Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.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: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.3 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.o.1351.2 |
$q$-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 \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | − 1.00000i | − 0.408248i | ||||||||
\(7\) | − 2.00000i | − 0.755929i | −0.925820 | − | 0.377964i | \(-0.876624\pi\) | ||||
0.925820 | − | 0.377964i | \(-0.123376\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | − 6.46410i | − 1.94900i | −0.224388 | − | 0.974500i | \(-0.572038\pi\) | ||||
0.224388 | − | 0.974500i | \(-0.427962\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | − 1.00000i | − 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 7.46410i | 1.71238i | 0.516659 | + | 0.856191i | \(0.327175\pi\) | ||||
−0.516659 | + | 0.856191i | \(0.672825\pi\) | |||||||
\(20\) | − 1.00000i | − 0.223607i | ||||||||
\(21\) | 2.00000i | 0.436436i | ||||||||
\(22\) | 6.46410 | 1.37815 | ||||||||
\(23\) | 3.73205 | 0.778186 | 0.389093 | − | 0.921198i | \(-0.372788\pi\) | ||||
0.389093 | + | 0.921198i | \(0.372788\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.00000i | 0.377964i | ||||||||
\(29\) | 0.267949 | 0.0497569 | 0.0248785 | − | 0.999690i | \(-0.492080\pi\) | ||||
0.0248785 | + | 0.999690i | \(0.492080\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | − 1.73205i | − 0.311086i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) | ||||
0.987829 | − | 0.155543i | \(-0.0497126\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 6.46410i | 1.12526i | ||||||||
\(34\) | − 4.00000i | − 0.685994i | ||||||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 9.19615i | − 1.51184i | −0.654665 | − | 0.755919i | \(-0.727190\pi\) | ||||
0.654665 | − | 0.755919i | \(-0.272810\pi\) | |||||||
\(38\) | −7.46410 | −1.21084 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | − 2.00000i | − 0.312348i | −0.987730 | − | 0.156174i | \(-0.950084\pi\) | ||||
0.987730 | − | 0.156174i | \(-0.0499160\pi\) | |||||||
\(42\) | −2.00000 | −0.308607 | ||||||||
\(43\) | 11.9282 | 1.81903 | 0.909517 | − | 0.415667i | \(-0.136452\pi\) | ||||
0.909517 | + | 0.415667i | \(0.136452\pi\) | |||||||
\(44\) | 6.46410i | 0.974500i | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 3.73205i | 0.550261i | ||||||||
\(47\) | − 3.53590i | − 0.515764i | −0.966176 | − | 0.257882i | \(-0.916975\pi\) | ||||
0.966176 | − | 0.257882i | \(-0.0830245\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.928203 | 0.127499 | 0.0637493 | − | 0.997966i | \(-0.479694\pi\) | ||||
0.0637493 | + | 0.997966i | \(0.479694\pi\) | |||||||
\(54\) | − 1.00000i | − 0.136083i | ||||||||
\(55\) | 6.46410 | 0.871619 | ||||||||
\(56\) | −2.00000 | −0.267261 | ||||||||
\(57\) | − 7.46410i | − 0.988644i | ||||||||
\(58\) | 0.267949i | 0.0351835i | ||||||||
\(59\) | 8.46410i | 1.10193i | 0.834528 | + | 0.550966i | \(0.185741\pi\) | ||||
−0.834528 | + | 0.550966i | \(0.814259\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | −10.3923 | −1.33060 | −0.665299 | − | 0.746577i | \(-0.731696\pi\) | ||||
−0.665299 | + | 0.746577i | \(0.731696\pi\) | |||||||
\(62\) | 1.73205 | 0.219971 | ||||||||
\(63\) | − 2.00000i | − 0.251976i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.46410 | −0.795676 | ||||||||
\(67\) | 11.4641i | 1.40056i | 0.713867 | + | 0.700281i | \(0.246942\pi\) | ||||
−0.713867 | + | 0.700281i | \(0.753058\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | −3.73205 | −0.449286 | ||||||||
\(70\) | 2.00000i | 0.239046i | ||||||||
\(71\) | − 12.3923i | − 1.47070i | −0.677690 | − | 0.735348i | \(-0.737019\pi\) | ||||
0.677690 | − | 0.735348i | \(-0.262981\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | 2.00000i | 0.234082i | 0.993127 | + | 0.117041i | \(0.0373409\pi\) | ||||
−0.993127 | + | 0.117041i | \(0.962659\pi\) | |||||||
\(74\) | 9.19615 | 1.06903 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | − 7.46410i | − 0.856191i | ||||||||
\(77\) | −12.9282 | −1.47331 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.9282 | −1.56705 | −0.783523 | − | 0.621363i | \(-0.786579\pi\) | ||||
−0.783523 | + | 0.621363i | \(0.786579\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.00000 | 0.220863 | ||||||||
\(83\) | 8.92820i | 0.979998i | 0.871723 | + | 0.489999i | \(0.163003\pi\) | ||||
−0.871723 | + | 0.489999i | \(0.836997\pi\) | |||||||
\(84\) | − 2.00000i | − 0.218218i | ||||||||
\(85\) | − 4.00000i | − 0.433861i | ||||||||
\(86\) | 11.9282i | 1.28625i | ||||||||
\(87\) | −0.267949 | −0.0287272 | ||||||||
\(88\) | −6.46410 | −0.689076 | ||||||||
\(89\) | 0.535898i | 0.0568051i | 0.999597 | + | 0.0284026i | \(0.00904203\pi\) | ||||
−0.999597 | + | 0.0284026i | \(0.990958\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.73205 | −0.389093 | ||||||||
\(93\) | 1.73205i | 0.179605i | ||||||||
\(94\) | 3.53590 | 0.364700 | ||||||||
\(95\) | −7.46410 | −0.765801 | ||||||||
\(96\) | − 1.00000i | − 0.102062i | ||||||||
\(97\) | 0.535898i | 0.0544122i | 0.999630 | + | 0.0272061i | \(0.00866105\pi\) | ||||
−0.999630 | + | 0.0272061i | \(0.991339\pi\) | |||||||
\(98\) | 3.00000i | 0.303046i | ||||||||
\(99\) | − 6.46410i | − 0.649667i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 2.92820 | 0.291367 | 0.145684 | − | 0.989331i | \(-0.453462\pi\) | ||||
0.145684 | + | 0.989331i | \(0.453462\pi\) | |||||||
\(102\) | 4.00000i | 0.396059i | ||||||||
\(103\) | −11.8564 | −1.16825 | −0.584123 | − | 0.811665i | \(-0.698562\pi\) | ||||
−0.584123 | + | 0.811665i | \(0.698562\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | 0.928203i | 0.0901551i | ||||||||
\(107\) | −7.85641 | −0.759507 | −0.379754 | − | 0.925088i | \(-0.623991\pi\) | ||||
−0.379754 | + | 0.925088i | \(0.623991\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | − 15.8564i | − 1.51877i | −0.650643 | − | 0.759384i | \(-0.725500\pi\) | ||||
0.650643 | − | 0.759384i | \(-0.274500\pi\) | |||||||
\(110\) | 6.46410i | 0.616328i | ||||||||
\(111\) | 9.19615i | 0.872860i | ||||||||
\(112\) | − 2.00000i | − 0.188982i | ||||||||
\(113\) | 0.803848 | 0.0756196 | 0.0378098 | − | 0.999285i | \(-0.487962\pi\) | ||||
0.0378098 | + | 0.999285i | \(0.487962\pi\) | |||||||
\(114\) | 7.46410 | 0.699077 | ||||||||
\(115\) | 3.73205i | 0.348016i | ||||||||
\(116\) | −0.267949 | −0.0248785 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.46410 | −0.779184 | ||||||||
\(119\) | 8.00000i | 0.733359i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −30.7846 | −2.79860 | ||||||||
\(122\) | − 10.3923i | − 0.940875i | ||||||||
\(123\) | 2.00000i | 0.180334i | ||||||||
\(124\) | 1.73205i | 0.155543i | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 2.00000 | 0.178174 | ||||||||
\(127\) | −4.92820 | −0.437307 | −0.218654 | − | 0.975803i | \(-0.570166\pi\) | ||||
−0.218654 | + | 0.975803i | \(0.570166\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −11.9282 | −1.05022 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.6603 | −1.63035 | −0.815177 | − | 0.579212i | \(-0.803360\pi\) | ||||
−0.815177 | + | 0.579212i | \(0.803360\pi\) | |||||||
\(132\) | − 6.46410i | − 0.562628i | ||||||||
\(133\) | 14.9282 | 1.29444 | ||||||||
\(134\) | −11.4641 | −0.990348 | ||||||||
\(135\) | − 1.00000i | − 0.0860663i | ||||||||
\(136\) | 4.00000i | 0.342997i | ||||||||
\(137\) | − 2.46410i | − 0.210522i | −0.994445 | − | 0.105261i | \(-0.966432\pi\) | ||||
0.994445 | − | 0.105261i | \(-0.0335679\pi\) | |||||||
\(138\) | − 3.73205i | − 0.317693i | ||||||||
\(139\) | −12.9282 | −1.09656 | −0.548278 | − | 0.836296i | \(-0.684716\pi\) | ||||
−0.548278 | + | 0.836296i | \(0.684716\pi\) | |||||||
\(140\) | −2.00000 | −0.169031 | ||||||||
\(141\) | 3.53590i | 0.297776i | ||||||||
\(142\) | 12.3923 | 1.03994 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.267949i | 0.0222520i | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | −3.00000 | −0.247436 | ||||||||
\(148\) | 9.19615i | 0.755919i | ||||||||
\(149\) | − 13.5359i | − 1.10890i | −0.832216 | − | 0.554452i | \(-0.812928\pi\) | ||||
0.832216 | − | 0.554452i | \(-0.187072\pi\) | |||||||
\(150\) | 1.00000i | 0.0816497i | ||||||||
\(151\) | − 10.3923i | − 0.845714i | −0.906196 | − | 0.422857i | \(-0.861027\pi\) | ||||
0.906196 | − | 0.422857i | \(-0.138973\pi\) | |||||||
\(152\) | 7.46410 | 0.605419 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | − 12.9282i | − 1.04178i | ||||||||
\(155\) | 1.73205 | 0.139122 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.00000 | −0.399043 | −0.199522 | − | 0.979893i | \(-0.563939\pi\) | ||||
−0.199522 | + | 0.979893i | \(0.563939\pi\) | |||||||
\(158\) | − 13.9282i | − 1.10807i | ||||||||
\(159\) | −0.928203 | −0.0736113 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | − 7.46410i | − 0.588254i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 15.0526i | 1.17901i | 0.807766 | + | 0.589504i | \(0.200677\pi\) | ||||
−0.807766 | + | 0.589504i | \(0.799323\pi\) | |||||||
\(164\) | 2.00000i | 0.156174i | ||||||||
\(165\) | −6.46410 | −0.503230 | ||||||||
\(166\) | −8.92820 | −0.692963 | ||||||||
\(167\) | − 16.3205i | − 1.26292i | −0.775409 | − | 0.631459i | \(-0.782456\pi\) | ||||
0.775409 | − | 0.631459i | \(-0.217544\pi\) | |||||||
\(168\) | 2.00000 | 0.154303 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 7.46410i | 0.570794i | ||||||||
\(172\) | −11.9282 | −0.909517 | ||||||||
\(173\) | 10.9282 | 0.830856 | 0.415428 | − | 0.909626i | \(-0.363632\pi\) | ||||
0.415428 | + | 0.909626i | \(0.363632\pi\) | |||||||
\(174\) | − 0.267949i | − 0.0203132i | ||||||||
\(175\) | 2.00000i | 0.151186i | ||||||||
\(176\) | − 6.46410i | − 0.487250i | ||||||||
\(177\) | − 8.46410i | − 0.636201i | ||||||||
\(178\) | −0.535898 | −0.0401673 | ||||||||
\(179\) | −19.7321 | −1.47484 | −0.737421 | − | 0.675433i | \(-0.763957\pi\) | ||||
−0.737421 | + | 0.675433i | \(0.763957\pi\) | |||||||
\(180\) | − 1.00000i | − 0.0745356i | ||||||||
\(181\) | −2.92820 | −0.217652 | −0.108826 | − | 0.994061i | \(-0.534709\pi\) | ||||
−0.108826 | + | 0.994061i | \(0.534709\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.3923 | 0.768221 | ||||||||
\(184\) | − 3.73205i | − 0.275130i | ||||||||
\(185\) | 9.19615 | 0.676115 | ||||||||
\(186\) | −1.73205 | −0.127000 | ||||||||
\(187\) | 25.8564i | 1.89081i | ||||||||
\(188\) | 3.53590i | 0.257882i | ||||||||
\(189\) | 2.00000i | 0.145479i | ||||||||
\(190\) | − 7.46410i | − 0.541503i | ||||||||
\(191\) | 21.4641 | 1.55309 | 0.776544 | − | 0.630063i | \(-0.216971\pi\) | ||||
0.776544 | + | 0.630063i | \(0.216971\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | − 11.3205i | − 0.814868i | −0.913235 | − | 0.407434i | \(-0.866424\pi\) | ||||
0.913235 | − | 0.407434i | \(-0.133576\pi\) | |||||||
\(194\) | −0.535898 | −0.0384753 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | − 4.39230i | − 0.312939i | −0.987683 | − | 0.156469i | \(-0.949989\pi\) | ||||
0.987683 | − | 0.156469i | \(-0.0500113\pi\) | |||||||
\(198\) | 6.46410 | 0.459384 | ||||||||
\(199\) | −5.07180 | −0.359530 | −0.179765 | − | 0.983710i | \(-0.557534\pi\) | ||||
−0.179765 | + | 0.983710i | \(0.557534\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | − 11.4641i | − 0.808615i | ||||||||
\(202\) | 2.92820i | 0.206028i | ||||||||
\(203\) | − 0.535898i | − 0.0376127i | ||||||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | 2.00000 | 0.139686 | ||||||||
\(206\) | − 11.8564i | − 0.826075i | ||||||||
\(207\) | 3.73205 | 0.259395 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 48.2487 | 3.33743 | ||||||||
\(210\) | − 2.00000i | − 0.138013i | ||||||||
\(211\) | −11.3205 | −0.779336 | −0.389668 | − | 0.920955i | \(-0.627410\pi\) | ||||
−0.389668 | + | 0.920955i | \(0.627410\pi\) | |||||||
\(212\) | −0.928203 | −0.0637493 | ||||||||
\(213\) | 12.3923i | 0.849107i | ||||||||
\(214\) | − 7.85641i | − 0.537053i | ||||||||
\(215\) | 11.9282i | 0.813497i | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −3.46410 | −0.235159 | ||||||||
\(218\) | 15.8564 | 1.07393 | ||||||||
\(219\) | − 2.00000i | − 0.135147i | ||||||||
\(220\) | −6.46410 | −0.435810 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −9.19615 | −0.617205 | ||||||||
\(223\) | 20.5359i | 1.37519i | 0.726097 | + | 0.687593i | \(0.241333\pi\) | ||||
−0.726097 | + | 0.687593i | \(0.758667\pi\) | |||||||
\(224\) | 2.00000 | 0.133631 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0.803848i | 0.0534711i | ||||||||
\(227\) | − 16.3923i | − 1.08800i | −0.839087 | − | 0.543998i | \(-0.816910\pi\) | ||||
0.839087 | − | 0.543998i | \(-0.183090\pi\) | |||||||
\(228\) | 7.46410i | 0.494322i | ||||||||
\(229\) | − 7.85641i | − 0.519166i | −0.965721 | − | 0.259583i | \(-0.916415\pi\) | ||||
0.965721 | − | 0.259583i | \(-0.0835851\pi\) | |||||||
\(230\) | −3.73205 | −0.246084 | ||||||||
\(231\) | 12.9282 | 0.850613 | ||||||||
\(232\) | − 0.267949i | − 0.0175917i | ||||||||
\(233\) | 6.12436 | 0.401220 | 0.200610 | − | 0.979671i | \(-0.435708\pi\) | ||||
0.200610 | + | 0.979671i | \(0.435708\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.53590 | 0.230657 | ||||||||
\(236\) | − 8.46410i | − 0.550966i | ||||||||
\(237\) | 13.9282 | 0.904734 | ||||||||
\(238\) | −8.00000 | −0.518563 | ||||||||
\(239\) | − 16.3923i | − 1.06033i | −0.847894 | − | 0.530165i | \(-0.822130\pi\) | ||||
0.847894 | − | 0.530165i | \(-0.177870\pi\) | |||||||
\(240\) | − 1.00000i | − 0.0645497i | ||||||||
\(241\) | 17.7321i | 1.14222i | 0.820873 | + | 0.571111i | \(0.193487\pi\) | ||||
−0.820873 | + | 0.571111i | \(0.806513\pi\) | |||||||
\(242\) | − 30.7846i | − 1.97891i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 10.3923 | 0.665299 | ||||||||
\(245\) | 3.00000i | 0.191663i | ||||||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.73205 | −0.109985 | ||||||||
\(249\) | − 8.92820i | − 0.565802i | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 15.7321 | 0.992998 | 0.496499 | − | 0.868037i | \(-0.334619\pi\) | ||||
0.496499 | + | 0.868037i | \(0.334619\pi\) | |||||||
\(252\) | 2.00000i | 0.125988i | ||||||||
\(253\) | − 24.1244i | − 1.51669i | ||||||||
\(254\) | − 4.92820i | − 0.309223i | ||||||||
\(255\) | 4.00000i | 0.250490i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.33975 | −0.333084 | −0.166542 | − | 0.986034i | \(-0.553260\pi\) | ||||
−0.166542 | + | 0.986034i | \(0.553260\pi\) | |||||||
\(258\) | − 11.9282i | − 0.742617i | ||||||||
\(259\) | −18.3923 | −1.14284 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.267949 | 0.0165856 | ||||||||
\(262\) | − 18.6603i | − 1.15283i | ||||||||
\(263\) | 6.12436 | 0.377644 | 0.188822 | − | 0.982011i | \(-0.439533\pi\) | ||||
0.188822 | + | 0.982011i | \(0.439533\pi\) | |||||||
\(264\) | 6.46410 | 0.397838 | ||||||||
\(265\) | 0.928203i | 0.0570191i | ||||||||
\(266\) | 14.9282i | 0.915307i | ||||||||
\(267\) | − 0.535898i | − 0.0327964i | ||||||||
\(268\) | − 11.4641i | − 0.700281i | ||||||||
\(269\) | 12.0000 | 0.731653 | 0.365826 | − | 0.930683i | \(-0.380786\pi\) | ||||
0.365826 | + | 0.930683i | \(0.380786\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | − 1.19615i | − 0.0726611i | −0.999340 | − | 0.0363305i | \(-0.988433\pi\) | ||||
0.999340 | − | 0.0363305i | \(-0.0115669\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.46410 | 0.148862 | ||||||||
\(275\) | 6.46410i | 0.389800i | ||||||||
\(276\) | 3.73205 | 0.224643 | ||||||||
\(277\) | −3.92820 | −0.236023 | −0.118011 | − | 0.993012i | \(-0.537652\pi\) | ||||
−0.118011 | + | 0.993012i | \(0.537652\pi\) | |||||||
\(278\) | − 12.9282i | − 0.775382i | ||||||||
\(279\) | − 1.73205i | − 0.103695i | ||||||||
\(280\) | − 2.00000i | − 0.119523i | ||||||||
\(281\) | − 8.92820i | − 0.532612i | −0.963889 | − | 0.266306i | \(-0.914197\pi\) | ||||
0.963889 | − | 0.266306i | \(-0.0858032\pi\) | |||||||
\(282\) | −3.53590 | −0.210560 | ||||||||
\(283\) | −9.92820 | −0.590170 | −0.295085 | − | 0.955471i | \(-0.595348\pi\) | ||||
−0.295085 | + | 0.955471i | \(0.595348\pi\) | |||||||
\(284\) | 12.3923i | 0.735348i | ||||||||
\(285\) | 7.46410 | 0.442135 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −0.267949 | −0.0157345 | ||||||||
\(291\) | − 0.535898i | − 0.0314149i | ||||||||
\(292\) | − 2.00000i | − 0.117041i | ||||||||
\(293\) | − 31.8564i | − 1.86107i | −0.366202 | − | 0.930536i | \(-0.619342\pi\) | ||||
0.366202 | − | 0.930536i | \(-0.380658\pi\) | |||||||
\(294\) | − 3.00000i | − 0.174964i | ||||||||
\(295\) | −8.46410 | −0.492799 | ||||||||
\(296\) | −9.19615 | −0.534516 | ||||||||
\(297\) | 6.46410i | 0.375085i | ||||||||
\(298\) | 13.5359 | 0.784114 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | − 23.8564i | − 1.37506i | ||||||||
\(302\) | 10.3923 | 0.598010 | ||||||||
\(303\) | −2.92820 | −0.168221 | ||||||||
\(304\) | 7.46410i | 0.428096i | ||||||||
\(305\) | − 10.3923i | − 0.595062i | ||||||||
\(306\) | − 4.00000i | − 0.228665i | ||||||||
\(307\) | 19.4641i | 1.11087i | 0.831558 | + | 0.555437i | \(0.187449\pi\) | ||||
−0.831558 | + | 0.555437i | \(0.812551\pi\) | |||||||
\(308\) | 12.9282 | 0.736653 | ||||||||
\(309\) | 11.8564 | 0.674487 | ||||||||
\(310\) | 1.73205i | 0.0983739i | ||||||||
\(311\) | −28.3923 | −1.60998 | −0.804990 | − | 0.593288i | \(-0.797829\pi\) | ||||
−0.804990 | + | 0.593288i | \(0.797829\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.0000 | −1.58265 | −0.791327 | − | 0.611393i | \(-0.790609\pi\) | ||||
−0.791327 | + | 0.611393i | \(0.790609\pi\) | |||||||
\(314\) | − 5.00000i | − 0.282166i | ||||||||
\(315\) | 2.00000 | 0.112687 | ||||||||
\(316\) | 13.9282 | 0.783523 | ||||||||
\(317\) | 14.5359i | 0.816417i | 0.912889 | + | 0.408209i | \(0.133846\pi\) | ||||
−0.912889 | + | 0.408209i | \(0.866154\pi\) | |||||||
\(318\) | − 0.928203i | − 0.0520511i | ||||||||
\(319\) | − 1.73205i | − 0.0969762i | ||||||||
\(320\) | − 1.00000i | − 0.0559017i | ||||||||
\(321\) | 7.85641 | 0.438502 | ||||||||
\(322\) | 7.46410 | 0.415958 | ||||||||
\(323\) | − 29.8564i | − 1.66125i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15.0526 | −0.833684 | ||||||||
\(327\) | 15.8564i | 0.876861i | ||||||||
\(328\) | −2.00000 | −0.110432 | ||||||||
\(329\) | −7.07180 | −0.389881 | ||||||||
\(330\) | − 6.46410i | − 0.355837i | ||||||||
\(331\) | − 16.7846i | − 0.922566i | −0.887253 | − | 0.461283i | \(-0.847389\pi\) | ||||
0.887253 | − | 0.461283i | \(-0.152611\pi\) | |||||||
\(332\) | − 8.92820i | − 0.489999i | ||||||||
\(333\) | − 9.19615i | − 0.503946i | ||||||||
\(334\) | 16.3205 | 0.893018 | ||||||||
\(335\) | −11.4641 | −0.626351 | ||||||||
\(336\) | 2.00000i | 0.109109i | ||||||||
\(337\) | 9.32051 | 0.507720 | 0.253860 | − | 0.967241i | \(-0.418300\pi\) | ||||
0.253860 | + | 0.967241i | \(0.418300\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.803848 | −0.0436590 | ||||||||
\(340\) | 4.00000i | 0.216930i | ||||||||
\(341\) | −11.1962 | −0.606306 | ||||||||
\(342\) | −7.46410 | −0.403612 | ||||||||
\(343\) | − 20.0000i | − 1.07990i | ||||||||
\(344\) | − 11.9282i | − 0.643126i | ||||||||
\(345\) | − 3.73205i | − 0.200927i | ||||||||
\(346\) | 10.9282i | 0.587504i | ||||||||
\(347\) | 1.60770 | 0.0863056 | 0.0431528 | − | 0.999068i | \(-0.486260\pi\) | ||||
0.0431528 | + | 0.999068i | \(0.486260\pi\) | |||||||
\(348\) | 0.267949 | 0.0143636 | ||||||||
\(349\) | − 21.4641i | − 1.14895i | −0.818523 | − | 0.574474i | \(-0.805207\pi\) | ||||
0.818523 | − | 0.574474i | \(-0.194793\pi\) | |||||||
\(350\) | −2.00000 | −0.106904 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.46410 | 0.344538 | ||||||||
\(353\) | − 2.00000i | − 0.106449i | −0.998583 | − | 0.0532246i | \(-0.983050\pi\) | ||||
0.998583 | − | 0.0532246i | \(-0.0169499\pi\) | |||||||
\(354\) | 8.46410 | 0.449862 | ||||||||
\(355\) | 12.3923 | 0.657715 | ||||||||
\(356\) | − 0.535898i | − 0.0284026i | ||||||||
\(357\) | − 8.00000i | − 0.423405i | ||||||||
\(358\) | − 19.7321i | − 1.04287i | ||||||||
\(359\) | 5.07180i | 0.267679i | 0.991003 | + | 0.133840i | \(0.0427307\pi\) | ||||
−0.991003 | + | 0.133840i | \(0.957269\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −36.7128 | −1.93225 | ||||||||
\(362\) | − 2.92820i | − 0.153903i | ||||||||
\(363\) | 30.7846 | 1.61577 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.00000 | −0.104685 | ||||||||
\(366\) | 10.3923i | 0.543214i | ||||||||
\(367\) | 15.6077 | 0.814715 | 0.407358 | − | 0.913269i | \(-0.366450\pi\) | ||||
0.407358 | + | 0.913269i | \(0.366450\pi\) | |||||||
\(368\) | 3.73205 | 0.194547 | ||||||||
\(369\) | − 2.00000i | − 0.104116i | ||||||||
\(370\) | 9.19615i | 0.478085i | ||||||||
\(371\) | − 1.85641i | − 0.0963798i | ||||||||
\(372\) | − 1.73205i | − 0.0898027i | ||||||||
\(373\) | −15.7846 | −0.817296 | −0.408648 | − | 0.912692i | \(-0.634000\pi\) | ||||
−0.408648 | + | 0.912692i | \(0.634000\pi\) | |||||||
\(374\) | −25.8564 | −1.33700 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | −3.53590 | −0.182350 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.00000 | −0.102869 | ||||||||
\(379\) | − 27.8564i | − 1.43089i | −0.698670 | − | 0.715444i | \(-0.746225\pi\) | ||||
0.698670 | − | 0.715444i | \(-0.253775\pi\) | |||||||
\(380\) | 7.46410 | 0.382900 | ||||||||
\(381\) | 4.92820 | 0.252479 | ||||||||
\(382\) | 21.4641i | 1.09820i | ||||||||
\(383\) | 25.3923i | 1.29749i | 0.761007 | + | 0.648743i | \(0.224705\pi\) | ||||
−0.761007 | + | 0.648743i | \(0.775295\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | − 12.9282i | − 0.658882i | ||||||||
\(386\) | 11.3205 | 0.576199 | ||||||||
\(387\) | 11.9282 | 0.606345 | ||||||||
\(388\) | − 0.535898i | − 0.0272061i | ||||||||
\(389\) | −23.7321 | −1.20326 | −0.601631 | − | 0.798774i | \(-0.705482\pi\) | ||||
−0.601631 | + | 0.798774i | \(0.705482\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.9282 | −0.754952 | ||||||||
\(392\) | − 3.00000i | − 0.151523i | ||||||||
\(393\) | 18.6603 | 0.941285 | ||||||||
\(394\) | 4.39230 | 0.221281 | ||||||||
\(395\) | − 13.9282i | − 0.700804i | ||||||||
\(396\) | 6.46410i | 0.324833i | ||||||||
\(397\) | 12.1244i | 0.608504i | 0.952592 | + | 0.304252i | \(0.0984065\pi\) | ||||
−0.952592 | + | 0.304252i | \(0.901594\pi\) | |||||||
\(398\) | − 5.07180i | − 0.254226i | ||||||||
\(399\) | −14.9282 | −0.747345 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 32.0000i | 1.59800i | 0.601329 | + | 0.799002i | \(0.294638\pi\) | ||||
−0.601329 | + | 0.799002i | \(0.705362\pi\) | |||||||
\(402\) | 11.4641 | 0.571777 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −2.92820 | −0.145684 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0.535898 | 0.0265962 | ||||||||
\(407\) | −59.4449 | −2.94657 | ||||||||
\(408\) | − 4.00000i | − 0.198030i | ||||||||
\(409\) | 4.00000i | 0.197787i | 0.995098 | + | 0.0988936i | \(0.0315304\pi\) | ||||
−0.995098 | + | 0.0988936i | \(0.968470\pi\) | |||||||
\(410\) | 2.00000i | 0.0987730i | ||||||||
\(411\) | 2.46410i | 0.121545i | ||||||||
\(412\) | 11.8564 | 0.584123 | ||||||||
\(413\) | 16.9282 | 0.832982 | ||||||||
\(414\) | 3.73205i | 0.183420i | ||||||||
\(415\) | −8.92820 | −0.438268 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.9282 | 0.633097 | ||||||||
\(418\) | 48.2487i | 2.35992i | ||||||||
\(419\) | 22.3923 | 1.09394 | 0.546968 | − | 0.837154i | \(-0.315782\pi\) | ||||
0.546968 | + | 0.837154i | \(0.315782\pi\) | |||||||
\(420\) | 2.00000 | 0.0975900 | ||||||||
\(421\) | 4.39230i | 0.214068i | 0.994255 | + | 0.107034i | \(0.0341353\pi\) | ||||
−0.994255 | + | 0.107034i | \(0.965865\pi\) | |||||||
\(422\) | − 11.3205i | − 0.551074i | ||||||||
\(423\) | − 3.53590i | − 0.171921i | ||||||||
\(424\) | − 0.928203i | − 0.0450775i | ||||||||
\(425\) | 4.00000 | 0.194029 | ||||||||
\(426\) | −12.3923 | −0.600409 | ||||||||
\(427\) | 20.7846i | 1.00584i | ||||||||
\(428\) | 7.85641 | 0.379754 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.9282 | −0.575229 | ||||||||
\(431\) | − 28.3923i | − 1.36761i | −0.729665 | − | 0.683805i | \(-0.760324\pi\) | ||||
0.729665 | − | 0.683805i | \(-0.239676\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 19.3205 | 0.928484 | 0.464242 | − | 0.885708i | \(-0.346327\pi\) | ||||
0.464242 | + | 0.885708i | \(0.346327\pi\) | |||||||
\(434\) | − 3.46410i | − 0.166282i | ||||||||
\(435\) | − 0.267949i | − 0.0128472i | ||||||||
\(436\) | 15.8564i | 0.759384i | ||||||||
\(437\) | 27.8564i | 1.33255i | ||||||||
\(438\) | 2.00000 | 0.0955637 | ||||||||
\(439\) | −17.8564 | −0.852240 | −0.426120 | − | 0.904667i | \(-0.640120\pi\) | ||||
−0.426120 | + | 0.904667i | \(0.640120\pi\) | |||||||
\(440\) | − 6.46410i | − 0.308164i | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.3923 | 0.778822 | 0.389411 | − | 0.921064i | \(-0.372679\pi\) | ||||
0.389411 | + | 0.921064i | \(0.372679\pi\) | |||||||
\(444\) | − 9.19615i | − 0.436430i | ||||||||
\(445\) | −0.535898 | −0.0254040 | ||||||||
\(446\) | −20.5359 | −0.972403 | ||||||||
\(447\) | 13.5359i | 0.640226i | ||||||||
\(448\) | 2.00000i | 0.0944911i | ||||||||
\(449\) | − 15.7128i | − 0.741533i | −0.928726 | − | 0.370767i | \(-0.879095\pi\) | ||||
0.928726 | − | 0.370767i | \(-0.120905\pi\) | |||||||
\(450\) | − 1.00000i | − 0.0471405i | ||||||||
\(451\) | −12.9282 | −0.608765 | ||||||||
\(452\) | −0.803848 | −0.0378098 | ||||||||
\(453\) | 10.3923i | 0.488273i | ||||||||
\(454\) | 16.3923 | 0.769329 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.46410 | −0.349539 | ||||||||
\(457\) | − 24.5359i | − 1.14774i | −0.818946 | − | 0.573870i | \(-0.805441\pi\) | ||||
0.818946 | − | 0.573870i | \(-0.194559\pi\) | |||||||
\(458\) | 7.85641 | 0.367106 | ||||||||
\(459\) | 4.00000 | 0.186704 | ||||||||
\(460\) | − 3.73205i | − 0.174008i | ||||||||
\(461\) | 0.464102i | 0.0216154i | 0.999942 | + | 0.0108077i | \(0.00344026\pi\) | ||||
−0.999942 | + | 0.0108077i | \(0.996560\pi\) | |||||||
\(462\) | 12.9282i | 0.601474i | ||||||||
\(463\) | 7.07180i | 0.328654i | 0.986406 | + | 0.164327i | \(0.0525453\pi\) | ||||
−0.986406 | + | 0.164327i | \(0.947455\pi\) | |||||||
\(464\) | 0.267949 | 0.0124392 | ||||||||
\(465\) | −1.73205 | −0.0803219 | ||||||||
\(466\) | 6.12436i | 0.283705i | ||||||||
\(467\) | −15.8564 | −0.733747 | −0.366873 | − | 0.930271i | \(-0.619572\pi\) | ||||
−0.366873 | + | 0.930271i | \(0.619572\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.9282 | 1.05873 | ||||||||
\(470\) | 3.53590i | 0.163099i | ||||||||
\(471\) | 5.00000 | 0.230388 | ||||||||
\(472\) | 8.46410 | 0.389592 | ||||||||
\(473\) | − 77.1051i | − 3.54530i | ||||||||
\(474\) | 13.9282i | 0.639744i | ||||||||
\(475\) | − 7.46410i | − 0.342476i | ||||||||
\(476\) | − 8.00000i | − 0.366679i | ||||||||
\(477\) | 0.928203 | 0.0424995 | ||||||||
\(478\) | 16.3923 | 0.749767 | ||||||||
\(479\) | − 5.46410i | − 0.249661i | −0.992178 | − | 0.124831i | \(-0.960161\pi\) | ||||
0.992178 | − | 0.124831i | \(-0.0398387\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −17.7321 | −0.807673 | ||||||||
\(483\) | 7.46410i | 0.339628i | ||||||||
\(484\) | 30.7846 | 1.39930 | ||||||||
\(485\) | −0.535898 | −0.0243339 | ||||||||
\(486\) | − 1.00000i | − 0.0453609i | ||||||||
\(487\) | 23.1769i | 1.05025i | 0.851026 | + | 0.525123i | \(0.175981\pi\) | ||||
−0.851026 | + | 0.525123i | \(0.824019\pi\) | |||||||
\(488\) | 10.3923i | 0.470438i | ||||||||
\(489\) | − 15.0526i | − 0.680700i | ||||||||
\(490\) | −3.00000 | −0.135526 | ||||||||
\(491\) | −17.3205 | −0.781664 | −0.390832 | − | 0.920462i | \(-0.627813\pi\) | ||||
−0.390832 | + | 0.920462i | \(0.627813\pi\) | |||||||
\(492\) | − 2.00000i | − 0.0901670i | ||||||||
\(493\) | −1.07180 | −0.0482713 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.46410 | 0.290540 | ||||||||
\(496\) | − 1.73205i | − 0.0777714i | ||||||||
\(497\) | −24.7846 | −1.11174 | ||||||||
\(498\) | 8.92820 | 0.400082 | ||||||||
\(499\) | 6.53590i | 0.292587i | 0.989241 | + | 0.146293i | \(0.0467344\pi\) | ||||
−0.989241 | + | 0.146293i | \(0.953266\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | 16.3205i | 0.729147i | ||||||||
\(502\) | 15.7321i | 0.702156i | ||||||||
\(503\) | −31.1769 | −1.39011 | −0.695055 | − | 0.718957i | \(-0.744620\pi\) | ||||
−0.695055 | + | 0.718957i | \(0.744620\pi\) | |||||||
\(504\) | −2.00000 | −0.0890871 | ||||||||
\(505\) | 2.92820i | 0.130303i | ||||||||
\(506\) | 24.1244 | 1.07246 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.92820 | 0.218654 | ||||||||
\(509\) | − 1.39230i | − 0.0617128i | −0.999524 | − | 0.0308564i | \(-0.990177\pi\) | ||||
0.999524 | − | 0.0308564i | \(-0.00982346\pi\) | |||||||
\(510\) | −4.00000 | −0.177123 | ||||||||
\(511\) | 4.00000 | 0.176950 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 7.46410i | − 0.329548i | ||||||||
\(514\) | − 5.33975i | − 0.235526i | ||||||||
\(515\) | − 11.8564i | − 0.522456i | ||||||||
\(516\) | 11.9282 | 0.525110 | ||||||||
\(517\) | −22.8564 | −1.00522 | ||||||||
\(518\) | − 18.3923i | − 0.808111i | ||||||||
\(519\) | −10.9282 | −0.479695 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.3205 | −0.758825 | −0.379413 | − | 0.925228i | \(-0.623874\pi\) | ||||
−0.379413 | + | 0.925228i | \(0.623874\pi\) | |||||||
\(522\) | 0.267949i | 0.0117278i | ||||||||
\(523\) | 11.7846 | 0.515305 | 0.257653 | − | 0.966238i | \(-0.417051\pi\) | ||||
0.257653 | + | 0.966238i | \(0.417051\pi\) | |||||||
\(524\) | 18.6603 | 0.815177 | ||||||||
\(525\) | − 2.00000i | − 0.0872872i | ||||||||
\(526\) | 6.12436i | 0.267035i | ||||||||
\(527\) | 6.92820i | 0.301797i | ||||||||
\(528\) | 6.46410i | 0.281314i | ||||||||
\(529\) | −9.07180 | −0.394426 | ||||||||
\(530\) | −0.928203 | −0.0403186 | ||||||||
\(531\) | 8.46410i | 0.367311i | ||||||||
\(532\) | −14.9282 | −0.647220 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.535898 | 0.0231906 | ||||||||
\(535\) | − 7.85641i | − 0.339662i | ||||||||
\(536\) | 11.4641 | 0.495174 | ||||||||
\(537\) | 19.7321 | 0.851501 | ||||||||
\(538\) | 12.0000i | 0.517357i | ||||||||
\(539\) | − 19.3923i | − 0.835286i | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | 26.9282i | 1.15773i | 0.815422 | + | 0.578867i | \(0.196505\pi\) | ||||
−0.815422 | + | 0.578867i | \(0.803495\pi\) | |||||||
\(542\) | 1.19615 | 0.0513791 | ||||||||
\(543\) | 2.92820 | 0.125661 | ||||||||
\(544\) | − 4.00000i | − 0.171499i | ||||||||
\(545\) | 15.8564 | 0.679214 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.9282 | 0.980339 | 0.490170 | − | 0.871627i | \(-0.336935\pi\) | ||||
0.490170 | + | 0.871627i | \(0.336935\pi\) | |||||||
\(548\) | 2.46410i | 0.105261i | ||||||||
\(549\) | −10.3923 | −0.443533 | ||||||||
\(550\) | −6.46410 | −0.275630 | ||||||||
\(551\) | 2.00000i | 0.0852029i | ||||||||
\(552\) | 3.73205i | 0.158847i | ||||||||
\(553\) | 27.8564i | 1.18457i | ||||||||
\(554\) | − 3.92820i | − 0.166893i | ||||||||
\(555\) | −9.19615 | −0.390355 | ||||||||
\(556\) | 12.9282 | 0.548278 | ||||||||
\(557\) | − 17.7128i | − 0.750516i | −0.926920 | − | 0.375258i | \(-0.877554\pi\) | ||||
0.926920 | − | 0.375258i | \(-0.122446\pi\) | |||||||
\(558\) | 1.73205 | 0.0733236 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | − 25.8564i | − 1.09166i | ||||||||
\(562\) | 8.92820 | 0.376614 | ||||||||
\(563\) | −4.67949 | −0.197217 | −0.0986085 | − | 0.995126i | \(-0.531439\pi\) | ||||
−0.0986085 | + | 0.995126i | \(0.531439\pi\) | |||||||
\(564\) | − 3.53590i | − 0.148888i | ||||||||
\(565\) | 0.803848i | 0.0338181i | ||||||||
\(566\) | − 9.92820i | − 0.417314i | ||||||||
\(567\) | − 2.00000i | − 0.0839921i | ||||||||
\(568\) | −12.3923 | −0.519970 | ||||||||
\(569\) | 29.3205 | 1.22918 | 0.614590 | − | 0.788847i | \(-0.289322\pi\) | ||||
0.614590 | + | 0.788847i | \(0.289322\pi\) | |||||||
\(570\) | 7.46410i | 0.312637i | ||||||||
\(571\) | −17.1769 | −0.718832 | −0.359416 | − | 0.933178i | \(-0.617024\pi\) | ||||
−0.359416 | + | 0.933178i | \(0.617024\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.4641 | −0.896676 | ||||||||
\(574\) | − 4.00000i | − 0.166957i | ||||||||
\(575\) | −3.73205 | −0.155637 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − 10.0000i | − 0.416305i | −0.978096 | − | 0.208153i | \(-0.933255\pi\) | ||||
0.978096 | − | 0.208153i | \(-0.0667451\pi\) | |||||||
\(578\) | − 1.00000i | − 0.0415945i | ||||||||
\(579\) | 11.3205i | 0.470464i | ||||||||
\(580\) | − 0.267949i | − 0.0111260i | ||||||||
\(581\) | 17.8564 | 0.740809 | ||||||||
\(582\) | 0.535898 | 0.0222137 | ||||||||
\(583\) | − 6.00000i | − 0.248495i | ||||||||
\(584\) | 2.00000 | 0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.8564 | 1.31598 | ||||||||
\(587\) | 2.39230i | 0.0987410i | 0.998781 | + | 0.0493705i | \(0.0157215\pi\) | ||||
−0.998781 | + | 0.0493705i | \(0.984278\pi\) | |||||||
\(588\) | 3.00000 | 0.123718 | ||||||||
\(589\) | 12.9282 | 0.532697 | ||||||||
\(590\) | − 8.46410i | − 0.348462i | ||||||||
\(591\) | 4.39230i | 0.180675i | ||||||||
\(592\) | − 9.19615i | − 0.377960i | ||||||||
\(593\) | 45.1051i | 1.85225i | 0.377223 | + | 0.926123i | \(0.376879\pi\) | ||||
−0.377223 | + | 0.926123i | \(0.623121\pi\) | |||||||
\(594\) | −6.46410 | −0.265225 | ||||||||
\(595\) | −8.00000 | −0.327968 | ||||||||
\(596\) | 13.5359i | 0.554452i | ||||||||
\(597\) | 5.07180 | 0.207575 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.3923 | −0.424618 | −0.212309 | − | 0.977203i | \(-0.568098\pi\) | ||||
−0.212309 | + | 0.977203i | \(0.568098\pi\) | |||||||
\(600\) | − 1.00000i | − 0.0408248i | ||||||||
\(601\) | −19.7846 | −0.807031 | −0.403516 | − | 0.914973i | \(-0.632212\pi\) | ||||
−0.403516 | + | 0.914973i | \(0.632212\pi\) | |||||||
\(602\) | 23.8564 | 0.972315 | ||||||||
\(603\) | 11.4641i | 0.466854i | ||||||||
\(604\) | 10.3923i | 0.422857i | ||||||||
\(605\) | − 30.7846i | − 1.25157i | ||||||||
\(606\) | − 2.92820i | − 0.118950i | ||||||||
\(607\) | −19.1769 | −0.778367 | −0.389183 | − | 0.921160i | \(-0.627243\pi\) | ||||
−0.389183 | + | 0.921160i | \(0.627243\pi\) | |||||||
\(608\) | −7.46410 | −0.302709 | ||||||||
\(609\) | 0.535898i | 0.0217157i | ||||||||
\(610\) | 10.3923 | 0.420772 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.00000 | 0.161690 | ||||||||
\(613\) | 39.0526i | 1.57732i | 0.614831 | + | 0.788659i | \(0.289224\pi\) | ||||
−0.614831 | + | 0.788659i | \(0.710776\pi\) | |||||||
\(614\) | −19.4641 | −0.785507 | ||||||||
\(615\) | −2.00000 | −0.0806478 | ||||||||
\(616\) | 12.9282i | 0.520892i | ||||||||
\(617\) | − 22.4641i | − 0.904371i | −0.891924 | − | 0.452185i | \(-0.850645\pi\) | ||||
0.891924 | − | 0.452185i | \(-0.149355\pi\) | |||||||
\(618\) | 11.8564i | 0.476935i | ||||||||
\(619\) | − 24.2487i | − 0.974638i | −0.873224 | − | 0.487319i | \(-0.837975\pi\) | ||||
0.873224 | − | 0.487319i | \(-0.162025\pi\) | |||||||
\(620\) | −1.73205 | −0.0695608 | ||||||||
\(621\) | −3.73205 | −0.149762 | ||||||||
\(622\) | − 28.3923i | − 1.13843i | ||||||||
\(623\) | 1.07180 | 0.0429406 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | − 28.0000i | − 1.11911i | ||||||||
\(627\) | −48.2487 | −1.92687 | ||||||||
\(628\) | 5.00000 | 0.199522 | ||||||||
\(629\) | 36.7846i | 1.46670i | ||||||||
\(630\) | 2.00000i | 0.0796819i | ||||||||
\(631\) | 31.4641i | 1.25257i | 0.779596 | + | 0.626283i | \(0.215425\pi\) | ||||
−0.779596 | + | 0.626283i | \(0.784575\pi\) | |||||||
\(632\) | 13.9282i | 0.554034i | ||||||||
\(633\) | 11.3205 | 0.449950 | ||||||||
\(634\) | −14.5359 | −0.577294 | ||||||||
\(635\) | − 4.92820i | − 0.195570i | ||||||||
\(636\) | 0.928203 | 0.0368057 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.73205 | 0.0685725 | ||||||||
\(639\) | − 12.3923i | − 0.490232i | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 0.143594 | 0.00567160 | 0.00283580 | − | 0.999996i | \(-0.499097\pi\) | ||||
0.00283580 | + | 0.999996i | \(0.499097\pi\) | |||||||
\(642\) | 7.85641i | 0.310068i | ||||||||
\(643\) | − 20.5359i | − 0.809857i | −0.914348 | − | 0.404928i | \(-0.867296\pi\) | ||||
0.914348 | − | 0.404928i | \(-0.132704\pi\) | |||||||
\(644\) | 7.46410i | 0.294127i | ||||||||
\(645\) | − 11.9282i | − 0.469673i | ||||||||
\(646\) | 29.8564 | 1.17468 | ||||||||
\(647\) | −13.3205 | −0.523683 | −0.261842 | − | 0.965111i | \(-0.584330\pi\) | ||||
−0.261842 | + | 0.965111i | \(0.584330\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | 54.7128 | 2.14767 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.46410 | 0.135769 | ||||||||
\(652\) | − 15.0526i | − 0.589504i | ||||||||
\(653\) | 4.24871 | 0.166265 | 0.0831325 | − | 0.996539i | \(-0.473508\pi\) | ||||
0.0831325 | + | 0.996539i | \(0.473508\pi\) | |||||||
\(654\) | −15.8564 | −0.620035 | ||||||||
\(655\) | − 18.6603i | − 0.729116i | ||||||||
\(656\) | − 2.00000i | − 0.0780869i | ||||||||
\(657\) | 2.00000i | 0.0780274i | ||||||||
\(658\) | − 7.07180i | − 0.275687i | ||||||||
\(659\) | −0.267949 | −0.0104378 | −0.00521891 | − | 0.999986i | \(-0.501661\pi\) | ||||
−0.00521891 | + | 0.999986i | \(0.501661\pi\) | |||||||
\(660\) | 6.46410 | 0.251615 | ||||||||
\(661\) | 8.67949i | 0.337593i | 0.985651 | + | 0.168797i | \(0.0539881\pi\) | ||||
−0.985651 | + | 0.168797i | \(0.946012\pi\) | |||||||
\(662\) | 16.7846 | 0.652352 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.92820 | 0.346481 | ||||||||
\(665\) | 14.9282i | 0.578891i | ||||||||
\(666\) | 9.19615 | 0.356344 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 16.3205i | 0.631459i | ||||||||
\(669\) | − 20.5359i | − 0.793964i | ||||||||
\(670\) | − 11.4641i | − 0.442897i | ||||||||
\(671\) | 67.1769i | 2.59334i | ||||||||
\(672\) | −2.00000 | −0.0771517 | ||||||||
\(673\) | 32.0000 | 1.23351 | 0.616755 | − | 0.787155i | \(-0.288447\pi\) | ||||
0.616755 | + | 0.787155i | \(0.288447\pi\) | |||||||
\(674\) | 9.32051i | 0.359013i | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.3923 | 1.24494 | 0.622469 | − | 0.782645i | \(-0.286130\pi\) | ||||
0.622469 | + | 0.782645i | \(0.286130\pi\) | |||||||
\(678\) | − 0.803848i | − 0.0308716i | ||||||||
\(679\) | 1.07180 | 0.0411318 | ||||||||
\(680\) | −4.00000 | −0.153393 | ||||||||
\(681\) | 16.3923i | 0.628154i | ||||||||
\(682\) | − 11.1962i | − 0.428723i | ||||||||
\(683\) | − 40.7846i | − 1.56058i | −0.625418 | − | 0.780290i | \(-0.715072\pi\) | ||||
0.625418 | − | 0.780290i | \(-0.284928\pi\) | |||||||
\(684\) | − 7.46410i | − 0.285397i | ||||||||
\(685\) | 2.46410 | 0.0941485 | ||||||||
\(686\) | 20.0000 | 0.763604 | ||||||||
\(687\) | 7.85641i | 0.299741i | ||||||||
\(688\) | 11.9282 | 0.454758 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.73205 | 0.142077 | ||||||||
\(691\) | 27.1769i | 1.03386i | 0.856028 | + | 0.516929i | \(0.172925\pi\) | ||||
−0.856028 | + | 0.516929i | \(0.827075\pi\) | |||||||
\(692\) | −10.9282 | −0.415428 | ||||||||
\(693\) | −12.9282 | −0.491102 | ||||||||
\(694\) | 1.60770i | 0.0610273i | ||||||||
\(695\) | − 12.9282i | − 0.490395i | ||||||||
\(696\) | 0.267949i | 0.0101566i | ||||||||
\(697\) | 8.00000i | 0.303022i | ||||||||
\(698\) | 21.4641 | 0.812428 | ||||||||
\(699\) | −6.12436 | −0.231644 | ||||||||
\(700\) | − 2.00000i | − 0.0755929i | ||||||||
\(701\) | −0.267949 | −0.0101203 | −0.00506015 | − | 0.999987i | \(-0.501611\pi\) | ||||
−0.00506015 | + | 0.999987i | \(0.501611\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 68.6410 | 2.58884 | ||||||||
\(704\) | 6.46410i | 0.243625i | ||||||||
\(705\) | −3.53590 | −0.133170 | ||||||||
\(706\) | 2.00000 | 0.0752710 | ||||||||
\(707\) | − 5.85641i | − 0.220253i | ||||||||
\(708\) | 8.46410i | 0.318100i | ||||||||
\(709\) | − 22.9282i | − 0.861087i | −0.902570 | − | 0.430543i | \(-0.858322\pi\) | ||||
0.902570 | − | 0.430543i | \(-0.141678\pi\) | |||||||
\(710\) | 12.3923i | 0.465075i | ||||||||
\(711\) | −13.9282 | −0.522348 | ||||||||
\(712\) | 0.535898 | 0.0200836 | ||||||||
\(713\) | − 6.46410i | − 0.242083i | ||||||||
\(714\) | 8.00000 | 0.299392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.7321 | 0.737421 | ||||||||
\(717\) | 16.3923i | 0.612182i | ||||||||
\(718\) | −5.07180 | −0.189278 | ||||||||
\(719\) | −34.6410 | −1.29189 | −0.645946 | − | 0.763383i | \(-0.723537\pi\) | ||||
−0.645946 | + | 0.763383i | \(0.723537\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | 23.7128i | 0.883111i | ||||||||
\(722\) | − 36.7128i | − 1.36631i | ||||||||
\(723\) | − 17.7321i | − 0.659462i | ||||||||
\(724\) | 2.92820 | 0.108826 | ||||||||
\(725\) | −0.267949 | −0.00995138 | ||||||||
\(726\) | 30.7846i | 1.14252i | ||||||||
\(727\) | −31.7128 | −1.17616 | −0.588082 | − | 0.808802i | \(-0.700117\pi\) | ||||
−0.588082 | + | 0.808802i | \(0.700117\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − 2.00000i | − 0.0740233i | ||||||||
\(731\) | −47.7128 | −1.76472 | ||||||||
\(732\) | −10.3923 | −0.384111 | ||||||||
\(733\) | − 50.9282i | − 1.88108i | −0.339688 | − | 0.940538i | \(-0.610322\pi\) | ||||
0.339688 | − | 0.940538i | \(-0.389678\pi\) | |||||||
\(734\) | 15.6077i | 0.576091i | ||||||||
\(735\) | − 3.00000i | − 0.110657i | ||||||||
\(736\) | 3.73205i | 0.137565i | ||||||||
\(737\) | 74.1051 | 2.72970 | ||||||||
\(738\) | 2.00000 | 0.0736210 | ||||||||
\(739\) | 19.3205i | 0.710716i | 0.934730 | + | 0.355358i | \(0.115641\pi\) | ||||
−0.934730 | + | 0.355358i | \(0.884359\pi\) | |||||||
\(740\) | −9.19615 | −0.338057 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.85641 | 0.0681508 | ||||||||
\(743\) | 40.4641i | 1.48448i | 0.670132 | + | 0.742242i | \(0.266237\pi\) | ||||
−0.670132 | + | 0.742242i | \(0.733763\pi\) | |||||||
\(744\) | 1.73205 | 0.0635001 | ||||||||
\(745\) | 13.5359 | 0.495917 | ||||||||
\(746\) | − 15.7846i | − 0.577916i | ||||||||
\(747\) | 8.92820i | 0.326666i | ||||||||
\(748\) | − 25.8564i | − 0.945404i | ||||||||
\(749\) | 15.7128i | 0.574134i | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 14.0718 | 0.513487 | 0.256744 | − | 0.966480i | \(-0.417350\pi\) | ||||
0.256744 | + | 0.966480i | \(0.417350\pi\) | |||||||
\(752\) | − 3.53590i | − 0.128941i | ||||||||
\(753\) | −15.7321 | −0.573308 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.3923 | 0.378215 | ||||||||
\(756\) | − 2.00000i | − 0.0727393i | ||||||||
\(757\) | −18.0000 | −0.654221 | −0.327111 | − | 0.944986i | \(-0.606075\pi\) | ||||
−0.327111 | + | 0.944986i | \(0.606075\pi\) | |||||||
\(758\) | 27.8564 | 1.01179 | ||||||||
\(759\) | 24.1244i | 0.875659i | ||||||||
\(760\) | 7.46410i | 0.270751i | ||||||||
\(761\) | 5.07180i | 0.183852i | 0.995766 | + | 0.0919262i | \(0.0293024\pi\) | ||||
−0.995766 | + | 0.0919262i | \(0.970698\pi\) | |||||||
\(762\) | 4.92820i | 0.178530i | ||||||||
\(763\) | −31.7128 | −1.14808 | ||||||||
\(764\) | −21.4641 | −0.776544 | ||||||||
\(765\) | − 4.00000i | − 0.144620i | ||||||||
\(766\) | −25.3923 | −0.917461 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 11.5885i | 0.417890i | 0.977927 | + | 0.208945i | \(0.0670030\pi\) | ||||
−0.977927 | + | 0.208945i | \(0.932997\pi\) | |||||||
\(770\) | 12.9282 | 0.465900 | ||||||||
\(771\) | 5.33975 | 0.192306 | ||||||||
\(772\) | 11.3205i | 0.407434i | ||||||||
\(773\) | 27.7128i | 0.996761i | 0.866959 | + | 0.498380i | \(0.166072\pi\) | ||||
−0.866959 | + | 0.498380i | \(0.833928\pi\) | |||||||
\(774\) | 11.9282i | 0.428750i | ||||||||
\(775\) | 1.73205i | 0.0622171i | ||||||||
\(776\) | 0.535898 | 0.0192376 | ||||||||
\(777\) | 18.3923 | 0.659820 | ||||||||
\(778\) | − 23.7321i | − 0.850835i | ||||||||
\(779\) | 14.9282 | 0.534858 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −80.1051 | −2.86639 | ||||||||
\(782\) | − 14.9282i | − 0.533831i | ||||||||
\(783\) | −0.267949 | −0.00957572 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | − 5.00000i | − 0.178458i | ||||||||
\(786\) | 18.6603i | 0.665589i | ||||||||
\(787\) | 1.73205i | 0.0617409i | 0.999523 | + | 0.0308705i | \(0.00982794\pi\) | ||||
−0.999523 | + | 0.0308705i | \(0.990172\pi\) | |||||||
\(788\) | 4.39230i | 0.156469i | ||||||||
\(789\) | −6.12436 | −0.218033 | ||||||||
\(790\) | 13.9282 | 0.495543 | ||||||||
\(791\) | − 1.60770i | − 0.0571631i | ||||||||
\(792\) | −6.46410 | −0.229692 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −12.1244 | −0.430277 | ||||||||
\(795\) | − 0.928203i | − 0.0329200i | ||||||||
\(796\) | 5.07180 | 0.179765 | ||||||||
\(797\) | −10.1436 | −0.359305 | −0.179652 | − | 0.983730i | \(-0.557497\pi\) | ||||
−0.179652 | + | 0.983730i | \(0.557497\pi\) | |||||||
\(798\) | − 14.9282i | − 0.528453i | ||||||||
\(799\) | 14.1436i | 0.500364i | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | 0.535898i | 0.0189350i | ||||||||
\(802\) | −32.0000 | −1.12996 | ||||||||
\(803\) | 12.9282 | 0.456226 | ||||||||
\(804\) | 11.4641i | 0.404308i | ||||||||
\(805\) | 7.46410 | 0.263075 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.0000 | −0.422420 | ||||||||
\(808\) | − 2.92820i | − 0.103014i | ||||||||
\(809\) | −42.7846 | −1.50423 | −0.752113 | − | 0.659034i | \(-0.770965\pi\) | ||||
−0.752113 | + | 0.659034i | \(0.770965\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 40.7846i | 1.43214i | 0.698028 | + | 0.716071i | \(0.254061\pi\) | ||||
−0.698028 | + | 0.716071i | \(0.745939\pi\) | |||||||
\(812\) | 0.535898i | 0.0188063i | ||||||||
\(813\) | 1.19615i | 0.0419509i | ||||||||
\(814\) | − 59.4449i | − 2.08354i | ||||||||
\(815\) | −15.0526 | −0.527268 | ||||||||
\(816\) | 4.00000 | 0.140028 | ||||||||
\(817\) | 89.0333i | 3.11488i | ||||||||
\(818\) | −4.00000 | −0.139857 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.00000 | −0.0698430 | ||||||||
\(821\) | − 14.6077i | − 0.509812i | −0.966966 | − | 0.254906i | \(-0.917955\pi\) | ||||
0.966966 | − | 0.254906i | \(-0.0820445\pi\) | |||||||
\(822\) | −2.46410 | −0.0859454 | ||||||||
\(823\) | 39.1769 | 1.36562 | 0.682811 | − | 0.730595i | \(-0.260757\pi\) | ||||
0.682811 | + | 0.730595i | \(0.260757\pi\) | |||||||
\(824\) | 11.8564i | 0.413037i | ||||||||
\(825\) | − 6.46410i | − 0.225051i | ||||||||
\(826\) | 16.9282i | 0.589008i | ||||||||
\(827\) | 17.3205i | 0.602293i | 0.953578 | + | 0.301147i | \(0.0973693\pi\) | ||||
−0.953578 | + | 0.301147i | \(0.902631\pi\) | |||||||
\(828\) | −3.73205 | −0.129698 | ||||||||
\(829\) | 16.5359 | 0.574315 | 0.287158 | − | 0.957883i | \(-0.407290\pi\) | ||||
0.287158 | + | 0.957883i | \(0.407290\pi\) | |||||||
\(830\) | − 8.92820i | − 0.309902i | ||||||||
\(831\) | 3.92820 | 0.136268 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.0000 | −0.415775 | ||||||||
\(834\) | 12.9282i | 0.447667i | ||||||||
\(835\) | 16.3205 | 0.564794 | ||||||||
\(836\) | −48.2487 | −1.66872 | ||||||||
\(837\) | 1.73205i | 0.0598684i | ||||||||
\(838\) | 22.3923i | 0.773529i | ||||||||
\(839\) | − 43.5692i | − 1.50418i | −0.659062 | − | 0.752088i | \(-0.729047\pi\) | ||||
0.659062 | − | 0.752088i | \(-0.270953\pi\) | |||||||
\(840\) | 2.00000i | 0.0690066i | ||||||||
\(841\) | −28.9282 | −0.997524 | ||||||||
\(842\) | −4.39230 | −0.151369 | ||||||||
\(843\) | 8.92820i | 0.307504i | ||||||||
\(844\) | 11.3205 | 0.389668 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.53590 | 0.121567 | ||||||||
\(847\) | 61.5692i | 2.11554i | ||||||||
\(848\) | 0.928203 | 0.0318746 | ||||||||
\(849\) | 9.92820 | 0.340735 | ||||||||
\(850\) | 4.00000i | 0.137199i | ||||||||
\(851\) | − 34.3205i | − 1.17649i | ||||||||
\(852\) | − 12.3923i | − 0.424553i | ||||||||
\(853\) | 43.8372i | 1.50096i | 0.660895 | + | 0.750478i | \(0.270177\pi\) | ||||
−0.660895 | + | 0.750478i | \(0.729823\pi\) | |||||||
\(854\) | −20.7846 | −0.711235 | ||||||||
\(855\) | −7.46410 | −0.255267 | ||||||||
\(856\) | 7.85641i | 0.268526i | ||||||||
\(857\) | 24.5167 | 0.837473 | 0.418737 | − | 0.908108i | \(-0.362473\pi\) | ||||
0.418737 | + | 0.908108i | \(0.362473\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.1769 | −1.20022 | −0.600110 | − | 0.799917i | \(-0.704877\pi\) | ||||
−0.600110 | + | 0.799917i | \(0.704877\pi\) | |||||||
\(860\) | − 11.9282i | − 0.406748i | ||||||||
\(861\) | 4.00000 | 0.136320 | ||||||||
\(862\) | 28.3923 | 0.967046 | ||||||||
\(863\) | 35.5359i | 1.20966i | 0.796356 | + | 0.604828i | \(0.206758\pi\) | ||||
−0.796356 | + | 0.604828i | \(0.793242\pi\) | |||||||
\(864\) | − 1.00000i | − 0.0340207i | ||||||||
\(865\) | 10.9282i | 0.371570i | ||||||||
\(866\) | 19.3205i | 0.656538i | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 3.46410 | 0.117579 | ||||||||
\(869\) | 90.0333i | 3.05417i | ||||||||
\(870\) | 0.267949 | 0.00908433 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −15.8564 | −0.536966 | ||||||||
\(873\) | 0.535898i | 0.0181374i | ||||||||
\(874\) | −27.8564 | −0.942257 | ||||||||
\(875\) | −2.00000 | −0.0676123 | ||||||||
\(876\) | 2.00000i | 0.0675737i | ||||||||
\(877\) | − 3.87564i | − 0.130871i | −0.997857 | − | 0.0654356i | \(-0.979156\pi\) | ||||
0.997857 | − | 0.0654356i | \(-0.0208437\pi\) | |||||||
\(878\) | − 17.8564i | − 0.602625i | ||||||||
\(879\) | 31.8564i | 1.07449i | ||||||||
\(880\) | 6.46410 | 0.217905 | ||||||||
\(881\) | −14.0000 | −0.471672 | −0.235836 | − | 0.971793i | \(-0.575783\pi\) | ||||
−0.235836 | + | 0.971793i | \(0.575783\pi\) | |||||||
\(882\) | 3.00000i | 0.101015i | ||||||||
\(883\) | 29.9282 | 1.00716 | 0.503582 | − | 0.863947i | \(-0.332015\pi\) | ||||
0.503582 | + | 0.863947i | \(0.332015\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.46410 | 0.284518 | ||||||||
\(886\) | 16.3923i | 0.550710i | ||||||||
\(887\) | 14.1244 | 0.474249 | 0.237125 | − | 0.971479i | \(-0.423795\pi\) | ||||
0.237125 | + | 0.971479i | \(0.423795\pi\) | |||||||
\(888\) | 9.19615 | 0.308603 | ||||||||
\(889\) | 9.85641i | 0.330573i | ||||||||
\(890\) | − 0.535898i | − 0.0179634i | ||||||||
\(891\) | − 6.46410i | − 0.216556i | ||||||||
\(892\) | − 20.5359i | − 0.687593i | ||||||||
\(893\) | 26.3923 | 0.883185 | ||||||||
\(894\) | −13.5359 | −0.452708 | ||||||||
\(895\) | − 19.7321i | − 0.659570i | ||||||||
\(896\) | −2.00000 | −0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.7128 | 0.524343 | ||||||||
\(899\) | − 0.464102i | − 0.0154787i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −3.71281 | −0.123692 | ||||||||
\(902\) | − 12.9282i | − 0.430462i | ||||||||
\(903\) | 23.8564i | 0.793891i | ||||||||
\(904\) | − 0.803848i | − 0.0267356i | ||||||||
\(905\) | − 2.92820i | − 0.0973368i | ||||||||
\(906\) | −10.3923 | −0.345261 | ||||||||
\(907\) | −20.8564 | −0.692526 | −0.346263 | − | 0.938138i | \(-0.612549\pi\) | ||||
−0.346263 | + | 0.938138i | \(0.612549\pi\) | |||||||
\(908\) | 16.3923i | 0.543998i | ||||||||
\(909\) | 2.92820 | 0.0971224 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.2487 | 0.803396 | 0.401698 | − | 0.915772i | \(-0.368420\pi\) | ||||
0.401698 | + | 0.915772i | \(0.368420\pi\) | |||||||
\(912\) | − 7.46410i | − 0.247161i | ||||||||
\(913\) | 57.7128 | 1.91002 | ||||||||
\(914\) | 24.5359 | 0.811575 | ||||||||
\(915\) | 10.3923i | 0.343559i | ||||||||
\(916\) | 7.85641i | 0.259583i | ||||||||
\(917\) | 37.3205i | 1.23243i | ||||||||
\(918\) | 4.00000i | 0.132020i | ||||||||
\(919\) | 14.6410 | 0.482963 | 0.241481 | − | 0.970405i | \(-0.422367\pi\) | ||||
0.241481 | + | 0.970405i | \(0.422367\pi\) | |||||||
\(920\) | 3.73205 | 0.123042 | ||||||||
\(921\) | − 19.4641i | − 0.641364i | ||||||||
\(922\) | −0.464102 | −0.0152844 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −12.9282 | −0.425307 | ||||||||
\(925\) | 9.19615i | 0.302368i | ||||||||
\(926\) | −7.07180 | −0.232394 | ||||||||
\(927\) | −11.8564 | −0.389415 | ||||||||
\(928\) | 0.267949i | 0.00879586i | ||||||||
\(929\) | − 6.14359i | − 0.201565i | −0.994908 | − | 0.100782i | \(-0.967865\pi\) | ||||
0.994908 | − | 0.100782i | \(-0.0321346\pi\) | |||||||
\(930\) | − 1.73205i | − 0.0567962i | ||||||||
\(931\) | 22.3923i | 0.733878i | ||||||||
\(932\) | −6.12436 | −0.200610 | ||||||||
\(933\) | 28.3923 | 0.929522 | ||||||||
\(934\) | − 15.8564i | − 0.518837i | ||||||||
\(935\) | −25.8564 | −0.845595 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.6410 | −0.804987 | −0.402493 | − | 0.915423i | \(-0.631856\pi\) | ||||
−0.402493 | + | 0.915423i | \(0.631856\pi\) | |||||||
\(938\) | 22.9282i | 0.748632i | ||||||||
\(939\) | 28.0000 | 0.913745 | ||||||||
\(940\) | −3.53590 | −0.115328 | ||||||||
\(941\) | − 14.7846i | − 0.481965i | −0.970530 | − | 0.240982i | \(-0.922530\pi\) | ||||
0.970530 | − | 0.240982i | \(-0.0774696\pi\) | |||||||
\(942\) | 5.00000i | 0.162909i | ||||||||
\(943\) | − 7.46410i | − 0.243065i | ||||||||
\(944\) | 8.46410i | 0.275483i | ||||||||
\(945\) | −2.00000 | −0.0650600 | ||||||||
\(946\) | 77.1051 | 2.50690 | ||||||||
\(947\) | − 9.46410i | − 0.307542i | −0.988107 | − | 0.153771i | \(-0.950858\pi\) | ||||
0.988107 | − | 0.153771i | \(-0.0491418\pi\) | |||||||
\(948\) | −13.9282 | −0.452367 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.46410 | 0.242167 | ||||||||
\(951\) | − 14.5359i | − 0.471359i | ||||||||
\(952\) | 8.00000 | 0.259281 | ||||||||
\(953\) | −12.2679 | −0.397398 | −0.198699 | − | 0.980061i | \(-0.563672\pi\) | ||||
−0.198699 | + | 0.980061i | \(0.563672\pi\) | |||||||
\(954\) | 0.928203i | 0.0300517i | ||||||||
\(955\) | 21.4641i | 0.694562i | ||||||||
\(956\) | 16.3923i | 0.530165i | ||||||||
\(957\) | 1.73205i | 0.0559893i | ||||||||
\(958\) | 5.46410 | 0.176537 | ||||||||
\(959\) | −4.92820 | −0.159140 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | 28.0000 | 0.903226 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.85641 | −0.253169 | ||||||||
\(964\) | − 17.7321i | − 0.571111i | ||||||||
\(965\) | 11.3205 | 0.364420 | ||||||||
\(966\) | −7.46410 | −0.240154 | ||||||||
\(967\) | − 41.4641i | − 1.33340i | −0.745328 | − | 0.666698i | \(-0.767707\pi\) | ||||
0.745328 | − | 0.666698i | \(-0.232293\pi\) | |||||||
\(968\) | 30.7846i | 0.989455i | ||||||||
\(969\) | 29.8564i | 0.959126i | ||||||||
\(970\) | − 0.535898i | − 0.0172067i | ||||||||
\(971\) | 4.53590 | 0.145564 | 0.0727820 | − | 0.997348i | \(-0.476812\pi\) | ||||
0.0727820 | + | 0.997348i | \(0.476812\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 25.8564i | 0.828918i | ||||||||
\(974\) | −23.1769 | −0.742636 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.3923 | −0.332650 | ||||||||
\(977\) | − 12.6077i | − 0.403356i | −0.979452 | − | 0.201678i | \(-0.935361\pi\) | ||||
0.979452 | − | 0.201678i | \(-0.0646394\pi\) | |||||||
\(978\) | 15.0526 | 0.481328 | ||||||||
\(979\) | 3.46410 | 0.110713 | ||||||||
\(980\) | − 3.00000i | − 0.0958315i | ||||||||
\(981\) | − 15.8564i | − 0.506256i | ||||||||
\(982\) | − 17.3205i | − 0.552720i | ||||||||
\(983\) | − 36.6077i | − 1.16760i | −0.811896 | − | 0.583802i | \(-0.801564\pi\) | ||||
0.811896 | − | 0.583802i | \(-0.198436\pi\) | |||||||
\(984\) | 2.00000 | 0.0637577 | ||||||||
\(985\) | 4.39230 | 0.139950 | ||||||||
\(986\) | − 1.07180i | − 0.0341330i | ||||||||
\(987\) | 7.07180 | 0.225098 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.5167 | 1.41555 | ||||||||
\(990\) | 6.46410i | 0.205443i | ||||||||
\(991\) | −52.8564 | −1.67904 | −0.839520 | − | 0.543329i | \(-0.817163\pi\) | ||||
−0.839520 | + | 0.543329i | \(0.817163\pi\) | |||||||
\(992\) | 1.73205 | 0.0549927 | ||||||||
\(993\) | 16.7846i | 0.532643i | ||||||||
\(994\) | − 24.7846i | − 0.786120i | ||||||||
\(995\) | − 5.07180i | − 0.160787i | ||||||||
\(996\) | 8.92820i | 0.282901i | ||||||||
\(997\) | 35.5692 | 1.12649 | 0.563244 | − | 0.826290i | \(-0.309553\pi\) | ||||
0.563244 | + | 0.826290i | \(0.309553\pi\) | |||||||
\(998\) | −6.53590 | −0.206890 | ||||||||
\(999\) | 9.19615i | 0.290953i |
(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 | 5070.2.b.o.1351.3 | 4 | ||
13.3 | even | 3 | 390.2.bb.b.121.1 | ✓ | 4 | ||
13.4 | even | 6 | 390.2.bb.b.361.1 | yes | 4 | ||
13.5 | odd | 4 | 5070.2.a.bg.1.2 | 2 | |||
13.8 | odd | 4 | 5070.2.a.y.1.1 | 2 | |||
13.12 | even | 2 | inner | 5070.2.b.o.1351.2 | 4 | ||
39.17 | odd | 6 | 1170.2.bs.e.361.2 | 4 | |||
39.29 | odd | 6 | 1170.2.bs.e.901.2 | 4 | |||
65.3 | odd | 12 | 1950.2.y.c.199.2 | 4 | |||
65.4 | even | 6 | 1950.2.bc.b.751.2 | 4 | |||
65.17 | odd | 12 | 1950.2.y.c.49.2 | 4 | |||
65.29 | even | 6 | 1950.2.bc.b.901.2 | 4 | |||
65.42 | odd | 12 | 1950.2.y.f.199.1 | 4 | |||
65.43 | odd | 12 | 1950.2.y.f.49.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.b.121.1 | ✓ | 4 | 13.3 | even | 3 | ||
390.2.bb.b.361.1 | yes | 4 | 13.4 | even | 6 | ||
1170.2.bs.e.361.2 | 4 | 39.17 | odd | 6 | |||
1170.2.bs.e.901.2 | 4 | 39.29 | odd | 6 | |||
1950.2.y.c.49.2 | 4 | 65.17 | odd | 12 | |||
1950.2.y.c.199.2 | 4 | 65.3 | odd | 12 | |||
1950.2.y.f.49.1 | 4 | 65.43 | odd | 12 | |||
1950.2.y.f.199.1 | 4 | 65.42 | odd | 12 | |||
1950.2.bc.b.751.2 | 4 | 65.4 | even | 6 | |||
1950.2.bc.b.901.2 | 4 | 65.29 | even | 6 | |||
5070.2.a.y.1.1 | 2 | 13.8 | odd | 4 | |||
5070.2.a.bg.1.2 | 2 | 13.5 | odd | 4 | |||
5070.2.b.o.1351.2 | 4 | 13.12 | even | 2 | inner | ||
5070.2.b.o.1351.3 | 4 | 1.1 | even | 1 | trivial |