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 | 1351.3 | ||
Root | \(-1.58114 - 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3042.1351 |
Dual form | 3042.2.b.j.1351.2 |
$q$-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 \(\left(\mathbb{Z}/3042\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | − 2.16228i | − 0.967000i | −0.875344 | − | 0.483500i | \(-0.839365\pi\) | ||||
0.875344 | − | 0.483500i | \(-0.160635\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 3.16228i | − 1.19523i | −0.801784 | − | 0.597614i | \(-0.796115\pi\) | ||||
0.801784 | − | 0.597614i | \(-0.203885\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.16228 | 0.683772 | ||||||||
\(11\) | − 5.16228i | − 1.55649i | −0.627964 | − | 0.778243i | \(-0.716111\pi\) | ||||
0.627964 | − | 0.778243i | \(-0.283889\pi\) | |||||||
\(12\) | 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 | ||||||||
\(19\) | − 1.16228i | − 0.266645i | −0.991073 | − | 0.133322i | \(-0.957435\pi\) | ||||
0.991073 | − | 0.133322i | \(-0.0425646\pi\) | |||||||
\(20\) | 2.16228i | 0.483500i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.16228 | 1.10060 | ||||||||
\(23\) | 0.837722 | 0.174677 | 0.0873386 | − | 0.996179i | \(-0.472164\pi\) | ||||
0.0873386 | + | 0.996179i | \(0.472164\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.324555 | 0.0649111 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.16228i | 0.597614i | ||||||||
\(29\) | 8.16228 | 1.51570 | 0.757848 | − | 0.652431i | \(-0.226251\pi\) | ||||
0.757848 | + | 0.652431i | \(0.226251\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 6.32456i | − 1.13592i | −0.823055 | − | 0.567962i | \(-0.807732\pi\) | ||||
0.823055 | − | 0.567962i | \(-0.192268\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 3.00000i | − 0.514496i | ||||||||
\(35\) | −6.83772 | −1.15579 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.1623i | 1.67067i | 0.549743 | + | 0.835334i | \(0.314726\pi\) | ||||
−0.549743 | + | 0.835334i | \(0.685274\pi\) | |||||||
\(38\) | 1.16228 | 0.188546 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.16228 | −0.341886 | ||||||||
\(41\) | 3.00000i | 0.468521i | 0.972174 | + | 0.234261i | \(0.0752669\pi\) | ||||
−0.972174 | + | 0.234261i | \(0.924733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.83772 | −0.432749 | −0.216374 | − | 0.976310i | \(-0.569423\pi\) | ||||
−0.216374 | + | 0.976310i | \(0.569423\pi\) | |||||||
\(44\) | 5.16228i | 0.778243i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.837722i | 0.123515i | ||||||||
\(47\) | − 11.1623i | − 1.62819i | −0.580735 | − | 0.814093i | \(-0.697235\pi\) | ||||
0.580735 | − | 0.814093i | \(-0.302765\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0.324555i | 0.0458991i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.48683 | −0.891035 | −0.445518 | − | 0.895273i | \(-0.646980\pi\) | ||||
−0.445518 | + | 0.895273i | \(0.646980\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.1623 | −1.50512 | ||||||||
\(56\) | −3.16228 | −0.422577 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.16228i | 1.07176i | ||||||||
\(59\) | − 10.3246i | − 1.34414i | −0.740486 | − | 0.672071i | \(-0.765405\pi\) | ||||
0.740486 | − | 0.672071i | \(-0.234595\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.16228 | −0.788999 | −0.394499 | − | 0.918896i | \(-0.629082\pi\) | ||||
−0.394499 | + | 0.918896i | \(0.629082\pi\) | |||||||
\(62\) | 6.32456 | 0.803219 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.16228i | 1.11935i | 0.828712 | + | 0.559675i | \(0.189074\pi\) | ||||
−0.828712 | + | 0.559675i | \(0.810926\pi\) | |||||||
\(68\) | 3.00000 | 0.363803 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − 6.83772i | − 0.817264i | ||||||||
\(71\) | − 0.837722i | − 0.0994194i | −0.998764 | − | 0.0497097i | \(-0.984170\pi\) | ||||
0.998764 | − | 0.0497097i | \(-0.0158296\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 1.00000i | − 0.117041i | −0.998286 | − | 0.0585206i | \(-0.981362\pi\) | ||||
0.998286 | − | 0.0585206i | \(-0.0186383\pi\) | |||||||
\(74\) | −10.1623 | −1.18134 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.16228i | 0.133322i | ||||||||
\(77\) | −16.3246 | −1.86036 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | − 2.16228i | − 0.241750i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.00000 | −0.331295 | ||||||||
\(83\) | 15.4868i | 1.69990i | 0.526863 | + | 0.849950i | \(0.323368\pi\) | ||||
−0.526863 | + | 0.849950i | \(0.676632\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.48683i | 0.703596i | ||||||||
\(86\) | − 2.83772i | − 0.305999i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.16228 | −0.550301 | ||||||||
\(89\) | − 12.0000i | − 1.27200i | −0.771690 | − | 0.635999i | \(-0.780588\pi\) | ||||
0.771690 | − | 0.635999i | \(-0.219412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.837722 | −0.0873386 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.1623 | 1.15130 | ||||||||
\(95\) | −2.51317 | −0.257845 | ||||||||
\(96\) | 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 | ||||||||
\(100\) | −0.324555 | −0.0324555 | ||||||||
\(101\) | 14.1623 | 1.40920 | 0.704600 | − | 0.709605i | \(-0.251127\pi\) | ||||
0.704600 | + | 0.709605i | \(0.251127\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.8114 | −1.55794 | −0.778971 | − | 0.627060i | \(-0.784258\pi\) | ||||
−0.778971 | + | 0.627060i | \(0.784258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − 6.48683i | − 0.630057i | ||||||||
\(107\) | −13.8114 | −1.33520 | −0.667599 | − | 0.744521i | \(-0.732678\pi\) | ||||
−0.667599 | + | 0.744521i | \(0.732678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.6491i | 1.78626i | 0.449798 | + | 0.893130i | \(0.351496\pi\) | ||||
−0.449798 | + | 0.893130i | \(0.648504\pi\) | |||||||
\(110\) | − 11.1623i | − 1.06428i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 3.16228i | − 0.298807i | ||||||||
\(113\) | −19.3246 | −1.81790 | −0.908951 | − | 0.416904i | \(-0.863115\pi\) | ||||
−0.908951 | + | 0.416904i | \(0.863115\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1.81139i | − 0.168913i | ||||||||
\(116\) | −8.16228 | −0.757848 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.3246 | 0.950452 | ||||||||
\(119\) | 9.48683i | 0.869657i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.6491 | −1.42265 | ||||||||
\(122\) | − 6.16228i | − 0.557906i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.32456i | 0.567962i | ||||||||
\(125\) | − 11.5132i | − 1.02977i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.67544 | 0.503614 | 0.251807 | − | 0.967777i | \(-0.418975\pi\) | ||||
0.251807 | + | 0.967777i | \(0.418975\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.64911 | 0.755676 | 0.377838 | − | 0.925872i | \(-0.376668\pi\) | ||||
0.377838 | + | 0.925872i | \(0.376668\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.67544 | −0.318701 | ||||||||
\(134\) | −9.16228 | −0.791500 | ||||||||
\(135\) | 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 | \(-0.413564\pi\) | ||||
0.268221 | + | 0.963357i | \(0.413564\pi\) | |||||||
\(140\) | 6.83772 | 0.577893 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.837722 | 0.0703001 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 17.6491i | − 1.46568i | ||||||||
\(146\) | 1.00000 | 0.0827606 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 10.1623i | − 0.835334i | ||||||||
\(149\) | − 18.4868i | − 1.51450i | −0.653125 | − | 0.757250i | \(-0.726542\pi\) | ||||
0.653125 | − | 0.757250i | \(-0.273458\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.16228i | 0.582858i | 0.956592 | + | 0.291429i | \(0.0941307\pi\) | ||||
−0.956592 | + | 0.291429i | \(0.905869\pi\) | |||||||
\(152\) | −1.16228 | −0.0942732 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − 16.3246i | − 1.31547i | ||||||||
\(155\) | −13.6754 | −1.09844 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.48683 | 0.677323 | 0.338662 | − | 0.940908i | \(-0.390026\pi\) | ||||
0.338662 | + | 0.940908i | \(0.390026\pi\) | |||||||
\(158\) | − 4.00000i | − 0.318223i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.16228 | 0.170943 | ||||||||
\(161\) | − 2.64911i | − 0.208779i | ||||||||
\(162\) | 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 | ||||||||
\(166\) | −15.4868 | −1.20201 | ||||||||
\(167\) | − 12.0000i | − 0.928588i | −0.885681 | − | 0.464294i | \(-0.846308\pi\) | ||||
0.885681 | − | 0.464294i | \(-0.153692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6.48683 | −0.497517 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.83772 | 0.216374 | ||||||||
\(173\) | −2.64911 | −0.201408 | −0.100704 | − | 0.994916i | \(-0.532110\pi\) | ||||
−0.100704 | + | 0.994916i | \(0.532110\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 1.02633i | − 0.0775836i | ||||||||
\(176\) | − 5.16228i | − 0.389121i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.0000 | 0.899438 | ||||||||
\(179\) | −3.48683 | −0.260618 | −0.130309 | − | 0.991473i | \(-0.541597\pi\) | ||||
−0.130309 | + | 0.991473i | \(0.541597\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.1623 | −0.755356 | −0.377678 | − | 0.925937i | \(-0.623277\pi\) | ||||
−0.377678 | + | 0.925937i | \(0.623277\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − 0.837722i | − 0.0617577i | ||||||||
\(185\) | 21.9737 | 1.61554 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.4868i | 1.13251i | ||||||||
\(188\) | 11.1623i | 0.814093i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − 2.51317i | − 0.182324i | ||||||||
\(191\) | −1.67544 | −0.121231 | −0.0606155 | − | 0.998161i | \(-0.519306\pi\) | ||||
−0.0606155 | + | 0.998161i | \(0.519306\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.9737i | 1.29377i | 0.762586 | + | 0.646886i | \(0.223929\pi\) | ||||
−0.762586 | + | 0.646886i | \(0.776071\pi\) | |||||||
\(194\) | −4.00000 | −0.287183 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | − 18.9737i | − 1.35182i | −0.736985 | − | 0.675909i | \(-0.763751\pi\) | ||||
0.736985 | − | 0.675909i | \(-0.236249\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.4868 | 1.80671 | 0.903357 | − | 0.428890i | \(-0.141095\pi\) | ||||
0.903357 | + | 0.428890i | \(0.141095\pi\) | |||||||
\(200\) | − 0.324555i | − 0.0229495i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.1623i | 0.996454i | ||||||||
\(203\) | − 25.8114i | − 1.81160i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.48683 | 0.453060 | ||||||||
\(206\) | − 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 | \(0.543966\pi\) | |||||||
\(212\) | 6.48683 | 0.445518 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − 13.8114i | − 0.944127i | ||||||||
\(215\) | 6.13594i | 0.418468i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.0000 | −1.35769 | ||||||||
\(218\) | −18.6491 | −1.26308 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.1623 | 0.752561 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.3246i | 0.959243i | 0.877475 | + | 0.479622i | \(0.159226\pi\) | ||||
−0.877475 | + | 0.479622i | \(0.840774\pi\) | |||||||
\(224\) | 3.16228 | 0.211289 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − 19.3246i | − 1.28545i | ||||||||
\(227\) | 3.48683i | 0.231429i | 0.993283 | + | 0.115715i | \(0.0369158\pi\) | ||||
−0.993283 | + | 0.115715i | \(0.963084\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.67544i | 0.639371i | 0.947524 | + | 0.319686i | \(0.103577\pi\) | ||||
−0.947524 | + | 0.319686i | \(0.896423\pi\) | |||||||
\(230\) | 1.81139 | 0.119439 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 8.16228i | − 0.535880i | ||||||||
\(233\) | 8.64911 | 0.566622 | 0.283311 | − | 0.959028i | \(-0.408567\pi\) | ||||
0.283311 | + | 0.959028i | \(0.408567\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.1359 | −1.57446 | ||||||||
\(236\) | 10.3246i | 0.672071i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.48683 | −0.614940 | ||||||||
\(239\) | − 2.51317i | − 0.162563i | −0.996691 | − | 0.0812816i | \(-0.974099\pi\) | ||||
0.996691 | − | 0.0812816i | \(-0.0259013\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.675445i | 0.0435092i | 0.999763 | + | 0.0217546i | \(0.00692525\pi\) | ||||
−0.999763 | + | 0.0217546i | \(0.993075\pi\) | |||||||
\(242\) | − 15.6491i | − 1.00596i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.16228 | 0.394499 | ||||||||
\(245\) | 6.48683i | 0.414429i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.32456 | −0.401610 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.5132 | 0.728157 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 4.32456i | − 0.271882i | ||||||||
\(254\) | 5.67544i | 0.356109i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.9737 | 0.996410 | 0.498205 | − | 0.867059i | \(-0.333993\pi\) | ||||
0.498205 | + | 0.867059i | \(0.333993\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 32.1359 | 1.99683 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.64911i | 0.534344i | ||||||||
\(263\) | 21.4868 | 1.32493 | 0.662467 | − | 0.749091i | \(-0.269509\pi\) | ||||
0.662467 | + | 0.749091i | \(0.269509\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.0263i | 0.861631i | ||||||||
\(266\) | − 3.67544i | − 0.225356i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 9.16228i | − 0.559675i | ||||||||
\(269\) | −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 | \(0.0615281\pi\) | ||||
−0.981376 | + | 0.192095i | \(0.938472\pi\) | |||||||
\(272\) | −3.00000 | −0.181902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.00000 | −0.181237 | ||||||||
\(275\) | − 1.67544i | − 0.101033i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.8114 | 1.25044 | 0.625218 | − | 0.780451i | \(-0.285010\pi\) | ||||
0.625218 | + | 0.780451i | \(0.285010\pi\) | |||||||
\(278\) | 6.32456i | 0.379322i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.83772i | 0.408632i | ||||||||
\(281\) | 13.3246i | 0.794876i | 0.917629 | + | 0.397438i | \(0.130101\pi\) | ||||
−0.917629 | + | 0.397438i | \(0.869899\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.16228 | 0.544641 | 0.272320 | − | 0.962207i | \(-0.412209\pi\) | ||||
0.272320 | + | 0.962207i | \(0.412209\pi\) | |||||||
\(284\) | 0.837722i | 0.0497097i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.48683 | 0.559990 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 17.6491 | 1.03639 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.00000i | 0.0585206i | ||||||||
\(293\) | − 8.16228i | − 0.476845i | −0.971161 | − | 0.238423i | \(-0.923370\pi\) | ||||
0.971161 | − | 0.238423i | \(-0.0766304\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.3246 | −1.29979 | ||||||||
\(296\) | 10.1623 | 0.590670 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 18.4868 | 1.07091 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.97367i | 0.517234i | ||||||||
\(302\) | −7.16228 | −0.412143 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 1.16228i | − 0.0666612i | ||||||||
\(305\) | 13.3246i | 0.762962i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 7.48683i | − 0.427296i | −0.976911 | − | 0.213648i | \(-0.931465\pi\) | ||||
0.976911 | − | 0.213648i | \(-0.0685346\pi\) | |||||||
\(308\) | 16.3246 | 0.930178 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 13.6754i | − 0.776713i | ||||||||
\(311\) | 2.51317 | 0.142509 | 0.0712543 | − | 0.997458i | \(-0.477300\pi\) | ||||
0.0712543 | + | 0.997458i | \(0.477300\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.00000 | −0.226093 | −0.113047 | − | 0.993590i | \(-0.536061\pi\) | ||||
−0.113047 | + | 0.993590i | \(0.536061\pi\) | |||||||
\(314\) | 8.48683i | 0.478940i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | − 6.48683i | − 0.364337i | −0.983267 | − | 0.182168i | \(-0.941688\pi\) | ||||
0.983267 | − | 0.182168i | \(-0.0583116\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 42.1359i | − 2.35916i | ||||||||
\(320\) | 2.16228i | 0.120875i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.64911 | 0.147629 | ||||||||
\(323\) | 3.48683i | 0.194013i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.0000 | 0.886158 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.00000 | 0.165647 | ||||||||
\(329\) | −35.2982 | −1.94605 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 26.9737i | − 1.48261i | −0.671170 | − | 0.741303i | \(-0.734208\pi\) | ||||
0.671170 | − | 0.741303i | \(-0.265792\pi\) | |||||||
\(332\) | − 15.4868i | − 0.849950i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | 19.8114 | 1.08241 | ||||||||
\(336\) | 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 | ||||||||
\(340\) | − 6.48683i | − 0.351798i | ||||||||
\(341\) | −32.6491 | −1.76805 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 12.6491i | − 0.682988i | ||||||||
\(344\) | 2.83772i | 0.153000i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 2.64911i | − 0.142417i | ||||||||
\(347\) | −3.48683 | −0.187183 | −0.0935915 | − | 0.995611i | \(-0.529835\pi\) | ||||
−0.0935915 | + | 0.995611i | \(0.529835\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 30.6491i | − 1.64061i | −0.571927 | − | 0.820305i | \(-0.693804\pi\) | ||||
0.571927 | − | 0.820305i | \(-0.306196\pi\) | |||||||
\(350\) | 1.02633 | 0.0548599 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.16228 | 0.275150 | ||||||||
\(353\) | 16.6754i | 0.887544i | 0.896140 | + | 0.443772i | \(0.146360\pi\) | ||||
−0.896140 | + | 0.443772i | \(0.853640\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.81139 | −0.0961385 | ||||||||
\(356\) | 12.0000i | 0.635999i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 3.48683i | − 0.184285i | ||||||||
\(359\) | 28.4605i | 1.50209i | 0.660252 | + | 0.751044i | \(0.270449\pi\) | ||||
−0.660252 | + | 0.751044i | \(0.729551\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.6491 | 0.928901 | ||||||||
\(362\) | − 10.1623i | − 0.534117i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.16228 | −0.113179 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.51317 | −0.339985 | −0.169992 | − | 0.985445i | \(-0.554374\pi\) | ||||
−0.169992 | + | 0.985445i | \(0.554374\pi\) | |||||||
\(368\) | 0.837722 | 0.0436693 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.9737i | 1.14236i | ||||||||
\(371\) | 20.5132i | 1.06499i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.48683 | 0.128763 | 0.0643817 | − | 0.997925i | \(-0.479492\pi\) | ||||
0.0643817 | + | 0.997925i | \(0.479492\pi\) | |||||||
\(374\) | −15.4868 | −0.800805 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.1623 | −0.575651 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 30.3246i | − 1.55767i | −0.627230 | − | 0.778834i | \(-0.715811\pi\) | ||||
0.627230 | − | 0.778834i | \(-0.284189\pi\) | |||||||
\(380\) | 2.51317 | 0.128923 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 1.67544i | − 0.0857232i | ||||||||
\(383\) | − 6.97367i | − 0.356338i | −0.984000 | − | 0.178169i | \(-0.942983\pi\) | ||||
0.984000 | − | 0.178169i | \(-0.0570173\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 35.2982i | 1.79896i | ||||||||
\(386\) | −17.9737 | −0.914836 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 4.00000i | − 0.203069i | ||||||||
\(389\) | −6.48683 | −0.328895 | −0.164448 | − | 0.986386i | \(-0.552584\pi\) | ||||
−0.164448 | + | 0.986386i | \(0.552584\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.51317 | −0.127096 | ||||||||
\(392\) | 3.00000i | 0.151523i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.9737 | 0.955879 | ||||||||
\(395\) | 8.64911i | 0.435184i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.0000i | 1.30490i | 0.757831 | + | 0.652451i | \(0.226259\pi\) | ||||
−0.757831 | + | 0.652451i | \(0.773741\pi\) | |||||||
\(398\) | 25.4868i | 1.27754i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.324555 | 0.0162278 | ||||||||
\(401\) | 15.0000i | 0.749064i | 0.927214 | + | 0.374532i | \(0.122197\pi\) | ||||
−0.927214 | + | 0.374532i | \(0.877803\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.1623 | −0.704600 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 25.8114 | 1.28100 | ||||||||
\(407\) | 52.4605 | 2.60037 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 27.3246i | − 1.35111i | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
0.737309 | − | 0.675556i | \(-0.236096\pi\) | |||||||
\(410\) | 6.48683i | 0.320362i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.8114 | 0.778971 | ||||||||
\(413\) | −32.6491 | −1.60656 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 33.4868 | 1.64380 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 6.00000i | − 0.293470i | ||||||||
\(419\) | −6.97367 | −0.340686 | −0.170343 | − | 0.985385i | \(-0.554488\pi\) | ||||
−0.170343 | + | 0.985385i | \(0.554488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.1623i | 1.47002i | 0.678057 | + | 0.735010i | \(0.262822\pi\) | ||||
−0.678057 | + | 0.735010i | \(0.737178\pi\) | |||||||
\(422\) | − 4.00000i | − 0.194717i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.48683i | 0.315028i | ||||||||
\(425\) | −0.973666 | −0.0472297 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.4868i | 0.943034i | ||||||||
\(428\) | 13.8114 | 0.667599 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.13594 | −0.295901 | ||||||||
\(431\) | 9.48683i | 0.456965i | 0.973548 | + | 0.228482i | \(0.0733763\pi\) | ||||
−0.973548 | + | 0.228482i | \(0.926624\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.32456 | −0.159768 | −0.0798840 | − | 0.996804i | \(-0.525455\pi\) | ||||
−0.0798840 | + | 0.996804i | \(0.525455\pi\) | |||||||
\(434\) | − 20.0000i | − 0.960031i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − 18.6491i | − 0.893130i | ||||||||
\(437\) | − 0.973666i | − 0.0465768i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.51317 | 0.310857 | 0.155428 | − | 0.987847i | \(-0.450324\pi\) | ||||
0.155428 | + | 0.987847i | \(0.450324\pi\) | |||||||
\(440\) | 11.1623i | 0.532141i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.9473 | −1.23002 | ||||||||
\(446\) | −14.3246 | −0.678287 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.16228i | 0.149404i | ||||||||
\(449\) | − 32.6491i | − 1.54081i | −0.637557 | − | 0.770403i | \(-0.720055\pi\) | ||||
0.637557 | − | 0.770403i | \(-0.279945\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.4868 | 0.729246 | ||||||||
\(452\) | 19.3246 | 0.908951 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.48683 | −0.163645 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 9.32456i | − 0.436184i | −0.975928 | − | 0.218092i | \(-0.930017\pi\) | ||||
0.975928 | − | 0.218092i | \(-0.0699833\pi\) | |||||||
\(458\) | −9.67544 | −0.452104 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.81139i | 0.0844564i | ||||||||
\(461\) | − 0.486833i | − 0.0226741i | −0.999936 | − | 0.0113370i | \(-0.996391\pi\) | ||||
0.999936 | − | 0.0113370i | \(-0.00360877\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.83772i | 0.410724i | 0.978686 | + | 0.205362i | \(0.0658371\pi\) | ||||
−0.978686 | + | 0.205362i | \(0.934163\pi\) | |||||||
\(464\) | 8.16228 | 0.378924 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.64911i | 0.400662i | ||||||||
\(467\) | 37.8114 | 1.74970 | 0.874851 | − | 0.484392i | \(-0.160959\pi\) | ||||
0.874851 | + | 0.484392i | \(0.160959\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.9737 | 1.33788 | ||||||||
\(470\) | − 24.1359i | − 1.11331i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.3246 | −0.475226 | ||||||||
\(473\) | 14.6491i | 0.673567i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 0.377223i | − 0.0173082i | ||||||||
\(476\) | − 9.48683i | − 0.434828i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.51317 | 0.114950 | ||||||||
\(479\) | 24.0000i | 1.09659i | 0.836286 | + | 0.548294i | \(0.184723\pi\) | ||||
−0.836286 | + | 0.548294i | \(0.815277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.675445 | −0.0307657 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.6491 | 0.711323 | ||||||||
\(485\) | 8.64911 | 0.392736 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 5.48683i | − 0.248632i | −0.992243 | − | 0.124316i | \(-0.960326\pi\) | ||||
0.992243 | − | 0.124316i | \(-0.0396737\pi\) | |||||||
\(488\) | 6.16228i | 0.278953i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.48683 | −0.293045 | ||||||||
\(491\) | −25.8114 | −1.16485 | −0.582426 | − | 0.812884i | \(-0.697896\pi\) | ||||
−0.582426 | + | 0.812884i | \(0.697896\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.4868 | −1.10283 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 6.32456i | − 0.283981i | ||||||||
\(497\) | −2.64911 | −0.118829 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.6491i | 0.566252i | 0.959083 | + | 0.283126i | \(0.0913715\pi\) | ||||
−0.959083 | + | 0.283126i | \(0.908629\pi\) | |||||||
\(500\) | 11.5132i | 0.514884i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 12.0000i | − 0.535586i | ||||||||
\(503\) | 31.8114 | 1.41840 | 0.709200 | − | 0.705007i | \(-0.249056\pi\) | ||||
0.709200 | + | 0.705007i | \(0.249056\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 30.6228i | − 1.36270i | ||||||||
\(506\) | 4.32456 | 0.192250 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.67544 | −0.251807 | ||||||||
\(509\) | − 21.8377i | − 0.967940i | −0.875085 | − | 0.483970i | \(-0.839194\pi\) | ||||
0.875085 | − | 0.483970i | \(-0.160806\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.16228 | −0.139891 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.9737i | 0.704568i | ||||||||
\(515\) | 34.1886i | 1.50653i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −57.6228 | −2.53425 | ||||||||
\(518\) | 32.1359i | 1.41197i | ||||||||
\(519\) | 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 | ||||||||
\(523\) | 1.16228 | 0.0508229 | 0.0254114 | − | 0.999677i | \(-0.491910\pi\) | ||||
0.0254114 | + | 0.999677i | \(0.491910\pi\) | |||||||
\(524\) | −8.64911 | −0.377838 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.4868i | 0.936870i | ||||||||
\(527\) | 18.9737i | 0.826506i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2982 | −0.969488 | ||||||||
\(530\) | −14.0263 | −0.609265 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.67544 | 0.159351 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.8641i | 1.29114i | ||||||||
\(536\) | 9.16228 | 0.395750 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 6.00000i | − 0.258678i | ||||||||
\(539\) | 15.4868i | 0.667065i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 34.4868i | − 1.48270i | −0.671116 | − | 0.741352i | \(-0.734185\pi\) | ||||
0.671116 | − | 0.741352i | \(-0.265815\pi\) | |||||||
\(542\) | −6.32456 | −0.271663 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 3.00000i | − 0.128624i | ||||||||
\(545\) | 40.3246 | 1.72731 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.18861 | −0.0935783 | −0.0467891 | − | 0.998905i | \(-0.514899\pi\) | ||||
−0.0467891 | + | 0.998905i | \(0.514899\pi\) | |||||||
\(548\) | − 3.00000i | − 0.128154i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.67544 | 0.0714412 | ||||||||
\(551\) | − 9.48683i | − 0.404153i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.6491i | 0.537895i | ||||||||
\(554\) | 20.8114i | 0.884191i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.32456 | −0.268221 | ||||||||
\(557\) | − 0.486833i | − 0.0206278i | −0.999947 | − | 0.0103139i | \(-0.996717\pi\) | ||||
0.999947 | − | 0.0103139i | \(-0.00328307\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −6.83772 | −0.288947 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.3246 | −0.562062 | ||||||||
\(563\) | 15.3509 | 0.646963 | 0.323481 | − | 0.946235i | \(-0.395147\pi\) | ||||
0.323481 | + | 0.946235i | \(0.395147\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 41.7851i | 1.75791i | ||||||||
\(566\) | 9.16228i | 0.385119i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.837722 | −0.0351500 | ||||||||
\(569\) | −23.2982 | −0.976712 | −0.488356 | − | 0.872644i | \(-0.662403\pi\) | ||||
−0.488356 | + | 0.872644i | \(0.662403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.13594 | −0.340479 | −0.170239 | − | 0.985403i | \(-0.554454\pi\) | ||||
−0.170239 | + | 0.985403i | \(0.554454\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.48683i | 0.395973i | ||||||||
\(575\) | 0.271887 | 0.0113385 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 25.6491i | − 1.06779i | −0.845552 | − | 0.533893i | \(-0.820728\pi\) | ||||
0.845552 | − | 0.533893i | \(-0.179272\pi\) | |||||||
\(578\) | − 8.00000i | − 0.332756i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 17.6491i | 0.732839i | ||||||||
\(581\) | 48.9737 | 2.03177 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.4868i | 1.38688i | ||||||||
\(584\) | −1.00000 | −0.0413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.16228 | 0.337181 | ||||||||
\(587\) | 3.35089i | 0.138306i | 0.997606 | + | 0.0691530i | \(0.0220297\pi\) | ||||
−0.997606 | + | 0.0691530i | \(0.977970\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.35089 | −0.302888 | ||||||||
\(590\) | − 22.3246i | − 0.919087i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.1623i | 0.417667i | ||||||||
\(593\) | − 13.3246i | − 0.547174i | −0.961847 | − | 0.273587i | \(-0.911790\pi\) | ||||
0.961847 | − | 0.273587i | \(-0.0882101\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.5132 | 0.840958 | ||||||||
\(596\) | 18.4868i | 0.757250i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.6228 | −1.61894 | −0.809471 | − | 0.587159i | \(-0.800246\pi\) | ||||
−0.809471 | + | 0.587159i | \(0.800246\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.2982 | 0.664818 | 0.332409 | − | 0.943135i | \(-0.392139\pi\) | ||||
0.332409 | + | 0.943135i | \(0.392139\pi\) | |||||||
\(602\) | −8.97367 | −0.365739 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − 7.16228i | − 0.291429i | ||||||||
\(605\) | 33.8377i | 1.37570i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.2982 | −1.35153 | −0.675767 | − | 0.737116i | \(-0.736187\pi\) | ||||
−0.675767 | + | 0.737116i | \(0.736187\pi\) | |||||||
\(608\) | 1.16228 | 0.0471366 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.3246 | −0.539495 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.51317i | − 0.0611162i | −0.999533 | − | 0.0305581i | \(-0.990272\pi\) | ||||
0.999533 | − | 0.0305581i | \(-0.00972847\pi\) | |||||||
\(614\) | 7.48683 | 0.302144 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.3246i | 0.657735i | ||||||||
\(617\) | 36.6228i | 1.47438i | 0.675687 | + | 0.737189i | \(0.263847\pi\) | ||||
−0.675687 | + | 0.737189i | \(0.736153\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 0.649111i | − 0.0260900i | −0.999915 | − | 0.0130450i | \(-0.995848\pi\) | ||||
0.999915 | − | 0.0130450i | \(-0.00415246\pi\) | |||||||
\(620\) | 13.6754 | 0.549219 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.51317i | 0.100769i | ||||||||
\(623\) | −37.9473 | −1.52033 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.2719 | −0.930875 | ||||||||
\(626\) | − 4.00000i | − 0.159872i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.48683 | −0.338662 | ||||||||
\(629\) | − 30.4868i | − 1.21559i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.2982i | 1.00711i | 0.863964 | + | 0.503553i | \(0.167974\pi\) | ||||
−0.863964 | + | 0.503553i | \(0.832026\pi\) | |||||||
\(632\) | 4.00000i | 0.159111i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.48683 | 0.257625 | ||||||||
\(635\) | − 12.2719i | − 0.486995i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 42.1359 | 1.66818 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.16228 | −0.0854715 | ||||||||
\(641\) | 41.6491 | 1.64504 | 0.822520 | − | 0.568735i | \(-0.192567\pi\) | ||||
0.822520 | + | 0.568735i | \(0.192567\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 20.0000i | − 0.788723i | −0.918955 | − | 0.394362i | \(-0.870966\pi\) | ||||
0.918955 | − | 0.394362i | \(-0.129034\pi\) | |||||||
\(644\) | 2.64911i | 0.104390i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.48683 | −0.137188 | ||||||||
\(647\) | −15.3509 | −0.603506 | −0.301753 | − | 0.953386i | \(-0.597572\pi\) | ||||
−0.301753 | + | 0.953386i | \(0.597572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −53.2982 | −2.09214 | ||||||||
\(650\) | 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 | ||||||||
\(655\) | − 18.7018i | − 0.730739i | ||||||||
\(656\) | 3.00000i | 0.117130i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 35.2982i | − 1.37607i | ||||||||
\(659\) | 42.9737 | 1.67402 | 0.837008 | − | 0.547190i | \(-0.184303\pi\) | ||||
0.837008 | + | 0.547190i | \(0.184303\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.51317i | 0.292228i | 0.989268 | + | 0.146114i | \(0.0466767\pi\) | ||||
−0.989268 | + | 0.146114i | \(0.953323\pi\) | |||||||
\(662\) | 26.9737 | 1.04836 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.4868 | 0.601006 | ||||||||
\(665\) | 7.94733i | 0.308184i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.83772 | 0.264758 | ||||||||
\(668\) | 12.0000i | 0.464294i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 19.8114i | 0.765381i | ||||||||
\(671\) | 31.8114i | 1.22807i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.3246 | −1.05328 | −0.526642 | − | 0.850087i | \(-0.676549\pi\) | ||||
−0.526642 | + | 0.850087i | \(0.676549\pi\) | |||||||
\(674\) | − 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 | ||||||||
\(680\) | 6.48683 | 0.248759 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 32.6491i | − 1.25020i | ||||||||
\(683\) | − 27.6228i | − 1.05696i | −0.848947 | − | 0.528478i | \(-0.822763\pi\) | ||||
0.848947 | − | 0.528478i | \(-0.177237\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.48683 | 0.247849 | ||||||||
\(686\) | 12.6491 | 0.482945 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.83772 | −0.108187 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 2.83772i | − 0.107952i | −0.998542 | − | 0.0539760i | \(-0.982811\pi\) | ||||
0.998542 | − | 0.0539760i | \(-0.0171895\pi\) | |||||||
\(692\) | 2.64911 | 0.100704 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − 3.48683i | − 0.132358i | ||||||||
\(695\) | − 13.6754i | − 0.518739i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 9.00000i | − 0.340899i | ||||||||
\(698\) | 30.6491 | 1.16009 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.02633i | 0.0387918i | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.8114 | 0.445475 | ||||||||
\(704\) | 5.16228i | 0.194561i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.6754 | −0.627589 | ||||||||
\(707\) | − 44.7851i | − 1.68432i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 11.4605i | − 0.430408i | −0.976569 | − | 0.215204i | \(-0.930958\pi\) | ||||
0.976569 | − | 0.215204i | \(-0.0690417\pi\) | |||||||
\(710\) | − 1.81139i | − 0.0679802i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.0000 | −0.449719 | ||||||||
\(713\) | − 5.29822i | − 0.198420i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.48683 | 0.130309 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28.4605 | −1.06214 | ||||||||
\(719\) | −25.6754 | −0.957533 | −0.478766 | − | 0.877942i | \(-0.658916\pi\) | ||||
−0.478766 | + | 0.877942i | \(0.658916\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 50.0000i | 1.86210i | ||||||||
\(722\) | 17.6491i | 0.656832i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.1623 | 0.377678 | ||||||||
\(725\) | 2.64911 | 0.0983855 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.1623 | 0.562338 | 0.281169 | − | 0.959658i | \(-0.409278\pi\) | ||||
0.281169 | + | 0.959658i | \(0.409278\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − 2.16228i | − 0.0800295i | ||||||||
\(731\) | 8.51317 | 0.314871 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.4605i | 1.30976i | 0.755731 | + | 0.654882i | \(0.227282\pi\) | ||||
−0.755731 | + | 0.654882i | \(0.772718\pi\) | |||||||
\(734\) | − 6.51317i | − 0.240405i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.837722i | 0.0308789i | ||||||||
\(737\) | 47.2982 | 1.74225 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.6228i | 0.868978i | 0.900677 | + | 0.434489i | \(0.143071\pi\) | ||||
−0.900677 | + | 0.434489i | \(0.856929\pi\) | |||||||
\(740\) | −21.9737 | −0.807768 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20.5132 | −0.753062 | ||||||||
\(743\) | − 10.3246i | − 0.378771i | −0.981903 | − | 0.189386i | \(-0.939350\pi\) | ||||
0.981903 | − | 0.189386i | \(-0.0606496\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −39.9737 | −1.46452 | ||||||||
\(746\) | 2.48683i | 0.0910494i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 15.4868i | − 0.566255i | ||||||||
\(749\) | 43.6754i | 1.59587i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.7851 | 1.12336 | 0.561681 | − | 0.827354i | \(-0.310155\pi\) | ||||
0.561681 | + | 0.827354i | \(0.310155\pi\) | |||||||
\(752\) | − 11.1623i | − 0.407046i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.4868 | 0.563624 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.35089 | −0.0490989 | −0.0245495 | − | 0.999699i | \(-0.507815\pi\) | ||||
−0.0245495 | + | 0.999699i | \(0.507815\pi\) | |||||||
\(758\) | 30.3246 | 1.10144 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.51317i | 0.0911621i | ||||||||
\(761\) | 12.0000i | 0.435000i | 0.976060 | + | 0.217500i | \(0.0697902\pi\) | ||||
−0.976060 | + | 0.217500i | \(0.930210\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 58.9737 | 2.13499 | ||||||||
\(764\) | 1.67544 | 0.0606155 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.97367 | 0.251969 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 28.6491i | − 1.03311i | −0.856253 | − | 0.516557i | \(-0.827214\pi\) | ||||
0.856253 | − | 0.516557i | \(-0.172786\pi\) | |||||||
\(770\) | −35.2982 | −1.27206 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 17.9737i | − 0.646886i | ||||||||
\(773\) | − 2.64911i | − 0.0952819i | −0.998865 | − | 0.0476409i | \(-0.984830\pi\) | ||||
0.998865 | − | 0.0476409i | \(-0.0151703\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 2.05267i | − 0.0737340i | ||||||||
\(776\) | 4.00000 | 0.143592 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 6.48683i | − 0.232564i | ||||||||
\(779\) | 3.48683 | 0.124929 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.32456 | −0.154745 | ||||||||
\(782\) | − 2.51317i | − 0.0898707i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | − 18.3509i | − 0.654971i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 46.9737i | − 1.67443i | −0.546874 | − | 0.837215i | \(-0.684182\pi\) | ||||
0.546874 | − | 0.837215i | \(-0.315818\pi\) | |||||||
\(788\) | 18.9737i | 0.675909i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.64911 | −0.307722 | ||||||||
\(791\) | 61.1096i | 2.17281i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −26.0000 | −0.922705 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −25.4868 | −0.903357 | ||||||||
\(797\) | 18.9737 | 0.672082 | 0.336041 | − | 0.941847i | \(-0.390912\pi\) | ||||
0.336041 | + | 0.941847i | \(0.390912\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.4868i | 1.18468i | ||||||||
\(800\) | 0.324555i | 0.0114748i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.0000 | −0.529668 | ||||||||
\(803\) | −5.16228 | −0.182173 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.72811 | −0.201889 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 14.1623i | − 0.498227i | ||||||||
\(809\) | −3.00000 | −0.105474 | −0.0527372 | − | 0.998608i | \(-0.516795\pi\) | ||||
−0.0527372 | + | 0.998608i | \(0.516795\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 38.9737i | − 1.36855i | −0.729224 | − | 0.684275i | \(-0.760119\pi\) | ||||
0.729224 | − | 0.684275i | \(-0.239881\pi\) | |||||||
\(812\) | 25.8114i | 0.905802i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 52.4605i | 1.83874i | ||||||||
\(815\) | −34.5964 | −1.21186 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.29822i | 0.115390i | ||||||||
\(818\) | 27.3246 | 0.955381 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.48683 | −0.226530 | ||||||||
\(821\) | − 14.6491i | − 0.511257i | −0.966775 | − | 0.255629i | \(-0.917718\pi\) | ||||
0.966775 | − | 0.255629i | \(-0.0822825\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.70178 | −0.0941781 | −0.0470890 | − | 0.998891i | \(-0.514994\pi\) | ||||
−0.0470890 | + | 0.998891i | \(0.514994\pi\) | |||||||
\(824\) | 15.8114i | 0.550816i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − 32.6491i | − 1.13601i | ||||||||
\(827\) | − 30.9737i | − 1.07706i | −0.842606 | − | 0.538530i | \(-0.818980\pi\) | ||||
0.842606 | − | 0.538530i | \(-0.181020\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.83772 | −0.202752 | −0.101376 | − | 0.994848i | \(-0.532325\pi\) | ||||
−0.101376 | + | 0.994848i | \(0.532325\pi\) | |||||||
\(830\) | 33.4868i | 1.16234i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.00000 | 0.311832 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.9473 | −0.897944 | ||||||||
\(836\) | 6.00000 | 0.207514 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 6.97367i | − 0.240901i | ||||||||
\(839\) | 20.6491i | 0.712886i | 0.934317 | + | 0.356443i | \(0.116011\pi\) | ||||
−0.934317 | + | 0.356443i | \(0.883989\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.6228 | 1.29734 | ||||||||
\(842\) | −30.1623 | −1.03946 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.00000 | 0.137686 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 49.4868i | 1.70039i | ||||||||
\(848\) | −6.48683 | −0.222759 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 0.973666i | − 0.0333965i | ||||||||
\(851\) | 8.51317i | 0.291828i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.8641i | 0.371978i | 0.982552 | + | 0.185989i | \(0.0595489\pi\) | ||||
−0.982552 | + | 0.185989i | \(0.940451\pi\) | |||||||
\(854\) | −19.4868 | −0.666826 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.8114i | 0.472064i | ||||||||
\(857\) | −0.350889 | −0.0119862 | −0.00599308 | − | 0.999982i | \(-0.501908\pi\) | ||||
−0.00599308 | + | 0.999982i | \(0.501908\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.4868 | 1.62023 | 0.810115 | − | 0.586271i | \(-0.199405\pi\) | ||||
0.810115 | + | 0.586271i | \(0.199405\pi\) | |||||||
\(860\) | − 6.13594i | − 0.209234i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.48683 | −0.323123 | ||||||||
\(863\) | 16.1886i | 0.551067i | 0.961292 | + | 0.275533i | \(0.0888545\pi\) | ||||
−0.961292 | + | 0.275533i | \(0.911146\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.72811i | 0.194762i | ||||||||
\(866\) | − 3.32456i | − 0.112973i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20.0000 | 0.678844 | ||||||||
\(869\) | 20.6491i | 0.700473i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 18.6491 | 0.631539 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.973666 | 0.0329347 | ||||||||
\(875\) | −36.4078 | −1.23081 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.864056i | 0.0291771i | 0.999894 | + | 0.0145886i | \(0.00464385\pi\) | ||||
−0.999894 | + | 0.0145886i | \(0.995356\pi\) | |||||||
\(878\) | 6.51317i | 0.219809i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −11.1623 | −0.376280 | ||||||||
\(881\) | −27.9737 | −0.942457 | −0.471228 | − | 0.882011i | \(-0.656189\pi\) | ||||
−0.471228 | + | 0.882011i | \(0.656189\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.6491 | 1.23334 | 0.616670 | − | 0.787221i | \(-0.288481\pi\) | ||||
0.616670 | + | 0.787221i | \(0.288481\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.6754 | −0.862097 | −0.431049 | − | 0.902329i | \(-0.641856\pi\) | ||||
−0.431049 | + | 0.902329i | \(0.641856\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − 17.9473i | − 0.601934i | ||||||||
\(890\) | − 25.9473i | − 0.869757i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 14.3246i | − 0.479622i | ||||||||
\(893\) | −12.9737 | −0.434147 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.53950i | 0.252018i | ||||||||
\(896\) | −3.16228 | −0.105644 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 32.6491 | 1.08951 | ||||||||
\(899\) | − 51.6228i | − 1.72172i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.4605 | 0.648323 | ||||||||
\(902\) | 15.4868i | 0.515655i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.3246i | 0.642725i | ||||||||
\(905\) | 21.9737i | 0.730429i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.2719 | 1.73566 | 0.867830 | − | 0.496862i | \(-0.165514\pi\) | ||||
0.867830 | + | 0.496862i | \(0.165514\pi\) | |||||||
\(908\) | − 3.48683i | − 0.115715i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.9473 | −0.859673 | −0.429837 | − | 0.902907i | \(-0.641429\pi\) | ||||
−0.429837 | + | 0.902907i | \(0.641429\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 79.9473 | 2.64587 | ||||||||
\(914\) | 9.32456 | 0.308429 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 9.67544i | − 0.319686i | ||||||||
\(917\) | − 27.3509i | − 0.903206i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.6491 | 0.945047 | 0.472523 | − | 0.881318i | \(-0.343343\pi\) | ||||
0.472523 | + | 0.881318i | \(0.343343\pi\) | |||||||
\(920\) | −1.81139 | −0.0597197 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.486833 | 0.0160330 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.29822i | 0.108445i | ||||||||
\(926\) | −8.83772 | −0.290426 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.16228i | 0.267940i | ||||||||
\(929\) | − 46.9473i | − 1.54029i | −0.637868 | − | 0.770146i | \(-0.720183\pi\) | ||||
0.637868 | − | 0.770146i | \(-0.279817\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.48683i | 0.114276i | ||||||||
\(932\) | −8.64911 | −0.283311 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 37.8114i | 1.23723i | ||||||||
\(935\) | 33.4868 | 1.09514 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.2982 | −1.18581 | −0.592906 | − | 0.805272i | \(-0.702019\pi\) | ||||
−0.592906 | + | 0.805272i | \(0.702019\pi\) | |||||||
\(938\) | 28.9737i | 0.946024i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 24.1359 | 0.787228 | ||||||||
\(941\) | 52.5964i | 1.71460i | 0.514821 | + | 0.857298i | \(0.327858\pi\) | ||||
−0.514821 | + | 0.857298i | \(0.672142\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.51317i | 0.0818400i | ||||||||
\(944\) | − 10.3246i | − 0.336036i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.6491 | −0.476284 | ||||||||
\(947\) | 18.9737i | 0.616561i | 0.951295 | + | 0.308281i | \(0.0997536\pi\) | ||||
−0.951295 | + | 0.308281i | \(0.900246\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.377223 | 0.0122387 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.48683 | 0.307470 | ||||||||
\(953\) | 23.2982 | 0.754703 | 0.377352 | − | 0.926070i | \(-0.376835\pi\) | ||||
0.377352 | + | 0.926070i | \(0.376835\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.62278i | 0.117230i | ||||||||
\(956\) | 2.51317i | 0.0812816i | ||||||||
\(957\) | 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 | ||||||||
\(964\) | − 0.675445i | − 0.0217546i | ||||||||
\(965\) | 38.8641 | 1.25108 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 53.4868i | − 1.72002i | −0.510277 | − | 0.860010i | \(-0.670457\pi\) | ||||
0.510277 | − | 0.860010i | \(-0.329543\pi\) | |||||||
\(968\) | 15.6491i | 0.502981i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.64911i | 0.277706i | ||||||||
\(971\) | −18.9737 | −0.608894 | −0.304447 | − | 0.952529i | \(-0.598472\pi\) | ||||
−0.304447 | + | 0.952529i | \(0.598472\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 20.0000i | − 0.641171i | ||||||||
\(974\) | 5.48683 | 0.175809 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.16228 | −0.197250 | ||||||||
\(977\) | 21.0000i | 0.671850i | 0.941889 | + | 0.335925i | \(0.109049\pi\) | ||||
−0.941889 | + | 0.335925i | \(0.890951\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −61.9473 | −1.97985 | ||||||||
\(980\) | − 6.48683i | − 0.207214i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 25.8114i | − 0.823674i | ||||||||
\(983\) | 39.6228i | 1.26377i | 0.775062 | + | 0.631885i | \(0.217719\pi\) | ||||
−0.775062 | + | 0.631885i | \(0.782281\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41.0263 | −1.30721 | ||||||||
\(986\) | − 24.4868i | − 0.779820i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.37722 | −0.0755913 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.7851 | −1.35911 | −0.679556 | − | 0.733624i | \(-0.737828\pi\) | ||||
−0.679556 | + | 0.733624i | \(0.737828\pi\) | |||||||
\(992\) | 6.32456 | 0.200805 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − 2.64911i | − 0.0840247i | ||||||||
\(995\) | − 55.1096i | − 1.74709i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.53950 | −0.0804268 | −0.0402134 | − | 0.999191i | \(-0.512804\pi\) | ||||
−0.0402134 | + | 0.999191i | \(0.512804\pi\) | |||||||
\(998\) | −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.1351.3 | 4 | ||
3.2 | odd | 2 | 3042.2.b.k.1351.2 | 4 | |||
13.5 | odd | 4 | 3042.2.a.x.1.1 | 2 | |||
13.7 | odd | 12 | 234.2.h.e.55.2 | yes | 4 | ||
13.8 | odd | 4 | 3042.2.a.r.1.2 | 2 | |||
13.11 | odd | 12 | 234.2.h.e.217.2 | yes | 4 | ||
13.12 | even | 2 | inner | 3042.2.b.j.1351.2 | 4 | ||
39.5 | even | 4 | 3042.2.a.q.1.2 | 2 | |||
39.8 | even | 4 | 3042.2.a.w.1.1 | 2 | |||
39.11 | even | 12 | 234.2.h.d.217.1 | yes | 4 | ||
39.20 | even | 12 | 234.2.h.d.55.1 | ✓ | 4 | ||
39.38 | odd | 2 | 3042.2.b.k.1351.3 | 4 | |||
52.7 | even | 12 | 1872.2.t.n.289.2 | 4 | |||
52.11 | even | 12 | 1872.2.t.n.1153.2 | 4 | |||
156.11 | odd | 12 | 1872.2.t.p.1153.1 | 4 | |||
156.59 | odd | 12 | 1872.2.t.p.289.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
234.2.h.d.55.1 | ✓ | 4 | 39.20 | even | 12 | ||
234.2.h.d.217.1 | yes | 4 | 39.11 | even | 12 | ||
234.2.h.e.55.2 | yes | 4 | 13.7 | odd | 12 | ||
234.2.h.e.217.2 | yes | 4 | 13.11 | odd | 12 | ||
1872.2.t.n.289.2 | 4 | 52.7 | even | 12 | |||
1872.2.t.n.1153.2 | 4 | 52.11 | even | 12 | |||
1872.2.t.p.289.1 | 4 | 156.59 | odd | 12 | |||
1872.2.t.p.1153.1 | 4 | 156.11 | odd | 12 | |||
3042.2.a.q.1.2 | 2 | 39.5 | even | 4 | |||
3042.2.a.r.1.2 | 2 | 13.8 | odd | 4 | |||
3042.2.a.w.1.1 | 2 | 39.8 | even | 4 | |||
3042.2.a.x.1.1 | 2 | 13.5 | odd | 4 | |||
3042.2.b.j.1351.2 | 4 | 13.12 | even | 2 | inner | ||
3042.2.b.j.1351.3 | 4 | 1.1 | even | 1 | trivial | ||
3042.2.b.k.1351.2 | 4 | 3.2 | odd | 2 | |||
3042.2.b.k.1351.3 | 4 | 39.38 | odd | 2 |