Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,3,Mod(41,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([0, 0, 11]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.41");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.t (of order \(16\), degree \(8\), 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: | \(3.70573159530\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{16})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{16}]$ |
Embedding invariants
Embedding label | 57.3 | ||
Character | \(\chi\) | \(=\) | 136.57 |
Dual form | 136.3.t.b.105.3 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{15}{16}\right)\) |
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 | ||||||||
\(3\) | 1.63930 | − | 0.326077i | 0.546433 | − | 0.108692i | 0.0858486 | − | 0.996308i | \(-0.472640\pi\) |
0.460584 | + | 0.887616i | \(0.347640\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.61793 | + | 6.91122i | −0.923585 | + | 1.38224i | 0.000476532 | 1.00000i | \(0.499848\pi\) | |
−0.924062 | + | 0.382243i | \(0.875152\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.96901 | + | 4.44344i | 0.424144 | + | 0.634777i | 0.980581 | − | 0.196113i | \(-0.0628320\pi\) |
−0.556437 | + | 0.830890i | \(0.687832\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.73394 | + | 2.37508i | −0.637104 | + | 0.263897i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.84284 | + | 14.2919i | −0.258440 | + | 1.29927i | 0.605570 | + | 0.795792i | \(0.292945\pi\) |
−0.864010 | + | 0.503475i | \(0.832055\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.6679 | − | 15.6679i | 1.20522 | − | 1.20522i | 0.232667 | − | 0.972556i | \(-0.425255\pi\) |
0.972556 | − | 0.232667i | \(-0.0747453\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.31657 | + | 12.8353i | −0.354438 | + | 0.855690i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 16.0654 | + | 5.55912i | 0.945022 | + | 0.327007i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −21.1674 | − | 8.76784i | −1.11408 | − | 0.461465i | −0.251736 | − | 0.967796i | \(-0.581001\pi\) |
−0.862339 | + | 0.506331i | \(0.831001\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.31600 | + | 6.31600i | 0.300762 | + | 0.300762i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 34.3844 | + | 6.83948i | 1.49497 | + | 0.297368i | 0.873792 | − | 0.486299i | \(-0.161654\pi\) |
0.621180 | + | 0.783668i | \(0.286654\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −16.8726 | − | 40.7340i | −0.674903 | − | 1.62936i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −21.1328 | + | 14.1205i | −0.782695 | + | 0.522980i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −11.1864 | − | 7.47449i | −0.385737 | − | 0.257741i | 0.347549 | − | 0.937662i | \(-0.387014\pi\) |
−0.733285 | + | 0.679921i | \(0.762014\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.22691 | + | 31.3048i | 0.200868 | + | 1.00983i | 0.941267 | + | 0.337664i | \(0.109637\pi\) |
−0.740399 | + | 0.672168i | \(0.765363\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 24.3557i | 0.738053i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −44.4202 | −1.26915 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 17.3336 | − | 3.44786i | 0.468474 | − | 0.0931854i | 0.0447924 | − | 0.998996i | \(-0.485737\pi\) |
0.423682 | + | 0.905811i | \(0.360737\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 20.5754 | − | 30.7933i | 0.527576 | − | 0.789573i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −26.6426 | − | 39.8734i | −0.649819 | − | 0.972523i | −0.999366 | − | 0.0356040i | \(-0.988665\pi\) |
0.349547 | − | 0.936919i | \(-0.386335\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 15.6376 | − | 6.47729i | 0.363664 | − | 0.150635i | −0.193366 | − | 0.981127i | \(-0.561941\pi\) |
0.557031 | + | 0.830492i | \(0.311941\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.0643 | − | 50.5964i | 0.223650 | − | 1.12436i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 49.2607 | − | 49.2607i | 1.04810 | − | 1.04810i | 0.0493173 | − | 0.998783i | \(-0.484295\pi\) |
0.998783 | − | 0.0493173i | \(-0.0157046\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.82237 | − | 18.8849i | 0.159640 | − | 0.385406i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 28.1487 | + | 3.87451i | 0.551934 | + | 0.0759708i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.90219 | − | 3.68741i | −0.167966 | − | 0.0695737i | 0.297116 | − | 0.954841i | \(-0.403975\pi\) |
−0.465082 | + | 0.885268i | \(0.653975\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −85.6466 | − | 85.6466i | −1.55721 | − | 1.55721i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −37.5587 | − | 7.47090i | −0.658925 | − | 0.131068i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.7735 | + | 33.2521i | 0.233449 | + | 0.563596i | 0.996579 | − | 0.0826498i | \(-0.0263383\pi\) |
−0.763130 | + | 0.646245i | \(0.776338\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.92989 | − | 1.95769i | 0.0480310 | − | 0.0320933i | −0.531323 | − | 0.847169i | \(-0.678305\pi\) |
0.579354 | + | 0.815076i | \(0.303305\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −27.5776 | − | 18.4268i | −0.437740 | − | 0.292489i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 35.9310 | + | 180.638i | 0.552785 | + | 2.77904i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 44.1965i | 0.659649i | 0.944042 | + | 0.329825i | \(0.106990\pi\) | ||||
−0.944042 | + | 0.329825i | \(0.893010\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 58.5965 | 0.849224 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 27.2022 | − | 5.41086i | 0.383130 | − | 0.0762093i | 0.000232228 | − | 1.00000i | \(-0.499926\pi\) |
0.382898 | + | 0.923791i | \(0.374926\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 22.0828 | − | 33.0492i | 0.302504 | − | 0.452729i | −0.648811 | − | 0.760950i | \(-0.724733\pi\) |
0.951315 | + | 0.308220i | \(0.0997334\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −40.9416 | − | 61.2734i | −0.545888 | − | 0.816979i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −71.9457 | + | 29.8009i | −0.934360 | + | 0.387025i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.9727 | + | 75.2727i | −0.189528 | + | 0.952819i | 0.762542 | + | 0.646938i | \(0.223951\pi\) |
−0.952070 | + | 0.305881i | \(0.901049\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.45855 | − | 9.45855i | 0.116772 | − | 0.116772i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17.9264 | + | 43.2783i | −0.215981 | + | 0.521425i | −0.994321 | − | 0.106418i | \(-0.966062\pi\) |
0.778340 | + | 0.627843i | \(0.216062\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −112.609 | + | 85.3596i | −1.32481 | + | 1.00423i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −20.7751 | − | 8.60531i | −0.238794 | − | 0.0989116i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 82.2618 | + | 82.2618i | 0.924290 | + | 0.924290i | 0.997329 | − | 0.0730393i | \(-0.0232698\pi\) |
−0.0730393 | + | 0.997329i | \(0.523270\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 116.138 | + | 23.1012i | 1.27624 | + | 0.253859i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20.4155 | + | 49.2875i | 0.219522 | + | 0.529973i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 158.346 | − | 105.803i | 1.66680 | − | 1.11372i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −39.3793 | − | 26.3124i | −0.405972 | − | 0.271262i | 0.335774 | − | 0.941943i | \(-0.391002\pi\) |
−0.741746 | + | 0.670681i | \(0.766002\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.6437 | − | 88.7011i | −0.178220 | − | 0.895971i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 61.1665i | 0.605609i | 0.953053 | + | 0.302804i | \(0.0979229\pi\) | ||||
−0.953053 | + | 0.302804i | \(0.902077\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 133.129 | 1.29251 | 0.646255 | − | 0.763122i | \(-0.276334\pi\) | ||||
0.646255 | + | 0.763122i | \(0.276334\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −72.8180 | + | 14.4844i | −0.693505 | + | 0.137947i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −55.0149 | + | 82.3356i | −0.514158 | + | 0.769492i | −0.994176 | − | 0.107767i | \(-0.965630\pi\) |
0.480018 | + | 0.877258i | \(0.340630\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.98036 | + | 7.45364i | 0.0456914 | + | 0.0683820i | 0.853612 | − | 0.520909i | \(-0.174407\pi\) |
−0.807921 | + | 0.589291i | \(0.799407\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 27.2906 | − | 11.3041i | 0.245861 | − | 0.101839i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 24.3650 | − | 122.491i | 0.215619 | − | 1.08399i | −0.709614 | − | 0.704591i | \(-0.751131\pi\) |
0.925233 | − | 0.379400i | \(-0.123869\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −206.054 | + | 206.054i | −1.79177 | + | 1.79177i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −52.6264 | + | 127.051i | −0.449798 | + | 1.08591i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 22.9966 | + | 87.8905i | 0.193249 | + | 0.738576i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −84.3883 | − | 34.9548i | −0.697424 | − | 0.288882i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −56.6770 | − | 56.6770i | −0.460788 | − | 0.460788i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 155.629 | + | 30.9566i | 1.24503 | + | 0.247653i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −60.6875 | − | 146.513i | −0.477854 | − | 1.15364i | −0.960613 | − | 0.277889i | \(-0.910365\pi\) |
0.482759 | − | 0.875753i | \(-0.339635\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 23.5226 | − | 15.7173i | 0.182345 | − | 0.121839i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −125.928 | − | 84.1427i | −0.961286 | − | 0.642311i | −0.0273026 | − | 0.999627i | \(-0.508692\pi\) |
−0.933983 | + | 0.357316i | \(0.883692\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.8870 | − | 120.088i | −0.179601 | − | 0.902917i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 211.260i | − | 1.56489i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 107.514 | 0.784772 | 0.392386 | − | 0.919801i | \(-0.371650\pi\) | ||||
0.392386 | + | 0.919801i | \(0.371650\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 26.2161 | − | 5.21470i | 0.188605 | − | 0.0375158i | −0.0998840 | − | 0.994999i | \(-0.531847\pi\) |
0.288489 | + | 0.957483i | \(0.406847\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 64.6903 | − | 96.8158i | 0.458796 | − | 0.686637i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 179.383 | + | 268.466i | 1.25443 | + | 1.87739i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 103.316 | − | 42.7947i | 0.712521 | − | 0.295136i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.66529 | − | 33.5087i | 0.0453421 | − | 0.227950i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 45.5277 | − | 45.5277i | 0.305555 | − | 0.305555i | −0.537628 | − | 0.843182i | \(-0.680679\pi\) |
0.843182 | + | 0.537628i | \(0.180679\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −27.1000 | + | 65.4252i | −0.179470 | + | 0.433280i | −0.987856 | − | 0.155374i | \(-0.950342\pi\) |
0.808385 | + | 0.588654i | \(0.200342\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −105.321 | + | 6.28082i | −0.688374 | + | 0.0410511i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −245.110 | − | 101.528i | −1.58135 | − | 0.655017i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −71.9058 | − | 71.9058i | −0.457999 | − | 0.457999i | 0.439999 | − | 0.897998i | \(-0.354979\pi\) |
−0.897998 | + | 0.439999i | \(0.854979\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.7957 | − | 3.14196i | −0.0993442 | − | 0.0197608i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 71.6967 | + | 173.091i | 0.445321 | + | 1.07510i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 202.124 | − | 135.055i | 1.24002 | − | 0.828558i | 0.249835 | − | 0.968288i | \(-0.419624\pi\) |
0.990190 | + | 0.139730i | \(0.0446236\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −168.328 | − | 112.473i | −1.02017 | − | 0.681655i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 29.3721 | + | 147.664i | 0.175881 | + | 0.884214i | 0.963430 | + | 0.267961i | \(0.0863499\pi\) |
−0.787549 | + | 0.616252i | \(0.788650\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 321.967i | − | 1.90513i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 142.197 | 0.831562 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −129.875 | + | 25.8337i | −0.750720 | + | 0.149328i | −0.555598 | − | 0.831451i | \(-0.687510\pi\) |
−0.195123 | + | 0.980779i | \(0.562510\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 130.904 | − | 195.912i | 0.748023 | − | 1.11950i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 33.4216 | + | 50.0190i | 0.188823 | + | 0.282593i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −143.287 | + | 59.3513i | −0.800485 | + | 0.331572i | −0.745150 | − | 0.666896i | \(-0.767622\pi\) |
−0.0553340 | + | 0.998468i | \(0.517622\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 38.2243 | − | 192.166i | 0.211184 | − | 1.06169i | −0.719115 | − | 0.694891i | \(-0.755453\pi\) |
0.930299 | − | 0.366802i | \(-0.119547\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.16461 | − | 4.16461i | 0.0227574 | − | 0.0227574i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −56.2162 | + | 135.718i | −0.303871 | + | 0.733610i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −125.122 | + | 213.802i | −0.669101 | + | 1.14332i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −125.487 | − | 51.9783i | −0.663951 | − | 0.275018i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −111.071 | − | 111.071i | −0.581523 | − | 0.581523i | 0.353799 | − | 0.935322i | \(-0.384890\pi\) |
−0.935322 | + | 0.353799i | \(0.884890\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −133.384 | − | 26.5317i | −0.691109 | − | 0.137470i | −0.162974 | − | 0.986630i | \(-0.552109\pi\) |
−0.528135 | + | 0.849160i | \(0.677109\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 117.803 | + | 284.403i | 0.604120 | + | 1.45848i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −114.722 | + | 76.6551i | −0.582347 | + | 0.389112i | −0.811564 | − | 0.584263i | \(-0.801384\pi\) |
0.229217 | + | 0.973375i | \(0.426384\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 72.6120 | + | 48.5178i | 0.364884 | + | 0.243808i | 0.724473 | − | 0.689303i | \(-0.242083\pi\) |
−0.359589 | + | 0.933111i | \(0.617083\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.4115 | + | 72.4513i | 0.0716988 | + | 0.360454i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 71.8977i | − | 0.354176i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 398.607 | 1.94443 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −213.402 | + | 42.4483i | −1.03093 | + | 0.205064i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 185.485 | − | 277.598i | 0.887488 | − | 1.32822i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −182.735 | − | 273.483i | −0.866044 | − | 1.29613i | −0.953940 | − | 0.299996i | \(-0.903015\pi\) |
0.0878969 | − | 0.996130i | \(-0.471985\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 42.8283 | − | 17.7400i | 0.201072 | − | 0.0832866i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −27.4472 | + | 137.986i | −0.127661 | + | 0.641797i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −120.613 | + | 120.613i | −0.555821 | + | 0.555821i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 25.4237 | − | 61.3783i | 0.116090 | − | 0.280266i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 338.811 | − | 164.611i | 1.53308 | − | 0.744846i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 330.436 | + | 136.871i | 1.48177 | + | 0.613771i | 0.969509 | − | 0.245056i | \(-0.0788064\pi\) |
0.512266 | + | 0.858827i | \(0.328806\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 193.493 | + | 193.493i | 0.859967 | + | 0.859967i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 197.677 | + | 39.3203i | 0.870822 | + | 0.173217i | 0.610223 | − | 0.792230i | \(-0.291080\pi\) |
0.260599 | + | 0.965447i | \(0.416080\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −57.0684 | − | 137.775i | −0.249207 | − | 0.601639i | 0.748930 | − | 0.662649i | \(-0.230568\pi\) |
−0.998137 | + | 0.0610101i | \(0.980568\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −108.223 | + | 72.3124i | −0.468499 | + | 0.313041i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −133.734 | − | 89.3582i | −0.573965 | − | 0.383511i | 0.234446 | − | 0.972129i | \(-0.424672\pi\) |
−0.808412 | + | 0.588618i | \(0.799672\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 112.969 | + | 567.934i | 0.480719 | + | 2.41674i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 128.277i | 0.541252i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −194.043 | −0.811897 | −0.405949 | − | 0.913896i | \(-0.633059\pi\) | ||||
−0.405949 | + | 0.913896i | \(0.633059\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.42729 | − | 0.880642i | 0.0183705 | − | 0.00365412i | −0.185897 | − | 0.982569i | \(-0.559519\pi\) |
0.204267 | + | 0.978915i | \(0.434519\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 139.505 | − | 208.784i | 0.574096 | − | 0.859195i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 94.3943 | + | 141.271i | 0.385283 | + | 0.576617i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −469.023 | + | 194.276i | −1.89888 | + | 0.786541i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.2748 | + | 76.7914i | −0.0613444 | + | 0.308399i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −123.725 | + | 123.725i | −0.492928 | + | 0.492928i | −0.909228 | − | 0.416299i | \(-0.863327\pi\) |
0.416299 | + | 0.909228i | \(0.363327\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −195.499 | + | 471.976i | −0.772722 | + | 1.86552i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −156.766 | + | 176.649i | −0.614769 | + | 0.692742i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −374.071 | − | 154.945i | −1.45553 | − | 0.602900i | −0.492022 | − | 0.870583i | \(-0.663742\pi\) |
−0.963507 | + | 0.267682i | \(0.913742\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 66.7838 | + | 66.7838i | 0.257853 | + | 0.257853i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 81.8944 | + | 16.2898i | 0.313772 | + | 0.0624131i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −127.880 | − | 308.730i | −0.486236 | − | 1.17388i | −0.956600 | − | 0.291405i | \(-0.905877\pi\) |
0.470364 | − | 0.882472i | \(-0.344123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 66.5941 | − | 44.4967i | 0.251298 | − | 0.167912i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 161.675 | + | 108.028i | 0.605526 | + | 0.404599i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 74.7720 | + | 375.904i | 0.277963 | + | 1.39741i | 0.827276 | + | 0.561796i | \(0.189889\pi\) |
−0.549313 | + | 0.835617i | \(0.685111\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 174.280i | 0.643099i | 0.946893 | + | 0.321550i | \(0.104204\pi\) | ||||
−0.946893 | + | 0.321550i | \(0.895796\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 197.917 | 0.724970 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 630.133 | − | 125.341i | 2.29139 | − | 0.455787i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −68.8045 | + | 102.973i | −0.248392 | + | 0.371744i | −0.934624 | − | 0.355638i | \(-0.884263\pi\) |
0.686232 | + | 0.727383i | \(0.259263\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −110.056 | − | 164.710i | −0.394466 | − | 0.590360i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −495.657 | + | 205.308i | −1.76390 | + | 0.730633i | −0.767976 | + | 0.640478i | \(0.778736\pi\) |
−0.995928 | + | 0.0901546i | \(0.971264\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 40.4243 | − | 203.227i | 0.142842 | − | 0.718116i | −0.841277 | − | 0.540605i | \(-0.818195\pi\) |
0.984119 | − | 0.177511i | \(-0.0568046\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 225.076 | − | 225.076i | 0.789742 | − | 0.789742i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 98.0730 | − | 236.769i | 0.341718 | − | 0.824980i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 227.192 | + | 178.619i | 0.786133 | + | 0.618058i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −73.1344 | − | 30.2932i | −0.251321 | − | 0.104100i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −226.842 | − | 226.842i | −0.774206 | − | 0.774206i | 0.204633 | − | 0.978839i | \(-0.434400\pi\) |
−0.978839 | + | 0.204633i | \(0.934400\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −293.418 | − | 58.3644i | −0.994636 | − | 0.197845i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −141.732 | − | 342.170i | −0.477211 | − | 1.15209i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 645.891 | − | 431.571i | 2.16017 | − | 1.44338i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 75.2095 | + | 50.2534i | 0.249866 | + | 0.166955i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.9450 | + | 100.270i | 0.0658250 | + | 0.330925i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 29.2896i | 0.0960314i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −290.459 | −0.946119 | −0.473060 | − | 0.881030i | \(-0.656850\pi\) | ||||
−0.473060 | + | 0.881030i | \(0.656850\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 218.237 | − | 43.4101i | 0.706270 | − | 0.140486i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 236.493 | − | 353.937i | 0.760428 | − | 1.13806i | −0.226042 | − | 0.974118i | \(-0.572579\pi\) |
0.986470 | − | 0.163943i | \(-0.0524214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 154.057 | + | 230.562i | 0.492195 | + | 0.736621i | 0.991543 | − | 0.129780i | \(-0.0414272\pi\) |
−0.499348 | + | 0.866401i | \(0.666427\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 254.703 | − | 105.501i | 0.808581 | − | 0.334925i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −47.2492 | + | 237.538i | −0.149051 | + | 0.749331i | 0.831877 | + | 0.554960i | \(0.187266\pi\) |
−0.980928 | + | 0.194371i | \(0.937734\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 138.626 | − | 138.626i | 0.434564 | − | 0.434564i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −63.3381 | + | 152.912i | −0.197315 | + | 0.476361i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −291.321 | − | 258.531i | −0.901923 | − | 0.800405i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −902.574 | − | 373.858i | −2.77715 | − | 1.15033i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.5948 | + | 10.5948i | 0.0323999 | + | 0.0323999i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 365.142 | + | 72.6314i | 1.10986 | + | 0.220764i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −49.7048 | − | 119.998i | −0.150166 | − | 0.362532i | 0.830840 | − | 0.556511i | \(-0.187860\pi\) |
−0.981006 | + | 0.193980i | \(0.937860\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −91.2006 | + | 60.9383i | −0.273876 | + | 0.182998i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −305.451 | − | 204.096i | −0.911795 | − | 0.609242i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −37.2805 | − | 187.422i | −0.110625 | − | 0.556148i | −0.995852 | − | 0.0909890i | \(-0.970997\pi\) |
0.885227 | − | 0.465159i | \(-0.154003\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 208.744i | − | 0.615764i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −465.108 | −1.36395 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 363.967 | − | 72.3975i | 1.06113 | − | 0.211071i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −270.594 | + | 404.973i | −0.784331 | + | 1.17383i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −281.533 | − | 421.344i | −0.811334 | − | 1.21425i | −0.973772 | − | 0.227528i | \(-0.926936\pi\) |
0.162438 | − | 0.986719i | \(-0.448064\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 594.610 | − | 246.296i | 1.70375 | − | 0.705718i | 0.703765 | − | 0.710433i | \(-0.251501\pi\) |
0.999989 | + | 0.00471518i | \(0.00150090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −109.868 | + | 552.344i | −0.313015 | + | 1.57363i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 276.652 | − | 276.652i | 0.783716 | − | 0.783716i | −0.196740 | − | 0.980456i | \(-0.563035\pi\) |
0.980456 | + | 0.196740i | \(0.0630354\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −88.2223 | + | 212.988i | −0.248514 | + | 0.599965i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 66.3575 | + | 136.580i | 0.185875 | + | 0.382578i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 69.2901 | + | 28.7009i | 0.193009 | + | 0.0799468i | 0.477094 | − | 0.878852i | \(-0.341690\pi\) |
−0.284086 | + | 0.958799i | \(0.591690\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 115.920 | + | 115.920i | 0.321107 | + | 0.321107i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −149.736 | − | 29.7843i | −0.412495 | − | 0.0820503i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 126.434 | + | 305.238i | 0.346394 | + | 0.836268i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −279.201 | + | 186.556i | −0.760766 | + | 0.508327i | −0.874406 | − | 0.485195i | \(-0.838749\pi\) |
0.113641 | + | 0.993522i | \(0.463749\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 247.469 | + | 165.354i | 0.670649 | + | 0.448113i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.0459 | − | 50.5042i | −0.0270779 | − | 0.136130i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 246.692i | − | 0.661372i | −0.943741 | − | 0.330686i | \(-0.892720\pi\) | ||
0.943741 | − | 0.330686i | \(-0.107280\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 265.217 | 0.707245 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −292.377 | + | 58.1573i | −0.775535 | + | 0.154263i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.66749 | + | 8.48200i | −0.0149538 | + | 0.0223799i | −0.838871 | − | 0.544330i | \(-0.816784\pi\) |
0.823917 | + | 0.566710i | \(0.191784\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −147.259 | − | 220.389i | −0.386507 | − | 0.578449i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −459.825 | + | 190.466i | −1.20059 | + | 0.497299i | −0.891189 | − | 0.453633i | \(-0.850128\pi\) |
−0.309398 | + | 0.950932i | \(0.600128\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 126.280 | − | 634.851i | 0.327999 | − | 1.64896i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −74.2808 | + | 74.2808i | −0.191940 | + | 0.191940i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 176.119 | − | 425.188i | 0.452747 | − | 1.09303i | −0.518526 | − | 0.855062i | \(-0.673519\pi\) |
0.971273 | − | 0.237967i | \(-0.0764810\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 514.376 | + | 301.026i | 1.31554 | + | 0.769886i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −233.871 | − | 96.8727i | −0.595093 | − | 0.246495i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −451.083 | − | 451.083i | −1.14198 | − | 1.14198i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 614.279 | + | 122.188i | 1.54730 | + | 0.307777i | 0.893561 | − | 0.448941i | \(-0.148199\pi\) |
0.653741 | + | 0.756719i | \(0.273199\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −78.3158 | − | 189.071i | −0.196280 | − | 0.473862i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −151.745 | + | 101.393i | −0.378418 | + | 0.252851i | −0.730203 | − | 0.683230i | \(-0.760575\pi\) |
0.351786 | + | 0.936081i | \(0.385575\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 588.043 | + | 392.918i | 1.45916 | + | 0.974982i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 21.6912 | + | 109.049i | 0.0535585 | + | 0.269257i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 257.532i | 0.632756i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.15321 | −0.00770956 | −0.00385478 | − | 0.999993i | \(-0.501227\pi\) | ||||
−0.00385478 | + | 0.999993i | \(0.501227\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 176.247 | − | 35.0577i | 0.428825 | − | 0.0852986i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −106.860 | + | 159.928i | −0.258741 | + | 0.387234i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −216.322 | − | 323.749i | −0.521259 | − | 0.780119i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 41.2756 | − | 17.0969i | 0.0989822 | − | 0.0409998i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.7759 | − | 79.3110i | 0.0376514 | − | 0.189286i | −0.957383 | − | 0.288823i | \(-0.906736\pi\) |
0.995034 | + | 0.0995367i | \(0.0317361\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −98.2149 | + | 98.2149i | −0.233290 | + | 0.233290i | −0.814064 | − | 0.580775i | \(-0.802750\pi\) |
0.580775 | + | 0.814064i | \(0.302750\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −165.460 | + | 399.456i | −0.391159 | + | 0.944340i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −44.6190 | − | 748.203i | −0.104986 | − | 1.76048i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.3977 | + | 7.20638i | 0.0407441 | + | 0.0168768i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 381.604 | + | 381.604i | 0.889519 | + | 0.889519i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 318.284 | + | 63.3106i | 0.738478 | + | 0.146892i | 0.549976 | − | 0.835180i | \(-0.314637\pi\) |
0.188502 | + | 0.982073i | \(0.439637\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 228.502 | + | 551.654i | 0.527719 | + | 1.27403i | 0.933014 | + | 0.359841i | \(0.117169\pi\) |
−0.405294 | + | 0.914186i | \(0.632831\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 155.411 | − | 103.842i | 0.357266 | − | 0.238718i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −667.861 | − | 446.251i | −1.52829 | − | 1.02117i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.5765 | + | 103.445i | 0.0468713 | + | 0.235638i | 0.997119 | − | 0.0758586i | \(-0.0241697\pi\) |
−0.950247 | + | 0.311497i | \(0.899170\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 126.864i | 0.287672i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 312.080 | 0.704469 | 0.352235 | − | 0.935912i | \(-0.385422\pi\) | ||||
0.352235 | + | 0.935912i | \(0.385422\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −948.408 | + | 188.650i | −2.13125 | + | 0.423933i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 59.7879 | − | 89.4790i | 0.133754 | − | 0.200177i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 261.386 | + | 391.192i | 0.582152 | + | 0.871252i | 0.999293 | − | 0.0375900i | \(-0.0119681\pi\) |
−0.417142 | + | 0.908842i | \(0.636968\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 645.609 | − | 267.420i | 1.43151 | − | 0.592949i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.0914 | + | 116.088i | −0.0509744 | + | 0.256265i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −695.972 | + | 695.972i | −1.52961 | + | 1.52961i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.5035 | + | 88.1273i | −0.0798764 | + | 0.192839i | −0.958773 | − | 0.284174i | \(-0.908281\pi\) |
0.878896 | + | 0.477013i | \(0.158281\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −418.003 | + | 109.371i | −0.910682 | + | 0.238281i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 658.460 | + | 272.743i | 1.42833 | + | 0.591634i | 0.956938 | − | 0.290291i | \(-0.0937520\pi\) |
0.471391 | + | 0.881924i | \(0.343752\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −133.625 | − | 133.625i | −0.288606 | − | 0.288606i | 0.547923 | − | 0.836529i | \(-0.315419\pi\) |
−0.836529 | + | 0.547923i | \(0.815419\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −434.914 | − | 86.5097i | −0.935298 | − | 0.186042i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 245.812 | + | 593.443i | 0.526364 | + | 1.27076i | 0.933890 | + | 0.357562i | \(0.116392\pi\) |
−0.407525 | + | 0.913194i | \(0.633608\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −196.384 | + | 131.220i | −0.418730 | + | 0.279786i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −141.322 | − | 94.4283i | −0.300046 | − | 0.200485i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 48.1179 | + | 241.905i | 0.101729 | + | 0.511427i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1010.17i | 2.12667i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 59.8025 | 0.125372 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −770.025 | + | 153.168i | −1.60757 | + | 0.319765i | −0.915578 | − | 0.402141i | \(-0.868266\pi\) |
−0.691991 | + | 0.721906i | \(0.743266\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 217.560 | − | 325.601i | 0.452307 | − | 0.676926i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 173.973 | + | 260.370i | 0.360193 | + | 0.539068i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 363.702 | − | 150.650i | 0.749900 | − | 0.310619i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.1911 | + | 136.699i | −0.0558338 | + | 0.280695i | −0.998609 | − | 0.0527349i | \(-0.983206\pi\) |
0.942775 | + | 0.333430i | \(0.108206\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 287.303 | − | 287.303i | 0.587533 | − | 0.587533i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 111.558 | − | 269.326i | 0.227207 | − | 0.548525i | −0.768629 | − | 0.639695i | \(-0.779061\pi\) |
0.995835 | + | 0.0911698i | \(0.0290606\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −138.162 | − | 182.267i | −0.280246 | − | 0.369709i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 694.510 | + | 287.675i | 1.40305 | + | 0.581162i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 104.807 | + | 104.807i | 0.210878 | + | 0.210878i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −474.259 | − | 94.3360i | −0.950419 | − | 0.189050i | −0.304548 | − | 0.952497i | \(-0.598506\pi\) |
−0.645871 | + | 0.763447i | \(0.723506\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 96.2994 | + | 232.487i | 0.192214 | + | 0.464047i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 328.366 | − | 219.407i | 0.652814 | − | 0.436196i | −0.184564 | − | 0.982820i | \(-0.559087\pi\) |
0.837378 | + | 0.546624i | \(0.184087\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −422.735 | − | 282.462i | −0.837099 | − | 0.559331i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −104.986 | − | 527.800i | −0.207073 | − | 1.04103i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 605.145i | − | 1.18889i | −0.804136 | − | 0.594445i | \(-0.797372\pi\) | ||
0.804136 | − | 0.594445i | \(-0.202628\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 212.416 | 0.415687 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 571.132 | − | 113.605i | 1.11332 | − | 0.221453i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −614.778 | + | 920.080i | −1.19374 | + | 1.78656i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 563.991 | + | 844.072i | 1.09089 | + | 1.63263i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −204.480 | + | 84.6982i | −0.393988 | + | 0.163195i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 151.096 | − | 759.610i | 0.290011 | − | 1.45798i | −0.511127 | − | 0.859505i | \(-0.670772\pi\) |
0.801138 | − | 0.598479i | \(-0.204228\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 390.295 | − | 390.295i | 0.746261 | − | 0.746261i | −0.227513 | − | 0.973775i | \(-0.573060\pi\) |
0.973775 | + | 0.227513i | \(0.0730596\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 150.709 | − | 363.843i | 0.287064 | − | 0.693034i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −73.9894 | + | 537.539i | −0.140397 | + | 1.02000i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 646.774 | + | 267.903i | 1.22263 | + | 0.506432i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −157.953 | − | 157.953i | −0.297463 | − | 0.297463i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1042.17 | − | 207.300i | −1.95528 | − | 0.388930i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −314.984 | − | 760.440i | −0.588756 | − | 1.42138i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −215.537 | + | 144.017i | −0.401372 | + | 0.268188i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 247.664 | + | 165.484i | 0.459488 | + | 0.307020i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −165.940 | − | 834.234i | −0.306727 | − | 1.54202i | −0.759566 | − | 0.650430i | \(-0.774589\pi\) |
0.452838 | − | 0.891593i | \(-0.350411\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 327.482i | − | 0.603098i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −74.5127 | −0.136721 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.1837 | + | 6.79956i | −0.0624930 | + | 0.0124306i | −0.226238 | − | 0.974072i | \(-0.572643\pi\) |
0.163745 | + | 0.986503i | \(0.447643\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.1502 | + | 18.1840i | −0.0221314 | + | 0.0331220i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 171.251 | + | 256.296i | 0.310801 | + | 0.465147i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −378.924 | + | 156.955i | −0.685214 | + | 0.283825i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −47.9007 | + | 240.813i | −0.0863075 | + | 0.433897i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.67112 | − | 6.67112i | 0.0119769 | − | 0.0119769i | −0.701093 | − | 0.713070i | \(-0.747304\pi\) |
0.713070 | + | 0.701093i | \(0.247304\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 143.522 | − | 346.494i | 0.256748 | − | 0.619846i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −135.396 | + | 391.284i | −0.241348 | + | 0.697476i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 644.559 | + | 266.985i | 1.14486 | + | 0.474218i | 0.872808 | − | 0.488063i | \(-0.162296\pi\) |
0.272056 | + | 0.962281i | \(0.412296\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 734.046 | + | 734.046i | 1.29920 | + | 1.29920i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 70.1110 | + | 13.9459i | 0.123653 | + | 0.0245960i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.2433 | − | 85.0848i | −0.0619390 | − | 0.149534i | 0.889880 | − | 0.456195i | \(-0.150788\pi\) |
−0.951819 | + | 0.306661i | \(0.900788\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −838.846 | + | 560.499i | −1.46908 | + | 0.981609i | −0.474216 | + | 0.880409i | \(0.657268\pi\) |
−0.994866 | + | 0.101201i | \(0.967732\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −218.296 | − | 145.861i | −0.380970 | − | 0.254556i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −301.553 | − | 1516.01i | −0.524441 | − | 2.63654i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 902.184i | 1.56358i | 0.623544 | + | 0.781788i | \(0.285692\pi\) | ||||
−0.623544 | + | 0.781788i | \(0.714308\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −227.308 | −0.392587 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −245.528 | + | 48.8385i | −0.422595 | + | 0.0840595i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 78.0077 | − | 116.747i | 0.133804 | − | 0.200252i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −635.054 | − | 950.426i | −1.08556 | − | 1.62466i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 382.237 | − | 158.328i | 0.651171 | − | 0.269724i | −0.0325470 | − | 0.999470i | \(-0.510362\pi\) |
0.683718 | + | 0.729746i | \(0.260362\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 142.668 | − | 717.238i | 0.242220 | − | 1.21772i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −163.069 | + | 163.069i | −0.275920 | + | 0.275920i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 306.441 | − | 739.813i | 0.516763 | − | 1.24758i | −0.423118 | − | 0.906075i | \(-0.639064\pi\) |
0.939881 | − | 0.341502i | \(-0.110936\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −713.627 | − | 246.937i | −1.19937 | − | 0.415021i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 134.853 | + | 55.8581i | 0.225885 | + | 0.0935646i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −74.2393 | − | 74.2393i | −0.123939 | − | 0.123939i | 0.642417 | − | 0.766356i | \(-0.277932\pi\) |
−0.766356 | + | 0.642417i | \(0.777932\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −155.429 | − | 30.9167i | −0.258617 | − | 0.0514422i | 0.0640787 | − | 0.997945i | \(-0.479589\pi\) |
−0.322696 | + | 0.946503i | \(0.604589\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −104.970 | − | 253.420i | −0.174080 | − | 0.420265i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 631.279 | − | 421.807i | 1.04344 | − | 0.697202i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 86.2065 | + | 57.6013i | 0.142021 | + | 0.0948951i | 0.624551 | − | 0.780984i | \(-0.285282\pi\) |
−0.482530 | + | 0.875879i | \(0.660282\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23.4442 | − | 117.862i | −0.0384962 | − | 0.193533i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1543.62i | − | 2.52639i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 106.904 | 0.174394 | 0.0871971 | − | 0.996191i | \(-0.472209\pi\) | ||||
0.0871971 | + | 0.996191i | \(0.472209\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 653.437 | − | 129.977i | 1.06250 | − | 0.211344i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −167.765 | + | 251.078i | −0.271904 | + | 0.406934i | −0.942143 | − | 0.335212i | \(-0.891192\pi\) |
0.670238 | + | 0.742146i | \(0.266192\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 161.719 | + | 242.029i | 0.261258 | + | 0.391001i | 0.938788 | − | 0.344494i | \(-0.111950\pi\) |
−0.677530 | + | 0.735495i | \(0.736950\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −823.213 | + | 340.986i | −1.32563 | + | 0.549092i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −121.289 | + | 609.761i | −0.194685 | + | 0.978750i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −153.221 | + | 153.221i | −0.245153 | + | 0.245153i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 213.547 | − | 515.549i | 0.340586 | − | 0.822246i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 297.637 | + | 40.9682i | 0.473191 | + | 0.0651322i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 58.1522 | + | 24.0874i | 0.0921588 | + | 0.0381734i | 0.428287 | − | 0.903643i | \(-0.359117\pi\) |
−0.336128 | + | 0.941816i | \(0.609117\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −388.734 | − | 388.734i | −0.614114 | − | 0.614114i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1292.83 | + | 257.160i | 2.03595 | + | 0.404976i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −173.326 | − | 418.447i | −0.272098 | − | 0.656902i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −143.125 | + | 95.6330i | −0.223983 | + | 0.149660i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.3553 | − | 22.2873i | −0.0520364 | − | 0.0347696i | 0.529280 | − | 0.848447i | \(-0.322462\pi\) |
−0.581316 | + | 0.813678i | \(0.697462\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −68.0029 | − | 341.873i | −0.105759 | − | 0.531685i | −0.996949 | − | 0.0780554i | \(-0.975129\pi\) |
0.891190 | − | 0.453630i | \(-0.149871\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 235.151i | 0.364575i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −383.840 | −0.593261 | −0.296631 | − | 0.954992i | \(-0.595863\pi\) | ||||
−0.296631 | + | 0.954992i | \(0.595863\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −514.393 | + | 102.319i | −0.792594 | + | 0.157657i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −158.392 | + | 237.050i | −0.243305 | + | 0.364132i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 181.018 | + | 270.913i | 0.277210 | + | 0.414874i | 0.943783 | − | 0.330565i | \(-0.107239\pi\) |
−0.666573 | + | 0.745440i | \(0.732239\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1163.06 | − | 481.754i | 1.77566 | − | 0.735502i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −48.1270 | + | 241.951i | −0.0732526 | + | 0.368266i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −505.846 | + | 505.846i | −0.767596 | + | 0.767596i | −0.977683 | − | 0.210086i | \(-0.932625\pi\) |
0.210086 | + | 0.977683i | \(0.432625\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −116.507 | + | 281.272i | −0.176258 | + | 0.425525i | −0.987176 | − | 0.159635i | \(-0.948968\pi\) |
0.810918 | + | 0.585160i | \(0.198968\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 501.736 | − | 380.325i | 0.756766 | − | 0.573642i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 940.262 | + | 389.469i | 1.41393 | + | 0.585668i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −333.514 | − | 333.514i | −0.500022 | − | 0.500022i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 586.313 | + | 116.625i | 0.876403 | + | 0.174327i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.6500 | + | 47.4392i | 0.0292846 | + | 0.0706993i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −665.108 | + | 444.411i | −0.988273 | + | 0.660343i | −0.940953 | − | 0.338537i | \(-0.890068\pi\) |
−0.0473200 | + | 0.998880i | \(0.515068\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 931.746 | + | 622.573i | 1.38036 | + | 0.922330i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.0546 | − | 146.067i | −0.0429167 | − | 0.215757i | 0.953376 | − | 0.301785i | \(-0.0975825\pi\) |
−0.996293 | + | 0.0860281i | \(0.972583\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 253.101i | − | 0.372756i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 336.872 | 0.494673 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −548.888 | + | 109.181i | −0.803643 | + | 0.159855i | −0.579788 | − | 0.814768i | \(-0.696864\pi\) |
−0.223856 | + | 0.974622i | \(0.571864\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −496.490 | + | 743.051i | −0.724804 | + | 1.08475i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −138.477 | − | 207.246i | −0.201568 | − | 0.301668i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −197.253 | + | 81.7047i | −0.286288 | + | 0.118584i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −139.685 | + | 702.242i | −0.202148 | + | 1.01627i | 0.737817 | + | 0.675000i | \(0.235857\pi\) |
−0.939966 | + | 0.341269i | \(0.889143\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 341.753 | − | 341.753i | 0.493150 | − | 0.493150i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −85.0240 | + | 205.266i | −0.122337 | + | 0.295347i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −206.362 | − | 788.691i | −0.296071 | − | 1.13155i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −248.368 | − | 102.877i | −0.355318 | − | 0.147178i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 83.2890 | + | 83.2890i | 0.118815 | + | 0.118815i | 0.764014 | − | 0.645200i | \(-0.223226\pi\) |
−0.645200 | + | 0.764014i | \(0.723226\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −397.137 | − | 78.9955i | −0.564918 | − | 0.112369i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 370.380 | + | 894.177i | 0.525362 | + | 1.26834i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −271.789 | + | 181.604i | −0.384426 | + | 0.256866i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 655.789 | + | 438.184i | 0.924949 | + | 0.618031i | 0.924175 | − | 0.381969i | \(-0.124754\pi\) |
0.000773505 | 1.00000i | \(0.499754\pi\) | ||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −92.9260 | − | 467.170i | −0.130698 | − | 0.657061i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1118.98i | 1.56940i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2683.81 | −3.75358 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −318.095 | + | 63.2731i | −0.443647 | + | 0.0882470i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −272.711 | + | 408.141i | −0.379292 | + | 0.567651i | −0.971173 | − | 0.238375i | \(-0.923385\pi\) |
0.591881 | + | 0.806025i | \(0.298385\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 395.260 | + | 591.548i | 0.548211 | + | 0.820455i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.97049 | − | 2.88727i | 0.00964107 | − | 0.00399346i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −115.723 | + | 581.779i | −0.159618 | + | 0.802454i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 836.092 | − | 836.092i | 1.15006 | − | 1.15006i | 0.163518 | − | 0.986540i | \(-0.447716\pi\) |
0.986540 | − | 0.163518i | \(-0.0522841\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 114.541 | − | 276.526i | 0.157120 | − | 0.379322i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 287.231 | − | 17.1290i | 0.392929 | − | 0.0234323i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 233.598 | + | 96.7596i | 0.318688 | + | 0.132005i | 0.536293 | − | 0.844032i | \(-0.319824\pi\) |
−0.217605 | + | 0.976037i | \(0.569824\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 200.806 | + | 200.806i | 0.273205 | + | 0.273205i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −631.653 | − | 125.644i | −0.857060 | − | 0.170480i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.19672 | + | 22.2029i | 0.0124448 | + | 0.0300445i | 0.929980 | − | 0.367611i | \(-0.119824\pi\) |
−0.917535 | + | 0.397655i | \(0.869824\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −705.520 | + | 471.414i | −0.952119 | + | 0.636186i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 414.988 | + | 277.286i | 0.558530 | + | 0.373198i | 0.802561 | − | 0.596569i | \(-0.203470\pi\) |
−0.244031 | + | 0.969767i | \(0.578470\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 104.408 | + | 524.895i | 0.140145 | + | 0.704557i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 290.732i | − | 0.389199i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −529.193 | −0.706532 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1176.01 | − | 233.924i | 1.56593 | − | 0.311483i | 0.665471 | − | 0.746423i | \(-0.268231\pi\) |
0.900459 | + | 0.434941i | \(0.143231\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −162.478 | + | 243.166i | −0.215775 | + | 0.322930i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −327.022 | − | 489.423i | −0.433142 | − | 0.648242i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 907.665 | − | 375.967i | 1.19903 | − | 0.496654i | 0.308344 | − | 0.951275i | \(-0.400225\pi\) |
0.890685 | + | 0.454621i | \(0.150225\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −166.581 | + | 837.457i | −0.219474 | + | 1.10337i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 96.4662 | − | 96.4662i | 0.126762 | − | 0.126762i | −0.640879 | − | 0.767642i | \(-0.721430\pi\) |
0.767642 | + | 0.640879i | \(0.221430\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.3330 | + | 44.2599i | −0.0240276 | + | 0.0580077i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 442.958 | − | 756.902i | 0.579029 | − | 0.989414i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 736.793 | + | 305.190i | 0.960617 | + | 0.397901i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 211.871 | + | 211.871i | 0.275515 | + | 0.275515i | 0.831315 | − | 0.555801i | \(-0.187588\pi\) |
−0.555801 | + | 0.831315i | \(0.687588\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −663.739 | − | 132.026i | −0.860880 | − | 0.171240i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −143.142 | − | 345.575i | −0.185177 | − | 0.447057i | 0.803842 | − | 0.594842i | \(-0.202786\pi\) |
−0.989019 | + | 0.147785i | \(0.952786\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1170.10 | − | 781.839i | 1.50981 | − | 1.00882i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 131.255 | + | 87.7020i | 0.168926 | + | 0.112873i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 214.351 | + | 1077.62i | 0.275162 | + | 1.38333i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 404.155i | 0.517484i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 341.942 | 0.436707 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 829.012 | − | 164.901i | 1.05607 | − | 0.210065i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 488.026 | − | 730.382i | 0.620109 | − | 0.928059i | −0.379886 | − | 0.925033i | \(-0.624037\pi\) |
0.999995 | − | 0.00302581i | \(-0.000963146\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −310.303 | − | 464.402i | −0.393287 | − | 0.588595i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 616.621 | − | 255.413i | 0.779546 | − | 0.322898i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.2323 | − | 76.5782i | 0.0192085 | − | 0.0965677i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 94.6583 | − | 94.6583i | 0.119067 | − | 0.119067i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.8659 | − | 81.7594i | 0.0424917 | − | 0.102584i | −0.901209 | − | 0.433385i | \(-0.857319\pi\) |
0.943700 | + | 0.330801i | \(0.107319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1065.24 | − | 517.546i | 1.33321 | − | 0.647742i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −667.062 | − | 276.306i | −0.832787 | − | 0.344952i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 409.560 | + | 409.560i | 0.510037 | + | 0.510037i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1527.36 | − | 303.811i | −1.89734 | − | 0.377405i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 245.147 | + | 591.838i | 0.303776 | + | 0.733380i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1156.53 | + | 772.769i | −1.42958 | + | 0.955216i | −0.430979 | + | 0.902362i | \(0.641832\pi\) |
−0.998602 | + | 0.0528535i | \(0.983168\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −441.389 | − | 294.927i | −0.544253 | − | 0.363658i | 0.252846 | − | 0.967506i | \(-0.418633\pi\) |
−0.797099 | + | 0.603848i | \(0.793633\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 56.8286 | + | 285.697i | 0.0698999 | + | 0.351411i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2020.60i | 2.47926i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −387.799 | −0.474662 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −720.793 | + | 143.375i | −0.880089 | + | 0.175061i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −201.598 | + | 301.713i | −0.245552 | + | 0.367494i | −0.933688 | − | 0.358087i | \(-0.883429\pi\) |
0.688136 | + | 0.725581i | \(0.258429\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −501.260 | − | 750.189i | −0.609065 | − | 0.911530i | 0.390895 | − | 0.920435i | \(-0.372165\pi\) |
−0.999960 | + | 0.00890509i | \(0.997165\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 992.106 | − | 410.944i | 1.20255 | − | 0.498114i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.1095 | − | 80.9880i | 0.0194795 | − | 0.0979299i | −0.969823 | − | 0.243812i | \(-0.921602\pi\) |
0.989302 | + | 0.145882i | \(0.0466020\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −667.698 | + | 667.698i | −0.805426 | + | 0.805426i | −0.983938 | − | 0.178511i | \(-0.942872\pi\) |
0.178511 | + | 0.983938i | \(0.442872\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −79.2140 | + | 191.239i | −0.0953236 | + | 0.230132i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 230.653 | − | 259.907i | 0.276894 | − | 0.312013i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1156.17 | − | 478.903i | −1.38464 | − | 0.573536i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −573.630 | − | 573.630i | −0.685340 | − | 0.685340i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1374.83 | − | 273.470i | −1.63865 | − | 0.325947i | −0.712087 | − | 0.702092i | \(-0.752250\pi\) |
−0.926561 | + | 0.376144i | \(0.877250\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −252.570 | − | 609.758i | −0.300321 | − | 0.725039i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −745.584 | + | 498.183i | −0.884441 | + | 0.590965i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2225.18 | + | 1486.82i | 2.63335 | + | 1.75955i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −95.2303 | − | 478.755i | −0.112432 | − | 0.565236i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 346.331i | − | 0.407928i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 619.585 | 0.728067 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1671.12 | − | 332.407i | 1.95911 | − | 0.389691i | 0.969790 | − | 0.243942i | \(-0.0784407\pi\) |
0.989322 | − | 0.145749i | \(-0.0465593\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −656.656 | + | 982.754i | −0.768018 | + | 1.14942i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −164.307 | − | 245.903i | −0.191723 | − | 0.286934i | 0.723137 | − | 0.690705i | \(-0.242700\pi\) |
−0.914860 | + | 0.403770i | \(0.867700\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −978.055 | + | 405.124i | −1.13860 | + | 0.471622i | −0.870695 | − | 0.491824i | \(-0.836330\pi\) |
−0.267902 | + | 0.963446i | \(0.586330\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 83.5660 | − | 420.115i | 0.0970570 | − | 0.487938i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 333.846 | − | 333.846i | 0.386844 | − | 0.386844i | −0.486716 | − | 0.873560i | \(-0.661805\pi\) |
0.873560 | + | 0.486716i | \(0.161805\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 421.209 | − | 1016.89i | 0.486947 | − | 1.17559i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 430.680 | + | 218.727i | 0.496747 | + | 0.252281i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1033.23 | − | 427.977i | −1.18898 | − | 0.492494i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 692.467 | + | 692.467i | 0.795025 | + | 0.795025i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 288.293 | + | 57.3450i | 0.330232 | + | 0.0656873i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 324.511 | + | 783.439i | 0.370870 | + | 0.895359i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 110.050 | − | 73.5328i | 0.125484 | − | 0.0838459i | −0.491244 | − | 0.871022i | \(-0.663458\pi\) |
0.616728 | + | 0.787176i | \(0.288458\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −445.830 | − | 297.894i | −0.507202 | − | 0.338901i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −290.402 | − | 1459.95i | −0.329628 | − | 1.65715i | −0.689602 | − | 0.724188i | \(-0.742215\pi\) |
0.359975 | − | 0.932962i | \(-0.382785\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 850.214i | 0.962870i | 0.876482 | + | 0.481435i | \(0.159884\pi\) | ||||
−0.876482 | + | 0.481435i | \(0.840116\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −500.030 | −0.565006 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −764.270 | + | 152.023i | −0.861635 | + | 0.171390i | −0.606079 | − | 0.795404i | \(-0.707259\pi\) |
−0.255556 | + | 0.966794i | \(0.582259\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 470.837 | − | 704.658i | 0.529626 | − | 0.792641i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 108.292 | + | 162.070i | 0.121540 | + | 0.181897i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1474.63 | + | 610.813i | −1.65132 | + | 0.684001i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 251.498 | − | 1264.37i | 0.281003 | − | 1.41270i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 918.084 | − | 918.084i | 1.02350 | − | 1.02350i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 164.331 | − | 396.730i | 0.182793 | − | 0.441301i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −122.518 | − | 108.728i | −0.135980 | − | 0.120675i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 139.677 | + | 57.8563i | 0.154682 | + | 0.0640712i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1151.59 | + | 1151.59i | 1.27247 | + | 1.27247i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 886.642 | + | 176.364i | 0.977555 | + | 0.194448i | 0.657916 | − | 0.753092i | \(-0.271438\pi\) |
0.319639 | + | 0.947539i | \(0.396438\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −145.275 | − | 350.725i | −0.159819 | − | 0.385836i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 641.980 | − | 428.957i | 0.704698 | − | 0.470864i | −0.150871 | − | 0.988553i | \(-0.548208\pi\) |
0.855569 | + | 0.517689i | \(0.173208\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −567.568 | − | 379.237i | −0.621652 | − | 0.415374i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.55065 | + | 48.0144i | 0.0104379 | + | 0.0524747i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 809.376i | − | 0.882634i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1260.71 | −1.37183 | −0.685913 | − | 0.727684i | \(-0.740597\pi\) | ||||
−0.685913 | + | 0.727684i | \(0.740597\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −476.148 | + | 94.7118i | −0.516991 | + | 0.102836i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 341.425 | − | 510.979i | 0.369908 | − | 0.553607i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −432.907 | − | 647.890i | −0.468007 | − | 0.700422i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −763.351 | + | 316.190i | −0.823464 | + | 0.341090i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.8279 | + | 235.420i | −0.0504067 | + | 0.253412i | −0.997770 | − | 0.0667496i | \(-0.978737\pi\) |
0.947363 | + | 0.320161i | \(0.103737\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −331.159 | + | 331.159i | −0.355703 | + | 0.355703i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 272.272 | − | 657.323i | 0.291825 | − | 0.704527i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −899.825 | − | 1852.06i | −0.962380 | − | 1.98082i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1368.87 | + | 567.005i | 1.46091 | + | 0.605128i | 0.964765 | − | 0.263113i | \(-0.0847492\pi\) |
0.496143 | + | 0.868241i | \(0.334749\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 327.726 | + | 327.726i | 0.349016 | + | 0.349016i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1508.49 | + | 300.056i | 1.60307 | + | 0.318870i | 0.913964 | − | 0.405794i | \(-0.133005\pi\) |
0.689102 | + | 0.724664i | \(0.258005\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −643.375 | − | 1553.24i | −0.682264 | − | 1.64713i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 938.722 | − | 627.234i | 0.993356 | − | 0.663740i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 195.098 | + | 130.360i | 0.206017 | + | 0.137656i | 0.654299 | − | 0.756236i | \(-0.272964\pi\) |
−0.448282 | + | 0.893892i | \(0.647964\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −171.821 | − | 863.804i | −0.181055 | − | 0.910225i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 404.802i | 0.425660i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −577.880 | −0.606380 | −0.303190 | − | 0.952930i | \(-0.598052\pi\) | ||||
−0.303190 | + | 0.952930i | \(0.598052\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1280.55 | − | 254.718i | 1.34089 | − | 0.266720i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 182.047 | − | 272.452i | 0.190226 | − | 0.284694i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 319.209 | + | 477.730i | 0.332856 | + | 0.498155i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −53.3672 | + | 22.1054i | −0.0555330 | + | 0.0230025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 119.899 | − | 602.772i | 0.124506 | − | 0.625931i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 799.324 | − | 799.324i | 0.828315 | − | 0.828315i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 290.511 | − | 701.356i | 0.300425 | − | 0.725290i | −0.699518 | − | 0.714615i | \(-0.746602\pi\) |
0.999943 | − | 0.0106752i | \(-0.00339810\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −561.863 | − | 328.816i | −0.579838 | − | 0.339336i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1394.29 | + | 577.535i | 1.43593 | + | 0.594783i | 0.958809 | − | 0.284052i | \(-0.0916788\pi\) |
0.477125 | + | 0.878835i | \(0.341679\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 101.007 | + | 101.007i | 0.103810 | + | 0.103810i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1601.50 | − | 318.557i | −1.64256 | − | 0.326725i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −533.687 | − | 1288.43i | −0.546251 | − | 1.31877i | −0.920248 | − | 0.391336i | \(-0.872013\pi\) |
0.373997 | − | 0.927430i | \(-0.377987\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1409.54 | + | 941.823i | −1.43977 | + | 0.962026i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −46.2601 | − | 30.9100i | −0.0471560 | − | 0.0315087i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 209.895 | + | 1055.21i | 0.213525 | + | 1.07346i | 0.927652 | + | 0.373446i | \(0.121824\pi\) |
−0.714127 | + | 0.700016i | \(0.753176\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1146.86i | − | 1.16432i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 622.261 | 0.630457 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 581.989 | − | 115.765i | 0.588462 | − | 0.117052i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −939.515 | + | 1406.08i | −0.948048 | + | 1.41885i | −0.0403703 | + | 0.999185i | \(0.512854\pi\) |
−0.907677 | + | 0.419669i | \(0.862146\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −120.610 | − | 180.505i | −0.121460 | − | 0.181778i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −670.633 | + | 277.785i | −0.674004 | + | 0.279181i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −140.134 | + | 704.501i | −0.140556 | + | 0.706620i | 0.844660 | + | 0.535303i | \(0.179802\pi\) |
−0.985216 | + | 0.171318i | \(0.945198\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −317.621 | + | 317.621i | −0.317938 | + | 0.317938i |
(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 | 136.3.t.b.57.3 | ✓ | 40 | |
4.3 | odd | 2 | 272.3.bh.g.193.3 | 40 | |||
17.3 | odd | 16 | inner | 136.3.t.b.105.3 | yes | 40 | |
68.3 | even | 16 | 272.3.bh.g.241.3 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.3.t.b.57.3 | ✓ | 40 | 1.1 | even | 1 | trivial | |
136.3.t.b.105.3 | yes | 40 | 17.3 | odd | 16 | inner | |
272.3.bh.g.193.3 | 40 | 4.3 | odd | 2 | |||
272.3.bh.g.241.3 | 40 | 68.3 | even | 16 |