Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [276,2,Mod(13,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("276.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 276.i (of order \(11\), degree \(10\), 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: | \(2.20387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{11})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{11}]$ |
Embedding invariants
Embedding label | 121.2 | ||
Root | \(-0.404188 + 2.81119i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 276.121 |
Dual form | 276.2.i.a.73.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(139\) | \(185\) |
\(\chi(n)\) | \(e\left(\frac{9}{11}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.959493 | − | 0.281733i | −0.553964 | − | 0.162658i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.332496 | + | 0.213682i | −0.148697 | + | 0.0955616i | −0.612874 | − | 0.790181i | \(-0.709987\pi\) |
0.464177 | + | 0.885743i | \(0.346350\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.440112 | + | 3.06105i | −0.166347 | + | 1.15697i | 0.720010 | + | 0.693964i | \(0.244137\pi\) |
−0.886356 | + | 0.463003i | \(0.846772\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.841254 | + | 0.540641i | 0.280418 | + | 0.180214i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.09466 | + | 2.39697i | 0.330053 | + | 0.722715i | 0.999803 | − | 0.0198719i | \(-0.00632584\pi\) |
−0.669750 | + | 0.742587i | \(0.733599\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.315289 | + | 2.19288i | 0.0874454 | + | 0.608196i | 0.985673 | + | 0.168666i | \(0.0539459\pi\) |
−0.898228 | + | 0.439530i | \(0.855145\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.379229 | − | 0.111352i | 0.0979165 | − | 0.0287509i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.42879 | − | 2.80297i | 0.589068 | − | 0.679821i | −0.380461 | − | 0.924797i | \(-0.624235\pi\) |
0.969529 | + | 0.244976i | \(0.0787802\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.61122 | + | 5.32163i | 1.05789 | + | 1.22087i | 0.974509 | + | 0.224348i | \(0.0720253\pi\) |
0.0833775 | + | 0.996518i | \(0.473429\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.28468 | − | 2.81306i | 0.280341 | − | 0.613860i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.06629 | + | 2.54269i | −0.847881 | + | 0.530187i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.01218 | + | 4.40606i | −0.402436 | + | 0.881213i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.654861 | − | 0.755750i | −0.126028 | − | 0.145444i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.37075 | − | 5.04411i | 0.811627 | − | 0.936668i | −0.187331 | − | 0.982297i | \(-0.559984\pi\) |
0.998958 | + | 0.0456288i | \(0.0145291\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.22075 | + | 0.652070i | −0.398858 | + | 0.117115i | −0.475009 | − | 0.879981i | \(-0.657555\pi\) |
0.0761510 | + | 0.997096i | \(0.475737\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.375014 | − | 2.60828i | −0.0652816 | − | 0.454044i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.507756 | − | 1.11183i | −0.0858264 | − | 0.187934i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.80517 | − | 3.08810i | −0.789966 | − | 0.507680i | 0.0823615 | − | 0.996603i | \(-0.473754\pi\) |
−0.872327 | + | 0.488922i | \(0.837390\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.315289 | − | 2.19288i | 0.0504866 | − | 0.351142i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.36514 | + | 1.51998i | −0.369372 | + | 0.237381i | −0.712138 | − | 0.702040i | \(-0.752273\pi\) |
0.342765 | + | 0.939421i | \(0.388636\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.75382 | + | 1.10222i | 0.572451 | + | 0.168087i | 0.555131 | − | 0.831763i | \(-0.312668\pi\) |
0.0173207 | + | 0.999850i | \(0.494486\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.395239 | −0.0589187 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.37944 | −0.638808 | −0.319404 | − | 0.947619i | \(-0.603483\pi\) | ||||
−0.319404 | + | 0.947619i | \(0.603483\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.45987 | − | 0.722282i | −0.351410 | − | 0.103183i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.12009 | + | 2.00516i | −0.436901 | + | 0.280779i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.80647 | − | 12.5643i | 0.248138 | − | 1.72584i | −0.360821 | − | 0.932635i | \(-0.617504\pi\) |
0.608959 | − | 0.793202i | \(-0.291587\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.876162 | − | 0.563075i | −0.118142 | − | 0.0759250i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.92516 | − | 6.40520i | −0.387446 | − | 0.848389i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.40772 | − | 9.79088i | −0.183269 | − | 1.27466i | −0.848968 | − | 0.528444i | \(-0.822776\pi\) |
0.665699 | − | 0.746220i | \(-0.268133\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.36499 | − | 1.86893i | 0.814954 | − | 0.239292i | 0.152412 | − | 0.988317i | \(-0.451296\pi\) |
0.662542 | + | 0.749025i | \(0.269478\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.02517 | + | 2.33718i | −0.255148 | + | 0.294456i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.573412 | − | 0.661753i | −0.0711231 | − | 0.0820804i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.559732 | − | 1.22564i | 0.0683822 | − | 0.149736i | −0.872355 | − | 0.488874i | \(-0.837408\pi\) |
0.940737 | + | 0.339138i | \(0.110135\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.61794 | − | 1.29408i | 0.555934 | − | 0.155790i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.25308 | + | 7.12324i | −0.386069 | + | 0.845374i | 0.612426 | + | 0.790528i | \(0.290194\pi\) |
−0.998495 | + | 0.0548454i | \(0.982533\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.16279 | + | 4.80412i | 0.487218 | + | 0.562280i | 0.945120 | − | 0.326723i | \(-0.105944\pi\) |
−0.457902 | + | 0.889003i | \(0.651399\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.17201 | − | 3.66069i | 0.366272 | − | 0.422700i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.81903 | + | 2.29587i | −0.891061 | + | 0.261639i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.05877 | − | 7.36392i | −0.119121 | − | 0.828505i | −0.958527 | − | 0.285001i | \(-0.908006\pi\) |
0.839406 | − | 0.543505i | \(-0.182903\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.415415 | + | 0.909632i | 0.0461572 | + | 0.101070i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.579976 | − | 0.372728i | −0.0636606 | − | 0.0409122i | 0.508423 | − | 0.861107i | \(-0.330229\pi\) |
−0.572084 | + | 0.820195i | \(0.693865\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.208617 | + | 1.45097i | −0.0226277 | + | 0.157379i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.61479 | + | 3.60841i | −0.601969 | + | 0.386862i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.91112 | + | 1.73566i | 0.626578 | + | 0.183980i | 0.579580 | − | 0.814915i | \(-0.303217\pi\) |
0.0469975 | + | 0.998895i | \(0.485035\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.85128 | −0.718210 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.31450 | 0.240002 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.67035 | − | 0.784086i | −0.273972 | − | 0.0804455i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.89824 | + | 3.14790i | −0.497340 | + | 0.319621i | −0.765152 | − | 0.643850i | \(-0.777336\pi\) |
0.267811 | + | 0.963471i | \(0.413700\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.375014 | + | 2.60828i | −0.0376904 | + | 0.262142i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.86524 | + | 5.05468i | 0.782620 | + | 0.502959i | 0.869902 | − | 0.493224i | \(-0.164182\pi\) |
−0.0872820 | + | 0.996184i | \(0.527818\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.945200 | + | 2.06970i | 0.0931334 | + | 0.203934i | 0.950466 | − | 0.310830i | \(-0.100607\pi\) |
−0.857332 | + | 0.514764i | \(0.827880\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.173949 | + | 1.20985i | 0.0169757 | + | 0.118069i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.1337 | − | 3.56279i | 1.17301 | − | 0.344428i | 0.363536 | − | 0.931580i | \(-0.381569\pi\) |
0.809476 | + | 0.587153i | \(0.199751\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.145524 | − | 0.167943i | 0.0139387 | − | 0.0160861i | −0.748737 | − | 0.662867i | \(-0.769340\pi\) |
0.762676 | + | 0.646781i | \(0.223885\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.74051 | + | 4.31678i | 0.355034 | + | 0.409731i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.84385 | − | 4.03747i | 0.173455 | − | 0.379813i | −0.802860 | − | 0.596167i | \(-0.796689\pi\) |
0.976315 | + | 0.216355i | \(0.0694167\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.808699 | − | 1.71433i | 0.0754116 | − | 0.159862i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.920324 | + | 2.01523i | −0.0850840 | + | 0.186308i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.51109 | + | 8.66826i | 0.688541 | + | 0.794618i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.65626 | − | 3.06549i | 0.241479 | − | 0.278681i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.69756 | − | 0.792075i | 0.243231 | − | 0.0714190i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.553697 | − | 3.85105i | −0.0495241 | − | 0.344448i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.38374 | − | 7.40936i | −0.300258 | − | 0.657474i | 0.698023 | − | 0.716075i | \(-0.254063\pi\) |
−0.998281 | + | 0.0586010i | \(0.981336\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.29123 | − | 2.11514i | −0.289776 | − | 0.186228i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.51207 | + | 17.4719i | −0.219481 | + | 1.52652i | 0.520480 | + | 0.853874i | \(0.325753\pi\) |
−0.739961 | + | 0.672650i | \(0.765156\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.3192 | + | 11.7731i | −1.58848 | + | 1.02085i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.379229 | + | 0.111352i | 0.0326388 | + | 0.00958362i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.3712 | −1.14238 | −0.571191 | − | 0.820817i | \(-0.693518\pi\) | ||||
−0.571191 | + | 0.820817i | \(0.693518\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 23.4118 | 1.98576 | 0.992881 | − | 0.119108i | \(-0.0380034\pi\) | ||||
0.992881 | + | 0.119108i | \(0.0380034\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.20205 | + | 1.23383i | 0.353876 | + | 0.103907i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.91115 | + | 3.15620i | −0.410691 | + | 0.263935i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.375419 | + | 2.61110i | −0.0311769 | + | 0.216840i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.15673 | + | 1.38605i | 0.177884 | + | 0.114319i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.60048 | + | 21.0221i | 0.786502 | + | 1.72220i | 0.686404 | + | 0.727221i | \(0.259188\pi\) |
0.100098 | + | 0.994978i | \(0.468084\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.80811 | − | 19.5308i | −0.228520 | − | 1.58939i | −0.704348 | − | 0.709855i | \(-0.748760\pi\) |
0.475827 | − | 0.879539i | \(-0.342149\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.55863 | − | 1.04491i | 0.287698 | − | 0.0844758i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.599053 | − | 0.691345i | 0.0481171 | − | 0.0555301i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.08803 | + | 3.56377i | 0.246451 | + | 0.284420i | 0.865475 | − | 0.500953i | \(-0.167017\pi\) |
−0.619023 | + | 0.785372i | \(0.712471\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.27306 | + | 11.5464i | −0.418181 | + | 0.915689i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.99367 | − | 13.5662i | −0.472367 | − | 1.06917i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.18435 | − | 6.97275i | 0.249417 | − | 0.546148i | −0.742967 | − | 0.669328i | \(-0.766582\pi\) |
0.992384 | + | 0.123180i | \(0.0393093\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.682034 | + | 0.787110i | 0.0530963 | + | 0.0612764i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.4153 | + | 15.4821i | −1.03811 | + | 1.19804i | −0.0582568 | + | 0.998302i | \(0.518554\pi\) |
−0.979850 | + | 0.199737i | \(0.935991\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.76408 | − | 2.27974i | 0.597237 | − | 0.175365i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00211 | + | 6.96986i | 0.0766336 | + | 0.532998i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.46235 | + | 14.1506i | 0.491323 | + | 1.07585i | 0.979193 | + | 0.202931i | \(0.0650468\pi\) |
−0.487870 | + | 0.872916i | \(0.662226\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.6016 | − | 8.09855i | −0.952590 | − | 0.612193i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.40772 | + | 9.79088i | −0.105810 | + | 0.735927i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.2018 | − | 7.84161i | 0.912004 | − | 0.586110i | 0.00167699 | − | 0.999999i | \(-0.499466\pi\) |
0.910327 | + | 0.413889i | \(0.135830\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.91748 | − | 1.44390i | −0.365513 | − | 0.107324i | 0.0938180 | − | 0.995589i | \(-0.470093\pi\) |
−0.459331 | + | 0.888265i | \(0.651911\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.63370 | −0.490378 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.25757 | 0.165980 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.37736 | + | 2.75344i | 0.685740 | + | 0.201352i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.60160 | − | 1.67195i | 0.189238 | − | 0.121616i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.24708 | − | 8.67363i | 0.0902355 | − | 0.627602i | −0.893645 | − | 0.448775i | \(-0.851861\pi\) |
0.983881 | − | 0.178827i | \(-0.0572303\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.40555 | + | 4.11659i | 0.461081 | + | 0.296319i | 0.750484 | − | 0.660888i | \(-0.229820\pi\) |
−0.289403 | + | 0.957207i | \(0.593457\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.363748 | + | 0.796496i | 0.0260485 | + | 0.0570383i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.03344 | − | 21.0981i | −0.216124 | − | 1.50318i | −0.752160 | − | 0.658980i | \(-0.770988\pi\) |
0.536036 | − | 0.844195i | \(-0.319921\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.3686 | − | 7.15526i | 1.72744 | − | 0.507223i | 0.741025 | − | 0.671478i | \(-0.234340\pi\) |
0.986418 | + | 0.164255i | \(0.0525220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.882362 | + | 1.01830i | −0.0622370 | + | 0.0718254i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.5167 | + | 15.5990i | 0.948683 | + | 1.09484i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.461605 | − | 1.01077i | 0.0322399 | − | 0.0705956i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.79546 | − | 0.0593580i | −0.333308 | − | 0.00412567i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.70809 | + | 16.8784i | −0.533180 | + | 1.16750i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.8102 | − | 14.7838i | −0.881891 | − | 1.01776i | −0.999694 | − | 0.0247197i | \(-0.992131\pi\) |
0.117803 | − | 0.993037i | \(-0.462415\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.12815 | − | 5.91821i | 0.351375 | − | 0.405509i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.48365 | + | 0.435640i | −0.101184 | + | 0.0297104i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.01864 | − | 7.08479i | −0.0691498 | − | 0.480947i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.64069 | − | 5.78231i | −0.178442 | − | 0.390733i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.91236 | + | 4.44230i | 0.464976 | + | 0.298822i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00285 | + | 6.97494i | −0.0671555 | + | 0.467077i | 0.928299 | + | 0.371835i | \(0.121271\pi\) |
−0.995454 | + | 0.0952414i | \(0.969638\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.07485 | + | 2.61875i | −0.271657 | + | 0.174583i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.6593 | − | 6.65336i | −1.50395 | − | 0.441599i | −0.576986 | − | 0.816754i | \(-0.695771\pi\) |
−0.926962 | + | 0.375156i | \(0.877589\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.5083 | −1.61956 | −0.809778 | − | 0.586736i | \(-0.800412\pi\) | ||||
−0.809778 | + | 0.586736i | \(0.800412\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.14913 | 0.536173 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.683723 | + | 0.200759i | 0.0447922 | + | 0.0131522i | 0.304052 | − | 0.952655i | \(-0.401660\pi\) |
−0.259260 | + | 0.965808i | \(0.583479\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.45615 | − | 0.935810i | 0.0949886 | − | 0.0610455i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.05877 | + | 7.36392i | −0.0687746 | + | 0.478338i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.28510 | − | 0.825882i | −0.0831261 | − | 0.0534219i | 0.498418 | − | 0.866937i | \(-0.333915\pi\) |
−0.581544 | + | 0.813515i | \(0.697551\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.3499 | − | 24.8528i | −0.731111 | − | 1.60091i | −0.797647 | − | 0.603125i | \(-0.793922\pi\) |
0.0665361 | − | 0.997784i | \(-0.478805\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.142315 | − | 0.989821i | −0.00912950 | − | 0.0634971i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.972235 | − | 0.285474i | 0.0621138 | − | 0.0182383i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.2158 | + | 11.7897i | −0.650019 | + | 0.750162i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.451473 | + | 0.521028i | 0.0286109 | + | 0.0330188i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.87995 | − | 21.6341i | 0.623617 | − | 1.36553i | −0.289243 | − | 0.957256i | \(-0.593403\pi\) |
0.912859 | − | 0.408274i | \(-0.133869\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.5460 | − | 6.96342i | −0.663020 | − | 0.437786i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.608951 | − | 1.33342i | 0.0381340 | − | 0.0835019i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.4861 | + | 12.1017i | 0.654108 | + | 0.754880i | 0.981803 | − | 0.189903i | \(-0.0608174\pi\) |
−0.327695 | + | 0.944783i | \(0.606272\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.5676 | − | 13.3498i | 0.718778 | − | 0.829514i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.40396 | − | 1.88037i | 0.396395 | − | 0.116392i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.96549 | − | 27.5806i | −0.244522 | − | 1.70069i | −0.628877 | − | 0.777505i | \(-0.716485\pi\) |
0.384354 | − | 0.923186i | \(-0.374424\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.08412 | + | 4.56358i | 0.128026 | + | 0.280339i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.18269 | − | 3.33071i | −0.317175 | − | 0.203836i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.678639 | − | 4.72004i | 0.0413774 | − | 0.287786i | −0.958618 | − | 0.284696i | \(-0.908107\pi\) |
0.999995 | − | 0.00308994i | \(-0.000983561\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.5864 | + | 6.80348i | −0.643080 | + | 0.413282i | −0.821132 | − | 0.570739i | \(-0.806657\pi\) |
0.178052 | + | 0.984021i | \(0.443020\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.57376 | + | 1.93023i | 0.397862 | + | 0.116823i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.7639 | −0.769691 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.2855 | −1.15875 | −0.579376 | − | 0.815060i | \(-0.696704\pi\) | ||||
−0.579376 | + | 0.815060i | \(0.696704\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.22075 | − | 0.652070i | −0.132953 | − | 0.0390384i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.56835 | − | 1.65058i | 0.153215 | − | 0.0984653i | −0.461787 | − | 0.886991i | \(-0.652792\pi\) |
0.615002 | + | 0.788526i | \(0.289155\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.33156 | − | 30.1266i | 0.257484 | − | 1.79084i | −0.293119 | − | 0.956076i | \(-0.594693\pi\) |
0.550603 | − | 0.834767i | \(-0.314398\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.34128 | + | 1.50465i | 0.138685 | + | 0.0891277i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.61181 | − | 7.90876i | −0.213198 | − | 0.466839i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.461716 | + | 3.21131i | 0.0271598 | + | 0.188900i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.58669 | − | 1.64040i | 0.327498 | − | 0.0961620i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.30169 | − | 6.11848i | 0.309728 | − | 0.357445i | −0.579449 | − | 0.815009i | \(-0.696732\pi\) |
0.889177 | + | 0.457563i | \(0.151278\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.56020 | + | 2.95462i | 0.149060 | + | 0.172025i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.09466 | − | 2.39697i | 0.0635187 | − | 0.139087i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.85787 | − | 8.11522i | −0.396601 | − | 0.469315i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.02605 | + | 11.0055i | −0.289697 | + | 0.634347i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.12257 | − | 7.06582i | −0.351732 | − | 0.405921i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.71698 | + | 1.98150i | −0.0983139 | + | 0.113460i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.75969 | − | 2.27845i | 0.442869 | − | 0.130038i | −0.0526927 | − | 0.998611i | \(-0.516780\pi\) |
0.495562 | + | 0.868573i | \(0.334962\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.323811 | − | 2.25216i | −0.0184210 | − | 0.128121i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.338709 | − | 0.741670i | −0.0192064 | − | 0.0420562i | 0.899786 | − | 0.436332i | \(-0.143723\pi\) |
−0.918992 | + | 0.394276i | \(0.870995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.3434 | + | 15.6445i | 1.37597 | + | 0.884281i | 0.999118 | − | 0.0419935i | \(-0.0133709\pi\) |
0.376850 | + | 0.926274i | \(0.377007\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.173949 | − | 1.20985i | 0.00980094 | − | 0.0681671i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.1679 | + | 18.7451i | −1.63823 | + | 1.05283i | −0.695903 | + | 0.718135i | \(0.744996\pi\) |
−0.942328 | + | 0.334692i | \(0.891368\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.8751 | + | 4.95498i | 0.944824 | + | 0.277425i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.6460 | −0.705830 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.1161 | 1.45314 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.2964 | − | 3.02330i | −0.571141 | − | 0.167702i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.186944 | + | 0.120142i | −0.0103380 | + | 0.00664386i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.92745 | − | 13.4057i | 0.106264 | − | 0.739080i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.7815 | + | 7.57152i | 0.647570 | + | 0.416168i | 0.822778 | − | 0.568363i | \(-0.192423\pi\) |
−0.175207 | + | 0.984532i | \(0.556060\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.37282 | − | 5.19575i | −0.130030 | − | 0.284725i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.0757893 | + | 0.527126i | 0.00414081 | + | 0.0288000i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.2111 | − | 3.29189i | 0.610710 | − | 0.179321i | 0.0382703 | − | 0.999267i | \(-0.487815\pi\) |
0.572440 | + | 0.819947i | \(0.305997\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.90665 | + | 3.35445i | −0.157867 | + | 0.182189i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.99396 | − | 4.60928i | −0.216285 | − | 0.249606i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.69921 | + | 12.4795i | −0.307729 | + | 0.673832i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.25892 | + | 1.41705i | −0.0677781 | + | 0.0762914i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.7515 | + | 27.9220i | −0.684538 | + | 1.49893i | 0.173223 | + | 0.984883i | \(0.444582\pi\) |
−0.857762 | + | 0.514048i | \(0.828145\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.4824 | + | 21.3299i | 0.989342 | + | 1.14176i | 0.989901 | + | 0.141762i | \(0.0452768\pi\) |
−0.000558286 | 1.00000i | \(0.500178\pi\) | ||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.45080 | − | 1.67431i | 0.0774380 | − | 0.0893682i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.1718 | + | 4.45484i | −0.807514 | + | 0.237107i | −0.659331 | − | 0.751853i | \(-0.729161\pi\) |
−0.148183 | + | 0.988960i | \(0.547342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.440476 | − | 3.06358i | −0.0233780 | − | 0.162598i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.76471 | − | 10.4333i | −0.252175 | − | 0.552187i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.567977 | + | 0.365017i | 0.0299767 | + | 0.0192648i | 0.555543 | − | 0.831488i | \(-0.312510\pi\) |
−0.525567 | + | 0.850752i | \(0.676147\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.35243 | + | 30.2718i | −0.229075 | + | 1.59325i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.41232 | + | 2.19296i | −0.179100 | + | 0.115101i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.41067 | − | 0.707836i | −0.126180 | − | 0.0370498i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.9235 | −0.778998 | −0.389499 | − | 0.921027i | \(-0.627352\pi\) | ||||
−0.389499 | + | 0.921027i | \(0.627352\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.81144 | −0.146358 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 37.6648 | + | 11.0594i | 1.95546 | + | 0.574175i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.57634 | − | 3.58369i | 0.288732 | − | 0.185557i | −0.388255 | − | 0.921552i | \(-0.626922\pi\) |
0.676986 | + | 0.735995i | \(0.263286\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.553697 | + | 3.85105i | −0.0285928 | + | 0.198867i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.4392 | + | 7.99418i | 0.640651 | + | 0.411721i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.67512 | + | 3.66799i | 0.0860449 | + | 0.188412i | 0.947763 | − | 0.318975i | \(-0.103339\pi\) |
−0.861718 | + | 0.507387i | \(0.830611\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.15922 | + | 8.06254i | 0.0593885 | + | 0.413056i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.86688 | + | 2.60355i | −0.453076 | + | 0.133035i | −0.500306 | − | 0.865849i | \(-0.666779\pi\) |
0.0472294 | + | 0.998884i | \(0.484961\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.10921 | − | 2.43416i | 0.107495 | − | 0.124056i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.56201 | + | 2.95671i | 0.130234 | + | 0.150298i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.71406 | − | 14.7017i | 0.340416 | − | 0.745407i | −0.659564 | − | 0.751648i | \(-0.729259\pi\) |
0.999981 | + | 0.00624068i | \(0.00198648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.74908 | + | 17.5734i | −0.139027 | + | 0.888723i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.33271 | − | 16.0564i | 0.369886 | − | 0.809938i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.92558 | + | 2.22223i | 0.0968862 | + | 0.111813i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.206863 | − | 0.238733i | 0.0103822 | − | 0.0119817i | −0.750535 | − | 0.660831i | \(-0.770204\pi\) |
0.760917 | + | 0.648849i | \(0.224749\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.8940 | − | 6.13504i | 1.04601 | − | 0.307136i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.204711 | + | 1.42380i | 0.0102228 | + | 0.0711011i | 0.994294 | − | 0.106672i | \(-0.0340196\pi\) |
−0.984071 | + | 0.177774i | \(0.943111\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.13009 | − | 4.66424i | −0.106107 | − | 0.232343i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.332496 | − | 0.213682i | −0.0165219 | − | 0.0106180i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.14205 | − | 14.8983i | 0.106178 | − | 0.738482i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.86910 | + | 1.20120i | −0.0924211 | + | 0.0593954i | −0.586035 | − | 0.810286i | \(-0.699312\pi\) |
0.493614 | + | 0.869681i | \(0.335676\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.8296 | + | 3.76711i | 0.632838 | + | 0.185818i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.5899 | 1.50523 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.272485 | 0.0133758 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.4635 | − | 6.59587i | −1.10004 | − | 0.323001i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.96288 | + | 5.76010i | −0.437866 | + | 0.281399i | −0.740944 | − | 0.671566i | \(-0.765622\pi\) |
0.303079 | + | 0.952965i | \(0.401985\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.54761 | + | 17.7190i | −0.124163 | + | 0.863572i | 0.828596 | + | 0.559846i | \(0.189140\pi\) |
−0.952759 | + | 0.303726i | \(0.901769\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.68422 | − | 2.36771i | −0.179133 | − | 0.115122i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.46291 | + | 16.3415i | 0.362004 | + | 0.792679i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.91957 | + | 20.3061i | 0.141288 | + | 0.982681i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.60142 | − | 1.64473i | 0.270439 | − | 0.0794081i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.11016 | + | 1.28119i | −0.0534744 | + | 0.0617128i | −0.781857 | − | 0.623458i | \(-0.785727\pi\) |
0.728382 | + | 0.685171i | \(0.240273\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.1428 | + | 23.2460i | 0.968001 | + | 1.11713i | 0.993079 | + | 0.117447i | \(0.0374709\pi\) |
−0.0250786 | + | 0.999685i | \(0.507984\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.09584 | − | 2.39956i | 0.0525417 | − | 0.115050i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −32.2818 | − | 9.91442i | −1.54425 | − | 0.474271i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.6426 | + | 25.4938i | −0.555672 | + | 1.21675i | 0.398411 | + | 0.917207i | \(0.369562\pi\) |
−0.954082 | + | 0.299544i | \(0.903165\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.67888 | − | 1.93753i | −0.0799465 | − | 0.0922632i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.96931 | + | 6.88895i | −0.283611 | + | 0.327304i | −0.879623 | − | 0.475671i | \(-0.842205\pi\) |
0.596013 | + | 0.802975i | \(0.296751\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.33630 | + | 0.686001i | −0.110751 | + | 0.0325196i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.28898 | − | 22.8753i | −0.155563 | − | 1.08197i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.2833 | − | 35.6554i | −0.768456 | − | 1.68268i | −0.730024 | − | 0.683422i | \(-0.760491\pi\) |
−0.0384319 | − | 0.999261i | \(-0.512236\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.23238 | − | 4.00531i | −0.293471 | − | 0.188602i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.80811 | + | 19.5308i | −0.131936 | + | 0.917637i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.27802 | − | 1.46400i | 0.106795 | − | 0.0686333i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.8827 | + | 8.77435i | 1.39785 | + | 0.410447i | 0.891946 | − | 0.452141i | \(-0.149340\pi\) |
0.505907 | + | 0.862588i | \(0.331158\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.70886 | −0.173115 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.9022 | 0.926939 | 0.463469 | − | 0.886113i | \(-0.346604\pi\) | ||||
0.463469 | + | 0.886113i | \(0.346604\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.03576 | + | 0.597752i | 0.0946097 | + | 0.0277799i | 0.328695 | − | 0.944436i | \(-0.393391\pi\) |
−0.234085 | + | 0.972216i | \(0.575209\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.769562 | + | 0.494567i | −0.0356876 | + | 0.0229350i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.25711 | − | 29.6089i | 0.196996 | − | 1.37013i | −0.615946 | − | 0.787789i | \(-0.711226\pi\) |
0.812941 | − | 0.582346i | \(-0.197865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.50541 | + | 2.25279i | 0.161865 | + | 0.104024i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.95891 | − | 4.28941i | −0.0902617 | − | 0.197646i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.46717 | + | 10.2044i | 0.0674603 | + | 0.469197i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −32.7261 | + | 9.60924i | −1.50157 | + | 0.440902i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.31246 | − | 9.59309i | 0.380601 | − | 0.439238i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.4583 | + | 23.6101i | 0.934764 | + | 1.07877i | 0.996739 | + | 0.0806972i | \(0.0257147\pi\) |
−0.0619749 | + | 0.998078i | \(0.519740\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.25682 | − | 11.5108i | 0.239690 | − | 0.524848i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.92885 | + | 14.7053i | 0.0877655 | + | 0.669113i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.955993 | − | 2.09333i | 0.0434094 | − | 0.0950533i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.50158 | + | 1.73291i | 0.0680429 | + | 0.0785257i | 0.788750 | − | 0.614714i | \(-0.210728\pi\) |
−0.720708 | + | 0.693239i | \(0.756183\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.01981 | + | 5.79317i | −0.227004 | + | 0.261976i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.7180 | + | 9.01961i | −1.38628 | + | 0.407049i | −0.887951 | − | 0.459938i | \(-0.847872\pi\) |
−0.498331 | + | 0.866987i | \(0.666053\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.52288 | − | 24.5022i | −0.158663 | − | 1.10352i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.432653 | − | 0.947378i | −0.0194463 | − | 0.0425815i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.3729 | − | 13.0929i | −0.913848 | − | 0.587295i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.53308 | + | 31.5283i | −0.202929 | + | 1.41140i | 0.592607 | + | 0.805492i | \(0.298099\pi\) |
−0.795535 | + | 0.605907i | \(0.792810\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.2337 | − | 11.0754i | 0.769944 | − | 0.494813i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.5336 | − | 6.32282i | −0.960134 | − | 0.281921i | −0.236134 | − | 0.971721i | \(-0.575880\pi\) |
−0.724000 | + | 0.689800i | \(0.757699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.69526 | −0.164437 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.09186 | −0.359372 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.2921 | + | 4.78378i | 0.722133 | + | 0.212037i | 0.622090 | − | 0.782946i | \(-0.286284\pi\) |
0.100043 | + | 0.994983i | \(0.468102\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.5377 | + | 10.6282i | −0.731586 | + | 0.470162i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00211 | − | 6.96986i | 0.0442444 | − | 0.307727i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.756534 | − | 0.486195i | −0.0333369 | − | 0.0214243i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.79401 | − | 10.4974i | −0.210840 | − | 0.461676i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.21390 | − | 15.3980i | −0.0971795 | − | 0.675898i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.8096 | − | 3.76125i | 0.561200 | − | 0.164783i | 0.0111844 | − | 0.999937i | \(-0.496440\pi\) |
0.550016 | + | 0.835154i | \(0.314622\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.27548 | + | 4.93417i | −0.186954 | + | 0.215756i | −0.841487 | − | 0.540277i | \(-0.818320\pi\) |
0.654534 | + | 0.756033i | \(0.272865\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.80951 | + | 11.3208i | 0.428122 | + | 0.494079i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.56599 | + | 7.80843i | −0.155337 | + | 0.340140i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.0695 | − | 20.6786i | 0.437803 | − | 0.899071i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.10910 | − | 8.99768i | 0.178320 | − | 0.390466i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.07884 | − | 4.70723i | −0.176674 | − | 0.203893i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.27311 | + | 3.77738i | −0.141509 | + | 0.163310i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.9168 | + | 4.08633i | −0.600553 | + | 0.176338i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.961430 | − | 6.68689i | −0.0414117 | − | 0.288025i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.25561 | − | 20.2670i | −0.397930 | − | 0.871345i | −0.997476 | − | 0.0710046i | \(-0.977379\pi\) |
0.599546 | − | 0.800340i | \(-0.295348\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.31149 | + | 2.77083i | 0.185024 | + | 0.118908i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.0124996 | + | 0.0869364i | −0.000535423 | + | 0.00372395i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.96660 | − | 2.54918i | 0.169600 | − | 0.108995i | −0.453087 | − | 0.891466i | \(-0.649677\pi\) |
0.622687 | + | 0.782471i | \(0.286041\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.36499 | + | 1.86893i | 0.271651 | + | 0.0797640i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 46.9974 | 2.00216 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.0073 | 0.978369 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.16613 | − | 0.636032i | −0.0919469 | − | 0.0269980i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.4469 | − | 8.64180i | 0.569764 | − | 0.366165i | −0.223816 | − | 0.974631i | \(-0.571851\pi\) |
0.793580 | + | 0.608467i | \(0.208215\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.23350 | + | 8.57919i | −0.0521716 | + | 0.362861i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.22177 | − | 5.28381i | −0.347124 | − | 0.223083i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.59556 | − | 5.68349i | −0.109390 | − | 0.239531i | 0.847018 | − | 0.531564i | \(-0.178395\pi\) |
−0.956408 | + | 0.292033i | \(0.905668\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.249662 | + | 1.73644i | 0.0105034 | + | 0.0730526i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.96726 | + | 0.871265i | −0.124613 | + | 0.0365897i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.55803 | − | 9.87649i | 0.358771 | − | 0.414044i | −0.547456 | − | 0.836834i | \(-0.684404\pi\) |
0.906228 | + | 0.422790i | \(0.138949\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.06617 | + | 4.69261i | 0.170164 | + | 0.196380i | 0.834426 | − | 0.551120i | \(-0.185799\pi\) |
−0.664262 | + | 0.747500i | \(0.731254\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.64021 | + | 7.97094i | −0.152072 | + | 0.332991i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.02113 | − | 23.0327i | −0.125990 | − | 0.960530i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.8091 | − | 41.1861i | 0.783031 | − | 1.71460i | 0.0874304 | − | 0.996171i | \(-0.472134\pi\) |
0.695601 | − | 0.718429i | \(-0.255138\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.98630 | − | 5.75449i | −0.207223 | − | 0.239149i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.39619 | − | 1.61129i | 0.0579238 | − | 0.0668477i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.0937 | − | 9.42357i | 1.32919 | − | 0.390284i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.124614 | − | 0.866712i | −0.00515217 | − | 0.0358341i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.87091 | + | 15.0452i | 0.283593 | + | 0.620982i | 0.996797 | − | 0.0799747i | \(-0.0254840\pi\) |
−0.713204 | + | 0.700957i | \(0.752757\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.7104 | − | 8.81115i | −0.564928 | − | 0.363057i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.03344 | + | 21.0981i | −0.124779 | + | 0.867859i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.4481 | + | 18.2825i | −1.16822 | + | 0.750772i | −0.973185 | − | 0.230023i | \(-0.926120\pi\) |
−0.195039 | + | 0.980795i | \(0.562483\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.34966 | − | 1.27718i | −0.178319 | − | 0.0523591i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25.3973 | −1.03944 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.1009 | −1.14817 | −0.574085 | − | 0.818796i | \(-0.694642\pi\) | ||||
−0.574085 | + | 0.818796i | \(0.694642\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.6957 | − | 7.25132i | −1.00736 | − | 0.295788i | −0.263887 | − | 0.964554i | \(-0.585005\pi\) |
−0.743473 | + | 0.668766i | \(0.766823\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.13351 | − | 0.728462i | 0.0461600 | − | 0.0296653i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.228156 | + | 1.58686i | −0.00927586 | + | 0.0645151i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.02454 | + | 4.51439i | 0.285117 | + | 0.183234i | 0.675380 | − | 0.737470i | \(-0.263980\pi\) |
−0.390263 | + | 0.920703i | \(0.627616\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.57437 | − | 18.7753i | −0.347451 | − | 0.760812i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.38079 | − | 9.60361i | −0.0558608 | − | 0.388520i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.17393 | + | 0.638325i | −0.0878044 | + | 0.0257817i | −0.325340 | − | 0.945597i | \(-0.605479\pi\) |
0.237535 | + | 0.971379i | \(0.423660\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.727675 | + | 0.839782i | −0.0293427 | + | 0.0338633i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.7560 | − | 32.0322i | −1.11742 | − | 1.28957i | −0.952931 | − | 0.303186i | \(-0.901950\pi\) |
−0.164484 | − | 0.986380i | \(-0.552596\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.39428 | + | 3.05306i | −0.0560410 | + | 0.122713i | −0.935581 | − | 0.353113i | \(-0.885123\pi\) |
0.879540 | + | 0.475825i | \(0.157851\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.58449 | + | 1.40799i | 0.183969 | + | 0.0565008i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.91450 | + | 17.3303i | −0.317088 | + | 0.694326i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.8530 | − | 17.1413i | −0.594121 | − | 0.685652i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.1510 | − | 14.0231i | 0.485266 | − | 0.560027i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.3266 | + | 5.96843i | −0.810475 | + | 0.237977i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.265066 | − | 1.84358i | −0.0105521 | − | 0.0733916i | 0.983865 | − | 0.178913i | \(-0.0572580\pi\) |
−0.994417 | + | 0.105521i | \(0.966349\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.12624 | + | 17.7940i | 0.322989 | + | 0.707247i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.70833 | + | 1.74054i | 0.107477 | + | 0.0690711i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.808311 | − | 5.62193i | 0.0320265 | − | 0.222749i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.58778 | + | 4.23371i | −0.260608 | + | 0.167483i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.9732 | − | 12.6181i | −1.69734 | − | 0.498384i | −0.717229 | − | 0.696837i | \(-0.754590\pi\) |
−0.980110 | + | 0.198454i | \(0.936408\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.1652 | −1.22904 | −0.614518 | − | 0.788903i | \(-0.710650\pi\) | ||||
−0.614518 | + | 0.788903i | \(0.710650\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.54629 | 0.0608851 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.7754 | + | 6.68747i | 0.895394 | + | 0.262911i | 0.696881 | − | 0.717187i | \(-0.254571\pi\) |
0.198513 | + | 0.980098i | \(0.436389\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.9275 | − | 14.0920i | 0.860730 | − | 0.553158i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.01864 | + | 7.08479i | −0.0399236 | + | 0.277675i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.4780 | + | 17.0164i | 1.03616 | + | 0.665902i | 0.944035 | − | 0.329846i | \(-0.106997\pi\) |
0.0921282 | + | 0.995747i | \(0.470633\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.89817 | − | 6.34611i | −0.113241 | − | 0.247963i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.904661 | + | 6.29206i | 0.0352942 | + | 0.245477i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.87364 | + | 2.31191i | −0.306714 | + | 0.0900592i | −0.431468 | − | 0.902128i | \(-0.642004\pi\) |
0.124754 | + | 0.992188i | \(0.460186\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.5124 | − | 14.4401i | 0.486677 | − | 0.561656i | −0.458297 | − | 0.888799i | \(-0.651541\pi\) |
0.944975 | + | 0.327143i | \(0.106086\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.38082 | − | 6.20980i | −0.208974 | − | 0.241168i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.57538 | − | 7.82899i | 0.138647 | − | 0.303595i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.94713 | + | 31.6243i | −0.191554 | + | 1.22450i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.92729 | − | 6.40987i | 0.113176 | − | 0.247820i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.4473 | + | 13.2109i | 0.441918 | + | 0.510000i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.6217 | − | 26.1068i | 0.872003 | − | 1.00634i | −0.127891 | − | 0.991788i | \(-0.540821\pi\) |
0.999894 | − | 0.0145567i | \(-0.00463371\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.64758 | − | 1.36465i | 0.178885 | − | 0.0525255i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.808364 | − | 5.62230i | −0.0310680 | − | 0.216082i | 0.968373 | − | 0.249506i | \(-0.0802681\pi\) |
−0.999441 | + | 0.0334233i | \(0.989359\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.48011 | − | 16.3792i | −0.287060 | − | 0.628575i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.8669 | + | 12.7677i | 0.761302 | + | 0.489259i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.17313 | − | 42.9350i | 0.236208 | − | 1.64286i | −0.434161 | − | 0.900835i | \(-0.642955\pi\) |
0.670369 | − | 0.742028i | \(-0.266136\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.44588 | − | 2.85720i | 0.169869 | − | 0.109168i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.5156 | + | 6.90479i | 0.897175 | + | 0.263434i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.1215 | 1.07135 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.6785 | −1.12902 | −0.564511 | − | 0.825425i | \(-0.690935\pi\) | ||||
−0.564511 | + | 0.825425i | \(0.690935\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.81903 | − | 2.29587i | −0.297020 | − | 0.0872131i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.78433 | + | 5.00269i | −0.295276 | + | 0.189763i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.48395 | + | 10.3211i | −0.0562087 | + | 0.390940i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.599467 | − | 0.385254i | −0.0226739 | − | 0.0145716i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.63854 | + | 21.1055i | 0.364043 | + | 0.797142i | 0.999684 | + | 0.0251573i | \(0.00800866\pi\) |
−0.635641 | + | 0.771985i | \(0.719264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.72400 | − | 39.8113i | −0.215885 | − | 1.50151i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.66081 | + | 0.487658i | −0.0625498 | + | 0.0183663i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.9342 | + | 21.8512i | −0.712094 | + | 0.821800i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.3462 | − | 31.5591i | −1.02701 | − | 1.18523i | −0.982508 | − | 0.186219i | \(-0.940377\pi\) |
−0.0444980 | − | 0.999009i | \(-0.514169\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.09054 | − | 6.76734i | 0.115904 | − | 0.253795i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.37219 | − | 8.29817i | 0.276091 | − | 0.310769i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.958513 | − | 2.09885i | 0.0358464 | − | 0.0784926i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.00036 | + | 1.15448i | 0.0373593 | + | 0.0431149i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.9557 | + | 20.7220i | −0.669635 | + | 0.772800i | −0.984319 | − | 0.176396i | \(-0.943556\pi\) |
0.314684 | + | 0.949196i | \(0.398101\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.75145 | + | 1.98240i | −0.251437 | + | 0.0738286i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.88830 | + | 27.0437i | 0.144607 | + | 1.00577i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.4299 | + | 29.4075i | 0.498775 | + | 1.09217i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.3465 | + | 12.4333i | 0.717523 | + | 0.461124i | 0.847774 | − | 0.530357i | \(-0.177942\pi\) |
−0.130252 | + | 0.991481i | \(0.541578\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.142315 | + | 0.989821i | −0.00527092 | + | 0.0366601i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.2067 | − | 7.84478i | 0.451482 | − | 0.290150i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.58286 | + | 2.52016i | 0.317015 | + | 0.0930841i | 0.436369 | − | 0.899768i | \(-0.356264\pi\) |
−0.119354 | + | 0.992852i | \(0.538082\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.01328 | −0.0373754 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.55055 | 0.130786 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.20386 | − | 1.82162i | −0.228213 | − | 0.0670093i | 0.165627 | − | 0.986188i | \(-0.447035\pi\) |
−0.393840 | + | 0.919179i | \(0.628853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.1236 | − | 8.43401i | 0.482107 | − | 0.309831i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.68094 | − | 39.5118i | 0.208414 | − | 1.44955i | −0.569921 | − | 0.821699i | \(-0.693026\pi\) |
0.778335 | − | 0.627849i | \(-0.216065\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.68417 | − | 4.93832i | −0.281526 | − | 0.180926i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.286395 | − | 0.627117i | −0.0104786 | − | 0.0229450i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.56565 | + | 38.7100i | 0.203365 | + | 1.41443i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.95344 | + | 0.573581i | −0.0712819 | + | 0.0209303i | −0.317179 | − | 0.948366i | \(-0.602736\pi\) |
0.245897 | + | 0.969296i | \(0.420917\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.5748 | + | 17.9742i | −0.567576 | + | 0.655017i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.10707 | + | 5.89387i | 0.185865 | + | 0.214500i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.37358 | + | 5.19741i | −0.0862692 | + | 0.188903i | −0.947850 | − | 0.318718i | \(-0.896748\pi\) |
0.861580 | + | 0.507621i | \(0.169475\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.15697 | + | 9.65249i | 0.296079 | + | 0.350363i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.9068 | + | 30.4517i | −0.504122 | + | 1.10387i | 0.470986 | + | 0.882141i | \(0.343898\pi\) |
−0.975108 | + | 0.221732i | \(0.928829\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.450036 | + | 0.519370i | 0.0162924 | + | 0.0188024i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.959952 | + | 1.10784i | −0.0347071 | + | 0.0400542i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.0264 | − | 6.17391i | 0.759219 | − | 0.222927i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.10383 | + | 21.5876i | 0.111927 | + | 0.778470i | 0.966042 | + | 0.258386i | \(0.0831905\pi\) |
−0.854115 | + | 0.520085i | \(0.825900\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.65195 | − | 14.5657i | −0.239564 | − | 0.524572i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.3238 | + | 10.4907i | 0.587127 | + | 0.377324i | 0.800219 | − | 0.599709i | \(-0.204717\pi\) |
−0.213091 | + | 0.977032i | \(0.568353\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.59548 | − | 11.0968i | 0.0573114 | − | 0.398610i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.8601 | + | 9.55002i | −0.533104 | + | 0.342605i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.9949 | − | 5.57742i | −0.680564 | − | 0.199832i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.6353 | −0.738388 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.67432 | −0.238521 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.78827 | − | 0.525084i | −0.0638261 | − | 0.0187410i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.19114 | − | 1.40816i | 0.0781055 | − | 0.0501954i | −0.501005 | − | 0.865444i | \(-0.667036\pi\) |
0.579111 | + | 0.815249i | \(0.303400\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.96549 | + | 27.5806i | −0.141175 | + | 0.981894i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.5474 | + | 7.42105i | 0.410578 | + | 0.263862i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.10516 | + | 13.3684i | 0.216800 | + | 0.474727i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.713987 | − | 4.96589i | −0.0253225 | − | 0.176122i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.5547 | − | 3.09913i | 0.373866 | − | 0.109777i | −0.0894012 | − | 0.995996i | \(-0.528495\pi\) |
0.463267 | + | 0.886219i | \(0.346677\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.6367 | + | 12.2755i | −0.376301 | + | 0.434275i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.03438 | + | 4.65593i | 0.142548 | + | 0.164509i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.95850 | + | 15.2370i | −0.245560 | + | 0.537702i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.89172 | + | 3.22996i | 0.172411 | + | 0.113841i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.98094 | + | 4.33765i | −0.0697323 | + | 0.152693i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.4667 | + | 29.3901i | 0.895361 | + | 1.03330i | 0.999250 | + | 0.0387128i | \(0.0123257\pi\) |
−0.103889 | + | 0.994589i | \(0.533129\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.2544 | + | 21.0667i | −0.640998 | + | 0.739751i | −0.979551 | − | 0.201196i | \(-0.935517\pi\) |
0.338553 | + | 0.940947i | \(0.390063\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.0744 | − | 3.54535i | 0.423466 | − | 0.124341i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.431170 | + | 2.99885i | 0.0151032 | + | 0.105045i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.4441 | + | 25.0590i | 0.400377 | + | 0.876703i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.76367 | − | 3.70408i | −0.201399 | − | 0.129431i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.69369 | − | 18.7350i | 0.0940105 | − | 0.653857i | −0.887267 | − | 0.461257i | \(-0.847399\pi\) |
0.981277 | − | 0.192601i | \(-0.0616922\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.6887 | − | 18.4371i | 1.00003 | − | 0.642677i | 0.0652322 | − | 0.997870i | \(-0.479221\pi\) |
0.934793 | + | 0.355193i | \(0.115585\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.2469 | + | 3.59600i | 0.426381 | + | 0.125197i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.79980 | −0.236452 | −0.118226 | − | 0.992987i | \(-0.537721\pi\) | ||||
−0.118226 | + | 0.992987i | \(0.537721\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.0129 | 1.00766 | 0.503829 | − | 0.863803i | \(-0.331924\pi\) | ||||
0.503829 | + | 0.863803i | \(0.331924\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.5043 | + | 5.43335i | 0.641906 | + | 0.188481i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.99904 | + | 5.14067i | −0.277150 | + | 0.178114i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.15229 | − | 8.01434i | 0.0398766 | − | 0.277348i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.94708 | + | 1.25131i | 0.0673009 | + | 0.0432517i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.50925 | + | 9.87387i | 0.155677 | + | 0.340884i | 0.971359 | − | 0.237615i | \(-0.0763658\pi\) |
−0.815683 | + | 0.578499i | \(0.803639\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.21250 | − | 15.3883i | −0.0762930 | − | 0.530630i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.92934 | + | 0.860131i | −0.100892 | + | 0.0296245i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.09439 | + | 2.41705i | −0.0720491 | + | 0.0831491i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.21456 | + | 9.48011i | 0.282256 | + | 0.325741i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.6438 | + | 27.6860i | −0.433933 | + | 0.950180i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.3913 | + | 0.339048i | 0.938962 | + | 0.0116224i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.6788 | − | 25.5730i | 0.399874 | − | 0.875602i | −0.597409 | − | 0.801937i | \(-0.703803\pi\) |
0.997283 | − | 0.0736653i | \(-0.0234696\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.82253 | − | 2.10332i | −0.0623293 | − | 0.0719319i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.1207 | + | 32.4530i | −0.960585 | + | 1.10857i | 0.0334425 | + | 0.999441i | \(0.489353\pi\) |
−0.994027 | + | 0.109133i | \(0.965193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.5555 | − | 8.97190i | 1.04254 | − | 0.306117i | 0.284740 | − | 0.958605i | \(-0.408093\pi\) |
0.757800 | + | 0.652487i | \(0.226274\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.23735 | + | 8.60596i | 0.0421688 | + | 0.293290i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.8967 | + | 41.3781i | 0.643252 | + | 1.40853i | 0.897338 | + | 0.441344i | \(0.145498\pi\) |
−0.254086 | + | 0.967182i | \(0.581775\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.17243 | − | 3.32412i | −0.175868 | − | 0.113023i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.461716 | − | 3.21131i | 0.0156807 | − | 0.109062i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.4921 | − | 10.5988i | 0.559457 | − | 0.359541i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.86417 | + | 0.840995i | 0.0970486 | + | 0.0284960i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.82254 | −0.197063 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.0319 | 0.406753 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.8598 | + | 3.18874i | 0.366711 | + | 0.107676i | 0.459896 | − | 0.887973i | \(-0.347887\pi\) |
−0.0931853 | + | 0.995649i | \(0.529705\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.81071 | + | 4.37698i | −0.229720 | + | 0.147632i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.31790 | + | 43.9419i | −0.212855 | + | 1.48044i | 0.550702 | + | 0.834702i | \(0.314360\pi\) |
−0.763558 | + | 0.645740i | \(0.776549\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.1828 | − | 25.8239i | −1.35226 | − | 0.869045i | −0.354442 | − | 0.935078i | \(-0.615329\pi\) |
−0.997817 | + | 0.0660331i | \(0.978966\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.62408 | − | 3.55623i | −0.0545927 | − | 0.119541i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.58184 | − | 11.0020i | −0.0531131 | − | 0.369410i | −0.998992 | − | 0.0448898i | \(-0.985706\pi\) |
0.945879 | − | 0.324520i | \(-0.105203\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.1696 | − | 7.09684i | 0.810623 | − | 0.238021i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.72563 | + | 1.99148i | −0.0578106 | + | 0.0667170i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.1946 | − | 23.3058i | −0.675786 | − | 0.779899i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.38143 | + | 5.21461i | −0.0796025 | + | 0.174305i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.29376 | + | 9.71858i | 0.143364 | + | 0.324494i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.41721 | + | 14.0517i | −0.214026 | + | 0.468651i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.8298 | − | 35.5795i | −1.02709 | − | 1.18532i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.92307 | − | 9.14371i | 0.263663 | − | 0.304284i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.94358 | − | 0.570686i | 0.0646068 | − | 0.0189703i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.30586 | + | 43.8582i | 0.209383 | + | 1.45629i | 0.775178 | + | 0.631743i | \(0.217660\pi\) |
−0.565795 | + | 0.824546i | \(0.691431\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.88389 | + | 8.50454i | 0.128821 | + | 0.282078i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.3349 | − | 7.92715i | −0.408673 | − | 0.262638i | 0.320113 | − | 0.947379i | \(-0.396279\pi\) |
−0.728787 | + | 0.684741i | \(0.759915\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.258542 | − | 1.79820i | 0.00855649 | − | 0.0595117i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.20568 | − | 1.41750i | 0.0729175 | − | 0.0468613i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −52.3766 | − | 15.3792i | −1.72963 | − | 0.507865i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.2726 | 1.09756 | 0.548781 | − | 0.835966i | \(-0.315092\pi\) | ||||
0.548781 | + | 0.835966i | \(0.315092\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.08728 | −0.266485 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.6461 | − | 4.88774i | −0.547913 | − | 0.160882i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.2752 | − | 14.9581i | 0.765285 | − | 0.491819i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.323811 | + | 2.25216i | −0.0106354 | + | 0.0739705i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.6126 | − | 24.8148i | −1.26684 | − | 0.814148i | −0.277634 | − | 0.960687i | \(-0.589550\pi\) |
−0.989205 | + | 0.146539i | \(0.953187\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.49927 | − | 16.4211i | −0.245779 | − | 0.538180i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.116037 | + | 0.807052i | 0.00379887 | + | 0.0264217i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.70630 | + | 1.08827i | −0.121209 | + | 0.0355901i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.1513 | − | 29.0262i | 0.821658 | − | 0.948244i | −0.177699 | − | 0.984085i | \(-0.556865\pi\) |
0.999358 | + | 0.0358409i | \(0.0114109\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.9497 | − | 21.8691i | −0.618400 | − | 0.713672i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.8427 | − | 41.2597i | 0.614253 | − | 1.34503i | −0.305373 | − | 0.952233i | \(-0.598781\pi\) |
0.919626 | − | 0.392794i | \(-0.128491\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.75250 | − | 12.1945i | 0.187327 | − | 0.397107i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.507756 | + | 1.11183i | −0.0165173 | + | 0.0361679i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.3370 | + | 14.2377i | 0.400899 | + | 0.462663i | 0.919924 | − | 0.392097i | \(-0.128250\pi\) |
−0.519025 | + | 0.854759i | \(0.673705\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.22239 | + | 10.6432i | −0.299371 | + | 0.345493i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.2675 | − | 9.76821i | 1.07877 | − | 0.316756i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.03248 | + | 35.0017i | 0.163018 | + | 1.13382i | 0.892904 | + | 0.450247i | \(0.148664\pi\) |
−0.729886 | + | 0.683569i | \(0.760427\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.43875 | + | 3.15043i | 0.0465569 | + | 0.101945i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.7956 | − | 9.50853i | −0.478273 | − | 0.307367i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.88485 | − | 40.9300i | 0.190032 | − | 1.32170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.5723 | + | 13.8637i | −0.695882 | + | 0.447216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.1337 | + | 3.56279i | 0.391004 | + | 0.114809i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.00946 | −0.0968780 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.7227 | −0.955817 | −0.477908 | − | 0.878410i | \(-0.658605\pi\) | ||||
−0.477908 | + | 0.878410i | \(0.658605\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −25.0582 | − | 7.35775i | −0.804985 | − | 0.236365i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.785865 | − | 0.505045i | 0.0252196 | − | 0.0162077i | −0.527970 | − | 0.849263i | \(-0.677047\pi\) |
0.553190 | + | 0.833055i | \(0.313410\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.3038 | + | 71.6646i | −0.330325 | + | 2.29746i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.02756 | + | 5.80166i | 0.289113 | + | 0.185802i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.3389 | + | 33.5876i | 0.490736 | + | 1.07456i | 0.979371 | + | 0.202073i | \(0.0647677\pi\) |
−0.488635 | + | 0.872488i | \(0.662505\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.31034 | + | 16.0688i | 0.0738388 | + | 0.513560i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.213220 | − | 0.0626069i | 0.00680758 | − | 0.00199888i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.46173 | − | 10.9194i | 0.301782 | − | 0.348276i | −0.584523 | − | 0.811377i | \(-0.698718\pi\) |
0.886305 | + | 0.463102i | \(0.153264\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.51689 | + | 6.36683i | 0.175783 | + | 0.202864i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.62619 | + | 12.3196i | −0.179084 | + | 0.392139i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.0667 | + | 5.06284i | −0.574488 | + | 0.160989i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.8065 | − | 25.8527i | 0.375047 | − | 0.821238i | −0.624156 | − | 0.781300i | \(-0.714557\pi\) |
0.999202 | − | 0.0399374i | \(-0.0127159\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.17114 | − | 10.5841i | −0.291037 | − | 0.335875i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.57350 | + | 7.58623i | −0.208394 | + | 0.240500i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.7175 | + | 8.43221i | −0.909491 | + | 0.267051i | −0.702827 | − | 0.711361i | \(-0.748079\pi\) |
−0.206665 | + | 0.978412i | \(0.566261\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.812891 | + | 5.65378i | 0.0257187 | + | 0.178878i |
(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 | 276.2.i.a.121.2 | yes | 20 | |
3.2 | odd | 2 | 828.2.q.c.397.1 | 20 | |||
23.2 | even | 11 | 6348.2.a.s.1.6 | 10 | |||
23.4 | even | 11 | inner | 276.2.i.a.73.2 | ✓ | 20 | |
23.21 | odd | 22 | 6348.2.a.t.1.5 | 10 | |||
69.50 | odd | 22 | 828.2.q.c.73.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.i.a.73.2 | ✓ | 20 | 23.4 | even | 11 | inner | |
276.2.i.a.121.2 | yes | 20 | 1.1 | even | 1 | trivial | |
828.2.q.c.73.1 | 20 | 69.50 | odd | 22 | |||
828.2.q.c.397.1 | 20 | 3.2 | odd | 2 | |||
6348.2.a.s.1.6 | 10 | 23.2 | even | 11 | |||
6348.2.a.t.1.5 | 10 | 23.21 | odd | 22 |