Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2200,2,Mod(1849,2200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2200.1849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2200.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.5670884447\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.96668224.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 15x^{4} + 61x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1849.1 | ||
Root | \(-2.75153i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2200.1849 |
Dual form | 2200.2.b.m.1849.6 |
$q$-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 \(\left(\mathbb{Z}/2200\mathbb{Z}\right)^\times\).
\(n\) | \(177\) | \(551\) | \(1101\) | \(1201\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 2.75153i | − 1.58860i | −0.607527 | − | 0.794299i | \(-0.707838\pi\) | ||||
0.607527 | − | 0.794299i | \(-0.292162\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.57093i | 1.34968i | 0.737962 | + | 0.674842i | \(0.235788\pi\) | ||||
−0.737962 | + | 0.674842i | \(0.764212\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.57093 | −1.52364 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.00000i | − 0.277350i | −0.990338 | − | 0.138675i | \(-0.955716\pi\) | ||||
0.990338 | − | 0.138675i | \(-0.0442844\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.751532i | 0.182273i | 0.995838 | + | 0.0911367i | \(0.0290500\pi\) | ||||
−0.995838 | + | 0.0911367i | \(0.970950\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.50306 | 0.574242 | 0.287121 | − | 0.957894i | \(-0.407302\pi\) | ||||
0.287121 | + | 0.957894i | \(0.407302\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.82552 | 2.14411 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 5.75153i | − 1.19928i | −0.800271 | − | 0.599639i | \(-0.795311\pi\) | ||||
0.800271 | − | 0.599639i | \(-0.204689\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.32246i | 0.831858i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.07399 | 0.756521 | 0.378261 | − | 0.925699i | \(-0.376522\pi\) | ||||
0.378261 | + | 0.925699i | \(0.376522\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.14186 | −1.10311 | −0.551555 | − | 0.834138i | \(-0.685965\pi\) | ||||
−0.551555 | + | 0.834138i | \(0.685965\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 2.75153i | − 0.478980i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.81940i | − 0.463506i | −0.972775 | − | 0.231753i | \(-0.925554\pi\) | ||||
0.972775 | − | 0.231753i | \(-0.0744461\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.75153 | −0.440598 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.18060 | 0.184379 | 0.0921896 | − | 0.995741i | \(-0.470613\pi\) | ||||
0.0921896 | + | 0.995741i | \(0.470613\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 7.68367i | − 1.17175i | −0.810402 | − | 0.585874i | \(-0.800751\pi\) | ||||
0.810402 | − | 0.585874i | \(-0.199249\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 9.82552i | − 1.43320i | −0.697484 | − | 0.716600i | \(-0.745697\pi\) | ||||
0.697484 | − | 0.716600i | \(-0.254303\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.75153 | −0.821647 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.06786 | 0.289559 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 14.2159i | − 1.95270i | −0.216202 | − | 0.976349i | \(-0.569367\pi\) | ||||
0.216202 | − | 0.976349i | \(-0.430633\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 6.88726i | − 0.912240i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.82552 | 1.27917 | 0.639587 | − | 0.768719i | \(-0.279105\pi\) | ||||
0.639587 | + | 0.768719i | \(0.279105\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.07399 | 0.905732 | 0.452866 | − | 0.891579i | \(-0.350402\pi\) | ||||
0.452866 | + | 0.891579i | \(0.350402\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 16.3225i | − 2.05644i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 14.6449i | − 1.78916i | −0.446906 | − | 0.894581i | \(-0.647474\pi\) | ||||
0.446906 | − | 0.894581i | \(-0.352526\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −15.8255 | −1.90517 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.81940 | 0.690635 | 0.345318 | − | 0.938486i | \(-0.387771\pi\) | ||||
0.345318 | + | 0.938486i | \(0.387771\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.7128i | 1.72200i | 0.508604 | + | 0.861001i | \(0.330162\pi\) | ||||
−0.508604 | + | 0.861001i | \(0.669838\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.57093i | 0.406945i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.89339 | 0.438041 | 0.219020 | − | 0.975720i | \(-0.429714\pi\) | ||||
0.219020 | + | 0.975720i | \(0.429714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.81940 | −0.202155 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.57706i | 0.612162i | 0.952006 | + | 0.306081i | \(0.0990178\pi\) | ||||
−0.952006 | + | 0.306081i | \(0.900982\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 11.2097i | − 1.20181i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.42907 | −0.787480 | −0.393740 | − | 0.919222i | \(-0.628819\pi\) | ||||
−0.393740 | + | 0.919222i | \(0.628819\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.57093 | 0.374335 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.8995i | 1.75240i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 0.609675i | − 0.0619031i | −0.999521 | − | 0.0309515i | \(-0.990146\pi\) | ||||
0.999521 | − | 0.0309515i | \(-0.00985375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.57093 | −0.459396 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.248468 | 0.0247235 | 0.0123617 | − | 0.999924i | \(-0.496065\pi\) | ||||
0.0123617 | + | 0.999924i | \(0.496065\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 17.5771i | − 1.73192i | −0.500114 | − | 0.865959i | \(-0.666709\pi\) | ||||
0.500114 | − | 0.865959i | \(-0.333291\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.7868i | 1.42949i | 0.699384 | + | 0.714746i | \(0.253458\pi\) | ||||
−0.699384 | + | 0.714746i | \(0.746542\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.42907 | −0.328445 | −0.164223 | − | 0.986423i | \(-0.552512\pi\) | ||||
−0.164223 | + | 0.986423i | \(0.552512\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.75766 | −0.736325 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.1867i | 1.33458i | 0.744800 | + | 0.667288i | \(0.232545\pi\) | ||||
−0.744800 | + | 0.667288i | \(0.767455\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.57093i | 0.422583i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.68367 | −0.246011 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 3.24847i | − 0.292904i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 18.8995i | − 1.67706i | −0.544855 | − | 0.838531i | \(-0.683415\pi\) | ||||
0.544855 | − | 0.838531i | \(-0.316585\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21.1419 | −1.86144 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.5322 | 1.79391 | 0.896953 | − | 0.442127i | \(-0.145776\pi\) | ||||
0.896953 | + | 0.442127i | \(0.145776\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.93826i | 0.775046i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 3.29334i | − 0.281369i | −0.990054 | − | 0.140685i | \(-0.955070\pi\) | ||||
0.990054 | − | 0.140685i | \(-0.0449304\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.4256 | −1.56284 | −0.781418 | − | 0.624008i | \(-0.785503\pi\) | ||||
−0.781418 | + | 0.624008i | \(0.785503\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −27.0352 | −2.27678 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1.00000i | − 0.0836242i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.8255i | 1.30527i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.36121 | −0.684977 | −0.342488 | − | 0.939522i | \(-0.611270\pi\) | ||||
−0.342488 | + | 0.939522i | \(0.611270\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.04487 | 0.410546 | 0.205273 | − | 0.978705i | \(-0.434192\pi\) | ||||
0.205273 | + | 0.978705i | \(0.434192\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 3.43520i | − 0.277719i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.2837i | 0.980347i | 0.871625 | + | 0.490174i | \(0.163067\pi\) | ||||
−0.871625 | + | 0.490174i | \(0.836933\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −39.1154 | −3.10205 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.5383 | 1.61865 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0801i | 0.946188i | 0.881012 | + | 0.473094i | \(0.156863\pi\) | ||||
−0.881012 | + | 0.473094i | \(0.843137\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 20.8317i | − 1.61200i | −0.591914 | − | 0.806001i | \(-0.701628\pi\) | ||||
0.591914 | − | 0.806001i | \(-0.298372\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.4413 | −0.874940 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2.50306i | − 0.190304i | −0.995463 | − | 0.0951522i | \(-0.969666\pi\) | ||||
0.995463 | − | 0.0951522i | \(-0.0303338\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 27.0352i | − 2.03209i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.5709 | 0.864852 | 0.432426 | − | 0.901669i | \(-0.357658\pi\) | ||||
0.432426 | + | 0.901669i | \(0.357658\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.4413 | −1.37073 | −0.685367 | − | 0.728198i | \(-0.740358\pi\) | ||||
−0.685367 | + | 0.728198i | \(0.740358\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 19.4643i | − 1.43884i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.751532i | 0.0549575i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.4352 | −1.12275 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.29334 | 0.238298 | 0.119149 | − | 0.992876i | \(-0.461983\pi\) | ||||
0.119149 | + | 0.992876i | \(0.461983\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.0061i | 1.65602i | 0.560715 | + | 0.828009i | \(0.310526\pi\) | ||||
−0.560715 | + | 0.828009i | \(0.689474\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.2546i | 0.944351i | 0.881505 | + | 0.472175i | \(0.156531\pi\) | ||||
−0.881505 | + | 0.472175i | \(0.843469\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.65455 | −0.117288 | −0.0586439 | − | 0.998279i | \(-0.518678\pi\) | ||||
−0.0586439 | + | 0.998279i | \(0.518678\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −40.2960 | −2.84226 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.5479i | 1.02107i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 26.2898i | 1.82727i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.50306 | 0.173141 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.9674 | −1.44345 | −0.721727 | − | 0.692178i | \(-0.756651\pi\) | ||||
−0.721727 | + | 0.692178i | \(0.756651\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 16.0123i | − 1.09714i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 21.9321i | − 1.48885i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 40.4827 | 2.73557 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.751532 | 0.0505535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.8317i | 0.859271i | 0.903002 | + | 0.429636i | \(0.141358\pi\) | ||||
−0.903002 | + | 0.429636i | \(0.858642\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.42907i | 0.625829i | 0.949781 | + | 0.312915i | \(0.101305\pi\) | ||||
−0.949781 | + | 0.312915i | \(0.898695\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.97701 | 0.328890 | 0.164445 | − | 0.986386i | \(-0.447417\pi\) | ||||
0.164445 | + | 0.986386i | \(0.447417\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.82552 | 0.646472 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.93214i | 0.257603i | 0.991670 | + | 0.128801i | \(0.0411130\pi\) | ||||
−0.991670 | + | 0.128801i | \(0.958887\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 10.7128i | − 0.695870i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.7189 | −1.79299 | −0.896494 | − | 0.443056i | \(-0.853894\pi\) | ||||
−0.896494 | + | 0.443056i | \(0.853894\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1189 | 0.780645 | 0.390322 | − | 0.920678i | \(-0.372364\pi\) | ||||
0.390322 | + | 0.920678i | \(0.372364\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.9735i | 1.15300i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 2.50306i | − 0.159266i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.3455 | 0.972478 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.1189 | 0.891175 | 0.445587 | − | 0.895238i | \(-0.352995\pi\) | ||||
0.445587 | + | 0.895238i | \(0.352995\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 5.75153i | − 0.361596i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 13.6062i | − 0.848730i | −0.905491 | − | 0.424365i | \(-0.860497\pi\) | ||||
0.905491 | − | 0.424365i | \(-0.139503\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0679 | 0.625587 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.6219 | −1.15267 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 28.6959i | − 1.76947i | −0.466098 | − | 0.884733i | \(-0.654340\pi\) | ||||
0.466098 | − | 0.884733i | \(-0.345660\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.4413i | 1.25099i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.39033 | 0.267683 | 0.133841 | − | 0.991003i | \(-0.457269\pi\) | ||||
0.133841 | + | 0.991003i | \(0.457269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.8317 | 1.14394 | 0.571971 | − | 0.820274i | \(-0.306179\pi\) | ||||
0.571971 | + | 0.820274i | \(0.306179\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 9.82552i | − 0.594668i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 22.1092i | − 1.32842i | −0.747548 | − | 0.664208i | \(-0.768769\pi\) | ||||
0.747548 | − | 0.664208i | \(-0.231231\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 28.0740 | 1.68075 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.18673 | −0.488379 | −0.244190 | − | 0.969727i | \(-0.578522\pi\) | ||||
−0.244190 | + | 0.969727i | \(0.578522\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 23.8934i | − 1.42031i | −0.704043 | − | 0.710157i | \(-0.748624\pi\) | ||||
0.704043 | − | 0.710157i | \(-0.251376\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.21585i | 0.248854i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.4352 | 0.966776 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.67754 | −0.0983391 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.99387i | 0.408586i | 0.978910 | + | 0.204293i | \(0.0654896\pi\) | ||||
−0.978910 | + | 0.204293i | \(0.934510\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.32246i | 0.250815i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.75153 | −0.332620 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.4378 | 1.58149 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 0.683667i | − 0.0392757i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 11.0352i | − 0.629815i | −0.949122 | − | 0.314907i | \(-0.898027\pi\) | ||||
0.949122 | − | 0.314907i | \(-0.101973\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −48.3638 | −2.75132 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.6449 | 1.34078 | 0.670390 | − | 0.742009i | \(-0.266127\pi\) | ||||
0.670390 | + | 0.742009i | \(0.266127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.50306i | 0.198005i | 0.995087 | + | 0.0990024i | \(0.0315652\pi\) | ||||
−0.995087 | + | 0.0990024i | \(0.968435\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.10048i | 0.0618092i | 0.999522 | + | 0.0309046i | \(0.00983881\pi\) | ||||
−0.999522 | + | 0.0309046i | \(0.990161\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.07399 | 0.228100 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 40.6863 | 2.27089 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.88113i | 0.104669i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.43520i | 0.521768i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 35.0862 | 1.93437 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.3225 | −0.677304 | −0.338652 | − | 0.940912i | \(-0.609971\pi\) | ||||
−0.338652 | + | 0.940912i | \(0.609971\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.8873i | 0.706218i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 10.0000i | − 0.544735i | −0.962193 | − | 0.272367i | \(-0.912193\pi\) | ||||
0.962193 | − | 0.272367i | \(-0.0878066\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 39.0352 | 2.12010 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.14186 | −0.332600 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.45819i | 0.240720i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.5709i | 0.835891i | 0.908472 | + | 0.417946i | \(0.137250\pi\) | ||||
−0.908472 | + | 0.417946i | \(0.862750\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.1541 | 0.650595 | 0.325297 | − | 0.945612i | \(-0.394536\pi\) | ||||
0.325297 | + | 0.945612i | \(0.394536\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.32246 | 0.230716 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0061i | 0.958370i | 0.877714 | + | 0.479185i | \(0.159068\pi\) | ||||
−0.877714 | + | 0.479185i | \(0.840932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.38420i | 0.390813i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.35508 | 0.388186 | 0.194093 | − | 0.980983i | \(-0.437824\pi\) | ||||
0.194093 | + | 0.980983i | \(0.437824\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.7347 | −0.670246 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2.75153i | − 0.144418i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.5322i | 1.48937i | 0.667417 | + | 0.744684i | \(0.267400\pi\) | ||||
−0.667417 | + | 0.744684i | \(0.732600\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.39645 | −0.280928 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 50.7638 | 2.63552 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 18.0510i | − 0.934645i | −0.884087 | − | 0.467323i | \(-0.845219\pi\) | ||||
0.884087 | − | 0.467323i | \(-0.154781\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 4.07399i | − 0.209821i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.32246 | 0.119297 | 0.0596484 | − | 0.998219i | \(-0.481002\pi\) | ||||
0.0596484 | + | 0.998219i | \(0.481002\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −52.0026 | −2.66418 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.67141i | 0.289796i | 0.989447 | + | 0.144898i | \(0.0462853\pi\) | ||||
−0.989447 | + | 0.144898i | \(0.953715\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 35.1215i | 1.78533i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.7347 | 1.35550 | 0.677751 | − | 0.735292i | \(-0.262955\pi\) | ||||
0.677751 | + | 0.735292i | \(0.262955\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.32246 | 0.218596 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 56.4950i | − 2.84979i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.89339i | 0.496535i | 0.968692 | + | 0.248267i | \(0.0798612\pi\) | ||||
−0.968692 | + | 0.248267i | \(0.920139\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 24.5939 | 1.23124 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.2572 | −1.36116 | −0.680580 | − | 0.732673i | \(-0.738272\pi\) | ||||
−0.680580 | + | 0.732673i | \(0.738272\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.14186i | 0.305948i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 2.81940i | − 0.139752i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.03875 | 0.100809 | 0.0504047 | − | 0.998729i | \(-0.483949\pi\) | ||||
0.0504047 | + | 0.998729i | \(0.483949\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.06174 | −0.446982 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 35.0862i | 1.72648i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 50.6986i | 2.48272i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.310204 | −0.0151545 | −0.00757723 | − | 0.999971i | \(-0.502412\pi\) | ||||
−0.00757723 | + | 0.999971i | \(0.502412\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.28109 | −0.403595 | −0.201798 | − | 0.979427i | \(-0.564678\pi\) | ||||
−0.201798 | + | 0.979427i | \(0.564678\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 44.9118i | 2.18369i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.2607i | 1.22245i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.75153 | −0.132845 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.45819 | 0.214743 | 0.107372 | − | 0.994219i | \(-0.465757\pi\) | ||||
0.107372 | + | 0.994219i | \(0.465757\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 22.9348i | − 1.10217i | −0.834448 | − | 0.551087i | \(-0.814213\pi\) | ||||
0.834448 | − | 0.551087i | \(-0.185787\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 14.3965i | − 0.688676i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.964753 | 0.0460451 | 0.0230226 | − | 0.999735i | \(-0.492671\pi\) | ||||
0.0230226 | + | 0.999735i | \(0.492671\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 26.2898 | 1.25190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.5092i | 1.73460i | 0.497782 | + | 0.867302i | \(0.334148\pi\) | ||||
−0.497782 | + | 0.867302i | \(0.665852\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 23.0061i | 1.08815i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.68017 | −0.409642 | −0.204821 | − | 0.978799i | \(-0.565661\pi\) | ||||
−0.204821 | + | 0.978799i | \(0.565661\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.18060 | 0.0555924 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 13.8811i | − 0.652193i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.4934i | 0.537640i | 0.963190 | + | 0.268820i | \(0.0866337\pi\) | ||||
−0.963190 | + | 0.268820i | \(0.913366\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.24847 | −0.151625 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.0571 | 1.16703 | 0.583513 | − | 0.812103i | \(-0.301678\pi\) | ||||
0.583513 | + | 0.812103i | \(0.301678\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 32.7868i | − 1.52373i | −0.647735 | − | 0.761865i | \(-0.724284\pi\) | ||||
0.647735 | − | 0.761865i | \(-0.275716\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 41.7603i | − 1.93244i | −0.257727 | − | 0.966218i | \(-0.582973\pi\) | ||||
0.257727 | − | 0.966218i | \(-0.417027\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 52.2960 | 2.41480 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 33.7990 | 1.55738 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 7.68367i | − 0.353295i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 64.9796i | 2.97521i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.96125 | −0.180994 | −0.0904972 | − | 0.995897i | \(-0.528846\pi\) | ||||
−0.0904972 | + | 0.995897i | \(0.528846\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.81940 | −0.128553 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 56.5118i | − 2.57138i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 22.7990i | − 1.03312i | −0.856250 | − | 0.516561i | \(-0.827212\pi\) | ||||
0.856250 | − | 0.516561i | \(-0.172788\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 33.2388 | 1.50311 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.4256 | −1.01205 | −0.506026 | − | 0.862518i | \(-0.668886\pi\) | ||||
−0.506026 | + | 0.862518i | \(0.668886\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.06174i | 0.137894i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.7807i | 0.932140i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.9321 | 1.07135 | 0.535675 | − | 0.844424i | \(-0.320057\pi\) | ||||
0.535675 | + | 0.844424i | \(0.320057\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −57.3190 | −2.56082 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.0766i | 1.02894i | 0.857510 | + | 0.514468i | \(0.172011\pi\) | ||||
−0.857510 | + | 0.514468i | \(0.827989\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 33.0184i | − 1.46640i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.2220 | −0.940648 | −0.470324 | − | 0.882494i | \(-0.655863\pi\) | ||||
−0.470324 | + | 0.882494i | \(0.655863\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −52.5383 | −2.32416 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.8194i | 0.477688i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 9.82552i | − 0.432126i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.88726 | −0.302317 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.1806 | 0.708885 | 0.354443 | − | 0.935078i | \(-0.384671\pi\) | ||||
0.354443 | + | 0.935078i | \(0.384671\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 31.8899i | − 1.39445i | −0.716854 | − | 0.697224i | \(-0.754418\pi\) | ||||
0.716854 | − | 0.697224i | \(-0.245582\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 4.61580i | − 0.201068i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.0801 | −0.438266 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −44.9118 | −1.94901 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.18060i | − 0.0511376i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 31.8378i | − 1.37390i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.75153 | −0.247736 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.4739 | 0.536297 | 0.268148 | − | 0.963378i | \(-0.413588\pi\) | ||||
0.268148 | + | 0.963378i | \(0.413588\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 50.7419i | 2.17754i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.1250i | 0.518427i | 0.965820 | + | 0.259214i | \(0.0834634\pi\) | ||||
−0.965820 | + | 0.259214i | \(0.916537\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −32.3347 | −1.38001 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.1975 | 0.434427 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.9030i | 0.591216i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.3673i | 1.20196i | 0.799263 | + | 0.600981i | \(0.205223\pi\) | ||||
−0.799263 | + | 0.600981i | \(0.794777\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.68367 | −0.324985 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.06786 | 0.0873053 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 4.08012i | − 0.171957i | −0.996297 | − | 0.0859783i | \(-0.972598\pi\) | ||||
0.996297 | − | 0.0859783i | \(-0.0274016\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 6.49694i | − 0.272846i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.0088 | 0.964577 | 0.482289 | − | 0.876012i | \(-0.339806\pi\) | ||||
0.482289 | + | 0.876012i | \(0.339806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.5322 | −1.44513 | −0.722563 | − | 0.691305i | \(-0.757036\pi\) | ||||
−0.722563 | + | 0.691305i | \(0.757036\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 9.06174i | − 0.378559i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 25.1710i | − 1.04788i | −0.851755 | − | 0.523941i | \(-0.824461\pi\) | ||||
0.851755 | − | 0.523941i | \(-0.175539\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 63.3021 | 2.63075 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.9153 | −0.826225 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 14.2159i | − 0.588760i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.2546i | 0.423252i | 0.977351 | + | 0.211626i | \(0.0678760\pi\) | ||||
−0.977351 | + | 0.211626i | \(0.932124\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.3735 | −0.633453 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36.4704 | 1.50019 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.9091i | 0.447985i | 0.974591 | + | 0.223992i | \(0.0719091\pi\) | ||||
−0.974591 | + | 0.223992i | \(0.928091\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.55254i | 0.186323i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.2607 | −1.19556 | −0.597780 | − | 0.801660i | \(-0.703951\pi\) | ||||
−0.597780 | + | 0.801660i | \(0.703951\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.2220 | −1.11041 | −0.555204 | − | 0.831714i | \(-0.687360\pi\) | ||||
−0.555204 | + | 0.831714i | \(0.687360\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 66.9409i | 2.72604i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 32.7347i | − 1.32866i | −0.747440 | − | 0.664330i | \(-0.768717\pi\) | ||||
0.747440 | − | 0.664330i | \(-0.231283\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 40.0291 | 1.62206 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.82552 | −0.397498 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.1894i | 0.573103i | 0.958065 | + | 0.286551i | \(0.0925089\pi\) | ||||
−0.958065 | + | 0.286551i | \(0.907491\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.4766i | 0.985390i | 0.870202 | + | 0.492695i | \(0.163988\pi\) | ||||
−0.870202 | + | 0.492695i | \(0.836012\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.7603 | −1.27655 | −0.638277 | − | 0.769807i | \(-0.720353\pi\) | ||||
−0.638277 | + | 0.769807i | \(0.720353\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 24.8608 | 0.997628 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 26.5287i | − 1.06285i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 6.88726i | − 0.275051i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.11887 | 0.0844848 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.0219 | −0.956296 | −0.478148 | − | 0.878279i | \(-0.658692\pi\) | ||||
−0.478148 | + | 0.878279i | \(0.658692\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 57.6924i | 2.29307i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.75153i | 0.227884i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −26.6000 | −1.05228 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.0061 | 0.632204 | 0.316102 | − | 0.948725i | \(-0.397626\pi\) | ||||
0.316102 | + | 0.948725i | \(0.397626\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.0836i | 0.437095i | 0.975826 | + | 0.218548i | \(0.0701319\pi\) | ||||
−0.975826 | + | 0.218548i | \(0.929868\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.0449i | 1.14187i | 0.820995 | + | 0.570936i | \(0.193420\pi\) | ||||
−0.820995 | + | 0.570936i | \(0.806580\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.82552 | 0.385686 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −60.3470 | −2.36518 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 50.3251i | 1.96937i | 0.174335 | + | 0.984686i | \(0.444223\pi\) | ||||
−0.174335 | + | 0.984686i | \(0.555777\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 67.2511i | − 2.62372i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.7189 | −1.04082 | −0.520411 | − | 0.853916i | \(-0.674221\pi\) | ||||
−0.520411 | + | 0.853916i | \(0.674221\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.83165 | −0.187930 | −0.0939648 | − | 0.995576i | \(-0.529954\pi\) | ||||
−0.0939648 | + | 0.995576i | \(0.529954\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 2.06786i | − 0.0803092i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 23.4317i | − 0.907279i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 35.3067 | 1.36504 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.07399 | 0.273088 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.7542i | 0.800014i | 0.916512 | + | 0.400007i | \(0.130992\pi\) | ||||
−0.916512 | + | 0.400007i | \(0.869008\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.53568i | 0.212754i | 0.994326 | + | 0.106377i | \(0.0339250\pi\) | ||||
−0.994326 | + | 0.106377i | \(0.966075\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.17710 | 0.0835496 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.9444 | 0.994191 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.0256i | 1.56980i | 0.619621 | + | 0.784901i | \(0.287286\pi\) | ||||
−0.619621 | + | 0.784901i | \(0.712714\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 13.6944i | − 0.522474i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.2159 | −0.541581 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 51.5180 | 1.95984 | 0.979918 | − | 0.199403i | \(-0.0639002\pi\) | ||||
0.979918 | + | 0.199403i | \(0.0639002\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 16.3225i | − 0.620039i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.887261i | 0.0336074i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.8194 | 0.409227 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.2450 | 0.726872 | 0.363436 | − | 0.931619i | \(-0.381603\pi\) | ||||
0.363436 | + | 0.931619i | \(0.381603\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 7.05713i | − 0.266165i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.887261i | 0.0333689i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.99387 | 0.337772 | 0.168886 | − | 0.985636i | \(-0.445983\pi\) | ||||
0.168886 | + | 0.985636i | \(0.445983\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.7964 | −0.667417 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 35.3251i | 1.32294i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 76.2695i | 2.84834i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.6837 | 0.398434 | 0.199217 | − | 0.979955i | \(-0.436160\pi\) | ||||
0.199217 | + | 0.979955i | \(0.436160\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 62.7664 | 2.33754 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 33.3455i | − 1.24013i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.98424i | 0.0735916i | 0.999323 | + | 0.0367958i | \(0.0117151\pi\) | ||||
−0.999323 | + | 0.0367958i | \(0.988285\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 43.9965 | 1.62950 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.77452 | 0.213578 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.8765i | 1.21432i | 0.794579 | + | 0.607161i | \(0.207692\pi\) | ||||
−0.794579 | + | 0.607161i | \(0.792308\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 14.6449i | − 0.539453i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.4352 | −1.15636 | −0.578181 | − | 0.815908i | \(-0.696237\pi\) | ||||
−0.578181 | + | 0.815908i | \(0.696237\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.88726 | −0.253010 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.3638i | 1.04057i | 0.853993 | + | 0.520284i | \(0.174174\pi\) | ||||
−0.853993 | + | 0.520284i | \(0.825826\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 25.4923i | − 0.932716i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −52.8025 | −1.92936 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.4291 | −0.635996 | −0.317998 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317998 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 38.8485i | − 1.41572i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 21.8838i | − 0.795379i | −0.917520 | − | 0.397689i | \(-0.869812\pi\) | ||||
0.917520 | − | 0.397689i | \(-0.130188\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.8255 | −0.574430 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.7224 | 1.18619 | 0.593093 | − | 0.805134i | \(-0.297907\pi\) | ||||
0.593093 | + | 0.805134i | \(0.297907\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 12.2450i | − 0.443298i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 9.82552i | − 0.354779i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.54181 | 0.344086 | 0.172043 | − | 0.985089i | \(-0.444963\pi\) | ||||
0.172043 | + | 0.985089i | \(0.444963\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −37.4378 | −1.34829 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.0556080i | 0.00200008i | 0.999999 | + | 0.00100004i | \(0.000318323\pi\) | ||||
−0.999999 | + | 0.00100004i | \(0.999682\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 27.7021i | − 0.993806i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.95513 | 0.105878 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.81940 | 0.208234 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.6097i | 0.629318i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.0970i | 0.787672i | 0.919181 | + | 0.393836i | \(0.128852\pi\) | ||||
−0.919181 | + | 0.393836i | \(0.871148\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −78.9578 | −2.81097 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −50.6598 | −1.80126 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 7.07399i | − 0.251205i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.7577i | 1.26660i | 0.773906 | + | 0.633301i | \(0.218300\pi\) | ||||
−0.773906 | + | 0.633301i | \(0.781700\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.38420 | 0.261234 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 33.9578 | 1.19984 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.7128i | 0.519203i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 12.0801i | − 0.425240i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.9286 | −0.876444 | −0.438222 | − | 0.898867i | \(-0.644392\pi\) | ||||
−0.438222 | + | 0.898867i | \(0.644392\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.6123 | 1.03983 | 0.519914 | − | 0.854218i | \(-0.325964\pi\) | ||||
0.519914 | + | 0.854218i | \(0.325964\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 51.8159i | − 1.81726i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 19.2327i | − 0.672867i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.3225 | −0.570353 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.328589 | 0.0114678 | 0.00573392 | − | 0.999984i | \(-0.498175\pi\) | ||||
0.00573392 | + | 0.999984i | \(0.498175\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.5797i | 1.48423i | 0.670270 | + | 0.742117i | \(0.266178\pi\) | ||||
−0.670270 | + | 0.742117i | \(0.733822\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 23.1867i | − 0.806282i | −0.915138 | − | 0.403141i | \(-0.867918\pi\) | ||||
0.915138 | − | 0.403141i | \(-0.132082\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.2546 | 1.25917 | 0.629587 | − | 0.776930i | \(-0.283224\pi\) | ||||
0.629587 | + | 0.776930i | \(0.283224\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −60.8343 | −2.11032 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 4.32246i | − 0.149764i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 26.5479i | − 0.917631i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.6607 | 0.471619 | 0.235809 | − | 0.971799i | \(-0.424226\pi\) | ||||
0.235809 | + | 0.971799i | \(0.424226\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.4026 | −0.427675 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.5261i | 0.775839i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.57093i | 0.122699i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −65.7434 | −2.25631 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.2159 | −0.555872 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 54.2476i | − 1.85740i | −0.370829 | − | 0.928701i | \(-0.620926\pi\) | ||||
0.370829 | − | 0.928701i | \(-0.379074\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.41221i | 0.219037i | 0.993985 | + | 0.109518i | \(0.0349309\pi\) | ||||
−0.993985 | + | 0.109518i | \(0.965069\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −51.5031 | −1.75726 | −0.878631 | − | 0.477501i | \(-0.841543\pi\) | ||||
−0.878631 | + | 0.477501i | \(0.841543\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.6000 | 0.395329 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 43.2837i | 1.47339i | 0.676223 | + | 0.736697i | \(0.263616\pi\) | ||||
−0.676223 | + | 0.736697i | \(0.736384\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 45.2220i | − 1.53582i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.89339 | 0.132074 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.6449 | −0.496224 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.78678i | 0.0943182i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.2511i | 0.346155i | 0.984908 | + | 0.173077i | \(0.0553711\pi\) | ||||
−0.984908 | + | 0.173077i | \(0.944629\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.2439 | 0.649079 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.19023 | 0.275936 | 0.137968 | − | 0.990437i | \(-0.455943\pi\) | ||||
0.137968 | + | 0.990437i | \(0.455943\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 6.76116i | − 0.227531i | −0.993508 | − | 0.113766i | \(-0.963709\pi\) | ||||
0.993508 | − | 0.113766i | \(-0.0362913\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 10.3225i | − 0.346594i | −0.984870 | − | 0.173297i | \(-0.944558\pi\) | ||||
0.984870 | − | 0.173297i | \(-0.0554421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 67.4888 | 2.26350 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.81940 | −0.0609521 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 24.5939i | − 0.823004i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.8255i | 0.528399i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.0219 | −0.834527 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.6837 | 0.355925 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 75.4961i | − 2.51235i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.9348i | 0.396287i | 0.980173 | + | 0.198144i | \(0.0634913\pi\) | ||||
−0.980173 | + | 0.198144i | \(0.936509\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.13573 | −0.0376698 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.35508 | −0.243685 | −0.121842 | − | 0.992549i | \(-0.538880\pi\) | ||||
−0.121842 | + | 0.992549i | \(0.538880\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.57706i | 0.184574i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 73.3190i | 2.42121i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.0184 | 0.825280 | 0.412640 | − | 0.910894i | \(-0.364607\pi\) | ||||
0.412640 | + | 0.910894i | \(0.364607\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.3638 | −1.00052 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 5.81940i | − 0.191548i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 80.3435i | 2.63883i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.42557 | −0.145198 | −0.0725992 | − | 0.997361i | \(-0.523129\pi\) | ||||
−0.0725992 | + | 0.997361i | \(0.523129\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.3965 | −0.471825 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 65.0598i | − 2.12996i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 40.3612i | − 1.31854i | −0.751905 | − | 0.659272i | \(-0.770865\pi\) | ||||
0.751905 | − | 0.659272i | \(-0.229135\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.63879 | 0.314550 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.2704 | 0.432601 | 0.216301 | − | 0.976327i | \(-0.430601\pi\) | ||||
0.216301 | + | 0.976327i | \(0.430601\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 6.79028i | − 0.221122i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4.81940i | − 0.156609i | −0.996929 | − | 0.0783047i | \(-0.975049\pi\) | ||||
0.996929 | − | 0.0783047i | \(-0.0249507\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.7128 | 0.477597 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.02801 | 0.0981900 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 16.0123i | − 0.518688i | −0.965785 | − | 0.259344i | \(-0.916494\pi\) | ||||
0.965785 | − | 0.259344i | \(-0.0835063\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 11.2097i | − 0.362359i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.7603 | 0.379760 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.72241 | 0.216852 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 67.5893i | − 2.17804i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.6211i | 1.62786i | 0.580960 | + | 0.813932i | \(0.302677\pi\) | ||||
−0.580960 | + | 0.813932i | \(0.697323\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.17600 | 0.166277 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.5249 | 0.883318 | 0.441659 | − | 0.897183i | \(-0.354390\pi\) | ||||
0.441659 | + | 0.897183i | \(0.354390\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 65.7964i | − 2.10934i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.1215i | 1.53954i | 0.638320 | + | 0.769772i | \(0.279630\pi\) | ||||
−0.638320 | + | 0.769772i | \(0.720370\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.42907 | −0.237434 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.6740 | 0.500434 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 12.8960i | − 0.411319i | −0.978624 | − | 0.205660i | \(-0.934066\pi\) | ||||
0.978624 | − | 0.205660i | \(-0.0659340\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 96.5409i | − 3.07293i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.1929 | −1.40525 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.53218 | 0.0486714 | 0.0243357 | − | 0.999704i | \(-0.492253\pi\) | ||||
0.0243357 | + | 0.999704i | \(0.492253\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.9056i | 1.07596i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.9831i | 1.01292i | 0.862265 | + | 0.506458i | \(0.169046\pi\) | ||||
−0.862265 | + | 0.506458i | \(0.830954\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.1867 | 0.385571 |
(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 | 2200.2.b.m.1849.1 | 6 | ||
4.3 | odd | 2 | 4400.2.b.bb.4049.6 | 6 | |||
5.2 | odd | 4 | 2200.2.a.u.1.1 | ✓ | 3 | ||
5.3 | odd | 4 | 2200.2.a.v.1.3 | yes | 3 | ||
5.4 | even | 2 | inner | 2200.2.b.m.1849.6 | 6 | ||
20.3 | even | 4 | 4400.2.a.by.1.1 | 3 | |||
20.7 | even | 4 | 4400.2.a.bz.1.3 | 3 | |||
20.19 | odd | 2 | 4400.2.b.bb.4049.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2200.2.a.u.1.1 | ✓ | 3 | 5.2 | odd | 4 | ||
2200.2.a.v.1.3 | yes | 3 | 5.3 | odd | 4 | ||
2200.2.b.m.1849.1 | 6 | 1.1 | even | 1 | trivial | ||
2200.2.b.m.1849.6 | 6 | 5.4 | even | 2 | inner | ||
4400.2.a.by.1.1 | 3 | 20.3 | even | 4 | |||
4400.2.a.bz.1.3 | 3 | 20.7 | even | 4 | |||
4400.2.b.bb.4049.1 | 6 | 20.19 | odd | 2 | |||
4400.2.b.bb.4049.6 | 6 | 4.3 | odd | 2 |