Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3450,2,Mod(2899,3450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3450, 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("3450.2899");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3450.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.5483886973\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2899.4 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3450.2899 |
Dual form | 3450.2.d.y.2899.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3450\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(1151\) | \(1201\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.44949i | 0.547856i | 0.961750 | + | 0.273928i | \(0.0883229\pi\) | ||||
−0.961750 | + | 0.273928i | \(0.911677\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 2.89898i | 0.804032i | 0.915633 | + | 0.402016i | \(0.131690\pi\) | ||||
−0.915633 | + | 0.402016i | \(0.868310\pi\) | |||||||
\(14\) | −1.44949 | −0.387392 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 5.44949i | − 1.32170i | −0.750520 | − | 0.660848i | \(-0.770197\pi\) | ||||
0.750520 | − | 0.660848i | \(-0.229803\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | −6.89898 | −1.58273 | −0.791367 | − | 0.611341i | \(-0.790630\pi\) | ||||
−0.791367 | + | 0.611341i | \(0.790630\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.44949 | 0.316305 | ||||||||
\(22\) | 2.00000i | 0.426401i | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.89898 | −0.568537 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − 1.44949i | − 0.273928i | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 2.00000i | − 0.348155i | ||||||||
\(34\) | 5.44949 | 0.934580 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 8.34847i | 1.37248i | 0.727375 | + | 0.686240i | \(0.240740\pi\) | ||||
−0.727375 | + | 0.686240i | \(0.759260\pi\) | |||||||
\(38\) | − 6.89898i | − 1.11916i | ||||||||
\(39\) | 2.89898 | 0.464208 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.89898 | −0.765092 | −0.382546 | − | 0.923936i | \(-0.624953\pi\) | ||||
−0.382546 | + | 0.923936i | \(0.624953\pi\) | |||||||
\(42\) | 1.44949i | 0.223661i | ||||||||
\(43\) | − 10.8990i | − 1.66208i | −0.556214 | − | 0.831039i | \(-0.687746\pi\) | ||||
0.556214 | − | 0.831039i | \(-0.312254\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | − 3.89898i | − 0.568725i | −0.958717 | − | 0.284362i | \(-0.908218\pi\) | ||||
0.958717 | − | 0.284362i | \(-0.0917819\pi\) | |||||||
\(48\) | − 1.00000i | − 0.144338i | ||||||||
\(49\) | 4.89898 | 0.699854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.44949 | −0.763081 | ||||||||
\(52\) | − 2.89898i | − 0.402016i | ||||||||
\(53\) | − 0.898979i | − 0.123484i | −0.998092 | − | 0.0617422i | \(-0.980334\pi\) | ||||
0.998092 | − | 0.0617422i | \(-0.0196656\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.44949 | 0.193696 | ||||||||
\(57\) | 6.89898i | 0.913792i | ||||||||
\(58\) | − 5.00000i | − 0.656532i | ||||||||
\(59\) | −10.0000 | −1.30189 | −0.650945 | − | 0.759125i | \(-0.725627\pi\) | ||||
−0.650945 | + | 0.759125i | \(0.725627\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.89898 | −0.627250 | −0.313625 | − | 0.949547i | \(-0.601543\pi\) | ||||
−0.313625 | + | 0.949547i | \(0.601543\pi\) | |||||||
\(62\) | 2.00000i | 0.254000i | ||||||||
\(63\) | − 1.44949i | − 0.182619i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.00000 | 0.246183 | ||||||||
\(67\) | − 2.00000i | − 0.244339i | −0.992509 | − | 0.122169i | \(-0.961015\pi\) | ||||
0.992509 | − | 0.122169i | \(-0.0389851\pi\) | |||||||
\(68\) | 5.44949i | 0.660848i | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7980 | 1.28148 | 0.640741 | − | 0.767757i | \(-0.278627\pi\) | ||||
0.640741 | + | 0.767757i | \(0.278627\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − 2.10102i | − 0.245906i | −0.992413 | − | 0.122953i | \(-0.960764\pi\) | ||||
0.992413 | − | 0.122953i | \(-0.0392364\pi\) | |||||||
\(74\) | −8.34847 | −0.970490 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.89898 | 0.791367 | ||||||||
\(77\) | 2.89898i | 0.330369i | ||||||||
\(78\) | 2.89898i | 0.328245i | ||||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 4.89898i | − 0.541002i | ||||||||
\(83\) | 2.55051i | 0.279955i | 0.990155 | + | 0.139977i | \(0.0447030\pi\) | ||||
−0.990155 | + | 0.139977i | \(0.955297\pi\) | |||||||
\(84\) | −1.44949 | −0.158152 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.8990 | 1.17527 | ||||||||
\(87\) | 5.00000i | 0.536056i | ||||||||
\(88\) | − 2.00000i | − 0.213201i | ||||||||
\(89\) | 10.3485 | 1.09694 | 0.548468 | − | 0.836172i | \(-0.315211\pi\) | ||||
0.548468 | + | 0.836172i | \(0.315211\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.20204 | −0.440494 | ||||||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | − 2.00000i | − 0.207390i | ||||||||
\(94\) | 3.89898 | 0.402149 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | − 12.6969i | − 1.28918i | −0.764529 | − | 0.644589i | \(-0.777028\pi\) | ||||
0.764529 | − | 0.644589i | \(-0.222972\pi\) | |||||||
\(98\) | 4.89898i | 0.494872i | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.6969 | −1.36290 | −0.681448 | − | 0.731866i | \(-0.738650\pi\) | ||||
−0.681448 | + | 0.731866i | \(0.738650\pi\) | |||||||
\(102\) | − 5.44949i | − 0.539580i | ||||||||
\(103\) | 13.2474i | 1.30531i | 0.757655 | + | 0.652655i | \(0.226345\pi\) | ||||
−0.757655 | + | 0.652655i | \(0.773655\pi\) | |||||||
\(104\) | 2.89898 | 0.284268 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.898979 | 0.0873166 | ||||||||
\(107\) | − 2.00000i | − 0.193347i | −0.995316 | − | 0.0966736i | \(-0.969180\pi\) | ||||
0.995316 | − | 0.0966736i | \(-0.0308203\pi\) | |||||||
\(108\) | − 1.00000i | − 0.0962250i | ||||||||
\(109\) | −3.44949 | −0.330401 | −0.165201 | − | 0.986260i | \(-0.552827\pi\) | ||||
−0.165201 | + | 0.986260i | \(0.552827\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.34847 | 0.792402 | ||||||||
\(112\) | 1.44949i | 0.136964i | ||||||||
\(113\) | − 14.3485i | − 1.34979i | −0.737914 | − | 0.674895i | \(-0.764189\pi\) | ||||
0.737914 | − | 0.674895i | \(-0.235811\pi\) | |||||||
\(114\) | −6.89898 | −0.646149 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.00000 | 0.464238 | ||||||||
\(117\) | − 2.89898i | − 0.268011i | ||||||||
\(118\) | − 10.0000i | − 0.920575i | ||||||||
\(119\) | 7.89898 | 0.724098 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | − 4.89898i | − 0.443533i | ||||||||
\(123\) | 4.89898i | 0.441726i | ||||||||
\(124\) | −2.00000 | −0.179605 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.44949 | 0.129131 | ||||||||
\(127\) | 1.79796i | 0.159543i | 0.996813 | + | 0.0797715i | \(0.0254191\pi\) | ||||
−0.996813 | + | 0.0797715i | \(0.974581\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −10.8990 | −0.959602 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.89898 | 0.777507 | 0.388754 | − | 0.921342i | \(-0.372906\pi\) | ||||
0.388754 | + | 0.921342i | \(0.372906\pi\) | |||||||
\(132\) | 2.00000i | 0.174078i | ||||||||
\(133\) | − 10.0000i | − 0.867110i | ||||||||
\(134\) | 2.00000 | 0.172774 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.44949 | −0.467290 | ||||||||
\(137\) | − 22.3485i | − 1.90936i | −0.297636 | − | 0.954679i | \(-0.596198\pi\) | ||||
0.297636 | − | 0.954679i | \(-0.403802\pi\) | |||||||
\(138\) | − 1.00000i | − 0.0851257i | ||||||||
\(139\) | −15.6969 | −1.33140 | −0.665698 | − | 0.746221i | \(-0.731866\pi\) | ||||
−0.665698 | + | 0.746221i | \(0.731866\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.89898 | −0.328353 | ||||||||
\(142\) | 10.7980i | 0.906145i | ||||||||
\(143\) | 5.79796i | 0.484850i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.10102 | 0.173882 | ||||||||
\(147\) | − 4.89898i | − 0.404061i | ||||||||
\(148\) | − 8.34847i | − 0.686240i | ||||||||
\(149\) | −20.0000 | −1.63846 | −0.819232 | − | 0.573462i | \(-0.805600\pi\) | ||||
−0.819232 | + | 0.573462i | \(0.805600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.6969 | −1.52154 | −0.760768 | − | 0.649024i | \(-0.775177\pi\) | ||||
−0.760768 | + | 0.649024i | \(0.775177\pi\) | |||||||
\(152\) | 6.89898i | 0.559581i | ||||||||
\(153\) | 5.44949i | 0.440565i | ||||||||
\(154\) | −2.89898 | −0.233606 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.89898 | −0.232104 | ||||||||
\(157\) | − 8.89898i | − 0.710216i | −0.934825 | − | 0.355108i | \(-0.884444\pi\) | ||||
0.934825 | − | 0.355108i | \(-0.115556\pi\) | |||||||
\(158\) | − 10.0000i | − 0.795557i | ||||||||
\(159\) | −0.898979 | −0.0712937 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.44949 | 0.114236 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | − 17.7980i | − 1.39404i | −0.717050 | − | 0.697022i | \(-0.754508\pi\) | ||||
0.717050 | − | 0.697022i | \(-0.245492\pi\) | |||||||
\(164\) | 4.89898 | 0.382546 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.55051 | −0.197958 | ||||||||
\(167\) | − 7.00000i | − 0.541676i | −0.962625 | − | 0.270838i | \(-0.912699\pi\) | ||||
0.962625 | − | 0.270838i | \(-0.0873008\pi\) | |||||||
\(168\) | − 1.44949i | − 0.111831i | ||||||||
\(169\) | 4.59592 | 0.353532 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.89898 | 0.527578 | ||||||||
\(172\) | 10.8990i | 0.831039i | ||||||||
\(173\) | 19.7980i | 1.50521i | 0.658472 | + | 0.752605i | \(0.271203\pi\) | ||||
−0.658472 | + | 0.752605i | \(0.728797\pi\) | |||||||
\(174\) | −5.00000 | −0.379049 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 10.0000i | 0.751646i | ||||||||
\(178\) | 10.3485i | 0.775651i | ||||||||
\(179\) | −3.10102 | −0.231781 | −0.115891 | − | 0.993262i | \(-0.536972\pi\) | ||||
−0.115891 | + | 0.993262i | \(0.536972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.3485 | −1.36383 | −0.681915 | − | 0.731431i | \(-0.738853\pi\) | ||||
−0.681915 | + | 0.731431i | \(0.738853\pi\) | |||||||
\(182\) | − 4.20204i | − 0.311476i | ||||||||
\(183\) | 4.89898i | 0.362143i | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.00000 | 0.146647 | ||||||||
\(187\) | − 10.8990i | − 0.797012i | ||||||||
\(188\) | 3.89898i | 0.284362i | ||||||||
\(189\) | −1.44949 | −0.105435 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.00000 | 0.144715 | 0.0723575 | − | 0.997379i | \(-0.476948\pi\) | ||||
0.0723575 | + | 0.997379i | \(0.476948\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | − 9.69694i | − 0.698001i | −0.937123 | − | 0.349000i | \(-0.886521\pi\) | ||||
0.937123 | − | 0.349000i | \(-0.113479\pi\) | |||||||
\(194\) | 12.6969 | 0.911587 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.89898 | −0.349927 | ||||||||
\(197\) | − 3.89898i | − 0.277791i | −0.990307 | − | 0.138895i | \(-0.955645\pi\) | ||||
0.990307 | − | 0.138895i | \(-0.0443552\pi\) | |||||||
\(198\) | − 2.00000i | − 0.142134i | ||||||||
\(199\) | −24.1464 | −1.71169 | −0.855847 | − | 0.517228i | \(-0.826964\pi\) | ||||
−0.855847 | + | 0.517228i | \(0.826964\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.00000 | −0.141069 | ||||||||
\(202\) | − 13.6969i | − 0.963713i | ||||||||
\(203\) | − 7.24745i | − 0.508671i | ||||||||
\(204\) | 5.44949 | 0.381541 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −13.2474 | −0.922993 | ||||||||
\(207\) | 1.00000i | 0.0695048i | ||||||||
\(208\) | 2.89898i | 0.201008i | ||||||||
\(209\) | −13.7980 | −0.954425 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.7980 | 0.743362 | 0.371681 | − | 0.928360i | \(-0.378781\pi\) | ||||
0.371681 | + | 0.928360i | \(0.378781\pi\) | |||||||
\(212\) | 0.898979i | 0.0617422i | ||||||||
\(213\) | − 10.7980i | − 0.739864i | ||||||||
\(214\) | 2.00000 | 0.136717 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.89898i | 0.196796i | ||||||||
\(218\) | − 3.44949i | − 0.233629i | ||||||||
\(219\) | −2.10102 | −0.141974 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.7980 | 1.06269 | ||||||||
\(222\) | 8.34847i | 0.560313i | ||||||||
\(223\) | − 24.6969i | − 1.65383i | −0.562327 | − | 0.826915i | \(-0.690094\pi\) | ||||
0.562327 | − | 0.826915i | \(-0.309906\pi\) | |||||||
\(224\) | −1.44949 | −0.0968481 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.3485 | 0.954446 | ||||||||
\(227\) | − 4.75255i | − 0.315438i | −0.987484 | − | 0.157719i | \(-0.949586\pi\) | ||||
0.987484 | − | 0.157719i | \(-0.0504140\pi\) | |||||||
\(228\) | − 6.89898i | − 0.456896i | ||||||||
\(229\) | −3.10102 | −0.204921 | −0.102461 | − | 0.994737i | \(-0.532672\pi\) | ||||
−0.102461 | + | 0.994737i | \(0.532672\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.89898 | 0.190739 | ||||||||
\(232\) | 5.00000i | 0.328266i | ||||||||
\(233\) | 26.6969i | 1.74897i | 0.485048 | + | 0.874487i | \(0.338802\pi\) | ||||
−0.485048 | + | 0.874487i | \(0.661198\pi\) | |||||||
\(234\) | 2.89898 | 0.189512 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.0000 | 0.650945 | ||||||||
\(237\) | 10.0000i | 0.649570i | ||||||||
\(238\) | 7.89898i | 0.512015i | ||||||||
\(239\) | 8.10102 | 0.524011 | 0.262006 | − | 0.965066i | \(-0.415616\pi\) | ||||
0.262006 | + | 0.965066i | \(0.415616\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.00000 | −0.515325 | −0.257663 | − | 0.966235i | \(-0.582952\pi\) | ||||
−0.257663 | + | 0.966235i | \(0.582952\pi\) | |||||||
\(242\) | − 7.00000i | − 0.449977i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 4.89898 | 0.313625 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.89898 | −0.312348 | ||||||||
\(247\) | − 20.0000i | − 1.27257i | ||||||||
\(248\) | − 2.00000i | − 0.127000i | ||||||||
\(249\) | 2.55051 | 0.161632 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.24745 | −0.331216 | −0.165608 | − | 0.986192i | \(-0.552959\pi\) | ||||
−0.165608 | + | 0.986192i | \(0.552959\pi\) | |||||||
\(252\) | 1.44949i | 0.0913093i | ||||||||
\(253\) | − 2.00000i | − 0.125739i | ||||||||
\(254\) | −1.79796 | −0.112814 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 8.20204i | − 0.511629i | −0.966726 | − | 0.255815i | \(-0.917656\pi\) | ||||
0.966726 | − | 0.255815i | \(-0.0823437\pi\) | |||||||
\(258\) | − 10.8990i | − 0.678541i | ||||||||
\(259\) | −12.1010 | −0.751921 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.00000 | 0.309492 | ||||||||
\(262\) | 8.89898i | 0.549781i | ||||||||
\(263\) | 19.7980i | 1.22079i | 0.792095 | + | 0.610397i | \(0.208990\pi\) | ||||
−0.792095 | + | 0.610397i | \(0.791010\pi\) | |||||||
\(264\) | −2.00000 | −0.123091 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 10.0000 | 0.613139 | ||||||||
\(267\) | − 10.3485i | − 0.633316i | ||||||||
\(268\) | 2.00000i | 0.122169i | ||||||||
\(269\) | −3.79796 | −0.231566 | −0.115783 | − | 0.993275i | \(-0.536938\pi\) | ||||
−0.115783 | + | 0.993275i | \(0.536938\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | − 5.44949i | − 0.330424i | ||||||||
\(273\) | 4.20204i | 0.254319i | ||||||||
\(274\) | 22.3485 | 1.35012 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | 25.5959i | 1.53791i | 0.639303 | + | 0.768955i | \(0.279223\pi\) | ||||
−0.639303 | + | 0.768955i | \(0.720777\pi\) | |||||||
\(278\) | − 15.6969i | − 0.941440i | ||||||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.752551 | −0.0448934 | −0.0224467 | − | 0.999748i | \(-0.507146\pi\) | ||||
−0.0224467 | + | 0.999748i | \(0.507146\pi\) | |||||||
\(282\) | − 3.89898i | − 0.232181i | ||||||||
\(283\) | − 11.5959i | − 0.689306i | −0.938730 | − | 0.344653i | \(-0.887997\pi\) | ||||
0.938730 | − | 0.344653i | \(-0.112003\pi\) | |||||||
\(284\) | −10.7980 | −0.640741 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.79796 | −0.342841 | ||||||||
\(287\) | − 7.10102i | − 0.419160i | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −12.6969 | −0.746879 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.6969 | −0.744308 | ||||||||
\(292\) | 2.10102i | 0.122953i | ||||||||
\(293\) | − 7.79796i | − 0.455562i | −0.973712 | − | 0.227781i | \(-0.926853\pi\) | ||||
0.973712 | − | 0.227781i | \(-0.0731470\pi\) | |||||||
\(294\) | 4.89898 | 0.285714 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.34847 | 0.485245 | ||||||||
\(297\) | 2.00000i | 0.116052i | ||||||||
\(298\) | − 20.0000i | − 1.15857i | ||||||||
\(299\) | 2.89898 | 0.167652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.7980 | 0.910579 | ||||||||
\(302\) | − 18.6969i | − 1.07589i | ||||||||
\(303\) | 13.6969i | 0.786869i | ||||||||
\(304\) | −6.89898 | −0.395684 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.44949 | −0.311527 | ||||||||
\(307\) | − 20.1010i | − 1.14723i | −0.819126 | − | 0.573613i | \(-0.805541\pi\) | ||||
0.819126 | − | 0.573613i | \(-0.194459\pi\) | |||||||
\(308\) | − 2.89898i | − 0.165185i | ||||||||
\(309\) | 13.2474 | 0.753621 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.5959 | 0.827659 | 0.413829 | − | 0.910355i | \(-0.364191\pi\) | ||||
0.413829 | + | 0.910355i | \(0.364191\pi\) | |||||||
\(312\) | − 2.89898i | − 0.164122i | ||||||||
\(313\) | 12.8990i | 0.729093i | 0.931185 | + | 0.364547i | \(0.118776\pi\) | ||||
−0.931185 | + | 0.364547i | \(0.881224\pi\) | |||||||
\(314\) | 8.89898 | 0.502198 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | 10.5959i | 0.595126i | 0.954702 | + | 0.297563i | \(0.0961738\pi\) | ||||
−0.954702 | + | 0.297563i | \(0.903826\pi\) | |||||||
\(318\) | − 0.898979i | − 0.0504123i | ||||||||
\(319\) | −10.0000 | −0.559893 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.00000 | −0.111629 | ||||||||
\(322\) | 1.44949i | 0.0807769i | ||||||||
\(323\) | 37.5959i | 2.09189i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.7980 | 0.985738 | ||||||||
\(327\) | 3.44949i | 0.190757i | ||||||||
\(328\) | 4.89898i | 0.270501i | ||||||||
\(329\) | 5.65153 | 0.311579 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.79796 | −0.373650 | −0.186825 | − | 0.982393i | \(-0.559820\pi\) | ||||
−0.186825 | + | 0.982393i | \(0.559820\pi\) | |||||||
\(332\) | − 2.55051i | − 0.139977i | ||||||||
\(333\) | − 8.34847i | − 0.457493i | ||||||||
\(334\) | 7.00000 | 0.383023 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.44949 | 0.0790761 | ||||||||
\(337\) | − 16.4949i | − 0.898534i | −0.893397 | − | 0.449267i | \(-0.851685\pi\) | ||||
0.893397 | − | 0.449267i | \(-0.148315\pi\) | |||||||
\(338\) | 4.59592i | 0.249985i | ||||||||
\(339\) | −14.3485 | −0.779302 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.00000 | 0.216612 | ||||||||
\(342\) | 6.89898i | 0.373054i | ||||||||
\(343\) | 17.2474i | 0.931275i | ||||||||
\(344\) | −10.8990 | −0.587634 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.7980 | −1.06434 | ||||||||
\(347\) | − 32.6969i | − 1.75526i | −0.479335 | − | 0.877632i | \(-0.659122\pi\) | ||||
0.479335 | − | 0.877632i | \(-0.340878\pi\) | |||||||
\(348\) | − 5.00000i | − 0.268028i | ||||||||
\(349\) | −13.1010 | −0.701282 | −0.350641 | − | 0.936510i | \(-0.614036\pi\) | ||||
−0.350641 | + | 0.936510i | \(0.614036\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.89898 | −0.154736 | ||||||||
\(352\) | 2.00000i | 0.106600i | ||||||||
\(353\) | 26.0000i | 1.38384i | 0.721974 | + | 0.691920i | \(0.243235\pi\) | ||||
−0.721974 | + | 0.691920i | \(0.756765\pi\) | |||||||
\(354\) | −10.0000 | −0.531494 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.3485 | −0.548468 | ||||||||
\(357\) | − 7.89898i | − 0.418058i | ||||||||
\(358\) | − 3.10102i | − 0.163894i | ||||||||
\(359\) | 6.20204 | 0.327331 | 0.163666 | − | 0.986516i | \(-0.447668\pi\) | ||||
0.163666 | + | 0.986516i | \(0.447668\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 28.5959 | 1.50505 | ||||||||
\(362\) | − 18.3485i | − 0.964374i | ||||||||
\(363\) | 7.00000i | 0.367405i | ||||||||
\(364\) | 4.20204 | 0.220247 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.89898 | −0.256074 | ||||||||
\(367\) | − 8.20204i | − 0.428143i | −0.976818 | − | 0.214072i | \(-0.931327\pi\) | ||||
0.976818 | − | 0.214072i | \(-0.0686726\pi\) | |||||||
\(368\) | − 1.00000i | − 0.0521286i | ||||||||
\(369\) | 4.89898 | 0.255031 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.30306 | 0.0676516 | ||||||||
\(372\) | 2.00000i | 0.103695i | ||||||||
\(373\) | 3.24745i | 0.168147i | 0.996460 | + | 0.0840733i | \(0.0267930\pi\) | ||||
−0.996460 | + | 0.0840733i | \(0.973207\pi\) | |||||||
\(374\) | 10.8990 | 0.563573 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.89898 | −0.201075 | ||||||||
\(377\) | − 14.4949i | − 0.746525i | ||||||||
\(378\) | − 1.44949i | − 0.0745537i | ||||||||
\(379\) | 38.2929 | 1.96697 | 0.983486 | − | 0.180984i | \(-0.0579284\pi\) | ||||
0.983486 | + | 0.180984i | \(0.0579284\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.79796 | 0.0921122 | ||||||||
\(382\) | 2.00000i | 0.102329i | ||||||||
\(383\) | 9.79796i | 0.500652i | 0.968162 | + | 0.250326i | \(0.0805379\pi\) | ||||
−0.968162 | + | 0.250326i | \(0.919462\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.69694 | 0.493561 | ||||||||
\(387\) | 10.8990i | 0.554026i | ||||||||
\(388\) | 12.6969i | 0.644589i | ||||||||
\(389\) | 23.7980 | 1.20660 | 0.603302 | − | 0.797513i | \(-0.293851\pi\) | ||||
0.603302 | + | 0.797513i | \(0.293851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.44949 | −0.275593 | ||||||||
\(392\) | − 4.89898i | − 0.247436i | ||||||||
\(393\) | − 8.89898i | − 0.448894i | ||||||||
\(394\) | 3.89898 | 0.196428 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.00000 | 0.100504 | ||||||||
\(397\) | 28.0000i | 1.40528i | 0.711546 | + | 0.702640i | \(0.247995\pi\) | ||||
−0.711546 | + | 0.702640i | \(0.752005\pi\) | |||||||
\(398\) | − 24.1464i | − 1.21035i | ||||||||
\(399\) | −10.0000 | −0.500626 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.6969 | −0.933681 | −0.466840 | − | 0.884342i | \(-0.654608\pi\) | ||||
−0.466840 | + | 0.884342i | \(0.654608\pi\) | |||||||
\(402\) | − 2.00000i | − 0.0997509i | ||||||||
\(403\) | 5.79796i | 0.288817i | ||||||||
\(404\) | 13.6969 | 0.681448 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.24745 | 0.359685 | ||||||||
\(407\) | 16.6969i | 0.827637i | ||||||||
\(408\) | 5.44949i | 0.269790i | ||||||||
\(409\) | −25.6969 | −1.27063 | −0.635316 | − | 0.772252i | \(-0.719130\pi\) | ||||
−0.635316 | + | 0.772252i | \(0.719130\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.3485 | −1.10237 | ||||||||
\(412\) | − 13.2474i | − 0.652655i | ||||||||
\(413\) | − 14.4949i | − 0.713247i | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.89898 | −0.142134 | ||||||||
\(417\) | 15.6969i | 0.768682i | ||||||||
\(418\) | − 13.7980i | − 0.674880i | ||||||||
\(419\) | −14.1464 | −0.691098 | −0.345549 | − | 0.938401i | \(-0.612307\pi\) | ||||
−0.345549 | + | 0.938401i | \(0.612307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.4949 | −0.608964 | −0.304482 | − | 0.952518i | \(-0.598483\pi\) | ||||
−0.304482 | + | 0.952518i | \(0.598483\pi\) | |||||||
\(422\) | 10.7980i | 0.525636i | ||||||||
\(423\) | 3.89898i | 0.189575i | ||||||||
\(424\) | −0.898979 | −0.0436583 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.7980 | 0.523163 | ||||||||
\(427\) | − 7.10102i | − 0.343642i | ||||||||
\(428\) | 2.00000i | 0.0966736i | ||||||||
\(429\) | 5.79796 | 0.279928 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.3031 | 0.544449 | 0.272225 | − | 0.962234i | \(-0.412241\pi\) | ||||
0.272225 | + | 0.962234i | \(0.412241\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 16.6969i | 0.802404i | 0.915990 | + | 0.401202i | \(0.131407\pi\) | ||||
−0.915990 | + | 0.401202i | \(0.868593\pi\) | |||||||
\(434\) | −2.89898 | −0.139155 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.44949 | 0.165201 | ||||||||
\(437\) | 6.89898i | 0.330023i | ||||||||
\(438\) | − 2.10102i | − 0.100391i | ||||||||
\(439\) | 10.6969 | 0.510537 | 0.255269 | − | 0.966870i | \(-0.417836\pi\) | ||||
0.255269 | + | 0.966870i | \(0.417836\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.89898 | −0.233285 | ||||||||
\(442\) | 15.7980i | 0.751432i | ||||||||
\(443\) | 5.30306i | 0.251956i | 0.992033 | + | 0.125978i | \(0.0402069\pi\) | ||||
−0.992033 | + | 0.125978i | \(0.959793\pi\) | |||||||
\(444\) | −8.34847 | −0.396201 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 24.6969 | 1.16943 | ||||||||
\(447\) | 20.0000i | 0.945968i | ||||||||
\(448\) | − 1.44949i | − 0.0684820i | ||||||||
\(449\) | −3.79796 | −0.179237 | −0.0896184 | − | 0.995976i | \(-0.528565\pi\) | ||||
−0.0896184 | + | 0.995976i | \(0.528565\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.79796 | −0.461368 | ||||||||
\(452\) | 14.3485i | 0.674895i | ||||||||
\(453\) | 18.6969i | 0.878459i | ||||||||
\(454\) | 4.75255 | 0.223048 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.89898 | 0.323074 | ||||||||
\(457\) | 0.404082i | 0.0189022i | 0.999955 | + | 0.00945108i | \(0.00300842\pi\) | ||||
−0.999955 | + | 0.00945108i | \(0.996992\pi\) | |||||||
\(458\) | − 3.10102i | − 0.144901i | ||||||||
\(459\) | 5.44949 | 0.254360 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.4949 | 1.00112 | 0.500559 | − | 0.865703i | \(-0.333128\pi\) | ||||
0.500559 | + | 0.865703i | \(0.333128\pi\) | |||||||
\(462\) | 2.89898i | 0.134873i | ||||||||
\(463\) | − 4.00000i | − 0.185896i | −0.995671 | − | 0.0929479i | \(-0.970371\pi\) | ||||
0.995671 | − | 0.0929479i | \(-0.0296290\pi\) | |||||||
\(464\) | −5.00000 | −0.232119 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −26.6969 | −1.23671 | ||||||||
\(467\) | − 29.9444i | − 1.38566i | −0.721100 | − | 0.692830i | \(-0.756363\pi\) | ||||
0.721100 | − | 0.692830i | \(-0.243637\pi\) | |||||||
\(468\) | 2.89898i | 0.134005i | ||||||||
\(469\) | 2.89898 | 0.133862 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.89898 | −0.410043 | ||||||||
\(472\) | 10.0000i | 0.460287i | ||||||||
\(473\) | − 21.7980i | − 1.00227i | ||||||||
\(474\) | −10.0000 | −0.459315 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.89898 | −0.362049 | ||||||||
\(477\) | 0.898979i | 0.0411614i | ||||||||
\(478\) | 8.10102i | 0.370532i | ||||||||
\(479\) | 30.0000 | 1.37073 | 0.685367 | − | 0.728197i | \(-0.259642\pi\) | ||||
0.685367 | + | 0.728197i | \(0.259642\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.2020 | −1.10352 | ||||||||
\(482\) | − 8.00000i | − 0.364390i | ||||||||
\(483\) | − 1.44949i | − 0.0659541i | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | − 15.1010i | − 0.684293i | −0.939647 | − | 0.342146i | \(-0.888846\pi\) | ||||
0.939647 | − | 0.342146i | \(-0.111154\pi\) | |||||||
\(488\) | 4.89898i | 0.221766i | ||||||||
\(489\) | −17.7980 | −0.804852 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.1010 | 1.13279 | 0.566397 | − | 0.824133i | \(-0.308337\pi\) | ||||
0.566397 | + | 0.824133i | \(0.308337\pi\) | |||||||
\(492\) | − 4.89898i | − 0.220863i | ||||||||
\(493\) | 27.2474i | 1.22716i | ||||||||
\(494\) | 20.0000 | 0.899843 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 15.6515i | 0.702067i | ||||||||
\(498\) | 2.55051i | 0.114291i | ||||||||
\(499\) | −21.8990 | −0.980333 | −0.490166 | − | 0.871629i | \(-0.663064\pi\) | ||||
−0.490166 | + | 0.871629i | \(0.663064\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.00000 | −0.312737 | ||||||||
\(502\) | − 5.24745i | − 0.234205i | ||||||||
\(503\) | − 14.6969i | − 0.655304i | −0.944798 | − | 0.327652i | \(-0.893743\pi\) | ||||
0.944798 | − | 0.327652i | \(-0.106257\pi\) | |||||||
\(504\) | −1.44949 | −0.0645654 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.00000 | 0.0889108 | ||||||||
\(507\) | − 4.59592i | − 0.204112i | ||||||||
\(508\) | − 1.79796i | − 0.0797715i | ||||||||
\(509\) | 15.0000 | 0.664863 | 0.332432 | − | 0.943127i | \(-0.392131\pi\) | ||||
0.332432 | + | 0.943127i | \(0.392131\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.04541 | 0.134721 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 6.89898i | − 0.304597i | ||||||||
\(514\) | 8.20204 | 0.361777 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.8990 | 0.479801 | ||||||||
\(517\) | − 7.79796i | − 0.342954i | ||||||||
\(518\) | − 12.1010i | − 0.531688i | ||||||||
\(519\) | 19.7980 | 0.869034 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.1464 | 1.14550 | 0.572748 | − | 0.819732i | \(-0.305877\pi\) | ||||
0.572748 | + | 0.819732i | \(0.305877\pi\) | |||||||
\(522\) | 5.00000i | 0.218844i | ||||||||
\(523\) | 16.0000i | 0.699631i | 0.936819 | + | 0.349816i | \(0.113756\pi\) | ||||
−0.936819 | + | 0.349816i | \(0.886244\pi\) | |||||||
\(524\) | −8.89898 | −0.388754 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.7980 | −0.863232 | ||||||||
\(527\) | − 10.8990i | − 0.474767i | ||||||||
\(528\) | − 2.00000i | − 0.0870388i | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.0000 | 0.433963 | ||||||||
\(532\) | 10.0000i | 0.433555i | ||||||||
\(533\) | − 14.2020i | − 0.615159i | ||||||||
\(534\) | 10.3485 | 0.447822 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.00000 | −0.0863868 | ||||||||
\(537\) | 3.10102i | 0.133819i | ||||||||
\(538\) | − 3.79796i | − 0.163742i | ||||||||
\(539\) | 9.79796 | 0.422028 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.5959 | −0.670521 | −0.335260 | − | 0.942125i | \(-0.608824\pi\) | ||||
−0.335260 | + | 0.942125i | \(0.608824\pi\) | |||||||
\(542\) | − 8.00000i | − 0.343629i | ||||||||
\(543\) | 18.3485i | 0.787408i | ||||||||
\(544\) | 5.44949 | 0.233645 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.20204 | −0.179831 | ||||||||
\(547\) | − 10.7980i | − 0.461687i | −0.972991 | − | 0.230844i | \(-0.925851\pi\) | ||||
0.972991 | − | 0.230844i | \(-0.0741486\pi\) | |||||||
\(548\) | 22.3485i | 0.954679i | ||||||||
\(549\) | 4.89898 | 0.209083 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.4949 | 1.46953 | ||||||||
\(552\) | 1.00000i | 0.0425628i | ||||||||
\(553\) | − 14.4949i | − 0.616386i | ||||||||
\(554\) | −25.5959 | −1.08747 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.6969 | 0.665698 | ||||||||
\(557\) | 28.6969i | 1.21593i | 0.793964 | + | 0.607964i | \(0.208014\pi\) | ||||
−0.793964 | + | 0.607964i | \(0.791986\pi\) | |||||||
\(558\) | − 2.00000i | − 0.0846668i | ||||||||
\(559\) | 31.5959 | 1.33636 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.8990 | −0.460155 | ||||||||
\(562\) | − 0.752551i | − 0.0317445i | ||||||||
\(563\) | 6.00000i | 0.252870i | 0.991975 | + | 0.126435i | \(0.0403535\pi\) | ||||
−0.991975 | + | 0.126435i | \(0.959647\pi\) | |||||||
\(564\) | 3.89898 | 0.164177 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.5959 | 0.487413 | ||||||||
\(567\) | 1.44949i | 0.0608728i | ||||||||
\(568\) | − 10.7980i | − 0.453072i | ||||||||
\(569\) | 44.4949 | 1.86532 | 0.932662 | − | 0.360753i | \(-0.117480\pi\) | ||||
0.932662 | + | 0.360753i | \(0.117480\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.6969 | 1.36832 | 0.684162 | − | 0.729330i | \(-0.260168\pi\) | ||||
0.684162 | + | 0.729330i | \(0.260168\pi\) | |||||||
\(572\) | − 5.79796i | − 0.242425i | ||||||||
\(573\) | − 2.00000i | − 0.0835512i | ||||||||
\(574\) | 7.10102 | 0.296391 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − 2.00000i | − 0.0832611i | −0.999133 | − | 0.0416305i | \(-0.986745\pi\) | ||||
0.999133 | − | 0.0416305i | \(-0.0132552\pi\) | |||||||
\(578\) | − 12.6969i | − 0.528123i | ||||||||
\(579\) | −9.69694 | −0.402991 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.69694 | −0.153375 | ||||||||
\(582\) | − 12.6969i | − 0.526305i | ||||||||
\(583\) | − 1.79796i | − 0.0744639i | ||||||||
\(584\) | −2.10102 | −0.0869408 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.79796 | 0.322131 | ||||||||
\(587\) | 4.89898i | 0.202203i | 0.994876 | + | 0.101101i | \(0.0322366\pi\) | ||||
−0.994876 | + | 0.101101i | \(0.967763\pi\) | |||||||
\(588\) | 4.89898i | 0.202031i | ||||||||
\(589\) | −13.7980 | −0.568535 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.89898 | −0.160383 | ||||||||
\(592\) | 8.34847i | 0.343120i | ||||||||
\(593\) | 43.5959i | 1.79027i | 0.445795 | + | 0.895135i | \(0.352921\pi\) | ||||
−0.445795 | + | 0.895135i | \(0.647079\pi\) | |||||||
\(594\) | −2.00000 | −0.0820610 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.0000 | 0.819232 | ||||||||
\(597\) | 24.1464i | 0.988248i | ||||||||
\(598\) | 2.89898i | 0.118548i | ||||||||
\(599\) | 21.3939 | 0.874130 | 0.437065 | − | 0.899430i | \(-0.356018\pi\) | ||||
0.437065 | + | 0.899430i | \(0.356018\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.0000 | 1.50926 | 0.754631 | − | 0.656150i | \(-0.227816\pi\) | ||||
0.754631 | + | 0.656150i | \(0.227816\pi\) | |||||||
\(602\) | 15.7980i | 0.643877i | ||||||||
\(603\) | 2.00000i | 0.0814463i | ||||||||
\(604\) | 18.6969 | 0.760768 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −13.6969 | −0.556400 | ||||||||
\(607\) | 18.0000i | 0.730597i | 0.930890 | + | 0.365299i | \(0.119033\pi\) | ||||
−0.930890 | + | 0.365299i | \(0.880967\pi\) | |||||||
\(608\) | − 6.89898i | − 0.279791i | ||||||||
\(609\) | −7.24745 | −0.293681 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.3031 | 0.457273 | ||||||||
\(612\) | − 5.44949i | − 0.220283i | ||||||||
\(613\) | 0.146428i | 0.00591418i | 0.999996 | + | 0.00295709i | \(0.000941272\pi\) | ||||
−0.999996 | + | 0.00295709i | \(0.999059\pi\) | |||||||
\(614\) | 20.1010 | 0.811211 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.89898 | 0.116803 | ||||||||
\(617\) | 12.4949i | 0.503026i | 0.967854 | + | 0.251513i | \(0.0809281\pi\) | ||||
−0.967854 | + | 0.251513i | \(0.919072\pi\) | |||||||
\(618\) | 13.2474i | 0.532891i | ||||||||
\(619\) | 44.4949 | 1.78840 | 0.894200 | − | 0.447667i | \(-0.147745\pi\) | ||||
0.894200 | + | 0.447667i | \(0.147745\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 14.5959i | 0.585243i | ||||||||
\(623\) | 15.0000i | 0.600962i | ||||||||
\(624\) | 2.89898 | 0.116052 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.8990 | −0.515547 | ||||||||
\(627\) | 13.7980i | 0.551037i | ||||||||
\(628\) | 8.89898i | 0.355108i | ||||||||
\(629\) | 45.4949 | 1.81400 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.4495 | 0.615034 | 0.307517 | − | 0.951543i | \(-0.400502\pi\) | ||||
0.307517 | + | 0.951543i | \(0.400502\pi\) | |||||||
\(632\) | 10.0000i | 0.397779i | ||||||||
\(633\) | − 10.7980i | − 0.429180i | ||||||||
\(634\) | −10.5959 | −0.420818 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.898979 | 0.0356469 | ||||||||
\(637\) | 14.2020i | 0.562705i | ||||||||
\(638\) | − 10.0000i | − 0.395904i | ||||||||
\(639\) | −10.7980 | −0.427161 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.5505 | −0.969687 | −0.484843 | − | 0.874601i | \(-0.661123\pi\) | ||||
−0.484843 | + | 0.874601i | \(0.661123\pi\) | |||||||
\(642\) | − 2.00000i | − 0.0789337i | ||||||||
\(643\) | 19.7980i | 0.780755i | 0.920655 | + | 0.390378i | \(0.127656\pi\) | ||||
−0.920655 | + | 0.390378i | \(0.872344\pi\) | |||||||
\(644\) | −1.44949 | −0.0571179 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −37.5959 | −1.47919 | ||||||||
\(647\) | 20.5959i | 0.809709i | 0.914381 | + | 0.404855i | \(0.132678\pi\) | ||||
−0.914381 | + | 0.404855i | \(0.867322\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | −20.0000 | −0.785069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.89898 | 0.113620 | ||||||||
\(652\) | 17.7980i | 0.697022i | ||||||||
\(653\) | 0.303062i | 0.0118597i | 0.999982 | + | 0.00592986i | \(0.00188754\pi\) | ||||
−0.999982 | + | 0.00592986i | \(0.998112\pi\) | |||||||
\(654\) | −3.44949 | −0.134886 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.89898 | −0.191273 | ||||||||
\(657\) | 2.10102i | 0.0819686i | ||||||||
\(658\) | 5.65153i | 0.220320i | ||||||||
\(659\) | 23.4495 | 0.913462 | 0.456731 | − | 0.889605i | \(-0.349020\pi\) | ||||
0.456731 | + | 0.889605i | \(0.349020\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.4495 | −0.834288 | −0.417144 | − | 0.908840i | \(-0.636969\pi\) | ||||
−0.417144 | + | 0.908840i | \(0.636969\pi\) | |||||||
\(662\) | − 6.79796i | − 0.264210i | ||||||||
\(663\) | − 15.7980i | − 0.613542i | ||||||||
\(664\) | 2.55051 | 0.0989790 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.34847 | 0.323497 | ||||||||
\(667\) | 5.00000i | 0.193601i | ||||||||
\(668\) | 7.00000i | 0.270838i | ||||||||
\(669\) | −24.6969 | −0.954839 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.79796 | −0.378246 | ||||||||
\(672\) | 1.44949i | 0.0559153i | ||||||||
\(673\) | − 26.5959i | − 1.02520i | −0.858628 | − | 0.512599i | \(-0.828683\pi\) | ||||
0.858628 | − | 0.512599i | \(-0.171317\pi\) | |||||||
\(674\) | 16.4949 | 0.635360 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.59592 | −0.176766 | ||||||||
\(677\) | − 33.3939i | − 1.28343i | −0.766943 | − | 0.641715i | \(-0.778223\pi\) | ||||
0.766943 | − | 0.641715i | \(-0.221777\pi\) | |||||||
\(678\) | − 14.3485i | − 0.551050i | ||||||||
\(679\) | 18.4041 | 0.706284 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.75255 | −0.182118 | ||||||||
\(682\) | 4.00000i | 0.153168i | ||||||||
\(683\) | − 7.10102i | − 0.271713i | −0.990729 | − | 0.135856i | \(-0.956621\pi\) | ||||
0.990729 | − | 0.135856i | \(-0.0433786\pi\) | |||||||
\(684\) | −6.89898 | −0.263789 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −17.2474 | −0.658511 | ||||||||
\(687\) | 3.10102i | 0.118311i | ||||||||
\(688\) | − 10.8990i | − 0.415520i | ||||||||
\(689\) | 2.60612 | 0.0992854 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.20204 | −0.350062 | −0.175031 | − | 0.984563i | \(-0.556003\pi\) | ||||
−0.175031 | + | 0.984563i | \(0.556003\pi\) | |||||||
\(692\) | − 19.7980i | − 0.752605i | ||||||||
\(693\) | − 2.89898i | − 0.110123i | ||||||||
\(694\) | 32.6969 | 1.24116 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.00000 | 0.189525 | ||||||||
\(697\) | 26.6969i | 1.01122i | ||||||||
\(698\) | − 13.1010i | − 0.495881i | ||||||||
\(699\) | 26.6969 | 1.00977 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0000 | −0.679851 | −0.339925 | − | 0.940452i | \(-0.610402\pi\) | ||||
−0.339925 | + | 0.940452i | \(0.610402\pi\) | |||||||
\(702\) | − 2.89898i | − 0.109415i | ||||||||
\(703\) | − 57.5959i | − 2.17227i | ||||||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.0000 | −0.978523 | ||||||||
\(707\) | − 19.8536i | − 0.746670i | ||||||||
\(708\) | − 10.0000i | − 0.375823i | ||||||||
\(709\) | −27.9444 | −1.04947 | −0.524737 | − | 0.851265i | \(-0.675836\pi\) | ||||
−0.524737 | + | 0.851265i | \(0.675836\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.0000 | 0.375029 | ||||||||
\(712\) | − 10.3485i | − 0.387825i | ||||||||
\(713\) | − 2.00000i | − 0.0749006i | ||||||||
\(714\) | 7.89898 | 0.295612 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.10102 | 0.115891 | ||||||||
\(717\) | − 8.10102i | − 0.302538i | ||||||||
\(718\) | 6.20204i | 0.231458i | ||||||||
\(719\) | −28.7980 | −1.07398 | −0.536991 | − | 0.843588i | \(-0.680439\pi\) | ||||
−0.536991 | + | 0.843588i | \(0.680439\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.2020 | −0.715121 | ||||||||
\(722\) | 28.5959i | 1.06423i | ||||||||
\(723\) | 8.00000i | 0.297523i | ||||||||
\(724\) | 18.3485 | 0.681915 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.00000 | −0.259794 | ||||||||
\(727\) | 39.3939i | 1.46104i | 0.682892 | + | 0.730519i | \(0.260722\pi\) | ||||
−0.682892 | + | 0.730519i | \(0.739278\pi\) | |||||||
\(728\) | 4.20204i | 0.155738i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −59.3939 | −2.19676 | ||||||||
\(732\) | − 4.89898i | − 0.181071i | ||||||||
\(733\) | 40.1464i | 1.48284i | 0.671040 | + | 0.741421i | \(0.265848\pi\) | ||||
−0.671040 | + | 0.741421i | \(0.734152\pi\) | |||||||
\(734\) | 8.20204 | 0.302743 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | − 4.00000i | − 0.147342i | ||||||||
\(738\) | 4.89898i | 0.180334i | ||||||||
\(739\) | −12.5959 | −0.463348 | −0.231674 | − | 0.972793i | \(-0.574420\pi\) | ||||
−0.231674 | + | 0.972793i | \(0.574420\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.0000 | −0.734718 | ||||||||
\(742\) | 1.30306i | 0.0478369i | ||||||||
\(743\) | 24.2929i | 0.891218i | 0.895228 | + | 0.445609i | \(0.147013\pi\) | ||||
−0.895228 | + | 0.445609i | \(0.852987\pi\) | |||||||
\(744\) | −2.00000 | −0.0733236 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.24745 | −0.118898 | ||||||||
\(747\) | − 2.55051i | − 0.0933183i | ||||||||
\(748\) | 10.8990i | 0.398506i | ||||||||
\(749\) | 2.89898 | 0.105926 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.2474 | −0.921292 | −0.460646 | − | 0.887584i | \(-0.652382\pi\) | ||||
−0.460646 | + | 0.887584i | \(0.652382\pi\) | |||||||
\(752\) | − 3.89898i | − 0.142181i | ||||||||
\(753\) | 5.24745i | 0.191228i | ||||||||
\(754\) | 14.4949 | 0.527873 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.44949 | 0.0527174 | ||||||||
\(757\) | 10.7526i | 0.390808i | 0.980723 | + | 0.195404i | \(0.0626018\pi\) | ||||
−0.980723 | + | 0.195404i | \(0.937398\pi\) | |||||||
\(758\) | 38.2929i | 1.39086i | ||||||||
\(759\) | −2.00000 | −0.0725954 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −50.0908 | −1.81579 | −0.907895 | − | 0.419197i | \(-0.862312\pi\) | ||||
−0.907895 | + | 0.419197i | \(0.862312\pi\) | |||||||
\(762\) | 1.79796i | 0.0651332i | ||||||||
\(763\) | − 5.00000i | − 0.181012i | ||||||||
\(764\) | −2.00000 | −0.0723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.79796 | −0.354015 | ||||||||
\(767\) | − 28.9898i | − 1.04676i | ||||||||
\(768\) | − 1.00000i | − 0.0360844i | ||||||||
\(769\) | −48.2929 | −1.74148 | −0.870742 | − | 0.491739i | \(-0.836361\pi\) | ||||
−0.870742 | + | 0.491739i | \(0.836361\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.20204 | −0.295389 | ||||||||
\(772\) | 9.69694i | 0.349000i | ||||||||
\(773\) | − 10.8990i | − 0.392009i | −0.980603 | − | 0.196005i | \(-0.937203\pi\) | ||||
0.980603 | − | 0.196005i | \(-0.0627967\pi\) | |||||||
\(774\) | −10.8990 | −0.391756 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.6969 | −0.455794 | ||||||||
\(777\) | 12.1010i | 0.434122i | ||||||||
\(778\) | 23.7980i | 0.853198i | ||||||||
\(779\) | 33.7980 | 1.21094 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.5959 | 0.772763 | ||||||||
\(782\) | − 5.44949i | − 0.194873i | ||||||||
\(783\) | − 5.00000i | − 0.178685i | ||||||||
\(784\) | 4.89898 | 0.174964 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.89898 | 0.317416 | ||||||||
\(787\) | 28.0000i | 0.998092i | 0.866575 | + | 0.499046i | \(0.166316\pi\) | ||||
−0.866575 | + | 0.499046i | \(0.833684\pi\) | |||||||
\(788\) | 3.89898i | 0.138895i | ||||||||
\(789\) | 19.7980 | 0.704826 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.7980 | 0.739490 | ||||||||
\(792\) | 2.00000i | 0.0710669i | ||||||||
\(793\) | − 14.2020i | − 0.504329i | ||||||||
\(794\) | −28.0000 | −0.993683 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.1464 | 0.855847 | ||||||||
\(797\) | 34.8990i | 1.23619i | 0.786105 | + | 0.618093i | \(0.212094\pi\) | ||||
−0.786105 | + | 0.618093i | \(0.787906\pi\) | |||||||
\(798\) | − 10.0000i | − 0.353996i | ||||||||
\(799\) | −21.2474 | −0.751681 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.3485 | −0.365645 | ||||||||
\(802\) | − 18.6969i | − 0.660212i | ||||||||
\(803\) | − 4.20204i | − 0.148287i | ||||||||
\(804\) | 2.00000 | 0.0705346 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.79796 | −0.204224 | ||||||||
\(807\) | 3.79796i | 0.133694i | ||||||||
\(808\) | 13.6969i | 0.481857i | ||||||||
\(809\) | −11.3939 | −0.400587 | −0.200294 | − | 0.979736i | \(-0.564190\pi\) | ||||
−0.200294 | + | 0.979736i | \(0.564190\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.7980 | 1.60818 | 0.804092 | − | 0.594505i | \(-0.202652\pi\) | ||||
0.804092 | + | 0.594505i | \(0.202652\pi\) | |||||||
\(812\) | 7.24745i | 0.254336i | ||||||||
\(813\) | 8.00000i | 0.280572i | ||||||||
\(814\) | −16.6969 | −0.585227 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5.44949 | −0.190770 | ||||||||
\(817\) | 75.1918i | 2.63063i | ||||||||
\(818\) | − 25.6969i | − 0.898472i | ||||||||
\(819\) | 4.20204 | 0.146831 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −51.7980 | −1.80776 | −0.903881 | − | 0.427785i | \(-0.859294\pi\) | ||||
−0.903881 | + | 0.427785i | \(0.859294\pi\) | |||||||
\(822\) | − 22.3485i | − 0.779492i | ||||||||
\(823\) | − 56.0908i | − 1.95520i | −0.210465 | − | 0.977601i | \(-0.567498\pi\) | ||||
0.210465 | − | 0.977601i | \(-0.432502\pi\) | |||||||
\(824\) | 13.2474 | 0.461497 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.4949 | 0.504342 | ||||||||
\(827\) | − 14.7526i | − 0.512996i | −0.966545 | − | 0.256498i | \(-0.917431\pi\) | ||||
0.966545 | − | 0.256498i | \(-0.0825688\pi\) | |||||||
\(828\) | − 1.00000i | − 0.0347524i | ||||||||
\(829\) | 33.1010 | 1.14965 | 0.574823 | − | 0.818278i | \(-0.305071\pi\) | ||||
0.574823 | + | 0.818278i | \(0.305071\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.5959 | 0.887913 | ||||||||
\(832\) | − 2.89898i | − 0.100504i | ||||||||
\(833\) | − 26.6969i | − 0.924994i | ||||||||
\(834\) | −15.6969 | −0.543541 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 13.7980 | 0.477212 | ||||||||
\(837\) | 2.00000i | 0.0691301i | ||||||||
\(838\) | − 14.1464i | − 0.488680i | ||||||||
\(839\) | 9.30306 | 0.321177 | 0.160589 | − | 0.987021i | \(-0.448661\pi\) | ||||
0.160589 | + | 0.987021i | \(0.448661\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | − 12.4949i | − 0.430603i | ||||||||
\(843\) | 0.752551i | 0.0259192i | ||||||||
\(844\) | −10.7980 | −0.371681 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.89898 | −0.134050 | ||||||||
\(847\) | − 10.1464i | − 0.348635i | ||||||||
\(848\) | − 0.898979i | − 0.0308711i | ||||||||
\(849\) | −11.5959 | −0.397971 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.34847 | 0.286182 | ||||||||
\(852\) | 10.7980i | 0.369932i | ||||||||
\(853\) | 44.9898i | 1.54042i | 0.637790 | + | 0.770211i | \(0.279849\pi\) | ||||
−0.637790 | + | 0.770211i | \(0.720151\pi\) | |||||||
\(854\) | 7.10102 | 0.242992 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.00000 | −0.0683586 | ||||||||
\(857\) | 42.4949i | 1.45160i | 0.687907 | + | 0.725799i | \(0.258530\pi\) | ||||
−0.687907 | + | 0.725799i | \(0.741470\pi\) | |||||||
\(858\) | 5.79796i | 0.197939i | ||||||||
\(859\) | −20.0000 | −0.682391 | −0.341196 | − | 0.939992i | \(-0.610832\pi\) | ||||
−0.341196 | + | 0.939992i | \(0.610832\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.10102 | −0.242002 | ||||||||
\(862\) | 11.3031i | 0.384984i | ||||||||
\(863\) | − 20.3939i | − 0.694216i | −0.937825 | − | 0.347108i | \(-0.887164\pi\) | ||||
0.937825 | − | 0.347108i | \(-0.112836\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.6969 | −0.567385 | ||||||||
\(867\) | 12.6969i | 0.431211i | ||||||||
\(868\) | − 2.89898i | − 0.0983978i | ||||||||
\(869\) | −20.0000 | −0.678454 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.79796 | 0.196456 | ||||||||
\(872\) | 3.44949i | 0.116814i | ||||||||
\(873\) | 12.6969i | 0.429726i | ||||||||
\(874\) | −6.89898 | −0.233361 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.10102 | 0.0709869 | ||||||||
\(877\) | − 9.59592i | − 0.324031i | −0.986788 | − | 0.162016i | \(-0.948201\pi\) | ||||
0.986788 | − | 0.162016i | \(-0.0517995\pi\) | |||||||
\(878\) | 10.6969i | 0.361004i | ||||||||
\(879\) | −7.79796 | −0.263019 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.1010 | −1.04782 | −0.523910 | − | 0.851774i | \(-0.675527\pi\) | ||||
−0.523910 | + | 0.851774i | \(0.675527\pi\) | |||||||
\(882\) | − 4.89898i | − 0.164957i | ||||||||
\(883\) | 48.5959i | 1.63538i | 0.575657 | + | 0.817691i | \(0.304746\pi\) | ||||
−0.575657 | + | 0.817691i | \(0.695254\pi\) | |||||||
\(884\) | −15.7980 | −0.531343 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.30306 | −0.178160 | ||||||||
\(887\) | − 10.1010i | − 0.339159i | −0.985517 | − | 0.169580i | \(-0.945759\pi\) | ||||
0.985517 | − | 0.169580i | \(-0.0542410\pi\) | |||||||
\(888\) | − 8.34847i | − 0.280156i | ||||||||
\(889\) | −2.60612 | −0.0874066 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00000 | 0.0670025 | ||||||||
\(892\) | 24.6969i | 0.826915i | ||||||||
\(893\) | 26.8990i | 0.900140i | ||||||||
\(894\) | −20.0000 | −0.668900 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.44949 | 0.0484241 | ||||||||
\(897\) | − 2.89898i | − 0.0967941i | ||||||||
\(898\) | − 3.79796i | − 0.126740i | ||||||||
\(899\) | −10.0000 | −0.333519 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.89898 | −0.163209 | ||||||||
\(902\) | − 9.79796i | − 0.326236i | ||||||||
\(903\) | − 15.7980i | − 0.525723i | ||||||||
\(904\) | −14.3485 | −0.477223 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −18.6969 | −0.621164 | ||||||||
\(907\) | 2.49490i | 0.0828417i | 0.999142 | + | 0.0414209i | \(0.0131884\pi\) | ||||
−0.999142 | + | 0.0414209i | \(0.986812\pi\) | |||||||
\(908\) | 4.75255i | 0.157719i | ||||||||
\(909\) | 13.6969 | 0.454299 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.3031 | 0.705802 | 0.352901 | − | 0.935661i | \(-0.385195\pi\) | ||||
0.352901 | + | 0.935661i | \(0.385195\pi\) | |||||||
\(912\) | 6.89898i | 0.228448i | ||||||||
\(913\) | 5.10102i | 0.168819i | ||||||||
\(914\) | −0.404082 | −0.0133658 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.10102 | 0.102461 | ||||||||
\(917\) | 12.8990i | 0.425962i | ||||||||
\(918\) | 5.44949i | 0.179860i | ||||||||
\(919\) | 27.9444 | 0.921800 | 0.460900 | − | 0.887452i | \(-0.347527\pi\) | ||||
0.460900 | + | 0.887452i | \(0.347527\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.1010 | −0.662351 | ||||||||
\(922\) | 21.4949i | 0.707897i | ||||||||
\(923\) | 31.3031i | 1.03035i | ||||||||
\(924\) | −2.89898 | −0.0953694 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.00000 | 0.131448 | ||||||||
\(927\) | − 13.2474i | − 0.435103i | ||||||||
\(928\) | − 5.00000i | − 0.164133i | ||||||||
\(929\) | 3.79796 | 0.124607 | 0.0623035 | − | 0.998057i | \(-0.480155\pi\) | ||||
0.0623035 | + | 0.998057i | \(0.480155\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.7980 | −1.10768 | ||||||||
\(932\) | − 26.6969i | − 0.874487i | ||||||||
\(933\) | − 14.5959i | − 0.477849i | ||||||||
\(934\) | 29.9444 | 0.979810 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.89898 | −0.0947561 | ||||||||
\(937\) | − 15.7980i | − 0.516097i | −0.966132 | − | 0.258048i | \(-0.916921\pi\) | ||||
0.966132 | − | 0.258048i | \(-0.0830794\pi\) | |||||||
\(938\) | 2.89898i | 0.0946550i | ||||||||
\(939\) | 12.8990 | 0.420942 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.00000 | 0.0651981 | 0.0325991 | − | 0.999469i | \(-0.489622\pi\) | ||||
0.0325991 | + | 0.999469i | \(0.489622\pi\) | |||||||
\(942\) | − 8.89898i | − 0.289944i | ||||||||
\(943\) | 4.89898i | 0.159533i | ||||||||
\(944\) | −10.0000 | −0.325472 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.7980 | 0.708713 | ||||||||
\(947\) | 0.404082i | 0.0131309i | 0.999978 | + | 0.00656545i | \(0.00208986\pi\) | ||||
−0.999978 | + | 0.00656545i | \(0.997910\pi\) | |||||||
\(948\) | − 10.0000i | − 0.324785i | ||||||||
\(949\) | 6.09082 | 0.197716 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.5959 | 0.343596 | ||||||||
\(952\) | − 7.89898i | − 0.256007i | ||||||||
\(953\) | 30.8434i | 0.999115i | 0.866281 | + | 0.499557i | \(0.166504\pi\) | ||||
−0.866281 | + | 0.499557i | \(0.833496\pi\) | |||||||
\(954\) | −0.898979 | −0.0291055 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8.10102 | −0.262006 | ||||||||
\(957\) | 10.0000i | 0.323254i | ||||||||
\(958\) | 30.0000i | 0.969256i | ||||||||
\(959\) | 32.3939 | 1.04605 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | − 24.2020i | − 0.780305i | ||||||||
\(963\) | 2.00000i | 0.0644491i | ||||||||
\(964\) | 8.00000 | 0.257663 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.44949 | 0.0466366 | ||||||||
\(967\) | − 29.5959i | − 0.951741i | −0.879515 | − | 0.475870i | \(-0.842133\pi\) | ||||
0.879515 | − | 0.475870i | \(-0.157867\pi\) | |||||||
\(968\) | 7.00000i | 0.224989i | ||||||||
\(969\) | 37.5959 | 1.20775 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.1464 | 0.839079 | 0.419539 | − | 0.907737i | \(-0.362192\pi\) | ||||
0.419539 | + | 0.907737i | \(0.362192\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | − 22.7526i | − 0.729413i | ||||||||
\(974\) | 15.1010 | 0.483868 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.89898 | −0.156813 | ||||||||
\(977\) | − 24.7526i | − 0.791904i | −0.918271 | − | 0.395952i | \(-0.870415\pi\) | ||||
0.918271 | − | 0.395952i | \(-0.129585\pi\) | |||||||
\(978\) | − 17.7980i | − 0.569116i | ||||||||
\(979\) | 20.6969 | 0.661477 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.44949 | 0.110134 | ||||||||
\(982\) | 25.1010i | 0.801006i | ||||||||
\(983\) | − 24.0000i | − 0.765481i | −0.923856 | − | 0.382741i | \(-0.874980\pi\) | ||||
0.923856 | − | 0.382741i | \(-0.125020\pi\) | |||||||
\(984\) | 4.89898 | 0.156174 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −27.2474 | −0.867736 | ||||||||
\(987\) | − 5.65153i | − 0.179890i | ||||||||
\(988\) | 20.0000i | 0.636285i | ||||||||
\(989\) | −10.8990 | −0.346567 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.2020 | 0.578207 | 0.289103 | − | 0.957298i | \(-0.406643\pi\) | ||||
0.289103 | + | 0.957298i | \(0.406643\pi\) | |||||||
\(992\) | 2.00000i | 0.0635001i | ||||||||
\(993\) | 6.79796i | 0.215727i | ||||||||
\(994\) | −15.6515 | −0.496436 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.55051 | −0.0808160 | ||||||||
\(997\) | 21.1010i | 0.668276i | 0.942524 | + | 0.334138i | \(0.108445\pi\) | ||||
−0.942524 | + | 0.334138i | \(0.891555\pi\) | |||||||
\(998\) | − 21.8990i | − 0.693200i | ||||||||
\(999\) | −8.34847 | −0.264134 |
(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 | 3450.2.d.y.2899.4 | 4 | ||
5.2 | odd | 4 | 3450.2.a.bf.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 3450.2.a.bl.1.2 | yes | 2 | ||
5.4 | even | 2 | inner | 3450.2.d.y.2899.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3450.2.a.bf.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
3450.2.a.bl.1.2 | yes | 2 | 5.3 | odd | 4 | ||
3450.2.d.y.2899.1 | 4 | 5.4 | even | 2 | inner | ||
3450.2.d.y.2899.4 | 4 | 1.1 | even | 1 | trivial |