Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(215,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.215");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.l (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 378) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 215.1 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.215 |
Dual form | 1134.2.l.e.269.3 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.22474 | − | 2.12132i | −0.547723 | − | 0.948683i | −0.998430 | − | 0.0560116i | \(-0.982162\pi\) |
0.450708 | − | 0.892672i | \(-0.351172\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.62132 | − | 0.358719i | 0.990766 | − | 0.135583i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.12132 | + | 1.22474i | −0.670820 | + | 0.387298i | ||||
\(11\) | 3.67423 | + | 2.12132i | 1.10782 | + | 0.639602i | 0.938265 | − | 0.345918i | \(-0.112432\pi\) |
0.169559 | + | 0.985520i | \(0.445766\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.62132 | + | 2.09077i | 1.00437 | + | 0.579875i | 0.909539 | − | 0.415618i | \(-0.136435\pi\) |
0.0948342 | + | 0.995493i | \(0.469768\pi\) | |||||||
\(14\) | −0.358719 | − | 2.62132i | −0.0958718 | − | 0.700577i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.22474 | − | 2.12132i | −0.297044 | − | 0.514496i | 0.678414 | − | 0.734680i | \(-0.262668\pi\) |
−0.975458 | + | 0.220184i | \(0.929334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.24264 | + | 2.44949i | 0.973329 | + | 0.561951i | 0.900249 | − | 0.435375i | \(-0.143384\pi\) |
0.0730792 | + | 0.997326i | \(0.476717\pi\) | |||||||
\(20\) | 1.22474 | + | 2.12132i | 0.273861 | + | 0.474342i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.12132 | − | 3.67423i | 0.452267 | − | 0.783349i | ||||
\(23\) | −5.19615 | + | 3.00000i | −1.08347 | + | 0.625543i | −0.931831 | − | 0.362892i | \(-0.881789\pi\) |
−0.151642 | + | 0.988436i | \(0.548456\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 2.09077 | − | 3.62132i | 0.410034 | − | 0.710199i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.62132 | + | 0.358719i | −0.495383 | + | 0.0677916i | ||||
\(29\) | 8.87039 | − | 5.12132i | 1.64719 | − | 0.951005i | 0.669007 | − | 0.743256i | \(-0.266719\pi\) |
0.978182 | − | 0.207750i | \(-0.0666139\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.61642i | 1.00874i | 0.863488 | + | 0.504369i | \(0.168275\pi\) | ||||
−0.863488 | + | 0.504369i | \(0.831725\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.12132 | + | 1.22474i | −0.363803 | + | 0.210042i | ||||
\(35\) | −3.97141 | − | 5.12132i | −0.671290 | − | 0.865661i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.62132 | − | 2.80821i | 0.266543 | − | 0.461667i | −0.701423 | − | 0.712745i | \(-0.747452\pi\) |
0.967967 | + | 0.251078i | \(0.0807851\pi\) | |||||||
\(38\) | 2.44949 | − | 4.24264i | 0.397360 | − | 0.688247i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.12132 | − | 1.22474i | 0.335410 | − | 0.193649i | ||||
\(41\) | 1.22474 | − | 2.12132i | 0.191273 | − | 0.331295i | −0.754399 | − | 0.656416i | \(-0.772072\pi\) |
0.945672 | + | 0.325121i | \(0.105405\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.50000 | − | 6.06218i | −0.533745 | − | 0.924473i | −0.999223 | − | 0.0394140i | \(-0.987451\pi\) |
0.465478 | − | 0.885059i | \(-0.345882\pi\) | |||||||
\(44\) | −3.67423 | − | 2.12132i | −0.553912 | − | 0.319801i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | + | 5.19615i | 0.442326 | + | 0.766131i | ||||
\(47\) | −7.94282 | −1.15858 | −0.579289 | − | 0.815122i | \(-0.696670\pi\) | ||||
−0.579289 | + | 0.815122i | \(0.696670\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.74264 | − | 1.88064i | 0.963234 | − | 0.268662i | ||||
\(50\) | 0.866025 | + | 0.500000i | 0.122474 | + | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.62132 | − | 2.09077i | −0.502187 | − | 0.289938i | ||||
\(53\) | 2.15232 | − | 1.24264i | 0.295643 | − | 0.170690i | −0.344841 | − | 0.938661i | \(-0.612067\pi\) |
0.640484 | + | 0.767971i | \(0.278734\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 10.3923i | − | 1.40130i | ||||||
\(56\) | 0.358719 | + | 2.62132i | 0.0479359 | + | 0.350289i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.12132 | − | 8.87039i | −0.672462 | − | 1.16474i | ||||
\(59\) | −2.44949 | −0.318896 | −0.159448 | − | 0.987206i | \(-0.550971\pi\) | ||||
−0.159448 | + | 0.987206i | \(0.550971\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.717439i | 0.0918586i | 0.998945 | + | 0.0459293i | \(0.0146249\pi\) | ||||
−0.998945 | + | 0.0459293i | \(0.985375\pi\) | |||||||
\(62\) | 5.61642 | 0.713286 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 10.2426i | − | 1.27044i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.48528 | −0.425795 | −0.212897 | − | 0.977075i | \(-0.568290\pi\) | ||||
−0.212897 | + | 0.977075i | \(0.568290\pi\) | |||||||
\(68\) | 1.22474 | + | 2.12132i | 0.148522 | + | 0.257248i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.12132 | + | 3.97141i | −0.612115 | + | 0.474674i | ||||
\(71\) | − | 12.7279i | − | 1.51053i | −0.655422 | − | 0.755263i | \(-0.727509\pi\) | ||
0.655422 | − | 0.755263i | \(-0.272491\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.2426 | + | 7.64564i | −1.54993 | + | 0.894855i | −0.551788 | + | 0.833984i | \(0.686054\pi\) |
−0.998146 | + | 0.0608704i | \(0.980612\pi\) | |||||||
\(74\) | −2.80821 | − | 1.62132i | −0.326448 | − | 0.188475i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.24264 | − | 2.44949i | −0.486664 | − | 0.280976i | ||||
\(77\) | 10.3923 | + | 4.24264i | 1.18431 | + | 0.483494i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.24264 | 1.03988 | 0.519939 | − | 0.854203i | \(-0.325955\pi\) | ||||
0.519939 | + | 0.854203i | \(0.325955\pi\) | |||||||
\(80\) | −1.22474 | − | 2.12132i | −0.136931 | − | 0.237171i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.12132 | − | 1.22474i | −0.234261 | − | 0.135250i | ||||
\(83\) | 2.74666 | + | 4.75736i | 0.301485 | + | 0.522188i | 0.976473 | − | 0.215641i | \(-0.0691842\pi\) |
−0.674987 | + | 0.737829i | \(0.735851\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | + | 5.19615i | −0.325396 | + | 0.563602i | ||||
\(86\) | −6.06218 | + | 3.50000i | −0.653701 | + | 0.377415i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.12132 | + | 3.67423i | −0.226134 | + | 0.391675i | ||||
\(89\) | 8.87039 | − | 15.3640i | 0.940259 | − | 1.62858i | 0.175283 | − | 0.984518i | \(-0.443916\pi\) |
0.764976 | − | 0.644059i | \(-0.222751\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.2426 | + | 4.18154i | 1.07372 | + | 0.438345i | ||||
\(92\) | 5.19615 | − | 3.00000i | 0.541736 | − | 0.312772i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.94282i | 0.819239i | ||||||||
\(95\) | − | 12.0000i | − | 1.23117i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.74264 | − | 3.31552i | 0.583077 | − | 0.336640i | −0.179278 | − | 0.983798i | \(-0.557376\pi\) |
0.762355 | + | 0.647159i | \(0.224043\pi\) | |||||||
\(98\) | −1.88064 | − | 6.74264i | −0.189973 | − | 0.681110i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −3.67423 | + | 6.36396i | −0.365600 | + | 0.633238i | −0.988872 | − | 0.148767i | \(-0.952470\pi\) |
0.623272 | + | 0.782005i | \(0.285803\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.37868 | + | 3.10538i | −0.529977 | + | 0.305982i | −0.741007 | − | 0.671497i | \(-0.765652\pi\) |
0.211030 | + | 0.977480i | \(0.432318\pi\) | |||||||
\(104\) | −2.09077 | + | 3.62132i | −0.205017 | + | 0.355100i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.24264 | − | 2.15232i | −0.120696 | − | 0.209051i | ||||
\(107\) | 12.5446 | + | 7.24264i | 1.21273 | + | 0.700173i | 0.963354 | − | 0.268233i | \(-0.0864397\pi\) |
0.249380 | + | 0.968406i | \(0.419773\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.86396 | − | 6.69258i | −0.370100 | − | 0.641033i | 0.619480 | − | 0.785012i | \(-0.287343\pi\) |
−0.989581 | + | 0.143980i | \(0.954010\pi\) | |||||||
\(110\) | −10.3923 | −0.990867 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.62132 | − | 0.358719i | 0.247691 | − | 0.0338958i | ||||
\(113\) | 1.52192 | + | 0.878680i | 0.143170 | + | 0.0826592i | 0.569874 | − | 0.821732i | \(-0.306992\pi\) |
−0.426704 | + | 0.904391i | \(0.640325\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.7279 | + | 7.34847i | 1.18688 | + | 0.685248i | ||||
\(116\) | −8.87039 | + | 5.12132i | −0.823595 | + | 0.475503i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.44949i | 0.225494i | ||||||||
\(119\) | −3.97141 | − | 5.12132i | −0.364058 | − | 0.469471i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0.717439 | 0.0649539 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 5.61642i | − | 0.504369i | ||||||
\(125\) | −9.79796 | −0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.7279 | 1.57310 | 0.786549 | − | 0.617527i | \(-0.211866\pi\) | ||||
0.786549 | + | 0.617527i | \(0.211866\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.2426 | −0.898339 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.0000 | + | 4.89898i | 1.04053 | + | 0.424795i | ||||
\(134\) | 3.48528i | 0.301082i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.12132 | − | 1.22474i | 0.181902 | − | 0.105021i | ||||
\(137\) | 5.19615 | + | 3.00000i | 0.443937 | + | 0.256307i | 0.705266 | − | 0.708942i | \(-0.250827\pi\) |
−0.261329 | + | 0.965250i | \(0.584161\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.98528 | − | 5.76500i | −0.846941 | − | 0.488981i | 0.0126769 | − | 0.999920i | \(-0.495965\pi\) |
−0.859617 | + | 0.510938i | \(0.829298\pi\) | |||||||
\(140\) | 3.97141 | + | 5.12132i | 0.335645 | + | 0.432831i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.7279 | −1.06810 | ||||||||
\(143\) | 8.87039 | + | 15.3640i | 0.741779 | + | 1.28480i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.7279 | − | 12.5446i | −1.80441 | − | 1.04177i | ||||
\(146\) | 7.64564 | + | 13.2426i | 0.632758 | + | 1.09597i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.62132 | + | 2.80821i | −0.133272 | + | 0.230833i | ||||
\(149\) | −6.71807 | + | 3.87868i | −0.550366 | + | 0.317754i | −0.749270 | − | 0.662265i | \(-0.769595\pi\) |
0.198904 | + | 0.980019i | \(0.436262\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.62132 | + | 14.9326i | −0.701593 | + | 1.21519i | 0.266314 | + | 0.963886i | \(0.414194\pi\) |
−0.967907 | + | 0.251309i | \(0.919139\pi\) | |||||||
\(152\) | −2.44949 | + | 4.24264i | −0.198680 | + | 0.344124i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.24264 | − | 10.3923i | 0.341882 | − | 0.837436i | ||||
\(155\) | 11.9142 | − | 6.87868i | 0.956973 | − | 0.552509i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.3923i | − | 0.829396i | −0.909959 | − | 0.414698i | \(-0.863887\pi\) | ||
0.909959 | − | 0.414698i | \(-0.136113\pi\) | |||||||
\(158\) | − | 9.24264i | − | 0.735305i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.12132 | + | 1.22474i | −0.167705 | + | 0.0968246i | ||||
\(161\) | −12.5446 | + | 9.72792i | −0.988655 | + | 0.766668i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.74264 | + | 6.48244i | −0.293146 | + | 0.507744i | −0.974552 | − | 0.224162i | \(-0.928036\pi\) |
0.681406 | + | 0.731906i | \(0.261369\pi\) | |||||||
\(164\) | −1.22474 | + | 2.12132i | −0.0956365 | + | 0.165647i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.75736 | − | 2.74666i | 0.369243 | − | 0.213182i | ||||
\(167\) | −10.0951 | + | 17.4853i | −0.781185 | + | 1.35305i | 0.150067 | + | 0.988676i | \(0.452051\pi\) |
−0.931252 | + | 0.364376i | \(0.881282\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.24264 | + | 3.88437i | 0.172511 | + | 0.298798i | ||||
\(170\) | 5.19615 | + | 3.00000i | 0.398527 | + | 0.230089i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.50000 | + | 6.06218i | 0.266872 | + | 0.462237i | ||||
\(173\) | −20.7846 | −1.58022 | −0.790112 | − | 0.612962i | \(-0.789978\pi\) | ||||
−0.790112 | + | 0.612962i | \(0.789978\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | + | 2.44949i | −0.0755929 | + | 0.185164i | ||||
\(176\) | 3.67423 | + | 2.12132i | 0.276956 | + | 0.159901i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.3640 | − | 8.87039i | −1.15158 | − | 0.664864i | ||||
\(179\) | −16.2189 | + | 9.36396i | −1.21225 | + | 0.699895i | −0.963250 | − | 0.268607i | \(-0.913437\pi\) |
−0.249004 | + | 0.968502i | \(0.580103\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.79796i | − | 0.728277i | −0.931345 | − | 0.364138i | \(-0.881364\pi\) | ||
0.931345 | − | 0.364138i | \(-0.118636\pi\) | |||||||
\(182\) | 4.18154 | − | 10.2426i | 0.309956 | − | 0.759235i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.00000 | − | 5.19615i | −0.221163 | − | 0.383065i | ||||
\(185\) | −7.94282 | −0.583967 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 10.3923i | − | 0.759961i | ||||||
\(188\) | 7.94282 | 0.579289 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.0000 | −0.870572 | ||||||||
\(191\) | 21.2132i | 1.53493i | 0.641089 | + | 0.767467i | \(0.278483\pi\) | ||||
−0.641089 | + | 0.767467i | \(0.721517\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.4853 | 1.11465 | 0.557327 | − | 0.830293i | \(-0.311827\pi\) | ||||
0.557327 | + | 0.830293i | \(0.311827\pi\) | |||||||
\(194\) | −3.31552 | − | 5.74264i | −0.238040 | − | 0.412298i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.74264 | + | 1.88064i | −0.481617 | + | 0.134331i | ||||
\(197\) | 16.9706i | 1.20910i | 0.796566 | + | 0.604551i | \(0.206648\pi\) | ||||
−0.796566 | + | 0.604551i | \(0.793352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.10660 | − | 1.79360i | 0.220221 | − | 0.127145i | −0.385832 | − | 0.922569i | \(-0.626085\pi\) |
0.606053 | + | 0.795425i | \(0.292752\pi\) | |||||||
\(200\) | −0.866025 | − | 0.500000i | −0.0612372 | − | 0.0353553i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.36396 | + | 3.67423i | 0.447767 | + | 0.258518i | ||||
\(203\) | 21.4150 | − | 16.6066i | 1.50304 | − | 1.16555i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | −0.419058 | ||||||||
\(206\) | 3.10538 | + | 5.37868i | 0.216362 | + | 0.374750i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.62132 | + | 2.09077i | 0.251093 | + | 0.144969i | ||||
\(209\) | 10.3923 | + | 18.0000i | 0.718851 | + | 1.24509i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.74264 | − | 11.6786i | 0.464183 | − | 0.803988i | −0.534982 | − | 0.844864i | \(-0.679682\pi\) |
0.999164 | + | 0.0408759i | \(0.0130148\pi\) | |||||||
\(212\) | −2.15232 | + | 1.24264i | −0.147822 | + | 0.0853449i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.24264 | − | 12.5446i | 0.495097 | − | 0.857533i | ||||
\(215\) | −8.57321 | + | 14.8492i | −0.584688 | + | 1.01271i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.01472 | + | 14.7224i | 0.136768 | + | 0.999424i | ||||
\(218\) | −6.69258 | + | 3.86396i | −0.453278 | + | 0.261700i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.3923i | 0.700649i | ||||||||
\(221\) | − | 10.2426i | − | 0.688995i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.00000 | − | 5.19615i | 0.602685 | − | 0.347960i | −0.167412 | − | 0.985887i | \(-0.553541\pi\) |
0.770097 | + | 0.637927i | \(0.220208\pi\) | |||||||
\(224\) | −0.358719 | − | 2.62132i | −0.0239680 | − | 0.175144i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.878680 | − | 1.52192i | 0.0584489 | − | 0.101236i | ||||
\(227\) | 2.15232 | − | 3.72792i | 0.142854 | − | 0.247431i | −0.785716 | − | 0.618587i | \(-0.787705\pi\) |
0.928570 | + | 0.371156i | \(0.121039\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.86396 | + | 4.54026i | −0.519665 | + | 0.300029i | −0.736798 | − | 0.676113i | \(-0.763663\pi\) |
0.217132 | + | 0.976142i | \(0.430330\pi\) | |||||||
\(230\) | 7.34847 | − | 12.7279i | 0.484544 | − | 0.839254i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.12132 | + | 8.87039i | 0.336231 | + | 0.582369i | ||||
\(233\) | 3.04384 | + | 1.75736i | 0.199408 | + | 0.115128i | 0.596379 | − | 0.802703i | \(-0.296605\pi\) |
−0.396971 | + | 0.917831i | \(0.629939\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.72792 | + | 16.8493i | 0.634580 | + | 1.09912i | ||||
\(236\) | 2.44949 | 0.159448 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.12132 | + | 3.97141i | −0.331966 | + | 0.257428i | ||||
\(239\) | 6.71807 | + | 3.87868i | 0.434556 | + | 0.250891i | 0.701286 | − | 0.712880i | \(-0.252610\pi\) |
−0.266730 | + | 0.963771i | \(0.585943\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.9853 | − | 9.22911i | −1.02970 | − | 0.594499i | −0.112803 | − | 0.993617i | \(-0.535983\pi\) |
−0.916899 | + | 0.399118i | \(0.869316\pi\) | |||||||
\(242\) | 6.06218 | − | 3.50000i | 0.389692 | − | 0.224989i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 0.717439i | − | 0.0459293i | ||||||
\(245\) | −12.2474 | − | 12.0000i | −0.782461 | − | 0.766652i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.2426 | + | 17.7408i | 0.651724 | + | 1.12882i | ||||
\(248\) | −5.61642 | −0.356643 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.79796i | 0.619677i | ||||||||
\(251\) | 5.49333 | 0.346736 | 0.173368 | − | 0.984857i | \(-0.444535\pi\) | ||||
0.173368 | + | 0.984857i | \(0.444535\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.4558 | −1.60040 | ||||||||
\(254\) | − | 17.7279i | − | 1.11235i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.15232 | + | 3.72792i | 0.134258 | + | 0.232541i | 0.925314 | − | 0.379203i | \(-0.123802\pi\) |
−0.791056 | + | 0.611744i | \(0.790468\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.24264 | − | 7.94282i | 0.201488 | − | 0.493543i | ||||
\(260\) | 10.2426i | 0.635222i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.2189 | − | 9.36396i | −1.00010 | − | 0.577407i | −0.0918204 | − | 0.995776i | \(-0.529269\pi\) |
−0.908277 | + | 0.418369i | \(0.862602\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.27208 | − | 3.04384i | −0.323861 | − | 0.186981i | ||||
\(266\) | 4.89898 | − | 12.0000i | 0.300376 | − | 0.735767i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.48528 | 0.212897 | ||||||||
\(269\) | 4.89898 | + | 8.48528i | 0.298696 | + | 0.517357i | 0.975838 | − | 0.218496i | \(-0.0701150\pi\) |
−0.677142 | + | 0.735853i | \(0.736782\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.3492 | + | 7.70719i | 0.810909 | + | 0.468178i | 0.847271 | − | 0.531160i | \(-0.178244\pi\) |
−0.0363626 | + | 0.999339i | \(0.511577\pi\) | |||||||
\(272\) | −1.22474 | − | 2.12132i | −0.0742611 | − | 0.128624i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.00000 | − | 5.19615i | 0.181237 | − | 0.313911i | ||||
\(275\) | −3.67423 | + | 2.12132i | −0.221565 | + | 0.127920i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.863961 | − | 1.49642i | 0.0519104 | − | 0.0899114i | −0.838903 | − | 0.544282i | \(-0.816802\pi\) |
0.890813 | + | 0.454370i | \(0.150136\pi\) | |||||||
\(278\) | −5.76500 | + | 9.98528i | −0.345762 | + | 0.598877i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.12132 | − | 3.97141i | 0.306057 | − | 0.237337i | ||||
\(281\) | 19.2627 | − | 11.1213i | 1.14912 | − | 0.663442i | 0.200444 | − | 0.979705i | \(-0.435761\pi\) |
0.948672 | + | 0.316263i | \(0.102428\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 23.3572i | − | 1.38844i | −0.719762 | − | 0.694220i | \(-0.755749\pi\) | ||
0.719762 | − | 0.694220i | \(-0.244251\pi\) | |||||||
\(284\) | 12.7279i | 0.755263i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.3640 | − | 8.87039i | 0.908490 | − | 0.524517i | ||||
\(287\) | 2.44949 | − | 6.00000i | 0.144589 | − | 0.354169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.50000 | − | 9.52628i | 0.323529 | − | 0.560369i | ||||
\(290\) | −12.5446 | + | 21.7279i | −0.736646 | + | 1.27591i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.2426 | − | 7.64564i | 0.774967 | − | 0.447427i | ||||
\(293\) | −3.97141 | + | 6.87868i | −0.232012 | + | 0.401857i | −0.958400 | − | 0.285428i | \(-0.907864\pi\) |
0.726388 | + | 0.687285i | \(0.241198\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.00000 | + | 5.19615i | 0.174667 | + | 0.302532i | ||||
\(296\) | 2.80821 | + | 1.62132i | 0.163224 | + | 0.0942373i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.87868 | + | 6.71807i | 0.224686 | + | 0.389167i | ||||
\(299\) | −25.0892 | −1.45095 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.3492 | − | 14.6354i | −0.654159 | − | 0.843570i | ||||
\(302\) | 14.9326 | + | 8.62132i | 0.859273 | + | 0.496101i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.24264 | + | 2.44949i | 0.243332 | + | 0.140488i | ||||
\(305\) | 1.52192 | − | 0.878680i | 0.0871448 | − | 0.0503131i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.57258i | 0.146825i | 0.997302 | + | 0.0734125i | \(0.0233890\pi\) | ||||
−0.997302 | + | 0.0734125i | \(0.976611\pi\) | |||||||
\(308\) | −10.3923 | − | 4.24264i | −0.592157 | − | 0.241747i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.87868 | − | 11.9142i | −0.390683 | − | 0.676682i | ||||
\(311\) | 17.1464 | 0.972285 | 0.486142 | − | 0.873880i | \(-0.338404\pi\) | ||||
0.486142 | + | 0.873880i | \(0.338404\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.594346i | 0.0335944i | 0.999859 | + | 0.0167972i | \(0.00534697\pi\) | ||||
−0.999859 | + | 0.0167972i | \(0.994653\pi\) | |||||||
\(314\) | −10.3923 | −0.586472 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.24264 | −0.519939 | ||||||||
\(317\) | 13.7574i | 0.772690i | 0.922354 | + | 0.386345i | \(0.126263\pi\) | ||||
−0.922354 | + | 0.386345i | \(0.873737\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 43.4558 | 2.43306 | ||||||||
\(320\) | 1.22474 | + | 2.12132i | 0.0684653 | + | 0.118585i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.72792 | + | 12.5446i | 0.542116 | + | 0.699084i | ||||
\(323\) | − | 12.0000i | − | 0.667698i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.62132 | + | 2.09077i | −0.200875 | + | 0.115975i | ||||
\(326\) | 6.48244 | + | 3.74264i | 0.359029 | + | 0.207286i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.12132 | + | 1.22474i | 0.117130 | + | 0.0676252i | ||||
\(329\) | −20.8207 | + | 2.84924i | −1.14788 | + | 0.157084i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | 0.549650 | 0.274825 | − | 0.961494i | \(-0.411380\pi\) | ||||
0.274825 | + | 0.961494i | \(0.411380\pi\) | |||||||
\(332\) | −2.74666 | − | 4.75736i | −0.150743 | − | 0.261094i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.4853 | + | 10.0951i | 0.956752 | + | 0.552381i | ||||
\(335\) | 4.26858 | + | 7.39340i | 0.233217 | + | 0.403944i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.7279 | + | 25.5095i | −0.802281 | + | 1.38959i | 0.115830 | + | 0.993269i | \(0.463047\pi\) |
−0.918111 | + | 0.396323i | \(0.870286\pi\) | |||||||
\(338\) | 3.88437 | − | 2.24264i | 0.211282 | − | 0.121984i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.00000 | − | 5.19615i | 0.162698 | − | 0.281801i | ||||
\(341\) | −11.9142 | + | 20.6360i | −0.645191 | + | 1.11750i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | − | 7.34847i | 0.917914 | − | 0.396780i | ||||
\(344\) | 6.06218 | − | 3.50000i | 0.326851 | − | 0.188707i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.7846i | 1.11739i | ||||||||
\(347\) | 28.9706i | 1.55522i | 0.628746 | + | 0.777611i | \(0.283568\pi\) | ||||
−0.628746 | + | 0.777611i | \(0.716432\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.1066 | + | 12.1859i | −1.12981 | + | 0.652296i | −0.943887 | − | 0.330268i | \(-0.892861\pi\) |
−0.185923 | + | 0.982564i | \(0.559528\pi\) | |||||||
\(350\) | 2.44949 | + | 1.00000i | 0.130931 | + | 0.0534522i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.12132 | − | 3.67423i | 0.113067 | − | 0.195837i | ||||
\(353\) | −15.2913 | + | 26.4853i | −0.813873 | + | 1.40967i | 0.0962614 | + | 0.995356i | \(0.469312\pi\) |
−0.910134 | + | 0.414313i | \(0.864022\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.0000 | + | 15.5885i | −1.43301 | + | 0.827349i | ||||
\(356\) | −8.87039 | + | 15.3640i | −0.470130 | + | 0.814288i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.36396 | + | 16.2189i | 0.494901 | + | 0.857193i | ||||
\(359\) | 2.15232 | + | 1.24264i | 0.113595 | + | 0.0655841i | 0.555721 | − | 0.831369i | \(-0.312442\pi\) |
−0.442126 | + | 0.896953i | \(0.645776\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.50000 | + | 4.33013i | 0.131579 | + | 0.227901i | ||||
\(362\) | −9.79796 | −0.514969 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.2426 | − | 4.18154i | −0.536860 | − | 0.219172i | ||||
\(365\) | 32.4377 | + | 18.7279i | 1.69787 | + | 0.980264i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.97056 | − | 4.60181i | −0.416060 | − | 0.240212i | 0.277330 | − | 0.960775i | \(-0.410550\pi\) |
−0.693390 | + | 0.720562i | \(0.743884\pi\) | |||||||
\(368\) | −5.19615 | + | 3.00000i | −0.270868 | + | 0.156386i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.94282i | 0.412927i | ||||||||
\(371\) | 5.19615 | − | 4.02944i | 0.269771 | − | 0.209198i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0000 | + | 19.0526i | 0.569558 | + | 0.986504i | 0.996610 | + | 0.0822766i | \(0.0262191\pi\) |
−0.427051 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(374\) | −10.3923 | −0.537373 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 7.94282i | − | 0.409619i | ||||||
\(377\) | 42.8300 | 2.20586 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.48528 | 0.487226 | 0.243613 | − | 0.969872i | \(-0.421667\pi\) | ||||
0.243613 | + | 0.969872i | \(0.421667\pi\) | |||||||
\(380\) | 12.0000i | 0.615587i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.2132 | 1.08536 | ||||||||
\(383\) | −7.64564 | − | 13.2426i | −0.390674 | − | 0.676667i | 0.601865 | − | 0.798598i | \(-0.294425\pi\) |
−0.992539 | + | 0.121931i | \(0.961091\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.72792 | − | 27.2416i | −0.189993 | − | 1.38836i | ||||
\(386\) | − | 15.4853i | − | 0.788180i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.74264 | + | 3.31552i | −0.291538 | + | 0.168320i | ||||
\(389\) | −28.1331 | − | 16.2426i | −1.42640 | − | 0.823535i | −0.429569 | − | 0.903034i | \(-0.641334\pi\) |
−0.996835 | + | 0.0794995i | \(0.974668\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.7279 | + | 7.34847i | 0.643679 | + | 0.371628i | ||||
\(392\) | 1.88064 | + | 6.74264i | 0.0949865 | + | 0.340555i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.9706 | 0.854965 | ||||||||
\(395\) | −11.3199 | − | 19.6066i | −0.569565 | − | 0.986515i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.8640 | − | 14.9326i | −1.29807 | − | 0.749444i | −0.318004 | − | 0.948090i | \(-0.603012\pi\) |
−0.980071 | + | 0.198646i | \(0.936346\pi\) | |||||||
\(398\) | −1.79360 | − | 3.10660i | −0.0899049 | − | 0.155720i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 24.4588 | − | 14.1213i | 1.22142 | − | 0.705185i | 0.256197 | − | 0.966625i | \(-0.417531\pi\) |
0.965220 | + | 0.261440i | \(0.0841972\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.7426 | + | 20.3389i | −0.584943 | + | 1.01315i | ||||
\(404\) | 3.67423 | − | 6.36396i | 0.182800 | − | 0.316619i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.6066 | − | 21.4150i | −0.824172 | − | 1.06281i | ||||
\(407\) | 11.9142 | − | 6.87868i | 0.590566 | − | 0.340963i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 13.5592i | − | 0.670461i | −0.942136 | − | 0.335230i | \(-0.891186\pi\) | ||
0.942136 | − | 0.335230i | \(-0.108814\pi\) | |||||||
\(410\) | 6.00000i | 0.296319i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.37868 | − | 3.10538i | 0.264989 | − | 0.152991i | ||||
\(413\) | −6.42090 | + | 0.878680i | −0.315952 | + | 0.0432370i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.72792 | − | 11.6531i | 0.330261 | − | 0.572028i | ||||
\(416\) | 2.09077 | − | 3.62132i | 0.102508 | − | 0.177550i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.0000 | − | 10.3923i | 0.880409 | − | 0.508304i | ||||
\(419\) | −6.42090 | + | 11.1213i | −0.313681 | + | 0.543312i | −0.979156 | − | 0.203108i | \(-0.934896\pi\) |
0.665475 | + | 0.746420i | \(0.268229\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.7279 | − | 23.7775i | −0.669058 | − | 1.15884i | −0.978168 | − | 0.207816i | \(-0.933364\pi\) |
0.309110 | − | 0.951026i | \(-0.399969\pi\) | |||||||
\(422\) | −11.6786 | − | 6.74264i | −0.568505 | − | 0.328227i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.24264 | + | 2.15232i | 0.0603480 | + | 0.104526i | ||||
\(425\) | 2.44949 | 0.118818 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.257359 | + | 1.88064i | 0.0124545 | + | 0.0910104i | ||||
\(428\) | −12.5446 | − | 7.24264i | −0.606367 | − | 0.350086i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.8492 | + | 8.57321i | 0.716094 | + | 0.413437i | ||||
\(431\) | 8.87039 | − | 5.12132i | 0.427272 | − | 0.246685i | −0.270912 | − | 0.962604i | \(-0.587325\pi\) |
0.698184 | + | 0.715919i | \(0.253992\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.8213i | 1.28895i | 0.764626 | + | 0.644475i | \(0.222924\pi\) | ||||
−0.764626 | + | 0.644475i | \(0.777076\pi\) | |||||||
\(434\) | 14.7224 | − | 2.01472i | 0.706699 | − | 0.0967096i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.86396 | + | 6.69258i | 0.185050 | + | 0.320516i | ||||
\(437\) | −29.3939 | −1.40610 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.0892i | 1.19744i | 0.800957 | + | 0.598722i | \(0.204325\pi\) | ||||
−0.800957 | + | 0.598722i | \(0.795675\pi\) | |||||||
\(440\) | 10.3923 | 0.495434 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.2426 | −0.487193 | ||||||||
\(443\) | − | 25.4558i | − | 1.20944i | −0.796437 | − | 0.604722i | \(-0.793284\pi\) | ||
0.796437 | − | 0.604722i | \(-0.206716\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −43.4558 | −2.06000 | ||||||||
\(446\) | −5.19615 | − | 9.00000i | −0.246045 | − | 0.426162i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.62132 | + | 0.358719i | −0.123846 | + | 0.0169479i | ||||
\(449\) | − | 30.7279i | − | 1.45014i | −0.688675 | − | 0.725070i | \(-0.741807\pi\) | ||
0.688675 | − | 0.725070i | \(-0.258193\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | − | 5.19615i | 0.423793 | − | 0.244677i | ||||
\(452\) | −1.52192 | − | 0.878680i | −0.0715850 | − | 0.0413296i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.72792 | − | 2.15232i | −0.174960 | − | 0.101013i | ||||
\(455\) | −3.67423 | − | 26.8492i | −0.172251 | − | 1.25871i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.0000 | −1.07589 | −0.537947 | − | 0.842978i | \(-0.680800\pi\) | ||||
−0.537947 | + | 0.842978i | \(0.680800\pi\) | |||||||
\(458\) | 4.54026 | + | 7.86396i | 0.212152 | + | 0.367459i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.7279 | − | 7.34847i | −0.593442 | − | 0.342624i | ||||
\(461\) | 21.1178 | + | 36.5772i | 0.983556 | + | 1.70357i | 0.648187 | + | 0.761482i | \(0.275528\pi\) |
0.335369 | + | 0.942087i | \(0.391139\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0000 | − | 19.0526i | 0.511213 | − | 0.885448i | −0.488702 | − | 0.872451i | \(-0.662530\pi\) |
0.999916 | − | 0.0129968i | \(-0.00413714\pi\) | |||||||
\(464\) | 8.87039 | − | 5.12132i | 0.411797 | − | 0.237751i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.75736 | − | 3.04384i | 0.0814081 | − | 0.141003i | ||||
\(467\) | −1.52192 | + | 2.63604i | −0.0704260 | + | 0.121981i | −0.899088 | − | 0.437768i | \(-0.855769\pi\) |
0.828662 | + | 0.559749i | \(0.189103\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.13604 | + | 1.25024i | −0.421863 | + | 0.0577306i | ||||
\(470\) | 16.8493 | − | 9.72792i | 0.777198 | − | 0.448716i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 2.44949i | − | 0.112747i | ||||||
\(473\) | − | 29.6985i | − | 1.36554i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.24264 | + | 2.44949i | −0.194666 | + | 0.112390i | ||||
\(476\) | 3.97141 | + | 5.12132i | 0.182029 | + | 0.234735i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.87868 | − | 6.71807i | 0.177407 | − | 0.307277i | ||||
\(479\) | 1.22474 | − | 2.12132i | 0.0559600 | − | 0.0969256i | −0.836688 | − | 0.547679i | \(-0.815511\pi\) |
0.892648 | + | 0.450754i | \(0.148845\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.7426 | − | 6.77962i | 0.535418 | − | 0.309124i | ||||
\(482\) | −9.22911 | + | 15.9853i | −0.420374 | + | 0.728110i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.50000 | − | 6.06218i | −0.159091 | − | 0.275554i | ||||
\(485\) | −14.0665 | − | 8.12132i | −0.638729 | − | 0.368770i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0000 | − | 19.0526i | −0.498458 | − | 0.863354i | 0.501541 | − | 0.865134i | \(-0.332767\pi\) |
−0.999998 | + | 0.00178012i | \(0.999433\pi\) | |||||||
\(488\) | −0.717439 | −0.0324769 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −12.0000 | + | 12.2474i | −0.542105 | + | 0.553283i | ||||
\(491\) | 0.891519 | + | 0.514719i | 0.0402337 | + | 0.0232289i | 0.519982 | − | 0.854177i | \(-0.325939\pi\) |
−0.479748 | + | 0.877406i | \(0.659272\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.7279 | − | 12.5446i | −0.978576 | − | 0.564981i | ||||
\(494\) | 17.7408 | − | 10.2426i | 0.798195 | − | 0.460838i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.61642i | 0.252185i | ||||||||
\(497\) | −4.56575 | − | 33.3640i | −0.204802 | − | 1.49658i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.2279 | − | 22.9114i | −0.592163 | − | 1.02566i | −0.993941 | − | 0.109919i | \(-0.964941\pi\) |
0.401777 | − | 0.915737i | \(-0.368393\pi\) | |||||||
\(500\) | 9.79796 | 0.438178 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 5.49333i | − | 0.245179i | ||||||
\(503\) | −20.1903 | −0.900239 | −0.450120 | − | 0.892968i | \(-0.648619\pi\) | ||||
−0.450120 | + | 0.892968i | \(0.648619\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | 25.4558i | 1.13165i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.7279 | −0.786549 | ||||||||
\(509\) | −14.9941 | − | 25.9706i | −0.664602 | − | 1.15112i | −0.979393 | − | 0.201964i | \(-0.935268\pi\) |
0.314791 | − | 0.949161i | \(-0.398066\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.9706 | + | 24.7921i | −1.41429 | + | 1.09674i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.72792 | − | 2.15232i | 0.164432 | − | 0.0949346i | ||||
\(515\) | 13.1750 | + | 7.60660i | 0.580561 | + | 0.335187i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.1838 | − | 16.8493i | −1.28350 | − | 0.741029i | ||||
\(518\) | −7.94282 | − | 3.24264i | −0.348987 | − | 0.142473i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.2426 | 0.449170 | ||||||||
\(521\) | −4.60181 | − | 7.97056i | −0.201609 | − | 0.349197i | 0.747438 | − | 0.664331i | \(-0.231284\pi\) |
−0.949047 | + | 0.315135i | \(0.897950\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.2574 | + | 8.80884i | 0.667158 | + | 0.385184i | 0.794999 | − | 0.606611i | \(-0.207471\pi\) |
−0.127841 | + | 0.991795i | \(0.540805\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.36396 | + | 16.2189i | −0.408288 | + | 0.707176i | ||||
\(527\) | 11.9142 | − | 6.87868i | 0.518992 | − | 0.299640i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | − | 11.2583i | 0.282609 | − | 0.489493i | ||||
\(530\) | −3.04384 | + | 5.27208i | −0.132216 | + | 0.229004i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.0000 | − | 4.89898i | −0.520266 | − | 0.212398i | ||||
\(533\) | 8.87039 | − | 5.12132i | 0.384219 | − | 0.221829i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 35.4815i | − | 1.53400i | ||||||
\(536\) | − | 3.48528i | − | 0.150541i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.48528 | − | 4.89898i | 0.365826 | − | 0.211210i | ||||
\(539\) | 28.7635 | + | 7.39340i | 1.23893 | + | 0.318456i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.7279 | + | 39.3659i | −0.977150 | + | 1.69247i | −0.304499 | + | 0.952513i | \(0.598489\pi\) |
−0.672651 | + | 0.739960i | \(0.734844\pi\) | |||||||
\(542\) | 7.70719 | − | 13.3492i | 0.331052 | − | 0.573399i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.12132 | + | 1.22474i | −0.0909509 | + | 0.0525105i | ||||
\(545\) | −9.46473 | + | 16.3934i | −0.405425 | + | 0.702216i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.01472 | − | 5.22165i | −0.128900 | − | 0.223261i | 0.794351 | − | 0.607460i | \(-0.207811\pi\) |
−0.923251 | + | 0.384198i | \(0.874478\pi\) | |||||||
\(548\) | −5.19615 | − | 3.00000i | −0.221969 | − | 0.128154i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.12132 | + | 3.67423i | 0.0904534 | + | 0.156670i | ||||
\(551\) | 50.1785 | 2.13768 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.2279 | − | 3.31552i | 1.03028 | − | 0.140990i | ||||
\(554\) | −1.49642 | − | 0.863961i | −0.0635770 | − | 0.0367062i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.98528 | + | 5.76500i | 0.423470 | + | 0.244491i | ||||
\(557\) | 18.3712 | − | 10.6066i | 0.778412 | − | 0.449416i | −0.0574555 | − | 0.998348i | \(-0.518299\pi\) |
0.835867 | + | 0.548932i | \(0.184965\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 29.2708i | − | 1.23802i | ||||||
\(560\) | −3.97141 | − | 5.12132i | −0.167823 | − | 0.216415i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.1213 | − | 19.2627i | −0.469125 | − | 0.812548i | ||||
\(563\) | −16.4800 | −0.694548 | −0.347274 | − | 0.937764i | \(-0.612893\pi\) | ||||
−0.347274 | + | 0.937764i | \(0.612893\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 4.30463i | − | 0.181097i | ||||||
\(566\) | −23.3572 | −0.981776 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.7279 | 0.534052 | ||||||||
\(569\) | 1.75736i | 0.0736723i | 0.999321 | + | 0.0368362i | \(0.0117280\pi\) | ||||
−0.999321 | + | 0.0368362i | \(0.988272\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0000 | −0.920671 | −0.460336 | − | 0.887745i | \(-0.652271\pi\) | ||||
−0.460336 | + | 0.887745i | \(0.652271\pi\) | |||||||
\(572\) | −8.87039 | − | 15.3640i | −0.370890 | − | 0.642399i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.00000 | − | 2.44949i | −0.250435 | − | 0.102240i | ||||
\(575\) | − | 6.00000i | − | 0.250217i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.2574 | − | 8.80884i | 0.635172 | − | 0.366717i | −0.147580 | − | 0.989050i | \(-0.547148\pi\) |
0.782752 | + | 0.622333i | \(0.213815\pi\) | |||||||
\(578\) | −9.52628 | − | 5.50000i | −0.396241 | − | 0.228770i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 21.7279 | + | 12.5446i | 0.902203 | + | 0.520887i | ||||
\(581\) | 8.90644 | + | 11.4853i | 0.369501 | + | 0.476490i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.5442 | 0.436694 | ||||||||
\(584\) | −7.64564 | − | 13.2426i | −0.316379 | − | 0.547984i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.87868 | + | 3.97141i | 0.284156 | + | 0.164057i | ||||
\(587\) | 5.82655 | + | 10.0919i | 0.240488 | + | 0.416537i | 0.960853 | − | 0.277058i | \(-0.0893594\pi\) |
−0.720366 | + | 0.693594i | \(0.756026\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.7574 | + | 23.8284i | −0.566862 | + | 0.981834i | ||||
\(590\) | 5.19615 | − | 3.00000i | 0.213922 | − | 0.123508i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.62132 | − | 2.80821i | 0.0666359 | − | 0.115417i | ||||
\(593\) | −11.3199 | + | 19.6066i | −0.464852 | + | 0.805147i | −0.999195 | − | 0.0401210i | \(-0.987226\pi\) |
0.534343 | + | 0.845268i | \(0.320559\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | + | 14.6969i | −0.245976 | + | 0.602516i | ||||
\(596\) | 6.71807 | − | 3.87868i | 0.275183 | − | 0.158877i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 25.0892i | 1.02598i | ||||||||
\(599\) | 20.4853i | 0.837006i | 0.908215 | + | 0.418503i | \(0.137445\pi\) | ||||
−0.908215 | + | 0.418503i | \(0.862555\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.9558 | − | 8.63476i | 0.610062 | − | 0.352219i | −0.162928 | − | 0.986638i | \(-0.552094\pi\) |
0.772990 | + | 0.634419i | \(0.218760\pi\) | |||||||
\(602\) | −14.6354 | + | 11.3492i | −0.596494 | + | 0.462561i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.62132 | − | 14.9326i | 0.350797 | − | 0.607597i | ||||
\(605\) | 8.57321 | − | 14.8492i | 0.348551 | − | 0.603708i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.7574 | + | 13.1390i | −0.923693 | + | 0.533294i | −0.884811 | − | 0.465950i | \(-0.845713\pi\) |
−0.0388815 | + | 0.999244i | \(0.512379\pi\) | |||||||
\(608\) | 2.44949 | − | 4.24264i | 0.0993399 | − | 0.172062i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.878680 | − | 1.52192i | −0.0355767 | − | 0.0616207i | ||||
\(611\) | −28.7635 | − | 16.6066i | −1.16365 | − | 0.671831i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.10660 | − | 12.3090i | −0.287033 | − | 0.497156i | 0.686067 | − | 0.727538i | \(-0.259336\pi\) |
−0.973100 | + | 0.230383i | \(0.926002\pi\) | |||||||
\(614\) | 2.57258 | 0.103821 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.24264 | + | 10.3923i | −0.170941 | + | 0.418718i | ||||
\(617\) | −3.67423 | − | 2.12132i | −0.147919 | − | 0.0854011i | 0.424214 | − | 0.905562i | \(-0.360551\pi\) |
−0.572133 | + | 0.820161i | \(0.693884\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.9853 | + | 16.1573i | 1.12482 | + | 0.649417i | 0.942628 | − | 0.333845i | \(-0.108346\pi\) |
0.182196 | + | 0.983262i | \(0.441680\pi\) | |||||||
\(620\) | −11.9142 | + | 6.87868i | −0.478487 | + | 0.276254i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 17.1464i | − | 0.687509i | ||||||
\(623\) | 17.7408 | − | 43.4558i | 0.710769 | − | 1.74102i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 0.594346 | 0.0237548 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.3923i | 0.414698i | ||||||||
\(629\) | −7.94282 | −0.316701 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.2426 | −0.925275 | −0.462637 | − | 0.886548i | \(-0.653097\pi\) | ||||
−0.462637 | + | 0.886548i | \(0.653097\pi\) | |||||||
\(632\) | 9.24264i | 0.367653i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.7574 | 0.546375 | ||||||||
\(635\) | −21.7122 | − | 37.6066i | −0.861622 | − | 1.49237i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.3492 | + | 7.28692i | 1.12324 | + | 0.288718i | ||||
\(638\) | − | 43.4558i | − | 1.72043i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.12132 | − | 1.22474i | 0.0838525 | − | 0.0484123i | ||||
\(641\) | 7.97887 | + | 4.60660i | 0.315146 | + | 0.181950i | 0.649227 | − | 0.760595i | \(-0.275092\pi\) |
−0.334081 | + | 0.942544i | \(0.608426\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.50000 | − | 0.866025i | −0.0591542 | − | 0.0341527i | 0.470131 | − | 0.882597i | \(-0.344207\pi\) |
−0.529285 | + | 0.848444i | \(0.677540\pi\) | |||||||
\(644\) | 12.5446 | − | 9.72792i | 0.494327 | − | 0.383334i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0000 | −0.472134 | ||||||||
\(647\) | −10.3923 | − | 18.0000i | −0.408564 | − | 0.707653i | 0.586165 | − | 0.810191i | \(-0.300637\pi\) |
−0.994729 | + | 0.102538i | \(0.967304\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | − | 5.19615i | −0.353281 | − | 0.203967i | ||||
\(650\) | 2.09077 | + | 3.62132i | 0.0820068 | + | 0.142040i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.74264 | − | 6.48244i | 0.146573 | − | 0.253872i | ||||
\(653\) | −12.5446 | + | 7.24264i | −0.490909 | + | 0.283426i | −0.724951 | − | 0.688800i | \(-0.758138\pi\) |
0.234043 | + | 0.972226i | \(0.424805\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.22474 | − | 2.12132i | 0.0478183 | − | 0.0828236i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.84924 | + | 20.8207i | 0.111075 | + | 0.811674i | ||||
\(659\) | −11.9142 | + | 6.87868i | −0.464112 | + | 0.267955i | −0.713772 | − | 0.700378i | \(-0.753015\pi\) |
0.249660 | + | 0.968334i | \(0.419681\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.89898i | 0.190548i | 0.995451 | + | 0.0952741i | \(0.0303728\pi\) | ||||
−0.995451 | + | 0.0952741i | \(0.969627\pi\) | |||||||
\(662\) | − | 10.0000i | − | 0.388661i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.75736 | + | 2.74666i | −0.184621 | + | 0.106591i | ||||
\(665\) | −4.30463 | − | 31.4558i | −0.166927 | − | 1.21981i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.7279 | + | 53.2223i | −1.18979 | + | 2.06078i | ||||
\(668\) | 10.0951 | − | 17.4853i | 0.390592 | − | 0.676526i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.39340 | − | 4.26858i | 0.285632 | − | 0.164910i | ||||
\(671\) | −1.52192 | + | 2.63604i | −0.0587530 | + | 0.101763i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.72792 | − | 4.72490i | −0.105154 | − | 0.182131i | 0.808647 | − | 0.588294i | \(-0.200200\pi\) |
−0.913801 | + | 0.406162i | \(0.866867\pi\) | |||||||
\(674\) | 25.5095 | + | 14.7279i | 0.982590 | + | 0.567298i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.24264 | − | 3.88437i | −0.0862554 | − | 0.149399i | ||||
\(677\) | 14.6969 | 0.564849 | 0.282425 | − | 0.959289i | \(-0.408861\pi\) | ||||
0.282425 | + | 0.959289i | \(0.408861\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.8640 | − | 10.7510i | 0.532050 | − | 0.412586i | ||||
\(680\) | −5.19615 | − | 3.00000i | −0.199263 | − | 0.115045i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 20.6360 | + | 11.9142i | 0.790195 | + | 0.456219i | ||||
\(683\) | 1.52192 | − | 0.878680i | 0.0582346 | − | 0.0336217i | −0.470600 | − | 0.882347i | \(-0.655963\pi\) |
0.528835 | + | 0.848725i | \(0.322629\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 14.6969i | − | 0.561541i | ||||||
\(686\) | −7.34847 | − | 17.0000i | −0.280566 | − | 0.649063i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.50000 | − | 6.06218i | −0.133436 | − | 0.231118i | ||||
\(689\) | 10.3923 | 0.395915 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.8213i | 1.02033i | 0.860077 | + | 0.510165i | \(0.170416\pi\) | ||||
−0.860077 | + | 0.510165i | \(0.829584\pi\) | |||||||
\(692\) | 20.7846 | 0.790112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.9706 | 1.09971 | ||||||||
\(695\) | 28.2426i | 1.07130i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.00000 | −0.227266 | ||||||||
\(698\) | 12.1859 | + | 21.1066i | 0.461243 | + | 0.798897i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00000 | − | 2.44949i | 0.0377964 | − | 0.0925820i | ||||
\(701\) | − | 3.51472i | − | 0.132749i | −0.997795 | − | 0.0663745i | \(-0.978857\pi\) | ||
0.997795 | − | 0.0663745i | \(-0.0211432\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.7574 | − | 7.94282i | 0.518869 | − | 0.299569i | ||||
\(704\) | −3.67423 | − | 2.12132i | −0.138478 | − | 0.0799503i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.4853 | + | 15.2913i | 0.996787 | + | 0.575495i | ||||
\(707\) | −7.34847 | + | 18.0000i | −0.276368 | + | 0.676960i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.2132 | −0.984458 | −0.492229 | − | 0.870466i | \(-0.663818\pi\) | ||||
−0.492229 | + | 0.870466i | \(0.663818\pi\) | |||||||
\(710\) | 15.5885 | + | 27.0000i | 0.585024 | + | 1.01329i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.3640 | + | 8.87039i | 0.575789 | + | 0.332432i | ||||
\(713\) | −16.8493 | − | 29.1838i | −0.631010 | − | 1.09294i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.7279 | − | 37.6339i | 0.812578 | − | 1.40743i | ||||
\(716\) | 16.2189 | − | 9.36396i | 0.606127 | − | 0.349948i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.24264 | − | 2.15232i | 0.0463749 | − | 0.0803237i | ||||
\(719\) | 5.52938 | − | 9.57716i | 0.206211 | − | 0.357168i | −0.744307 | − | 0.667838i | \(-0.767220\pi\) |
0.950518 | + | 0.310670i | \(0.100553\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.9853 | + | 10.0696i | −0.483597 | + | 0.375013i | ||||
\(722\) | 4.33013 | − | 2.50000i | 0.161151 | − | 0.0930404i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.79796i | 0.364138i | ||||||||
\(725\) | 10.2426i | 0.380402i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.3198 | + | 22.7013i | −1.45829 | + | 0.841945i | −0.998927 | − | 0.0463038i | \(-0.985256\pi\) |
−0.459363 | + | 0.888248i | \(0.651922\pi\) | |||||||
\(728\) | −4.18154 | + | 10.2426i | −0.154978 | + | 0.379618i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18.7279 | − | 32.4377i | 0.693151 | − | 1.20057i | ||||
\(731\) | −8.57321 | + | 14.8492i | −0.317092 | + | 0.549219i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.8640 | + | 8.00436i | −0.512077 | + | 0.295648i | −0.733687 | − | 0.679488i | \(-0.762202\pi\) |
0.221610 | + | 0.975135i | \(0.428869\pi\) | |||||||
\(734\) | −4.60181 | + | 7.97056i | −0.169856 | + | 0.294199i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.00000 | + | 5.19615i | 0.110581 | + | 0.191533i | ||||
\(737\) | −12.8057 | − | 7.39340i | −0.471706 | − | 0.272339i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.2279 | − | 36.7678i | −0.780882 | − | 1.35253i | −0.931429 | − | 0.363924i | \(-0.881437\pi\) |
0.150547 | − | 0.988603i | \(-0.451897\pi\) | |||||||
\(740\) | 7.94282 | 0.291984 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.02944 | − | 5.19615i | −0.147925 | − | 0.190757i | ||||
\(743\) | −5.82655 | − | 3.36396i | −0.213755 | − | 0.123412i | 0.389300 | − | 0.921111i | \(-0.372717\pi\) |
−0.603055 | + | 0.797699i | \(0.706050\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.4558 | + | 9.50079i | 0.602895 | + | 0.348082i | ||||
\(746\) | 19.0526 | − | 11.0000i | 0.697564 | − | 0.402739i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.3923i | 0.379980i | ||||||||
\(749\) | 35.4815 | + | 14.4853i | 1.29647 | + | 0.529281i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.27208 | − | 2.20330i | −0.0464188 | − | 0.0803997i | 0.841882 | − | 0.539661i | \(-0.181448\pi\) |
−0.888301 | + | 0.459261i | \(0.848114\pi\) | |||||||
\(752\) | −7.94282 | −0.289645 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 42.8300i | − | 1.55978i | ||||||
\(755\) | 42.2357 | 1.53711 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.2426 | 1.49899 | 0.749495 | − | 0.662010i | \(-0.230297\pi\) | ||||
0.749495 | + | 0.662010i | \(0.230297\pi\) | |||||||
\(758\) | − | 9.48528i | − | 0.344521i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.0000 | 0.435286 | ||||||||
\(761\) | 12.2474 | + | 21.2132i | 0.443970 | + | 0.768978i | 0.997980 | − | 0.0635319i | \(-0.0202365\pi\) |
−0.554010 | + | 0.832510i | \(0.686903\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.5294 | − | 16.1573i | −0.453596 | − | 0.584934i | ||||
\(764\) | − | 21.2132i | − | 0.767467i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.2426 | + | 7.64564i | −0.478476 | + | 0.276248i | ||||
\(767\) | −8.87039 | − | 5.12132i | −0.320291 | − | 0.184920i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.02944 | − | 0.594346i | −0.0371225 | − | 0.0214327i | 0.481324 | − | 0.876543i | \(-0.340156\pi\) |
−0.518446 | + | 0.855110i | \(0.673489\pi\) | |||||||
\(770\) | −27.2416 | + | 3.72792i | −0.981718 | + | 0.134345i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.4853 | −0.557327 | ||||||||
\(773\) | −4.89898 | − | 8.48528i | −0.176204 | − | 0.305194i | 0.764373 | − | 0.644774i | \(-0.223049\pi\) |
−0.940577 | + | 0.339580i | \(0.889715\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.86396 | − | 2.80821i | −0.174719 | − | 0.100874i | ||||
\(776\) | 3.31552 | + | 5.74264i | 0.119020 | + | 0.206149i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16.2426 | + | 28.1331i | −0.582327 | + | 1.00862i | ||||
\(779\) | 10.3923 | − | 6.00000i | 0.372343 | − | 0.214972i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.0000 | − | 46.7654i | 0.966136 | − | 1.67340i | ||||
\(782\) | 7.34847 | − | 12.7279i | 0.262781 | − | 0.455150i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.74264 | − | 1.88064i | 0.240809 | − | 0.0671656i | ||||
\(785\) | −22.0454 | + | 12.7279i | −0.786834 | + | 0.454279i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.9357i | 0.389814i | 0.980822 | + | 0.194907i | \(0.0624406\pi\) | ||||
−0.980822 | + | 0.194907i | \(0.937559\pi\) | |||||||
\(788\) | − | 16.9706i | − | 0.604551i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −19.6066 | + | 11.3199i | −0.697572 | + | 0.402743i | ||||
\(791\) | 4.30463 | + | 1.75736i | 0.153055 | + | 0.0624845i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.50000 | + | 2.59808i | −0.0532666 | + | 0.0922604i | ||||
\(794\) | −14.9326 | + | 25.8640i | −0.529937 | + | 0.917878i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.10660 | + | 1.79360i | −0.110111 | + | 0.0635724i | ||||
\(797\) | 1.52192 | − | 2.63604i | 0.0539091 | − | 0.0933733i | −0.837812 | − | 0.545960i | \(-0.816165\pi\) |
0.891721 | + | 0.452586i | \(0.149499\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.72792 | + | 16.8493i | 0.344149 | + | 0.596084i | ||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.1213 | − | 24.4588i | −0.498641 | − | 0.863672i | ||||
\(803\) | −64.8754 | −2.28940 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 36.0000 | + | 14.6969i | 1.26883 | + | 0.517999i | ||||
\(806\) | 20.3389 | + | 11.7426i | 0.716405 | + | 0.413617i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.36396 | − | 3.67423i | −0.223883 | − | 0.129259i | ||||
\(809\) | −2.15232 | + | 1.24264i | −0.0756714 | + | 0.0436889i | −0.537358 | − | 0.843354i | \(-0.680578\pi\) |
0.461687 | + | 0.887043i | \(0.347244\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | −21.4150 | + | 16.6066i | −0.751519 | + | 0.582777i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.87868 | − | 11.9142i | −0.241098 | − | 0.417593i | ||||
\(815\) | 18.3351 | 0.642251 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 34.2929i | − | 1.19976i | ||||||
\(818\) | −13.5592 | −0.474087 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | 10.9706i | 0.382875i | 0.981505 | + | 0.191438i | \(0.0613150\pi\) | ||||
−0.981505 | + | 0.191438i | \(0.938685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.2426 | −0.391894 | −0.195947 | − | 0.980615i | \(-0.562778\pi\) | ||||
−0.195947 | + | 0.980615i | \(0.562778\pi\) | |||||||
\(824\) | −3.10538 | − | 5.37868i | −0.108181 | − | 0.187375i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.878680 | + | 6.42090i | 0.0305732 | + | 0.223412i | ||||
\(827\) | 20.4853i | 0.712343i | 0.934421 | + | 0.356172i | \(0.115918\pi\) | ||||
−0.934421 | + | 0.356172i | \(0.884082\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.48528 | + | 4.89898i | −0.294706 | + | 0.170149i | −0.640062 | − | 0.768323i | \(-0.721091\pi\) |
0.345356 | + | 0.938472i | \(0.387758\pi\) | |||||||
\(830\) | −11.6531 | − | 6.72792i | −0.404485 | − | 0.233530i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.62132 | − | 2.09077i | −0.125547 | − | 0.0724844i | ||||
\(833\) | −12.2474 | − | 12.0000i | −0.424349 | − | 0.415775i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.4558 | 1.71149 | ||||||||
\(836\) | −10.3923 | − | 18.0000i | −0.359425 | − | 0.622543i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11.1213 | + | 6.42090i | 0.384180 | + | 0.221806i | ||||
\(839\) | −2.74666 | − | 4.75736i | −0.0948253 | − | 0.164242i | 0.814710 | − | 0.579868i | \(-0.196896\pi\) |
−0.909536 | + | 0.415626i | \(0.863563\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.9558 | − | 65.7415i | 1.30882 | − | 2.26695i | ||||
\(842\) | −23.7775 | + | 13.7279i | −0.819425 | + | 0.473095i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.74264 | + | 11.6786i | −0.232091 | + | 0.401994i | ||||
\(845\) | 5.49333 | − | 9.51472i | 0.188976 | − | 0.327316i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.3492 | + | 14.6354i | 0.389965 | + | 0.502878i | ||||
\(848\) | 2.15232 | − | 1.24264i | 0.0739109 | − | 0.0426725i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 2.44949i | − | 0.0840168i | ||||||
\(851\) | 19.4558i | 0.666938i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.4853 | + | 25.6836i | −1.52315 | + | 0.879389i | −0.523522 | + | 0.852012i | \(0.675382\pi\) |
−0.999625 | + | 0.0273771i | \(0.991285\pi\) | |||||||
\(854\) | 1.88064 | − | 0.257359i | 0.0643541 | − | 0.00880665i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.24264 | + | 12.5446i | −0.247548 | + | 0.428766i | ||||
\(857\) | −3.37706 | + | 5.84924i | −0.115358 | + | 0.199806i | −0.917923 | − | 0.396759i | \(-0.870135\pi\) |
0.802565 | + | 0.596565i | \(0.203468\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.47056 | − | 5.46783i | 0.323131 | − | 0.186560i | −0.329656 | − | 0.944101i | \(-0.606933\pi\) |
0.652787 | + | 0.757541i | \(0.273599\pi\) | |||||||
\(860\) | 8.57321 | − | 14.8492i | 0.292344 | − | 0.506355i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.12132 | − | 8.87039i | −0.174433 | − | 0.302127i | ||||
\(863\) | −11.6531 | − | 6.72792i | −0.396676 | − | 0.229021i | 0.288373 | − | 0.957518i | \(-0.406886\pi\) |
−0.685049 | + | 0.728497i | \(0.740219\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.4558 | + | 44.0908i | 0.865525 | + | 1.49913i | ||||
\(866\) | 26.8213 | 0.911425 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.01472 | − | 14.7224i | −0.0683840 | − | 0.499712i | ||||
\(869\) | 33.9596 | + | 19.6066i | 1.15200 | + | 0.665108i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.6213 | − | 7.28692i | −0.427657 | − | 0.246908i | ||||
\(872\) | 6.69258 | − | 3.86396i | 0.226639 | − | 0.130850i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 29.3939i | 0.994263i | ||||||||
\(875\) | −25.6836 | + | 3.51472i | −0.868264 | + | 0.118819i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.89340 | + | 3.27946i | 0.0639355 | + | 0.110740i | 0.896221 | − | 0.443607i | \(-0.146301\pi\) |
−0.832286 | + | 0.554347i | \(0.812968\pi\) | |||||||
\(878\) | 25.0892 | 0.846721 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 10.3923i | − | 0.350325i | ||||||
\(881\) | 4.30463 | 0.145027 | 0.0725134 | − | 0.997367i | \(-0.476898\pi\) | ||||
0.0725134 | + | 0.997367i | \(0.476898\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.00000 | −0.0673054 | −0.0336527 | − | 0.999434i | \(-0.510714\pi\) | ||||
−0.0336527 | + | 0.999434i | \(0.510714\pi\) | |||||||
\(884\) | 10.2426i | 0.344497i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.4558 | −0.855206 | ||||||||
\(887\) | 14.9941 | + | 25.9706i | 0.503453 | + | 0.872006i | 0.999992 | + | 0.00399177i | \(0.00127062\pi\) |
−0.496539 | + | 0.868014i | \(0.665396\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 46.4706 | − | 6.35935i | 1.55857 | − | 0.213286i | ||||
\(890\) | 43.4558i | 1.45664i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.00000 | + | 5.19615i | −0.301342 | + | 0.173980i | ||||
\(893\) | −33.6985 | − | 19.4558i | −1.12768 | − | 0.651065i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 39.7279 | + | 22.9369i | 1.32796 | + | 0.766697i | ||||
\(896\) | 0.358719 | + | 2.62132i | 0.0119840 | + | 0.0875722i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30.7279 | −1.02540 | ||||||||
\(899\) | 28.7635 | + | 49.8198i | 0.959316 | + | 1.66158i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.27208 | − | 3.04384i | −0.175638 | − | 0.101405i | ||||
\(902\) | −5.19615 | − | 9.00000i | −0.173013 | − | 0.299667i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.878680 | + | 1.52192i | −0.0292245 | + | 0.0506182i | ||||
\(905\) | −20.7846 | + | 12.0000i | −0.690904 | + | 0.398893i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.74264 | + | 3.01834i | −0.0578634 | + | 0.100222i | −0.893506 | − | 0.449051i | \(-0.851762\pi\) |
0.835643 | + | 0.549273i | \(0.185095\pi\) | |||||||
\(908\) | −2.15232 | + | 3.72792i | −0.0714271 | + | 0.123715i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −26.8492 | + | 3.67423i | −0.890044 | + | 0.121800i | ||||
\(911\) | 1.52192 | − | 0.878680i | 0.0504234 | − | 0.0291120i | −0.474576 | − | 0.880214i | \(-0.657399\pi\) |
0.525000 | + | 0.851102i | \(0.324065\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.3062i | 0.771323i | ||||||||
\(914\) | 23.0000i | 0.760772i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.86396 | − | 4.54026i | 0.259833 | − | 0.150014i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.136039 | + | 0.235626i | −0.00448751 | + | 0.00777260i | −0.868260 | − | 0.496109i | \(-0.834762\pi\) |
0.863773 | + | 0.503881i | \(0.168095\pi\) | |||||||
\(920\) | −7.34847 | + | 12.7279i | −0.242272 | + | 0.419627i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 36.5772 | − | 21.1178i | 1.20460 | − | 0.695479i | ||||
\(923\) | 26.6112 | − | 46.0919i | 0.875917 | − | 1.51713i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.62132 | + | 2.80821i | 0.0533087 | + | 0.0923334i | ||||
\(926\) | −19.0526 | − | 11.0000i | −0.626106 | − | 0.361482i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.12132 | − | 8.87039i | −0.168116 | − | 0.291185i | ||||
\(929\) | 33.6264 | 1.10325 | 0.551623 | − | 0.834093i | \(-0.314009\pi\) | ||||
0.551623 | + | 0.834093i | \(0.314009\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.2132 | + | 8.53716i | 1.08852 | + | 0.279794i | ||||
\(932\) | −3.04384 | − | 1.75736i | −0.0997042 | − | 0.0575642i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.63604 | + | 1.52192i | 0.0862538 | + | 0.0497987i | ||||
\(935\) | −22.0454 | + | 12.7279i | −0.720962 | + | 0.416248i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.0992i | 1.73468i | 0.497719 | + | 0.867338i | \(0.334171\pi\) | ||||
−0.497719 | + | 0.867338i | \(0.665829\pi\) | |||||||
\(938\) | 1.25024 | + | 9.13604i | 0.0408217 | + | 0.298302i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.72792 | − | 16.8493i | −0.317290 | − | 0.549562i | ||||
\(941\) | −21.4511 | −0.699285 | −0.349642 | − | 0.936883i | \(-0.613697\pi\) | ||||
−0.349642 | + | 0.936883i | \(0.613697\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.6969i | 0.478598i | ||||||||
\(944\) | −2.44949 | −0.0797241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.6985 | −0.965581 | ||||||||
\(947\) | 7.75736i | 0.252080i | 0.992025 | + | 0.126040i | \(0.0402268\pi\) | ||||
−0.992025 | + | 0.126040i | \(0.959773\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −63.9411 | −2.07562 | ||||||||
\(950\) | 2.44949 | + | 4.24264i | 0.0794719 | + | 0.137649i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.12132 | − | 3.97141i | 0.165983 | − | 0.128714i | ||||
\(953\) | 34.9706i | 1.13281i | 0.824128 | + | 0.566404i | \(0.191666\pi\) | ||||
−0.824128 | + | 0.566404i | \(0.808334\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.0000 | − | 25.9808i | 1.45617 | − | 0.840718i | ||||
\(956\) | −6.71807 | − | 3.87868i | −0.217278 | − | 0.125445i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.12132 | − | 1.22474i | −0.0685367 | − | 0.0395697i | ||||
\(959\) | 14.6969 | + | 6.00000i | 0.474589 | + | 0.193750i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.544156 | −0.0175534 | ||||||||
\(962\) | −6.77962 | − | 11.7426i | −0.218584 | − | 0.378598i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.9853 | + | 9.22911i | 0.514851 | + | 0.297250i | ||||
\(965\) | −18.9655 | − | 32.8492i | −0.610522 | − | 1.05745i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.34924 | + | 14.4613i | −0.268494 | + | 0.465044i | −0.968473 | − | 0.249119i | \(-0.919859\pi\) |
0.699979 | + | 0.714163i | \(0.253192\pi\) | |||||||
\(968\) | −6.06218 | + | 3.50000i | −0.194846 | + | 0.112494i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.12132 | + | 14.0665i | −0.260760 | + | 0.451649i | ||||
\(971\) | 0.594346 | − | 1.02944i | 0.0190735 | − | 0.0330362i | −0.856331 | − | 0.516427i | \(-0.827262\pi\) |
0.875405 | + | 0.483391i | \(0.160595\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.2426 | − | 11.5300i | −0.905417 | − | 0.369635i | ||||
\(974\) | −19.0526 | + | 11.0000i | −0.610483 | + | 0.352463i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.717439i | 0.0229647i | ||||||||
\(977\) | − | 6.00000i | − | 0.191957i | −0.995383 | − | 0.0959785i | \(-0.969402\pi\) | ||
0.995383 | − | 0.0959785i | \(-0.0305980\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 65.1838 | − | 37.6339i | 2.08328 | − | 1.20278i | ||||
\(980\) | 12.2474 | + | 12.0000i | 0.391230 | + | 0.383326i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.514719 | − | 0.891519i | 0.0164253 | − | 0.0284495i | ||||
\(983\) | −9.16756 | + | 15.8787i | −0.292400 | + | 0.506451i | −0.974377 | − | 0.224922i | \(-0.927787\pi\) |
0.681977 | + | 0.731374i | \(0.261120\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.0000 | − | 20.7846i | 1.14706 | − | 0.662253i | ||||
\(986\) | −12.5446 | + | 21.7279i | −0.399502 | + | 0.691958i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.2426 | − | 17.7408i | −0.325862 | − | 0.564409i | ||||
\(989\) | 36.3731 | + | 21.0000i | 1.15660 | + | 0.667761i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.1066 | − | 19.2372i | −0.352813 | − | 0.611090i | 0.633928 | − | 0.773392i | \(-0.281441\pi\) |
−0.986741 | + | 0.162302i | \(0.948108\pi\) | |||||||
\(992\) | 5.61642 | 0.178321 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −33.3640 | + | 4.56575i | −1.05824 | + | 0.144817i | ||||
\(995\) | −7.60959 | − | 4.39340i | −0.241240 | − | 0.139280i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.13604 | − | 2.38794i | −0.130990 | − | 0.0756269i | 0.433073 | − | 0.901359i | \(-0.357429\pi\) |
−0.564063 | + | 0.825732i | \(0.690762\pi\) | |||||||
\(998\) | −22.9114 | + | 13.2279i | −0.725249 | + | 0.418723i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1134.2.l.e.215.1 | 8 | ||
3.2 | odd | 2 | inner | 1134.2.l.e.215.4 | 8 | ||
7.3 | odd | 6 | 1134.2.t.f.1025.3 | 8 | |||
9.2 | odd | 6 | 1134.2.t.f.593.3 | 8 | |||
9.4 | even | 3 | 378.2.k.d.215.3 | yes | 8 | ||
9.5 | odd | 6 | 378.2.k.d.215.2 | ✓ | 8 | ||
9.7 | even | 3 | 1134.2.t.f.593.2 | 8 | |||
21.17 | even | 6 | 1134.2.t.f.1025.2 | 8 | |||
63.5 | even | 6 | 2646.2.d.d.2645.8 | 8 | |||
63.23 | odd | 6 | 2646.2.d.d.2645.6 | 8 | |||
63.31 | odd | 6 | 378.2.k.d.269.2 | yes | 8 | ||
63.38 | even | 6 | inner | 1134.2.l.e.269.3 | 8 | ||
63.40 | odd | 6 | 2646.2.d.d.2645.1 | 8 | |||
63.52 | odd | 6 | inner | 1134.2.l.e.269.2 | 8 | ||
63.58 | even | 3 | 2646.2.d.d.2645.3 | 8 | |||
63.59 | even | 6 | 378.2.k.d.269.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.k.d.215.2 | ✓ | 8 | 9.5 | odd | 6 | ||
378.2.k.d.215.3 | yes | 8 | 9.4 | even | 3 | ||
378.2.k.d.269.2 | yes | 8 | 63.31 | odd | 6 | ||
378.2.k.d.269.3 | yes | 8 | 63.59 | even | 6 | ||
1134.2.l.e.215.1 | 8 | 1.1 | even | 1 | trivial | ||
1134.2.l.e.215.4 | 8 | 3.2 | odd | 2 | inner | ||
1134.2.l.e.269.2 | 8 | 63.52 | odd | 6 | inner | ||
1134.2.l.e.269.3 | 8 | 63.38 | even | 6 | inner | ||
1134.2.t.f.593.2 | 8 | 9.7 | even | 3 | |||
1134.2.t.f.593.3 | 8 | 9.2 | odd | 6 | |||
1134.2.t.f.1025.2 | 8 | 21.17 | even | 6 | |||
1134.2.t.f.1025.3 | 8 | 7.3 | odd | 6 | |||
2646.2.d.d.2645.1 | 8 | 63.40 | odd | 6 | |||
2646.2.d.d.2645.3 | 8 | 63.58 | even | 3 | |||
2646.2.d.d.2645.6 | 8 | 63.23 | odd | 6 | |||
2646.2.d.d.2645.8 | 8 | 63.5 | even | 6 |