Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3042,2,Mod(1351,3042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3042, 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("3042.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3042 = 2 \cdot 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3042.b (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: | \(24.2904922949\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 234) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.4 | ||
Root | \(1.58114 + 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3042.1351 |
Dual form | 3042.2.b.j.1351.1 |
$q$-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 \(\left(\mathbb{Z}/3042\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 4.16228i | 1.86143i | 0.365749 | + | 0.930714i | \(0.380813\pi\) | ||||
−0.365749 | + | 0.930714i | \(0.619187\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.16228i | 1.19523i | 0.801784 | + | 0.597614i | \(0.203885\pi\) | ||||
−0.801784 | + | 0.597614i | \(0.796115\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.16228 | −1.31623 | ||||||||
\(11\) | 1.16228i | 0.350440i | 0.984529 | + | 0.175220i | \(0.0560637\pi\) | ||||
−0.984529 | + | 0.175220i | \(0.943936\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −3.16228 | −0.845154 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.16228i | 1.18431i | 0.805825 | + | 0.592154i | \(0.201722\pi\) | ||||
−0.805825 | + | 0.592154i | \(0.798278\pi\) | |||||||
\(20\) | − 4.16228i | − 0.930714i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.16228 | −0.247798 | ||||||||
\(23\) | 7.16228 | 1.49344 | 0.746719 | − | 0.665140i | \(-0.231628\pi\) | ||||
0.746719 | + | 0.665140i | \(0.231628\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.3246 | −2.46491 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 3.16228i | − 0.597614i | ||||||||
\(29\) | 1.83772 | 0.341256 | 0.170628 | − | 0.985335i | \(-0.445420\pi\) | ||||
0.170628 | + | 0.985335i | \(0.445420\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.32456i | 1.13592i | 0.823055 | + | 0.567962i | \(0.192268\pi\) | ||||
−0.823055 | + | 0.567962i | \(0.807732\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 3.00000i | − 0.514496i | ||||||||
\(35\) | −13.1623 | −2.22483 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.83772i | 0.630918i | 0.948939 | + | 0.315459i | \(0.102158\pi\) | ||||
−0.948939 | + | 0.315459i | \(0.897842\pi\) | |||||||
\(38\) | −5.16228 | −0.837432 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.16228 | 0.658114 | ||||||||
\(41\) | 3.00000i | 0.468521i | 0.972174 | + | 0.234261i | \(0.0752669\pi\) | ||||
−0.972174 | + | 0.234261i | \(0.924733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.16228 | −1.39723 | −0.698617 | − | 0.715496i | \(-0.746201\pi\) | ||||
−0.698617 | + | 0.715496i | \(0.746201\pi\) | |||||||
\(44\) | − 1.16228i | − 0.175220i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.16228i | 1.05602i | ||||||||
\(47\) | − 4.83772i | − 0.705654i | −0.935689 | − | 0.352827i | \(-0.885220\pi\) | ||||
0.935689 | − | 0.352827i | \(-0.114780\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | − 12.3246i | − 1.74296i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.4868 | 1.71520 | 0.857599 | − | 0.514319i | \(-0.171955\pi\) | ||||
0.857599 | + | 0.514319i | \(0.171955\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.83772 | −0.652318 | ||||||||
\(56\) | 3.16228 | 0.422577 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.83772i | 0.241305i | ||||||||
\(59\) | 2.32456i | 0.302631i | 0.988485 | + | 0.151316i | \(0.0483510\pi\) | ||||
−0.988485 | + | 0.151316i | \(0.951649\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.162278 | 0.0207775 | 0.0103888 | − | 0.999946i | \(-0.496693\pi\) | ||||
0.0103888 | + | 0.999946i | \(0.496693\pi\) | |||||||
\(62\) | −6.32456 | −0.803219 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.83772i | 0.346683i | 0.984862 | + | 0.173341i | \(0.0554564\pi\) | ||||
−0.984862 | + | 0.173341i | \(0.944544\pi\) | |||||||
\(68\) | 3.00000 | 0.363803 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − 13.1623i | − 1.57319i | ||||||||
\(71\) | − 7.16228i | − 0.850006i | −0.905192 | − | 0.425003i | \(-0.860273\pi\) | ||||
0.905192 | − | 0.425003i | \(-0.139727\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 1.00000i | − 0.117041i | −0.998286 | − | 0.0585206i | \(-0.981362\pi\) | ||||
0.998286 | − | 0.0585206i | \(-0.0186383\pi\) | |||||||
\(74\) | −3.83772 | −0.446126 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 5.16228i | − 0.592154i | ||||||||
\(77\) | −3.67544 | −0.418856 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 4.16228i | 0.465357i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.00000 | −0.331295 | ||||||||
\(83\) | − 3.48683i | − 0.382730i | −0.981519 | − | 0.191365i | \(-0.938709\pi\) | ||||
0.981519 | − | 0.191365i | \(-0.0612914\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 12.4868i | − 1.35439i | ||||||||
\(86\) | − 9.16228i | − 0.987994i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.16228 | 0.123899 | ||||||||
\(89\) | − 12.0000i | − 1.27200i | −0.771690 | − | 0.635999i | \(-0.780588\pi\) | ||||
0.771690 | − | 0.635999i | \(-0.219412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.16228 | −0.746719 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.83772 | 0.498973 | ||||||||
\(95\) | −21.4868 | −2.20450 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.00000i | 0.406138i | 0.979164 | + | 0.203069i | \(0.0650917\pi\) | ||||
−0.979164 | + | 0.203069i | \(0.934908\pi\) | |||||||
\(98\) | − 3.00000i | − 0.303046i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 12.3246 | 1.23246 | ||||||||
\(101\) | 7.83772 | 0.779883 | 0.389941 | − | 0.920840i | \(-0.372495\pi\) | ||||
0.389941 | + | 0.920840i | \(0.372495\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.8114 | 1.55794 | 0.778971 | − | 0.627060i | \(-0.215742\pi\) | ||||
0.778971 | + | 0.627060i | \(0.215742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.4868i | 1.21283i | ||||||||
\(107\) | 17.8114 | 1.72189 | 0.860946 | − | 0.508696i | \(-0.169872\pi\) | ||||
0.860946 | + | 0.508696i | \(0.169872\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 6.64911i | − 0.636869i | −0.947945 | − | 0.318435i | \(-0.896843\pi\) | ||||
0.947945 | − | 0.318435i | \(-0.103157\pi\) | |||||||
\(110\) | − 4.83772i | − 0.461259i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.16228i | 0.298807i | ||||||||
\(113\) | −6.67544 | −0.627973 | −0.313987 | − | 0.949427i | \(-0.601665\pi\) | ||||
−0.313987 | + | 0.949427i | \(0.601665\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 29.8114i | 2.77993i | ||||||||
\(116\) | −1.83772 | −0.170628 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.32456 | −0.213993 | ||||||||
\(119\) | − 9.48683i | − 0.869657i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.64911 | 0.877192 | ||||||||
\(122\) | 0.162278i | 0.0146919i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 6.32456i | − 0.567962i | ||||||||
\(125\) | − 30.4868i | − 2.72683i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.3246 | 1.62604 | 0.813021 | − | 0.582235i | \(-0.197822\pi\) | ||||
0.813021 | + | 0.582235i | \(0.197822\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.6491 | −1.45464 | −0.727320 | − | 0.686299i | \(-0.759234\pi\) | ||||
−0.727320 | + | 0.686299i | \(0.759234\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.3246 | −1.41552 | ||||||||
\(134\) | −2.83772 | −0.245142 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000i | 0.257248i | ||||||||
\(137\) | 3.00000i | 0.256307i | 0.991754 | + | 0.128154i | \(0.0409051\pi\) | ||||
−0.991754 | + | 0.128154i | \(0.959095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.32456 | −0.536442 | −0.268221 | − | 0.963357i | \(-0.586436\pi\) | ||||
−0.268221 | + | 0.963357i | \(0.586436\pi\) | |||||||
\(140\) | 13.1623 | 1.11242 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.16228 | 0.601045 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.64911i | 0.635224i | ||||||||
\(146\) | 1.00000 | 0.0827606 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 3.83772i | − 0.315459i | ||||||||
\(149\) | 0.486833i | 0.0398829i | 0.999801 | + | 0.0199415i | \(0.00634798\pi\) | ||||
−0.999801 | + | 0.0199415i | \(0.993652\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.837722i | 0.0681729i | 0.999419 | + | 0.0340864i | \(0.0108522\pi\) | ||||
−0.999419 | + | 0.0340864i | \(0.989148\pi\) | |||||||
\(152\) | 5.16228 | 0.418716 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − 3.67544i | − 0.296176i | ||||||||
\(155\) | −26.3246 | −2.11444 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.4868 | −0.836940 | −0.418470 | − | 0.908231i | \(-0.637434\pi\) | ||||
−0.418470 | + | 0.908231i | \(0.637434\pi\) | |||||||
\(158\) | − 4.00000i | − 0.318223i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.16228 | −0.329057 | ||||||||
\(161\) | 22.6491i | 1.78500i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 16.0000i | − 1.25322i | −0.779334 | − | 0.626608i | \(-0.784443\pi\) | ||||
0.779334 | − | 0.626608i | \(-0.215557\pi\) | |||||||
\(164\) | − 3.00000i | − 0.234261i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.48683 | 0.270631 | ||||||||
\(167\) | − 12.0000i | − 0.928588i | −0.885681 | − | 0.464294i | \(-0.846308\pi\) | ||||
0.885681 | − | 0.464294i | \(-0.153692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 12.4868 | 0.957696 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.16228 | 0.698617 | ||||||||
\(173\) | 22.6491 | 1.72198 | 0.860990 | − | 0.508622i | \(-0.169845\pi\) | ||||
0.860990 | + | 0.508622i | \(0.169845\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 38.9737i | − 2.94613i | ||||||||
\(176\) | 1.16228i | 0.0876100i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.0000 | 0.899438 | ||||||||
\(179\) | 15.4868 | 1.15754 | 0.578770 | − | 0.815491i | \(-0.303533\pi\) | ||||
0.578770 | + | 0.815491i | \(0.303533\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.83772 | −0.285256 | −0.142628 | − | 0.989776i | \(-0.545555\pi\) | ||||
−0.142628 | + | 0.989776i | \(0.545555\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − 7.16228i | − 0.528010i | ||||||||
\(185\) | −15.9737 | −1.17441 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.48683i | − 0.254982i | ||||||||
\(188\) | 4.83772i | 0.352827i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − 21.4868i | − 1.55882i | ||||||||
\(191\) | −14.3246 | −1.03649 | −0.518244 | − | 0.855233i | \(-0.673414\pi\) | ||||
−0.518244 | + | 0.855233i | \(0.673414\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 19.9737i | − 1.43774i | −0.695147 | − | 0.718868i | \(-0.744661\pi\) | ||||
0.695147 | − | 0.718868i | \(-0.255339\pi\) | |||||||
\(194\) | −4.00000 | −0.287183 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | 18.9737i | 1.35182i | 0.736985 | + | 0.675909i | \(0.236249\pi\) | ||||
−0.736985 | + | 0.675909i | \(0.763751\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.51317 | 0.461706 | 0.230853 | − | 0.972989i | \(-0.425848\pi\) | ||||
0.230853 | + | 0.972989i | \(0.425848\pi\) | |||||||
\(200\) | 12.3246i | 0.871478i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.83772i | 0.551460i | ||||||||
\(203\) | 5.81139i | 0.407879i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.4868 | −0.872118 | ||||||||
\(206\) | 15.8114i | 1.10163i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | −12.4868 | −0.857599 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17.8114i | 1.21756i | ||||||||
\(215\) | − 38.1359i | − 2.60085i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.0000 | −1.35769 | ||||||||
\(218\) | 6.64911 | 0.450335 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.83772 | 0.326159 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.67544i | 0.112196i | 0.998425 | + | 0.0560980i | \(0.0178659\pi\) | ||||
−0.998425 | + | 0.0560980i | \(0.982134\pi\) | |||||||
\(224\) | −3.16228 | −0.211289 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − 6.67544i | − 0.444044i | ||||||||
\(227\) | − 15.4868i | − 1.02790i | −0.857821 | − | 0.513949i | \(-0.828182\pi\) | ||||
0.857821 | − | 0.513949i | \(-0.171818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.3246i | 1.47525i | 0.675212 | + | 0.737624i | \(0.264052\pi\) | ||||
−0.675212 | + | 0.737624i | \(0.735948\pi\) | |||||||
\(230\) | −29.8114 | −1.96570 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 1.83772i | − 0.120652i | ||||||||
\(233\) | −16.6491 | −1.09072 | −0.545360 | − | 0.838202i | \(-0.683607\pi\) | ||||
−0.545360 | + | 0.838202i | \(0.683607\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.1359 | 1.31352 | ||||||||
\(236\) | − 2.32456i | − 0.151316i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.48683 | 0.614940 | ||||||||
\(239\) | − 21.4868i | − 1.38987i | −0.719074 | − | 0.694934i | \(-0.755434\pi\) | ||||
0.719074 | − | 0.694934i | \(-0.244566\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.3246i | 0.858310i | 0.903231 | + | 0.429155i | \(0.141189\pi\) | ||||
−0.903231 | + | 0.429155i | \(0.858811\pi\) | |||||||
\(242\) | 9.64911i | 0.620268i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.162278 | −0.0103888 | ||||||||
\(245\) | − 12.4868i | − 0.797754i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 6.32456 | 0.401610 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 30.4868 | 1.92816 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.32456i | 0.523360i | ||||||||
\(254\) | 18.3246i | 1.14978i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.9737 | −1.37068 | −0.685340 | − | 0.728223i | \(-0.740346\pi\) | ||||
−0.685340 | + | 0.728223i | \(0.740346\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.1359 | −0.754091 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 16.6491i | − 1.02859i | ||||||||
\(263\) | 2.51317 | 0.154969 | 0.0774843 | − | 0.996994i | \(-0.475311\pi\) | ||||
0.0774843 | + | 0.996994i | \(0.475311\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 51.9737i | 3.19272i | ||||||||
\(266\) | − 16.3246i | − 1.00092i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 2.83772i | − 0.173341i | ||||||||
\(269\) | −6.00000 | −0.365826 | −0.182913 | − | 0.983129i | \(-0.558553\pi\) | ||||
−0.182913 | + | 0.983129i | \(0.558553\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 6.32456i | − 0.384189i | −0.981376 | − | 0.192095i | \(-0.938472\pi\) | ||||
0.981376 | − | 0.192095i | \(-0.0615281\pi\) | |||||||
\(272\) | −3.00000 | −0.181902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.00000 | −0.181237 | ||||||||
\(275\) | − 14.3246i | − 0.863803i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.8114 | −0.649593 | −0.324797 | − | 0.945784i | \(-0.605296\pi\) | ||||
−0.324797 | + | 0.945784i | \(0.605296\pi\) | |||||||
\(278\) | − 6.32456i | − 0.379322i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 13.1623i | 0.786597i | ||||||||
\(281\) | 0.675445i | 0.0402937i | 0.999797 | + | 0.0201468i | \(0.00641337\pi\) | ||||
−0.999797 | + | 0.0201468i | \(0.993587\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.83772 | 0.168685 | 0.0843425 | − | 0.996437i | \(-0.473121\pi\) | ||||
0.0843425 | + | 0.996437i | \(0.473121\pi\) | |||||||
\(284\) | 7.16228i | 0.425003i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.48683 | −0.559990 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | −7.64911 | −0.449171 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.00000i | 0.0585206i | ||||||||
\(293\) | − 1.83772i | − 0.107361i | −0.998558 | − | 0.0536804i | \(-0.982905\pi\) | ||||
0.998558 | − | 0.0536804i | \(-0.0170952\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.67544 | −0.563326 | ||||||||
\(296\) | 3.83772 | 0.223063 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.486833 | −0.0282015 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 28.9737i | − 1.67001i | ||||||||
\(302\) | −0.837722 | −0.0482055 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.16228i | 0.296077i | ||||||||
\(305\) | 0.675445i | 0.0386758i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.4868i | 0.655588i | 0.944749 | + | 0.327794i | \(0.106305\pi\) | ||||
−0.944749 | + | 0.327794i | \(0.893695\pi\) | |||||||
\(308\) | 3.67544 | 0.209428 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 26.3246i | − 1.49513i | ||||||||
\(311\) | 21.4868 | 1.21841 | 0.609203 | − | 0.793014i | \(-0.291489\pi\) | ||||
0.609203 | + | 0.793014i | \(0.291489\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.00000 | −0.226093 | −0.113047 | − | 0.993590i | \(-0.536061\pi\) | ||||
−0.113047 | + | 0.993590i | \(0.536061\pi\) | |||||||
\(314\) | − 10.4868i | − 0.591806i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | 12.4868i | 0.701330i | 0.936501 | + | 0.350665i | \(0.114044\pi\) | ||||
−0.936501 | + | 0.350665i | \(0.885956\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.13594i | 0.119590i | ||||||||
\(320\) | − 4.16228i | − 0.232678i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −22.6491 | −1.26219 | ||||||||
\(323\) | − 15.4868i | − 0.861710i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.0000 | 0.886158 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.00000 | 0.165647 | ||||||||
\(329\) | 15.2982 | 0.843418 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.9737i | 0.603167i | 0.953440 | + | 0.301584i | \(0.0975152\pi\) | ||||
−0.953440 | + | 0.301584i | \(0.902485\pi\) | |||||||
\(332\) | 3.48683i | 0.191365i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | −11.8114 | −0.645325 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.0000 | −0.599208 | −0.299604 | − | 0.954064i | \(-0.596855\pi\) | ||||
−0.299604 | + | 0.954064i | \(0.596855\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.4868i | 0.677194i | ||||||||
\(341\) | −7.35089 | −0.398073 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.6491i | 0.682988i | ||||||||
\(344\) | 9.16228i | 0.493997i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.6491i | 1.21762i | ||||||||
\(347\) | 15.4868 | 0.831377 | 0.415688 | − | 0.909507i | \(-0.363541\pi\) | ||||
0.415688 | + | 0.909507i | \(0.363541\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 5.35089i | − 0.286427i | −0.989692 | − | 0.143213i | \(-0.954257\pi\) | ||||
0.989692 | − | 0.143213i | \(-0.0457435\pi\) | |||||||
\(350\) | 38.9737 | 2.08323 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.16228 | −0.0619496 | ||||||||
\(353\) | 29.3246i | 1.56079i | 0.625288 | + | 0.780394i | \(0.284982\pi\) | ||||
−0.625288 | + | 0.780394i | \(0.715018\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.8114 | 1.58222 | ||||||||
\(356\) | 12.0000i | 0.635999i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.4868i | 0.818505i | ||||||||
\(359\) | − 28.4605i | − 1.50209i | −0.660252 | − | 0.751044i | \(-0.729551\pi\) | ||||
0.660252 | − | 0.751044i | \(-0.270449\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.64911 | −0.402585 | ||||||||
\(362\) | − 3.83772i | − 0.201706i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.16228 | 0.217864 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.4868 | −1.33040 | −0.665201 | − | 0.746664i | \(-0.731654\pi\) | ||||
−0.665201 | + | 0.746664i | \(0.731654\pi\) | |||||||
\(368\) | 7.16228 | 0.373360 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 15.9737i | − 0.830431i | ||||||||
\(371\) | 39.4868i | 2.05005i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.4868 | −0.853656 | −0.426828 | − | 0.904333i | \(-0.640369\pi\) | ||||
−0.426828 | + | 0.904333i | \(0.640369\pi\) | |||||||
\(374\) | 3.48683 | 0.180300 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.83772 | −0.249486 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 17.6754i | − 0.907927i | −0.891020 | − | 0.453963i | \(-0.850010\pi\) | ||||
0.891020 | − | 0.453963i | \(-0.149990\pi\) | |||||||
\(380\) | 21.4868 | 1.10225 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 14.3246i | − 0.732908i | ||||||||
\(383\) | 30.9737i | 1.58268i | 0.611376 | + | 0.791340i | \(0.290616\pi\) | ||||
−0.611376 | + | 0.791340i | \(0.709384\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − 15.2982i | − 0.779670i | ||||||||
\(386\) | 19.9737 | 1.01663 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 4.00000i | − 0.203069i | ||||||||
\(389\) | 12.4868 | 0.633108 | 0.316554 | − | 0.948575i | \(-0.397474\pi\) | ||||
0.316554 | + | 0.948575i | \(0.397474\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.4868 | −1.08664 | ||||||||
\(392\) | 3.00000i | 0.151523i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.9737 | −0.955879 | ||||||||
\(395\) | − 16.6491i | − 0.837708i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.0000i | 1.30490i | 0.757831 | + | 0.652451i | \(0.226259\pi\) | ||||
−0.757831 | + | 0.652451i | \(0.773741\pi\) | |||||||
\(398\) | 6.51317i | 0.326476i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.3246 | −0.616228 | ||||||||
\(401\) | 15.0000i | 0.749064i | 0.927214 | + | 0.374532i | \(0.122197\pi\) | ||||
−0.927214 | + | 0.374532i | \(0.877803\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −7.83772 | −0.389941 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.81139 | −0.288414 | ||||||||
\(407\) | −4.46050 | −0.221099 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 14.6754i | − 0.725654i | −0.931857 | − | 0.362827i | \(-0.881812\pi\) | ||||
0.931857 | − | 0.362827i | \(-0.118188\pi\) | |||||||
\(410\) | − 12.4868i | − 0.616681i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.8114 | −0.778971 | ||||||||
\(413\) | −7.35089 | −0.361714 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.5132 | 0.712423 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 6.00000i | − 0.293470i | ||||||||
\(419\) | 30.9737 | 1.51316 | 0.756581 | − | 0.653900i | \(-0.226868\pi\) | ||||
0.756581 | + | 0.653900i | \(0.226868\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.8377i | 1.16178i | 0.813982 | + | 0.580890i | \(0.197295\pi\) | ||||
−0.813982 | + | 0.580890i | \(0.802705\pi\) | |||||||
\(422\) | − 4.00000i | − 0.194717i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − 12.4868i | − 0.606414i | ||||||||
\(425\) | 36.9737 | 1.79349 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.513167i | 0.0248339i | ||||||||
\(428\) | −17.8114 | −0.860946 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 38.1359 | 1.83908 | ||||||||
\(431\) | − 9.48683i | − 0.456965i | −0.973548 | − | 0.228482i | \(-0.926624\pi\) | ||||
0.973548 | − | 0.228482i | \(-0.0733763\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.32456 | 0.448110 | 0.224055 | − | 0.974577i | \(-0.428071\pi\) | ||||
0.224055 | + | 0.974577i | \(0.428071\pi\) | |||||||
\(434\) | − 20.0000i | − 0.960031i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.64911i | 0.318435i | ||||||||
\(437\) | 36.9737i | 1.76869i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.4868 | 1.21642 | 0.608210 | − | 0.793776i | \(-0.291888\pi\) | ||||
0.608210 | + | 0.793776i | \(0.291888\pi\) | |||||||
\(440\) | 4.83772i | 0.230629i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 49.9473 | 2.36773 | ||||||||
\(446\) | −1.67544 | −0.0793346 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 3.16228i | − 0.149404i | ||||||||
\(449\) | − 7.35089i | − 0.346910i | −0.984842 | − | 0.173455i | \(-0.944507\pi\) | ||||
0.984842 | − | 0.173455i | \(-0.0554931\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.48683 | −0.164189 | ||||||||
\(452\) | 6.67544 | 0.313987 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.4868 | 0.726833 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.32456i | 0.155516i | 0.996972 | + | 0.0777581i | \(0.0247762\pi\) | ||||
−0.996972 | + | 0.0777581i | \(0.975224\pi\) | |||||||
\(458\) | −22.3246 | −1.04316 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 29.8114i | − 1.38996i | ||||||||
\(461\) | 18.4868i | 0.861018i | 0.902586 | + | 0.430509i | \(0.141666\pi\) | ||||
−0.902586 | + | 0.430509i | \(0.858334\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.1623i | 0.704651i | 0.935878 | + | 0.352325i | \(0.114609\pi\) | ||||
−0.935878 | + | 0.352325i | \(0.885391\pi\) | |||||||
\(464\) | 1.83772 | 0.0853141 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − 16.6491i | − 0.771255i | ||||||||
\(467\) | 6.18861 | 0.286375 | 0.143187 | − | 0.989696i | \(-0.454265\pi\) | ||||
0.143187 | + | 0.989696i | \(0.454265\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.97367 | −0.414365 | ||||||||
\(470\) | 20.1359i | 0.928802i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.32456 | 0.106996 | ||||||||
\(473\) | − 10.6491i | − 0.489647i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 63.6228i | − 2.91921i | ||||||||
\(476\) | 9.48683i | 0.434828i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 21.4868 | 0.982785 | ||||||||
\(479\) | 24.0000i | 1.09659i | 0.836286 | + | 0.548294i | \(0.184723\pi\) | ||||
−0.836286 | + | 0.548294i | \(0.815277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −13.3246 | −0.606917 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.64911 | −0.438596 | ||||||||
\(485\) | −16.6491 | −0.755997 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.4868i | 0.611147i | 0.952169 | + | 0.305573i | \(0.0988481\pi\) | ||||
−0.952169 | + | 0.305573i | \(0.901152\pi\) | |||||||
\(488\) | − 0.162278i | − 0.00734596i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 12.4868 | 0.564098 | ||||||||
\(491\) | 5.81139 | 0.262264 | 0.131132 | − | 0.991365i | \(-0.458139\pi\) | ||||
0.131132 | + | 0.991365i | \(0.458139\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.51317 | −0.248301 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.32456i | 0.283981i | ||||||||
\(497\) | 22.6491 | 1.01595 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 12.6491i | − 0.566252i | −0.959083 | − | 0.283126i | \(-0.908629\pi\) | ||||
0.959083 | − | 0.283126i | \(-0.0913715\pi\) | |||||||
\(500\) | 30.4868i | 1.36341i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 12.0000i | − 0.535586i | ||||||||
\(503\) | 0.188612 | 0.00840978 | 0.00420489 | − | 0.999991i | \(-0.498662\pi\) | ||||
0.00420489 | + | 0.999991i | \(0.498662\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.6228i | 1.45169i | ||||||||
\(506\) | −8.32456 | −0.370072 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.3246 | −0.813021 | ||||||||
\(509\) | − 28.1623i | − 1.24827i | −0.781316 | − | 0.624136i | \(-0.785451\pi\) | ||||
0.781316 | − | 0.624136i | \(-0.214549\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.16228 | 0.139891 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 21.9737i | − 0.969217i | ||||||||
\(515\) | 65.8114i | 2.90000i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.62278 | 0.247289 | ||||||||
\(518\) | − 12.1359i | − 0.533223i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.0000 | 1.18289 | 0.591446 | − | 0.806345i | \(-0.298557\pi\) | ||||
0.591446 | + | 0.806345i | \(0.298557\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.16228 | −0.225731 | −0.112865 | − | 0.993610i | \(-0.536003\pi\) | ||||
−0.112865 | + | 0.993610i | \(0.536003\pi\) | |||||||
\(524\) | 16.6491 | 0.727320 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.51317i | 0.109579i | ||||||||
\(527\) | − 18.9737i | − 0.826506i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.2982 | 1.23036 | ||||||||
\(530\) | −51.9737 | −2.25759 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 16.3246 | 0.707759 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 74.1359i | 3.20518i | ||||||||
\(536\) | 2.83772 | 0.122571 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 6.00000i | − 0.258678i | ||||||||
\(539\) | − 3.48683i | − 0.150189i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 15.5132i | − 0.666963i | −0.942757 | − | 0.333482i | \(-0.891777\pi\) | ||||
0.942757 | − | 0.333482i | \(-0.108223\pi\) | |||||||
\(542\) | 6.32456 | 0.271663 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 3.00000i | − 0.128624i | ||||||||
\(545\) | 27.6754 | 1.18549 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.8114 | −1.44567 | −0.722835 | − | 0.691020i | \(-0.757161\pi\) | ||||
−0.722835 | + | 0.691020i | \(0.757161\pi\) | |||||||
\(548\) | − 3.00000i | − 0.128154i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 14.3246 | 0.610801 | ||||||||
\(551\) | 9.48683i | 0.404153i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 12.6491i | − 0.537895i | ||||||||
\(554\) | − 10.8114i | − 0.459332i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.32456 | 0.268221 | ||||||||
\(557\) | 18.4868i | 0.783312i | 0.920112 | + | 0.391656i | \(0.128098\pi\) | ||||
−0.920112 | + | 0.391656i | \(0.871902\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −13.1623 | −0.556208 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.675445 | −0.0284919 | ||||||||
\(563\) | 40.6491 | 1.71316 | 0.856578 | − | 0.516018i | \(-0.172586\pi\) | ||||
0.856578 | + | 0.516018i | \(0.172586\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 27.7851i | − 1.16893i | ||||||||
\(566\) | 2.83772i | 0.119278i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.16228 | −0.300522 | ||||||||
\(569\) | 27.2982 | 1.14440 | 0.572200 | − | 0.820114i | \(-0.306090\pi\) | ||||
0.572200 | + | 0.820114i | \(0.306090\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.1359 | 1.51224 | 0.756121 | − | 0.654432i | \(-0.227092\pi\) | ||||
0.756121 | + | 0.654432i | \(0.227092\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − 9.48683i | − 0.395973i | ||||||||
\(575\) | −88.2719 | −3.68119 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 0.350889i | − 0.0146077i | −0.999973 | − | 0.00730386i | \(-0.997675\pi\) | ||||
0.999973 | − | 0.00730386i | \(-0.00232491\pi\) | |||||||
\(578\) | − 8.00000i | − 0.332756i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 7.64911i | − 0.317612i | ||||||||
\(581\) | 11.0263 | 0.457449 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.5132i | 0.601074i | ||||||||
\(584\) | −1.00000 | −0.0413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.83772 | 0.0759156 | ||||||||
\(587\) | 28.6491i | 1.18248i | 0.806497 | + | 0.591238i | \(0.201360\pi\) | ||||
−0.806497 | + | 0.591238i | \(0.798640\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.6491 | −1.34528 | ||||||||
\(590\) | − 9.67544i | − 0.398332i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.83772i | 0.157729i | ||||||||
\(593\) | − 0.675445i | − 0.0277372i | −0.999904 | − | 0.0138686i | \(-0.995585\pi\) | ||||
0.999904 | − | 0.0138686i | \(-0.00441465\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 39.4868 | 1.61880 | ||||||||
\(596\) | − 0.486833i | − 0.0199415i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.6228 | 0.965200 | 0.482600 | − | 0.875841i | \(-0.339692\pi\) | ||||
0.482600 | + | 0.875841i | \(0.339692\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.2982 | −1.39905 | −0.699527 | − | 0.714606i | \(-0.746606\pi\) | ||||
−0.699527 | + | 0.714606i | \(0.746606\pi\) | |||||||
\(602\) | 28.9737 | 1.18088 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − 0.837722i | − 0.0340864i | ||||||||
\(605\) | 40.1623i | 1.63283i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.2982 | 0.702113 | 0.351057 | − | 0.936354i | \(-0.385822\pi\) | ||||
0.351057 | + | 0.936354i | \(0.385822\pi\) | |||||||
\(608\) | −5.16228 | −0.209358 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.675445 | −0.0273480 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 20.4868i | − 0.827455i | −0.910401 | − | 0.413728i | \(-0.864227\pi\) | ||||
0.910401 | − | 0.413728i | \(-0.135773\pi\) | |||||||
\(614\) | −11.4868 | −0.463571 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.67544i | 0.148088i | ||||||||
\(617\) | − 26.6228i | − 1.07179i | −0.844284 | − | 0.535896i | \(-0.819974\pi\) | ||||
0.844284 | − | 0.535896i | \(-0.180026\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.6491i | 0.990731i | 0.868685 | + | 0.495366i | \(0.164966\pi\) | ||||
−0.868685 | + | 0.495366i | \(0.835034\pi\) | |||||||
\(620\) | 26.3246 | 1.05722 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.4868i | 0.861544i | ||||||||
\(623\) | 37.9473 | 1.52033 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 65.2719 | 2.61088 | ||||||||
\(626\) | − 4.00000i | − 0.159872i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.4868 | 0.418470 | ||||||||
\(629\) | − 11.5132i | − 0.459060i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 25.2982i | − 1.00711i | −0.863964 | − | 0.503553i | \(-0.832026\pi\) | ||||
0.863964 | − | 0.503553i | \(-0.167974\pi\) | |||||||
\(632\) | 4.00000i | 0.159111i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.4868 | −0.495915 | ||||||||
\(635\) | 76.2719i | 3.02676i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.13594 | −0.0845628 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.16228 | 0.164528 | ||||||||
\(641\) | 16.3509 | 0.645821 | 0.322911 | − | 0.946429i | \(-0.395339\pi\) | ||||
0.322911 | + | 0.946429i | \(0.395339\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 20.0000i | − 0.788723i | −0.918955 | − | 0.394362i | \(-0.870966\pi\) | ||||
0.918955 | − | 0.394362i | \(-0.129034\pi\) | |||||||
\(644\) | − 22.6491i | − 0.892500i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.4868 | 0.609321 | ||||||||
\(647\) | −40.6491 | −1.59808 | −0.799041 | − | 0.601277i | \(-0.794659\pi\) | ||||
−0.799041 | + | 0.601277i | \(0.794659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.70178 | −0.106054 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.0000i | 0.626608i | ||||||||
\(653\) | −30.0000 | −1.17399 | −0.586995 | − | 0.809590i | \(-0.699689\pi\) | ||||
−0.586995 | + | 0.809590i | \(0.699689\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 69.2982i | − 2.70771i | ||||||||
\(656\) | 3.00000i | 0.117130i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.2982i | 0.596387i | ||||||||
\(659\) | 5.02633 | 0.195798 | 0.0978991 | − | 0.995196i | \(-0.468788\pi\) | ||||
0.0978991 | + | 0.995196i | \(0.468788\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.4868i | 1.03022i | 0.857125 | + | 0.515109i | \(0.172249\pi\) | ||||
−0.857125 | + | 0.515109i | \(0.827751\pi\) | |||||||
\(662\) | −10.9737 | −0.426504 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.48683 | −0.135315 | ||||||||
\(665\) | − 67.9473i | − 2.63488i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.1623 | 0.509645 | ||||||||
\(668\) | 12.0000i | 0.464294i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 11.8114i | − 0.456314i | ||||||||
\(671\) | 0.188612i | 0.00728127i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.6754 | −0.565697 | −0.282848 | − | 0.959165i | \(-0.591279\pi\) | ||||
−0.282848 | + | 0.959165i | \(0.591279\pi\) | |||||||
\(674\) | − 11.0000i | − 0.423704i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.0000 | −0.691796 | −0.345898 | − | 0.938272i | \(-0.612426\pi\) | ||||
−0.345898 | + | 0.938272i | \(0.612426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.6491 | −0.485428 | ||||||||
\(680\) | −12.4868 | −0.478848 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 7.35089i | − 0.281480i | ||||||||
\(683\) | 35.6228i | 1.36307i | 0.731787 | + | 0.681534i | \(0.238687\pi\) | ||||
−0.731787 | + | 0.681534i | \(0.761313\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.4868 | −0.477097 | ||||||||
\(686\) | −12.6491 | −0.482945 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.16228 | −0.349309 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 9.16228i | − 0.348549i | −0.984697 | − | 0.174275i | \(-0.944242\pi\) | ||||
0.984697 | − | 0.174275i | \(-0.0557581\pi\) | |||||||
\(692\) | −22.6491 | −0.860990 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.4868i | 0.587872i | ||||||||
\(695\) | − 26.3246i | − 0.998547i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 9.00000i | − 0.340899i | ||||||||
\(698\) | 5.35089 | 0.202534 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 38.9737i | 1.47307i | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.8114 | −0.747201 | ||||||||
\(704\) | − 1.16228i | − 0.0438050i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −29.3246 | −1.10364 | ||||||||
\(707\) | 24.7851i | 0.932138i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.4605i | 1.70730i | 0.520843 | + | 0.853652i | \(0.325618\pi\) | ||||
−0.520843 | + | 0.853652i | \(0.674382\pi\) | |||||||
\(710\) | 29.8114i | 1.11880i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.0000 | −0.449719 | ||||||||
\(713\) | 45.2982i | 1.69643i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.4868 | −0.578770 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.4605 | 1.06214 | ||||||||
\(719\) | −38.3246 | −1.42926 | −0.714632 | − | 0.699500i | \(-0.753406\pi\) | ||||
−0.714632 | + | 0.699500i | \(0.753406\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 50.0000i | 1.86210i | ||||||||
\(722\) | − 7.64911i | − 0.284670i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.83772 | 0.142628 | ||||||||
\(725\) | −22.6491 | −0.841167 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.83772 | 0.327773 | 0.163886 | − | 0.986479i | \(-0.447597\pi\) | ||||
0.163886 | + | 0.986479i | \(0.447597\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.16228i | 0.154053i | ||||||||
\(731\) | 27.4868 | 1.01664 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 21.4605i | − 0.792662i | −0.918108 | − | 0.396331i | \(-0.870283\pi\) | ||||
0.918108 | − | 0.396331i | \(-0.129717\pi\) | |||||||
\(734\) | − 25.4868i | − 0.940736i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.16228i | 0.264005i | ||||||||
\(737\) | −3.29822 | −0.121492 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 39.6228i | − 1.45755i | −0.684755 | − | 0.728774i | \(-0.740091\pi\) | ||||
0.684755 | − | 0.728774i | \(-0.259909\pi\) | |||||||
\(740\) | 15.9737 | 0.587204 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −39.4868 | −1.44961 | ||||||||
\(743\) | 2.32456i | 0.0852797i | 0.999091 | + | 0.0426398i | \(0.0135768\pi\) | ||||
−0.999091 | + | 0.0426398i | \(0.986423\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.02633 | −0.0742391 | ||||||||
\(746\) | − 16.4868i | − 0.603626i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.48683i | 0.127491i | ||||||||
\(749\) | 56.3246i | 2.05805i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.7851 | −1.41529 | −0.707643 | − | 0.706570i | \(-0.750242\pi\) | ||||
−0.707643 | + | 0.706570i | \(0.750242\pi\) | |||||||
\(752\) | − 4.83772i | − 0.176414i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.48683 | −0.126899 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.6491 | −0.968578 | −0.484289 | − | 0.874908i | \(-0.660922\pi\) | ||||
−0.484289 | + | 0.874908i | \(0.660922\pi\) | |||||||
\(758\) | 17.6754 | 0.642001 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 21.4868i | 0.779409i | ||||||||
\(761\) | 12.0000i | 0.435000i | 0.976060 | + | 0.217500i | \(0.0697902\pi\) | ||||
−0.976060 | + | 0.217500i | \(0.930210\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.0263 | 0.761204 | ||||||||
\(764\) | 14.3246 | 0.518244 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.9737 | −1.11912 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 3.35089i | − 0.120836i | −0.998173 | − | 0.0604181i | \(-0.980757\pi\) | ||||
0.998173 | − | 0.0604181i | \(-0.0192434\pi\) | |||||||
\(770\) | 15.2982 | 0.551310 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 19.9737i | 0.718868i | ||||||||
\(773\) | 22.6491i | 0.814632i | 0.913287 | + | 0.407316i | \(0.133535\pi\) | ||||
−0.913287 | + | 0.407316i | \(0.866465\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 77.9473i | − 2.79995i | ||||||||
\(776\) | 4.00000 | 0.143592 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.4868i | 0.447675i | ||||||||
\(779\) | −15.4868 | −0.554873 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.32456 | 0.297876 | ||||||||
\(782\) | − 21.4868i | − 0.768368i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | − 43.6491i | − 1.55790i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 9.02633i | − 0.321754i | −0.986974 | − | 0.160877i | \(-0.948568\pi\) | ||||
0.986974 | − | 0.160877i | \(-0.0514323\pi\) | |||||||
\(788\) | − 18.9737i | − 0.675909i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 16.6491 | 0.592349 | ||||||||
\(791\) | − 21.1096i | − 0.750571i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −26.0000 | −0.922705 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.51317 | −0.230853 | ||||||||
\(797\) | −18.9737 | −0.672082 | −0.336041 | − | 0.941847i | \(-0.609088\pi\) | ||||
−0.336041 | + | 0.941847i | \(0.609088\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.5132i | 0.513439i | ||||||||
\(800\) | − 12.3246i | − 0.435739i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.0000 | −0.529668 | ||||||||
\(803\) | 1.16228 | 0.0410159 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −94.2719 | −3.32265 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 7.83772i | − 0.275730i | ||||||||
\(809\) | −3.00000 | −0.105474 | −0.0527372 | − | 0.998608i | \(-0.516795\pi\) | ||||
−0.0527372 | + | 0.998608i | \(0.516795\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1.02633i | − 0.0360395i | −0.999838 | − | 0.0180197i | \(-0.994264\pi\) | ||||
0.999838 | − | 0.0180197i | \(-0.00573617\pi\) | |||||||
\(812\) | − 5.81139i | − 0.203940i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − 4.46050i | − 0.156340i | ||||||||
\(815\) | 66.5964 | 2.33277 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 47.2982i | − 1.65476i | ||||||||
\(818\) | 14.6754 | 0.513115 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.4868 | 0.436059 | ||||||||
\(821\) | 10.6491i | 0.371657i | 0.982582 | + | 0.185828i | \(0.0594968\pi\) | ||||
−0.982582 | + | 0.185828i | \(0.940503\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −53.2982 | −1.85786 | −0.928930 | − | 0.370256i | \(-0.879270\pi\) | ||||
−0.928930 | + | 0.370256i | \(0.879270\pi\) | |||||||
\(824\) | − 15.8114i | − 0.550816i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − 7.35089i | − 0.255770i | ||||||||
\(827\) | 6.97367i | 0.242498i | 0.992622 | + | 0.121249i | \(0.0386900\pi\) | ||||
−0.992622 | + | 0.121249i | \(0.961310\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.1623 | −0.422413 | −0.211207 | − | 0.977441i | \(-0.567739\pi\) | ||||
−0.211207 | + | 0.977441i | \(0.567739\pi\) | |||||||
\(830\) | 14.5132i | 0.503759i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.00000 | 0.311832 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.9473 | 1.72850 | ||||||||
\(836\) | 6.00000 | 0.207514 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 30.9737i | 1.06997i | ||||||||
\(839\) | − 4.64911i | − 0.160505i | −0.996775 | − | 0.0802526i | \(-0.974427\pi\) | ||||
0.996775 | − | 0.0802526i | \(-0.0255727\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.6228 | −0.883544 | ||||||||
\(842\) | −23.8377 | −0.821502 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.00000 | 0.137686 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.5132i | 1.04844i | ||||||||
\(848\) | 12.4868 | 0.428800 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 36.9737i | 1.26819i | ||||||||
\(851\) | 27.4868i | 0.942236i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 55.1359i | 1.88782i | 0.330205 | + | 0.943909i | \(0.392882\pi\) | ||||
−0.330205 | + | 0.943909i | \(0.607118\pi\) | |||||||
\(854\) | −0.513167 | −0.0175602 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − 17.8114i | − 0.608781i | ||||||||
\(857\) | −25.6491 | −0.876157 | −0.438078 | − | 0.898937i | \(-0.644341\pi\) | ||||
−0.438078 | + | 0.898937i | \(0.644341\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.5132 | 0.972857 | 0.486428 | − | 0.873720i | \(-0.338299\pi\) | ||||
0.486428 | + | 0.873720i | \(0.338299\pi\) | |||||||
\(860\) | 38.1359i | 1.30042i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.48683 | 0.323123 | ||||||||
\(863\) | 47.8114i | 1.62752i | 0.581202 | + | 0.813759i | \(0.302583\pi\) | ||||
−0.581202 | + | 0.813759i | \(0.697417\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 94.2719i | 3.20534i | ||||||||
\(866\) | 9.32456i | 0.316861i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20.0000 | 0.678844 | ||||||||
\(869\) | − 4.64911i | − 0.157710i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.64911 | −0.225167 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −36.9737 | −1.25065 | ||||||||
\(875\) | 96.4078 | 3.25918 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.1359i | 1.52413i | 0.647499 | + | 0.762066i | \(0.275815\pi\) | ||||
−0.647499 | + | 0.762066i | \(0.724185\pi\) | |||||||
\(878\) | 25.4868i | 0.860139i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.83772 | −0.163080 | ||||||||
\(881\) | 9.97367 | 0.336021 | 0.168011 | − | 0.985785i | \(-0.446266\pi\) | ||||
0.168011 | + | 0.985785i | \(0.446266\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.3509 | 0.381988 | 0.190994 | − | 0.981591i | \(-0.438829\pi\) | ||||
0.190994 | + | 0.981591i | \(0.438829\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.3246 | −1.28681 | −0.643406 | − | 0.765525i | \(-0.722479\pi\) | ||||
−0.643406 | + | 0.765525i | \(0.722479\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 57.9473i | 1.94349i | ||||||||
\(890\) | 49.9473i | 1.67424i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 1.67544i | − 0.0560980i | ||||||||
\(893\) | 24.9737 | 0.835712 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 64.4605i | 2.15468i | ||||||||
\(896\) | 3.16228 | 0.105644 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.35089 | 0.245302 | ||||||||
\(899\) | 11.6228i | 0.387641i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.4605 | −1.24799 | ||||||||
\(902\) | − 3.48683i | − 0.116099i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.67544i | 0.222022i | ||||||||
\(905\) | − 15.9737i | − 0.530983i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.2719 | −1.20439 | −0.602194 | − | 0.798350i | \(-0.705707\pi\) | ||||
−0.602194 | + | 0.798350i | \(0.705707\pi\) | |||||||
\(908\) | 15.4868i | 0.513949i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.9473 | 1.65483 | 0.827414 | − | 0.561592i | \(-0.189811\pi\) | ||||
0.827414 | + | 0.561592i | \(0.189811\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.05267 | 0.134124 | ||||||||
\(914\) | −3.32456 | −0.109967 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 22.3246i | − 0.737624i | ||||||||
\(917\) | − 52.6491i | − 1.73863i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.35089 | 0.110536 | 0.0552678 | − | 0.998472i | \(-0.482399\pi\) | ||||
0.0552678 | + | 0.998472i | \(0.482399\pi\) | |||||||
\(920\) | 29.8114 | 0.982852 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.4868 | −0.608831 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 47.2982i | − 1.55516i | ||||||||
\(926\) | −15.1623 | −0.498263 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.83772i | 0.0603262i | ||||||||
\(929\) | 28.9473i | 0.949731i | 0.880058 | + | 0.474866i | \(0.157503\pi\) | ||||
−0.880058 | + | 0.474866i | \(0.842497\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 15.4868i | − 0.507560i | ||||||||
\(932\) | 16.6491 | 0.545360 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.18861i | 0.202498i | ||||||||
\(935\) | 14.5132 | 0.474631 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.2982 | 0.467103 | 0.233551 | − | 0.972344i | \(-0.424965\pi\) | ||||
0.233551 | + | 0.972344i | \(0.424965\pi\) | |||||||
\(938\) | − 8.97367i | − 0.293001i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −20.1359 | −0.656762 | ||||||||
\(941\) | − 48.5964i | − 1.58420i | −0.610392 | − | 0.792099i | \(-0.708988\pi\) | ||||
0.610392 | − | 0.792099i | \(-0.291012\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.4868i | 0.699708i | ||||||||
\(944\) | 2.32456i | 0.0756578i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.6491 | 0.346232 | ||||||||
\(947\) | − 18.9737i | − 0.616561i | −0.951295 | − | 0.308281i | \(-0.900246\pi\) | ||||
0.951295 | − | 0.308281i | \(-0.0997536\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 63.6228 | 2.06420 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.48683 | −0.307470 | ||||||||
\(953\) | −27.2982 | −0.884276 | −0.442138 | − | 0.896947i | \(-0.645780\pi\) | ||||
−0.442138 | + | 0.896947i | \(0.645780\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 59.6228i | − 1.92935i | ||||||||
\(956\) | 21.4868i | 0.694934i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.0000 | −0.775405 | ||||||||
\(959\) | −9.48683 | −0.306346 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | −0.290323 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 13.3246i | − 0.429155i | ||||||||
\(965\) | 83.1359 | 2.67624 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 34.5132i | − 1.10987i | −0.831894 | − | 0.554934i | \(-0.812743\pi\) | ||||
0.831894 | − | 0.554934i | \(-0.187257\pi\) | |||||||
\(968\) | − 9.64911i | − 0.310134i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − 16.6491i | − 0.534571i | ||||||||
\(971\) | 18.9737 | 0.608894 | 0.304447 | − | 0.952529i | \(-0.401528\pi\) | ||||
0.304447 | + | 0.952529i | \(0.401528\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 20.0000i | − 0.641171i | ||||||||
\(974\) | −13.4868 | −0.432146 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.162278 | 0.00519438 | ||||||||
\(977\) | 21.0000i | 0.671850i | 0.941889 | + | 0.335925i | \(0.109049\pi\) | ||||
−0.941889 | + | 0.335925i | \(0.890951\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.9473 | 0.445759 | ||||||||
\(980\) | 12.4868i | 0.398877i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.81139i | 0.185449i | ||||||||
\(983\) | − 23.6228i | − 0.753450i | −0.926325 | − | 0.376725i | \(-0.877050\pi\) | ||||
0.926325 | − | 0.376725i | \(-0.122950\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −78.9737 | −2.51631 | ||||||||
\(986\) | − 5.51317i | − 0.175575i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −65.6228 | −2.08668 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.7851 | 0.850855 | 0.425428 | − | 0.904992i | \(-0.360124\pi\) | ||||
0.425428 | + | 0.904992i | \(0.360124\pi\) | |||||||
\(992\) | −6.32456 | −0.200805 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 22.6491i | 0.718386i | ||||||||
\(995\) | 27.1096i | 0.859432i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −59.4605 | −1.88313 | −0.941566 | − | 0.336827i | \(-0.890646\pi\) | ||||
−0.941566 | + | 0.336827i | \(0.890646\pi\) | |||||||
\(998\) | 12.6491 | 0.400401 | ||||||||
\(999\) | 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 | 3042.2.b.j.1351.4 | 4 | ||
3.2 | odd | 2 | 3042.2.b.k.1351.1 | 4 | |||
13.5 | odd | 4 | 3042.2.a.x.1.2 | 2 | |||
13.7 | odd | 12 | 234.2.h.e.55.1 | yes | 4 | ||
13.8 | odd | 4 | 3042.2.a.r.1.1 | 2 | |||
13.11 | odd | 12 | 234.2.h.e.217.1 | yes | 4 | ||
13.12 | even | 2 | inner | 3042.2.b.j.1351.1 | 4 | ||
39.5 | even | 4 | 3042.2.a.q.1.1 | 2 | |||
39.8 | even | 4 | 3042.2.a.w.1.2 | 2 | |||
39.11 | even | 12 | 234.2.h.d.217.2 | yes | 4 | ||
39.20 | even | 12 | 234.2.h.d.55.2 | ✓ | 4 | ||
39.38 | odd | 2 | 3042.2.b.k.1351.4 | 4 | |||
52.7 | even | 12 | 1872.2.t.n.289.1 | 4 | |||
52.11 | even | 12 | 1872.2.t.n.1153.1 | 4 | |||
156.11 | odd | 12 | 1872.2.t.p.1153.2 | 4 | |||
156.59 | odd | 12 | 1872.2.t.p.289.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
234.2.h.d.55.2 | ✓ | 4 | 39.20 | even | 12 | ||
234.2.h.d.217.2 | yes | 4 | 39.11 | even | 12 | ||
234.2.h.e.55.1 | yes | 4 | 13.7 | odd | 12 | ||
234.2.h.e.217.1 | yes | 4 | 13.11 | odd | 12 | ||
1872.2.t.n.289.1 | 4 | 52.7 | even | 12 | |||
1872.2.t.n.1153.1 | 4 | 52.11 | even | 12 | |||
1872.2.t.p.289.2 | 4 | 156.59 | odd | 12 | |||
1872.2.t.p.1153.2 | 4 | 156.11 | odd | 12 | |||
3042.2.a.q.1.1 | 2 | 39.5 | even | 4 | |||
3042.2.a.r.1.1 | 2 | 13.8 | odd | 4 | |||
3042.2.a.w.1.2 | 2 | 39.8 | even | 4 | |||
3042.2.a.x.1.2 | 2 | 13.5 | odd | 4 | |||
3042.2.b.j.1351.1 | 4 | 13.12 | even | 2 | inner | ||
3042.2.b.j.1351.4 | 4 | 1.1 | even | 1 | trivial | ||
3042.2.b.k.1351.1 | 4 | 3.2 | odd | 2 | |||
3042.2.b.k.1351.4 | 4 | 39.38 | odd | 2 |