Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(1,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.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: | \(32.0519513713\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 14x^{6} + 28x^{5} + 43x^{4} - 90x^{3} - 23x^{2} + 82x - 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.34121\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4014.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.350247 | 0.156635 | 0.0783176 | − | 0.996928i | \(-0.475045\pi\) | ||||
0.0783176 | + | 0.996928i | \(0.475045\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.21437 | 1.21492 | 0.607459 | − | 0.794351i | \(-0.292189\pi\) | ||||
0.607459 | + | 0.794351i | \(0.292189\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.350247 | −0.110758 | ||||||||
\(11\) | 3.33410 | 1.00527 | 0.502634 | − | 0.864499i | \(-0.332364\pi\) | ||||
0.502634 | + | 0.864499i | \(0.332364\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.79431 | −1.32970 | −0.664852 | − | 0.746975i | \(-0.731505\pi\) | ||||
−0.664852 | + | 0.746975i | \(0.731505\pi\) | |||||||
\(14\) | −3.21437 | −0.859076 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.65967 | −0.402530 | −0.201265 | − | 0.979537i | \(-0.564505\pi\) | ||||
−0.201265 | + | 0.979537i | \(0.564505\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.44882 | −1.47946 | −0.739730 | − | 0.672903i | \(-0.765047\pi\) | ||||
−0.739730 | + | 0.672903i | \(0.765047\pi\) | |||||||
\(20\) | 0.350247 | 0.0783176 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.33410 | −0.710832 | ||||||||
\(23\) | 7.13194 | 1.48711 | 0.743556 | − | 0.668674i | \(-0.233138\pi\) | ||||
0.743556 | + | 0.668674i | \(0.233138\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.87733 | −0.975465 | ||||||||
\(26\) | 4.79431 | 0.940242 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.21437 | 0.607459 | ||||||||
\(29\) | 2.80668 | 0.521187 | 0.260593 | − | 0.965449i | \(-0.416082\pi\) | ||||
0.260593 | + | 0.965449i | \(0.416082\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.66261 | 1.19664 | 0.598320 | − | 0.801257i | \(-0.295835\pi\) | ||||
0.598320 | + | 0.801257i | \(0.295835\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.65967 | 0.284632 | ||||||||
\(35\) | 1.12582 | 0.190299 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.669487 | −0.110063 | −0.0550315 | − | 0.998485i | \(-0.517526\pi\) | ||||
−0.0550315 | + | 0.998485i | \(0.517526\pi\) | |||||||
\(38\) | 6.44882 | 1.04614 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.350247 | −0.0553789 | ||||||||
\(41\) | 0.589936 | 0.0921326 | 0.0460663 | − | 0.998938i | \(-0.485331\pi\) | ||||
0.0460663 | + | 0.998938i | \(0.485331\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.08795 | −0.623406 | −0.311703 | − | 0.950180i | \(-0.600899\pi\) | ||||
−0.311703 | + | 0.950180i | \(0.600899\pi\) | |||||||
\(44\) | 3.33410 | 0.502634 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.13194 | −1.05155 | ||||||||
\(47\) | 7.50921 | 1.09533 | 0.547665 | − | 0.836697i | \(-0.315517\pi\) | ||||
0.547665 | + | 0.836697i | \(0.315517\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.33217 | 0.476024 | ||||||||
\(50\) | 4.87733 | 0.689758 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.79431 | −0.664852 | ||||||||
\(53\) | 7.08046 | 0.972576 | 0.486288 | − | 0.873799i | \(-0.338351\pi\) | ||||
0.486288 | + | 0.873799i | \(0.338351\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.16776 | 0.157460 | ||||||||
\(56\) | −3.21437 | −0.429538 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.80668 | −0.368535 | ||||||||
\(59\) | 5.66381 | 0.737365 | 0.368682 | − | 0.929555i | \(-0.379809\pi\) | ||||
0.368682 | + | 0.929555i | \(0.379809\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.64659 | −0.210825 | −0.105412 | − | 0.994429i | \(-0.533616\pi\) | ||||
−0.105412 | + | 0.994429i | \(0.533616\pi\) | |||||||
\(62\) | −6.66261 | −0.846152 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.67919 | −0.208278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.99722 | 1.22135 | 0.610677 | − | 0.791880i | \(-0.290897\pi\) | ||||
0.610677 | + | 0.791880i | \(0.290897\pi\) | |||||||
\(68\) | −1.65967 | −0.201265 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.12582 | −0.134562 | ||||||||
\(71\) | 10.6585 | 1.26493 | 0.632466 | − | 0.774588i | \(-0.282043\pi\) | ||||
0.632466 | + | 0.774588i | \(0.282043\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.63197 | 0.776213 | 0.388107 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388107 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(74\) | 0.669487 | 0.0778263 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.44882 | −0.739730 | ||||||||
\(77\) | 10.7170 | 1.22132 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.4826 | 1.62942 | 0.814712 | − | 0.579866i | \(-0.196895\pi\) | ||||
0.814712 | + | 0.579866i | \(0.196895\pi\) | |||||||
\(80\) | 0.350247 | 0.0391588 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.589936 | −0.0651476 | ||||||||
\(83\) | 8.59600 | 0.943533 | 0.471767 | − | 0.881723i | \(-0.343616\pi\) | ||||
0.471767 | + | 0.881723i | \(0.343616\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.581295 | −0.0630503 | ||||||||
\(86\) | 4.08795 | 0.440815 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.33410 | −0.355416 | ||||||||
\(89\) | 0.107172 | 0.0113602 | 0.00568011 | − | 0.999984i | \(-0.498192\pi\) | ||||
0.00568011 | + | 0.999984i | \(0.498192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.4107 | −1.61548 | ||||||||
\(92\) | 7.13194 | 0.743556 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.50921 | −0.774516 | ||||||||
\(95\) | −2.25868 | −0.231736 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.0990721 | −0.0100593 | −0.00502963 | − | 0.999987i | \(-0.501601\pi\) | ||||
−0.00502963 | + | 0.999987i | \(0.501601\pi\) | |||||||
\(98\) | −3.33217 | −0.336600 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.87733 | −0.487733 | ||||||||
\(101\) | −18.0388 | −1.79493 | −0.897465 | − | 0.441086i | \(-0.854594\pi\) | ||||
−0.897465 | + | 0.441086i | \(0.854594\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.76745 | 0.174152 | 0.0870761 | − | 0.996202i | \(-0.472248\pi\) | ||||
0.0870761 | + | 0.996202i | \(0.472248\pi\) | |||||||
\(104\) | 4.79431 | 0.470121 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.08046 | −0.687715 | ||||||||
\(107\) | −19.3478 | −1.87043 | −0.935213 | − | 0.354085i | \(-0.884792\pi\) | ||||
−0.935213 | + | 0.354085i | \(0.884792\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.73637 | −0.166314 | −0.0831572 | − | 0.996536i | \(-0.526500\pi\) | ||||
−0.0831572 | + | 0.996536i | \(0.526500\pi\) | |||||||
\(110\) | −1.16776 | −0.111341 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.21437 | 0.303729 | ||||||||
\(113\) | −10.6213 | −0.999164 | −0.499582 | − | 0.866267i | \(-0.666513\pi\) | ||||
−0.499582 | + | 0.866267i | \(0.666513\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.49794 | 0.232934 | ||||||||
\(116\) | 2.80668 | 0.260593 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.66381 | −0.521396 | ||||||||
\(119\) | −5.33480 | −0.489040 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.116202 | 0.0105638 | ||||||||
\(122\) | 1.64659 | 0.149075 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.66261 | 0.598320 | ||||||||
\(125\) | −3.45950 | −0.309427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.09477 | 0.540823 | 0.270412 | − | 0.962745i | \(-0.412840\pi\) | ||||
0.270412 | + | 0.962745i | \(0.412840\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.67919 | 0.147275 | ||||||||
\(131\) | 10.3181 | 0.901499 | 0.450749 | − | 0.892651i | \(-0.351157\pi\) | ||||
0.450749 | + | 0.892651i | \(0.351157\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.7289 | −1.79742 | ||||||||
\(134\) | −9.99722 | −0.863628 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.65967 | 0.142316 | ||||||||
\(137\) | −2.82222 | −0.241119 | −0.120559 | − | 0.992706i | \(-0.538469\pi\) | ||||
−0.120559 | + | 0.992706i | \(0.538469\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.98204 | −0.168114 | −0.0840572 | − | 0.996461i | \(-0.526788\pi\) | ||||
−0.0840572 | + | 0.996461i | \(0.526788\pi\) | |||||||
\(140\) | 1.12582 | 0.0951494 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.6585 | −0.894441 | ||||||||
\(143\) | −15.9847 | −1.33671 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.983030 | 0.0816362 | ||||||||
\(146\) | −6.63197 | −0.548866 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.669487 | −0.0550315 | ||||||||
\(149\) | 13.7074 | 1.12296 | 0.561479 | − | 0.827491i | \(-0.310233\pi\) | ||||
0.561479 | + | 0.827491i | \(0.310233\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.4598 | 1.42086 | 0.710428 | − | 0.703770i | \(-0.248501\pi\) | ||||
0.710428 | + | 0.703770i | \(0.248501\pi\) | |||||||
\(152\) | 6.44882 | 0.523068 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.7170 | −0.863602 | ||||||||
\(155\) | 2.33356 | 0.187436 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.3567 | 1.06598 | 0.532989 | − | 0.846122i | \(-0.321069\pi\) | ||||
0.532989 | + | 0.846122i | \(0.321069\pi\) | |||||||
\(158\) | −14.4826 | −1.15218 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.350247 | −0.0276895 | ||||||||
\(161\) | 22.9247 | 1.80672 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.76239 | 0.451345 | 0.225673 | − | 0.974203i | \(-0.427542\pi\) | ||||
0.225673 | + | 0.974203i | \(0.427542\pi\) | |||||||
\(164\) | 0.589936 | 0.0460663 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.59600 | −0.667179 | ||||||||
\(167\) | 19.3205 | 1.49506 | 0.747532 | − | 0.664226i | \(-0.231239\pi\) | ||||
0.747532 | + | 0.664226i | \(0.231239\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.98545 | 0.768111 | ||||||||
\(170\) | 0.581295 | 0.0445833 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.08795 | −0.311703 | ||||||||
\(173\) | 9.74463 | 0.740870 | 0.370435 | − | 0.928858i | \(-0.379209\pi\) | ||||
0.370435 | + | 0.928858i | \(0.379209\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.6775 | −1.18511 | ||||||||
\(176\) | 3.33410 | 0.251317 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.107172 | −0.00803289 | ||||||||
\(179\) | 1.08363 | 0.0809945 | 0.0404973 | − | 0.999180i | \(-0.487106\pi\) | ||||
0.0404973 | + | 0.999180i | \(0.487106\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.7767 | −1.02401 | −0.512006 | − | 0.858982i | \(-0.671097\pi\) | ||||
−0.512006 | + | 0.858982i | \(0.671097\pi\) | |||||||
\(182\) | 15.4107 | 1.14232 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.13194 | −0.525773 | ||||||||
\(185\) | −0.234486 | −0.0172397 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.53351 | −0.404650 | ||||||||
\(188\) | 7.50921 | 0.547665 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.25868 | 0.163862 | ||||||||
\(191\) | 11.9517 | 0.864795 | 0.432397 | − | 0.901683i | \(-0.357668\pi\) | ||||
0.432397 | + | 0.901683i | \(0.357668\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.0497 | −1.73113 | −0.865567 | − | 0.500793i | \(-0.833042\pi\) | ||||
−0.865567 | + | 0.500793i | \(0.833042\pi\) | |||||||
\(194\) | 0.0990721 | 0.00711296 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.33217 | 0.238012 | ||||||||
\(197\) | −7.92447 | −0.564595 | −0.282298 | − | 0.959327i | \(-0.591097\pi\) | ||||
−0.282298 | + | 0.959327i | \(0.591097\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.100817 | −0.00714674 | −0.00357337 | − | 0.999994i | \(-0.501137\pi\) | ||||
−0.00357337 | + | 0.999994i | \(0.501137\pi\) | |||||||
\(200\) | 4.87733 | 0.344879 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18.0388 | 1.26921 | ||||||||
\(203\) | 9.02169 | 0.633199 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.206623 | 0.0144312 | ||||||||
\(206\) | −1.76745 | −0.123144 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.79431 | −0.332426 | ||||||||
\(209\) | −21.5010 | −1.48725 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.3981 | −1.06005 | −0.530024 | − | 0.847983i | \(-0.677817\pi\) | ||||
−0.530024 | + | 0.847983i | \(0.677817\pi\) | |||||||
\(212\) | 7.08046 | 0.486288 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.3478 | 1.32259 | ||||||||
\(215\) | −1.43179 | −0.0976473 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.4161 | 1.45382 | ||||||||
\(218\) | 1.73637 | 0.117602 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.16776 | 0.0787302 | ||||||||
\(221\) | 7.95699 | 0.535245 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00000 | 0.0669650 | ||||||||
\(224\) | −3.21437 | −0.214769 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.6213 | 0.706516 | ||||||||
\(227\) | −3.07847 | −0.204325 | −0.102163 | − | 0.994768i | \(-0.532576\pi\) | ||||
−0.102163 | + | 0.994768i | \(0.532576\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.5684 | 1.22703 | 0.613516 | − | 0.789682i | \(-0.289755\pi\) | ||||
0.613516 | + | 0.789682i | \(0.289755\pi\) | |||||||
\(230\) | −2.49794 | −0.164709 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.80668 | −0.184267 | ||||||||
\(233\) | −19.5683 | −1.28196 | −0.640981 | − | 0.767557i | \(-0.721472\pi\) | ||||
−0.640981 | + | 0.767557i | \(0.721472\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.63008 | 0.171567 | ||||||||
\(236\) | 5.66381 | 0.368682 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.33480 | 0.345804 | ||||||||
\(239\) | 18.5672 | 1.20101 | 0.600505 | − | 0.799621i | \(-0.294966\pi\) | ||||
0.600505 | + | 0.799621i | \(0.294966\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.634708 | −0.0408852 | −0.0204426 | − | 0.999791i | \(-0.506508\pi\) | ||||
−0.0204426 | + | 0.999791i | \(0.506508\pi\) | |||||||
\(242\) | −0.116202 | −0.00746972 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.64659 | −0.105412 | ||||||||
\(245\) | 1.16708 | 0.0745621 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.9177 | 1.96724 | ||||||||
\(248\) | −6.66261 | −0.423076 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.45950 | 0.218798 | ||||||||
\(251\) | 9.07437 | 0.572769 | 0.286385 | − | 0.958115i | \(-0.407546\pi\) | ||||
0.286385 | + | 0.958115i | \(0.407546\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.7786 | 1.49495 | ||||||||
\(254\) | −6.09477 | −0.382420 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.7825 | 1.17162 | 0.585810 | − | 0.810448i | \(-0.300776\pi\) | ||||
0.585810 | + | 0.810448i | \(0.300776\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.15198 | −0.133717 | ||||||||
\(260\) | −1.67919 | −0.104139 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.3181 | −0.637456 | ||||||||
\(263\) | −0.476195 | −0.0293634 | −0.0146817 | − | 0.999892i | \(-0.504674\pi\) | ||||
−0.0146817 | + | 0.999892i | \(0.504674\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.47991 | 0.152340 | ||||||||
\(266\) | 20.7289 | 1.27097 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.99722 | 0.610677 | ||||||||
\(269\) | 16.0647 | 0.979482 | 0.489741 | − | 0.871868i | \(-0.337091\pi\) | ||||
0.489741 | + | 0.871868i | \(0.337091\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.6687 | 0.891057 | 0.445529 | − | 0.895268i | \(-0.353016\pi\) | ||||
0.445529 | + | 0.895268i | \(0.353016\pi\) | |||||||
\(272\) | −1.65967 | −0.100632 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.82222 | 0.170497 | ||||||||
\(275\) | −16.2615 | −0.980604 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.1320 | −0.728942 | −0.364471 | − | 0.931215i | \(-0.618750\pi\) | ||||
−0.364471 | + | 0.931215i | \(0.618750\pi\) | |||||||
\(278\) | 1.98204 | 0.118875 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.12582 | −0.0672808 | ||||||||
\(281\) | 7.26142 | 0.433180 | 0.216590 | − | 0.976263i | \(-0.430507\pi\) | ||||
0.216590 | + | 0.976263i | \(0.430507\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −32.8202 | −1.95096 | −0.975480 | − | 0.220089i | \(-0.929365\pi\) | ||||
−0.975480 | + | 0.220089i | \(0.929365\pi\) | |||||||
\(284\) | 10.6585 | 0.632466 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.9847 | 0.945196 | ||||||||
\(287\) | 1.89627 | 0.111933 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.2455 | −0.837970 | ||||||||
\(290\) | −0.983030 | −0.0577255 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.63197 | 0.388107 | ||||||||
\(293\) | 0.225898 | 0.0131971 | 0.00659855 | − | 0.999978i | \(-0.497900\pi\) | ||||
0.00659855 | + | 0.999978i | \(0.497900\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.98373 | 0.115497 | ||||||||
\(296\) | 0.669487 | 0.0389131 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.7074 | −0.794051 | ||||||||
\(299\) | −34.1927 | −1.97742 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.1402 | −0.757387 | ||||||||
\(302\) | −17.4598 | −1.00470 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.44882 | −0.369865 | ||||||||
\(305\) | −0.576714 | −0.0330226 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.7531 | −0.784930 | −0.392465 | − | 0.919767i | \(-0.628378\pi\) | ||||
−0.392465 | + | 0.919767i | \(0.628378\pi\) | |||||||
\(308\) | 10.7170 | 0.610659 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.33356 | −0.132537 | ||||||||
\(311\) | −6.47772 | −0.367318 | −0.183659 | − | 0.982990i | \(-0.558794\pi\) | ||||
−0.183659 | + | 0.982990i | \(0.558794\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.0231 | −0.736109 | −0.368055 | − | 0.929804i | \(-0.619976\pi\) | ||||
−0.368055 | + | 0.929804i | \(0.619976\pi\) | |||||||
\(314\) | −13.3567 | −0.753760 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.4826 | 0.814712 | ||||||||
\(317\) | 9.33785 | 0.524466 | 0.262233 | − | 0.965005i | \(-0.415541\pi\) | ||||
0.262233 | + | 0.965005i | \(0.415541\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.35773 | 0.523932 | ||||||||
\(320\) | 0.350247 | 0.0195794 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −22.9247 | −1.27754 | ||||||||
\(323\) | 10.7029 | 0.595527 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.3834 | 1.29708 | ||||||||
\(326\) | −5.76239 | −0.319149 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.589936 | −0.0325738 | ||||||||
\(329\) | 24.1374 | 1.33074 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.0987 | 1.54444 | 0.772221 | − | 0.635354i | \(-0.219146\pi\) | ||||
0.772221 | + | 0.635354i | \(0.219146\pi\) | |||||||
\(332\) | 8.59600 | 0.471767 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.3205 | −1.05717 | ||||||||
\(335\) | 3.50149 | 0.191307 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.9674 | 1.03322 | 0.516609 | − | 0.856221i | \(-0.327194\pi\) | ||||
0.516609 | + | 0.856221i | \(0.327194\pi\) | |||||||
\(338\) | −9.98545 | −0.543137 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.581295 | −0.0315252 | ||||||||
\(341\) | 22.2138 | 1.20294 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.7898 | −0.636588 | ||||||||
\(344\) | 4.08795 | 0.220407 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.74463 | −0.523874 | ||||||||
\(347\) | 18.3610 | 0.985669 | 0.492834 | − | 0.870123i | \(-0.335961\pi\) | ||||
0.492834 | + | 0.870123i | \(0.335961\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.1613 | −1.50744 | −0.753720 | − | 0.657196i | \(-0.771743\pi\) | ||||
−0.753720 | + | 0.657196i | \(0.771743\pi\) | |||||||
\(350\) | 15.6775 | 0.837999 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.33410 | −0.177708 | ||||||||
\(353\) | 5.84323 | 0.311004 | 0.155502 | − | 0.987836i | \(-0.450301\pi\) | ||||
0.155502 | + | 0.987836i | \(0.450301\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.73311 | 0.198133 | ||||||||
\(356\) | 0.107172 | 0.00568011 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.08363 | −0.0572718 | ||||||||
\(359\) | −15.8671 | −0.837435 | −0.418717 | − | 0.908117i | \(-0.637520\pi\) | ||||
−0.418717 | + | 0.908117i | \(0.637520\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.5873 | 1.18880 | ||||||||
\(362\) | 13.7767 | 0.724086 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −15.4107 | −0.807740 | ||||||||
\(365\) | 2.32283 | 0.121582 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.90055 | 0.412405 | 0.206203 | − | 0.978509i | \(-0.433889\pi\) | ||||
0.206203 | + | 0.978509i | \(0.433889\pi\) | |||||||
\(368\) | 7.13194 | 0.371778 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.234486 | 0.0121903 | ||||||||
\(371\) | 22.7592 | 1.18160 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.3810 | −0.589285 | −0.294643 | − | 0.955608i | \(-0.595201\pi\) | ||||
−0.294643 | + | 0.955608i | \(0.595201\pi\) | |||||||
\(374\) | 5.53351 | 0.286131 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.50921 | −0.387258 | ||||||||
\(377\) | −13.4561 | −0.693024 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.6721 | 0.753658 | 0.376829 | − | 0.926283i | \(-0.377014\pi\) | ||||
0.376829 | + | 0.926283i | \(0.377014\pi\) | |||||||
\(380\) | −2.25868 | −0.115868 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.9517 | −0.611502 | ||||||||
\(383\) | −19.0623 | −0.974036 | −0.487018 | − | 0.873392i | \(-0.661915\pi\) | ||||
−0.487018 | + | 0.873392i | \(0.661915\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.75360 | 0.191301 | ||||||||
\(386\) | 24.0497 | 1.22410 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.0990721 | −0.00502963 | ||||||||
\(389\) | 6.04386 | 0.306436 | 0.153218 | − | 0.988192i | \(-0.451036\pi\) | ||||
0.153218 | + | 0.988192i | \(0.451036\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.8367 | −0.598607 | ||||||||
\(392\) | −3.33217 | −0.168300 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.92447 | 0.399229 | ||||||||
\(395\) | 5.07250 | 0.255225 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.8374 | 1.44731 | 0.723653 | − | 0.690164i | \(-0.242462\pi\) | ||||
0.723653 | + | 0.690164i | \(0.242462\pi\) | |||||||
\(398\) | 0.100817 | 0.00505351 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.87733 | −0.243866 | ||||||||
\(401\) | 4.13124 | 0.206304 | 0.103152 | − | 0.994666i | \(-0.467107\pi\) | ||||
0.103152 | + | 0.994666i | \(0.467107\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31.9426 | −1.59118 | ||||||||
\(404\) | −18.0388 | −0.897465 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.02169 | −0.447739 | ||||||||
\(407\) | −2.23213 | −0.110643 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.1566 | 0.996681 | 0.498340 | − | 0.866981i | \(-0.333943\pi\) | ||||
0.498340 | + | 0.866981i | \(0.333943\pi\) | |||||||
\(410\) | −0.206623 | −0.0102044 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.76745 | 0.0870761 | ||||||||
\(413\) | 18.2056 | 0.895837 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.01072 | 0.147791 | ||||||||
\(416\) | 4.79431 | 0.235061 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 21.5010 | 1.05165 | ||||||||
\(419\) | −13.7607 | −0.672253 | −0.336127 | − | 0.941817i | \(-0.609117\pi\) | ||||
−0.336127 | + | 0.941817i | \(0.609117\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.59634 | −0.0778007 | −0.0389003 | − | 0.999243i | \(-0.512385\pi\) | ||||
−0.0389003 | + | 0.999243i | \(0.512385\pi\) | |||||||
\(422\) | 15.3981 | 0.749567 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.08046 | −0.343857 | ||||||||
\(425\) | 8.09477 | 0.392654 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.29276 | −0.256134 | ||||||||
\(428\) | −19.3478 | −0.935213 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.43179 | 0.0690471 | ||||||||
\(431\) | 36.7445 | 1.76992 | 0.884959 | − | 0.465669i | \(-0.154186\pi\) | ||||
0.884959 | + | 0.465669i | \(0.154186\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.4318 | 0.645490 | 0.322745 | − | 0.946486i | \(-0.395394\pi\) | ||||
0.322745 | + | 0.946486i | \(0.395394\pi\) | |||||||
\(434\) | −21.4161 | −1.02800 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.73637 | −0.0831572 | ||||||||
\(437\) | −45.9926 | −2.20012 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.9136 | 1.04588 | 0.522938 | − | 0.852371i | \(-0.324836\pi\) | ||||
0.522938 | + | 0.852371i | \(0.324836\pi\) | |||||||
\(440\) | −1.16776 | −0.0556706 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.95699 | −0.378476 | ||||||||
\(443\) | −1.80133 | −0.0855839 | −0.0427919 | − | 0.999084i | \(-0.513625\pi\) | ||||
−0.0427919 | + | 0.999084i | \(0.513625\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.0375367 | 0.00177941 | ||||||||
\(446\) | −1.00000 | −0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.21437 | 0.151865 | ||||||||
\(449\) | 19.3399 | 0.912709 | 0.456354 | − | 0.889798i | \(-0.349155\pi\) | ||||
0.456354 | + | 0.889798i | \(0.349155\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.96690 | 0.0926179 | ||||||||
\(452\) | −10.6213 | −0.499582 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.07847 | 0.144480 | ||||||||
\(455\) | −5.39755 | −0.253041 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.7852 | 0.691624 | 0.345812 | − | 0.938304i | \(-0.387603\pi\) | ||||
0.345812 | + | 0.938304i | \(0.387603\pi\) | |||||||
\(458\) | −18.5684 | −0.867642 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.49794 | 0.116467 | ||||||||
\(461\) | −11.6231 | −0.541339 | −0.270670 | − | 0.962672i | \(-0.587245\pi\) | ||||
−0.270670 | + | 0.962672i | \(0.587245\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.0117 | −0.837074 | −0.418537 | − | 0.908200i | \(-0.637457\pi\) | ||||
−0.418537 | + | 0.908200i | \(0.637457\pi\) | |||||||
\(464\) | 2.80668 | 0.130297 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.5683 | 0.906484 | ||||||||
\(467\) | 28.5900 | 1.32299 | 0.661493 | − | 0.749951i | \(-0.269923\pi\) | ||||
0.661493 | + | 0.749951i | \(0.269923\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.1347 | 1.48384 | ||||||||
\(470\) | −2.63008 | −0.121316 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.66381 | −0.260698 | ||||||||
\(473\) | −13.6296 | −0.626690 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31.4530 | 1.44316 | ||||||||
\(476\) | −5.33480 | −0.244520 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.5672 | −0.849242 | ||||||||
\(479\) | −36.8616 | −1.68425 | −0.842124 | − | 0.539284i | \(-0.818695\pi\) | ||||
−0.842124 | + | 0.539284i | \(0.818695\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.20973 | 0.146351 | ||||||||
\(482\) | 0.634708 | 0.0289102 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.116202 | 0.00528189 | ||||||||
\(485\) | −0.0346997 | −0.00157563 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.16658 | 0.415378 | 0.207689 | − | 0.978195i | \(-0.433406\pi\) | ||||
0.207689 | + | 0.978195i | \(0.433406\pi\) | |||||||
\(488\) | 1.64659 | 0.0745377 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.16708 | −0.0527234 | ||||||||
\(491\) | −21.2418 | −0.958630 | −0.479315 | − | 0.877643i | \(-0.659115\pi\) | ||||
−0.479315 | + | 0.877643i | \(0.659115\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.65816 | −0.209793 | ||||||||
\(494\) | −30.9177 | −1.39105 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.66261 | 0.299160 | ||||||||
\(497\) | 34.2604 | 1.53679 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.75001 | −0.123107 | −0.0615536 | − | 0.998104i | \(-0.519606\pi\) | ||||
−0.0615536 | + | 0.998104i | \(0.519606\pi\) | |||||||
\(500\) | −3.45950 | −0.154714 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.07437 | −0.405009 | ||||||||
\(503\) | −10.5226 | −0.469178 | −0.234589 | − | 0.972095i | \(-0.575374\pi\) | ||||
−0.234589 | + | 0.972095i | \(0.575374\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.31804 | −0.281149 | ||||||||
\(506\) | −23.7786 | −1.05709 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.09477 | 0.270412 | ||||||||
\(509\) | −21.7076 | −0.962172 | −0.481086 | − | 0.876673i | \(-0.659758\pi\) | ||||
−0.481086 | + | 0.876673i | \(0.659758\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.3176 | 0.943035 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.7825 | −0.828461 | ||||||||
\(515\) | 0.619045 | 0.0272784 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.0364 | 1.10110 | ||||||||
\(518\) | 2.15198 | 0.0945525 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.67919 | 0.0736375 | ||||||||
\(521\) | −18.2299 | −0.798666 | −0.399333 | − | 0.916806i | \(-0.630758\pi\) | ||||
−0.399333 | + | 0.916806i | \(0.630758\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.2016 | 0.664720 | 0.332360 | − | 0.943153i | \(-0.392155\pi\) | ||||
0.332360 | + | 0.943153i | \(0.392155\pi\) | |||||||
\(524\) | 10.3181 | 0.450749 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.476195 | 0.0207631 | ||||||||
\(527\) | −11.0577 | −0.481683 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.8645 | 1.21150 | ||||||||
\(530\) | −2.47991 | −0.107720 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −20.7289 | −0.898711 | ||||||||
\(533\) | −2.82834 | −0.122509 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.77652 | −0.292975 | ||||||||
\(536\) | −9.99722 | −0.431814 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.0647 | −0.692599 | ||||||||
\(539\) | 11.1098 | 0.478532 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.4860 | 1.13872 | 0.569362 | − | 0.822087i | \(-0.307190\pi\) | ||||
0.569362 | + | 0.822087i | \(0.307190\pi\) | |||||||
\(542\) | −14.6687 | −0.630073 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.65967 | 0.0711579 | ||||||||
\(545\) | −0.608159 | −0.0260507 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.6800 | −1.22627 | −0.613134 | − | 0.789979i | \(-0.710092\pi\) | ||||
−0.613134 | + | 0.789979i | \(0.710092\pi\) | |||||||
\(548\) | −2.82222 | −0.120559 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 16.2615 | 0.693392 | ||||||||
\(551\) | −18.0997 | −0.771075 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 46.5525 | 1.97962 | ||||||||
\(554\) | 12.1320 | 0.515440 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.98204 | −0.0840572 | ||||||||
\(557\) | −12.9805 | −0.550000 | −0.275000 | − | 0.961444i | \(-0.588678\pi\) | ||||
−0.275000 | + | 0.961444i | \(0.588678\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.5989 | 0.828945 | ||||||||
\(560\) | 1.12582 | 0.0475747 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.26142 | −0.306304 | ||||||||
\(563\) | 10.8955 | 0.459191 | 0.229596 | − | 0.973286i | \(-0.426260\pi\) | ||||
0.229596 | + | 0.973286i | \(0.426260\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.72006 | −0.156504 | ||||||||
\(566\) | 32.8202 | 1.37954 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.6585 | −0.447221 | ||||||||
\(569\) | 0.263419 | 0.0110431 | 0.00552156 | − | 0.999985i | \(-0.498242\pi\) | ||||
0.00552156 | + | 0.999985i | \(0.498242\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.6277 | 0.570303 | 0.285151 | − | 0.958483i | \(-0.407956\pi\) | ||||
0.285151 | + | 0.958483i | \(0.407956\pi\) | |||||||
\(572\) | −15.9847 | −0.668354 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.89627 | −0.0791489 | ||||||||
\(575\) | −34.7848 | −1.45063 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.6443 | 1.69204 | 0.846022 | − | 0.533149i | \(-0.178991\pi\) | ||||
0.846022 | + | 0.533149i | \(0.178991\pi\) | |||||||
\(578\) | 14.2455 | 0.592534 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.983030 | 0.0408181 | ||||||||
\(581\) | 27.6307 | 1.14631 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.6069 | 0.977699 | ||||||||
\(584\) | −6.63197 | −0.274433 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.225898 | −0.00933176 | ||||||||
\(587\) | −26.5700 | −1.09666 | −0.548330 | − | 0.836262i | \(-0.684736\pi\) | ||||
−0.548330 | + | 0.836262i | \(0.684736\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.9660 | −1.77038 | ||||||||
\(590\) | −1.98373 | −0.0816689 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.669487 | −0.0275157 | ||||||||
\(593\) | −0.233160 | −0.00957474 | −0.00478737 | − | 0.999989i | \(-0.501524\pi\) | ||||
−0.00478737 | + | 0.999989i | \(0.501524\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.86850 | −0.0766009 | ||||||||
\(596\) | 13.7074 | 0.561479 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 34.1927 | 1.39825 | ||||||||
\(599\) | −30.6750 | −1.25335 | −0.626673 | − | 0.779282i | \(-0.715584\pi\) | ||||
−0.626673 | + | 0.779282i | \(0.715584\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.5223 | −0.510797 | −0.255399 | − | 0.966836i | \(-0.582207\pi\) | ||||
−0.255399 | + | 0.966836i | \(0.582207\pi\) | |||||||
\(602\) | 13.1402 | 0.535553 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.4598 | 0.710428 | ||||||||
\(605\) | 0.0406993 | 0.00165466 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.0716 | −1.01762 | −0.508812 | − | 0.860878i | \(-0.669915\pi\) | ||||
−0.508812 | + | 0.860878i | \(0.669915\pi\) | |||||||
\(608\) | 6.44882 | 0.261534 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.576714 | 0.0233505 | ||||||||
\(611\) | −36.0015 | −1.45647 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.0877 | −0.811336 | −0.405668 | − | 0.914021i | \(-0.632961\pi\) | ||||
−0.405668 | + | 0.914021i | \(0.632961\pi\) | |||||||
\(614\) | 13.7531 | 0.555029 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.7170 | −0.431801 | ||||||||
\(617\) | −7.66162 | −0.308445 | −0.154223 | − | 0.988036i | \(-0.549287\pi\) | ||||
−0.154223 | + | 0.988036i | \(0.549287\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.5002 | −0.703390 | −0.351695 | − | 0.936115i | \(-0.614395\pi\) | ||||
−0.351695 | + | 0.936115i | \(0.614395\pi\) | |||||||
\(620\) | 2.33356 | 0.0937179 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.47772 | 0.259733 | ||||||||
\(623\) | 0.344491 | 0.0138017 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.1750 | 0.926998 | ||||||||
\(626\) | 13.0231 | 0.520508 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.3567 | 0.532989 | ||||||||
\(629\) | 1.11113 | 0.0443036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.04290 | 0.160945 | 0.0804726 | − | 0.996757i | \(-0.474357\pi\) | ||||
0.0804726 | + | 0.996757i | \(0.474357\pi\) | |||||||
\(632\) | −14.4826 | −0.576088 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.33785 | −0.370853 | ||||||||
\(635\) | 2.13468 | 0.0847120 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.9755 | −0.632971 | ||||||||
\(638\) | −9.35773 | −0.370476 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.350247 | −0.0138447 | ||||||||
\(641\) | −39.0608 | −1.54281 | −0.771404 | − | 0.636346i | \(-0.780445\pi\) | ||||
−0.771404 | + | 0.636346i | \(0.780445\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −49.2168 | −1.94092 | −0.970461 | − | 0.241258i | \(-0.922440\pi\) | ||||
−0.970461 | + | 0.241258i | \(0.922440\pi\) | |||||||
\(644\) | 22.9247 | 0.903359 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.7029 | −0.421101 | ||||||||
\(647\) | 34.3816 | 1.35168 | 0.675840 | − | 0.737049i | \(-0.263781\pi\) | ||||
0.675840 | + | 0.737049i | \(0.263781\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.8837 | 0.741249 | ||||||||
\(650\) | −23.3834 | −0.917174 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.76239 | 0.225673 | ||||||||
\(653\) | 36.9090 | 1.44436 | 0.722180 | − | 0.691705i | \(-0.243140\pi\) | ||||
0.722180 | + | 0.691705i | \(0.243140\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.61389 | 0.141206 | ||||||||
\(656\) | 0.589936 | 0.0230331 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −24.1374 | −0.940973 | ||||||||
\(659\) | 27.6927 | 1.07876 | 0.539378 | − | 0.842064i | \(-0.318660\pi\) | ||||
0.539378 | + | 0.842064i | \(0.318660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.290938 | 0.0113162 | 0.00565808 | − | 0.999984i | \(-0.498199\pi\) | ||||
0.00565808 | + | 0.999984i | \(0.498199\pi\) | |||||||
\(662\) | −28.0987 | −1.09209 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.59600 | −0.333589 | ||||||||
\(665\) | −7.26023 | −0.281540 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.0170 | 0.775063 | ||||||||
\(668\) | 19.3205 | 0.747532 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.50149 | −0.135275 | ||||||||
\(671\) | −5.48990 | −0.211935 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.3379 | −0.783968 | −0.391984 | − | 0.919972i | \(-0.628211\pi\) | ||||
−0.391984 | + | 0.919972i | \(0.628211\pi\) | |||||||
\(674\) | −18.9674 | −0.730596 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.98545 | 0.384056 | ||||||||
\(677\) | −37.5843 | −1.44448 | −0.722240 | − | 0.691642i | \(-0.756888\pi\) | ||||
−0.722240 | + | 0.691642i | \(0.756888\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.318454 | −0.0122212 | ||||||||
\(680\) | 0.581295 | 0.0222917 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −22.2138 | −0.850610 | ||||||||
\(683\) | 29.3744 | 1.12398 | 0.561991 | − | 0.827144i | \(-0.310036\pi\) | ||||
0.561991 | + | 0.827144i | \(0.310036\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.988475 | −0.0377677 | ||||||||
\(686\) | 11.7898 | 0.450135 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.08795 | −0.155852 | ||||||||
\(689\) | −33.9459 | −1.29324 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.7978 | −1.32377 | −0.661885 | − | 0.749605i | \(-0.730243\pi\) | ||||
−0.661885 | + | 0.749605i | \(0.730243\pi\) | |||||||
\(692\) | 9.74463 | 0.370435 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.3610 | −0.696973 | ||||||||
\(695\) | −0.694203 | −0.0263326 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.979101 | −0.0370861 | ||||||||
\(698\) | 28.1613 | 1.06592 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −15.6775 | −0.592555 | ||||||||
\(701\) | 25.3023 | 0.955655 | 0.477827 | − | 0.878454i | \(-0.341424\pi\) | ||||
0.477827 | + | 0.878454i | \(0.341424\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.31740 | 0.162834 | ||||||||
\(704\) | 3.33410 | 0.125659 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.84323 | −0.219913 | ||||||||
\(707\) | −57.9834 | −2.18069 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.8439 | 0.970588 | 0.485294 | − | 0.874351i | \(-0.338713\pi\) | ||||
0.485294 | + | 0.874351i | \(0.338713\pi\) | |||||||
\(710\) | −3.73311 | −0.140101 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.107172 | −0.00401645 | ||||||||
\(713\) | 47.5173 | 1.77954 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.59860 | −0.209376 | ||||||||
\(716\) | 1.08363 | 0.0404973 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.8671 | 0.592156 | ||||||||
\(719\) | 16.0692 | 0.599280 | 0.299640 | − | 0.954052i | \(-0.403133\pi\) | ||||
0.299640 | + | 0.954052i | \(0.403133\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.68124 | 0.211581 | ||||||||
\(722\) | −22.5873 | −0.840611 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.7767 | −0.512006 | ||||||||
\(725\) | −13.6891 | −0.508400 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.4748 | 1.46404 | 0.732019 | − | 0.681284i | \(-0.238578\pi\) | ||||
0.732019 | + | 0.681284i | \(0.238578\pi\) | |||||||
\(728\) | 15.4107 | 0.571158 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.32283 | −0.0859717 | ||||||||
\(731\) | 6.78465 | 0.250939 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.7914 | −1.61747 | −0.808735 | − | 0.588173i | \(-0.799848\pi\) | ||||
−0.808735 | + | 0.588173i | \(0.799848\pi\) | |||||||
\(734\) | −7.90055 | −0.291614 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.13194 | −0.262887 | ||||||||
\(737\) | 33.3317 | 1.22779 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.68664 | −0.245972 | −0.122986 | − | 0.992408i | \(-0.539247\pi\) | ||||
−0.122986 | + | 0.992408i | \(0.539247\pi\) | |||||||
\(740\) | −0.234486 | −0.00861987 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −22.7592 | −0.835517 | ||||||||
\(743\) | 24.1544 | 0.886138 | 0.443069 | − | 0.896488i | \(-0.353890\pi\) | ||||
0.443069 | + | 0.896488i | \(0.353890\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.80099 | 0.175895 | ||||||||
\(746\) | 11.3810 | 0.416688 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.53351 | −0.202325 | ||||||||
\(749\) | −62.1911 | −2.27241 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.32458 | 0.121316 | 0.0606578 | − | 0.998159i | \(-0.480680\pi\) | ||||
0.0606578 | + | 0.998159i | \(0.480680\pi\) | |||||||
\(752\) | 7.50921 | 0.273833 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.4561 | 0.490042 | ||||||||
\(755\) | 6.11523 | 0.222556 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.9677 | 1.34361 | 0.671806 | − | 0.740727i | \(-0.265519\pi\) | ||||
0.671806 | + | 0.740727i | \(0.265519\pi\) | |||||||
\(758\) | −14.6721 | −0.532916 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.25868 | 0.0819309 | ||||||||
\(761\) | −37.4329 | −1.35694 | −0.678471 | − | 0.734627i | \(-0.737357\pi\) | ||||
−0.678471 | + | 0.734627i | \(0.737357\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.58134 | −0.202058 | ||||||||
\(764\) | 11.9517 | 0.432397 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.0623 | 0.688747 | ||||||||
\(767\) | −27.1541 | −0.980477 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.2615 | −1.12732 | −0.563660 | − | 0.826007i | \(-0.690607\pi\) | ||||
−0.563660 | + | 0.826007i | \(0.690607\pi\) | |||||||
\(770\) | −3.75360 | −0.135270 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −24.0497 | −0.865567 | ||||||||
\(773\) | −6.58037 | −0.236679 | −0.118340 | − | 0.992973i | \(-0.537757\pi\) | ||||
−0.118340 | + | 0.992973i | \(0.537757\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.4957 | −1.16728 | ||||||||
\(776\) | 0.0990721 | 0.00355648 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.04386 | −0.216683 | ||||||||
\(779\) | −3.80439 | −0.136307 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.5365 | 1.27159 | ||||||||
\(782\) | 11.8367 | 0.423279 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.33217 | 0.119006 | ||||||||
\(785\) | 4.67813 | 0.166970 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.8855 | −1.24353 | −0.621767 | − | 0.783202i | \(-0.713585\pi\) | ||||
−0.621767 | + | 0.783202i | \(0.713585\pi\) | |||||||
\(788\) | −7.92447 | −0.282298 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.07250 | −0.180471 | ||||||||
\(791\) | −34.1407 | −1.21390 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.89428 | 0.280334 | ||||||||
\(794\) | −28.8374 | −1.02340 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.100817 | −0.00357337 | ||||||||
\(797\) | −49.6370 | −1.75823 | −0.879116 | − | 0.476608i | \(-0.841866\pi\) | ||||
−0.879116 | + | 0.476608i | \(0.841866\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.4628 | −0.440903 | ||||||||
\(800\) | 4.87733 | 0.172440 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.13124 | −0.145879 | ||||||||
\(803\) | 22.1116 | 0.780303 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.02930 | 0.282996 | ||||||||
\(806\) | 31.9426 | 1.12513 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18.0388 | 0.634604 | ||||||||
\(809\) | 19.2533 | 0.676911 | 0.338455 | − | 0.940982i | \(-0.390096\pi\) | ||||
0.338455 | + | 0.940982i | \(0.390096\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.4871 | 0.684286 | 0.342143 | − | 0.939648i | \(-0.388847\pi\) | ||||
0.342143 | + | 0.939648i | \(0.388847\pi\) | |||||||
\(812\) | 9.02169 | 0.316599 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.23213 | 0.0782363 | ||||||||
\(815\) | 2.01826 | 0.0706966 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.3624 | 0.922305 | ||||||||
\(818\) | −20.1566 | −0.704760 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.206623 | 0.00721560 | ||||||||
\(821\) | 17.7292 | 0.618754 | 0.309377 | − | 0.950939i | \(-0.399879\pi\) | ||||
0.309377 | + | 0.950939i | \(0.399879\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.0400 | −1.25628 | −0.628138 | − | 0.778102i | \(-0.716183\pi\) | ||||
−0.628138 | + | 0.778102i | \(0.716183\pi\) | |||||||
\(824\) | −1.76745 | −0.0615721 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.2056 | −0.633453 | ||||||||
\(827\) | 35.3287 | 1.22850 | 0.614250 | − | 0.789111i | \(-0.289459\pi\) | ||||
0.614250 | + | 0.789111i | \(0.289459\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.5468 | 0.539964 | 0.269982 | − | 0.962865i | \(-0.412982\pi\) | ||||
0.269982 | + | 0.962865i | \(0.412982\pi\) | |||||||
\(830\) | −3.01072 | −0.104504 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.79431 | −0.166213 | ||||||||
\(833\) | −5.53031 | −0.191614 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.76694 | 0.234180 | ||||||||
\(836\) | −21.5010 | −0.743627 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.7607 | 0.475355 | ||||||||
\(839\) | −43.6500 | −1.50697 | −0.753483 | − | 0.657467i | \(-0.771628\pi\) | ||||
−0.753483 | + | 0.657467i | \(0.771628\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.1226 | −0.728364 | ||||||||
\(842\) | 1.59634 | 0.0550134 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15.3981 | −0.530024 | ||||||||
\(845\) | 3.49737 | 0.120313 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.373515 | 0.0128341 | ||||||||
\(848\) | 7.08046 | 0.243144 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.09477 | −0.277648 | ||||||||
\(851\) | −4.77474 | −0.163676 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.5327 | 0.771506 | 0.385753 | − | 0.922602i | \(-0.373942\pi\) | ||||
0.385753 | + | 0.922602i | \(0.373942\pi\) | |||||||
\(854\) | 5.29276 | 0.181114 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.3478 | 0.661296 | ||||||||
\(857\) | −24.7850 | −0.846641 | −0.423321 | − | 0.905980i | \(-0.639136\pi\) | ||||
−0.423321 | + | 0.905980i | \(0.639136\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.8346 | −0.983824 | −0.491912 | − | 0.870645i | \(-0.663702\pi\) | ||||
−0.491912 | + | 0.870645i | \(0.663702\pi\) | |||||||
\(860\) | −1.43179 | −0.0488237 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −36.7445 | −1.25152 | ||||||||
\(863\) | 39.4609 | 1.34326 | 0.671632 | − | 0.740885i | \(-0.265593\pi\) | ||||
0.671632 | + | 0.740885i | \(0.265593\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.41303 | 0.116046 | ||||||||
\(866\) | −13.4318 | −0.456430 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 21.4161 | 0.726909 | ||||||||
\(869\) | 48.2865 | 1.63801 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −47.9298 | −1.62404 | ||||||||
\(872\) | 1.73637 | 0.0588010 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 45.9926 | 1.55572 | ||||||||
\(875\) | −11.1201 | −0.375929 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −37.5489 | −1.26793 | −0.633967 | − | 0.773360i | \(-0.718575\pi\) | ||||
−0.633967 | + | 0.773360i | \(0.718575\pi\) | |||||||
\(878\) | −21.9136 | −0.739547 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.16776 | 0.0393651 | ||||||||
\(881\) | −33.8608 | −1.14080 | −0.570399 | − | 0.821368i | \(-0.693211\pi\) | ||||
−0.570399 | + | 0.821368i | \(0.693211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.0649 | −1.14637 | −0.573187 | − | 0.819425i | \(-0.694293\pi\) | ||||
−0.573187 | + | 0.819425i | \(0.694293\pi\) | |||||||
\(884\) | 7.95699 | 0.267623 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.80133 | 0.0605169 | ||||||||
\(887\) | −19.0289 | −0.638928 | −0.319464 | − | 0.947598i | \(-0.603503\pi\) | ||||
−0.319464 | + | 0.947598i | \(0.603503\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.5908 | 0.657056 | ||||||||
\(890\) | −0.0375367 | −0.00125823 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.00000 | 0.0334825 | ||||||||
\(893\) | −48.4255 | −1.62050 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.379539 | 0.0126866 | ||||||||
\(896\) | −3.21437 | −0.107385 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.3399 | −0.645382 | ||||||||
\(899\) | 18.6998 | 0.623673 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.7512 | −0.391491 | ||||||||
\(902\) | −1.96690 | −0.0654908 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.6213 | 0.353258 | ||||||||
\(905\) | −4.82524 | −0.160396 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.3405 | −1.30628 | −0.653141 | − | 0.757237i | \(-0.726549\pi\) | ||||
−0.653141 | + | 0.757237i | \(0.726549\pi\) | |||||||
\(908\) | −3.07847 | −0.102163 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.39755 | 0.178927 | ||||||||
\(911\) | 45.3243 | 1.50166 | 0.750831 | − | 0.660495i | \(-0.229653\pi\) | ||||
0.750831 | + | 0.660495i | \(0.229653\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.6599 | 0.948504 | ||||||||
\(914\) | −14.7852 | −0.489052 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.5684 | 0.613516 | ||||||||
\(917\) | 33.1663 | 1.09525 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.4526 | −1.10350 | −0.551749 | − | 0.834010i | \(-0.686039\pi\) | ||||
−0.551749 | + | 0.834010i | \(0.686039\pi\) | |||||||
\(920\) | −2.49794 | −0.0823546 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.6231 | 0.382785 | ||||||||
\(923\) | −51.1002 | −1.68198 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.26531 | 0.107363 | ||||||||
\(926\) | 18.0117 | 0.591901 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.80668 | −0.0921337 | ||||||||
\(929\) | 0.357135 | 0.0117172 | 0.00585860 | − | 0.999983i | \(-0.498135\pi\) | ||||
0.00585860 | + | 0.999983i | \(0.498135\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.4885 | −0.704259 | ||||||||
\(932\) | −19.5683 | −0.640981 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −28.5900 | −0.935492 | ||||||||
\(935\) | −1.93809 | −0.0633825 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.9547 | 0.423212 | 0.211606 | − | 0.977355i | \(-0.432131\pi\) | ||||
0.211606 | + | 0.977355i | \(0.432131\pi\) | |||||||
\(938\) | −32.1347 | −1.04924 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.63008 | 0.0857837 | ||||||||
\(941\) | 21.7300 | 0.708377 | 0.354189 | − | 0.935174i | \(-0.384757\pi\) | ||||
0.354189 | + | 0.935174i | \(0.384757\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.20739 | 0.137011 | ||||||||
\(944\) | 5.66381 | 0.184341 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.6296 | 0.443137 | ||||||||
\(947\) | −40.0061 | −1.30002 | −0.650012 | − | 0.759924i | \(-0.725236\pi\) | ||||
−0.650012 | + | 0.759924i | \(0.725236\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.7958 | −1.03213 | ||||||||
\(950\) | −31.4530 | −1.02047 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.33480 | 0.172902 | ||||||||
\(953\) | −40.6002 | −1.31517 | −0.657585 | − | 0.753380i | \(-0.728422\pi\) | ||||
−0.657585 | + | 0.753380i | \(0.728422\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.18605 | 0.135457 | ||||||||
\(956\) | 18.5672 | 0.600505 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36.8616 | 1.19094 | ||||||||
\(959\) | −9.07167 | −0.292939 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.3903 | 0.431946 | ||||||||
\(962\) | −3.20973 | −0.103486 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.634708 | −0.0204426 | ||||||||
\(965\) | −8.42333 | −0.271157 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.5187 | −0.884940 | −0.442470 | − | 0.896783i | \(-0.645898\pi\) | ||||
−0.442470 | + | 0.896783i | \(0.645898\pi\) | |||||||
\(968\) | −0.116202 | −0.00373486 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.0346997 | 0.00111414 | ||||||||
\(971\) | −7.20664 | −0.231272 | −0.115636 | − | 0.993292i | \(-0.536891\pi\) | ||||
−0.115636 | + | 0.993292i | \(0.536891\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.37100 | −0.204245 | ||||||||
\(974\) | −9.16658 | −0.293716 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.64659 | −0.0527061 | ||||||||
\(977\) | 46.0399 | 1.47295 | 0.736474 | − | 0.676466i | \(-0.236489\pi\) | ||||
0.736474 | + | 0.676466i | \(0.236489\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.357322 | 0.0114201 | ||||||||
\(980\) | 1.16708 | 0.0372810 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21.2418 | 0.677854 | ||||||||
\(983\) | −31.4981 | −1.00463 | −0.502316 | − | 0.864684i | \(-0.667519\pi\) | ||||
−0.502316 | + | 0.864684i | \(0.667519\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.77552 | −0.0884355 | ||||||||
\(986\) | 4.65816 | 0.148346 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 30.9177 | 0.983622 | ||||||||
\(989\) | −29.1550 | −0.927074 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.4685 | −1.57142 | −0.785709 | − | 0.618597i | \(-0.787702\pi\) | ||||
−0.785709 | + | 0.618597i | \(0.787702\pi\) | |||||||
\(992\) | −6.66261 | −0.211538 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −34.2604 | −1.08667 | ||||||||
\(995\) | −0.0353109 | −0.00111943 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.19903 | 0.0379735 | 0.0189868 | − | 0.999820i | \(-0.493956\pi\) | ||||
0.0189868 | + | 0.999820i | \(0.493956\pi\) | |||||||
\(998\) | 2.75001 | 0.0870499 | ||||||||
\(999\) | 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 | 4014.2.a.x.1.4 | ✓ | 8 | |
3.2 | odd | 2 | 4014.2.a.y.1.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4014.2.a.x.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
4014.2.a.y.1.5 | yes | 8 | 3.2 | odd | 2 |