Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(165,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.i (of order \(3\), degree \(2\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 821.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.821 |
Dual form | 1148.2.i.b.165.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | 0.973494 | − | 0.228714i | \(-0.0734519\pi\) |
−0.684819 | + | 0.728714i | \(0.740119\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | −0.732294 | − | 0.680989i | \(-0.761550\pi\) |
0.955901 | + | 0.293691i | \(0.0948835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | + | 1.73205i | −0.755929 | + | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50000 | + | 4.33013i | 0.753778 | + | 1.30558i | 0.945979 | + | 0.324227i | \(0.105104\pi\) |
−0.192201 | + | 0.981356i | \(0.561563\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.50000 | + | 2.59808i | 0.363803 | + | 0.630126i | 0.988583 | − | 0.150675i | \(-0.0481447\pi\) |
−0.624780 | + | 0.780801i | \(0.714811\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.50000 | − | 2.59808i | 0.344124 | − | 0.596040i | −0.641071 | − | 0.767482i | \(-0.721509\pi\) |
0.985194 | + | 0.171442i | \(0.0548427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.50000 | − | 0.866025i | −0.545545 | − | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | −0.809177 | − | 0.587565i | \(-0.800087\pi\) |
0.913434 | + | 0.406986i | \(0.133420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | + | 3.46410i | 0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.0000 | −1.85695 | −0.928477 | − | 0.371391i | \(-0.878881\pi\) | ||||
−0.928477 | + | 0.371391i | \(0.878881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.50000 | + | 9.52628i | 0.987829 | + | 1.71097i | 0.628619 | + | 0.777714i | \(0.283621\pi\) |
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.50000 | + | 4.33013i | −0.435194 | + | 0.753778i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.500000 | + | 2.59808i | 0.0845154 | + | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.50000 | + | 6.06218i | −0.575396 | + | 0.996616i | 0.420602 | + | 0.907245i | \(0.361819\pi\) |
−0.995998 | + | 0.0893706i | \(0.971514\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | − | 1.73205i | −0.160128 | − | 0.277350i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | − | 1.73205i | −0.149071 | − | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.50000 | − | 6.06218i | 0.510527 | − | 0.884260i | −0.489398 | − | 0.872060i | \(-0.662783\pi\) |
0.999926 | − | 0.0121990i | \(-0.00388317\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.50000 | + | 2.59808i | −0.210042 | + | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.50000 | + | 9.52628i | 0.755483 | + | 1.30854i | 0.945134 | + | 0.326683i | \(0.105931\pi\) |
−0.189651 | + | 0.981852i | \(0.560736\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00000 | 0.674200 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | 0.397360 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.50000 | + | 6.06218i | 0.455661 | + | 0.789228i | 0.998726 | − | 0.0504625i | \(-0.0160695\pi\) |
−0.543065 | + | 0.839691i | \(0.682736\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | − | 0.866025i | 0.0640184 | − | 0.110883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | + | 5.19615i | 0.125988 | + | 0.654654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | + | 1.73205i | −0.124035 | + | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.50000 | − | 6.06218i | −0.427593 | − | 0.740613i | 0.569066 | − | 0.822292i | \(-0.307305\pi\) |
−0.996659 | + | 0.0816792i | \(0.973972\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.50000 | + | 4.33013i | 0.292603 | + | 0.506803i | 0.974424 | − | 0.224716i | \(-0.0721453\pi\) |
−0.681822 | + | 0.731519i | \(0.738812\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.00000 | + | 3.46410i | −0.230940 | + | 0.400000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.5000 | − | 4.33013i | −1.42451 | − | 0.493464i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.50000 | + | 7.79423i | −0.506290 | + | 0.876919i | 0.493684 | + | 0.869641i | \(0.335650\pi\) |
−0.999974 | + | 0.00727784i | \(0.997683\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00000 | 0.325396 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.00000 | − | 8.66025i | −0.536056 | − | 0.928477i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.50000 | − | 2.59808i | 0.159000 | − | 0.275396i | −0.775509 | − | 0.631337i | \(-0.782506\pi\) |
0.934508 | + | 0.355942i | \(0.115840\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | − | 3.46410i | 0.419314 | − | 0.363137i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.50000 | + | 9.52628i | −0.570323 | + | 0.987829i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.50000 | − | 2.59808i | −0.153897 | − | 0.266557i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.0000 | 1.00504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.50000 | + | 9.52628i | 0.547270 | + | 0.947900i | 0.998460 | + | 0.0554722i | \(0.0176664\pi\) |
−0.451190 | + | 0.892428i | \(0.649000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.500000 | − | 0.866025i | 0.0492665 | − | 0.0853320i | −0.840341 | − | 0.542059i | \(-0.817645\pi\) |
0.889607 | + | 0.456727i | \(0.150978\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | + | 1.73205i | −0.195180 | + | 0.169031i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.50000 | − | 11.2583i | 0.628379 | − | 1.08838i | −0.359498 | − | 0.933146i | \(-0.617052\pi\) |
0.987877 | − | 0.155238i | \(-0.0496145\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.50000 | − | 14.7224i | −0.814152 | − | 1.41015i | −0.909935 | − | 0.414751i | \(-0.863869\pi\) |
0.0957826 | − | 0.995402i | \(-0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.00000 | −0.664411 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.500000 | − | 0.866025i | −0.0466252 | − | 0.0807573i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | + | 3.46410i | −0.184900 | + | 0.320256i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.50000 | − | 2.59808i | −0.687524 | − | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.500000 | − | 0.866025i | −0.0450835 | − | 0.0780869i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.00000 | + | 6.92820i | 0.352180 | + | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.50000 | + | 2.59808i | −0.131056 | + | 0.226995i | −0.924084 | − | 0.382190i | \(-0.875170\pi\) |
0.793028 | + | 0.609185i | \(0.208503\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.50000 | + | 7.79423i | 0.130066 | + | 0.675845i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.50000 | − | 4.33013i | 0.215166 | − | 0.372678i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.50000 | − | 7.79423i | −0.384461 | − | 0.665906i | 0.607233 | − | 0.794524i | \(-0.292279\pi\) |
−0.991694 | + | 0.128618i | \(0.958946\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.0000 | −1.69638 | −0.848189 | − | 0.529694i | \(-0.822307\pi\) | ||||
−0.848189 | + | 0.529694i | \(0.822307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.00000 | 0.589506 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.00000 | − | 8.66025i | −0.418121 | − | 0.724207i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.00000 | + | 8.66025i | −0.415227 | + | 0.719195i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.50000 | − | 2.59808i | 0.536111 | − | 0.214286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.50000 | − | 6.06218i | 0.286731 | − | 0.496633i | −0.686296 | − | 0.727322i | \(-0.740765\pi\) |
0.973028 | + | 0.230689i | \(0.0740980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.50000 | + | 4.33013i | 0.203447 | + | 0.352381i | 0.949637 | − | 0.313353i | \(-0.101452\pi\) |
−0.746190 | + | 0.665733i | \(0.768119\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.00000 | 0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.0000 | 0.883541 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.50000 | + | 2.59808i | 0.119713 | + | 0.207349i | 0.919654 | − | 0.392730i | \(-0.128469\pi\) |
−0.799941 | + | 0.600079i | \(0.795136\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.50000 | + | 9.52628i | −0.436178 | + | 0.755483i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.500000 | + | 2.59808i | 0.0394055 | + | 0.204757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.50000 | − | 14.7224i | 0.665771 | − | 1.15315i | −0.313304 | − | 0.949653i | \(-0.601436\pi\) |
0.979076 | − | 0.203497i | \(-0.0652307\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.50000 | + | 4.33013i | 0.194625 | + | 0.337100i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.0000 | 1.23812 | 0.619059 | − | 0.785345i | \(-0.287514\pi\) | ||||
0.619059 | + | 0.785345i | \(0.287514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | − | 5.19615i | −0.229416 | − | 0.397360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5000 | − | 18.1865i | 0.798300 | − | 1.38270i | −0.122422 | − | 0.992478i | \(-0.539066\pi\) |
0.920722 | − | 0.390218i | \(-0.127601\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0000 | − | 3.46410i | −0.755929 | − | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.50000 | + | 6.06218i | −0.263076 | + | 0.455661i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.50000 | − | 6.06218i | −0.261602 | − | 0.453108i | 0.705066 | − | 0.709142i | \(-0.250918\pi\) |
−0.966668 | + | 0.256034i | \(0.917584\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.50000 | + | 6.06218i | 0.257325 | + | 0.445700i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.50000 | + | 12.9904i | −0.548454 | + | 0.949951i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.0000 | + | 8.66025i | −0.727393 | + | 0.629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.500000 | + | 0.866025i | −0.0361787 | + | 0.0626634i | −0.883548 | − | 0.468341i | \(-0.844852\pi\) |
0.847369 | + | 0.531004i | \(0.178185\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.50000 | − | 14.7224i | −0.611843 | − | 1.05974i | −0.990930 | − | 0.134382i | \(-0.957095\pi\) |
0.379086 | − | 0.925361i | \(-0.376238\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.00000 | −0.143223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.0000 | 1.85242 | 0.926212 | − | 0.377004i | \(-0.123046\pi\) | ||||
0.926212 | + | 0.377004i | \(0.123046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5000 | + | 18.1865i | 0.744325 | + | 1.28921i | 0.950509 | + | 0.310696i | \(0.100562\pi\) |
−0.206184 | + | 0.978513i | \(0.566105\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.50000 | − | 6.06218i | 0.246871 | − | 0.427593i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.0000 | − | 17.3205i | 1.40372 | − | 1.21566i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.500000 | + | 0.866025i | −0.0349215 | + | 0.0604858i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | − | 1.73205i | −0.0695048 | − | 0.120386i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.0000 | 1.03757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.00000 | − | 10.3923i | −0.411113 | − | 0.712069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.00000 | − | 6.92820i | 0.272798 | − | 0.472500i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −27.5000 | − | 9.52628i | −1.86682 | − | 0.646686i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.50000 | + | 4.33013i | −0.168934 | + | 0.292603i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | − | 5.19615i | −0.201802 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.00000 | 0.533333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.50000 | + | 7.79423i | 0.298675 | + | 0.517321i | 0.975833 | − | 0.218517i | \(-0.0701218\pi\) |
−0.677158 | + | 0.735838i | \(0.736789\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.5000 | − | 23.3827i | 0.892105 | − | 1.54517i | 0.0547581 | − | 0.998500i | \(-0.482561\pi\) |
0.837347 | − | 0.546672i | \(-0.184105\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.50000 | − | 12.9904i | −0.164488 | − | 0.854704i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.50000 | + | 11.2583i | −0.425829 | + | 0.737558i | −0.996497 | − | 0.0836229i | \(-0.973351\pi\) |
0.570668 | + | 0.821181i | \(0.306684\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.50000 | − | 6.06218i | −0.228315 | − | 0.395453i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.00000 | −0.584613 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.50000 | − | 16.4545i | −0.611949 | − | 1.05993i | −0.990912 | − | 0.134515i | \(-0.957053\pi\) |
0.378963 | − | 0.925412i | \(-0.376281\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.00000 | − | 13.8564i | 0.513200 | − | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.50000 | − | 4.33013i | −0.351382 | − | 0.276642i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.00000 | + | 5.19615i | −0.190885 | + | 0.330623i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.00000 | 0.314347 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.50000 | + | 2.59808i | 0.0939336 | + | 0.162698i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.50000 | − | 6.06218i | 0.218324 | − | 0.378148i | −0.735972 | − | 0.677012i | \(-0.763274\pi\) |
0.954296 | + | 0.298864i | \(0.0966077\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.50000 | − | 18.1865i | −0.217479 | − | 1.13006i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.0000 | + | 17.3205i | −0.618984 | + | 1.07211i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.50000 | − | 16.4545i | −0.585795 | − | 1.01463i | −0.994776 | − | 0.102084i | \(-0.967449\pi\) |
0.408981 | − | 0.912543i | \(-0.365884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.0000 | 0.675725 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.00000 | 0.183597 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.50000 | − | 9.52628i | −0.335341 | − | 0.580828i | 0.648209 | − | 0.761462i | \(-0.275518\pi\) |
−0.983550 | + | 0.180635i | \(0.942185\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5000 | − | 21.6506i | 0.759321 | − | 1.31518i | −0.183876 | − | 0.982949i | \(-0.558865\pi\) |
0.943197 | − | 0.332233i | \(-0.107802\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.00000 | + | 1.73205i | 0.302614 | + | 0.104828i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.0000 | + | 17.3205i | −0.603023 | + | 1.04447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.5000 | − | 19.9186i | −0.690968 | − | 1.19679i | −0.971521 | − | 0.236953i | \(-0.923851\pi\) |
0.280553 | − | 0.959839i | \(-0.409482\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.0000 | 1.31711 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.0000 | −0.835170 | −0.417585 | − | 0.908638i | \(-0.637123\pi\) | ||||
−0.417585 | + | 0.908638i | \(0.637123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.50000 | − | 14.7224i | −0.505273 | − | 0.875158i | −0.999981 | − | 0.00609896i | \(-0.998059\pi\) |
0.494709 | − | 0.869059i | \(-0.335275\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.50000 | − | 2.59808i | 0.0888523 | − | 0.153897i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.00000 | − | 1.73205i | 0.118056 | − | 0.102240i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.00000 | + | 1.73205i | 0.0586210 | + | 0.101535i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.0000 | −1.05157 | −0.525786 | − | 0.850617i | \(-0.676229\pi\) | ||||
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.00000 | 0.407556 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.5000 | + | 21.6506i | 0.725324 | + | 1.25630i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.00000 | + | 1.73205i | −0.0578315 | + | 0.100167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0000 | + | 13.8564i | −0.922225 | + | 0.798670i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.50000 | + | 9.52628i | −0.315967 | + | 0.547270i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.500000 | − | 0.866025i | −0.0286299 | − | 0.0495885i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0000 | 0.684876 | 0.342438 | − | 0.939540i | \(-0.388747\pi\) | ||||
0.342438 | + | 0.939540i | \(0.388747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.500000 | + | 0.866025i | 0.0283524 | + | 0.0491078i | 0.879853 | − | 0.475245i | \(-0.157641\pi\) |
−0.851501 | + | 0.524353i | \(0.824307\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.50000 | − | 9.52628i | 0.310878 | − | 0.538457i | −0.667674 | − | 0.744453i | \(-0.732710\pi\) |
0.978553 | + | 0.205996i | \(0.0660435\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.00000 | + | 1.73205i | 0.281718 | + | 0.0975900i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.50000 | + | 14.7224i | −0.477408 | + | 0.826894i | −0.999665 | − | 0.0258939i | \(-0.991757\pi\) |
0.522257 | + | 0.852788i | \(0.325090\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.0000 | − | 43.3013i | −1.39973 | − | 2.42441i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.0000 | 0.725589 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.00000 | 0.500773 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | − | 6.92820i | −0.221880 | − | 0.384308i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.50000 | − | 14.7224i | 0.470051 | − | 0.814152i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.50000 | + | 18.1865i | 0.192961 | + | 1.00266i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.50000 | − | 2.59808i | 0.0824475 | − | 0.142803i | −0.821853 | − | 0.569699i | \(-0.807060\pi\) |
0.904301 | + | 0.426896i | \(0.140393\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.00000 | + | 12.1244i | 0.383598 | + | 0.664411i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.00000 | −0.382451 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0000 | −0.762629 | −0.381314 | − | 0.924445i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.00000 | + | 5.19615i | 0.162938 | + | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.5000 | + | 47.6314i | −1.48921 | + | 2.57938i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.500000 | − | 0.866025i | 0.0269191 | − | 0.0466252i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.50000 | + | 7.79423i | 0.241573 | + | 0.418416i | 0.961162 | − | 0.275983i | \(-0.0890035\pi\) |
−0.719590 | + | 0.694399i | \(0.755670\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.0000 | −0.533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.50000 | + | 7.79423i | 0.239511 | + | 0.414845i | 0.960574 | − | 0.278024i | \(-0.0896796\pi\) |
−0.721063 | + | 0.692869i | \(0.756346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | + | 10.3923i | −0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.50000 | − | 7.79423i | −0.0793884 | − | 0.412514i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.5000 | − | 25.1147i | 0.765281 | − | 1.32551i | −0.174817 | − | 0.984601i | \(-0.555933\pi\) |
0.940098 | − | 0.340904i | \(-0.110733\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.00000 | + | 8.66025i | 0.263158 | + | 0.455803i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.0000 | −0.734809 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.00000 | 0.261712 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.50000 | + | 12.9904i | 0.391497 | + | 0.678092i | 0.992647 | − | 0.121044i | \(-0.0386241\pi\) |
−0.601150 | + | 0.799136i | \(0.705291\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.00000 | + | 1.73205i | −0.0520579 | + | 0.0901670i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.5000 | − | 9.52628i | −1.42773 | − | 0.494580i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.50000 | + | 16.4545i | −0.491891 | + | 0.851981i | −0.999956 | − | 0.00933789i | \(-0.997028\pi\) |
0.508065 | + | 0.861319i | \(0.330361\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.50000 | + | 7.79423i | 0.232379 | + | 0.402492i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.0000 | 1.03005 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.00000 | + | 3.46410i | 0.102463 | + | 0.177471i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.5000 | − | 23.3827i | 0.689818 | − | 1.19480i | −0.282079 | − | 0.959391i | \(-0.591024\pi\) |
0.971897 | − | 0.235408i | \(-0.0756427\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.0000 | + | 8.66025i | −0.509647 | + | 0.441367i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.00000 | − | 13.8564i | 0.406663 | − | 0.704361i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.50000 | − | 2.59808i | −0.0760530 | − | 0.131728i | 0.825491 | − | 0.564416i | \(-0.190898\pi\) |
−0.901544 | + | 0.432688i | \(0.857565\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.00000 | 0.151717 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.00000 | −0.151330 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.50000 | + | 7.79423i | 0.226420 | + | 0.392170i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.5000 | + | 25.1147i | −0.727734 | + | 1.26047i | 0.230105 | + | 0.973166i | \(0.426093\pi\) |
−0.957839 | + | 0.287307i | \(0.907240\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.00000 | + | 5.19615i | −0.300376 | + | 0.260133i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.50000 | − | 11.2583i | 0.324595 | − | 0.562214i | −0.656836 | − | 0.754034i | \(-0.728105\pi\) |
0.981430 | + | 0.191820i | \(0.0614388\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.0000 | − | 19.0526i | −0.547949 | − | 0.949076i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −35.0000 | −1.73489 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.5000 | − | 30.3109i | −0.865319 | − | 1.49878i | −0.866730 | − | 0.498778i | \(-0.833782\pi\) |
0.00141047 | − | 0.999999i | \(-0.499551\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.50000 | − | 7.79423i | 0.221969 | − | 0.384461i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.5000 | − | 6.06218i | −0.861119 | − | 0.298300i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.0000 | − | 17.3205i | −0.489702 | − | 0.848189i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.0000 | −0.877266 | −0.438633 | − | 0.898666i | \(-0.644537\pi\) | ||||
−0.438633 | + | 0.898666i | \(0.644537\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.00000 | − | 12.1244i | −0.340352 | − | 0.589506i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00000 | + | 10.3923i | −0.291043 | + | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.500000 | + | 2.59808i | 0.0241967 | + | 0.125730i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.00000 | − | 8.66025i | 0.241402 | − | 0.418121i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.5000 | + | 30.3109i | 0.842945 | + | 1.46002i | 0.887394 | + | 0.461012i | \(0.152514\pi\) |
−0.0444483 | + | 0.999012i | \(0.514153\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.0000 | −0.479463 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.50000 | − | 2.59808i | −0.0717547 | − | 0.124283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.50000 | − | 6.06218i | 0.167046 | − | 0.289332i | −0.770334 | − | 0.637641i | \(-0.779911\pi\) |
0.937380 | + | 0.348309i | \(0.113244\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.0000 | − | 8.66025i | −0.523810 | − | 0.412393i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.5000 | + | 33.7750i | −0.926473 | + | 1.60470i | −0.137298 | + | 0.990530i | \(0.543842\pi\) |
−0.789175 | + | 0.614168i | \(0.789492\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.50000 | − | 2.59808i | −0.0711068 | − | 0.123161i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.00000 | 0.331089 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.0000 | 1.03824 | 0.519122 | − | 0.854700i | \(-0.326259\pi\) | ||||
0.519122 | + | 0.854700i | \(0.326259\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.50000 | − | 4.33013i | −0.117720 | − | 0.203898i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.50000 | + | 4.33013i | −0.117460 | + | 0.203447i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.00000 | − | 5.19615i | −0.0468807 | − | 0.243599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.50000 | + | 4.33013i | −0.116945 | + | 0.202555i | −0.918556 | − | 0.395292i | \(-0.870643\pi\) |
0.801611 | + | 0.597847i | \(0.203977\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.50000 | + | 12.9904i | 0.350070 | + | 0.606339i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.00000 | 0.0931493 | 0.0465746 | − | 0.998915i | \(-0.485169\pi\) | ||||
0.0465746 | + | 0.998915i | \(0.485169\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.50000 | + | 9.52628i | 0.255056 | + | 0.441771i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.5000 | − | 28.5788i | 0.763529 | − | 1.32247i | −0.177492 | − | 0.984122i | \(-0.556798\pi\) |
0.941021 | − | 0.338349i | \(-0.109868\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.5000 | + | 6.06218i | 0.808075 | + | 0.279925i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.50000 | + | 2.59808i | −0.0691164 | + | 0.119713i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.0000 | + | 34.6410i | 0.919601 | + | 1.59280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.0000 | 0.550598 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.0000 | 1.00731 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.50000 | + | 14.7224i | 0.388375 | + | 0.672685i | 0.992231 | − | 0.124408i | \(-0.0397032\pi\) |
−0.603856 | + | 0.797093i | \(0.706370\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.00000 | − | 12.1244i | 0.319173 | − | 0.552823i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.00000 | + | 1.73205i | −0.0910032 | + | 0.0788110i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.00000 | − | 1.73205i | 0.0454077 | − | 0.0786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.5000 | + | 30.3109i | 0.793001 | + | 1.37352i | 0.924101 | + | 0.382148i | \(0.124816\pi\) |
−0.131100 | + | 0.991369i | \(0.541851\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.0000 | 0.768767 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.0000 | −0.902587 | −0.451294 | − | 0.892375i | \(-0.649037\pi\) | ||||
−0.451294 | + | 0.892375i | \(0.649037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.0000 | − | 25.9808i | −0.675566 | − | 1.17011i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.00000 | − | 8.66025i | 0.224733 | − | 0.389249i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.0000 | − | 20.7846i | 1.07655 | − | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.50000 | − | 2.59808i | 0.0671492 | − | 0.116306i | −0.830496 | − | 0.557024i | \(-0.811943\pi\) |
0.897645 | + | 0.440719i | \(0.145276\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.00000 | + | 13.8564i | 0.357414 | + | 0.619059i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 40.0000 | 1.78351 | 0.891756 | − | 0.452517i | \(-0.149474\pi\) | ||||
0.891756 | + | 0.452517i | \(0.149474\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.0000 | 0.489494 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.50000 | − | 7.79423i | −0.199852 | − | 0.346154i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.50000 | + | 4.33013i | −0.110811 | + | 0.191930i | −0.916097 | − | 0.400956i | \(-0.868678\pi\) |
0.805287 | + | 0.592886i | \(0.202011\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.5000 | − | 4.33013i | −0.552967 | − | 0.191554i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.50000 | − | 12.9904i | 0.331133 | − | 0.573539i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.500000 | − | 0.866025i | −0.0220326 | − | 0.0381616i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.0000 | 1.53930 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.0000 | 0.921798 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.5000 | + | 23.3827i | 0.591446 | + | 1.02441i | 0.994038 | + | 0.109035i | \(0.0347759\pi\) |
−0.402592 | + | 0.915379i | \(0.631891\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.5000 | + | 33.7750i | −0.852675 | + | 1.47688i | 0.0261094 | + | 0.999659i | \(0.491688\pi\) |
−0.878785 | + | 0.477218i | \(0.841645\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.00000 | − | 10.3923i | −0.0872872 | − | 0.453557i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.5000 | + | 28.5788i | −0.718751 | + | 1.24491i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | + | 19.0526i | 0.478261 | + | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.0000 | 0.607548 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.00000 | 0.0866296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.50000 | − | 11.2583i | −0.281020 | − | 0.486740i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.50000 | − | 6.06218i | 0.151036 | − | 0.261602i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.5000 | − | 12.9904i | 1.39987 | − | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.50000 | + | 9.52628i | −0.236463 | + | 0.409567i | −0.959697 | − | 0.281037i | \(-0.909322\pi\) |
0.723234 | + | 0.690604i | \(0.242655\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.0000 | − | 19.0526i | −0.472055 | − | 0.817624i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.0000 | −0.728200 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.00000 | −0.171028 | −0.0855138 | − | 0.996337i | \(-0.527253\pi\) | ||||
−0.0855138 | + | 0.996337i | \(0.527253\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.00000 | − | 1.73205i | −0.0426790 | − | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.0000 | + | 25.9808i | −0.639021 | + | 1.10682i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.50000 | − | 23.3827i | −0.191359 | − | 0.994333i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.50000 | + | 6.06218i | −0.148567 | + | 0.257325i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.5000 | − | 28.5788i | −0.699127 | − | 1.21092i | −0.968769 | − | 0.247964i | \(-0.920239\pi\) |
0.269642 | − | 0.962961i | \(-0.413095\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.0000 | −0.633300 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.5000 | + | 21.6506i | 0.526812 | + | 0.912465i | 0.999512 | + | 0.0312419i | \(0.00994622\pi\) |
−0.472700 | + | 0.881224i | \(0.656720\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.00000 | − | 5.19615i | 0.126211 | − | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.50000 | + | 0.866025i | 0.104990 | + | 0.0363696i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.50000 | + | 12.9904i | −0.314416 | + | 0.544585i | −0.979313 | − | 0.202350i | \(-0.935142\pi\) |
0.664897 | + | 0.746935i | \(0.268475\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.50000 | − | 12.9904i | −0.313865 | − | 0.543631i | 0.665330 | − | 0.746549i | \(-0.268291\pi\) |
−0.979196 | + | 0.202919i | \(0.934957\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.00000 | −0.0417756 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.5000 | + | 33.7750i | 0.811796 | + | 1.40607i | 0.911606 | + | 0.411065i | \(0.134843\pi\) |
−0.0998105 | + | 0.995006i | \(0.531824\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.50000 | − | 14.7224i | 0.353248 | − | 0.611843i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.5000 | + | 47.6314i | −1.13893 | + | 1.97269i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | + | 3.46410i | 0.0826898 | + | 0.143223i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.0000 | 1.48588 | 0.742940 | − | 0.669359i | \(-0.233431\pi\) | ||||
0.742940 | + | 0.669359i | \(0.233431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.0000 | 1.35974 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.0000 | + | 22.5167i | 0.534749 | + | 0.926212i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.50000 | + | 4.33013i | −0.102663 | + | 0.177817i | −0.912781 | − | 0.408450i | \(-0.866070\pi\) |
0.810118 | + | 0.586267i | \(0.199403\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | + | 5.19615i | −0.245976 | + | 0.213021i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.5000 | + | 18.1865i | −0.429736 | + | 0.744325i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.50000 | − | 7.79423i | −0.183865 | − | 0.318464i | 0.759328 | − | 0.650708i | \(-0.225528\pi\) |
−0.943193 | + | 0.332244i | \(0.892194\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.0000 | −0.570124 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | + | 12.1244i | 0.284590 | + | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.5000 | + | 30.3109i | −0.710303 | + | 1.23028i | 0.254440 | + | 0.967088i | \(0.418109\pi\) |
−0.964743 | + | 0.263193i | \(0.915225\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25.0000 | + | 8.66025i | 1.01305 | + | 0.350931i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.00000 | + | 12.1244i | −0.283190 | + | 0.490499i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.5000 | − | 23.3827i | −0.545260 | − | 0.944418i | −0.998591 | − | 0.0530754i | \(-0.983098\pi\) |
0.453331 | − | 0.891342i | \(-0.350236\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.00000 | −0.0403239 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.50000 | + | 9.52628i | 0.221064 | + | 0.382893i | 0.955131 | − | 0.296183i | \(-0.0957138\pi\) |
−0.734068 | + | 0.679076i | \(0.762380\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.50000 | − | 4.33013i | 0.100322 | − | 0.173762i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.50000 | + | 7.79423i | 0.0600962 | + | 0.312269i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | + | 9.52628i | −0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.50000 | + | 12.9904i | 0.299521 | + | 0.518786i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.0000 | −0.837325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.00000 | − | 10.3923i | −0.238479 | − | 0.413057i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.00000 | − | 3.46410i | 0.0793676 | − | 0.137469i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.00000 | + | 13.8564i | −0.0792429 | + | 0.549011i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.0000 | + | 20.7846i | −0.474713 | + | 0.822226i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.50000 | + | 12.9904i | 0.296232 | + | 0.513089i | 0.975271 | − | 0.221013i | \(-0.0709364\pi\) |
−0.679039 | + | 0.734103i | \(0.737603\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.0000 | −1.41970 | −0.709851 | − | 0.704352i | \(-0.751238\pi\) | ||||
−0.709851 | + | 0.704352i | \(0.751238\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.00000 | 0.315000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.50000 | + | 16.4545i | 0.373484 | + | 0.646892i | 0.990099 | − | 0.140372i | \(-0.0448299\pi\) |
−0.616615 | + | 0.787265i | \(0.711497\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.5000 | + | 30.3109i | −0.686935 | + | 1.18981i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.50000 | − | 28.5788i | −0.215562 | − | 1.12009i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.50000 | + | 7.79423i | −0.176099 | + | 0.305012i | −0.940541 | − | 0.339680i | \(-0.889681\pi\) |
0.764442 | + | 0.644692i | \(0.223014\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.50000 | + | 2.59808i | 0.0586098 | + | 0.101515i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.0000 | 0.390137 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.00000 | −0.155818 | −0.0779089 | − | 0.996960i | \(-0.524824\pi\) | ||||
−0.0779089 | + | 0.996960i | \(0.524824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.5000 | − | 44.1673i | −0.991835 | − | 1.71791i | −0.606359 | − | 0.795191i | \(-0.707371\pi\) |
−0.385476 | − | 0.922718i | \(-0.625963\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.00000 | − | 5.19615i | 0.116510 | − | 0.201802i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.50000 | + | 2.59808i | 0.290838 | + | 0.100749i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.00000 | + | 8.66025i | −0.193601 | + | 0.335326i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.00000 | + | 6.92820i | 0.154649 | + | 0.267860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.00000 | 0.193023 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.0000 | 1.31060 | 0.655302 | − | 0.755367i | \(-0.272541\pi\) | ||||
0.655302 | + | 0.755367i | \(0.272541\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.0000 | + | 17.3205i | 0.384900 | + | 0.666667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.50000 | + | 12.9904i | −0.288248 | + | 0.499261i | −0.973392 | − | 0.229147i | \(-0.926406\pi\) |
0.685143 | + | 0.728408i | \(0.259740\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.00000 | + | 3.46410i | −0.153506 | + | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.50000 | + | 7.79423i | −0.172440 | + | 0.298675i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.5000 | − | 26.8468i | −0.593091 | − | 1.02726i | −0.993813 | − | 0.111064i | \(-0.964574\pi\) |
0.400722 | − | 0.916200i | \(-0.368759\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.00000 | −0.343872 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.0000 | 1.03011 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.0000 | − | 19.0526i | −0.419067 | − | 0.725845i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.50000 | + | 7.79423i | −0.171188 | + | 0.296506i | −0.938835 | − | 0.344366i | \(-0.888094\pi\) |
0.767647 | + | 0.640872i | \(0.221427\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −20.0000 | + | 17.3205i | −0.759737 | + | 0.657952i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.0000 | + | 17.3205i | −0.379322 | + | 0.657004i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.50000 | − | 2.59808i | −0.0568166 | − | 0.0984092i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.0000 | −0.491705 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.0000 | 1.88847 | 0.944237 | − | 0.329267i | \(-0.106802\pi\) | ||||
0.944237 | + | 0.329267i | \(0.106802\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.5000 | + | 18.1865i | 0.396015 | + | 0.685918i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.50000 | − | 6.06218i | 0.131818 | − | 0.228315i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.5000 | − | 9.52628i | −1.03424 | − | 0.358273i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.50000 | − | 16.4545i | 0.356780 | − | 0.617961i | −0.630641 | − | 0.776075i | \(-0.717208\pi\) |
0.987421 | + | 0.158114i | \(0.0505412\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.00000 | + | 15.5885i | 0.337526 | + | 0.584613i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.0000 | 0.411953 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.0000 | −0.373979 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.00000 | − | 13.8564i | −0.298765 | − | 0.517477i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.50000 | − | 9.52628i | 0.205115 | − | 0.355270i | −0.745054 | − | 0.667004i | \(-0.767576\pi\) |
0.950169 | + | 0.311734i | \(0.100910\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.500000 | + | 2.59808i | 0.0186210 | + | 0.0967574i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.50000 | − | 16.4545i | 0.353309 | − | 0.611949i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.0000 | − | 34.6410i | −0.742781 | − | 1.28654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0000 | 1.18681 | 0.593407 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593407 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0000 | + | 20.7846i | 0.443836 | + | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.50000 | + | 2.59808i | −0.0554038 | + | 0.0959621i | −0.892397 | − | 0.451251i | \(-0.850978\pi\) |
0.836993 | + | 0.547213i | \(0.184311\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.00000 | − | 6.92820i | 0.0368856 | − | 0.255551i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.5000 | − | 30.3109i | 0.644621 | − | 1.11652i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.50000 | + | 12.9904i | 0.275892 | + | 0.477859i | 0.970360 | − | 0.241665i | \(-0.0776935\pi\) |
−0.694468 | + | 0.719524i | \(0.744360\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.00000 | −0.220416 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −48.0000 | −1.76095 | −0.880475 | − | 0.474093i | \(-0.842776\pi\) | ||||
−0.880475 | + | 0.474093i | \(0.842776\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.50000 | − | 6.06218i | −0.128230 | − | 0.222101i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.50000 | + | 33.7750i | 0.237505 | + | 1.23411i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.50000 | − | 6.06218i | 0.127717 | − | 0.221212i | −0.795075 | − | 0.606511i | \(-0.792568\pi\) |
0.922792 | + | 0.385299i | \(0.125902\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.0000 | + | 20.7846i | 0.437304 | + | 0.757433i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.00000 | 0.181969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.0000 | −1.38113 | −0.690567 | − | 0.723269i | \(-0.742639\pi\) | ||||
−0.690567 | + | 0.723269i | \(0.742639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.50000 | + | 4.33013i | 0.0907443 | + | 0.157174i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.5000 | − | 42.4352i | 0.888124 | − | 1.53828i | 0.0460340 | − | 0.998940i | \(-0.485342\pi\) |
0.842090 | − | 0.539337i | \(-0.181325\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.5000 | + | 14.7224i | 1.53860 | + | 0.532988i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.00000 | − | 5.19615i | 0.108465 | − | 0.187867i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.00000 | − | 12.1244i | −0.252755 | − | 0.437785i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.0000 | −0.360609 | −0.180305 | − | 0.983611i | \(-0.557708\pi\) | ||||
−0.180305 | + | 0.983611i | \(0.557708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.00000 | 0.252099 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.50000 | + | 16.4545i | 0.341691 | + | 0.591827i | 0.984747 | − | 0.173993i | \(-0.0556670\pi\) |
−0.643056 | + | 0.765819i | \(0.722334\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.0000 | + | 38.1051i | −0.790263 | + | 1.36878i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.0000 | − | 12.1244i | 0.502247 | − | 0.434959i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.50000 | + | 2.59808i | −0.0537431 | + | 0.0930857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.0000 | − | 51.9615i | −1.07348 | − | 1.85933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −50.0000 | −1.78685 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.00000 | 0.107075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.5000 | + | 40.7032i | 0.837685 | + | 1.45091i | 0.891826 | + | 0.452379i | \(0.149425\pi\) |
−0.0541413 | + | 0.998533i | \(0.517242\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.50000 | − | 16.4545i | 0.338209 | − | 0.585795i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | + | 10.3923i | −0.426671 | + | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.00000 | + | 1.73205i | −0.0355110 | + | 0.0615069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.50000 | + | 9.52628i | 0.195065 | + | 0.337862i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.00000 | 0.0708436 | 0.0354218 | − | 0.999372i | \(-0.488723\pi\) | ||||
0.0354218 | + | 0.999372i | \(0.488723\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.0000 | 0.742927 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00000 | − | 5.19615i | −0.106000 | − | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.5000 | + | 21.6506i | −0.441115 | + | 0.764034i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.50000 | + | 0.866025i | 0.0881134 | + | 0.0305234i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.50000 | − | 9.52628i | 0.193609 | − | 0.335341i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.5000 | + | 26.8468i | 0.544951 | + | 0.943883i | 0.998610 | + | 0.0527074i | \(0.0167851\pi\) |
−0.453659 | + | 0.891175i | \(0.649882\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.0000 | −0.421377 | −0.210688 | − | 0.977553i | \(-0.567571\pi\) | ||||
−0.210688 | + | 0.977553i | \(0.567571\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.0000 | 0.876788 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.50000 | − | 14.7224i | −0.297742 | − | 0.515704i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000 | − | 20.7846i | 0.419827 | − | 0.727161i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.00000 | − | 10.3923i | −0.0698857 | − | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.50000 | − | 14.7224i | 0.296652 | − | 0.513816i | −0.678716 | − | 0.734401i | \(-0.737463\pi\) |
0.975368 | + | 0.220585i | \(0.0707965\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.50000 | + | 4.33013i | 0.0871445 | + | 0.150939i | 0.906303 | − | 0.422628i | \(-0.138892\pi\) |
−0.819159 | + | 0.573567i | \(0.805559\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −20.0000 | −0.696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.5000 | − | 44.1673i | −0.885652 | − | 1.53399i | −0.844965 | − | 0.534822i | \(-0.820379\pi\) |
−0.0406866 | − | 0.999172i | \(-0.512955\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.5000 | − | 19.9186i | 0.398931 | − | 0.690968i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.5000 | − | 7.79423i | 0.675635 | − | 0.270054i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.00000 | − | 13.8564i | 0.276851 | − | 0.479521i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27.5000 | + | 47.6314i | 0.950539 | + | 1.64638i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.00000 | 0.276191 | 0.138095 | − | 0.990419i | \(-0.455902\pi\) | ||||
0.138095 | + | 0.990419i | \(0.455902\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 71.0000 | 2.44828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.00000 | − | 12.1244i | −0.241093 | − | 0.417585i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.50000 | + | 7.79423i | −0.154805 | + | 0.268130i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.00000 | − | 36.3731i | −0.240523 | − | 1.24979i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.50000 | − | 14.7224i | 0.291719 | − | 0.505273i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.50000 | + | 6.06218i | 0.119978 | + | 0.207809i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.0000 | −0.479351 | −0.239675 | − | 0.970853i | \(-0.577041\pi\) | ||||
−0.239675 | + | 0.970853i | \(0.577041\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.00000 | −0.205196 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.50000 | + | 11.2583i | 0.222036 | + | 0.384577i | 0.955426 | − | 0.295231i | \(-0.0953965\pi\) |
−0.733390 | + | 0.679808i | \(0.762063\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.50000 | + | 9.52628i | −0.187658 | + | 0.325032i | −0.944469 | − | 0.328601i | \(-0.893423\pi\) |
0.756811 | + | 0.653633i | \(0.226756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.50000 | + | 0.866025i | 0.0851998 | + | 0.0295141i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.5000 | − | 38.9711i | 0.765909 | − | 1.32659i | −0.173856 | − | 0.984771i | \(-0.555623\pi\) |
0.939765 | − | 0.341822i | \(-0.111044\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.5000 | − | 18.1865i | −0.357011 | − | 0.618361i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −45.0000 | −1.52652 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.00000 | + | 12.1244i | 0.237186 | + | 0.410818i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.00000 | − | 3.46410i | 0.0676897 | − | 0.117242i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.0000 | + | 15.5885i | −0.608511 | + | 0.526986i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.50000 | + | 9.52628i | −0.185722 | + | 0.321680i | −0.943820 | − | 0.330461i | \(-0.892796\pi\) |
0.758098 | + | 0.652141i | \(0.226129\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.00000 | − | 15.5885i | −0.303562 | − | 0.525786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.0000 | −1.68454 | −0.842271 | − | 0.539054i | \(-0.818782\pi\) | ||||
−0.842271 | + | 0.539054i | \(0.818782\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.0000 | −1.07689 | −0.538443 | − | 0.842662i | \(-0.680987\pi\) | ||||
−0.538443 | + | 0.842662i | \(0.680987\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.50000 | + | 6.06218i | 0.117651 | + | 0.203778i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.5000 | − | 37.2391i | 0.721899 | − | 1.25037i | −0.238338 | − | 0.971182i | \(-0.576603\pi\) |
0.960238 | − | 0.279184i | \(-0.0900640\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.00000 | + | 6.92820i | −0.268311 | + | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.50000 | − | 4.33013i | 0.0837532 | − | 0.145065i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.5000 | − | 18.1865i | −0.351369 | − | 0.608589i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.00000 | −0.233984 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.00000 | −0.0667781 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −55.0000 | − | 95.2628i | −1.83435 | − | 3.17719i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.5000 | + | 28.5788i | −0.549695 | + | 0.952099i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.0000 | − | 6.92820i | −0.665558 | − | 0.230556i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.0000 | + | 19.0526i | −0.365652 | + | 0.633328i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.50000 | − | 14.7224i | −0.282238 | − | 0.488850i | 0.689698 | − | 0.724097i | \(-0.257743\pi\) |
−0.971936 | + | 0.235247i | \(0.924410\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.0000 | 0.729694 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.0000 | −0.927681 | −0.463841 | − | 0.885919i | \(-0.653529\pi\) | ||||
−0.463841 | + | 0.885919i | \(0.653529\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.500000 | − | 0.866025i | 0.0165295 | − | 0.0286299i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.50000 | − | 7.79423i | −0.0495344 | − | 0.257388i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.50000 | + | 4.33013i | −0.0824674 | + | 0.142838i | −0.904309 | − | 0.426878i | \(-0.859613\pi\) |
0.821842 | + | 0.569716i | \(0.192947\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.00000 | + | 10.3923i | 0.197707 | + | 0.342438i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.0000 | 0.789970 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.0000 | −0.920634 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.00000 | − | 1.73205i | −0.0328443 | − | 0.0568880i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.50000 | + | 14.7224i | −0.278876 | + | 0.483027i | −0.971106 | − | 0.238650i | \(-0.923295\pi\) |
0.692230 | + | 0.721677i | \(0.256628\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.5000 | − | 12.9904i | −0.540766 | − | 0.425743i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.500000 | + | 0.866025i | −0.0163693 | + | 0.0283524i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.50000 | + | 12.9904i | 0.245276 | + | 0.424831i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.00000 | 0.196011 | 0.0980057 | − | 0.995186i | \(-0.468754\pi\) | ||||
0.0980057 | + | 0.995186i | \(0.468754\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.0000 | 0.358971 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.5000 | − | 23.3827i | −0.440087 | − | 0.762254i | 0.557608 | − | 0.830104i | \(-0.311719\pi\) |
−0.997695 | + | 0.0678506i | \(0.978386\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.500000 | + | 0.866025i | −0.0162822 | + | 0.0282017i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.50000 | + | 12.9904i | 0.0813250 | + | 0.422577i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.50000 | + | 12.9904i | −0.243717 | + | 0.422131i | −0.961770 | − | 0.273858i | \(-0.911700\pi\) |
0.718053 | + | 0.695988i | \(0.245034\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.00000 | − | 8.66025i | −0.162307 | − | 0.281124i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.0000 | −0.551263 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.0000 | 0.971795 | 0.485898 | − | 0.874016i | \(-0.338493\pi\) | ||||
0.485898 | + | 0.874016i | \(0.338493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.500000 | + | 0.866025i | 0.0161796 | + | 0.0280239i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.0000 | − | 43.3013i | 0.808135 | − | 1.39973i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.5000 | + | 7.79423i | 0.726563 | + | 0.251689i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −45.0000 | + | 77.9423i | −1.45161 | + | 2.51427i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.0000 | − | 22.5167i | −0.418919 | − | 0.725589i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.0000 | −0.547249 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.00000 | 0.128631 | 0.0643157 | − | 0.997930i | \(-0.479514\pi\) | ||||
0.0643157 | + | 0.997930i | \(0.479514\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.50000 | + | 7.79423i | 0.144561 | + | 0.250387i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.50000 | − | 9.52628i | 0.176503 | − | 0.305713i | −0.764177 | − | 0.645006i | \(-0.776855\pi\) |
0.940681 | + | 0.339294i | \(0.110188\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 40.0000 | − | 34.6410i | 1.28234 | − | 1.11054i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.00000 | − | 6.92820i | 0.128103 | − | 0.221880i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.50000 | + | 6.06218i | 0.111975 | + | 0.193946i | 0.916566 | − | 0.399882i | \(-0.130949\pi\) |
−0.804592 | + | 0.593829i | \(0.797616\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.0000 | 0.479402 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.0000 | −1.08554 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.50000 | + | 9.52628i | 0.175423 | + | 0.303841i | 0.940307 | − | 0.340326i | \(-0.110537\pi\) |
−0.764885 | + | 0.644167i | \(0.777204\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.0000 | − | 22.5167i | 0.414214 | − | 0.717440i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.0000 | + | 12.1244i | −0.445625 | + | 0.385922i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.00000 | − | 6.92820i | 0.127193 | − | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.50000 | + | 11.2583i | 0.206479 | + | 0.357633i | 0.950603 | − | 0.310409i | \(-0.100466\pi\) |
−0.744124 | + | 0.668042i | \(0.767133\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.00000 | 0.0952021 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.0000 | 0.665745 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.5000 | − | 32.0429i | −0.585901 | − | 1.01481i | −0.994762 | − | 0.102214i | \(-0.967407\pi\) |
0.408862 | − | 0.912596i | \(-0.365926\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17.5000 | + | 30.3109i | −0.553675 | + | 0.958994i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1148.2.i.b.821.1 | yes | 2 | |
7.2 | even | 3 | 8036.2.a.a.1.1 | 1 | |||
7.4 | even | 3 | inner | 1148.2.i.b.165.1 | ✓ | 2 | |
7.5 | odd | 6 | 8036.2.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.b.165.1 | ✓ | 2 | 7.4 | even | 3 | inner | |
1148.2.i.b.821.1 | yes | 2 | 1.1 | even | 1 | trivial | |
8036.2.a.a.1.1 | 1 | 7.2 | even | 3 | |||
8036.2.a.e.1.1 | 1 | 7.5 | odd | 6 |