Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(549,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bb (of order \(6\), degree \(2\), 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: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1049.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.1049 |
Dual form | 1300.2.bb.b.549.1 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | 0.228714 | − | 0.973494i | \(-0.426548\pi\) |
−0.728714 | + | 0.684819i | \(0.759881\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.866025 | − | 0.500000i | 0.327327 | − | 0.188982i | −0.327327 | − | 0.944911i | \(-0.606148\pi\) |
0.654654 | + | 0.755929i | \(0.272814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | − | 1.73205i | −0.333333 | − | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.46410 | + | 1.00000i | −0.960769 | + | 0.277350i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.59808 | − | 1.50000i | 0.630126 | − | 0.363803i | −0.150675 | − | 0.988583i | \(-0.548145\pi\) |
0.780801 | + | 0.624780i | \(0.214811\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50000 | + | 4.33013i | 0.573539 | + | 0.993399i | 0.996199 | + | 0.0871106i | \(0.0277634\pi\) |
−0.422659 | + | 0.906289i | \(0.638903\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.79423 | − | 4.50000i | −1.62521 | − | 0.938315i | −0.985496 | − | 0.169701i | \(-0.945720\pi\) |
−0.639713 | − | 0.768613i | \(-0.720947\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000i | 0.962250i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.50000 | + | 7.79423i | −0.835629 | + | 1.44735i | 0.0578882 | + | 0.998323i | \(0.481563\pi\) |
−0.893517 | + | 0.449029i | \(0.851770\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.59808 | − | 1.50000i | 0.452267 | − | 0.261116i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.06218 | − | 3.50000i | −0.996616 | − | 0.575396i | −0.0893706 | − | 0.995998i | \(-0.528486\pi\) |
−0.907245 | + | 0.420602i | \(0.861819\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.50000 | + | 0.866025i | 0.560449 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | + | 2.59808i | −0.234261 | + | 0.405751i | −0.959058 | − | 0.283211i | \(-0.908600\pi\) |
0.724797 | + | 0.688963i | \(0.241934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.866025 | + | 0.500000i | −0.132068 | + | 0.0762493i | −0.564578 | − | 0.825380i | \(-0.690961\pi\) |
0.432511 | + | 0.901629i | \(0.357628\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | + | 5.19615i | −0.428571 | + | 0.742307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.00000i | − | 0.662266i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.50000 | + | 7.79423i | 0.585850 | + | 1.01472i | 0.994769 | + | 0.102151i | \(0.0325726\pi\) |
−0.408919 | + | 0.912571i | \(0.634094\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | + | 0.866025i | 0.0640184 | + | 0.110883i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.73205 | − | 1.00000i | −0.218218 | − | 0.125988i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.33013 | + | 2.50000i | 0.529009 | + | 0.305424i | 0.740613 | − | 0.671932i | \(-0.234535\pi\) |
−0.211604 | + | 0.977356i | \(0.567869\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.50000 | + | 7.79423i | 0.541736 | + | 0.938315i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.50000 | − | 7.79423i | −0.534052 | − | 0.925005i | −0.999209 | − | 0.0397765i | \(-0.987335\pi\) |
0.465157 | − | 0.885228i | \(-0.345998\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000i | 0.234082i | 0.993127 | + | 0.117041i | \(0.0373409\pi\) | ||||
−0.993127 | + | 0.117041i | \(0.962659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.00000i | 0.341882i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.79423 | − | 4.50000i | 0.835629 | − | 0.482451i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.50000 | − | 2.59808i | 0.159000 | − | 0.275396i | −0.775509 | − | 0.631337i | \(-0.782506\pi\) |
0.934508 | + | 0.355942i | \(0.115840\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.50000 | + | 2.59808i | −0.262071 | + | 0.272352i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.92820 | − | 4.00000i | −0.718421 | − | 0.414781i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.7224 | + | 8.50000i | −1.49484 | + | 0.863044i | −0.999982 | − | 0.00593185i | \(-0.998112\pi\) |
−0.494854 | + | 0.868976i | \(0.664778\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.00000 | 0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.50000 | + | 12.9904i | −0.746278 | + | 1.29259i | 0.203317 | + | 0.979113i | \(0.434828\pi\) |
−0.949595 | + | 0.313478i | \(0.898506\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000i | 0.788263i | 0.919054 | + | 0.394132i | \(0.128955\pi\) | ||||
−0.919054 | + | 0.394132i | \(0.871045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.59808 | − | 1.50000i | −0.251166 | − | 0.145010i | 0.369132 | − | 0.929377i | \(-0.379655\pi\) |
−0.620298 | + | 0.784366i | \(0.712988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.50000 | + | 6.06218i | 0.332205 | + | 0.575396i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.9904 | + | 7.50000i | −1.22203 | + | 0.705541i | −0.965351 | − | 0.260955i | \(-0.915962\pi\) |
−0.256681 | + | 0.966496i | \(0.582629\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.19615 | + | 5.00000i | 0.480384 | + | 0.462250i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.50000 | − | 2.59808i | 0.137505 | − | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.59808 | − | 1.50000i | 0.234261 | − | 0.135250i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.7224 | + | 8.50000i | 1.30640 | + | 0.754253i | 0.981494 | − | 0.191492i | \(-0.0613325\pi\) |
0.324910 | + | 0.945745i | \(0.394666\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.00000 | 0.0880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.33013 | + | 2.50000i | 0.375470 | + | 0.216777i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.59808 | − | 1.50000i | 0.221969 | − | 0.128154i | −0.384893 | − | 0.922961i | \(-0.625762\pi\) |
0.606861 | + | 0.794808i | \(0.292428\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50000 | + | 4.33013i | 0.212047 | + | 0.367277i | 0.952355 | − | 0.304991i | \(-0.0986536\pi\) |
−0.740308 | + | 0.672268i | \(0.765320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.59808 | − | 10.5000i | 0.217262 | − | 0.878054i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.19615 | − | 3.00000i | 0.428571 | − | 0.247436i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.50000 | − | 7.79423i | −0.368654 | − | 0.638528i | 0.620701 | − | 0.784047i | \(-0.286848\pi\) |
−0.989355 | + | 0.145519i | \(0.953515\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.0000 | 1.62758 | 0.813788 | − | 0.581161i | \(-0.197401\pi\) | ||||
0.813788 | + | 0.581161i | \(0.197401\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.19615 | − | 3.00000i | −0.420084 | − | 0.242536i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 14.0000i | − | 1.11732i | −0.829396 | − | 0.558661i | \(-0.811315\pi\) | ||
0.829396 | − | 0.558661i | \(-0.188685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.00000 | − | 5.19615i | 0.237915 | − | 0.412082i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.00000 | −0.709299 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.866025 | + | 0.500000i | −0.0678323 | + | 0.0391630i | −0.533533 | − | 0.845780i | \(-0.679136\pi\) |
0.465700 | + | 0.884943i | \(0.345802\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.9904 | − | 7.50000i | −1.00523 | − | 0.580367i | −0.0954356 | − | 0.995436i | \(-0.530424\pi\) |
−0.909790 | + | 0.415068i | \(0.863758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000 | − | 6.92820i | 0.846154 | − | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.00000 | − | 8.66025i | 0.382360 | − | 0.662266i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.1865 | − | 10.5000i | 1.38270 | − | 0.798300i | 0.390218 | − | 0.920722i | \(-0.372399\pi\) |
0.992478 | + | 0.122422i | \(0.0390662\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 9.00000i | − | 0.676481i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.50000 | − | 12.9904i | 0.560576 | − | 0.970947i | −0.436870 | − | 0.899525i | \(-0.643913\pi\) |
0.997446 | − | 0.0714220i | \(-0.0227537\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.00000i | − | 0.0739221i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.00000i | 0.658145i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.50000 | + | 4.33013i | 0.181848 | + | 0.314970i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.50000 | + | 2.59808i | 0.108536 | + | 0.187990i | 0.915177 | − | 0.403051i | \(-0.132050\pi\) |
−0.806641 | + | 0.591041i | \(0.798717\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.33013 | − | 2.50000i | −0.311689 | − | 0.179954i | 0.335993 | − | 0.941865i | \(-0.390928\pi\) |
−0.647682 | + | 0.761911i | \(0.724262\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.59808 | − | 1.50000i | −0.185105 | − | 0.106871i | 0.404584 | − | 0.914501i | \(-0.367416\pi\) |
−0.589689 | + | 0.807630i | \(0.700750\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.50000 | − | 6.06218i | −0.248108 | − | 0.429736i | 0.714893 | − | 0.699234i | \(-0.246476\pi\) |
−0.963001 | + | 0.269498i | \(0.913142\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.50000 | − | 4.33013i | −0.176336 | − | 0.305424i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.00000i | 0.631676i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.0000i | 1.25109i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.0000 | −1.03757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.5000 | − | 21.6506i | 0.860535 | − | 1.49049i | −0.0108774 | − | 0.999941i | \(-0.503462\pi\) |
0.871413 | − | 0.490550i | \(-0.163204\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.00000i | 0.616670i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.92820 | − | 4.00000i | 0.470317 | − | 0.271538i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.00000 | − | 1.73205i | 0.0675737 | − | 0.117041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.50000 | + | 7.79423i | −0.504505 | + | 0.524297i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.4545 | + | 9.50000i | 1.10187 | + | 0.636167i | 0.936713 | − | 0.350100i | \(-0.113852\pi\) |
0.165161 | + | 0.986267i | \(0.447186\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.9904 | + | 7.50000i | −0.862202 | + | 0.497792i | −0.864749 | − | 0.502204i | \(-0.832523\pi\) |
0.00254715 | + | 0.999997i | \(0.499189\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0000 | 1.45380 | 0.726900 | − | 0.686743i | \(-0.240960\pi\) | ||||
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.50000 | − | 2.59808i | 0.0986928 | − | 0.170941i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6.00000i | − | 0.393073i | −0.980497 | − | 0.196537i | \(-0.937031\pi\) | ||
0.980497 | − | 0.196537i | \(-0.0629694\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.92820 | + | 4.00000i | 0.450035 | + | 0.259828i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5000 | − | 19.9186i | −0.740780 | − | 1.28307i | −0.952141 | − | 0.305661i | \(-0.901123\pi\) |
0.211360 | − | 0.977408i | \(-0.432211\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.8564 | − | 8.00000i | 0.888889 | − | 0.513200i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.9904 | − | 12.5000i | −0.826558 | − | 0.795356i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.50000 | − | 7.79423i | −0.284037 | − | 0.491967i | 0.688338 | − | 0.725390i | \(-0.258341\pi\) |
−0.972375 | + | 0.233423i | \(0.925007\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.3827 | − | 13.5000i | 1.47006 | − | 0.848738i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.3827 | − | 13.5000i | −1.45857 | − | 0.842107i | −0.459631 | − | 0.888110i | \(-0.652018\pi\) |
−0.998941 | + | 0.0460033i | \(0.985352\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.00000 | −0.434959 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.0000 | 1.11417 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.59808 | + | 1.50000i | 0.160204 | + | 0.0924940i | 0.577959 | − | 0.816066i | \(-0.303849\pi\) |
−0.417755 | + | 0.908560i | \(0.637183\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.59808 | + | 1.50000i | −0.159000 | + | 0.0917985i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.5000 | − | 18.1865i | −0.640196 | − | 1.10885i | −0.985389 | − | 0.170321i | \(-0.945520\pi\) |
0.345192 | − | 0.938532i | \(-0.387814\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.50000 | − | 11.2583i | 0.394847 | − | 0.683895i | −0.598235 | − | 0.801321i | \(-0.704131\pi\) |
0.993082 | + | 0.117426i | \(0.0374643\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.46410 | − | 1.00000i | 0.209657 | − | 0.0605228i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.4545 | − | 9.50000i | 0.988654 | − | 0.570800i | 0.0837823 | − | 0.996484i | \(-0.473300\pi\) |
0.904872 | + | 0.425684i | \(0.139967\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.00000 | − | 13.8564i | −0.478947 | − | 0.829561i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.7224 | − | 8.50000i | −0.875158 | − | 0.505273i | −0.00609896 | − | 0.999981i | \(-0.501941\pi\) |
−0.869059 | + | 0.494709i | \(0.835275\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.00000i | 0.177084i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.0000 | 0.996558 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.59808 | + | 1.50000i | −0.151781 | + | 0.0876309i | −0.573967 | − | 0.818878i | \(-0.694596\pi\) |
0.422186 | + | 0.906509i | \(0.361263\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.9904 | − | 7.50000i | −0.753778 | − | 0.435194i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 31.5000 | + | 7.79423i | 1.82169 | + | 0.450752i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.500000 | + | 0.866025i | −0.0288195 | + | 0.0499169i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.9904 | − | 7.50000i | 0.746278 | − | 0.430864i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000i | 0.228292i | 0.993464 | + | 0.114146i | \(0.0364132\pi\) | ||||
−0.993464 | + | 0.114146i | \(0.963587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | − | 6.92820i | 0.227552 | − | 0.394132i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 10.0000i | − | 0.565233i | −0.959233 | − | 0.282617i | \(-0.908798\pi\) | ||
0.959233 | − | 0.282617i | \(-0.0912024\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.0000i | 1.01098i | 0.862832 | + | 0.505490i | \(0.168688\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.5000 | − | 23.3827i | −0.755855 | − | 1.30918i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.50000 | + | 2.59808i | 0.0837218 | + | 0.145010i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.9904 | + | 7.50000i | 0.722804 | + | 0.417311i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.1244 | + | 7.00000i | 0.670478 | + | 0.387101i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.50000 | + | 16.4545i | 0.522167 | + | 0.904420i | 0.999667 | + | 0.0257885i | \(0.00820965\pi\) |
−0.477500 | + | 0.878632i | \(0.658457\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.0000i | 0.767195i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0000i | 1.19842i | 0.800593 | + | 0.599208i | \(0.204518\pi\) | ||||
−0.800593 | + | 0.599208i | \(0.795482\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.0000 | 0.814688 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | + | 20.7846i | −0.649836 | + | 1.12555i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000i | 0.701934i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.79423 | − | 4.50000i | 0.418416 | − | 0.241573i | −0.275983 | − | 0.961162i | \(-0.589003\pi\) |
0.694399 | + | 0.719590i | \(0.255670\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.5000 | − | 30.3109i | 0.936754 | − | 1.62250i | 0.165277 | − | 0.986247i | \(-0.447148\pi\) |
0.771477 | − | 0.636257i | \(-0.219518\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | − | 17.3205i | −0.266880 | − | 0.924500i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.3827 | + | 13.5000i | 1.24453 | + | 0.718532i | 0.970014 | − | 0.243049i | \(-0.0781475\pi\) |
0.274521 | + | 0.961581i | \(0.411481\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.59808 | + | 1.50000i | −0.137505 | + | 0.0793884i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | + | 5.19615i | −0.157895 | + | 0.273482i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.00000i | − | 0.104973i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.7224 | + | 8.50000i | 0.768505 | + | 0.443696i | 0.832341 | − | 0.554264i | \(-0.187000\pi\) |
−0.0638362 | + | 0.997960i | \(0.520334\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.00000 | + | 5.19615i | 0.155752 | + | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.33013 | − | 2.50000i | 0.224205 | − | 0.129445i | −0.383691 | − | 0.923462i | \(-0.625347\pi\) |
0.607896 | + | 0.794017i | \(0.292014\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.79423 | − | 31.5000i | 0.401423 | − | 1.62233i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.50000 | − | 9.52628i | 0.282516 | − | 0.489332i | −0.689488 | − | 0.724297i | \(-0.742164\pi\) |
0.972004 | + | 0.234965i | \(0.0754976\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.50000 | − | 14.7224i | −0.435468 | − | 0.754253i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.1865 | + | 10.5000i | −0.929288 | + | 0.536525i | −0.886586 | − | 0.462563i | \(-0.846930\pi\) |
−0.0427020 | + | 0.999088i | \(0.513597\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.73205 | + | 1.00000i | 0.0880451 | + | 0.0508329i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.0000 | −1.36545 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.1147 | + | 14.5000i | −1.26047 | + | 0.727734i | −0.973166 | − | 0.230105i | \(-0.926093\pi\) |
−0.287307 | + | 0.957839i | \(0.592760\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.50000 | − | 4.33013i | −0.125157 | − | 0.216777i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.50000 | + | 12.9904i | −0.374532 | + | 0.648709i | −0.990257 | − | 0.139253i | \(-0.955530\pi\) |
0.615725 | + | 0.787961i | \(0.288863\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.7128 | + | 8.00000i | −1.38047 | + | 0.398508i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.1865 | − | 10.5000i | 0.901473 | − | 0.520466i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.5000 | − | 21.6506i | −0.618085 | − | 1.07056i | −0.989835 | − | 0.142222i | \(-0.954575\pi\) |
0.371750 | − | 0.928333i | \(-0.378758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.00000 | −0.147979 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.79423 | + | 4.50000i | 0.383529 | + | 0.221431i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 5.00000i | − | 0.244851i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.5000 | + | 18.1865i | −0.512959 | + | 0.888470i | 0.486928 | + | 0.873442i | \(0.338117\pi\) |
−0.999887 | + | 0.0150285i | \(0.995216\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.00000 | 0.0974740 | 0.0487370 | − | 0.998812i | \(-0.484480\pi\) | ||||
0.0487370 | + | 0.998812i | \(0.484480\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.866025 | + | 0.500000i | 0.0419099 | + | 0.0241967i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.50000 | + | 7.79423i | −0.362103 | + | 0.376309i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.50000 | + | 2.59808i | −0.0722525 | + | 0.125145i | −0.899888 | − | 0.436121i | \(-0.856352\pi\) |
0.827636 | + | 0.561266i | \(0.189685\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.33013 | − | 2.50000i | 0.208093 | − | 0.120142i | −0.392332 | − | 0.919824i | \(-0.628332\pi\) |
0.600425 | + | 0.799681i | \(0.294998\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 45.0000i | − | 2.15264i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.500000 | + | 0.866025i | −0.0238637 | + | 0.0413331i | −0.877711 | − | 0.479191i | \(-0.840930\pi\) |
0.853847 | + | 0.520524i | \(0.174263\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.0000 | 0.571429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.0000i | 0.570137i | 0.958507 | + | 0.285069i | \(0.0920164\pi\) | ||||
−0.958507 | + | 0.285069i | \(0.907984\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.00000i | 0.425685i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.50000 | + | 12.9904i | 0.353947 | + | 0.613054i | 0.986937 | − | 0.161106i | \(-0.0515060\pi\) |
−0.632990 | + | 0.774160i | \(0.718173\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.50000 | − | 7.79423i | −0.211897 | − | 0.367016i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.3205 | − | 10.0000i | −0.813788 | − | 0.469841i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.5070 | + | 20.5000i | 1.66095 | + | 0.958950i | 0.972263 | + | 0.233890i | \(0.0751456\pi\) |
0.688686 | + | 0.725059i | \(0.258188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.50000 | + | 12.9904i | 0.350070 | + | 0.606339i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.50000 | − | 12.9904i | −0.349310 | − | 0.605022i | 0.636817 | − | 0.771015i | \(-0.280251\pi\) |
−0.986127 | + | 0.165992i | \(0.946917\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 40.0000i | − | 1.85896i | −0.368875 | − | 0.929479i | \(-0.620257\pi\) | ||
0.368875 | − | 0.929479i | \(-0.379743\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.0000i | 0.555294i | 0.960683 | + | 0.277647i | \(0.0895545\pi\) | ||||
−0.960683 | + | 0.277647i | \(0.910445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.00000 | 0.230879 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.00000 | + | 12.1244i | −0.322543 | + | 0.558661i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 3.00000i | − | 0.137940i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.3923 | − | 6.00000i | 0.475831 | − | 0.274721i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.50000 | − | 12.9904i | 0.342684 | − | 0.593546i | −0.642246 | − | 0.766498i | \(-0.721997\pi\) |
0.984930 | + | 0.172953i | \(0.0553307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.5000 | + | 6.06218i | 1.11710 | + | 0.276412i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.79423 | + | 4.50000i | 0.354650 | + | 0.204757i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.3109 | + | 17.5000i | −1.37352 | + | 0.793001i | −0.991369 | − | 0.131100i | \(-0.958149\pi\) |
−0.382148 | + | 0.924101i | \(0.624816\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.00000 | 0.0452216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.50000 | + | 12.9904i | −0.338470 | + | 0.586248i | −0.984145 | − | 0.177365i | \(-0.943243\pi\) |
0.645675 | + | 0.763612i | \(0.276576\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.0000i | 1.21602i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.79423 | − | 4.50000i | −0.349619 | − | 0.201853i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.50000 | + | 12.9904i | 0.335075 | + | 0.580367i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.7750 | − | 19.5000i | 1.50595 | − | 0.869462i | 0.505976 | − | 0.862547i | \(-0.331132\pi\) |
0.999976 | − | 0.00691465i | \(-0.00220102\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.9904 | + | 0.500000i | −0.576923 | + | 0.0222058i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.5000 | + | 28.5788i | −0.731350 | + | 1.26673i | 0.224957 | + | 0.974369i | \(0.427776\pi\) |
−0.956306 | + | 0.292366i | \(0.905557\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.00000 | + | 1.73205i | 0.0442374 | + | 0.0766214i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −21.6506 | + | 12.5000i | −0.955899 | + | 0.551888i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.0000 | −0.921798 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.33013 | − | 2.50000i | −0.189343 | − | 0.109317i | 0.402332 | − | 0.915494i | \(-0.368200\pi\) |
−0.591675 | + | 0.806177i | \(0.701533\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.7846 | − | 12.0000i | 0.905392 | − | 0.522728i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29.0000 | + | 50.2295i | 1.26087 | + | 2.18389i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.00000 | − | 15.5885i | 0.390567 | − | 0.676481i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.59808 | − | 10.5000i | 0.112535 | − | 0.454805i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.9904 | + | 7.50000i | −0.560576 | + | 0.323649i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.00000 | − | 15.5885i | −0.387657 | − | 0.671442i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.66025 | + | 5.00000i | 0.371647 | + | 0.214571i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.0000i | 1.19719i | 0.801050 | + | 0.598597i | \(0.204275\pi\) | ||||
−0.801050 | + | 0.598597i | \(0.795725\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.00000 | − | 1.73205i | 0.0426790 | − | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −45.0000 | −1.91706 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.92820 | + | 4.00000i | −0.294617 | + | 0.170097i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.7750 | − | 19.5000i | −1.43109 | − | 0.826242i | −0.433888 | − | 0.900967i | \(-0.642859\pi\) |
−0.997204 | + | 0.0747252i | \(0.976192\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.50000 | − | 2.59808i | 0.105739 | − | 0.109887i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.50000 | − | 7.79423i | 0.189990 | − | 0.329073i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.5788 | + | 16.5000i | −1.20445 | + | 0.695392i | −0.961542 | − | 0.274656i | \(-0.911436\pi\) |
−0.242912 | + | 0.970048i | \(0.578103\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.5000 | + | 28.5788i | −0.691716 | + | 1.19809i | 0.279559 | + | 0.960128i | \(0.409812\pi\) |
−0.971275 | + | 0.237959i | \(0.923522\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.0000 | 1.84134 | 0.920671 | − | 0.390339i | \(-0.127642\pi\) | ||||
0.920671 | + | 0.390339i | \(0.127642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 3.00000i | − | 0.125327i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.0000i | 0.915872i | 0.888985 | + | 0.457936i | \(0.151411\pi\) | ||||
−0.888985 | + | 0.457936i | \(0.848589\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.50000 | + | 4.33013i | 0.103896 | + | 0.179954i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.5885 | − | 9.00000i | −0.645608 | − | 0.372742i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.3827 | − | 13.5000i | −0.965107 | − | 0.557205i | −0.0673658 | − | 0.997728i | \(-0.521459\pi\) |
−0.897741 | + | 0.440524i | \(0.854793\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.0000 | + | 34.6410i | 0.824086 | + | 1.42736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.50000 | + | 2.59808i | 0.0617018 | + | 0.106871i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 6.00000i | − | 0.246390i | −0.992382 | − | 0.123195i | \(-0.960686\pi\) | ||
0.992382 | − | 0.123195i | \(-0.0393141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.00000i | 0.286491i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.500000 | − | 0.866025i | 0.0203954 | − | 0.0353259i | −0.855648 | − | 0.517559i | \(-0.826841\pi\) |
0.876043 | + | 0.482233i | \(0.160174\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 10.0000i | − | 0.407231i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.9186 | + | 11.5000i | −0.808470 | + | 0.466771i | −0.846424 | − | 0.532509i | \(-0.821249\pi\) |
0.0379540 | + | 0.999279i | \(0.487916\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.50000 | − | 7.79423i | 0.182349 | − | 0.315838i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.1147 | − | 14.5000i | −1.01437 | − | 0.585649i | −0.101905 | − | 0.994794i | \(-0.532494\pi\) |
−0.912470 | + | 0.409145i | \(0.865827\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.3827 | − | 13.5000i | 0.941351 | − | 0.543490i | 0.0509678 | − | 0.998700i | \(-0.483769\pi\) |
0.890384 | + | 0.455211i | \(0.150436\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.0000 | 1.12542 | 0.562708 | − | 0.826656i | \(-0.309760\pi\) | ||||
0.562708 | + | 0.826656i | \(0.309760\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.5000 | − | 38.9711i | 0.902894 | − | 1.56386i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 3.00000i | − | 0.120192i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.9904 | + | 7.50000i | 0.518786 | + | 0.299521i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.0000 | −0.837325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.50000 | + | 6.06218i | 0.139333 | + | 0.241331i | 0.927244 | − | 0.374457i | \(-0.122171\pi\) |
−0.787911 | + | 0.615789i | \(0.788838\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.6506 | + | 12.5000i | −0.860535 | + | 0.496830i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.19615 | − | 21.0000i | 0.205879 | − | 0.832050i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.00000 | + | 15.5885i | −0.356034 | + | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.50000 | − | 2.59808i | −0.0592464 | − | 0.102618i | 0.834881 | − | 0.550431i | \(-0.185536\pi\) |
−0.894127 | + | 0.447813i | \(0.852203\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.6506 | + | 12.5000i | −0.853818 | + | 0.492952i | −0.861937 | − | 0.507015i | \(-0.830749\pi\) |
0.00811944 | + | 0.999967i | \(0.497415\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.3827 | − | 13.5000i | −0.919268 | − | 0.530740i | −0.0358667 | − | 0.999357i | \(-0.511419\pi\) |
−0.883402 | + | 0.468617i | \(0.844753\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.0000 | −1.05984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.00000 | −0.313545 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.3827 | + | 13.5000i | 0.915035 | + | 0.528296i | 0.882048 | − | 0.471160i | \(-0.156165\pi\) |
0.0329874 | + | 0.999456i | \(0.489498\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.46410 | − | 2.00000i | 0.135147 | − | 0.0780274i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.5000 | + | 38.9711i | 0.876476 | + | 1.51810i | 0.855183 | + | 0.518327i | \(0.173445\pi\) |
0.0212930 | + | 0.999773i | \(0.493222\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.5000 | + | 30.3109i | −0.680671 | + | 1.17896i | 0.294105 | + | 0.955773i | \(0.404978\pi\) |
−0.974776 | + | 0.223184i | \(0.928355\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.3923 | − | 3.00000i | 0.403604 | − | 0.116510i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 70.1481 | − | 40.5000i | 2.71614 | − | 1.56817i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.50000 | − | 16.4545i | −0.367291 | − | 0.636167i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.00000 | −0.115814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.4545 | + | 9.50000i | 0.634274 | + | 0.366198i | 0.782405 | − | 0.622770i | \(-0.213993\pi\) |
−0.148132 | + | 0.988968i | \(0.547326\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.0000i | 0.691796i | 0.938272 | + | 0.345898i | \(0.112426\pi\) | ||||
−0.938272 | + | 0.345898i | \(0.887574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.50000 | + | 14.7224i | −0.326200 | + | 0.564995i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.0000 | 0.574801 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.1865 | + | 10.5000i | −0.695888 | + | 0.401771i | −0.805814 | − | 0.592168i | \(-0.798272\pi\) |
0.109926 | + | 0.993940i | \(0.464939\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.0526 | − | 11.0000i | −0.726900 | − | 0.419676i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.00000 | − | 20.7846i | −0.228582 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.5000 | + | 19.9186i | −0.437481 | + | 0.757739i | −0.997494 | − | 0.0707446i | \(-0.977462\pi\) |
0.560014 | + | 0.828483i | \(0.310796\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.19615 | − | 3.00000i | 0.197386 | − | 0.113961i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000i | 0.340899i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.00000 | + | 5.19615i | −0.113470 | + | 0.196537i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 35.0000i | − | 1.32005i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.0000i | 0.564133i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.5000 | + | 30.3109i | 0.657226 | + | 1.13835i | 0.981331 | + | 0.192328i | \(0.0616038\pi\) |
−0.324104 | + | 0.946021i | \(0.605063\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000 | + | 13.8564i | 0.300023 | + | 0.519656i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −62.3538 | − | 36.0000i | −2.33517 | − | 1.34821i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.7846 | + | 12.0000i | 0.776215 | + | 0.448148i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.5000 | + | 38.9711i | 0.839108 | + | 1.45338i | 0.890641 | + | 0.454707i | \(0.150256\pi\) |
−0.0515326 | + | 0.998671i | \(0.516411\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00000 | + | 6.92820i | 0.148968 | + | 0.258020i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.0000i | 0.855379i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.00000i | − | 0.296704i | −0.988935 | − | 0.148352i | \(-0.952603\pi\) | ||
0.988935 | − | 0.148352i | \(-0.0473968\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.50000 | + | 2.59808i | −0.0554795 | + | 0.0960933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 34.0000i | − | 1.25582i | −0.778287 | − | 0.627909i | \(-0.783911\pi\) | ||
0.778287 | − | 0.627909i | \(-0.216089\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.9904 | + | 7.50000i | −0.478507 | + | 0.276266i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.50000 | − | 9.52628i | 0.202321 | − | 0.350430i | −0.746955 | − | 0.664875i | \(-0.768485\pi\) |
0.949276 | + | 0.314445i | \(0.101818\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.00000 | + | 17.3205i | 0.183680 | + | 0.636285i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.5788 | − | 16.5000i | −1.04846 | − | 0.605326i | −0.126239 | − | 0.992000i | \(-0.540291\pi\) |
−0.922217 | + | 0.386674i | \(0.873624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.00000 | −0.109618 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.50000 | − | 11.2583i | 0.237188 | − | 0.410822i | −0.722718 | − | 0.691143i | \(-0.757107\pi\) |
0.959906 | + | 0.280321i | \(0.0904408\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.00000i | 0.327978i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.33013 | + | 2.50000i | 0.157381 | + | 0.0908640i | 0.576622 | − | 0.817011i | \(-0.304370\pi\) |
−0.419241 | + | 0.907875i | \(0.637704\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −27.0000 | −0.980038 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.50000 | + | 7.79423i | 0.163125 | + | 0.282541i | 0.935988 | − | 0.352032i | \(-0.114509\pi\) |
−0.772863 | + | 0.634573i | \(0.781176\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.1244 | + | 7.00000i | −0.438931 | + | 0.253417i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.3827 | − | 22.5000i | −0.844300 | − | 0.812428i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.50000 | − | 9.52628i | 0.198335 | − | 0.343526i | −0.749654 | − | 0.661830i | \(-0.769780\pi\) |
0.947989 | + | 0.318304i | \(0.103113\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.5000 | + | 23.3827i | 0.486191 | + | 0.842107i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.9904 | + | 7.50000i | −0.467232 | + | 0.269756i | −0.715080 | − | 0.699043i | \(-0.753610\pi\) |
0.247849 | + | 0.968799i | \(0.420276\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.06218 | + | 3.50000i | 0.217479 | + | 0.125562i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.0000 | −0.537431 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.0000 | 0.966136 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −38.9711 | − | 22.5000i | −1.39272 | − | 0.804084i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.4352 | − | 24.5000i | 1.51265 | − | 0.873331i | 0.512763 | − | 0.858530i | \(-0.328622\pi\) |
0.999890 | − | 0.0148003i | \(-0.00471124\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.50000 | − | 2.59808i | −0.0534014 | − | 0.0924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.50000 | + | 12.9904i | −0.266669 | + | 0.461885i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.59808 | − | 2.50000i | −0.0922604 | − | 0.0887776i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.3827 | − | 13.5000i | 0.828257 | − | 0.478195i | −0.0249984 | − | 0.999687i | \(-0.507958\pi\) |
0.853256 | + | 0.521493i | \(0.174625\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.00000 | −0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.19615 | − | 3.00000i | −0.183368 | − | 0.105868i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.0000i | 0.739235i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.5000 | − | 33.7750i | 0.685583 | − | 1.18747i | −0.287670 | − | 0.957730i | \(-0.592880\pi\) |
0.973253 | − | 0.229736i | \(-0.0737862\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0000 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.2583 | + | 6.50000i | −0.394847 | + | 0.227965i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.33013 | − | 2.50000i | −0.151492 | − | 0.0874639i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.00000 | + | 1.73205i | 0.244600 | + | 0.0605228i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.5000 | − | 18.1865i | 0.366453 | − | 0.634714i | −0.622556 | − | 0.782576i | \(-0.713906\pi\) |
0.989008 | + | 0.147861i | \(0.0472389\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.7032 | − | 23.5000i | 1.41882 | − | 0.819159i | 0.422628 | − | 0.906303i | \(-0.361108\pi\) |
0.996196 | + | 0.0871445i | \(0.0277742\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 12.0000i | − | 0.417281i | −0.977992 | − | 0.208640i | \(-0.933096\pi\) | ||
0.977992 | − | 0.208640i | \(-0.0669038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.50000 | − | 9.52628i | 0.191023 | − | 0.330861i | −0.754567 | − | 0.656223i | \(-0.772153\pi\) |
0.945589 | + | 0.325362i | \(0.105486\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.0000 | −0.659103 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0000i | 0.623663i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 40.0000i | 1.38260i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.50000 | − | 12.9904i | −0.258929 | − | 0.448478i | 0.707026 | − | 0.707187i | \(-0.250036\pi\) |
−0.965955 | + | 0.258709i | \(0.916703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | − | 45.0333i | −0.896552 | − | 1.55287i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.5885 | + | 9.00000i | 0.536895 | + | 0.309976i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.73205 | + | 1.00000i | 0.0595140 | + | 0.0343604i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.50000 | + | 14.7224i | 0.291719 | + | 0.505273i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.5000 | + | 54.5596i | 1.07981 | + | 1.87028i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.0000i | 0.479351i | 0.970853 | + | 0.239675i | \(0.0770410\pi\) | ||||
−0.970853 | + | 0.239675i | \(0.922959\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.0000i | 1.43469i | 0.696717 | + | 0.717346i | \(0.254643\pi\) | ||||
−0.696717 | + | 0.717346i | \(0.745357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.00000 | −0.272956 | −0.136478 | − | 0.990643i | \(-0.543578\pi\) | ||||
−0.136478 | + | 0.990643i | \(0.543578\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.50000 | − | 2.59808i | 0.0511199 | − | 0.0885422i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.0000i | 1.63394i | 0.576681 | + | 0.816970i | \(0.304348\pi\) | ||||
−0.576681 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.92820 | − | 4.00000i | 0.235294 | − | 0.135847i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0000 | − | 20.7846i | 0.407072 | − | 0.705070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.5000 | − | 4.33013i | −0.592965 | − | 0.146721i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.4449 | + | 17.0000i | 0.996558 | + | 0.575363i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.7224 | + | 8.50000i | −0.497141 | + | 0.287025i | −0.727532 | − | 0.686074i | \(-0.759333\pi\) |
0.230391 | + | 0.973098i | \(0.425999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.00000 | 0.101187 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.50000 | + | 2.59808i | −0.0505363 | + | 0.0875314i | −0.890187 | − | 0.455595i | \(-0.849426\pi\) |
0.839651 | + | 0.543127i | \(0.182760\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 56.0000i | 1.88455i | 0.334840 | + | 0.942275i | \(0.391318\pi\) | ||||
−0.334840 | + | 0.942275i | \(0.608682\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.5788 | + | 16.5000i | 0.959583 | + | 0.554016i | 0.896045 | − | 0.443964i | \(-0.146428\pi\) |
0.0635387 | + | 0.997979i | \(0.479761\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.0000 | 0.570162 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50000 | − | 2.59808i | −0.0502519 | − | 0.0870388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.3827 | − | 22.5000i | −0.780725 | − | 0.751253i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36.0000 | + | 62.3538i | −1.20067 | + | 2.07962i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.00000 | + | 15.5885i | 0.299833 | + | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.866025 | − | 0.500000i | 0.0288195 | − | 0.0166390i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.6314 | − | 27.5000i | −1.58157 | − | 0.913123i | −0.994630 | − | 0.103495i | \(-0.966997\pi\) |
−0.586945 | − | 0.809627i | \(-0.699669\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 30.0000 | 0.995037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.50000 | − | 6.06218i | −0.115454 | − | 0.199973i | 0.802507 | − | 0.596643i | \(-0.203499\pi\) |
−0.917961 | + | 0.396670i | \(0.870166\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.00000 | − | 3.46410i | 0.0659022 | − | 0.114146i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.3827 | + | 22.5000i | 0.769650 | + | 0.740597i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.8564 | − | 8.00000i | 0.455104 | − | 0.262754i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.50000 | + | 2.59808i | 0.0492134 | + | 0.0852401i | 0.889583 | − | 0.456774i | \(-0.150995\pi\) |
−0.840369 | + | 0.542014i | \(0.817662\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.0000 | −0.983210 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.3923 | − | 6.00000i | −0.340229 | − | 0.196431i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.0000i | 0.718709i | 0.933201 | + | 0.359354i | \(0.117003\pi\) | ||||
−0.933201 | + | 0.359354i | \(0.882997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.00000 | + | 8.66025i | −0.163169 | + | 0.282617i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.0000 | 0.586783 | 0.293392 | − | 0.955992i | \(-0.405216\pi\) | ||||
0.293392 | + | 0.955992i | \(0.405216\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.3827 | − | 13.5000i | 0.761445 | − | 0.439620i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.1673 | − | 25.5000i | −1.43524 | − | 0.828639i | −0.437730 | − | 0.899106i | \(-0.644217\pi\) |
−0.997514 | + | 0.0704677i | \(0.977551\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.00000 | − | 6.92820i | −0.0649227 | − | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.00000 | − | 15.5885i | 0.291845 | − | 0.505490i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.1865 | − | 10.5000i | 0.589120 | − | 0.340128i | −0.175630 | − | 0.984456i | \(-0.556196\pi\) |
0.764749 | + | 0.644328i | \(0.222863\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.0000i | 0.872786i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.50000 | − | 2.59808i | 0.0484375 | − | 0.0838963i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.00000i | 0.193347i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.00000i | 0.128631i | 0.997930 | + | 0.0643157i | \(0.0204865\pi\) | ||||
−0.997930 | + | 0.0643157i | \(0.979514\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.50000 | − | 12.9904i | −0.240935 | − | 0.417311i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.50000 | + | 12.9904i | 0.240686 | + | 0.416881i | 0.960910 | − | 0.276861i | \(-0.0892941\pi\) |
−0.720224 | + | 0.693742i | \(0.755961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.33013 | + | 2.50000i | 0.138817 | + | 0.0801463i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.59808 | − | 1.50000i | −0.0831198 | − | 0.0479893i | 0.457864 | − | 0.889022i | \(-0.348615\pi\) |
−0.540984 | + | 0.841033i | \(0.681948\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.50000 | + | 7.79423i | 0.143821 | + | 0.249105i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0000 | + | 24.2487i | 0.446986 | + | 0.774202i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 48.0000i | − | 1.53096i | −0.643458 | − | 0.765481i | \(-0.722501\pi\) | ||
0.643458 | − | 0.765481i | \(-0.277499\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.00000 | 0.286183 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.5000 | − | 42.4352i | 0.778268 | − | 1.34800i | −0.154671 | − | 0.987966i | \(-0.549432\pi\) |
0.932939 | − | 0.360034i | \(-0.117235\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 19.0000i | − | 0.602947i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.33013 | + | 2.50000i | −0.137136 | + | 0.0791758i | −0.566999 | − | 0.823719i | \(-0.691896\pi\) |
0.429862 | + | 0.902895i | \(0.358562\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 17.5000 | − | 30.3109i | 0.553675 | − | 0.958994i |
(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 | 1300.2.bb.b.1049.1 | 4 | ||
5.2 | odd | 4 | 260.2.i.a.61.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1300.2.i.d.1101.1 | 2 | |||
5.4 | even | 2 | inner | 1300.2.bb.b.1049.2 | 4 | ||
13.3 | even | 3 | inner | 1300.2.bb.b.549.2 | 4 | ||
15.2 | even | 4 | 2340.2.q.f.1621.1 | 2 | |||
20.7 | even | 4 | 1040.2.q.i.321.1 | 2 | |||
65.3 | odd | 12 | 1300.2.i.d.601.1 | 2 | |||
65.7 | even | 12 | 3380.2.f.d.3041.1 | 2 | |||
65.17 | odd | 12 | 3380.2.a.i.1.1 | 1 | |||
65.22 | odd | 12 | 3380.2.a.f.1.1 | 1 | |||
65.29 | even | 6 | inner | 1300.2.bb.b.549.1 | 4 | ||
65.32 | even | 12 | 3380.2.f.d.3041.2 | 2 | |||
65.42 | odd | 12 | 260.2.i.a.81.1 | yes | 2 | ||
195.107 | even | 12 | 2340.2.q.f.2161.1 | 2 | |||
260.107 | even | 12 | 1040.2.q.i.81.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.i.a.61.1 | ✓ | 2 | 5.2 | odd | 4 | ||
260.2.i.a.81.1 | yes | 2 | 65.42 | odd | 12 | ||
1040.2.q.i.81.1 | 2 | 260.107 | even | 12 | |||
1040.2.q.i.321.1 | 2 | 20.7 | even | 4 | |||
1300.2.i.d.601.1 | 2 | 65.3 | odd | 12 | |||
1300.2.i.d.1101.1 | 2 | 5.3 | odd | 4 | |||
1300.2.bb.b.549.1 | 4 | 65.29 | even | 6 | inner | ||
1300.2.bb.b.549.2 | 4 | 13.3 | even | 3 | inner | ||
1300.2.bb.b.1049.1 | 4 | 1.1 | even | 1 | trivial | ||
1300.2.bb.b.1049.2 | 4 | 5.4 | even | 2 | inner | ||
2340.2.q.f.1621.1 | 2 | 15.2 | even | 4 | |||
2340.2.q.f.2161.1 | 2 | 195.107 | even | 12 | |||
3380.2.a.f.1.1 | 1 | 65.22 | odd | 12 | |||
3380.2.a.i.1.1 | 1 | 65.17 | odd | 12 | |||
3380.2.f.d.3041.1 | 2 | 65.7 | even | 12 | |||
3380.2.f.d.3041.2 | 2 | 65.32 | even | 12 |