Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [170,2,Mod(69,170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(170, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("170.69");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 170 = 2 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 170.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.35745683436\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 69.2 | ||
Root | \(1.32001 + 1.32001i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 170.69 |
Dual form | 170.2.c.b.69.5 |
$q$-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 \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).
\(n\) | \(71\) | \(137\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0.484862i | 0.279935i | 0.990156 | + | 0.139968i | \(0.0446998\pi\) | ||||
−0.990156 | + | 0.139968i | \(0.955300\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.80487 | + | 1.32001i | 0.807164 | + | 0.590327i | ||||
\(6\) | 0.484862 | 0.197944 | ||||||||
\(7\) | − | 2.64002i | − | 0.997835i | −0.866649 | − | 0.498918i | \(-0.833731\pi\) | ||
0.866649 | − | 0.498918i | \(-0.166269\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 2.76491 | 0.921636 | ||||||||
\(10\) | 1.32001 | − | 1.80487i | 0.417424 | − | 0.570751i | ||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | − | 0.484862i | − | 0.139968i | ||||||
\(13\) | 0.484862i | 0.134477i | 0.997737 | + | 0.0672383i | \(0.0214188\pi\) | ||||
−0.997737 | + | 0.0672383i | \(0.978581\pi\) | |||||||
\(14\) | −2.64002 | −0.705576 | ||||||||
\(15\) | −0.640023 | + | 0.875115i | −0.165253 | + | 0.225954i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 1.00000i | − | 0.242536i | ||||||
\(18\) | − | 2.76491i | − | 0.651695i | ||||||
\(19\) | −5.76491 | −1.32256 | −0.661280 | − | 0.750139i | \(-0.729987\pi\) | ||||
−0.661280 | + | 0.750139i | \(0.729987\pi\) | |||||||
\(20\) | −1.80487 | − | 1.32001i | −0.403582 | − | 0.295164i | ||||
\(21\) | 1.28005 | 0.279329 | ||||||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | − | 1.35998i | − | 0.283575i | −0.989897 | − | 0.141787i | \(-0.954715\pi\) | ||
0.989897 | − | 0.141787i | \(-0.0452849\pi\) | |||||||
\(24\) | −0.484862 | −0.0989720 | ||||||||
\(25\) | 1.51514 | + | 4.76491i | 0.303028 | + | 0.952982i | ||||
\(26\) | 0.484862 | 0.0950893 | ||||||||
\(27\) | 2.79518i | 0.537934i | ||||||||
\(28\) | 2.64002i | 0.498918i | ||||||||
\(29\) | −8.15516 | −1.51438 | −0.757188 | − | 0.653197i | \(-0.773427\pi\) | ||||
−0.757188 | + | 0.653197i | \(0.773427\pi\) | |||||||
\(30\) | 0.875115 | + | 0.640023i | 0.159773 | + | 0.116852i | ||||
\(31\) | −2.09461 | −0.376203 | −0.188101 | − | 0.982150i | \(-0.560233\pi\) | ||||
−0.188101 | + | 0.982150i | \(0.560233\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0.969724i | 0.168807i | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 3.48486 | − | 4.76491i | 0.589049 | − | 0.805417i | ||||
\(36\) | −2.76491 | −0.460818 | ||||||||
\(37\) | 11.1396i | 1.83133i | 0.401939 | + | 0.915667i | \(0.368337\pi\) | ||||
−0.401939 | + | 0.915667i | \(0.631663\pi\) | |||||||
\(38\) | 5.76491i | 0.935192i | ||||||||
\(39\) | −0.235091 | −0.0376447 | ||||||||
\(40\) | −1.32001 | + | 1.80487i | −0.208712 | + | 0.285376i | ||||
\(41\) | −0.249771 | −0.0390077 | −0.0195038 | − | 0.999810i | \(-0.506209\pi\) | ||||
−0.0195038 | + | 0.999810i | \(0.506209\pi\) | |||||||
\(42\) | − | 1.28005i | − | 0.197516i | ||||||
\(43\) | 1.03028i | 0.157116i | 0.996910 | + | 0.0785578i | \(0.0250315\pi\) | ||||
−0.996910 | + | 0.0785578i | \(0.974968\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | 4.99031 | + | 3.64971i | 0.743912 | + | 0.544067i | ||||
\(46\) | −1.35998 | −0.200518 | ||||||||
\(47\) | − | 6.01468i | − | 0.877331i | −0.898650 | − | 0.438666i | \(-0.855451\pi\) | ||
0.898650 | − | 0.438666i | \(-0.144549\pi\) | |||||||
\(48\) | 0.484862i | 0.0699838i | ||||||||
\(49\) | 0.0302761 | 0.00432516 | ||||||||
\(50\) | 4.76491 | − | 1.51514i | 0.673860 | − | 0.214273i | ||||
\(51\) | 0.484862 | 0.0678943 | ||||||||
\(52\) | − | 0.484862i | − | 0.0672383i | ||||||
\(53\) | − | 7.70436i | − | 1.05827i | −0.848536 | − | 0.529137i | \(-0.822516\pi\) | ||
0.848536 | − | 0.529137i | \(-0.177484\pi\) | |||||||
\(54\) | 2.79518 | 0.380376 | ||||||||
\(55\) | 3.60975 | + | 2.64002i | 0.486738 | + | 0.355981i | ||||
\(56\) | 2.64002 | 0.352788 | ||||||||
\(57\) | − | 2.79518i | − | 0.370231i | ||||||
\(58\) | 8.15516i | 1.07083i | ||||||||
\(59\) | −8.73463 | −1.13715 | −0.568576 | − | 0.822631i | \(-0.692506\pi\) | ||||
−0.568576 | + | 0.822631i | \(0.692506\pi\) | |||||||
\(60\) | 0.640023 | − | 0.875115i | 0.0826267 | − | 0.112977i | ||||
\(61\) | −11.3747 | −1.45638 | −0.728188 | − | 0.685378i | \(-0.759637\pi\) | ||||
−0.728188 | + | 0.685378i | \(0.759637\pi\) | |||||||
\(62\) | 2.09461i | 0.266016i | ||||||||
\(63\) | − | 7.29942i | − | 0.919641i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.640023 | + | 0.875115i | −0.0793851 | + | 0.108545i | ||||
\(66\) | 0.969724 | 0.119365 | ||||||||
\(67\) | 4.96972i | 0.607148i | 0.952808 | + | 0.303574i | \(0.0981800\pi\) | ||||
−0.952808 | + | 0.303574i | \(0.901820\pi\) | |||||||
\(68\) | 1.00000i | 0.121268i | ||||||||
\(69\) | 0.659401 | 0.0793825 | ||||||||
\(70\) | −4.76491 | − | 3.48486i | −0.569516 | − | 0.416521i | ||||
\(71\) | 8.34438 | 0.990296 | 0.495148 | − | 0.868809i | \(-0.335114\pi\) | ||||
0.495148 | + | 0.868809i | \(0.335114\pi\) | |||||||
\(72\) | 2.76491i | 0.325848i | ||||||||
\(73\) | 0.484862i | 0.0567488i | 0.999597 | + | 0.0283744i | \(0.00903306\pi\) | ||||
−0.999597 | + | 0.0283744i | \(0.990967\pi\) | |||||||
\(74\) | 11.1396 | 1.29495 | ||||||||
\(75\) | −2.31032 | + | 0.734633i | −0.266773 | + | 0.0848281i | ||||
\(76\) | 5.76491 | 0.661280 | ||||||||
\(77\) | − | 5.28005i | − | 0.601717i | ||||||
\(78\) | 0.235091i | 0.0266188i | ||||||||
\(79\) | −9.85952 | −1.10928 | −0.554641 | − | 0.832090i | \(-0.687144\pi\) | ||||
−0.554641 | + | 0.832090i | \(0.687144\pi\) | |||||||
\(80\) | 1.80487 | + | 1.32001i | 0.201791 | + | 0.147582i | ||||
\(81\) | 6.93945 | 0.771050 | ||||||||
\(82\) | 0.249771i | 0.0275826i | ||||||||
\(83\) | − | 17.5298i | − | 1.92415i | −0.272790 | − | 0.962074i | \(-0.587946\pi\) | ||
0.272790 | − | 0.962074i | \(-0.412054\pi\) | |||||||
\(84\) | −1.28005 | −0.139665 | ||||||||
\(85\) | 1.32001 | − | 1.80487i | 0.143175 | − | 0.195766i | ||||
\(86\) | 1.03028 | 0.111098 | ||||||||
\(87\) | − | 3.95413i | − | 0.423927i | ||||||
\(88\) | 2.00000i | 0.213201i | ||||||||
\(89\) | 8.73463 | 0.925869 | 0.462935 | − | 0.886392i | \(-0.346796\pi\) | ||||
0.462935 | + | 0.886392i | \(0.346796\pi\) | |||||||
\(90\) | 3.64971 | − | 4.99031i | 0.384713 | − | 0.526025i | ||||
\(91\) | 1.28005 | 0.134185 | ||||||||
\(92\) | 1.35998i | 0.141787i | ||||||||
\(93\) | − | 1.01560i | − | 0.105312i | ||||||
\(94\) | −6.01468 | −0.620367 | ||||||||
\(95\) | −10.4049 | − | 7.60975i | −1.06752 | − | 0.780744i | ||||
\(96\) | 0.484862 | 0.0494860 | ||||||||
\(97\) | − | 6.73463i | − | 0.683798i | −0.939737 | − | 0.341899i | \(-0.888930\pi\) | ||
0.939737 | − | 0.341899i | \(-0.111070\pi\) | |||||||
\(98\) | − | 0.0302761i | − | 0.00305835i | ||||||
\(99\) | 5.52982 | 0.555768 | ||||||||
\(100\) | −1.51514 | − | 4.76491i | −0.151514 | − | 0.476491i | ||||
\(101\) | 13.5298 | 1.34627 | 0.673134 | − | 0.739521i | \(-0.264948\pi\) | ||||
0.673134 | + | 0.739521i | \(0.264948\pi\) | |||||||
\(102\) | − | 0.484862i | − | 0.0480085i | ||||||
\(103\) | − | 11.2195i | − | 1.10549i | −0.833351 | − | 0.552745i | \(-0.813580\pi\) | ||
0.833351 | − | 0.552745i | \(-0.186420\pi\) | |||||||
\(104\) | −0.484862 | −0.0475446 | ||||||||
\(105\) | 2.31032 | + | 1.68968i | 0.225464 | + | 0.164896i | ||||
\(106\) | −7.70436 | −0.748313 | ||||||||
\(107\) | 19.4693i | 1.88216i | 0.338177 | + | 0.941082i | \(0.390190\pi\) | ||||
−0.338177 | + | 0.941082i | \(0.609810\pi\) | |||||||
\(108\) | − | 2.79518i | − | 0.268967i | ||||||
\(109\) | 12.6547 | 1.21210 | 0.606050 | − | 0.795426i | \(-0.292753\pi\) | ||||
0.606050 | + | 0.795426i | \(0.292753\pi\) | |||||||
\(110\) | 2.64002 | − | 3.60975i | 0.251716 | − | 0.344176i | ||||
\(111\) | −5.40115 | −0.512655 | ||||||||
\(112\) | − | 2.64002i | − | 0.249459i | ||||||
\(113\) | 7.51514i | 0.706965i | 0.935441 | + | 0.353482i | \(0.115003\pi\) | ||||
−0.935441 | + | 0.353482i | \(0.884997\pi\) | |||||||
\(114\) | −2.79518 | −0.261793 | ||||||||
\(115\) | 1.79518 | − | 2.45459i | 0.167402 | − | 0.228891i | ||||
\(116\) | 8.15516 | 0.757188 | ||||||||
\(117\) | 1.34060i | 0.123938i | ||||||||
\(118\) | 8.73463i | 0.804088i | ||||||||
\(119\) | −2.64002 | −0.242011 | ||||||||
\(120\) | −0.875115 | − | 0.640023i | −0.0798867 | − | 0.0584259i | ||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 11.3747i | 1.02981i | ||||||||
\(123\) | − | 0.121104i | − | 0.0109196i | ||||||
\(124\) | 2.09461 | 0.188101 | ||||||||
\(125\) | −3.55510 | + | 10.6001i | −0.317978 | + | 0.948098i | ||||
\(126\) | −7.29942 | −0.650284 | ||||||||
\(127\) | 14.7952i | 1.31286i | 0.754387 | + | 0.656430i | \(0.227934\pi\) | ||||
−0.754387 | + | 0.656430i | \(0.772066\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −0.499542 | −0.0439822 | ||||||||
\(130\) | 0.875115 | + | 0.640023i | 0.0767526 | + | 0.0561338i | ||||
\(131\) | −2.49954 | −0.218386 | −0.109193 | − | 0.994021i | \(-0.534827\pi\) | ||||
−0.109193 | + | 0.994021i | \(0.534827\pi\) | |||||||
\(132\) | − | 0.969724i | − | 0.0844036i | ||||||
\(133\) | 15.2195i | 1.31970i | ||||||||
\(134\) | 4.96972 | 0.429319 | ||||||||
\(135\) | −3.68968 | + | 5.04496i | −0.317557 | + | 0.434201i | ||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | − | 2.06055i | − | 0.176045i | −0.996118 | − | 0.0880224i | \(-0.971945\pi\) | ||
0.996118 | − | 0.0880224i | \(-0.0280547\pi\) | |||||||
\(138\) | − | 0.659401i | − | 0.0561319i | ||||||
\(139\) | 15.5904 | 1.32236 | 0.661179 | − | 0.750228i | \(-0.270056\pi\) | ||||
0.661179 | + | 0.750228i | \(0.270056\pi\) | |||||||
\(140\) | −3.48486 | + | 4.76491i | −0.294525 | + | 0.402708i | ||||
\(141\) | 2.91629 | 0.245596 | ||||||||
\(142\) | − | 8.34438i | − | 0.700245i | ||||||
\(143\) | 0.969724i | 0.0810924i | ||||||||
\(144\) | 2.76491 | 0.230409 | ||||||||
\(145\) | −14.7190 | − | 10.7649i | −1.22235 | − | 0.893977i | ||||
\(146\) | 0.484862 | 0.0401275 | ||||||||
\(147\) | 0.0146797i | 0.00121076i | ||||||||
\(148\) | − | 11.1396i | − | 0.915667i | ||||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | 0.734633 | + | 2.31032i | 0.0599825 | + | 0.188637i | ||||
\(151\) | −15.8401 | −1.28905 | −0.644526 | − | 0.764582i | \(-0.722945\pi\) | ||||
−0.644526 | + | 0.764582i | \(0.722945\pi\) | |||||||
\(152\) | − | 5.76491i | − | 0.467596i | ||||||
\(153\) | − | 2.76491i | − | 0.223530i | ||||||
\(154\) | −5.28005 | −0.425478 | ||||||||
\(155\) | −3.78051 | − | 2.76491i | −0.303657 | − | 0.222083i | ||||
\(156\) | 0.235091 | 0.0188224 | ||||||||
\(157\) | − | 1.34060i | − | 0.106991i | −0.998568 | − | 0.0534957i | \(-0.982964\pi\) | ||
0.998568 | − | 0.0534957i | \(-0.0170364\pi\) | |||||||
\(158\) | 9.85952i | 0.784381i | ||||||||
\(159\) | 3.73555 | 0.296248 | ||||||||
\(160\) | 1.32001 | − | 1.80487i | 0.104356 | − | 0.142688i | ||||
\(161\) | −3.59037 | −0.282961 | ||||||||
\(162\) | − | 6.93945i | − | 0.545215i | ||||||
\(163\) | 16.2498i | 1.27278i | 0.771367 | + | 0.636390i | \(0.219573\pi\) | ||||
−0.771367 | + | 0.636390i | \(0.780427\pi\) | |||||||
\(164\) | 0.249771 | 0.0195038 | ||||||||
\(165\) | −1.28005 | + | 1.75023i | −0.0996515 | + | 0.136255i | ||||
\(166\) | −17.5298 | −1.36058 | ||||||||
\(167\) | 2.95035i | 0.228305i | 0.993463 | + | 0.114152i | \(0.0364152\pi\) | ||||
−0.993463 | + | 0.114152i | \(0.963585\pi\) | |||||||
\(168\) | 1.28005i | 0.0987578i | ||||||||
\(169\) | 12.7649 | 0.981916 | ||||||||
\(170\) | −1.80487 | − | 1.32001i | −0.138427 | − | 0.101240i | ||||
\(171\) | −15.9394 | −1.21892 | ||||||||
\(172\) | − | 1.03028i | − | 0.0785578i | ||||||
\(173\) | − | 6.14048i | − | 0.466852i | −0.972375 | − | 0.233426i | \(-0.925006\pi\) | ||
0.972375 | − | 0.233426i | \(-0.0749937\pi\) | |||||||
\(174\) | −3.95413 | −0.299762 | ||||||||
\(175\) | 12.5795 | − | 4.00000i | 0.950919 | − | 0.302372i | ||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | − | 4.23509i | − | 0.318329i | ||||||
\(178\) | − | 8.73463i | − | 0.654688i | ||||||
\(179\) | 15.5904 | 1.16528 | 0.582639 | − | 0.812731i | \(-0.302020\pi\) | ||||
0.582639 | + | 0.812731i | \(0.302020\pi\) | |||||||
\(180\) | −4.99031 | − | 3.64971i | −0.371956 | − | 0.272033i | ||||
\(181\) | 4.10929 | 0.305441 | 0.152721 | − | 0.988269i | \(-0.451197\pi\) | ||||
0.152721 | + | 0.988269i | \(0.451197\pi\) | |||||||
\(182\) | − | 1.28005i | − | 0.0948834i | ||||||
\(183\) | − | 5.51514i | − | 0.407691i | ||||||
\(184\) | 1.35998 | 0.100259 | ||||||||
\(185\) | −14.7044 | + | 20.1055i | −1.08109 | + | 1.47819i | ||||
\(186\) | −1.01560 | −0.0744671 | ||||||||
\(187\) | − | 2.00000i | − | 0.146254i | ||||||
\(188\) | 6.01468i | 0.438666i | ||||||||
\(189\) | 7.37935 | 0.536769 | ||||||||
\(190\) | −7.60975 | + | 10.4049i | −0.552069 | + | 0.754853i | ||||
\(191\) | 6.06055 | 0.438526 | 0.219263 | − | 0.975666i | \(-0.429635\pi\) | ||||
0.219263 | + | 0.975666i | \(0.429635\pi\) | |||||||
\(192\) | − | 0.484862i | − | 0.0349919i | ||||||
\(193\) | 12.5601i | 0.904095i | 0.891994 | + | 0.452048i | \(0.149306\pi\) | ||||
−0.891994 | + | 0.452048i | \(0.850694\pi\) | |||||||
\(194\) | −6.73463 | −0.483518 | ||||||||
\(195\) | −0.424310 | − | 0.310323i | −0.0303855 | − | 0.0222227i | ||||
\(196\) | −0.0302761 | −0.00216258 | ||||||||
\(197\) | − | 26.0487i | − | 1.85590i | −0.372710 | − | 0.927948i | \(-0.621571\pi\) | ||
0.372710 | − | 0.927948i | \(-0.378429\pi\) | |||||||
\(198\) | − | 5.52982i | − | 0.392987i | ||||||
\(199\) | −3.37466 | −0.239223 | −0.119612 | − | 0.992821i | \(-0.538165\pi\) | ||||
−0.119612 | + | 0.992821i | \(0.538165\pi\) | |||||||
\(200\) | −4.76491 | + | 1.51514i | −0.336930 | + | 0.107136i | ||||
\(201\) | −2.40963 | −0.169962 | ||||||||
\(202\) | − | 13.5298i | − | 0.951955i | ||||||
\(203\) | 21.5298i | 1.51110i | ||||||||
\(204\) | −0.484862 | −0.0339471 | ||||||||
\(205\) | −0.450805 | − | 0.329700i | −0.0314856 | − | 0.0230273i | ||||
\(206\) | −11.2195 | −0.781699 | ||||||||
\(207\) | − | 3.76021i | − | 0.261353i | ||||||
\(208\) | 0.484862i | 0.0336191i | ||||||||
\(209\) | −11.5298 | −0.797534 | ||||||||
\(210\) | 1.68968 | − | 2.31032i | 0.116599 | − | 0.159427i | ||||
\(211\) | 18.0294 | 1.24119 | 0.620596 | − | 0.784130i | \(-0.286891\pi\) | ||||
0.620596 | + | 0.784130i | \(0.286891\pi\) | |||||||
\(212\) | 7.70436i | 0.529137i | ||||||||
\(213\) | 4.04587i | 0.277219i | ||||||||
\(214\) | 19.4693 | 1.33089 | ||||||||
\(215\) | −1.35998 | + | 1.85952i | −0.0927496 | + | 0.126818i | ||||
\(216\) | −2.79518 | −0.190188 | ||||||||
\(217\) | 5.52982i | 0.375388i | ||||||||
\(218\) | − | 12.6547i | − | 0.857085i | ||||||
\(219\) | −0.235091 | −0.0158860 | ||||||||
\(220\) | −3.60975 | − | 2.64002i | −0.243369 | − | 0.177990i | ||||
\(221\) | 0.484862 | 0.0326153 | ||||||||
\(222\) | 5.40115i | 0.362502i | ||||||||
\(223\) | − | 23.2947i | − | 1.55993i | −0.625823 | − | 0.779965i | \(-0.715237\pi\) | ||
0.625823 | − | 0.779965i | \(-0.284763\pi\) | |||||||
\(224\) | −2.64002 | −0.176394 | ||||||||
\(225\) | 4.18922 | + | 13.1745i | 0.279281 | + | 0.878303i | ||||
\(226\) | 7.51514 | 0.499900 | ||||||||
\(227\) | 17.4839i | 1.16045i | 0.814456 | + | 0.580225i | \(0.197035\pi\) | ||||
−0.814456 | + | 0.580225i | \(0.802965\pi\) | |||||||
\(228\) | 2.79518i | 0.185116i | ||||||||
\(229\) | −0.719953 | −0.0475758 | −0.0237879 | − | 0.999717i | \(-0.507573\pi\) | ||||
−0.0237879 | + | 0.999717i | \(0.507573\pi\) | |||||||
\(230\) | −2.45459 | − | 1.79518i | −0.161851 | − | 0.118371i | ||||
\(231\) | 2.56009 | 0.168442 | ||||||||
\(232\) | − | 8.15516i | − | 0.535413i | ||||||
\(233\) | − | 11.0450i | − | 0.723579i | −0.932260 | − | 0.361790i | \(-0.882166\pi\) | ||
0.932260 | − | 0.361790i | \(-0.117834\pi\) | |||||||
\(234\) | 1.34060 | 0.0876377 | ||||||||
\(235\) | 7.93945 | − | 10.8557i | 0.517912 | − | 0.708150i | ||||
\(236\) | 8.73463 | 0.568576 | ||||||||
\(237\) | − | 4.78051i | − | 0.310527i | ||||||
\(238\) | 2.64002i | 0.171127i | ||||||||
\(239\) | 5.59037 | 0.361611 | 0.180805 | − | 0.983519i | \(-0.442130\pi\) | ||||
0.180805 | + | 0.983519i | \(0.442130\pi\) | |||||||
\(240\) | −0.640023 | + | 0.875115i | −0.0413133 | + | 0.0564884i | ||||
\(241\) | −8.37088 | −0.539215 | −0.269608 | − | 0.962970i | \(-0.586894\pi\) | ||||
−0.269608 | + | 0.962970i | \(0.586894\pi\) | |||||||
\(242\) | 7.00000i | 0.449977i | ||||||||
\(243\) | 11.7502i | 0.753778i | ||||||||
\(244\) | 11.3747 | 0.728188 | ||||||||
\(245\) | 0.0546445 | + | 0.0399648i | 0.00349111 | + | 0.00255326i | ||||
\(246\) | −0.121104 | −0.00772133 | ||||||||
\(247\) | − | 2.79518i | − | 0.177853i | ||||||
\(248\) | − | 2.09461i | − | 0.133008i | ||||||
\(249\) | 8.49954 | 0.538637 | ||||||||
\(250\) | 10.6001 | + | 3.55510i | 0.670407 | + | 0.224844i | ||||
\(251\) | 19.4693 | 1.22889 | 0.614445 | − | 0.788960i | \(-0.289380\pi\) | ||||
0.614445 | + | 0.788960i | \(0.289380\pi\) | |||||||
\(252\) | 7.29942i | 0.459821i | ||||||||
\(253\) | − | 2.71995i | − | 0.171002i | ||||||
\(254\) | 14.7952 | 0.928332 | ||||||||
\(255\) | 0.875115 | + | 0.640023i | 0.0548018 | + | 0.0400798i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 13.9394i | − | 0.869519i | −0.900547 | − | 0.434759i | \(-0.856833\pi\) | ||
0.900547 | − | 0.434759i | \(-0.143167\pi\) | |||||||
\(258\) | 0.499542i | 0.0311001i | ||||||||
\(259\) | 29.4087 | 1.82737 | ||||||||
\(260\) | 0.640023 | − | 0.875115i | 0.0396926 | − | 0.0542723i | ||||
\(261\) | −22.5483 | −1.39570 | ||||||||
\(262\) | 2.49954i | 0.154422i | ||||||||
\(263\) | − | 16.2645i | − | 1.00291i | −0.865184 | − | 0.501454i | \(-0.832798\pi\) | ||
0.865184 | − | 0.501454i | \(-0.167202\pi\) | |||||||
\(264\) | −0.969724 | −0.0596824 | ||||||||
\(265\) | 10.1698 | − | 13.9054i | 0.624728 | − | 0.854201i | ||||
\(266\) | 15.2195 | 0.933167 | ||||||||
\(267\) | 4.23509i | 0.259183i | ||||||||
\(268\) | − | 4.96972i | − | 0.303574i | ||||||
\(269\) | −10.4049 | −0.634400 | −0.317200 | − | 0.948359i | \(-0.602743\pi\) | ||||
−0.317200 | + | 0.948359i | \(0.602743\pi\) | |||||||
\(270\) | 5.04496 | + | 3.68968i | 0.307026 | + | 0.224547i | ||||
\(271\) | −24.0294 | −1.45968 | −0.729840 | − | 0.683618i | \(-0.760405\pi\) | ||||
−0.729840 | + | 0.683618i | \(0.760405\pi\) | |||||||
\(272\) | − | 1.00000i | − | 0.0606339i | ||||||
\(273\) | 0.620646i | 0.0375632i | ||||||||
\(274\) | −2.06055 | −0.124483 | ||||||||
\(275\) | 3.03028 | + | 9.52982i | 0.182733 | + | 0.574670i | ||||
\(276\) | −0.659401 | −0.0396913 | ||||||||
\(277\) | − | 18.9503i | − | 1.13862i | −0.822124 | − | 0.569308i | \(-0.807211\pi\) | ||
0.822124 | − | 0.569308i | \(-0.192789\pi\) | |||||||
\(278\) | − | 15.5904i | − | 0.935048i | ||||||
\(279\) | −5.79140 | −0.346722 | ||||||||
\(280\) | 4.76491 | + | 3.48486i | 0.284758 | + | 0.208260i | ||||
\(281\) | 19.6438 | 1.17185 | 0.585926 | − | 0.810365i | \(-0.300731\pi\) | ||||
0.585926 | + | 0.810365i | \(0.300731\pi\) | |||||||
\(282\) | − | 2.91629i | − | 0.173663i | ||||||
\(283\) | 25.7943i | 1.53331i | 0.642059 | + | 0.766655i | \(0.278080\pi\) | ||||
−0.642059 | + | 0.766655i | \(0.721920\pi\) | |||||||
\(284\) | −8.34438 | −0.495148 | ||||||||
\(285\) | 3.68968 | − | 5.04496i | 0.218558 | − | 0.298837i | ||||
\(286\) | 0.969724 | 0.0573410 | ||||||||
\(287\) | 0.659401i | 0.0389232i | ||||||||
\(288\) | − | 2.76491i | − | 0.162924i | ||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −10.7649 | + | 14.7190i | −0.632137 | + | 0.864332i | ||||
\(291\) | 3.26537 | 0.191419 | ||||||||
\(292\) | − | 0.484862i | − | 0.0283744i | ||||||
\(293\) | − | 22.9239i | − | 1.33923i | −0.742710 | − | 0.669613i | \(-0.766460\pi\) | ||
0.742710 | − | 0.669613i | \(-0.233540\pi\) | |||||||
\(294\) | 0.0146797 | 0.000856139 | ||||||||
\(295\) | −15.7649 | − | 11.5298i | −0.917868 | − | 0.671292i | ||||
\(296\) | −11.1396 | −0.647474 | ||||||||
\(297\) | 5.59037i | 0.324386i | ||||||||
\(298\) | 10.0000i | 0.579284i | ||||||||
\(299\) | 0.659401 | 0.0381341 | ||||||||
\(300\) | 2.31032 | − | 0.734633i | 0.133387 | − | 0.0424140i | ||||
\(301\) | 2.71995 | 0.156775 | ||||||||
\(302\) | 15.8401i | 0.911498i | ||||||||
\(303\) | 6.56009i | 0.376868i | ||||||||
\(304\) | −5.76491 | −0.330640 | ||||||||
\(305\) | −20.5298 | − | 15.0147i | −1.17553 | − | 0.859738i | ||||
\(306\) | −2.76491 | −0.158059 | ||||||||
\(307\) | 10.4702i | 0.597565i | 0.954321 | + | 0.298782i | \(0.0965805\pi\) | ||||
−0.954321 | + | 0.298782i | \(0.903420\pi\) | |||||||
\(308\) | 5.28005i | 0.300859i | ||||||||
\(309\) | 5.43991 | 0.309465 | ||||||||
\(310\) | −2.76491 | + | 3.78051i | −0.157036 | + | 0.214718i | ||||
\(311\) | −9.73841 | −0.552215 | −0.276107 | − | 0.961127i | \(-0.589045\pi\) | ||||
−0.276107 | + | 0.961127i | \(0.589045\pi\) | |||||||
\(312\) | − | 0.235091i | − | 0.0133094i | ||||||
\(313\) | 9.50046i | 0.536998i | 0.963280 | + | 0.268499i | \(0.0865275\pi\) | ||||
−0.963280 | + | 0.268499i | \(0.913472\pi\) | |||||||
\(314\) | −1.34060 | −0.0756544 | ||||||||
\(315\) | 9.63533 | − | 13.1745i | 0.542889 | − | 0.742301i | ||||
\(316\) | 9.85952 | 0.554641 | ||||||||
\(317\) | − | 13.0790i | − | 0.734591i | −0.930104 | − | 0.367295i | \(-0.880284\pi\) | ||
0.930104 | − | 0.367295i | \(-0.119716\pi\) | |||||||
\(318\) | − | 3.73555i | − | 0.209479i | ||||||
\(319\) | −16.3103 | −0.913203 | ||||||||
\(320\) | −1.80487 | − | 1.32001i | −0.100896 | − | 0.0737909i | ||||
\(321\) | −9.43991 | −0.526884 | ||||||||
\(322\) | 3.59037i | 0.200083i | ||||||||
\(323\) | 5.76491i | 0.320768i | ||||||||
\(324\) | −6.93945 | −0.385525 | ||||||||
\(325\) | −2.31032 | + | 0.734633i | −0.128154 | + | 0.0407501i | ||||
\(326\) | 16.2498 | 0.899992 | ||||||||
\(327\) | 6.13578i | 0.339310i | ||||||||
\(328\) | − | 0.249771i | − | 0.0137913i | ||||||
\(329\) | −15.8789 | −0.875432 | ||||||||
\(330\) | 1.75023 | + | 1.28005i | 0.0963469 | + | 0.0704643i | ||||
\(331\) | 24.8851 | 1.36781 | 0.683904 | − | 0.729572i | \(-0.260281\pi\) | ||||
0.683904 | + | 0.729572i | \(0.260281\pi\) | |||||||
\(332\) | 17.5298i | 0.962074i | ||||||||
\(333\) | 30.7999i | 1.68782i | ||||||||
\(334\) | 2.95035 | 0.161436 | ||||||||
\(335\) | −6.56009 | + | 8.96972i | −0.358416 | + | 0.490068i | ||||
\(336\) | 1.28005 | 0.0698323 | ||||||||
\(337\) | − | 27.5445i | − | 1.50044i | −0.661186 | − | 0.750222i | \(-0.729947\pi\) | ||
0.661186 | − | 0.750222i | \(-0.270053\pi\) | |||||||
\(338\) | − | 12.7649i | − | 0.694320i | ||||||
\(339\) | −3.64380 | −0.197904 | ||||||||
\(340\) | −1.32001 | + | 1.80487i | −0.0715877 | + | 0.0978830i | ||||
\(341\) | −4.18922 | −0.226859 | ||||||||
\(342\) | 15.9394i | 0.861907i | ||||||||
\(343\) | − | 18.5601i | − | 1.00215i | ||||||
\(344\) | −1.03028 | −0.0555488 | ||||||||
\(345\) | 1.19014 | + | 0.870417i | 0.0640747 | + | 0.0468617i | ||||
\(346\) | −6.14048 | −0.330114 | ||||||||
\(347\) | − | 4.48486i | − | 0.240760i | −0.992728 | − | 0.120380i | \(-0.961589\pi\) | ||
0.992728 | − | 0.120380i | \(-0.0384113\pi\) | |||||||
\(348\) | 3.95413i | 0.211963i | ||||||||
\(349\) | −34.2186 | −1.83168 | −0.915839 | − | 0.401545i | \(-0.868473\pi\) | ||||
−0.915839 | + | 0.401545i | \(0.868473\pi\) | |||||||
\(350\) | −4.00000 | − | 12.5795i | −0.213809 | − | 0.672401i | ||||
\(351\) | −1.35528 | −0.0723394 | ||||||||
\(352\) | − | 2.00000i | − | 0.106600i | ||||||
\(353\) | − | 4.90917i | − | 0.261289i | −0.991429 | − | 0.130644i | \(-0.958295\pi\) | ||
0.991429 | − | 0.130644i | \(-0.0417046\pi\) | |||||||
\(354\) | −4.23509 | −0.225093 | ||||||||
\(355\) | 15.0606 | + | 11.0147i | 0.799331 | + | 0.584599i | ||||
\(356\) | −8.73463 | −0.462935 | ||||||||
\(357\) | − | 1.28005i | − | 0.0677473i | ||||||
\(358\) | − | 15.5904i | − | 0.823977i | ||||||
\(359\) | 13.7796 | 0.727259 | 0.363629 | − | 0.931544i | \(-0.381537\pi\) | ||||
0.363629 | + | 0.931544i | \(0.381537\pi\) | |||||||
\(360\) | −3.64971 | + | 4.99031i | −0.192357 | + | 0.263012i | ||||
\(361\) | 14.2342 | 0.749167 | ||||||||
\(362\) | − | 4.10929i | − | 0.215979i | ||||||
\(363\) | − | 3.39403i | − | 0.178141i | ||||||
\(364\) | −1.28005 | −0.0670927 | ||||||||
\(365\) | −0.640023 | + | 0.875115i | −0.0335004 | + | 0.0458056i | ||||
\(366\) | −5.51514 | −0.288281 | ||||||||
\(367\) | 4.39025i | 0.229169i | 0.993413 | + | 0.114585i | \(0.0365537\pi\) | ||||
−0.993413 | + | 0.114585i | \(0.963446\pi\) | |||||||
\(368\) | − | 1.35998i | − | 0.0708937i | ||||||
\(369\) | −0.690594 | −0.0359509 | ||||||||
\(370\) | 20.1055 | + | 14.7044i | 1.04524 | + | 0.764443i | ||||
\(371\) | −20.3397 | −1.05598 | ||||||||
\(372\) | 1.01560i | 0.0526562i | ||||||||
\(373\) | 0.220411i | 0.0114125i | 0.999984 | + | 0.00570623i | \(0.00181636\pi\) | ||||
−0.999984 | + | 0.00570623i | \(0.998184\pi\) | |||||||
\(374\) | −2.00000 | −0.103418 | ||||||||
\(375\) | −5.13957 | − | 1.72373i | −0.265406 | − | 0.0890132i | ||||
\(376\) | 6.01468 | 0.310183 | ||||||||
\(377\) | − | 3.95413i | − | 0.203648i | ||||||
\(378\) | − | 7.37935i | − | 0.379553i | ||||||
\(379\) | −26.3103 | −1.35147 | −0.675735 | − | 0.737144i | \(-0.736174\pi\) | ||||
−0.675735 | + | 0.737144i | \(0.736174\pi\) | |||||||
\(380\) | 10.4049 | + | 7.60975i | 0.533762 | + | 0.390372i | ||||
\(381\) | −7.17362 | −0.367516 | ||||||||
\(382\) | − | 6.06055i | − | 0.310085i | ||||||
\(383\) | 36.1433i | 1.84684i | 0.383793 | + | 0.923419i | \(0.374618\pi\) | ||||
−0.383793 | + | 0.923419i | \(0.625382\pi\) | |||||||
\(384\) | −0.484862 | −0.0247430 | ||||||||
\(385\) | 6.96972 | − | 9.52982i | 0.355210 | − | 0.485684i | ||||
\(386\) | 12.5601 | 0.639292 | ||||||||
\(387\) | 2.84862i | 0.144803i | ||||||||
\(388\) | 6.73463i | 0.341899i | ||||||||
\(389\) | −3.77959 | −0.191633 | −0.0958164 | − | 0.995399i | \(-0.530546\pi\) | ||||
−0.0958164 | + | 0.995399i | \(0.530546\pi\) | |||||||
\(390\) | −0.310323 | + | 0.424310i | −0.0157138 | + | 0.0214858i | ||||
\(391\) | −1.35998 | −0.0687770 | ||||||||
\(392\) | 0.0302761i | 0.00152917i | ||||||||
\(393\) | − | 1.21193i | − | 0.0611339i | ||||||
\(394\) | −26.0487 | −1.31232 | ||||||||
\(395\) | −17.7952 | − | 13.0147i | −0.895373 | − | 0.654840i | ||||
\(396\) | −5.52982 | −0.277884 | ||||||||
\(397\) | 12.2304i | 0.613826i | 0.951738 | + | 0.306913i | \(0.0992960\pi\) | ||||
−0.951738 | + | 0.306913i | \(0.900704\pi\) | |||||||
\(398\) | 3.37466i | 0.169156i | ||||||||
\(399\) | −7.37935 | −0.369430 | ||||||||
\(400\) | 1.51514 | + | 4.76491i | 0.0757569 | + | 0.238245i | ||||
\(401\) | −11.7796 | −0.588245 | −0.294122 | − | 0.955768i | \(-0.595027\pi\) | ||||
−0.294122 | + | 0.955768i | \(0.595027\pi\) | |||||||
\(402\) | 2.40963i | 0.120181i | ||||||||
\(403\) | − | 1.01560i | − | 0.0505905i | ||||||
\(404\) | −13.5298 | −0.673134 | ||||||||
\(405\) | 12.5248 | + | 9.16015i | 0.622364 | + | 0.455172i | ||||
\(406\) | 21.5298 | 1.06851 | ||||||||
\(407\) | 22.2791i | 1.10434i | ||||||||
\(408\) | 0.484862i | 0.0240042i | ||||||||
\(409\) | 15.7649 | 0.779525 | 0.389762 | − | 0.920916i | \(-0.372557\pi\) | ||||
0.389762 | + | 0.920916i | \(0.372557\pi\) | |||||||
\(410\) | −0.329700 | + | 0.450805i | −0.0162827 | + | 0.0222637i | ||||
\(411\) | 0.999083 | 0.0492811 | ||||||||
\(412\) | 11.2195i | 0.552745i | ||||||||
\(413\) | 23.0596i | 1.13469i | ||||||||
\(414\) | −3.76021 | −0.184804 | ||||||||
\(415\) | 23.1396 | − | 31.6391i | 1.13588 | − | 1.55310i | ||||
\(416\) | 0.484862 | 0.0237723 | ||||||||
\(417\) | 7.55918i | 0.370175i | ||||||||
\(418\) | 11.5298i | 0.563942i | ||||||||
\(419\) | −18.1892 | −0.888601 | −0.444301 | − | 0.895878i | \(-0.646548\pi\) | ||||
−0.444301 | + | 0.895878i | \(0.646548\pi\) | |||||||
\(420\) | −2.31032 | − | 1.68968i | −0.112732 | − | 0.0824478i | ||||
\(421\) | 9.03028 | 0.440109 | 0.220054 | − | 0.975488i | \(-0.429377\pi\) | ||||
0.220054 | + | 0.975488i | \(0.429377\pi\) | |||||||
\(422\) | − | 18.0294i | − | 0.877655i | ||||||
\(423\) | − | 16.6300i | − | 0.808580i | ||||||
\(424\) | 7.70436 | 0.374157 | ||||||||
\(425\) | 4.76491 | − | 1.51514i | 0.231132 | − | 0.0734950i | ||||
\(426\) | 4.04587 | 0.196023 | ||||||||
\(427\) | 30.0294i | 1.45322i | ||||||||
\(428\) | − | 19.4693i | − | 0.941082i | ||||||
\(429\) | −0.470182 | −0.0227006 | ||||||||
\(430\) | 1.85952 | + | 1.35998i | 0.0896739 | + | 0.0655839i | ||||
\(431\) | 20.4196 | 0.983578 | 0.491789 | − | 0.870714i | \(-0.336343\pi\) | ||||
0.491789 | + | 0.870714i | \(0.336343\pi\) | |||||||
\(432\) | 2.79518i | 0.134483i | ||||||||
\(433\) | − | 11.5904i | − | 0.556998i | −0.960437 | − | 0.278499i | \(-0.910163\pi\) | ||
0.960437 | − | 0.278499i | \(-0.0898368\pi\) | |||||||
\(434\) | 5.52982 | 0.265440 | ||||||||
\(435\) | 5.21949 | − | 7.13670i | 0.250256 | − | 0.342179i | ||||
\(436\) | −12.6547 | −0.606050 | ||||||||
\(437\) | 7.84014i | 0.375045i | ||||||||
\(438\) | 0.235091i | 0.0112331i | ||||||||
\(439\) | 2.01938 | 0.0963796 | 0.0481898 | − | 0.998838i | \(-0.484655\pi\) | ||||
0.0481898 | + | 0.998838i | \(0.484655\pi\) | |||||||
\(440\) | −2.64002 | + | 3.60975i | −0.125858 | + | 0.172088i | ||||
\(441\) | 0.0837106 | 0.00398622 | ||||||||
\(442\) | − | 0.484862i | − | 0.0230625i | ||||||
\(443\) | 27.4087i | 1.30223i | 0.758980 | + | 0.651114i | \(0.225698\pi\) | ||||
−0.758980 | + | 0.651114i | \(0.774302\pi\) | |||||||
\(444\) | 5.40115 | 0.256327 | ||||||||
\(445\) | 15.7649 | + | 11.5298i | 0.747328 | + | 0.546566i | ||||
\(446\) | −23.2947 | −1.10304 | ||||||||
\(447\) | − | 4.84862i | − | 0.229332i | ||||||
\(448\) | 2.64002i | 0.124729i | ||||||||
\(449\) | −29.7190 | −1.40253 | −0.701264 | − | 0.712902i | \(-0.747381\pi\) | ||||
−0.701264 | + | 0.712902i | \(0.747381\pi\) | |||||||
\(450\) | 13.1745 | − | 4.18922i | 0.621054 | − | 0.197482i | ||||
\(451\) | −0.499542 | −0.0235225 | ||||||||
\(452\) | − | 7.51514i | − | 0.353482i | ||||||
\(453\) | − | 7.68028i | − | 0.360851i | ||||||
\(454\) | 17.4839 | 0.820562 | ||||||||
\(455\) | 2.31032 | + | 1.68968i | 0.108310 | + | 0.0792133i | ||||
\(456\) | 2.79518 | 0.130897 | ||||||||
\(457\) | 39.4693i | 1.84629i | 0.384447 | + | 0.923147i | \(0.374392\pi\) | ||||
−0.384447 | + | 0.923147i | \(0.625608\pi\) | |||||||
\(458\) | 0.719953i | 0.0336412i | ||||||||
\(459\) | 2.79518 | 0.130468 | ||||||||
\(460\) | −1.79518 | + | 2.45459i | −0.0837009 | + | 0.114446i | ||||
\(461\) | 14.6888 | 0.684124 | 0.342062 | − | 0.939677i | \(-0.388875\pi\) | ||||
0.342062 | + | 0.939677i | \(0.388875\pi\) | |||||||
\(462\) | − | 2.56009i | − | 0.119106i | ||||||
\(463\) | − | 35.1055i | − | 1.63149i | −0.578411 | − | 0.815746i | \(-0.696327\pi\) | ||
0.578411 | − | 0.815746i | \(-0.303673\pi\) | |||||||
\(464\) | −8.15516 | −0.378594 | ||||||||
\(465\) | 1.34060 | − | 1.83302i | 0.0621688 | − | 0.0850044i | ||||
\(466\) | −11.0450 | −0.511648 | ||||||||
\(467\) | − | 9.96881i | − | 0.461301i | −0.973037 | − | 0.230651i | \(-0.925915\pi\) | ||
0.973037 | − | 0.230651i | \(-0.0740855\pi\) | |||||||
\(468\) | − | 1.34060i | − | 0.0619692i | ||||||
\(469\) | 13.1202 | 0.605834 | ||||||||
\(470\) | −10.8557 | − | 7.93945i | −0.500738 | − | 0.366219i | ||||
\(471\) | 0.650006 | 0.0299507 | ||||||||
\(472\) | − | 8.73463i | − | 0.402044i | ||||||
\(473\) | 2.06055i | 0.0947443i | ||||||||
\(474\) | −4.78051 | −0.219576 | ||||||||
\(475\) | −8.73463 | − | 27.4693i | −0.400772 | − | 1.26038i | ||||
\(476\) | 2.64002 | 0.121005 | ||||||||
\(477\) | − | 21.3018i | − | 0.975344i | ||||||
\(478\) | − | 5.59037i | − | 0.255698i | ||||||
\(479\) | 2.28383 | 0.104351 | 0.0521754 | − | 0.998638i | \(-0.483385\pi\) | ||||
0.0521754 | + | 0.998638i | \(0.483385\pi\) | |||||||
\(480\) | 0.875115 | + | 0.640023i | 0.0399433 | + | 0.0292129i | ||||
\(481\) | −5.40115 | −0.246271 | ||||||||
\(482\) | 8.37088i | 0.381283i | ||||||||
\(483\) | − | 1.74083i | − | 0.0792107i | ||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 8.88979 | − | 12.1552i | 0.403665 | − | 0.551937i | ||||
\(486\) | 11.7502 | 0.533001 | ||||||||
\(487\) | − | 10.8292i | − | 0.490720i | −0.969432 | − | 0.245360i | \(-0.921094\pi\) | ||
0.969432 | − | 0.245360i | \(-0.0789061\pi\) | |||||||
\(488\) | − | 11.3747i | − | 0.514906i | ||||||
\(489\) | −7.87890 | −0.356296 | ||||||||
\(490\) | 0.0399648 | − | 0.0546445i | 0.00180543 | − | 0.00246859i | ||||
\(491\) | 24.7952 | 1.11899 | 0.559496 | − | 0.828833i | \(-0.310995\pi\) | ||||
0.559496 | + | 0.828833i | \(0.310995\pi\) | |||||||
\(492\) | 0.121104i | 0.00545981i | ||||||||
\(493\) | 8.15516i | 0.367290i | ||||||||
\(494\) | −2.79518 | −0.125761 | ||||||||
\(495\) | 9.98062 | + | 7.29942i | 0.448596 | + | 0.328085i | ||||
\(496\) | −2.09461 | −0.0940507 | ||||||||
\(497\) | − | 22.0294i | − | 0.988152i | ||||||
\(498\) | − | 8.49954i | − | 0.380874i | ||||||
\(499\) | −5.15138 | −0.230607 | −0.115304 | − | 0.993330i | \(-0.536784\pi\) | ||||
−0.115304 | + | 0.993330i | \(0.536784\pi\) | |||||||
\(500\) | 3.55510 | − | 10.6001i | 0.158989 | − | 0.474049i | ||||
\(501\) | −1.43051 | −0.0639105 | ||||||||
\(502\) | − | 19.4693i | − | 0.868956i | ||||||
\(503\) | 29.0109i | 1.29353i | 0.762688 | + | 0.646766i | \(0.223879\pi\) | ||||
−0.762688 | + | 0.646766i | \(0.776121\pi\) | |||||||
\(504\) | 7.29942 | 0.325142 | ||||||||
\(505\) | 24.4196 | + | 17.8595i | 1.08666 | + | 0.794738i | ||||
\(506\) | −2.71995 | −0.120917 | ||||||||
\(507\) | 6.18922i | 0.274873i | ||||||||
\(508\) | − | 14.7952i | − | 0.656430i | ||||||
\(509\) | 27.4693 | 1.21755 | 0.608777 | − | 0.793341i | \(-0.291660\pi\) | ||||
0.608777 | + | 0.793341i | \(0.291660\pi\) | |||||||
\(510\) | 0.640023 | − | 0.875115i | 0.0283407 | − | 0.0387507i | ||||
\(511\) | 1.28005 | 0.0566259 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 16.1140i | − | 0.711450i | ||||||
\(514\) | −13.9394 | −0.614843 | ||||||||
\(515\) | 14.8099 | − | 20.2498i | 0.652601 | − | 0.892312i | ||||
\(516\) | 0.499542 | 0.0219911 | ||||||||
\(517\) | − | 12.0294i | − | 0.529051i | ||||||
\(518\) | − | 29.4087i | − | 1.29214i | ||||||
\(519\) | 2.97729 | 0.130688 | ||||||||
\(520\) | −0.875115 | − | 0.640023i | −0.0383763 | − | 0.0280669i | ||||
\(521\) | 5.68968 | 0.249269 | 0.124635 | − | 0.992203i | \(-0.460224\pi\) | ||||
0.124635 | + | 0.992203i | \(0.460224\pi\) | |||||||
\(522\) | 22.5483i | 0.986911i | ||||||||
\(523\) | − | 7.52982i | − | 0.329256i | −0.986356 | − | 0.164628i | \(-0.947358\pi\) | ||
0.986356 | − | 0.164628i | \(-0.0526424\pi\) | |||||||
\(524\) | 2.49954 | 0.109193 | ||||||||
\(525\) | 1.93945 | + | 6.09931i | 0.0846444 | + | 0.266196i | ||||
\(526\) | −16.2645 | −0.709164 | ||||||||
\(527\) | 2.09461i | 0.0912426i | ||||||||
\(528\) | 0.969724i | 0.0422018i | ||||||||
\(529\) | 21.1505 | 0.919585 | ||||||||
\(530\) | −13.9054 | − | 10.1698i | −0.604012 | − | 0.441750i | ||||
\(531\) | −24.1505 | −1.04804 | ||||||||
\(532\) | − | 15.2195i | − | 0.659849i | ||||||
\(533\) | − | 0.121104i | − | 0.00524561i | ||||||
\(534\) | 4.23509 | 0.183270 | ||||||||
\(535\) | −25.6997 | + | 35.1396i | −1.11109 | + | 1.51922i | ||||
\(536\) | −4.96972 | −0.214659 | ||||||||
\(537\) | 7.55918i | 0.326203i | ||||||||
\(538\) | 10.4049i | 0.448588i | ||||||||
\(539\) | 0.0605522 | 0.00260817 | ||||||||
\(540\) | 3.68968 | − | 5.04496i | 0.158778 | − | 0.217100i | ||||
\(541\) | 26.0100 | 1.11826 | 0.559128 | − | 0.829081i | \(-0.311136\pi\) | ||||
0.559128 | + | 0.829081i | \(0.311136\pi\) | |||||||
\(542\) | 24.0294i | 1.03215i | ||||||||
\(543\) | 1.99244i | 0.0855037i | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 22.8401 | + | 16.7044i | 0.978364 | + | 0.715536i | ||||
\(546\) | 0.620646 | 0.0265612 | ||||||||
\(547\) | − | 11.5833i | − | 0.495264i | −0.968854 | − | 0.247632i | \(-0.920348\pi\) | ||
0.968854 | − | 0.247632i | \(-0.0796524\pi\) | |||||||
\(548\) | 2.06055i | 0.0880224i | ||||||||
\(549\) | −31.4499 | −1.34225 | ||||||||
\(550\) | 9.52982 | − | 3.03028i | 0.406353 | − | 0.129211i | ||||
\(551\) | 47.0138 | 2.00285 | ||||||||
\(552\) | 0.659401i | 0.0280660i | ||||||||
\(553\) | 26.0294i | 1.10688i | ||||||||
\(554\) | −18.9503 | −0.805123 | ||||||||
\(555\) | −9.74840 | − | 7.12958i | −0.413796 | − | 0.302634i | ||||
\(556\) | −15.5904 | −0.661179 | ||||||||
\(557\) | 5.95413i | 0.252284i | 0.992012 | + | 0.126142i | \(0.0402596\pi\) | ||||
−0.992012 | + | 0.126142i | \(0.959740\pi\) | |||||||
\(558\) | 5.79140i | 0.245170i | ||||||||
\(559\) | −0.499542 | −0.0211284 | ||||||||
\(560\) | 3.48486 | − | 4.76491i | 0.147262 | − | 0.201354i | ||||
\(561\) | 0.969724 | 0.0409418 | ||||||||
\(562\) | − | 19.6438i | − | 0.828624i | ||||||
\(563\) | 34.5289i | 1.45522i | 0.685991 | + | 0.727610i | \(0.259369\pi\) | ||||
−0.685991 | + | 0.727610i | \(0.740631\pi\) | |||||||
\(564\) | −2.91629 | −0.122798 | ||||||||
\(565\) | −9.92007 | + | 13.5639i | −0.417340 | + | 0.570637i | ||||
\(566\) | 25.7943 | 1.08421 | ||||||||
\(567\) | − | 18.3203i | − | 0.769380i | ||||||
\(568\) | 8.34438i | 0.350122i | ||||||||
\(569\) | −12.7952 | −0.536402 | −0.268201 | − | 0.963363i | \(-0.586429\pi\) | ||||
−0.268201 | + | 0.963363i | \(0.586429\pi\) | |||||||
\(570\) | −5.04496 | − | 3.68968i | −0.211310 | − | 0.154544i | ||||
\(571\) | −4.22041 | −0.176619 | −0.0883094 | − | 0.996093i | \(-0.528146\pi\) | ||||
−0.0883094 | + | 0.996093i | \(0.528146\pi\) | |||||||
\(572\) | − | 0.969724i | − | 0.0405462i | ||||||
\(573\) | 2.93853i | 0.122759i | ||||||||
\(574\) | 0.659401 | 0.0275229 | ||||||||
\(575\) | 6.48016 | − | 2.06055i | 0.270242 | − | 0.0859310i | ||||
\(576\) | −2.76491 | −0.115205 | ||||||||
\(577\) | − | 35.5592i | − | 1.48035i | −0.672415 | − | 0.740174i | \(-0.734743\pi\) | ||
0.672415 | − | 0.740174i | \(-0.265257\pi\) | |||||||
\(578\) | 1.00000i | 0.0415945i | ||||||||
\(579\) | −6.08991 | −0.253088 | ||||||||
\(580\) | 14.7190 | + | 10.7649i | 0.611175 | + | 0.446989i | ||||
\(581\) | −46.2791 | −1.91998 | ||||||||
\(582\) | − | 3.26537i | − | 0.135354i | ||||||
\(583\) | − | 15.4087i | − | 0.638164i | ||||||
\(584\) | −0.484862 | −0.0200637 | ||||||||
\(585\) | −1.76961 | + | 2.41961i | −0.0731642 | + | 0.100039i | ||||
\(586\) | −22.9239 | −0.946976 | ||||||||
\(587\) | − | 43.6803i | − | 1.80288i | −0.432906 | − | 0.901439i | \(-0.642512\pi\) | ||
0.432906 | − | 0.901439i | \(-0.357488\pi\) | |||||||
\(588\) | − | 0.0146797i | − | 0.000605382i | ||||||
\(589\) | 12.0752 | 0.497551 | ||||||||
\(590\) | −11.5298 | + | 15.7649i | −0.474675 | + | 0.649031i | ||||
\(591\) | 12.6300 | 0.519530 | ||||||||
\(592\) | 11.1396i | 0.457833i | ||||||||
\(593\) | − | 20.1505i | − | 0.827480i | −0.910395 | − | 0.413740i | \(-0.864222\pi\) | ||
0.910395 | − | 0.413740i | \(-0.135778\pi\) | |||||||
\(594\) | 5.59037 | 0.229376 | ||||||||
\(595\) | −4.76491 | − | 3.48486i | −0.195342 | − | 0.142865i | ||||
\(596\) | 10.0000 | 0.409616 | ||||||||
\(597\) | − | 1.63624i | − | 0.0669669i | ||||||
\(598\) | − | 0.659401i | − | 0.0269649i | ||||||
\(599\) | −33.4986 | −1.36872 | −0.684358 | − | 0.729146i | \(-0.739918\pi\) | ||||
−0.684358 | + | 0.729146i | \(0.739918\pi\) | |||||||
\(600\) | −0.734633 | − | 2.31032i | −0.0299913 | − | 0.0943185i | ||||
\(601\) | 7.93945 | 0.323857 | 0.161928 | − | 0.986803i | \(-0.448229\pi\) | ||||
0.161928 | + | 0.986803i | \(0.448229\pi\) | |||||||
\(602\) | − | 2.71995i | − | 0.110857i | ||||||
\(603\) | 13.7408i | 0.559570i | ||||||||
\(604\) | 15.8401 | 0.644526 | ||||||||
\(605\) | −12.6341 | − | 9.24008i | −0.513650 | − | 0.375663i | ||||
\(606\) | 6.56009 | 0.266486 | ||||||||
\(607\) | 38.9797i | 1.58214i | 0.611727 | + | 0.791069i | \(0.290475\pi\) | ||||
−0.611727 | + | 0.791069i | \(0.709525\pi\) | |||||||
\(608\) | 5.76491i | 0.233798i | ||||||||
\(609\) | −10.4390 | −0.423009 | ||||||||
\(610\) | −15.0147 | + | 20.5298i | −0.607927 | + | 0.831228i | ||||
\(611\) | 2.91629 | 0.117980 | ||||||||
\(612\) | 2.76491i | 0.111765i | ||||||||
\(613\) | − | 28.5142i | − | 1.15168i | −0.817563 | − | 0.575839i | \(-0.804675\pi\) | ||
0.817563 | − | 0.575839i | \(-0.195325\pi\) | |||||||
\(614\) | 10.4702 | 0.422542 | ||||||||
\(615\) | 0.159859 | − | 0.218578i | 0.00644615 | − | 0.00881392i | ||||
\(616\) | 5.28005 | 0.212739 | ||||||||
\(617\) | − | 1.07615i | − | 0.0433241i | −0.999765 | − | 0.0216621i | \(-0.993104\pi\) | ||
0.999765 | − | 0.0216621i | \(-0.00689579\pi\) | |||||||
\(618\) | − | 5.43991i | − | 0.218825i | ||||||
\(619\) | 0.719953 | 0.0289374 | 0.0144687 | − | 0.999895i | \(-0.495394\pi\) | ||||
0.0144687 | + | 0.999895i | \(0.495394\pi\) | |||||||
\(620\) | 3.78051 | + | 2.76491i | 0.151829 | + | 0.111041i | ||||
\(621\) | 3.80139 | 0.152544 | ||||||||
\(622\) | 9.73841i | 0.390475i | ||||||||
\(623\) | − | 23.0596i | − | 0.923865i | ||||||
\(624\) | −0.235091 | −0.00941118 | ||||||||
\(625\) | −20.4087 | + | 14.4390i | −0.816349 | + | 0.577560i | ||||
\(626\) | 9.50046 | 0.379715 | ||||||||
\(627\) | − | 5.59037i | − | 0.223258i | ||||||
\(628\) | 1.34060i | 0.0534957i | ||||||||
\(629\) | 11.1396 | 0.444164 | ||||||||
\(630\) | −13.1745 | − | 9.63533i | −0.524886 | − | 0.383881i | ||||
\(631\) | 3.81078 | 0.151705 | 0.0758524 | − | 0.997119i | \(-0.475832\pi\) | ||||
0.0758524 | + | 0.997119i | \(0.475832\pi\) | |||||||
\(632\) | − | 9.85952i | − | 0.392191i | ||||||
\(633\) | 8.74175i | 0.347453i | ||||||||
\(634\) | −13.0790 | −0.519434 | ||||||||
\(635\) | −19.5298 | + | 26.7034i | −0.775017 | + | 1.05969i | ||||
\(636\) | −3.73555 | −0.148124 | ||||||||
\(637\) | 0.0146797i | 0.000581632i | ||||||||
\(638\) | 16.3103i | 0.645732i | ||||||||
\(639\) | 23.0715 | 0.912692 | ||||||||
\(640\) | −1.32001 | + | 1.80487i | −0.0521780 | + | 0.0713439i | ||||
\(641\) | 35.7796 | 1.41321 | 0.706604 | − | 0.707609i | \(-0.250226\pi\) | ||||
0.706604 | + | 0.707609i | \(0.250226\pi\) | |||||||
\(642\) | 9.43991i | 0.372563i | ||||||||
\(643\) | − | 11.3094i | − | 0.445999i | −0.974819 | − | 0.223000i | \(-0.928415\pi\) | ||
0.974819 | − | 0.223000i | \(-0.0715849\pi\) | |||||||
\(644\) | 3.59037 | 0.141480 | ||||||||
\(645\) | −0.901610 | − | 0.659401i | −0.0355008 | − | 0.0259639i | ||||
\(646\) | 5.76491 | 0.226817 | ||||||||
\(647\) | 49.4528i | 1.94419i | 0.234591 | + | 0.972094i | \(0.424625\pi\) | ||||
−0.234591 | + | 0.972094i | \(0.575375\pi\) | |||||||
\(648\) | 6.93945i | 0.272607i | ||||||||
\(649\) | −17.4693 | −0.685729 | ||||||||
\(650\) | 0.734633 | + | 2.31032i | 0.0288147 | + | 0.0906183i | ||||
\(651\) | −2.68120 | −0.105084 | ||||||||
\(652\) | − | 16.2498i | − | 0.636390i | ||||||
\(653\) | 46.1311i | 1.80525i | 0.430429 | + | 0.902624i | \(0.358362\pi\) | ||||
−0.430429 | + | 0.902624i | \(0.641638\pi\) | |||||||
\(654\) | 6.13578 | 0.239928 | ||||||||
\(655\) | −4.51136 | − | 3.29942i | −0.176273 | − | 0.128919i | ||||
\(656\) | −0.249771 | −0.00975191 | ||||||||
\(657\) | 1.34060i | 0.0523018i | ||||||||
\(658\) | 15.8789i | 0.619024i | ||||||||
\(659\) | 23.6732 | 0.922176 | 0.461088 | − | 0.887355i | \(-0.347459\pi\) | ||||
0.461088 | + | 0.887355i | \(0.347459\pi\) | |||||||
\(660\) | 1.28005 | − | 1.75023i | 0.0498258 | − | 0.0681276i | ||||
\(661\) | −32.1287 | −1.24966 | −0.624830 | − | 0.780761i | \(-0.714832\pi\) | ||||
−0.624830 | + | 0.780761i | \(0.714832\pi\) | |||||||
\(662\) | − | 24.8851i | − | 0.967187i | ||||||
\(663\) | 0.235091i | 0.00913018i | ||||||||
\(664\) | 17.5298 | 0.680289 | ||||||||
\(665\) | −20.0899 | + | 27.4693i | −0.779053 | + | 1.06521i | ||||
\(666\) | 30.7999 | 1.19347 | ||||||||
\(667\) | 11.0908i | 0.429439i | ||||||||
\(668\) | − | 2.95035i | − | 0.114152i | ||||||
\(669\) | 11.2947 | 0.436679 | ||||||||
\(670\) | 8.96972 | + | 6.56009i | 0.346531 | + | 0.253439i | ||||
\(671\) | −22.7493 | −0.878227 | ||||||||
\(672\) | − | 1.28005i | − | 0.0493789i | ||||||
\(673\) | 47.7631i | 1.84113i | 0.390588 | + | 0.920566i | \(0.372272\pi\) | ||||
−0.390588 | + | 0.920566i | \(0.627728\pi\) | |||||||
\(674\) | −27.5445 | −1.06097 | ||||||||
\(675\) | −13.3188 | + | 4.23509i | −0.512641 | + | 0.163009i | ||||
\(676\) | −12.7649 | −0.490958 | ||||||||
\(677\) | 8.82168i | 0.339045i | 0.985526 | + | 0.169522i | \(0.0542225\pi\) | ||||
−0.985526 | + | 0.169522i | \(0.945778\pi\) | |||||||
\(678\) | 3.64380i | 0.139939i | ||||||||
\(679\) | −17.7796 | −0.682318 | ||||||||
\(680\) | 1.80487 | + | 1.32001i | 0.0692137 | + | 0.0506201i | ||||
\(681\) | −8.47730 | −0.324851 | ||||||||
\(682\) | 4.18922i | 0.160413i | ||||||||
\(683\) | − | 28.5142i | − | 1.09107i | −0.838089 | − | 0.545533i | \(-0.816327\pi\) | ||
0.838089 | − | 0.545533i | \(-0.183673\pi\) | |||||||
\(684\) | 15.9394 | 0.609460 | ||||||||
\(685\) | 2.71995 | − | 3.71904i | 0.103924 | − | 0.142097i | ||||
\(686\) | −18.5601 | −0.708628 | ||||||||
\(687\) | − | 0.349078i | − | 0.0133182i | ||||||
\(688\) | 1.03028i | 0.0392789i | ||||||||
\(689\) | 3.73555 | 0.142313 | ||||||||
\(690\) | 0.870417 | − | 1.19014i | 0.0331362 | − | 0.0453077i | ||||
\(691\) | −50.4078 | −1.91760 | −0.958801 | − | 0.284077i | \(-0.908313\pi\) | ||||
−0.958801 | + | 0.284077i | \(0.908313\pi\) | |||||||
\(692\) | 6.14048i | 0.233426i | ||||||||
\(693\) | − | 14.5988i | − | 0.554564i | ||||||
\(694\) | −4.48486 | −0.170243 | ||||||||
\(695\) | 28.1386 | + | 20.5795i | 1.06736 | + | 0.780624i | ||||
\(696\) | 3.95413 | 0.149881 | ||||||||
\(697\) | 0.249771i | 0.00946075i | ||||||||
\(698\) | 34.2186i | 1.29519i | ||||||||
\(699\) | 5.35528 | 0.202555 | ||||||||
\(700\) | −12.5795 | + | 4.00000i | −0.475459 | + | 0.151186i | ||||
\(701\) | 10.4702 | 0.395453 | 0.197727 | − | 0.980257i | \(-0.436644\pi\) | ||||
0.197727 | + | 0.980257i | \(0.436644\pi\) | |||||||
\(702\) | 1.35528i | 0.0511517i | ||||||||
\(703\) | − | 64.2186i | − | 2.42205i | ||||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | 5.26353 | + | 3.84954i | 0.198236 | + | 0.144982i | ||||
\(706\) | −4.90917 | −0.184759 | ||||||||
\(707\) | − | 35.7190i | − | 1.34335i | ||||||
\(708\) | 4.23509i | 0.159164i | ||||||||
\(709\) | 5.90539 | 0.221782 | 0.110891 | − | 0.993833i | \(-0.464630\pi\) | ||||
0.110891 | + | 0.993833i | \(0.464630\pi\) | |||||||
\(710\) | 11.0147 | − | 15.0606i | 0.413374 | − | 0.565212i | ||||
\(711\) | −27.2607 | −1.02235 | ||||||||
\(712\) | 8.73463i | 0.327344i | ||||||||
\(713\) | 2.84862i | 0.106682i | ||||||||
\(714\) | −1.28005 | −0.0479046 | ||||||||
\(715\) | −1.28005 | + | 1.75023i | −0.0478710 | + | 0.0654549i | ||||
\(716\) | −15.5904 | −0.582639 | ||||||||
\(717\) | 2.71056i | 0.101228i | ||||||||
\(718\) | − | 13.7796i | − | 0.514250i | ||||||
\(719\) | 43.8354 | 1.63479 | 0.817393 | − | 0.576080i | \(-0.195418\pi\) | ||||
0.817393 | + | 0.576080i | \(0.195418\pi\) | |||||||
\(720\) | 4.99031 | + | 3.64971i | 0.185978 | + | 0.136017i | ||||
\(721\) | −29.6197 | −1.10310 | ||||||||
\(722\) | − | 14.2342i | − | 0.529741i | ||||||
\(723\) | − | 4.05872i | − | 0.150945i | ||||||
\(724\) | −4.10929 | −0.152721 | ||||||||
\(725\) | −12.3562 | − | 38.8586i | −0.458898 | − | 1.44317i | ||||
\(726\) | −3.39403 | −0.125964 | ||||||||
\(727\) | 6.60597i | 0.245002i | 0.992468 | + | 0.122501i | \(0.0390914\pi\) | ||||
−0.992468 | + | 0.122501i | \(0.960909\pi\) | |||||||
\(728\) | 1.28005i | 0.0474417i | ||||||||
\(729\) | 15.1211 | 0.560041 | ||||||||
\(730\) | 0.875115 | + | 0.640023i | 0.0323894 | + | 0.0236883i | ||||
\(731\) | 1.03028 | 0.0381061 | ||||||||
\(732\) | 5.51514i | 0.203845i | ||||||||
\(733\) | 44.6188i | 1.64803i | 0.566565 | + | 0.824017i | \(0.308272\pi\) | ||||
−0.566565 | + | 0.824017i | \(0.691728\pi\) | |||||||
\(734\) | 4.39025 | 0.162047 | ||||||||
\(735\) | −0.0193774 | + | 0.0264951i | −0.000714747 | + | 0.000977285i | ||||
\(736\) | −1.35998 | −0.0501294 | ||||||||
\(737\) | 9.93945i | 0.366124i | ||||||||
\(738\) | 0.690594i | 0.0254211i | ||||||||
\(739\) | −34.4149 | −1.26597 | −0.632987 | − | 0.774163i | \(-0.718171\pi\) | ||||
−0.632987 | + | 0.774163i | \(0.718171\pi\) | |||||||
\(740\) | 14.7044 | − | 20.1055i | 0.540543 | − | 0.739093i | ||||
\(741\) | 1.35528 | 0.0497874 | ||||||||
\(742\) | 20.3397i | 0.746693i | ||||||||
\(743\) | − | 28.0412i | − | 1.02873i | −0.857571 | − | 0.514365i | \(-0.828027\pi\) | ||
0.857571 | − | 0.514365i | \(-0.171973\pi\) | |||||||
\(744\) | 1.01560 | 0.0372336 | ||||||||
\(745\) | −18.0487 | − | 13.2001i | −0.661255 | − | 0.483615i | ||||
\(746\) | 0.220411 | 0.00806983 | ||||||||
\(747\) | − | 48.4683i | − | 1.77336i | ||||||
\(748\) | 2.00000i | 0.0731272i | ||||||||
\(749\) | 51.3993 | 1.87809 | ||||||||
\(750\) | −1.72373 | + | 5.13957i | −0.0629419 | + | 0.187670i | ||||
\(751\) | −47.4040 | −1.72980 | −0.864899 | − | 0.501947i | \(-0.832617\pi\) | ||||
−0.864899 | + | 0.501947i | \(0.832617\pi\) | |||||||
\(752\) | − | 6.01468i | − | 0.219333i | ||||||
\(753\) | 9.43991i | 0.344009i | ||||||||
\(754\) | −3.95413 | −0.144001 | ||||||||
\(755\) | −28.5895 | − | 20.9092i | −1.04048 | − | 0.760963i | ||||
\(756\) | −7.37935 | −0.268385 | ||||||||
\(757\) | 35.9759i | 1.30757i | 0.756682 | + | 0.653784i | \(0.226819\pi\) | ||||
−0.756682 | + | 0.653784i | \(0.773181\pi\) | |||||||
\(758\) | 26.3103i | 0.955634i | ||||||||
\(759\) | 1.31880 | 0.0478695 | ||||||||
\(760\) | 7.60975 | − | 10.4049i | 0.276035 | − | 0.377427i | ||||
\(761\) | 13.1807 | 0.477801 | 0.238901 | − | 0.971044i | \(-0.423213\pi\) | ||||
0.238901 | + | 0.971044i | \(0.423213\pi\) | |||||||
\(762\) | 7.17362i | 0.259873i | ||||||||
\(763\) | − | 33.4087i | − | 1.20948i | ||||||
\(764\) | −6.06055 | −0.219263 | ||||||||
\(765\) | 3.64971 | − | 4.99031i | 0.131956 | − | 0.180425i | ||||
\(766\) | 36.1433 | 1.30591 | ||||||||
\(767\) | − | 4.23509i | − | 0.152920i | ||||||
\(768\) | 0.484862i | 0.0174959i | ||||||||
\(769\) | 6.11399 | 0.220476 | 0.110238 | − | 0.993905i | \(-0.464839\pi\) | ||||
0.110238 | + | 0.993905i | \(0.464839\pi\) | |||||||
\(770\) | −9.52982 | − | 6.96972i | −0.343431 | − | 0.251171i | ||||
\(771\) | 6.75871 | 0.243409 | ||||||||
\(772\) | − | 12.5601i | − | 0.452048i | ||||||
\(773\) | − | 44.5601i | − | 1.60272i | −0.598186 | − | 0.801358i | \(-0.704111\pi\) | ||
0.598186 | − | 0.801358i | \(-0.295889\pi\) | |||||||
\(774\) | 2.84862 | 0.102392 | ||||||||
\(775\) | −3.17362 | − | 9.98062i | −0.114000 | − | 0.358515i | ||||
\(776\) | 6.73463 | 0.241759 | ||||||||
\(777\) | 14.2592i | 0.511545i | ||||||||
\(778\) | 3.77959i | 0.135505i | ||||||||
\(779\) | 1.43991 | 0.0515900 | ||||||||
\(780\) | 0.424310 | + | 0.310323i | 0.0151927 | + | 0.0111113i | ||||
\(781\) | 16.6888 | 0.597171 | ||||||||
\(782\) | 1.35998i | 0.0486327i | ||||||||
\(783\) | − | 22.7952i | − | 0.814633i | ||||||
\(784\) | 0.0302761 | 0.00108129 | ||||||||
\(785\) | 1.76961 | − | 2.41961i | 0.0631600 | − | 0.0863597i | ||||
\(786\) | −1.21193 | −0.0432282 | ||||||||
\(787\) | − | 26.3856i | − | 0.940543i | −0.882522 | − | 0.470272i | \(-0.844156\pi\) | ||
0.882522 | − | 0.470272i | \(-0.155844\pi\) | |||||||
\(788\) | 26.0487i | 0.927948i | ||||||||
\(789\) | 7.88601 | 0.280750 | ||||||||
\(790\) | −13.0147 | + | 17.7952i | −0.463042 | + | 0.633124i | ||||
\(791\) | 19.8401 | 0.705434 | ||||||||
\(792\) | 5.52982i | 0.196494i | ||||||||
\(793\) | − | 5.51514i | − | 0.195848i | ||||||
\(794\) | 12.2304 | 0.434040 | ||||||||
\(795\) | 6.74219 | + | 4.93097i | 0.239121 | + | 0.174883i | ||||
\(796\) | 3.37466 | 0.119612 | ||||||||
\(797\) | 12.4390i | 0.440612i | 0.975431 | + | 0.220306i | \(0.0707055\pi\) | ||||
−0.975431 | + | 0.220306i | \(0.929294\pi\) | |||||||
\(798\) | 7.37935i | 0.261226i | ||||||||
\(799\) | −6.01468 | −0.212784 | ||||||||
\(800\) | 4.76491 | − | 1.51514i | 0.168465 | − | 0.0535682i | ||||
\(801\) | 24.1505 | 0.853315 | ||||||||
\(802\) | 11.7796i | 0.415952i | ||||||||
\(803\) | 0.969724i | 0.0342208i | ||||||||
\(804\) | 2.40963 | 0.0849811 | ||||||||
\(805\) | −6.48016 | − | 4.73933i | −0.228396 | − | 0.167039i | ||||
\(806\) | −1.01560 | −0.0357729 | ||||||||
\(807\) | − | 5.04496i | − | 0.177591i | ||||||
\(808\) | 13.5298i | 0.475977i | ||||||||
\(809\) | −5.96125 | −0.209586 | −0.104793 | − | 0.994494i | \(-0.533418\pi\) | ||||
−0.104793 | + | 0.994494i | \(0.533418\pi\) | |||||||
\(810\) | 9.16015 | − | 12.5248i | 0.321855 | − | 0.440078i | ||||
\(811\) | −27.8089 | −0.976504 | −0.488252 | − | 0.872703i | \(-0.662365\pi\) | ||||
−0.488252 | + | 0.872703i | \(0.662365\pi\) | |||||||
\(812\) | − | 21.5298i | − | 0.755548i | ||||||
\(813\) | − | 11.6509i | − | 0.408616i | ||||||
\(814\) | 22.2791 | 0.780883 | ||||||||
\(815\) | −21.4499 | + | 29.3288i | −0.751357 | + | 1.02734i | ||||
\(816\) | 0.484862 | 0.0169736 | ||||||||
\(817\) | − | 5.93945i | − | 0.207795i | ||||||
\(818\) | − | 15.7649i | − | 0.551207i | ||||||
\(819\) | 3.53921 | 0.123670 | ||||||||
\(820\) | 0.450805 | + | 0.329700i | 0.0157428 | + | 0.0115136i | ||||
\(821\) | −9.05677 | −0.316083 | −0.158042 | − | 0.987432i | \(-0.550518\pi\) | ||||
−0.158042 | + | 0.987432i | \(0.550518\pi\) | |||||||
\(822\) | − | 0.999083i | − | 0.0348470i | ||||||
\(823\) | 6.54828i | 0.228259i | 0.993466 | + | 0.114129i | \(0.0364078\pi\) | ||||
−0.993466 | + | 0.114129i | \(0.963592\pi\) | |||||||
\(824\) | 11.2195 | 0.390850 | ||||||||
\(825\) | −4.62065 | + | 1.46927i | −0.160870 | + | 0.0511533i | ||||
\(826\) | 23.0596 | 0.802347 | ||||||||
\(827\) | 15.7115i | 0.546341i | 0.961966 | + | 0.273171i | \(0.0880724\pi\) | ||||
−0.961966 | + | 0.273171i | \(0.911928\pi\) | |||||||
\(828\) | 3.76021i | 0.130676i | ||||||||
\(829\) | 1.87890 | 0.0652567 | 0.0326284 | − | 0.999468i | \(-0.489612\pi\) | ||||
0.0326284 | + | 0.999468i | \(0.489612\pi\) | |||||||
\(830\) | −31.6391 | − | 23.1396i | −1.09821 | − | 0.803186i | ||||
\(831\) | 9.18830 | 0.318739 | ||||||||
\(832\) | − | 0.484862i | − | 0.0168096i | ||||||
\(833\) | − | 0.0302761i | − | 0.00104900i | ||||||
\(834\) | 7.55918 | 0.261753 | ||||||||
\(835\) | −3.89449 | + | 5.32500i | −0.134774 | + | 0.184279i | ||||
\(836\) | 11.5298 | 0.398767 | ||||||||
\(837\) | − | 5.85482i | − | 0.202372i | ||||||
\(838\) | 18.1892i | 0.628336i | ||||||||
\(839\) | 48.6841 | 1.68076 | 0.840380 | − | 0.541997i | \(-0.182332\pi\) | ||||
0.840380 | + | 0.541997i | \(0.182332\pi\) | |||||||
\(840\) | −1.68968 | + | 2.31032i | −0.0582994 | + | 0.0797137i | ||||
\(841\) | 37.5067 | 1.29333 | ||||||||
\(842\) | − | 9.03028i | − | 0.311204i | ||||||
\(843\) | 9.52453i | 0.328042i | ||||||||
\(844\) | −18.0294 | −0.620596 | ||||||||
\(845\) | 23.0390 | + | 16.8498i | 0.792567 | + | 0.579652i | ||||
\(846\) | −16.6300 | −0.571753 | ||||||||
\(847\) | 18.4802i | 0.634986i | ||||||||
\(848\) | − | 7.70436i | − | 0.264569i | ||||||
\(849\) | −12.5067 | −0.429227 | ||||||||
\(850\) | −1.51514 | − | 4.76491i | −0.0519688 | − | 0.163435i | ||||
\(851\) | 15.1495 | 0.519320 | ||||||||
\(852\) | − | 4.04587i | − | 0.138609i | ||||||
\(853\) | − | 35.9494i | − | 1.23089i | −0.788182 | − | 0.615443i | \(-0.788977\pi\) | ||
0.788182 | − | 0.615443i | \(-0.211023\pi\) | |||||||
\(854\) | 30.0294 | 1.02758 | ||||||||
\(855\) | −28.7687 | − | 21.0403i | −0.983868 | − | 0.719562i | ||||
\(856\) | −19.4693 | −0.665446 | ||||||||
\(857\) | − | 13.4158i | − | 0.458276i | −0.973394 | − | 0.229138i | \(-0.926409\pi\) | ||
0.973394 | − | 0.229138i | \(-0.0735907\pi\) | |||||||
\(858\) | 0.470182i | 0.0160518i | ||||||||
\(859\) | 23.8860 | 0.814980 | 0.407490 | − | 0.913210i | \(-0.366404\pi\) | ||||
0.407490 | + | 0.913210i | \(0.366404\pi\) | |||||||
\(860\) | 1.35998 | − | 1.85952i | 0.0463748 | − | 0.0634090i | ||||
\(861\) | −0.319718 | −0.0108960 | ||||||||
\(862\) | − | 20.4196i | − | 0.695495i | ||||||
\(863\) | 15.5979i | 0.530960i | 0.964116 | + | 0.265480i | \(0.0855304\pi\) | ||||
−0.964116 | + | 0.265480i | \(0.914470\pi\) | |||||||
\(864\) | 2.79518 | 0.0950941 | ||||||||
\(865\) | 8.10551 | − | 11.0828i | 0.275596 | − | 0.376826i | ||||
\(866\) | −11.5904 | −0.393857 | ||||||||
\(867\) | − | 0.484862i | − | 0.0164668i | ||||||
\(868\) | − | 5.52982i | − | 0.187694i | ||||||
\(869\) | −19.7190 | −0.668922 | ||||||||
\(870\) | −7.13670 | − | 5.21949i | −0.241957 | − | 0.176957i | ||||
\(871\) | −2.40963 | −0.0816472 | ||||||||
\(872\) | 12.6547i | 0.428542i | ||||||||
\(873\) | − | 18.6206i | − | 0.630213i | ||||||
\(874\) | 7.84014 | 0.265197 | ||||||||
\(875\) | 27.9844 | + | 9.38555i | 0.946046 | + | 0.317290i | ||||
\(876\) | 0.235091 | 0.00794299 | ||||||||
\(877\) | 33.3893i | 1.12748i | 0.825953 | + | 0.563739i | \(0.190638\pi\) | ||||
−0.825953 | + | 0.563739i | \(0.809362\pi\) | |||||||
\(878\) | − | 2.01938i | − | 0.0681507i | ||||||
\(879\) | 11.1149 | 0.374896 | ||||||||
\(880\) | 3.60975 | + | 2.64002i | 0.121685 | + | 0.0889952i | ||||
\(881\) | −35.1202 | −1.18323 | −0.591615 | − | 0.806221i | \(-0.701509\pi\) | ||||
−0.591615 | + | 0.806221i | \(0.701509\pi\) | |||||||
\(882\) | − | 0.0837106i | − | 0.00281868i | ||||||
\(883\) | 22.2110i | 0.747460i | 0.927537 | + | 0.373730i | \(0.121921\pi\) | ||||
−0.927537 | + | 0.373730i | \(0.878079\pi\) | |||||||
\(884\) | −0.484862 | −0.0163077 | ||||||||
\(885\) | 5.59037 | − | 7.64380i | 0.187918 | − | 0.256944i | ||||
\(886\) | 27.4087 | 0.920814 | ||||||||
\(887\) | − | 5.17076i | − | 0.173617i | −0.996225 | − | 0.0868085i | \(-0.972333\pi\) | ||
0.996225 | − | 0.0868085i | \(-0.0276668\pi\) | |||||||
\(888\) | − | 5.40115i | − | 0.181251i | ||||||
\(889\) | 39.0596 | 1.31002 | ||||||||
\(890\) | 11.5298 | − | 15.7649i | 0.386480 | − | 0.528441i | ||||
\(891\) | 13.8789 | 0.464960 | ||||||||
\(892\) | 23.2947i | 0.779965i | ||||||||
\(893\) | 34.6741i | 1.16032i | ||||||||
\(894\) | −4.84862 | −0.162162 | ||||||||
\(895\) | 28.1386 | + | 20.5795i | 0.940571 | + | 0.687896i | ||||
\(896\) | 2.64002 | 0.0881970 | ||||||||
\(897\) | 0.319718i | 0.0106751i | ||||||||
\(898\) | 29.7190i | 0.991737i | ||||||||
\(899\) | 17.0819 | 0.569713 | ||||||||
\(900\) | −4.18922 | − | 13.1745i | −0.139641 | − | 0.439151i | ||||
\(901\) | −7.70436 | −0.256669 | ||||||||
\(902\) | 0.499542i | 0.0166329i | ||||||||
\(903\) | 1.31880i | 0.0438870i | ||||||||
\(904\) | −7.51514 | −0.249950 | ||||||||
\(905\) | 7.41675 | + | 5.42431i | 0.246541 | + | 0.180310i | ||||
\(906\) | −7.68028 | −0.255160 | ||||||||
\(907\) | − | 3.85482i | − | 0.127997i | −0.997950 | − | 0.0639986i | \(-0.979615\pi\) | ||
0.997950 | − | 0.0639986i | \(-0.0203853\pi\) | |||||||
\(908\) | − | 17.4839i | − | 0.580225i | ||||||
\(909\) | 37.4087 | 1.24077 | ||||||||
\(910\) | 1.68968 | − | 2.31032i | 0.0560122 | − | 0.0765865i | ||||
\(911\) | −22.6400 | −0.750097 | −0.375049 | − | 0.927005i | \(-0.622374\pi\) | ||||
−0.375049 | + | 0.927005i | \(0.622374\pi\) | |||||||
\(912\) | − | 2.79518i | − | 0.0925578i | ||||||
\(913\) | − | 35.0596i | − | 1.16030i | ||||||
\(914\) | 39.4693 | 1.30553 | ||||||||
\(915\) | 7.28005 | − | 9.95413i | 0.240671 | − | 0.329073i | ||||
\(916\) | 0.719953 | 0.0237879 | ||||||||
\(917\) | 6.59885i | 0.217913i | ||||||||
\(918\) | − | 2.79518i | − | 0.0922549i | ||||||
\(919\) | −31.5298 | −1.04007 | −0.520036 | − | 0.854144i | \(-0.674082\pi\) | ||||
−0.520036 | + | 0.854144i | \(0.674082\pi\) | |||||||
\(920\) | 2.45459 | + | 1.79518i | 0.0809253 | + | 0.0591855i | ||||
\(921\) | −5.07659 | −0.167279 | ||||||||
\(922\) | − | 14.6888i | − | 0.483749i | ||||||
\(923\) | 4.04587i | 0.133172i | ||||||||
\(924\) | −2.56009 | −0.0842209 | ||||||||
\(925\) | −53.0790 | + | 16.8780i | −1.74523 | + | 0.554945i | ||||
\(926\) | −35.1055 | −1.15364 | ||||||||
\(927\) | − | 31.0209i | − | 1.01886i | ||||||
\(928\) | 8.15516i | 0.267706i | ||||||||
\(929\) | 11.1589 | 0.366113 | 0.183057 | − | 0.983102i | \(-0.441401\pi\) | ||||
0.183057 | + | 0.983102i | \(0.441401\pi\) | |||||||
\(930\) | −1.83302 | − | 1.34060i | −0.0601072 | − | 0.0439600i | ||||
\(931\) | −0.174539 | −0.00572028 | ||||||||
\(932\) | 11.0450i | 0.361790i | ||||||||
\(933\) | − | 4.72179i | − | 0.154584i | ||||||
\(934\) | −9.96881 | −0.326189 | ||||||||
\(935\) | 2.64002 | − | 3.60975i | 0.0863380 | − | 0.118051i | ||||
\(936\) | −1.34060 | −0.0438189 | ||||||||
\(937\) | 24.5307i | 0.801384i | 0.916213 | + | 0.400692i | \(0.131230\pi\) | ||||
−0.916213 | + | 0.400692i | \(0.868770\pi\) | |||||||
\(938\) | − | 13.1202i | − | 0.428389i | ||||||
\(939\) | −4.60641 | −0.150325 | ||||||||
\(940\) | −7.93945 | + | 10.8557i | −0.258956 | + | 0.354075i | ||||
\(941\) | 35.3747 | 1.15318 | 0.576590 | − | 0.817033i | \(-0.304383\pi\) | ||||
0.576590 | + | 0.817033i | \(0.304383\pi\) | |||||||
\(942\) | − | 0.650006i | − | 0.0211783i | ||||||
\(943\) | 0.339682i | 0.0110616i | ||||||||
\(944\) | −8.73463 | −0.284288 | ||||||||
\(945\) | 13.3188 | + | 9.74083i | 0.433261 | + | 0.316869i | ||||
\(946\) | 2.06055 | 0.0669943 | ||||||||
\(947\) | − | 2.23509i | − | 0.0726307i | −0.999340 | − | 0.0363154i | \(-0.988438\pi\) | ||
0.999340 | − | 0.0363154i | \(-0.0115621\pi\) | |||||||
\(948\) | 4.78051i | 0.155264i | ||||||||
\(949\) | −0.235091 | −0.00763138 | ||||||||
\(950\) | −27.4693 | + | 8.73463i | −0.891221 | + | 0.283389i | ||||
\(951\) | 6.34152 | 0.205638 | ||||||||
\(952\) | − | 2.64002i | − | 0.0855637i | ||||||
\(953\) | − | 5.65092i | − | 0.183051i | −0.995803 | − | 0.0915257i | \(-0.970826\pi\) | ||
0.995803 | − | 0.0915257i | \(-0.0291744\pi\) | |||||||
\(954\) | −21.3018 | −0.689673 | ||||||||
\(955\) | 10.9385 | + | 8.00000i | 0.353963 | + | 0.258874i | ||||
\(956\) | −5.59037 | −0.180805 | ||||||||
\(957\) | − | 7.90826i | − | 0.255638i | ||||||
\(958\) | − | 2.28383i | − | 0.0737871i | ||||||
\(959\) | −5.43991 | −0.175664 | ||||||||
\(960\) | 0.640023 | − | 0.875115i | 0.0206567 | − | 0.0282442i | ||||
\(961\) | −26.6126 | −0.858471 | ||||||||
\(962\) | 5.40115i | 0.174140i | ||||||||
\(963\) | 53.8307i | 1.73467i | ||||||||
\(964\) | 8.37088 | 0.269608 | ||||||||
\(965\) | −16.5795 | + | 22.6694i | −0.533712 | + | 0.729753i | ||||
\(966\) | −1.74083 | −0.0560104 | ||||||||
\(967\) | 40.9991i | 1.31844i | 0.751949 | + | 0.659221i | \(0.229114\pi\) | ||||
−0.751949 | + | 0.659221i | \(0.770886\pi\) | |||||||
\(968\) | − | 7.00000i | − | 0.224989i | ||||||
\(969\) | −2.79518 | −0.0897943 | ||||||||
\(970\) | −12.1552 | − | 8.88979i | −0.390279 | − | 0.285434i | ||||
\(971\) | −45.3846 | −1.45646 | −0.728231 | − | 0.685332i | \(-0.759657\pi\) | ||||
−0.728231 | + | 0.685332i | \(0.759657\pi\) | |||||||
\(972\) | − | 11.7502i | − | 0.376889i | ||||||
\(973\) | − | 41.1589i | − | 1.31950i | ||||||
\(974\) | −10.8292 | −0.346991 | ||||||||
\(975\) | −0.356195 | − | 1.12019i | −0.0114074 | − | 0.0358747i | ||||
\(976\) | −11.3747 | −0.364094 | ||||||||
\(977\) | − | 4.72752i | − | 0.151247i | −0.997136 | − | 0.0756233i | \(-0.975905\pi\) | ||
0.997136 | − | 0.0756233i | \(-0.0240946\pi\) | |||||||
\(978\) | 7.87890i | 0.251939i | ||||||||
\(979\) | 17.4693 | 0.558320 | ||||||||
\(980\) | −0.0546445 | − | 0.0399648i | −0.00174556 | − | 0.00127663i | ||||
\(981\) | 34.9891 | 1.11712 | ||||||||
\(982\) | − | 24.7952i | − | 0.791246i | ||||||
\(983\) | − | 14.3297i | − | 0.457046i | −0.973538 | − | 0.228523i | \(-0.926610\pi\) | ||
0.973538 | − | 0.228523i | \(-0.0733897\pi\) | |||||||
\(984\) | 0.121104 | 0.00386067 | ||||||||
\(985\) | 34.3846 | − | 47.0147i | 1.09559 | − | 1.49801i | ||||
\(986\) | 8.15516 | 0.259713 | ||||||||
\(987\) | − | 7.69907i | − | 0.245064i | ||||||
\(988\) | 2.79518i | 0.0889267i | ||||||||
\(989\) | 1.40115 | 0.0445540 | ||||||||
\(990\) | 7.29942 | − | 9.98062i | 0.231991 | − | 0.317205i | ||||
\(991\) | 16.8827 | 0.536296 | 0.268148 | − | 0.963378i | \(-0.413588\pi\) | ||||
0.268148 | + | 0.963378i | \(0.413588\pi\) | |||||||
\(992\) | 2.09461i | 0.0665039i | ||||||||
\(993\) | 12.0658i | 0.382898i | ||||||||
\(994\) | −22.0294 | −0.698729 | ||||||||
\(995\) | −6.09083 | − | 4.45459i | −0.193092 | − | 0.141220i | ||||
\(996\) | −8.49954 | −0.269318 | ||||||||
\(997\) | 18.5189i | 0.586500i | 0.956036 | + | 0.293250i | \(0.0947368\pi\) | ||||
−0.956036 | + | 0.293250i | \(0.905263\pi\) | |||||||
\(998\) | 5.15138i | 0.163064i | ||||||||
\(999\) | −31.1371 | −0.985136 |
(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 | 170.2.c.b.69.2 | ✓ | 6 | |
3.2 | odd | 2 | 1530.2.d.g.919.4 | 6 | |||
4.3 | odd | 2 | 1360.2.e.c.1089.3 | 6 | |||
5.2 | odd | 4 | 850.2.a.q.1.2 | 3 | |||
5.3 | odd | 4 | 850.2.a.p.1.2 | 3 | |||
5.4 | even | 2 | inner | 170.2.c.b.69.5 | yes | 6 | |
15.2 | even | 4 | 7650.2.a.dj.1.3 | 3 | |||
15.8 | even | 4 | 7650.2.a.do.1.1 | 3 | |||
15.14 | odd | 2 | 1530.2.d.g.919.1 | 6 | |||
20.3 | even | 4 | 6800.2.a.bp.1.2 | 3 | |||
20.7 | even | 4 | 6800.2.a.bk.1.2 | 3 | |||
20.19 | odd | 2 | 1360.2.e.c.1089.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
170.2.c.b.69.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
170.2.c.b.69.5 | yes | 6 | 5.4 | even | 2 | inner | |
850.2.a.p.1.2 | 3 | 5.3 | odd | 4 | |||
850.2.a.q.1.2 | 3 | 5.2 | odd | 4 | |||
1360.2.e.c.1089.3 | 6 | 4.3 | odd | 2 | |||
1360.2.e.c.1089.4 | 6 | 20.19 | odd | 2 | |||
1530.2.d.g.919.1 | 6 | 15.14 | odd | 2 | |||
1530.2.d.g.919.4 | 6 | 3.2 | odd | 2 | |||
6800.2.a.bk.1.2 | 3 | 20.7 | even | 4 | |||
6800.2.a.bp.1.2 | 3 | 20.3 | even | 4 | |||
7650.2.a.dj.1.3 | 3 | 15.2 | even | 4 | |||
7650.2.a.do.1.1 | 3 | 15.8 | even | 4 |