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: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 14 x^{14} - 8 x^{13} + 136 x^{12} - 87 x^{11} + 706 x^{10} - 568 x^{9} + 2685 x^{8} - 2100 x^{7} + 5529 x^{6} - 4919 x^{5} + 8145 x^{4} - 5182 x^{3} + 2775 x^{2} + \cdots + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 165.8 | ||
Root | \(-1.43353 + 2.48295i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.165 |
Dual form | 1148.2.i.d.821.8 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.43353 | − | 2.48295i | 0.827650 | − | 1.43353i | −0.0722278 | − | 0.997388i | \(-0.523011\pi\) |
0.899877 | − | 0.436143i | \(-0.143656\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.601031 | − | 1.04102i | −0.268789 | − | 0.465557i | 0.699760 | − | 0.714378i | \(-0.253290\pi\) |
−0.968549 | + | 0.248821i | \(0.919957\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.46485 | + | 0.961519i | −0.931625 | + | 0.363420i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.61002 | − | 4.52069i | −0.870008 | − | 1.50690i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.423540 | − | 0.733593i | 0.127702 | − | 0.221187i | −0.795084 | − | 0.606500i | \(-0.792573\pi\) |
0.922786 | + | 0.385313i | \(0.125907\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.77566 | −0.492479 | −0.246239 | − | 0.969209i | \(-0.579195\pi\) | ||||
−0.246239 | + | 0.969209i | \(0.579195\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.44639 | −0.889853 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.665195 | + | 1.15215i | −0.161334 | + | 0.279438i | −0.935347 | − | 0.353731i | \(-0.884913\pi\) |
0.774014 | + | 0.633169i | \(0.218246\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.56015 | − | 4.43430i | −0.587338 | − | 1.01730i | −0.994580 | − | 0.103979i | \(-0.966843\pi\) |
0.407242 | − | 0.913320i | \(-0.366491\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.14604 | + | 7.49846i | −0.250086 | + | 1.63630i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.408156 | + | 0.706947i | 0.0851064 | + | 0.147409i | 0.905437 | − | 0.424482i | \(-0.139544\pi\) |
−0.820330 | + | 0.571890i | \(0.806210\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.77752 | − | 3.07876i | 0.355505 | − | 0.615752i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.36501 | −1.22495 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.14823 | −1.51309 | −0.756544 | − | 0.653942i | \(-0.773114\pi\) | ||||
−0.756544 | + | 0.653942i | \(0.773114\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.94452 | + | 5.10006i | −0.528852 | + | 0.915998i | 0.470582 | + | 0.882356i | \(0.344044\pi\) |
−0.999434 | + | 0.0336419i | \(0.989289\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.21432 | − | 2.10326i | −0.211385 | − | 0.366130i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.48241 | + | 1.98805i | 0.419604 | + | 0.336041i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.829482 | − | 1.43670i | −0.136366 | − | 0.236193i | 0.789752 | − | 0.613426i | \(-0.210209\pi\) |
−0.926118 | + | 0.377233i | \(0.876876\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.54546 | + | 4.40887i | −0.407600 | + | 0.705983i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.82843 | −0.583831 | −0.291915 | − | 0.956444i | \(-0.594293\pi\) | ||||
−0.291915 | + | 0.956444i | \(0.594293\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.13741 | + | 5.43415i | −0.467698 | + | 0.810076i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.33648 | − | 4.04690i | −0.340810 | − | 0.590301i | 0.643773 | − | 0.765216i | \(-0.277368\pi\) |
−0.984583 | + | 0.174916i | \(0.944035\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.15096 | − | 4.74000i | 0.735852 | − | 0.677142i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.90716 | + | 3.30329i | 0.267055 | + | 0.462553i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.82475 | − | 3.16055i | 0.250648 | − | 0.434136i | −0.713056 | − | 0.701107i | \(-0.752690\pi\) |
0.963704 | + | 0.266971i | \(0.0860229\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.01824 | −0.137300 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.6802 | −1.94444 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.425709 | − | 0.737349i | 0.0554225 | − | 0.0959946i | −0.836983 | − | 0.547229i | \(-0.815683\pi\) |
0.892406 | + | 0.451234i | \(0.149016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.56564 | + | 7.90792i | 0.584570 | + | 1.01250i | 0.994929 | + | 0.100581i | \(0.0320701\pi\) |
−0.410359 | + | 0.911924i | \(0.634597\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.7800 | + | 8.63324i | 1.35816 | + | 1.08769i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.06723 | + | 1.84849i | 0.132373 | + | 0.229277i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.19546 | − | 7.26675i | 0.512557 | − | 0.887775i | −0.487337 | − | 0.873214i | \(-0.662032\pi\) |
0.999894 | − | 0.0145610i | \(-0.00463506\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.34042 | 0.281753 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.66604 | 0.197723 | 0.0988615 | − | 0.995101i | \(-0.468480\pi\) | ||||
0.0988615 | + | 0.995101i | \(0.468480\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.54331 | + | 2.67310i | −0.180631 | + | 0.312863i | −0.942096 | − | 0.335344i | \(-0.891147\pi\) |
0.761464 | + | 0.648207i | \(0.224481\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.09627 | − | 8.82700i | −0.588466 | − | 1.01925i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.338599 | + | 2.21544i | −0.0385870 | + | 0.252472i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.06100 | − | 7.03386i | −0.456898 | − | 0.791371i | 0.541897 | − | 0.840445i | \(-0.317706\pi\) |
−0.998795 | + | 0.0490737i | \(0.984373\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.29437 | + | 2.24192i | −0.143819 | + | 0.249102i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.90385 | 0.428503 | 0.214251 | − | 0.976779i | \(-0.431269\pi\) | ||||
0.214251 | + | 0.976779i | \(0.431269\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.59921 | 0.173459 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.6807 | + | 20.2316i | −1.25231 | + | 2.16906i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.76473 | + | 8.25275i | 0.505060 | + | 0.874790i | 0.999983 | + | 0.00585279i | \(0.00186301\pi\) |
−0.494923 | + | 0.868937i | \(0.664804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.37673 | − | 1.70733i | 0.458806 | − | 0.178977i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.44213 | + | 14.6222i | 0.875408 | + | 1.51625i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.07746 | + | 5.33031i | −0.315740 | + | 0.546878i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.3723 | 1.35776 | 0.678878 | − | 0.734251i | \(-0.262466\pi\) | ||||
0.678878 | + | 0.734251i | \(0.262466\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.42180 | −0.444407 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.37820 | + | 2.38712i | −0.137136 | + | 0.237527i | −0.926411 | − | 0.376513i | \(-0.877123\pi\) |
0.789275 | + | 0.614040i | \(0.210456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.730755 | + | 1.26570i | 0.0720034 | + | 0.124714i | 0.899779 | − | 0.436345i | \(-0.143727\pi\) |
−0.827776 | + | 0.561059i | \(0.810394\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.49483 | − | 3.31377i | 0.829010 | − | 0.323390i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.31141 | − | 10.9317i | −0.610147 | − | 1.05681i | −0.991215 | − | 0.132258i | \(-0.957777\pi\) |
0.381069 | − | 0.924547i | \(-0.375556\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.2890 | − | 17.8210i | 0.985504 | − | 1.70694i | 0.345831 | − | 0.938297i | \(-0.387597\pi\) |
0.639674 | − | 0.768647i | \(-0.279069\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.75635 | −0.451453 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.11456 | 0.387065 | 0.193532 | − | 0.981094i | \(-0.438006\pi\) | ||||
0.193532 | + | 0.981094i | \(0.438006\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.490629 | − | 0.849795i | 0.0457514 | − | 0.0792438i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.63451 | + | 8.02720i | 0.428460 | + | 0.742115i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.531791 | − | 3.47948i | 0.0487492 | − | 0.318963i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.14123 | + | 8.90487i | 0.467384 | + | 0.809533i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.43353 | − | 2.48295i | 0.129257 | − | 0.223880i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.2837 | −0.919802 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.96838 | 0.174665 | 0.0873327 | − | 0.996179i | \(-0.472166\pi\) | ||||
0.0873327 | + | 0.996179i | \(0.472166\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.48818 | + | 9.50580i | −0.483207 | + | 0.836939i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.58282 | − | 11.4018i | −0.575143 | − | 0.996178i | −0.996026 | − | 0.0890625i | \(-0.971613\pi\) |
0.420883 | − | 0.907115i | \(-0.361720\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.5740 | + | 8.46826i | 0.916886 | + | 0.734291i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.82557 | + | 6.62608i | 0.329253 | + | 0.570282i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.07245 | + | 3.58958i | −0.177061 | + | 0.306679i | −0.940873 | − | 0.338761i | \(-0.889992\pi\) |
0.763812 | + | 0.645439i | \(0.223326\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.0961 | −1.02598 | −0.512990 | − | 0.858394i | \(-0.671462\pi\) | ||||
−0.512990 | + | 0.858394i | \(0.671462\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.3977 | −1.12829 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.752062 | + | 1.30261i | −0.0628906 | + | 0.108930i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.89734 | + | 8.48244i | 0.406702 | + | 0.704429i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.38510 | − | 19.5845i | −0.361677 | − | 1.61530i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.55140 | − | 6.15120i | −0.290942 | − | 0.503926i | 0.683091 | − | 0.730333i | \(-0.260635\pi\) |
−0.974033 | + | 0.226407i | \(0.927302\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.85040 | − | 8.40113i | 0.394720 | − | 0.683674i | −0.598346 | − | 0.801238i | \(-0.704175\pi\) |
0.993065 | + | 0.117564i | \(0.0375084\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.94470 | 0.561446 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.07900 | 0.568599 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.46100 | − | 2.53052i | 0.116600 | − | 0.201958i | −0.801818 | − | 0.597568i | \(-0.796134\pi\) |
0.918418 | + | 0.395611i | \(0.129467\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.23166 | − | 9.06151i | −0.414898 | − | 0.718624i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.68579 | − | 1.35007i | −0.132859 | − | 0.106400i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.78609 | − | 16.9500i | −0.766506 | − | 1.32763i | −0.939447 | − | 0.342695i | \(-0.888660\pi\) |
0.172941 | − | 0.984932i | \(-0.444673\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.45968 | + | 2.52825i | −0.113636 | + | 0.196824i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.8666 | −1.15042 | −0.575208 | − | 0.818007i | \(-0.695079\pi\) | ||||
−0.575208 | + | 0.818007i | \(0.695079\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.84704 | −0.757465 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.3641 | + | 23.1473i | −1.02198 | + | 1.77012i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.21200 | − | 14.2236i | −0.624347 | − | 1.08140i | −0.988667 | − | 0.150126i | \(-0.952032\pi\) |
0.364320 | − | 0.931274i | \(-0.381301\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.42104 | + | 9.29780i | −0.107421 | + | 0.702848i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.22053 | − | 2.11402i | −0.0917409 | − | 0.158900i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.8807 | − | 22.3101i | 0.962750 | − | 1.66753i | 0.247207 | − | 0.968963i | \(-0.420487\pi\) |
0.715543 | − | 0.698569i | \(-0.246180\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.11304 | 0.157061 | 0.0785305 | − | 0.996912i | \(-0.474977\pi\) | ||||
0.0785305 | + | 0.996912i | \(0.474977\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26.1799 | 1.93528 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.997089 | + | 1.72701i | −0.0733074 | + | 0.126972i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.563474 | + | 0.975965i | 0.0412053 | + | 0.0713696i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 15.6888 | − | 6.12007i | 1.14119 | − | 0.445170i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.26542 | − | 16.0482i | −0.670422 | − | 1.16121i | −0.977785 | − | 0.209613i | \(-0.932780\pi\) |
0.307362 | − | 0.951593i | \(-0.400554\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.43037 | + | 2.47747i | −0.102960 | + | 0.178332i | −0.912903 | − | 0.408177i | \(-0.866165\pi\) |
0.809943 | + | 0.586509i | \(0.199498\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.11960 | 0.438234 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.05021 | 0.573553 | 0.286777 | − | 0.957997i | \(-0.407416\pi\) | ||||
0.286777 | + | 0.957997i | \(0.407416\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.395395 | − | 0.684845i | 0.0280288 | − | 0.0485474i | −0.851671 | − | 0.524077i | \(-0.824410\pi\) |
0.879700 | + | 0.475530i | \(0.157744\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.0286 | − | 20.8342i | −0.848435 | − | 1.46953i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.0842 | − | 7.83468i | 1.40963 | − | 0.549886i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.601031 | − | 1.04102i | −0.0419778 | − | 0.0727078i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.13059 | − | 3.69030i | 0.148086 | − | 0.256493i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.33730 | −0.300017 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.9976 | 1.23900 | 0.619502 | − | 0.784995i | \(-0.287334\pi\) | ||||
0.619502 | + | 0.784995i | \(0.287334\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.38833 | − | 4.13670i | 0.163645 | − | 0.283442i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.30101 | + | 3.98546i | 0.156927 | + | 0.271806i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.35400 | − | 15.4021i | 0.159800 | − | 1.04556i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.42478 | + | 7.66394i | 0.298999 | + | 0.517881i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.18116 | − | 2.04583i | 0.0794533 | − | 0.137617i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.5976 | 1.37932 | 0.689659 | − | 0.724134i | \(-0.257760\pi\) | ||||
0.689659 | + | 0.724134i | \(0.257760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.5575 | −1.23717 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.545207 | − | 0.944326i | 0.0361867 | − | 0.0626771i | −0.847365 | − | 0.531011i | \(-0.821812\pi\) |
0.883552 | + | 0.468334i | \(0.155146\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.78465 | + | 11.7514i | 0.448342 | + | 0.776552i | 0.998278 | − | 0.0586551i | \(-0.0186812\pi\) |
−0.549936 | + | 0.835207i | \(0.685348\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.01542 | + | 4.01662i | 0.329991 | + | 0.264274i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.74924 | − | 15.1541i | −0.573182 | − | 0.992780i | −0.996237 | − | 0.0866761i | \(-0.972375\pi\) |
0.423055 | − | 0.906104i | \(-0.360958\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.80859 | + | 4.86462i | −0.183212 | + | 0.317333i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −23.2863 | −1.51261 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.17257 | 0.334586 | 0.167293 | − | 0.985907i | \(-0.446497\pi\) | ||||
0.167293 | + | 0.985907i | \(0.446497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7092 | + | 20.2810i | −0.754257 | + | 1.30641i | 0.191486 | + | 0.981495i | \(0.438669\pi\) |
−0.945743 | + | 0.324916i | \(0.894664\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.83647 | − | 10.1091i | −0.374410 | − | 0.648497i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.03031 | − | 2.51335i | −0.513037 | − | 0.160572i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.54594 | + | 7.87380i | 0.289251 | + | 0.500998i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.59629 | − | 9.69305i | 0.354650 | − | 0.614272i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.39194 | −0.277217 | −0.138608 | − | 0.990347i | \(-0.544263\pi\) | ||||
−0.138608 | + | 0.990347i | \(0.544263\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.691482 | 0.0434731 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.29252 | − | 3.97076i | 0.143563 | − | 0.248659i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.66509 | + | 16.7404i | 0.602892 | + | 1.04424i | 0.992381 | + | 0.123208i | \(0.0393183\pi\) |
−0.389489 | + | 0.921031i | \(0.627348\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.42597 | + | 2.74370i | 0.212879 | + | 0.170485i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.2671 | + | 36.8356i | 1.31640 | + | 2.28007i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.14257 | + | 3.71103i | −0.132116 | + | 0.228832i | −0.924492 | − | 0.381201i | \(-0.875511\pi\) |
0.792376 | + | 0.610033i | \(0.208844\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.38692 | −0.269486 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.3215 | 1.67205 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.09292 | − | 8.82120i | 0.310521 | − | 0.537838i | −0.667954 | − | 0.744202i | \(-0.732830\pi\) |
0.978475 | + | 0.206364i | \(0.0661632\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.7973 | + | 25.6297i | 0.898873 | + | 1.55689i | 0.828937 | + | 0.559342i | \(0.188946\pi\) |
0.0699357 | + | 0.997552i | \(0.477721\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.03497 | − | 13.3147i | 0.123162 | − | 0.805842i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.50570 | − | 2.60796i | −0.0907974 | − | 0.157266i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.00530 | + | 5.20532i | −0.180571 | + | 0.312758i | −0.942075 | − | 0.335402i | \(-0.891128\pi\) |
0.761504 | + | 0.648160i | \(0.224461\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30.7411 | 1.84042 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.4365 | −1.45776 | −0.728881 | − | 0.684641i | \(-0.759959\pi\) | ||||
−0.728881 | + | 0.684641i | \(0.759959\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.195832 | − | 0.339192i | 0.0116410 | − | 0.0201628i | −0.860146 | − | 0.510048i | \(-0.829628\pi\) |
0.871787 | + | 0.489885i | \(0.162961\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.82326 | + | 15.2823i | 0.522645 | + | 0.905247i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.46485 | + | 0.961519i | −0.145495 | + | 0.0567566i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.61503 | + | 13.1896i | 0.447943 | + | 0.775860i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.1697 | − | 33.2029i | 1.12375 | − | 1.94639i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.12533 | 0.0657427 | 0.0328713 | − | 0.999460i | \(-0.489535\pi\) | ||||
0.0328713 | + | 0.999460i | \(0.489535\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.02346 | −0.0595879 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.69584 | + | 4.66932i | −0.156428 | + | 0.270942i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.724745 | − | 1.25530i | −0.0419131 | − | 0.0725956i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.43651 | − | 3.68111i | 0.543911 | − | 0.212176i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.95139 | + | 6.84401i | 0.227002 | + | 0.393178i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.48818 | − | 9.50581i | 0.314252 | − | 0.544301i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.8412 | −0.618740 | −0.309370 | − | 0.950942i | \(-0.600118\pi\) | ||||
−0.309370 | + | 0.950942i | \(0.600118\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.19024 | 0.238374 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.82635 | − | 4.89538i | 0.160268 | − | 0.277592i | −0.774697 | − | 0.632333i | \(-0.782098\pi\) |
0.934965 | + | 0.354741i | \(0.115431\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.70635 | + | 4.68753i | 0.152972 | + | 0.264955i | 0.932319 | − | 0.361638i | \(-0.117782\pi\) |
−0.779347 | + | 0.626593i | \(0.784449\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.50820 | − | 16.4110i | 0.141321 | − | 0.924658i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.3641 | + | 21.4153i | 0.694439 | + | 1.20280i | 0.970369 | + | 0.241626i | \(0.0776808\pi\) |
−0.275930 | + | 0.961178i | \(0.588986\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.45110 | + | 5.97748i | −0.193225 | + | 0.334675i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −36.1904 | −2.01995 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.81199 | 0.379029 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.15627 | + | 5.46682i | −0.175078 | + | 0.303245i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −29.4991 | − | 51.0940i | −1.63130 | − | 2.82550i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.65023 | + | 7.72843i | 0.532035 | + | 0.426082i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.94191 | + | 15.4879i | 0.491492 | + | 0.851289i | 0.999952 | − | 0.00979641i | \(-0.00311834\pi\) |
−0.508460 | + | 0.861086i | \(0.669785\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.32993 | + | 7.49966i | −0.237279 | + | 0.410979i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.0864 | −0.551080 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.1922 | −1.20888 | −0.604442 | − | 0.796649i | \(-0.706604\pi\) | ||||
−0.604442 | + | 0.796649i | \(0.706604\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.89834 | − | 10.2162i | 0.320354 | − | 0.554870i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.49425 | + | 4.32016i | 0.135071 | + | 0.233950i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.13876 | + | 16.6361i | −0.439452 | + | 0.898266i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.40666 | − | 2.43641i | −0.0757323 | − | 0.131172i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.6538 | − | 23.6491i | 0.732975 | − | 1.26955i | −0.222632 | − | 0.974903i | \(-0.571465\pi\) |
0.955606 | − | 0.294647i | \(-0.0952020\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.0020 | 1.23127 | 0.615633 | − | 0.788033i | \(-0.288900\pi\) | ||||
0.615633 | + | 0.788033i | \(0.288900\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.3021 | 0.603260 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.6241 | − | 20.1336i | 0.618689 | − | 1.07160i | −0.371036 | − | 0.928618i | \(-0.620997\pi\) |
0.989725 | − | 0.142982i | \(-0.0456692\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.00134 | − | 1.73438i | −0.0531458 | − | 0.0920513i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.87703 | − | 6.30835i | −0.416897 | − | 0.333873i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.2417 | + | 17.7392i | 0.540538 | + | 0.936240i | 0.998873 | + | 0.0474602i | \(0.0151127\pi\) |
−0.458335 | + | 0.888780i | \(0.651554\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.60870 | + | 6.25045i | −0.189932 | + | 0.328971i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.4804 | 1.54732 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.71032 | 0.194207 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.202540 | + | 0.350809i | −0.0105725 | + | 0.0183121i | −0.871263 | − | 0.490816i | \(-0.836699\pi\) |
0.860691 | + | 0.509128i | \(0.170032\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.61002 | − | 4.52069i | −0.135872 | − | 0.235338i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.45879 | + | 9.54482i | −0.0757368 | + | 0.495542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.35692 | + | 2.35026i | 0.0702589 | + | 0.121692i | 0.899015 | − | 0.437918i | \(-0.144284\pi\) |
−0.828756 | + | 0.559610i | \(0.810951\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.7420 | + | 25.5339i | −0.761274 | + | 1.31856i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.4685 | 0.745164 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.2270 | 0.525327 | 0.262663 | − | 0.964888i | \(-0.415399\pi\) | ||||
0.262663 | + | 0.964888i | \(0.415399\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.82173 | − | 4.88738i | 0.144562 | − | 0.250388i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.5025 | − | 28.5832i | −0.843241 | − | 1.46054i | −0.887140 | − | 0.461500i | \(-0.847311\pi\) |
0.0438996 | − | 0.999036i | \(-0.486022\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.50982 | − | 0.979059i | 0.127912 | − | 0.0498975i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.99230 | + | 17.3072i | 0.507937 | + | 0.879773i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.6827 | + | 23.6992i | −0.693742 | + | 1.20160i | 0.276861 | + | 0.960910i | \(0.410706\pi\) |
−0.970603 | + | 0.240686i | \(0.922628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.08601 | −0.0549221 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −37.7467 | −1.90407 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.88158 | + | 8.45514i | −0.245619 | + | 0.425424i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.34821 | + | 12.7275i | 0.368796 | + | 0.638774i | 0.989378 | − | 0.145368i | \(-0.0464367\pi\) |
−0.620582 | + | 0.784142i | \(0.713103\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 36.1845 | − | 14.1153i | 1.81149 | − | 0.706648i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.70877 | + | 8.15582i | 0.235145 | + | 0.407282i | 0.959315 | − | 0.282339i | \(-0.0911103\pi\) |
−0.724170 | + | 0.689621i | \(0.757777\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.22846 | − | 9.05596i | 0.260448 | − | 0.451109i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.11183 | 0.154628 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.40527 | −0.0696569 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.7879 | − | 25.6133i | 0.731213 | − | 1.26650i | −0.225152 | − | 0.974324i | \(-0.572288\pi\) |
0.956365 | − | 0.292174i | \(-0.0943788\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.94183 | + | 10.2916i | 0.293089 | + | 0.507645i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.340333 | + | 2.22678i | −0.0167467 | + | 0.109573i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.34633 | − | 4.06397i | −0.115177 | − | 0.199492i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.3402 | + | 30.0341i | −0.849152 | + | 1.47078i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.4890 | 0.658979 | 0.329489 | − | 0.944159i | \(-0.393123\pi\) | ||||
0.329489 | + | 0.944159i | \(0.393123\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.6752 | 0.666489 | 0.333244 | − | 0.942841i | \(-0.391857\pi\) | ||||
0.333244 | + | 0.942841i | \(0.391857\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.1965 | + | 21.1250i | −0.593015 | + | 1.02713i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.36480 | + | 4.09595i | 0.114710 | + | 0.198683i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.8572 | − | 15.1019i | −0.912565 | − | 0.730831i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.15621 | + | 3.73466i | 0.104103 | + | 0.180311i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.86833 | − | 15.3604i | 0.427173 | − | 0.739885i | −0.569448 | − | 0.822027i | \(-0.692843\pi\) |
0.996621 | + | 0.0821427i | \(0.0261763\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.5658 | 0.603874 | 0.301937 | − | 0.953328i | \(-0.402367\pi\) | ||||
0.301937 | + | 0.953328i | \(0.402367\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 28.0820 | 1.34643 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.08988 | − | 3.61978i | 0.0999725 | − | 0.173157i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.276998 | − | 0.479774i | −0.0132204 | − | 0.0228984i | 0.859340 | − | 0.511405i | \(-0.170875\pi\) |
−0.872560 | + | 0.488507i | \(0.837542\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −34.8722 | − | 10.9144i | −1.66058 | − | 0.519734i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.7952 | + | 30.8222i | 0.845477 | + | 1.46441i | 0.885206 | + | 0.465199i | \(0.154017\pi\) |
−0.0397291 | + | 0.999210i | \(0.512650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.72750 | − | 9.92032i | 0.271510 | − | 0.470268i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.3642 | −0.963191 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.72773 | 0.459080 | 0.229540 | − | 0.973299i | \(-0.426278\pi\) | ||||
0.229540 | + | 0.973299i | \(0.426278\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.423540 | − | 0.733593i | 0.0199437 | − | 0.0345435i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.9064 | − | 24.0866i | −0.653379 | − | 1.13169i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.40791 | − | 3.53009i | −0.206646 | − | 0.165493i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.4013 | + | 31.8721i | 0.860778 | + | 1.49091i | 0.871179 | + | 0.490966i | \(0.163356\pi\) |
−0.0104002 | + | 0.999946i | \(0.503311\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.23398 | − | 7.33346i | 0.197625 | − | 0.342297i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.6797 | −1.56862 | −0.784310 | − | 0.620369i | \(-0.786983\pi\) | ||||
−0.784310 | + | 0.620369i | \(0.786983\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.14990 | 0.146388 | 0.0731942 | − | 0.997318i | \(-0.476681\pi\) | ||||
0.0731942 | + | 0.997318i | \(0.476681\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.1480 | − | 17.5768i | 0.470601 | − | 0.815104i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.3931 | − | 28.3937i | −0.758584 | − | 1.31391i | −0.943573 | − | 0.331165i | \(-0.892558\pi\) |
0.184989 | − | 0.982741i | \(-0.440775\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.35406 | + | 21.9455i | −0.154876 | + | 1.01335i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.18877 | − | 7.25517i | −0.193008 | − | 0.334301i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.62149 | + | 2.80851i | −0.0745564 | + | 0.129135i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.2029 | −0.835205 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.0505 | −0.872264 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.91416 | − | 13.7077i | 0.361607 | − | 0.626322i | −0.626618 | − | 0.779326i | \(-0.715562\pi\) |
0.988226 | + | 0.153004i | \(0.0488948\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.47287 | + | 2.55109i | 0.0671573 | + | 0.116320i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.76878 | + | 2.25036i | −0.262488 | + | 0.102395i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.03720 | − | 13.9208i | −0.364950 | − | 0.632113i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.85215 | + | 10.1362i | −0.265186 | + | 0.459316i | −0.967612 | − | 0.252440i | \(-0.918767\pi\) |
0.702426 | + | 0.711757i | \(0.252100\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −56.1146 | −2.53759 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.0759 | −1.13166 | −0.565830 | − | 0.824522i | \(-0.691444\pi\) | ||||
−0.565830 | + | 0.824522i | \(0.691444\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.42017 | − | 9.38800i | 0.244112 | − | 0.422814i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.65764 | + | 4.60316i | 0.119452 | + | 0.206897i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.10655 | + | 1.60193i | −0.184204 | + | 0.0718565i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0710 | + | 27.8357i | 0.719435 | + | 1.24610i | 0.961224 | + | 0.275769i | \(0.0889324\pi\) |
−0.241789 | + | 0.970329i | \(0.577734\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.3118 | + | 36.9131i | −0.952141 | + | 1.64916i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.8480 | −0.929567 | −0.464784 | − | 0.885424i | \(-0.653868\pi\) | ||||
−0.464784 | + | 0.885424i | \(0.653868\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.31337 | 0.147443 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.1160 | + | 24.4497i | −0.626915 | + | 1.08585i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.3549 | + | 24.8634i | 0.636270 | + | 1.10205i | 0.986244 | + | 0.165293i | \(0.0528571\pi\) |
−0.349974 | + | 0.936759i | \(0.613810\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.23380 | − | 8.07271i | 0.0545802 | − | 0.357116i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.2954 | + | 28.2244i | 0.719458 | + | 1.24614i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.878413 | − | 1.52146i | 0.0387075 | − | 0.0670434i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.95837 | −0.174089 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −47.0886 | −2.06696 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.325114 | + | 0.563115i | −0.0142435 | + | 0.0246705i | −0.873059 | − | 0.487614i | \(-0.837867\pi\) |
0.858816 | + | 0.512285i | \(0.171201\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.33127 | − | 5.76993i | −0.145666 | − | 0.252301i | 0.783955 | − | 0.620818i | \(-0.213199\pi\) |
−0.929621 | + | 0.368516i | \(0.879866\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 21.0489 | + | 16.8571i | 0.918647 | + | 0.735702i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.91736 | − | 6.78507i | −0.170643 | − | 0.295562i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1668 | − | 19.3415i | 0.485514 | − | 0.840935i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.44444 | −0.192872 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.77566 | −0.0769122 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.58670 | + | 13.1406i | −0.328002 | + | 0.568116i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −36.9298 | − | 63.9643i | −1.59364 | − | 2.76026i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.29559 | − | 5.78629i | −0.0558049 | − | 0.249233i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.9160 | + | 29.2993i | 0.727274 | + | 1.25968i | 0.958031 | + | 0.286665i | \(0.0925465\pi\) |
−0.230757 | + | 0.973012i | \(0.574120\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.02911 | − | 5.24657i | 0.129991 | − | 0.225152i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.7360 | −1.05957 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.0612 | −1.32808 | −0.664040 | − | 0.747697i | \(-0.731160\pi\) | ||||
−0.664040 | + | 0.747697i | \(0.731160\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.8328 | − | 41.2797i | 1.01716 | − | 1.76177i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.8607 | + | 36.1317i | 0.888694 | + | 1.53926i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.7729 | + | 13.4327i | 0.713258 | + | 0.571216i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.85872 | + | 4.95144i | 0.121346 | + | 0.210177i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.1148 | − | 22.7155i | 0.555692 | − | 0.962488i | −0.442157 | − | 0.896938i | \(-0.645787\pi\) |
0.997849 | − | 0.0655498i | \(-0.0208801\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.79798 | 0.287524 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.23103 | 0.136414 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.59923 | + | 13.1623i | −0.320269 | + | 0.554723i | −0.980544 | − | 0.196302i | \(-0.937107\pi\) |
0.660274 | + | 0.751025i | \(0.270440\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.47298 | − | 4.28332i | −0.104039 | − | 0.180201i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.03478 | − | 6.77054i | 0.0434569 | − | 0.284336i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.0806 | − | 24.3882i | −0.590288 | − | 1.02241i | −0.994193 | − | 0.107607i | \(-0.965681\pi\) |
0.403906 | − | 0.914801i | \(-0.367652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.9883 | − | 25.9604i | 0.627239 | − | 1.08641i | −0.360864 | − | 0.932619i | \(-0.617518\pi\) |
0.988103 | − | 0.153792i | \(-0.0491486\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −53.1291 | −2.21950 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.90203 | 0.121023 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.6161 | + | 20.1197i | −0.483585 | + | 0.837595i | −0.999822 | − | 0.0188513i | \(-0.993999\pi\) |
0.516237 | + | 0.856446i | \(0.327332\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.10095 | + | 7.10305i | 0.170430 | + | 0.295193i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.62239 | + | 3.75362i | −0.399204 | + | 0.155726i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.54571 | − | 2.67724i | −0.0640166 | − | 0.110880i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.57096 | − | 9.64919i | 0.230331 | − | 0.398945i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.8264 | −1.23107 | −0.615533 | − | 0.788111i | \(-0.711059\pi\) | ||||
−0.615533 | + | 0.788111i | \(0.711059\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.1536 | 1.24246 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.5402 | − | 19.9882i | 0.474701 | − | 0.822207i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.00043 | + | 1.73279i | 0.0410825 | + | 0.0711570i | 0.885836 | − | 0.463999i | \(-0.153586\pi\) |
−0.844753 | + | 0.535156i | \(0.820253\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.94182 | + | 1.53767i | −0.161599 | + | 0.0630384i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.13362 | − | 1.96349i | −0.0463961 | − | 0.0803604i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.6729 | + | 30.6103i | −0.722094 | + | 1.25070i | 0.238065 | + | 0.971249i | \(0.423487\pi\) |
−0.960159 | + | 0.279454i | \(0.909847\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.2751 | −0.459920 | −0.229960 | − | 0.973200i | \(-0.573860\pi\) | ||||
−0.229960 | + | 0.973200i | \(0.573860\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −43.8010 | −1.78371 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.18008 | − | 10.7042i | 0.251256 | − | 0.435188i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.60312 | − | 9.70489i | −0.227424 | − | 0.393909i | 0.729620 | − | 0.683853i | \(-0.239697\pi\) |
−0.957044 | + | 0.289943i | \(0.906364\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.33817 | − | 61.0992i | 0.378402 | − | 2.47586i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.14878 | + | 7.18590i | 0.167842 | + | 0.290711i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.89025 | − | 6.73812i | 0.157126 | − | 0.272150i | −0.776705 | − | 0.629864i | \(-0.783110\pi\) |
0.933831 | + | 0.357714i | \(0.116444\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.44639 | −0.138972 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.9869 | −1.65007 | −0.825035 | − | 0.565082i | \(-0.808845\pi\) | ||||
−0.825035 | + | 0.565082i | \(0.808845\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.65595 | − | 13.2605i | 0.307719 | − | 0.532985i | −0.670144 | − | 0.742231i | \(-0.733768\pi\) |
0.977863 | + | 0.209246i | \(0.0671011\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.59792 | − | 4.49973i | −0.104251 | − | 0.180568i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.6795 | − | 15.7604i | −0.788443 | − | 0.631428i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.70679 | − | 4.68830i | −0.108272 | − | 0.187532i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.21765 | + | 10.7693i | −0.248309 | + | 0.430084i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.20707 | 0.0880016 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.4649 | −0.814696 | −0.407348 | − | 0.913273i | \(-0.633546\pi\) | ||||
−0.407348 | + | 0.913273i | \(0.633546\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.8001 | − | 44.6871i | 1.02546 | − | 1.77615i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.18306 | − | 2.04911i | −0.0469482 | − | 0.0813166i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.14635 | + | 8.41661i | −0.362391 | + | 0.333478i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.34841 | − | 7.53167i | −0.172021 | − | 0.297948i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.358245 | + | 0.620499i | −0.0141498 | + | 0.0245082i | −0.873014 | − | 0.487696i | \(-0.837838\pi\) |
0.858864 | + | 0.512204i | \(0.171171\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.2936 | −1.70733 | −0.853667 | − | 0.520819i | \(-0.825627\pi\) | ||||
−0.853667 | + | 0.520819i | \(0.825627\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.1943 | 0.519524 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.371451 | + | 0.643372i | −0.0146032 | + | 0.0252936i | −0.873235 | − | 0.487300i | \(-0.837982\pi\) |
0.858631 | + | 0.512593i | \(0.171315\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.360609 | − | 0.624593i | −0.0141551 | − | 0.0245174i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −34.8681 | − | 27.9242i | −1.36659 | − | 1.09444i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.0663 | − | 43.4161i | −0.980919 | − | 1.69900i | −0.658828 | − | 0.752294i | \(-0.728948\pi\) |
−0.322091 | − | 0.946709i | \(-0.604386\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.91296 | + | 13.7056i | −0.309185 | + | 0.535524i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.1123 | 0.628602 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.7410 | 0.574226 | 0.287113 | − | 0.957897i | \(-0.407304\pi\) | ||||
0.287113 | + | 0.957897i | \(0.407304\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.79181 | + | 13.4958i | −0.303066 | + | 0.524926i | −0.976829 | − | 0.214022i | \(-0.931344\pi\) |
0.673763 | + | 0.738948i | \(0.264677\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.38646 | − | 5.86551i | −0.131519 | − | 0.227798i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.46027 | − | 16.0974i | 0.0954053 | − | 0.624232i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.32575 | − | 5.76037i | −0.128774 | − | 0.223042i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 29.5273 | − | 51.1428i | 1.14159 | − | 1.97730i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.73492 | 0.298603 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.12856 | 0.313333 | 0.156666 | − | 0.987652i | \(-0.449925\pi\) | ||||
0.156666 | + | 0.987652i | \(0.449925\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.3140 | + | 19.5963i | −0.435474 | + | 0.754263i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.7593 | + | 39.4202i | 0.874709 | + | 1.51504i | 0.857072 | + | 0.515196i | \(0.172281\pi\) |
0.0176367 | + | 0.999844i | \(0.494386\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.9608 | + | 12.8578i | −1.26492 | + | 0.493436i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.56314 | − | 2.70744i | −0.0598997 | − | 0.103749i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.76614 | − | 16.9155i | 0.373691 | − | 0.647252i | −0.616439 | − | 0.787403i | \(-0.711425\pi\) |
0.990130 | + | 0.140151i | \(0.0447587\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.98242 | 0.190368 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 38.9040 | 1.48428 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.24012 | + | 5.61206i | −0.123439 | + | 0.213802i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.5181 | + | 19.9499i | 0.438168 | + | 0.758930i | 0.997548 | − | 0.0699814i | \(-0.0222940\pi\) |
−0.559380 | + | 0.828911i | \(0.688961\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.8991 | − | 4.25164i | 0.414021 | − | 0.161506i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.27015 | + | 12.5923i | 0.275773 | + | 0.477652i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.665195 | + | 1.15215i | −0.0251961 | + | 0.0436409i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −50.1692 | −1.89758 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.2873 | 0.501854 | 0.250927 | − | 0.968006i | \(-0.419265\pi\) | ||||
0.250927 | + | 0.968006i | \(0.419265\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.24719 | + | 7.35635i | −0.160186 | + | 0.277450i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.05241 | + | 13.9472i | 0.303271 | + | 0.525281i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.10180 | − | 7.20905i | 0.0414376 | − | 0.271124i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.5437 | + | 21.7263i | 0.471089 | + | 0.815949i | 0.999453 | − | 0.0330682i | \(-0.0105279\pi\) |
−0.528364 | + | 0.849018i | \(0.677195\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.1986 | + | 36.7171i | −0.795010 | + | 1.37700i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.80730 | −0.180035 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.80805 | 0.0676172 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.41505 | − | 12.8432i | 0.276920 | − | 0.479639i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.22565 | + | 12.5152i | 0.269471 | + | 0.466738i | 0.968725 | − | 0.248135i | \(-0.0798177\pi\) |
−0.699254 | + | 0.714873i | \(0.746484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.01820 | − | 2.41714i | −0.112404 | − | 0.0900189i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 33.5710 | + | 58.1468i | 1.24852 | + | 2.16250i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.4837 | + | 25.0865i | −0.537910 | + | 0.931687i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.3781 | −0.496167 | −0.248084 | − | 0.968739i | \(-0.579801\pi\) | ||||
−0.248084 | + | 0.968739i | \(0.579801\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.2333 | −1.52716 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.54666 | − | 4.41094i | 0.0941915 | − | 0.163144i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.9828 | − | 29.4151i | −0.627275 | − | 1.08647i | −0.988096 | − | 0.153837i | \(-0.950837\pi\) |
0.360821 | − | 0.932635i | \(-0.382496\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.7522 | + | 16.3359i | −0.654800 | + | 0.602557i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.55389 | − | 6.15552i | −0.130909 | − | 0.226741i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.80161 | + | 6.58459i | −0.139845 | + | 0.242218i | −0.927438 | − | 0.373978i | \(-0.877994\pi\) |
0.787593 | + | 0.616196i | \(0.211327\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.0670 | 0.957595 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.92565 | 0.327450 | 0.163725 | − | 0.986506i | \(-0.447649\pi\) | ||||
0.163725 | + | 0.986506i | \(0.447649\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.26900 | + | 7.39413i | −0.156404 | + | 0.270900i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.1891 | − | 17.6481i | −0.372801 | − | 0.645710i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.0677 | + | 20.8764i | 0.952492 | + | 0.762807i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.54662 | − | 9.60703i | −0.202399 | − | 0.350566i | 0.746902 | − | 0.664934i | \(-0.231540\pi\) |
−0.949301 | + | 0.314369i | \(0.898207\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.29598 | + | 10.9050i | −0.229438 | + | 0.397399i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.6610 | −0.424386 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.86787 | 0.140580 | 0.0702900 | − | 0.997527i | \(-0.477608\pi\) | ||||
0.0702900 | + | 0.997527i | \(0.477608\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.991261 | − | 1.71691i | 0.0359805 | − | 0.0623200i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.9211 | + | 43.1646i | 0.903390 | + | 1.56472i | 0.823064 | + | 0.567949i | \(0.192263\pi\) |
0.0803258 | + | 0.996769i | \(0.474404\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.22552 | + | 53.8191i | −0.297784 | + | 1.94838i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.17398 | − | 7.22955i | −0.150911 | − | 0.261385i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.755912 | + | 1.30928i | −0.0272944 | + | 0.0472753i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 48.6248 | 1.75345 | 0.876727 | − | 0.480988i | \(-0.159722\pi\) | ||||
0.876727 | + | 0.480988i | \(0.159722\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 55.4208 | 1.99593 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.8943 | − | 20.6015i | 0.427808 | − | 0.740984i | −0.568870 | − | 0.822427i | \(-0.692619\pi\) |
0.996678 | + | 0.0814427i | \(0.0259528\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.4679 | + | 18.1310i | 0.376018 | + | 0.651283i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.7237 | − | 4.57332i | 0.420585 | − | 0.164067i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.56015 | − | 4.43430i | −0.0917268 | − | 0.158875i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.705636 | − | 1.22220i | 0.0252496 | − | 0.0437337i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 51.8636 | 1.85345 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.51242 | −0.125364 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.10531 | + | 12.3068i | −0.253277 | + | 0.438689i | −0.964426 | − | 0.264352i | \(-0.914842\pi\) |
0.711149 | + | 0.703041i | \(0.248175\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.14287 | + | 10.6398i | 0.218692 | + | 0.378786i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.1418 | + | 3.95622i | −0.360599 | + | 0.140667i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.10701 | − | 14.0417i | −0.287888 | − | 0.498637i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.28879 | + | 10.8925i | −0.223040 | + | 0.386317i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −52.4563 | −1.85810 | −0.929049 | − | 0.369956i | \(-0.879373\pi\) | ||||
−0.929049 | + | 0.369956i | \(0.879373\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.21686 | 0.219937 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.8721 | − | 43.0797i | 0.878812 | − | 1.52215i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.30731 | + | 2.26433i | 0.0461340 | + | 0.0799064i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.392234 | + | 2.56636i | −0.0138244 | + | 0.0904525i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.6017 | − | 25.2909i | −0.514005 | − | 0.890282i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.1383 | + | 31.4164i | −0.637707 | + | 1.10454i | 0.348228 | + | 0.937410i | \(0.386784\pi\) |
−0.985935 | + | 0.167131i | \(0.946550\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.3129 | −0.888857 | −0.444428 | − | 0.895814i | \(-0.646593\pi\) | ||||
−0.444428 | + | 0.895814i | \(0.646593\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 84.8496 | 2.97581 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.7635 | + | 20.3750i | −0.412057 | + | 0.713704i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.80135 | + | 16.9764i | 0.342906 | + | 0.593930i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −19.1417 | − | 15.3297i | −0.668864 | − | 0.535662i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.2657 | + | 40.2974i | 0.811979 | + | 1.40639i | 0.911477 | + | 0.411351i | \(0.134943\pi\) |
−0.0994979 | + | 0.995038i | \(0.531724\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.4627 | − | 23.3181i | 0.469280 | − | 0.812817i | −0.530103 | − | 0.847933i | \(-0.677847\pi\) |
0.999383 | + | 0.0351160i | \(0.0111801\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.63389 | −0.300594 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.99334 | −0.104089 | −0.0520444 | − | 0.998645i | \(-0.516574\pi\) | ||||
−0.0520444 | + | 0.998645i | \(0.516574\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.3597 | + | 21.4076i | −0.429270 | + | 0.743518i | −0.996809 | − | 0.0798290i | \(-0.974563\pi\) |
0.567538 | + | 0.823347i | \(0.307896\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.61637 | + | 14.9240i | 0.298899 | + | 0.517707i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.03480 | + | 9.08772i | 0.0705016 | + | 0.314871i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.93532 | + | 15.4764i | 0.309219 | + | 0.535584i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.7419 | − | 32.4619i | 0.647815 | − | 1.12205i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.82342 | −0.235571 | −0.117785 | − | 0.993039i | \(-0.537579\pi\) | ||||
−0.117785 | + | 0.993039i | \(0.537579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.3937 | 1.28944 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −35.0305 | + | 60.6747i | −1.20652 | + | 2.08975i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.91838 | + | 10.2509i | 0.203598 | + | 0.352643i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.2345 | − | 17.0058i | −0.729628 | − | 0.584325i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.561464 | − | 0.972483i | −0.0192694 | − | 0.0333755i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.677116 | − | 1.17280i | 0.0232112 | − | 0.0402030i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.11780 | −0.243709 | −0.121854 | − | 0.992548i | \(-0.538884\pi\) | ||||
−0.121854 | + | 0.992548i | \(0.538884\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 32.1289 | 1.09879 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.6216 | − | 25.3253i | 0.499464 | − | 0.865097i | −0.500536 | − | 0.865716i | \(-0.666864\pi\) |
1.00000 | 0.000619066i | \(0.000197055\pi\) | ||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.3171 | + | 45.5825i | 0.897927 | + | 1.55525i | 0.830140 | + | 0.557555i | \(0.188260\pi\) |
0.0677863 | + | 0.997700i | \(0.478406\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.14604 | + | 7.49846i | −0.0390568 | + | 0.255547i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.6440 | − | 18.4360i | −0.362326 | − | 0.627567i | 0.626017 | − | 0.779809i | \(-0.284684\pi\) |
−0.988343 | + | 0.152242i | \(0.951351\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.87133 | + | 17.0977i | −0.335635 | + | 0.581338i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 43.6655 | 1.48296 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.87999 | −0.233388 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.44970 | + | 12.9033i | −0.252423 | + | 0.437210i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −34.9021 | − | 60.4523i | −1.18126 | − | 2.04600i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 25.3478 | − | 9.88797i | 0.856911 | − | 0.334274i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.7075 | − | 35.8664i | −0.699242 | − | 1.21112i | −0.968729 | − | 0.248119i | \(-0.920187\pi\) |
0.269487 | − | 0.963004i | \(-0.413146\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.61320 | − | 2.79415i | 0.0544119 | − | 0.0942442i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.0441 | 0.944831 | 0.472415 | − | 0.881376i | \(-0.343382\pi\) | ||||
0.472415 | + | 0.881376i | \(0.343382\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.7112 | 1.43735 | 0.718674 | − | 0.695347i | \(-0.244750\pi\) | ||||
0.718674 | + | 0.695347i | \(0.244750\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.46716 | + | 2.54119i | −0.0493179 | + | 0.0854212i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.7012 | + | 23.7311i | 0.460040 | + | 0.796813i | 0.998962 | − | 0.0455427i | \(-0.0145017\pi\) |
−0.538922 | + | 0.842355i | \(0.681168\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.85176 | + | 1.89263i | −0.162723 | + | 0.0634768i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.09644 | + | 1.89908i | 0.0367320 | + | 0.0636216i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.9635 | + | 20.7213i | −0.400342 | + | 0.693412i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.9668 | −1.03511 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.15578 | −0.138757 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.9926 | − | 41.5565i | 0.800200 | − | 1.38599i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.42763 | + | 4.20477i | 0.0808760 | + | 0.140081i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.38753 | − | 28.7074i | 0.146008 | − | 0.955321i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.27000 | − | 2.19971i | −0.0422163 | − | 0.0731208i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.9462 | − | 32.8158i | 0.629099 | − | 1.08963i | −0.358634 | − | 0.933478i | \(-0.616757\pi\) |
0.987733 | − | 0.156153i | \(-0.0499092\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.3886 | 0.477238 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.0315 | 1.06125 | 0.530626 | − | 0.847606i | \(-0.321957\pi\) | ||||
0.530626 | + | 0.847606i | \(0.321957\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.65344 | − | 2.86383i | 0.0547207 | − | 0.0947791i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.7350 | − | 27.2537i | −0.520182 | − | 0.900981i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.1887 | + | 21.7742i | 0.897849 | + | 0.719046i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.55296 | + | 9.61802i | 0.183175 | + | 0.317269i | 0.942960 | − | 0.332906i | \(-0.108029\pi\) |
−0.759785 | + | 0.650175i | \(0.774696\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.5412 | + | 26.9181i | −0.512100 | + | 0.886983i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.95832 | −0.0973744 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.89769 | −0.193915 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.81458 | − | 6.60704i | 0.125287 | − | 0.217004i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.47383 | + | 9.48096i | 0.179591 | + | 0.311060i | 0.941740 | − | 0.336341i | \(-0.109189\pi\) |
−0.762150 | + | 0.647401i | \(0.775856\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.2058 | − | 10.7059i | −1.12105 | − | 0.350870i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.10333 | − | 14.0354i | −0.265291 | − | 0.459497i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.677331 | − | 1.17317i | 0.0221511 | − | 0.0383668i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.2474 | 1.02081 | 0.510404 | − | 0.859935i | \(-0.329496\pi\) | ||||
0.510404 | + | 0.859935i | \(0.329496\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.5185 | 0.506429 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.0361 | + | 52.0240i | −0.979147 | + | 1.69593i | −0.313639 | + | 0.949542i | \(0.601548\pi\) |
−0.665508 | + | 0.746391i | \(0.731785\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.408156 | + | 0.706947i | 0.0132914 | + | 0.0230214i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.8006 | − | 12.6539i | −0.513992 | − | 0.411632i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.2131 | + | 24.6178i | 0.461864 | + | 0.799971i | 0.999054 | − | 0.0434899i | \(-0.0138476\pi\) |
−0.537190 | + | 0.843461i | \(0.680514\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.74040 | − | 4.74651i | 0.0889571 | − | 0.154078i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 70.8975 | 2.29901 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.26316 | 0.267670 | 0.133835 | − | 0.991004i | \(-0.457271\pi\) | ||||
0.133835 | + | 0.991004i | \(0.457271\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.1376 | + | 19.2909i | −0.360405 | + | 0.624239i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.89452 | + | 17.1378i | 0.319845 | + | 0.553987i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.65682 | − | 10.8405i | 0.0535014 | − | 0.350057i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.84042 | − | 3.18769i | −0.0593683 | − | 0.102829i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −32.9458 | + | 57.0639i | −1.06166 | + | 1.83886i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.43878 | 0.110698 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.49199 | −0.0801369 | −0.0400684 | − | 0.999197i | \(-0.512758\pi\) | ||||
−0.0400684 | + | 0.999197i | \(0.512758\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.76520 | − | 16.9138i | 0.313703 | − | 0.543350i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.2701 | − | 50.6974i | −0.939323 | − | 1.62696i | −0.766737 | − | 0.641962i | \(-0.778121\pi\) |
−0.172587 | − | 0.984994i | \(-0.555212\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.8151 | − | 11.6307i | 0.955830 | − | 0.372862i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.04923 | + | 15.6737i | 0.289807 | + | 0.501961i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.2617 | − | 31.6302i | 0.584244 | − | 1.01194i | −0.410726 | − | 0.911759i | \(-0.634725\pi\) |
0.994969 | − | 0.100181i | \(-0.0319421\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.07221 | 0.257989 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −107.418 | −3.42959 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.3570 | + | 45.6516i | −0.840657 | + | 1.45606i | 0.0486839 | + | 0.998814i | \(0.484497\pi\) |
−0.889340 | + | 0.457246i | \(0.848836\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.83842 | − | 8.38040i | −0.154165 | − | 0.267022i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 33.0232 | − | 12.8821i | 1.05114 | − | 0.410042i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.56260 | − | 2.70650i | −0.0496877 | − | 0.0860617i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.00757 | − | 12.1375i | 0.222603 | − | 0.385559i | −0.732995 | − | 0.680234i | \(-0.761878\pi\) |
0.955598 | + | 0.294675i | \(0.0952114\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 51.2741 | 1.62713 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.950580 | −0.0301354 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.1037 | − | 50.4092i | 0.921725 | − | 1.59647i | 0.124979 | − | 0.992159i | \(-0.460114\pi\) |
0.796746 | − | 0.604315i | \(-0.206553\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.27966 | + | 9.14464i | 0.167041 | + | 0.289324i |
(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.d.165.8 | ✓ | 16 | |
7.2 | even | 3 | inner | 1148.2.i.d.821.8 | yes | 16 | |
7.3 | odd | 6 | 8036.2.a.n.1.8 | 8 | |||
7.4 | even | 3 | 8036.2.a.m.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.d.165.8 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1148.2.i.d.821.8 | yes | 16 | 7.2 | even | 3 | inner | |
8036.2.a.m.1.1 | 8 | 7.4 | even | 3 | |||
8036.2.a.n.1.8 | 8 | 7.3 | odd | 6 |