Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,3,Mod(17,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.t (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.71936845953\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 113.11 | ||
Character | \(\chi\) | \(=\) | 320.113 |
Dual form | 320.3.t.a.17.11 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 0.119786 | 0.0399285 | 0.0199643 | − | 0.999801i | \(-0.493645\pi\) | ||||
0.0199643 | + | 0.999801i | \(0.493645\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.18046 | − | 3.85807i | −0.636091 | − | 0.771614i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.73972 | + | 4.73972i | 0.677103 | + | 0.677103i | 0.959344 | − | 0.282241i | \(-0.0910777\pi\) |
−0.282241 | + | 0.959344i | \(0.591078\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.98565 | −0.998406 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.49487 | − | 2.49487i | −0.226806 | − | 0.226806i | 0.584551 | − | 0.811357i | \(-0.301271\pi\) |
−0.811357 | + | 0.584551i | \(0.801271\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.4567 | −1.41974 | −0.709871 | − | 0.704331i | \(-0.751247\pi\) | ||||
−0.709871 | + | 0.704331i | \(0.751247\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.380972 | − | 0.462141i | −0.0253982 | − | 0.0308094i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 10.7165 | − | 10.7165i | 0.630385 | − | 0.630385i | −0.317780 | − | 0.948165i | \(-0.602937\pi\) |
0.948165 | + | 0.317780i | \(0.102937\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.469722 | + | 0.469722i | 0.0247222 | + | 0.0247222i | 0.719360 | − | 0.694638i | \(-0.244435\pi\) |
−0.694638 | + | 0.719360i | \(0.744435\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.567750 | + | 0.567750i | 0.0270357 | + | 0.0270357i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −27.9445 | + | 27.9445i | −1.21498 | + | 1.21498i | −0.245608 | + | 0.969369i | \(0.578988\pi\) |
−0.969369 | + | 0.245608i | \(0.921012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.76941 | + | 24.5408i | −0.190776 | + | 0.981634i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.15442 | −0.0797934 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −15.6079 | − | 15.6079i | −0.538203 | − | 0.538203i | 0.384798 | − | 0.923001i | \(-0.374271\pi\) |
−0.923001 | + | 0.384798i | \(0.874271\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −49.2667 | −1.58925 | −0.794624 | − | 0.607102i | \(-0.792332\pi\) | ||||
−0.794624 | + | 0.607102i | \(0.792332\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.298849 | − | 0.298849i | −0.00905602 | − | 0.00905602i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.21171 | − | 33.3606i | 0.0917630 | − | 0.953161i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −29.1310 | −0.787325 | −0.393662 | − | 0.919255i | \(-0.628792\pi\) | ||||
−0.393662 | + | 0.919255i | \(0.628792\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.21084 | −0.0566882 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16.4684i | 0.401669i | 0.979625 | + | 0.200834i | \(0.0643653\pi\) | ||||
−0.979625 | + | 0.200834i | \(0.935635\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.48974i | 0.104413i | 0.998636 | + | 0.0522063i | \(0.0166253\pi\) | ||||
−0.998636 | + | 0.0522063i | \(0.983375\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 28.5785 | + | 34.6673i | 0.635077 | + | 0.770384i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 40.6666 | − | 40.6666i | 0.865246 | − | 0.865246i | −0.126695 | − | 0.991942i | \(-0.540437\pi\) |
0.991942 | + | 0.126695i | \(0.0404370\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 4.07009i | − | 0.0830632i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.28369 | − | 1.28369i | 0.0251703 | − | 0.0251703i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 78.7038i | − | 1.48498i | −0.669859 | − | 0.742488i | \(-0.733646\pi\) | ||
0.669859 | − | 0.742488i | \(-0.266354\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.69056 | + | 17.5602i | −0.0307374 | + | 0.319276i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0562658 | + | 0.0562658i | 0.000987120 | + | 0.000987120i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.26583 | − | 3.26583i | 0.0553530 | − | 0.0553530i | −0.678888 | − | 0.734241i | \(-0.737538\pi\) |
0.734241 | + | 0.678888i | \(0.237538\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −23.0393 | + | 23.0393i | −0.377694 | + | 0.377694i | −0.870269 | − | 0.492576i | \(-0.836055\pi\) |
0.492576 | + | 0.870269i | \(0.336055\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −42.5895 | − | 42.5895i | −0.676023 | − | 0.676023i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 58.7006 | + | 71.2071i | 0.903086 | + | 1.09549i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 58.9247i | − | 0.879474i | −0.898127 | − | 0.439737i | \(-0.855072\pi\) | ||
0.898127 | − | 0.439737i | \(-0.144928\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.34734 | + | 3.34734i | −0.0485122 | + | 0.0485122i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 76.8059i | 1.08177i | 0.841096 | + | 0.540886i | \(0.181911\pi\) | ||||
−0.841096 | + | 0.540886i | \(0.818089\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −18.7472 | + | 18.7472i | −0.256811 | + | 0.256811i | −0.823756 | − | 0.566945i | \(-0.808125\pi\) |
0.566945 | + | 0.823756i | \(0.308125\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.571306 | + | 2.93964i | −0.00761742 | + | 0.0391952i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 23.6499i | − | 0.307142i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 141.697i | 1.79363i | 0.442407 | + | 0.896815i | \(0.354125\pi\) | ||||
−0.442407 | + | 0.896815i | \(0.645875\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 80.6128 | 0.995220 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 120.053 | 1.44642 | 0.723210 | − | 0.690628i | \(-0.242666\pi\) | ||||
0.723210 | + | 0.690628i | \(0.242666\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −75.4286 | − | 7.26169i | −0.887396 | − | 0.0854316i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.86960 | − | 1.86960i | −0.0214897 | − | 0.0214897i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 87.7260 | 0.985686 | 0.492843 | − | 0.870118i | \(-0.335958\pi\) | ||||
0.492843 | + | 0.870118i | \(0.335958\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −87.4794 | − | 87.4794i | −0.961312 | − | 0.961312i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.90143 | −0.0634563 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.318290 | − | 3.30615i | 0.00335043 | − | 0.0348015i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 34.6438 | − | 34.6438i | 0.357153 | − | 0.357153i | −0.505609 | − | 0.862762i | \(-0.668732\pi\) |
0.862762 | + | 0.505609i | \(0.168732\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 22.4180 | + | 22.4180i | 0.226444 | + | 0.226444i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −29.5707 | − | 29.5707i | −0.292780 | − | 0.292780i | 0.545398 | − | 0.838177i | \(-0.316379\pi\) |
−0.838177 | + | 0.545398i | \(0.816379\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 48.5504 | − | 48.5504i | 0.471363 | − | 0.471363i | −0.430992 | − | 0.902356i | \(-0.641836\pi\) |
0.902356 | + | 0.430992i | \(0.141836\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.384716 | − | 3.99612i | 0.00366396 | − | 0.0380583i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 62.1016 | 0.580389 | 0.290194 | − | 0.956968i | \(-0.406280\pi\) | ||||
0.290194 | + | 0.956968i | \(0.406280\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 31.6457 | + | 31.6457i | 0.290327 | + | 0.290327i | 0.837209 | − | 0.546882i | \(-0.184186\pi\) |
−0.546882 | + | 0.837209i | \(0.684186\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.48947 | −0.0314367 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −56.1211 | − | 56.1211i | −0.496647 | − | 0.496647i | 0.413745 | − | 0.910393i | \(-0.364220\pi\) |
−0.910393 | + | 0.413745i | \(0.864220\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 196.688 | + | 18.9356i | 1.71033 | + | 0.164657i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 165.845 | 1.41748 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 101.587 | 0.853671 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 108.551i | − | 0.897118i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.97268i | 0.0160380i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 109.849 | − | 59.6503i | 0.878793 | − | 0.477202i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 60.1440 | − | 60.1440i | 0.473575 | − | 0.473575i | −0.429495 | − | 0.903069i | \(-0.641308\pi\) |
0.903069 | + | 0.429495i | \(0.141308\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.537806i | 0.00416904i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −129.876 | + | 129.876i | −0.991422 | + | 0.991422i | −0.999964 | − | 0.00854147i | \(-0.997281\pi\) |
0.00854147 | + | 0.999964i | \(0.497281\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.45270i | 0.0334789i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.85204 | + | 8.31191i | 0.0507558 | + | 0.0615697i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −69.8267 | − | 69.8267i | −0.509684 | − | 0.509684i | 0.404745 | − | 0.914429i | \(-0.367360\pi\) |
−0.914429 | + | 0.404745i | \(0.867360\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.8371 | + | 16.8371i | −0.121130 | + | 0.121130i | −0.765073 | − | 0.643943i | \(-0.777297\pi\) |
0.643943 | + | 0.765073i | \(0.277297\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.87127 | − | 4.87127i | 0.0345480 | − | 0.0345480i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 46.0469 | + | 46.0469i | 0.322006 | + | 0.322006i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.5761 | + | 109.857i | −0.0729389 | + | 0.757631i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 0.487538i | − | 0.00331659i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −126.048 | + | 126.048i | −0.845963 | + | 0.845963i | −0.989627 | − | 0.143664i | \(-0.954112\pi\) |
0.143664 | + | 0.989627i | \(0.454112\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 170.000i | − | 1.12583i | −0.826516 | − | 0.562914i | \(-0.809680\pi\) | ||
0.826516 | − | 0.562914i | \(-0.190320\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −96.2951 | + | 96.2951i | −0.629380 | + | 0.629380i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 156.690 | + | 190.074i | 1.01091 | + | 1.22629i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.1854i | − | 0.0776137i | −0.999247 | − | 0.0388069i | \(-0.987644\pi\) | ||
0.999247 | − | 0.0388069i | \(-0.0123557\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 9.42757i | − | 0.0592929i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −264.898 | −1.64533 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −285.780 | −1.75325 | −0.876627 | − | 0.481170i | \(-0.840212\pi\) | ||||
−0.876627 | + | 0.481170i | \(0.840212\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.202504 | + | 2.10345i | −0.00122730 | + | 0.0127482i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −102.579 | − | 102.579i | −0.614248 | − | 0.614248i | 0.329802 | − | 0.944050i | \(-0.393018\pi\) |
−0.944050 | + | 0.329802i | \(0.893018\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 171.648 | 1.01567 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.22075 | − | 4.22075i | −0.0246828 | − | 0.0246828i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −68.3056 | −0.394830 | −0.197415 | − | 0.980320i | \(-0.563255\pi\) | ||||
−0.197415 | + | 0.980320i | \(0.563255\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −138.922 | + | 93.7110i | −0.793842 | + | 0.535492i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.391199 | − | 0.391199i | 0.00221016 | − | 0.00221016i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −165.892 | − | 165.892i | −0.926773 | − | 0.926773i | 0.0707227 | − | 0.997496i | \(-0.477469\pi\) |
−0.997496 | + | 0.0707227i | \(0.977469\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 101.633 | + | 101.633i | 0.561506 | + | 0.561506i | 0.929735 | − | 0.368229i | \(-0.120036\pi\) |
−0.368229 | + | 0.929735i | \(0.620036\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.75978 | + | 2.75978i | −0.0150807 | + | 0.0150807i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 92.6499 | + | 112.389i | 0.500810 | + | 0.607511i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −53.4726 | −0.285950 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.2114 | − | 10.2114i | −0.0540283 | − | 0.0540283i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 144.454 | 0.756301 | 0.378151 | − | 0.925744i | \(-0.376560\pi\) | ||||
0.378151 | + | 0.925744i | \(0.376560\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −32.7772 | − | 32.7772i | −0.169830 | − | 0.169830i | 0.617075 | − | 0.786905i | \(-0.288318\pi\) |
−0.786905 | + | 0.617075i | \(0.788318\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.03148 | + | 8.52958i | 0.0360589 | + | 0.0437414i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 335.205 | 1.70155 | 0.850775 | − | 0.525530i | \(-0.176133\pi\) | ||||
0.850775 | + | 0.525530i | \(0.176133\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −184.734 | −0.928313 | −0.464156 | − | 0.885753i | \(-0.653642\pi\) | ||||
−0.464156 | + | 0.885753i | \(0.653642\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 7.05833i | − | 0.0351161i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 147.954i | − | 0.728838i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 63.5363 | − | 52.3771i | 0.309933 | − | 0.255498i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 251.099 | − | 251.099i | 1.21304 | − | 1.21304i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2.34378i | − | 0.0112143i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −187.999 | + | 187.999i | −0.890989 | + | 0.890989i | −0.994616 | − | 0.103627i | \(-0.966955\pi\) |
0.103627 | + | 0.994616i | \(0.466955\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.20023i | 0.0431936i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.3217 | − | 14.2794i | 0.0805662 | − | 0.0664159i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −233.510 | − | 233.510i | −1.07608 | − | 1.07608i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.24564 | + | 2.24564i | −0.0102541 | + | 0.0102541i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −197.791 | + | 197.791i | −0.894984 | + | 0.894984i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −282.322 | − | 282.322i | −1.26602 | − | 1.26602i | −0.948128 | − | 0.317889i | \(-0.897026\pi\) |
−0.317889 | − | 0.948128i | \(-0.602974\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 42.8563 | − | 220.515i | 0.190472 | − | 0.980069i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 146.872i | 0.647015i | 0.946226 | + | 0.323507i | \(0.104862\pi\) | ||||
−0.946226 | + | 0.323507i | \(0.895138\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −194.697 | + | 194.697i | −0.850205 | + | 0.850205i | −0.990158 | − | 0.139953i | \(-0.955305\pi\) |
0.139953 | + | 0.990158i | \(0.455305\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 2.83292i | − | 0.0122637i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 87.0218 | − | 87.0218i | 0.373484 | − | 0.373484i | −0.495260 | − | 0.868745i | \(-0.664927\pi\) |
0.868745 | + | 0.495260i | \(0.164927\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −286.233 | − | 27.5563i | −1.21801 | − | 0.117261i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.9732i | 0.0716169i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 334.837i | 1.40099i | 0.713657 | + | 0.700495i | \(0.247037\pi\) | ||||
−0.713657 | + | 0.700495i | \(0.752963\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −378.876 | −1.57210 | −0.786049 | − | 0.618164i | \(-0.787877\pi\) | ||||
−0.786049 | + | 0.618164i | \(0.787877\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 29.0460 | 0.119531 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.7027 | + | 12.9448i | −0.0640927 | + | 0.0528357i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.66949 | − | 8.66949i | −0.0350991 | − | 0.0350991i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.3806 | 0.0577534 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 181.937 | + | 181.937i | 0.724849 | + | 0.724849i | 0.969589 | − | 0.244740i | \(-0.0787026\pi\) |
−0.244740 | + | 0.969589i | \(0.578703\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 139.435 | 0.551128 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.03526 | − | 0.869845i | −0.0354324 | − | 0.00341116i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 38.2528 | − | 38.2528i | 0.148843 | − | 0.148843i | −0.628758 | − | 0.777601i | \(-0.716436\pi\) |
0.777601 | + | 0.628758i | \(0.216436\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −138.073 | − | 138.073i | −0.533100 | − | 0.533100i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 140.247 | + | 140.247i | 0.537345 | + | 0.537345i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −165.962 | + | 165.962i | −0.631034 | + | 0.631034i | −0.948327 | − | 0.317294i | \(-0.897226\pi\) |
0.317294 | + | 0.948327i | \(0.397226\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −303.645 | + | 250.314i | −1.14583 | + | 0.944580i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.5083 | 0.0393570 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −310.294 | − | 310.294i | −1.15351 | − | 1.15351i | −0.985844 | − | 0.167665i | \(-0.946377\pi\) |
−0.167665 | − | 0.985844i | \(-0.553623\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 272.486 | 1.00548 | 0.502741 | − | 0.864437i | \(-0.332325\pi\) | ||||
0.502741 | + | 0.864437i | \(0.332325\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.4788 | − | 10.4788i | −0.0383838 | − | 0.0383838i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 73.1251 | − | 49.3270i | 0.265910 | − | 0.179371i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −143.172 | −0.516868 | −0.258434 | − | 0.966029i | \(-0.583206\pi\) | ||||
−0.258434 | + | 0.966029i | \(0.583206\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 442.693 | 1.58671 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 139.408i | − | 0.496115i | −0.968745 | − | 0.248057i | \(-0.920208\pi\) | ||
0.968745 | − | 0.248057i | \(-0.0797921\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 336.283i | 1.18828i | 0.804362 | + | 0.594140i | \(0.202507\pi\) | ||||
−0.804362 | + | 0.594140i | \(0.797493\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.0381266 | − | 0.396029i | 0.000133777 | − | 0.00138957i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −78.0557 | + | 78.0557i | −0.271971 | + | 0.271971i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 59.3116i | 0.205230i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.14983 | − | 4.14983i | 0.0142606 | − | 0.0142606i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 33.1195i | − | 0.113036i | −0.998402 | − | 0.0565179i | \(-0.982000\pi\) | ||
0.998402 | − | 0.0565179i | \(-0.0179998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.9866 | − | 2.21297i | −0.0779207 | − | 0.00750161i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.37499 | + | 5.37499i | 0.0180976 | + | 0.0180976i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 515.762 | − | 515.762i | 1.72496 | − | 1.72496i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.2801 | + | 21.2801i | −0.0706981 | + | 0.0706981i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.54215 | − | 3.54215i | −0.0116903 | − | 0.0116903i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 162.163 | + | 15.6118i | 0.531681 | + | 0.0511862i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 479.642i | 1.56235i | 0.624310 | + | 0.781176i | \(0.285380\pi\) | ||||
−0.624310 | + | 0.781176i | \(0.714620\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.81564 | − | 5.81564i | 0.0188208 | − | 0.0188208i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 328.043i | − | 1.05480i | −0.849617 | − | 0.527401i | \(-0.823167\pi\) | ||
0.849617 | − | 0.527401i | \(-0.176833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −90.2171 | + | 90.2171i | −0.288233 | + | 0.288233i | −0.836381 | − | 0.548148i | \(-0.815333\pi\) |
0.548148 | + | 0.836381i | \(0.315333\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −28.8593 | + | 299.767i | −0.0916167 | + | 0.951642i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 324.328i | − | 1.02312i | −0.859249 | − | 0.511558i | \(-0.829068\pi\) | ||
0.859249 | − | 0.511558i | \(-0.170932\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 77.8792i | 0.244135i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.43887 | 0.0231741 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.0676 | 0.0311690 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 88.0274 | − | 452.942i | 0.270853 | − | 1.39367i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.79069 | + | 3.79069i | 0.0115923 | + | 0.0115923i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 385.496 | 1.17172 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −248.635 | − | 248.635i | −0.751162 | − | 0.751162i | 0.223534 | − | 0.974696i | \(-0.428241\pi\) |
−0.974696 | + | 0.223534i | \(0.928241\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 261.761 | 0.786069 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −227.336 | + | 187.407i | −0.678614 | + | 0.559425i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −82.9415 | + | 82.9415i | −0.246117 | + | 0.246117i | −0.819375 | − | 0.573258i | \(-0.805679\pi\) |
0.573258 | + | 0.819375i | \(0.305679\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.72250 | − | 6.72250i | −0.0198304 | − | 0.0198304i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 122.914 | + | 122.914i | 0.360451 | + | 0.360451i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 251.537 | − | 251.537i | 0.733345 | − | 0.733345i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 23.5604 | + | 2.26821i | 0.0682909 | + | 0.00657452i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −288.892 | −0.832540 | −0.416270 | − | 0.909241i | \(-0.636663\pi\) | ||||
−0.416270 | + | 0.909241i | \(0.636663\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 345.135 | + | 345.135i | 0.988927 | + | 0.988927i | 0.999939 | − | 0.0110128i | \(-0.00350555\pi\) |
−0.0110128 | + | 0.999939i | \(0.503506\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 39.7634 | 0.113286 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 242.242 | + | 242.242i | 0.686239 | + | 0.686239i | 0.961399 | − | 0.275159i | \(-0.0887306\pi\) |
−0.275159 | + | 0.961399i | \(0.588731\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 296.322 | − | 244.278i | 0.834711 | − | 0.688106i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.1686 | 0.0340858 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −221.083 | −0.615831 | −0.307916 | − | 0.951414i | \(-0.599631\pi\) | ||||
−0.307916 | + | 0.951414i | \(0.599631\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 360.559i | − | 0.998778i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 13.0029i | − | 0.0358206i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 131.953 | + | 12.7034i | 0.361514 | + | 0.0348038i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 71.5971 | − | 71.5971i | 0.195087 | − | 0.195087i | −0.602803 | − | 0.797890i | \(-0.705949\pi\) |
0.797890 | + | 0.602803i | \(0.205949\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 147.980i | − | 0.401028i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 373.034 | − | 373.034i | 1.00548 | − | 1.00548i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 174.847i | − | 0.468758i | −0.972145 | − | 0.234379i | \(-0.924694\pi\) | ||
0.972145 | − | 0.234379i | \(-0.0753056\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.1583 | − | 7.14524i | 0.0350889 | − | 0.0190540i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 288.070 | + | 288.070i | 0.764110 | + | 0.764110i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −329.561 | + | 329.561i | −0.869553 | + | 0.869553i | −0.992423 | − | 0.122870i | \(-0.960790\pi\) |
0.122870 | + | 0.992423i | \(0.460790\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.20438 | − | 7.20438i | 0.0189091 | − | 0.0189091i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.40406 | + | 1.40406i | 0.00366594 | + | 0.00366594i | 0.708937 | − | 0.705271i | \(-0.249175\pi\) |
−0.705271 | + | 0.708937i | \(0.749175\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −91.2431 | + | 75.2175i | −0.236995 | + | 0.195370i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 40.3433i | − | 0.104246i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −276.184 | + | 276.184i | −0.709984 | + | 0.709984i | −0.966532 | − | 0.256548i | \(-0.917415\pi\) |
0.256548 | + | 0.966532i | \(0.417415\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 598.936i | 1.53181i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.5573 | + | 15.5573i | −0.0395860 | + | 0.0395860i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 546.676 | − | 450.660i | 1.38399 | − | 1.14091i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 692.870i | 1.74526i | 0.488378 | + | 0.872632i | \(0.337589\pi\) | ||||
−0.488378 | + | 0.872632i | \(0.662411\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.533369i | 0.00133676i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 755.828 | 1.88486 | 0.942429 | − | 0.334407i | \(-0.108536\pi\) | ||||
0.942429 | + | 0.334407i | \(0.108536\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 909.298 | 2.25632 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −256.385 | − | 311.010i | −0.633050 | − | 0.767925i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 72.6780 | + | 72.6780i | 0.178570 | + | 0.178570i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 43.3293 | 0.105940 | 0.0529698 | − | 0.998596i | \(-0.483131\pi\) | ||||
0.0529698 | + | 0.998596i | \(0.483131\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.36423 | − | 8.36423i | −0.0203509 | − | 0.0203509i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.9582 | 0.0749594 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −381.823 | − | 463.172i | −0.920055 | − | 1.11608i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.01684 | + | 2.01684i | −0.00483655 | + | 0.00483655i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −345.453 | − | 345.453i | −0.824471 | − | 0.824471i | 0.162274 | − | 0.986746i | \(-0.448117\pi\) |
−0.986746 | + | 0.162274i | \(0.948117\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −371.173 | − | 371.173i | −0.881645 | − | 0.881645i | 0.112056 | − | 0.993702i | \(-0.464256\pi\) |
−0.993702 | + | 0.112056i | \(0.964256\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −365.416 | + | 365.416i | −0.863867 | + | 0.863867i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 211.881 | + | 314.104i | 0.498544 | + | 0.739069i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −218.400 | −0.511475 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.51575 | + | 5.51575i | 0.0128572 | + | 0.0128572i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 150.726 | 0.349712 | 0.174856 | − | 0.984594i | \(-0.444054\pi\) | ||||
0.174856 | + | 0.984594i | \(0.444054\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 249.306 | + | 249.306i | 0.575765 | + | 0.575765i | 0.933734 | − | 0.357969i | \(-0.116531\pi\) |
−0.357969 | + | 0.933734i | \(0.616531\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.26687 | + | 13.1592i | −0.00291234 | + | 0.0302511i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26.2522 | −0.0600738 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 106.380 | 0.242324 | 0.121162 | − | 0.992633i | \(-0.461338\pi\) | ||||
0.121162 | + | 0.992633i | \(0.461338\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 36.5725i | 0.0829307i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 235.281i | − | 0.531108i | −0.964096 | − | 0.265554i | \(-0.914445\pi\) | ||
0.964096 | − | 0.265554i | \(-0.0855548\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −279.009 | − | 338.453i | −0.626986 | − | 0.760569i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.0988 | + | 15.0988i | −0.0337780 | + | 0.0337780i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 78.1899i | 0.174142i | 0.996202 | + | 0.0870712i | \(0.0277508\pi\) | ||||
−0.996202 | + | 0.0870712i | \(0.972249\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 41.0865 | − | 41.0865i | 0.0911009 | − | 0.0911009i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 20.3635i | − | 0.0449526i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −59.2774 | + | 615.726i | −0.130280 | + | 1.35324i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −401.924 | − | 401.924i | −0.879483 | − | 0.879483i | 0.113998 | − | 0.993481i | \(-0.463634\pi\) |
−0.993481 | + | 0.113998i | \(0.963634\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −23.0879 | + | 23.0879i | −0.0503005 | + | 0.0503005i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 158.945 | − | 158.945i | 0.344783 | − | 0.344783i | −0.513379 | − | 0.858162i | \(-0.671606\pi\) |
0.858162 | + | 0.513379i | \(0.171606\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 200.675 | + | 200.675i | 0.433422 | + | 0.433422i | 0.889791 | − | 0.456369i | \(-0.150850\pi\) |
−0.456369 | + | 0.889791i | \(0.650850\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.7692 | + | 22.7681i | 0.0403640 | + | 0.0489638i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 188.298i | − | 0.403208i | −0.979467 | − | 0.201604i | \(-0.935385\pi\) | ||
0.979467 | − | 0.201604i | \(-0.0646154\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 279.287 | − | 279.287i | 0.595494 | − | 0.595494i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1.45963i | − | 0.00309900i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.2013 | − | 11.2013i | 0.0236814 | − | 0.0236814i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.7677 | + | 9.28707i | −0.0289845 | + | 0.0195517i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 707.204i | 1.48261i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 175.422i | 0.366225i | 0.983092 | + | 0.183112i | \(0.0586172\pi\) | ||||
−0.983092 | + | 0.183112i | \(0.941383\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 537.661 | 1.11780 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −31.7309 | −0.0656955 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −243.842 | − | 23.4752i | −0.502766 | − | 0.0484025i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −53.3922 | − | 53.3922i | −0.109635 | − | 0.109635i | 0.650161 | − | 0.759796i | \(-0.274701\pi\) |
−0.759796 | + | 0.650161i | \(0.774701\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −34.2324 | −0.0700048 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −96.7903 | − | 96.7903i | −0.197129 | − | 0.197129i | 0.601639 | − | 0.798768i | \(-0.294515\pi\) |
−0.798768 | + | 0.601639i | \(0.794515\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −334.525 | −0.678550 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.1908 | − | 157.790i | 0.0306884 | − | 0.318767i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −364.038 | + | 364.038i | −0.732472 | + | 0.732472i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 139.686 | + | 139.686i | 0.279931 | + | 0.279931i | 0.833081 | − | 0.553150i | \(-0.186574\pi\) |
−0.553150 | + | 0.833081i | \(0.686574\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.2875 | − | 12.2875i | −0.0245260 | − | 0.0245260i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 319.688 | − | 319.688i | 0.635562 | − | 0.635562i | −0.313895 | − | 0.949458i | \(-0.601634\pi\) |
0.949458 | + | 0.313895i | \(0.101634\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.0376 | + | 208.134i | −0.0396784 | + | 0.412147i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.5610 | 0.0405542 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −702.440 | − | 702.440i | −1.38004 | − | 1.38004i | −0.844529 | − | 0.535510i | \(-0.820119\pi\) |
−0.535510 | − | 0.844529i | \(-0.679881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −177.713 | −0.347775 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.01198 | − | 1.01198i | −0.00197267 | − | 0.00197267i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −341.723 | − | 32.8985i | −0.663541 | − | 0.0638806i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −202.915 | −0.392486 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.18202 | −0.0157650 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 614.419i | 1.17931i | 0.807656 | + | 0.589654i | \(0.200736\pi\) | ||||
−0.807656 | + | 0.589654i | \(0.799264\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 178.970i | 0.342199i | 0.985254 | + | 0.171100i | \(0.0547320\pi\) | ||||
−0.985254 | + | 0.171100i | \(0.945268\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −16.6409 | + | 11.2252i | −0.0316969 | + | 0.0213814i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −527.968 | + | 527.968i | −1.00184 | + | 1.00184i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1032.79i | − | 1.95234i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −29.3456 | + | 29.3456i | −0.0552648 | + | 0.0552648i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 303.952i | − | 0.570266i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −197.511 | − | 239.592i | −0.369180 | − | 0.447836i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.8715 | − | 19.8715i | −0.0370047 | − | 0.0370047i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.1543 | + | 10.1543i | −0.0188392 | + | 0.0188392i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 216.557 | − | 216.557i | 0.400291 | − | 0.400291i | −0.478045 | − | 0.878336i | \(-0.658654\pi\) |
0.878336 | + | 0.478045i | \(0.158654\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.1741 | + | 12.1741i | 0.0224201 | + | 0.0224201i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.4436 | − | 222.739i | 0.0393460 | − | 0.408695i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 204.888i | 0.374567i | 0.982306 | + | 0.187284i | \(0.0599683\pi\) | ||||
−0.982306 | + | 0.187284i | \(0.940032\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 207.023 | − | 207.023i | 0.377091 | − | 0.377091i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 14.6627i | − | 0.0266111i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −671.603 | + | 671.603i | −1.21447 | + | 1.21447i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.0981 | + | 13.4626i | 0.0199966 | + | 0.0242570i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 345.777i | − | 0.620784i | −0.950609 | − | 0.310392i | \(-0.899540\pi\) | ||
0.950609 | − | 0.310392i | \(-0.100460\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 82.8656i | − | 0.148239i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.40525 | −0.0114176 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 319.750 | 0.567940 | 0.283970 | − | 0.958833i | \(-0.408348\pi\) | ||||
0.283970 | + | 0.958833i | \(0.408348\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38.0285 | + | 395.010i | −0.0673071 | + | 0.699133i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 382.082 | + | 382.082i | 0.673866 | + | 0.673866i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 146.472 | 0.257420 | 0.128710 | − | 0.991682i | \(-0.458916\pi\) | ||||
0.128710 | + | 0.991682i | \(0.458916\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 221.670 | + | 221.670i | 0.388214 | + | 0.388214i | 0.874050 | − | 0.485836i | \(-0.161485\pi\) |
−0.485836 | + | 0.874050i | \(0.661485\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.3034 | 0.0301980 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −552.502 | − | 819.060i | −0.960873 | − | 1.42445i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −293.131 | + | 293.131i | −0.508026 | + | 0.508026i | −0.913920 | − | 0.405894i | \(-0.866960\pi\) |
0.405894 | + | 0.913920i | \(0.366960\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.92624 | − | 3.92624i | −0.00678107 | − | 0.00678107i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 569.017 | + | 569.017i | 0.979375 | + | 0.979375i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −196.355 | + | 196.355i | −0.336801 | + | 0.336801i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −527.463 | − | 639.842i | −0.901646 | − | 1.09375i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −176.460 | −0.300614 | −0.150307 | − | 0.988639i | \(-0.548026\pi\) | ||||
−0.150307 | + | 0.988639i | \(0.548026\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.1416 | − | 23.1416i | −0.0392897 | − | 0.0392897i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 40.1528 | 0.0679404 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −311.192 | − | 311.192i | −0.524776 | − | 0.524776i | 0.394234 | − | 0.919010i | \(-0.371010\pi\) |
−0.919010 | + | 0.394234i | \(0.871010\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −323.092 | − | 391.929i | −0.543012 | − | 0.658704i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.1285 | −0.0370661 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −550.344 | −0.918771 | −0.459386 | − | 0.888237i | \(-0.651930\pi\) | ||||
−0.459386 | + | 0.888237i | \(0.651930\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 440.349i | − | 0.732693i | −0.930478 | − | 0.366347i | \(-0.880608\pi\) | ||
0.930478 | − | 0.366347i | \(-0.119392\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 529.477i | 0.878071i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −418.799 | + | 345.243i | −0.692229 | + | 0.570649i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.8864 | − | 12.8864i | 0.0212296 | − | 0.0212296i | −0.696412 | − | 0.717642i | \(-0.745221\pi\) |
0.717642 | + | 0.696412i | \(0.245221\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 17.7228i | − | 0.0291014i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −750.569 | + | 750.569i | −1.22843 | + | 1.22843i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 228.861i | 0.373346i | 0.982422 | + | 0.186673i | \(0.0597706\pi\) | ||||
−0.982422 | + | 0.186673i | \(0.940229\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.61073 | − | 6.27402i | 0.0123752 | − | 0.0102017i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 236.901 | + | 236.901i | 0.383957 | + | 0.383957i | 0.872525 | − | 0.488569i | \(-0.162481\pi\) |
−0.488569 | + | 0.872525i | \(0.662481\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 204.389 | − | 204.389i | 0.330192 | − | 0.330192i | −0.522468 | − | 0.852659i | \(-0.674988\pi\) |
0.852659 | + | 0.522468i | \(0.174988\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 60.2042 | − | 60.2042i | 0.0969471 | − | 0.0969471i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 415.797 | + | 415.797i | 0.667411 | + | 0.667411i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −579.505 | − | 234.091i | −0.927209 | − | 0.374545i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 0.280751i | − | 0.000447769i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −312.184 | + | 312.184i | −0.496317 | + | 0.496317i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 219.606i | 0.348029i | 0.984743 | + | 0.174014i | \(0.0556739\pi\) | ||||
−0.984743 | + | 0.174014i | \(0.944326\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.5195 | + | 22.5195i | −0.0355759 | + | 0.0355759i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −423.325 | − | 40.7545i | −0.666654 | − | 0.0641803i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 75.1203i | 0.117928i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 690.151i | − | 1.08005i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −399.195 | −0.622770 | −0.311385 | − | 0.950284i | \(-0.600793\pi\) | ||||
−0.311385 | + | 0.950284i | \(0.600793\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −864.637 | −1.34469 | −0.672346 | − | 0.740237i | \(-0.734713\pi\) | ||||
−0.672346 | + | 0.740237i | \(0.734713\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.07489 | − | 1.71047i | 0.00321689 | − | 0.00265189i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −569.775 | − | 569.775i | −0.880641 | − | 0.880641i | 0.112959 | − | 0.993600i | \(-0.463967\pi\) |
−0.993600 | + | 0.112959i | \(0.963967\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.2956 | −0.0251088 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27.9711 | − | 27.9711i | −0.0429664 | − | 0.0429664i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 139.259 | 0.213261 | 0.106630 | − | 0.994299i | \(-0.465994\pi\) | ||||
0.106630 | + | 0.994299i | \(0.465994\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 914.138 | + | 88.0061i | 1.39563 | + | 0.134361i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 168.456 | − | 168.456i | 0.256402 | − | 0.256402i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 348.410 | + | 348.410i | 0.528695 | + | 0.528695i | 0.920183 | − | 0.391488i | \(-0.128040\pi\) |
−0.391488 | + | 0.920183i | \(0.628040\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 270.659 | + | 270.659i | 0.409469 | + | 0.409469i | 0.881553 | − | 0.472084i | \(-0.156498\pi\) |
−0.472084 | + | 0.881553i | \(0.656498\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −23.6926 | + | 23.6926i | −0.0357354 | + | 0.0357354i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.1788 | − | 14.1616i | 0.0258328 | − | 0.0212956i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 872.309 | 1.30781 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −33.8181 | − | 33.8181i | −0.0505502 | − | 0.0505502i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 114.960 | 0.171326 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.4792 | − | 29.4792i | −0.0438027 | − | 0.0438027i | 0.684866 | − | 0.728669i | \(-0.259861\pi\) |
−0.728669 | + | 0.684866i | \(0.759861\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.2753 | − | 52.8713i | 0.0152227 | − | 0.0783278i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −519.409 | −0.767221 | −0.383611 | − | 0.923495i | \(-0.625319\pi\) | ||||
−0.383611 | + | 0.923495i | \(0.625319\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 328.404 | 0.483659 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.5932i | 0.0258343i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 254.873i | − | 0.373167i | −0.982439 | − | 0.186583i | \(-0.940259\pi\) | ||
0.982439 | − | 0.186583i | \(-0.0597415\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −47.3157 | + | 491.477i | −0.0690739 | + | 0.717485i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.3219 | + | 23.3219i | −0.0339474 | + | 0.0339474i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1452.61i | 2.10828i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 422.293 | − | 422.293i | 0.611133 | − | 0.611133i | −0.332108 | − | 0.943241i | \(-0.607760\pi\) |
0.943241 | + | 0.332108i | \(0.107760\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 212.510i | 0.306652i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 118.508 | + | 11.4091i | 0.170516 | + | 0.0164160i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 176.484 | + | 176.484i | 0.253206 | + | 0.253206i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.4240 | − | 10.4240i | 0.0149127 | − | 0.0149127i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 203.994 | − | 203.994i | 0.291004 | − | 0.291004i | −0.546473 | − | 0.837477i | \(-0.684030\pi\) |
0.837477 | + | 0.546473i | \(0.184030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.6835 | − | 13.6835i | −0.0194644 | − | 0.0194644i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −34.2865 | − | 3.30084i | −0.0486334 | − | 0.00468205i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 280.314i | − | 0.396484i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 407.106 | − | 407.106i | 0.574197 | − | 0.574197i | −0.359101 | − | 0.933299i | \(-0.616917\pi\) |
0.933299 | + | 0.359101i | \(0.116917\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1273.24i | − | 1.79077i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1376.73 | − | 1376.73i | 1.93090 | − | 1.93090i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.2021 | − | 324.102i | 0.0436392 | − | 0.453290i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 40.1086i | 0.0559394i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 725.464i | 1.00899i | 0.863415 | + | 0.504495i | \(0.168321\pi\) | ||||
−0.863415 | + | 0.504495i | \(0.831679\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 460.231 | 0.638323 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −45.3838 | −0.0627716 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 457.471 | − | 308.590i | 0.630995 | − | 0.425642i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 442.782 | + | 442.782i | 0.609054 | + | 0.609054i | 0.942699 | − | 0.333645i | \(-0.108279\pi\) |
−0.333645 | + | 0.942699i | \(0.608279\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −722.036 | −0.990447 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 48.1145 | + | 48.1145i | 0.0658201 | + | 0.0658201i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 358.600 | 0.489222 | 0.244611 | − | 0.969621i | \(-0.421340\pi\) | ||||
0.244611 | + | 0.969621i | \(0.421340\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.88096 | + | 1.55059i | −0.00255913 | + | 0.00210965i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −147.009 | + | 147.009i | −0.199470 | + | 0.199470i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −575.294 | − | 575.294i | −0.778477 | − | 0.778477i | 0.201095 | − | 0.979572i | \(-0.435550\pi\) |
−0.979572 | + | 0.201095i | \(0.935550\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.03848 | − | 1.03848i | −0.00140146 | − | 0.00140146i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −55.8927 | + | 55.8927i | −0.0752258 | + | 0.0752258i | −0.743719 | − | 0.668493i | \(-0.766940\pi\) |
0.668493 | + | 0.743719i | \(0.266940\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 887.195 | + | 85.4124i | 1.19087 | + | 0.114647i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1078.75 | −1.44411 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 294.344 | + | 294.344i | 0.392983 | + | 0.392983i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 63.5053 | 0.0845610 | 0.0422805 | − | 0.999106i | \(-0.486538\pi\) | ||||
0.0422805 | + | 0.999106i | \(0.486538\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21.7934 | + | 21.7934i | 0.0289421 | + | 0.0289421i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −655.872 | + | 540.677i | −0.868704 | + | 0.716129i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 495.675 | 0.654789 | 0.327395 | − | 0.944888i | \(-0.393829\pi\) | ||||
0.327395 | + | 0.944888i | \(0.393829\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.7023 | 0.0220057 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 228.669i | 0.300485i | 0.988649 | + | 0.150243i | \(0.0480055\pi\) | ||||
−0.988649 | + | 0.150243i | \(0.951995\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 299.983i | 0.393163i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 677.775 | + | 65.2510i | 0.885981 | + | 0.0852954i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −60.2763 | + | 60.2763i | −0.0785871 | + | 0.0785871i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 804.229i | − | 1.04581i | −0.852391 | − | 0.522906i | \(-0.824848\pi\) | ||
0.852391 | − | 0.522906i | \(-0.175152\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.58213 | − | 4.58213i | 0.00594310 | − | 0.00594310i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 186.546i | 0.241328i | 0.992693 | + | 0.120664i | \(0.0385023\pi\) | ||||
−0.992693 | + | 0.120664i | \(0.961498\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 234.973 | − | 1209.05i | 0.303191 | − | 1.56006i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.5391 | − | 16.5391i | −0.0212859 | − | 0.0212859i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.73557 | + | 7.73557i | −0.00993013 | + | 0.00993013i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 191.620 | − | 191.620i | 0.245353 | − | 0.245353i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33.6260 | + | 33.6260i | 0.0429450 | + | 0.0429450i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −47.0120 | + | 38.7550i | −0.0598878 | + | 0.0493694i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1134.28i | 1.44127i | 0.693315 | + | 0.720635i | \(0.256150\pi\) | ||||
−0.693315 | + | 0.720635i | \(0.743850\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.8798 | + | 19.8798i | −0.0251962 | + | 0.0251962i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 531.997i | − | 0.672563i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 425.229 | − | 425.229i | 0.536228 | − | 0.536228i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −36.3722 | + | 29.9840i | −0.0457512 | + | 0.0377157i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 250.905i | − | 0.314812i | −0.987534 | − | 0.157406i | \(-0.949687\pi\) | ||
0.987534 | − | 0.157406i | \(-0.0503132\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 871.610i | − | 1.09088i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −788.276 | −0.984114 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 93.5435 | 0.116493 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 842.496 | + | 1022.00i | 1.04658 | + | 1.26956i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −37.1687 | − | 37.1687i | −0.0460579 | − | 0.0460579i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1099.77 | −1.35942 | −0.679712 | − | 0.733479i | \(-0.737895\pi\) | ||||
−0.679712 | + | 0.733479i | \(0.737895\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 376.722 | + | 376.722i | 0.464515 | + | 0.464515i | 0.900132 | − | 0.435617i | \(-0.143470\pi\) |
−0.435617 | + | 0.900132i | \(0.643470\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.6399 | 0.0401474 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 908.912 | + | 1102.56i | 1.11523 | + | 1.35284i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.10893 | + | 2.10893i | −0.00258131 | + | 0.00258131i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 786.059 | + | 786.059i | 0.959779 | + | 0.959779i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −164.380 | − | 164.380i | −0.200220 | − | 0.200220i | 0.599874 | − | 0.800094i | \(-0.295217\pi\) |
−0.800094 | + | 0.599874i | \(0.795217\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 794.892 | − | 794.892i | 0.965847 | − | 0.965847i | −0.0335887 | − | 0.999436i | \(-0.510694\pi\) |
0.999436 | + | 0.0335887i | \(0.0106936\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.75933 | − | 5.90867i | 0.0106174 | − | 0.00716202i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 696.994 | 0.842798 | 0.421399 | − | 0.906875i | \(-0.361539\pi\) | ||||
0.421399 | + | 0.906875i | \(0.361539\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 857.248 | + | 857.248i | 1.03407 | + | 1.03407i | 0.999399 | + | 0.0346759i | \(0.0110399\pi\) |
0.0346759 | + | 0.999399i | \(0.488960\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.1500 | −0.0206378 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −43.6173 | − | 43.6173i | −0.0523617 | − | 0.0523617i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −69.5094 | + | 722.008i | −0.0832448 | + | 0.864681i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 106.141 | 0.126811 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 428.122 | 0.510277 | 0.255139 | − | 0.966905i | \(-0.417879\pi\) | ||||
0.255139 | + | 0.966905i | \(0.417879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 353.787i | − | 0.420675i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 16.6991i | − | 0.0198091i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −545.919 | − | 662.231i | −0.646058 | − | 0.783705i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 514.503 | − | 514.503i | 0.607441 | − | 0.607441i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 40.2818i | 0.0474462i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 814.051 | − | 814.051i | 0.956582 | − | 0.956582i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1569.13i | 1.83955i | 0.392451 | + | 0.919773i | \(0.371627\pi\) | ||||
−0.392451 | + | 0.919773i | \(0.628373\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.86005 | + | 29.7079i | −0.00334508 | + | 0.0347461i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −454.985 | − | 454.985i | −0.530904 | − | 0.530904i | 0.389937 | − | 0.920841i | \(-0.372497\pi\) |
−0.920841 | + | 0.389937i | \(0.872497\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −620.538 | + | 620.538i | −0.722396 | + | 0.722396i | −0.969093 | − | 0.246697i | \(-0.920655\pi\) |
0.246697 | + | 0.969093i | \(0.420655\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.34995 | + | 9.34995i | −0.0108594 | + | 0.0108594i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 234.305 | + | 234.305i | 0.271500 | + | 0.271500i | 0.829704 | − | 0.558204i | \(-0.188509\pi\) |
−0.558204 | + | 0.829704i | \(0.688509\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 217.243 | + | 263.528i | 0.251148 | + | 0.304656i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.10467i | 0.00819454i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 353.514 | − | 353.514i | 0.406806 | − | 0.406806i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1087.55i | 1.24863i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −311.297 | + | 311.297i | −0.356584 | + | 0.356584i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 803.380 | + | 237.929i | 0.918149 | + | 0.271918i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1505.10i | − | 1.71620i | −0.513485 | − | 0.858098i | \(-0.671646\pi\) | ||
0.513485 | − | 0.858098i | \(-0.328354\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 3.96723i | − | 0.00451335i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1589.76 | −1.80450 | −0.902250 | − | 0.431213i | \(-0.858086\pi\) | ||||
−0.902250 | + | 0.431213i | \(0.858086\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −512.240 | −0.580114 | −0.290057 | − | 0.957009i | \(-0.593674\pi\) | ||||
−0.290057 | + | 0.957009i | \(0.593674\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.75346 | − | 0.265082i | −0.00311126 | − | 0.000299528i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −495.921 | − | 495.921i | −0.559099 | − | 0.559099i | 0.369952 | − | 0.929051i | \(-0.379374\pi\) |
−0.929051 | + | 0.369952i | \(0.879374\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 570.132 | 0.641318 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −201.118 | − | 201.118i | −0.225722 | − | 0.225722i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 38.2039 | 0.0427816 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −112.411 | + | 1167.64i | −0.125599 | + | 1.30462i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 61.7808 | − | 61.7808i | 0.0688749 | − | 0.0688749i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 768.949 | + | 768.949i | 0.855338 | + | 0.855338i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −843.432 | − | 843.432i | −0.936106 | − | 0.936106i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.54905 | + | 2.54905i | −0.00282287 | + | 0.00282287i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 68.8678 | − | 715.344i | 0.0760970 | − | 0.790435i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 530.597 | 0.585002 | 0.292501 | − | 0.956265i | \(-0.405512\pi\) | ||||
0.292501 | + | 0.956265i | \(0.405512\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 265.712 | + | 265.712i | 0.292313 | + | 0.292313i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −964.958 | −1.05923 | −0.529615 | − | 0.848238i | \(-0.677663\pi\) | ||||
−0.529615 | + | 0.848238i | \(0.677663\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −299.516 | − | 299.516i | −0.328057 | − | 0.328057i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.4248 | + | 1.87007i | 0.0212292 | + | 0.00204379i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1231.15 | −1.34259 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.377866 | 0.000411171 | 0.000205586 | − | 1.00000i | \(-0.499935\pi\) | ||||
0.000205586 | 1.00000i | \(0.499935\pi\) | ||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 57.4542i | 0.0623824i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1417.58i | − | 1.53584i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 138.938 | − | 714.899i | 0.150203 | − | 0.772864i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −436.257 | + | 436.257i | −0.470612 | + | 0.470612i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 170.314i | 0.183330i | 0.995790 | + | 0.0916650i | \(0.0292189\pi\) | ||||
−0.995790 | + | 0.0916650i | \(0.970781\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.91181 | − | 1.91181i | 0.00205350 | − | 0.00205350i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 39.2948i | − | 0.0421166i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 170.067 | + | 206.301i | 0.181890 | + | 0.220643i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1277.81 | + | 1277.81i | 1.36372 | + | 1.36372i | 0.869119 | + | 0.494603i | \(0.164686\pi\) |
0.494603 | + | 0.869119i | \(0.335314\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.8067 | + | 10.8067i | −0.0115087 | + | 0.0115087i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −557.710 | + | 557.710i | −0.592678 | + | 0.592678i | −0.938354 | − | 0.345676i | \(-0.887650\pi\) |
0.345676 | + | 0.938354i | \(0.387650\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −460.201 | − | 460.201i | −0.488018 | − | 0.488018i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.91937 | + | 71.8729i | −0.00732208 | + | 0.0760559i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 978.575i | − | 1.03334i | −0.856184 | − | 0.516671i | \(-0.827171\pi\) | ||
0.856184 | − | 0.516671i | \(-0.172829\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 346.011 | − | 346.011i | 0.364606 | − | 0.364606i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 38.8498i | − | 0.0408515i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −82.0352 | + | 82.0352i | −0.0860810 | + | 0.0860810i | −0.748836 | − | 0.662755i | \(-0.769387\pi\) |
0.662755 | + | 0.748836i | \(0.269387\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −459.428 | − | 557.312i | −0.481077 | − | 0.583573i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.32880i | 0.00974796i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 661.919i | − | 0.690217i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1466.20 | 1.52571 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −558.024 | −0.579464 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.2103 | + | 230.703i | −0.0230159 | + | 0.239071i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 241.731 | + | 241.731i | 0.249980 | + | 0.249980i | 0.820962 | − | 0.570982i | \(-0.193438\pi\) |
−0.570982 | + | 0.820962i | \(0.693438\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.20595 | 0.00124453 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 970.962 | + | 970.962i | 0.999961 | + | 0.999961i | 1.00000 | 3.91262e-5i | \(-1.24543e-5\pi\) | |
−3.91262e−5 | 1.00000i | \(0.500012\pi\) | ||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −159.606 | −0.164035 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.5444 | − | 54.2559i | 0.0108148 | − | 0.0556470i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1199.24 | − | 1199.24i | 1.22747 | − | 1.22747i | 0.262558 | − | 0.964916i | \(-0.415434\pi\) |
0.964916 | − | 0.262558i | \(-0.0845662\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −218.865 | − | 218.865i | −0.223559 | − | 0.223559i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −284.357 | − | 284.357i | −0.289864 | − | 0.289864i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 269.570 | − | 269.570i | 0.274232 | − | 0.274232i | −0.556569 | − | 0.830801i | \(-0.687883\pi\) |
0.830801 | + | 0.556569i | \(0.187883\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1066.11 | − | 1293.25i | −1.08234 | − | 1.31294i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 46.1769 | 0.0467851 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −125.463 | − | 125.463i | −0.126859 | − | 0.126859i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 514.885 | 0.519561 | 0.259781 | − | 0.965668i | \(-0.416350\pi\) | ||||
0.259781 | + | 0.965668i | \(0.416350\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29.7828 | − | 29.7828i | −0.0299928 | − | 0.0299928i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 587.539 | + | 712.718i | 0.590491 | + | 0.716299i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1154.22 | 1.15769 | 0.578845 | − | 0.815437i | \(-0.303504\pi\) | ||||
0.578845 | + | 0.815437i | \(0.303504\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 62.7605 | 0.0628233 |
(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 | 320.3.t.a.113.11 | 44 | ||
4.3 | odd | 2 | 80.3.t.a.53.5 | yes | 44 | ||
5.2 | odd | 4 | 320.3.i.a.177.12 | 44 | |||
8.3 | odd | 2 | 640.3.t.b.353.11 | 44 | |||
8.5 | even | 2 | 640.3.t.a.353.12 | 44 | |||
16.3 | odd | 4 | 80.3.i.a.13.16 | ✓ | 44 | ||
16.5 | even | 4 | 640.3.i.a.33.12 | 44 | |||
16.11 | odd | 4 | 640.3.i.b.33.11 | 44 | |||
16.13 | even | 4 | 320.3.i.a.273.11 | 44 | |||
20.3 | even | 4 | 400.3.i.b.357.7 | 44 | |||
20.7 | even | 4 | 80.3.i.a.37.16 | yes | 44 | ||
20.19 | odd | 2 | 400.3.t.b.293.18 | 44 | |||
40.27 | even | 4 | 640.3.i.b.97.12 | 44 | |||
40.37 | odd | 4 | 640.3.i.a.97.11 | 44 | |||
80.3 | even | 4 | 400.3.t.b.157.18 | 44 | |||
80.19 | odd | 4 | 400.3.i.b.93.7 | 44 | |||
80.27 | even | 4 | 640.3.t.b.417.11 | 44 | |||
80.37 | odd | 4 | 640.3.t.a.417.12 | 44 | |||
80.67 | even | 4 | 80.3.t.a.77.5 | yes | 44 | ||
80.77 | odd | 4 | inner | 320.3.t.a.17.11 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.3.i.a.13.16 | ✓ | 44 | 16.3 | odd | 4 | ||
80.3.i.a.37.16 | yes | 44 | 20.7 | even | 4 | ||
80.3.t.a.53.5 | yes | 44 | 4.3 | odd | 2 | ||
80.3.t.a.77.5 | yes | 44 | 80.67 | even | 4 | ||
320.3.i.a.177.12 | 44 | 5.2 | odd | 4 | |||
320.3.i.a.273.11 | 44 | 16.13 | even | 4 | |||
320.3.t.a.17.11 | 44 | 80.77 | odd | 4 | inner | ||
320.3.t.a.113.11 | 44 | 1.1 | even | 1 | trivial | ||
400.3.i.b.93.7 | 44 | 80.19 | odd | 4 | |||
400.3.i.b.357.7 | 44 | 20.3 | even | 4 | |||
400.3.t.b.157.18 | 44 | 80.3 | even | 4 | |||
400.3.t.b.293.18 | 44 | 20.19 | odd | 2 | |||
640.3.i.a.33.12 | 44 | 16.5 | even | 4 | |||
640.3.i.a.97.11 | 44 | 40.37 | odd | 4 | |||
640.3.i.b.33.11 | 44 | 16.11 | odd | 4 | |||
640.3.i.b.97.12 | 44 | 40.27 | even | 4 | |||
640.3.t.a.353.12 | 44 | 8.5 | even | 2 | |||
640.3.t.a.417.12 | 44 | 80.37 | odd | 4 | |||
640.3.t.b.353.11 | 44 | 8.3 | odd | 2 | |||
640.3.t.b.417.11 | 44 | 80.27 | even | 4 |