Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(249,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.bh (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: | \(11.1790562830\) |
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 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 849.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.849 |
Dual form | 1400.2.bh.b.249.2 |
$q$-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 \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 | \(-0.573452\pi\) |
0.728714 | + | 0.684819i | \(0.240119\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866025 | + | 2.50000i | −0.327327 | + | 0.944911i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 1.73205i | −0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | + | 2.00000i | −0.840168 | + | 0.485071i | −0.857321 | − | 0.514782i | \(-0.827873\pi\) |
0.0171533 | + | 0.999853i | \(0.494540\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | + | 1.73205i | −0.229416 | + | 0.397360i | −0.957635 | − | 0.287984i | \(-0.907015\pi\) |
0.728219 | + | 0.685344i | \(0.240348\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.500000 | + | 2.59808i | 0.109109 | + | 0.566947i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.866025 | − | 0.500000i | −0.180579 | − | 0.104257i | 0.406986 | − | 0.913434i | \(-0.366580\pi\) |
−0.587565 | + | 0.809177i | \(0.699913\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000i | 0.962250i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.00000 | −1.67126 | −0.835629 | − | 0.549294i | \(-0.814897\pi\) | ||||
−0.835629 | + | 0.549294i | \(0.814897\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | − | 3.46410i | −0.359211 | − | 0.622171i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.73205 | − | 1.00000i | −0.301511 | − | 0.174078i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.46410 | + | 2.00000i | 0.569495 | + | 0.328798i | 0.756948 | − | 0.653476i | \(-0.226690\pi\) |
−0.187453 | + | 0.982274i | \(0.560023\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | 0.0780869 | − | 0.996947i | \(-0.475119\pi\) | ||||
0.0780869 | + | 0.996947i | \(0.475119\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.00000i | 1.37249i | 0.727372 | + | 0.686244i | \(0.240742\pi\) | ||||
−0.727372 | + | 0.686244i | \(0.759258\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.50000 | − | 4.33013i | −0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | + | 3.46410i | −0.280056 | + | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.66025 | + | 5.00000i | −1.18958 | + | 0.686803i | −0.958211 | − | 0.286064i | \(-0.907653\pi\) |
−0.231367 | + | 0.972867i | \(0.574320\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000i | 0.264906i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.00000 | − | 8.66025i | −0.650945 | − | 1.12747i | −0.982894 | − | 0.184172i | \(-0.941040\pi\) |
0.331949 | − | 0.943297i | \(-0.392294\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.50000 | + | 7.79423i | −0.576166 | + | 0.997949i | 0.419748 | + | 0.907641i | \(0.362118\pi\) |
−0.995914 | + | 0.0903080i | \(0.971215\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.46410 | − | 4.00000i | −0.436436 | − | 0.503953i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.33013 | + | 2.50000i | −0.529009 | + | 0.305424i | −0.740613 | − | 0.671932i | \(-0.765465\pi\) |
0.211604 | + | 0.977356i | \(0.432131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0000 | 1.66149 | 0.830747 | − | 0.556650i | \(-0.187914\pi\) | ||||
0.830747 | + | 0.556650i | \(0.187914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.3923 | − | 6.00000i | 1.21633 | − | 0.702247i | 0.252197 | − | 0.967676i | \(-0.418847\pi\) |
0.964130 | + | 0.265429i | \(0.0855136\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.19615 | − | 1.00000i | 0.592157 | − | 0.113961i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.00000 | − | 12.1244i | 0.787562 | − | 1.36410i | −0.139895 | − | 0.990166i | \(-0.544677\pi\) |
0.927457 | − | 0.373930i | \(-0.121990\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.0000i | 1.20741i | 0.797209 | + | 0.603703i | \(0.206309\pi\) | ||||
−0.797209 | + | 0.603703i | \(0.793691\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.79423 | + | 4.50000i | −0.835629 | + | 0.482451i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.50000 | + | 12.9904i | −0.794998 | + | 1.37698i | 0.127842 | + | 0.991795i | \(0.459195\pi\) |
−0.922840 | + | 0.385183i | \(0.874138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.46410 | − | 2.00000i | −0.359211 | − | 0.207390i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.0000i | 1.82762i | 0.406138 | + | 0.913812i | \(0.366875\pi\) | ||||
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.50000 | − | 2.59808i | −0.149256 | − | 0.258518i | 0.781697 | − | 0.623658i | \(-0.214354\pi\) |
−0.930953 | + | 0.365140i | \(0.881021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.2583 | + | 6.50000i | 1.10932 | + | 0.640464i | 0.938652 | − | 0.344865i | \(-0.112075\pi\) |
0.170664 | + | 0.985329i | \(0.445409\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.79423 | + | 4.50000i | 0.753497 | + | 0.435031i | 0.826956 | − | 0.562267i | \(-0.190071\pi\) |
−0.0734594 | + | 0.997298i | \(0.523404\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.500000 | − | 0.866025i | −0.0478913 | − | 0.0829502i | 0.841086 | − | 0.540901i | \(-0.181917\pi\) |
−0.888977 | + | 0.457951i | \(0.848583\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000i | 0.188144i | 0.995565 | + | 0.0940721i | \(0.0299884\pi\) | ||||
−0.995565 | + | 0.0940721i | \(0.970012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.00000 | − | 10.3923i | −0.183340 | − | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.866025 | − | 0.500000i | 0.0780869 | − | 0.0450835i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.00000i | − | 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.50000 | + | 7.79423i | 0.396203 | + | 0.686244i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | − | 6.92820i | 0.349482 | − | 0.605320i | −0.636676 | − | 0.771132i | \(-0.719691\pi\) |
0.986157 | + | 0.165812i | \(0.0530244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.46410 | − | 4.00000i | −0.300376 | − | 0.346844i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.3923 | + | 6.00000i | −0.887875 | + | 0.512615i | −0.873247 | − | 0.487278i | \(-0.837990\pi\) |
−0.0146279 | + | 0.999893i | \(0.504656\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | 0.169638 | 0.0848189 | − | 0.996396i | \(-0.472969\pi\) | ||||
0.0848189 | + | 0.996396i | \(0.472969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.92820 | − | 1.00000i | −0.571429 | − | 0.0824786i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.50000 | + | 4.33013i | −0.204808 | + | 0.354738i | −0.950072 | − | 0.312032i | \(-0.898990\pi\) |
0.745264 | + | 0.666770i | \(0.232324\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | − | 6.92820i | −0.325515 | − | 0.563809i | 0.656101 | − | 0.754673i | \(-0.272204\pi\) |
−0.981617 | + | 0.190864i | \(0.938871\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 8.00000i | − | 0.646762i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.73205 | + | 1.00000i | −0.138233 | + | 0.0798087i | −0.567521 | − | 0.823359i | \(-0.692098\pi\) |
0.429289 | + | 0.903167i | \(0.358764\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.00000 | + | 8.66025i | −0.396526 | + | 0.686803i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00000 | − | 1.73205i | 0.157622 | − | 0.136505i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.3205 | + | 10.0000i | 1.35665 | + | 0.783260i | 0.989170 | − | 0.146772i | \(-0.0468885\pi\) |
0.367477 | + | 0.930033i | \(0.380222\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 17.0000i | − | 1.31550i | −0.753237 | − | 0.657750i | \(-0.771508\pi\) | ||
0.753237 | − | 0.657750i | \(-0.228492\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | − | 3.46410i | −0.152944 | − | 0.264906i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.8564 | − | 8.00000i | −1.05348 | − | 0.608229i | −0.129861 | − | 0.991532i | \(-0.541453\pi\) |
−0.923622 | + | 0.383304i | \(0.874786\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.66025 | − | 5.00000i | −0.650945 | − | 0.375823i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000 | + | 10.3923i | 0.448461 | + | 0.776757i | 0.998286 | − | 0.0585225i | \(-0.0186389\pi\) |
−0.549825 | + | 0.835280i | \(0.685306\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.0000 | −1.85824 | −0.929118 | − | 0.369784i | \(-0.879432\pi\) | ||||
−0.929118 | + | 0.369784i | \(0.879432\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.00000i | 0.665299i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.92820 | + | 4.00000i | 0.506640 | + | 0.292509i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.5000 | − | 4.33013i | −0.909241 | − | 0.314970i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.00000 | + | 15.5885i | −0.651217 | + | 1.12794i | 0.331611 | + | 0.943416i | \(0.392408\pi\) |
−0.982828 | + | 0.184525i | \(0.940925\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.1244 | + | 7.00000i | −0.872730 | + | 0.503871i | −0.868255 | − | 0.496119i | \(-0.834758\pi\) |
−0.00447566 | + | 0.999990i | \(0.501425\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.0000i | − | 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.00000 | − | 3.46410i | −0.141776 | − | 0.245564i | 0.786389 | − | 0.617731i | \(-0.211948\pi\) |
−0.928166 | + | 0.372168i | \(0.878615\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.50000 | + | 4.33013i | −0.176336 | + | 0.305424i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.79423 | − | 22.5000i | 0.547048 | − | 1.57919i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.73205 | − | 1.00000i | 0.120386 | − | 0.0695048i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | 0.137686 | 0.0688428 | − | 0.997628i | \(-0.478069\pi\) | ||||
0.0688428 | + | 0.997628i | \(0.478069\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.1244 | − | 7.00000i | 0.830747 | − | 0.479632i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.3923 | − | 2.00000i | 0.705476 | − | 0.135769i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.00000 | − | 10.3923i | 0.405442 | − | 0.702247i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 4.00000i | − | 0.267860i | −0.990991 | − | 0.133930i | \(-0.957240\pi\) | ||
0.990991 | − | 0.133930i | \(-0.0427597\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.3205 | − | 10.0000i | 1.14960 | − | 0.663723i | 0.200812 | − | 0.979630i | \(-0.435642\pi\) |
0.948790 | + | 0.315906i | \(0.102309\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.00000 | + | 8.66025i | −0.330409 | + | 0.572286i | −0.982592 | − | 0.185776i | \(-0.940520\pi\) |
0.652183 | + | 0.758062i | \(0.273853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.00000 | − | 3.46410i | 0.263181 | − | 0.227921i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.92820 | − | 4.00000i | −0.453882 | − | 0.262049i | 0.255586 | − | 0.966786i | \(-0.417731\pi\) |
−0.709468 | + | 0.704737i | \(0.751065\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 14.0000i | − | 0.909398i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0000 | + | 19.0526i | 0.708572 | + | 1.22728i | 0.965387 | + | 0.260822i | \(0.0839937\pi\) |
−0.256814 | + | 0.966461i | \(0.582673\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.8564 | − | 8.00000i | −0.888889 | − | 0.513200i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.50000 | + | 9.52628i | 0.348548 | + | 0.603703i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.00000 | 0.504956 | 0.252478 | − | 0.967603i | \(-0.418755\pi\) | ||||
0.252478 | + | 0.967603i | \(0.418755\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000i | 0.125739i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.00000 | + | 6.92820i | −0.497096 | + | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.00000 | − | 15.5885i | 0.557086 | − | 0.964901i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.866025 | + | 0.500000i | −0.0534014 | + | 0.0308313i | −0.526463 | − | 0.850198i | \(-0.676482\pi\) |
0.473062 | + | 0.881029i | \(0.343149\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.0000i | 0.917985i | ||||||||
\(268\) | 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 | ||||||||
\(271\) | −11.0000 | + | 19.0526i | −0.668202 | + | 1.15736i | 0.310204 | + | 0.950670i | \(0.399603\pi\) |
−0.978406 | + | 0.206691i | \(0.933731\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.2487 | − | 14.0000i | 1.45696 | − | 0.841178i | 0.458103 | − | 0.888899i | \(-0.348529\pi\) |
0.998861 | + | 0.0477206i | \(0.0151957\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.46410 | + | 2.00000i | −0.205919 | + | 0.118888i | −0.599414 | − | 0.800439i | \(-0.704600\pi\) |
0.393494 | + | 0.919327i | \(0.371266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.866025 | + | 2.50000i | −0.0511199 | + | 0.147570i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.500000 | + | 0.866025i | −0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.00000 | + | 15.5885i | 0.527589 | + | 0.913812i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.0000i | 0.701047i | 0.936554 | + | 0.350524i | \(0.113996\pi\) | ||||
−0.936554 | + | 0.350524i | \(0.886004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.66025 | − | 5.00000i | 0.502519 | − | 0.290129i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.5000 | − | 7.79423i | −1.29688 | − | 0.449252i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.59808 | − | 1.50000i | −0.149256 | − | 0.0861727i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.0000i | − | 1.19853i | −0.800549 | − | 0.599267i | \(-0.795459\pi\) | ||
0.800549 | − | 0.599267i | \(-0.204541\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.0000 | 0.739544 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.0000 | − | 22.5167i | −0.737162 | − | 1.27680i | −0.953768 | − | 0.300544i | \(-0.902832\pi\) |
0.216606 | − | 0.976259i | \(-0.430501\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.8564 | − | 8.00000i | −0.783210 | − | 0.452187i | 0.0543564 | − | 0.998522i | \(-0.482689\pi\) |
−0.837567 | + | 0.546335i | \(0.816023\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.8564 | − | 8.00000i | −0.778253 | − | 0.449325i | 0.0575576 | − | 0.998342i | \(-0.481669\pi\) |
−0.835811 | + | 0.549017i | \(0.815002\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | + | 15.5885i | 0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.00000 | 0.502331 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.00000i | − | 0.445132i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.866025 | − | 0.500000i | −0.0478913 | − | 0.0276501i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.92820 | + | 4.00000i | −0.379663 | + | 0.219199i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000i | 0.108947i | 0.998515 | + | 0.0544735i | \(0.0173480\pi\) | ||||
−0.998515 | + | 0.0544735i | \(0.982652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.00000 | + | 1.73205i | 0.0543125 | + | 0.0940721i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.00000 | + | 6.92820i | −0.216612 | + | 0.375183i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.5885 | − | 10.0000i | 0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.06218 | − | 3.50000i | 0.325435 | − | 0.187890i | −0.328378 | − | 0.944547i | \(-0.606502\pi\) |
0.653812 | + | 0.756657i | \(0.273169\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.0000 | 1.01705 | 0.508523 | − | 0.861048i | \(-0.330192\pi\) | ||||
0.508523 | + | 0.861048i | \(0.330192\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.1244 | − | 7.00000i | 0.645314 | − | 0.372572i | −0.141344 | − | 0.989960i | \(-0.545142\pi\) |
0.786659 | + | 0.617388i | \(0.211809\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.92820 | − | 8.00000i | −0.366679 | − | 0.423405i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.00000 | − | 10.3923i | 0.316668 | − | 0.548485i | −0.663123 | − | 0.748511i | \(-0.730769\pi\) |
0.979791 | + | 0.200026i | \(0.0641026\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 7.00000i | − | 0.367405i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.06218 | + | 3.50000i | −0.316443 | + | 0.182699i | −0.649806 | − | 0.760100i | \(-0.725150\pi\) |
0.333363 | + | 0.942799i | \(0.391817\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.00000 | + | 1.73205i | −0.0520579 | + | 0.0901670i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.00000 | − | 25.9808i | −0.259587 | − | 1.34885i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.2487 | + | 14.0000i | 1.25555 | + | 0.724893i | 0.972206 | − | 0.234126i | \(-0.0752227\pi\) |
0.283344 | + | 0.959018i | \(0.408556\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.0000 | 1.54100 | 0.770498 | − | 0.637442i | \(-0.220007\pi\) | ||||
0.770498 | + | 0.637442i | \(0.220007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | − | 6.92820i | −0.204926 | − | 0.354943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.1865 | − | 10.5000i | −0.929288 | − | 0.536525i | −0.0427020 | − | 0.999088i | \(-0.513597\pi\) |
−0.886586 | + | 0.462563i | \(0.846930\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.5885 | − | 9.00000i | −0.792406 | − | 0.457496i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.0000 | + | 22.5167i | 0.659126 | + | 1.14164i | 0.980842 | + | 0.194804i | \(0.0624070\pi\) |
−0.321716 | + | 0.946836i | \(0.604260\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.00000 | 0.202289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 8.00000i | − | 0.403547i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.19615 | + | 3.00000i | 0.260787 | + | 0.150566i | 0.624694 | − | 0.780870i | \(-0.285224\pi\) |
−0.363906 | + | 0.931436i | \(0.618557\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.00000 | − | 1.73205i | −0.250313 | − | 0.0867110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.50000 | − | 14.7224i | 0.424470 | − | 0.735203i | −0.571901 | − | 0.820323i | \(-0.693794\pi\) |
0.996371 | + | 0.0851195i | \(0.0271272\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 8.00000i | − | 0.396545i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.5000 | − | 18.1865i | −0.519192 | − | 0.899266i | −0.999751 | − | 0.0223042i | \(-0.992900\pi\) |
0.480560 | − | 0.876962i | \(-0.340434\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | + | 10.3923i | −0.295958 | + | 0.512615i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 25.9808 | − | 5.00000i | 1.27843 | − | 0.246034i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.73205 | − | 1.00000i | 0.0848189 | − | 0.0489702i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.0000 | −0.781651 | −0.390826 | − | 0.920465i | \(-0.627810\pi\) | ||||
−0.390826 | + | 0.920465i | \(0.627810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.0000 | −1.31590 | −0.657950 | − | 0.753062i | \(-0.728576\pi\) | ||||
−0.657950 | + | 0.753062i | \(0.728576\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.5885 | − | 18.0000i | −0.754378 | − | 0.871081i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.00000 | − | 12.1244i | −0.337178 | − | 0.584010i | 0.646723 | − | 0.762725i | \(-0.276139\pi\) |
−0.983901 | + | 0.178716i | \(0.942806\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.0000i | 1.44171i | 0.693087 | + | 0.720854i | \(0.256250\pi\) | ||||
−0.693087 | + | 0.720854i | \(0.743750\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.73205 | − | 1.00000i | 0.0828552 | − | 0.0478365i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.0000 | + | 24.2487i | −0.668184 | + | 1.15733i | 0.310228 | + | 0.950662i | \(0.399595\pi\) |
−0.978412 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.0000 | − | 5.19615i | 0.619048 | − | 0.247436i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.52628 | + | 5.50000i | 0.452607 | + | 0.261313i | 0.708931 | − | 0.705278i | \(-0.249178\pi\) |
−0.256323 | + | 0.966591i | \(0.582511\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.00000i | 0.236492i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 41.0000 | 1.93491 | 0.967455 | − | 0.253044i | \(-0.0814317\pi\) | ||||
0.967455 | + | 0.253044i | \(0.0814317\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.00000 | − | 1.73205i | −0.0470882 | − | 0.0815591i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.92820 | − | 4.00000i | −0.325515 | − | 0.187936i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.92820 | + | 4.00000i | 0.324088 | + | 0.187112i | 0.653213 | − | 0.757174i | \(-0.273421\pi\) |
−0.329125 | + | 0.944286i | \(0.606754\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.0000 | − | 17.3205i | −0.466760 | − | 0.808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.00000 | 0.0931493 | 0.0465746 | − | 0.998915i | \(-0.485169\pi\) | ||||
0.0465746 | + | 0.998915i | \(0.485169\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.0000i | 1.81248i | 0.422760 | + | 0.906242i | \(0.361061\pi\) | ||||
−0.422760 | + | 0.906242i | \(0.638939\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.06218 | − | 3.50000i | −0.280524 | − | 0.161961i | 0.353137 | − | 0.935572i | \(-0.385115\pi\) |
−0.633661 | + | 0.773611i | \(0.718448\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.50000 | − | 12.9904i | −0.115439 | − | 0.599840i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.00000 | + | 1.73205i | −0.0460776 | + | 0.0798087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.5885 | − | 9.00000i | 0.716758 | − | 0.413820i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 20.0000i | − | 0.915737i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.00000 | − | 13.8564i | −0.365529 | − | 0.633115i | 0.623332 | − | 0.781958i | \(-0.285779\pi\) |
−0.988861 | + | 0.148842i | \(0.952445\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.866025 | − | 2.50000i | 0.0394055 | − | 0.113754i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.92820 | − | 4.00000i | 0.313947 | − | 0.181257i | −0.334744 | − | 0.942309i | \(-0.608650\pi\) |
0.648691 | + | 0.761052i | \(0.275317\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.0000 | 0.904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.0000 | −0.902587 | −0.451294 | − | 0.892375i | \(-0.649037\pi\) | ||||
−0.451294 | + | 0.892375i | \(0.649037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.1769 | − | 18.0000i | 1.40414 | − | 0.810679i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.1244 | + | 35.0000i | −0.543852 | + | 1.56996i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.0000 | + | 32.9090i | −0.850557 | + | 1.47321i | 0.0301498 | + | 0.999545i | \(0.490402\pi\) |
−0.880707 | + | 0.473662i | \(0.842932\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.50000 | − | 14.7224i | −0.379752 | − | 0.657750i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 23.0000i | − | 1.02552i | −0.858532 | − | 0.512760i | \(-0.828623\pi\) | ||
0.858532 | − | 0.512760i | \(-0.171377\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.2583 | − | 6.50000i | 0.500000 | − | 0.288675i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.50000 | + | 12.9904i | −0.332432 | + | 0.575789i | −0.982988 | − | 0.183669i | \(-0.941202\pi\) |
0.650556 | + | 0.759458i | \(0.274536\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | + | 31.1769i | 0.265424 | + | 1.37919i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.66025 | − | 5.00000i | −0.382360 | − | 0.220755i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.0000 | −0.702322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.0000 | + | 36.3731i | 0.920027 | + | 1.59353i | 0.799370 | + | 0.600839i | \(0.205167\pi\) |
0.120656 | + | 0.992694i | \(0.461500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.2487 | − | 14.0000i | −1.06032 | − | 0.612177i | −0.134801 | − | 0.990873i | \(-0.543039\pi\) |
−0.925521 | + | 0.378695i | \(0.876373\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.8564 | + | 8.00000i | 0.603595 | + | 0.348485i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | − | 19.0526i | −0.478261 | − | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.0000 | 0.867926 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.3923 | + | 6.00000i | 0.448461 | + | 0.258919i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.00000 | + | 13.8564i | −0.0861461 | + | 0.596838i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.50000 | − | 11.2583i | 0.279457 | − | 0.484033i | −0.691793 | − | 0.722096i | \(-0.743179\pi\) |
0.971250 | + | 0.238062i | \(0.0765123\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.6506 | + | 12.5000i | −0.929118 | + | 0.536426i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.0000i | 1.49649i | 0.663421 | + | 0.748246i | \(0.269104\pi\) | ||||
−0.663421 | + | 0.748246i | \(0.730896\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.00000 | − | 15.5885i | −0.384111 | − | 0.665299i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.00000 | − | 15.5885i | 0.383413 | − | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.2487 | + | 28.0000i | 1.03116 | + | 1.19068i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.9808 | + | 15.0000i | −1.10084 | + | 0.635570i | −0.936442 | − | 0.350824i | \(-0.885902\pi\) |
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.9711 | + | 22.5000i | −1.64244 | + | 0.948262i | −0.662474 | + | 0.749085i | \(0.730494\pi\) |
−0.979963 | + | 0.199177i | \(0.936173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.59808 | − | 0.500000i | 0.109109 | − | 0.0209980i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.0000 | − | 39.8372i | 0.964210 | − | 1.67006i | 0.252488 | − | 0.967600i | \(-0.418751\pi\) |
0.711722 | − | 0.702461i | \(-0.247915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.0000 | + | 22.5167i | 0.544033 | + | 0.942293i | 0.998667 | + | 0.0516146i | \(0.0164367\pi\) |
−0.454634 | + | 0.890678i | \(0.650230\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.0000i | 0.751961i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.73205 | + | 1.00000i | −0.0721062 | + | 0.0416305i | −0.535620 | − | 0.844459i | \(-0.679922\pi\) |
0.463513 | + | 0.886090i | \(0.346589\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.00000 | + | 12.1244i | −0.290910 | + | 0.503871i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.5000 | − | 9.52628i | −1.14089 | − | 0.395217i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.3205 | + | 10.0000i | 0.717342 | + | 0.414158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.00000 | 0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.00000 | − | 15.5885i | −0.370211 | − | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.5885 | − | 9.00000i | −0.640141 | − | 0.369586i | 0.144528 | − | 0.989501i | \(-0.453834\pi\) |
−0.784669 | + | 0.619915i | \(0.787167\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.46410 | − | 2.00000i | −0.141776 | − | 0.0818546i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.00000 | + | 3.46410i | 0.0817178 | + | 0.141539i | 0.903988 | − | 0.427558i | \(-0.140626\pi\) |
−0.822270 | + | 0.569097i | \(0.807293\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0000 | 0.407909 | 0.203954 | − | 0.978980i | \(-0.434621\pi\) | ||||
0.203954 | + | 0.978980i | \(0.434621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 10.0000i | − | 0.407231i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.3827 | + | 13.5000i | 0.949074 | + | 0.547948i | 0.892793 | − | 0.450467i | \(-0.148742\pi\) |
0.0562808 | + | 0.998415i | \(0.482076\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.50000 | − | 23.3827i | −0.182349 | − | 0.947514i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.3205 | + | 10.0000i | −0.699569 | + | 0.403896i | −0.807187 | − | 0.590296i | \(-0.799011\pi\) |
0.107618 | + | 0.994192i | \(0.465678\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.0000i | 0.483102i | 0.970388 | + | 0.241551i | \(0.0776561\pi\) | ||||
−0.970388 | + | 0.241551i | \(0.922344\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.0000 | − | 29.4449i | −0.683288 | − | 1.18349i | −0.973972 | − | 0.226670i | \(-0.927216\pi\) |
0.290684 | − | 0.956819i | \(-0.406117\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.50000 | − | 4.33013i | 0.100322 | − | 0.173762i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.9808 | − | 30.0000i | −1.04090 | − | 1.20192i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.46410 | − | 2.00000i | 0.138343 | − | 0.0798723i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.00000 | −0.0796187 | −0.0398094 | − | 0.999207i | \(-0.512675\pi\) | ||||
−0.0398094 | + | 0.999207i | \(0.512675\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.73205 | − | 1.00000i | 0.0688428 | − | 0.0397464i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.0000 | + | 24.2487i | −0.553831 | + | 0.959264i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.50000 | + | 16.4545i | 0.375227 | + | 0.649913i | 0.990361 | − | 0.138510i | \(-0.0442313\pi\) |
−0.615134 | + | 0.788423i | \(0.710898\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 4.00000i | − | 0.157745i | −0.996885 | − | 0.0788723i | \(-0.974868\pi\) | ||
0.996885 | − | 0.0788723i | \(-0.0251319\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.9186 | + | 11.5000i | −0.783080 | + | 0.452112i | −0.837521 | − | 0.546405i | \(-0.815996\pi\) |
0.0544405 | + | 0.998517i | \(0.482662\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.0000 | + | 17.3205i | −0.392534 | + | 0.679889i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.00000 | − | 6.92820i | 0.313545 | − | 0.271538i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.1769 | − | 18.0000i | −1.22005 | − | 0.704394i | −0.255119 | − | 0.966910i | \(-0.582115\pi\) |
−0.964928 | + | 0.262515i | \(0.915448\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 24.0000i | 0.936329i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.00000 | −0.0779089 | −0.0389545 | − | 0.999241i | \(-0.512403\pi\) | ||||
−0.0389545 | + | 0.999241i | \(0.512403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.50000 | + | 2.59808i | 0.0583432 | + | 0.101053i | 0.893722 | − | 0.448622i | \(-0.148085\pi\) |
−0.835379 | + | 0.549675i | \(0.814752\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.79423 | + | 4.50000i | 0.301794 | + | 0.174241i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.00000 | − | 3.46410i | −0.0773245 | − | 0.133930i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.0000 | 0.694882 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.0000i | 0.925132i | 0.886585 | + | 0.462566i | \(0.153071\pi\) | ||||
−0.886585 | + | 0.462566i | \(0.846929\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.7846 | − | 12.0000i | −0.798817 | − | 0.461197i | 0.0442400 | − | 0.999021i | \(-0.485913\pi\) |
−0.843057 | + | 0.537823i | \(0.819247\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −45.0000 | − | 15.5885i | −1.72694 | − | 0.598230i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.0000 | − | 17.3205i | 0.383201 | − | 0.663723i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.79423 | − | 4.50000i | 0.298238 | − | 0.172188i | −0.343413 | − | 0.939184i | \(-0.611583\pi\) |
0.641651 | + | 0.766997i | \(0.278250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.0000i | 0.381524i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.0000 | + | 43.3013i | −0.951045 | + | 1.64726i | −0.207875 | + | 0.978155i | \(0.566655\pi\) |
−0.743170 | + | 0.669102i | \(0.766679\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.46410 | + | 10.0000i | −0.131590 | + | 0.379869i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.46410 | + | 2.00000i | −0.131212 | + | 0.0757554i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.00000 | −0.302588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.00000 | 0.339925 | 0.169963 | − | 0.985451i | \(-0.445635\pi\) | ||||
0.169963 | + | 0.985451i | \(0.445635\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.92820 | + | 4.00000i | −0.261302 | + | 0.150863i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.79423 | − | 1.50000i | 0.293132 | − | 0.0564133i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.5000 | − | 18.1865i | 0.394336 | − | 0.683010i | −0.598680 | − | 0.800988i | \(-0.704308\pi\) |
0.993016 | + | 0.117978i | \(0.0376414\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.0000 | + | 24.2487i | 0.525041 | + | 0.909398i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.00000i | 0.149801i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.7846 | − | 12.0000i | 0.776215 | − | 0.448148i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.0000 | + | 36.3731i | −0.783168 | + | 1.35649i | 0.146920 | + | 0.989148i | \(0.453064\pi\) |
−0.930087 | + | 0.367338i | \(0.880269\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.0000 | + | 22.5167i | −0.968291 | + | 0.838564i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.0526 | + | 11.0000i | 0.708572 | + | 0.409094i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.0000i | 1.14973i | 0.818250 | + | 0.574863i | \(0.194945\pi\) | ||||
−0.818250 | + | 0.574863i | \(0.805055\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.0000 | − | 31.1769i | −0.665754 | − | 1.15312i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.5167 | + | 13.0000i | 0.831672 | + | 0.480166i | 0.854425 | − | 0.519575i | \(-0.173910\pi\) |
−0.0227529 | + | 0.999741i | \(0.507243\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.66025 | + | 5.00000i | 0.319005 | + | 0.184177i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.00000 | + | 8.66025i | 0.183928 | + | 0.318573i | 0.943215 | − | 0.332184i | \(-0.107785\pi\) |
−0.759287 | + | 0.650756i | \(0.774452\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.0000i | 0.990534i | 0.868741 | + | 0.495267i | \(0.164930\pi\) | ||||
−0.868741 | + | 0.495267i | \(0.835070\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.0526 | − | 11.0000i | −0.697097 | − | 0.402469i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.0000 | + | 15.5885i | −0.657706 | + | 0.569590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.00000 | + | 10.3923i | −0.218943 | + | 0.379221i | −0.954485 | − | 0.298259i | \(-0.903594\pi\) |
0.735542 | + | 0.677479i | \(0.236928\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.92820 | − | 4.00000i | 0.252478 | − | 0.145768i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.0000i | 0.872295i | 0.899875 | + | 0.436147i | \(0.143657\pi\) | ||||
−0.899875 | + | 0.436147i | \(0.856343\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.00000 | + | 1.73205i | 0.0362977 | + | 0.0628695i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.00000 | − | 5.19615i | 0.108750 | − | 0.188360i | −0.806514 | − | 0.591215i | \(-0.798649\pi\) |
0.915264 | + | 0.402854i | \(0.131982\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.59808 | − | 0.500000i | 0.0940567 | − | 0.0181012i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.0000 | −1.22607 | −0.613036 | − | 0.790055i | \(-0.710052\pi\) | ||||
−0.613036 | + | 0.790055i | \(0.710052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.46410 | + | 10.0000i | −0.124274 | + | 0.358748i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.00000 | + | 1.73205i | −0.0358287 | + | 0.0620572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.0000 | − | 24.2487i | −0.500959 | − | 0.867687i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 45.0000i | − | 1.60817i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.9711 | + | 22.5000i | −1.38917 | + | 0.802038i | −0.993222 | − | 0.116234i | \(-0.962918\pi\) |
−0.395949 | + | 0.918272i | \(0.629584\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.500000 | + | 0.866025i | −0.0178005 | + | 0.0308313i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.00000 | − | 1.73205i | −0.177780 | − | 0.0615846i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 8.00000i | − | 0.283375i | −0.989911 | − | 0.141687i | \(-0.954747\pi\) | ||
0.989911 | − | 0.141687i | \(-0.0452527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.0000 | − | 25.9808i | −0.529999 | − | 0.917985i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −20.7846 | − | 12.0000i | −0.733473 | − | 0.423471i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.1865 | − | 10.5000i | −0.640196 | − | 0.369618i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.50000 | + | 11.2583i | 0.228528 | + | 0.395822i | 0.957372 | − | 0.288858i | \(-0.0932755\pi\) |
−0.728844 | + | 0.684680i | \(0.759942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.0000 | −1.54505 | −0.772524 | − | 0.634985i | \(-0.781006\pi\) | ||||
−0.772524 | + | 0.634985i | \(0.781006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.0000i | 0.771574i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.5885 | − | 9.00000i | −0.545371 | − | 0.314870i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0000 | + | 25.9808i | −0.523504 | + | 0.906735i | 0.476122 | + | 0.879379i | \(0.342042\pi\) |
−0.999626 | + | 0.0273557i | \(0.991291\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.4352 | − | 24.5000i | 1.47920 | − | 0.854016i | 0.479477 | − | 0.877555i | \(-0.340826\pi\) |
0.999723 | + | 0.0235383i | \(0.00749316\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.0000i | 0.591148i | 0.955320 | + | 0.295574i | \(0.0955109\pi\) | ||||
−0.955320 | + | 0.295574i | \(0.904489\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.00000 | + | 1.73205i | 0.0347314 | + | 0.0601566i | 0.882869 | − | 0.469620i | \(-0.155609\pi\) |
−0.848137 | + | 0.529777i | \(0.822276\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.0000 | − | 24.2487i | 0.485655 | − | 0.841178i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.7128 | + | 4.00000i | 0.960192 | + | 0.138592i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.3205 | − | 10.0000i | 0.598684 | − | 0.345651i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.0000 | −0.345238 | −0.172619 | − | 0.984989i | \(-0.555223\pi\) | ||||
−0.172619 | + | 0.984989i | \(0.555223\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.5885 | − | 9.00000i | 0.536895 | − | 0.309976i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.1244 | + | 14.0000i | 0.416598 | + | 0.481046i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.00000 | + | 3.46410i | −0.0686398 | + | 0.118888i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.00000 | − | 3.46410i | −0.0685591 | − | 0.118748i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.0000i | 1.30110i | 0.759465 | + | 0.650548i | \(0.225461\pi\) | ||||
−0.759465 | + | 0.650548i | \(0.774539\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.9808 | + | 15.0000i | −0.887486 | + | 0.512390i | −0.873119 | − | 0.487507i | \(-0.837907\pi\) |
−0.0143666 | + | 0.999897i | \(0.504573\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0000 | − | 34.6410i | 0.682391 | − | 1.18194i | −0.291858 | − | 0.956462i | \(-0.594273\pi\) |
0.974249 | − | 0.225475i | \(-0.0723932\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.500000 | + | 2.59808i | 0.0170400 | + | 0.0885422i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.866025 | + | 0.500000i | 0.0294798 | + | 0.0170202i | 0.514667 | − | 0.857390i | \(-0.327915\pi\) |
−0.485188 | + | 0.874410i | \(0.661249\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.00000i | 0.0339618i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.0000 | −0.949835 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −31.1769 | − | 18.0000i | −1.05518 | − | 0.609208i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.19615 | + | 3.00000i | 0.175462 | + | 0.101303i | 0.585159 | − | 0.810919i | \(-0.301032\pi\) |
−0.409697 | + | 0.912222i | \(0.634366\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.00000 | + | 10.3923i | 0.202375 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.0000 | 0.572745 | 0.286372 | − | 0.958118i | \(-0.407551\pi\) | ||||
0.286372 | + | 0.958118i | \(0.407551\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000i | 0.673054i | 0.941674 | + | 0.336527i | \(0.109252\pi\) | ||||
−0.941674 | + | 0.336527i | \(0.890748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.9904 | + | 7.50000i | 0.436174 | + | 0.251825i | 0.701974 | − | 0.712203i | \(-0.252302\pi\) |
−0.265799 | + | 0.964028i | \(0.585636\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | + | 6.92820i | 0.670778 | + | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | + | 1.73205i | −0.0335013 | + | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.0000 | + | 31.1769i | 0.600334 | + | 1.03981i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.0000 | − | 34.6410i | 0.666297 | − | 1.15406i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −23.3827 | + | 4.50000i | −0.778127 | + | 0.149751i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.06218 | + | 3.50000i | −0.201291 | + | 0.116216i | −0.597258 | − | 0.802049i | \(-0.703743\pi\) |
0.395966 | + | 0.918265i | \(0.370410\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.0526 | − | 11.0000i | 0.630548 | − | 0.364047i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.8564 | + | 16.0000i | 0.457579 | + | 0.528367i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.0000 | − | 36.3731i | 0.692726 | − | 1.19984i | −0.278215 | − | 0.960519i | \(-0.589743\pi\) |
0.970941 | − | 0.239318i | \(-0.0769238\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.5000 | − | 18.1865i | −0.345987 | − | 0.599267i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.5167 | + | 13.0000i | −0.739544 | + | 0.426976i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.50000 | + | 11.2583i | −0.213258 | + | 0.369374i | −0.952732 | − | 0.303811i | \(-0.901741\pi\) |
0.739474 | + | 0.673185i | \(0.235074\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.0000 | − | 5.19615i | 0.426058 | − | 0.170297i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.5167 | − | 13.0000i | −0.737162 | − | 0.425601i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4.00000i | − | 0.130674i | −0.997863 | − | 0.0653372i | \(-0.979188\pi\) | ||
0.997863 | − | 0.0653372i | \(-0.0208123\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.0000 | −0.522140 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.0000 | + | 25.9808i | 0.488986 | + | 0.846949i | 0.999920 | − | 0.0126715i | \(-0.00403357\pi\) |
−0.510934 | + | 0.859620i | \(0.670700\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.866025 | − | 0.500000i | −0.0282017 | − | 0.0162822i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.33013 | + | 2.50000i | 0.140710 | + | 0.0812391i | 0.568702 | − | 0.822543i | \(-0.307446\pi\) |
−0.427992 | + | 0.903782i | \(0.640779\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.0000 | −0.518836 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.0000i | 0.907009i | 0.891254 | + | 0.453504i | \(0.149826\pi\) | ||||
−0.891254 | + | 0.453504i | \(0.850174\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.5885 | + | 9.00000i | 0.503903 | + | 0.290929i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.00000 | − | 31.1769i | −0.193750 | − | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.5885 | + | 9.00000i | −0.502331 | + | 0.290021i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 55.0000i | − | 1.76868i | −0.466843 | − | 0.884340i | \(-0.654609\pi\) | ||
0.466843 | − | 0.884340i | \(-0.345391\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.00000 | − | 6.92820i | −0.128499 | − | 0.222566i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.00000 | − | 6.92820i | 0.128366 | − | 0.222337i | −0.794678 | − | 0.607032i | \(-0.792360\pi\) |
0.923044 | + | 0.384695i | \(0.125693\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.73205 | + | 5.00000i | −0.0555270 | + | 0.160293i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.3731 | + | 21.0000i | −1.16368 | + | 0.671850i | −0.952183 | − | 0.305530i | \(-0.901167\pi\) |
−0.211495 | + | 0.977379i | \(0.567833\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.0000 | 0.958804 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.59808 | − | 1.50000i | 0.0828658 | − | 0.0478426i | −0.457995 | − | 0.888955i | \(-0.651432\pi\) |
0.540860 | + | 0.841112i | \(0.318099\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.50000 | − | 7.79423i | 0.143092 | − | 0.247842i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | + | 34.6410i | 0.635321 | + | 1.10041i | 0.986447 | + | 0.164080i | \(0.0524655\pi\) |
−0.351126 | + | 0.936328i | \(0.614201\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.66025 | + | 5.00000i | −0.274273 | + | 0.158352i | −0.630828 | − | 0.775923i | \(-0.717285\pi\) |
0.356555 | + | 0.934274i | \(0.383951\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.0000 | + | 17.3205i | −0.316386 | + | 0.547997i |
(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 | 1400.2.bh.b.849.2 | 4 | ||
5.2 | odd | 4 | 280.2.q.a.121.1 | yes | 2 | ||
5.3 | odd | 4 | 1400.2.q.e.401.1 | 2 | |||
5.4 | even | 2 | inner | 1400.2.bh.b.849.1 | 4 | ||
7.4 | even | 3 | inner | 1400.2.bh.b.249.1 | 4 | ||
15.2 | even | 4 | 2520.2.bi.a.1801.1 | 2 | |||
20.7 | even | 4 | 560.2.q.h.401.1 | 2 | |||
35.2 | odd | 12 | 1960.2.a.i.1.1 | 1 | |||
35.4 | even | 6 | inner | 1400.2.bh.b.249.2 | 4 | ||
35.12 | even | 12 | 1960.2.a.e.1.1 | 1 | |||
35.17 | even | 12 | 1960.2.q.k.361.1 | 2 | |||
35.18 | odd | 12 | 1400.2.q.e.1201.1 | 2 | |||
35.23 | odd | 12 | 9800.2.a.r.1.1 | 1 | |||
35.27 | even | 4 | 1960.2.q.k.961.1 | 2 | |||
35.32 | odd | 12 | 280.2.q.a.81.1 | ✓ | 2 | ||
35.33 | even | 12 | 9800.2.a.bc.1.1 | 1 | |||
105.32 | even | 12 | 2520.2.bi.a.361.1 | 2 | |||
140.47 | odd | 12 | 3920.2.a.y.1.1 | 1 | |||
140.67 | even | 12 | 560.2.q.h.81.1 | 2 | |||
140.107 | even | 12 | 3920.2.a.m.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.a.81.1 | ✓ | 2 | 35.32 | odd | 12 | ||
280.2.q.a.121.1 | yes | 2 | 5.2 | odd | 4 | ||
560.2.q.h.81.1 | 2 | 140.67 | even | 12 | |||
560.2.q.h.401.1 | 2 | 20.7 | even | 4 | |||
1400.2.q.e.401.1 | 2 | 5.3 | odd | 4 | |||
1400.2.q.e.1201.1 | 2 | 35.18 | odd | 12 | |||
1400.2.bh.b.249.1 | 4 | 7.4 | even | 3 | inner | ||
1400.2.bh.b.249.2 | 4 | 35.4 | even | 6 | inner | ||
1400.2.bh.b.849.1 | 4 | 5.4 | even | 2 | inner | ||
1400.2.bh.b.849.2 | 4 | 1.1 | even | 1 | trivial | ||
1960.2.a.e.1.1 | 1 | 35.12 | even | 12 | |||
1960.2.a.i.1.1 | 1 | 35.2 | odd | 12 | |||
1960.2.q.k.361.1 | 2 | 35.17 | even | 12 | |||
1960.2.q.k.961.1 | 2 | 35.27 | even | 4 | |||
2520.2.bi.a.361.1 | 2 | 105.32 | even | 12 | |||
2520.2.bi.a.1801.1 | 2 | 15.2 | even | 4 | |||
3920.2.a.m.1.1 | 1 | 140.107 | even | 12 | |||
3920.2.a.y.1.1 | 1 | 140.47 | odd | 12 | |||
9800.2.a.r.1.1 | 1 | 35.23 | odd | 12 | |||
9800.2.a.bc.1.1 | 1 | 35.33 | even | 12 |