Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [306,2,Mod(271,306)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(306, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("306.271");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 306 = 2 \cdot 3^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 306.b (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: | \(2.44342230185\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 271.1 | ||
Root | \(-1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 306.271 |
Dual form | 306.2.b.b.271.2 |
$q$-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 \(\left(\mathbb{Z}/306\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(137\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | − | 1.41421i | − | 0.632456i | −0.948683 | − | 0.316228i | \(-0.897584\pi\) | ||
0.948683 | − | 0.316228i | \(-0.102416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.24264i | 1.60357i | 0.597614 | + | 0.801784i | \(0.296115\pi\) | ||||
−0.597614 | + | 0.801784i | \(0.703885\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.41421i | 0.447214i | ||||||||
\(11\) | 2.82843i | 0.852803i | 0.904534 | + | 0.426401i | \(0.140219\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | − | 4.24264i | − | 1.13389i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.00000 | − | 2.82843i | 0.727607 | − | 0.685994i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | − | 1.41421i | − | 0.316228i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2.82843i | − | 0.603023i | ||||||
\(23\) | 7.07107i | 1.47442i | 0.675664 | + | 0.737210i | \(0.263857\pi\) | ||||
−0.675664 | + | 0.737210i | \(0.736143\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.24264i | 0.801784i | ||||||||
\(29\) | 7.07107i | 1.31306i | 0.754298 | + | 0.656532i | \(0.227977\pi\) | ||||
−0.754298 | + | 0.656532i | \(0.772023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.24264i | − | 0.762001i | −0.924575 | − | 0.381000i | \(-0.875580\pi\) | ||
0.924575 | − | 0.381000i | \(-0.124420\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.00000 | + | 2.82843i | −0.514496 | + | 0.485071i | ||||
\(35\) | 6.00000 | 1.01419 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.24264i | 0.697486i | 0.937218 | + | 0.348743i | \(0.113391\pi\) | ||||
−0.937218 | + | 0.348743i | \(0.886609\pi\) | |||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.41421i | 0.223607i | ||||||||
\(41\) | − | 5.65685i | − | 0.883452i | −0.897150 | − | 0.441726i | \(-0.854366\pi\) | ||
0.897150 | − | 0.441726i | \(-0.145634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 2.82843i | 0.426401i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 7.07107i | − | 1.04257i | ||||||
\(47\) | 12.0000 | 1.75038 | 0.875190 | − | 0.483779i | \(-0.160736\pi\) | ||||
0.875190 | + | 0.483779i | \(0.160736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.0000 | −1.57143 | ||||||||
\(50\) | −3.00000 | −0.424264 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | − | 4.24264i | − | 0.566947i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 7.07107i | − | 0.928477i | ||||||
\(59\) | −6.00000 | −0.781133 | −0.390567 | − | 0.920575i | \(-0.627721\pi\) | ||||
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 12.7279i | − | 1.62964i | −0.579712 | − | 0.814822i | \(-0.696835\pi\) | ||
0.579712 | − | 0.814822i | \(-0.303165\pi\) | |||||||
\(62\) | 4.24264i | 0.538816i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | − | 2.82843i | − | 0.350823i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.0000 | −1.22169 | −0.610847 | − | 0.791748i | \(-0.709171\pi\) | ||||
−0.610847 | + | 0.791748i | \(0.709171\pi\) | |||||||
\(68\) | 3.00000 | − | 2.82843i | 0.363803 | − | 0.342997i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.00000 | −0.717137 | ||||||||
\(71\) | − | 1.41421i | − | 0.167836i | −0.996473 | − | 0.0839181i | \(-0.973257\pi\) | ||
0.996473 | − | 0.0839181i | \(-0.0267434\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | − | 4.24264i | − | 0.493197i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | −12.0000 | −1.36753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.7279i | − | 1.43200i | −0.698099 | − | 0.716002i | \(-0.745970\pi\) | ||
0.698099 | − | 0.716002i | \(-0.254030\pi\) | |||||||
\(80\) | − | 1.41421i | − | 0.158114i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.65685i | 0.624695i | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | − | 4.24264i | −0.433861 | − | 0.460179i | ||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 2.82843i | − | 0.301511i | ||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.48528i | 0.889499i | ||||||||
\(92\) | 7.07107i | 0.737210i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.0000 | −1.23771 | ||||||||
\(95\) | − | 2.82843i | − | 0.290191i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.48528i | 0.861550i | 0.902459 | + | 0.430775i | \(0.141760\pi\) | ||||
−0.902459 | + | 0.430775i | \(0.858240\pi\) | |||||||
\(98\) | 11.0000 | 1.11117 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.00000 | 0.300000 | ||||||||
\(101\) | −18.0000 | −1.79107 | −0.895533 | − | 0.444994i | \(-0.853206\pi\) | ||||
−0.895533 | + | 0.444994i | \(0.853206\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 2.82843i | 0.273434i | 0.990610 | + | 0.136717i | \(0.0436552\pi\) | ||||
−0.990610 | + | 0.136717i | \(0.956345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.24264i | 0.406371i | 0.979140 | + | 0.203186i | \(0.0651295\pi\) | ||||
−0.979140 | + | 0.203186i | \(0.934871\pi\) | |||||||
\(110\) | −4.00000 | −0.381385 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.24264i | 0.400892i | ||||||||
\(113\) | − | 14.1421i | − | 1.33038i | −0.746674 | − | 0.665190i | \(-0.768350\pi\) | ||
0.746674 | − | 0.665190i | \(-0.231650\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.0000 | 0.932505 | ||||||||
\(116\) | 7.07107i | 0.656532i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | 12.0000 | + | 12.7279i | 1.10004 | + | 1.16677i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | 12.7279i | 1.15233i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 4.24264i | − | 0.381000i | ||||||
\(125\) | − | 11.3137i | − | 1.01193i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.0000 | 1.77471 | 0.887357 | − | 0.461084i | \(-0.152539\pi\) | ||||
0.887357 | + | 0.461084i | \(0.152539\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.82843i | 0.248069i | ||||||||
\(131\) | − | 14.1421i | − | 1.23560i | −0.786334 | − | 0.617802i | \(-0.788023\pi\) | ||
0.786334 | − | 0.617802i | \(-0.211977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.48528i | 0.735767i | ||||||||
\(134\) | 10.0000 | 0.863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00000 | + | 2.82843i | −0.257248 | + | 0.242536i | ||||
\(137\) | 12.0000 | 1.02523 | 0.512615 | − | 0.858619i | \(-0.328677\pi\) | ||||
0.512615 | + | 0.858619i | \(0.328677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8.48528i | − | 0.719712i | −0.933008 | − | 0.359856i | \(-0.882826\pi\) | ||
0.933008 | − | 0.359856i | \(-0.117174\pi\) | |||||||
\(140\) | 6.00000 | 0.507093 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.41421i | 0.118678i | ||||||||
\(143\) | 5.65685i | 0.473050i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0000 | 0.830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.24264i | 0.348743i | ||||||||
\(149\) | 18.0000 | 1.47462 | 0.737309 | − | 0.675556i | \(-0.236096\pi\) | ||||
0.737309 | + | 0.675556i | \(0.236096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | −2.00000 | −0.162221 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.0000 | 0.966988 | ||||||||
\(155\) | −6.00000 | −0.481932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 12.7279i | 1.01258i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.41421i | 0.111803i | ||||||||
\(161\) | −30.0000 | −2.36433 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.9706i | 1.32924i | 0.747183 | + | 0.664619i | \(0.231406\pi\) | ||||
−0.747183 | + | 0.664619i | \(0.768594\pi\) | |||||||
\(164\) | − | 5.65685i | − | 0.441726i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | −0.465690 | ||||||||
\(167\) | 24.0416i | 1.86040i | 0.367057 | + | 0.930199i | \(0.380366\pi\) | ||||
−0.367057 | + | 0.930199i | \(0.619634\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 4.00000 | + | 4.24264i | 0.306786 | + | 0.325396i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.00000 | −0.304997 | ||||||||
\(173\) | − | 9.89949i | − | 0.752645i | −0.926489 | − | 0.376322i | \(-0.877189\pi\) | ||
0.926489 | − | 0.376322i | \(-0.122811\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.7279i | 0.962140i | ||||||||
\(176\) | 2.82843i | 0.213201i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.00000 | 0.449719 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.2132i | 1.57676i | 0.615185 | + | 0.788382i | \(0.289081\pi\) | ||||
−0.615185 | + | 0.788382i | \(0.710919\pi\) | |||||||
\(182\) | − | 8.48528i | − | 0.628971i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 7.07107i | − | 0.521286i | ||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000 | + | 8.48528i | 0.585018 | + | 0.620505i | ||||
\(188\) | 12.0000 | 0.875190 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.82843i | 0.205196i | ||||||||
\(191\) | 12.0000 | 0.868290 | 0.434145 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434145 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 25.4558i | − | 1.83235i | −0.400776 | − | 0.916176i | \(-0.631260\pi\) | ||
0.400776 | − | 0.916176i | \(-0.368740\pi\) | |||||||
\(194\) | − | 8.48528i | − | 0.609208i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.0000 | −0.785714 | ||||||||
\(197\) | − | 9.89949i | − | 0.705310i | −0.935753 | − | 0.352655i | \(-0.885279\pi\) | ||
0.935753 | − | 0.352655i | \(-0.114721\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 4.24264i | − | 0.300753i | −0.988629 | − | 0.150376i | \(-0.951951\pi\) | ||
0.988629 | − | 0.150376i | \(-0.0480486\pi\) | |||||||
\(200\) | −3.00000 | −0.212132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18.0000 | 1.26648 | ||||||||
\(203\) | −30.0000 | −2.10559 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.00000 | −0.558744 | ||||||||
\(206\) | 4.00000 | 0.278693 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | 5.65685i | 0.391293i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 8.48528i | − | 0.584151i | −0.956395 | − | 0.292075i | \(-0.905654\pi\) | ||
0.956395 | − | 0.292075i | \(-0.0943458\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 2.82843i | − | 0.193347i | ||||||
\(215\) | 5.65685i | 0.385794i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0000 | 1.22192 | ||||||||
\(218\) | − | 4.24264i | − | 0.287348i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.00000 | 0.269680 | ||||||||
\(221\) | 6.00000 | − | 5.65685i | 0.403604 | − | 0.380521i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | − | 4.24264i | − | 0.283473i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.1421i | 0.940721i | ||||||||
\(227\) | − | 22.6274i | − | 1.50183i | −0.660396 | − | 0.750917i | \(-0.729612\pi\) | ||
0.660396 | − | 0.750917i | \(-0.270388\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | −10.0000 | −0.659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 7.07107i | − | 0.464238i | ||||||
\(233\) | 2.82843i | 0.185296i | 0.995699 | + | 0.0926482i | \(0.0295332\pi\) | ||||
−0.995699 | + | 0.0926482i | \(0.970467\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 16.9706i | − | 1.10704i | ||||||
\(236\) | −6.00000 | −0.390567 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.0000 | − | 12.7279i | −0.777844 | − | 0.825029i | ||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.48528i | 0.546585i | 0.961931 | + | 0.273293i | \(0.0881127\pi\) | ||||
−0.961931 | + | 0.273293i | \(0.911887\pi\) | |||||||
\(242\) | −3.00000 | −0.192847 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 12.7279i | − | 0.814822i | ||||||
\(245\) | 15.5563i | 0.993859i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | 0.254514 | ||||||||
\(248\) | 4.24264i | 0.269408i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.3137i | 0.715542i | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.0000 | −1.25739 | ||||||||
\(254\) | −20.0000 | −1.25491 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.0000 | −1.11847 | ||||||||
\(260\) | − | 2.82843i | − | 0.175412i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.1421i | 0.873704i | ||||||||
\(263\) | −12.0000 | −0.739952 | −0.369976 | − | 0.929041i | \(-0.620634\pi\) | ||||
−0.369976 | + | 0.929041i | \(0.620634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.48528i | 0.521247i | ||||||||
\(266\) | − | 8.48528i | − | 0.520266i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.0000 | −0.610847 | ||||||||
\(269\) | − | 18.3848i | − | 1.12094i | −0.828175 | − | 0.560470i | \(-0.810621\pi\) | ||
0.828175 | − | 0.560470i | \(-0.189379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 3.00000 | − | 2.82843i | 0.181902 | − | 0.171499i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 8.48528i | 0.511682i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 21.2132i | − | 1.27458i | −0.770625 | − | 0.637289i | \(-0.780056\pi\) | ||
0.770625 | − | 0.637289i | \(-0.219944\pi\) | |||||||
\(278\) | 8.48528i | 0.508913i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.00000 | −0.358569 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 8.48528i | − | 0.504398i | −0.967675 | − | 0.252199i | \(-0.918846\pi\) | ||
0.967675 | − | 0.252199i | \(-0.0811537\pi\) | |||||||
\(284\) | − | 1.41421i | − | 0.0839181i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 5.65685i | − | 0.334497i | ||||||
\(287\) | 24.0000 | 1.41668 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | − | 16.9706i | 0.0588235 | − | 0.998268i | ||||
\(290\) | −10.0000 | −0.587220 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.0000 | 1.05157 | 0.525786 | − | 0.850617i | \(-0.323771\pi\) | ||||
0.525786 | + | 0.850617i | \(0.323771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.48528i | 0.494032i | ||||||||
\(296\) | − | 4.24264i | − | 0.246598i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.0000 | −1.04271 | ||||||||
\(299\) | 14.1421i | 0.817861i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 16.9706i | − | 0.978167i | ||||||
\(302\) | 16.0000 | 0.920697 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | −18.0000 | −1.03068 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.00000 | −0.228292 | −0.114146 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(308\) | −12.0000 | −0.683763 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.00000 | 0.340777 | ||||||||
\(311\) | − | 1.41421i | − | 0.0801927i | −0.999196 | − | 0.0400963i | \(-0.987234\pi\) | ||
0.999196 | − | 0.0400963i | \(-0.0127665\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 25.4558i | − | 1.43885i | −0.694570 | − | 0.719425i | \(-0.744406\pi\) | ||
0.694570 | − | 0.719425i | \(-0.255594\pi\) | |||||||
\(314\) | −14.0000 | −0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 12.7279i | − | 0.716002i | ||||||
\(317\) | 32.5269i | 1.82689i | 0.406958 | + | 0.913447i | \(0.366589\pi\) | ||||
−0.406958 | + | 0.913447i | \(0.633411\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.0000 | −1.11979 | ||||||||
\(320\) | − | 1.41421i | − | 0.0790569i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 30.0000 | 1.67183 | ||||||||
\(323\) | 6.00000 | − | 5.65685i | 0.333849 | − | 0.314756i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00000 | 0.332820 | ||||||||
\(326\) | − | 16.9706i | − | 0.939913i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.65685i | 0.312348i | ||||||||
\(329\) | 50.9117i | 2.80685i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | 6.00000 | 0.329293 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 24.0416i | − | 1.31550i | ||||||
\(335\) | 14.1421i | 0.772667i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.9411i | 1.84889i | 0.381314 | + | 0.924445i | \(0.375472\pi\) | ||||
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | 9.00000 | 0.489535 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.00000 | − | 4.24264i | −0.216930 | − | 0.230089i | ||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.9706i | − | 0.916324i | ||||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.89949i | 0.532200i | ||||||||
\(347\) | − | 22.6274i | − | 1.21470i | −0.794433 | − | 0.607352i | \(-0.792232\pi\) | ||
0.794433 | − | 0.607352i | \(-0.207768\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.0000 | 1.39175 | 0.695874 | − | 0.718164i | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(350\) | − | 12.7279i | − | 0.680336i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 2.82843i | − | 0.150756i | ||||||
\(353\) | 18.0000 | 0.958043 | 0.479022 | − | 0.877803i | \(-0.340992\pi\) | ||||
0.479022 | + | 0.877803i | \(0.340992\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.00000 | −0.106149 | ||||||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | 12.0000 | 0.633336 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | − | 21.2132i | − | 1.11494i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.48528i | 0.444750i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.2132i | 1.10732i | 0.832743 | + | 0.553660i | \(0.186769\pi\) | ||||
−0.832743 | + | 0.553660i | \(0.813231\pi\) | |||||||
\(368\) | 7.07107i | 0.368605i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.00000 | −0.311925 | ||||||||
\(371\) | − | 25.4558i | − | 1.32160i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | −8.00000 | − | 8.48528i | −0.413670 | − | 0.438763i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.0000 | −0.618853 | ||||||||
\(377\) | 14.1421i | 0.728357i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | − | 2.82843i | − | 0.145095i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.0000 | −0.613973 | ||||||||
\(383\) | −12.0000 | −0.613171 | −0.306586 | − | 0.951843i | \(-0.599187\pi\) | ||||
−0.306586 | + | 0.951843i | \(0.599187\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.9706i | 0.864900i | ||||||||
\(386\) | 25.4558i | 1.29567i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.48528i | 0.430775i | ||||||||
\(389\) | 18.0000 | 0.912636 | 0.456318 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456318 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.0000 | + | 21.2132i | 1.01144 | + | 1.07280i | ||||
\(392\) | 11.0000 | 0.555584 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.89949i | 0.498729i | ||||||||
\(395\) | −18.0000 | −0.905678 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.2132i | 1.06466i | 0.846537 | + | 0.532330i | \(0.178683\pi\) | ||||
−0.846537 | + | 0.532330i | \(0.821317\pi\) | |||||||
\(398\) | 4.24264i | 0.212664i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | 11.3137i | 0.564980i | 0.959270 | + | 0.282490i | \(0.0911603\pi\) | ||||
−0.959270 | + | 0.282490i | \(0.908840\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8.48528i | − | 0.422682i | ||||||
\(404\) | −18.0000 | −0.895533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 30.0000 | 1.48888 | ||||||||
\(407\) | −12.0000 | −0.594818 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.0000 | −0.791149 | −0.395575 | − | 0.918434i | \(-0.629455\pi\) | ||||
−0.395575 | + | 0.918434i | \(0.629455\pi\) | |||||||
\(410\) | 8.00000 | 0.395092 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | − | 25.4558i | − | 1.25260i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.48528i | − | 0.416526i | ||||||
\(416\) | −2.00000 | −0.0980581 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 5.65685i | − | 0.276686i | ||||||
\(419\) | − | 22.6274i | − | 1.10542i | −0.833373 | − | 0.552711i | \(-0.813593\pi\) | ||
0.833373 | − | 0.552711i | \(-0.186407\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.0000 | 1.26716 | 0.633581 | − | 0.773676i | \(-0.281584\pi\) | ||||
0.633581 | + | 0.773676i | \(0.281584\pi\) | |||||||
\(422\) | 8.48528i | 0.413057i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | 9.00000 | − | 8.48528i | 0.436564 | − | 0.411597i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 54.0000 | 2.61324 | ||||||||
\(428\) | 2.82843i | 0.136717i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 5.65685i | − | 0.272798i | ||||||
\(431\) | − | 1.41421i | − | 0.0681203i | −0.999420 | − | 0.0340601i | \(-0.989156\pi\) | ||
0.999420 | − | 0.0340601i | \(-0.0108438\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.0000 | −0.768911 | −0.384455 | − | 0.923144i | \(-0.625611\pi\) | ||||
−0.384455 | + | 0.923144i | \(0.625611\pi\) | |||||||
\(434\) | −18.0000 | −0.864028 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.24264i | 0.203186i | ||||||||
\(437\) | 14.1421i | 0.676510i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.24264i | − | 0.202490i | −0.994862 | − | 0.101245i | \(-0.967717\pi\) | ||
0.994862 | − | 0.101245i | \(-0.0322826\pi\) | |||||||
\(440\) | −4.00000 | −0.190693 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.00000 | + | 5.65685i | −0.285391 | + | 0.269069i | ||||
\(443\) | −12.0000 | −0.570137 | −0.285069 | − | 0.958507i | \(-0.592016\pi\) | ||||
−0.285069 | + | 0.958507i | \(0.592016\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.48528i | 0.402241i | ||||||||
\(446\) | −8.00000 | −0.378811 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.24264i | 0.200446i | ||||||||
\(449\) | − | 5.65685i | − | 0.266963i | −0.991051 | − | 0.133482i | \(-0.957384\pi\) | ||
0.991051 | − | 0.133482i | \(-0.0426157\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.0000 | 0.753411 | ||||||||
\(452\) | − | 14.1421i | − | 0.665190i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.6274i | 1.06196i | ||||||||
\(455\) | 12.0000 | 0.562569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.00000 | 0.374224 | 0.187112 | − | 0.982339i | \(-0.440087\pi\) | ||||
0.187112 | + | 0.982339i | \(0.440087\pi\) | |||||||
\(458\) | 10.0000 | 0.467269 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.0000 | 0.466252 | ||||||||
\(461\) | −6.00000 | −0.279448 | −0.139724 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139724 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | −0.185896 | −0.0929479 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929479 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(464\) | 7.07107i | 0.328266i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 2.82843i | − | 0.131024i | ||||||
\(467\) | −36.0000 | −1.66588 | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 42.4264i | − | 1.95907i | ||||||
\(470\) | 16.9706i | 0.782794i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.00000 | 0.276172 | ||||||||
\(473\) | − | 11.3137i | − | 0.520205i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.00000 | 0.275299 | ||||||||
\(476\) | 12.0000 | + | 12.7279i | 0.550019 | + | 0.583383i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −24.0000 | −1.09773 | ||||||||
\(479\) | − | 9.89949i | − | 0.452319i | −0.974090 | − | 0.226160i | \(-0.927383\pi\) | ||
0.974090 | − | 0.226160i | \(-0.0726171\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.48528i | 0.386896i | ||||||||
\(482\) | − | 8.48528i | − | 0.386494i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.00000 | 0.136364 | ||||||||
\(485\) | 12.0000 | 0.544892 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.24264i | 0.192252i | 0.995369 | + | 0.0961262i | \(0.0306452\pi\) | ||||
−0.995369 | + | 0.0961262i | \(0.969355\pi\) | |||||||
\(488\) | 12.7279i | 0.576166i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 15.5563i | − | 0.702764i | ||||||
\(491\) | −36.0000 | −1.62466 | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0000 | + | 21.2132i | 0.900755 | + | 0.955395i | ||||
\(494\) | −4.00000 | −0.179969 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 4.24264i | − | 0.190500i | ||||||
\(497\) | 6.00000 | 0.269137 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.48528i | 0.379853i | 0.981798 | + | 0.189927i | \(0.0608250\pi\) | ||||
−0.981798 | + | 0.189927i | \(0.939175\pi\) | |||||||
\(500\) | − | 11.3137i | − | 0.505964i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | 15.5563i | 0.693623i | 0.937935 | + | 0.346812i | \(0.112736\pi\) | ||||
−0.937935 | + | 0.346812i | \(0.887264\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.4558i | 1.13277i | ||||||||
\(506\) | 20.0000 | 0.889108 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.0000 | 0.887357 | ||||||||
\(509\) | 6.00000 | 0.265945 | 0.132973 | − | 0.991120i | \(-0.457548\pi\) | ||||
0.132973 | + | 0.991120i | \(0.457548\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.65685i | 0.249271i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.9411i | 1.49273i | ||||||||
\(518\) | 18.0000 | 0.790875 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.82843i | 0.124035i | ||||||||
\(521\) | − | 5.65685i | − | 0.247831i | −0.992293 | − | 0.123916i | \(-0.960455\pi\) | ||
0.992293 | − | 0.123916i | \(-0.0395452\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.0000 | −1.48672 | −0.743358 | − | 0.668894i | \(-0.766768\pi\) | ||||
−0.743358 | + | 0.668894i | \(0.766768\pi\) | |||||||
\(524\) | − | 14.1421i | − | 0.617802i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0000 | 0.523225 | ||||||||
\(527\) | −12.0000 | − | 12.7279i | −0.522728 | − | 0.554437i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −27.0000 | −1.17391 | ||||||||
\(530\) | − | 8.48528i | − | 0.368577i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.48528i | 0.367884i | ||||||||
\(533\) | − | 11.3137i | − | 0.490051i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.00000 | 0.172935 | ||||||||
\(536\) | 10.0000 | 0.431934 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18.3848i | 0.792624i | ||||||||
\(539\) | − | 31.1127i | − | 1.34012i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 21.2132i | − | 0.912027i | −0.889973 | − | 0.456013i | \(-0.849277\pi\) | ||
0.889973 | − | 0.456013i | \(-0.150723\pi\) | |||||||
\(542\) | 16.0000 | 0.687259 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.00000 | + | 2.82843i | −0.128624 | + | 0.121268i | ||||
\(545\) | 6.00000 | 0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.48528i | 0.362804i | 0.983409 | + | 0.181402i | \(0.0580636\pi\) | ||||
−0.983409 | + | 0.181402i | \(0.941936\pi\) | |||||||
\(548\) | 12.0000 | 0.512615 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 8.48528i | − | 0.361814i | ||||||
\(551\) | 14.1421i | 0.602475i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 54.0000 | 2.29631 | ||||||||
\(554\) | 21.2132i | 0.901263i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 8.48528i | − | 0.359856i | ||||||
\(557\) | −18.0000 | −0.762684 | −0.381342 | − | 0.924434i | \(-0.624538\pi\) | ||||
−0.381342 | + | 0.924434i | \(0.624538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 6.00000 | 0.253546 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | −30.0000 | −1.26435 | −0.632175 | − | 0.774826i | \(-0.717837\pi\) | ||||
−0.632175 | + | 0.774826i | \(0.717837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.0000 | −0.841406 | ||||||||
\(566\) | 8.48528i | 0.356663i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.41421i | 0.0593391i | ||||||||
\(569\) | 36.0000 | 1.50920 | 0.754599 | − | 0.656186i | \(-0.227831\pi\) | ||||
0.754599 | + | 0.656186i | \(0.227831\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 16.9706i | − | 0.710196i | −0.934829 | − | 0.355098i | \(-0.884448\pi\) | ||
0.934829 | − | 0.355098i | \(-0.115552\pi\) | |||||||
\(572\) | 5.65685i | 0.236525i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −24.0000 | −1.00174 | ||||||||
\(575\) | 21.2132i | 0.884652i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | −1.00000 | + | 16.9706i | −0.0415945 | + | 0.705882i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.0000 | 0.415227 | ||||||||
\(581\) | 25.4558i | 1.05609i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 16.9706i | − | 0.702849i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 8.48528i | − | 0.349630i | ||||||
\(590\) | − | 8.48528i | − | 0.349334i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.24264i | 0.174371i | ||||||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.0000 | − | 16.9706i | 0.737928 | − | 0.695725i | ||||
\(596\) | 18.0000 | 0.737309 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 14.1421i | − | 0.578315i | ||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 33.9411i | − | 1.38449i | −0.721664 | − | 0.692244i | \(-0.756622\pi\) | ||
0.721664 | − | 0.692244i | \(-0.243378\pi\) | |||||||
\(602\) | 16.9706i | 0.691669i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16.0000 | −0.651031 | ||||||||
\(605\) | − | 4.24264i | − | 0.172488i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 12.7279i | − | 0.516610i | −0.966063 | − | 0.258305i | \(-0.916836\pi\) | ||
0.966063 | − | 0.258305i | \(-0.0831640\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.0000 | 0.728799 | ||||||||
\(611\) | 24.0000 | 0.970936 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −46.0000 | −1.85792 | −0.928961 | − | 0.370177i | \(-0.879297\pi\) | ||||
−0.928961 | + | 0.370177i | \(0.879297\pi\) | |||||||
\(614\) | 4.00000 | 0.161427 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.0000 | 0.483494 | ||||||||
\(617\) | 2.82843i | 0.113868i | 0.998378 | + | 0.0569341i | \(0.0181325\pi\) | ||||
−0.998378 | + | 0.0569341i | \(0.981868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.9411i | 1.36421i | 0.731255 | + | 0.682105i | \(0.238935\pi\) | ||||
−0.731255 | + | 0.682105i | \(0.761065\pi\) | |||||||
\(620\) | −6.00000 | −0.240966 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.41421i | 0.0567048i | ||||||||
\(623\) | − | 25.4558i | − | 1.01987i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 25.4558i | 1.01742i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.0000 | 0.558661 | ||||||||
\(629\) | 12.0000 | + | 12.7279i | 0.478471 | + | 0.507495i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 12.7279i | 0.506290i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 32.5269i | − | 1.29181i | ||||||
\(635\) | − | 28.2843i | − | 1.12243i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.0000 | −0.871672 | ||||||||
\(638\) | 20.0000 | 0.791808 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.41421i | 0.0559017i | ||||||||
\(641\) | − | 22.6274i | − | 0.893729i | −0.894602 | − | 0.446865i | \(-0.852541\pi\) | ||
0.894602 | − | 0.446865i | \(-0.147459\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | −30.0000 | −1.18217 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | + | 5.65685i | −0.236067 | + | 0.222566i | ||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 16.9706i | − | 0.666153i | ||||||
\(650\) | −6.00000 | −0.235339 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.9706i | 0.664619i | ||||||||
\(653\) | − | 1.41421i | − | 0.0553425i | −0.999617 | − | 0.0276712i | \(-0.991191\pi\) | ||
0.999617 | − | 0.0276712i | \(-0.00880915\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.0000 | −0.781465 | ||||||||
\(656\) | − | 5.65685i | − | 0.220863i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 50.9117i | − | 1.98474i | ||||||
\(659\) | −30.0000 | −1.16863 | −0.584317 | − | 0.811525i | \(-0.698638\pi\) | ||||
−0.584317 | + | 0.811525i | \(0.698638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0000 | 0.544537 | 0.272268 | − | 0.962221i | \(-0.412226\pi\) | ||||
0.272268 | + | 0.962221i | \(0.412226\pi\) | |||||||
\(662\) | 4.00000 | 0.155464 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 12.0000 | 0.465340 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −50.0000 | −1.93601 | ||||||||
\(668\) | 24.0416i | 0.930199i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 14.1421i | − | 0.546358i | ||||||
\(671\) | 36.0000 | 1.38976 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.4558i | 0.981251i | 0.871371 | + | 0.490625i | \(0.163232\pi\) | ||||
−0.871371 | + | 0.490625i | \(0.836768\pi\) | |||||||
\(674\) | − | 33.9411i | − | 1.30736i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 49.4975i | 1.90234i | 0.308664 | + | 0.951171i | \(0.400118\pi\) | ||||
−0.308664 | + | 0.951171i | \(0.599882\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.0000 | −1.38155 | ||||||||
\(680\) | 4.00000 | + | 4.24264i | 0.153393 | + | 0.162698i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.0000 | −0.459504 | ||||||||
\(683\) | − | 5.65685i | − | 0.216454i | −0.994126 | − | 0.108227i | \(-0.965483\pi\) | ||
0.994126 | − | 0.108227i | \(-0.0345173\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 16.9706i | − | 0.648412i | ||||||
\(686\) | 16.9706i | 0.647939i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.00000 | −0.152499 | ||||||||
\(689\) | −12.0000 | −0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 25.4558i | − | 0.968386i | −0.874961 | − | 0.484193i | \(-0.839113\pi\) | ||
0.874961 | − | 0.484193i | \(-0.160887\pi\) | |||||||
\(692\) | − | 9.89949i | − | 0.376322i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.6274i | 0.858925i | ||||||||
\(695\) | −12.0000 | −0.455186 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.0000 | − | 16.9706i | −0.606043 | − | 0.642806i | ||||
\(698\) | −26.0000 | −0.984115 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12.7279i | 0.481070i | ||||||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.48528i | 0.320028i | ||||||||
\(704\) | 2.82843i | 0.106600i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.0000 | −0.677439 | ||||||||
\(707\) | − | 76.3675i | − | 2.87210i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 12.7279i | − | 0.478007i | −0.971019 | − | 0.239004i | \(-0.923179\pi\) | ||
0.971019 | − | 0.239004i | \(-0.0768208\pi\) | |||||||
\(710\) | 2.00000 | 0.0750587 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.00000 | 0.224860 | ||||||||
\(713\) | 30.0000 | 1.12351 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.00000 | 0.299183 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.0000 | −0.447836 | ||||||||
\(719\) | 32.5269i | 1.21305i | 0.795065 | + | 0.606525i | \(0.207437\pi\) | ||||
−0.795065 | + | 0.606525i | \(0.792563\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 16.9706i | − | 0.632017i | ||||||
\(722\) | 15.0000 | 0.558242 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21.2132i | 0.788382i | ||||||||
\(725\) | 21.2132i | 0.787839i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.0000 | 0.741759 | 0.370879 | − | 0.928681i | \(-0.379056\pi\) | ||||
0.370879 | + | 0.928681i | \(0.379056\pi\) | |||||||
\(728\) | − | 8.48528i | − | 0.314485i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | + | 11.3137i | −0.443836 | + | 0.418453i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.0000 | −0.369358 | −0.184679 | − | 0.982799i | \(-0.559125\pi\) | ||||
−0.184679 | + | 0.982799i | \(0.559125\pi\) | |||||||
\(734\) | − | 21.2132i | − | 0.782994i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 7.07107i | − | 0.260643i | ||||||
\(737\) | − | 28.2843i | − | 1.04186i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.0000 | −0.367856 | −0.183928 | − | 0.982940i | \(-0.558881\pi\) | ||||
−0.183928 | + | 0.982940i | \(0.558881\pi\) | |||||||
\(740\) | 6.00000 | 0.220564 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 25.4558i | 0.934513i | ||||||||
\(743\) | − | 26.8701i | − | 0.985767i | −0.870095 | − | 0.492883i | \(-0.835943\pi\) | ||
0.870095 | − | 0.492883i | \(-0.164057\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 25.4558i | − | 0.932630i | ||||||
\(746\) | 10.0000 | 0.366126 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.00000 | + | 8.48528i | 0.292509 | + | 0.310253i | ||||
\(749\) | −12.0000 | −0.438470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.6985i | 1.08371i | 0.840471 | + | 0.541857i | \(0.182278\pi\) | ||||
−0.840471 | + | 0.541857i | \(0.817722\pi\) | |||||||
\(752\) | 12.0000 | 0.437595 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 14.1421i | − | 0.515026i | ||||||
\(755\) | 22.6274i | 0.823496i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.82843i | 0.102598i | ||||||||
\(761\) | 12.0000 | 0.435000 | 0.217500 | − | 0.976060i | \(-0.430210\pi\) | ||||
0.217500 | + | 0.976060i | \(0.430210\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.0000 | −0.651644 | ||||||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0000 | 0.433578 | ||||||||
\(767\) | −12.0000 | −0.433295 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.0000 | 1.80305 | 0.901523 | − | 0.432731i | \(-0.142450\pi\) | ||||
0.901523 | + | 0.432731i | \(0.142450\pi\) | |||||||
\(770\) | − | 16.9706i | − | 0.611577i | ||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 25.4558i | − | 0.916176i | ||||||
\(773\) | −18.0000 | −0.647415 | −0.323708 | − | 0.946157i | \(-0.604929\pi\) | ||||
−0.323708 | + | 0.946157i | \(0.604929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 12.7279i | − | 0.457200i | ||||||
\(776\) | − | 8.48528i | − | 0.304604i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18.0000 | −0.645331 | ||||||||
\(779\) | − | 11.3137i | − | 0.405356i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | −20.0000 | − | 21.2132i | −0.715199 | − | 0.758583i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −11.0000 | −0.392857 | ||||||||
\(785\) | − | 19.7990i | − | 0.706656i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.4558i | 0.907403i | 0.891154 | + | 0.453701i | \(0.149897\pi\) | ||||
−0.891154 | + | 0.453701i | \(0.850103\pi\) | |||||||
\(788\) | − | 9.89949i | − | 0.352655i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 18.0000 | 0.640411 | ||||||||
\(791\) | 60.0000 | 2.13335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 25.4558i | − | 0.903964i | ||||||
\(794\) | − | 21.2132i | − | 0.752828i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 4.24264i | − | 0.150376i | ||||||
\(797\) | −30.0000 | −1.06265 | −0.531327 | − | 0.847167i | \(-0.678307\pi\) | ||||
−0.531327 | + | 0.847167i | \(0.678307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.0000 | − | 33.9411i | 1.27359 | − | 1.20075i | ||||
\(800\) | −3.00000 | −0.106066 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 11.3137i | − | 0.399501i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 42.4264i | 1.49533i | ||||||||
\(806\) | 8.48528i | 0.298881i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18.0000 | 0.633238 | ||||||||
\(809\) | 45.2548i | 1.59108i | 0.605904 | + | 0.795538i | \(0.292811\pi\) | ||||
−0.605904 | + | 0.795538i | \(0.707189\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.9411i | 1.19183i | 0.803046 | + | 0.595917i | \(0.203211\pi\) | ||||
−0.803046 | + | 0.595917i | \(0.796789\pi\) | |||||||
\(812\) | −30.0000 | −1.05279 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.0000 | 0.420600 | ||||||||
\(815\) | 24.0000 | 0.840683 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | −0.279885 | ||||||||
\(818\) | 16.0000 | 0.559427 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.00000 | −0.279372 | ||||||||
\(821\) | 15.5563i | 0.542920i | 0.962450 | + | 0.271460i | \(0.0875065\pi\) | ||||
−0.962450 | + | 0.271460i | \(0.912493\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.24264i | 0.147889i | 0.997262 | + | 0.0739446i | \(0.0235588\pi\) | ||||
−0.997262 | + | 0.0739446i | \(0.976441\pi\) | |||||||
\(824\) | 4.00000 | 0.139347 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 25.4558i | 0.885722i | ||||||||
\(827\) | 19.7990i | 0.688478i | 0.938882 | + | 0.344239i | \(0.111863\pi\) | ||||
−0.938882 | + | 0.344239i | \(0.888137\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0000 | 0.486240 | 0.243120 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243120 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(830\) | 8.48528i | 0.294528i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | −33.0000 | + | 31.1127i | −1.14338 | + | 1.07799i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.0000 | 1.17662 | ||||||||
\(836\) | 5.65685i | 0.195646i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.6274i | 0.781651i | ||||||||
\(839\) | 15.5563i | 0.537065i | 0.963271 | + | 0.268532i | \(0.0865386\pi\) | ||||
−0.963271 | + | 0.268532i | \(0.913461\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | −26.0000 | −0.896019 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 8.48528i | − | 0.292075i | ||||||
\(845\) | 12.7279i | 0.437854i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.7279i | 0.437337i | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.00000 | + | 8.48528i | −0.308697 | + | 0.291043i | ||||
\(851\) | −30.0000 | −1.02839 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.6985i | 1.01686i | 0.861104 | + | 0.508428i | \(0.169773\pi\) | ||||
−0.861104 | + | 0.508428i | \(0.830227\pi\) | |||||||
\(854\) | −54.0000 | −1.84784 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 2.82843i | − | 0.0966736i | ||||||
\(857\) | − | 22.6274i | − | 0.772938i | −0.922302 | − | 0.386469i | \(-0.873695\pi\) | ||
0.922302 | − | 0.386469i | \(-0.126305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | −0.136478 | −0.0682391 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682391 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(860\) | 5.65685i | 0.192897i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.41421i | 0.0481683i | ||||||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.0000 | −0.476014 | ||||||||
\(866\) | 16.0000 | 0.543702 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18.0000 | 0.610960 | ||||||||
\(869\) | 36.0000 | 1.22122 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.0000 | −0.677674 | ||||||||
\(872\) | − | 4.24264i | − | 0.143674i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 14.1421i | − | 0.478365i | ||||||
\(875\) | 48.0000 | 1.62270 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 12.7279i | − | 0.429791i | −0.976637 | − | 0.214896i | \(-0.931059\pi\) | ||
0.976637 | − | 0.214896i | \(-0.0689412\pi\) | |||||||
\(878\) | 4.24264i | 0.143182i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.00000 | 0.134840 | ||||||||
\(881\) | − | 14.1421i | − | 0.476461i | −0.971209 | − | 0.238230i | \(-0.923433\pi\) | ||
0.971209 | − | 0.238230i | \(-0.0765673\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.0000 | 0.874970 | 0.437485 | − | 0.899226i | \(-0.355869\pi\) | ||||
0.437485 | + | 0.899226i | \(0.355869\pi\) | |||||||
\(884\) | 6.00000 | − | 5.65685i | 0.201802 | − | 0.190261i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0000 | 0.403148 | ||||||||
\(887\) | − | 1.41421i | − | 0.0474846i | −0.999718 | − | 0.0237423i | \(-0.992442\pi\) | ||
0.999718 | − | 0.0237423i | \(-0.00755813\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 84.8528i | 2.84587i | ||||||||
\(890\) | − | 8.48528i | − | 0.284427i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.00000 | 0.267860 | ||||||||
\(893\) | 24.0000 | 0.803129 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.9706i | 0.567263i | ||||||||
\(896\) | − | 4.24264i | − | 0.141737i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.65685i | 0.188772i | ||||||||
\(899\) | 30.0000 | 1.00056 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.0000 | + | 16.9706i | −0.599667 | + | 0.565371i | ||||
\(902\) | −16.0000 | −0.532742 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.1421i | 0.470360i | ||||||||
\(905\) | 30.0000 | 0.997234 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 42.4264i | − | 1.40875i | −0.709830 | − | 0.704373i | \(-0.751228\pi\) | ||
0.709830 | − | 0.704373i | \(-0.248772\pi\) | |||||||
\(908\) | − | 22.6274i | − | 0.750917i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.0000 | −0.397796 | ||||||||
\(911\) | 15.5563i | 0.515405i | 0.966224 | + | 0.257702i | \(0.0829654\pi\) | ||||
−0.966224 | + | 0.257702i | \(0.917035\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.9706i | 0.561644i | ||||||||
\(914\) | −8.00000 | −0.264616 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | 60.0000 | 1.98137 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.0000 | 0.659739 | 0.329870 | − | 0.944027i | \(-0.392995\pi\) | ||||
0.329870 | + | 0.944027i | \(0.392995\pi\) | |||||||
\(920\) | −10.0000 | −0.329690 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.00000 | 0.197599 | ||||||||
\(923\) | − | 2.82843i | − | 0.0930988i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.7279i | 0.418491i | ||||||||
\(926\) | 4.00000 | 0.131448 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 7.07107i | − | 0.232119i | ||||||
\(929\) | − | 22.6274i | − | 0.742381i | −0.928557 | − | 0.371191i | \(-0.878950\pi\) | ||
0.928557 | − | 0.371191i | \(-0.121050\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.0000 | −0.721021 | ||||||||
\(932\) | 2.82843i | 0.0926482i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 36.0000 | 1.17796 | ||||||||
\(935\) | 12.0000 | − | 11.3137i | 0.392442 | − | 0.369998i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.00000 | −0.130674 | −0.0653372 | − | 0.997863i | \(-0.520812\pi\) | ||||
−0.0653372 | + | 0.997863i | \(0.520812\pi\) | |||||||
\(938\) | 42.4264i | 1.38527i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 16.9706i | − | 0.553519i | ||||||
\(941\) | − | 1.41421i | − | 0.0461020i | −0.999734 | − | 0.0230510i | \(-0.992662\pi\) | ||
0.999734 | − | 0.0230510i | \(-0.00733802\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.0000 | 1.30258 | ||||||||
\(944\) | −6.00000 | −0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.3137i | 0.367840i | ||||||||
\(947\) | 53.7401i | 1.74632i | 0.487435 | + | 0.873160i | \(0.337933\pi\) | ||||
−0.487435 | + | 0.873160i | \(0.662067\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −6.00000 | −0.194666 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.0000 | − | 12.7279i | −0.388922 | − | 0.412514i | ||||
\(953\) | −42.0000 | −1.36051 | −0.680257 | − | 0.732974i | \(-0.738132\pi\) | ||||
−0.680257 | + | 0.732974i | \(0.738132\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 16.9706i | − | 0.549155i | ||||||
\(956\) | 24.0000 | 0.776215 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.89949i | 0.319838i | ||||||||
\(959\) | 50.9117i | 1.64402i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.0000 | 0.419355 | ||||||||
\(962\) | − | 8.48528i | − | 0.273576i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.48528i | 0.273293i | ||||||||
\(965\) | −36.0000 | −1.15888 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | −3.00000 | −0.0964237 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.0000 | −0.385297 | ||||||||
\(971\) | 42.0000 | 1.34784 | 0.673922 | − | 0.738802i | \(-0.264608\pi\) | ||||
0.673922 | + | 0.738802i | \(0.264608\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.0000 | 1.15411 | ||||||||
\(974\) | − | 4.24264i | − | 0.135943i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 12.7279i | − | 0.407411i | ||||||
\(977\) | 60.0000 | 1.91957 | 0.959785 | − | 0.280736i | \(-0.0905785\pi\) | ||||
0.959785 | + | 0.280736i | \(0.0905785\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 16.9706i | − | 0.542382i | ||||||
\(980\) | 15.5563i | 0.496929i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.0000 | 1.14881 | ||||||||
\(983\) | − | 9.89949i | − | 0.315745i | −0.987460 | − | 0.157872i | \(-0.949537\pi\) | ||
0.987460 | − | 0.157872i | \(-0.0504635\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.0000 | −0.446077 | ||||||||
\(986\) | −20.0000 | − | 21.2132i | −0.636930 | − | 0.675566i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.00000 | 0.127257 | ||||||||
\(989\) | − | 28.2843i | − | 0.899388i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 12.7279i | − | 0.404316i | −0.979353 | − | 0.202158i | \(-0.935205\pi\) | ||
0.979353 | − | 0.202158i | \(-0.0647954\pi\) | |||||||
\(992\) | 4.24264i | 0.134704i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.00000 | −0.190308 | ||||||||
\(995\) | −6.00000 | −0.190213 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 29.6985i | − | 0.940560i | −0.882517 | − | 0.470280i | \(-0.844153\pi\) | ||
0.882517 | − | 0.470280i | \(-0.155847\pi\) | |||||||
\(998\) | − | 8.48528i | − | 0.268597i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 306.2.b.b.271.1 | ✓ | 2 | |
3.2 | odd | 2 | 306.2.b.c.271.2 | yes | 2 | ||
4.3 | odd | 2 | 2448.2.c.k.577.1 | 2 | |||
12.11 | even | 2 | 2448.2.c.i.577.2 | 2 | |||
17.4 | even | 4 | 5202.2.a.bd.1.1 | 2 | |||
17.13 | even | 4 | 5202.2.a.bd.1.2 | 2 | |||
17.16 | even | 2 | inner | 306.2.b.b.271.2 | yes | 2 | |
51.38 | odd | 4 | 5202.2.a.t.1.2 | 2 | |||
51.47 | odd | 4 | 5202.2.a.t.1.1 | 2 | |||
51.50 | odd | 2 | 306.2.b.c.271.1 | yes | 2 | ||
68.67 | odd | 2 | 2448.2.c.k.577.2 | 2 | |||
204.203 | even | 2 | 2448.2.c.i.577.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
306.2.b.b.271.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
306.2.b.b.271.2 | yes | 2 | 17.16 | even | 2 | inner | |
306.2.b.c.271.1 | yes | 2 | 51.50 | odd | 2 | ||
306.2.b.c.271.2 | yes | 2 | 3.2 | odd | 2 | ||
2448.2.c.i.577.1 | 2 | 204.203 | even | 2 | |||
2448.2.c.i.577.2 | 2 | 12.11 | even | 2 | |||
2448.2.c.k.577.1 | 2 | 4.3 | odd | 2 | |||
2448.2.c.k.577.2 | 2 | 68.67 | odd | 2 | |||
5202.2.a.t.1.1 | 2 | 51.47 | odd | 4 | |||
5202.2.a.t.1.2 | 2 | 51.38 | odd | 4 | |||
5202.2.a.bd.1.1 | 2 | 17.4 | even | 4 | |||
5202.2.a.bd.1.2 | 2 | 17.13 | even | 4 |