Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.r (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: | \(8.04892052375\) |
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: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(1.68614 - 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.337 |
Dual form | 1008.2.r.f.673.2 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.68614 | + | 0.396143i | 0.973494 | + | 0.228714i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.18614 | + | 3.78651i | −0.977672 | + | 1.69338i | −0.306851 | + | 0.951757i | \(0.599275\pi\) |
−0.670820 | + | 0.741620i | \(0.734058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.68614 | + | 1.33591i | 0.895380 | + | 0.445302i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.686141 | − | 1.18843i | −0.206879 | − | 0.358325i | 0.743851 | − | 0.668346i | \(-0.232997\pi\) |
−0.950730 | + | 0.310021i | \(0.899664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | + | 1.73205i | −0.277350 | + | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.18614 | + | 5.51856i | −1.33906 | + | 1.42489i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 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 | \(0.694430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.500000 | + | 1.65831i | 0.109109 | + | 0.361873i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.813859 | + | 1.40965i | −0.169701 | + | 0.293931i | −0.938315 | − | 0.345782i | \(-0.887614\pi\) |
0.768613 | + | 0.639713i | \(0.220947\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.05842 | − | 12.2255i | −1.41168 | − | 2.44511i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | + | 3.31662i | 0.769800 | + | 0.638285i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.37228 | + | 7.57301i | 0.811912 | + | 1.40627i | 0.911524 | + | 0.411247i | \(0.134907\pi\) |
−0.0996117 | + | 0.995026i | \(0.531760\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | − | 1.73205i | 0.179605 | − | 0.311086i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.941745 | + | 0.336327i | \(0.109185\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.686141 | − | 2.27567i | −0.119442 | − | 0.396143i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.37228 | −0.739050 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.37228 | + | 2.52434i | −0.379869 | + | 0.404218i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.31386 | + | 4.00772i | −0.361364 | + | 0.625901i | −0.988186 | − | 0.153262i | \(-0.951022\pi\) |
0.626821 | + | 0.779163i | \(0.284356\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.05842 | − | 7.02939i | −0.618904 | − | 1.07197i | −0.989686 | − | 0.143253i | \(-0.954244\pi\) |
0.370783 | − | 0.928720i | \(-0.379090\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.9307 | + | 7.25061i | −1.62945 | + | 1.08086i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.31386 | + | 0.543620i | 0.324005 | + | 0.0761221i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.74456 | −1.20116 | −0.600579 | − | 0.799565i | \(-0.705063\pi\) | ||||
−0.600579 | + | 0.799565i | \(0.705063\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | 0.809040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.43070 | − | 1.98072i | −1.11667 | − | 0.262352i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.05842 | + | 8.76144i | −0.658550 | + | 1.14064i | 0.322441 | + | 0.946590i | \(0.395497\pi\) |
−0.980991 | + | 0.194053i | \(0.937837\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.55842 | − | 2.69927i | −0.199535 | − | 0.345606i | 0.748842 | − | 0.662748i | \(-0.230610\pi\) |
−0.948378 | + | 0.317142i | \(0.897277\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.186141 | + | 2.99422i | 0.0234515 | + | 0.377236i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.37228 | − | 7.57301i | −0.542315 | − | 0.939317i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.05842 | + | 1.83324i | −0.129307 | + | 0.223966i | −0.923408 | − | 0.383819i | \(-0.874609\pi\) |
0.794101 | + | 0.607785i | \(0.207942\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.93070 | + | 2.05446i | −0.232429 | + | 0.247327i | ||||
\(70\) | 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 | \(-0.249108\pi\) | ||||
0.709085 | + | 0.705123i | \(0.249108\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.05842 | − | 23.4101i | −0.815036 | − | 2.70317i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.686141 | − | 1.18843i | 0.0781930 | − | 0.135434i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.55842 | − | 4.43132i | −0.287845 | − | 0.498562i | 0.685450 | − | 0.728120i | \(-0.259605\pi\) |
−0.973295 | + | 0.229557i | \(0.926272\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.43070 | + | 7.17687i | 0.603411 | + | 0.797430i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.74456 | + | 15.1460i | 0.959840 | + | 1.66249i | 0.722881 | + | 0.690973i | \(0.242818\pi\) |
0.236960 | + | 0.971519i | \(0.423849\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | + | 5.19615i | −0.325396 | + | 0.563602i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.37228 | + | 14.5012i | 0.468758 | + | 1.55469i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.7446 | 1.56292 | 0.781460 | − | 0.623955i | \(-0.214475\pi\) | ||||
0.781460 | + | 0.623955i | \(0.214475\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.37228 | − | 2.52434i | 0.245994 | − | 0.261762i | ||||
\(94\) | 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 | \(-0.0314725\pi\) |
−0.583046 | + | 0.812439i | \(0.698139\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.255437 | − | 4.10891i | −0.0256724 | − | 0.412961i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.813859 | − | 1.40965i | −0.0809820 | − | 0.140265i | 0.822690 | − | 0.568490i | \(-0.192472\pi\) |
−0.903672 | + | 0.428225i | \(0.859139\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.00000 | + | 8.66025i | −0.492665 | + | 0.853320i | −0.999964 | − | 0.00844953i | \(-0.997310\pi\) |
0.507300 | + | 0.861770i | \(0.330644\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.37228 | − | 1.73205i | −0.719461 | − | 0.169031i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 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 | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.37228 | + | 0.792287i | 0.320083 | + | 0.0752006i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.18614 | − | 3.78651i | 0.205655 | − | 0.356205i | −0.744686 | − | 0.667415i | \(-0.767401\pi\) |
0.950341 | + | 0.311210i | \(0.100734\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.55842 | − | 6.16337i | −0.331825 | − | 0.574737i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.00000 | + | 3.31662i | −0.462250 | + | 0.306622i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.686141 | + | 1.18843i | 0.0628984 | + | 0.108943i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.55842 | − | 7.89542i | 0.414402 | − | 0.717765i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.48913 | + | 5.84096i | −0.494938 | + | 0.526662i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 39.8614 | 3.56531 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.11684 | −0.276575 | −0.138288 | − | 0.990392i | \(-0.544160\pi\) | ||||
−0.138288 | + | 0.990392i | \(0.544160\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.05842 | − | 13.4603i | −0.357324 | − | 1.18511i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.813859 | + | 1.40965i | −0.0711072 | + | 0.123161i | −0.899387 | − | 0.437154i | \(-0.855987\pi\) |
0.828280 | + | 0.560315i | \(0.189320\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.50000 | − | 4.33013i | −0.216777 | − | 0.375470i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −21.3030 | + | 7.89542i | −1.83347 | + | 0.679529i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.31386 | − | 9.20387i | −0.453994 | − | 0.786340i | 0.544636 | − | 0.838672i | \(-0.316668\pi\) |
−0.998630 | + | 0.0523324i | \(0.983334\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.61684 | − | 11.4607i | 0.561233 | − | 0.972085i | −0.436156 | − | 0.899871i | \(-0.643660\pi\) |
0.997389 | − | 0.0722136i | \(-0.0230063\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.74456 | 0.229512 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −38.2337 | −3.17513 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.18614 | + | 1.26217i | −0.0978312 | + | 0.104102i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.62772 | + | 2.81929i | −0.133348 | + | 0.230965i | −0.924965 | − | 0.380052i | \(-0.875906\pi\) |
0.791617 | + | 0.611017i | \(0.209239\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.55842 | + | 7.89542i | 0.370959 | + | 0.642520i | 0.989713 | − | 0.143065i | \(-0.0456957\pi\) |
−0.618754 | + | 0.785585i | \(0.712362\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.68614 | + | 1.83324i | 0.298007 | + | 0.148209i | ||||
\(154\) | 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 | \(-0.951855\pi\) |
0.624781 | + | 0.780800i | \(0.285188\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.7446 | − | 3.46410i | −1.16932 | − | 0.274721i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.62772 | −0.128282 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.2337 | 1.42817 | 0.714086 | − | 0.700058i | \(-0.246842\pi\) | ||||
0.714086 | + | 0.700058i | \(0.246842\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.1168 | + | 2.37686i | 0.787595 | + | 0.185038i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.74456 | + | 4.75372i | −0.212381 | + | 0.367854i | −0.952459 | − | 0.304666i | \(-0.901455\pi\) |
0.740078 | + | 0.672521i | \(0.234788\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.4307 | − | 6.67954i | −1.02707 | − | 0.510797i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.00000 | + | 5.19615i | 0.228086 | + | 0.395056i | 0.957241 | − | 0.289292i | \(-0.0934200\pi\) |
−0.729155 | + | 0.684349i | \(0.760087\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.05842 | − | 12.2255i | 0.533567 | − | 0.924164i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.0000 | + | 12.7692i | −0.901975 | + | 0.959789i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −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 | \(-0.489550\pi\) | ||||
0.0328222 | + | 0.999461i | \(0.489550\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.55842 | − | 5.16870i | −0.115202 | − | 0.382081i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.37228 | + | 7.57301i | −0.321457 | + | 0.556779i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.941578 | − | 1.63086i | −0.0688550 | − | 0.119260i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.872281 | + | 5.12241i | −0.0634491 | + | 0.372601i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.55842 | − | 16.5557i | −0.691623 | − | 1.19793i | −0.971306 | − | 0.237834i | \(-0.923563\pi\) |
0.279683 | − | 0.960092i | \(-0.409771\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.50000 | − | 6.06218i | 0.251936 | − | 0.436365i | −0.712123 | − | 0.702055i | \(-0.752266\pi\) |
0.964059 | + | 0.265689i | \(0.0855996\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.37228 | − | 14.5012i | −0.313106 | − | 1.03845i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000 | 0.708881 | 0.354441 | − | 0.935079i | \(-0.384671\pi\) | ||||
0.354441 | + | 0.935079i | \(0.384671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.51087 | + | 2.67181i | −0.177103 | + | 0.188455i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.37228 | + | 7.57301i | −0.306874 | + | 0.531521i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.1168 | − | 17.5229i | −0.706591 | − | 1.22385i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.06930 | + | 2.69927i | −0.282836 | + | 0.187612i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.43070 | + | 5.94215i | 0.237307 | + | 0.411027i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | + | 13.8564i | −0.550743 | + | 0.953914i | 0.447478 | + | 0.894295i | \(0.352322\pi\) |
−0.998221 | + | 0.0596196i | \(0.981011\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.0000 | + | 2.81929i | 0.822226 | + | 0.193175i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 35.4891 | 2.42034 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.4307 | + | 4.80001i | 1.38058 | + | 0.324355i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.37228 | + | 2.37686i | −0.0923096 | + | 0.159885i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.00000 | − | 3.46410i | −0.133930 | − | 0.231973i | 0.791258 | − | 0.611482i | \(-0.209426\pi\) |
−0.925188 | + | 0.379509i | \(0.876093\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.62772 | − | 42.2689i | −0.175181 | − | 2.81793i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.12772 | − | 10.6135i | −0.406711 | − | 0.704444i | 0.587808 | − | 0.809000i | \(-0.299991\pi\) |
−0.994519 | + | 0.104556i | \(0.966658\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.44158 | − | 2.49689i | 0.0952622 | − | 0.164999i | −0.814456 | − | 0.580226i | \(-0.802964\pi\) |
0.909718 | + | 0.415227i | \(0.136298\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.62772 | − | 1.73205i | 0.107096 | − | 0.113961i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.255437 | −0.0167343 | −0.00836713 | − | 0.999965i | \(-0.502663\pi\) | ||||
−0.00836713 | + | 0.999965i | \(0.502663\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.55842 | − | 8.48533i | −0.166187 | − | 0.551181i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.93070 | − | 8.54023i | 0.318941 | − | 0.552421i | −0.661327 | − | 0.750098i | \(-0.730006\pi\) |
0.980267 | + | 0.197677i | \(0.0633396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.05842 | − | 15.6896i | −0.583504 | − | 1.01066i | −0.995060 | − | 0.0992745i | \(-0.968348\pi\) |
0.411556 | − | 0.911385i | \(-0.364986\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.31386 | + | 14.2525i | 0.405034 | + | 0.914302i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.18614 | − | 3.78651i | −0.139667 | − | 0.241911i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.00000 | − | 8.66025i | 0.318142 | − | 0.551039i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.74456 | + | 29.0024i | 0.554164 | + | 1.83795i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.00000 | 0.568075 | 0.284037 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284037 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.23369 | 0.140431 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.11684 | + | 7.57301i | −0.445674 | + | 0.474240i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.43070 | − | 5.94215i | 0.214001 | − | 0.370661i | −0.738962 | − | 0.673747i | \(-0.764684\pi\) |
0.952963 | + | 0.303086i | \(0.0980170\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.00000 | + | 1.73205i | 0.0621370 | + | 0.107624i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.62772 | + | 26.1831i | 0.100753 | + | 1.62070i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.81386 | + | 6.60580i | 0.235173 | + | 0.407331i | 0.959323 | − | 0.282311i | \(-0.0911011\pi\) |
−0.724150 | + | 0.689642i | \(0.757768\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.1168 | − | 33.1113i | 1.17434 | − | 2.03401i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.8614 | + | 5.84096i | 1.52149 | + | 0.357461i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −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 | 0 | ||||||||
\(273\) | −3.37228 | − | 0.792287i | −0.204100 | − | 0.0479514i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.68614 | + | 16.7769i | −0.584096 | + | 1.01168i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.11684 | + | 10.5947i | 0.367526 | + | 0.636573i | 0.989178 | − | 0.146720i | \(-0.0468717\pi\) |
−0.621652 | + | 0.783293i | \(0.713538\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.00000 | − | 3.31662i | 0.299342 | − | 0.198561i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.18614 | − | 14.1788i | −0.488344 | − | 0.845837i | 0.511566 | − | 0.859244i | \(-0.329066\pi\) |
−0.999910 | + | 0.0134071i | \(0.995732\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.5584 | − | 23.4839i | 0.805965 | − | 1.39597i | −0.109673 | − | 0.993968i | \(-0.534981\pi\) |
0.915638 | − | 0.402004i | \(-0.131686\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 25.9307 | − | 27.5928i | 1.53600 | − | 1.63446i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.62772 | −0.273166 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1168 | −0.889226 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.05842 | + | 13.4603i | 0.237909 | + | 0.789055i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.18614 | − | 8.98266i | 0.302978 | − | 0.524773i | −0.673831 | − | 0.738885i | \(-0.735353\pi\) |
0.976809 | + | 0.214113i | \(0.0686859\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.1168 | − | 38.3075i | −1.28769 | − | 2.23035i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.19702 | − | 7.02939i | 0.0694579 | − | 0.407887i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.62772 | − | 2.81929i | −0.0941334 | − | 0.163044i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.05842 | − | 7.02939i | 0.233924 | − | 0.405167i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.813859 | − | 2.69927i | −0.0467550 | − | 0.155069i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 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 | ||||||||
\(309\) | −11.8614 | + | 12.6217i | −0.674772 | + | 0.718023i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.11684 | − | 7.13058i | 0.233445 | − | 0.404338i | −0.725375 | − | 0.688354i | \(-0.758334\pi\) |
0.958820 | + | 0.284016i | \(0.0916668\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0584 | + | 17.4217i | 0.568536 | + | 0.984733i | 0.996711 | + | 0.0810370i | \(0.0258232\pi\) |
−0.428175 | + | 0.903696i | \(0.640843\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.7446 | − | 5.84096i | −0.661731 | − | 0.329101i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.00000 | + | 5.19615i | 0.168497 | + | 0.291845i | 0.937892 | − | 0.346929i | \(-0.112775\pi\) |
−0.769395 | + | 0.638774i | \(0.779442\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.00000 | − | 10.3923i | 0.335936 | − | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.4307 | + | 2.92048i | 0.693814 | + | 0.163005i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.86141 | −0.381779 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.2337 | 1.56612 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.6060 | + | 5.54601i | 1.30541 | + | 0.306695i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.1168 | + | 19.2549i | 0.611037 | + | 1.05835i | 0.991066 | + | 0.133373i | \(0.0425807\pi\) |
−0.380029 | + | 0.924975i | \(0.624086\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.37228 | + | 2.67181i | 0.294399 | + | 0.146415i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.62772 | − | 8.01544i | −0.252839 | − | 0.437930i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.05842 | − | 7.02939i | 0.221076 | − | 0.382915i | −0.734059 | − | 0.679086i | \(-0.762376\pi\) |
0.955135 | + | 0.296171i | \(0.0957097\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.18614 | − | 5.51856i | 0.281672 | − | 0.299727i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.74456 | −0.148626 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.55842 | − | 11.8020i | −0.191579 | − | 0.635396i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.05842 | + | 8.76144i | −0.271550 | + | 0.470339i | −0.969259 | − | 0.246043i | \(-0.920870\pi\) |
0.697709 | + | 0.716382i | \(0.254203\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.0000 | + | 19.0526i | 0.588817 | + | 1.01986i | 0.994388 | + | 0.105797i | \(0.0337393\pi\) |
−0.405571 | + | 0.914063i | \(0.632927\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.74456 | + | 3.61158i | −0.520126 | + | 0.192772i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.68614 | + | 11.5807i | 0.355867 | + | 0.616380i | 0.987266 | − | 0.159078i | \(-0.0508522\pi\) |
−0.631399 | + | 0.775458i | \(0.717519\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.5584 | + | 26.9480i | −0.825755 | + | 1.43025i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.686141 | + | 2.27567i | 0.0363144 | + | 0.120441i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −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 | 0 | ||||||||
\(363\) | 10.8139 | − | 11.5070i | 0.567580 | − | 0.603961i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.4891 | + | 45.8805i | −1.38650 | + | 2.40150i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.11684 | − | 10.5947i | −0.319297 | − | 0.553038i | 0.661045 | − | 0.750346i | \(-0.270113\pi\) |
−0.980341 | + | 0.197308i | \(0.936780\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.5693 | + | 7.67420i | −0.602274 | + | 0.399503i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.37228 | − | 7.57301i | −0.226998 | − | 0.393171i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | − | 8.66025i | 0.258890 | − | 0.448411i | −0.707055 | − | 0.707159i | \(-0.749977\pi\) |
0.965945 | + | 0.258748i | \(0.0833099\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 67.2119 | + | 15.7908i | 3.47081 | + | 0.815435i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.4891 | −0.900736 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.11684 | 0.416934 | 0.208467 | − | 0.978029i | \(-0.433153\pi\) | ||||
0.208467 | + | 0.978029i | \(0.433153\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.25544 | − | 1.23472i | −0.269244 | − | 0.0632565i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.3723 | + | 28.3576i | −0.836584 | + | 1.44901i | 0.0561493 | + | 0.998422i | \(0.482118\pi\) |
−0.892734 | + | 0.450584i | \(0.851216\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.00000 | + | 5.19615i | 0.152894 | + | 0.264820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.51087 | − | 24.3036i | −0.0768021 | − | 1.23542i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.48913 | − | 9.50744i | −0.278310 | − | 0.482047i | 0.692655 | − | 0.721269i | \(-0.256441\pi\) |
−0.970965 | + | 0.239222i | \(0.923107\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.11684 | + | 1.93443i | −0.0564812 | + | 0.0978284i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.93070 | + | 2.05446i | −0.0973911 | + | 0.103634i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.3723 | 1.12567 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.50000 | − | 8.29156i | −0.125157 | − | 0.415097i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.87228 | − | 10.1711i | 0.293248 | − | 0.507920i | −0.681328 | − | 0.731978i | \(-0.738597\pi\) |
0.974576 | + | 0.224058i | \(0.0719306\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.00000 | + | 3.46410i | 0.0996271 | + | 0.172559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −39.0475 | + | 4.87375i | −1.94029 | + | 0.242178i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.37228 | − | 2.37686i | −0.0680215 | − | 0.117817i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.1753 | − | 19.3561i | 0.552581 | − | 0.957099i | −0.445506 | − | 0.895279i | \(-0.646976\pi\) |
0.998087 | − | 0.0618200i | \(-0.0196905\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.31386 | − | 17.6241i | −0.262113 | − | 0.869332i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.1168 | −0.497817 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −76.4674 | −3.75364 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.6970 | − | 16.7031i | 0.768686 | − | 0.817957i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.30298 | + | 10.9171i | −0.307921 | + | 0.533335i | −0.977907 | − | 0.209039i | \(-0.932967\pi\) |
0.669986 | + | 0.742373i | \(0.266300\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.1168 | − | 29.6472i | −0.834224 | − | 1.44492i | −0.894661 | − | 0.446746i | \(-0.852583\pi\) |
0.0604368 | − | 0.998172i | \(-0.480751\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.68614 | − | 16.7769i | −0.469847 | − | 0.813799i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.55842 | − | 2.69927i | 0.0754173 | − | 0.130627i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.62772 | + | 1.08724i | 0.223428 | + | 0.0524925i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 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 | \(-0.660590\pi\) | ||||
−0.483377 | + | 0.875412i | \(0.660590\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −64.4674 | − | 15.1460i | −3.09097 | − | 0.726196i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.06930 | − | 7.04823i | 0.194661 | − | 0.337162i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000 | + | 6.92820i | 0.190910 | + | 0.330665i | 0.945552 | − | 0.325471i | \(-0.105523\pi\) |
−0.754642 | + | 0.656136i | \(0.772190\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.50000 | + | 1.65831i | −0.119048 | + | 0.0789673i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.0584 | − | 34.7422i | −0.953004 | − | 1.65065i | −0.738870 | − | 0.673848i | \(-0.764640\pi\) |
−0.214134 | − | 0.976804i | \(-0.568693\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.2337 | + | 55.8304i | −1.52802 | + | 2.64661i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.86141 | + | 4.10891i | −0.182638 | + | 0.194345i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.0000 | 1.55737 | 0.778683 | − | 0.627417i | \(-0.215888\pi\) | ||||
0.778683 | + | 0.627417i | \(0.215888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.35053 | 0.299035 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.55842 | + | 15.1186i | 0.214173 | + | 0.710333i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.37228 | − | 7.57301i | 0.204976 | − | 0.355028i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.7337 | + | 30.7156i | 0.829547 | + | 1.43682i | 0.898394 | + | 0.439190i | \(0.144735\pi\) |
−0.0688472 | + | 0.997627i | \(0.521932\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.48913 | + | 4.55134i | 0.256210 | + | 0.212438i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.06930 | − | 1.85208i | −0.0498021 | − | 0.0862598i | 0.840050 | − | 0.542509i | \(-0.182526\pi\) |
−0.889852 | + | 0.456250i | \(0.849192\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.5584 | + | 20.0198i | −0.537165 | + | 0.930398i | 0.461890 | + | 0.886937i | \(0.347172\pi\) |
−0.999055 | + | 0.0434604i | \(0.986162\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.37228 | + | 14.5012i | 0.202760 | + | 0.672478i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.0951 | −1.53146 | −0.765729 | − | 0.643163i | \(-0.777622\pi\) | ||||
−0.765729 | + | 0.643163i | \(0.777622\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.11684 | −0.0977468 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.8139 | + | 11.5070i | −0.498276 | + | 0.530214i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.56930 | + | 9.64630i | −0.256077 | + | 0.443538i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 35.2921 | + | 61.1277i | 1.61931 | + | 2.80473i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.4891 | − | 11.6819i | −1.07549 | − | 0.534879i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.3723 | + | 28.3576i | 0.748069 | + | 1.29569i | 0.948747 | + | 0.316036i | \(0.102352\pi\) |
−0.200679 | + | 0.979657i | \(0.564315\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | + | 3.46410i | −0.0911922 | + | 0.157949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.74456 | − | 0.644810i | −0.124882 | − | 0.0293399i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −35.4891 | −1.61148 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.3505 | −1.60189 | −0.800943 | − | 0.598741i | \(-0.795668\pi\) | ||||
−0.800943 | + | 0.598741i | \(0.795668\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 30.7446 | + | 7.22316i | 1.39032 | + | 0.326642i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.6861 | + | 21.9730i | −0.572518 | + | 0.991629i | 0.423789 | + | 0.905761i | \(0.360700\pi\) |
−0.996306 | + | 0.0858685i | \(0.972634\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.00000 | + | 10.3923i | 0.270226 | + | 0.468046i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.1168 | + | 8.01544i | 0.724398 | + | 0.360267i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.55842 | + | 6.16337i | 0.159617 | + | 0.276465i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.05842 | − | 15.6896i | 0.405511 | − | 0.702365i | −0.588870 | − | 0.808228i | \(-0.700427\pi\) |
0.994381 | + | 0.105863i | \(0.0337604\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.51087 | + | 6.92820i | −0.290884 | + | 0.309529i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.2337 | 1.43723 | 0.718615 | − | 0.695409i | \(-0.244777\pi\) | ||||
0.718615 | + | 0.695409i | \(0.244777\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.11684 | 0.316695 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.50000 | + | 14.9248i | 0.199852 | + | 0.662834i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.4891 | − | 25.0959i | 0.642219 | − | 1.11236i | −0.342717 | − | 0.939439i | \(-0.611347\pi\) |
0.984936 | − | 0.172918i | \(-0.0553194\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.05842 | + | 10.4935i | 0.268009 | + | 0.464205i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.0000 | − | 16.5831i | −0.883022 | − | 0.732163i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −21.8614 | − | 37.8651i | −0.963329 | − | 1.66853i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.00000 | + | 9.94987i | 0.131685 | + | 0.436751i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −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 | 0 | ||||||||
\(525\) | 16.7446 | − | 17.8178i | 0.730793 | − | 0.777634i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.37228 | − | 2.37686i | 0.0597775 | − | 0.103538i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.1753 | + | 17.6241i | 0.442403 | + | 0.766264i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −25.2921 | + | 16.7769i | −1.09758 | + | 0.728055i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.62772 | − | 8.01544i | −0.200449 | − | 0.347187i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.1168 | + | 27.9152i | −0.696792 | + | 1.20688i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.48913 | − | 1.28962i | −0.236873 | − | 0.0556512i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.37228 | 0.0591083 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.23369 | −0.268007 | −0.134004 | − | 0.990981i | \(-0.542783\pi\) | ||||
−0.134004 | + | 0.990981i | \(0.542783\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.48913 | + | 0.349857i | 0.0639045 | + | 0.0150138i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −30.6060 | + | 53.0111i | −1.31102 | + | 2.27075i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.05842 | + | 15.6896i | 0.387310 | + | 0.670841i | 0.992087 | − | 0.125554i | \(-0.0400709\pi\) |
−0.604777 | + | 0.796395i | \(0.706738\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.580171 | − | 9.33252i | −0.0247611 | − | 0.398302i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.8614 | − | 37.8651i | −0.931327 | − | 1.61311i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.55842 | − | 4.43132i | 0.108795 | − | 0.188439i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.3723 | + | 11.0371i | −0.440279 | + | 0.468499i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.4891 | 1.24949 | 0.624747 | − | 0.780827i | \(-0.285202\pi\) | ||||
0.624747 | + | 0.780827i | \(0.285202\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.2337 | 0.686612 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.941578 | − | 3.12286i | −0.0397535 | − | 0.131847i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.50000 | − | 2.59808i | 0.0632175 | − | 0.109496i | −0.832684 | − | 0.553748i | \(-0.813197\pi\) |
0.895902 | + | 0.444252i | \(0.146530\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.55842 | + | 16.5557i | 0.402126 | + | 0.696502i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.50000 | + | 8.29156i | −0.146986 | + | 0.348213i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.05842 | − | 13.9576i | −0.337827 | − | 0.585133i | 0.646197 | − | 0.763171i | \(-0.276358\pi\) |
−0.984024 | + | 0.178038i | \(0.943025\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.1753 | + | 19.3561i | −0.467670 | + | 0.810029i | −0.999318 | − | 0.0369371i | \(-0.988240\pi\) |
0.531647 | + | 0.846966i | \(0.321573\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.55842 | − | 31.7017i | −0.399309 | − | 1.32436i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.9783 | 0.958259 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.88316 | 0.411441 | 0.205721 | − | 0.978611i | \(-0.434046\pi\) | ||||
0.205721 | + | 0.978611i | \(0.434046\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.30298 | − | 8.83518i | 0.345060 | − | 0.367178i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.74456 | + | 15.1460i | −0.362786 | + | 0.628363i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.00000 | + | 10.3923i | 0.248495 | + | 0.430405i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.62772 | − | 26.1831i | −0.0672979 | − | 1.08254i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.24456 | + | 12.5480i | 0.299015 | + | 0.517909i | 0.975911 | − | 0.218170i | \(-0.0700086\pi\) |
−0.676896 | + | 0.736079i | \(0.736675\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.00000 | + | 8.66025i | −0.206021 | + | 0.356840i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.1168 | − | 2.37686i | −0.416151 | − | 0.0977710i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.7446 | 0.605487 | 0.302743 | − | 0.953072i | \(-0.402098\pi\) | ||||
0.302743 | + | 0.953072i | \(0.402098\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | −0.245976 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.8614 | + | 3.96143i | 0.690091 | + | 0.162131i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | − | 20.7846i | 0.490307 | − | 0.849236i | −0.509631 | − | 0.860393i | \(-0.670218\pi\) |
0.999938 | + | 0.0111569i | \(0.00355143\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.0584 | − | 20.8858i | −0.491873 | − | 0.851950i | 0.508083 | − | 0.861308i | \(-0.330354\pi\) |
−0.999956 | + | 0.00935863i | \(0.997021\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.29211 | + | 3.51039i | −0.215511 | + | 0.142954i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.9307 | + | 34.5210i | 0.810298 | + | 1.40348i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.1168 | − | 19.2549i | 0.451219 | − | 0.781534i | −0.547243 | − | 0.836974i | \(-0.684323\pi\) |
0.998462 | + | 0.0554398i | \(0.0176561\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.3723 | + | 11.0371i | −0.420306 | + | 0.447246i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.2337 | −1.46346 | −0.731732 | − | 0.681592i | \(-0.761288\pi\) | ||||
−0.731732 | + | 0.681592i | \(0.761288\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.1168 | − | 33.5538i | −0.407951 | − | 1.35302i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.43070 | + | 16.3345i | −0.379666 | + | 0.657600i | −0.991014 | − | 0.133762i | \(-0.957294\pi\) |
0.611348 | + | 0.791362i | \(0.290628\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.7337 | + | 39.3759i | 0.913744 | + | 1.58265i | 0.808730 | + | 0.588180i | \(0.200156\pi\) |
0.105014 | + | 0.994471i | \(0.466511\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.93070 | + | 2.93932i | −0.318248 | + | 0.117951i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.37228 | + | 12.7692i | 0.295364 | + | 0.511586i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −51.8505 | + | 89.8078i | −2.07402 | + | 3.59231i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.43070 | + | 11.3784i | 0.137009 | + | 0.454408i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.74456 | 0.109433 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.3505 | 1.48690 | 0.743451 | − | 0.668791i | \(-0.233188\pi\) | ||||
0.743451 | + | 0.668791i | \(0.233188\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.9783 | + | 20.1947i | −0.754318 | + | 0.802667i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.81386 | − | 11.8020i | 0.270400 | − | 0.468346i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | − | 1.73205i | −0.0396214 | − | 0.0686264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.1168 | + | 9.50744i | 0.756251 | + | 0.376109i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.1060 | − | 29.6284i | −0.675645 | − | 1.17025i | −0.976280 | − | 0.216512i | \(-0.930532\pi\) |
0.300635 | − | 0.953739i | \(-0.402802\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.1753 | − | 22.8202i | 0.519582 | − | 0.899942i | −0.480159 | − | 0.877181i | \(-0.659421\pi\) |
0.999741 | − | 0.0227606i | \(-0.00724556\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 59.8397 | + | 14.0588i | 2.35618 | + | 0.553564i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.48913 | −0.215800 | −0.107900 | − | 0.994162i | \(-0.534413\pi\) | ||||
−0.107900 | + | 0.994162i | \(0.534413\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.8832 | 0.544962 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.37228 | + | 0.792287i | 0.132170 | + | 0.0310522i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.3723 | − | 23.1615i | 0.523298 | − | 0.906378i | −0.476335 | − | 0.879264i | \(-0.658035\pi\) |
0.999632 | − | 0.0271143i | \(-0.00863179\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.55842 | − | 6.16337i | −0.139039 | − | 0.240823i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 32.5475 | + | 16.1870i | 1.26980 | + | 0.631514i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.3723 | − | 17.9653i | −0.404047 | − | 0.699829i | 0.590163 | − | 0.807284i | \(-0.299063\pi\) |
−0.994210 | + | 0.107454i | \(0.965730\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.5584 | + | 23.4839i | −0.527361 | + | 0.913417i | 0.472130 | + | 0.881529i | \(0.343485\pi\) |
−0.999491 | + | 0.0318879i | \(0.989848\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.25544 | + | 3.46410i | −0.126431 | + | 0.134535i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21.8614 | 0.847749 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.2337 | −0.551131 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.00000 | − | 6.63325i | −0.0773245 | − | 0.256456i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.13859 | + | 3.70415i | −0.0825595 | + | 0.142997i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.44158 | + | 2.49689i | 0.0555687 | + | 0.0962479i | 0.892472 | − | 0.451103i | \(-0.148969\pi\) |
−0.836903 | + | 0.547351i | \(0.815636\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.3139 | − | 72.3123i | 0.473961 | − | 2.78330i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.2337 | − | 29.8496i | −0.662344 | − | 1.14721i | −0.979998 | − | 0.199007i | \(-0.936228\pi\) |
0.317654 | − | 0.948207i | \(-0.397105\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.05842 | + | 7.02939i | −0.155748 | + | 0.269763i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.12772 | − | 20.3233i | −0.234815 | − | 0.778792i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −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 | ||||||||
\(687\) | 3.41983 | − | 3.63903i | 0.130475 | − | 0.138838i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.74456 | − | 15.1460i | 0.333141 | − | 0.577018i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.5584 | − | 20.0198i | −0.439703 | − | 0.761588i | 0.557963 | − | 0.829866i | \(-0.311583\pi\) |
−0.997666 | + | 0.0682775i | \(0.978250\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.43070 | − | 2.27567i | 0.130322 | − | 0.0864456i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.9307 | + | 50.1094i | 1.09740 | + | 1.90076i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.17527 | + | 5.49972i | −0.120272 | + | 0.208317i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.430703 | − | 0.101190i | −0.0162907 | − | 0.00382735i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.2337 | −1.44407 | −0.722033 | − | 0.691858i | \(-0.756792\pi\) | ||||
−0.722033 | + | 0.691858i | \(0.756792\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.0000 | −0.377157 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.813859 | − | 1.40965i | 0.0306083 | − | 0.0530152i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.0000 | − | 38.1051i | −0.826227 | − | 1.43107i | −0.900978 | − | 0.433865i | \(-0.857149\pi\) |
0.0747503 | − | 0.997202i | \(-0.476184\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.952453 | − | 15.3210i | −0.0357198 | − | 0.574581i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.62772 | + | 2.81929i | 0.0609585 | + | 0.105583i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.00000 | + | 10.3923i | −0.224387 | + | 0.388650i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.6970 | − | 12.4468i | 0.436833 | − | 0.464833i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.74456 | −0.102355 | −0.0511775 | − | 0.998690i | \(-0.516297\pi\) | ||||
−0.0511775 | + | 0.998690i | \(0.516297\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0000 | −0.372419 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.05842 | − | 30.0434i | −0.336886 | − | 1.11733i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 61.7228 | − | 106.907i | 2.29233 | − | 3.97043i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.1168 | − | 31.3793i | −0.671917 | − | 1.16379i | −0.977360 | − | 0.211583i | \(-0.932138\pi\) |
0.305443 | − | 0.952210i | \(-0.401195\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.00000 | + | 26.5330i | 0.185185 | + | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.56930 | − | 9.64630i | −0.205988 | − | 0.356781i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.5584 | − | 35.6082i | 0.759343 | − | 1.31522i | −0.183844 | − | 0.982956i | \(-0.558854\pi\) |
0.943186 | − | 0.332265i | \(-0.107813\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.18614 | − | 7.25061i | −0.0806370 | − | 0.267443i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.90491 | 0.107004 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.11684 | 0.298583 | 0.149291 | − | 0.988793i | \(-0.452301\pi\) | ||||
0.149291 | + | 0.988793i | \(0.452301\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.8614 | − | 12.6217i | 0.435740 | − | 0.463669i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.86141 | + | 11.8843i | −0.251721 | + | 0.435993i | −0.964000 | − | 0.265904i | \(-0.914330\pi\) |
0.712279 | + | 0.701896i | \(0.247663\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.11684 | − | 12.3267i | −0.260741 | − | 0.451617i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.25544 | + | 52.3663i | 0.119110 | + | 1.91598i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.68614 | + | 6.38458i | 0.134689 | + | 0.233288i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.55842 | + | 14.8236i | −0.312301 | + | 0.540922i | −0.978860 | − | 0.204531i | \(-0.934433\pi\) |
0.666559 | + | 0.745452i | \(0.267766\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.1753 | + | 3.56529i | 0.553017 | + | 0.129926i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.8614 | −1.45071 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.2337 | 1.68039 | 0.840196 | − | 0.542283i | \(-0.182440\pi\) | ||||
0.840196 | + | 0.542283i | \(0.182440\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.76631 | + | 0.884861i | 0.136708 | + | 0.0321184i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.7446 | + | 30.7345i | −0.643240 | + | 1.11412i | 0.341465 | + | 0.939894i | \(0.389077\pi\) |
−0.984705 | + | 0.174230i | \(0.944256\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.00000 | + | 12.1244i | 0.253417 | + | 0.438931i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.0000 | + | 9.94987i | −0.542326 | + | 0.359738i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.1168 | − | 17.5229i | −0.365298 | − | 0.632715i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.00000 | − | 8.66025i | 0.180305 | − | 0.312297i | −0.761680 | − | 0.647954i | \(-0.775625\pi\) |
0.941984 | + | 0.335657i | \(0.108958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.13859 | − | 8.66025i | 0.293104 | − | 0.311891i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −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 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.00000 | + | 3.31662i | 0.0358748 | + | 0.118983i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.5693 | − | 20.0386i | 0.414513 | − | 0.717958i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.88316 | − | 8.45787i | −0.174733 | − | 0.302647i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.62772 | + | 44.7933i | −0.272592 | + | 1.60078i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.9307 | − | 34.5210i | −0.711357 | − | 1.23211i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.00000 | + | 3.46410i | −0.0712923 | + | 0.123482i | −0.899468 | − | 0.436987i | \(-0.856046\pi\) |
0.828176 | + | 0.560469i | \(0.189379\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.81386 | + | 12.6491i | 0.135777 | + | 0.450321i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.37228 | 0.155460 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.23369 | 0.221365 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 45.3505 | − | 48.2574i | 1.60842 | − | 1.71151i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.06930 | − | 7.04823i | 0.144142 | − | 0.249661i | −0.784911 | − | 0.619609i | \(-0.787291\pi\) |
0.929052 | + | 0.369948i | \(0.120624\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 39.6060 | + | 19.6974i | 1.39941 | + | 0.695972i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.31386 | − | 14.4000i | −0.293390 | − | 0.508166i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.55842 | − | 6.16337i | 0.125418 | − | 0.217230i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.74456 | − | 0.644810i | −0.0966132 | − | 0.0226984i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.86141 | −0.241234 | −0.120617 | − | 0.992699i | \(-0.538487\pi\) | ||||
−0.120617 | + | 0.992699i | \(0.538487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.1168 | −1.47892 | −0.739461 | − | 0.673199i | \(-0.764920\pi\) | ||||
−0.739461 | + | 0.673199i | \(0.764920\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.3723 | − | 6.43087i | −0.959988 | − | 0.225540i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −39.8614 | + | 69.0420i | −1.39628 | + | 2.41844i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.2921 | + | 35.1470i | 0.709931 | + | 1.22964i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.37228 | − | 2.67181i | −0.187723 | − | 0.0933608i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.88316 | + | 3.26172i | 0.0657226 | + | 0.113835i | 0.897014 | − | 0.442002i | \(-0.145731\pi\) |
−0.831292 | + | 0.555836i | \(0.812398\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.11684 | + | 10.5947i | −0.213220 | + | 0.369307i | −0.952720 | − | 0.303848i | \(-0.901728\pi\) |
0.739501 | + | 0.673156i | \(0.235062\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22.9783 | + | 24.4511i | −0.800000 | + | 0.851278i | ||||
\(826\) | 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 | \(-0.576840\pi\) | ||||
−0.239062 | + | 0.971004i | \(0.576840\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.11684 | + | 20.2873i | 0.212191 | + | 0.703758i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.686141 | + | 1.18843i | −0.0237734 | + | 0.0411767i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.0000 | − | 20.7846i | −0.415277 | − | 0.719281i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.74456 | − | 3.61158i | 0.336821 | − | 0.124834i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.74456 | + | 4.75372i | 0.0947528 | + | 0.164117i | 0.909505 | − | 0.415692i | \(-0.136461\pi\) |
−0.814753 | + | 0.579809i | \(0.803127\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.7337 | + | 41.1080i | −0.818403 | + | 1.41752i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.18614 | − | 27.1504i | −0.281946 | − | 0.935108i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −39.3505 | −1.35370 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.11684 | 0.313258 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 32.1644 | − | 34.2260i | 1.10388 | − | 1.17463i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.62772 | + | 2.81929i | −0.0557975 | + | 0.0966441i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.5584 | + | 30.4121i | 0.601189 | + | 1.04129i | 0.992641 | + | 0.121091i | \(0.0386394\pi\) |
−0.391452 | + | 0.920198i | \(0.628027\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 54.6535 | − | 36.2530i | 1.86911 | − | 1.23983i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.9783 | + | 34.6033i | 0.682444 | + | 1.18203i | 0.974233 | + | 0.225545i | \(0.0724163\pi\) |
−0.291789 | + | 0.956483i | \(0.594250\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.9416 | − | 29.3437i | 0.578039 | − | 1.00119i | −0.417665 | − | 0.908601i | \(-0.637151\pi\) |
0.995704 | − | 0.0925921i | \(-0.0295153\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.80298 | − | 1.83324i | −0.265925 | − | 0.0624767i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −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 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.4891 | − | 5.98844i | −0.865656 | − | 0.203378i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.51087 | + | 6.08101i | −0.119098 | + | 0.206284i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.11684 | − | 3.66648i | −0.0717265 | − | 0.124234i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.51087 | + | 24.3036i | 0.0511354 | + | 0.822553i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.9307 | + | 34.5210i | 0.673781 | + | 1.16702i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.3505 | − | 50.8366i | 0.991097 | − | 1.71663i | 0.380245 | − | 0.924886i | \(-0.375840\pi\) |
0.610852 | − | 0.791744i | \(-0.290827\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.3030 | − | 13.0916i | 0.414969 | − | 0.441568i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −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 | \(-0.262435\pi\) | ||||
0.678952 | + | 0.734183i | \(0.262435\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −22.1168 | − | 73.3533i | −0.743450 | − | 2.46574i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.8614 | − | 22.2766i | 0.431844 | − | 0.747975i | −0.565188 | − | 0.824962i | \(-0.691197\pi\) |
0.997032 | + | 0.0769865i | \(0.0245298\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.55842 | − | 2.69927i | −0.0522678 | − | 0.0905305i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.80298 | − | 11.3784i | 0.160906 | − | 0.381189i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.11684 | − | 12.3267i | 0.237890 | − | 0.412037i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.62772 | − | 5.39853i | −0.0543479 | − | 0.180252i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.4891 | 0.583295 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.62772 | − | 10.2448i | 0.320390 | − | 0.340927i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.93070 | + | 3.34408i | −0.0641787 | + | 0.111161i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.0584 | − | 22.6179i | −0.433598 | − | 0.751013i | 0.563582 | − | 0.826060i | \(-0.309423\pi\) |
−0.997180 | + | 0.0750466i | \(0.976089\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.302985 | − | 4.87375i | −0.0100494 | − | 0.161652i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.8139 | − | 32.5866i | −0.623331 | − | 1.07964i | −0.988861 | − | 0.148841i | \(-0.952446\pi\) |
0.365530 | − | 0.930800i | \(-0.380888\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000 | − | 20.7846i | 0.397142 | − | 0.687870i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22.9783 | + | 5.39853i | 0.759638 | + | 0.178470i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.62772 | −0.0537520 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.1168 | 1.55424 | 0.777121 | − | 0.629352i | \(-0.216679\pi\) | ||||
0.777121 | + | 0.629352i | \(0.216679\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.9198 | + | 5.14987i | 0.722283 | + | 0.169694i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.11684 | + | 12.3267i | −0.234254 | + | 0.405739i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.1168 | − | 24.4511i | −0.464159 | − | 0.803947i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25.0000 | + | 16.5831i | −0.821108 | + | 0.544661i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.1168 | − | 38.3075i | −0.725630 | − | 1.25683i | −0.958714 | − | 0.284372i | \(-0.908215\pi\) |
0.233084 | − | 0.972457i | \(-0.425118\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.50000 | − | 4.33013i | 0.0819342 | − | 0.141914i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.76631 | − | 10.3923i | 0.319735 | − | 0.340229i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.23369 | 0.269270 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.4674 | 0.995326 | 0.497663 | − | 0.867371i | \(-0.334192\pi\) | ||||
0.497663 | + | 0.867371i | \(0.334192\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.0584 | + | 33.3600i | 0.328244 | + | 1.08866i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.55842 | + | 16.5557i | −0.311596 | + | 0.539699i | −0.978708 | − | 0.205258i | \(-0.934197\pi\) |
0.667112 | + | 0.744957i | \(0.267530\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.76631 | − | 6.52344i | −0.122648 | − | 0.212433i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17.4891 | − | 14.5012i | −0.568921 | − | 0.471725i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.0584 | + | 29.5461i | 0.554324 | + | 0.960118i | 0.997956 | + | 0.0639085i | \(0.0203566\pi\) |
−0.443632 | + | 0.896209i | \(0.646310\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.1168 | + | 20.9870i | −0.393329 | + | 0.681267i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.00000 | + | 9.94987i | 0.0972817 | + | 0.322647i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.1168 | 0.910794 | 0.455397 | − | 0.890288i | \(-0.349497\pi\) | ||||
0.455397 | + | 0.890288i | \(0.349497\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 83.5842 | 2.70472 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.2337 | − | 15.1460i | 0.460110 | − | 0.489602i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.31386 | − | 9.20387i | 0.171593 | − | 0.297209i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.8030 | + | 9.84868i | 0.638142 | + | 0.317369i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.3030 | + | 26.5055i | 0.492621 | + | 0.853244i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.4416 | − | 26.7456i | 0.496568 | − | 0.860080i | −0.503424 | − | 0.864039i | \(-0.667927\pi\) |
0.999992 | + | 0.00395879i | \(0.00126012\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.5693 | − | 2.71810i | −0.371659 | − | 0.0873180i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.62772 | −0.0522360 | −0.0261180 | − | 0.999659i | \(-0.508315\pi\) | ||||
−0.0261180 | + | 0.999659i | \(0.508315\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.2337 | 0.424253 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 47.6060 | + | 11.1846i | 1.52461 | + | 0.358194i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.0584 | + | 34.7422i | −0.641726 | + | 1.11150i | 0.343322 | + | 0.939218i | \(0.388448\pi\) |
−0.985047 | + | 0.172284i | \(0.944885\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.1168 | − | 17.5229i | −0.323336 | − | 0.560034i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.6060 | + | 18.7027i | 1.20067 | + | 0.597131i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.6277 | − | 33.9962i | −0.626027 | − | 1.08431i | −0.988341 | − | 0.152255i | \(-0.951347\pi\) |
0.362314 | − | 0.932056i | \(-0.381987\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.1168 | − | 22.7190i | 0.417937 | − | 0.723889i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.2119 | 0.420115 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48.4674 | −1.53962 | −0.769808 | − | 0.638275i | \(-0.779648\pi\) | ||||
−0.769808 | + | 0.638275i | \(0.779648\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.1168 | + | 36.8704i | 0.352782 | + | 1.17005i | ||||
\(994\) | 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 | \(-0.140847\pi\) |
−0.822665 | + | 0.568527i | \(0.807514\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.00000 | + | 6.63325i | 0.253109 | + | 0.209867i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))