Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(249,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.bh (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{36})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{6} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 249.5 | ||
Root | \(0.984808 + 0.173648i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1400.249 |
Dual form | 1400.2.bh.h.849.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.16679 | + | 0.673648i | 0.673648 | + | 0.388931i | 0.797458 | − | 0.603375i | \(-0.206178\pi\) |
−0.123809 | + | 0.992306i | \(0.539511\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0412527 | + | 2.64543i | 0.0155920 | + | 0.999878i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.592396 | − | 1.02606i | −0.197465 | − | 0.342020i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.705737 | + | 1.22237i | −0.212788 | + | 0.368559i | −0.952586 | − | 0.304270i | \(-0.901588\pi\) |
0.739798 | + | 0.672829i | \(0.234921\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.47565i | 1.79602i | 0.439972 | + | 0.898011i | \(0.354988\pi\) | ||||
−0.439972 | + | 0.898011i | \(0.645012\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.24843 | − | 1.29813i | −0.545325 | − | 0.314844i | 0.201909 | − | 0.979404i | \(-0.435285\pi\) |
−0.747234 | + | 0.664561i | \(0.768619\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.581252 | + | 1.00676i | 0.133348 | + | 0.230966i | 0.924965 | − | 0.380052i | \(-0.124094\pi\) |
−0.791617 | + | 0.611018i | \(0.790760\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.73396 | + | 3.11446i | −0.378380 | + | 0.679631i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.36310 | − | 0.786989i | 0.284227 | − | 0.164099i | −0.351108 | − | 0.936335i | \(-0.614195\pi\) |
0.635335 | + | 0.772236i | \(0.280862\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.63816i | − | 1.08506i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.22668 | −1.15627 | −0.578133 | − | 0.815943i | \(-0.696218\pi\) | ||||
−0.578133 | + | 0.815943i | \(0.696218\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.49273 | + | 4.31753i | −0.447707 | + | 0.775451i | −0.998236 | − | 0.0593647i | \(-0.981093\pi\) |
0.550530 | + | 0.834816i | \(0.314426\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.64690 | + | 0.950837i | −0.286688 | + | 0.165519i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.34013 | + | 4.23783i | −1.20671 | + | 0.696694i | −0.962039 | − | 0.272912i | \(-0.912013\pi\) |
−0.244671 | + | 0.969606i | \(0.578680\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.36231 | + | 7.55574i | −0.698529 | + | 1.20989i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.57398 | 0.558162 | 0.279081 | − | 0.960268i | \(-0.409970\pi\) | ||||
0.279081 | + | 0.960268i | \(0.409970\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.24897i | 1.10546i | 0.833361 | + | 0.552729i | \(0.186413\pi\) | ||||
−0.833361 | + | 0.552729i | \(0.813587\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.47740 | − | 5.47178i | 1.38242 | − | 0.798141i | 0.389976 | − | 0.920825i | \(-0.372483\pi\) |
0.992446 | + | 0.122684i | \(0.0391501\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99660 | + | 0.218262i | −0.999514 | + | 0.0311803i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.74897 | − | 3.02931i | −0.244905 | − | 0.424188i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.0731 | + | 6.39306i | 1.52101 | + | 0.878154i | 0.999693 | + | 0.0247889i | \(0.00789137\pi\) |
0.521314 | + | 0.853365i | \(0.325442\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.56624i | 0.207453i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.02094 | + | 1.76833i | −0.132916 | + | 0.230217i | −0.924799 | − | 0.380455i | \(-0.875767\pi\) |
0.791884 | + | 0.610672i | \(0.209101\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.307934 | + | 0.533356i | 0.0394268 | + | 0.0682893i | 0.885065 | − | 0.465467i | \(-0.154113\pi\) |
−0.845639 | + | 0.533756i | \(0.820780\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.68993 | − | 1.60947i | 0.338900 | − | 0.202774i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.26871 | − | 3.04189i | −0.643675 | − | 0.371626i | 0.142354 | − | 0.989816i | \(-0.454533\pi\) |
−0.786029 | + | 0.618190i | \(0.787866\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.12061 | 0.255292 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.27631 | −0.982217 | −0.491109 | − | 0.871098i | \(-0.663408\pi\) | ||||
−0.491109 | + | 0.871098i | \(0.663408\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.04628 | + | 1.75877i | 0.356540 | + | 0.205849i | 0.667562 | − | 0.744554i | \(-0.267338\pi\) |
−0.311022 | + | 0.950403i | \(0.600671\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.26281 | − | 1.81655i | −0.371832 | − | 0.207015i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.439693 | + | 0.761570i | 0.0494693 | + | 0.0856833i | 0.889700 | − | 0.456546i | \(-0.150914\pi\) |
−0.840230 | + | 0.542229i | \(0.817580\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.02094 | − | 3.50038i | 0.224549 | − | 0.388931i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.90167i | 0.428264i | 0.976805 | + | 0.214132i | \(0.0686923\pi\) | ||||
−0.976805 | + | 0.214132i | \(0.931308\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.26525 | − | 4.19459i | −0.778916 | − | 0.449708i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.98158 | + | 5.16425i | 0.316047 | + | 0.547410i | 0.979660 | − | 0.200667i | \(-0.0643109\pi\) |
−0.663612 | + | 0.748077i | \(0.730978\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.1309 | + | 0.267138i | −1.79580 | + | 0.0280037i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.81699 | + | 3.35844i | −0.603194 | + | 0.348254i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.23442i | 0.328406i | 0.986427 | + | 0.164203i | \(0.0525052\pi\) | ||||
−0.986427 | + | 0.164203i | \(0.947495\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.67230 | 0.168073 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.26604 | + | 12.5852i | −0.722998 | + | 1.25227i | 0.236794 | + | 0.971560i | \(0.423903\pi\) |
−0.959793 | + | 0.280710i | \(0.909430\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.8335 | − | 7.98680i | 1.36306 | − | 0.786962i | 0.373029 | − | 0.927820i | \(-0.378319\pi\) |
0.990030 | + | 0.140857i | \(0.0449859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.4418 | − | 8.91534i | 1.49282 | − | 0.861879i | 0.492852 | − | 0.870113i | \(-0.335954\pi\) |
0.999966 | + | 0.00823431i | \(0.00262109\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.11721 | − | 10.5953i | 0.585923 | − | 1.01485i | −0.408837 | − | 0.912607i | \(-0.634066\pi\) |
0.994760 | − | 0.102240i | \(-0.0326011\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.4192 | −1.08386 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.29086i | 0.403650i | 0.979422 | + | 0.201825i | \(0.0646872\pi\) | ||||
−0.979422 | + | 0.201825i | \(0.935313\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.64441 | − | 3.83615i | 0.614276 | − | 0.354652i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.34137 | − | 6.00162i | 0.306303 | − | 0.550168i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.50387 | + | 7.80093i | 0.409443 | + | 0.709176i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.17009 | + | 2.40760i | 0.376005 | + | 0.217086i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.89899i | 0.878393i | 0.898391 | + | 0.439196i | \(0.144737\pi\) | ||||
−0.898391 | + | 0.439196i | \(0.855263\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.88326 | + | 8.45805i | −0.429947 | + | 0.744690i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.98293 | − | 13.8268i | −0.697471 | − | 1.20806i | −0.969340 | − | 0.245722i | \(-0.920975\pi\) |
0.271869 | − | 0.962334i | \(-0.412358\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.63933 | + | 1.57919i | −0.228859 | + | 0.136933i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.0175 | − | 6.36097i | −0.941290 | − | 0.543454i | −0.0509256 | − | 0.998702i | \(-0.516217\pi\) |
−0.890364 | + | 0.455248i | \(0.849550\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.65270 | −0.649094 | −0.324547 | − | 0.945870i | \(-0.605212\pi\) | ||||
−0.324547 | + | 0.945870i | \(0.605212\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.7442 | 1.24169 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.91566 | − | 4.57011i | −0.661941 | − | 0.382172i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.31061 | − | 4.45858i | −0.685448 | − | 0.367737i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.64543 | + | 2.84997i | 0.134799 | + | 0.233478i | 0.925521 | − | 0.378697i | \(-0.123628\pi\) |
−0.790722 | + | 0.612176i | \(0.790295\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.36231 | − | 16.2160i | 0.761894 | − | 1.31964i | −0.179979 | − | 0.983670i | \(-0.557603\pi\) |
0.941873 | − | 0.335969i | \(-0.109064\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.07604i | 0.248683i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.2011 | + | 9.35369i | 1.29299 | + | 0.746506i | 0.979182 | − | 0.202982i | \(-0.0650633\pi\) |
0.313804 | + | 0.949488i | \(0.398397\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.61334 | + | 14.9187i | 0.683082 | + | 1.18313i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.13816 | + | 3.57353i | 0.168510 | + | 0.281634i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.62760 | − | 0.939693i | 0.127483 | − | 0.0736024i | −0.434902 | − | 0.900478i | \(-0.643217\pi\) |
0.562385 | + | 0.826875i | \(0.309884\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.25402i | − | 0.0970392i | −0.998822 | − | 0.0485196i | \(-0.984550\pi\) | ||
0.998822 | − | 0.0485196i | \(-0.0154503\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −28.9341 | −2.22570 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.688663 | − | 1.19280i | 0.0526634 | − | 0.0912156i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.17350 | + | 0.677519i | −0.0892193 | + | 0.0515108i | −0.543946 | − | 0.839120i | \(-0.683070\pi\) |
0.454727 | + | 0.890631i | \(0.349737\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.38246 | + | 1.37551i | −0.179077 | + | 0.103390i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.70233 | − | 9.87673i | 0.426212 | − | 0.738222i | −0.570320 | − | 0.821422i | \(-0.693181\pi\) |
0.996533 | + | 0.0832008i | \(0.0265143\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.40373 | 0.698974 | 0.349487 | − | 0.936941i | \(-0.386356\pi\) | ||||
0.349487 | + | 0.936941i | \(0.386356\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.829755i | 0.0613373i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.17360 | − | 1.83228i | 0.232077 | − | 0.133990i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.9153 | − | 0.232589i | 1.08493 | − | 0.0169184i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.3871 | + | 21.4551i | 0.896301 | + | 1.55244i | 0.832186 | + | 0.554496i | \(0.187089\pi\) |
0.0641148 | + | 0.997943i | \(0.479578\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.50779 | − | 5.48932i | −0.684385 | − | 0.395130i | 0.117120 | − | 0.993118i | \(-0.462634\pi\) |
−0.801505 | + | 0.597988i | \(0.795967\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.1019i | 1.71719i | 0.512652 | + | 0.858596i | \(0.328663\pi\) | ||||
−0.512652 | + | 0.858596i | \(0.671337\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.89780 | − | 8.48324i | 0.347196 | − | 0.601361i | −0.638554 | − | 0.769577i | \(-0.720467\pi\) |
0.985750 | + | 0.168216i | \(0.0538005\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.09833 | − | 7.09851i | −0.289074 | − | 0.500690i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.256867 | − | 16.4722i | −0.0180285 | − | 1.15613i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.61500 | − | 0.932419i | −0.112250 | − | 0.0648076i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.64084 | −0.113500 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.68954 | 0.460527 | 0.230263 | − | 0.973128i | \(-0.426041\pi\) | ||||
0.230263 | + | 0.973128i | \(0.426041\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.65674 | − | 5.57532i | −0.661669 | − | 0.382015i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.5245 | − | 6.41622i | −0.782337 | − | 0.435562i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.36959 | + | 4.10424i | 0.160122 | + | 0.277339i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.40626 | − | 14.5601i | 0.565466 | − | 0.979416i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 25.4911i | − | 1.70701i | −0.521083 | − | 0.853506i | \(-0.674472\pi\) | ||
0.521083 | − | 0.853506i | \(-0.325528\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.82034 | − | 5.66978i | −0.651799 | − | 0.376316i | 0.137346 | − | 0.990523i | \(-0.456143\pi\) |
−0.789145 | + | 0.614207i | \(0.789476\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.82160 | − | 4.88716i | −0.186457 | − | 0.322953i | 0.757610 | − | 0.652708i | \(-0.226367\pi\) |
−0.944066 | + | 0.329755i | \(0.893034\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.58331 | − | 4.31753i | −0.169969 | − | 0.284072i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.97210 | + | 5.18004i | −0.587782 | + | 0.339356i | −0.764220 | − | 0.644956i | \(-0.776876\pi\) |
0.176438 | + | 0.984312i | \(0.443542\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.18479i | 0.0769605i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.2422 | 0.791880 | 0.395940 | − | 0.918276i | \(-0.370419\pi\) | ||||
0.395940 | + | 0.918276i | \(0.370419\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.92989 | + | 15.4670i | −0.575225 | + | 0.996319i | 0.420792 | + | 0.907157i | \(0.361752\pi\) |
−0.996017 | + | 0.0891618i | \(0.971581\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.93231 | + | 5.73442i | −0.637158 | + | 0.367863i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.51941 | + | 3.76399i | −0.414820 | + | 0.239497i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.62836 | + | 4.55245i | −0.166565 | + | 0.288500i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.7888 | 1.05970 | 0.529850 | − | 0.848091i | \(-0.322248\pi\) | ||||
0.529850 | + | 0.848091i | \(0.322248\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.22163i | 0.139673i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.8699 | − | 9.16250i | 0.989939 | − | 0.571541i | 0.0846826 | − | 0.996408i | \(-0.473012\pi\) |
0.905256 | + | 0.424867i | \(0.139679\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.5137 | − | 19.2430i | −0.715425 | − | 1.19570i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.68866 | + | 6.38895i | 0.228323 | + | 0.395466i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.7089 | + | 6.76011i | 0.721999 | + | 0.416847i | 0.815488 | − | 0.578774i | \(-0.196469\pi\) |
−0.0934888 | + | 0.995620i | \(0.529802\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.03415i | 0.491682i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.8824 | − | 24.0450i | 0.846424 | − | 1.46605i | −0.0379556 | − | 0.999279i | \(-0.512085\pi\) |
0.884379 | − | 0.466769i | \(-0.154582\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.93969 | − | 13.7520i | −0.482302 | − | 0.835372i | 0.517492 | − | 0.855688i | \(-0.326866\pi\) |
−0.999794 | + | 0.0203167i | \(0.993533\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −20.1681 | − | 11.2285i | −1.22063 | − | 0.679579i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.4690 | + | 8.35369i | 0.869359 | + | 0.501925i | 0.867135 | − | 0.498073i | \(-0.165959\pi\) |
0.00222396 | + | 0.999998i | \(0.499292\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.90673 | 0.353626 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.0155 | 1.90988 | 0.954942 | − | 0.296793i | \(-0.0959172\pi\) | ||||
0.954942 | + | 0.296793i | \(0.0959172\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.27287 | − | 5.35369i | −0.551215 | − | 0.318244i | 0.198397 | − | 0.980122i | \(-0.436426\pi\) |
−0.749612 | + | 0.661878i | \(0.769760\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.147436 | + | 9.45471i | 0.00870288 | + | 0.558094i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.12970 | − | 8.88490i | −0.301747 | − | 0.522641i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.17886 | + | 3.77390i | −0.127727 | + | 0.221230i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.20439i | 0.479306i | 0.970859 | + | 0.239653i | \(0.0770336\pi\) | ||||
−0.970859 | + | 0.239653i | \(0.922966\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.89193 | + | 3.97906i | 0.399910 | + | 0.230888i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.09627 | + | 8.82699i | 0.294725 | + | 0.510478i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.1766 | + | 0.299039i | −1.10532 | + | 0.0172363i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.9559 | + | 9.78952i | −0.974093 | + | 0.562393i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.3678i | 1.50489i | 0.658654 | + | 0.752446i | \(0.271126\pi\) | ||||
−0.658654 | + | 0.752446i | \(0.728874\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 21.5212 | 1.22430 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.33275 | − | 12.7007i | 0.415802 | − | 0.720190i | −0.579710 | − | 0.814823i | \(-0.696834\pi\) |
0.995512 | + | 0.0946325i | \(0.0301676\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.4313 | − | 15.2601i | 1.49399 | − | 0.862553i | 0.494009 | − | 0.869457i | \(-0.335531\pi\) |
0.999976 | + | 0.00690417i | \(0.00219768\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.6113 | + | 8.43582i | −0.820651 | + | 0.473803i | −0.850641 | − | 0.525747i | \(-0.823786\pi\) |
0.0299900 | + | 0.999550i | \(0.490452\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.39440 | − | 7.61132i | 0.246039 | − | 0.426152i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.0232 | 1.34085 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.01817i | − | 0.167935i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.2750 | − | 8.24170i | 0.789411 | − | 0.455767i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.8662 | + | 24.8461i | 0.819599 | + | 1.36981i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.18779 | − | 12.4496i | −0.395076 | − | 0.684292i | 0.598035 | − | 0.801470i | \(-0.295949\pi\) |
−0.993111 | + | 0.117178i | \(0.962615\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.69653 | + | 5.02094i | 0.476567 | + | 0.275146i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.2909i | 0.996367i | 0.867072 | + | 0.498183i | \(0.165999\pi\) | ||||
−0.867072 | + | 0.498183i | \(0.834001\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.89053 | + | 5.00654i | −0.156992 | + | 0.271918i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.51842 | − | 6.09408i | −0.190533 | − | 0.330013i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.866025 | − | 18.5000i | −0.0467610 | − | 0.998906i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.8795 | + | 15.5189i | 1.44297 | + | 0.833097i | 0.998047 | − | 0.0624727i | \(-0.0198986\pi\) |
0.444920 | + | 0.895570i | \(0.353232\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.3286 | 1.14170 | 0.570848 | − | 0.821056i | \(-0.306615\pi\) | ||||
0.570848 | + | 0.821056i | \(0.306615\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 36.5107 | 1.94880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.9916 | − | 17.3157i | −1.59629 | − | 0.921620i | −0.992193 | − | 0.124712i | \(-0.960199\pi\) |
−0.604100 | − | 0.796908i | \(-0.706467\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.94166 | − | 4.75174i | 0.420317 | − | 0.251489i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.3576 | − | 19.6719i | −0.599429 | − | 1.03824i | −0.992905 | − | 0.118907i | \(-0.962061\pi\) |
0.393476 | − | 0.919335i | \(-0.371272\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.82429 | − | 15.2841i | 0.464436 | − | 0.804428i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.1361i | 0.636980i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.5913 | − | 15.3525i | −1.38806 | − | 0.801395i | −0.394960 | − | 0.918698i | \(-0.629242\pi\) |
−0.993096 | + | 0.117304i | \(0.962575\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.11721 | − | 3.66712i | −0.110218 | − | 0.190903i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.4556 | + | 29.5568i | −0.854331 | + | 1.53451i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.0433 | − | 8.68526i | 0.778913 | − | 0.449706i | −0.0571319 | − | 0.998367i | \(-0.518196\pi\) |
0.836045 | + | 0.548661i | \(0.184862\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 40.3218i | − | 2.07668i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.78880 | −0.143251 | −0.0716255 | − | 0.997432i | \(-0.522819\pi\) | ||||
−0.0716255 | + | 0.997432i | \(0.522819\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.66843 | + | 11.5501i | −0.341634 | + | 0.591728i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.39160 | − | 2.53549i | 0.224400 | − | 0.129558i | −0.383586 | − | 0.923505i | \(-0.625311\pi\) |
0.607986 | + | 0.793948i | \(0.291978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.43788 | − | 4.29426i | 0.378089 | − | 0.218290i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.29948 | + | 7.44691i | −0.217992 | + | 0.377574i | −0.954194 | − | 0.299189i | \(-0.903284\pi\) |
0.736202 | + | 0.676762i | \(0.236617\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.08647 | −0.206661 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 21.5107i | − | 1.08507i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.22913 | − | 1.28699i | 0.111877 | − | 0.0645921i | −0.443017 | − | 0.896513i | \(-0.646092\pi\) |
0.554894 | + | 0.831921i | \(0.312759\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.14337 | + | 0.0646115i | −0.207428 | + | 0.00323462i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.7310 | − | 25.5149i | −0.735632 | − | 1.27415i | −0.954446 | − | 0.298385i | \(-0.903552\pi\) |
0.218814 | − | 0.975767i | \(-0.429781\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −27.9588 | − | 16.1420i | −1.39273 | − | 0.804092i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 11.9632i | − | 0.592992i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.92602 | − | 5.06802i | 0.144682 | − | 0.250597i | −0.784572 | − | 0.620038i | \(-0.787117\pi\) |
0.929254 | + | 0.369440i | \(0.120451\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.57011 | − | 14.8439i | −0.422732 | − | 0.732194i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.72010 | − | 2.62789i | −0.232261 | − | 0.129310i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.92912 | − | 5.15523i | −0.437261 | − | 0.252453i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.03952 | 0.0507841 | 0.0253921 | − | 0.999678i | \(-0.491917\pi\) | ||||
0.0253921 | + | 0.999678i | \(0.491917\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.1566 | −1.56722 | −0.783609 | − | 0.621254i | \(-0.786623\pi\) | ||||
−0.783609 | + | 0.621254i | \(0.786623\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.2288 | − | 6.48293i | −0.545961 | − | 0.315211i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.39825 | + | 0.836619i | −0.0676663 | + | 0.0404868i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.15729 | − | 10.6647i | −0.297277 | − | 0.514898i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.230085 | + | 0.398519i | −0.0110828 | + | 0.0191960i | −0.871514 | − | 0.490371i | \(-0.836861\pi\) |
0.860431 | + | 0.509567i | \(0.170195\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 24.6509i | − | 1.18465i | −0.805699 | − | 0.592325i | \(-0.798210\pi\) | ||
0.805699 | − | 0.592325i | \(-0.201790\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.58461 | + | 0.914878i | 0.0758024 | + | 0.0437645i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.9572 | + | 25.9067i | 0.713870 | + | 1.23646i | 0.963394 | + | 0.268090i | \(0.0863925\pi\) |
−0.249524 | + | 0.968369i | \(0.580274\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.36871 | + | 7.04963i | 0.208034 | + | 0.335697i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.9005 | − | 6.29339i | 0.517897 | − | 0.299008i | −0.218177 | − | 0.975909i | \(-0.570011\pi\) |
0.736074 | + | 0.676901i | \(0.236678\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.43376i | 0.209710i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.4783 | −1.15520 | −0.577602 | − | 0.816318i | \(-0.696011\pi\) | ||||
−0.577602 | + | 0.816318i | \(0.696011\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.52229 | + | 4.36873i | −0.118770 | + | 0.205716i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.8478 | − | 12.6138i | 1.02650 | − | 0.592648i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.0403 | + | 20.2306i | −1.63912 | + | 0.946345i | −0.657980 | + | 0.753035i | \(0.728589\pi\) |
−0.981138 | + | 0.193310i | \(0.938078\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.31908 | + | 12.6770i | −0.341625 | + | 0.591712i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.22668 | −0.243431 | −0.121715 | − | 0.992565i | \(-0.538840\pi\) | ||||
−0.121715 | + | 0.992565i | \(0.538840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.0547i | 1.86150i | 0.365658 | + | 0.930749i | \(0.380844\pi\) | ||||
−0.365658 | + | 0.930749i | \(0.619156\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.8199 | − | 10.2883i | 0.824607 | − | 0.476087i | −0.0273953 | − | 0.999625i | \(-0.508721\pi\) |
0.852003 | + | 0.523537i | \(0.175388\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.82976 | − | 14.0635i | 0.361545 | − | 0.649391i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.6022 | + | 21.8276i | 0.580679 | + | 1.00576i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.86094 | − | 5.11587i | −0.407427 | − | 0.235228i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 15.1489i | − | 0.693620i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.3020 | − | 19.5756i | 0.516402 | − | 0.894434i | −0.483417 | − | 0.875390i | \(-0.660604\pi\) |
0.999819 | − | 0.0190438i | \(-0.00606219\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.4427 | − | 47.5321i | −1.25128 | − | 2.16728i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.0874810 | + | 5.60994i | 0.00398052 | + | 0.255261i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.4403 | + | 12.9559i | 1.01687 | + | 0.587087i | 0.913194 | − | 0.407524i | \(-0.133608\pi\) |
0.103671 | + | 0.994612i | \(0.466941\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.53209 | 0.114505 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.7297 | 1.79298 | 0.896488 | − | 0.443069i | \(-0.146110\pi\) | ||||
0.896488 | + | 0.443069i | \(0.146110\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.0003 | + | 8.08306i | 0.630541 | + | 0.364043i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.341420 | − | 21.8944i | −0.0153148 | − | 0.982098i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.0963 | + | 17.4872i | 0.451971 | + | 0.782837i | 0.998508 | − | 0.0545980i | \(-0.0173877\pi\) |
−0.546537 | + | 0.837435i | \(0.684054\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.844770 | − | 1.46318i | 0.0377415 | − | 0.0653703i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.29086i | 0.325083i | 0.986702 | + | 0.162542i | \(0.0519692\pi\) | ||||
−0.986702 | + | 0.162542i | \(0.948031\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −33.7601 | − | 19.4914i | −1.49934 | − | 0.865643i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.27126 | + | 5.66599i | 0.144996 | + | 0.251140i | 0.929371 | − | 0.369146i | \(-0.120350\pi\) |
−0.784375 | + | 0.620286i | \(0.787016\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.52704 | + | 8.13127i | −0.200264 | + | 0.359706i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.67626 | − | 3.27719i | 0.250613 | − | 0.144691i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.4466i | 0.679339i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.82564 | −0.0801366 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.87939 | + | 10.1834i | −0.257581 | + | 0.446143i | −0.965593 | − | 0.260057i | \(-0.916259\pi\) |
0.708013 | + | 0.706200i | \(0.249592\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.852618 | + | 0.492259i | −0.0372824 | + | 0.0215250i | −0.518525 | − | 0.855062i | \(-0.673519\pi\) |
0.481243 | + | 0.876587i | \(0.340185\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.2095 | − | 6.47178i | 0.488292 | − | 0.281915i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.2613 | + | 17.7731i | −0.446143 | + | 0.772743i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.41921 | 0.104985 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.1438i | 1.00247i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.3069 | − | 7.68273i | 0.574234 | − | 0.331534i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.67096 | − | 8.70648i | 0.201192 | − | 0.375015i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.10488 | − | 14.0381i | −0.348456 | − | 0.603544i | 0.637519 | − | 0.770434i | \(-0.279961\pi\) |
−0.985975 | + | 0.166891i | \(0.946627\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.9722 | + | 6.33481i | 0.470863 | + | 0.271853i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.3337i | 1.25422i | 0.778932 | + | 0.627109i | \(0.215762\pi\) | ||||
−0.778932 | + | 0.627109i | \(0.784238\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.364837 | − | 0.631917i | 0.0155709 | − | 0.0269696i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.61927 | − | 6.26876i | −0.154186 | − | 0.267058i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.99654 | + | 1.19459i | −0.0849016 | + | 0.0507992i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.2990 | + | 6.52347i | 0.478753 | + | 0.276408i | 0.719897 | − | 0.694081i | \(-0.244189\pi\) |
−0.241144 | + | 0.970489i | \(0.577522\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −46.9418 | −1.98543 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.93725 | 0.208451 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.3323 | + | 13.4709i | 0.983339 | + | 0.567731i | 0.903276 | − | 0.429059i | \(-0.141155\pi\) |
0.0800623 | + | 0.996790i | \(0.474488\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.34337 | + | 5.20187i | 0.392385 | + | 0.218458i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.61633 | + | 11.4598i | 0.277371 | + | 0.480421i | 0.970731 | − | 0.240171i | \(-0.0772035\pi\) |
−0.693359 | + | 0.720592i | \(0.743870\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.16385 | − | 5.47995i | 0.132403 | − | 0.229329i | −0.792199 | − | 0.610262i | \(-0.791064\pi\) |
0.924602 | + | 0.380934i | \(0.124397\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.3783i | 1.39440i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.36208 | + | 3.09580i | 0.223226 | + | 0.128880i | 0.607443 | − | 0.794363i | \(-0.292195\pi\) |
−0.384217 | + | 0.923243i | \(0.625529\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.39574 | − | 12.8098i | −0.307357 | − | 0.532357i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.3216 | + | 0.160954i | −0.428212 | + | 0.00667752i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.6294 | + | 9.02363i | −0.647303 | + | 0.373721i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.6186i | 1.09867i | 0.835604 | + | 0.549333i | \(0.185118\pi\) | ||||
−0.835604 | + | 0.549333i | \(0.814882\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.79561 | −0.238804 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.2362 | + | 28.1220i | −0.667869 | + | 1.15678i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.7317 | − | 6.77332i | 0.481764 | − | 0.278147i | −0.239387 | − | 0.970924i | \(-0.576946\pi\) |
0.721152 | + | 0.692777i | \(0.243613\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.4294 | − | 6.59879i | 0.467776 | − | 0.270071i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.8007 | + | 25.6355i | −0.604739 | + | 1.04744i | 0.387354 | + | 0.921931i | \(0.373389\pi\) |
−0.992093 | + | 0.125507i | \(0.959944\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.9050 | −0.852732 | −0.426366 | − | 0.904551i | \(-0.640206\pi\) | ||||
−0.426366 | + | 0.904551i | \(0.640206\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.20801i | 0.293533i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.2192 | + | 18.6018i | −1.30774 | + | 0.755023i | −0.981718 | − | 0.190340i | \(-0.939041\pi\) |
−0.326020 | + | 0.945363i | \(0.605708\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.7968 | − | 19.3927i | 0.437508 | − | 0.785833i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.4334 | + | 61.3724i | 1.43348 | + | 2.48286i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.6152 | + | 13.0569i | 0.913420 | + | 0.527363i | 0.881530 | − | 0.472128i | \(-0.156514\pi\) |
0.0318902 | + | 0.999491i | \(0.489847\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 25.4698i | − | 1.02537i | −0.858575 | − | 0.512687i | \(-0.828650\pi\) | ||
0.858575 | − | 0.512687i | \(-0.171350\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.51455 | − | 13.0156i | 0.302035 | − | 0.523140i | −0.674562 | − | 0.738219i | \(-0.735667\pi\) |
0.976597 | + | 0.215078i | \(0.0690007\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.43717 | − | 7.68540i | −0.178057 | − | 0.308404i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.5387 | + | 8.10060i | −0.542415 | + | 0.324544i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.91453 | − | 1.10535i | −0.0764588 | − | 0.0441435i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.0051 | 0.877399 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.605762 | 0.0241150 | 0.0120575 | − | 0.999927i | \(-0.496162\pi\) | ||||
0.0120575 | + | 0.999927i | \(0.496162\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.80531 | + | 4.50640i | 0.310233 | + | 0.179113i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.41339 | − | 45.3075i | −0.0560005 | − | 1.79515i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.90286 | + | 8.49200i | 0.193954 | + | 0.335938i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.3772 | + | 19.7058i | −0.449371 | + | 0.778333i | −0.998345 | − | 0.0575060i | \(-0.981685\pi\) |
0.548974 | + | 0.835839i | \(0.315019\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.85204i | − | 0.0730375i | −0.999333 | − | 0.0365187i | \(-0.988373\pi\) | ||
0.999333 | − | 0.0365187i | \(-0.0116269\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.79098 | − | 3.34343i | −0.227667 | − | 0.131444i | 0.381828 | − | 0.924233i | \(-0.375295\pi\) |
−0.609495 | + | 0.792790i | \(0.708628\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.44104 | − | 2.49595i | −0.0565656 | − | 0.0979746i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.12449 | − | 15.2499i | −0.357617 | − | 0.597690i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.55461 | + | 5.51636i | −0.373901 | + | 0.215872i | −0.675161 | − | 0.737670i | \(-0.735926\pi\) |
0.301260 | + | 0.953542i | \(0.402593\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4.16756i | − | 0.162592i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.5202 | 0.526673 | 0.263337 | − | 0.964704i | \(-0.415177\pi\) | ||||
0.263337 | + | 0.964704i | \(0.415177\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.0692 | + | 36.4930i | −0.819498 | + | 1.41941i | 0.0865545 | + | 0.996247i | \(0.472414\pi\) |
−0.906053 | + | 0.423165i | \(0.860919\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19.6167 | − | 11.3257i | 0.761851 | − | 0.439855i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.48762 | + | 4.90033i | −0.328642 | + | 0.189742i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.1721 | − | 29.7429i | 0.663910 | − | 1.14993i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.869280 | −0.0335582 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.8494i | 0.726589i | 0.931674 | + | 0.363295i | \(0.118348\pi\) | ||||
−0.931674 | + | 0.363295i | \(0.881652\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.6298 | + | 12.4880i | −0.831301 | + | 0.479952i | −0.854298 | − | 0.519784i | \(-0.826013\pi\) |
0.0229968 | + | 0.999736i | \(0.492679\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.55644 | + | 0.133429i | −0.328366 | + | 0.00512052i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.63887 | − | 13.2309i | −0.292722 | − | 0.507010i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.8321 | + | 8.56330i | 0.567533 | + | 0.327666i | 0.756164 | − | 0.654383i | \(-0.227071\pi\) |
−0.188630 | + | 0.982048i | \(0.560405\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7.60307i | − | 0.290075i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41.3992 | + | 71.7055i | −1.57718 | + | 2.73176i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.80500 | + | 11.7866i | 0.258874 | + | 0.448383i | 0.965941 | − | 0.258764i | \(-0.0833151\pi\) |
−0.707066 | + | 0.707147i | \(0.749982\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0689870 | + | 4.42396i | 0.00262060 | + | 0.168052i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.03585 | − | 4.63950i | −0.304380 | − | 0.175734i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.9581 | −0.527944 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.86247 | 0.145884 | 0.0729418 | − | 0.997336i | \(-0.476761\pi\) | ||||
0.0729418 | + | 0.997336i | \(0.476761\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.53293 | − | 4.92649i | −0.321826 | − | 0.185806i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33.5929 | − | 18.7026i | −1.26339 | − | 0.703385i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.8935 | − | 18.8681i | −0.409115 | − | 0.708608i | 0.585676 | − | 0.810545i | \(-0.300829\pi\) |
−0.994791 | + | 0.101938i | \(0.967496\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.520945 | − | 0.902302i | 0.0195369 | − | 0.0338390i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.84699i | 0.293872i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.2841 | + | 8.24691i | 0.533448 | + | 0.307987i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.3926 | − | 43.9814i | −0.946986 | − | 1.64023i | −0.751725 | − | 0.659476i | \(-0.770778\pi\) |
−0.195260 | − | 0.980751i | \(-0.562555\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.6992 | + | 36.2662i | 0.808120 | + | 1.35062i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.8387 | + | 12.0312i | −0.774998 | + | 0.447446i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.1607i | 1.41530i | 0.706561 | + | 0.707652i | \(0.250245\pi\) | ||||
−0.706561 | + | 0.707652i | \(0.749755\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.5776 | −1.02139 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.41013 | − | 16.2988i | 0.348046 | − | 0.602834i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.3318 | − | 7.69712i | 0.492421 | − | 0.284300i | −0.233157 | − | 0.972439i | \(-0.574906\pi\) |
0.725578 | + | 0.688140i | \(0.241572\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.43664 | − | 4.29355i | 0.273932 | − | 0.158155i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.0749 | + | 38.2349i | −0.812039 | + | 1.40649i | 0.0993961 | + | 0.995048i | \(0.468309\pi\) |
−0.911435 | + | 0.411444i | \(0.865024\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.1424 | −0.372591 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 53.0378i | 1.94577i | 0.231296 | + | 0.972884i | \(0.425704\pi\) | ||||
−0.231296 | + | 0.972884i | \(0.574296\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.00335 | − | 2.31134i | 0.146475 | − | 0.0845674i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.2219 | + | 40.4825i | 0.885050 | + | 1.47920i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.85844 | − | 8.41507i | −0.177287 | − | 0.307070i | 0.763663 | − | 0.645615i | \(-0.223399\pi\) |
−0.940950 | + | 0.338545i | \(0.890065\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.5891 | + | 11.3097i | 0.713865 | + | 0.412150i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.2030i | 0.806980i | 0.914984 | + | 0.403490i | \(0.132203\pi\) | ||||
−0.914984 | + | 0.403490i | \(0.867797\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.49660 | + | 2.59218i | −0.0543230 | + | 0.0940902i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.5273 | − | 32.0903i | −0.671616 | − | 1.16327i | −0.977446 | − | 0.211186i | \(-0.932267\pi\) |
0.305830 | − | 0.952086i | \(-0.401066\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.2815 | + | 15.7456i | 1.02386 | + | 0.570028i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.4511 | − | 6.61128i | −0.413474 | − | 0.238720i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.7948 | −1.50716 | −0.753579 | − | 0.657357i | \(-0.771674\pi\) | ||||
−0.753579 | + | 0.657357i | \(0.771674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.6892 | 0.889160 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.1396 | − | 15.6691i | −0.976144 | − | 0.563577i | −0.0750402 | − | 0.997181i | \(-0.523909\pi\) |
−0.901104 | + | 0.433603i | \(0.857242\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.471073 | − | 30.2087i | −0.0168997 | − | 1.08373i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.07738 | + | 3.59813i | 0.0744299 | + | 0.128916i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.84090 | − | 10.1167i | 0.209004 | − | 0.362005i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 35.1070i | 1.25462i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.4531 | − | 12.3859i | −0.764720 | − | 0.441511i | 0.0662679 | − | 0.997802i | \(-0.478891\pi\) |
−0.830988 | + | 0.556291i | \(0.812224\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.10788 | + | 15.7753i | 0.324249 | + | 0.561616i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.3512 | + | 0.177009i | −0.403601 | + | 0.00629373i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.45383 | + | 1.99407i | −0.122649 | + | 0.0708115i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.07697i | 0.179836i | 0.995949 | + | 0.0899178i | \(0.0286604\pi\) | ||||
−0.995949 | + | 0.0899178i | \(0.971340\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.4124 | −1.00516 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.53256 | − | 6.11857i | 0.124817 | − | 0.216189i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.29975 | + | 2.48246i | −0.151735 | + | 0.0876041i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.3957 | − | 18.7037i | 1.14038 | − | 0.658401i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.47519 | − | 2.55510i | 0.0518647 | − | 0.0898324i | −0.838927 | − | 0.544243i | \(-0.816817\pi\) |
0.890792 | + | 0.454411i | \(0.150150\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.1753 | −0.462647 | −0.231324 | − | 0.972877i | \(-0.574306\pi\) | ||||
−0.231324 | + | 0.972877i | \(0.574306\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 21.3942i | − | 0.750329i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.29796 | + | 4.21348i | −0.255323 | + | 0.147411i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.4224 | + | 17.4191i | 0.364187 | + | 0.608672i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.8032 | + | 20.4437i | 0.411934 | + | 0.713491i | 0.995101 | − | 0.0988615i | \(-0.0315201\pi\) |
−0.583167 | + | 0.812352i | \(0.698187\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.88511 | + | 2.82042i | 0.170284 | + | 0.0983137i | 0.582720 | − | 0.812673i | \(-0.301988\pi\) |
−0.412436 | + | 0.910987i | \(0.635322\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 19.2368i | − | 0.668929i | −0.942408 | − | 0.334464i | \(-0.891445\pi\) | ||
0.942408 | − | 0.334464i | \(-0.108555\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.6762 | − | 23.6878i | 0.474993 | − | 0.822712i | −0.524597 | − | 0.851351i | \(-0.675784\pi\) |
0.999590 | + | 0.0286386i | \(0.00911719\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.2549 | + | 19.4941i | 0.390428 | + | 0.676241i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.0147 | + | 8.59177i | 0.554877 | + | 0.297687i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24.3429 | + | 14.0544i | 0.841414 | + | 0.485790i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.5425 | −0.571111 | −0.285556 | − | 0.958362i | \(-0.592178\pi\) | ||||
−0.285556 | + | 0.958362i | \(0.592178\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.77156 | 0.336950 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 37.3554 | + | 21.5672i | 1.28659 | + | 0.742813i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.4510 | + | 12.2365i | −0.702705 | + | 0.420450i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.21301 | − | 12.4933i | −0.247550 | − | 0.428769i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.67024 | + | 11.5532i | −0.228653 | + | 0.396039i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.633103i | 0.0216770i | 0.999941 | + | 0.0108385i | \(0.00345008\pi\) | ||||
−0.999941 | + | 0.0108385i | \(0.996550\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.33099 | − | 3.07785i | −0.182103 | − | 0.105137i | 0.406177 | − | 0.913794i | \(-0.366862\pi\) |
−0.588280 | + | 0.808657i | \(0.700195\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.7554 | − | 22.0929i | −0.435208 | − | 0.753802i | 0.562105 | − | 0.827066i | \(-0.309992\pi\) |
−0.997313 | + | 0.0732643i | \(0.976658\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.19712 | + | 11.1310i | −0.211197 | + | 0.379344i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.0391 | + | 6.37346i | −0.375777 | + | 0.216955i | −0.675979 | − | 0.736921i | \(-0.736279\pi\) |
0.300202 | + | 0.953876i | \(0.402946\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 13.8225i | − | 0.469435i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.24123 | −0.0421058 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.6982 | − | 34.1183i | 0.667449 | − | 1.15605i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.31871 | − | 1.91606i | 0.112321 | − | 0.0648488i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.8769 | + | 21.2909i | −1.24524 | + | 0.718941i | −0.970157 | − | 0.242478i | \(-0.922040\pi\) |
−0.275086 | + | 0.961420i | \(0.588706\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.52687 | + | 9.57283i | −0.186417 | + | 0.322883i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.0033 | −0.775001 | −0.387500 | − | 0.921870i | \(-0.626661\pi\) | ||||
−0.387500 | + | 0.921870i | \(0.626661\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.92303i | − | 0.0647151i | −0.999476 | − | 0.0323575i | \(-0.989698\pi\) | ||
0.999476 | − | 0.0323575i | \(-0.0103015\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.9725 | − | 10.3764i | 0.603459 | − | 0.348407i | −0.166942 | − | 0.985967i | \(-0.553389\pi\) |
0.770401 | + | 0.637560i | \(0.220056\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.1871 | + | 0.408360i | −0.878286 | + | 0.0136959i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.85251 | + | 4.94069i | 0.0955627 | + | 0.165519i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.0175 | + | 6.36097i | 0.368687 | + | 0.212862i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.7324i | 0.458510i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.5214 | − | 26.8839i | 0.517668 | − | 0.896627i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.5981 | − | 28.7487i | −0.552962 | − | 0.957759i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −22.5766 | − | 12.5694i | −0.751303 | − | 0.418283i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.25876 | + | 1.88144i | 0.108205 | + | 0.0624723i | 0.553126 | − | 0.833098i | \(-0.313435\pi\) |
−0.444921 | + | 0.895570i | \(0.646768\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.2175 | 0.571069 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.0618 | −0.631546 | −0.315773 | − | 0.948835i | \(-0.602264\pi\) | ||||
−0.315773 | + | 0.948835i | \(0.602264\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.76930 | − | 2.75356i | −0.157841 | − | 0.0911294i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.2486 | − | 21.6887i | 1.19703 | − | 0.716223i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.61334 | + | 16.6508i | 0.317115 | + | 0.549259i | 0.979885 | − | 0.199564i | \(-0.0639526\pi\) |
−0.662770 | + | 0.748823i | \(0.730619\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.7626 | + | 30.7658i | −0.585299 | + | 1.01377i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 53.5945i | − | 1.76408i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.3899 | − | 9.46270i | −0.538314 | − | 0.310796i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.1621 | + | 45.3141i | 0.858350 | + | 1.48671i | 0.873502 | + | 0.486821i | \(0.161844\pi\) |
−0.0151511 | + | 0.999885i | \(0.504823\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.28652 | − | 6.91701i | −0.140485 | − | 0.226696i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.1116 | − | 9.87939i | 0.560209 | − | 0.323437i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 36.0145i | − | 1.17654i | −0.808663 | − | 0.588272i | \(-0.799808\pi\) | ||
0.808663 | − | 0.588272i | \(-0.200192\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 41.1198 | 1.34189 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.4108 | + | 26.6922i | −0.502376 | + | 0.870141i | 0.497620 | + | 0.867395i | \(0.334207\pi\) |
−0.999996 | + | 0.00274619i | \(0.999126\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.87171 | − | 2.81268i | 0.158645 | − | 0.0915935i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.03341 | + | 3.48339i | −0.196060 | + | 0.113195i | −0.594816 | − | 0.803862i | \(-0.702775\pi\) |
0.398757 | + | 0.917057i | \(0.369442\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.3892 | + | 19.7266i | −0.369709 | + | 0.640354i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.7311 | −0.737107 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.84491i | 0.221728i | 0.993836 | + | 0.110864i | \(0.0353619\pi\) | ||||
−0.993836 | + | 0.110864i | \(0.964638\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.2547 | − | 5.92056i | 0.331488 | − | 0.191384i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.3730 | − | 29.4085i | 0.528711 | − | 0.949649i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.07263 | + | 5.32196i | 0.0991172 | + | 0.171676i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.2954 | − | 10.5628i | −0.589560 | − | 0.340383i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 19.2909i | − | 0.620352i | −0.950679 | − | 0.310176i | \(-0.899612\pi\) | ||
0.950679 | − | 0.310176i | \(-0.100388\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.03318 | − | 3.52158i | 0.0653153 | − | 0.113129i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.3726 | − | 37.0184i | −0.685879 | − | 1.18798i | −0.973160 | − | 0.230130i | \(-0.926085\pi\) |
0.287281 | − | 0.957846i | \(-0.407249\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.315695 | − | 20.2447i | −0.0101207 | − | 0.649015i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.8382 | − | 6.25743i | −0.346744 | − | 0.200193i | 0.316506 | − | 0.948590i | \(-0.397490\pi\) |
−0.663250 | + | 0.748398i | \(0.730824\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.41685 | −0.269004 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.4953 | −0.462798 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.2334 | + | 14.5685i | 0.804821 | + | 0.464663i | 0.845154 | − | 0.534523i | \(-0.179509\pi\) |
−0.0403333 | + | 0.999186i | \(0.512842\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.608239 | + | 39.0048i | 0.0193604 | + | 1.24154i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.70486 | + | 9.88111i | 0.181404 | + | 0.314201i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.0107 | + | 51.9801i | −0.953322 | + | 1.65120i | −0.215161 | + | 0.976579i | \(0.569028\pi\) |
−0.738161 | + | 0.674624i | \(0.764306\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 19.3682i | − | 0.614630i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.8296 | + | 17.7995i | 0.976383 | + | 0.563715i | 0.901176 | − | 0.433453i | \(-0.142705\pi\) |
0.0752070 | + | 0.997168i | \(0.476038\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 23.8935 | + | 41.3848i | 0.755958 | + | 1.30936i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1400.2.bh.h.249.5 | 12 | ||
5.2 | odd | 4 | 1400.2.q.k.1201.2 | yes | 6 | ||
5.3 | odd | 4 | 1400.2.q.i.1201.2 | yes | 6 | ||
5.4 | even | 2 | inner | 1400.2.bh.h.249.2 | 12 | ||
7.2 | even | 3 | inner | 1400.2.bh.h.849.2 | 12 | ||
35.2 | odd | 12 | 1400.2.q.k.401.2 | yes | 6 | ||
35.3 | even | 12 | 9800.2.a.cb.1.2 | 3 | |||
35.9 | even | 6 | inner | 1400.2.bh.h.849.5 | 12 | ||
35.17 | even | 12 | 9800.2.a.ch.1.2 | 3 | |||
35.18 | odd | 12 | 9800.2.a.ci.1.2 | 3 | |||
35.23 | odd | 12 | 1400.2.q.i.401.2 | ✓ | 6 | ||
35.32 | odd | 12 | 9800.2.a.cc.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.q.i.401.2 | ✓ | 6 | 35.23 | odd | 12 | ||
1400.2.q.i.1201.2 | yes | 6 | 5.3 | odd | 4 | ||
1400.2.q.k.401.2 | yes | 6 | 35.2 | odd | 12 | ||
1400.2.q.k.1201.2 | yes | 6 | 5.2 | odd | 4 | ||
1400.2.bh.h.249.2 | 12 | 5.4 | even | 2 | inner | ||
1400.2.bh.h.249.5 | 12 | 1.1 | even | 1 | trivial | ||
1400.2.bh.h.849.2 | 12 | 7.2 | even | 3 | inner | ||
1400.2.bh.h.849.5 | 12 | 35.9 | even | 6 | inner | ||
9800.2.a.cb.1.2 | 3 | 35.3 | even | 12 | |||
9800.2.a.cc.1.2 | 3 | 35.32 | odd | 12 | |||
9800.2.a.ch.1.2 | 3 | 35.17 | even | 12 | |||
9800.2.a.ci.1.2 | 3 | 35.18 | odd | 12 |