Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(223,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.223");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.p (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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.10 | ||
Character | \(\chi\) | \(=\) | 1344.223 |
Dual form | 1344.4.p.d.223.9 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 15.4018 | 1.37758 | 0.688789 | − | 0.724962i | \(-0.258143\pi\) | ||||
0.688789 | + | 0.724962i | \(0.258143\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.29285 | + | 17.4184i | 0.339782 | + | 0.940504i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.8703 | −0.462418 | −0.231209 | − | 0.972904i | \(-0.574268\pi\) | ||||
−0.231209 | + | 0.972904i | \(0.574268\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.10290 | 0.194207 | 0.0971034 | − | 0.995274i | \(-0.469042\pi\) | ||||
0.0971034 | + | 0.995274i | \(0.469042\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 46.2054i | 0.795345i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 73.9573i | 1.05513i | 0.849513 | + | 0.527567i | \(0.176896\pi\) | ||||
−0.849513 | + | 0.527567i | \(0.823104\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 151.262i | − | 1.82641i | −0.407499 | − | 0.913206i | \(-0.633599\pi\) | ||
0.407499 | − | 0.913206i | \(-0.366401\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −52.2551 | + | 18.8786i | −0.543000 | + | 0.196173i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.264643i | − | 0.00239921i | −0.999999 | − | 0.00119960i | \(-0.999618\pi\) | ||
0.999999 | − | 0.00119960i | \(-0.000381846\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 112.215 | 0.897721 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 27.0000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 279.925i | 1.79244i | 0.443607 | + | 0.896221i | \(0.353699\pi\) | ||||
−0.443607 | + | 0.896221i | \(0.646301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 147.800 | 0.856311 | 0.428156 | − | 0.903705i | \(-0.359164\pi\) | ||||
0.428156 | + | 0.903705i | \(0.359164\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 50.6110i | − | 0.266977i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 96.9212 | + | 268.274i | 0.468076 | + | 1.29562i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 418.498i | 1.85948i | 0.368221 | + | 0.929738i | \(0.379967\pi\) | ||||
−0.368221 | + | 0.929738i | \(0.620033\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 27.3087i | 0.112125i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 164.377i | 0.626131i | 0.949731 | + | 0.313066i | \(0.101356\pi\) | ||||
−0.949731 | + | 0.313066i | \(0.898644\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −266.668 | −0.945731 | −0.472865 | − | 0.881135i | \(-0.656780\pi\) | ||||
−0.472865 | + | 0.881135i | \(0.656780\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −138.616 | −0.459193 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −277.719 | −0.861903 | −0.430952 | − | 0.902375i | \(-0.641822\pi\) | ||||
−0.430952 | + | 0.902375i | \(0.641822\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −263.800 | + | 219.223i | −0.769096 | + | 0.639133i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −221.872 | −0.609182 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 276.852i | − | 0.717519i | −0.933430 | − | 0.358760i | \(-0.883200\pi\) | ||
0.933430 | − | 0.358760i | \(-0.116800\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −259.833 | −0.637017 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 453.785 | 1.05448 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 212.008i | − | 0.467815i | −0.972259 | − | 0.233908i | \(-0.924849\pi\) | ||
0.972259 | − | 0.233908i | \(-0.0751513\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 174.541 | 0.366355 | 0.183177 | − | 0.983080i | \(-0.441362\pi\) | ||||
0.183177 | + | 0.983080i | \(0.441362\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −56.6357 | − | 156.765i | −0.113261 | − | 0.313501i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 140.201 | 0.267535 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 317.501 | 0.578940 | 0.289470 | − | 0.957187i | \(-0.406521\pi\) | ||||
0.289470 | + | 0.957187i | \(0.406521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.793928 | 0.00138518 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 106.093i | 0.177338i | 0.996061 | + | 0.0886688i | \(0.0282613\pi\) | ||||
−0.996061 | + | 0.0886688i | \(0.971739\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 755.118i | 1.21068i | 0.795966 | + | 0.605342i | \(0.206964\pi\) | ||||
−0.795966 | + | 0.605342i | \(0.793036\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 336.645i | 0.518299i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −106.163 | − | 293.854i | −0.157121 | − | 0.434906i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 194.202i | 0.276575i | 0.990392 | + | 0.138288i | \(0.0441598\pi\) | ||||
−0.990392 | + | 0.138288i | \(0.955840\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 997.764i | 1.31950i | 0.751484 | + | 0.659752i | \(0.229339\pi\) | ||||
−0.751484 | + | 0.659752i | \(0.770661\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1139.08i | 1.45353i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −839.776 | −1.03487 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 988.320i | − | 1.17710i | −0.808462 | − | 0.588549i | \(-0.799700\pi\) | ||
0.808462 | − | 0.588549i | \(-0.200300\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 57.2832 | + | 158.558i | 0.0659880 | + | 0.182652i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 443.400i | 0.494391i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 2329.70i | − | 2.51602i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1021.78i | 1.06954i | 0.844996 | + | 0.534772i | \(0.179602\pi\) | ||||
−0.844996 | + | 0.534772i | \(0.820398\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 151.833 | 0.154139 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 914.669 | 0.901118 | 0.450559 | − | 0.892747i | \(-0.351225\pi\) | ||||
0.450559 | + | 0.892747i | \(0.351225\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 469.098 | 0.448753 | 0.224377 | − | 0.974503i | \(-0.427965\pi\) | ||||
0.224377 | + | 0.974503i | \(0.427965\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −804.823 | + | 290.763i | −0.748025 | + | 0.270244i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1553.58 | 1.40364 | 0.701822 | − | 0.712352i | \(-0.252370\pi\) | ||||
0.701822 | + | 0.712352i | \(0.252370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1424.25i | − | 1.25155i | −0.780005 | − | 0.625773i | \(-0.784784\pi\) | ||
0.780005 | − | 0.625773i | \(-0.215216\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1255.49 | −1.07357 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 784.755 | 0.653305 | 0.326653 | − | 0.945144i | \(-0.394079\pi\) | ||||
0.326653 | + | 0.945144i | \(0.394079\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.07597i | − | 0.00330510i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −81.9261 | −0.0647356 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1288.22 | + | 465.402i | −0.992358 | + | 0.358516i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1046.39 | −0.786170 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −493.131 | −0.361497 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −196.910 | −0.140897 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2509.27i | − | 1.75324i | −0.481182 | − | 0.876620i | \(-0.659793\pi\) | ||
0.481182 | − | 0.876620i | \(-0.340207\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 800.003i | − | 0.546018i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2050.10i | 1.36731i | 0.729805 | + | 0.683655i | \(0.239611\pi\) | ||||
−0.729805 | + | 0.683655i | \(0.760389\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2634.73 | − | 951.868i | 1.71775 | − | 0.620582i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 415.848i | − | 0.265115i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2516.47 | −1.56932 | −0.784658 | − | 0.619929i | \(-0.787161\pi\) | ||||
−0.784658 | + | 0.619929i | \(0.787161\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 270.678i | 0.165170i | 0.996584 | + | 0.0825849i | \(0.0263176\pi\) | ||||
−0.996584 | + | 0.0825849i | \(0.973682\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 833.157i | − | 0.497620i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −153.569 | −0.0898048 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4311.35i | 2.46923i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −657.668 | − | 791.400i | −0.369004 | − | 0.444038i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 238.893i | − | 0.131348i | −0.997841 | − | 0.0656742i | \(-0.979080\pi\) | ||
0.997841 | − | 0.0656742i | \(-0.0209198\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2859.49i | 1.54107i | 0.637397 | + | 0.770535i | \(0.280011\pi\) | ||||
−0.637397 | + | 0.770535i | \(0.719989\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 665.616i | − | 0.351711i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2276.38 | 1.17964 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −566.367 | −0.287904 | −0.143952 | − | 0.989585i | \(-0.545981\pi\) | ||||
−0.143952 | + | 0.989585i | \(0.545981\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 830.555 | 0.414260 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.60965 | − | 1.66536i | 0.00225647 | − | 0.000815208i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1330.25 | −0.639222 | −0.319611 | − | 0.947549i | \(-0.603552\pi\) | ||||
−0.319611 | + | 0.947549i | \(0.603552\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 779.500i | − | 0.367782i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2770.08 | −1.28356 | −0.641782 | − | 0.766887i | \(-0.721805\pi\) | ||||
−0.641782 | + | 0.766887i | \(0.721805\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2114.14 | −0.962284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1361.36i | 0.608804i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1389.16 | 0.610498 | 0.305249 | − | 0.952273i | \(-0.401260\pi\) | ||||
0.305249 | + | 0.952273i | \(0.401260\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 706.153 | + | 1954.61i | 0.305029 | + | 0.844310i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 636.024 | 0.270093 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2337.71 | −0.976136 | −0.488068 | − | 0.872806i | \(-0.662298\pi\) | ||||
−0.488068 | + | 0.872806i | \(0.662298\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3318.66 | 1.36284 | 0.681420 | − | 0.731893i | \(-0.261363\pi\) | ||||
0.681420 | + | 0.731893i | \(0.261363\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 523.622i | 0.211515i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6445.62i | 2.56157i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1247.69i | − | 0.487913i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 470.296 | − | 169.907i | 0.181000 | − | 0.0653911i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1614.06i | − | 0.611463i | −0.952118 | − | 0.305731i | \(-0.901099\pi\) | ||
0.952118 | − | 0.305731i | \(-0.0989010\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1248.70 | −0.465719 | −0.232859 | − | 0.972510i | \(-0.574808\pi\) | ||||
−0.232859 | + | 0.972510i | \(0.574808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 420.603i | 0.154461i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4151.12i | 1.50129i | 0.660703 | + | 0.750647i | \(0.270258\pi\) | ||||
−0.660703 | + | 0.750647i | \(0.729742\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2928.99 | −1.04337 | −0.521685 | − | 0.853138i | \(-0.674696\pi\) | ||||
−0.521685 | + | 0.853138i | \(0.674696\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 952.504i | 0.334251i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4875.85 | + | 1761.53i | −1.68580 | + | 0.609040i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2531.70i | 0.862545i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.38178i | 0.000799737i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2551.84i | 0.844566i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3360.79 | 1.09652 | 0.548261 | − | 0.836307i | \(-0.315290\pi\) | ||||
0.548261 | + | 0.836307i | \(0.315290\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −318.280 | −0.102386 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4107.16 | −1.30282 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 930.083 | + | 2574.43i | 0.290959 | + | 0.805364i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2265.35 | −0.698988 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 673.226i | 0.204914i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2329.45 | −0.699515 | −0.349757 | − | 0.936840i | \(-0.613736\pi\) | ||||
−0.349757 | + | 0.936840i | \(0.613736\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1009.94 | −0.299240 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 832.888i | 0.243528i | 0.992559 | + | 0.121764i | \(0.0388550\pi\) | ||||
−0.992559 | + | 0.121764i | \(0.961145\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1434.36 | 0.413908 | 0.206954 | − | 0.978351i | \(-0.433645\pi\) | ||||
0.206954 | + | 0.978351i | \(0.433645\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 881.562 | − | 318.488i | 0.251093 | − | 0.0907140i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2388.42 | 0.671547 | 0.335773 | − | 0.941943i | \(-0.391002\pi\) | ||||
0.335773 | + | 0.941943i | \(0.391002\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4277.37 | −1.18734 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −582.606 | −0.159681 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4808.99i | − | 1.30154i | −0.759276 | − | 0.650769i | \(-0.774447\pi\) | ||
0.759276 | − | 0.650769i | \(-0.225553\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 2269.59i | − | 0.606627i | −0.952891 | − | 0.303313i | \(-0.901907\pi\) | ||
0.952891 | − | 0.303313i | \(-0.0980929\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4062.99 | + | 3376.42i | −1.05949 | + | 0.880455i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1376.92i | − | 0.354702i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2993.29 | −0.761816 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2242.07i | − | 0.563818i | −0.959441 | − | 0.281909i | \(-0.909032\pi\) | ||
0.959441 | − | 0.281909i | \(-0.0909676\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.46461i | 0.00110944i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3417.23 | −0.839196 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 787.861i | 0.191227i | 0.995419 | + | 0.0956136i | \(0.0304813\pi\) | ||||
−0.995419 | + | 0.0956136i | \(0.969519\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7289.56 | + | 2633.54i | −1.74885 | + | 0.631817i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 2519.33i | − | 0.597481i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6696.97i | 1.57016i | 0.619392 | + | 0.785082i | \(0.287379\pi\) | ||||
−0.619392 | + | 0.785082i | \(0.712621\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4264.01i | − | 0.988439i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2964.96 | 0.679597 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4374.92 | 0.991612 | 0.495806 | − | 0.868433i | \(-0.334873\pi\) | ||||
0.495806 | + | 0.868433i | \(0.334873\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8058.24 | −1.80629 | −0.903143 | − | 0.429340i | \(-0.858746\pi\) | ||||
−0.903143 | + | 0.429340i | \(0.858746\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −475.673 | + | 171.850i | −0.105454 | + | 0.0380982i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1893.11 | −0.415122 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4224.44i | − | 0.916324i | −0.888869 | − | 0.458162i | \(-0.848508\pi\) | ||
0.888869 | − | 0.458162i | \(-0.151492\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1330.20 | −0.285437 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3763.77 | 0.799031 | 0.399516 | − | 0.916726i | \(-0.369178\pi\) | ||||
0.399516 | + | 0.916726i | \(0.369178\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1604.16i | − | 0.336952i | −0.985706 | − | 0.168476i | \(-0.946115\pi\) | ||
0.985706 | − | 0.168476i | \(-0.0538846\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6989.10 | 1.45263 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2863.18 | + | 1034.40i | −0.588879 | + | 0.212748i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −556.685 | −0.113309 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3065.33 | −0.617502 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3124.58 | −0.623004 | −0.311502 | − | 0.950245i | \(-0.600832\pi\) | ||||
−0.311502 | + | 0.950245i | \(0.600832\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3265.30i | − | 0.644452i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 455.499i | 0.0889924i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 2.40902i | − | 0.000465943i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1678.10 | − | 4644.92i | −0.321342 | − | 0.889464i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2744.01i | 0.520261i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2688.24 | 0.504683 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9789.14i | 1.81986i | 0.414767 | + | 0.909928i | \(0.363863\pi\) | ||||
−0.414767 | + | 0.909928i | \(0.636137\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1407.29i | 0.259088i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3916.61 | 0.714117 | 0.357059 | − | 0.934082i | \(-0.383780\pi\) | ||||
0.357059 | + | 0.934082i | \(0.383780\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5571.72i | 1.00617i | 0.864236 | + | 0.503087i | \(0.167802\pi\) | ||||
−0.864236 | + | 0.503087i | \(0.832198\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −872.290 | − | 2414.47i | −0.156025 | − | 0.431873i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10110.5i | 1.79136i | 0.444700 | + | 0.895680i | \(0.353310\pi\) | ||||
−0.444700 | + | 0.895680i | \(0.646690\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4722.44i | − | 0.828858i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4660.73i | 0.810395i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11186.9 | 1.92711 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1021.48 | 0.174344 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4272.75 | 0.722580 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1747.64 | − | 4837.41i | −0.292859 | − | 0.810624i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −396.980 | −0.0659214 | −0.0329607 | − | 0.999457i | \(-0.510494\pi\) | ||||
−0.0329607 | + | 0.999457i | \(0.510494\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 3766.48i | − | 0.619825i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4890.09 | 0.797535 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7848.71 | 1.26868 | 0.634342 | − | 0.773053i | \(-0.281271\pi\) | ||||
0.634342 | + | 0.773053i | \(0.281271\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2354.26i | 0.377186i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2493.43 | −0.395974 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5478.56 | − | 3215.44i | −0.862432 | − | 0.506173i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.2279 | 0.00190820 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12522.0 | 1.93722 | 0.968609 | − | 0.248591i | \(-0.0799674\pi\) | ||||
0.968609 | + | 0.248591i | \(0.0799674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5091.86 | −0.780978 | −0.390489 | − | 0.920608i | \(-0.627694\pi\) | ||||
−0.390489 | + | 0.920608i | \(0.627694\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 245.778i | − | 0.0373751i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9690.22i | 1.46107i | 0.682874 | + | 0.730536i | \(0.260730\pi\) | ||||
−0.682874 | + | 0.730536i | \(0.739270\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1634.03i | 0.244296i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1396.21 | − | 3864.65i | −0.206989 | − | 0.572938i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9222.74i | − | 1.35587i | −0.735122 | − | 0.677935i | \(-0.762875\pi\) | ||
0.735122 | − | 0.677935i | \(-0.237125\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16021.1 | −2.33578 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3139.18i | − | 0.453895i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11630.2i | 1.66781i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2968.62 | 0.422236 | 0.211118 | − | 0.977461i | \(-0.432289\pi\) | ||||
0.211118 | + | 0.977461i | \(0.432289\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1479.39i | − | 0.208710i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4822.31 | − | 1742.19i | 0.674830 | − | 0.243800i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2883.02i | − | 0.400207i | −0.979775 | − | 0.200103i | \(-0.935872\pi\) | ||
0.979775 | − | 0.200103i | \(-0.0641278\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 590.730i | − | 0.0813471i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2548.13i | 0.348105i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2727.26 | 0.369630 | 0.184815 | − | 0.982773i | \(-0.440831\pi\) | ||||
0.184815 | + | 0.982773i | \(0.440831\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7527.81 | 1.01223 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10418.3 | 1.38995 | 0.694976 | − | 0.719033i | \(-0.255415\pi\) | ||||
0.694976 | + | 0.719033i | \(0.255415\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1635.09 | − | 4525.88i | −0.216447 | − | 0.599117i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2400.01 | 0.315244 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 9095.84i | − | 1.18555i | −0.805369 | − | 0.592773i | \(-0.798033\pi\) | ||
0.805369 | − | 0.592773i | \(-0.201967\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.5723 | 0.00253149 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6150.29 | −0.789417 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2991.06i | 0.381004i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1349.74 | 0.170633 | 0.0853167 | − | 0.996354i | \(-0.472810\pi\) | ||||
0.0853167 | + | 0.996354i | \(0.472810\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2855.60 | + | 7904.20i | 0.358293 | + | 0.991742i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1830.81 | 0.227996 | 0.113998 | − | 0.993481i | \(-0.463634\pi\) | ||||
0.113998 | + | 0.993481i | \(0.463634\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1345.41 | 0.166301 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1247.54 | 0.153064 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7060.20i | − | 0.859855i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 14709.9i | − | 1.77838i | −0.457542 | − | 0.889188i | \(-0.651270\pi\) | ||
0.457542 | − | 0.889188i | \(-0.348730\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 7549.40i | − | 0.906045i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3692.84 | − | 1334.14i | 0.439982 | − | 0.158955i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15367.3i | 1.81772i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −812.034 | −0.0953608 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6721.49i | 0.783690i | 0.920031 | + | 0.391845i | \(0.128163\pi\) | ||||
−0.920031 | + | 0.391845i | \(0.871837\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4541.66i | 0.525765i | 0.964828 | + | 0.262882i | \(0.0846731\pi\) | ||||
−0.964828 | + | 0.262882i | \(0.915327\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2499.47 | 0.287301 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8299.13i | 0.947216i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1098.36 | + | 3040.22i | 0.124481 | + | 0.344558i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 460.707i | − | 0.0518488i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10747.7i | − | 1.20116i | −0.799564 | − | 0.600580i | \(-0.794936\pi\) | ||
0.799564 | − | 0.600580i | \(-0.205064\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10058.7i | − | 1.11638i | −0.829714 | − | 0.558188i | \(-0.811497\pi\) | ||
0.829714 | − | 0.558188i | \(-0.188503\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12934.1 | −1.42561 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −40.0303 | −0.00438194 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2944.00 | 0.320067 | 0.160034 | − | 0.987112i | \(-0.448840\pi\) | ||||
0.160034 | + | 0.987112i | \(0.448840\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2374.20 | − | 1973.00i | 0.256365 | − | 0.213044i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8667.71 | 0.929606 | 0.464803 | − | 0.885414i | \(-0.346125\pi\) | ||||
0.464803 | + | 0.885414i | \(0.346125\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 15221.9i | − | 1.62154i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 716.680 | 0.0758340 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2980.91 | 0.313314 | 0.156657 | − | 0.987653i | \(-0.449928\pi\) | ||||
0.156657 | + | 0.987653i | \(0.449928\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2773.10i | − | 0.289534i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8578.46 | −0.889738 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 882.263 | + | 2442.07i | 0.0909036 | + | 0.251618i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5915.60 | 0.605515 | 0.302757 | − | 0.953068i | \(-0.402093\pi\) | ||||
0.302757 | + | 0.953068i | \(0.402093\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1996.85 | 0.203061 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5755.48 | 0.581474 | 0.290737 | − | 0.956803i | \(-0.406099\pi\) | ||||
0.290737 | + | 0.956803i | \(0.406099\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6502.53i | 0.652696i | 0.945250 | + | 0.326348i | \(0.105818\pi\) | ||||
−0.945250 | + | 0.326348i | \(0.894182\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6829.15i | 0.681063i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4507.81i | 0.446674i | 0.974741 | + | 0.223337i | \(0.0716950\pi\) | ||||
−0.974741 | + | 0.223337i | \(0.928305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1997.99 | + | 5530.36i | 0.196713 | + | 0.544495i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1699.10i | − | 0.166222i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4498.77 | 0.437323 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 16973.9i | − | 1.63961i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2491.67i | 0.239173i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2320.76 | −0.221375 | −0.110687 | − | 0.993855i | \(-0.535305\pi\) | ||||
−0.110687 | + | 0.993855i | \(0.535305\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3809.54i | 0.361123i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.99607 | + | 13.8289i | 0.000470661 | + | 0.00130277i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15737.2i | 1.47338i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8971.64i | − | 0.834792i | −0.908725 | − | 0.417396i | \(-0.862943\pi\) | ||
0.908725 | − | 0.417396i | \(-0.137057\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 3990.75i | − | 0.369055i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11942.9 | 1.09771 | 0.548857 | − | 0.835916i | \(-0.315063\pi\) | ||||
0.548857 | + | 0.835916i | \(0.315063\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20702.5 | −1.89127 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2338.50 | 0.212339 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1847.98 | + | 667.630i | −0.166787 | + | 0.0602561i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4865.01 | −0.436448 | −0.218224 | − | 0.975899i | \(-0.570026\pi\) | ||||
−0.218224 | + | 0.975899i | \(0.570026\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 8310.24i | − | 0.741066i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5302.73 | −0.470054 | −0.235027 | − | 0.971989i | \(-0.575518\pi\) | ||||
−0.235027 | + | 0.971989i | \(0.575518\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14087.5 | 1.24136 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 6342.41i | − | 0.555575i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13255.3 | −1.15428 | −0.577142 | − | 0.816644i | \(-0.695832\pi\) | ||||
−0.577142 | + | 0.816644i | \(0.695832\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13152.9 | + | 4751.85i | −1.13865 | + | 0.411368i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4084.07 | −0.351493 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7224.95 | 0.618193 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4685.21 | 0.398560 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4167.49i | 0.352471i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 17961.3i | − | 1.51036i | −0.655517 | − | 0.755181i | \(-0.727549\pi\) | ||
0.655517 | − | 0.755181i | \(-0.272451\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 15183.8i | − | 1.26948i | −0.772724 | − | 0.634742i | \(-0.781106\pi\) | ||
0.772724 | − | 0.634742i | \(-0.218894\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5863.82 | + | 2118.46i | −0.487463 | + | 0.176109i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10930.9i | 0.903523i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12166.9 | 0.999994 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1908.07i | 0.155938i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1496.31i | 0.121599i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23927.9 | 1.93363 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 7013.12i | − | 0.563572i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4450.40 | − | 3698.36i | 0.355644 | − | 0.295547i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1840.34i | 0.146252i | 0.997323 | + | 0.0731262i | \(0.0232976\pi\) | ||||
−0.997323 | + | 0.0731262i | \(0.976702\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9955.98i | 0.786836i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 21936.0i | − | 1.72410i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17887.3 | −1.39818 | −0.699091 | − | 0.715033i | \(-0.746412\pi\) | ||||
−0.699091 | + | 0.715033i | \(0.746412\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1570.87 | −0.122118 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42342.0 | 3.27374 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3382.69 | + | 1222.09i | −0.260120 | + | 0.0939753i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19336.8 | −1.47893 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12246.4i | 0.931590i | 0.884893 | + | 0.465795i | \(0.154232\pi\) | ||||
−0.884893 | + | 0.465795i | \(0.845768\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2427.45 | −0.183667 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3743.06 | 0.281697 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18024.0i | 1.34924i | 0.738165 | + | 0.674621i | \(0.235693\pi\) | ||||
−0.738165 | + | 0.674621i | \(0.764307\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12086.6 | 0.899979 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 509.721 | + | 1410.89i | 0.0377536 | + | 0.104500i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21534.4 | 1.58659 | 0.793294 | − | 0.608839i | \(-0.208364\pi\) | ||||
0.793294 | + | 0.608839i | \(0.208364\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5542.36 | −0.406201 | −0.203100 | − | 0.979158i | \(-0.565102\pi\) | ||||
−0.203100 | + | 0.979158i | \(0.565102\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4842.19 | 0.353028 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 29.6969i | − | 0.00215382i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 10857.0i | − | 0.783334i | −0.920107 | − | 0.391667i | \(-0.871898\pi\) | ||
0.920107 | − | 0.391667i | \(-0.128102\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 3746.11i | − | 0.268883i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17379.4 | + | 6278.78i | −1.24100 | + | 0.448344i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4670.58i | 0.331794i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1261.81 | −0.0891784 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 2426.15i | − | 0.170593i | −0.996356 | − | 0.0852963i | \(-0.972816\pi\) | ||
0.996356 | − | 0.0852963i | \(-0.0271837\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 22356.5i | − | 1.56398i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12453.4 | −0.866773 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 6562.03i | − | 0.454418i | −0.973846 | − | 0.227209i | \(-0.927040\pi\) | ||
0.973846 | − | 0.227209i | \(-0.0729601\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19840.8 | + | 7168.03i | −1.36705 | + | 0.493883i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 8786.97i | − | 0.602390i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 14414.2i | − | 0.983222i | −0.870815 | − | 0.491611i | \(-0.836408\pi\) | ||
0.870815 | − | 0.491611i | \(-0.163592\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 206.035i | 0.0139839i | 0.999976 | + | 0.00699196i | \(0.00222563\pi\) | ||||
−0.999976 | + | 0.00699196i | \(0.997774\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2857.51 | −0.192980 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16116.3 | −1.08301 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9273.66 | 0.620109 | 0.310055 | − | 0.950719i | \(-0.399653\pi\) | ||||
0.310055 | + | 0.950719i | \(0.399653\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5284.59 | − | 14627.5i | −0.351629 | − | 0.973297i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2528.05 | −0.167388 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1780.49i | 0.117314i | 0.998278 | + | 0.0586568i | \(0.0186817\pi\) | ||||
−0.998278 | + | 0.0586568i | \(0.981318\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7595.10 | −0.497990 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10288.9 | −0.671338 | −0.335669 | − | 0.941980i | \(-0.608962\pi\) | ||||
−0.335669 | + | 0.941980i | \(0.608962\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 28693.8i | − | 1.86317i | −0.363525 | − | 0.931585i | \(-0.618427\pi\) | ||
0.363525 | − | 0.931585i | \(-0.381573\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.14535 | −0.000461728 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17214.9 | − | 6219.35i | 1.10706 | − | 0.399956i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17059.7 | −1.09182 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7655.51 | −0.487610 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30951.0 | −1.96200 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22169.2i | 1.39864i | 0.714808 | + | 0.699320i | \(0.246514\pi\) | ||||
−0.714808 | + | 0.699320i | \(0.753486\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10082.4i | 0.633077i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 38647.2i | − | 2.41523i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2401.34 | + | 1995.56i | −0.149364 | + | 0.124124i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 954.841i | − | 0.0591125i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15310.8 | 0.943430 | 0.471715 | − | 0.881751i | \(-0.343635\pi\) | ||||
0.471715 | + | 0.881751i | \(0.343635\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.01281i | 0.000552769i | 1.00000 | 0.000276385i | \(8.79760e-5\pi\) | |||||
−1.00000 | 0.000276385i | \(0.999912\pi\) | ||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 12321.5i | − | 0.752182i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20077.1 | −1.21996 | −0.609979 | − | 0.792417i | \(-0.708822\pi\) | ||||
−0.609979 | + | 0.792417i | \(0.708822\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3576.65i | 0.216326i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7723.30 | + | 2790.25i | −0.464977 | + | 0.167985i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1796.00i | − | 0.107631i | −0.998551 | − | 0.0538154i | \(-0.982862\pi\) | ||
0.998551 | − | 0.0538154i | \(-0.0171383\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 31575.1i | 1.88358i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6796.06i | − | 0.403561i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12136.5 | 0.717405 | 0.358703 | − | 0.933452i | \(-0.383219\pi\) | ||||
0.358703 | + | 0.933452i | \(0.383219\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18080.9 | 1.06394 | 0.531970 | − | 0.846763i | \(-0.321452\pi\) | ||||
0.531970 | + | 0.846763i | \(0.321452\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2019.68 | −0.118307 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 40579.6 | − | 14660.5i | 2.36633 | − | 0.854900i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 74.0802 | 0.00430045 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 6988.36i | − | 0.403865i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2944.56 | −0.169409 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25019.4 | −1.43303 | −0.716513 | − | 0.697573i | \(-0.754263\pi\) | ||||
−0.716513 | + | 0.697573i | \(0.754263\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 3029.81i | − | 0.172766i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28258.5 | 1.60423 | 0.802114 | − | 0.597170i | \(-0.203708\pi\) | ||||
0.802114 | + | 0.597170i | \(0.203708\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17797.7 | + | 6429.89i | −1.00591 | + | 0.363412i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2498.67 | −0.140601 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14966.8 | 0.838491 | 0.419245 | − | 0.907873i | \(-0.362295\pi\) | ||||
0.419245 | + | 0.907873i | \(0.362295\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38758.1 | −2.16185 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4303.07i | 0.238970i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 2520.15i | − | 0.139347i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11414.7i | 0.628415i | 0.949354 | + | 0.314208i | \(0.101739\pi\) | ||||
−0.949354 | + | 0.314208i | \(0.898261\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 955.463 | + | 2644.69i | 0.0523738 | + | 0.144969i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4168.92i | 0.227534i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12156.9 | −0.660653 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7165.25i | 0.387718i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 26445.0i | − | 1.42484i | −0.701753 | − | 0.712420i | \(-0.747599\pi\) | ||
0.701753 | − | 0.712420i | \(-0.252401\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 63302.7 | 3.39617 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 12832.1i | − | 0.685511i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5755.88 | + | 15932.1i | 0.306184 | + | 0.847506i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 4251.03i | − | 0.225177i | −0.993642 | − | 0.112589i | \(-0.964086\pi\) | ||
0.993642 | − | 0.112589i | \(-0.0359143\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1747.82i | − | 0.0921918i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 39.1142i | − | 0.00205447i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2365.24 | −0.123713 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14427.0 | 0.751443 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14049.0 | 0.728703 | 0.364352 | − | 0.931261i | \(-0.381291\pi\) | ||||
0.364352 | + | 0.931261i | \(0.381291\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2951.96 | + | 8170.92i | 0.152478 | + | 0.422054i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6808.76 | 0.350236 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 31411.9i | 1.60911i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22710.8 | 1.15859 | 0.579295 | − | 0.815118i | \(-0.303328\pi\) | ||||
0.579295 | + | 0.815118i | \(0.303328\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 19722.0i | − | 0.997873i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34196.7 | 1.72317 | 0.861586 | − | 0.507611i | \(-0.169471\pi\) | ||||
0.861586 | + | 0.507611i | \(0.169471\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10129.3 | − | 12189.0i | −0.508331 | − | 0.611697i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5356.35 | −0.267712 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33629.7 | 1.67400 | 0.837001 | − | 0.547201i | \(-0.184307\pi\) | ||||
0.837001 | + | 0.547201i | \(0.184307\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4130.76 | 0.204787 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 12955.5i | − | 0.639693i | −0.947469 | − | 0.319846i | \(-0.896369\pi\) | ||
0.947469 | − | 0.319846i | \(-0.103631\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 3679.39i | − | 0.180943i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 8979.87i | − | 0.439835i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9776.43 | + | 27060.8i | 0.476933 | + | 1.32013i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 13497.2i | − | 0.655820i | −0.944709 | − | 0.327910i | \(-0.893656\pi\) | ||
0.944709 | − | 0.327910i | \(-0.106344\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6726.21 | 0.325520 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 44041.2i | 2.12295i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 35571.1i | − | 1.70786i | −0.520386 | − | 0.853931i | \(-0.674212\pi\) | ||
0.520386 | − | 0.853931i | \(-0.325788\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.3938 | −0.000640534 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16927.8i | 0.806348i | 0.915123 | + | 0.403174i | \(0.132093\pi\) | ||||
−0.915123 | + | 0.403174i | \(0.867907\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24808.1 | − | 8962.60i | 1.17708 | − | 0.425253i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 10251.7i | − | 0.484510i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1929.89i | − | 0.0908529i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 15208.9i | − | 0.713197i | −0.934258 | − | 0.356599i | \(-0.883936\pi\) | ||
0.934258 | − | 0.356599i | \(-0.116064\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2363.58 | −0.110405 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10234.0 | −0.476187 | −0.238093 | − | 0.971242i | \(-0.576522\pi\) | ||||
−0.238093 | + | 0.971242i | \(0.576522\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16585.4 | 0.768728 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7900.63 | − | 21868.7i | −0.364780 | − | 1.00970i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24864.0 | 1.14357 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1789.83i | − | 0.0820041i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7557.99 | 0.344956 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8723.06 | −0.396611 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 26421.8i | − | 1.19674i | −0.801220 | − | 0.598370i | \(-0.795815\pi\) | ||
0.801220 | − | 0.598370i | \(-0.204185\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20090.9 | −0.906534 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4938.34 | + | 13669.2i | 0.221981 | + | 0.614437i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1588.83 | 0.0711486 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12792.0 | 0.570675 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4607.96 | 0.204796 | 0.102398 | − | 0.994744i | \(-0.467348\pi\) | ||||
0.102398 | + | 0.994744i | \(0.467348\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 20539.3i | − | 0.909424i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8894.88i | 0.392366i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 12739.1i | − | 0.559842i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 70.9968 | − | 25.6495i | 0.00310846 | − | 0.00112301i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13124.8i | 0.572507i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16750.3 | −0.727947 | −0.363974 | − | 0.931409i | \(-0.618580\pi\) | ||||
−0.363974 | + | 0.931409i | \(0.618580\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 25091.7i | − | 1.08642i | −0.839596 | − | 0.543211i | \(-0.817209\pi\) | ||
0.839596 | − | 0.543211i | \(-0.182791\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 24174.7i | − | 1.04286i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20488.2 | −0.880578 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40336.6i | 1.72729i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −515.549 | − | 1427.02i | −0.0219960 | − | 0.0608841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1843.11i | − | 0.0783495i | −0.999232 | − | 0.0391747i | \(-0.987527\pi\) | ||
0.999232 | − | 0.0391747i | \(-0.0124729\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 3958.61i | − | 0.167665i | −0.996480 | − | 0.0838327i | \(-0.973284\pi\) | ||
0.996480 | − | 0.0838327i | \(-0.0267161\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 5679.32i | − | 0.239671i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −655.225 | −0.0275507 | −0.0137753 | − | 0.999905i | \(-0.504385\pi\) | ||||
−0.0137753 | + | 0.999905i | \(0.504385\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8380.73 | 0.351115 | 0.175558 | − | 0.984469i | \(-0.443827\pi\) | ||||
0.175558 | + | 0.984469i | \(0.443827\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12673.3 | 0.529040 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16213.1 | − | 19509.9i | −0.674371 | − | 0.811500i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −42664.2 | −1.76821 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 3990.60i | − | 0.164797i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19219.3 | −0.790850 | −0.395425 | − | 0.918498i | \(-0.629403\pi\) | ||||
−0.395425 | + | 0.918498i | \(0.629403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −53969.2 | −2.21285 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11291.3i | 0.461321i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −32561.5 | −1.32562 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6584.79 | − | 18226.4i | −0.267126 | − | 0.739396i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4812.48 | 0.194539 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 110.752 | 0.00446127 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16201.1 | 0.650312 | 0.325156 | − | 0.945660i | \(-0.394583\pi\) | ||||
0.325156 | + | 0.945660i | \(0.394583\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 20967.3i | 0.838675i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40564.8i | 1.61688i | 0.588578 | + | 0.808440i | \(0.299688\pi\) | ||||
−0.588578 | + | 0.808440i | \(0.700312\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33166.6i | 1.31738i | 0.752414 | + | 0.658690i | \(0.228889\pi\) | ||||
−0.752414 | + | 0.658690i | \(0.771111\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3103.20 | − | 8589.55i | −0.122830 | − | 0.339990i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 26307.1i | − | 1.03767i | −0.854876 | − | 0.518833i | \(-0.826367\pi\) | ||
0.854876 | − | 0.518833i | \(-0.173633\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21395.6 | 0.841009 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 1670.06i | − | 0.0654188i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 3276.26i | − | 0.127893i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2890.18 | 0.112434 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 9196.00i | − | 0.356515i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1239.13 | − | 3429.85i | −0.0478744 | − | 0.132515i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 30669.7i | − | 1.18089i | −0.807077 | − | 0.590447i | \(-0.798952\pi\) | ||
0.807077 | − | 0.590447i | \(-0.201048\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 9373.75i | − | 0.359692i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 31170.9i | − | 1.19202i | −0.802975 | − | 0.596012i | \(-0.796751\pi\) | ||
0.802975 | − | 0.596012i | \(-0.203249\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21907.1 | −0.834920 | −0.417460 | − | 0.908695i | \(-0.637080\pi\) | ||||
−0.417460 | + | 0.908695i | \(0.637080\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9795.91 | 0.372075 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1265.56 | 0.0479069 | 0.0239535 | − | 0.999713i | \(-0.492375\pi\) | ||||
0.0239535 | + | 0.999713i | \(0.492375\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 43707.4 | − | 15790.5i | 1.64893 | − | 0.595720i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1366.50 | −0.0513798 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42008.2i | 1.57419i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −36004.8 | −1.34470 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.22705 | 0.000269012 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 41372.9i | 1.53489i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20475.2 | 0.757079 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13934.8 | − | 5034.30i | 0.513532 | − | 0.185527i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 51113.3 | 1.87742 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11720.3 | 0.429068 | 0.214534 | − | 0.976716i | \(-0.431177\pi\) | ||||
0.214534 | + | 0.976716i | \(0.431177\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8232.02 | −0.300373 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30432.4i | 1.10677i | 0.832924 | + | 0.553387i | \(0.186665\pi\) | ||||
−0.832924 | + | 0.553387i | \(0.813335\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 16832.6i | − | 0.610162i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8064.72i | 0.291379i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −35709.3 | + | 12900.9i | −1.28596 | + | 0.464588i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14099.5i | 0.506092i | 0.967454 | + | 0.253046i | \(0.0814324\pi\) | ||||
−0.967454 | + | 0.253046i | \(0.918568\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29367.4 | −1.05069 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 965.757i | 0.0344402i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 46961.8i | 1.66929i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4221.88 | −0.149584 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44727.9i | 1.57963i | 0.613347 | + | 0.789813i | \(0.289823\pi\) | ||||
−0.613347 | + | 0.789813i | \(0.710177\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33160.0 | + | 39902.9i | 1.16732 | + | 1.40469i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11749.8i | 0.412296i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 19216.6i | − | 0.672138i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 56196.2i | − | 1.95929i | −0.200748 | − | 0.979643i | \(-0.564337\pi\) | ||
0.200748 | − | 0.979643i | \(-0.435663\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16715.2 | −0.580915 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4005.38 | 0.138758 | 0.0693792 | − | 0.997590i | \(-0.477898\pi\) | ||||
0.0693792 | + | 0.997590i | \(0.477898\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.5012 | 0.00150222 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7243.40 | − | 2616.87i | 0.249342 | − | 0.0900813i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10996.3 | 0.377332 | 0.188666 | − | 0.982041i | \(-0.439584\pi\) | ||||
0.188666 | + | 0.982041i | \(0.439584\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6873.76i | 0.235123i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30331.4 | −1.03424 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54721.9 | 1.86004 | 0.930020 | − | 0.367510i | \(-0.119790\pi\) | ||||
0.930020 | + | 0.367510i | \(0.119790\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 24859.4i | − | 0.842338i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14167.3 | 0.478541 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15835.7 | − | 43832.8i | −0.533225 | − | 1.47595i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7946.19 | −0.266731 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13982.2 | −0.467882 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19232.3 | −0.641564 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20511.0i | 0.682098i | 0.940046 | + | 0.341049i | \(0.110782\pi\) | ||||
−0.940046 | + | 0.341049i | \(0.889218\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33560.7i | 1.11262i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 15402.6i | − | 0.509055i | −0.967066 | − | 0.254527i | \(-0.918080\pi\) | ||
0.967066 | − | 0.254527i | \(-0.0819199\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4714.77 | + | 1703.34i | −0.155343 | + | 0.0561217i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3064.45i | 0.100657i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30243.1 | 0.990341 | 0.495171 | − | 0.868796i | \(-0.335106\pi\) | ||||
0.495171 | + | 0.868796i | \(0.335106\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16673.3i | 0.544311i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12818.3i | 0.417182i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31981.0 | 1.03767 | 0.518837 | − | 0.854873i | \(-0.326365\pi\) | ||||
0.518837 | + | 0.854873i | \(0.326365\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 63934.7i | 2.06815i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14512.2 | − | 5242.93i | 0.468014 | − | 0.169082i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 70.5716i | 0.00226901i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 33096.4i | − | 1.06089i | −0.847719 | − | 0.530445i | \(-0.822025\pi\) | ||
0.847719 | − | 0.530445i | \(-0.177975\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 1190.94i | − | 0.0380598i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45111.7 | −1.43732 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −59677.3 | −1.89569 | −0.947843 | − | 0.318739i | \(-0.896741\pi\) | ||||
−0.947843 | + | 0.318739i | \(0.896741\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11299.4 | 0.357856 |
(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 | 1344.4.p.d.223.10 | yes | 32 | |
4.3 | odd | 2 | inner | 1344.4.p.d.223.11 | yes | 32 | |
7.6 | odd | 2 | 1344.4.p.c.223.13 | ✓ | 32 | ||
8.3 | odd | 2 | 1344.4.p.c.223.14 | yes | 32 | ||
8.5 | even | 2 | 1344.4.p.c.223.29 | yes | 32 | ||
28.27 | even | 2 | 1344.4.p.c.223.30 | yes | 32 | ||
56.13 | odd | 2 | inner | 1344.4.p.d.223.12 | yes | 32 | |
56.27 | even | 2 | inner | 1344.4.p.d.223.9 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.p.c.223.13 | ✓ | 32 | 7.6 | odd | 2 | ||
1344.4.p.c.223.14 | yes | 32 | 8.3 | odd | 2 | ||
1344.4.p.c.223.29 | yes | 32 | 8.5 | even | 2 | ||
1344.4.p.c.223.30 | yes | 32 | 28.27 | even | 2 | ||
1344.4.p.d.223.9 | yes | 32 | 56.27 | even | 2 | inner | |
1344.4.p.d.223.10 | yes | 32 | 1.1 | even | 1 | trivial | |
1344.4.p.d.223.11 | yes | 32 | 4.3 | odd | 2 | inner | |
1344.4.p.d.223.12 | yes | 32 | 56.13 | odd | 2 | inner |