Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(379,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.e (of order \(2\), degree \(1\), 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: | \(10.9235349965\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.319794774016000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{10} + 2x^{8} + 8x^{4} - 32x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.12 | ||
Root | \(-1.37364 - 0.336338i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1368.379 |
Dual form | 1368.2.e.e.379.11 |
$q$-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 \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.37364 | + | 0.336338i | 0.971308 | + | 0.237827i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.77375 | + | 0.924013i | 0.886877 | + | 0.462006i | ||||
\(5\) | − | 3.04222i | − | 1.36052i | −0.732970 | − | 0.680261i | \(-0.761866\pi\) | ||
0.732970 | − | 0.680261i | \(-0.238134\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.23607i | − | 0.845154i | −0.906327 | − | 0.422577i | \(-0.861126\pi\) | ||
0.906327 | − | 0.422577i | \(-0.138874\pi\) | |||||||
\(8\) | 2.12571 | + | 1.86584i | 0.751552 | + | 0.659673i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.02321 | − | 4.17890i | 0.323569 | − | 1.32149i | ||||
\(11\) | 2.29240 | 0.691185 | 0.345593 | − | 0.938385i | \(-0.387678\pi\) | ||||
0.345593 | + | 0.938385i | \(0.387678\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.09769 | 0.859146 | 0.429573 | − | 0.903032i | \(-0.358664\pi\) | ||||
0.429573 | + | 0.903032i | \(0.358664\pi\) | |||||||
\(14\) | 0.752075 | − | 3.07154i | 0.201000 | − | 0.820905i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.29240 | + | 3.27794i | 0.573100 | + | 0.819485i | ||||
\(17\) | −5.58480 | −1.35451 | −0.677257 | − | 0.735747i | \(-0.736831\pi\) | ||||
−0.677257 | + | 0.735747i | \(0.736831\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.29240 | − | 0.758478i | −0.984744 | − | 0.174007i | ||||
\(20\) | 2.81105 | − | 5.39615i | 0.628570 | − | 1.20662i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.14893 | + | 0.771022i | 0.671353 | + | 0.164382i | ||||
\(23\) | − | 5.51401i | − | 1.14975i | −0.818241 | − | 0.574875i | \(-0.805051\pi\) | ||
0.818241 | − | 0.574875i | \(-0.194949\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.25511 | −0.851021 | ||||||||
\(26\) | 4.25511 | + | 1.04187i | 0.834495 | + | 0.204328i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.06615 | − | 3.96623i | 0.390467 | − | 0.749548i | ||||
\(29\) | 1.85457 | 0.344385 | 0.172193 | − | 0.985063i | \(-0.444915\pi\) | ||||
0.172193 | + | 0.985063i | \(0.444915\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.25142 | 0.763578 | 0.381789 | − | 0.924250i | \(-0.375308\pi\) | ||||
0.381789 | + | 0.924250i | \(0.375308\pi\) | |||||||
\(32\) | 2.04643 | + | 5.27372i | 0.361761 | + | 0.932271i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.67149 | − | 1.87838i | −1.31565 | − | 0.322140i | ||||
\(35\) | −6.80261 | −1.14985 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.24312 | −0.204368 | −0.102184 | − | 0.994766i | \(-0.532583\pi\) | ||||
−0.102184 | + | 0.994766i | \(0.532583\pi\) | |||||||
\(38\) | −5.64109 | − | 2.48557i | −0.915106 | − | 0.403213i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.67629 | − | 6.46688i | 0.897500 | − | 1.02250i | ||||
\(41\) | − | 8.33272i | − | 1.30135i | −0.759355 | − | 0.650676i | \(-0.774486\pi\) | ||
0.759355 | − | 0.650676i | \(-0.225514\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.87720 | 0.743767 | 0.371883 | − | 0.928279i | \(-0.378712\pi\) | ||||
0.371883 | + | 0.928279i | \(0.378712\pi\) | |||||||
\(44\) | 4.06615 | + | 2.11821i | 0.612996 | + | 0.319332i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.85457 | − | 7.57424i | 0.273442 | − | 1.11676i | ||||
\(47\) | 9.36238i | 1.36564i | 0.730585 | + | 0.682822i | \(0.239247\pi\) | ||||
−0.730585 | + | 0.682822i | \(0.760753\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | −5.84497 | − | 1.43115i | −0.826603 | − | 0.202396i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.49455 | + | 2.86231i | 0.761956 | + | 0.396931i | ||||
\(53\) | −11.4420 | −1.57168 | −0.785838 | − | 0.618432i | \(-0.787768\pi\) | ||||
−0.785838 | + | 0.618432i | \(0.787768\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.97399i | − | 0.940373i | ||||||
\(56\) | 4.17214 | − | 4.75323i | 0.557526 | − | 0.635178i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.54751 | + | 0.623763i | 0.334504 | + | 0.0819041i | ||||
\(59\) | − | 2.49721i | − | 0.325110i | −0.986700 | − | 0.162555i | \(-0.948027\pi\) | ||
0.986700 | − | 0.162555i | \(-0.0519734\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.26613i | − | 0.290149i | −0.989421 | − | 0.145074i | \(-0.953658\pi\) | ||
0.989421 | − | 0.145074i | \(-0.0463422\pi\) | |||||||
\(62\) | 5.83991 | + | 1.42992i | 0.741669 | + | 0.181599i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.03730 | + | 7.93247i | 0.129662 | + | 0.991558i | ||||
\(65\) | − | 9.42387i | − | 1.16889i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.49015i | 0.548560i | 0.961650 | + | 0.274280i | \(0.0884394\pi\) | ||||
−0.961650 | + | 0.274280i | \(0.911561\pi\) | |||||||
\(68\) | −9.90606 | − | 5.16043i | −1.20129 | − | 0.625794i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.34431 | − | 2.28798i | −1.11686 | − | 0.273466i | ||||
\(71\) | 14.6982 | 1.74436 | 0.872180 | − | 0.489186i | \(-0.162706\pi\) | ||||
0.872180 | + | 0.489186i | \(0.162706\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.51021 | 0.176757 | 0.0883784 | − | 0.996087i | \(-0.471832\pi\) | ||||
0.0883784 | + | 0.996087i | \(0.471832\pi\) | |||||||
\(74\) | −1.70760 | − | 0.418110i | −0.198504 | − | 0.0486043i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.91282 | − | 5.31159i | −0.792955 | − | 0.609281i | ||||
\(77\) | − | 5.12597i | − | 0.584158i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.5314 | 1.29738 | 0.648690 | − | 0.761053i | \(-0.275317\pi\) | ||||
0.648690 | + | 0.761053i | \(0.275317\pi\) | |||||||
\(80\) | 9.97222 | − | 6.97399i | 1.11493 | − | 0.779716i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.80261 | − | 11.4461i | 0.309497 | − | 1.26401i | ||||
\(83\) | −2.00000 | −0.219529 | −0.109764 | − | 0.993958i | \(-0.535010\pi\) | ||||
−0.109764 | + | 0.993958i | \(0.535010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.9902i | 1.84285i | ||||||||
\(86\) | 6.69951 | + | 1.64039i | 0.722426 | + | 0.176888i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.87298 | + | 4.27725i | 0.519462 | + | 0.455956i | ||||
\(89\) | 5.29881i | 0.561673i | 0.959756 | + | 0.280836i | \(0.0906118\pi\) | ||||
−0.959756 | + | 0.280836i | \(0.909388\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.92665i | − | 0.726111i | ||||||
\(92\) | 5.09501 | − | 9.78049i | 0.531192 | − | 1.01969i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.14893 | + | 12.8605i | −0.324787 | + | 1.32646i | ||||
\(95\) | −2.30746 | + | 13.0584i | −0.236740 | + | 1.33977i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.17375i | 0.119176i | 0.998223 | + | 0.0595881i | \(0.0189787\pi\) | ||||
−0.998223 | + | 0.0595881i | \(0.981021\pi\) | |||||||
\(98\) | 2.74727 | + | 0.672676i | 0.277516 | + | 0.0679506i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.54751 | − | 3.93177i | −0.754751 | − | 0.393177i | ||||
\(101\) | 12.6403i | 1.25776i | 0.777503 | + | 0.628880i | \(0.216486\pi\) | ||||
−0.777503 | + | 0.628880i | \(0.783514\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.70914 | 0.365473 | 0.182736 | − | 0.983162i | \(-0.441505\pi\) | ||||
0.182736 | + | 0.983162i | \(0.441505\pi\) | |||||||
\(104\) | 6.58480 | + | 5.77980i | 0.645693 | + | 0.566756i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.7171 | − | 3.84837i | −1.52658 | − | 0.373787i | ||||
\(107\) | 11.1343i | 1.07639i | 0.842819 | + | 0.538197i | \(0.180895\pi\) | ||||
−0.842819 | + | 0.538197i | \(0.819105\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.4420 | −1.09594 | −0.547971 | − | 0.836497i | \(-0.684600\pi\) | ||||
−0.547971 | + | 0.836497i | \(0.684600\pi\) | |||||||
\(110\) | 2.34562 | − | 9.57973i | 0.223646 | − | 0.913391i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.32970 | − | 5.12597i | 0.692591 | − | 0.484358i | ||||
\(113\) | 17.5348i | 1.64954i | 0.565471 | + | 0.824768i | \(0.308694\pi\) | ||||
−0.565471 | + | 0.824768i | \(0.691306\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.7748 | −1.56426 | ||||||||
\(116\) | 3.28955 | + | 1.71365i | 0.305427 | + | 0.159108i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.839908 | − | 3.43026i | 0.0773198 | − | 0.315781i | ||||
\(119\) | 12.4880i | 1.14477i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.74489 | −0.522263 | ||||||||
\(122\) | 0.762188 | − | 3.11284i | 0.0690052 | − | 0.281824i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.54097 | + | 3.92837i | 0.677200 | + | 0.352778i | ||||
\(125\) | − | 2.26613i | − | 0.202689i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.84974 | 0.252873 | 0.126437 | − | 0.991975i | \(-0.459646\pi\) | ||||
0.126437 | + | 0.991975i | \(0.459646\pi\) | |||||||
\(128\) | −1.24312 | + | 11.2452i | −0.109878 | + | 0.993945i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.16961 | − | 12.9450i | 0.277993 | − | 1.13535i | ||||
\(131\) | −7.97222 | −0.696536 | −0.348268 | − | 0.937395i | \(-0.613230\pi\) | ||||
−0.348268 | + | 0.937395i | \(0.613230\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.69601 | + | 9.59810i | −0.147063 | + | 0.832261i | ||||
\(134\) | −1.51021 | + | 6.16784i | −0.130462 | + | 0.532820i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.8717 | − | 10.4203i | −1.01799 | − | 0.893537i | ||||
\(137\) | −9.19003 | −0.785157 | −0.392578 | − | 0.919719i | \(-0.628417\pi\) | ||||
−0.392578 | + | 0.919719i | \(0.628417\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.89762 | −0.330592 | −0.165296 | − | 0.986244i | \(-0.552858\pi\) | ||||
−0.165296 | + | 0.986244i | \(0.552858\pi\) | |||||||
\(140\) | −12.0662 | − | 6.28570i | −1.01978 | − | 0.531238i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 20.1900 | + | 4.94358i | 1.69431 | + | 0.414856i | ||||
\(143\) | 7.10116 | 0.593829 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 5.64202i | − | 0.468544i | ||||||
\(146\) | 2.07448 | + | 0.507941i | 0.171685 | + | 0.0420375i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.20499 | − | 1.14866i | −0.181249 | − | 0.0944193i | ||||
\(149\) | 10.4343i | 0.854813i | 0.904060 | + | 0.427406i | \(0.140573\pi\) | ||||
−0.904060 | + | 0.427406i | \(0.859427\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.9891 | 0.894279 | 0.447140 | − | 0.894464i | \(-0.352443\pi\) | ||||
0.447140 | + | 0.894464i | \(0.352443\pi\) | |||||||
\(152\) | −7.70921 | − | 9.62123i | −0.625299 | − | 0.780385i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.72406 | − | 7.04121i | 0.138929 | − | 0.567397i | ||||
\(155\) | − | 12.9338i | − | 1.03886i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.77980i | 0.461278i | 0.973039 | + | 0.230639i | \(0.0740816\pi\) | ||||
−0.973039 | + | 0.230639i | \(0.925918\pi\) | |||||||
\(158\) | 15.8399 | + | 3.87844i | 1.26016 | + | 0.308552i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 16.0438 | − | 6.22569i | 1.26838 | − | 0.492184i | ||||
\(161\) | −12.3297 | −0.971716 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.65940 | 0.521604 | 0.260802 | − | 0.965392i | \(-0.416013\pi\) | ||||
0.260802 | + | 0.965392i | \(0.416013\pi\) | |||||||
\(164\) | 7.69954 | − | 14.7802i | 0.601233 | − | 1.15414i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.74727 | − | 0.672676i | −0.213230 | − | 0.0522098i | ||||
\(167\) | 1.94397 | 0.150429 | 0.0752143 | − | 0.997167i | \(-0.476036\pi\) | ||||
0.0752143 | + | 0.997167i | \(0.476036\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.40429 | −0.261869 | ||||||||
\(170\) | −5.71445 | + | 23.3384i | −0.438279 | + | 1.78997i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.65096 | + | 4.50660i | 0.659629 | + | 0.343625i | ||||
\(173\) | 20.5765 | 1.56440 | 0.782201 | − | 0.623026i | \(-0.214097\pi\) | ||||
0.782201 | + | 0.623026i | \(0.214097\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.51470i | 0.719244i | ||||||||
\(176\) | 5.25511 | + | 7.51436i | 0.396118 | + | 0.566416i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.78219 | + | 7.27864i | −0.133581 | + | 0.545557i | ||||
\(179\) | 8.72610i | 0.652220i | 0.945332 | + | 0.326110i | \(0.105738\pi\) | ||||
−0.945332 | + | 0.326110i | \(0.894262\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.50284 | −0.632011 | −0.316006 | − | 0.948757i | \(-0.602342\pi\) | ||||
−0.316006 | + | 0.948757i | \(0.602342\pi\) | |||||||
\(182\) | 2.32970 | − | 9.51470i | 0.172689 | − | 0.705277i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.2882 | − | 11.7212i | 0.758460 | − | 0.864098i | ||||
\(185\) | 3.78185i | 0.278047i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.8026 | −0.936220 | ||||||||
\(188\) | −8.65096 | + | 16.6066i | −0.630936 | + | 1.21116i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.56166 | + | 17.1614i | −0.548580 | + | 1.24502i | ||||
\(191\) | − | 11.2405i | − | 0.813332i | −0.913577 | − | 0.406666i | \(-0.866691\pi\) | ||
0.913577 | − | 0.406666i | \(-0.133309\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.76773i | 0.559134i | 0.960126 | + | 0.279567i | \(0.0901909\pi\) | ||||
−0.960126 | + | 0.279567i | \(0.909809\pi\) | |||||||
\(194\) | −0.394777 | + | 1.61230i | −0.0283433 | + | 0.115757i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.54751 | + | 1.84803i | 0.253393 | + | 0.132002i | ||||
\(197\) | − | 3.63592i | − | 0.259048i | −0.991576 | − | 0.129524i | \(-0.958655\pi\) | ||
0.991576 | − | 0.129524i | \(-0.0413450\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.46068i | 0.387097i | 0.981091 | + | 0.193549i | \(0.0619997\pi\) | ||||
−0.981091 | + | 0.193549i | \(0.938000\pi\) | |||||||
\(200\) | −9.04512 | − | 7.93934i | −0.639587 | − | 0.561396i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.25142 | + | 17.3632i | −0.299129 | + | 1.22167i | ||||
\(203\) | − | 4.14695i | − | 0.291059i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −25.3500 | −1.77052 | ||||||||
\(206\) | 5.09501 | + | 1.24753i | 0.354986 | + | 0.0869193i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.10116 | + | 10.1541i | 0.492377 | + | 0.704057i | ||||
\(209\) | −9.83991 | − | 1.73874i | −0.680641 | − | 0.120271i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 15.3420i | − | 1.05619i | −0.849187 | − | 0.528093i | \(-0.822907\pi\) | ||
0.849187 | − | 0.528093i | \(-0.177093\pi\) | |||||||
\(212\) | −20.2952 | − | 10.5725i | −1.39388 | − | 0.726124i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.74489 | + | 15.2945i | −0.255996 | + | 1.04551i | ||||
\(215\) | − | 14.8375i | − | 1.01191i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 9.50647i | − | 0.645341i | ||||||
\(218\) | −15.7171 | − | 3.84837i | −1.06450 | − | 0.260645i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.44406 | − | 12.3701i | 0.434458 | − | 0.833995i | ||||
\(221\) | −17.3000 | −1.16372 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.4468 | 0.699570 | 0.349785 | − | 0.936830i | \(-0.386255\pi\) | ||||
0.349785 | + | 0.936830i | \(0.386255\pi\) | |||||||
\(224\) | 11.7924 | − | 4.57596i | 0.787913 | − | 0.305744i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.89762 | + | 24.0864i | −0.392304 | + | 1.60221i | ||||
\(227\) | 0.193492i | 0.0128425i | 0.999979 | + | 0.00642124i | \(0.00204396\pi\) | ||||
−0.999979 | + | 0.00642124i | \(0.997956\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 19.3185i | − | 1.27660i | −0.769788 | − | 0.638300i | \(-0.779638\pi\) | ||
0.769788 | − | 0.638300i | \(-0.220362\pi\) | |||||||
\(230\) | −23.0425 | − | 5.64202i | −1.51938 | − | 0.372023i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.94228 | + | 3.46033i | 0.258824 | + | 0.227182i | ||||
\(233\) | 12.4247 | 0.813970 | 0.406985 | − | 0.913435i | \(-0.366580\pi\) | ||||
0.406985 | + | 0.913435i | \(0.366580\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.4824 | 1.85799 | ||||||||
\(236\) | 2.30746 | − | 4.42944i | 0.150203 | − | 0.288332i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.20019 | + | 17.1540i | −0.272258 | + | 1.11193i | ||||
\(239\) | 0.152323i | 0.00985293i | 0.999988 | + | 0.00492647i | \(0.00156815\pi\) | ||||
−0.999988 | + | 0.00492647i | \(0.998432\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 11.9754i | − | 0.771403i | −0.922624 | − | 0.385701i | \(-0.873959\pi\) | ||
0.922624 | − | 0.385701i | \(-0.126041\pi\) | |||||||
\(242\) | −7.89140 | − | 1.93223i | −0.507278 | − | 0.124208i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.09394 | − | 4.01956i | 0.134051 | − | 0.257326i | ||||
\(245\) | − | 6.08444i | − | 0.388721i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.2965 | − | 2.34953i | −0.846039 | − | 0.149497i | ||||
\(248\) | 9.03730 | + | 7.93247i | 0.573869 | + | 0.503712i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.762188 | − | 3.11284i | 0.0482050 | − | 0.196874i | ||||
\(251\) | −7.82303 | −0.493785 | −0.246893 | − | 0.969043i | \(-0.579410\pi\) | ||||
−0.246893 | + | 0.969043i | \(0.579410\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 12.6403i | − | 0.794690i | ||||||
\(254\) | 3.91450 | + | 0.958475i | 0.245618 | + | 0.0601401i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.48979 | + | 15.0287i | −0.343112 | + | 0.939295i | ||||
\(257\) | 13.4097i | 0.836477i | 0.908337 | + | 0.418239i | \(0.137352\pi\) | ||||
−0.908337 | + | 0.418239i | \(0.862648\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.77971i | 0.172723i | ||||||||
\(260\) | 8.70777 | − | 16.7156i | 0.540033 | − | 1.03666i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.9509 | − | 2.68136i | −0.676551 | − | 0.165655i | ||||
\(263\) | 4.11416i | 0.253690i | 0.991923 | + | 0.126845i | \(0.0404851\pi\) | ||||
−0.991923 | + | 0.126845i | \(0.959515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 34.8090i | 2.13830i | ||||||||
\(266\) | −5.55791 | + | 12.6139i | −0.340777 | + | 0.773406i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.14896 | + | 7.96443i | −0.253438 | + | 0.486505i | ||||
\(269\) | −26.4345 | −1.61174 | −0.805871 | − | 0.592091i | \(-0.798302\pi\) | ||||
−0.805871 | + | 0.592091i | \(0.798302\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 19.2952i | − | 1.17210i | −0.810275 | − | 0.586050i | \(-0.800682\pi\) | ||
0.810275 | − | 0.586050i | \(-0.199318\pi\) | |||||||
\(272\) | −12.8026 | − | 18.3067i | −0.776272 | − | 1.11000i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.6238 | − | 3.09096i | −0.762629 | − | 0.186732i | ||||
\(275\) | −9.75441 | −0.588213 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.7106i | 1.60488i | 0.596731 | + | 0.802441i | \(0.296466\pi\) | ||||
−0.596731 | + | 0.802441i | \(0.703534\pi\) | |||||||
\(278\) | −5.35392 | − | 1.31092i | −0.321107 | − | 0.0786238i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −14.4604 | − | 12.6926i | −0.864173 | − | 0.758526i | ||||
\(281\) | 23.4424i | 1.39846i | 0.714899 | + | 0.699228i | \(0.246473\pi\) | ||||
−0.714899 | + | 0.699228i | \(0.753527\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.5366 | −0.685780 | −0.342890 | − | 0.939376i | \(-0.611406\pi\) | ||||
−0.342890 | + | 0.939376i | \(0.611406\pi\) | |||||||
\(284\) | 26.0710 | + | 13.5814i | 1.54703 | + | 0.805905i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.75441 | + | 2.38839i | 0.576790 | + | 0.141228i | ||||
\(287\) | −18.6325 | −1.09984 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.1900 | 0.834707 | ||||||||
\(290\) | 1.89762 | − | 7.75008i | 0.111432 | − | 0.455100i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.67874 | + | 1.39545i | 0.156761 | + | 0.0816627i | ||||
\(293\) | −11.7793 | −0.688156 | −0.344078 | − | 0.938941i | \(-0.611808\pi\) | ||||
−0.344078 | + | 0.938941i | \(0.611808\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.59707 | −0.442319 | ||||||||
\(296\) | −2.64252 | − | 2.31947i | −0.153593 | − | 0.134816i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.50946 | + | 14.3330i | −0.203298 | + | 0.830286i | ||||
\(299\) | − | 17.0807i | − | 0.987803i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 10.9058i | − | 0.628598i | ||||||
\(302\) | 15.0950 | + | 3.69605i | 0.868620 | + | 0.212684i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.35366 | − | 15.8090i | −0.421761 | − | 0.906707i | ||||
\(305\) | −6.89408 | −0.394754 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.16669i | − | 0.180733i | −0.995909 | − | 0.0903663i | \(-0.971196\pi\) | ||
0.995909 | − | 0.0903663i | \(-0.0288038\pi\) | |||||||
\(308\) | 4.73646 | − | 9.09220i | 0.269885 | − | 0.518076i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.35012 | − | 17.7663i | 0.247070 | − | 1.00906i | ||||
\(311\) | − | 9.73483i | − | 0.552012i | −0.961156 | − | 0.276006i | \(-0.910989\pi\) | ||
0.961156 | − | 0.276006i | \(-0.0890109\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.0299 | −1.18868 | −0.594341 | − | 0.804213i | \(-0.702587\pi\) | ||||
−0.594341 | + | 0.804213i | \(0.702587\pi\) | |||||||
\(314\) | −1.94397 | + | 7.93934i | −0.109704 | + | 0.448043i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.4538 | + | 10.6551i | 1.15062 | + | 0.599398i | ||||
\(317\) | 10.1989 | 0.572825 | 0.286412 | − | 0.958106i | \(-0.407537\pi\) | ||||
0.286412 | + | 0.958106i | \(0.407537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.25142 | 0.238034 | ||||||||
\(320\) | 24.1323 | − | 3.15568i | 1.34904 | − | 0.176408i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −16.9365 | − | 4.14695i | −0.943835 | − | 0.231100i | ||||
\(323\) | 23.9722 | + | 4.23595i | 1.33385 | + | 0.235695i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.1810 | −0.731151 | ||||||||
\(326\) | 9.14759 | + | 2.23981i | 0.506638 | + | 0.124052i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.5475 | − | 17.7130i | 0.858467 | − | 0.978034i | ||||
\(329\) | 20.9349 | 1.15418 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.4100i | 1.72645i | 0.504819 | + | 0.863225i | \(0.331559\pi\) | ||||
−0.504819 | + | 0.863225i | \(0.668441\pi\) | |||||||
\(332\) | −3.54751 | − | 1.84803i | −0.194695 | − | 0.101424i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.67030 | + | 0.653830i | 0.146112 | + | 0.0357760i | ||||
\(335\) | 13.6600 | 0.746328 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0554i | 1.25591i | 0.778251 | + | 0.627954i | \(0.216107\pi\) | ||||
−0.778251 | + | 0.627954i | \(0.783893\pi\) | |||||||
\(338\) | −4.67626 | − | 1.14499i | −0.254355 | − | 0.0622794i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −15.6992 | + | 30.1364i | −0.851407 | + | 1.63438i | ||||
\(341\) | 9.74597 | 0.527774 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.1246i | − | 1.08663i | ||||||
\(344\) | 10.3675 | + | 9.10007i | 0.558980 | + | 0.490643i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 28.2646 | + | 6.92066i | 1.51952 | + | 0.372057i | ||||
\(347\) | −29.3319 | −1.57462 | −0.787308 | − | 0.616560i | \(-0.788526\pi\) | ||||
−0.787308 | + | 0.616560i | \(0.788526\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 11.9865i | − | 0.641622i | −0.947143 | − | 0.320811i | \(-0.896045\pi\) | ||
0.947143 | − | 0.320811i | \(-0.103955\pi\) | |||||||
\(350\) | −3.20016 | + | 13.0697i | −0.171056 | + | 0.698607i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.69124 | + | 12.0895i | 0.250044 | + | 0.644372i | ||||
\(353\) | 12.5197 | 0.666358 | 0.333179 | − | 0.942864i | \(-0.391879\pi\) | ||||
0.333179 | + | 0.942864i | \(0.391879\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 44.7153i | − | 2.37324i | ||||||
\(356\) | −4.89617 | + | 9.39878i | −0.259496 | + | 0.498134i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.93492 | + | 11.9865i | −0.155115 | + | 0.633506i | ||||
\(359\) | − | 16.0173i | − | 0.845358i | −0.906279 | − | 0.422679i | \(-0.861090\pi\) | ||
0.906279 | − | 0.422679i | \(-0.138910\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.8494 | + | 6.51138i | 0.939443 | + | 0.342704i | ||||
\(362\) | −11.6798 | − | 2.85983i | −0.613878 | − | 0.150309i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.40032 | − | 12.2862i | 0.335468 | − | 0.643971i | ||||
\(365\) | − | 4.59439i | − | 0.240481i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.0338i | 1.46335i | 0.681652 | + | 0.731677i | \(0.261262\pi\) | ||||
−0.681652 | + | 0.731677i | \(0.738738\pi\) | |||||||
\(368\) | 18.0746 | − | 12.6403i | 0.942203 | − | 0.658922i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.27198 | + | 5.19489i | −0.0661272 | + | 0.270070i | ||||
\(371\) | 25.5850i | 1.32831i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.7697 | −0.712966 | −0.356483 | − | 0.934302i | \(-0.616024\pi\) | ||||
−0.356483 | + | 0.934302i | \(0.616024\pi\) | |||||||
\(374\) | −17.5861 | − | 4.30601i | −0.909357 | − | 0.222658i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.4687 | + | 19.9017i | −0.900879 | + | 1.02635i | ||||
\(377\) | 5.74489 | 0.295877 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.8817i | 1.53492i | 0.641097 | + | 0.767460i | \(0.278480\pi\) | ||||
−0.641097 | + | 0.767460i | \(0.721520\pi\) | |||||||
\(380\) | −16.1590 | + | 21.0303i | −0.828940 | + | 1.07883i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.78060 | − | 15.4403i | 0.193432 | − | 0.789996i | ||||
\(383\) | 8.72800 | 0.445980 | 0.222990 | − | 0.974821i | \(-0.428418\pi\) | ||||
0.222990 | + | 0.974821i | \(0.428418\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.5943 | −0.794760 | ||||||||
\(386\) | −2.61259 | + | 10.6700i | −0.132977 | + | 0.543091i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.08456 | + | 2.08194i | −0.0550602 | + | 0.105695i | ||||
\(389\) | 20.6261i | 1.04579i | 0.852398 | + | 0.522893i | \(0.175147\pi\) | ||||
−0.852398 | + | 0.522893i | \(0.824853\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.7947i | 1.55735i | ||||||||
\(392\) | 4.25142 | + | 3.73168i | 0.214729 | + | 0.188478i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.22290 | − | 4.99443i | 0.0616087 | − | 0.251616i | ||||
\(395\) | − | 35.0810i | − | 1.76512i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 23.3793i | − | 1.17337i | −0.809814 | − | 0.586686i | \(-0.800432\pi\) | ||
0.809814 | − | 0.586686i | \(-0.199568\pi\) | |||||||
\(398\) | −1.83663 | + | 7.50099i | −0.0920622 | + | 0.375990i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.75441 | − | 13.9480i | −0.487720 | − | 0.697399i | ||||
\(401\) | 3.17309i | 0.158457i | 0.996856 | + | 0.0792283i | \(0.0252456\pi\) | ||||
−0.996856 | + | 0.0792283i | \(0.974754\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.1696 | 0.656025 | ||||||||
\(404\) | −11.6798 | + | 22.4208i | −0.581093 | + | 1.11548i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.39478 | − | 5.69640i | 0.0692216 | − | 0.282707i | ||||
\(407\) | −2.84974 | −0.141256 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 8.55450i | − | 0.422993i | −0.977379 | − | 0.211496i | \(-0.932166\pi\) | ||
0.977379 | − | 0.211496i | \(-0.0678337\pi\) | |||||||
\(410\) | −34.8216 | − | 8.52616i | −1.71972 | − | 0.421077i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.57910 | + | 3.42729i | 0.324129 | + | 0.168851i | ||||
\(413\) | −5.58394 | −0.274768 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.08444i | 0.298673i | ||||||||
\(416\) | 6.33921 | + | 16.3364i | 0.310805 | + | 0.800957i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12.9317 | − | 5.69793i | −0.632508 | − | 0.278695i | ||||
\(419\) | 35.5497 | 1.73671 | 0.868357 | − | 0.495939i | \(-0.165176\pi\) | ||||
0.868357 | + | 0.495939i | \(0.165176\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.6265 | −1.39517 | −0.697584 | − | 0.716503i | \(-0.745742\pi\) | ||||
−0.697584 | + | 0.716503i | \(0.745742\pi\) | |||||||
\(422\) | 5.16009 | − | 21.0743i | 0.251189 | − | 1.02588i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −24.3223 | − | 21.3489i | −1.18120 | − | 1.03679i | ||||
\(425\) | 23.7639 | 1.15272 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.06723 | −0.245221 | ||||||||
\(428\) | −10.2882 | + | 19.7495i | −0.497301 | + | 0.954630i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.99043 | − | 20.3814i | 0.240660 | − | 0.982877i | ||||
\(431\) | 31.5656 | 1.52046 | 0.760230 | − | 0.649654i | \(-0.225086\pi\) | ||||
0.760230 | + | 0.649654i | \(0.225086\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.4868i | 0.888418i | 0.895923 | + | 0.444209i | \(0.146515\pi\) | ||||
−0.895923 | + | 0.444209i | \(0.853485\pi\) | |||||||
\(434\) | 3.19739 | − | 13.0584i | 0.153480 | − | 0.626825i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −20.2952 | − | 10.5725i | −0.971966 | − | 0.506332i | ||||
\(437\) | −4.18225 | + | 23.6683i | −0.200064 | + | 1.13221i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.6256 | 0.507132 | 0.253566 | − | 0.967318i | \(-0.418396\pi\) | ||||
0.253566 | + | 0.967318i | \(0.418396\pi\) | |||||||
\(440\) | 13.0123 | − | 14.8247i | 0.620339 | − | 0.706739i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −23.7639 | − | 5.81865i | −1.13033 | − | 0.276765i | ||||
\(443\) | 28.7470 | 1.36581 | 0.682907 | − | 0.730506i | \(-0.260716\pi\) | ||||
0.682907 | + | 0.730506i | \(0.260716\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.1201 | 0.764168 | ||||||||
\(446\) | 14.3501 | + | 3.51366i | 0.679498 | + | 0.166377i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 17.7375 | − | 2.31947i | 0.838020 | − | 0.109584i | ||||
\(449\) | − | 28.2150i | − | 1.33155i | −0.746153 | − | 0.665775i | \(-0.768101\pi\) | ||
0.746153 | − | 0.665775i | \(-0.231899\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 19.1019i | − | 0.899475i | ||||||
\(452\) | −16.2024 | + | 31.1024i | −0.762096 | + | 1.46293i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.0650786 | + | 0.265787i | −0.00305429 | + | 0.0124740i | ||||
\(455\) | −21.0724 | −0.987890 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.1154 | 1.08129 | 0.540647 | − | 0.841249i | \(-0.318179\pi\) | ||||
0.540647 | + | 0.841249i | \(0.318179\pi\) | |||||||
\(458\) | 6.49753 | − | 26.5365i | 0.303610 | − | 1.23997i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −29.7544 | − | 15.5002i | −1.38731 | − | 0.722698i | ||||
\(461\) | 1.90136i | 0.0885550i | 0.999019 | + | 0.0442775i | \(0.0140986\pi\) | ||||
−0.999019 | + | 0.0442775i | \(0.985901\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 20.5572i | − | 0.955374i | −0.878530 | − | 0.477687i | \(-0.841475\pi\) | ||
0.878530 | − | 0.477687i | \(-0.158525\pi\) | |||||||
\(464\) | 4.25142 | + | 6.07918i | 0.197367 | + | 0.282219i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.0670 | + | 4.17890i | 0.790615 | + | 0.193584i | ||||
\(467\) | −15.1228 | −0.699800 | −0.349900 | − | 0.936787i | \(-0.613784\pi\) | ||||
−0.349900 | + | 0.936787i | \(0.613784\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0403 | 0.463617 | ||||||||
\(470\) | 39.1245 | + | 9.57973i | 1.80468 | + | 0.441880i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.65940 | − | 5.30836i | 0.214466 | − | 0.244337i | ||||
\(473\) | 11.1805 | 0.514080 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.2646 | + | 3.22740i | 0.838038 | + | 0.148083i | ||||
\(476\) | −11.5391 | + | 22.1506i | −0.528892 | + | 1.01527i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.0512319 | + | 0.209236i | −0.00234329 | + | 0.00957023i | ||||
\(479\) | − | 17.4171i | − | 0.795808i | −0.917427 | − | 0.397904i | \(-0.869738\pi\) | ||
0.917427 | − | 0.397904i | \(-0.130262\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.85081 | −0.175582 | ||||||||
\(482\) | 4.02778 | − | 16.4498i | 0.183460 | − | 0.749270i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.1900 | − | 5.30836i | −0.463183 | − | 0.241289i | ||||
\(485\) | 3.57080 | 0.162142 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 42.3759 | 1.92023 | 0.960117 | − | 0.279597i | \(-0.0902010\pi\) | ||||
0.960117 | + | 0.279597i | \(0.0902010\pi\) | |||||||
\(488\) | 4.22824 | − | 4.81715i | 0.191403 | − | 0.218062i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.04643 | − | 8.35781i | 0.0924483 | − | 0.377567i | ||||
\(491\) | 6.65940 | 0.300534 | 0.150267 | − | 0.988645i | \(-0.451987\pi\) | ||||
0.150267 | + | 0.988645i | \(0.451987\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.3574 | −0.466475 | ||||||||
\(494\) | −17.4744 | − | 7.69954i | −0.786210 | − | 0.346419i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.74597 | + | 13.9359i | 0.437607 | + | 0.625741i | ||||
\(497\) | − | 32.8662i | − | 1.47425i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.5028 | −0.873067 | −0.436534 | − | 0.899688i | \(-0.643794\pi\) | ||||
−0.436534 | + | 0.899688i | \(0.643794\pi\) | |||||||
\(500\) | 2.09394 | − | 4.01956i | 0.0936437 | − | 0.179760i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.7460 | − | 2.63118i | −0.479617 | − | 0.117435i | ||||
\(503\) | − | 18.8238i | − | 0.839310i | −0.907684 | − | 0.419655i | \(-0.862151\pi\) | ||
0.907684 | − | 0.419655i | \(-0.137849\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 38.4546 | 1.71121 | ||||||||
\(506\) | 4.25142 | − | 17.3632i | 0.188999 | − | 0.771889i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.05473 | + | 2.63319i | 0.224267 | + | 0.116829i | ||||
\(509\) | −19.8091 | −0.878021 | −0.439011 | − | 0.898482i | \(-0.644671\pi\) | ||||
−0.439011 | + | 0.898482i | \(0.644671\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 3.37693i | − | 0.149387i | ||||||
\(512\) | −12.5957 | + | 18.7976i | −0.556657 | + | 0.830743i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.51021 | + | 18.4201i | −0.198937 | + | 0.812477i | ||||
\(515\) | − | 11.2840i | − | 0.497234i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.4623i | 0.943913i | ||||||||
\(518\) | −0.934921 | + | 3.81831i | −0.0410781 | + | 0.167767i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17.5834 | − | 20.0324i | 0.771084 | − | 0.878480i | ||||
\(521\) | − | 29.7708i | − | 1.30428i | −0.758097 | − | 0.652141i | \(-0.773871\pi\) | ||
0.758097 | − | 0.652141i | \(-0.226129\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.05365i | − | 0.0898000i | −0.998991 | − | 0.0449000i | \(-0.985703\pi\) | ||
0.998991 | − | 0.0449000i | \(-0.0142969\pi\) | |||||||
\(524\) | −14.1407 | − | 7.36643i | −0.617741 | − | 0.321804i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.38375 | + | 5.65136i | −0.0603343 | + | 0.246411i | ||||
\(527\) | −23.7434 | −1.03428 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.40429 | −0.321926 | ||||||||
\(530\) | −11.7076 | + | 47.8149i | −0.508546 | + | 2.07695i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.8771 | + | 15.4575i | −0.514936 | + | 0.670169i | ||||
\(533\) | − | 25.8122i | − | 1.11805i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.8730 | 1.46446 | ||||||||
\(536\) | −8.37790 | + | 9.54477i | −0.361870 | + | 0.412271i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −36.3114 | − | 8.89094i | −1.56550 | − | 0.383316i | ||||
\(539\) | 4.58480 | 0.197481 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 24.9916i | − | 1.07447i | −0.843432 | − | 0.537236i | \(-0.819468\pi\) | ||
0.843432 | − | 0.537236i | \(-0.180532\pi\) | |||||||
\(542\) | 6.48971 | − | 26.5046i | 0.278757 | − | 1.13847i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −11.4289 | − | 29.4527i | −0.490010 | − | 1.26277i | ||||
\(545\) | 34.8090i | 1.49105i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.0893i | 1.11550i | 0.830010 | + | 0.557749i | \(0.188335\pi\) | ||||
−0.830010 | + | 0.557749i | \(0.811665\pi\) | |||||||
\(548\) | −16.3008 | − | 8.49170i | −0.696337 | − | 0.362747i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −13.3990 | − | 3.28078i | −0.571336 | − | 0.139893i | ||||
\(551\) | −7.96057 | − | 1.40665i | −0.339131 | − | 0.0599254i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 25.7849i | − | 1.09649i | ||||||
\(554\) | −8.98378 | + | 36.6906i | −0.381684 | + | 1.55883i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.91342 | − | 3.60145i | −0.293195 | − | 0.152736i | ||||
\(557\) | − | 10.9058i | − | 0.462092i | −0.972943 | − | 0.231046i | \(-0.925785\pi\) | ||
0.972943 | − | 0.231046i | \(-0.0742148\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.1081 | 0.639004 | ||||||||
\(560\) | −15.5943 | − | 22.2986i | −0.658980 | − | 0.942286i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.88457 | + | 32.2013i | −0.332590 | + | 1.35833i | ||||
\(563\) | 27.7390i | 1.16906i | 0.811372 | + | 0.584531i | \(0.198721\pi\) | ||||
−0.811372 | + | 0.584531i | \(0.801279\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 53.3448 | 2.24423 | ||||||||
\(566\) | −15.8471 | − | 3.88020i | −0.666103 | − | 0.163097i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 31.2442 | + | 27.4245i | 1.31098 | + | 1.15071i | ||||
\(569\) | − | 45.2675i | − | 1.89771i | −0.315712 | − | 0.948855i | \(-0.602243\pi\) | ||
0.315712 | − | 0.948855i | \(-0.397757\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.80997 | −0.326837 | −0.163419 | − | 0.986557i | \(-0.552252\pi\) | ||||
−0.163419 | + | 0.986557i | \(0.552252\pi\) | |||||||
\(572\) | 12.5957 | + | 6.56156i | 0.526653 | + | 0.274353i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −25.5943 | − | 6.26683i | −1.06829 | − | 0.261572i | ||||
\(575\) | 23.4627i | 0.978462i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.1696 | −0.506627 | −0.253314 | − | 0.967384i | \(-0.581520\pi\) | ||||
−0.253314 | + | 0.967384i | \(0.581520\pi\) | |||||||
\(578\) | 19.4919 | + | 4.77265i | 0.810758 | + | 0.198516i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.21329 | − | 10.0075i | 0.216470 | − | 0.415541i | ||||
\(581\) | 4.47214i | 0.185535i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.2296 | −1.08632 | ||||||||
\(584\) | 3.21027 | + | 2.81781i | 0.132842 | + | 0.116602i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.1805 | − | 3.96184i | −0.668411 | − | 0.163662i | ||||
\(587\) | 6.84345 | 0.282459 | 0.141230 | − | 0.989977i | \(-0.454894\pi\) | ||||
0.141230 | + | 0.989977i | \(0.454894\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.2488 | − | 3.22461i | −0.751929 | − | 0.132868i | ||||
\(590\) | −10.4356 | − | 2.55519i | −0.429628 | − | 0.105195i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.84974 | − | 4.07488i | −0.117123 | − | 0.167477i | ||||
\(593\) | −17.0950 | −0.702008 | −0.351004 | − | 0.936374i | \(-0.614160\pi\) | ||||
−0.351004 | + | 0.936374i | \(0.614160\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 37.9912 | 1.55749 | ||||||||
\(596\) | −9.64144 | + | 18.5079i | −0.394929 | + | 0.758114i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.74489 | − | 23.4627i | 0.234926 | − | 0.959461i | ||||
\(599\) | −1.76518 | −0.0721232 | −0.0360616 | − | 0.999350i | \(-0.511481\pi\) | ||||
−0.0360616 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 48.7011i | − | 1.98656i | −0.115731 | − | 0.993281i | \(-0.536921\pi\) | ||
0.115731 | − | 0.993281i | \(-0.463079\pi\) | |||||||
\(602\) | 3.66802 | − | 14.9805i | 0.149497 | − | 0.610562i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19.4919 | + | 10.1541i | 0.793116 | + | 0.413163i | ||||
\(605\) | 17.4772i | 0.710551i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −45.9062 | −1.86328 | −0.931638 | − | 0.363387i | \(-0.881620\pi\) | ||||
−0.931638 | + | 0.363387i | \(0.881620\pi\) | |||||||
\(608\) | −4.78410 | − | 24.1891i | −0.194021 | − | 0.980997i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.46996 | − | 2.31874i | −0.383427 | − | 0.0938831i | ||||
\(611\) | 29.0018i | 1.17329i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.9308i | 0.845386i | 0.906273 | + | 0.422693i | \(0.138915\pi\) | ||||
−0.906273 | + | 0.422693i | \(0.861085\pi\) | |||||||
\(614\) | 1.06508 | − | 4.34988i | 0.0429831 | − | 0.175547i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.56422 | − | 10.8963i | 0.385353 | − | 0.439025i | ||||
\(617\) | −32.8048 | −1.32067 | −0.660335 | − | 0.750971i | \(-0.729586\pi\) | ||||
−0.660335 | + | 0.750971i | \(0.729586\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0190 | 0.885020 | 0.442510 | − | 0.896764i | \(-0.354088\pi\) | ||||
0.442510 | + | 0.896764i | \(0.354088\pi\) | |||||||
\(620\) | 11.9510 | − | 22.9413i | 0.479962 | − | 0.921345i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.27419 | − | 13.3721i | 0.131283 | − | 0.536173i | ||||
\(623\) | 11.8485 | 0.474700 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.1696 | −1.12678 | ||||||||
\(626\) | −28.8875 | − | 7.07317i | −1.15458 | − | 0.282701i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.34060 | + | 10.2519i | −0.213113 | + | 0.409097i | ||||
\(629\) | 6.94260 | 0.276819 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 9.72716i | − | 0.387232i | −0.981077 | − | 0.193616i | \(-0.937978\pi\) | ||
0.981077 | − | 0.193616i | \(-0.0620216\pi\) | |||||||
\(632\) | 24.5124 | + | 21.5157i | 0.975049 | + | 0.855847i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.0095 | + | 3.43026i | 0.556389 | + | 0.136233i | ||||
\(635\) | − | 8.66953i | − | 0.344040i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.19539 | 0.245470 | ||||||||
\(638\) | 5.83991 | + | 1.42992i | 0.231204 | + | 0.0566109i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 34.2104 | + | 3.78185i | 1.35228 | + | 0.149491i | ||||
\(641\) | 15.1485i | 0.598329i | 0.954202 | + | 0.299165i | \(0.0967080\pi\) | ||||
−0.954202 | + | 0.299165i | \(0.903292\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.46201 | −0.0576560 | −0.0288280 | − | 0.999584i | \(-0.509178\pi\) | ||||
−0.0288280 | + | 0.999584i | \(0.509178\pi\) | |||||||
\(644\) | −21.8698 | − | 11.3928i | −0.861793 | − | 0.448939i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 31.5044 | + | 13.8814i | 1.23952 | + | 0.546157i | ||||
\(647\) | 7.90920i | 0.310943i | 0.987840 | + | 0.155471i | \(0.0496897\pi\) | ||||
−0.987840 | + | 0.155471i | \(0.950310\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 5.72462i | − | 0.224711i | ||||||
\(650\) | −18.1059 | − | 4.43328i | −0.710173 | − | 0.173887i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.8121 | + | 6.15337i | 0.462599 | + | 0.240984i | ||||
\(653\) | − | 32.5505i | − | 1.27380i | −0.770947 | − | 0.636900i | \(-0.780217\pi\) | ||
0.770947 | − | 0.636900i | \(-0.219783\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.2532i | 0.947653i | ||||||||
\(656\) | 27.3142 | − | 19.1019i | 1.06644 | − | 0.745805i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 28.7570 | + | 7.04121i | 1.12106 | + | 0.274495i | ||||
\(659\) | − | 12.8731i | − | 0.501463i | −0.968057 | − | 0.250731i | \(-0.919329\pi\) | ||
0.968057 | − | 0.250731i | \(-0.0806711\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.01313 | −0.0783019 | −0.0391509 | − | 0.999233i | \(-0.512465\pi\) | ||||
−0.0391509 | + | 0.999233i | \(0.512465\pi\) | |||||||
\(662\) | −10.5644 | + | 43.1459i | −0.410596 | + | 1.67691i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.25142 | − | 3.73168i | −0.164987 | − | 0.144817i | ||||
\(665\) | 29.1995 | + | 5.15963i | 1.13231 | + | 0.200082i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 10.2261i | − | 0.395957i | ||||||
\(668\) | 3.44812 | + | 1.79625i | 0.133412 | + | 0.0694990i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.7639 | + | 4.59439i | 0.724914 | + | 0.177497i | ||||
\(671\) | − | 5.19489i | − | 0.200547i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 21.9254i | − | 0.845163i | −0.906325 | − | 0.422582i | \(-0.861124\pi\) | ||
0.906325 | − | 0.422582i | \(-0.138876\pi\) | |||||||
\(674\) | −7.75441 | + | 31.6697i | −0.298689 | + | 1.21987i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.03837 | − | 3.14561i | −0.232245 | − | 0.120985i | ||||
\(677\) | 42.2401 | 1.62342 | 0.811710 | − | 0.584061i | \(-0.198537\pi\) | ||||
0.811710 | + | 0.584061i | \(0.198537\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.62458 | 0.100722 | ||||||||
\(680\) | −31.7010 | + | 36.1163i | −1.21568 | + | 1.38500i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 13.3874 | + | 3.27794i | 0.512631 | + | 0.125519i | ||||
\(683\) | 6.89837i | 0.263959i | 0.991252 | + | 0.131979i | \(0.0421332\pi\) | ||||
−0.991252 | + | 0.131979i | \(0.957867\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.9581i | 1.06822i | ||||||||
\(686\) | 6.76867 | − | 27.6439i | 0.258429 | − | 1.05545i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.1805 | + | 15.9872i | 0.426253 | + | 0.609506i | ||||
\(689\) | −35.4437 | −1.35030 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.4620 | −1.34904 | −0.674519 | − | 0.738257i | \(-0.735649\pi\) | ||||
−0.674519 | + | 0.738257i | \(0.735649\pi\) | |||||||
\(692\) | 36.4976 | + | 19.0129i | 1.38743 | + | 0.722764i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −40.2913 | − | 9.86542i | −1.52944 | − | 0.374486i | ||||
\(695\) | 11.8574i | 0.449778i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46.5366i | 1.76270i | ||||||||
\(698\) | 4.03151 | − | 16.4651i | 0.152595 | − | 0.623213i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.79171 | + | 16.8767i | −0.332295 | + | 0.637881i | ||||
\(701\) | 10.3586i | 0.391239i | 0.980680 | + | 0.195619i | \(0.0626717\pi\) | ||||
−0.980680 | + | 0.195619i | \(0.937328\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.33598 | + | 0.942881i | 0.201250 | + | 0.0355614i | ||||
\(704\) | 2.37790 | + | 18.1844i | 0.0896205 | + | 0.685350i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.1975 | + | 4.21086i | 0.647238 | + | 0.158478i | ||||
\(707\) | 28.2646 | 1.06300 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.24822i | 0.197101i | 0.995132 | + | 0.0985506i | \(0.0314206\pi\) | ||||
−0.995132 | + | 0.0985506i | \(0.968579\pi\) | |||||||
\(710\) | 15.0394 | − | 61.4225i | 0.564420 | − | 2.30515i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.88672 | + | 11.2637i | −0.370520 | + | 0.422126i | ||||
\(713\) | − | 23.4424i | − | 0.877924i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 21.6033i | − | 0.807917i | ||||||
\(716\) | −8.06303 | + | 15.4780i | −0.301330 | + | 0.578438i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.38721 | − | 22.0019i | 0.201049 | − | 0.821103i | ||||
\(719\) | − | 4.31981i | − | 0.161102i | −0.996750 | − | 0.0805509i | \(-0.974332\pi\) | ||
0.996750 | − | 0.0805509i | \(-0.0256680\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 8.29390i | − | 0.308881i | ||||||
\(722\) | 22.3286 | + | 14.9477i | 0.830984 | + | 0.556296i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15.0819 | − | 7.85674i | −0.560516 | − | 0.291993i | ||||
\(725\) | −7.89140 | −0.293079 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.37763i | 0.273621i | 0.990597 | + | 0.136811i | \(0.0436852\pi\) | ||||
−0.990597 | + | 0.136811i | \(0.956315\pi\) | |||||||
\(728\) | 12.9240 | − | 14.7241i | 0.478996 | − | 0.545710i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.54527 | − | 6.31102i | 0.0571930 | − | 0.233581i | ||||
\(731\) | −27.2382 | −1.00744 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 6.72268i | − | 0.248308i | −0.992263 | − | 0.124154i | \(-0.960378\pi\) | ||
0.992263 | − | 0.124154i | \(-0.0396216\pi\) | |||||||
\(734\) | −9.42884 | + | 38.5083i | −0.348025 | + | 1.42137i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 29.0793 | − | 11.2840i | 1.07188 | − | 0.415935i | ||||
\(737\) | 10.2932i | 0.379156i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.1622 | 1.33025 | 0.665125 | − | 0.746732i | \(-0.268378\pi\) | ||||
0.665125 | + | 0.746732i | \(0.268378\pi\) | |||||||
\(740\) | −3.49448 | + | 6.70807i | −0.128460 | + | 0.246594i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.60522 | + | 35.1445i | −0.315908 | + | 1.29020i | ||||
\(743\) | 11.6697 | 0.428120 | 0.214060 | − | 0.976821i | \(-0.431331\pi\) | ||||
0.214060 | + | 0.976821i | \(0.431331\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.7435 | 1.16299 | ||||||||
\(746\) | −18.9145 | − | 4.63126i | −0.692509 | − | 0.169563i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22.7087 | − | 11.8298i | −0.830311 | − | 0.432539i | ||||
\(749\) | 24.8971 | 0.909720 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.36451 | −0.305225 | −0.152613 | − | 0.988286i | \(-0.548769\pi\) | ||||
−0.152613 | + | 0.988286i | \(0.548769\pi\) | |||||||
\(752\) | −30.6893 | + | 21.4623i | −1.11912 | + | 0.782651i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.89140 | + | 1.93223i | 0.287388 | + | 0.0703676i | ||||
\(755\) | − | 33.4312i | − | 1.21669i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 44.5991i | − | 1.62098i | −0.585751 | − | 0.810491i | \(-0.699200\pi\) | ||
0.585751 | − | 0.810491i | \(-0.300800\pi\) | |||||||
\(758\) | −10.0504 | + | 41.0466i | −0.365045 | + | 1.49088i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −29.2699 | + | 23.4531i | −1.06173 | + | 0.850734i | ||||
\(761\) | 40.6243 | 1.47263 | 0.736314 | − | 0.676640i | \(-0.236565\pi\) | ||||
0.736314 | + | 0.676640i | \(0.236565\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.5850i | 0.926240i | ||||||||
\(764\) | 10.3863 | − | 19.9378i | 0.375765 | − | 0.721325i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.9891 | + | 2.93556i | 0.433184 | + | 0.106066i | ||||
\(767\) | − | 7.73560i | − | 0.279316i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.7748 | 0.496733 | 0.248367 | − | 0.968666i | \(-0.420106\pi\) | ||||
0.248367 | + | 0.968666i | \(0.420106\pi\) | |||||||
\(770\) | −21.4209 | − | 5.24496i | −0.771956 | − | 0.189015i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.17748 | + | 13.7780i | −0.258323 | + | 0.495883i | ||||
\(773\) | −22.7684 | −0.818923 | −0.409462 | − | 0.912327i | \(-0.634283\pi\) | ||||
−0.409462 | + | 0.912327i | \(0.634283\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.0902 | −0.649821 | ||||||||
\(776\) | −2.19003 | + | 2.49505i | −0.0786174 | + | 0.0895672i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.93735 | + | 28.3328i | −0.248716 | + | 1.01578i | ||||
\(779\) | −6.32018 | + | 35.7674i | −0.226444 | + | 1.28150i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.6943 | 1.20568 | ||||||||
\(782\) | −10.3574 | + | 42.3007i | −0.370380 | + | 1.51267i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.58480 | + | 6.55588i | 0.163743 | + | 0.234139i | ||||
\(785\) | 17.5834 | 0.627579 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 6.09611i | − | 0.217303i | −0.994080 | − | 0.108651i | \(-0.965347\pi\) | ||
0.994080 | − | 0.108651i | \(-0.0346532\pi\) | |||||||
\(788\) | 3.35963 | − | 6.44922i | 0.119682 | − | 0.229744i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.7991 | − | 48.1885i | 0.419792 | − | 1.71447i | ||||
\(791\) | 39.2090 | 1.39411 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 7.01979i | − | 0.249280i | ||||||
\(794\) | 7.86335 | − | 32.1146i | 0.279060 | − | 1.13971i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.04573 | + | 9.68590i | −0.178841 | + | 0.343307i | ||||
\(797\) | −17.2798 | −0.612081 | −0.306041 | − | 0.952018i | \(-0.599004\pi\) | ||||
−0.306041 | + | 0.952018i | \(0.599004\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 52.2871i | − | 1.84978i | ||||||
\(800\) | −8.70777 | − | 22.4402i | −0.307866 | − | 0.793382i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.06723 | + | 4.35867i | −0.0376852 | + | 0.153910i | ||||
\(803\) | 3.46201 | 0.122172 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 37.5097i | 1.32204i | ||||||||
\(806\) | 18.0902 | + | 4.42944i | 0.637202 | + | 0.156020i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −23.5848 | + | 26.8697i | −0.829710 | + | 0.945272i | ||||
\(809\) | 39.3801 | 1.38453 | 0.692264 | − | 0.721644i | \(-0.256613\pi\) | ||||
0.692264 | + | 0.721644i | \(0.256613\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.9452i | 0.735484i | 0.929928 | + | 0.367742i | \(0.119869\pi\) | ||||
−0.929928 | + | 0.367742i | \(0.880131\pi\) | |||||||
\(812\) | 3.83183 | − | 7.35566i | 0.134471 | − | 0.258133i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.91450 | − | 0.958475i | −0.137203 | − | 0.0335945i | ||||
\(815\) | − | 20.2594i | − | 0.709654i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.9349 | − | 3.69925i | −0.732420 | − | 0.129420i | ||||
\(818\) | 2.87720 | − | 11.7508i | 0.100599 | − | 0.410856i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −44.9646 | − | 23.4237i | −1.57023 | − | 0.817991i | ||||
\(821\) | − | 52.2181i | − | 1.82243i | −0.411936 | − | 0.911213i | \(-0.635147\pi\) | ||
0.411936 | − | 0.911213i | \(-0.364853\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 39.5789i | − | 1.37963i | −0.723983 | − | 0.689817i | \(-0.757691\pi\) | ||
0.723983 | − | 0.689817i | \(-0.242309\pi\) | |||||||
\(824\) | 7.88457 | + | 6.92066i | 0.274672 | + | 0.241093i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.67030 | − | 1.87809i | −0.266884 | − | 0.0653472i | ||||
\(827\) | 19.5172i | 0.678680i | 0.940664 | + | 0.339340i | \(0.110204\pi\) | ||||
−0.940664 | + | 0.339340i | \(0.889796\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.0759 | −0.870921 | −0.435461 | − | 0.900208i | \(-0.643414\pi\) | ||||
−0.435461 | + | 0.900208i | \(0.643414\pi\) | |||||||
\(830\) | −2.04643 | + | 8.35781i | −0.0710326 | + | 0.290104i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.21323 | + | 24.5724i | 0.111399 | + | 0.851893i | ||||
\(833\) | −11.1696 | −0.387004 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 5.91397i | − | 0.204661i | ||||||
\(836\) | −15.8470 | − | 12.1763i | −0.548078 | − | 0.421126i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 48.8323 | + | 11.9567i | 1.68688 | + | 0.413038i | ||||
\(839\) | −10.0833 | −0.348115 | −0.174057 | − | 0.984736i | \(-0.555688\pi\) | ||||
−0.174057 | + | 0.984736i | \(0.555688\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.5606 | −0.881399 | ||||||||
\(842\) | −39.3223 | − | 9.62817i | −1.35514 | − | 0.331809i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.1762 | − | 27.2129i | 0.487964 | − | 0.936706i | ||||
\(845\) | 10.3566i | 0.356278i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.8460i | 0.441393i | ||||||||
\(848\) | −26.2296 | − | 37.5061i | −0.900728 | − | 1.28797i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 32.6430 | + | 7.99271i | 1.11965 | + | 0.274148i | ||||
\(851\) | 6.85459i | 0.234972i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 38.4525i | − | 1.31659i | −0.752760 | − | 0.658295i | \(-0.771278\pi\) | ||
0.752760 | − | 0.658295i | \(-0.228722\pi\) | |||||||
\(854\) | −6.96053 | − | 1.70430i | −0.238185 | − | 0.0583201i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.7748 | + | 23.6683i | −0.710069 | + | 0.808967i | ||||
\(857\) | 42.6333i | 1.45633i | 0.685404 | + | 0.728163i | \(0.259626\pi\) | ||||
−0.685404 | + | 0.728163i | \(0.740374\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.5570 | −0.974353 | −0.487176 | − | 0.873304i | \(-0.661973\pi\) | ||||
−0.487176 | + | 0.873304i | \(0.661973\pi\) | |||||||
\(860\) | 13.7101 | − | 26.3181i | 0.467509 | − | 0.897440i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 43.3596 | + | 10.6167i | 1.47683 | + | 0.361607i | ||||
\(863\) | 17.0521 | 0.580459 | 0.290229 | − | 0.956957i | \(-0.406268\pi\) | ||||
0.290229 | + | 0.956957i | \(0.406268\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 62.5982i | − | 2.12840i | ||||||
\(866\) | −6.21781 | + | 25.3941i | −0.211290 | + | 0.862927i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.78410 | − | 16.8621i | 0.298152 | − | 0.572338i | ||||
\(869\) | 26.4345 | 0.896730 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.9091i | 0.471293i | ||||||||
\(872\) | −24.3223 | − | 21.3489i | −0.823658 | − | 0.722964i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.7055 | + | 31.1050i | −0.463594 | + | 1.05214i | ||||
\(875\) | −5.06723 | −0.171304 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.5160 | 0.355099 | 0.177550 | − | 0.984112i | \(-0.443183\pi\) | ||||
0.177550 | + | 0.984112i | \(0.443183\pi\) | |||||||
\(878\) | 14.5957 | + | 3.57379i | 0.492581 | + | 0.120610i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 22.8603 | − | 15.9872i | 0.770622 | − | 0.538928i | ||||
\(881\) | −37.5943 | −1.26658 | −0.633292 | − | 0.773913i | \(-0.718297\pi\) | ||||
−0.633292 | + | 0.773913i | \(0.718297\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.2720 | −0.446638 | −0.223319 | − | 0.974745i | \(-0.571689\pi\) | ||||
−0.223319 | + | 0.974745i | \(0.571689\pi\) | |||||||
\(884\) | −30.6860 | − | 15.9854i | −1.03208 | − | 0.537648i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.4880 | + | 9.66873i | 1.32662 | + | 0.324827i | ||||
\(887\) | −27.6777 | −0.929325 | −0.464662 | − | 0.885488i | \(-0.653824\pi\) | ||||
−0.464662 | + | 0.885488i | \(0.653824\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.37220i | − | 0.213717i | ||||||
\(890\) | 22.1432 | + | 5.42182i | 0.742242 | + | 0.181740i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.5301 | + | 9.65298i | 0.620432 | + | 0.323206i | ||||
\(893\) | 7.10116 | − | 40.1871i | 0.237631 | − | 1.34481i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.5467 | 0.887359 | ||||||||
\(896\) | 25.1450 | + | 2.77971i | 0.840037 | + | 0.0928635i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.48979 | − | 38.7572i | 0.316678 | − | 1.29334i | ||||
\(899\) | 7.88457 | 0.262965 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 63.9012 | 2.12886 | ||||||||
\(902\) | 6.42471 | − | 26.2391i | 0.213919 | − | 0.873667i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −32.7171 | + | 37.2739i | −1.08815 | + | 1.23971i | ||||
\(905\) | 25.8675i | 0.859866i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 44.3324i | − | 1.47203i | −0.676963 | − | 0.736017i | \(-0.736704\pi\) | ||
0.676963 | − | 0.736017i | \(-0.263296\pi\) | |||||||
\(908\) | −0.178789 | + | 0.343206i | −0.00593331 | + | 0.0113897i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −28.9458 | − | 7.08746i | −0.959545 | − | 0.234947i | ||||
\(911\) | −40.9742 | −1.35754 | −0.678768 | − | 0.734353i | \(-0.737486\pi\) | ||||
−0.678768 | + | 0.734353i | \(0.737486\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.58480 | −0.151735 | ||||||||
\(914\) | 31.7522 | + | 7.77460i | 1.05027 | + | 0.257161i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.8505 | − | 34.2662i | 0.589797 | − | 1.13219i | ||||
\(917\) | 17.8264i | 0.588680i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 37.2439i | − | 1.22856i | −0.789087 | − | 0.614281i | \(-0.789446\pi\) | ||
0.789087 | − | 0.614281i | \(-0.210554\pi\) | |||||||
\(920\) | −35.6584 | − | 31.2991i | −1.17562 | − | 1.03190i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.639499 | + | 2.61177i | −0.0210608 | + | 0.0860141i | ||||
\(923\) | 45.5306 | 1.49866 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.28962 | 0.173922 | ||||||||
\(926\) | 6.91417 | − | 28.2381i | 0.227214 | − | 0.927962i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.79525 | + | 9.78049i | 0.124585 | + | 0.321060i | ||||
\(929\) | 3.86033 | 0.126653 | 0.0633266 | − | 0.997993i | \(-0.479829\pi\) | ||||
0.0633266 | + | 0.997993i | \(0.479829\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.58480 | − | 1.51696i | −0.281356 | − | 0.0497162i | ||||
\(932\) | 22.0384 | + | 11.4806i | 0.721891 | + | 0.376059i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −20.7732 | − | 5.08637i | −0.679721 | − | 0.166431i | ||||
\(935\) | 38.9484i | 1.27375i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.6798 | 0.675580 | 0.337790 | − | 0.941221i | \(-0.390321\pi\) | ||||
0.337790 | + | 0.941221i | \(0.390321\pi\) | |||||||
\(938\) | 13.7917 | + | 3.37693i | 0.450315 | + | 0.110261i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 50.5208 | + | 26.3181i | 1.64781 | + | 0.858402i | ||||
\(941\) | 9.29308 | 0.302946 | 0.151473 | − | 0.988461i | \(-0.451598\pi\) | ||||
0.151473 | + | 0.988461i | \(0.451598\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −45.9467 | −1.49623 | ||||||||
\(944\) | 8.18572 | − | 5.72462i | 0.266422 | − | 0.186320i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.3580 | + | 3.76043i | 0.499330 | + | 0.122262i | ||||
\(947\) | −37.3934 | −1.21512 | −0.607561 | − | 0.794273i | \(-0.707852\pi\) | ||||
−0.607561 | + | 0.794273i | \(0.707852\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.67817 | 0.151860 | ||||||||
\(950\) | 24.0034 | + | 10.5764i | 0.778775 | + | 0.343143i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −23.3006 | + | 26.5459i | −0.755176 | + | 0.860357i | ||||
\(953\) | − | 6.08558i | − | 0.197131i | −0.995131 | − | 0.0985656i | \(-0.968575\pi\) | ||
0.995131 | − | 0.0985656i | \(-0.0314254\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34.1960 | −1.10656 | ||||||||
\(956\) | −0.140748 | + | 0.270183i | −0.00455212 | + | 0.00873833i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.85804 | − | 23.9248i | 0.189265 | − | 0.772974i | ||||
\(959\) | 20.5495i | 0.663579i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.9254 | −0.416949 | ||||||||
\(962\) | −5.28962 | − | 1.29518i | −0.170544 | − | 0.0417581i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.0654 | − | 21.2414i | 0.356393 | − | 0.684139i | ||||
\(965\) | 23.6312 | 0.760714 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.0088i | 0.579124i | 0.957159 | + | 0.289562i | \(0.0935097\pi\) | ||||
−0.957159 | + | 0.289562i | \(0.906490\pi\) | |||||||
\(968\) | −12.2120 | − | 10.7190i | −0.392508 | − | 0.344523i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.90499 | + | 1.20100i | 0.157490 | + | 0.0385617i | ||||
\(971\) | − | 55.6999i | − | 1.78749i | −0.448572 | − | 0.893747i | \(-0.648067\pi\) | ||
0.448572 | − | 0.893747i | \(-0.351933\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.71535i | 0.279401i | ||||||||
\(974\) | 58.2091 | + | 14.2526i | 1.86514 | + | 0.456684i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.42826 | − | 5.19489i | 0.237773 | − | 0.166284i | ||||
\(977\) | − | 33.1269i | − | 1.05982i | −0.848053 | − | 0.529911i | \(-0.822225\pi\) | ||
0.848053 | − | 0.529911i | \(-0.177775\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.1470i | 0.388220i | ||||||||
\(980\) | 5.62210 | − | 10.7923i | 0.179591 | − | 0.344747i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.14759 | + | 2.23981i | 0.291911 | + | 0.0714752i | ||||
\(983\) | −26.2760 | −0.838073 | −0.419037 | − | 0.907969i | \(-0.637632\pi\) | ||||
−0.419037 | + | 0.907969i | \(0.637632\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.0613 | −0.352441 | ||||||||
\(986\) | −14.2273 | − | 3.48359i | −0.453090 | − | 0.110940i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.4138 | − | 16.4537i | −0.681264 | − | 0.523461i | ||||
\(989\) | − | 26.8929i | − | 0.855146i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.6714 | −1.51433 | −0.757166 | − | 0.653222i | \(-0.773417\pi\) | ||||
−0.757166 | + | 0.653222i | \(0.773417\pi\) | |||||||
\(992\) | 8.70024 | + | 22.4208i | 0.276233 | + | 0.711862i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 11.0542 | − | 45.1463i | 0.350617 | − | 1.43195i | ||||
\(995\) | 16.6126 | 0.526654 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 2.73758i | − | 0.0866999i | −0.999060 | − | 0.0433499i | \(-0.986197\pi\) | ||
0.999060 | − | 0.0433499i | \(-0.0138030\pi\) | |||||||
\(998\) | −26.7898 | − | 6.55955i | −0.848017 | − | 0.207639i | ||||
\(999\) | 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 | 1368.2.e.e.379.12 | 12 | ||
3.2 | odd | 2 | 152.2.b.c.75.1 | ✓ | 12 | ||
4.3 | odd | 2 | 5472.2.e.e.5167.4 | 12 | |||
8.3 | odd | 2 | inner | 1368.2.e.e.379.2 | 12 | ||
8.5 | even | 2 | 5472.2.e.e.5167.9 | 12 | |||
12.11 | even | 2 | 608.2.b.c.303.2 | 12 | |||
19.18 | odd | 2 | inner | 1368.2.e.e.379.1 | 12 | ||
24.5 | odd | 2 | 608.2.b.c.303.1 | 12 | |||
24.11 | even | 2 | 152.2.b.c.75.11 | yes | 12 | ||
57.56 | even | 2 | 152.2.b.c.75.12 | yes | 12 | ||
76.75 | even | 2 | 5472.2.e.e.5167.3 | 12 | |||
152.37 | odd | 2 | 5472.2.e.e.5167.10 | 12 | |||
152.75 | even | 2 | inner | 1368.2.e.e.379.11 | 12 | ||
228.227 | odd | 2 | 608.2.b.c.303.12 | 12 | |||
456.227 | odd | 2 | 152.2.b.c.75.2 | yes | 12 | ||
456.341 | even | 2 | 608.2.b.c.303.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.b.c.75.1 | ✓ | 12 | 3.2 | odd | 2 | ||
152.2.b.c.75.2 | yes | 12 | 456.227 | odd | 2 | ||
152.2.b.c.75.11 | yes | 12 | 24.11 | even | 2 | ||
152.2.b.c.75.12 | yes | 12 | 57.56 | even | 2 | ||
608.2.b.c.303.1 | 12 | 24.5 | odd | 2 | |||
608.2.b.c.303.2 | 12 | 12.11 | even | 2 | |||
608.2.b.c.303.11 | 12 | 456.341 | even | 2 | |||
608.2.b.c.303.12 | 12 | 228.227 | odd | 2 | |||
1368.2.e.e.379.1 | 12 | 19.18 | odd | 2 | inner | ||
1368.2.e.e.379.2 | 12 | 8.3 | odd | 2 | inner | ||
1368.2.e.e.379.11 | 12 | 152.75 | even | 2 | inner | ||
1368.2.e.e.379.12 | 12 | 1.1 | even | 1 | trivial | ||
5472.2.e.e.5167.3 | 12 | 76.75 | even | 2 | |||
5472.2.e.e.5167.4 | 12 | 4.3 | odd | 2 | |||
5472.2.e.e.5167.9 | 12 | 8.5 | even | 2 | |||
5472.2.e.e.5167.10 | 12 | 152.37 | odd | 2 |