Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(337,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.c (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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 16x^{10} + 96x^{8} + 266x^{6} + 332x^{4} + 141x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.2 | ||
Root | \(0.908891i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.337 |
Dual form | 1183.2.c.h.337.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.08281i | − 1.47277i | −0.676564 | − | 0.736384i | \(-0.736532\pi\) | ||||
0.676564 | − | 0.736384i | \(-0.263468\pi\) | |||||||
\(3\) | −0.0911085 | −0.0526015 | −0.0263008 | − | 0.999654i | \(-0.508373\pi\) | ||||
−0.0263008 | + | 0.999654i | \(0.508373\pi\) | |||||||
\(4\) | −2.33809 | −1.16904 | ||||||||
\(5\) | 2.63777i | 1.17964i | 0.807533 | + | 0.589822i | \(0.200802\pi\) | ||||
−0.807533 | + | 0.589822i | \(0.799198\pi\) | |||||||
\(6\) | 0.189762i | 0.0774698i | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0.704173i | 0.248963i | ||||||||
\(9\) | −2.99170 | −0.997233 | ||||||||
\(10\) | 5.49396 | 1.73734 | ||||||||
\(11\) | − 3.44676i | − 1.03924i | −0.854399 | − | 0.519618i | \(-0.826074\pi\) | ||||
0.854399 | − | 0.519618i | \(-0.173926\pi\) | |||||||
\(12\) | 0.213020 | 0.0614935 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.08281 | 0.556654 | ||||||||
\(15\) | − 0.240323i | − 0.0620511i | ||||||||
\(16\) | −3.20952 | −0.802380 | ||||||||
\(17\) | 4.83445 | 1.17253 | 0.586264 | − | 0.810120i | \(-0.300598\pi\) | ||||
0.586264 | + | 0.810120i | \(0.300598\pi\) | |||||||
\(18\) | 6.23113i | 1.46869i | ||||||||
\(19\) | − 2.42330i | − 0.555944i | −0.960589 | − | 0.277972i | \(-0.910338\pi\) | ||||
0.960589 | − | 0.277972i | \(-0.0896622\pi\) | |||||||
\(20\) | − 6.16733i | − 1.37906i | ||||||||
\(21\) | − 0.0911085i | − 0.0198815i | ||||||||
\(22\) | −7.17893 | −1.53055 | ||||||||
\(23\) | 6.84789 | 1.42788 | 0.713942 | − | 0.700205i | \(-0.246908\pi\) | ||||
0.713942 | + | 0.700205i | \(0.246908\pi\) | |||||||
\(24\) | − 0.0641561i | − 0.0130958i | ||||||||
\(25\) | −1.95781 | −0.391562 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.545895 | 0.105057 | ||||||||
\(28\) | − 2.33809i | − 0.441857i | ||||||||
\(29\) | 4.64785 | 0.863084 | 0.431542 | − | 0.902093i | \(-0.357970\pi\) | ||||
0.431542 | + | 0.902093i | \(0.357970\pi\) | |||||||
\(30\) | −0.500546 | −0.0913869 | ||||||||
\(31\) | − 8.43394i | − 1.51478i | −0.652962 | − | 0.757390i | \(-0.726474\pi\) | ||||
0.652962 | − | 0.757390i | \(-0.273526\pi\) | |||||||
\(32\) | 8.09316i | 1.43068i | ||||||||
\(33\) | 0.314029i | 0.0546654i | ||||||||
\(34\) | − 10.0692i | − 1.72686i | ||||||||
\(35\) | −2.63777 | −0.445864 | ||||||||
\(36\) | 6.99486 | 1.16581 | ||||||||
\(37\) | − 1.51646i | − 0.249305i | −0.992200 | − | 0.124652i | \(-0.960218\pi\) | ||||
0.992200 | − | 0.124652i | \(-0.0397816\pi\) | |||||||
\(38\) | −5.04727 | −0.818776 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.85744 | −0.293687 | ||||||||
\(41\) | − 10.4384i | − 1.63020i | −0.579317 | − | 0.815102i | \(-0.696681\pi\) | ||||
0.579317 | − | 0.815102i | \(-0.303319\pi\) | |||||||
\(42\) | −0.189762 | −0.0292808 | ||||||||
\(43\) | 0.451785 | 0.0688966 | 0.0344483 | − | 0.999406i | \(-0.489033\pi\) | ||||
0.0344483 | + | 0.999406i | \(0.489033\pi\) | |||||||
\(44\) | 8.05882i | 1.21491i | ||||||||
\(45\) | − 7.89140i | − 1.17638i | ||||||||
\(46\) | − 14.2628i | − 2.10294i | ||||||||
\(47\) | − 2.56938i | − 0.374782i | −0.982285 | − | 0.187391i | \(-0.939997\pi\) | ||||
0.982285 | − | 0.187391i | \(-0.0600032\pi\) | |||||||
\(48\) | 0.292415 | 0.0422064 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 4.07774i | 0.576679i | ||||||||
\(51\) | −0.440460 | −0.0616767 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.3402 | −1.42033 | −0.710166 | − | 0.704035i | \(-0.751380\pi\) | ||||
−0.710166 | + | 0.704035i | \(0.751380\pi\) | |||||||
\(54\) | − 1.13699i | − 0.154725i | ||||||||
\(55\) | 9.09173 | 1.22593 | ||||||||
\(56\) | −0.704173 | −0.0940990 | ||||||||
\(57\) | 0.220783i | 0.0292435i | ||||||||
\(58\) | − 9.68058i | − 1.27112i | ||||||||
\(59\) | − 12.7994i | − 1.66634i | −0.553016 | − | 0.833171i | \(-0.686523\pi\) | ||||
0.553016 | − | 0.833171i | \(-0.313477\pi\) | |||||||
\(60\) | 0.561896i | 0.0725405i | ||||||||
\(61\) | −0.984619 | −0.126068 | −0.0630338 | − | 0.998011i | \(-0.520078\pi\) | ||||
−0.0630338 | + | 0.998011i | \(0.520078\pi\) | |||||||
\(62\) | −17.5663 | −2.23092 | ||||||||
\(63\) | − 2.99170i | − 0.376919i | ||||||||
\(64\) | 10.4375 | 1.30468 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.654061 | 0.0805094 | ||||||||
\(67\) | − 1.28567i | − 0.157069i | −0.996911 | − | 0.0785346i | \(-0.974976\pi\) | ||||
0.996911 | − | 0.0785346i | \(-0.0250241\pi\) | |||||||
\(68\) | −11.3034 | −1.37074 | ||||||||
\(69\) | −0.623901 | −0.0751089 | ||||||||
\(70\) | 5.49396i | 0.656654i | ||||||||
\(71\) | 12.0794i | 1.43356i | 0.697301 | + | 0.716779i | \(0.254384\pi\) | ||||
−0.697301 | + | 0.716779i | \(0.745616\pi\) | |||||||
\(72\) | − 2.10667i | − 0.248274i | ||||||||
\(73\) | − 5.18381i | − 0.606719i | −0.952876 | − | 0.303360i | \(-0.901892\pi\) | ||||
0.952876 | − | 0.303360i | \(-0.0981083\pi\) | |||||||
\(74\) | −3.15850 | −0.367168 | ||||||||
\(75\) | 0.178373 | 0.0205967 | ||||||||
\(76\) | 5.66589i | 0.649923i | ||||||||
\(77\) | 3.44676 | 0.392794 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.74733 | 1.09666 | 0.548330 | − | 0.836262i | \(-0.315264\pi\) | ||||
0.548330 | + | 0.836262i | \(0.315264\pi\) | |||||||
\(80\) | − 8.46596i | − 0.946523i | ||||||||
\(81\) | 8.92536 | 0.991707 | ||||||||
\(82\) | −21.7412 | −2.40091 | ||||||||
\(83\) | − 13.2658i | − 1.45611i | −0.685520 | − | 0.728054i | \(-0.740425\pi\) | ||||
0.685520 | − | 0.728054i | \(-0.259575\pi\) | |||||||
\(84\) | 0.213020i | 0.0232424i | ||||||||
\(85\) | 12.7522i | 1.38317i | ||||||||
\(86\) | − 0.940982i | − 0.101469i | ||||||||
\(87\) | −0.423459 | −0.0453995 | ||||||||
\(88\) | 2.42711 | 0.258731 | ||||||||
\(89\) | 16.0403i | 1.70027i | 0.526567 | + | 0.850134i | \(0.323479\pi\) | ||||
−0.526567 | + | 0.850134i | \(0.676521\pi\) | |||||||
\(90\) | −16.4363 | −1.73254 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −16.0110 | −1.66926 | ||||||||
\(93\) | 0.768404i | 0.0796798i | ||||||||
\(94\) | −5.35152 | −0.551967 | ||||||||
\(95\) | 6.39210 | 0.655816 | ||||||||
\(96\) | − 0.737356i | − 0.0752560i | ||||||||
\(97\) | 14.9407i | 1.51700i | 0.651672 | + | 0.758501i | \(0.274068\pi\) | ||||
−0.651672 | + | 0.758501i | \(0.725932\pi\) | |||||||
\(98\) | 2.08281i | 0.210395i | ||||||||
\(99\) | 10.3117i | 1.03636i | ||||||||
\(100\) | 4.57753 | 0.457753 | ||||||||
\(101\) | 5.58103 | 0.555334 | 0.277667 | − | 0.960677i | \(-0.410439\pi\) | ||||
0.277667 | + | 0.960677i | \(0.410439\pi\) | |||||||
\(102\) | 0.917393i | 0.0908355i | ||||||||
\(103\) | 15.0233 | 1.48029 | 0.740144 | − | 0.672448i | \(-0.234757\pi\) | ||||
0.740144 | + | 0.672448i | \(0.234757\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.240323 | 0.0234531 | ||||||||
\(106\) | 21.5366i | 2.09182i | ||||||||
\(107\) | −12.0550 | −1.16540 | −0.582701 | − | 0.812687i | \(-0.698004\pi\) | ||||
−0.582701 | + | 0.812687i | \(0.698004\pi\) | |||||||
\(108\) | −1.27635 | −0.122817 | ||||||||
\(109\) | − 14.7918i | − 1.41679i | −0.705815 | − | 0.708397i | \(-0.749419\pi\) | ||||
0.705815 | − | 0.708397i | \(-0.250581\pi\) | |||||||
\(110\) | − 18.9363i | − 1.80551i | ||||||||
\(111\) | 0.138163i | 0.0131138i | ||||||||
\(112\) | − 3.20952i | − 0.303271i | ||||||||
\(113\) | −10.4878 | −0.986608 | −0.493304 | − | 0.869857i | \(-0.664211\pi\) | ||||
−0.493304 | + | 0.869857i | \(0.664211\pi\) | |||||||
\(114\) | 0.459850 | 0.0430689 | ||||||||
\(115\) | 18.0631i | 1.68440i | ||||||||
\(116\) | −10.8671 | −1.00898 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −26.6587 | −2.45413 | ||||||||
\(119\) | 4.83445i | 0.443174i | ||||||||
\(120\) | 0.169229 | 0.0154484 | ||||||||
\(121\) | −0.880123 | −0.0800112 | ||||||||
\(122\) | 2.05077i | 0.185668i | ||||||||
\(123\) | 0.951027i | 0.0857512i | ||||||||
\(124\) | 19.7193i | 1.77085i | ||||||||
\(125\) | 8.02459i | 0.717741i | ||||||||
\(126\) | −6.23113 | −0.555114 | ||||||||
\(127\) | 5.86506 | 0.520440 | 0.260220 | − | 0.965549i | \(-0.416205\pi\) | ||||
0.260220 | + | 0.965549i | \(0.416205\pi\) | |||||||
\(128\) | − 5.55289i | − 0.490811i | ||||||||
\(129\) | −0.0411615 | −0.00362407 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.38898 | 0.121356 | 0.0606778 | − | 0.998157i | \(-0.480674\pi\) | ||||
0.0606778 | + | 0.998157i | \(0.480674\pi\) | |||||||
\(132\) | − 0.734227i | − 0.0639062i | ||||||||
\(133\) | 2.42330 | 0.210127 | ||||||||
\(134\) | −2.67780 | −0.231326 | ||||||||
\(135\) | 1.43994i | 0.123931i | ||||||||
\(136\) | 3.40429i | 0.291915i | ||||||||
\(137\) | 12.4476i | 1.06347i | 0.846910 | + | 0.531736i | \(0.178460\pi\) | ||||
−0.846910 | + | 0.531736i | \(0.821540\pi\) | |||||||
\(138\) | 1.29947i | 0.110618i | ||||||||
\(139\) | 7.98054 | 0.676900 | 0.338450 | − | 0.940984i | \(-0.390097\pi\) | ||||
0.338450 | + | 0.940984i | \(0.390097\pi\) | |||||||
\(140\) | 6.16733 | 0.521234 | ||||||||
\(141\) | 0.234092i | 0.0197141i | ||||||||
\(142\) | 25.1590 | 2.11130 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 9.60192 | 0.800160 | ||||||||
\(145\) | 12.2599i | 1.01813i | ||||||||
\(146\) | −10.7969 | −0.893556 | ||||||||
\(147\) | 0.0911085 | 0.00751450 | ||||||||
\(148\) | 3.54562i | 0.291448i | ||||||||
\(149\) | − 9.36477i | − 0.767192i | −0.923501 | − | 0.383596i | \(-0.874686\pi\) | ||||
0.923501 | − | 0.383596i | \(-0.125314\pi\) | |||||||
\(150\) | − 0.371517i | − 0.0303342i | ||||||||
\(151\) | − 12.5890i | − 1.02448i | −0.858843 | − | 0.512239i | \(-0.828816\pi\) | ||||
0.858843 | − | 0.512239i | \(-0.171184\pi\) | |||||||
\(152\) | 1.70642 | 0.138409 | ||||||||
\(153\) | −14.4632 | −1.16928 | ||||||||
\(154\) | − 7.17893i | − 0.578495i | ||||||||
\(155\) | 22.2468 | 1.78690 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.31025 | 0.503613 | 0.251807 | − | 0.967778i | \(-0.418975\pi\) | ||||
0.251807 | + | 0.967778i | \(0.418975\pi\) | |||||||
\(158\) | − 20.3018i | − 1.61513i | ||||||||
\(159\) | 0.942077 | 0.0747116 | ||||||||
\(160\) | −21.3479 | −1.68770 | ||||||||
\(161\) | 6.84789i | 0.539690i | ||||||||
\(162\) | − 18.5898i | − 1.46055i | ||||||||
\(163\) | 11.5904i | 0.907829i | 0.891045 | + | 0.453915i | \(0.149973\pi\) | ||||
−0.891045 | + | 0.453915i | \(0.850027\pi\) | |||||||
\(164\) | 24.4059i | 1.90578i | ||||||||
\(165\) | −0.828334 | −0.0644857 | ||||||||
\(166\) | −27.6301 | −2.14451 | ||||||||
\(167\) | 4.38945i | 0.339666i | 0.985473 | + | 0.169833i | \(0.0543228\pi\) | ||||
−0.985473 | + | 0.169833i | \(0.945677\pi\) | |||||||
\(168\) | 0.0641561 | 0.00494975 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 26.5603 | 2.03708 | ||||||||
\(171\) | 7.24979i | 0.554405i | ||||||||
\(172\) | −1.05631 | −0.0805432 | ||||||||
\(173\) | 19.7818 | 1.50398 | 0.751990 | − | 0.659175i | \(-0.229094\pi\) | ||||
0.751990 | + | 0.659175i | \(0.229094\pi\) | |||||||
\(174\) | 0.881983i | 0.0668630i | ||||||||
\(175\) | − 1.95781i | − 0.147996i | ||||||||
\(176\) | 11.0624i | 0.833862i | ||||||||
\(177\) | 1.16614i | 0.0876521i | ||||||||
\(178\) | 33.4088 | 2.50410 | ||||||||
\(179\) | −6.46685 | −0.483355 | −0.241678 | − | 0.970357i | \(-0.577698\pi\) | ||||
−0.241678 | + | 0.970357i | \(0.577698\pi\) | |||||||
\(180\) | 18.4508i | 1.37524i | ||||||||
\(181\) | −20.9234 | −1.55522 | −0.777612 | − | 0.628745i | \(-0.783569\pi\) | ||||
−0.777612 | + | 0.628745i | \(0.783569\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0897072 | 0.00663135 | ||||||||
\(184\) | 4.82210i | 0.355490i | ||||||||
\(185\) | 4.00007 | 0.294091 | ||||||||
\(186\) | 1.60044 | 0.117350 | ||||||||
\(187\) | − 16.6632i | − 1.21853i | ||||||||
\(188\) | 6.00743i | 0.438137i | ||||||||
\(189\) | 0.545895i | 0.0397080i | ||||||||
\(190\) | − 13.3135i | − 0.965865i | ||||||||
\(191\) | −19.6754 | −1.42366 | −0.711831 | − | 0.702351i | \(-0.752134\pi\) | ||||
−0.711831 | + | 0.702351i | \(0.752134\pi\) | |||||||
\(192\) | −0.950941 | −0.0686282 | ||||||||
\(193\) | − 14.8701i | − 1.07038i | −0.844733 | − | 0.535188i | \(-0.820241\pi\) | ||||
0.844733 | − | 0.535188i | \(-0.179759\pi\) | |||||||
\(194\) | 31.1187 | 2.23419 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.33809 | 0.167006 | ||||||||
\(197\) | 14.9442i | 1.06473i | 0.846515 | + | 0.532365i | \(0.178697\pi\) | ||||
−0.846515 | + | 0.532365i | \(0.821303\pi\) | |||||||
\(198\) | 21.4772 | 1.52632 | ||||||||
\(199\) | −9.08903 | −0.644305 | −0.322152 | − | 0.946688i | \(-0.604406\pi\) | ||||
−0.322152 | + | 0.946688i | \(0.604406\pi\) | |||||||
\(200\) | − 1.37864i | − 0.0974842i | ||||||||
\(201\) | 0.117135i | 0.00826207i | ||||||||
\(202\) | − 11.6242i | − 0.817877i | ||||||||
\(203\) | 4.64785i | 0.326215i | ||||||||
\(204\) | 1.02983 | 0.0721028 | ||||||||
\(205\) | 27.5341 | 1.92306 | ||||||||
\(206\) | − 31.2906i | − 2.18012i | ||||||||
\(207\) | −20.4868 | −1.42393 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.35253 | −0.577757 | ||||||||
\(210\) | − 0.500546i | − 0.0345410i | ||||||||
\(211\) | −3.39540 | −0.233749 | −0.116875 | − | 0.993147i | \(-0.537288\pi\) | ||||
−0.116875 | + | 0.993147i | \(0.537288\pi\) | |||||||
\(212\) | 24.1762 | 1.66043 | ||||||||
\(213\) | − 1.10053i | − 0.0754073i | ||||||||
\(214\) | 25.1083i | 1.71637i | ||||||||
\(215\) | 1.19170i | 0.0812735i | ||||||||
\(216\) | 0.384404i | 0.0261554i | ||||||||
\(217\) | 8.43394 | 0.572533 | ||||||||
\(218\) | −30.8084 | −2.08661 | ||||||||
\(219\) | 0.472289i | 0.0319144i | ||||||||
\(220\) | −21.2573 | −1.43317 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.287766 | 0.0193136 | ||||||||
\(223\) | − 5.64878i | − 0.378270i | −0.981951 | − | 0.189135i | \(-0.939432\pi\) | ||||
0.981951 | − | 0.189135i | \(-0.0605684\pi\) | |||||||
\(224\) | −8.09316 | −0.540747 | ||||||||
\(225\) | 5.85718 | 0.390478 | ||||||||
\(226\) | 21.8440i | 1.45304i | ||||||||
\(227\) | 13.2468i | 0.879222i | 0.898188 | + | 0.439611i | \(0.144884\pi\) | ||||
−0.898188 | + | 0.439611i | \(0.855116\pi\) | |||||||
\(228\) | − 0.516211i | − 0.0341869i | ||||||||
\(229\) | 1.66636i | 0.110116i | 0.998483 | + | 0.0550580i | \(0.0175344\pi\) | ||||
−0.998483 | + | 0.0550580i | \(0.982466\pi\) | |||||||
\(230\) | 37.6220 | 2.48072 | ||||||||
\(231\) | −0.314029 | −0.0206616 | ||||||||
\(232\) | 3.27289i | 0.214876i | ||||||||
\(233\) | −12.0833 | −0.791600 | −0.395800 | − | 0.918337i | \(-0.629533\pi\) | ||||
−0.395800 | + | 0.918337i | \(0.629533\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.77742 | 0.442110 | ||||||||
\(236\) | 29.9262i | 1.94803i | ||||||||
\(237\) | −0.888065 | −0.0576860 | ||||||||
\(238\) | 10.0692 | 0.652692 | ||||||||
\(239\) | 14.8457i | 0.960287i | 0.877190 | + | 0.480143i | \(0.159415\pi\) | ||||
−0.877190 | + | 0.480143i | \(0.840585\pi\) | |||||||
\(240\) | 0.771321i | 0.0497886i | ||||||||
\(241\) | − 20.4472i | − 1.31712i | −0.752528 | − | 0.658560i | \(-0.771166\pi\) | ||||
0.752528 | − | 0.658560i | \(-0.228834\pi\) | |||||||
\(242\) | 1.83313i | 0.117838i | ||||||||
\(243\) | −2.45086 | −0.157223 | ||||||||
\(244\) | 2.30213 | 0.147379 | ||||||||
\(245\) | − 2.63777i | − 0.168521i | ||||||||
\(246\) | 1.98081 | 0.126292 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 5.93895 | 0.377124 | ||||||||
\(249\) | 1.20862i | 0.0765935i | ||||||||
\(250\) | 16.7137 | 1.05707 | ||||||||
\(251\) | 6.03670 | 0.381033 | 0.190517 | − | 0.981684i | \(-0.438984\pi\) | ||||
0.190517 | + | 0.981684i | \(0.438984\pi\) | |||||||
\(252\) | 6.99486i | 0.440635i | ||||||||
\(253\) | − 23.6030i | − 1.48391i | ||||||||
\(254\) | − 12.2158i | − 0.766487i | ||||||||
\(255\) | − 1.16183i | − 0.0727566i | ||||||||
\(256\) | 9.30930 | 0.581831 | ||||||||
\(257\) | 1.99555 | 0.124479 | 0.0622396 | − | 0.998061i | \(-0.480176\pi\) | ||||
0.0622396 | + | 0.998061i | \(0.480176\pi\) | |||||||
\(258\) | 0.0857314i | 0.00533741i | ||||||||
\(259\) | 1.51646 | 0.0942283 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.9050 | −0.860696 | ||||||||
\(262\) | − 2.89298i | − 0.178729i | ||||||||
\(263\) | 12.8872 | 0.794661 | 0.397331 | − | 0.917676i | \(-0.369937\pi\) | ||||
0.397331 | + | 0.917676i | \(0.369937\pi\) | |||||||
\(264\) | −0.221130 | −0.0136096 | ||||||||
\(265\) | − 27.2749i | − 1.67549i | ||||||||
\(266\) | − 5.04727i | − 0.309468i | ||||||||
\(267\) | − 1.46141i | − 0.0894367i | ||||||||
\(268\) | 3.00600i | 0.183621i | ||||||||
\(269\) | −24.4694 | −1.49193 | −0.745963 | − | 0.665988i | \(-0.768010\pi\) | ||||
−0.745963 | + | 0.665988i | \(0.768010\pi\) | |||||||
\(270\) | 2.99912 | 0.182521 | ||||||||
\(271\) | − 14.2847i | − 0.867734i | −0.900977 | − | 0.433867i | \(-0.857149\pi\) | ||||
0.900977 | − | 0.433867i | \(-0.142851\pi\) | |||||||
\(272\) | −15.5163 | −0.940813 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.9260 | 1.56625 | ||||||||
\(275\) | 6.74809i | 0.406925i | ||||||||
\(276\) | 1.45874 | 0.0878056 | ||||||||
\(277\) | 26.5784 | 1.59694 | 0.798469 | − | 0.602035i | \(-0.205643\pi\) | ||||
0.798469 | + | 0.602035i | \(0.205643\pi\) | |||||||
\(278\) | − 16.6219i | − 0.996917i | ||||||||
\(279\) | 25.2318i | 1.51059i | ||||||||
\(280\) | − 1.85744i | − 0.111003i | ||||||||
\(281\) | 9.68696i | 0.577876i | 0.957348 | + | 0.288938i | \(0.0933021\pi\) | ||||
−0.957348 | + | 0.288938i | \(0.906698\pi\) | |||||||
\(282\) | 0.487569 | 0.0290343 | ||||||||
\(283\) | 9.01853 | 0.536096 | 0.268048 | − | 0.963406i | \(-0.413621\pi\) | ||||
0.268048 | + | 0.963406i | \(0.413621\pi\) | |||||||
\(284\) | − 28.2426i | − 1.67589i | ||||||||
\(285\) | −0.582375 | −0.0344969 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.4384 | 0.616159 | ||||||||
\(288\) | − 24.2123i | − 1.42672i | ||||||||
\(289\) | 6.37195 | 0.374820 | ||||||||
\(290\) | 25.5351 | 1.49947 | ||||||||
\(291\) | − 1.36123i | − 0.0797966i | ||||||||
\(292\) | 12.1202i | 0.709282i | ||||||||
\(293\) | − 3.36723i | − 0.196716i | −0.995151 | − | 0.0983579i | \(-0.968641\pi\) | ||||
0.995151 | − | 0.0983579i | \(-0.0313590\pi\) | |||||||
\(294\) | − 0.189762i | − 0.0110671i | ||||||||
\(295\) | 33.7619 | 1.96569 | ||||||||
\(296\) | 1.06785 | 0.0620675 | ||||||||
\(297\) | − 1.88157i | − 0.109180i | ||||||||
\(298\) | −19.5050 | −1.12989 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.417052 | −0.0240785 | ||||||||
\(301\) | 0.451785i | 0.0260405i | ||||||||
\(302\) | −26.2204 | −1.50882 | ||||||||
\(303\) | −0.508480 | −0.0292114 | ||||||||
\(304\) | 7.77764i | 0.446078i | ||||||||
\(305\) | − 2.59720i | − 0.148715i | ||||||||
\(306\) | 30.1241i | 1.72208i | ||||||||
\(307\) | − 5.27364i | − 0.300983i | −0.988611 | − | 0.150491i | \(-0.951914\pi\) | ||||
0.988611 | − | 0.150491i | \(-0.0480856\pi\) | |||||||
\(308\) | −8.05882 | −0.459194 | ||||||||
\(309\) | −1.36875 | −0.0778654 | ||||||||
\(310\) | − 46.3357i | − 2.63169i | ||||||||
\(311\) | −9.31654 | −0.528292 | −0.264146 | − | 0.964483i | \(-0.585090\pi\) | ||||
−0.264146 | + | 0.964483i | \(0.585090\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.0327 | −1.75407 | −0.877037 | − | 0.480423i | \(-0.840483\pi\) | ||||
−0.877037 | + | 0.480423i | \(0.840483\pi\) | |||||||
\(314\) | − 13.1430i | − 0.741705i | ||||||||
\(315\) | 7.89140 | 0.444630 | ||||||||
\(316\) | −22.7901 | −1.28204 | ||||||||
\(317\) | 9.22067i | 0.517884i | 0.965893 | + | 0.258942i | \(0.0833739\pi\) | ||||
−0.965893 | + | 0.258942i | \(0.916626\pi\) | |||||||
\(318\) | − 1.96217i | − 0.110033i | ||||||||
\(319\) | − 16.0200i | − 0.896948i | ||||||||
\(320\) | 27.5316i | 1.53906i | ||||||||
\(321\) | 1.09831 | 0.0613019 | ||||||||
\(322\) | 14.2628 | 0.794837 | ||||||||
\(323\) | − 11.7153i | − 0.651859i | ||||||||
\(324\) | −20.8683 | −1.15935 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 24.1406 | 1.33702 | ||||||||
\(327\) | 1.34765i | 0.0745255i | ||||||||
\(328\) | 7.35043 | 0.405860 | ||||||||
\(329\) | 2.56938 | 0.141654 | ||||||||
\(330\) | 1.72526i | 0.0949725i | ||||||||
\(331\) | 15.3888i | 0.845848i | 0.906165 | + | 0.422924i | \(0.138996\pi\) | ||||
−0.906165 | + | 0.422924i | \(0.861004\pi\) | |||||||
\(332\) | 31.0166i | 1.70225i | ||||||||
\(333\) | 4.53680i | 0.248615i | ||||||||
\(334\) | 9.14238 | 0.500249 | ||||||||
\(335\) | 3.39129 | 0.185286 | ||||||||
\(336\) | 0.292415i | 0.0159525i | ||||||||
\(337\) | −9.97038 | −0.543121 | −0.271561 | − | 0.962421i | \(-0.587540\pi\) | ||||
−0.271561 | + | 0.962421i | \(0.587540\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.955527 | 0.0518971 | ||||||||
\(340\) | − 29.8157i | − 1.61698i | ||||||||
\(341\) | −29.0697 | −1.57421 | ||||||||
\(342\) | 15.0999 | 0.816510 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0.318135i | 0.0171527i | ||||||||
\(345\) | − 1.64571i | − 0.0886018i | ||||||||
\(346\) | − 41.2016i | − 2.21501i | ||||||||
\(347\) | 18.3587 | 0.985547 | 0.492773 | − | 0.870158i | \(-0.335983\pi\) | ||||
0.492773 | + | 0.870158i | \(0.335983\pi\) | |||||||
\(348\) | 0.990084 | 0.0530741 | ||||||||
\(349\) | 3.91068i | 0.209334i | 0.994507 | + | 0.104667i | \(0.0333776\pi\) | ||||
−0.994507 | + | 0.104667i | \(0.966622\pi\) | |||||||
\(350\) | −4.07774 | −0.217964 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 27.8951 | 1.48682 | ||||||||
\(353\) | − 25.6384i | − 1.36459i | −0.731075 | − | 0.682297i | \(-0.760981\pi\) | ||||
0.731075 | − | 0.682297i | \(-0.239019\pi\) | |||||||
\(354\) | 2.42884 | 0.129091 | ||||||||
\(355\) | −31.8625 | −1.69109 | ||||||||
\(356\) | − 37.5036i | − 1.98769i | ||||||||
\(357\) | − 0.440460i | − 0.0233116i | ||||||||
\(358\) | 13.4692i | 0.711870i | ||||||||
\(359\) | 17.5435i | 0.925908i | 0.886382 | + | 0.462954i | \(0.153210\pi\) | ||||
−0.886382 | + | 0.462954i | \(0.846790\pi\) | |||||||
\(360\) | 5.55691 | 0.292875 | ||||||||
\(361\) | 13.1276 | 0.690927 | ||||||||
\(362\) | 43.5794i | 2.29048i | ||||||||
\(363\) | 0.0801867 | 0.00420871 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.6737 | 0.715713 | ||||||||
\(366\) | − 0.186843i | − 0.00976643i | ||||||||
\(367\) | 12.0095 | 0.626890 | 0.313445 | − | 0.949606i | \(-0.398517\pi\) | ||||
0.313445 | + | 0.949606i | \(0.398517\pi\) | |||||||
\(368\) | −21.9784 | −1.14571 | ||||||||
\(369\) | 31.2286i | 1.62569i | ||||||||
\(370\) | − 8.33138i | − 0.433128i | ||||||||
\(371\) | − 10.3402i | − 0.536835i | ||||||||
\(372\) | − 1.79660i | − 0.0931492i | ||||||||
\(373\) | 6.58590 | 0.341005 | 0.170503 | − | 0.985357i | \(-0.445461\pi\) | ||||
0.170503 | + | 0.985357i | \(0.445461\pi\) | |||||||
\(374\) | −34.7062 | −1.79461 | ||||||||
\(375\) | − 0.731108i | − 0.0377543i | ||||||||
\(376\) | 1.80929 | 0.0933068 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.13699 | 0.0584807 | ||||||||
\(379\) | 11.1382i | 0.572130i | 0.958210 | + | 0.286065i | \(0.0923473\pi\) | ||||
−0.958210 | + | 0.286065i | \(0.907653\pi\) | |||||||
\(380\) | −14.9453 | −0.766678 | ||||||||
\(381\) | −0.534357 | −0.0273759 | ||||||||
\(382\) | 40.9801i | 2.09672i | ||||||||
\(383\) | − 5.16337i | − 0.263836i | −0.991261 | − | 0.131918i | \(-0.957886\pi\) | ||||
0.991261 | − | 0.131918i | \(-0.0421135\pi\) | |||||||
\(384\) | 0.505916i | 0.0258174i | ||||||||
\(385\) | 9.09173i | 0.463358i | ||||||||
\(386\) | −30.9716 | −1.57642 | ||||||||
\(387\) | −1.35161 | −0.0687060 | ||||||||
\(388\) | − 34.9327i | − 1.77344i | ||||||||
\(389\) | 3.90202 | 0.197840 | 0.0989200 | − | 0.995095i | \(-0.468461\pi\) | ||||
0.0989200 | + | 0.995095i | \(0.468461\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.1058 | 1.67423 | ||||||||
\(392\) | − 0.704173i | − 0.0355661i | ||||||||
\(393\) | −0.126548 | −0.00638349 | ||||||||
\(394\) | 31.1259 | 1.56810 | ||||||||
\(395\) | 25.7112i | 1.29367i | ||||||||
\(396\) | − 24.1096i | − 1.21155i | ||||||||
\(397\) | 6.09215i | 0.305756i | 0.988245 | + | 0.152878i | \(0.0488542\pi\) | ||||
−0.988245 | + | 0.152878i | \(0.951146\pi\) | |||||||
\(398\) | 18.9307i | 0.948911i | ||||||||
\(399\) | −0.220783 | −0.0110530 | ||||||||
\(400\) | 6.28363 | 0.314181 | ||||||||
\(401\) | − 14.5534i | − 0.726761i | −0.931641 | − | 0.363380i | \(-0.881623\pi\) | ||||
0.931641 | − | 0.363380i | \(-0.118377\pi\) | |||||||
\(402\) | 0.243970 | 0.0121681 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −13.0489 | −0.649210 | ||||||||
\(405\) | 23.5430i | 1.16986i | ||||||||
\(406\) | 9.68058 | 0.480439 | ||||||||
\(407\) | −5.22687 | −0.259086 | ||||||||
\(408\) | − 0.310160i | − 0.0153552i | ||||||||
\(409\) | 29.5278i | 1.46006i | 0.683417 | + | 0.730028i | \(0.260493\pi\) | ||||
−0.683417 | + | 0.730028i | \(0.739507\pi\) | |||||||
\(410\) | − 57.3481i | − 2.83222i | ||||||||
\(411\) | − 1.13408i | − 0.0559403i | ||||||||
\(412\) | −35.1258 | −1.73052 | ||||||||
\(413\) | 12.7994 | 0.629818 | ||||||||
\(414\) | 42.6701i | 2.09712i | ||||||||
\(415\) | 34.9920 | 1.71769 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.727095 | −0.0356060 | ||||||||
\(418\) | 17.3967i | 0.850901i | ||||||||
\(419\) | 31.8847 | 1.55767 | 0.778835 | − | 0.627229i | \(-0.215811\pi\) | ||||
0.778835 | + | 0.627229i | \(0.215811\pi\) | |||||||
\(420\) | −0.561896 | −0.0274177 | ||||||||
\(421\) | − 16.0318i | − 0.781344i | −0.920530 | − | 0.390672i | \(-0.872243\pi\) | ||||
0.920530 | − | 0.390672i | \(-0.127757\pi\) | |||||||
\(422\) | 7.07197i | 0.344258i | ||||||||
\(423\) | 7.68681i | 0.373745i | ||||||||
\(424\) | − 7.28126i | − 0.353609i | ||||||||
\(425\) | −9.46494 | −0.459117 | ||||||||
\(426\) | −2.29220 | −0.111057 | ||||||||
\(427\) | − 0.984619i | − 0.0476491i | ||||||||
\(428\) | 28.1857 | 1.36241 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.48209 | 0.119697 | ||||||||
\(431\) | 20.3260i | 0.979069i | 0.871984 | + | 0.489535i | \(0.162833\pi\) | ||||
−0.871984 | + | 0.489535i | \(0.837167\pi\) | |||||||
\(432\) | −1.75206 | −0.0842960 | ||||||||
\(433\) | 13.9077 | 0.668364 | 0.334182 | − | 0.942509i | \(-0.391540\pi\) | ||||
0.334182 | + | 0.942509i | \(0.391540\pi\) | |||||||
\(434\) | − 17.5663i | − 0.843208i | ||||||||
\(435\) | − 1.11698i | − 0.0535553i | ||||||||
\(436\) | 34.5844i | 1.65629i | ||||||||
\(437\) | − 16.5945i | − 0.793823i | ||||||||
\(438\) | 0.983688 | 0.0470024 | ||||||||
\(439\) | 11.3492 | 0.541669 | 0.270835 | − | 0.962626i | \(-0.412700\pi\) | ||||
0.270835 | + | 0.962626i | \(0.412700\pi\) | |||||||
\(440\) | 6.40215i | 0.305210i | ||||||||
\(441\) | 2.99170 | 0.142462 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.8184 | −1.03662 | −0.518311 | − | 0.855192i | \(-0.673439\pi\) | ||||
−0.518311 | + | 0.855192i | \(0.673439\pi\) | |||||||
\(444\) | − 0.323036i | − 0.0153306i | ||||||||
\(445\) | −42.3105 | −2.00571 | ||||||||
\(446\) | −11.7653 | −0.557104 | ||||||||
\(447\) | 0.853210i | 0.0403554i | ||||||||
\(448\) | 10.4375i | 0.493123i | ||||||||
\(449\) | 11.0754i | 0.522680i | 0.965247 | + | 0.261340i | \(0.0841644\pi\) | ||||
−0.965247 | + | 0.261340i | \(0.915836\pi\) | |||||||
\(450\) | − 12.1994i | − 0.575084i | ||||||||
\(451\) | −35.9786 | −1.69417 | ||||||||
\(452\) | 24.5214 | 1.15339 | ||||||||
\(453\) | 1.14696i | 0.0538891i | ||||||||
\(454\) | 27.5906 | 1.29489 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.155470 | −0.00728053 | ||||||||
\(457\) | 6.02903i | 0.282026i | 0.990008 | + | 0.141013i | \(0.0450359\pi\) | ||||
−0.990008 | + | 0.141013i | \(0.954964\pi\) | |||||||
\(458\) | 3.47070 | 0.162175 | ||||||||
\(459\) | 2.63910 | 0.123183 | ||||||||
\(460\) | − 42.2332i | − 1.96913i | ||||||||
\(461\) | − 31.2543i | − 1.45566i | −0.685759 | − | 0.727829i | \(-0.740529\pi\) | ||||
0.685759 | − | 0.727829i | \(-0.259471\pi\) | |||||||
\(462\) | 0.654061i | 0.0304297i | ||||||||
\(463\) | 16.0896i | 0.747746i | 0.927480 | + | 0.373873i | \(0.121970\pi\) | ||||
−0.927480 | + | 0.373873i | \(0.878030\pi\) | |||||||
\(464\) | −14.9174 | −0.692521 | ||||||||
\(465\) | −2.02687 | −0.0939938 | ||||||||
\(466\) | 25.1671i | 1.16584i | ||||||||
\(467\) | 5.18604 | 0.239981 | 0.119991 | − | 0.992775i | \(-0.461714\pi\) | ||||
0.119991 | + | 0.992775i | \(0.461714\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.28567 | 0.0593665 | ||||||||
\(470\) | − 14.1161i | − 0.651125i | ||||||||
\(471\) | −0.574918 | −0.0264908 | ||||||||
\(472\) | 9.01299 | 0.414857 | ||||||||
\(473\) | − 1.55719i | − 0.0715998i | ||||||||
\(474\) | 1.84967i | 0.0849581i | ||||||||
\(475\) | 4.74436i | 0.217686i | ||||||||
\(476\) | − 11.3034i | − 0.518090i | ||||||||
\(477\) | 30.9347 | 1.41640 | ||||||||
\(478\) | 30.9207 | 1.41428 | ||||||||
\(479\) | − 4.15275i | − 0.189744i | −0.995489 | − | 0.0948720i | \(-0.969756\pi\) | ||||
0.995489 | − | 0.0948720i | \(-0.0302442\pi\) | |||||||
\(480\) | 1.94497 | 0.0887754 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −42.5876 | −1.93981 | ||||||||
\(483\) | − 0.623901i | − 0.0283885i | ||||||||
\(484\) | 2.05780 | 0.0935366 | ||||||||
\(485\) | −39.4101 | −1.78952 | ||||||||
\(486\) | 5.10467i | 0.231553i | ||||||||
\(487\) | − 6.52104i | − 0.295496i | −0.989025 | − | 0.147748i | \(-0.952797\pi\) | ||||
0.989025 | − | 0.147748i | \(-0.0472025\pi\) | |||||||
\(488\) | − 0.693342i | − 0.0313861i | ||||||||
\(489\) | − 1.05598i | − 0.0477532i | ||||||||
\(490\) | −5.49396 | −0.248192 | ||||||||
\(491\) | −18.9254 | −0.854091 | −0.427046 | − | 0.904230i | \(-0.640446\pi\) | ||||
−0.427046 | + | 0.904230i | \(0.640446\pi\) | |||||||
\(492\) | − 2.22358i | − 0.100247i | ||||||||
\(493\) | 22.4698 | 1.01199 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −27.1997 | −1.22254 | ||||||||
\(496\) | 27.0689i | 1.21543i | ||||||||
\(497\) | −12.0794 | −0.541834 | ||||||||
\(498\) | 2.51733 | 0.112804 | ||||||||
\(499\) | 36.1116i | 1.61658i | 0.588785 | + | 0.808290i | \(0.299606\pi\) | ||||
−0.588785 | + | 0.808290i | \(0.700394\pi\) | |||||||
\(500\) | − 18.7622i | − 0.839071i | ||||||||
\(501\) | − 0.399916i | − 0.0178669i | ||||||||
\(502\) | − 12.5733i | − 0.561173i | ||||||||
\(503\) | 13.8545 | 0.617743 | 0.308872 | − | 0.951104i | \(-0.400049\pi\) | ||||
0.308872 | + | 0.951104i | \(0.400049\pi\) | |||||||
\(504\) | 2.10667 | 0.0938386 | ||||||||
\(505\) | 14.7215i | 0.655096i | ||||||||
\(506\) | −49.1605 | −2.18545 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.7130 | −0.608417 | ||||||||
\(509\) | 10.1964i | 0.451948i | 0.974133 | + | 0.225974i | \(0.0725564\pi\) | ||||
−0.974133 | + | 0.225974i | \(0.927444\pi\) | |||||||
\(510\) | −2.41987 | −0.107154 | ||||||||
\(511\) | 5.18381 | 0.229318 | ||||||||
\(512\) | − 30.4953i | − 1.34771i | ||||||||
\(513\) | − 1.32287i | − 0.0584061i | ||||||||
\(514\) | − 4.15635i | − 0.183329i | ||||||||
\(515\) | 39.6279i | 1.74621i | ||||||||
\(516\) | 0.0962392 | 0.00423669 | ||||||||
\(517\) | −8.85602 | −0.389487 | ||||||||
\(518\) | − 3.15850i | − 0.138776i | ||||||||
\(519\) | −1.80229 | −0.0791116 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.6356 | −1.78028 | −0.890139 | − | 0.455688i | \(-0.849393\pi\) | ||||
−0.890139 | + | 0.455688i | \(0.849393\pi\) | |||||||
\(522\) | 28.9614i | 1.26760i | ||||||||
\(523\) | 25.0743 | 1.09642 | 0.548210 | − | 0.836340i | \(-0.315309\pi\) | ||||
0.548210 | + | 0.836340i | \(0.315309\pi\) | |||||||
\(524\) | −3.24755 | −0.141870 | ||||||||
\(525\) | 0.178373i | 0.00778484i | ||||||||
\(526\) | − 26.8416i | − 1.17035i | ||||||||
\(527\) | − 40.7735i | − 1.77612i | ||||||||
\(528\) | − 1.00788i | − 0.0438624i | ||||||||
\(529\) | 23.8936 | 1.03885 | ||||||||
\(530\) | −56.8085 | −2.46760 | ||||||||
\(531\) | 38.2920i | 1.66173i | ||||||||
\(532\) | −5.66589 | −0.245648 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.04383 | −0.131719 | ||||||||
\(535\) | − 31.7983i | − 1.37476i | ||||||||
\(536\) | 0.905331 | 0.0391043 | ||||||||
\(537\) | 0.589185 | 0.0254252 | ||||||||
\(538\) | 50.9650i | 2.19726i | ||||||||
\(539\) | 3.44676i | 0.148462i | ||||||||
\(540\) | − 3.36671i | − 0.144880i | ||||||||
\(541\) | − 22.0722i | − 0.948959i | −0.880267 | − | 0.474479i | \(-0.842636\pi\) | ||||
0.880267 | − | 0.474479i | \(-0.157364\pi\) | |||||||
\(542\) | −29.7523 | −1.27797 | ||||||||
\(543\) | 1.90630 | 0.0818071 | ||||||||
\(544\) | 39.1260i | 1.67751i | ||||||||
\(545\) | 39.0172 | 1.67131 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.9107 | −0.552022 | −0.276011 | − | 0.961154i | \(-0.589013\pi\) | ||||
−0.276011 | + | 0.961154i | \(0.589013\pi\) | |||||||
\(548\) | − 29.1036i | − 1.24325i | ||||||||
\(549\) | 2.94568 | 0.125719 | ||||||||
\(550\) | 14.0550 | 0.599306 | ||||||||
\(551\) | − 11.2631i | − 0.479826i | ||||||||
\(552\) | − 0.439334i | − 0.0186993i | ||||||||
\(553\) | 9.74733i | 0.414499i | ||||||||
\(554\) | − 55.3576i | − 2.35192i | ||||||||
\(555\) | −0.364440 | −0.0154696 | ||||||||
\(556\) | −18.6592 | −0.791326 | ||||||||
\(557\) | − 23.4061i | − 0.991746i | −0.868395 | − | 0.495873i | \(-0.834848\pi\) | ||||
0.868395 | − | 0.495873i | \(-0.165152\pi\) | |||||||
\(558\) | 52.5530 | 2.22475 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8.46596 | 0.357752 | ||||||||
\(561\) | 1.51816i | 0.0640967i | ||||||||
\(562\) | 20.1761 | 0.851077 | ||||||||
\(563\) | −42.3634 | −1.78541 | −0.892703 | − | 0.450645i | \(-0.851194\pi\) | ||||
−0.892703 | + | 0.450645i | \(0.851194\pi\) | |||||||
\(564\) | − 0.547328i | − 0.0230467i | ||||||||
\(565\) | − 27.6643i | − 1.16385i | ||||||||
\(566\) | − 18.7839i | − 0.789545i | ||||||||
\(567\) | 8.92536i | 0.374830i | ||||||||
\(568\) | −8.50596 | −0.356902 | ||||||||
\(569\) | −24.3356 | −1.02020 | −0.510101 | − | 0.860115i | \(-0.670392\pi\) | ||||
−0.510101 | + | 0.860115i | \(0.670392\pi\) | |||||||
\(570\) | 1.21298i | 0.0508059i | ||||||||
\(571\) | −9.71777 | −0.406676 | −0.203338 | − | 0.979109i | \(-0.565179\pi\) | ||||
−0.203338 | + | 0.979109i | \(0.565179\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.79260 | 0.0748868 | ||||||||
\(574\) | − 21.7412i | − 0.907459i | ||||||||
\(575\) | −13.4069 | −0.559105 | ||||||||
\(576\) | −31.2257 | −1.30107 | ||||||||
\(577\) | 4.39680i | 0.183041i | 0.995803 | + | 0.0915206i | \(0.0291727\pi\) | ||||
−0.995803 | + | 0.0915206i | \(0.970827\pi\) | |||||||
\(578\) | − 13.2715i | − 0.552023i | ||||||||
\(579\) | 1.35480i | 0.0563034i | ||||||||
\(580\) | − 28.6648i | − 1.19024i | ||||||||
\(581\) | 13.2658 | 0.550357 | ||||||||
\(582\) | −2.83518 | −0.117522 | ||||||||
\(583\) | 35.6400i | 1.47606i | ||||||||
\(584\) | 3.65030 | 0.151050 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.01330 | −0.289717 | ||||||||
\(587\) | − 13.2174i | − 0.545540i | −0.962079 | − | 0.272770i | \(-0.912060\pi\) | ||||
0.962079 | − | 0.272770i | \(-0.0879397\pi\) | |||||||
\(588\) | −0.213020 | −0.00878479 | ||||||||
\(589\) | −20.4380 | −0.842133 | ||||||||
\(590\) | − 70.3194i | − 2.89501i | ||||||||
\(591\) | − 1.36154i | − 0.0560065i | ||||||||
\(592\) | 4.86711i | 0.200037i | ||||||||
\(593\) | − 5.35235i | − 0.219795i | −0.993943 | − | 0.109897i | \(-0.964948\pi\) | ||||
0.993943 | − | 0.109897i | \(-0.0350522\pi\) | |||||||
\(594\) | −3.91894 | −0.160796 | ||||||||
\(595\) | −12.7522 | −0.522787 | ||||||||
\(596\) | 21.8957i | 0.896881i | ||||||||
\(597\) | 0.828088 | 0.0338914 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.81933 | 0.401207 | 0.200604 | − | 0.979673i | \(-0.435710\pi\) | ||||
0.200604 | + | 0.979673i | \(0.435710\pi\) | |||||||
\(600\) | 0.125605i | 0.00512782i | ||||||||
\(601\) | −28.2788 | −1.15352 | −0.576758 | − | 0.816915i | \(-0.695682\pi\) | ||||
−0.576758 | + | 0.816915i | \(0.695682\pi\) | |||||||
\(602\) | 0.940982 | 0.0383516 | ||||||||
\(603\) | 3.84633i | 0.156635i | ||||||||
\(604\) | 29.4342i | 1.19766i | ||||||||
\(605\) | − 2.32156i | − 0.0943848i | ||||||||
\(606\) | 1.05907i | 0.0430216i | ||||||||
\(607\) | 8.70338 | 0.353259 | 0.176630 | − | 0.984277i | \(-0.443480\pi\) | ||||
0.176630 | + | 0.984277i | \(0.443480\pi\) | |||||||
\(608\) | 19.6122 | 0.795379 | ||||||||
\(609\) | − 0.423459i | − 0.0171594i | ||||||||
\(610\) | −5.40946 | −0.219023 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 33.8163 | 1.36694 | ||||||||
\(613\) | − 28.8798i | − 1.16644i | −0.812313 | − | 0.583222i | \(-0.801792\pi\) | ||||
0.812313 | − | 0.583222i | \(-0.198208\pi\) | |||||||
\(614\) | −10.9840 | −0.443277 | ||||||||
\(615\) | −2.50859 | −0.101156 | ||||||||
\(616\) | 2.42711i | 0.0977911i | ||||||||
\(617\) | 24.5573i | 0.988641i | 0.869280 | + | 0.494320i | \(0.164583\pi\) | ||||
−0.869280 | + | 0.494320i | \(0.835417\pi\) | |||||||
\(618\) | 2.85084i | 0.114678i | ||||||||
\(619\) | 16.7008i | 0.671262i | 0.941994 | + | 0.335631i | \(0.108949\pi\) | ||||
−0.941994 | + | 0.335631i | \(0.891051\pi\) | |||||||
\(620\) | −52.0149 | −2.08897 | ||||||||
\(621\) | 3.73823 | 0.150010 | ||||||||
\(622\) | 19.4046i | 0.778052i | ||||||||
\(623\) | −16.0403 | −0.642641 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.9560 | −1.23824 | ||||||||
\(626\) | 64.6352i | 2.58334i | ||||||||
\(627\) | 0.760987 | 0.0303909 | ||||||||
\(628\) | −14.7539 | −0.588746 | ||||||||
\(629\) | − 7.33126i | − 0.292317i | ||||||||
\(630\) | − 16.4363i | − 0.654837i | ||||||||
\(631\) | − 26.7848i | − 1.06629i | −0.846025 | − | 0.533143i | \(-0.821011\pi\) | ||||
0.846025 | − | 0.533143i | \(-0.178989\pi\) | |||||||
\(632\) | 6.86380i | 0.273027i | ||||||||
\(633\) | 0.309350 | 0.0122956 | ||||||||
\(634\) | 19.2049 | 0.762723 | ||||||||
\(635\) | 15.4707i | 0.613934i | ||||||||
\(636\) | −2.20266 | −0.0873411 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −33.3666 | −1.32100 | ||||||||
\(639\) | − 36.1378i | − 1.42959i | ||||||||
\(640\) | 14.6472 | 0.578982 | ||||||||
\(641\) | −2.23814 | −0.0884012 | −0.0442006 | − | 0.999023i | \(-0.514074\pi\) | ||||
−0.0442006 | + | 0.999023i | \(0.514074\pi\) | |||||||
\(642\) | − 2.28758i | − 0.0902834i | ||||||||
\(643\) | − 34.6442i | − 1.36623i | −0.730309 | − | 0.683117i | \(-0.760624\pi\) | ||||
0.730309 | − | 0.683117i | \(-0.239376\pi\) | |||||||
\(644\) | − 16.0110i | − 0.630921i | ||||||||
\(645\) | − 0.108574i | − 0.00427511i | ||||||||
\(646\) | −24.4008 | −0.960037 | ||||||||
\(647\) | 19.0383 | 0.748473 | 0.374236 | − | 0.927333i | \(-0.377905\pi\) | ||||
0.374236 | + | 0.927333i | \(0.377905\pi\) | |||||||
\(648\) | 6.28499i | 0.246898i | ||||||||
\(649\) | −44.1164 | −1.73172 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.768404 | −0.0301161 | ||||||||
\(652\) | − 27.0994i | − 1.06129i | ||||||||
\(653\) | 0.112802 | 0.00441429 | 0.00220715 | − | 0.999998i | \(-0.499297\pi\) | ||||
0.00220715 | + | 0.999998i | \(0.499297\pi\) | |||||||
\(654\) | 2.80691 | 0.109759 | ||||||||
\(655\) | 3.66380i | 0.143157i | ||||||||
\(656\) | 33.5023i | 1.30804i | ||||||||
\(657\) | 15.5084i | 0.605041i | ||||||||
\(658\) | − 5.35152i | − 0.208624i | ||||||||
\(659\) | 8.44907 | 0.329129 | 0.164565 | − | 0.986366i | \(-0.447378\pi\) | ||||
0.164565 | + | 0.986366i | \(0.447378\pi\) | |||||||
\(660\) | 1.93672 | 0.0753867 | ||||||||
\(661\) | 19.0576i | 0.741256i | 0.928781 | + | 0.370628i | \(0.120858\pi\) | ||||
−0.928781 | + | 0.370628i | \(0.879142\pi\) | |||||||
\(662\) | 32.0520 | 1.24574 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.34139 | 0.362516 | ||||||||
\(665\) | 6.39210i | 0.247875i | ||||||||
\(666\) | 9.44927 | 0.366152 | ||||||||
\(667\) | 31.8280 | 1.23238 | ||||||||
\(668\) | − 10.2629i | − 0.397084i | ||||||||
\(669\) | 0.514652i | 0.0198976i | ||||||||
\(670\) | − 7.06340i | − 0.272883i | ||||||||
\(671\) | 3.39374i | 0.131014i | ||||||||
\(672\) | 0.737356 | 0.0284441 | ||||||||
\(673\) | −4.66145 | −0.179686 | −0.0898428 | − | 0.995956i | \(-0.528636\pi\) | ||||
−0.0898428 | + | 0.995956i | \(0.528636\pi\) | |||||||
\(674\) | 20.7664i | 0.799891i | ||||||||
\(675\) | −1.06876 | −0.0411365 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.2159 | −0.546360 | −0.273180 | − | 0.961963i | \(-0.588075\pi\) | ||||
−0.273180 | + | 0.961963i | \(0.588075\pi\) | |||||||
\(678\) | − 1.99018i | − 0.0764323i | ||||||||
\(679\) | −14.9407 | −0.573373 | ||||||||
\(680\) | −8.97972 | −0.344357 | ||||||||
\(681\) | − 1.20690i | − 0.0462484i | ||||||||
\(682\) | 60.5467i | 2.31845i | ||||||||
\(683\) | 47.4878i | 1.81707i | 0.417807 | + | 0.908536i | \(0.362799\pi\) | ||||
−0.417807 | + | 0.908536i | \(0.637201\pi\) | |||||||
\(684\) | − 16.9507i | − 0.648124i | ||||||||
\(685\) | −32.8339 | −1.25452 | ||||||||
\(686\) | −2.08281 | −0.0795220 | ||||||||
\(687\) | − 0.151819i | − 0.00579227i | ||||||||
\(688\) | −1.45001 | −0.0552813 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −3.42769 | −0.130490 | ||||||||
\(691\) | 6.11055i | 0.232456i | 0.993223 | + | 0.116228i | \(0.0370804\pi\) | ||||
−0.993223 | + | 0.116228i | \(0.962920\pi\) | |||||||
\(692\) | −46.2515 | −1.75822 | ||||||||
\(693\) | −10.3117 | −0.391707 | ||||||||
\(694\) | − 38.2376i | − 1.45148i | ||||||||
\(695\) | 21.0508i | 0.798502i | ||||||||
\(696\) | − 0.298188i | − 0.0113028i | ||||||||
\(697\) | − 50.4640i | − 1.91146i | ||||||||
\(698\) | 8.14519 | 0.308300 | ||||||||
\(699\) | 1.10089 | 0.0416394 | ||||||||
\(700\) | 4.57753i | 0.173014i | ||||||||
\(701\) | −46.9469 | −1.77316 | −0.886580 | − | 0.462575i | \(-0.846926\pi\) | ||||
−0.886580 | + | 0.462575i | \(0.846926\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.67484 | −0.138599 | ||||||||
\(704\) | − 35.9753i | − 1.35587i | ||||||||
\(705\) | −0.617481 | −0.0232557 | ||||||||
\(706\) | −53.3998 | −2.00973 | ||||||||
\(707\) | 5.58103i | 0.209896i | ||||||||
\(708\) | − 2.72653i | − 0.102469i | ||||||||
\(709\) | − 42.2551i | − 1.58692i | −0.608620 | − | 0.793462i | \(-0.708276\pi\) | ||||
0.608620 | − | 0.793462i | \(-0.291724\pi\) | |||||||
\(710\) | 66.3635i | 2.49058i | ||||||||
\(711\) | −29.1611 | −1.09363 | ||||||||
\(712\) | −11.2951 | −0.423303 | ||||||||
\(713\) | − 57.7547i | − 2.16293i | ||||||||
\(714\) | −0.917393 | −0.0343326 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.1201 | 0.565063 | ||||||||
\(717\) | − 1.35257i | − 0.0505125i | ||||||||
\(718\) | 36.5396 | 1.36365 | ||||||||
\(719\) | −29.1865 | −1.08847 | −0.544237 | − | 0.838932i | \(-0.683181\pi\) | ||||
−0.544237 | + | 0.838932i | \(0.683181\pi\) | |||||||
\(720\) | 25.3276i | 0.943904i | ||||||||
\(721\) | 15.0233i | 0.559496i | ||||||||
\(722\) | − 27.3423i | − 1.01757i | ||||||||
\(723\) | 1.86291i | 0.0692825i | ||||||||
\(724\) | 48.9207 | 1.81812 | ||||||||
\(725\) | −9.09960 | −0.337951 | ||||||||
\(726\) | − 0.167013i | − 0.00619845i | ||||||||
\(727\) | 21.5693 | 0.799961 | 0.399981 | − | 0.916524i | \(-0.369017\pi\) | ||||
0.399981 | + | 0.916524i | \(0.369017\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.5528 | −0.983437 | ||||||||
\(730\) | − 28.4796i | − 1.05408i | ||||||||
\(731\) | 2.18413 | 0.0807831 | ||||||||
\(732\) | −0.209743 | −0.00775234 | ||||||||
\(733\) | − 7.73466i | − 0.285686i | −0.989745 | − | 0.142843i | \(-0.954376\pi\) | ||||
0.989745 | − | 0.142843i | \(-0.0456244\pi\) | |||||||
\(734\) | − 25.0135i | − 0.923263i | ||||||||
\(735\) | 0.240323i | 0.00886444i | ||||||||
\(736\) | 55.4211i | 2.04285i | ||||||||
\(737\) | −4.43138 | −0.163232 | ||||||||
\(738\) | 65.0431 | 2.39427 | ||||||||
\(739\) | 17.0608i | 0.627591i | 0.949491 | + | 0.313796i | \(0.101601\pi\) | ||||
−0.949491 | + | 0.313796i | \(0.898399\pi\) | |||||||
\(740\) | −9.35251 | −0.343805 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −21.5366 | −0.790633 | ||||||||
\(743\) | 42.3773i | 1.55467i | 0.629085 | + | 0.777337i | \(0.283430\pi\) | ||||
−0.629085 | + | 0.777337i | \(0.716570\pi\) | |||||||
\(744\) | −0.541089 | −0.0198373 | ||||||||
\(745\) | 24.7021 | 0.905014 | ||||||||
\(746\) | − 13.7172i | − 0.502221i | ||||||||
\(747\) | 39.6872i | 1.45208i | ||||||||
\(748\) | 38.9600i | 1.42452i | ||||||||
\(749\) | − 12.0550i | − 0.440480i | ||||||||
\(750\) | −1.52276 | −0.0556033 | ||||||||
\(751\) | −13.6368 | −0.497615 | −0.248807 | − | 0.968553i | \(-0.580039\pi\) | ||||
−0.248807 | + | 0.968553i | \(0.580039\pi\) | |||||||
\(752\) | 8.24647i | 0.300718i | ||||||||
\(753\) | −0.549995 | −0.0200429 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.2068 | 1.20852 | ||||||||
\(756\) | − 1.27635i | − 0.0464204i | ||||||||
\(757\) | −3.57825 | −0.130054 | −0.0650269 | − | 0.997884i | \(-0.520713\pi\) | ||||
−0.0650269 | + | 0.997884i | \(0.520713\pi\) | |||||||
\(758\) | 23.1987 | 0.842614 | ||||||||
\(759\) | 2.15044i | 0.0780558i | ||||||||
\(760\) | 4.50114i | 0.163274i | ||||||||
\(761\) | 10.5161i | 0.381207i | 0.981667 | + | 0.190603i | \(0.0610444\pi\) | ||||
−0.981667 | + | 0.190603i | \(0.938956\pi\) | |||||||
\(762\) | 1.11296i | 0.0403184i | ||||||||
\(763\) | 14.7918 | 0.535497 | ||||||||
\(764\) | 46.0028 | 1.66432 | ||||||||
\(765\) | − 38.1506i | − 1.37934i | ||||||||
\(766\) | −10.7543 | −0.388569 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.848157 | −0.0306052 | ||||||||
\(769\) | 19.9912i | 0.720901i | 0.932778 | + | 0.360451i | \(0.117377\pi\) | ||||
−0.932778 | + | 0.360451i | \(0.882623\pi\) | |||||||
\(770\) | 18.9363 | 0.682418 | ||||||||
\(771\) | −0.181812 | −0.00654779 | ||||||||
\(772\) | 34.7677i | 1.25132i | ||||||||
\(773\) | − 44.5679i | − 1.60300i | −0.597998 | − | 0.801498i | \(-0.704037\pi\) | ||||
0.597998 | − | 0.801498i | \(-0.295963\pi\) | |||||||
\(774\) | 2.81513i | 0.101188i | ||||||||
\(775\) | 16.5120i | 0.593130i | ||||||||
\(776\) | −10.5209 | −0.377677 | ||||||||
\(777\) | −0.138163 | −0.00495655 | ||||||||
\(778\) | − 8.12715i | − 0.291372i | ||||||||
\(779\) | −25.2954 | −0.906302 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.6346 | 1.48980 | ||||||||
\(782\) | − 68.9531i | − 2.46576i | ||||||||
\(783\) | 2.53724 | 0.0906734 | ||||||||
\(784\) | 3.20952 | 0.114626 | ||||||||
\(785\) | 16.6450i | 0.594085i | ||||||||
\(786\) | 0.263575i | 0.00940140i | ||||||||
\(787\) | − 37.0091i | − 1.31923i | −0.751602 | − | 0.659617i | \(-0.770719\pi\) | ||||
0.751602 | − | 0.659617i | \(-0.229281\pi\) | |||||||
\(788\) | − 34.9409i | − 1.24472i | ||||||||
\(789\) | −1.17414 | −0.0418004 | ||||||||
\(790\) | 53.5514 | 1.90527 | ||||||||
\(791\) | − 10.4878i | − 0.372903i | ||||||||
\(792\) | −7.26118 | −0.258015 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 12.6888 | 0.450308 | ||||||||
\(795\) | 2.48498i | 0.0881331i | ||||||||
\(796\) | 21.2510 | 0.753220 | ||||||||
\(797\) | 5.86398 | 0.207713 | 0.103856 | − | 0.994592i | \(-0.466882\pi\) | ||||
0.103856 | + | 0.994592i | \(0.466882\pi\) | |||||||
\(798\) | 0.459850i | 0.0162785i | ||||||||
\(799\) | − 12.4215i | − 0.439443i | ||||||||
\(800\) | − 15.8449i | − 0.560200i | ||||||||
\(801\) | − 47.9877i | − 1.69556i | ||||||||
\(802\) | −30.3119 | −1.07035 | ||||||||
\(803\) | −17.8673 | −0.630524 | ||||||||
\(804\) | − 0.273872i | − 0.00965873i | ||||||||
\(805\) | −18.0631 | −0.636642 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.22937 | 0.0784775 | ||||||||
\(808\) | 3.93001i | 0.138257i | ||||||||
\(809\) | 1.17991 | 0.0414835 | 0.0207417 | − | 0.999785i | \(-0.493397\pi\) | ||||
0.0207417 | + | 0.999785i | \(0.493397\pi\) | |||||||
\(810\) | 49.0356 | 1.72293 | ||||||||
\(811\) | 24.4596i | 0.858894i | 0.903092 | + | 0.429447i | \(0.141292\pi\) | ||||
−0.903092 | + | 0.429447i | \(0.858708\pi\) | |||||||
\(812\) | − 10.8671i | − 0.381360i | ||||||||
\(813\) | 1.30146i | 0.0456441i | ||||||||
\(814\) | 10.8866i | 0.381574i | ||||||||
\(815\) | −30.5727 | −1.07092 | ||||||||
\(816\) | 1.41366 | 0.0494882 | ||||||||
\(817\) | − 1.09481i | − 0.0383026i | ||||||||
\(818\) | 61.5008 | 2.15032 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −64.3770 | −2.24814 | ||||||||
\(821\) | 45.2922i | 1.58071i | 0.612651 | + | 0.790354i | \(0.290103\pi\) | ||||
−0.612651 | + | 0.790354i | \(0.709897\pi\) | |||||||
\(822\) | −2.36208 | −0.0823870 | ||||||||
\(823\) | 28.5033 | 0.993563 | 0.496781 | − | 0.867876i | \(-0.334515\pi\) | ||||
0.496781 | + | 0.867876i | \(0.334515\pi\) | |||||||
\(824\) | 10.5790i | 0.368536i | ||||||||
\(825\) | − 0.614808i | − 0.0214049i | ||||||||
\(826\) | − 26.6587i | − 0.927575i | ||||||||
\(827\) | 0.594562i | 0.0206749i | 0.999947 | + | 0.0103375i | \(0.00329058\pi\) | ||||
−0.999947 | + | 0.0103375i | \(0.996709\pi\) | |||||||
\(828\) | 47.9000 | 1.66464 | ||||||||
\(829\) | 40.7651 | 1.41583 | 0.707915 | − | 0.706298i | \(-0.249636\pi\) | ||||
0.707915 | + | 0.706298i | \(0.249636\pi\) | |||||||
\(830\) | − 72.8816i | − 2.52976i | ||||||||
\(831\) | −2.42151 | −0.0840014 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.83445 | −0.167504 | ||||||||
\(834\) | 1.51440i | 0.0524393i | ||||||||
\(835\) | −11.5783 | −0.400685 | ||||||||
\(836\) | 19.5290 | 0.675423 | ||||||||
\(837\) | − 4.60404i | − 0.159139i | ||||||||
\(838\) | − 66.4097i | − 2.29408i | ||||||||
\(839\) | 48.1410i | 1.66201i | 0.556264 | + | 0.831005i | \(0.312234\pi\) | ||||
−0.556264 | + | 0.831005i | \(0.687766\pi\) | |||||||
\(840\) | 0.169229i | 0.00583895i | ||||||||
\(841\) | −7.39749 | −0.255086 | ||||||||
\(842\) | −33.3912 | −1.15074 | ||||||||
\(843\) | − 0.882565i | − 0.0303971i | ||||||||
\(844\) | 7.93875 | 0.273263 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 16.0101 | 0.550440 | ||||||||
\(847\) | − 0.880123i | − 0.0302414i | ||||||||
\(848\) | 33.1870 | 1.13965 | ||||||||
\(849\) | −0.821665 | −0.0281995 | ||||||||
\(850\) | 19.7136i | 0.676172i | ||||||||
\(851\) | − 10.3846i | − 0.355978i | ||||||||
\(852\) | 2.57314i | 0.0881544i | ||||||||
\(853\) | 15.8090i | 0.541291i | 0.962679 | + | 0.270645i | \(0.0872371\pi\) | ||||
−0.962679 | + | 0.270645i | \(0.912763\pi\) | |||||||
\(854\) | −2.05077 | −0.0701760 | ||||||||
\(855\) | −19.1233 | −0.654002 | ||||||||
\(856\) | − 8.48880i | − 0.290141i | ||||||||
\(857\) | 43.5809 | 1.48870 | 0.744348 | − | 0.667792i | \(-0.232761\pi\) | ||||
0.744348 | + | 0.667792i | \(0.232761\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 57.5101 | 1.96222 | 0.981110 | − | 0.193449i | \(-0.0619673\pi\) | ||||
0.981110 | + | 0.193449i | \(0.0619673\pi\) | |||||||
\(860\) | − 2.78631i | − 0.0950123i | ||||||||
\(861\) | −0.951027 | −0.0324109 | ||||||||
\(862\) | 42.3352 | 1.44194 | ||||||||
\(863\) | 16.1116i | 0.548444i | 0.961666 | + | 0.274222i | \(0.0884203\pi\) | ||||
−0.961666 | + | 0.274222i | \(0.911580\pi\) | |||||||
\(864\) | 4.41801i | 0.150304i | ||||||||
\(865\) | 52.1797i | 1.77416i | ||||||||
\(866\) | − 28.9672i | − 0.984344i | ||||||||
\(867\) | −0.580538 | −0.0197161 | ||||||||
\(868\) | −19.7193 | −0.669317 | ||||||||
\(869\) | − 33.5967i | − 1.13969i | ||||||||
\(870\) | −2.32646 | −0.0788745 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.4159 | 0.352728 | ||||||||
\(873\) | − 44.6982i | − 1.51280i | ||||||||
\(874\) | −34.5632 | −1.16912 | ||||||||
\(875\) | −8.02459 | −0.271281 | ||||||||
\(876\) | − 1.10425i | − 0.0373093i | ||||||||
\(877\) | − 44.0382i | − 1.48706i | −0.668700 | − | 0.743532i | \(-0.733149\pi\) | ||||
0.668700 | − | 0.743532i | \(-0.266851\pi\) | |||||||
\(878\) | − 23.6383i | − 0.797753i | ||||||||
\(879\) | 0.306784i | 0.0103476i | ||||||||
\(880\) | −29.1801 | −0.983661 | ||||||||
\(881\) | 21.2905 | 0.717295 | 0.358647 | − | 0.933473i | \(-0.383238\pi\) | ||||
0.358647 | + | 0.933473i | \(0.383238\pi\) | |||||||
\(882\) | − 6.23113i | − 0.209813i | ||||||||
\(883\) | −4.28392 | −0.144165 | −0.0720827 | − | 0.997399i | \(-0.522965\pi\) | ||||
−0.0720827 | + | 0.997399i | \(0.522965\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.07599 | −0.103398 | ||||||||
\(886\) | 45.4434i | 1.52670i | ||||||||
\(887\) | −37.0660 | −1.24455 | −0.622276 | − | 0.782798i | \(-0.713792\pi\) | ||||
−0.622276 | + | 0.782798i | \(0.713792\pi\) | |||||||
\(888\) | −0.0972902 | −0.00326485 | ||||||||
\(889\) | 5.86506i | 0.196708i | ||||||||
\(890\) | 88.1247i | 2.95395i | ||||||||
\(891\) | − 30.7635i | − 1.03062i | ||||||||
\(892\) | 13.2073i | 0.442215i | ||||||||
\(893\) | −6.22638 | −0.208358 | ||||||||
\(894\) | 1.77707 | 0.0594342 | ||||||||
\(895\) | − 17.0580i | − 0.570187i | ||||||||
\(896\) | 5.55289 | 0.185509 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.0679 | 0.769787 | ||||||||
\(899\) | − 39.1997i | − 1.30738i | ||||||||
\(900\) | −13.6946 | −0.456486 | ||||||||
\(901\) | −49.9891 | −1.66538 | ||||||||
\(902\) | 74.9365i | 2.49511i | ||||||||
\(903\) | − 0.0411615i | − 0.00136977i | ||||||||
\(904\) | − 7.38521i | − 0.245629i | ||||||||
\(905\) | − 55.1910i | − 1.83461i | ||||||||
\(906\) | 2.38891 | 0.0793661 | ||||||||
\(907\) | 0.906355 | 0.0300950 | 0.0150475 | − | 0.999887i | \(-0.495210\pi\) | ||||
0.0150475 | + | 0.999887i | \(0.495210\pi\) | |||||||
\(908\) | − 30.9722i | − 1.02785i | ||||||||
\(909\) | −16.6968 | −0.553797 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.1318 | 1.56155 | 0.780773 | − | 0.624815i | \(-0.214826\pi\) | ||||
0.780773 | + | 0.624815i | \(0.214826\pi\) | |||||||
\(912\) | − 0.708609i | − 0.0234644i | ||||||||
\(913\) | −45.7239 | −1.51324 | ||||||||
\(914\) | 12.5573 | 0.415359 | ||||||||
\(915\) | 0.236627i | 0.00782263i | ||||||||
\(916\) | − 3.89609i | − 0.128730i | ||||||||
\(917\) | 1.38898i | 0.0458681i | ||||||||
\(918\) | − 5.49674i | − 0.181420i | ||||||||
\(919\) | 52.5207 | 1.73250 | 0.866249 | − | 0.499613i | \(-0.166524\pi\) | ||||
0.866249 | + | 0.499613i | \(0.166524\pi\) | |||||||
\(920\) | −12.7196 | −0.419352 | ||||||||
\(921\) | 0.480474i | 0.0158321i | ||||||||
\(922\) | −65.0967 | −2.14385 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.734227 | 0.0241543 | ||||||||
\(925\) | 2.96894i | 0.0976182i | ||||||||
\(926\) | 33.5115 | 1.10126 | ||||||||
\(927\) | −44.9451 | −1.47619 | ||||||||
\(928\) | 37.6158i | 1.23480i | ||||||||
\(929\) | 4.76389i | 0.156298i | 0.996942 | + | 0.0781491i | \(0.0249010\pi\) | ||||
−0.996942 | + | 0.0781491i | \(0.975099\pi\) | |||||||
\(930\) | 4.22158i | 0.138431i | ||||||||
\(931\) | 2.42330i | 0.0794205i | ||||||||
\(932\) | 28.2517 | 0.925415 | ||||||||
\(933\) | 0.848816 | 0.0277890 | ||||||||
\(934\) | − 10.8015i | − 0.353437i | ||||||||
\(935\) | 43.9536 | 1.43744 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.8844 | 1.56432 | 0.782158 | − | 0.623080i | \(-0.214119\pi\) | ||||
0.782158 | + | 0.623080i | \(0.214119\pi\) | |||||||
\(938\) | − 2.67780i | − 0.0874331i | ||||||||
\(939\) | 2.82735 | 0.0922670 | ||||||||
\(940\) | −15.8462 | −0.516846 | ||||||||
\(941\) | 8.54785i | 0.278652i | 0.990247 | + | 0.139326i | \(0.0444936\pi\) | ||||
−0.990247 | + | 0.139326i | \(0.955506\pi\) | |||||||
\(942\) | 1.19744i | 0.0390148i | ||||||||
\(943\) | − 71.4810i | − 2.32774i | ||||||||
\(944\) | 41.0800i | 1.33704i | ||||||||
\(945\) | −1.43994 | −0.0468413 | ||||||||
\(946\) | −3.24333 | −0.105450 | ||||||||
\(947\) | 11.7381i | 0.381437i | 0.981645 | + | 0.190718i | \(0.0610817\pi\) | ||||
−0.981645 | + | 0.190718i | \(0.938918\pi\) | |||||||
\(948\) | 2.07637 | 0.0674375 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 9.88160 | 0.320601 | ||||||||
\(951\) | − 0.840081i | − 0.0272415i | ||||||||
\(952\) | −3.40429 | −0.110334 | ||||||||
\(953\) | 39.2912 | 1.27277 | 0.636383 | − | 0.771373i | \(-0.280430\pi\) | ||||
0.636383 | + | 0.771373i | \(0.280430\pi\) | |||||||
\(954\) | − 64.4310i | − 2.08603i | ||||||||
\(955\) | − 51.8991i | − 1.67942i | ||||||||
\(956\) | − 34.7105i | − 1.12262i | ||||||||
\(957\) | 1.45956i | 0.0471808i | ||||||||
\(958\) | −8.64938 | −0.279449 | ||||||||
\(959\) | −12.4476 | −0.401955 | ||||||||
\(960\) | − 2.50836i | − 0.0809569i | ||||||||
\(961\) | −40.1314 | −1.29456 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.0650 | 1.16218 | ||||||||
\(964\) | 47.8073i | 1.53977i | ||||||||
\(965\) | 39.2240 | 1.26266 | ||||||||
\(966\) | −1.29947 | −0.0418096 | ||||||||
\(967\) | 6.78097i | 0.218061i | 0.994038 | + | 0.109031i | \(0.0347747\pi\) | ||||
−0.994038 | + | 0.109031i | \(0.965225\pi\) | |||||||
\(968\) | − 0.619758i | − 0.0199198i | ||||||||
\(969\) | 1.06737i | 0.0342888i | ||||||||
\(970\) | 82.0838i | 2.63555i | ||||||||
\(971\) | −5.36908 | −0.172302 | −0.0861511 | − | 0.996282i | \(-0.527457\pi\) | ||||
−0.0861511 | + | 0.996282i | \(0.527457\pi\) | |||||||
\(972\) | 5.73033 | 0.183800 | ||||||||
\(973\) | 7.98054i | 0.255844i | ||||||||
\(974\) | −13.5821 | −0.435197 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.16016 | 0.101154 | ||||||||
\(977\) | 22.6247i | 0.723828i | 0.932212 | + | 0.361914i | \(0.117877\pi\) | ||||
−0.932212 | + | 0.361914i | \(0.882123\pi\) | |||||||
\(978\) | −2.19941 | −0.0703294 | ||||||||
\(979\) | 55.2870 | 1.76698 | ||||||||
\(980\) | 6.16733i | 0.197008i | ||||||||
\(981\) | 44.2525i | 1.41287i | ||||||||
\(982\) | 39.4180i | 1.25788i | ||||||||
\(983\) | 25.8113i | 0.823254i | 0.911352 | + | 0.411627i | \(0.135039\pi\) | ||||
−0.911352 | + | 0.411627i | \(0.864961\pi\) | |||||||
\(984\) | −0.669687 | −0.0213488 | ||||||||
\(985\) | −39.4193 | −1.25600 | ||||||||
\(986\) | − 46.8003i | − 1.49043i | ||||||||
\(987\) | −0.234092 | −0.00745124 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.09378 | 0.0983764 | ||||||||
\(990\) | 56.6518i | 1.80051i | ||||||||
\(991\) | 45.2014 | 1.43587 | 0.717936 | − | 0.696110i | \(-0.245087\pi\) | ||||
0.717936 | + | 0.696110i | \(0.245087\pi\) | |||||||
\(992\) | 68.2572 | 2.16717 | ||||||||
\(993\) | − 1.40206i | − 0.0444929i | ||||||||
\(994\) | 25.1590i | 0.797995i | ||||||||
\(995\) | − 23.9747i | − 0.760050i | ||||||||
\(996\) | − 2.82587i | − 0.0895412i | ||||||||
\(997\) | 12.9965 | 0.411604 | 0.205802 | − | 0.978594i | \(-0.434020\pi\) | ||||
0.205802 | + | 0.978594i | \(0.434020\pi\) | |||||||
\(998\) | 75.2136 | 2.38085 | ||||||||
\(999\) | − 0.827828i | − 0.0261913i |
(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 | 1183.2.c.h.337.2 | 12 | ||
13.5 | odd | 4 | 1183.2.a.o.1.1 | yes | 6 | ||
13.8 | odd | 4 | 1183.2.a.n.1.6 | ✓ | 6 | ||
13.12 | even | 2 | inner | 1183.2.c.h.337.11 | 12 | ||
91.34 | even | 4 | 8281.2.a.cb.1.6 | 6 | |||
91.83 | even | 4 | 8281.2.a.cg.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.a.n.1.6 | ✓ | 6 | 13.8 | odd | 4 | ||
1183.2.a.o.1.1 | yes | 6 | 13.5 | odd | 4 | ||
1183.2.c.h.337.2 | 12 | 1.1 | even | 1 | trivial | ||
1183.2.c.h.337.11 | 12 | 13.12 | even | 2 | inner | ||
8281.2.a.cb.1.6 | 6 | 91.34 | even | 4 | |||
8281.2.a.cg.1.1 | 6 | 91.83 | even | 4 |