Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(737,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.737");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.r (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.15 | ||
Character | \(\chi\) | \(=\) | 1380.737 |
Dual form | 1380.2.r.c.1013.15 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.727046 | − | 1.57207i | −0.419760 | − | 0.907635i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.08694 | − | 1.95412i | 0.486093 | − | 0.873907i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.39152 | + | 2.39152i | 0.903911 | + | 0.903911i | 0.995772 | − | 0.0918611i | \(-0.0292816\pi\) |
−0.0918611 | + | 0.995772i | \(0.529282\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.94281 | + | 2.28593i | −0.647603 | + | 0.761978i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.03033i | − | 0.913680i | −0.889549 | − | 0.456840i | \(-0.848981\pi\) | ||
0.889549 | − | 0.456840i | \(-0.151019\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0771350 | − | 0.0771350i | 0.0213934 | − | 0.0213934i | −0.696329 | − | 0.717723i | \(-0.745185\pi\) |
0.717723 | + | 0.696329i | \(0.245185\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.86226 | − | 0.288012i | −0.997231 | − | 0.0743645i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.23292 | − | 1.23292i | 0.299026 | − | 0.299026i | −0.541606 | − | 0.840632i | \(-0.682184\pi\) |
0.840632 | + | 0.541606i | \(0.182184\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.48755i | − | 0.800098i | −0.916494 | − | 0.400049i | \(-0.868993\pi\) | ||
0.916494 | − | 0.400049i | \(-0.131007\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.02090 | − | 5.49839i | 0.440996 | − | 1.19985i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.707107 | + | 0.707107i | 0.147442 | + | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.63713 | − | 4.24800i | −0.527426 | − | 0.849601i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00616 | + | 1.39226i | 0.963436 | + | 0.267940i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.96661 | 0.550886 | 0.275443 | − | 0.961317i | \(-0.411175\pi\) | ||||
0.275443 | + | 0.961317i | \(0.411175\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.61431 | 0.289939 | 0.144969 | − | 0.989436i | \(-0.453692\pi\) | ||||
0.144969 | + | 0.989436i | \(0.453692\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.76390 | + | 2.20319i | −0.829288 | + | 0.383526i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.27275 | − | 2.07387i | 1.22932 | − | 0.350549i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.20541 | − | 3.20541i | −0.526967 | − | 0.526967i | 0.392700 | − | 0.919667i | \(-0.371541\pi\) |
−0.919667 | + | 0.392700i | \(0.871541\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.177342 | − | 0.0651809i | −0.0283975 | − | 0.0104373i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.20816i | 0.344857i | 0.985022 | + | 0.172428i | \(0.0551614\pi\) | ||||
−0.985022 | + | 0.172428i | \(0.944839\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.58947 | − | 6.58947i | 1.00488 | − | 1.00488i | 0.00489686 | − | 0.999988i | \(-0.498441\pi\) |
0.999988 | − | 0.00489686i | \(-0.00155873\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.35526 | + | 6.28114i | 0.351102 | + | 0.936337i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.02234 | − | 4.02234i | 0.586719 | − | 0.586719i | −0.350022 | − | 0.936741i | \(-0.613826\pi\) |
0.936741 | + | 0.350022i | \(0.113826\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.43876i | 0.634109i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.83462 | − | 1.04184i | −0.396926 | − | 0.145887i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.02954 | − | 2.02954i | −0.278779 | − | 0.278779i | 0.553842 | − | 0.832621i | \(-0.313161\pi\) |
−0.832621 | + | 0.553842i | \(0.813161\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.92162 | − | 3.29379i | −0.798471 | − | 0.444134i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.48267 | + | 2.53560i | −0.726197 | + | 0.335849i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.09767 | −0.663661 | −0.331830 | − | 0.943339i | \(-0.607666\pi\) | ||||
−0.331830 | + | 0.943339i | \(0.607666\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.81766 | 0.360764 | 0.180382 | − | 0.983597i | \(-0.442267\pi\) | ||||
0.180382 | + | 0.983597i | \(0.442267\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.1131 | + | 0.820588i | −1.27414 | + | 0.103384i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0668897 | − | 0.234571i | −0.00829664 | − | 0.0290950i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.824194 | + | 0.824194i | 0.100691 | + | 0.100691i | 0.755658 | − | 0.654967i | \(-0.227317\pi\) |
−0.654967 | + | 0.755658i | \(0.727317\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.597523 | − | 1.62572i | 0.0719333 | − | 0.195714i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.280915i | − | 0.0333384i | −0.999861 | − | 0.0166692i | \(-0.994694\pi\) | ||
0.999861 | − | 0.0166692i | \(-0.00530622\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.78399 | + | 7.78399i | −0.911047 | + | 0.911047i | −0.996355 | − | 0.0853074i | \(-0.972813\pi\) |
0.0853074 | + | 0.996355i | \(0.472813\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.76085 | + | 7.23425i | −0.549735 | + | 0.835339i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.24711 | − | 7.24711i | 0.825885 | − | 0.825885i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.52181i | 0.508744i | 0.967106 | + | 0.254372i | \(0.0818687\pi\) | ||||
−0.967106 | + | 0.254372i | \(0.918131\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.45098 | − | 8.88227i | −0.161220 | − | 0.986918i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.1188 | − | 12.1188i | −1.33021 | − | 1.33021i | −0.905174 | − | 0.425041i | \(-0.860260\pi\) |
−0.425041 | − | 0.905174i | \(-0.639740\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.06916 | − | 3.74936i | −0.115966 | − | 0.406675i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.15686 | − | 4.66372i | −0.231240 | − | 0.500003i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.16782 | −0.759788 | −0.379894 | − | 0.925030i | \(-0.624040\pi\) | ||||
−0.379894 | + | 0.925030i | \(0.624040\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.368940 | 0.0386754 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.17368 | − | 2.53781i | −0.121705 | − | 0.263158i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.81507 | − | 3.79075i | −0.699211 | − | 0.388922i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.7971 | − | 10.7971i | −1.09628 | − | 1.09628i | −0.994842 | − | 0.101434i | \(-0.967657\pi\) |
−0.101434 | − | 0.994842i | \(-0.532343\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.92714 | + | 5.88736i | 0.696204 | + | 0.591702i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.94622i | 0.790678i | 0.918535 | + | 0.395339i | \(0.129373\pi\) | ||||
−0.918535 | + | 0.395339i | \(0.870627\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.30248 | − | 6.30248i | 0.621002 | − | 0.621002i | −0.324786 | − | 0.945788i | \(-0.605292\pi\) |
0.945788 | + | 0.324786i | \(0.105292\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.54789 | − | 9.92547i | −0.834189 | − | 0.968627i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.89565 | − | 7.89565i | 0.763301 | − | 0.763301i | −0.213616 | − | 0.976918i | \(-0.568524\pi\) |
0.976918 | + | 0.213616i | \(0.0685242\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.66158i | 0.925411i | 0.886512 | + | 0.462706i | \(0.153121\pi\) | ||||
−0.886512 | + | 0.462706i | \(0.846879\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.70865 | + | 7.36961i | −0.257094 | + | 0.699493i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.24425 | − | 7.24425i | −0.681482 | − | 0.681482i | 0.278852 | − | 0.960334i | \(-0.410046\pi\) |
−0.960334 | + | 0.278852i | \(0.910046\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.15035 | − | 0.613187i | 0.200521 | − | 0.0571800i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0264668 | + | 0.326184i | 0.00244686 | + | 0.0301557i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.89709 | 0.540585 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.81707 | 0.165188 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.47138 | − | 1.60543i | 0.313004 | − | 0.144757i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1675 | + | 0.535940i | −0.998850 | + | 0.0479359i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9189 | + | 10.9189i | 0.968899 | + | 0.968899i | 0.999531 | − | 0.0306321i | \(-0.00975201\pi\) |
−0.0306321 | + | 0.999531i | \(0.509752\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.1500 | − | 5.56827i | −1.33388 | − | 0.490258i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.3152i | 1.33809i | 0.743221 | + | 0.669046i | \(0.233297\pi\) | ||||
−0.743221 | + | 0.669046i | \(0.766703\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.34055 | − | 8.34055i | 0.723217 | − | 0.723217i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.16201 | − | 8.26931i | 0.702474 | − | 0.711709i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.66668 | + | 7.66668i | −0.655009 | + | 0.655009i | −0.954195 | − | 0.299186i | \(-0.903285\pi\) |
0.299186 | + | 0.954195i | \(0.403285\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 19.7232i | − | 1.67290i | −0.548045 | − | 0.836449i | \(-0.684628\pi\) | ||
0.548045 | − | 0.836449i | \(-0.315372\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.24783 | − | 3.39898i | −0.778808 | − | 0.286246i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.233745 | − | 0.233745i | −0.0195467 | − | 0.0195467i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.22452 | − | 5.79710i | 0.267782 | − | 0.481423i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.97805 | − | 3.22718i | 0.575540 | − | 0.266174i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.62678 | −0.624810 | −0.312405 | − | 0.949949i | \(-0.601135\pi\) | ||||
−0.312405 | + | 0.949949i | \(0.601135\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.8732 | −1.12898 | −0.564492 | − | 0.825439i | \(-0.690928\pi\) | ||||
−0.564492 | + | 0.825439i | \(0.690928\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.423043 | + | 5.21368i | 0.0342010 | + | 0.421501i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.75465 | − | 3.15455i | 0.140937 | − | 0.253379i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.2735 | + | 12.2735i | 0.979533 | + | 0.979533i | 0.999795 | − | 0.0202615i | \(-0.00644988\pi\) |
−0.0202615 | + | 0.999795i | \(0.506450\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.71501 | + | 4.66615i | −0.136009 | + | 0.370050i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.38212i | 0.266549i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.0286 | − | 14.0286i | 1.09881 | − | 1.09881i | 0.104254 | − | 0.994551i | \(-0.466754\pi\) |
0.994551 | − | 0.104254i | \(-0.0332456\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.872774 | + | 11.7039i | −0.0679454 | + | 0.911150i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.2691 | − | 17.2691i | 1.33632 | − | 1.33632i | 0.436725 | − | 0.899595i | \(-0.356138\pi\) |
0.899595 | − | 0.436725i | \(-0.143862\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9881i | 0.999085i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.97230 | + | 6.77564i | 0.609657 | + | 0.518146i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.58768 | + | 7.58768i | 0.576880 | + | 0.576880i | 0.934042 | − | 0.357162i | \(-0.116256\pi\) |
−0.357162 | + | 0.934042i | \(0.616256\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.85244 | − | 16.4660i | 0.291217 | − | 1.24471i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.70624 | + | 8.01390i | 0.278578 | + | 0.602362i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 24.3028 | 1.81648 | 0.908239 | − | 0.418452i | \(-0.137427\pi\) | ||||
0.908239 | + | 0.418452i | \(0.137427\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.08837 | 0.526874 | 0.263437 | − | 0.964677i | \(-0.415144\pi\) | ||||
0.263437 | + | 0.964677i | \(0.415144\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.04857 | − | 4.42956i | −0.151434 | − | 0.327442i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.74783 | + | 2.77966i | −0.716675 | + | 0.204365i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.73615 | − | 3.73615i | −0.273214 | − | 0.273214i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.64273 | + | 15.3020i | 0.628666 | + | 1.11305i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.6573i | 1.06057i | 0.847820 | + | 0.530284i | \(0.177915\pi\) | ||||
−0.847820 | + | 0.530284i | \(0.822085\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.09665 | − | 8.09665i | 0.582810 | − | 0.582810i | −0.352865 | − | 0.935674i | \(-0.614792\pi\) |
0.935674 | + | 0.352865i | \(0.114792\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.320131 | + | 0.275699i | −0.0229251 | + | 0.0197432i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.59195 | + | 5.59195i | −0.398410 | + | 0.398410i | −0.877672 | − | 0.479262i | \(-0.840904\pi\) |
0.479262 | + | 0.877672i | \(0.340904\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.3085i | 0.943418i | 0.881754 | + | 0.471709i | \(0.156363\pi\) | ||||
−0.881754 | + | 0.471709i | \(0.843637\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.696464 | − | 1.89492i | 0.0491248 | − | 0.133657i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.09472 | + | 7.09472i | 0.497952 | + | 0.497952i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.31500 | + | 2.40013i | 0.301373 | + | 0.167633i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.99017 | + | 0.242625i | −0.207831 | + | 0.0168636i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.5684 | −0.731034 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0331 | 0.966079 | 0.483040 | − | 0.875599i | \(-0.339533\pi\) | ||||
0.483040 | + | 0.875599i | \(0.339533\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.441618 | + | 0.204238i | −0.0302591 | + | 0.0139941i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.71424 | − | 20.0389i | −0.389708 | − | 1.36664i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.86066 | + | 3.86066i | 0.262079 | + | 0.262079i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.8963 | + | 6.57767i | 1.20932 | + | 0.444477i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 0.190202i | − | 0.0127944i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.706985 | + | 0.706985i | −0.0473432 | + | 0.0473432i | −0.730382 | − | 0.683039i | \(-0.760658\pi\) |
0.683039 | + | 0.730382i | \(0.260658\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.8341 | + | 2.22476i | 0.988940 | + | 0.148317i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.1219 | + | 13.1219i | −0.870934 | + | 0.870934i | −0.992574 | − | 0.121641i | \(-0.961184\pi\) |
0.121641 | + | 0.992574i | \(0.461184\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.6439i | 1.62851i | 0.580506 | + | 0.814256i | \(0.302855\pi\) | ||||
−0.580506 | + | 0.814256i | \(0.697145\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.6620 | − | 6.12399i | −1.09628 | − | 0.402929i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.56833 | − | 4.56833i | −0.299282 | − | 0.299282i | 0.541451 | − | 0.840732i | \(-0.317875\pi\) |
−0.840732 | + | 0.541451i | \(0.817875\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.48808 | − | 12.2322i | −0.227537 | − | 0.797938i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.10861 | − | 3.28757i | 0.461754 | − | 0.213550i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.76665 | 0.308329 | 0.154164 | − | 0.988045i | \(-0.450731\pi\) | ||||
0.154164 | + | 0.988045i | \(0.450731\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.97265 | −0.384732 | −0.192366 | − | 0.981323i | \(-0.561616\pi\) | ||||
−0.192366 | + | 0.981323i | \(0.561616\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.9086 | + | 8.73886i | −0.828088 | + | 0.560598i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.67386 | + | 4.82466i | 0.554152 | + | 0.308236i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.269012 | − | 0.269012i | −0.0171168 | − | 0.0171168i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.2407 | + | 27.8626i | −0.648979 | + | 1.76572i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.5096i | 0.915841i | 0.888993 | + | 0.457920i | \(0.151406\pi\) | ||||
−0.888993 | + | 0.457920i | \(0.848594\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.14277 | − | 2.14277i | 0.134715 | − | 0.134715i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.11693 | + | 4.40674i | −0.320435 | + | 0.275961i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.30591 | + | 7.30591i | −0.455730 | + | 0.455730i | −0.897251 | − | 0.441521i | \(-0.854439\pi\) |
0.441521 | + | 0.897251i | \(0.354439\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 15.3316i | − | 0.952661i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.76356 | + | 6.78147i | −0.356755 | + | 0.419763i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.5283 | + | 18.5283i | 1.14250 | + | 1.14250i | 0.987991 | + | 0.154510i | \(0.0493798\pi\) |
0.154510 | + | 0.987991i | \(0.450620\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.17194 | + | 1.75997i | −0.379140 | + | 0.108114i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.21133 | + | 11.2683i | 0.318928 | + | 0.689610i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.3813 | 0.876846 | 0.438423 | − | 0.898769i | \(-0.355537\pi\) | ||||
0.438423 | + | 0.898769i | \(0.355537\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.9841 | −1.09246 | −0.546228 | − | 0.837636i | \(-0.683937\pi\) | ||||
−0.546228 | + | 0.837636i | \(0.683937\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.268236 | − | 0.580000i | −0.0162344 | − | 0.0351032i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.8729 | + | 7.99139i | −0.776264 | + | 0.481899i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.62499 | + | 4.62499i | 0.277888 | + | 0.277888i | 0.832266 | − | 0.554377i | \(-0.187043\pi\) |
−0.554377 | + | 0.832266i | \(0.687043\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.13630 | + | 3.69020i | −0.187765 | + | 0.220927i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.31170i | 0.257215i | 0.991696 | + | 0.128607i | \(0.0410507\pi\) | ||||
−0.991696 | + | 0.128607i | \(0.958949\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.0057 | − | 18.0057i | 1.07033 | − | 1.07033i | 0.0729938 | − | 0.997332i | \(-0.476745\pi\) |
0.997332 | − | 0.0729938i | \(-0.0232553\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00446 | + | 13.4698i | −0.0594989 | + | 0.797883i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.28087 | + | 5.28087i | −0.311720 | + | 0.311720i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.9598i | 0.821167i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.12379 | + | 24.8237i | −0.534846 | + | 1.45519i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.9659 | − | 20.9659i | −1.22484 | − | 1.22484i | −0.965892 | − | 0.258947i | \(-0.916625\pi\) |
−0.258947 | − | 0.965892i | \(-0.583375\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.54086 | + | 9.96144i | −0.322601 | + | 0.579978i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.21900 | − | 15.1703i | 0.244811 | − | 0.880272i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.109085 | 0.00630857 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.5177 | 1.81665 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.4920 | − | 5.77726i | 0.717647 | − | 0.331895i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.06262 | − | 5.50603i | 0.175365 | − | 0.315274i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.96829 | + | 2.96829i | 0.169409 | + | 0.169409i | 0.786720 | − | 0.617310i | \(-0.211778\pi\) |
−0.617310 | + | 0.786720i | \(0.711778\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.4901 | − | 5.32575i | −0.824315 | − | 0.302971i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 12.0420i | − | 0.682837i | −0.939911 | − | 0.341418i | \(-0.889093\pi\) | ||
0.939911 | − | 0.341418i | \(-0.110907\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.9634 | − | 11.9634i | 0.676213 | − | 0.676213i | −0.282928 | − | 0.959141i | \(-0.591306\pi\) |
0.959141 | + | 0.282928i | \(0.0913059\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.38883 | + | 20.6542i | −0.529001 | + | 1.16373i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.4069 | + | 20.4069i | −1.14616 | + | 1.14616i | −0.158862 | + | 0.987301i | \(0.550783\pi\) |
−0.987301 | + | 0.158862i | \(0.949217\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.98982i | − | 0.503334i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.1530 | − | 6.67202i | −1.01320 | − | 0.372396i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.29985 | − | 4.29985i | −0.239250 | − | 0.239250i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.531085 | − | 0.124255i | −0.0294593 | − | 0.00689241i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.1887 | − | 7.02441i | 0.839936 | − | 0.388451i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.2391 | 1.06068 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.7917 | −1.03288 | −0.516442 | − | 0.856322i | \(-0.672744\pi\) | ||||
−0.516442 | + | 0.856322i | \(0.672744\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.5549 | − | 1.09985i | 0.742802 | − | 0.0602716i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.50642 | − | 0.714722i | 0.136940 | − | 0.0390494i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.0203458 | − | 0.0203458i | −0.00110830 | − | 0.00110830i | 0.706552 | − | 0.707661i | \(-0.250249\pi\) |
−0.707661 | + | 0.706552i | \(0.750249\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.12157 | + | 16.6554i | −0.332478 | + | 0.904596i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4.89190i | − | 0.264911i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.12525 | − | 6.12525i | 0.330733 | − | 0.330733i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.52737 | − | 2.93469i | −0.136069 | − | 0.157998i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.83783 | − | 2.83783i | 0.152343 | − | 0.152343i | −0.626821 | − | 0.779164i | \(-0.715644\pi\) |
0.779164 | + | 0.626821i | \(0.215644\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 13.9751i | − | 0.748069i | −0.927415 | − | 0.374034i | \(-0.877974\pi\) | ||
0.927415 | − | 0.374034i | \(-0.122026\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.493541 | − | 0.278758i | 0.0263433 | − | 0.0148790i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.04195 | + | 6.04195i | 0.321581 | + | 0.321581i | 0.849373 | − | 0.527793i | \(-0.176980\pi\) |
−0.527793 | + | 0.849373i | \(0.676980\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.548940 | − | 0.305337i | −0.0291347 | − | 0.0162056i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.28745 | − | 9.27064i | −0.226916 | − | 0.490654i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.0378 | 0.635331 | 0.317665 | − | 0.948203i | \(-0.397101\pi\) | ||||
0.317665 | + | 0.948203i | \(0.397101\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.83702 | 0.359843 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.32109 | − | 2.85656i | −0.0693394 | − | 0.149931i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.75010 | + | 23.6715i | 0.353316 | + | 1.23902i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.185005 | + | 0.185005i | 0.00965719 | + | 0.00965719i | 0.711919 | − | 0.702262i | \(-0.247826\pi\) |
−0.702262 | + | 0.711919i | \(0.747826\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.04771 | − | 4.29004i | −0.262773 | − | 0.223330i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 9.70739i | − | 0.503983i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.3645 | − | 16.3645i | 0.847322 | − | 0.847322i | −0.142476 | − | 0.989798i | \(-0.545506\pi\) |
0.989798 | + | 0.142476i | \(0.0455065\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.96181 | + | 17.1664i | 0.462786 | + | 0.886470i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.228829 | − | 0.228829i | 0.0117853 | − | 0.0117853i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 19.3612i | − | 0.994518i | −0.867602 | − | 0.497259i | \(-0.834340\pi\) | ||
0.867602 | − | 0.497259i | \(-0.165660\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.22677 | − | 25.1039i | 0.472702 | − | 1.28611i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.9821 | + | 10.9821i | 0.561157 | + | 0.561157i | 0.929636 | − | 0.368479i | \(-0.120121\pi\) |
−0.368479 | + | 0.929636i | \(0.620121\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.28453 | − | 22.0389i | −0.320289 | − | 1.12320i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.26100 | + | 27.8652i | 0.114933 | + | 1.41647i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.3592 | −0.525230 | −0.262615 | − | 0.964901i | \(-0.584585\pi\) | ||||
−0.262615 | + | 0.964901i | \(0.584585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.74361 | 0.0881779 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 24.0765 | − | 11.1348i | 1.21450 | − | 0.561678i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.83615 | + | 4.91493i | 0.444595 | + | 0.247297i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.51490 | + | 5.51490i | 0.276785 | + | 0.276785i | 0.831824 | − | 0.555039i | \(-0.187297\pi\) |
−0.555039 | + | 0.831824i | \(0.687297\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.1759 | − | 7.04797i | −0.959995 | − | 0.352840i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.0585i | 1.30130i | 0.759378 | + | 0.650650i | \(0.225503\pi\) | ||||
−0.759378 | + | 0.650650i | \(0.774497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.124520 | − | 0.124520i | 0.00620277 | − | 0.00620277i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.9341 | − | 6.81909i | −0.940843 | − | 0.338843i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.71347 | + | 9.71347i | −0.481479 | + | 0.481479i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.72894i | 0.431618i | 0.976436 | + | 0.215809i | \(0.0692389\pi\) | ||||
−0.976436 | + | 0.215809i | \(0.930761\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.6266 | + | 6.47854i | 0.869456 | + | 0.319563i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.1912 | − | 12.1912i | −0.599890 | − | 0.599890i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −36.8540 | + | 10.5092i | −1.80909 | + | 0.515875i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −31.0062 | + | 14.3396i | −1.51838 | + | 0.702215i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.3008 | 0.991758 | 0.495879 | − | 0.868392i | \(-0.334846\pi\) | ||||
0.495879 | + | 0.868392i | \(0.334846\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.0673 | 0.831810 | 0.415905 | − | 0.909408i | \(-0.363465\pi\) | ||||
0.415905 | + | 0.909408i | \(0.363465\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.38016 | + | 17.0095i | 0.0671057 | + | 0.827028i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.48879 | − | 1.98607i | −0.411767 | − | 0.0963385i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.73850 | + | 6.73850i | 0.326099 | + | 0.326099i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.197520 | + | 0.537406i | −0.00953636 | + | 0.0259462i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.7241i | 0.612900i | 0.951887 | + | 0.306450i | \(0.0991412\pi\) | ||||
−0.951887 | + | 0.306450i | \(0.900859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.8008 | − | 21.8008i | 1.04768 | − | 1.04768i | 0.0488738 | − | 0.998805i | \(-0.484437\pi\) |
0.998805 | − | 0.0488738i | \(-0.0155632\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.4578 | − | 0.854421i | −0.549361 | − | 0.0409663i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.46607 | − | 2.46607i | 0.117968 | − | 0.117968i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 25.1349i | − | 1.19963i | −0.800140 | − | 0.599813i | \(-0.795242\pi\) | ||
0.800140 | − | 0.599813i | \(-0.204758\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.1467 | − | 8.62367i | −0.483177 | − | 0.410651i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.8865 | + | 13.8865i | 0.659766 | + | 0.659766i | 0.955325 | − | 0.295559i | \(-0.0955058\pi\) |
−0.295559 | + | 0.955325i | \(0.595506\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.79098 | + | 14.0068i | −0.369328 | + | 0.663984i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.54502 | + | 11.9898i | 0.262270 | + | 0.567100i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.2061 | 0.528846 | 0.264423 | − | 0.964407i | \(-0.414818\pi\) | ||||
0.264423 | + | 0.964407i | \(0.414818\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.69147 | 0.315089 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.0864 | + | 21.8096i | 0.473902 | + | 1.02470i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.401015 | − | 0.720951i | 0.0187999 | − | 0.0337987i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.697802 | − | 0.697802i | −0.0326418 | − | 0.0326418i | 0.690598 | − | 0.723239i | \(-0.257348\pi\) |
−0.723239 | + | 0.690598i | \(0.757348\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.88870 | − | 4.45564i | 0.368213 | − | 0.207971i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.47325i | − | 0.348064i | −0.984740 | − | 0.174032i | \(-0.944320\pi\) | ||
0.984740 | − | 0.174032i | \(-0.0556796\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.8330 | + | 19.8330i | −0.921718 | + | 0.921718i | −0.997151 | − | 0.0754333i | \(-0.975966\pi\) |
0.0754333 | + | 0.997151i | \(0.475966\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.23488 | − | 0.464941i | −0.289136 | − | 0.0215611i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.5294 | + | 23.5294i | −1.08881 | + | 1.08881i | −0.0931582 | + | 0.995651i | \(0.529696\pi\) |
−0.995651 | + | 0.0931582i | \(0.970304\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.94216i | 0.182032i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.3714 | − | 28.2182i | 0.477890 | − | 1.30023i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.9683 | − | 19.9683i | −0.918143 | − | 0.918143i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.8151 | + | 9.19712i | −0.679764 | + | 0.421993i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.58241 | − | 0.696384i | 0.392962 | − | 0.0318852i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.0000 | 0.685369 | 0.342684 | − | 0.939451i | \(-0.388664\pi\) | ||||
0.342684 | + | 0.939451i | \(0.388664\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.494499 | −0.0225472 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.31694 | − | 2.45896i | 0.241929 | − | 0.111886i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −32.8345 | + | 9.36297i | −1.49094 | + | 0.425150i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.3336 | + | 14.3336i | 0.649518 | + | 0.649518i | 0.952876 | − | 0.303359i | \(-0.0981080\pi\) |
−0.303359 | + | 0.952876i | \(0.598108\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −32.2534 | − | 11.8545i | −1.45855 | − | 0.536080i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.10767i | 0.230506i | 0.993336 | + | 0.115253i | \(0.0367678\pi\) | ||||
−0.993336 | + | 0.115253i | \(0.963232\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.65758 | − | 3.65758i | 0.164729 | − | 0.164729i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 19.0340 | − | 7.13723i | 0.855513 | − | 0.320795i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.671814 | − | 0.671814i | 0.0301350 | − | 0.0301350i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.6445i | 1.28231i | 0.767413 | + | 0.641153i | \(0.221543\pi\) | ||||
−0.767413 | + | 0.641153i | \(0.778457\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −39.7036 | − | 14.5928i | −1.77382 | − | 0.651957i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.07906 | + | 2.07906i | 0.0927009 | + | 0.0927009i | 0.751936 | − | 0.659236i | \(-0.229120\pi\) |
−0.659236 | + | 0.751936i | \(0.729120\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.5278 | + | 8.63705i | 0.690979 | + | 0.384343i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.4182 | − | 9.44294i | 0.906804 | − | 0.419376i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.28928 | 0.411740 | 0.205870 | − | 0.978579i | \(-0.433998\pi\) | ||||
0.205870 | + | 0.978579i | \(0.433998\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −37.2312 | −1.64701 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.85556 | − | 17.4592i | 0.214378 | − | 0.770843i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.46537 | − | 19.1662i | −0.240833 | − | 0.844563i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.1890 | − | 12.1890i | −0.536074 | − | 0.536074i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.41177 | − | 17.4449i | 0.281446 | − | 0.765748i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.84496i | 0.0808293i | 0.999183 | + | 0.0404146i | \(0.0128679\pi\) | ||||
−0.999183 | + | 0.0404146i | \(0.987132\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.5854 | + | 10.5854i | −0.462867 | + | 0.462867i | −0.899594 | − | 0.436727i | \(-0.856137\pi\) |
0.436727 | + | 0.899594i | \(0.356137\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −28.6865 | + | 5.91520i | −1.25198 | + | 0.258160i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.99031 | − | 1.99031i | 0.0866991 | − | 0.0866991i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.90381 | − | 11.6529i | 0.429789 | − | 0.505695i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.170326 | + | 0.170326i | 0.00737766 | + | 0.00737766i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.84693 | − | 24.0111i | −0.296018 | − | 1.03809i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17.6693 | − | 38.2057i | −0.762485 | − | 1.64870i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.4509 | 0.579373 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.75571 | −0.333444 | −0.166722 | − | 0.986004i | \(-0.553318\pi\) | ||||
−0.166722 | + | 0.986004i | \(0.553318\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.15357 | − | 11.1434i | −0.221161 | − | 0.478210i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.8798 | + | 10.5015i | 0.808723 | + | 0.449837i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.1659 | + | 24.1659i | 1.03326 | + | 1.03326i | 0.999427 | + | 0.0338337i | \(0.0107717\pi\) |
0.0338337 | + | 0.999427i | \(0.489228\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.47418 | + | 6.44098i | −0.233632 | + | 0.274894i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.3462i | − | 0.440763i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.8140 | + | 10.8140i | −0.459859 | + | 0.459859i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.4569 | + | 13.3033i | 0.486320 | + | 0.564695i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.9800 | − | 24.9800i | 1.05844 | − | 1.05844i | 0.0602526 | − | 0.998183i | \(-0.480809\pi\) |
0.998183 | − | 0.0602526i | \(-0.0191906\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.01656i | − | 0.0429958i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.15714 | + | 8.58983i | −0.133294 | + | 0.362663i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.7657 | − | 14.7657i | −0.622301 | − | 0.622301i | 0.323818 | − | 0.946119i | \(-0.395033\pi\) |
−0.946119 | + | 0.323818i | \(0.895033\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.0302 | + | 6.28205i | −0.926816 | + | 0.264288i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.7721 | − | 24.7122i | 0.746357 | − | 1.03781i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.29060 | 0.305638 | 0.152819 | − | 0.988254i | \(-0.451165\pi\) | ||||
0.152819 | + | 0.988254i | \(0.451165\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −46.9287 | −1.96390 | −0.981952 | − | 0.189131i | \(-0.939433\pi\) | ||||
−0.981952 | + | 0.189131i | \(0.939433\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.0423 | − | 10.6565i | 0.962608 | − | 0.445184i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.13906 | − | 4.86853i | 0.0475021 | − | 0.203032i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.2223 | + | 25.2223i | 1.05002 | + | 1.05002i | 0.998681 | + | 0.0513387i | \(0.0163488\pi\) |
0.0513387 | + | 0.998681i | \(0.483651\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.6151 | − | 6.84187i | −0.773619 | − | 0.284338i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 57.9649i | − | 2.40479i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.15019 | + | 6.15019i | −0.254715 | + | 0.254715i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.666169 | + | 0.302822i | 0.0275427 | + | 0.0125202i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.8174 | + | 27.8174i | −1.14815 | + | 1.14815i | −0.161232 | + | 0.986917i | \(0.551547\pi\) |
−0.986917 | + | 0.161232i | \(0.948453\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 5.62998i | − | 0.231979i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.8565 | + | 4.72534i | 0.528848 | + | 0.194374i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.05842 | + | 6.05842i | 0.248789 | + | 0.248789i | 0.820474 | − | 0.571684i | \(-0.193710\pi\) |
−0.571684 | + | 0.820474i | \(0.693710\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.40977 | − | 11.5236i | 0.262775 | − | 0.472421i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.9220 | − | 9.67592i | 0.856279 | − | 0.396009i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.3845 | 0.546875 | 0.273438 | − | 0.961890i | \(-0.411839\pi\) | ||||
0.273438 | + | 0.961890i | \(0.411839\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.1321 | −1.71860 | −0.859302 | − | 0.511469i | \(-0.829102\pi\) | ||||
−0.859302 | + | 0.511469i | \(0.829102\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.48530 | + | 0.282801i | −0.141933 | + | 0.0115165i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.97504 | − | 3.55077i | 0.0802970 | − | 0.144359i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.68751 | − | 8.68751i | −0.352615 | − | 0.352615i | 0.508467 | − | 0.861082i | \(-0.330213\pi\) |
−0.861082 | + | 0.508467i | \(0.830213\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.99521 | − | 16.3116i | 0.242938 | − | 0.660979i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 0.620527i | − | 0.0251038i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.5196 | + | 24.5196i | −0.990336 | + | 0.990336i | −0.999954 | − | 0.00961775i | \(-0.996939\pi\) |
0.00961775 | + | 0.999954i | \(0.496939\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.635978 | − | 8.52849i | 0.0256451 | − | 0.343902i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.8654 | − | 12.8654i | 0.517941 | − | 0.517941i | −0.399007 | − | 0.916948i | \(-0.630645\pi\) |
0.916948 | + | 0.399007i | \(0.130645\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.6382i | 0.789324i | 0.918826 | + | 0.394662i | \(0.129138\pi\) | ||||
−0.918826 | + | 0.394662i | \(0.870862\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.55542 | + | 4.52436i | 0.102545 | + | 0.181556i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.1420 | − | 17.1420i | −0.686780 | − | 0.686780i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0911 | + | 22.4051i | −0.443643 | + | 0.896204i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.68373 | + | 16.6143i | 0.306859 | + | 0.663512i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.90400 | −0.315153 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.6366 | 0.940956 | 0.470478 | − | 0.882412i | \(-0.344081\pi\) | ||||
0.470478 | + | 0.882412i | \(0.344081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.2027 | − | 22.0610i | −0.405521 | − | 0.876847i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 33.2051 | − | 9.46865i | 1.31770 | − | 0.375752i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.342384 | + | 0.342384i | 0.0135657 | + | 0.0135657i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.642152 | + | 0.545764i | 0.0254032 | + | 0.0215901i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.7717i | 1.09692i | 0.836178 | + | 0.548458i | \(0.184785\pi\) | ||||
−0.836178 | + | 0.548458i | \(0.815215\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.98288 | − | 3.98288i | 0.157069 | − | 0.157069i | −0.624197 | − | 0.781267i | \(-0.714574\pi\) |
0.781267 | + | 0.624197i | \(0.214574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −27.3481 | + | 23.5524i | −1.07683 | + | 0.927375i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.0330 | − | 10.0330i | 0.394438 | − | 0.394438i | −0.481828 | − | 0.876266i | \(-0.660027\pi\) |
0.876266 | + | 0.481828i | \(0.160027\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.4477i | 0.606374i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.26235 | − | 8.87610i | 0.127862 | − | 0.347882i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22.2164 | − | 22.2164i | −0.869396 | − | 0.869396i | 0.123010 | − | 0.992405i | \(-0.460745\pi\) |
−0.992405 | + | 0.123010i | \(0.960745\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.9276 | + | 16.6466i | 1.16937 | + | 0.650438i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.67087 | − | 32.9165i | −0.104201 | − | 1.28419i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.69071 | −0.104815 | −0.0524077 | − | 0.998626i | \(-0.516690\pi\) | ||||
−0.0524077 | + | 0.998626i | \(0.516690\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.8779 | 0.461996 | 0.230998 | − | 0.972954i | \(-0.425801\pi\) | ||||
0.230998 | + | 0.972954i | \(0.425801\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.299010 | + | 0.138285i | −0.0116126 | + | 0.00537056i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.23273 | − | 25.3640i | −0.280473 | − | 0.983576i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.09771 | + | 2.09771i | 0.0812237 | + | 0.0812237i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.62544 | + | 0.597420i | 0.0628432 | + | 0.0230976i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 8.53845i | − | 0.329623i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.4110 | − | 14.4110i | 0.555505 | − | 0.555505i | −0.372519 | − | 0.928024i | \(-0.621506\pi\) |
0.928024 | + | 0.372519i | \(0.121506\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.28759 | − | 24.9377i | −0.280499 | − | 0.959854i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.2268 | − | 12.2268i | 0.469913 | − | 0.469913i | −0.431974 | − | 0.901886i | \(-0.642183\pi\) |
0.901886 | + | 0.431974i | \(0.142183\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 51.6429i | − | 1.98187i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30.1689 | + | 11.0884i | 1.15607 | + | 0.424907i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.4350 | + | 14.4350i | 0.552338 | + | 0.552338i | 0.927115 | − | 0.374777i | \(-0.122281\pi\) |
−0.374777 | + | 0.927115i | \(0.622281\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.64837 | + | 23.3148i | 0.254021 | + | 0.890813i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 38.7419 | − | 17.9172i | 1.47810 | − | 0.683584i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.313097 | −0.0119281 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.2465 | −0.541961 | −0.270980 | − | 0.962585i | \(-0.587348\pi\) | ||||
−0.270980 | + | 0.962585i | \(0.587348\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.48666 | + | 30.6462i | 0.0944603 | + | 1.16415i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −38.5413 | − | 21.4379i | −1.46196 | − | 0.813185i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.72248 | + | 2.72248i | 0.103121 | + | 0.103121i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.86036 | + | 10.5031i | −0.146012 | + | 0.397265i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 19.9558i | − | 0.753721i | −0.926270 | − | 0.376861i | \(-0.877004\pi\) | ||
0.926270 | − | 0.376861i | \(-0.122996\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.1790 | + | 11.1790i | −0.421625 | + | 0.421625i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.6938 | + | 14.3768i | −0.628726 | + | 0.541463i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.0036 | + | 19.0036i | −0.714702 | + | 0.714702i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 32.1595i | − | 1.20778i | −0.797069 | − | 0.603888i | \(-0.793618\pi\) | ||
0.797069 | − | 0.603888i | \(-0.206382\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.3366 | − | 8.78502i | −0.387652 | − | 0.329464i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.14149 | + | 1.14149i | 0.0427491 | + | 0.0427491i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.710830 | + | 0.202698i | −0.0265835 | + | 0.00758048i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.46557 | − | 7.49351i | −0.129424 | − | 0.279850i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.0312 | 1.08268 | 0.541341 | − | 0.840803i | \(-0.317917\pi\) | ||||
0.541341 | + | 0.840803i | \(0.317917\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.1451 | 1.12266 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.34239 | + | 9.38942i | 0.161495 | + | 0.349196i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.82334 | − | 12.6022i | −0.290552 | − | 0.468033i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.23331 | + | 8.23331i | 0.305357 | + | 0.305357i | 0.843105 | − | 0.537749i | \(-0.180725\pi\) |
−0.537749 | + | 0.843105i | \(0.680725\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.1232 | + | 13.9397i | 0.856417 | + | 0.516285i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 16.2485i | − | 0.600973i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.96783 | + | 9.96783i | −0.368170 | + | 0.368170i | −0.866810 | − | 0.498639i | \(-0.833833\pi\) |
0.498639 | + | 0.866810i | \(0.333833\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.27842 | − | 17.1437i | 0.0471552 | − | 0.632353i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.49758 | − | 2.49758i | 0.0919997 | − | 0.0919997i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.4383i | 1.78183i | 0.454168 | + | 0.890916i | \(0.349937\pi\) | ||||
−0.454168 | + | 0.890916i | \(0.650063\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.227322 | + | 0.618489i | −0.00835087 | + | 0.0227208i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.6600 | − | 23.6600i | −0.867999 | − | 0.867999i | 0.124251 | − | 0.992251i | \(-0.460347\pi\) |
−0.992251 | + | 0.124251i | \(0.960347\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.28984 | + | 14.9036i | −0.303716 | + | 0.546026i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 51.2474 | − | 4.15826i | 1.87505 | − | 0.152143i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 37.7653 | 1.37991 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.5562 | −0.750106 | −0.375053 | − | 0.927003i | \(-0.622376\pi\) | ||||
−0.375053 | + | 0.927003i | \(0.622376\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.8102 | − | 10.5492i | 0.831249 | − | 0.384433i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.0793 | + | 27.1098i | −0.548791 | + | 0.986626i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.68775 | + | 2.68775i | 0.0976880 | + | 0.0976880i | 0.754262 | − | 0.656574i | \(-0.227995\pi\) |
−0.656574 | + | 0.754262i | \(0.727995\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.92648 | − | 1.81069i | −0.178820 | − | 0.0657240i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.9845i | 0.941936i | 0.882150 | + | 0.470968i | \(0.156095\pi\) | ||||
−0.882150 | + | 0.470968i | \(0.843905\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −23.1059 | + | 23.1059i | −0.836489 | + | 0.836489i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.6480 | + | 4.84028i | 0.384978 | + | 0.175001i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.393209 | + | 0.393209i | −0.0141979 | + | 0.0141979i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.7478i | 0.964552i | 0.876019 | + | 0.482276i | \(0.160190\pi\) | ||||
−0.876019 | + | 0.482276i | \(0.839810\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.7971 | + | 6.17368i | 0.604934 | + | 0.222340i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.6146 | − | 26.6146i | −0.957260 | − | 0.957260i | 0.0418634 | − | 0.999123i | \(-0.486671\pi\) |
−0.999123 | + | 0.0418634i | \(0.986671\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.25715 | − | 6.85759i | −0.152921 | − | 0.246332i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.1024 | + | 11.1468i | −0.864669 | + | 0.399889i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.70106 | 0.275919 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.851266 | −0.0304607 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.8513 | + | 4.13028i | 0.530743 | + | 0.147604i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 37.3244 | − | 10.6433i | 1.33217 | − | 0.379876i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.6714 | − | 33.6714i | −1.20025 | − | 1.20025i | −0.974089 | − | 0.226166i | \(-0.927381\pi\) |
−0.226166 | − | 0.974089i | \(-0.572619\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.6568 | − | 42.5986i | 0.557398 | − | 1.51655i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 34.6496i | − | 1.23200i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.217340 | − | 0.217340i | 0.00771797 | − | 0.00771797i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.25408 | + | 8.42315i | 0.257276 | + | 0.298738i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.75184 | − | 8.75184i | 0.310006 | − | 0.310006i | −0.534906 | − | 0.844912i | \(-0.679653\pi\) |
0.844912 | + | 0.534906i | \(0.179653\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 9.91842i | − | 0.350888i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.9257 | − | 16.3852i | 0.492041 | − | 0.578941i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.5881 | + | 23.5881i | 0.832406 | + | 0.832406i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.60906 | + | 3.67616i | 0.232939 | + | 0.129568i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.4559 | − | 22.6085i | −0.368065 | − | 0.795856i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.2305 | −1.44959 | −0.724793 | − | 0.688967i | \(-0.758065\pi\) | ||||
−0.724793 | + | 0.688967i | \(0.758065\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.02401 | 0.211532 | 0.105766 | − | 0.994391i | \(-0.466271\pi\) | ||||
0.105766 | + | 0.994391i | \(0.466271\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.0753 | + | 28.2723i | 0.458570 | + | 0.991552i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.1653 | − | 42.6617i | −0.426131 | − | 1.49438i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.9811 | − | 22.9811i | −0.804006 | − | 0.804006i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.716780 | + | 0.843372i | −0.0250463 | + | 0.0294698i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.2374i | 1.05529i | 0.849464 | + | 0.527646i | \(0.176925\pi\) | ||||
−0.849464 | + | 0.527646i | \(0.823075\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.7362 | + | 37.7362i | −1.31540 | + | 1.31540i | −0.398030 | + | 0.917372i | \(0.630306\pi\) |
−0.917372 | + | 0.398030i | \(0.869694\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21.9222 | + | 14.4270i | 0.763233 | + | 0.502282i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.5789 | + | 10.5789i | −0.367864 | + | 0.367864i | −0.866698 | − | 0.498834i | \(-0.833762\pi\) |
0.498834 | + | 0.866698i | \(0.333762\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.3511i | 1.22780i | 0.789385 | + | 0.613898i | \(0.210399\pi\) | ||||
−0.789385 | + | 0.613898i | \(0.789601\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.90823 | − | 10.6334i | 0.135575 | − | 0.368868i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.47262 | + | 5.47262i | 0.189615 | + | 0.189615i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.9753 | − | 52.5161i | −0.518243 | − | 1.81740i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.08149 | + | 2.24753i | 0.279337 | + | 0.0776860i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.2840 | −1.08005 | −0.540023 | − | 0.841651i | \(-0.681584\pi\) | ||||
−0.540023 | + | 0.841651i | \(0.681584\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.1992 | −0.696525 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.77830 | − | 3.13480i | 0.233457 | − | 0.107968i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.3802 | + | 14.1173i | 0.873107 | + | 0.485649i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.34557 | + | 4.34557i | 0.149316 | + | 0.149316i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −41.3971 | − | 15.2152i | −1.42075 | − | 0.522186i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.53314i | − | 0.155394i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.7408 | − | 33.7408i | 1.15526 | − | 1.15526i | 0.169781 | − | 0.985482i | \(-0.445694\pi\) |
0.985482 | − | 0.169781i | \(-0.0543061\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.9058 | − | 8.21409i | 0.749162 | − | 0.280916i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.92962 | + | 5.92962i | −0.202552 | + | 0.202552i | −0.801092 | − | 0.598541i | \(-0.795748\pi\) |
0.598541 | + | 0.801092i | \(0.295748\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 40.4897i | − | 1.38149i | −0.723098 | − | 0.690745i | \(-0.757283\pi\) | ||
0.723098 | − | 0.690745i | \(-0.242717\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.1413 | + | 4.46246i | 0.413775 | + | 0.152080i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.1926 | − | 37.1926i | −1.26605 | − | 1.26605i | −0.948111 | − | 0.317939i | \(-0.897009\pi\) |
−0.317939 | − | 0.948111i | \(-0.602991\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.0745 | − | 6.57986i | 0.784558 | − | 0.223722i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.9458 | − | 10.1494i | 0.745320 | − | 0.344693i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.7026 | 0.464829 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.127148 | 0.00430826 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 45.6580 | − | 3.70473i | 1.54529 | − | 0.125386i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.9890 | − | 25.4256i | −0.946201 | − | 0.859542i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.18800 | − | 6.18800i | −0.208954 | − | 0.208954i | 0.594869 | − | 0.803823i | \(-0.297204\pi\) |
−0.803823 | + | 0.594869i | \(0.797204\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.7167 | + | 48.2029i | −0.597568 | + | 1.62584i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 17.5166i | − | 0.590151i | −0.955474 | − | 0.295075i | \(-0.904655\pi\) | ||
0.955474 | − | 0.295075i | \(-0.0953447\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.1033 | − | 21.1033i | 0.710183 | − | 0.710183i | −0.256390 | − | 0.966573i | \(-0.582533\pi\) |
0.966573 | + | 0.256390i | \(0.0825331\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.6885 | + | 1.46819i | 0.661823 | + | 0.0493528i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.12505 | − | 7.12505i | 0.239236 | − | 0.239236i | −0.577298 | − | 0.816534i | \(-0.695893\pi\) |
0.816534 | + | 0.577298i | \(0.195893\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 52.2258i | 1.75160i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.9162 | + | 4.39696i | −0.901728 | + | 0.147304i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.0281 | − | 14.0281i | −0.469433 | − | 0.469433i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.4157 | − | 47.4905i | 0.882978 | − | 1.58743i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0793100 | − | 0.171490i | −0.00264808 | − | 0.00572588i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.78903 | 0.159723 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.00451 | −0.166724 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −22.9148 | − | 49.5481i | −0.762558 | − | 1.64886i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.70462 | − | 13.8515i | 0.256110 | − | 0.460439i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.4316 | − | 25.4316i | −0.844444 | − | 0.844444i | 0.144989 | − | 0.989433i | \(-0.453685\pi\) |
−0.989433 | + | 0.144989i | \(0.953685\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.1645 | − | 15.4380i | −0.602479 | − | 0.512046i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 54.9857i | − | 1.82176i | −0.412676 | − | 0.910878i | \(-0.635406\pi\) | ||
0.412676 | − | 0.910878i | \(-0.364594\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.7241 | + | 36.7241i | −1.21539 | + | 1.21539i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.8825 | − | 0.811521i | −0.359765 | − | 0.0268280i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.6266 | + | 36.6266i | −1.20952 | + | 1.20952i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 3.51450i | − | 0.115933i | −0.998319 | − | 0.0579663i | \(-0.981538\pi\) | ||
0.998319 | − | 0.0579663i | \(-0.0184616\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.50828 | − | 6.82445i | 0.0826507 | − | 0.224873i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.0216683 | − | 0.0216683i | −0.000713222 | − | 0.000713222i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.16351 | + | 22.0697i | −0.169775 | + | 0.725647i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.16253 | + | 26.6516i | 0.0710268 | + | 0.875352i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48.7325 | 1.59886 | 0.799432 | − | 0.600757i | \(-0.205134\pi\) | ||||
0.799432 | + | 0.600757i | \(0.205134\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.4804 | 0.507349 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.9308 | + | 8.75505i | −0.619767 | + | 0.286627i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.3618 | + | 3.23990i | −0.371571 | + | 0.105956i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.2348 | − | 23.2348i | −0.759049 | − | 0.759049i | 0.217100 | − | 0.976149i | \(-0.430340\pi\) |
−0.976149 | + | 0.217100i | \(0.930340\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.5053 | − | 10.1094i | −0.897601 | − | 0.329907i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.8466i | 0.418786i | 0.977832 | + | 0.209393i | \(0.0671488\pi\) | ||||
−0.977832 | + | 0.209393i | \(0.932851\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.56141 | + | 1.56141i | −0.0508464 | + | 0.0508464i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 39.2959 | − | 0.256617i | 1.27830 | − | 0.00834775i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.0951 | + | 26.0951i | −0.847978 | + | 0.847978i | −0.989881 | − | 0.141903i | \(-0.954678\pi\) |
0.141903 | + | 0.989881i | \(0.454678\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.20084i | 0.0389808i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 46.9177 | + | 17.2443i | 1.52141 | + | 0.559185i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.4710 | + | 19.4710i | 0.630729 | + | 0.630729i | 0.948251 | − | 0.317522i | \(-0.102851\pi\) |
−0.317522 | + | 0.948251i | \(0.602851\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.6421 | + | 15.9316i | 0.926837 | + | 0.515535i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.1326 | + | 6.53601i | −0.456843 | + | 0.211279i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36.6701 | −1.18414 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3940 | −0.915936 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.70919 | + | 33.3887i | 0.0873023 | + | 1.07594i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.02123 | − | 24.6224i | −0.226021 | − | 0.792622i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.68778 | − | 6.68778i | −0.215065 | − | 0.215065i | 0.591350 | − | 0.806415i | \(-0.298595\pi\) |
−0.806415 | + | 0.591350i | \(0.798595\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.63348 | + | 9.88585i | −0.116724 | + | 0.317579i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.9373i | 1.34583i | 0.739718 | + | 0.672916i | \(0.234959\pi\) | ||||
−0.739718 | + | 0.672916i | \(0.765041\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 47.1684 | − | 47.1684i | 1.51215 | − | 1.51215i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.190786 | + | 0.925241i | 0.00611003 | + | 0.0296314i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.90198 | + | 4.90198i | −0.156828 | + | 0.156828i | −0.781160 | − | 0.624331i | \(-0.785371\pi\) |
0.624331 | + | 0.781160i | \(0.285371\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.7209i | 0.694203i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22.0857 | − | 18.7706i | −0.705143 | − | 0.599299i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.32411 | + | 8.32411i | 0.265498 | + | 0.265498i | 0.827283 | − | 0.561785i | \(-0.189885\pi\) |
−0.561785 | + | 0.827283i | \(0.689885\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.84921 | + | 17.0054i | 0.154509 | + | 0.541838i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.9877 | − | 30.2451i | −0.445232 | − | 0.962713i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.31892 | 0.296324 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.1511 | −0.481289 | −0.240645 | − | 0.970613i | \(-0.577359\pi\) | ||||
−0.240645 | + | 0.970613i | \(0.577359\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.6624 | + | 29.5418i | 0.433563 | + | 0.937481i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.0064 | + | 14.4656i | 0.824459 | + | 0.458589i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.3556 | − | 11.3556i | −0.359635 | − | 0.359635i | 0.504043 | − | 0.863678i | \(-0.331845\pi\) |
−0.863678 | + | 0.504043i | \(0.831845\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.5841 | − | 20.5096i | −0.366503 | − | 0.648894i |
(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 | 1380.2.r.c.737.15 | ✓ | 80 | |
3.2 | odd | 2 | inner | 1380.2.r.c.737.36 | yes | 80 | |
5.3 | odd | 4 | inner | 1380.2.r.c.1013.36 | yes | 80 | |
15.8 | even | 4 | inner | 1380.2.r.c.1013.15 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.r.c.737.15 | ✓ | 80 | 1.1 | even | 1 | trivial | |
1380.2.r.c.737.36 | yes | 80 | 3.2 | odd | 2 | inner | |
1380.2.r.c.1013.15 | yes | 80 | 15.8 | even | 4 | inner | |
1380.2.r.c.1013.36 | yes | 80 | 5.3 | odd | 4 | inner |