Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(883,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.883");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.f (of order \(3\), 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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 883.1 | ||
Root | \(1.68614 + 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.883 |
Dual form | 2646.2.f.j.1765.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −2.18614 | − | 3.78651i | −0.977672 | − | 1.69338i | −0.670820 | − | 0.741620i | \(-0.734058\pi\) |
−0.306851 | − | 0.951757i | \(-0.599275\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.37228 | 1.38264 | ||||||||
\(11\) | −0.686141 | + | 1.18843i | −0.206879 | + | 0.358325i | −0.950730 | − | 0.310021i | \(-0.899664\pi\) |
0.743851 | + | 0.668346i | \(0.232997\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | + | 1.73205i | 0.277350 | + | 0.480384i | 0.970725 | − | 0.240192i | \(-0.0772105\pi\) |
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.37228 | 0.332827 | 0.166414 | − | 0.986056i | \(-0.446781\pi\) | ||||
0.166414 | + | 0.986056i | \(0.446781\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.00000 | −1.14708 | −0.573539 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573539 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(20\) | −2.18614 | + | 3.78651i | −0.488836 | + | 0.846689i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.686141 | − | 1.18843i | −0.146286 | − | 0.253374i | ||||
\(23\) | −0.813859 | − | 1.40965i | −0.169701 | − | 0.293931i | 0.768613 | − | 0.639713i | \(-0.220947\pi\) |
−0.938315 | + | 0.345782i | \(0.887614\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.05842 | + | 12.2255i | −1.41168 | + | 2.44511i | ||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.37228 | + | 7.57301i | −0.811912 | + | 1.40627i | 0.0996117 | + | 0.995026i | \(0.468240\pi\) |
−0.911524 | + | 0.411247i | \(0.865093\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | + | 1.73205i | 0.179605 | + | 0.311086i | 0.941745 | − | 0.336327i | \(-0.109185\pi\) |
−0.762140 | + | 0.647412i | \(0.775851\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.686141 | + | 1.18843i | −0.117672 | + | 0.203814i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 2.50000 | − | 4.33013i | 0.405554 | − | 0.702439i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.18614 | − | 3.78651i | −0.345659 | − | 0.598699i | ||||
\(41\) | −2.31386 | − | 4.00772i | −0.361364 | − | 0.625901i | 0.626821 | − | 0.779163i | \(-0.284356\pi\) |
−0.988186 | + | 0.153262i | \(0.951022\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.05842 | − | 7.02939i | 0.618904 | − | 1.07197i | −0.370783 | − | 0.928720i | \(-0.620910\pi\) |
0.989686 | − | 0.143253i | \(-0.0457562\pi\) | |||||||
\(44\) | 1.37228 | 0.206879 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.62772 | 0.239994 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −7.05842 | − | 12.2255i | −0.998212 | − | 1.72895i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.00000 | − | 1.73205i | 0.138675 | − | 0.240192i | ||||
\(53\) | 8.74456 | 1.20116 | 0.600579 | − | 0.799565i | \(-0.294937\pi\) | ||||
0.600579 | + | 0.799565i | \(0.294937\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | 0.809040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.37228 | − | 7.57301i | −0.574109 | − | 0.994385i | ||||
\(59\) | 5.05842 | + | 8.76144i | 0.658550 | + | 1.14064i | 0.980991 | + | 0.194053i | \(0.0621634\pi\) |
−0.322441 | + | 0.946590i | \(0.604503\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.55842 | − | 2.69927i | 0.199535 | − | 0.345606i | −0.748842 | − | 0.662748i | \(-0.769390\pi\) |
0.948378 | + | 0.317142i | \(0.102723\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.37228 | − | 7.57301i | 0.542315 | − | 0.939317i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.05842 | + | 1.83324i | 0.129307 | + | 0.223966i | 0.923408 | − | 0.383819i | \(-0.125391\pi\) |
−0.794101 | + | 0.607785i | \(0.792058\pi\) | |||||||
\(68\) | −0.686141 | − | 1.18843i | −0.0832068 | − | 0.144118i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.11684 | 0.844614 | 0.422307 | − | 0.906453i | \(-0.361220\pi\) | ||||
0.422307 | + | 0.906453i | \(0.361220\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.1168 | −1.41817 | −0.709085 | − | 0.705123i | \(-0.750892\pi\) | ||||
−0.709085 | + | 0.705123i | \(0.750892\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.50000 | + | 4.33013i | 0.286770 | + | 0.496700i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.55842 | − | 4.43132i | 0.287845 | − | 0.498562i | −0.685450 | − | 0.728120i | \(-0.740395\pi\) |
0.973295 | + | 0.229557i | \(0.0737279\pi\) | |||||||
\(80\) | 4.37228 | 0.488836 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.62772 | 0.511046 | ||||||||
\(83\) | −8.74456 | + | 15.1460i | −0.959840 | + | 1.66249i | −0.236960 | + | 0.971519i | \(0.576151\pi\) |
−0.722881 | + | 0.690973i | \(0.757182\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | − | 5.19615i | −0.325396 | − | 0.563602i | ||||
\(86\) | 4.05842 | + | 7.02939i | 0.437631 | + | 0.757999i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.686141 | + | 1.18843i | −0.0731428 | + | 0.126687i | ||||
\(89\) | 14.7446 | 1.56292 | 0.781460 | − | 0.623955i | \(-0.214475\pi\) | ||||
0.781460 | + | 0.623955i | \(0.214475\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.813859 | + | 1.40965i | −0.0848507 | + | 0.146966i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.9307 | + | 18.9325i | 1.12147 | + | 1.94244i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.05842 | + | 7.02939i | −0.412070 | + | 0.713727i | −0.995116 | − | 0.0987127i | \(-0.968528\pi\) |
0.583046 | + | 0.812439i | \(0.301861\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 14.1168 | 1.41168 | ||||||||
\(101\) | −0.813859 | + | 1.40965i | −0.0809820 | + | 0.140265i | −0.903672 | − | 0.428225i | \(-0.859139\pi\) |
0.822690 | + | 0.568490i | \(0.192472\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.00000 | − | 8.66025i | −0.492665 | − | 0.853320i | 0.507300 | − | 0.861770i | \(-0.330644\pi\) |
−0.999964 | + | 0.00844953i | \(0.997310\pi\) | |||||||
\(104\) | 1.00000 | + | 1.73205i | 0.0980581 | + | 0.169842i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.37228 | + | 7.57301i | −0.424674 | + | 0.735556i | ||||
\(107\) | 7.37228 | 0.712705 | 0.356353 | − | 0.934352i | \(-0.384020\pi\) | ||||
0.356353 | + | 0.934352i | \(0.384020\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | −3.00000 | + | 5.19615i | −0.286039 | + | 0.495434i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.18614 | − | 3.78651i | −0.205655 | − | 0.356205i | 0.744686 | − | 0.667415i | \(-0.232599\pi\) |
−0.950341 | + | 0.311210i | \(0.899266\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.55842 | + | 6.16337i | −0.331825 | + | 0.574737i | ||||
\(116\) | 8.74456 | 0.811912 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.1168 | −0.931331 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.55842 | + | 7.89542i | 0.414402 | + | 0.717765i | ||||
\(122\) | 1.55842 | + | 2.69927i | 0.141093 | + | 0.244380i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.00000 | − | 1.73205i | 0.0898027 | − | 0.155543i | ||||
\(125\) | 39.8614 | 3.56531 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.11684 | 0.276575 | 0.138288 | − | 0.990392i | \(-0.455840\pi\) | ||||
0.138288 | + | 0.990392i | \(0.455840\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.37228 | + | 7.57301i | 0.383474 | + | 0.664197i | ||||
\(131\) | 0.813859 | + | 1.40965i | 0.0711072 | + | 0.123161i | 0.899387 | − | 0.437154i | \(-0.144013\pi\) |
−0.828280 | + | 0.560315i | \(0.810680\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.11684 | −0.182867 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.37228 | 0.117672 | ||||||||
\(137\) | 5.31386 | − | 9.20387i | 0.453994 | − | 0.786340i | −0.544636 | − | 0.838672i | \(-0.683332\pi\) |
0.998630 | + | 0.0523324i | \(0.0166655\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.61684 | + | 11.4607i | 0.561233 | + | 0.972085i | 0.997389 | + | 0.0722136i | \(0.0230063\pi\) |
−0.436156 | + | 0.899871i | \(0.643660\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.55842 | + | 6.16337i | −0.298616 | + | 0.517218i | ||||
\(143\) | −2.74456 | −0.229512 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 38.2337 | 3.17513 | ||||||||
\(146\) | 6.05842 | − | 10.4935i | 0.501399 | − | 0.868448i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | − | 1.73205i | −0.0821995 | − | 0.142374i | ||||
\(149\) | 1.62772 | + | 2.81929i | 0.133348 | + | 0.230965i | 0.924965 | − | 0.380052i | \(-0.124094\pi\) |
−0.791617 | + | 0.611017i | \(0.790761\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.55842 | + | 7.89542i | −0.370959 | + | 0.642520i | −0.989713 | − | 0.143065i | \(-0.954304\pi\) |
0.618754 | + | 0.785585i | \(0.287638\pi\) | |||||||
\(152\) | −5.00000 | −0.405554 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.37228 | − | 7.57301i | 0.351190 | − | 0.608279i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.55842 | + | 7.89542i | 0.363802 | + | 0.630123i | 0.988583 | − | 0.150677i | \(-0.0481453\pi\) |
−0.624781 | + | 0.780800i | \(0.714812\pi\) | |||||||
\(158\) | 2.55842 | + | 4.43132i | 0.203537 | + | 0.352537i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.18614 | + | 3.78651i | −0.172830 | + | 0.299350i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.2337 | −1.42817 | −0.714086 | − | 0.700058i | \(-0.753158\pi\) | ||||
−0.714086 | + | 0.700058i | \(0.753158\pi\) | |||||||
\(164\) | −2.31386 | + | 4.00772i | −0.180682 | + | 0.312951i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.74456 | − | 15.1460i | −0.678710 | − | 1.17556i | ||||
\(167\) | 2.74456 | + | 4.75372i | 0.212381 | + | 0.367854i | 0.952459 | − | 0.304666i | \(-0.0985450\pi\) |
−0.740078 | + | 0.672521i | \(0.765212\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | − | 7.79423i | 0.346154 | − | 0.599556i | ||||
\(170\) | 6.00000 | 0.460179 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.11684 | −0.618904 | ||||||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.686141 | − | 1.18843i | −0.0517198 | − | 0.0895813i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.37228 | + | 12.7692i | −0.552576 | + | 0.957089i | ||||
\(179\) | −3.25544 | −0.243323 | −0.121661 | − | 0.992572i | \(-0.538822\pi\) | ||||
−0.121661 | + | 0.992572i | \(0.538822\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.883156 | −0.0656445 | −0.0328222 | − | 0.999461i | \(-0.510450\pi\) | ||||
−0.0328222 | + | 0.999461i | \(0.510450\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.813859 | − | 1.40965i | −0.0599985 | − | 0.103920i | ||||
\(185\) | −4.37228 | − | 7.57301i | −0.321457 | − | 0.556779i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.941578 | + | 1.63086i | −0.0688550 | + | 0.119260i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −21.8614 | −1.58599 | ||||||||
\(191\) | −9.55842 | + | 16.5557i | −0.691623 | + | 1.19793i | 0.279683 | + | 0.960092i | \(0.409771\pi\) |
−0.971306 | + | 0.237834i | \(0.923563\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.50000 | + | 6.06218i | 0.251936 | + | 0.436365i | 0.964059 | − | 0.265689i | \(-0.0855996\pi\) |
−0.712123 | + | 0.702055i | \(0.752266\pi\) | |||||||
\(194\) | −4.05842 | − | 7.02939i | −0.291378 | − | 0.504681i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000 | 0.708881 | 0.354441 | − | 0.935079i | \(-0.384671\pi\) | ||||
0.354441 | + | 0.935079i | \(0.384671\pi\) | |||||||
\(200\) | −7.05842 | + | 12.2255i | −0.499106 | + | 0.864477i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.813859 | − | 1.40965i | −0.0572629 | − | 0.0991823i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.1168 | + | 17.5229i | −0.706591 | + | 1.22385i | ||||
\(206\) | 10.0000 | 0.696733 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.00000 | −0.138675 | ||||||||
\(209\) | 3.43070 | − | 5.94215i | 0.237307 | − | 0.411027i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | + | 13.8564i | 0.550743 | + | 0.953914i | 0.998221 | + | 0.0596196i | \(0.0189888\pi\) |
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | −4.37228 | − | 7.57301i | −0.300290 | − | 0.520117i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.68614 | + | 6.38458i | −0.251979 | + | 0.436441i | ||||
\(215\) | −35.4891 | −2.42034 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.00000 | + | 12.1244i | −0.474100 | + | 0.821165i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.00000 | − | 5.19615i | −0.202260 | − | 0.350325i | ||||
\(221\) | 1.37228 | + | 2.37686i | 0.0923096 | + | 0.159885i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.00000 | + | 3.46410i | −0.133930 | + | 0.231973i | −0.925188 | − | 0.379509i | \(-0.876093\pi\) |
0.791258 | + | 0.611482i | \(0.209426\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.37228 | 0.290840 | ||||||||
\(227\) | 6.12772 | − | 10.6135i | 0.406711 | − | 0.704444i | −0.587808 | − | 0.809000i | \(-0.700009\pi\) |
0.994519 | + | 0.104556i | \(0.0333423\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.44158 | − | 2.49689i | −0.0952622 | − | 0.164999i | 0.814456 | − | 0.580226i | \(-0.197036\pi\) |
−0.909718 | + | 0.415227i | \(0.863702\pi\) | |||||||
\(230\) | −3.55842 | − | 6.16337i | −0.234635 | − | 0.406400i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.37228 | + | 7.57301i | −0.287054 | + | 0.497193i | ||||
\(233\) | 0.255437 | 0.0167343 | 0.00836713 | − | 0.999965i | \(-0.497337\pi\) | ||||
0.00836713 | + | 0.999965i | \(0.497337\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.05842 | − | 8.76144i | 0.329275 | − | 0.570321i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.93070 | + | 8.54023i | 0.318941 | + | 0.552421i | 0.980267 | − | 0.197677i | \(-0.0633396\pi\) |
−0.661327 | + | 0.750098i | \(0.730006\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.05842 | − | 15.6896i | 0.583504 | − | 1.01066i | −0.411556 | − | 0.911385i | \(-0.635014\pi\) |
0.995060 | − | 0.0992745i | \(-0.0316522\pi\) | |||||||
\(242\) | −9.11684 | −0.586053 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.11684 | −0.199535 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.00000 | − | 8.66025i | −0.318142 | − | 0.551039i | ||||
\(248\) | 1.00000 | + | 1.73205i | 0.0635001 | + | 0.109985i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −19.9307 | + | 34.5210i | −1.26053 | + | 2.18330i | ||||
\(251\) | −9.00000 | −0.568075 | −0.284037 | − | 0.958813i | \(-0.591674\pi\) | ||||
−0.284037 | + | 0.958813i | \(0.591674\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.23369 | 0.140431 | ||||||||
\(254\) | −1.55842 | + | 2.69927i | −0.0977841 | + | 0.169367i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 3.43070 | + | 5.94215i | 0.214001 | + | 0.370661i | 0.952963 | − | 0.303086i | \(-0.0980170\pi\) |
−0.738962 | + | 0.673747i | \(0.764684\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8.74456 | −0.542315 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.62772 | −0.100561 | ||||||||
\(263\) | 3.81386 | − | 6.60580i | 0.235173 | − | 0.407331i | −0.724150 | − | 0.689642i | \(-0.757768\pi\) |
0.959323 | + | 0.282311i | \(0.0911011\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.1168 | − | 33.1113i | −1.17434 | − | 2.03401i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.05842 | − | 1.83324i | 0.0646534 | − | 0.111983i | ||||
\(269\) | −1.62772 | −0.0992438 | −0.0496219 | − | 0.998768i | \(-0.515802\pi\) | ||||
−0.0496219 | + | 0.998768i | \(0.515802\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.2337 | −0.986126 | −0.493063 | − | 0.869994i | \(-0.664123\pi\) | ||||
−0.493063 | + | 0.869994i | \(0.664123\pi\) | |||||||
\(272\) | −0.686141 | + | 1.18843i | −0.0416034 | + | 0.0720592i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.31386 | + | 9.20387i | 0.321022 | + | 0.556026i | ||||
\(275\) | −9.68614 | − | 16.7769i | −0.584096 | − | 1.01168i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.11684 | − | 10.5947i | 0.367526 | − | 0.636573i | −0.621652 | − | 0.783293i | \(-0.713538\pi\) |
0.989178 | + | 0.146720i | \(0.0468717\pi\) | |||||||
\(278\) | −13.2337 | −0.793704 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.18614 | − | 14.1788i | 0.488344 | − | 0.845837i | −0.511566 | − | 0.859244i | \(-0.670934\pi\) |
0.999910 | + | 0.0134071i | \(0.00426773\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.5584 | + | 23.4839i | 0.805965 | + | 1.39597i | 0.915638 | + | 0.402004i | \(0.131686\pi\) |
−0.109673 | + | 0.993968i | \(0.534981\pi\) | |||||||
\(284\) | −3.55842 | − | 6.16337i | −0.211153 | − | 0.365729i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.37228 | − | 2.37686i | 0.0811447 | − | 0.140547i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1168 | −0.889226 | ||||||||
\(290\) | −19.1168 | + | 33.1113i | −1.12258 | + | 1.94437i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.05842 | + | 10.4935i | 0.354542 | + | 0.614085i | ||||
\(293\) | 5.18614 | + | 8.98266i | 0.302978 | + | 0.524773i | 0.976809 | − | 0.214113i | \(-0.0686859\pi\) |
−0.673831 | + | 0.738885i | \(0.735353\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.1168 | − | 38.3075i | 1.28769 | − | 2.23035i | ||||
\(296\) | 2.00000 | 0.116248 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.25544 | −0.188582 | ||||||||
\(299\) | 1.62772 | − | 2.81929i | 0.0941334 | − | 0.163044i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4.55842 | − | 7.89542i | −0.262308 | − | 0.454330i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.50000 | − | 4.33013i | 0.143385 | − | 0.248350i | ||||
\(305\) | −13.6277 | −0.780321 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.0000 | 0.741949 | 0.370975 | − | 0.928643i | \(-0.379024\pi\) | ||||
0.370975 | + | 0.928643i | \(0.379024\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.37228 | + | 7.57301i | 0.248329 | + | 0.430118i | ||||
\(311\) | −4.11684 | − | 7.13058i | −0.233445 | − | 0.404338i | 0.725375 | − | 0.688354i | \(-0.241666\pi\) |
−0.958820 | + | 0.284016i | \(0.908333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0584 | + | 17.4217i | −0.568536 | + | 0.984733i | 0.428175 | + | 0.903696i | \(0.359157\pi\) |
−0.996711 | + | 0.0810370i | \(0.974177\pi\) | |||||||
\(314\) | −9.11684 | −0.514493 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.11684 | −0.287845 | ||||||||
\(317\) | −3.00000 | + | 5.19615i | −0.168497 | + | 0.291845i | −0.937892 | − | 0.346929i | \(-0.887225\pi\) |
0.769395 | + | 0.638774i | \(0.220558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | − | 10.3923i | −0.335936 | − | 0.581857i | ||||
\(320\) | −2.18614 | − | 3.78651i | −0.122209 | − | 0.211672i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.86141 | −0.381779 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −28.2337 | −1.56612 | ||||||||
\(326\) | 9.11684 | − | 15.7908i | 0.504935 | − | 0.874574i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.31386 | − | 4.00772i | −0.127762 | − | 0.221289i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.1168 | + | 19.2549i | −0.611037 | + | 1.05835i | 0.380029 | + | 0.924975i | \(0.375914\pi\) |
−0.991066 | + | 0.133373i | \(0.957419\pi\) | |||||||
\(332\) | 17.4891 | 0.959840 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.48913 | −0.300352 | ||||||||
\(335\) | 4.62772 | − | 8.01544i | 0.252839 | − | 0.437930i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.05842 | + | 7.02939i | 0.221076 | + | 0.382915i | 0.955135 | − | 0.296171i | \(-0.0957097\pi\) |
−0.734059 | + | 0.679086i | \(0.762376\pi\) | |||||||
\(338\) | 4.50000 | + | 7.79423i | 0.244768 | + | 0.423950i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.00000 | + | 5.19615i | −0.162698 | + | 0.281801i | ||||
\(341\) | −2.74456 | −0.148626 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.05842 | − | 7.02939i | 0.218815 | − | 0.378999i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.00000 | + | 5.19615i | 0.161281 | + | 0.279347i | ||||
\(347\) | −5.05842 | − | 8.76144i | −0.271550 | − | 0.470339i | 0.697709 | − | 0.716382i | \(-0.254203\pi\) |
−0.969259 | + | 0.246043i | \(0.920870\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.0000 | + | 19.0526i | −0.588817 | + | 1.01986i | 0.405571 | + | 0.914063i | \(0.367073\pi\) |
−0.994388 | + | 0.105797i | \(0.966261\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.37228 | 0.0731428 | ||||||||
\(353\) | 6.68614 | − | 11.5807i | 0.355867 | − | 0.616380i | −0.631399 | − | 0.775458i | \(-0.717519\pi\) |
0.987266 | + | 0.159078i | \(0.0508522\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.5584 | − | 26.9480i | −0.825755 | − | 1.43025i | ||||
\(356\) | −7.37228 | − | 12.7692i | −0.390730 | − | 0.676764i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.62772 | − | 2.81929i | 0.0860276 | − | 0.149004i | ||||
\(359\) | −21.8614 | −1.15380 | −0.576900 | − | 0.816814i | \(-0.695738\pi\) | ||||
−0.576900 | + | 0.816814i | \(0.695738\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | 0.441578 | − | 0.764836i | 0.0232088 | − | 0.0401989i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.4891 | + | 45.8805i | 1.38650 | + | 2.40150i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.11684 | + | 10.5947i | −0.319297 | + | 0.553038i | −0.980341 | − | 0.197308i | \(-0.936780\pi\) |
0.661045 | + | 0.750346i | \(0.270113\pi\) | |||||||
\(368\) | 1.62772 | 0.0848507 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.74456 | 0.454608 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | + | 8.66025i | 0.258890 | + | 0.448411i | 0.965945 | − | 0.258748i | \(-0.0833099\pi\) |
−0.707055 | + | 0.707159i | \(0.749977\pi\) | |||||||
\(374\) | −0.941578 | − | 1.63086i | −0.0486878 | − | 0.0843298i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.4891 | −0.900736 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.11684 | −0.416934 | −0.208467 | − | 0.978029i | \(-0.566847\pi\) | ||||
−0.208467 | + | 0.978029i | \(0.566847\pi\) | |||||||
\(380\) | 10.9307 | − | 18.9325i | 0.560733 | − | 0.971218i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.55842 | − | 16.5557i | −0.489051 | − | 0.847062i | ||||
\(383\) | 16.3723 | + | 28.3576i | 0.836584 | + | 1.44901i | 0.892734 | + | 0.450584i | \(0.148784\pi\) |
−0.0561493 | + | 0.998422i | \(0.517882\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.00000 | −0.356291 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.11684 | 0.412070 | ||||||||
\(389\) | 5.48913 | − | 9.50744i | 0.278310 | − | 0.482047i | −0.692655 | − | 0.721269i | \(-0.743559\pi\) |
0.970965 | + | 0.239222i | \(0.0768925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.11684 | − | 1.93443i | −0.0564812 | − | 0.0978284i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.00000 | + | 5.19615i | −0.151138 | + | 0.261778i | ||||
\(395\) | −22.3723 | −1.12567 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.0000 | 1.10415 | 0.552074 | − | 0.833795i | \(-0.313837\pi\) | ||||
0.552074 | + | 0.833795i | \(0.313837\pi\) | |||||||
\(398\) | −5.00000 | + | 8.66025i | −0.250627 | + | 0.434099i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.05842 | − | 12.2255i | −0.352921 | − | 0.611277i | ||||
\(401\) | −5.87228 | − | 10.1711i | −0.293248 | − | 0.507920i | 0.681328 | − | 0.731978i | \(-0.261403\pi\) |
−0.974576 | + | 0.224058i | \(0.928069\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.00000 | + | 3.46410i | −0.0996271 | + | 0.172559i | ||||
\(404\) | 1.62772 | 0.0809820 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.37228 | + | 2.37686i | −0.0680215 | + | 0.117817i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.1753 | − | 19.3561i | −0.552581 | − | 0.957099i | −0.998087 | − | 0.0618200i | \(-0.980310\pi\) |
0.445506 | − | 0.895279i | \(-0.353024\pi\) | |||||||
\(410\) | −10.1168 | − | 17.5229i | −0.499635 | − | 0.865394i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.00000 | + | 8.66025i | −0.246332 | + | 0.426660i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 76.4674 | 3.75364 | ||||||||
\(416\) | 1.00000 | − | 1.73205i | 0.0490290 | − | 0.0849208i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.43070 | + | 5.94215i | 0.167801 | + | 0.290640i | ||||
\(419\) | 6.30298 | + | 10.9171i | 0.307921 | + | 0.533335i | 0.977907 | − | 0.209039i | \(-0.0670334\pi\) |
−0.669986 | + | 0.742373i | \(0.733700\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.1168 | + | 29.6472i | −0.834224 | + | 1.44492i | 0.0604368 | + | 0.998172i | \(0.480751\pi\) |
−0.894661 | + | 0.446746i | \(0.852583\pi\) | |||||||
\(422\) | −16.0000 | −0.778868 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.74456 | 0.424674 | ||||||||
\(425\) | −9.68614 | + | 16.7769i | −0.469847 | + | 0.813799i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.68614 | − | 6.38458i | −0.178176 | − | 0.308610i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 17.7446 | − | 30.7345i | 0.855719 | − | 1.48215i | ||||
\(431\) | 6.51087 | 0.313618 | 0.156809 | − | 0.987629i | \(-0.449879\pi\) | ||||
0.156809 | + | 0.987629i | \(0.449879\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.1168 | 0.966754 | 0.483377 | − | 0.875412i | \(-0.339410\pi\) | ||||
0.483377 | + | 0.875412i | \(0.339410\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.00000 | − | 12.1244i | −0.335239 | − | 0.580651i | ||||
\(437\) | 4.06930 | + | 7.04823i | 0.194661 | + | 0.337162i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000 | − | 6.92820i | 0.190910 | − | 0.330665i | −0.754642 | − | 0.656136i | \(-0.772190\pi\) |
0.945552 | + | 0.325471i | \(0.105523\pi\) | |||||||
\(440\) | 6.00000 | 0.286039 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.74456 | −0.130546 | ||||||||
\(443\) | −20.0584 | + | 34.7422i | −0.953004 | + | 1.65065i | −0.214134 | + | 0.976804i | \(0.568693\pi\) |
−0.738870 | + | 0.673848i | \(0.764640\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.2337 | − | 55.8304i | −1.52802 | − | 2.64661i | ||||
\(446\) | −2.00000 | − | 3.46410i | −0.0947027 | − | 0.164030i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.0000 | −1.55737 | −0.778683 | − | 0.627417i | \(-0.784112\pi\) | ||||
−0.778683 | + | 0.627417i | \(0.784112\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.35053 | 0.299035 | ||||||||
\(452\) | −2.18614 | + | 3.78651i | −0.102827 | + | 0.178102i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.12772 | + | 10.6135i | 0.287588 | + | 0.498117i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.7337 | − | 30.7156i | 0.829547 | − | 1.43682i | −0.0688472 | − | 0.997627i | \(-0.521932\pi\) |
0.898394 | − | 0.439190i | \(-0.144735\pi\) | |||||||
\(458\) | 2.88316 | 0.134721 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.11684 | 0.331825 | ||||||||
\(461\) | −1.06930 | + | 1.85208i | −0.0498021 | + | 0.0862598i | −0.889852 | − | 0.456250i | \(-0.849192\pi\) |
0.840050 | + | 0.542509i | \(0.182526\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.5584 | + | 20.0198i | 0.537165 | + | 0.930398i | 0.999055 | + | 0.0434604i | \(0.0138382\pi\) |
−0.461890 | + | 0.886937i | \(0.652828\pi\) | |||||||
\(464\) | −4.37228 | − | 7.57301i | −0.202978 | − | 0.351568i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.127719 | + | 0.221215i | −0.00591645 | + | 0.0102476i | ||||
\(467\) | 33.0951 | 1.53146 | 0.765729 | − | 0.643163i | \(-0.222378\pi\) | ||||
0.765729 | + | 0.643163i | \(0.222378\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.05842 | + | 8.76144i | 0.232833 | + | 0.403278i | ||||
\(473\) | 5.56930 | + | 9.64630i | 0.256077 | + | 0.443538i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 35.2921 | − | 61.1277i | 1.61931 | − | 2.80473i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.86141 | −0.451050 | ||||||||
\(479\) | −16.3723 | + | 28.3576i | −0.748069 | + | 1.29569i | 0.200679 | + | 0.979657i | \(0.435685\pi\) |
−0.948747 | + | 0.316036i | \(0.897648\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | + | 3.46410i | 0.0911922 | + | 0.157949i | ||||
\(482\) | 9.05842 | + | 15.6896i | 0.412600 | + | 0.714644i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.55842 | − | 7.89542i | 0.207201 | − | 0.358883i | ||||
\(485\) | 35.4891 | 1.61148 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.3505 | 1.60189 | 0.800943 | − | 0.598741i | \(-0.204332\pi\) | ||||
0.800943 | + | 0.598741i | \(0.204332\pi\) | |||||||
\(488\) | 1.55842 | − | 2.69927i | 0.0705464 | − | 0.122190i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.6861 | − | 21.9730i | −0.572518 | − | 0.991629i | −0.996306 | − | 0.0858685i | \(-0.972634\pi\) |
0.423789 | − | 0.905761i | \(-0.360700\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.00000 | + | 10.3923i | −0.270226 | + | 0.468046i | ||||
\(494\) | 10.0000 | 0.449921 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.05842 | − | 15.6896i | −0.405511 | − | 0.702365i | 0.588870 | − | 0.808228i | \(-0.299573\pi\) |
−0.994381 | + | 0.105863i | \(0.966240\pi\) | |||||||
\(500\) | −19.9307 | − | 34.5210i | −0.891328 | − | 1.54383i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.50000 | − | 7.79423i | 0.200845 | − | 0.347873i | ||||
\(503\) | −32.2337 | −1.43723 | −0.718615 | − | 0.695409i | \(-0.755223\pi\) | ||||
−0.718615 | + | 0.695409i | \(0.755223\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.11684 | 0.316695 | ||||||||
\(506\) | −1.11684 | + | 1.93443i | −0.0496498 | + | 0.0859959i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.55842 | − | 2.69927i | −0.0691438 | − | 0.119761i | ||||
\(509\) | 14.4891 | + | 25.0959i | 0.642219 | + | 1.11236i | 0.984936 | + | 0.172918i | \(0.0553194\pi\) |
−0.342717 | + | 0.939439i | \(0.611347\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.86141 | −0.302644 | ||||||||
\(515\) | −21.8614 | + | 37.8651i | −0.963329 | + | 1.66853i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.37228 | − | 7.57301i | 0.191737 | − | 0.332099i | ||||
\(521\) | −24.8614 | −1.08920 | −0.544599 | − | 0.838697i | \(-0.683318\pi\) | ||||
−0.544599 | + | 0.838697i | \(0.683318\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.1168 | 1.53555 | 0.767776 | − | 0.640718i | \(-0.221363\pi\) | ||||
0.767776 | + | 0.640718i | \(0.221363\pi\) | |||||||
\(524\) | 0.813859 | − | 1.40965i | 0.0355536 | − | 0.0615807i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.81386 | + | 6.60580i | 0.166292 | + | 0.288026i | ||||
\(527\) | 1.37228 | + | 2.37686i | 0.0597775 | + | 0.103538i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.1753 | − | 17.6241i | 0.442403 | − | 0.766264i | ||||
\(530\) | 38.2337 | 1.66077 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.62772 | − | 8.01544i | 0.200449 | − | 0.347187i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.1168 | − | 27.9152i | −0.696792 | − | 1.20688i | ||||
\(536\) | 1.05842 | + | 1.83324i | 0.0457169 | + | 0.0791839i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.813859 | − | 1.40965i | 0.0350880 | − | 0.0607741i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.23369 | −0.268007 | −0.134004 | − | 0.990981i | \(-0.542783\pi\) | ||||
−0.134004 | + | 0.990981i | \(0.542783\pi\) | |||||||
\(542\) | 8.11684 | − | 14.0588i | 0.348648 | − | 0.603877i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.686141 | − | 1.18843i | −0.0294180 | − | 0.0509535i | ||||
\(545\) | −30.6060 | − | 53.0111i | −1.31102 | − | 2.27075i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.05842 | + | 15.6896i | −0.387310 | + | 0.670841i | −0.992087 | − | 0.125554i | \(-0.959929\pi\) |
0.604777 | + | 0.796395i | \(0.293262\pi\) | |||||||
\(548\) | −10.6277 | −0.453994 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 19.3723 | 0.826037 | ||||||||
\(551\) | 21.8614 | − | 37.8651i | 0.931327 | − | 1.61311i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.11684 | + | 10.5947i | 0.259880 | + | 0.450125i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.61684 | − | 11.4607i | 0.280617 | − | 0.486042i | ||||
\(557\) | −29.4891 | −1.24949 | −0.624747 | − | 0.780827i | \(-0.714798\pi\) | ||||
−0.624747 | + | 0.780827i | \(0.714798\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.2337 | 0.686612 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.18614 | + | 14.1788i | 0.345312 | + | 0.598097i | ||||
\(563\) | −1.50000 | − | 2.59808i | −0.0632175 | − | 0.109496i | 0.832684 | − | 0.553748i | \(-0.186803\pi\) |
−0.895902 | + | 0.444252i | \(0.853470\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.55842 | + | 16.5557i | −0.402126 | + | 0.696502i | ||||
\(566\) | −27.1168 | −1.13981 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.11684 | 0.298616 | ||||||||
\(569\) | 8.05842 | − | 13.9576i | 0.337827 | − | 0.585133i | −0.646197 | − | 0.763171i | \(-0.723642\pi\) |
0.984024 | + | 0.178038i | \(0.0569749\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.1753 | + | 19.3561i | 0.467670 | + | 0.810029i | 0.999318 | − | 0.0369371i | \(-0.0117601\pi\) |
−0.531647 | + | 0.846966i | \(0.678427\pi\) | |||||||
\(572\) | 1.37228 | + | 2.37686i | 0.0573780 | + | 0.0993815i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.9783 | 0.958259 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.88316 | −0.411441 | −0.205721 | − | 0.978611i | \(-0.565954\pi\) | ||||
−0.205721 | + | 0.978611i | \(0.565954\pi\) | |||||||
\(578\) | 7.55842 | − | 13.0916i | 0.314389 | − | 0.544538i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −19.1168 | − | 33.1113i | −0.793784 | − | 1.37487i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.00000 | + | 10.3923i | −0.248495 | + | 0.430405i | ||||
\(584\) | −12.1168 | −0.501399 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.3723 | −0.428475 | ||||||||
\(587\) | −7.24456 | + | 12.5480i | −0.299015 | + | 0.517909i | −0.975911 | − | 0.218170i | \(-0.929991\pi\) |
0.676896 | + | 0.736079i | \(0.263325\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.00000 | − | 8.66025i | −0.206021 | − | 0.356840i | ||||
\(590\) | 22.1168 | + | 38.3075i | 0.910536 | + | 1.57709i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.00000 | + | 1.73205i | −0.0410997 | + | 0.0711868i | ||||
\(593\) | 14.7446 | 0.605487 | 0.302743 | − | 0.953072i | \(-0.402098\pi\) | ||||
0.302743 | + | 0.953072i | \(0.402098\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.62772 | − | 2.81929i | 0.0666740 | − | 0.115483i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.62772 | + | 2.81929i | 0.0665624 | + | 0.115289i | ||||
\(599\) | 12.0000 | + | 20.7846i | 0.490307 | + | 0.849236i | 0.999938 | − | 0.0111569i | \(-0.00355143\pi\) |
−0.509631 | + | 0.860393i | \(0.670218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.0584 | − | 20.8858i | 0.491873 | − | 0.851950i | −0.508083 | − | 0.861308i | \(-0.669646\pi\) |
0.999956 | + | 0.00935863i | \(0.00297899\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.11684 | 0.370959 | ||||||||
\(605\) | 19.9307 | − | 34.5210i | 0.810298 | − | 1.40348i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.1168 | + | 19.2549i | 0.451219 | + | 0.781534i | 0.998462 | − | 0.0554398i | \(-0.0176561\pi\) |
−0.547243 | + | 0.836974i | \(0.684323\pi\) | |||||||
\(608\) | 2.50000 | + | 4.33013i | 0.101388 | + | 0.175610i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.81386 | − | 11.8020i | 0.275885 | − | 0.477847i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.2337 | −1.46346 | −0.731732 | − | 0.681592i | \(-0.761288\pi\) | ||||
−0.731732 | + | 0.681592i | \(0.761288\pi\) | |||||||
\(614\) | −6.50000 | + | 11.2583i | −0.262319 | + | 0.454349i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.43070 | + | 16.3345i | 0.379666 | + | 0.657600i | 0.991014 | − | 0.133762i | \(-0.0427056\pi\) |
−0.611348 | + | 0.791362i | \(0.709372\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.7337 | − | 39.3759i | 0.913744 | − | 1.58265i | 0.105014 | − | 0.994471i | \(-0.466511\pi\) |
0.808730 | − | 0.588180i | \(-0.200156\pi\) | |||||||
\(620\) | −8.74456 | −0.351190 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.23369 | 0.330141 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −51.8505 | − | 89.8078i | −2.07402 | − | 3.59231i | ||||
\(626\) | −10.0584 | − | 17.4217i | −0.402015 | − | 0.696311i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.55842 | − | 7.89542i | 0.181901 | − | 0.315061i | ||||
\(629\) | 2.74456 | 0.109433 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.3505 | −1.48690 | −0.743451 | − | 0.668791i | \(-0.766812\pi\) | ||||
−0.743451 | + | 0.668791i | \(0.766812\pi\) | |||||||
\(632\) | 2.55842 | − | 4.43132i | 0.101769 | − | 0.176268i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.00000 | − | 5.19615i | −0.119145 | − | 0.206366i | ||||
\(635\) | −6.81386 | − | 11.8020i | −0.270400 | − | 0.468346i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.0000 | 0.475085 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.37228 | 0.172830 | ||||||||
\(641\) | 17.1060 | − | 29.6284i | 0.675645 | − | 1.17025i | −0.300635 | − | 0.953739i | \(-0.597198\pi\) |
0.976280 | − | 0.216512i | \(-0.0694682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.1753 | + | 22.8202i | 0.519582 | + | 0.899942i | 0.999741 | + | 0.0227606i | \(0.00724556\pi\) |
−0.480159 | + | 0.877181i | \(0.659421\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.43070 | − | 5.94215i | 0.134979 | − | 0.233791i | ||||
\(647\) | 5.48913 | 0.215800 | 0.107900 | − | 0.994162i | \(-0.465587\pi\) | ||||
0.107900 | + | 0.994162i | \(0.465587\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.8832 | −0.544962 | ||||||||
\(650\) | 14.1168 | − | 24.4511i | 0.553708 | − | 0.959051i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.11684 | + | 15.7908i | 0.357043 | + | 0.618417i | ||||
\(653\) | −13.3723 | − | 23.1615i | −0.523298 | − | 0.906378i | −0.999632 | − | 0.0271143i | \(-0.991368\pi\) |
0.476335 | − | 0.879264i | \(-0.341965\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.55842 | − | 6.16337i | 0.139039 | − | 0.240823i | ||||
\(656\) | 4.62772 | 0.180682 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3723 | + | 17.9653i | −0.404047 | + | 0.699829i | −0.994210 | − | 0.107454i | \(-0.965730\pi\) |
0.590163 | + | 0.807284i | \(0.299063\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.5584 | + | 23.4839i | 0.527361 | + | 0.913417i | 0.999491 | + | 0.0318879i | \(0.0101520\pi\) |
−0.472130 | + | 0.881529i | \(0.656515\pi\) | |||||||
\(662\) | −11.1168 | − | 19.2549i | −0.432068 | − | 0.748364i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.74456 | + | 15.1460i | −0.339355 | + | 0.587780i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.2337 | 0.551131 | ||||||||
\(668\) | 2.74456 | − | 4.75372i | 0.106190 | − | 0.183927i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.62772 | + | 8.01544i | 0.178784 | + | 0.309664i | ||||
\(671\) | 2.13859 | + | 3.70415i | 0.0825595 | + | 0.142997i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.44158 | − | 2.49689i | 0.0555687 | − | 0.0962479i | −0.836903 | − | 0.547351i | \(-0.815636\pi\) |
0.892472 | + | 0.451103i | \(0.148969\pi\) | |||||||
\(674\) | −8.11684 | −0.312649 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −17.2337 | + | 29.8496i | −0.662344 | + | 1.14721i | 0.317654 | + | 0.948207i | \(0.397105\pi\) |
−0.979998 | + | 0.199007i | \(0.936228\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.00000 | − | 5.19615i | −0.115045 | − | 0.199263i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.37228 | − | 2.37686i | 0.0525474 | − | 0.0910147i | ||||
\(683\) | −29.8397 | −1.14178 | −0.570891 | − | 0.821026i | \(-0.693402\pi\) | ||||
−0.570891 | + | 0.821026i | \(0.693402\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46.4674 | −1.77543 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.05842 | + | 7.02939i | 0.154726 | + | 0.267993i | ||||
\(689\) | 8.74456 | + | 15.1460i | 0.333141 | + | 0.577018i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.5584 | + | 20.0198i | −0.439703 | + | 0.761588i | −0.997666 | − | 0.0682775i | \(-0.978250\pi\) |
0.557963 | + | 0.829866i | \(0.311583\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.1168 | 0.384030 | ||||||||
\(695\) | 28.9307 | − | 50.1094i | 1.09740 | − | 1.90076i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.17527 | − | 5.49972i | −0.120272 | − | 0.208317i | ||||
\(698\) | −11.0000 | − | 19.0526i | −0.416356 | − | 0.721150i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.2337 | 1.44407 | 0.722033 | − | 0.691858i | \(-0.243208\pi\) | ||||
0.722033 | + | 0.691858i | \(0.243208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.0000 | −0.377157 | ||||||||
\(704\) | −0.686141 | + | 1.18843i | −0.0258599 | + | 0.0447907i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.68614 | + | 11.5807i | 0.251636 | + | 0.435847i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.0000 | + | 38.1051i | −0.826227 | + | 1.43107i | 0.0747503 | + | 0.997202i | \(0.476184\pi\) |
−0.900978 | + | 0.433865i | \(0.857149\pi\) | |||||||
\(710\) | 31.1168 | 1.16779 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.7446 | 0.552576 | ||||||||
\(713\) | 1.62772 | − | 2.81929i | 0.0609585 | − | 0.105583i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | + | 10.3923i | 0.224387 | + | 0.388650i | ||||
\(716\) | 1.62772 | + | 2.81929i | 0.0608307 | + | 0.105362i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.9307 | − | 18.9325i | 0.407930 | − | 0.706556i | ||||
\(719\) | 2.74456 | 0.102355 | 0.0511775 | − | 0.998690i | \(-0.483703\pi\) | ||||
0.0511775 | + | 0.998690i | \(0.483703\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.00000 | + | 5.19615i | −0.111648 | + | 0.193381i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.441578 | + | 0.764836i | 0.0164111 | + | 0.0284249i | ||||
\(725\) | −61.7228 | − | 106.907i | −2.29233 | − | 3.97043i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.1168 | + | 31.3793i | −0.671917 | + | 1.16379i | 0.305443 | + | 0.952210i | \(0.401195\pi\) |
−0.977360 | + | 0.211583i | \(0.932138\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −52.9783 | −1.96081 | ||||||||
\(731\) | 5.56930 | − | 9.64630i | 0.205988 | − | 0.356781i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.5584 | − | 35.6082i | −0.759343 | − | 1.31522i | −0.943186 | − | 0.332265i | \(-0.892187\pi\) |
0.183844 | − | 0.982956i | \(-0.441146\pi\) | |||||||
\(734\) | −6.11684 | − | 10.5947i | −0.225777 | − | 0.391057i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.813859 | + | 1.40965i | −0.0299993 | + | 0.0519602i | ||||
\(737\) | −2.90491 | −0.107004 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.11684 | −0.298583 | −0.149291 | − | 0.988793i | \(-0.547699\pi\) | ||||
−0.149291 | + | 0.988793i | \(0.547699\pi\) | |||||||
\(740\) | −4.37228 | + | 7.57301i | −0.160728 | + | 0.278390i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.86141 | − | 11.8843i | −0.251721 | − | 0.435993i | 0.712279 | − | 0.701896i | \(-0.247663\pi\) |
−0.964000 | + | 0.265904i | \(0.914330\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.11684 | − | 12.3267i | 0.260741 | − | 0.451617i | ||||
\(746\) | −10.0000 | −0.366126 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.88316 | 0.0688550 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.55842 | + | 14.8236i | 0.312301 | + | 0.540922i | 0.978860 | − | 0.204531i | \(-0.0655668\pi\) |
−0.666559 | + | 0.745452i | \(0.732234\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.74456 | − | 15.1460i | 0.318458 | − | 0.551586i | ||||
\(755\) | 39.8614 | 1.45071 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.2337 | 1.68039 | 0.840196 | − | 0.542283i | \(-0.182440\pi\) | ||||
0.840196 | + | 0.542283i | \(0.182440\pi\) | |||||||
\(758\) | 4.05842 | − | 7.02939i | 0.147409 | − | 0.255319i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.9307 | + | 18.9325i | 0.396498 | + | 0.686755i | ||||
\(761\) | −17.7446 | − | 30.7345i | −0.643240 | − | 1.11412i | −0.984705 | − | 0.174230i | \(-0.944256\pi\) |
0.341465 | − | 0.939894i | \(-0.389077\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 19.1168 | 0.691623 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.7446 | −1.18311 | ||||||||
\(767\) | −10.1168 | + | 17.5229i | −0.365298 | + | 0.632715i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.00000 | − | 8.66025i | −0.180305 | − | 0.312297i | 0.761680 | − | 0.647954i | \(-0.224375\pi\) |
−0.941984 | + | 0.335657i | \(0.891042\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.50000 | − | 6.06218i | 0.125968 | − | 0.218183i | ||||
\(773\) | −39.8614 | −1.43372 | −0.716858 | − | 0.697220i | \(-0.754420\pi\) | ||||
−0.716858 | + | 0.697220i | \(0.754420\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.2337 | −1.01418 | ||||||||
\(776\) | −4.05842 | + | 7.02939i | −0.145689 | + | 0.252341i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.48913 | + | 9.50744i | 0.196795 | + | 0.340858i | ||||
\(779\) | 11.5693 | + | 20.0386i | 0.414513 | + | 0.717958i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.88316 | + | 8.45787i | −0.174733 | + | 0.302647i | ||||
\(782\) | 2.23369 | 0.0798765 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.9307 | − | 34.5210i | 0.711357 | − | 1.23211i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.00000 | − | 3.46410i | −0.0712923 | − | 0.123482i | 0.828176 | − | 0.560469i | \(-0.189379\pi\) |
−0.899468 | + | 0.436987i | \(0.856046\pi\) | |||||||
\(788\) | −3.00000 | − | 5.19615i | −0.106871 | − | 0.185105i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.1861 | − | 19.3750i | 0.397985 | − | 0.689330i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.23369 | 0.221365 | ||||||||
\(794\) | −11.0000 | + | 19.0526i | −0.390375 | + | 0.676150i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.00000 | − | 8.66025i | −0.177220 | − | 0.306955i | ||||
\(797\) | 4.06930 | + | 7.04823i | 0.144142 | + | 0.249661i | 0.929052 | − | 0.369948i | \(-0.120624\pi\) |
−0.784911 | + | 0.619609i | \(0.787291\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 14.1168 | 0.499106 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.7446 | 0.414715 | ||||||||
\(803\) | 8.31386 | − | 14.4000i | 0.293390 | − | 0.508166i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.00000 | − | 3.46410i | −0.0704470 | − | 0.122018i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.813859 | + | 1.40965i | −0.0286315 | + | 0.0495912i | ||||
\(809\) | 6.86141 | 0.241234 | 0.120617 | − | 0.992699i | \(-0.461513\pi\) | ||||
0.120617 | + | 0.992699i | \(0.461513\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.1168 | −1.47892 | −0.739461 | − | 0.673199i | \(-0.764920\pi\) | ||||
−0.739461 | + | 0.673199i | \(0.764920\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.37228 | − | 2.37686i | −0.0480984 | − | 0.0833089i | ||||
\(815\) | 39.8614 | + | 69.0420i | 1.39628 | + | 2.41844i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.2921 | + | 35.1470i | −0.709931 | + | 1.22964i | ||||
\(818\) | 22.3505 | 0.781468 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.2337 | 0.706591 | ||||||||
\(821\) | −1.88316 | + | 3.26172i | −0.0657226 | + | 0.113835i | −0.897014 | − | 0.442002i | \(-0.854269\pi\) |
0.831292 | + | 0.555836i | \(0.187602\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.11684 | + | 10.5947i | 0.213220 | + | 0.369307i | 0.952720 | − | 0.303848i | \(-0.0982716\pi\) |
−0.739501 | + | 0.673156i | \(0.764938\pi\) | |||||||
\(824\) | −5.00000 | − | 8.66025i | −0.174183 | − | 0.301694i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.7663 | 0.478124 | 0.239062 | − | 0.971004i | \(-0.423160\pi\) | ||||
0.239062 | + | 0.971004i | \(0.423160\pi\) | |||||||
\(830\) | −38.2337 | + | 66.2227i | −1.32711 | + | 2.29862i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000 | + | 1.73205i | 0.0346688 | + | 0.0600481i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0000 | − | 20.7846i | 0.415277 | − | 0.719281i | ||||
\(836\) | −6.86141 | −0.237307 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.6060 | −0.435466 | ||||||||
\(839\) | −2.74456 | + | 4.75372i | −0.0947528 | + | 0.164117i | −0.909505 | − | 0.415692i | \(-0.863539\pi\) |
0.814753 | + | 0.579809i | \(0.196873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.7337 | − | 41.1080i | −0.818403 | − | 1.41752i | ||||
\(842\) | −17.1168 | − | 29.6472i | −0.589885 | − | 1.02171i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.00000 | − | 13.8564i | 0.275371 | − | 0.476957i | ||||
\(845\) | −39.3505 | −1.35370 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.37228 | + | 7.57301i | −0.150145 | + | 0.260058i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.68614 | − | 16.7769i | −0.332232 | − | 0.575443i | ||||
\(851\) | −1.62772 | − | 2.81929i | −0.0557975 | − | 0.0966441i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.5584 | + | 30.4121i | −0.601189 | + | 1.04129i | 0.391452 | + | 0.920198i | \(0.371973\pi\) |
−0.992641 | + | 0.121091i | \(0.961361\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.37228 | 0.251979 | ||||||||
\(857\) | 19.9783 | − | 34.6033i | 0.682444 | − | 1.18203i | −0.291789 | − | 0.956483i | \(-0.594250\pi\) |
0.974233 | − | 0.225545i | \(-0.0724163\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.9416 | + | 29.3437i | 0.578039 | + | 1.00119i | 0.995704 | + | 0.0925921i | \(0.0295153\pi\) |
−0.417665 | + | 0.908601i | \(0.637151\pi\) | |||||||
\(860\) | 17.7446 | + | 30.7345i | 0.605085 | + | 1.04804i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.25544 | + | 5.63858i | −0.110881 | + | 0.192051i | ||||
\(863\) | −9.86141 | −0.335686 | −0.167843 | − | 0.985814i | \(-0.553680\pi\) | ||||
−0.167843 | + | 0.985814i | \(0.553680\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.2337 | −0.891972 | ||||||||
\(866\) | −10.0584 | + | 17.4217i | −0.341799 | + | 0.592013i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.51087 | + | 6.08101i | 0.119098 | + | 0.206284i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.11684 | + | 3.66648i | −0.0717265 | + | 0.124234i | ||||
\(872\) | 14.0000 | 0.474100 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.13859 | −0.275292 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.3505 | + | 50.8366i | 0.991097 | + | 1.71663i | 0.610852 | + | 0.791744i | \(0.290827\pi\) |
0.380245 | + | 0.924886i | \(0.375840\pi\) | |||||||
\(878\) | 4.00000 | + | 6.92820i | 0.134993 | + | 0.233816i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.00000 | + | 5.19615i | −0.101130 | + | 0.175162i | ||||
\(881\) | −20.2337 | −0.681690 | −0.340845 | − | 0.940119i | \(-0.610713\pi\) | ||||
−0.340845 | + | 0.940119i | \(0.610713\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.3505 | −1.35790 | −0.678952 | − | 0.734183i | \(-0.737565\pi\) | ||||
−0.678952 | + | 0.734183i | \(0.737565\pi\) | |||||||
\(884\) | 1.37228 | − | 2.37686i | 0.0461548 | − | 0.0799425i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.0584 | − | 34.7422i | −0.673876 | − | 1.16719i | ||||
\(887\) | −12.8614 | − | 22.2766i | −0.431844 | − | 0.747975i | 0.565188 | − | 0.824962i | \(-0.308803\pi\) |
−0.997032 | + | 0.0769865i | \(0.975470\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 64.4674 | 2.16095 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.00000 | 0.133930 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.11684 | + | 12.3267i | 0.237890 | + | 0.412037i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.5000 | − | 28.5788i | 0.550612 | − | 0.953688i | ||||
\(899\) | −17.4891 | −0.583295 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | −3.17527 | + | 5.49972i | −0.105725 | + | 0.183121i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.18614 | − | 3.78651i | −0.0727100 | − | 0.125937i | ||||
\(905\) | 1.93070 | + | 3.34408i | 0.0641787 | + | 0.111161i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.0584 | − | 22.6179i | 0.433598 | − | 0.751013i | −0.563582 | − | 0.826060i | \(-0.690577\pi\) |
0.997180 | + | 0.0750466i | \(0.0239105\pi\) | |||||||
\(908\) | −12.2554 | −0.406711 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.8139 | + | 32.5866i | −0.623331 | + | 1.07964i | 0.365530 | + | 0.930800i | \(0.380888\pi\) |
−0.988861 | + | 0.148841i | \(0.952446\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.0000 | − | 20.7846i | −0.397142 | − | 0.687870i | ||||
\(914\) | 17.7337 | + | 30.7156i | 0.586578 | + | 1.01598i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.44158 | + | 2.49689i | −0.0476311 | + | 0.0824994i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.1168 | −1.55424 | −0.777121 | − | 0.629352i | \(-0.783321\pi\) | ||||
−0.777121 | + | 0.629352i | \(0.783321\pi\) | |||||||
\(920\) | −3.55842 | + | 6.16337i | −0.117318 | + | 0.203200i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.06930 | − | 1.85208i | −0.0352154 | − | 0.0609949i | ||||
\(923\) | 7.11684 | + | 12.3267i | 0.234254 | + | 0.405739i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.1168 | + | 24.4511i | −0.464159 | + | 0.803947i | ||||
\(926\) | −23.1168 | −0.759667 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.74456 | 0.287054 | ||||||||
\(929\) | −22.1168 | + | 38.3075i | −0.725630 | + | 1.25683i | 0.233084 | + | 0.972457i | \(0.425118\pi\) |
−0.958714 | + | 0.284372i | \(0.908215\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.127719 | − | 0.221215i | −0.00418356 | − | 0.00724615i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.5475 | + | 28.6612i | −0.541452 | + | 0.937823i | ||||
\(935\) | 8.23369 | 0.269270 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.4674 | −0.995326 | −0.497663 | − | 0.867371i | \(-0.665808\pi\) | ||||
−0.497663 | + | 0.867371i | \(0.665808\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.55842 | − | 16.5557i | −0.311596 | − | 0.539699i | 0.667112 | − | 0.744957i | \(-0.267530\pi\) |
−0.978708 | + | 0.205258i | \(0.934197\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.76631 | + | 6.52344i | −0.122648 | + | 0.212433i | ||||
\(944\) | −10.1168 | −0.329275 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.1386 | −0.362147 | ||||||||
\(947\) | 17.0584 | − | 29.5461i | 0.554324 | − | 0.960118i | −0.443632 | − | 0.896209i | \(-0.646310\pi\) |
0.997956 | − | 0.0639085i | \(-0.0203566\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.1168 | − | 20.9870i | −0.393329 | − | 0.681267i | ||||
\(950\) | 35.2921 | + | 61.1277i | 1.14503 | + | 1.98325i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.1168 | −0.910794 | −0.455397 | − | 0.890288i | \(-0.650503\pi\) | ||||
−0.455397 | + | 0.890288i | \(0.650503\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 83.5842 | 2.70472 | ||||||||
\(956\) | 4.93070 | − | 8.54023i | 0.159470 | − | 0.276211i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.3723 | − | 28.3576i | −0.528964 | − | 0.916193i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | −4.00000 | −0.128965 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.1168 | −0.583504 | ||||||||
\(965\) | 15.3030 | − | 26.5055i | 0.492621 | − | 0.853244i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.4416 | − | 26.7456i | −0.496568 | − | 0.860080i | 0.503424 | − | 0.864039i | \(-0.332073\pi\) |
−0.999992 | + | 0.00395879i | \(0.998740\pi\) | |||||||
\(968\) | 4.55842 | + | 7.89542i | 0.146513 | + | 0.253768i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −17.7446 | + | 30.7345i | −0.569744 | + | 0.986825i | ||||
\(971\) | 1.62772 | 0.0522360 | 0.0261180 | − | 0.999659i | \(-0.491685\pi\) | ||||
0.0261180 | + | 0.999659i | \(0.491685\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −17.6753 | + | 30.6145i | −0.566352 | + | 0.980951i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.55842 | + | 2.69927i | 0.0498839 | + | 0.0864014i | ||||
\(977\) | 20.0584 | + | 34.7422i | 0.641726 | + | 1.11150i | 0.985047 | + | 0.172284i | \(0.0551146\pi\) |
−0.343322 | + | 0.939218i | \(0.611552\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.1168 | + | 17.5229i | −0.323336 | + | 0.560034i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 25.3723 | 0.809662 | ||||||||
\(983\) | 19.6277 | − | 33.9962i | 0.626027 | − | 1.08431i | −0.362314 | − | 0.932056i | \(-0.618013\pi\) |
0.988341 | − | 0.152255i | \(-0.0486534\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.1168 | − | 22.7190i | −0.417937 | − | 0.723889i | ||||
\(986\) | −6.00000 | − | 10.3923i | −0.191079 | − | 0.330958i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.00000 | + | 8.66025i | −0.159071 | + | 0.275519i | ||||
\(989\) | −13.2119 | −0.420115 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.4674 | 1.53962 | 0.769808 | − | 0.638275i | \(-0.220352\pi\) | ||||
0.769808 | + | 0.638275i | \(0.220352\pi\) | |||||||
\(992\) | 1.00000 | − | 1.73205i | 0.0317500 | − | 0.0549927i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.8614 | − | 37.8651i | −0.693053 | − | 1.20040i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.55842 | + | 4.43132i | −0.0810260 | + | 0.140341i | −0.903691 | − | 0.428185i | \(-0.859153\pi\) |
0.822665 | + | 0.568527i | \(0.192486\pi\) | |||||||
\(998\) | 18.1168 | 0.573479 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))