847163 | − | 0.322238i | ||||
\(221\) | −0.737136 | −0.0495852 | ||||||||
\(222\) | −5.09649 | −0.342054 | ||||||||
\(223\) | − | 4.64198i | − | 0.310850i | −0.987848 | − | 0.155425i | \(-0.950325\pi\) | ||
0.987848 | − | 0.155425i | \(-0.0496747\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.4304 | 0.762029 | ||||||||
\(226\) | 0.749179i | 0.0498346i | ||||||||
\(227\) | 13.0638 | 0.867075 | 0.433537 | − | 0.901136i | \(-0.357265\pi\) | ||||
0.433537 | + | 0.901136i | \(0.357265\pi\) | |||||||
\(228\) | − | 4.37877i | − | 0.289991i | ||||||
\(229\) | 9.68676i | 0.640119i | 0.947397 | + | 0.320060i | \(0.103703\pi\) | ||||
−0.947397 | + | 0.320060i | \(0.896297\pi\) | |||||||
\(230\) | −14.5255 | −0.957781 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.75703 | 0.377967 | ||||||||
\(233\) | 21.6421i | 1.41782i | 0.705298 | + | 0.708911i | \(0.250813\pi\) | ||||
−0.705298 | + | 0.708911i | \(0.749187\pi\) | |||||||
\(234\) | 3.91265i | 0.255778i | ||||||||
\(235\) | −17.7386 | −1.15714 | ||||||||
\(236\) | 4.99905i | 0.325411i | ||||||||
\(237\) | 8.55410 | 0.555648 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.6397i | 0.688225i | 0.938928 | + | 0.344112i | \(0.111820\pi\) | ||||
−0.938928 | + | 0.344112i | \(0.888180\pi\) | |||||||
\(240\) | 4.05345 | 0.261649 | ||||||||
\(241\) | 5.68711 | 0.366339 | 0.183169 | − | 0.983081i | \(-0.441364\pi\) | ||||
0.183169 | + | 0.983081i | \(0.441364\pi\) | |||||||
\(242\) | 7.31050 | − | 8.21928i | 0.469937 | − | 0.528355i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 7.95115 | 0.509020 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.14212 | −0.519123 | ||||||||
\(247\) | −17.1326 | −1.09012 | ||||||||
\(248\) | 3.21035 | 0.203857 | ||||||||
\(249\) | 12.5690i | 0.796525i | ||||||||
\(250\) | −26.0655 | −1.64852 | ||||||||
\(251\) | − | 0.576257i | − | 0.0363730i | −0.999835 | − | 0.0181865i | \(-0.994211\pi\) | ||
0.999835 | − | 0.0181865i | \(-0.00578927\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.22541 | − | 11.1086i | 0.265649 | − | 0.698391i | ||||
\(254\) | −6.79955 | −0.426642 | ||||||||
\(255\) | 0.763662 | 0.0478224 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.2114i | 1.38551i | 0.721174 | + | 0.692754i | \(0.243603\pi\) | ||||
−0.721174 | + | 0.692754i | \(0.756397\pi\) | |||||||
\(258\) | − | 3.21078i | − | 0.199894i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 15.8597i | − | 0.983579i | ||||||
\(261\) | − | 5.75703i | − | 0.356351i | ||||||
\(262\) | 21.7846i | 1.34585i | ||||||||
\(263\) | − | 21.1657i | − | 1.30513i | −0.757731 | − | 0.652567i | \(-0.773692\pi\) | ||
0.757731 | − | 0.652567i | \(-0.226308\pi\) | |||||||
\(264\) | −1.17914 | + | 3.09994i | −0.0725708 | + | 0.190788i | ||||
\(265\) | − | 11.5003i | − | 0.706456i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.2616 | −0.872793 | ||||||||
\(268\) | 6.50120 | 0.397124 | ||||||||
\(269\) | − | 16.9288i | − | 1.03217i | −0.856538 | − | 0.516084i | \(-0.827389\pi\) | ||
0.856538 | − | 0.516084i | \(-0.172611\pi\) | |||||||
\(270\) | − | 4.05345i | − | 0.246685i | ||||||
\(271\) | −12.9849 | −0.788777 | −0.394389 | − | 0.918944i | \(-0.629044\pi\) | ||||
−0.394389 | + | 0.918944i | \(0.629044\pi\) | |||||||
\(272\) | 0.188398 | 0.0114233 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.02179i | 0.424202i | ||||||||
\(275\) | 13.4780 | − | 35.4337i | 0.812756 | − | 2.13673i | ||||
\(276\) | 3.58348i | 0.215700i | ||||||||
\(277\) | 25.5474i | 1.53500i | 0.641051 | + | 0.767498i | \(0.278499\pi\) | ||||
−0.641051 | + | 0.767498i | \(0.721501\pi\) | |||||||
\(278\) | 15.5729i | 0.934000i | ||||||||
\(279\) | − | 3.21035i | − | 0.192199i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.87709i | − | 0.410253i | −0.978735 | − | 0.205126i | \(-0.934239\pi\) | ||
0.978735 | − | 0.205126i | \(-0.0657606\pi\) | |||||||
\(282\) | 4.37618i | 0.260598i | ||||||||
\(283\) | −13.6656 | −0.812337 | −0.406168 | − | 0.913798i | \(-0.633135\pi\) | ||||
−0.406168 | + | 0.913798i | \(0.633135\pi\) | |||||||
\(284\) | −16.2739 | −0.965681 | ||||||||
\(285\) | 17.7491 | 1.05137 | ||||||||
\(286\) | 12.1290 | + | 4.61355i | 0.717202 | + | 0.272805i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −16.9645 | −0.997912 | ||||||||
\(290\) | 23.3358i | 1.37033i | ||||||||
\(291\) | −17.4901 | −1.02529 | ||||||||
\(292\) | −12.3419 | −0.722253 | ||||||||
\(293\) | 9.49826 | 0.554894 | 0.277447 | − | 0.960741i | \(-0.410512\pi\) | ||||
0.277447 | + | 0.960741i | \(0.410512\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.2634 | −1.17978 | ||||||||
\(296\) | − | 5.09649i | − | 0.296228i | ||||||
\(297\) | 3.09994 | + | 1.17914i | 0.179877 | + | 0.0684204i | ||||
\(298\) | −0.875307 | −0.0507052 | ||||||||
\(299\) | 14.0209 | 0.810851 | ||||||||
\(300\) | 11.4304i | 0.659937i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.1267 | 1.04308 | ||||||||
\(303\) | − | 2.87801i | − | 0.165337i | ||||||
\(304\) | 4.37877 | 0.251140 | ||||||||
\(305\) | 32.2296i | 1.84546i | ||||||||
\(306\) | − | 0.188398i | − | 0.0107700i | ||||||
\(307\) | −17.4551 | −0.996216 | −0.498108 | − | 0.867115i | \(-0.665972\pi\) | ||||
−0.498108 | + | 0.867115i | \(0.665972\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.7997 | −1.01259 | ||||||||
\(310\) | 13.0130i | 0.739088i | ||||||||
\(311\) | 10.1883i | 0.577724i | 0.957371 | + | 0.288862i | \(0.0932768\pi\) | ||||
−0.957371 | + | 0.288862i | \(0.906723\pi\) | |||||||
\(312\) | −3.91265 | −0.221510 | ||||||||
\(313\) | − | 19.8187i | − | 1.12022i | −0.828418 | − | 0.560111i | \(-0.810759\pi\) | ||
0.828418 | − | 0.560111i | \(-0.189241\pi\) | |||||||
\(314\) | 8.01869 | 0.452521 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.55410i | 0.481206i | ||||||||
\(317\) | −15.5000 | −0.870566 | −0.435283 | − | 0.900294i | \(-0.643352\pi\) | ||||
−0.435283 | + | 0.900294i | \(0.643352\pi\) | |||||||
\(318\) | −2.83716 | −0.159100 | ||||||||
\(319\) | −17.8465 | − | 6.78832i | −0.999209 | − | 0.380073i | ||||
\(320\) | 4.05345i | 0.226595i | ||||||||
\(321\) | −6.46948 | −0.361091 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.824952 | 0.0459015 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 44.7233 | 2.48080 | ||||||||
\(326\) | − | 3.40939i | − | 0.188828i | ||||||
\(327\) | −17.4531 | −0.965160 | ||||||||
\(328\) | − | 8.14212i | − | 0.449573i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −12.5655 | − | 4.77956i | −0.691705 | − | 0.263106i | ||||
\(331\) | −22.3460 | −1.22825 | −0.614123 | − | 0.789211i | \(-0.710490\pi\) | ||||
−0.614123 | + | 0.789211i | \(0.710490\pi\) | |||||||
\(332\) | −12.5690 | −0.689811 | ||||||||
\(333\) | −5.09649 | −0.279286 | ||||||||
\(334\) | − | 11.1360i | − | 0.609333i | ||||||
\(335\) | 26.3523i | 1.43978i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 21.9009i | − | 1.19302i | −0.802607 | − | 0.596508i | \(-0.796555\pi\) | ||
0.802607 | − | 0.596508i | \(-0.203445\pi\) | |||||||
\(338\) | 2.30884i | 0.125584i | ||||||||
\(339\) | 0.749179i | 0.0406898i | ||||||||
\(340\) | 0.763662i | 0.0414154i | ||||||||
\(341\) | −9.95190 | − | 3.78544i | −0.538925 | − | 0.204993i | ||||
\(342\) | − | 4.37877i | − | 0.236777i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.21078 | 0.173114 | ||||||||
\(345\) | −14.5255 | −0.782025 | ||||||||
\(346\) | 5.89901i | 0.317133i | ||||||||
\(347\) | 7.73409i | 0.415188i | 0.978215 | + | 0.207594i | \(0.0665633\pi\) | ||||
−0.978215 | + | 0.207594i | \(0.933437\pi\) | |||||||
\(348\) | 5.75703 | 0.308609 | ||||||||
\(349\) | −20.8125 | −1.11406 | −0.557032 | − | 0.830491i | \(-0.688060\pi\) | ||||
−0.557032 | + | 0.830491i | \(0.688060\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.91265i | 0.208842i | ||||||||
\(352\) | −3.09994 | − | 1.17914i | −0.165227 | − | 0.0628481i | ||||
\(353\) | 29.2347i | 1.55600i | 0.628261 | + | 0.778002i | \(0.283767\pi\) | ||||
−0.628261 | + | 0.778002i | \(0.716233\pi\) | |||||||
\(354\) | 4.99905i | 0.265697i | ||||||||
\(355\) | − | 65.9656i | − | 3.50109i | ||||||
\(356\) | − | 14.2616i | − | 0.755861i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 3.92282i | − | 0.207328i | ||||||
\(359\) | − | 34.8045i | − | 1.83691i | −0.395527 | − | 0.918454i | \(-0.629438\pi\) | ||
0.395527 | − | 0.918454i | \(-0.370562\pi\) | |||||||
\(360\) | 4.05345 | 0.213635 | ||||||||
\(361\) | 0.173600 | 0.00913684 | ||||||||
\(362\) | 13.8033 | 0.725484 | ||||||||
\(363\) | 7.31050 | − | 8.21928i | 0.383702 | − | 0.431400i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 50.0271i | − | 2.61854i | ||||||
\(366\) | 7.95115 | 0.415613 | ||||||||
\(367\) | − | 28.5311i | − | 1.48931i | −0.667449 | − | 0.744656i | \(-0.732614\pi\) | ||
0.667449 | − | 0.744656i | \(-0.267386\pi\) | |||||||
\(368\) | −3.58348 | −0.186802 | ||||||||
\(369\) | −8.14212 | −0.423862 | ||||||||
\(370\) | 20.6584 | 1.07398 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.21035 | 0.166449 | ||||||||
\(373\) | 28.0262i | 1.45114i | 0.688148 | + | 0.725570i | \(0.258424\pi\) | ||||
−0.688148 | + | 0.725570i | \(0.741576\pi\) | |||||||
\(374\) | −0.584023 | − | 0.222147i | −0.0301991 | − | 0.0114869i | ||||
\(375\) | −26.0655 | −1.34601 | ||||||||
\(376\) | −4.37618 | −0.225684 | ||||||||
\(377\) | − | 22.5252i | − | 1.16011i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.1317 | 0.674529 | 0.337265 | − | 0.941410i | \(-0.390498\pi\) | ||||
0.337265 | + | 0.941410i | \(0.390498\pi\) | |||||||
\(380\) | 17.7491i | 0.910510i | ||||||||
\(381\) | −6.79955 | −0.348352 | ||||||||
\(382\) | − | 9.49736i | − | 0.485927i | ||||||
\(383\) | 11.9092i | 0.608533i | 0.952587 | + | 0.304266i | \(0.0984113\pi\) | ||||
−0.952587 | + | 0.304266i | \(0.901589\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.5397 | −0.689155 | ||||||||
\(387\) | − | 3.21078i | − | 0.163213i | ||||||
\(388\) | − | 17.4901i | − | 0.887926i | ||||||
\(389\) | 36.7446 | 1.86303 | 0.931513 | − | 0.363709i | \(-0.118490\pi\) | ||||
0.931513 | + | 0.363709i | \(0.118490\pi\) | |||||||
\(390\) | − | 15.8597i | − | 0.803089i | ||||||
\(391\) | −0.675122 | −0.0341424 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.7846i | 1.09889i | ||||||||
\(394\) | −26.1952 | −1.31970 | ||||||||
\(395\) | −34.6736 | −1.74462 | ||||||||
\(396\) | −1.17914 | + | 3.09994i | −0.0592538 | + | 0.155778i | ||||
\(397\) | − | 38.5547i | − | 1.93500i | −0.252865 | − | 0.967502i | \(-0.581373\pi\) | ||
0.252865 | − | 0.967502i | \(-0.418627\pi\) | |||||||
\(398\) | −6.10803 | −0.306168 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11.4304 | −0.571522 | ||||||||
\(401\) | 13.9262 | 0.695441 | 0.347720 | − | 0.937598i | \(-0.386956\pi\) | ||||
0.347720 | + | 0.937598i | \(0.386956\pi\) | |||||||
\(402\) | 6.50120 | 0.324250 | ||||||||
\(403\) | − | 12.5610i | − | 0.625707i | ||||||
\(404\) | 2.87801 | 0.143186 | ||||||||
\(405\) | − | 4.05345i | − | 0.201417i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.00946 | + | 15.7988i | −0.297878 | + | 0.783119i | ||||
\(408\) | 0.188398 | 0.00932710 | ||||||||
\(409\) | −8.35551 | −0.413153 | −0.206577 | − | 0.978430i | \(-0.566232\pi\) | ||||
−0.206577 | + | 0.978430i | \(0.566232\pi\) | |||||||
\(410\) | 33.0037 | 1.62993 | ||||||||
\(411\) | 7.02179i | 0.346359i | ||||||||
\(412\) | − | 17.7997i | − | 0.876927i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.58348i | 0.176119i | ||||||||
\(415\) | − | 50.9476i | − | 2.50092i | ||||||
\(416\) | − | 3.91265i | − | 0.191834i | ||||||
\(417\) | 15.5729i | 0.762608i | ||||||||
\(418\) | −13.5739 | − | 5.16316i | −0.663922 | − | 0.252538i | ||||
\(419\) | − | 0.503760i | − | 0.0246103i | −0.999924 | − | 0.0123052i | \(-0.996083\pi\) | ||
0.999924 | − | 0.0123052i | \(-0.00391695\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0435 | 0.879386 | 0.439693 | − | 0.898148i | \(-0.355087\pi\) | ||||
0.439693 | + | 0.898148i | \(0.355087\pi\) | |||||||
\(422\) | 19.8676 | 0.967138 | ||||||||
\(423\) | 4.37618i | 0.212777i | ||||||||
\(424\) | − | 2.83716i | − | 0.137785i | ||||||
\(425\) | −2.15347 | −0.104459 | ||||||||
\(426\) | −16.2739 | −0.788475 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 6.46948i | − | 0.312714i | ||||||
\(429\) | 12.1290 | + | 4.61355i | 0.585593 | + | 0.222744i | ||||
\(430\) | 13.0147i | 0.627626i | ||||||||
\(431\) | 23.7641i | 1.14468i | 0.820017 | + | 0.572339i | \(0.193964\pi\) | ||||
−0.820017 | + | 0.572339i | \(0.806036\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | − | 13.2596i | − | 0.637218i | −0.947886 | − | 0.318609i | \(-0.896784\pi\) | ||
0.947886 | − | 0.318609i | \(-0.103216\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 23.3358i | 1.11887i | ||||||||
\(436\) | − | 17.4531i | − | 0.835853i | ||||||
\(437\) | −15.6912 | −0.750614 | ||||||||
\(438\) | −12.3419 | −0.589717 | ||||||||
\(439\) | 18.6515 | 0.890187 | 0.445093 | − | 0.895484i | \(-0.353170\pi\) | ||||
0.445093 | + | 0.895484i | \(0.353170\pi\) | |||||||
\(440\) | 4.77956 | − | 12.5655i | 0.227857 | − | 0.599035i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 0.737136i | − | 0.0350620i | ||||||
\(443\) | −12.0548 | −0.572740 | −0.286370 | − | 0.958119i | \(-0.592449\pi\) | ||||
−0.286370 | + | 0.958119i | \(0.592449\pi\) | |||||||
\(444\) | − | 5.09649i | − | 0.241869i | ||||||
\(445\) | 57.8085 | 2.74038 | ||||||||
\(446\) | 4.64198 | 0.219804 | ||||||||
\(447\) | −0.875307 | −0.0414006 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.9760 | 1.32027 | 0.660135 | − | 0.751147i | \(-0.270499\pi\) | ||||
0.660135 | + | 0.751147i | \(0.270499\pi\) | |||||||
\(450\) | 11.4304i | 0.538836i | ||||||||
\(451\) | −9.60066 | + | 25.2401i | −0.452078 | + | 1.18851i | ||||
\(452\) | −0.749179 | −0.0352384 | ||||||||
\(453\) | 18.1267 | 0.851668 | ||||||||
\(454\) | 13.0638i | 0.613114i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.37877 | 0.205055 | ||||||||
\(457\) | 15.8979i | 0.743670i | 0.928299 | + | 0.371835i | \(0.121271\pi\) | ||||
−0.928299 | + | 0.371835i | \(0.878729\pi\) | |||||||
\(458\) | −9.68676 | −0.452633 | ||||||||
\(459\) | − | 0.188398i | − | 0.00879367i | ||||||
\(460\) | − | 14.5255i | − | 0.677254i | ||||||
\(461\) | −37.1843 | −1.73184 | −0.865922 | − | 0.500179i | \(-0.833267\pi\) | ||||
−0.865922 | + | 0.500179i | \(0.833267\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.4293 | −1.27475 | −0.637374 | − | 0.770555i | \(-0.719979\pi\) | ||||
−0.637374 | + | 0.770555i | \(0.719979\pi\) | |||||||
\(464\) | 5.75703i | 0.267263i | ||||||||
\(465\) | 13.0130i | 0.603463i | ||||||||
\(466\) | −21.6421 | −1.00255 | ||||||||
\(467\) | 15.3698i | 0.711231i | 0.934632 | + | 0.355616i | \(0.115729\pi\) | ||||
−0.934632 | + | 0.355616i | \(0.884271\pi\) | |||||||
\(468\) | −3.91265 | −0.180862 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 17.7386i | − | 0.818221i | ||||||
\(471\) | 8.01869 | 0.369482 | ||||||||
\(472\) | −4.99905 | −0.230100 | ||||||||
\(473\) | −9.95322 | − | 3.78594i | −0.457650 | − | 0.174078i | ||||
\(474\) | 8.55410i | 0.392903i | ||||||||
\(475\) | −50.0512 | −2.29651 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.83716 | −0.129905 | ||||||||
\(478\) | −10.6397 | −0.486648 | ||||||||
\(479\) | 36.8475 | 1.68360 | 0.841802 | − | 0.539786i | \(-0.181495\pi\) | ||||
0.841802 | + | 0.539786i | \(0.181495\pi\) | |||||||
\(480\) | 4.05345i | 0.185014i | ||||||||
\(481\) | −19.9408 | −0.909222 | ||||||||
\(482\) | 5.68711i | 0.259041i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.21928 | + | 7.31050i | 0.373604 | + | 0.332296i | ||||
\(485\) | 70.8953 | 3.21919 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 12.1267 | 0.549511 | 0.274756 | − | 0.961514i | \(-0.411403\pi\) | ||||
0.274756 | + | 0.961514i | \(0.411403\pi\) | |||||||
\(488\) | 7.95115i | 0.359932i | ||||||||
\(489\) | − | 3.40939i | − | 0.154178i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.1431i | 1.72138i | 0.509133 | + | 0.860688i | \(0.329966\pi\) | ||||
−0.509133 | + | 0.860688i | \(0.670034\pi\) | |||||||
\(492\) | − | 8.14212i | − | 0.367075i | ||||||
\(493\) | 1.08461i | 0.0488485i | ||||||||
\(494\) | − | 17.1326i | − | 0.770832i | ||||||
\(495\) | −12.5655 | − | 4.77956i | −0.564775 | − | 0.214825i | ||||
\(496\) | 3.21035i | 0.144149i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −12.5690 | −0.563228 | ||||||||
\(499\) | 6.48858 | 0.290469 | 0.145234 | − | 0.989397i | \(-0.453606\pi\) | ||||
0.145234 | + | 0.989397i | \(0.453606\pi\) | |||||||
\(500\) | − | 26.0655i | − | 1.16568i | ||||||
\(501\) | − | 11.1360i | − | 0.497518i | ||||||
\(502\) | 0.576257 | 0.0257196 | ||||||||
\(503\) | 30.9319 | 1.37919 | 0.689593 | − | 0.724197i | \(-0.257789\pi\) | ||||
0.689593 | + | 0.724197i | \(0.257789\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.6659i | 0.519124i | ||||||||
\(506\) | 11.1086 | + | 4.22541i | 0.493837 | + | 0.187843i | ||||
\(507\) | 2.30884i | 0.102539i | ||||||||
\(508\) | − | 6.79955i | − | 0.301681i | ||||||
\(509\) | 12.3663i | 0.548128i | 0.961711 | + | 0.274064i | \(0.0883680\pi\) | ||||
−0.961711 | + | 0.274064i | \(0.911632\pi\) | |||||||
\(510\) | 0.763662i | 0.0338155i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 4.37877i | − | 0.193327i | ||||||
\(514\) | −22.2114 | −0.979702 | ||||||||
\(515\) | 72.1500 | 3.17931 | ||||||||
\(516\) | 3.21078 | 0.141347 | ||||||||
\(517\) | 13.5659 | + | 5.16010i | 0.596627 | + | 0.226941i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.89901i | 0.258938i | ||||||||
\(520\) | 15.8597 | 0.695495 | ||||||||
\(521\) | − | 32.9604i | − | 1.44402i | −0.691882 | − | 0.722011i | \(-0.743218\pi\) | ||
0.691882 | − | 0.722011i | \(-0.256782\pi\) | |||||||
\(522\) | 5.75703 | 0.251978 | ||||||||
\(523\) | 11.7372 | 0.513231 | 0.256615 | − | 0.966514i | \(-0.417393\pi\) | ||||
0.256615 | + | 0.966514i | \(0.417393\pi\) | |||||||
\(524\) | −21.7846 | −0.951663 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.1657 | 0.922869 | ||||||||
\(527\) | 0.604824i | 0.0263465i | ||||||||
\(528\) | −3.09994 | − | 1.17914i | −0.134908 | − | 0.0513153i | ||||
\(529\) | −10.1586 | −0.441680 | ||||||||
\(530\) | 11.5003 | 0.499540 | ||||||||
\(531\) | 4.99905i | 0.216941i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −31.8573 | −1.37989 | ||||||||
\(534\) | − | 14.2616i | − | 0.617158i | ||||||
\(535\) | 26.2237 | 1.13375 | ||||||||
\(536\) | 6.50120i | 0.280809i | ||||||||
\(537\) | − | 3.92282i | − | 0.169282i | ||||||
\(538\) | 16.9288 | 0.729853 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.05345 | 0.174433 | ||||||||
\(541\) | 4.32833i | 0.186089i | 0.995662 | + | 0.0930447i | \(0.0296600\pi\) | ||||
−0.995662 | + | 0.0930447i | \(0.970340\pi\) | |||||||
\(542\) | − | 12.9849i | − | 0.557750i | ||||||
\(543\) | 13.8033 | 0.592355 | ||||||||
\(544\) | 0.188398i | 0.00807750i | ||||||||
\(545\) | 70.7453 | 3.03040 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.00956i | 0.214193i | 0.994249 | + | 0.107097i | \(0.0341554\pi\) | ||||
−0.994249 | + | 0.107097i | \(0.965845\pi\) | |||||||
\(548\) | −7.02179 | −0.299956 | ||||||||
\(549\) | 7.95115 | 0.339347 | ||||||||
\(550\) | 35.4337 | + | 13.4780i | 1.51090 | + | 0.574706i | ||||
\(551\) | 25.2087i | 1.07393i | ||||||||
\(552\) | −3.58348 | −0.152523 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −25.5474 | −1.08541 | ||||||||
\(555\) | 20.6584 | 0.876899 | ||||||||
\(556\) | −15.5729 | −0.660438 | ||||||||
\(557\) | − | 16.5353i | − | 0.700622i | −0.936633 | − | 0.350311i | \(-0.886076\pi\) | ||
0.936633 | − | 0.350311i | \(-0.113924\pi\) | |||||||
\(558\) | 3.21035 | 0.135905 | ||||||||
\(559\) | − | 12.5627i | − | 0.531344i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.584023 | − | 0.222147i | −0.0246575 | − | 0.00937905i | ||||
\(562\) | 6.87709 | 0.290093 | ||||||||
\(563\) | −25.9643 | −1.09427 | −0.547133 | − | 0.837046i | \(-0.684281\pi\) | ||||
−0.547133 | + | 0.837046i | \(0.684281\pi\) | |||||||
\(564\) | −4.37618 | −0.184270 | ||||||||
\(565\) | − | 3.03676i | − | 0.127757i | ||||||
\(566\) | − | 13.6656i | − | 0.574409i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 16.2739i | − | 0.682839i | ||||||
\(569\) | 32.5397i | 1.36414i | 0.731289 | + | 0.682068i | \(0.238919\pi\) | ||||
−0.731289 | + | 0.682068i | \(0.761081\pi\) | |||||||
\(570\) | 17.7491i | 0.743428i | ||||||||
\(571\) | 8.55851i | 0.358163i | 0.983834 | + | 0.179081i | \(0.0573125\pi\) | ||||
−0.983834 | + | 0.179081i | \(0.942687\pi\) | |||||||
\(572\) | −4.61355 | + | 12.1290i | −0.192902 | + | 0.507139i | ||||
\(573\) | − | 9.49736i | − | 0.396758i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 40.9608 | 1.70818 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 4.95164i | − | 0.206139i | −0.994674 | − | 0.103070i | \(-0.967134\pi\) | ||
0.994674 | − | 0.103070i | \(-0.0328665\pi\) | |||||||
\(578\) | − | 16.9645i | − | 0.705630i | ||||||
\(579\) | −13.5397 | −0.562693 | ||||||||
\(580\) | −23.3358 | −0.968967 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 17.4901i | − | 0.724989i | ||||||
\(583\) | −3.34539 | + | 8.79502i | −0.138552 | + | 0.364253i | ||||
\(584\) | − | 12.3419i | − | 0.510710i | ||||||
\(585\) | − | 15.8597i | − | 0.655719i | ||||||
\(586\) | 9.49826i | 0.392370i | ||||||||
\(587\) | 7.93396i | 0.327469i | 0.986504 | + | 0.163735i | \(0.0523541\pi\) | ||||
−0.986504 | + | 0.163735i | \(0.947646\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.0574i | 0.579224i | ||||||||
\(590\) | − | 20.2634i | − | 0.834231i | ||||||
\(591\) | −26.1952 | −1.07753 | ||||||||
\(592\) | 5.09649 | 0.209465 | ||||||||
\(593\) | −21.3377 | −0.876233 | −0.438117 | − | 0.898918i | \(-0.644354\pi\) | ||||
−0.438117 | + | 0.898918i | \(0.644354\pi\) | |||||||
\(594\) | −1.17914 | + | 3.09994i | −0.0483805 | + | 0.127192i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 0.875307i | − | 0.0358540i | ||||||
\(597\) | −6.10803 | −0.249985 | ||||||||
\(598\) | 14.0209i | 0.573358i | ||||||||
\(599\) | 18.6966 | 0.763924 | 0.381962 | − | 0.924178i | \(-0.375249\pi\) | ||||
0.381962 | + | 0.924178i | \(0.375249\pi\) | |||||||
\(600\) | −11.4304 | −0.466646 | ||||||||
\(601\) | −2.99879 | −0.122323 | −0.0611616 | − | 0.998128i | \(-0.519480\pi\) | ||||
−0.0611616 | + | 0.998128i | \(0.519480\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.50120 | 0.264749 | ||||||||
\(604\) | 18.1267i | 0.737566i | ||||||||
\(605\) | −29.6327 | + | 33.3164i | −1.20474 | + | 1.35451i | ||||
\(606\) | 2.87801 | 0.116911 | ||||||||
\(607\) | −21.9575 | −0.891227 | −0.445613 | − | 0.895225i | \(-0.647014\pi\) | ||||
−0.445613 | + | 0.895225i | \(0.647014\pi\) | |||||||
\(608\) | 4.37877i | 0.177582i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −32.2296 | −1.30494 | ||||||||
\(611\) | 17.1225i | 0.692700i | ||||||||
\(612\) | 0.188398 | 0.00761554 | ||||||||
\(613\) | 29.8421i | 1.20531i | 0.798002 | + | 0.602655i | \(0.205890\pi\) | ||||
−0.798002 | + | 0.602655i | \(0.794110\pi\) | |||||||
\(614\) | − | 17.4551i | − | 0.704431i | ||||||
\(615\) | 33.0037 | 1.33084 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.7509 | −0.996435 | −0.498218 | − | 0.867052i | \(-0.666012\pi\) | ||||
−0.498218 | + | 0.867052i | \(0.666012\pi\) | |||||||
\(618\) | − | 17.7997i | − | 0.716008i | ||||||
\(619\) | − | 19.8562i | − | 0.798086i | −0.916932 | − | 0.399043i | \(-0.869342\pi\) | ||
0.916932 | − | 0.399043i | \(-0.130658\pi\) | |||||||
\(620\) | −13.0130 | −0.522614 | ||||||||
\(621\) | 3.58348i | 0.143800i | ||||||||
\(622\) | −10.1883 | −0.408512 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 3.91265i | − | 0.156631i | ||||||
\(625\) | 48.5028 | 1.94011 | ||||||||
\(626\) | 19.8187 | 0.792116 | ||||||||
\(627\) | −13.5739 | − | 5.16316i | −0.542090 | − | 0.206197i | ||||
\(628\) | 8.01869i | 0.319981i | ||||||||
\(629\) | 0.960170 | 0.0382845 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.2358 | 1.08424 | 0.542120 | − | 0.840301i | \(-0.317622\pi\) | ||||
0.542120 | + | 0.840301i | \(0.317622\pi\) | |||||||
\(632\) | −8.55410 | −0.340264 | ||||||||
\(633\) | 19.8676 | 0.789665 | ||||||||
\(634\) | − | 15.5000i | − | 0.615583i | ||||||
\(635\) | 27.5616 | 1.09375 | ||||||||
\(636\) | − | 2.83716i | − | 0.112501i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.78832 | − | 17.8465i | 0.268752 | − | 0.706548i | ||||
\(639\) | −16.2739 | −0.643787 | ||||||||
\(640\) | −4.05345 | −0.160227 | ||||||||
\(641\) | 38.3259 | 1.51378 | 0.756892 | − | 0.653540i | \(-0.226717\pi\) | ||||
0.756892 | + | 0.653540i | \(0.226717\pi\) | |||||||
\(642\) | − | 6.46948i | − | 0.255330i | ||||||
\(643\) | 48.9151i | 1.92902i | 0.264039 | + | 0.964512i | \(0.414945\pi\) | ||||
−0.264039 | + | 0.964512i | \(0.585055\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.0147i | 0.512454i | ||||||||
\(646\) | 0.824952i | 0.0324573i | ||||||||
\(647\) | − | 38.0347i | − | 1.49530i | −0.664094 | − | 0.747649i | \(-0.731183\pi\) | ||
0.664094 | − | 0.747649i | \(-0.268817\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | 15.4968 | + | 5.89456i | 0.608302 | + | 0.231382i | ||||
\(650\) | 44.7233i | 1.75419i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.40939 | 0.133522 | ||||||||
\(653\) | −19.7568 | −0.773143 | −0.386572 | − | 0.922259i | \(-0.626341\pi\) | ||||
−0.386572 | + | 0.922259i | \(0.626341\pi\) | |||||||
\(654\) | − | 17.4531i | − | 0.682471i | ||||||
\(655\) | − | 88.3026i | − | 3.45027i | ||||||
\(656\) | 8.14212 | 0.317896 | ||||||||
\(657\) | −12.3419 | −0.481502 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.6746i | 1.66237i | 0.555999 | + | 0.831183i | \(0.312336\pi\) | ||||
−0.555999 | + | 0.831183i | \(0.687664\pi\) | |||||||
\(660\) | 4.77956 | − | 12.5655i | 0.186044 | − | 0.489110i | ||||
\(661\) | − | 40.6501i | − | 1.58110i | −0.612395 | − | 0.790552i | \(-0.709794\pi\) | ||
0.612395 | − | 0.790552i | \(-0.290206\pi\) | |||||||
\(662\) | − | 22.3460i | − | 0.868501i | ||||||
\(663\) | − | 0.737136i | − | 0.0286280i | ||||||
\(664\) | − | 12.5690i | − | 0.487770i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 5.09649i | − | 0.197485i | ||||||
\(667\) | − | 20.6302i | − | 0.798805i | ||||||
\(668\) | 11.1360 | 0.430863 | ||||||||
\(669\) | 4.64198 | 0.179469 | ||||||||
\(670\) | −26.3523 | −1.01808 | ||||||||
\(671\) | 9.37548 | − | 24.6481i | 0.361936 | − | 0.951529i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.6669i | 0.681011i | 0.940243 | + | 0.340505i | \(0.110598\pi\) | ||||
−0.940243 | + | 0.340505i | \(0.889402\pi\) | |||||||
\(674\) | 21.9009 | 0.843589 | ||||||||
\(675\) | 11.4304i | 0.439958i | ||||||||
\(676\) | −2.30884 | −0.0888015 | ||||||||
\(677\) | −12.3507 | −0.474677 | −0.237338 | − | 0.971427i | \(-0.576275\pi\) | ||||
−0.237338 | + | 0.971427i | \(0.576275\pi\) | |||||||
\(678\) | −0.749179 | −0.0287720 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.763662 | −0.0292851 | ||||||||
\(681\) | 13.0638i | 0.500606i | ||||||||
\(682\) | 3.78544 | − | 9.95190i | 0.144952 | − | 0.381078i | ||||
\(683\) | 11.9147 | 0.455904 | 0.227952 | − | 0.973672i | \(-0.426797\pi\) | ||||
0.227952 | + | 0.973672i | \(0.426797\pi\) | |||||||
\(684\) | 4.37877 | 0.167426 | ||||||||
\(685\) | − | 28.4625i | − | 1.08750i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.68676 | −0.369573 | ||||||||
\(688\) | 3.21078i | 0.122410i | ||||||||
\(689\) | −11.1008 | −0.422907 | ||||||||
\(690\) | − | 14.5255i | − | 0.552975i | ||||||
\(691\) | 40.8856i | 1.55536i | 0.628660 | + | 0.777680i | \(0.283604\pi\) | ||||
−0.628660 | + | 0.777680i | \(0.716396\pi\) | |||||||
\(692\) | −5.89901 | −0.224247 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.73409 | −0.293582 | ||||||||
\(695\) | − | 63.1239i | − | 2.39443i | ||||||
\(696\) | 5.75703i | 0.218220i | ||||||||
\(697\) | 1.53396 | 0.0581029 | ||||||||
\(698\) | − | 20.8125i | − | 0.787763i | ||||||
\(699\) | −21.6421 | −0.818580 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 35.4801i | − | 1.34007i | −0.742331 | − | 0.670033i | \(-0.766280\pi\) | ||
0.742331 | − | 0.670033i | \(-0.233720\pi\) | |||||||
\(702\) | −3.91265 | −0.147674 | ||||||||
\(703\) | 22.3164 | 0.841678 | ||||||||
\(704\) | 1.17914 | − | 3.09994i | 0.0444403 | − | 0.116833i | ||||
\(705\) | − | 17.7386i | − | 0.668074i | ||||||
\(706\) | −29.2347 | −1.10026 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.99905 | −0.187876 | ||||||||
\(709\) | −39.7202 | −1.49172 | −0.745861 | − | 0.666102i | \(-0.767962\pi\) | ||||
−0.745861 | + | 0.666102i | \(0.767962\pi\) | |||||||
\(710\) | 65.9656 | 2.47564 | ||||||||
\(711\) | 8.55410i | 0.320804i | ||||||||
\(712\) | 14.2616 | 0.534474 | ||||||||
\(713\) | − | 11.5042i | − | 0.430837i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −49.1642 | − | 18.7008i | −1.83864 | − | 0.699369i | ||||
\(716\) | 3.92282 | 0.146603 | ||||||||
\(717\) | −10.6397 | −0.397347 | ||||||||
\(718\) | 34.8045 | 1.29889 | ||||||||
\(719\) | − | 0.852683i | − | 0.0317997i | −0.999874 | − | 0.0158999i | \(-0.994939\pi\) | ||
0.999874 | − | 0.0158999i | \(-0.00506130\pi\) | |||||||
\(720\) | 4.05345i | 0.151063i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.173600i | 0.00646072i | ||||||||
\(723\) | 5.68711i | 0.211506i | ||||||||
\(724\) | 13.8033i | 0.512994i | ||||||||
\(725\) | − | 65.8054i | − | 2.44395i | ||||||
\(726\) | 8.21928 | + | 7.31050i | 0.305046 | + | 0.271318i | ||||
\(727\) | − | 45.9492i | − | 1.70416i | −0.523411 | − | 0.852080i | \(-0.675341\pi\) | ||
0.523411 | − | 0.852080i | \(-0.324659\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 50.0271 | 1.85159 | ||||||||
\(731\) | 0.604905i | 0.0223732i | ||||||||
\(732\) | 7.95115i | 0.293883i | ||||||||
\(733\) | −1.39257 | −0.0514359 | −0.0257179 | − | 0.999669i | \(-0.508187\pi\) | ||||
−0.0257179 | + | 0.999669i | \(0.508187\pi\) | |||||||
\(734\) | 28.5311 | 1.05310 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 3.58348i | − | 0.132089i | ||||||
\(737\) | 7.66579 | − | 20.1533i | 0.282373 | − | 0.742358i | ||||
\(738\) | − | 8.14212i | − | 0.299716i | ||||||
\(739\) | 17.6182i | 0.648096i | 0.946041 | + | 0.324048i | \(0.105044\pi\) | ||||
−0.946041 | + | 0.324048i | \(0.894956\pi\) | |||||||
\(740\) | 20.6584i | 0.759417i | ||||||||
\(741\) | − | 17.1326i | − | 0.629381i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.42362i | 0.0522274i | 0.999659 | + | 0.0261137i | \(0.00831320\pi\) | ||||
−0.999659 | + | 0.0261137i | \(0.991687\pi\) | |||||||
\(744\) | 3.21035i | 0.117697i | ||||||||
\(745\) | 3.54801 | 0.129989 | ||||||||
\(746\) | −28.0262 | −1.02611 | ||||||||
\(747\) | −12.5690 | −0.459874 | ||||||||
\(748\) | 0.222147 | − | 0.584023i | 0.00812250 | − | 0.0213540i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 26.0655i | − | 0.951776i | ||||||
\(751\) | 33.3920 | 1.21849 | 0.609246 | − | 0.792981i | \(-0.291472\pi\) | ||||
0.609246 | + | 0.792981i | \(0.291472\pi\) | |||||||
\(752\) | − | 4.37618i | − | 0.159583i | ||||||
\(753\) | 0.576257 | 0.0210000 | ||||||||
\(754\) | 22.5252 | 0.820321 | ||||||||
\(755\) | −73.4758 | −2.67406 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.9154 | −0.433074 | −0.216537 | − | 0.976274i | \(-0.569476\pi\) | ||||
−0.216537 | + | 0.976274i | \(0.569476\pi\) | |||||||
\(758\) | 13.1317i | 0.476964i | ||||||||
\(759\) | 11.1086 | + | 4.22541i | 0.403216 | + | 0.153373i | ||||
\(760\) | −17.7491 | −0.643828 | ||||||||
\(761\) | 17.3932 | 0.630504 | 0.315252 | − | 0.949008i | \(-0.397911\pi\) | ||||
0.315252 | + | 0.949008i | \(0.397911\pi\) | |||||||
\(762\) | − | 6.79955i | − | 0.246322i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 9.49736 | 0.343602 | ||||||||
\(765\) | 0.763662i | 0.0276103i | ||||||||
\(766\) | −11.9092 | −0.430298 | ||||||||
\(767\) | 19.5596i | 0.706255i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 51.8599 | 1.87012 | 0.935059 | − | 0.354493i | \(-0.115346\pi\) | ||||
0.935059 | + | 0.354493i | \(0.115346\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.2114 | −0.799923 | ||||||||
\(772\) | − | 13.5397i | − | 0.487306i | ||||||
\(773\) | − | 1.68049i | − | 0.0604430i | −0.999543 | − | 0.0302215i | \(-0.990379\pi\) | ||
0.999543 | − | 0.0302215i | \(-0.00962126\pi\) | |||||||
\(774\) | 3.21078 | 0.115409 | ||||||||
\(775\) | − | 36.6957i | − | 1.31815i | ||||||
\(776\) | 17.4901 | 0.627859 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 36.7446i | 1.31736i | ||||||||
\(779\) | 35.6524 | 1.27738 | ||||||||
\(780\) | 15.8597 | 0.567869 | ||||||||
\(781\) | −19.1892 | + | 50.4483i | −0.686643 | + | 1.80518i | ||||
\(782\) | − | 0.675122i | − | 0.0241423i | ||||||
\(783\) | 5.75703 | 0.205739 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −32.5033 | −1.16009 | ||||||||
\(786\) | −21.7846 | −0.777029 | ||||||||
\(787\) | −0.926397 | −0.0330225 | −0.0165112 | − | 0.999864i | \(-0.505256\pi\) | ||||
−0.0165112 | + | 0.999864i | \(0.505256\pi\) | |||||||
\(788\) | − | 26.1952i | − | 0.933165i | ||||||
\(789\) | 21.1657 | 0.753519 | ||||||||
\(790\) | − | 34.6736i | − | 1.23363i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.09994 | − | 1.17914i | −0.110152 | − | 0.0418988i | ||||
\(793\) | 31.1101 | 1.10475 | ||||||||
\(794\) | 38.5547 | 1.36825 | ||||||||
\(795\) | 11.5003 | 0.407873 | ||||||||
\(796\) | − | 6.10803i | − | 0.216493i | ||||||
\(797\) | − | 12.5708i | − | 0.445280i | −0.974901 | − | 0.222640i | \(-0.928533\pi\) | ||
0.974901 | − | 0.222640i | \(-0.0714674\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 0.824464i | − | 0.0291674i | ||||||
\(800\) | − | 11.4304i | − | 0.404127i | ||||||
\(801\) | − | 14.2616i | − | 0.503907i | ||||||
\(802\) | 13.9262i | 0.491751i | ||||||||
\(803\) | −14.5527 | + | 38.2591i | −0.513555 | + | 1.35013i | ||||
\(804\) | 6.50120i | 0.229280i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.5610 | 0.442442 | ||||||||
\(807\) | 16.9288 | 0.595922 | ||||||||
\(808\) | 2.87801i | 0.101248i | ||||||||
\(809\) | 13.3055i | 0.467798i | 0.972261 | + | 0.233899i | \(0.0751484\pi\) | ||||
−0.972261 | + | 0.233899i | \(0.924852\pi\) | |||||||
\(810\) | 4.05345 | 0.142424 | ||||||||
\(811\) | −11.8888 | −0.417471 | −0.208735 | − | 0.977972i | \(-0.566935\pi\) | ||||
−0.208735 | + | 0.977972i | \(0.566935\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 12.9849i | − | 0.455401i | ||||||
\(814\) | −15.7988 | − | 6.00946i | −0.553749 | − | 0.210631i | ||||
\(815\) | 13.8198i | 0.484085i | ||||||||
\(816\) | 0.188398i | 0.00659525i | ||||||||
\(817\) | 14.0592i | 0.491871i | ||||||||
\(818\) | − | 8.35551i | − | 0.292143i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 33.0037i | 1.15254i | ||||||||
\(821\) | 29.1262i | 1.01651i | 0.861206 | + | 0.508256i | \(0.169710\pi\) | ||||
−0.861206 | + | 0.508256i | \(0.830290\pi\) | |||||||
\(822\) | −7.02179 | −0.244913 | ||||||||
\(823\) | 5.45802 | 0.190255 | 0.0951273 | − | 0.995465i | \(-0.469674\pi\) | ||||
0.0951273 | + | 0.995465i | \(0.469674\pi\) | |||||||
\(824\) | 17.7997 | 0.620081 | ||||||||
\(825\) | 35.4337 | + | 13.4780i | 1.23364 | + | 0.469245i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.0567i | 0.940852i | 0.882439 | + | 0.470426i | \(0.155900\pi\) | ||||
−0.882439 | + | 0.470426i | \(0.844100\pi\) | |||||||
\(828\) | −3.58348 | −0.124535 | ||||||||
\(829\) | 24.6755i | 0.857016i | 0.903538 | + | 0.428508i | \(0.140961\pi\) | ||||
−0.903538 | + | 0.428508i | \(0.859039\pi\) | |||||||
\(830\) | 50.9476 | 1.76842 | ||||||||
\(831\) | −25.5474 | −0.886230 | ||||||||
\(832\) | 3.91265 | 0.135647 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −15.5729 | −0.539245 | ||||||||
\(835\) | 45.1391i | 1.56210i | ||||||||
\(836\) | 5.16316 | − | 13.5739i | 0.178572 | − | 0.469464i | ||||
\(837\) | 3.21035 | 0.110966 | ||||||||
\(838\) | 0.503760 | 0.0174021 | ||||||||
\(839\) | − | 33.2478i | − | 1.14784i | −0.818911 | − | 0.573920i | \(-0.805422\pi\) | ||
0.818911 | − | 0.573920i | \(-0.194578\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.14337 | −0.142875 | ||||||||
\(842\) | 18.0435i | 0.621820i | ||||||||
\(843\) | 6.87709 | 0.236860 | ||||||||
\(844\) | 19.8676i | 0.683870i | ||||||||
\(845\) | − | 9.35876i | − | 0.321951i | ||||||
\(846\) | −4.37618 | −0.150456 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.83716 | 0.0974284 | ||||||||
\(849\) | − | 13.6656i | − | 0.469003i | ||||||
\(850\) | − | 2.15347i | − | 0.0738636i | ||||||
\(851\) | −18.2632 | −0.626055 | ||||||||
\(852\) | − | 16.2739i | − | 0.557536i | ||||||
\(853\) | −12.5236 | −0.428802 | −0.214401 | − | 0.976746i | \(-0.568780\pi\) | ||||
−0.214401 | + | 0.976746i | \(0.568780\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17.7491i | 0.607007i | ||||||||
\(856\) | 6.46948 | 0.221122 | ||||||||
\(857\) | 35.1338 | 1.20015 | 0.600073 | − | 0.799945i | \(-0.295138\pi\) | ||||
0.600073 | + | 0.799945i | \(0.295138\pi\) | |||||||
\(858\) | −4.61355 | + | 12.1290i | −0.157504 | + | 0.414077i | ||||
\(859\) | 3.08712i | 0.105331i | 0.998612 | + | 0.0526656i | \(0.0167718\pi\) | ||||
−0.998612 | + | 0.0526656i | \(0.983228\pi\) | |||||||
\(860\) | −13.0147 | −0.443798 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.7641 | −0.809409 | ||||||||
\(863\) | 16.5450 | 0.563200 | 0.281600 | − | 0.959532i | \(-0.409135\pi\) | ||||
0.281600 | + | 0.959532i | \(0.409135\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | − | 23.9113i | − | 0.813010i | ||||||
\(866\) | 13.2596 | 0.450581 | ||||||||
\(867\) | − | 16.9645i | − | 0.576145i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.5172 | + | 10.0864i | 0.899535 | + | 0.342159i | ||||
\(870\) | −23.3358 | −0.791158 | ||||||||
\(871\) | 25.4369 | 0.861897 | ||||||||
\(872\) | 17.4531 | 0.591037 | ||||||||
\(873\) | − | 17.4901i | − | 0.591951i | ||||||
\(874\) | − | 15.6912i | − | 0.530764i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 12.3419i | − | 0.416993i | ||||||
\(877\) | − | 0.198470i | − | 0.00670185i | −0.999994 | − | 0.00335092i | \(-0.998933\pi\) | ||
0.999994 | − | 0.00335092i | \(-0.00106663\pi\) | |||||||
\(878\) | 18.6515i | 0.629457i | ||||||||
\(879\) | 9.49826i | 0.320368i | ||||||||
\(880\) | 12.5655 | + | 4.77956i | 0.423581 | + | 0.161119i | ||||
\(881\) | − | 35.4245i | − | 1.19348i | −0.802434 | − | 0.596741i | \(-0.796462\pi\) | ||
0.802434 | − | 0.596741i | \(-0.203538\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.00799 | −0.235838 | −0.117919 | − | 0.993023i | \(-0.537622\pi\) | ||||
−0.117919 | + | 0.993023i | \(0.537622\pi\) | |||||||
\(884\) | 0.737136 | 0.0247926 | ||||||||
\(885\) | − | 20.2634i | − | 0.681147i | ||||||
\(886\) | − | 12.0548i | − | 0.404989i | ||||||
\(887\) | −5.25368 | −0.176401 | −0.0882007 | − | 0.996103i | \(-0.528112\pi\) | ||||
−0.0882007 | + | 0.996103i | \(0.528112\pi\) | |||||||
\(888\) | 5.09649 | 0.171027 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 57.8085i | 1.93774i | ||||||||
\(891\) | −1.17914 | + | 3.09994i | −0.0395025 | + | 0.103852i | ||||
\(892\) | 4.64198i | 0.155425i | ||||||||
\(893\) | − | 19.1623i | − | 0.641240i | ||||||
\(894\) | − | 0.875307i | − | 0.0292746i | ||||||
\(895\) | 15.9010i | 0.531510i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.0209i | 0.468145i | ||||||||
\(898\) | 27.9760i | 0.933572i | ||||||||
\(899\) | −18.4821 | −0.616412 | ||||||||
\(900\) | −11.4304 | −0.381015 | ||||||||
\(901\) | 0.534515 | 0.0178073 | ||||||||
\(902\) | −25.2401 | − | 9.60066i | −0.840403 | − | 0.319667i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 0.749179i | − | 0.0249173i | ||||||
\(905\) | −55.9508 | −1.85987 | ||||||||
\(906\) | 18.1267i | 0.602220i | ||||||||
\(907\) | −28.2027 | −0.936455 | −0.468228 | − | 0.883608i | \(-0.655107\pi\) | ||||
−0.468228 | + | 0.883608i | \(0.655107\pi\) | |||||||
\(908\) | −13.0638 | −0.433537 | ||||||||
\(909\) | 2.87801 | 0.0954576 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.22257 | −0.0736369 | −0.0368184 | − | 0.999322i | \(-0.511722\pi\) | ||||
−0.0368184 | + | 0.999322i | \(0.511722\pi\) | |||||||
\(912\) | 4.37877i | 0.144995i | ||||||||
\(913\) | −14.8205 | + | 38.9630i | −0.490487 | + | 1.28949i | ||||
\(914\) | −15.8979 | −0.525854 | ||||||||
\(915\) | −32.2296 | −1.06548 | ||||||||
\(916\) | − | 9.68676i | − | 0.320060i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.188398 | 0.00621807 | ||||||||
\(919\) | 43.5488i | 1.43654i | 0.695763 | + | 0.718271i | \(0.255066\pi\) | ||||
−0.695763 | + | 0.718271i | \(0.744934\pi\) | |||||||
\(920\) | 14.5255 | 0.478891 | ||||||||
\(921\) | − | 17.4551i | − | 0.575166i | ||||||
\(922\) | − | 37.1843i | − | 1.22460i | ||||||
\(923\) | −63.6743 | −2.09586 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −58.2552 | −1.91542 | ||||||||
\(926\) | − | 27.4293i | − | 0.901383i | ||||||
\(927\) | − | 17.7997i | − | 0.584618i | ||||||
\(928\) | −5.75703 | −0.188984 | ||||||||
\(929\) | − | 30.4460i | − | 0.998902i | −0.866342 | − | 0.499451i | \(-0.833535\pi\) | ||
0.866342 | − | 0.499451i | \(-0.166465\pi\) | |||||||
\(930\) | −13.0130 | −0.426713 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 21.6421i | − | 0.708911i | ||||||
\(933\) | −10.1883 | −0.333549 | ||||||||
\(934\) | −15.3698 | −0.502916 | ||||||||
\(935\) | 2.36731 | + | 0.900461i | 0.0774193 | + | 0.0294482i | ||||
\(936\) | − | 3.91265i | − | 0.127889i | ||||||
\(937\) | −30.3254 | −0.990688 | −0.495344 | − | 0.868697i | \(-0.664958\pi\) | ||||
−0.495344 | + | 0.868697i | \(0.664958\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.8187 | 0.646760 | ||||||||
\(940\) | 17.7386 | 0.578569 | ||||||||
\(941\) | 3.23897 | 0.105588 | 0.0527938 | − | 0.998605i | \(-0.483187\pi\) | ||||
0.0527938 | + | 0.998605i | \(0.483187\pi\) | |||||||
\(942\) | 8.01869i | 0.261263i | ||||||||
\(943\) | −29.1772 | −0.950139 | ||||||||
\(944\) | − | 4.99905i | − | 0.162705i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.78594 | − | 9.95322i | 0.123092 | − | 0.323607i | ||||
\(947\) | −33.4714 | −1.08767 | −0.543837 | − | 0.839191i | \(-0.683029\pi\) | ||||
−0.543837 | + | 0.839191i | \(0.683029\pi\) | |||||||
\(948\) | −8.55410 | −0.277824 | ||||||||
\(949\) | −48.2894 | −1.56754 | ||||||||
\(950\) | − | 50.0512i | − | 1.62388i | ||||||
\(951\) | − | 15.5000i | − | 0.502622i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 28.4159i | − | 0.920482i | −0.887794 | − | 0.460241i | \(-0.847763\pi\) | ||
0.887794 | − | 0.460241i | \(-0.152237\pi\) | |||||||
\(954\) | − | 2.83716i | − | 0.0918564i | ||||||
\(955\) | 38.4970i | 1.24573i | ||||||||
\(956\) | − | 10.6397i | − | 0.344112i | ||||||
\(957\) | 6.78832 | − | 17.8465i | 0.219435 | − | 0.576894i | ||||
\(958\) | 36.8475i | 1.19049i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −4.05345 | −0.130824 | ||||||||
\(961\) | 20.6937 | 0.667537 | ||||||||
\(962\) | − | 19.9408i | − | 0.642917i | ||||||
\(963\) | − | 6.46948i | − | 0.208476i | ||||||
\(964\) | −5.68711 | −0.183169 | ||||||||
\(965\) | 54.8827 | 1.76674 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 9.93397i | − | 0.319455i | −0.987161 | − | 0.159728i | \(-0.948938\pi\) | ||
0.987161 | − | 0.159728i | \(-0.0510616\pi\) | |||||||
\(968\) | −7.31050 | + | 8.21928i | −0.234968 | + | 0.264178i | ||||
\(969\) | 0.824952i | 0.0265013i | ||||||||
\(970\) | 70.8953i | 2.27631i | ||||||||
\(971\) | − | 61.7684i | − | 1.98224i | −0.132957 | − | 0.991122i | \(-0.542447\pi\) | ||
0.132957 | − | 0.991122i | \(-0.457553\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12.1267i | 0.388563i | ||||||||
\(975\) | 44.7233i | 1.43229i | ||||||||
\(976\) | −7.95115 | −0.254510 | ||||||||
\(977\) | −10.0719 | −0.322228 | −0.161114 | − | 0.986936i | \(-0.551509\pi\) | ||||
−0.161114 | + | 0.986936i | \(0.551509\pi\) | |||||||
\(978\) | 3.40939 | 0.109020 | ||||||||
\(979\) | −44.2100 | − | 16.8163i | −1.41296 | − | 0.537451i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 17.4531i | − | 0.557235i | ||||||
\(982\) | −38.1431 | −1.21720 | ||||||||
\(983\) | − | 26.2075i | − | 0.835890i | −0.908472 | − | 0.417945i | \(-0.862750\pi\) | ||
0.908472 | − | 0.417945i | \(-0.137250\pi\) | |||||||
\(984\) | 8.14212 | 0.259561 | ||||||||
\(985\) | 106.181 | 3.38320 | ||||||||
\(986\) | −1.08461 | −0.0345411 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.1326 | 0.545060 | ||||||||
\(989\) | − | 11.5058i | − | 0.365862i | ||||||
\(990\) | 4.77956 | − | 12.5655i | 0.151905 | − | 0.399356i | ||||
\(991\) | 7.65843 | 0.243278 | 0.121639 | − | 0.992574i | \(-0.461185\pi\) | ||||
0.121639 | + | 0.992574i | \(0.461185\pi\) | |||||||
\(992\) | −3.21035 | −0.101929 | ||||||||
\(993\) | − | 22.3460i | − | 0.709128i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.7586 | 0.784900 | ||||||||
\(996\) | − | 12.5690i | − | 0.398263i | ||||||
\(997\) | 11.7961 | 0.373586 | 0.186793 | − | 0.982399i | \(-0.440191\pi\) | ||||
0.186793 | + | 0.982399i | \(0.440191\pi\) | |||||||
\(998\) | 6.48858i | 0.205392i | ||||||||
\(999\) | − | 5.09649i | − | 0.161246i |
(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 | 3234.2.e.c.2155.13 | yes | 24 | |
7.6 | odd | 2 | 3234.2.e.d.2155.24 | yes | 24 | ||
11.10 | odd | 2 | 3234.2.e.d.2155.1 | yes | 24 | ||
77.76 | even | 2 | inner | 3234.2.e.c.2155.12 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.e.c.2155.12 | ✓ | 24 | 77.76 | even | 2 | inner | |
3234.2.e.c.2155.13 | yes | 24 | 1.1 | even | 1 | trivial | |
3234.2.e.d.2155.1 | yes | 24 | 11.10 | odd | 2 | ||
3234.2.e.d.2155.24 | yes | 24 | 7.6 | odd | 2 |