Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(2157,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4004.2157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.m (of order \(2\), degree \(1\), 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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2157.20 | ||
Character | \(\chi\) | \(=\) | 4004.2157 |
Dual form | 4004.2.m.b.2157.19 |
$q$-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 \(\left(\mathbb{Z}/4004\mathbb{Z}\right)^\times\).
\(n\) | \(365\) | \(925\) | \(2003\) | \(3433\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.726270 | 0.419312 | 0.209656 | − | 0.977775i | \(-0.432766\pi\) | ||||
0.209656 | + | 0.977775i | \(0.432766\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.96350i | 1.32532i | 0.748922 | + | 0.662658i | \(0.230572\pi\) | ||||
−0.748922 | + | 0.662658i | \(0.769428\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.47253 | −0.824177 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.483609 | − | 3.57297i | −0.134129 | − | 0.990964i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.15230i | 0.555721i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.91968 | 1.19320 | 0.596599 | − | 0.802539i | \(-0.296518\pi\) | ||||
0.596599 | + | 0.802539i | \(0.296518\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.32548i | 1.45116i | 0.688136 | + | 0.725582i | \(0.258429\pi\) | ||||
−0.688136 | + | 0.725582i | \(0.741571\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.726270i | − | 0.158485i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.763996 | 0.159304 | 0.0796521 | − | 0.996823i | \(-0.474619\pi\) | ||||
0.0796521 | + | 0.996823i | \(0.474619\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.78231 | −0.756461 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.97454 | −0.764900 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.71850 | 1.24759 | 0.623797 | − | 0.781586i | \(-0.285589\pi\) | ||||
0.623797 | + | 0.781586i | \(0.285589\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.63535i | − | 1.01214i | −0.862493 | − | 0.506070i | \(-0.831098\pi\) | ||
0.862493 | − | 0.506070i | \(-0.168902\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.726270i | − | 0.126427i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.96350 | 0.500922 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.09762i | 1.16684i | 0.812170 | + | 0.583421i | \(0.198286\pi\) | ||||
−0.812170 | + | 0.583421i | \(0.801714\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.351231 | − | 2.59494i | −0.0562419 | − | 0.415523i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.75835i | 1.21165i | 0.795598 | + | 0.605825i | \(0.207157\pi\) | ||||
−0.795598 | + | 0.605825i | \(0.792843\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.96634 | 0.299864 | 0.149932 | − | 0.988696i | \(-0.452095\pi\) | ||||
0.149932 | + | 0.988696i | \(0.452095\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 7.32734i | − | 1.09230i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.93798i | 1.44960i | 0.688958 | + | 0.724802i | \(0.258069\pi\) | ||||
−0.688958 | + | 0.724802i | \(0.741931\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.57302 | 0.500323 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.03131 | −0.828464 | −0.414232 | − | 0.910171i | \(-0.635950\pi\) | ||||
−0.414232 | + | 0.910171i | \(0.635950\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.96350 | 0.399598 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.59400i | 0.608491i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.32831i | 0.563498i | 0.959488 | + | 0.281749i | \(0.0909145\pi\) | ||||
−0.959488 | + | 0.281749i | \(0.909085\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.15178 | −0.915692 | −0.457846 | − | 0.889032i | \(-0.651379\pi\) | ||||
−0.457846 | + | 0.889032i | \(0.651379\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.47253i | 0.311510i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.5885 | − | 1.43317i | 1.31334 | − | 0.177763i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.48905i | − | 1.03710i | −0.855047 | − | 0.518551i | \(-0.826472\pi\) | ||
0.855047 | − | 0.518551i | \(-0.173528\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.554867 | 0.0667982 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.48248i | 1.00668i | 0.864087 | + | 0.503342i | \(0.167897\pi\) | ||||
−0.864087 | + | 0.503342i | \(0.832103\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.437137i | − | 0.0511630i | −0.999673 | − | 0.0255815i | \(-0.991856\pi\) | ||
0.999673 | − | 0.0255815i | \(-0.00814373\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.74697 | −0.317193 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.91924 | 0.328440 | 0.164220 | − | 0.986424i | \(-0.447489\pi\) | ||||
0.164220 | + | 0.986424i | \(0.447489\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.53101 | 0.503446 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.2024i | 1.77845i | 0.457473 | + | 0.889224i | \(0.348755\pi\) | ||||
−0.457473 | + | 0.889224i | \(0.651245\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.5795i | 1.58136i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.87945 | 0.523132 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.41370i | 0.573851i | 0.957953 | + | 0.286925i | \(0.0926332\pi\) | ||||
−0.957953 | + | 0.286925i | \(0.907367\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.57297 | + | 0.483609i | −0.374549 | + | 0.0506960i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 4.09279i | − | 0.424402i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.7455 | −1.92325 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.24011i | − | 0.938191i | −0.883147 | − | 0.469096i | \(-0.844580\pi\) | ||
0.883147 | − | 0.469096i | \(-0.155420\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.47253i | 0.248499i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.22666 | −0.221561 | −0.110781 | − | 0.993845i | \(-0.535335\pi\) | ||||
−0.110781 | + | 0.993845i | \(0.535335\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.86947 | 0.676869 | 0.338434 | − | 0.940990i | \(-0.390103\pi\) | ||||
0.338434 | + | 0.940990i | \(0.390103\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.15230 | 0.210043 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.5787 | 1.40938 | 0.704688 | − | 0.709518i | \(-0.251087\pi\) | ||||
0.704688 | + | 0.709518i | \(0.251087\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.7570i | 1.03033i | 0.857090 | + | 0.515166i | \(0.172270\pi\) | ||||
−0.857090 | + | 0.515166i | \(0.827730\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.15479i | 0.489271i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.08338 | −0.854492 | −0.427246 | − | 0.904135i | \(-0.640516\pi\) | ||||
−0.427246 | + | 0.904135i | \(0.640516\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.26410i | 0.211128i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.19574 | + | 8.83429i | 0.110546 | + | 0.816730i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 4.91968i | − | 0.450987i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.63465i | 0.508060i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.60863i | 0.322766i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.18388 | 0.548730 | 0.274365 | − | 0.961626i | \(-0.411532\pi\) | ||||
0.274365 | + | 0.961626i | \(0.411532\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.42809 | 0.125737 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.46908 | −0.652577 | −0.326288 | − | 0.945270i | \(-0.605798\pi\) | ||||
−0.326288 | + | 0.945270i | \(0.605798\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.32548 | 0.548488 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 11.7785i | − | 1.01373i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.21732i | 0.616617i | 0.951286 | + | 0.308308i | \(0.0997629\pi\) | ||||
−0.951286 | + | 0.308308i | \(0.900237\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.64119 | −0.224023 | −0.112011 | − | 0.993707i | \(-0.535729\pi\) | ||||
−0.112011 | + | 0.993707i | \(0.535729\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.21766i | 0.607836i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.57297 | + | 0.483609i | −0.298787 | + | 0.0404414i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.9103i | 1.65346i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.726270 | −0.0599017 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 10.1639i | − | 0.832659i | −0.909214 | − | 0.416329i | \(-0.863316\pi\) | ||
0.909214 | − | 0.416329i | \(-0.136684\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.2313i | 0.832611i | 0.909225 | + | 0.416305i | \(0.136675\pi\) | ||||
−0.909225 | + | 0.416305i | \(0.863325\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.1641 | −0.983407 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.7003 | 1.34140 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.66954 | −0.771714 | −0.385857 | − | 0.922559i | \(-0.626094\pi\) | ||||
−0.385857 | + | 0.922559i | \(0.626094\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.38036 | −0.347385 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 0.763996i | − | 0.0602113i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.94966i | 0.231035i | 0.993305 | + | 0.115518i | \(0.0368527\pi\) | ||||
−0.993305 | + | 0.115518i | \(0.963147\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.15230 | 0.167556 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.6935i | 1.29178i | 0.763430 | + | 0.645891i | \(0.223514\pi\) | ||||
−0.763430 | + | 0.645891i | \(0.776486\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5322 | + | 3.45584i | −0.964019 | + | 0.265834i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 15.6399i | − | 1.19602i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.2932 | −1.16272 | −0.581361 | − | 0.813646i | \(-0.697480\pi\) | ||||
−0.581361 | + | 0.813646i | \(0.697480\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.78231i | 0.285915i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.14352i | 0.236282i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.49826 | −0.111985 | −0.0559927 | − | 0.998431i | \(-0.517832\pi\) | ||||
−0.0559927 | + | 0.998431i | \(0.517832\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.0631 | −1.56561 | −0.782805 | − | 0.622267i | \(-0.786212\pi\) | ||||
−0.782805 | + | 0.622267i | \(0.786212\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.19412 | −0.383961 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.0338 | −1.54643 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.91968i | − | 0.359763i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.97454i | 0.289105i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.42418 | 0.464837 | 0.232419 | − | 0.972616i | \(-0.425336\pi\) | ||||
0.232419 | + | 0.972616i | \(0.425336\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 3.03861i | − | 0.218724i | −0.994002 | − | 0.109362i | \(-0.965119\pi\) | ||
0.994002 | − | 0.109362i | \(-0.0348807\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.69010 | − | 1.04087i | 0.550699 | − | 0.0745383i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 16.9844i | − | 1.21009i | −0.796191 | − | 0.605045i | \(-0.793155\pi\) | ||
0.796191 | − | 0.605045i | \(-0.206845\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.342520 | −0.0242806 | −0.0121403 | − | 0.999926i | \(-0.503864\pi\) | ||||
−0.0121403 | + | 0.999926i | \(0.503864\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 6.16534i | − | 0.434870i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 6.71850i | − | 0.471547i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.9918 | −1.60582 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.88900 | −0.131295 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.32548 | 0.437542 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.75600 | −0.533945 | −0.266973 | − | 0.963704i | \(-0.586023\pi\) | ||||
−0.266973 | + | 0.963704i | \(0.586023\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.16057i | 0.422115i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.82724i | 0.397414i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.63535 | −0.382553 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 0.317479i | − | 0.0214533i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.37921 | − | 17.5779i | −0.160043 | − | 1.18242i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.96125i | 0.265265i | 0.991165 | + | 0.132632i | \(0.0423430\pi\) | ||||
−0.991165 | + | 0.132632i | \(0.957657\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.35187 | 0.623458 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.40000i | 0.292038i | 0.989282 | + | 0.146019i | \(0.0466461\pi\) | ||||
−0.989282 | + | 0.146019i | \(0.953354\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.91264i | 0.258555i | 0.991608 | + | 0.129277i | \(0.0412658\pi\) | ||||
−0.991608 | + | 0.129277i | \(0.958734\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.726270 | −0.0477851 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.8867 | −0.844234 | −0.422117 | − | 0.906541i | \(-0.638713\pi\) | ||||
−0.422117 | + | 0.906541i | \(0.638713\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.4512 | −1.92118 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.12016 | 0.137719 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 26.1370i | − | 1.69066i | −0.534242 | − | 0.845332i | \(-0.679403\pi\) | ||
0.534242 | − | 0.845332i | \(-0.320597\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20.5354i | − | 1.32280i | −0.750032 | − | 0.661401i | \(-0.769962\pi\) | ||
0.750032 | − | 0.661401i | \(-0.230038\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2143 | 0.976001 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 2.96350i | − | 0.189331i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.6007 | − | 3.05906i | 1.43805 | − | 0.194643i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.7673i | 0.745724i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.2009 | 1.71691 | 0.858453 | − | 0.512893i | \(-0.171426\pi\) | ||||
0.858453 | + | 0.512893i | \(0.171426\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.763996i | − | 0.0480320i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.5886i | 0.663085i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.9853 | 0.685242 | 0.342621 | − | 0.939474i | \(-0.388685\pi\) | ||||
0.342621 | + | 0.939474i | \(0.388685\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.09762 | 0.441025 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.6117 | −1.02824 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.16621 | 0.380225 | 0.190112 | − | 0.981762i | \(-0.439115\pi\) | ||||
0.190112 | + | 0.981762i | \(0.439115\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 17.8738i | − | 1.09798i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.93181i | 0.240623i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.0961 | 0.859455 | 0.429728 | − | 0.902959i | \(-0.358610\pi\) | ||||
0.429728 | + | 0.902959i | \(0.358610\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.2242i | 1.71450i | 0.514901 | + | 0.857249i | \(0.327829\pi\) | ||||
−0.514901 | + | 0.857249i | \(0.672171\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.59494 | + | 0.351231i | −0.157053 | + | 0.0212575i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.78231i | 0.228082i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.01644 | 0.361493 | 0.180746 | − | 0.983530i | \(-0.442149\pi\) | ||||
0.180746 | + | 0.983530i | \(0.442149\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.9336i | 0.834182i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.4529i | 1.16046i | 0.814451 | + | 0.580232i | \(0.197038\pi\) | ||||
−0.814451 | + | 0.580232i | \(0.802962\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.4758 | −1.39549 | −0.697747 | − | 0.716344i | \(-0.745814\pi\) | ||||
−0.697747 | + | 0.716344i | \(0.745814\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.6143 | −0.806442 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.75835 | 0.457961 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.20330 | 0.423723 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 6.71081i | − | 0.393395i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.05645i | − | 0.0617185i | −0.999524 | − | 0.0308592i | \(-0.990176\pi\) | ||
0.999524 | − | 0.0308592i | \(-0.00982436\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.8269 | −0.746813 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.97454i | 0.230626i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.369475 | − | 2.72974i | −0.0213673 | − | 0.157865i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.96634i | − | 0.113338i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.61716 | −0.0929033 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 21.1943i | − | 1.21358i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 0.356927i | − | 0.0203709i | −0.999948 | − | 0.0101854i | \(-0.996758\pi\) | ||
0.999948 | − | 0.0101854i | \(-0.00324218\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.98909 | 0.283819 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.0350 | 1.87324 | 0.936621 | − | 0.350343i | \(-0.113935\pi\) | ||||
0.936621 | + | 0.350343i | \(0.113935\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.66203 | 0.376560 | 0.188280 | − | 0.982115i | \(-0.439709\pi\) | ||||
0.188280 | + | 0.982115i | \(0.439709\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.32734 | −0.412849 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 29.1498i | − | 1.63722i | −0.574351 | − | 0.818609i | \(-0.694745\pi\) | ||
0.574351 | − | 0.818609i | \(-0.305255\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.71850i | − | 0.376164i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.5881 | 0.590968 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 31.1194i | 1.73153i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.82916 | + | 13.5141i | 0.101463 | + | 0.749626i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.81248i | 0.432031i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.93798 | 0.547899 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.2592i | 1.05858i | 0.848440 | + | 0.529292i | \(0.177542\pi\) | ||||
−0.848440 | + | 0.529292i | \(0.822458\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 17.5491i | − | 0.961685i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.1573 | 1.37449 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.1061 | 1.74893 | 0.874465 | − | 0.485089i | \(-0.161213\pi\) | ||||
0.874465 | + | 0.485089i | \(0.161213\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.59698 | −0.358299 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.63535 | −0.305171 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.64435i | 0.0885286i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.0697 | 0.701621 | 0.350810 | − | 0.936447i | \(-0.385906\pi\) | ||||
0.350810 | + | 0.936447i | \(0.385906\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.7152i | 1.69768i | 0.528652 | + | 0.848839i | \(0.322698\pi\) | ||||
−0.528652 | + | 0.848839i | \(0.677302\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.92212 | + | 14.2009i | 0.102595 | + | 0.757988i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.5166i | 0.985537i | 0.870160 | + | 0.492769i | \(0.164015\pi\) | ||||
−0.870160 | + | 0.492769i | \(0.835985\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.1378 | −1.33418 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 3.57302i | − | 0.189104i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.8442i | 1.31123i | 0.755096 | + | 0.655614i | \(0.227590\pi\) | ||||
−0.755096 | + | 0.655614i | \(0.772410\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −21.0117 | −1.10588 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.726270 | −0.0381193 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.29545 | 0.0678071 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.1723 | 0.844187 | 0.422093 | − | 0.906552i | \(-0.361295\pi\) | ||||
0.422093 | + | 0.906552i | \(0.361295\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 19.1828i | − | 0.998615i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.03131i | 0.313130i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.3452 | 1.51944 | 0.759718 | − | 0.650253i | \(-0.225337\pi\) | ||||
0.759718 | + | 0.650253i | \(0.225337\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.62084i | 0.135340i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.24913 | − | 24.0050i | −0.167339 | − | 1.23632i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.9422i | 0.716165i | 0.933690 | + | 0.358083i | \(0.116569\pi\) | ||||
−0.933690 | + | 0.358083i | \(0.883431\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.49116 | 0.230089 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 9.38159i | − | 0.479377i | −0.970850 | − | 0.239688i | \(-0.922955\pi\) | ||
0.970850 | − | 0.239688i | \(-0.0770453\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 2.96350i | − | 0.151034i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.86184 | −0.247141 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.5581 | 1.54936 | 0.774679 | − | 0.632355i | \(-0.217911\pi\) | ||||
0.774679 | + | 0.632355i | \(0.217911\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.75862 | 0.190082 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.42457 | −0.273633 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.65116i | 0.435287i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.84234i | − | 0.192841i | −0.995341 | − | 0.0964207i | \(-0.969261\pi\) | ||
0.995341 | − | 0.0964207i | \(-0.0307394\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.59400 | 0.229988 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.75461i | 0.287371i | 0.989623 | + | 0.143686i | \(0.0458954\pi\) | ||||
−0.989623 | + | 0.143686i | \(0.954105\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.1350 | + | 2.72531i | −1.00299 | + | 0.135757i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.4276i | 0.667224i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.09762 | 0.351816 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.5803i | 1.51210i | 0.654515 | + | 0.756049i | \(0.272873\pi\) | ||||
−0.654515 | + | 0.756049i | \(0.727127\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.24172i | 0.258555i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.32831 | 0.212982 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −48.0158 | −2.35700 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.91822 | −0.0939355 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −39.9466 | −1.95152 | −0.975759 | − | 0.218847i | \(-0.929770\pi\) | ||||
−0.975759 | + | 0.218847i | \(0.929770\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 30.3486i | − | 1.47910i | −0.673101 | − | 0.739551i | \(-0.735038\pi\) | ||
0.673101 | − | 0.739551i | \(-0.264962\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 24.5720i | − | 1.19473i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.6078 | −0.902609 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.15178i | 0.346099i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.59494 | + | 0.351231i | −0.125285 | + | 0.0169576i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 35.6955i | − | 1.71939i | −0.510806 | − | 0.859696i | \(-0.670653\pi\) | ||
0.510806 | − | 0.859696i | \(-0.329347\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.3314 | 1.74598 | 0.872989 | − | 0.487740i | \(-0.162179\pi\) | ||||
0.872989 | + | 0.487740i | \(0.162179\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.4602i | 0.693314i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.83264i | 0.231176i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.8340 | −0.946626 | −0.473313 | − | 0.880894i | \(-0.656942\pi\) | ||||
−0.473313 | + | 0.880894i | \(0.656942\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.47253 | 0.117740 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.64529 | 0.458262 | 0.229131 | − | 0.973396i | \(-0.426412\pi\) | ||||
0.229131 | + | 0.973396i | \(0.426412\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.0435 | −0.760534 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 7.38173i | − | 0.349144i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 26.7295i | − | 1.26144i | −0.776009 | − | 0.630722i | \(-0.782759\pi\) | ||
0.776009 | − | 0.630722i | \(-0.217241\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.75835 | 0.365326 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.43068i | 0.349124i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.43317 | − | 10.5885i | −0.0671882 | − | 0.496396i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 41.1316i | 1.92406i | 0.272950 | + | 0.962028i | \(0.412001\pi\) | ||||
−0.272950 | + | 0.962028i | \(0.587999\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.5535 | −0.912677 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 12.7142i | − | 0.592158i | −0.955163 | − | 0.296079i | \(-0.904321\pi\) | ||
0.955163 | − | 0.296079i | \(-0.0956792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.55527i | 0.444071i | 0.975039 | + | 0.222036i | \(0.0712701\pi\) | ||||
−0.975039 | + | 0.222036i | \(0.928730\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.1290 | 0.562467 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.9493 | 0.645495 | 0.322748 | − | 0.946485i | \(-0.395393\pi\) | ||||
0.322748 | + | 0.946485i | \(0.395393\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.48905 | −0.391988 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.02270 | −0.323589 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.96634i | − | 0.0904124i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 23.9249i | − | 1.09775i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.9126 | 0.682802 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 18.8755i | − | 0.862446i | −0.902245 | − | 0.431223i | \(-0.858082\pi\) | ||
0.902245 | − | 0.431223i | \(-0.141918\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.3596 | − | 3.43248i | 1.15630 | − | 0.156507i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 0.554867i | − | 0.0252473i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27.3830 | 1.24340 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 28.8145i | − | 1.30571i | −0.757483 | − | 0.652855i | \(-0.773571\pi\) | ||
0.757483 | − | 0.652855i | \(-0.226429\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.14225i | 0.0968758i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.5351 | −0.971865 | −0.485932 | − | 0.873996i | \(-0.661520\pi\) | ||||
−0.485932 | + | 0.873996i | \(0.661520\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.0529 | 1.48863 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.32734 | −0.329339 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.48248 | 0.380491 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.9872i | 1.16335i | 0.813423 | + | 0.581673i | \(0.197602\pi\) | ||||
−0.813423 | + | 0.581673i | \(0.802398\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.1240i | 0.541659i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.5711 | 1.76439 | 0.882193 | − | 0.470887i | \(-0.156066\pi\) | ||||
0.882193 | + | 0.470887i | \(0.156066\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 6.59871i | − | 0.293639i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.10179 | + | 2.50988i | −0.404225 | + | 0.111467i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 16.2151i | − | 0.718721i | −0.933199 | − | 0.359360i | \(-0.882995\pi\) | ||
0.933199 | − | 0.359360i | \(-0.117005\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.437137 | −0.0193378 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 25.1408i | − | 1.10999i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.3576i | 0.897064i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.93798 | 0.437072 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.1070 | −0.487544 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.8071 | 1.17444 | 0.587220 | − | 0.809427i | \(-0.300222\pi\) | ||||
0.587220 | + | 0.809427i | \(0.300222\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.569536 | −0.0249041 | −0.0124520 | − | 0.999922i | \(-0.503964\pi\) | ||||
−0.0124520 | + | 0.999922i | \(0.503964\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.74697i | 0.119888i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 27.7242i | − | 1.20768i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.4163 | −0.974622 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 10.7019i | − | 0.464422i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.7204 | − | 3.75201i | 1.20070 | − | 0.162518i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 43.2039i | 1.86787i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.08814 | −0.0469568 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000i | 0.0430730i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 24.1535i | − | 1.03844i | −0.854641 | − | 0.519220i | \(-0.826223\pi\) | ||
0.854641 | − | 0.519220i | \(-0.173777\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.2975 | −0.656479 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −31.8783 | −1.36552 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.19909 | −0.307811 | −0.153905 | − | 0.988086i | \(-0.549185\pi\) | ||||
−0.153905 | + | 0.988086i | \(0.549185\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.6830 | 0.754692 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.4977i | 1.81046i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.91924i | − | 0.124139i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.2762 | −0.648439 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 17.8131i | − | 0.754766i | −0.926057 | − | 0.377383i | \(-0.876824\pi\) | ||
0.926057 | − | 0.377383i | \(-0.123176\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.950940 | − | 7.02567i | −0.0402205 | − | 0.297154i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 3.57302i | − | 0.150853i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.6963 | −0.492941 | −0.246471 | − | 0.969150i | \(-0.579271\pi\) | ||||
−0.246471 | + | 0.969150i | \(0.579271\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 26.9185i | − | 1.13247i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 4.53101i | − | 0.190285i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.4110 | −1.48451 | −0.742253 | − | 0.670120i | \(-0.766243\pi\) | ||||
−0.742253 | + | 0.670120i | \(0.766243\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.2151 | −0.469336 | −0.234668 | − | 0.972076i | \(-0.575400\pi\) | ||||
−0.234668 | + | 0.972076i | \(0.575400\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.66569 | 0.194912 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.88967 | −0.120507 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 21.0166i | − | 0.874932i | −0.899235 | − | 0.437466i | \(-0.855876\pi\) | ||
0.899235 | − | 0.437466i | \(-0.144124\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 2.20685i | − | 0.0917135i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.2024 | 0.672190 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.03131i | 0.249791i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −26.1804 | + | 3.54357i | −1.08242 | + | 0.146509i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 22.3533i | − | 0.922619i | −0.887239 | − | 0.461309i | \(-0.847380\pi\) | ||
0.887239 | − | 0.461309i | \(-0.152620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.6463 | 1.46878 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 12.3353i | − | 0.507405i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 13.4125i | − | 0.550786i | −0.961332 | − | 0.275393i | \(-0.911192\pi\) | ||
0.961332 | − | 0.275393i | \(-0.0888080\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.5795 | 0.597700 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.248762 | −0.0101812 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.4283 | −0.752962 | −0.376481 | − | 0.926424i | \(-0.622866\pi\) | ||||
−0.376481 | + | 0.926424i | \(0.622866\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.4793 | 0.753786 | 0.376893 | − | 0.926257i | \(-0.376992\pi\) | ||||
0.376893 | + | 0.926257i | \(0.376992\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.9894i | 0.854756i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 2.96350i | − | 0.120483i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.05677 | −0.327014 | −0.163507 | − | 0.986542i | \(-0.552281\pi\) | ||||
−0.163507 | + | 0.986542i | \(0.552281\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 4.87945i | − | 0.197725i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.5081 | − | 4.80610i | 1.43650 | − | 0.194434i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.0743i | 0.689626i | 0.938671 | + | 0.344813i | \(0.112058\pi\) | ||||
−0.938671 | + | 0.344813i | \(0.887942\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16.6983 | −0.673339 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 36.2886i | − | 1.46092i | −0.682953 | − | 0.730462i | \(-0.739305\pi\) | ||
0.682953 | − | 0.730462i | \(-0.260695\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.1271i | 1.00994i | 0.863136 | + | 0.504972i | \(0.168497\pi\) | ||||
−0.863136 | + | 0.504972i | \(0.831503\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.03653 | −0.121852 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.41370 | 0.216895 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.6057 | −1.18423 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.59400 | 0.183467 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.9181i | 1.39227i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.66774i | − | 0.106201i | −0.998589 | − | 0.0531005i | \(-0.983090\pi\) | ||
0.998589 | − | 0.0531005i | \(-0.0169104\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.63295 | −0.223890 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.3259i | 0.727241i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.483609 | + | 3.57297i | 0.0191613 | + | 0.141566i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 20.9732i | − | 0.829687i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.7926 | −0.426281 | −0.213141 | − | 0.977022i | \(-0.568369\pi\) | ||||
−0.213141 | + | 0.977022i | \(0.568369\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.9566i | 0.826449i | 0.910629 | + | 0.413224i | \(0.135598\pi\) | ||||
−0.910629 | + | 0.413224i | \(0.864402\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.23215i | 0.166641i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.2358 | 0.834866 | 0.417433 | − | 0.908708i | \(-0.362930\pi\) | ||||
0.417433 | + | 0.908708i | \(0.362930\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.32831 | 0.169901 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.09279 | −0.160409 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.8540 | −0.659546 | −0.329773 | − | 0.944060i | \(-0.606972\pi\) | ||||
−0.329773 | + | 0.944060i | \(0.606972\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 22.1346i | − | 0.864870i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.08084i | 0.0421674i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.138324 | 0.00538832 | 0.00269416 | − | 0.999996i | \(-0.499142\pi\) | ||||
0.00269416 | + | 0.999996i | \(0.499142\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 24.1473i | − | 0.939221i | −0.882874 | − | 0.469610i | \(-0.844394\pi\) | ||
0.882874 | − | 0.469610i | \(-0.155606\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.72794 | − | 12.7663i | −0.0671078 | − | 0.495802i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18.7455i | 0.726920i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.13291 | 0.198747 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.87694i | 0.111229i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.15178i | 0.276091i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.2043 | 1.62685 | 0.813427 | − | 0.581667i | \(-0.197599\pi\) | ||||
0.813427 | + | 0.581667i | \(0.197599\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.0329 | 0.578617 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.5801 | 0.637223 | 0.318612 | − | 0.947885i | \(-0.396783\pi\) | ||||
0.318612 | + | 0.947885i | \(0.396783\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.24011 | −0.354603 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.19559i | 0.122455i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.96449i | 0.0751693i | 0.999293 | + | 0.0375846i | \(0.0119664\pi\) | ||||
−0.999293 | + | 0.0375846i | \(0.988034\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.3885 | −0.817212 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.84163i | 0.108415i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.91680 | + | 21.5497i | 0.111121 | + | 0.820978i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.2966i | 1.57100i | 0.618865 | + | 0.785498i | \(0.287593\pi\) | ||||
−0.618865 | + | 0.785498i | \(0.712407\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.47253 | 0.0939237 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 7.82716i | − | 0.296901i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.1686i | 1.44574i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.35920 | −0.353998 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.2844 | −0.652821 | −0.326411 | − | 0.945228i | \(-0.605839\pi\) | ||||
−0.326411 | + | 0.945228i | \(0.605839\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −44.8959 | −1.69328 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −21.3895 | −0.805575 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.22666i | 0.0837423i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 45.9143i | − | 1.72435i | −0.506613 | − | 0.862173i | \(-0.669103\pi\) | ||
0.506613 | − | 0.862173i | \(-0.330897\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.21792 | −0.270693 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4.30539i | − | 0.161238i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.43317 | − | 10.5885i | −0.0535977 | − | 0.395987i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 18.9825i | − | 0.708916i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.5039 | 1.43595 | 0.717976 | − | 0.696068i | \(-0.245069\pi\) | ||||
0.717976 | + | 0.696068i | \(0.245069\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 6.86947i | − | 0.255832i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 14.9142i | − | 0.554667i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −25.4114 | −0.943757 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.2100 | 0.564108 | 0.282054 | − | 0.959399i | \(-0.408984\pi\) | ||||
0.282054 | + | 0.959399i | \(0.408984\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.54331 | −0.0941968 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.67377 | 0.357797 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 43.5219i | − | 1.60752i | −0.594955 | − | 0.803759i | \(-0.702830\pi\) | ||
0.594955 | − | 0.803759i | \(-0.297170\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 2.15230i | − | 0.0793887i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.48905 | −0.312698 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 18.2929i | − | 0.672916i | −0.941698 | − | 0.336458i | \(-0.890771\pi\) | ||
0.941698 | − | 0.336458i | \(-0.109229\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.4142 | − | 2.22170i | 0.602992 | − | 0.0816163i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.14492i | 0.225435i | 0.993627 | + | 0.112718i | \(0.0359556\pi\) | ||||
−0.993627 | + | 0.112718i | \(0.964044\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30.1207 | 1.10354 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 40.0610i | − | 1.46576i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 14.5787i | − | 0.532694i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.0322 | 0.730986 | 0.365493 | − | 0.930814i | \(-0.380900\pi\) | ||||
0.365493 | + | 0.930814i | \(0.380900\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.7552 | 0.719919 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −30.3204 | −1.10347 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.4448 | −1.32461 | −0.662305 | − | 0.749234i | \(-0.730422\pi\) | ||||
−0.662305 | + | 0.749234i | \(0.730422\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 0.554867i | − | 0.0201404i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 17.5763i | − | 0.637142i | −0.947899 | − | 0.318571i | \(-0.896797\pi\) | ||
0.947899 | − | 0.318571i | \(-0.103203\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.7570 | 0.389429 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 36.0482i | − | 1.30333i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.4649 | − | 2.09321i | 0.558406 | − | 0.0755815i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 18.7179i | − | 0.674984i | −0.941328 | − | 0.337492i | \(-0.890421\pi\) | ||
0.941328 | − | 0.337492i | \(-0.109579\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.97827 | 0.287330 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.15430i | 0.293290i | 0.989189 | + | 0.146645i | \(0.0468475\pi\) | ||||
−0.989189 | + | 0.146645i | \(0.953153\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.3146i | 0.765644i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.15479 | 0.184927 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −49.0752 | −1.75830 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.48248 | 0.303527 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −26.7029 | −0.954285 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 28.6556i | − | 1.02276i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 45.0189i | − | 1.60475i | −0.596820 | − | 0.802375i | \(-0.703569\pi\) | ||
0.596820 | − | 0.802375i | \(-0.296431\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.47833 | 0.159433 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.08338i | 0.322968i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.45867 | + | 25.5531i | 0.122821 | + | 0.907418i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 12.9812i | − | 0.460395i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.6870 | −0.768194 | −0.384097 | − | 0.923293i | \(-0.625487\pi\) | ||||
−0.384097 | + | 0.923293i | \(0.625487\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.8917i | 1.72966i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 13.3855i | − | 0.472955i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.437137 | −0.0154262 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.26410 | 0.0797990 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.2376 | 0.360380 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.2729 | −1.48623 | −0.743117 | − | 0.669161i | \(-0.766654\pi\) | ||||
−0.743117 | + | 0.669161i | \(0.766654\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 17.4347i | − | 0.612215i | −0.951997 | − | 0.306107i | \(-0.900973\pi\) | ||
0.951997 | − | 0.306107i | \(-0.0990266\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.4984i | 0.718910i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.74130 | −0.306194 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.4380i | 0.435152i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.83429 | − | 1.19574i | 0.308695 | − | 0.0417825i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 0.272128i | − | 0.00949734i | −0.999989 | − | 0.00474867i | \(-0.998488\pi\) | ||
0.999989 | − | 0.00474867i | \(-0.00151155\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.1727 | 1.40033 | 0.700167 | − | 0.713979i | \(-0.253109\pi\) | ||||
0.700167 | + | 0.713979i | \(0.253109\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.74697i | 0.0956374i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.21908i | 0.146712i | 0.997306 | + | 0.0733559i | \(0.0233709\pi\) | ||||
−0.997306 | + | 0.0733559i | \(0.976629\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.2263 | 0.910878 | 0.455439 | − | 0.890267i | \(-0.349482\pi\) | ||||
0.455439 | + | 0.890267i | \(0.349482\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.36956 | 0.151578 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.91968 | −0.170457 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −49.4711 | −1.71202 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.3979i | 0.774185i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 23.1046i | − | 0.797661i | −0.917025 | − | 0.398830i | \(-0.869416\pi\) | ||
0.917025 | − | 0.398830i | \(-0.130584\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.1383 | 0.556493 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.1281i | 0.486597i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.2414 | − | 37.1392i | −0.352314 | − | 1.27763i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.0498 | −0.585147 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.42256i | 0.185883i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.1300i | 0.346845i | 0.984848 | + | 0.173423i | \(0.0554826\pi\) | ||||
−0.984848 | + | 0.173423i | \(0.944517\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 46.3489 | 1.58510 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.6379 | 0.875772 | 0.437886 | − | 0.899030i | \(-0.355727\pi\) | ||||
0.437886 | + | 0.899030i | \(0.355727\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.0070 | −1.26266 | −0.631331 | − | 0.775514i | \(-0.717491\pi\) | ||||
−0.631331 | + | 0.775514i | \(0.717491\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.63465 | 0.192029 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.3294i | 0.896262i | 0.893968 | + | 0.448131i | \(0.147910\pi\) | ||||
−0.893968 | + | 0.448131i | \(0.852090\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 45.3214i | − | 1.54097i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.23154 | 0.177672 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.91924i | − | 0.0990285i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.3311 | + | 4.10538i | −1.02773 | + | 0.139106i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.8465i | 0.773236i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.60863 | 0.121994 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.30338i | − | 0.0440121i | −0.999758 | − | 0.0220061i | \(-0.992995\pi\) | ||
0.999758 | − | 0.0220061i | \(-0.00700531\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 0.767268i | − | 0.0258793i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.9213 | −0.671167 | −0.335583 | − | 0.942010i | \(-0.608933\pi\) | ||||
−0.335583 | + | 0.942010i | \(0.608933\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.7982 | 0.497999 | 0.248999 | − | 0.968504i | \(-0.419898\pi\) | ||||
0.248999 | + | 0.968504i | \(0.419898\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.31581 | −0.313148 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.8158 | −1.47119 | −0.735595 | − | 0.677421i | \(-0.763097\pi\) | ||||
−0.735595 | + | 0.677421i | \(0.763097\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.18388i | − | 0.207401i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 4.53101i | − | 0.151795i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −62.8625 | −2.10361 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 4.44009i | − | 0.148416i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.268339 | − | 1.98252i | −0.00895958 | − | 0.0661946i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 37.8611i | − | 1.26274i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.6721 | −0.988523 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1.42809i | − | 0.0475239i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 62.4205i | − | 2.07493i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.2132 | −1.56769 | −0.783844 | − | 0.620958i | \(-0.786744\pi\) | ||||
−0.783844 | + | 0.620958i | \(0.786744\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.50550 | 0.182606 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.6688 | −0.419735 | −0.209867 | − | 0.977730i | \(-0.567303\pi\) | ||||
−0.209867 | + | 0.977730i | \(0.567303\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.2024 | 0.536222 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 15.3928i | − | 0.508869i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.46908i | 0.246651i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.6094 | 1.76841 | 0.884206 | − | 0.467097i | \(-0.154700\pi\) | ||||
0.884206 | + | 0.467097i | \(0.154700\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 0.259225i | − | 0.00854176i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.3076 | − | 4.10221i | 0.997588 | − | 0.135026i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 26.8454i | − | 0.882671i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.9850 | −0.557860 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.0062i | 1.70627i | 0.521692 | + | 0.853134i | \(0.325301\pi\) | ||||
−0.521692 | + | 0.853134i | \(0.674699\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 6.32548i | − | 0.207309i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.9923 | 0.785473 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.5795 | 0.476799 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.8918 | −0.878517 | −0.439259 | − | 0.898361i | \(-0.644759\pi\) | ||||
−0.439259 | + | 0.898361i | \(0.644759\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.83843 | 0.157896 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 15.8480i | − | 0.516630i | −0.966061 | − | 0.258315i | \(-0.916833\pi\) | ||
0.966061 | − | 0.258315i | \(-0.0831672\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.92735i | 0.193021i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.7785 | −0.383155 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 2.83310i | − | 0.0920634i | −0.998940 | − | 0.0460317i | \(-0.985342\pi\) | ||
0.998940 | − | 0.0460317i | \(-0.0146575\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.56188 | + | 0.211403i | −0.0507007 | + | 0.00686245i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 21.1707i | − | 0.686506i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.26334 | 0.235283 | 0.117641 | − | 0.993056i | \(-0.462467\pi\) | ||||
0.117641 | + | 0.993056i | \(0.462467\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.0380i | 0.616056i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 4.87945i | − | 0.157730i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.21732 | 0.233059 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.757201 | −0.0244258 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −36.0463 | −1.16158 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.00490 | 0.289878 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 35.4836i | − | 1.14108i | −0.821271 | − | 0.570539i | \(-0.806734\pi\) | ||
0.821271 | − | 0.570539i | \(-0.193266\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22.6010i | 0.726050i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.5557 | −1.55823 | −0.779113 | − | 0.626883i | \(-0.784330\pi\) | ||||
−0.779113 | + | 0.626883i | \(0.784330\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.64119i | 0.0846727i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.32846 | + | 9.81486i | 0.0425448 | + | 0.314327i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 20.9442i | − | 0.670066i | −0.942206 | − | 0.335033i | \(-0.891253\pi\) | ||
0.942206 | − | 0.335033i | \(-0.108747\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.41370 | 0.173023 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 26.5970i | − | 0.849177i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.13085i | 0.291229i | 0.989341 | + | 0.145615i | \(0.0465159\pi\) | ||||
−0.989341 | + | 0.145615i | \(0.953484\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 50.3332 | 1.60375 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.21766 | 0.229741 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.50227 | 0.0477696 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.9738 | −0.729788 | −0.364894 | − | 0.931049i | \(-0.618895\pi\) | ||||
−0.364894 | + | 0.931049i | \(0.618895\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.9874i | 0.443877i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1.01506i | − | 0.0321795i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −59.3596 | −1.87994 | −0.939969 | − | 0.341259i | \(-0.889147\pi\) | ||||
−0.939969 | + | 0.341259i | \(0.889147\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 28.2098i | − | 0.892517i |
(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 | 4004.2.m.b.2157.20 | yes | 30 | |
13.12 | even | 2 | inner | 4004.2.m.b.2157.19 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.m.b.2157.19 | ✓ | 30 | 13.12 | even | 2 | inner | |
4004.2.m.b.2157.20 | yes | 30 | 1.1 | even | 1 | trivial |