Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4788,2,Mod(1,4788)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4788, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4788.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4788 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4788.a (trivial) |
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: | yes |
Analytic conductor: | \(38.2323724878\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.874032\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4788.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.874032 | 0.390879 | 0.195440 | − | 0.980716i | \(-0.437387\pi\) | ||||
0.195440 | + | 0.980716i | \(0.437387\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82843 | 0.852803 | 0.426401 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.23607 | 0.342824 | 0.171412 | − | 0.985199i | \(-0.445167\pi\) | ||||
0.171412 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.70246 | −0.897978 | −0.448989 | − | 0.893537i | \(-0.648216\pi\) | ||||
−0.448989 | + | 0.893537i | \(0.648216\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82843 | −0.589768 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.23607 | −0.847214 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.19859 | −1.33674 | −0.668372 | − | 0.743827i | \(-0.733009\pi\) | ||||
−0.668372 | + | 0.743827i | \(0.733009\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.70820 | −1.02522 | −0.512612 | − | 0.858620i | \(-0.671322\pi\) | ||||
−0.512612 | + | 0.858620i | \(0.671322\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.874032 | −0.147738 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.48528 | 1.32518 | 0.662589 | − | 0.748983i | \(-0.269458\pi\) | ||||
0.662589 | + | 0.748983i | \(0.269458\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.763932 | −0.116499 | −0.0582493 | − | 0.998302i | \(-0.518552\pi\) | ||||
−0.0582493 | + | 0.998302i | \(0.518552\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.45052 | −0.795041 | −0.397520 | − | 0.917593i | \(-0.630129\pi\) | ||||
−0.397520 | + | 0.917593i | \(0.630129\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.37016 | 0.600288 | 0.300144 | − | 0.953894i | \(-0.402965\pi\) | ||||
0.300144 | + | 0.953894i | \(0.402965\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.47214 | 0.333343 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.8098 | −1.92808 | −0.964038 | − | 0.265764i | \(-0.914376\pi\) | ||||
−0.964038 | + | 0.265764i | \(0.914376\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.4721 | −1.59689 | −0.798447 | − | 0.602066i | \(-0.794345\pi\) | ||||
−0.798447 | + | 0.602066i | \(0.794345\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.08036 | 0.134003 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.4164 | 1.39474 | 0.697368 | − | 0.716713i | \(-0.254354\pi\) | ||||
0.697368 | + | 0.716713i | \(0.254354\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.03476 | −0.360160 | −0.180080 | − | 0.983652i | \(-0.557636\pi\) | ||||
−0.180080 | + | 0.983652i | \(0.557636\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.94427 | 0.812766 | 0.406383 | − | 0.913703i | \(-0.366790\pi\) | ||||
0.406383 | + | 0.913703i | \(0.366790\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.82843 | −0.322329 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.52786 | −0.171898 | −0.0859491 | − | 0.996300i | \(-0.527392\pi\) | ||||
−0.0859491 | + | 0.996300i | \(0.527392\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.78282 | 0.524983 | 0.262491 | − | 0.964934i | \(-0.415456\pi\) | ||||
0.262491 | + | 0.964934i | \(0.415456\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.23607 | −0.351001 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.48528 | 0.899438 | 0.449719 | − | 0.893170i | \(-0.351524\pi\) | ||||
0.449719 | + | 0.893170i | \(0.351524\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.23607 | −0.129575 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.874032 | 0.0896738 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.52786 | −0.358200 | −0.179100 | − | 0.983831i | \(-0.557319\pi\) | ||||
−0.179100 | + | 0.983831i | \(0.557319\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.5123 | 1.84204 | 0.921021 | − | 0.389513i | \(-0.127357\pi\) | ||||
0.921021 | + | 0.389513i | \(0.127357\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.9443 | −1.27544 | −0.637719 | − | 0.770270i | \(-0.720122\pi\) | ||||
−0.637719 | + | 0.770270i | \(0.720122\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.6035 | 1.41177 | 0.705887 | − | 0.708324i | \(-0.250549\pi\) | ||||
0.705887 | + | 0.708324i | \(0.250549\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.9443 | −1.81453 | −0.907266 | − | 0.420557i | \(-0.861835\pi\) | ||||
−0.907266 | + | 0.420557i | \(0.861835\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.54173 | −0.145034 | −0.0725170 | − | 0.997367i | \(-0.523103\pi\) | ||||
−0.0725170 | + | 0.997367i | \(0.523103\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.47214 | −0.230528 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.70246 | 0.339404 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.07262 | −0.722037 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.41641 | 0.658100 | 0.329050 | − | 0.944313i | \(-0.393272\pi\) | ||||
0.329050 | + | 0.944313i | \(0.393272\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.03476 | 0.265148 | 0.132574 | − | 0.991173i | \(-0.457676\pi\) | ||||
0.132574 | + | 0.991173i | \(0.457676\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.16073 | −0.184603 | −0.0923016 | − | 0.995731i | \(-0.529422\pi\) | ||||
−0.0923016 | + | 0.995731i | \(0.529422\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.94427 | −0.419368 | −0.209684 | − | 0.977769i | \(-0.567243\pi\) | ||||
−0.209684 | + | 0.977769i | \(0.567243\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.49613 | 0.292361 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.29180 | −0.522505 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.24419 | −0.429621 | −0.214810 | − | 0.976656i | \(-0.568913\pi\) | ||||
−0.214810 | + | 0.976656i | \(0.568913\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.52786 | −0.124336 | −0.0621679 | − | 0.998066i | \(-0.519801\pi\) | ||||
−0.0621679 | + | 0.998066i | \(0.519801\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.98915 | −0.400738 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.00000 | −0.478852 | −0.239426 | − | 0.970915i | \(-0.576959\pi\) | ||||
−0.239426 | + | 0.970915i | \(0.576959\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.82843 | 0.222911 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −25.1246 | −1.96791 | −0.983956 | − | 0.178413i | \(-0.942904\pi\) | ||||
−0.983956 | + | 0.178413i | \(0.942904\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.90879 | −0.302471 | −0.151236 | − | 0.988498i | \(-0.548325\pi\) | ||||
−0.151236 | + | 0.988498i | \(0.548325\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.1344 | −1.60682 | −0.803409 | − | 0.595428i | \(-0.796983\pi\) | ||||
−0.803409 | + | 0.595428i | \(0.796983\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.23607 | 0.320217 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.61125 | −0.568891 | −0.284446 | − | 0.958692i | \(-0.591810\pi\) | ||||
−0.284446 | + | 0.958692i | \(0.591810\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.9443 | −1.11080 | −0.555399 | − | 0.831584i | \(-0.687435\pi\) | ||||
−0.555399 | + | 0.831584i | \(0.687435\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.90879 | −0.287380 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.4721 | −0.765798 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.6305 | 1.78220 | 0.891101 | − | 0.453805i | \(-0.149934\pi\) | ||||
0.891101 | + | 0.453805i | \(0.149934\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.0000 | −1.29567 | −0.647834 | − | 0.761781i | \(-0.724325\pi\) | ||||
−0.647834 | + | 0.761781i | \(0.724325\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.81758 | −0.556980 | −0.278490 | − | 0.960439i | \(-0.589834\pi\) | ||||
−0.278490 | + | 0.960439i | \(0.589834\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.19859 | 0.505242 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.41641 | 0.517984 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.82843 | 0.195646 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.52786 | 0.105182 | 0.0525912 | − | 0.998616i | \(-0.483252\pi\) | ||||
0.0525912 | + | 0.998616i | \(0.483252\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.667701 | −0.0455368 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.70820 | 0.387498 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.57649 | −0.307848 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.763932 | 0.0511567 | 0.0255783 | − | 0.999673i | \(-0.491857\pi\) | ||||
0.0255783 | + | 0.999673i | \(0.491857\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.0540 | 1.33103 | 0.665516 | − | 0.746383i | \(-0.268211\pi\) | ||||
0.665516 | + | 0.746383i | \(0.268211\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.3607 | 1.21331 | 0.606654 | − | 0.794966i | \(-0.292511\pi\) | ||||
0.606654 | + | 0.794966i | \(0.292511\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.7186 | −1.22630 | −0.613149 | − | 0.789967i | \(-0.710097\pi\) | ||||
−0.613149 | + | 0.789967i | \(0.710097\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.76393 | −0.310765 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.3863 | −1.25400 | −0.626999 | − | 0.779020i | \(-0.715717\pi\) | ||||
−0.626999 | + | 0.779020i | \(0.715717\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.8885 | −1.53880 | −0.769398 | − | 0.638769i | \(-0.779444\pi\) | ||||
−0.769398 | + | 0.638769i | \(0.779444\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.874032 | 0.0558399 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.23607 | 0.0786491 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.618993 | −0.0390705 | −0.0195352 | − | 0.999809i | \(-0.506219\pi\) | ||||
−0.0195352 | + | 0.999809i | \(0.506219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.3941 | 0.773121 | 0.386560 | − | 0.922264i | \(-0.373663\pi\) | ||||
0.386560 | + | 0.922264i | \(0.373663\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.47214 | 0.277885 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.0509 | 1.11307 | 0.556534 | − | 0.830825i | \(-0.312131\pi\) | ||||
0.556534 | + | 0.830825i | \(0.312131\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.81966 | 0.234640 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.73722 | −0.410775 | −0.205388 | − | 0.978681i | \(-0.565846\pi\) | ||||
−0.205388 | + | 0.978681i | \(0.565846\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.8328 | 1.62998 | 0.814989 | − | 0.579477i | \(-0.196743\pi\) | ||||
0.814989 | + | 0.579477i | \(0.196743\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.9814 | −0.722506 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.2361 | −1.75663 | −0.878313 | − | 0.478087i | \(-0.841330\pi\) | ||||
−0.878313 | + | 0.478087i | \(0.841330\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.5927 | 1.16880 | 0.584400 | − | 0.811466i | \(-0.301330\pi\) | ||||
0.584400 | + | 0.811466i | \(0.301330\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.47214 | −0.146953 | −0.0734766 | − | 0.997297i | \(-0.523409\pi\) | ||||
−0.0734766 | + | 0.997297i | \(0.523409\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.48528 | −0.500870 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.29180 | −0.193635 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.1266 | 1.64318 | 0.821588 | − | 0.570081i | \(-0.193088\pi\) | ||||
0.821588 | + | 0.570081i | \(0.193088\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.9443 | −0.753645 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.49613 | −0.202186 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.763932 | 0.0440323 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.9010 | −0.624192 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.70820 | 0.554076 | 0.277038 | − | 0.960859i | \(-0.410647\pi\) | ||||
0.277038 | + | 0.960859i | \(0.410647\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.03476 | 0.172085 | 0.0860427 | − | 0.996291i | \(-0.472578\pi\) | ||||
0.0860427 | + | 0.996291i | \(0.472578\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.8885 | −1.12417 | −0.562083 | − | 0.827081i | \(-0.690000\pi\) | ||||
−0.562083 | + | 0.827081i | \(0.690000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −31.9867 | −1.79655 | −0.898277 | − | 0.439430i | \(-0.855180\pi\) | ||||
−0.898277 | + | 0.439430i | \(0.855180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.3607 | −1.13998 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.70246 | −0.206010 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.23607 | −0.290445 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.45052 | 0.300497 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.8885 | 0.763383 | 0.381692 | − | 0.924290i | \(-0.375342\pi\) | ||||
0.381692 | + | 0.924290i | \(0.375342\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.97831 | 0.545173 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.9443 | 0.596172 | 0.298086 | − | 0.954539i | \(-0.403652\pi\) | ||||
0.298086 | + | 0.954539i | \(0.403652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.1452 | −0.874314 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.3786 | −1.41608 | −0.708038 | − | 0.706174i | \(-0.750420\pi\) | ||||
−0.708038 | + | 0.706174i | \(0.750420\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.41641 | 0.504049 | 0.252024 | − | 0.967721i | \(-0.418904\pi\) | ||||
0.252024 | + | 0.967721i | \(0.418904\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.0270 | −0.533684 | −0.266842 | − | 0.963740i | \(-0.585980\pi\) | ||||
−0.266842 | + | 0.963740i | \(0.585980\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.65248 | −0.140779 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 35.9442 | 1.89706 | 0.948532 | − | 0.316682i | \(-0.102569\pi\) | ||||
0.948532 | + | 0.316682i | \(0.102569\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.06952 | 0.317693 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.41641 | 0.178335 | 0.0891675 | − | 0.996017i | \(-0.471579\pi\) | ||||
0.0891675 | + | 0.996017i | \(0.471579\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.37016 | −0.226887 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.9443 | −1.18801 | −0.594005 | − | 0.804462i | \(-0.702454\pi\) | ||||
−0.594005 | + | 0.804462i | \(0.702454\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.89794 | −0.458267 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.583592 | 0.0299771 | 0.0149886 | − | 0.999888i | \(-0.495229\pi\) | ||||
0.0149886 | + | 0.999888i | \(0.495229\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.08347 | 0.157558 | 0.0787789 | − | 0.996892i | \(-0.474898\pi\) | ||||
0.0787789 | + | 0.996892i | \(0.474898\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.47214 | −0.125992 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.8933 | 0.907226 | 0.453613 | − | 0.891199i | \(-0.350135\pi\) | ||||
0.453613 | + | 0.891199i | \(0.350135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.4721 | 0.529599 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.33540 | −0.0671914 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.0000 | −0.903394 | −0.451697 | − | 0.892171i | \(-0.649181\pi\) | ||||
−0.451697 | + | 0.892171i | \(0.649181\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.8369 | 1.24029 | 0.620147 | − | 0.784486i | \(-0.287073\pi\) | ||||
0.620147 | + | 0.784486i | \(0.287073\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.05573 | −0.351471 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.6491 | −0.626993 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.1246 | 0.747864 | 0.373932 | − | 0.927456i | \(-0.378009\pi\) | ||||
0.373932 | + | 0.927456i | \(0.378009\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.8098 | 0.728744 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.18034 | 0.205205 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.6870 | −0.864065 | −0.432033 | − | 0.901858i | \(-0.642203\pi\) | ||||
−0.432033 | + | 0.901858i | \(0.642203\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.6839 | 0.760779 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.4721 | 0.603569 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.7565 | 1.14431 | 0.572155 | − | 0.820146i | \(-0.306108\pi\) | ||||
0.572155 | + | 0.820146i | \(0.306108\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.8885 | 1.14801 | 0.574005 | − | 0.818852i | \(-0.305389\pi\) | ||||
0.574005 | + | 0.818852i | \(0.305389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.82843 | −0.135302 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.1246 | −1.19913 | −0.599566 | − | 0.800325i | \(-0.704660\pi\) | ||||
−0.599566 | + | 0.800325i | \(0.704660\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.5393 | −1.35594 | −0.677972 | − | 0.735088i | \(-0.737141\pi\) | ||||
−0.677972 | + | 0.735088i | \(0.737141\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.41641 | 0.351571 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.3190 | 1.47804 | 0.739018 | − | 0.673685i | \(-0.235290\pi\) | ||||
0.739018 | + | 0.673685i | \(0.235290\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.0000 | 1.13012 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.08036 | −0.0506482 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.5967 | −0.823141 | −0.411571 | − | 0.911378i | \(-0.635020\pi\) | ||||
−0.411571 | + | 0.911378i | \(0.635020\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.9017 | −1.85841 | −0.929204 | − | 0.369566i | \(-0.879506\pi\) | ||||
−0.929204 | + | 0.369566i | \(0.879506\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.8885 | 0.645455 | 0.322728 | − | 0.946492i | \(-0.395400\pi\) | ||||
0.322728 | + | 0.946492i | \(0.395400\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.5014 | 1.08752 | 0.543759 | − | 0.839242i | \(-0.317001\pi\) | ||||
0.543759 | + | 0.839242i | \(0.317001\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.4164 | −0.527161 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.16073 | −0.0993503 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.23607 | −0.194364 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.9389 | 0.728267 | 0.364134 | − | 0.931347i | \(-0.381365\pi\) | ||||
0.364134 | + | 0.931347i | \(0.381365\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.52786 | −0.252049 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.08347 | −0.140013 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.8885 | −1.71689 | −0.858447 | − | 0.512902i | \(-0.828570\pi\) | ||||
−0.858447 | + | 0.512902i | \(0.828570\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.8608 | 1.48299 | 0.741493 | − | 0.670961i | \(-0.234118\pi\) | ||||
0.741493 | + | 0.670961i | \(0.234118\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.6525 | 1.20037 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.03476 | 0.136128 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.8885 | −0.800801 | −0.400401 | − | 0.916340i | \(-0.631129\pi\) | ||||
−0.400401 | + | 0.916340i | \(0.631129\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.7456 | −1.28170 | −0.640852 | − | 0.767664i | \(-0.721419\pi\) | ||||
−0.640852 | + | 0.767664i | \(0.721419\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.1803 | 0.720016 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.2117 | −0.895866 | −0.447933 | − | 0.894067i | \(-0.647840\pi\) | ||||
−0.447933 | + | 0.894067i | \(0.647840\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.94427 | −0.307197 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.3137 | −0.498542 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.4164 | −0.678013 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.2333 | −0.448331 | −0.224166 | − | 0.974551i | \(-0.571966\pi\) | ||||
−0.224166 | + | 0.974551i | \(0.571966\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.1803 | −0.707517 | −0.353758 | − | 0.935337i | \(-0.615097\pi\) | ||||
−0.353758 | + | 0.935337i | \(0.615097\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.1344 | 0.920629 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.4884 | 0.454302 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.7639 | 0.551833 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.82843 | 0.121829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.5279 | 0.667595 | 0.333798 | − | 0.942645i | \(-0.391670\pi\) | ||||
0.333798 | + | 0.942645i | \(0.391670\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.5579 | −0.709263 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.5836 | 0.709063 | 0.354532 | − | 0.935044i | \(-0.384640\pi\) | ||||
0.354532 | + | 0.935044i | \(0.384640\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.19859 | −0.306670 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.52786 | 0.0649714 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.5579 | 0.701581 | 0.350790 | − | 0.936454i | \(-0.385913\pi\) | ||||
0.350790 | + | 0.936454i | \(0.385913\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.944272 | −0.0399384 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −34.8639 | −1.46934 | −0.734668 | − | 0.678426i | \(-0.762662\pi\) | ||||
−0.734668 | + | 0.678426i | \(0.762662\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.34752 | −0.0566908 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.03476 | −0.127224 | −0.0636118 | − | 0.997975i | \(-0.520262\pi\) | ||||
−0.0636118 | + | 0.997975i | \(0.520262\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.8885 | 1.58559 | 0.792793 | − | 0.609491i | \(-0.208626\pi\) | ||||
0.792793 | + | 0.609491i | \(0.208626\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.9814 | 0.499659 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.8328 | −1.03380 | −0.516902 | − | 0.856045i | \(-0.672915\pi\) | ||||
−0.516902 | + | 0.856045i | \(0.672915\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.78282 | −0.198425 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.3607 | 0.511927 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.1074 | −0.458451 | −0.229225 | − | 0.973373i | \(-0.573619\pi\) | ||||
−0.229225 | + | 0.973373i | \(0.573619\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.70820 | −0.235202 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.7456 | −1.18044 | −0.590221 | − | 0.807242i | \(-0.700959\pi\) | ||||
−0.590221 | + | 0.807242i | \(0.700959\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.23607 | 0.132666 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.1908 | 0.579822 | 0.289911 | − | 0.957054i | \(-0.406374\pi\) | ||||
0.289911 | + | 0.957054i | \(0.406374\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.4164 | 1.19992 | 0.599960 | − | 0.800030i | \(-0.295183\pi\) | ||||
0.599960 | + | 0.800030i | \(0.295183\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.62210 | −0.106603 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.0000 | 0.487065 | 0.243532 | − | 0.969893i | \(-0.421694\pi\) | ||||
0.243532 | + | 0.969893i | \(0.421694\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.73722 | −0.272559 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.1803 | −1.21897 | −0.609486 | − | 0.792797i | \(-0.708624\pi\) | ||||
−0.609486 | + | 0.792797i | \(0.708624\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.1081 | −1.61469 | −0.807345 | − | 0.590080i | \(-0.799096\pi\) | ||||
−0.807345 | + | 0.590080i | \(0.799096\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.7771 | 1.43800 | 0.719001 | − | 0.695009i | \(-0.244600\pi\) | ||||
0.719001 | + | 0.695009i | \(0.244600\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.48528 | −0.339956 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.1246 | 0.564984 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.5579 | 0.660207 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.5967 | −0.461659 | −0.230830 | − | 0.972994i | \(-0.574144\pi\) | ||||
−0.230830 | + | 0.972994i | \(0.574144\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.48218 | 0.257237 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.23607 | 0.0489748 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.9095 | −1.29985 | −0.649923 | − | 0.760000i | \(-0.725199\pi\) | ||||
−0.649923 | + | 0.760000i | \(0.725199\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.5279 | 1.47995 | 0.739977 | − | 0.672632i | \(-0.234836\pi\) | ||||
0.739977 | + | 0.672632i | \(0.234836\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.86319 | 0.230506 | 0.115253 | − | 0.993336i | \(-0.463232\pi\) | ||||
0.115253 | + | 0.993336i | \(0.463232\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.8885 | −1.64427 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.2920 | 0.833221 | 0.416610 | − | 0.909085i | \(-0.363218\pi\) | ||||
0.416610 | + | 0.909085i | \(0.363218\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.65248 | 0.103641 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.0965 | −0.627032 | −0.313516 | − | 0.949583i | \(-0.601507\pi\) | ||||
−0.313516 | + | 0.949583i | \(0.601507\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.7639 | 0.574250 | 0.287125 | − | 0.957893i | \(-0.407300\pi\) | ||||
0.287125 | + | 0.957893i | \(0.407300\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.874032 | −0.0338935 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.3607 | 0.788369 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −35.2765 | −1.36184 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.8328 | −0.957235 | −0.478617 | − | 0.878024i | \(-0.658862\pi\) | ||||
−0.478617 | + | 0.878024i | \(0.658862\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.5610 | −0.713357 | −0.356679 | − | 0.934227i | \(-0.616091\pi\) | ||||
−0.356679 | + | 0.934227i | \(0.616091\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.52786 | 0.135387 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.3299 | 1.00748 | 0.503742 | − | 0.863854i | \(-0.331956\pi\) | ||||
0.503742 | + | 0.863854i | \(0.331956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.88854 | −0.0721576 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.40182 | 0.205793 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.32145 | −0.163922 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −31.4164 | −1.18998 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.6414 | 0.741844 | 0.370922 | − | 0.928664i | \(-0.379042\pi\) | ||||
0.370922 | + | 0.928664i | \(0.379042\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.47214 | −0.168670 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.5123 | −0.696227 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.7082 | −1.04060 | −0.520302 | − | 0.853983i | \(-0.674181\pi\) | ||||
−0.520302 | + | 0.853983i | \(0.674181\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.1452 | 0.604644 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.05573 | 0.114278 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.8229 | −1.03762 | −0.518810 | − | 0.854890i | \(-0.673625\pi\) | ||||
−0.518810 | + | 0.854890i | \(0.673625\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.9443 | 0.482070 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 30.4937 | 1.13251 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.52786 | −0.205017 | −0.102509 | − | 0.994732i | \(-0.532687\pi\) | ||||
−0.102509 | + | 0.994732i | \(0.532687\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.82843 | 0.104613 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.8328 | 0.473991 | 0.236995 | − | 0.971511i | \(-0.423837\pi\) | ||||
0.236995 | + | 0.971511i | \(0.423837\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.2905 | 1.18944 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.1246 | −0.924224 | −0.462112 | − | 0.886822i | \(-0.652908\pi\) | ||||
−0.462112 | + | 0.886822i | \(0.652908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.2681 | 0.486760 | 0.243380 | − | 0.969931i | \(-0.421744\pi\) | ||||
0.243380 | + | 0.969931i | \(0.421744\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.58359 | −0.167930 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.6035 | −0.533600 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.3607 | −0.597010 | −0.298505 | − | 0.954408i | \(-0.596488\pi\) | ||||
−0.298505 | + | 0.954408i | \(0.596488\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.33540 | −0.0486003 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.3050 | 1.57395 | 0.786973 | − | 0.616988i | \(-0.211647\pi\) | ||||
0.786973 | + | 0.616988i | \(0.211647\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.60815 | −0.203295 | −0.101648 | − | 0.994820i | \(-0.532411\pi\) | ||||
−0.101648 | + | 0.994820i | \(0.532411\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.9443 | 0.685829 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.3060 | −0.660990 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.8885 | 1.43842 | 0.719209 | − | 0.694794i | \(-0.244504\pi\) | ||||
0.719209 | + | 0.694794i | \(0.244504\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.2719 | 1.59235 | 0.796175 | − | 0.605067i | \(-0.206854\pi\) | ||||
0.796175 | + | 0.605067i | \(0.206854\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.1803 | 0.868583 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.48528 | 0.304017 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.58359 | −0.307145 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.24419 | −0.187173 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.1246 | 1.89369 | 0.946844 | − | 0.321693i | \(-0.104252\pi\) | ||||
0.946844 | + | 0.321693i | \(0.104252\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.54173 | 0.0548177 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.4164 | −0.547453 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 48.5933 | 1.72126 | 0.860632 | − | 0.509227i | \(-0.170069\pi\) | ||||
0.860632 | + | 0.509227i | \(0.170069\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.1803 | 0.713929 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.6414 | 0.693129 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.47214 | 0.0871313 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.83153 | 0.169868 | 0.0849338 | − | 0.996387i | \(-0.472932\pi\) | ||||
0.0849338 | + | 0.996387i | \(0.472932\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.9597 | −0.769215 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.763932 | −0.0267266 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.0618 | −0.455859 | −0.227930 | − | 0.973678i | \(-0.573196\pi\) | ||||
−0.227930 | + | 0.973678i | \(0.573196\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.180340 | 0.00628625 | 0.00314313 | − | 0.999995i | \(-0.499000\pi\) | ||||
0.00314313 | + | 0.999995i | \(0.499000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.6761 | −0.788526 | −0.394263 | − | 0.918998i | \(-0.629000\pi\) | ||||
−0.394263 | + | 0.918998i | \(0.629000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.5279 | 0.678231 | 0.339115 | − | 0.940745i | \(-0.389872\pi\) | ||||
0.339115 | + | 0.940745i | \(0.389872\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.70246 | −0.128283 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.41641 | −0.118230 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.1452 | 0.557396 | 0.278698 | − | 0.960379i | \(-0.410097\pi\) | ||||
0.278698 | + | 0.960379i | \(0.410097\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.8197 | 0.786885 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.0270 | −0.344940 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.00000 | 0.103081 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.6491 | 0.433606 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.3607 | −0.628658 | −0.314329 | − | 0.949314i | \(-0.601779\pi\) | ||||
−0.314329 | + | 0.949314i | \(0.601779\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.7618 | 1.49487 | 0.747437 | − | 0.664332i | \(-0.231284\pi\) | ||||
0.747437 | + | 0.664332i | \(0.231284\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.3050 | 1.40931 | 0.704653 | − | 0.709552i | \(-0.251103\pi\) | ||||
0.704653 | + | 0.709552i | \(0.251103\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −52.5508 | −1.78885 | −0.894426 | − | 0.447217i | \(-0.852415\pi\) | ||||
−0.894426 | + | 0.447217i | \(0.852415\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.4721 | −0.628071 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.32145 | −0.146595 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.1115 | 0.478148 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.07262 | 0.272904 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.00000 | 0.202606 | 0.101303 | − | 0.994856i | \(-0.467699\pi\) | ||||
0.101303 | + | 0.994856i | \(0.467699\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.0656 | 1.48461 | 0.742303 | − | 0.670064i | \(-0.233733\pi\) | ||||
0.742303 | + | 0.670064i | \(0.233733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.9443 | 1.78172 | 0.890858 | − | 0.454281i | \(-0.150104\pi\) | ||||
0.890858 | + | 0.454281i | \(0.150104\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 53.9952 | 1.81298 | 0.906490 | − | 0.422227i | \(-0.138752\pi\) | ||||
0.906490 | + | 0.422227i | \(0.138752\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.41641 | −0.248738 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.45052 | −0.182395 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.65248 | −0.222368 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 41.0910 | 1.37046 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.1803 | −0.539045 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.0618 | −0.434188 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.9443 | −0.695443 | −0.347722 | − | 0.937598i | \(-0.613045\pi\) | ||||
−0.347722 | + | 0.937598i | \(0.613045\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.1877 | 0.403798 | 0.201899 | − | 0.979406i | \(-0.435289\pi\) | ||||
0.201899 | + | 0.979406i | \(0.435289\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.5279 | 0.447707 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.03476 | −0.100217 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.0557 | −0.364695 | −0.182347 | − | 0.983234i | \(-0.558370\pi\) | ||||
−0.182347 | + | 0.983234i | \(0.558370\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.75117 | −0.123471 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.9443 | 0.622884 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.4428 | 0.408234 | 0.204117 | − | 0.978946i | \(-0.434568\pi\) | ||||
0.204117 | + | 0.978946i | \(0.434568\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.15298 | −0.299335 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.94427 | 0.226859 | 0.113430 | − | 0.993546i | \(-0.463816\pi\) | ||||
0.113430 | + | 0.993546i | \(0.463816\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.90569 | 0.0621236 | 0.0310618 | − | 0.999517i | \(-0.490111\pi\) | ||||
0.0310618 | + | 0.999517i | \(0.490111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.0000 | −0.781548 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.6011 | −1.35185 | −0.675927 | − | 0.736969i | \(-0.736256\pi\) | ||||
−0.675927 | + | 0.736969i | \(0.736256\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.58359 | 0.278635 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.9281 | −0.677926 | −0.338963 | − | 0.940800i | \(-0.610076\pi\) | ||||
−0.338963 | + | 0.940800i | \(0.610076\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.5279 | 0.696625 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.16073 | 0.0697735 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.58359 | 0.0510836 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.7326 | −0.506450 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.5410 | 0.531923 | 0.265962 | − | 0.963984i | \(-0.414311\pi\) | ||||
0.265962 | + | 0.963984i | \(0.414311\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.3137 | −0.363074 | −0.181537 | − | 0.983384i | \(-0.558107\pi\) | ||||
−0.181537 | + | 0.983384i | \(0.558107\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.94427 | 0.158506 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.0888 | −0.738676 | −0.369338 | − | 0.929295i | \(-0.620415\pi\) | ||||
−0.369338 | + | 0.929295i | \(0.620415\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.0000 | 0.767043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.32145 | −0.137833 | −0.0689165 | − | 0.997622i | \(-0.521954\pi\) | ||||
−0.0689165 | + | 0.997622i | \(0.521954\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.83282 | −0.217712 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.16073 | 0.0687071 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.88854 | 0.187056 | 0.0935279 | − | 0.995617i | \(-0.470186\pi\) | ||||
0.0935279 | + | 0.995617i | \(0.470186\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.99226 | 0.221669 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.7771 | −0.563006 | −0.281503 | − | 0.959560i | \(-0.590833\pi\) | ||||
−0.281503 | + | 0.959560i | \(0.590833\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4788.2.a.q.1.3 | yes | 4 | |
3.2 | odd | 2 | inner | 4788.2.a.q.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4788.2.a.q.1.2 | ✓ | 4 | 3.2 | odd | 2 | inner | |
4788.2.a.q.1.3 | yes | 4 | 1.1 | even | 1 | trivial |