Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(701,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.701");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.e (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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 701.6 | ||
Character | \(\chi\) | \(=\) | 1050.701 |
Dual form | 1050.3.e.e.701.8 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | 2.22285 | + | 2.01468i | 0.740949 | + | 0.671561i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.84919 | − | 3.14358i | 0.474865 | − | 0.523930i | ||||
\(7\) | −2.64575 | −0.377964 | ||||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0.882103 | + | 8.95667i | 0.0980115 | + | 0.995185i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 6.10339i | − | 0.554853i | −0.960747 | − | 0.277427i | \(-0.910518\pi\) | ||
0.960747 | − | 0.277427i | \(-0.0894816\pi\) | |||||||
\(12\) | −4.44570 | − | 4.02937i | −0.370475 | − | 0.335781i | ||||
\(13\) | −6.09265 | −0.468666 | −0.234333 | − | 0.972156i | \(-0.575291\pi\) | ||||
−0.234333 | + | 0.972156i | \(0.575291\pi\) | |||||||
\(14\) | 3.74166i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 7.30179i | − | 0.429517i | −0.976667 | − | 0.214758i | \(-0.931104\pi\) | ||
0.976667 | − | 0.214758i | \(-0.0688964\pi\) | |||||||
\(18\) | 12.6666 | − | 1.24748i | 0.703702 | − | 0.0693046i | ||||
\(19\) | −31.7506 | −1.67109 | −0.835543 | − | 0.549424i | \(-0.814847\pi\) | ||||
−0.835543 | + | 0.549424i | \(0.814847\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.88110 | − | 5.33035i | −0.280052 | − | 0.253826i | ||||
\(22\) | −8.63149 | −0.392341 | ||||||||
\(23\) | − | 33.8856i | − | 1.47329i | −0.676280 | − | 0.736644i | \(-0.736409\pi\) | ||
0.676280 | − | 0.736644i | \(-0.263591\pi\) | |||||||
\(24\) | −5.69838 | + | 6.28716i | −0.237433 | + | 0.261965i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.61631i | 0.331397i | ||||||||
\(27\) | −16.0841 | + | 21.6865i | −0.595706 | + | 0.803202i | ||||
\(28\) | 5.29150 | 0.188982 | ||||||||
\(29\) | − | 41.0122i | − | 1.41421i | −0.707106 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707106 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 42.9120 | 1.38426 | 0.692129 | − | 0.721774i | \(-0.256673\pi\) | ||||
0.692129 | + | 0.721774i | \(0.256673\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 12.2964 | − | 13.5669i | 0.372618 | − | 0.411118i | ||||
\(34\) | −10.3263 | −0.303714 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.76421 | − | 17.9133i | −0.0490057 | − | 0.497593i | ||||
\(37\) | 18.1246 | 0.489854 | 0.244927 | − | 0.969542i | \(-0.421236\pi\) | ||||
0.244927 | + | 0.969542i | \(0.421236\pi\) | |||||||
\(38\) | 44.9022i | 1.18164i | ||||||||
\(39\) | −13.5430 | − | 12.2748i | −0.347257 | − | 0.314738i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 36.4331i | − | 0.888612i | −0.895875 | − | 0.444306i | \(-0.853450\pi\) | ||
0.895875 | − | 0.444306i | \(-0.146550\pi\) | |||||||
\(42\) | −7.53825 | + | 8.31713i | −0.179482 | + | 0.198027i | ||||
\(43\) | −17.7024 | −0.411684 | −0.205842 | − | 0.978585i | \(-0.565993\pi\) | ||||
−0.205842 | + | 0.978585i | \(0.565993\pi\) | |||||||
\(44\) | 12.2068i | 0.277427i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −47.9215 | −1.04177 | ||||||||
\(47\) | − | 45.3150i | − | 0.964149i | −0.876130 | − | 0.482074i | \(-0.839884\pi\) | ||
0.876130 | − | 0.482074i | \(-0.160116\pi\) | |||||||
\(48\) | 8.89139 | + | 8.05873i | 0.185237 | + | 0.167890i | ||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.7108 | − | 16.2308i | 0.288447 | − | 0.318250i | ||||
\(52\) | 12.1853 | 0.234333 | ||||||||
\(53\) | − | 18.1388i | − | 0.342242i | −0.985250 | − | 0.171121i | \(-0.945261\pi\) | ||
0.985250 | − | 0.171121i | \(-0.0547390\pi\) | |||||||
\(54\) | 30.6693 | + | 22.7463i | 0.567950 | + | 0.421228i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 7.48331i | − | 0.133631i | ||||||
\(57\) | −70.5769 | − | 63.9675i | −1.23819 | − | 1.12224i | ||||
\(58\) | −58.0000 | −1.00000 | ||||||||
\(59\) | 4.22725i | 0.0716482i | 0.999358 | + | 0.0358241i | \(0.0114056\pi\) | ||||
−0.999358 | + | 0.0358241i | \(0.988594\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 16.8936 | 0.276944 | 0.138472 | − | 0.990366i | \(-0.455781\pi\) | ||||
0.138472 | + | 0.990366i | \(0.455781\pi\) | |||||||
\(62\) | − | 60.6867i | − | 0.978818i | ||||||
\(63\) | −2.33383 | − | 23.6971i | −0.0370449 | − | 0.376145i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −19.1865 | − | 17.3897i | −0.290704 | − | 0.263481i | ||||
\(67\) | −17.1392 | −0.255810 | −0.127905 | − | 0.991786i | \(-0.540825\pi\) | ||||
−0.127905 | + | 0.991786i | \(0.540825\pi\) | |||||||
\(68\) | 14.6036i | 0.214758i | ||||||||
\(69\) | 68.2688 | − | 75.3226i | 0.989404 | − | 1.09163i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 113.824i | 1.60316i | 0.597890 | + | 0.801578i | \(0.296006\pi\) | ||||
−0.597890 | + | 0.801578i | \(0.703994\pi\) | |||||||
\(72\) | −25.3333 | + | 2.49497i | −0.351851 | + | 0.0346523i | ||||
\(73\) | −105.073 | −1.43935 | −0.719675 | − | 0.694311i | \(-0.755709\pi\) | ||||
−0.719675 | + | 0.694311i | \(0.755709\pi\) | |||||||
\(74\) | − | 25.6320i | − | 0.346379i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 63.5013 | 0.835543 | ||||||||
\(77\) | 16.1480i | 0.209715i | ||||||||
\(78\) | −17.3591 | + | 19.1527i | −0.222553 | + | 0.245548i | ||||
\(79\) | 74.8132 | 0.947003 | 0.473501 | − | 0.880793i | \(-0.342990\pi\) | ||||
0.473501 | + | 0.880793i | \(0.342990\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −79.4438 | + | 15.8014i | −0.980787 | + | 0.195079i | ||||
\(82\) | −51.5242 | −0.628344 | ||||||||
\(83\) | − | 76.5950i | − | 0.922831i | −0.887184 | − | 0.461416i | \(-0.847342\pi\) | ||
0.887184 | − | 0.461416i | \(-0.152658\pi\) | |||||||
\(84\) | 11.7622 | + | 10.6607i | 0.140026 | + | 0.126913i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 25.0350i | 0.291104i | ||||||||
\(87\) | 82.6266 | − | 91.1639i | 0.949732 | − | 1.04786i | ||||
\(88\) | 17.2630 | 0.196170 | ||||||||
\(89\) | 26.8568i | 0.301762i | 0.988552 | + | 0.150881i | \(0.0482110\pi\) | ||||
−0.988552 | + | 0.150881i | \(0.951789\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.1196 | 0.177139 | ||||||||
\(92\) | 67.7713i | 0.736644i | ||||||||
\(93\) | 95.3868 | + | 86.4541i | 1.02566 | + | 0.929614i | ||||
\(94\) | −64.0851 | −0.681756 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 11.3968 | − | 12.5743i | 0.118716 | − | 0.130983i | ||||
\(97\) | −120.087 | −1.23801 | −0.619005 | − | 0.785387i | \(-0.712464\pi\) | ||||
−0.619005 | + | 0.785387i | \(0.712464\pi\) | |||||||
\(98\) | − | 9.89949i | − | 0.101015i | ||||||
\(99\) | 54.6660 | − | 5.38382i | 0.552182 | − | 0.0543820i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 162.983i | − | 1.61369i | −0.590764 | − | 0.806844i | \(-0.701174\pi\) | ||
0.590764 | − | 0.806844i | \(-0.298826\pi\) | |||||||
\(102\) | −22.9538 | − | 20.8042i | −0.225037 | − | 0.203963i | ||||
\(103\) | −186.379 | −1.80951 | −0.904753 | − | 0.425937i | \(-0.859944\pi\) | ||||
−0.904753 | + | 0.425937i | \(0.859944\pi\) | |||||||
\(104\) | − | 17.2326i | − | 0.165698i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −25.6522 | −0.242002 | ||||||||
\(107\) | − | 164.926i | − | 1.54136i | −0.637221 | − | 0.770681i | \(-0.719916\pi\) | ||
0.637221 | − | 0.770681i | \(-0.280084\pi\) | |||||||
\(108\) | 32.1681 | − | 43.3729i | 0.297853 | − | 0.401601i | ||||
\(109\) | 96.6905 | 0.887069 | 0.443535 | − | 0.896257i | \(-0.353724\pi\) | ||||
0.443535 | + | 0.896257i | \(0.353724\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 40.2882 | + | 36.5153i | 0.362957 | + | 0.328967i | ||||
\(112\) | −10.5830 | −0.0944911 | ||||||||
\(113\) | − | 112.284i | − | 0.993660i | −0.867848 | − | 0.496830i | \(-0.834497\pi\) | ||
0.867848 | − | 0.496830i | \(-0.165503\pi\) | |||||||
\(114\) | −90.4637 | + | 99.8107i | −0.793541 | + | 0.875533i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 82.0245i | 0.707107i | ||||||||
\(117\) | −5.37435 | − | 54.5699i | −0.0459346 | − | 0.466409i | ||||
\(118\) | 5.97823 | 0.0506629 | ||||||||
\(119\) | 19.3187i | 0.162342i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 83.7487 | 0.692138 | ||||||||
\(122\) | − | 23.8911i | − | 0.195829i | ||||||
\(123\) | 73.4012 | − | 80.9852i | 0.596757 | − | 0.658417i | ||||
\(124\) | −85.8240 | −0.692129 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −33.5128 | + | 3.30053i | −0.265974 | + | 0.0261947i | ||||
\(127\) | −197.632 | −1.55616 | −0.778078 | − | 0.628167i | \(-0.783805\pi\) | ||||
−0.778078 | + | 0.628167i | \(0.783805\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | −39.3497 | − | 35.6647i | −0.305037 | − | 0.276471i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 38.0418i | 0.290396i | 0.989403 | + | 0.145198i | \(0.0463819\pi\) | ||||
−0.989403 | + | 0.145198i | \(0.953618\pi\) | |||||||
\(132\) | −24.5928 | + | 27.1338i | −0.186309 | + | 0.205559i | ||||
\(133\) | 84.0043 | 0.631611 | ||||||||
\(134\) | 24.2385i | 0.180885i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.6526 | 0.151857 | ||||||||
\(137\) | − | 43.7923i | − | 0.319652i | −0.987145 | − | 0.159826i | \(-0.948907\pi\) | ||
0.987145 | − | 0.159826i | \(-0.0510933\pi\) | |||||||
\(138\) | −106.522 | − | 96.5467i | −0.771901 | − | 0.699614i | ||||
\(139\) | 175.928 | 1.26567 | 0.632836 | − | 0.774286i | \(-0.281891\pi\) | ||||
0.632836 | + | 0.774286i | \(0.281891\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 91.2953 | − | 100.728i | 0.647485 | − | 0.714385i | ||||
\(142\) | 160.972 | 1.13360 | ||||||||
\(143\) | 37.1858i | 0.260041i | ||||||||
\(144\) | 3.52841 | + | 35.8267i | 0.0245029 | + | 0.248796i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 148.595i | 1.01777i | ||||||||
\(147\) | 15.5599 | + | 14.1028i | 0.105850 | + | 0.0959373i | ||||
\(148\) | −36.2492 | −0.244927 | ||||||||
\(149\) | 150.593i | 1.01069i | 0.862917 | + | 0.505345i | \(0.168635\pi\) | ||||
−0.862917 | + | 0.505345i | \(0.831365\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.63028 | −0.0372866 | −0.0186433 | − | 0.999826i | \(-0.505935\pi\) | ||||
−0.0186433 | + | 0.999826i | \(0.505935\pi\) | |||||||
\(152\) | − | 89.8044i | − | 0.590818i | ||||||
\(153\) | 65.3997 | − | 6.44093i | 0.427449 | − | 0.0420976i | ||||
\(154\) | 22.8368 | 0.148291 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 27.0861 | + | 24.5495i | 0.173629 | + | 0.157369i | ||||
\(157\) | −119.059 | −0.758341 | −0.379170 | − | 0.925327i | \(-0.623791\pi\) | ||||
−0.379170 | + | 0.925327i | \(0.623791\pi\) | |||||||
\(158\) | − | 105.802i | − | 0.669632i | ||||||
\(159\) | 36.5440 | − | 40.3199i | 0.229837 | − | 0.253584i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 89.6530i | 0.556851i | ||||||||
\(162\) | 22.3466 | + | 112.350i | 0.137942 | + | 0.693521i | ||||
\(163\) | 74.5829 | 0.457564 | 0.228782 | − | 0.973478i | \(-0.426526\pi\) | ||||
0.228782 | + | 0.973478i | \(0.426526\pi\) | |||||||
\(164\) | 72.8662i | 0.444306i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −108.322 | −0.652540 | ||||||||
\(167\) | 114.419i | 0.685144i | 0.939492 | + | 0.342572i | \(0.111298\pi\) | ||||
−0.939492 | + | 0.342572i | \(0.888702\pi\) | |||||||
\(168\) | 15.0765 | − | 16.6343i | 0.0897411 | − | 0.0990135i | ||||
\(169\) | −131.880 | −0.780353 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −28.0074 | − | 284.380i | −0.163786 | − | 1.66304i | ||||
\(172\) | 35.4048 | 0.205842 | ||||||||
\(173\) | 173.820i | 1.00474i | 0.864653 | + | 0.502370i | \(0.167538\pi\) | ||||
−0.864653 | + | 0.502370i | \(0.832462\pi\) | |||||||
\(174\) | −128.925 | − | 116.852i | −0.740950 | − | 0.671562i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 24.4136i | − | 0.138713i | ||||||
\(177\) | −8.51656 | + | 9.39652i | −0.0481162 | + | 0.0530877i | ||||
\(178\) | 37.9812 | 0.213378 | ||||||||
\(179\) | − | 134.192i | − | 0.749677i | −0.927090 | − | 0.374838i | \(-0.877698\pi\) | ||
0.927090 | − | 0.374838i | \(-0.122302\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −199.113 | −1.10007 | −0.550036 | − | 0.835141i | \(-0.685386\pi\) | ||||
−0.550036 | + | 0.835141i | \(0.685386\pi\) | |||||||
\(182\) | − | 22.7966i | − | 0.125256i | ||||||
\(183\) | 37.5518 | + | 34.0352i | 0.205201 | + | 0.185985i | ||||
\(184\) | 95.8431 | 0.520886 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 122.265 | − | 134.897i | 0.657336 | − | 0.725255i | ||||
\(187\) | −44.5656 | −0.238319 | ||||||||
\(188\) | 90.6300i | 0.482074i | ||||||||
\(189\) | 42.5544 | − | 57.3770i | 0.225156 | − | 0.303582i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 224.206i | 1.17385i | 0.809640 | + | 0.586927i | \(0.199662\pi\) | ||||
−0.809640 | + | 0.586927i | \(0.800338\pi\) | |||||||
\(192\) | −17.7828 | − | 16.1175i | −0.0926187 | − | 0.0839451i | ||||
\(193\) | 340.124 | 1.76230 | 0.881149 | − | 0.472838i | \(-0.156770\pi\) | ||||
0.881149 | + | 0.472838i | \(0.156770\pi\) | |||||||
\(194\) | 169.829i | 0.875405i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 115.404i | 0.585805i | 0.956142 | + | 0.292903i | \(0.0946212\pi\) | ||||
−0.956142 | + | 0.292903i | \(0.905379\pi\) | |||||||
\(198\) | −7.61387 | − | 77.3094i | −0.0384539 | − | 0.390452i | ||||
\(199\) | −186.569 | −0.937534 | −0.468767 | − | 0.883322i | \(-0.655302\pi\) | ||||
−0.468767 | + | 0.883322i | \(0.655302\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −38.0979 | − | 34.5301i | −0.189542 | − | 0.171792i | ||||
\(202\) | −230.492 | −1.14105 | ||||||||
\(203\) | 108.508i | 0.534523i | ||||||||
\(204\) | −29.4216 | + | 32.4615i | −0.144223 | + | 0.159125i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 263.580i | 1.27951i | ||||||||
\(207\) | 303.502 | − | 29.8906i | 1.46620 | − | 0.144399i | ||||
\(208\) | −24.3706 | −0.117166 | ||||||||
\(209\) | 193.787i | 0.927208i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −348.892 | −1.65352 | −0.826759 | − | 0.562556i | \(-0.809818\pi\) | ||||
−0.826759 | + | 0.562556i | \(0.809818\pi\) | |||||||
\(212\) | 36.2777i | 0.171121i | ||||||||
\(213\) | −229.320 | + | 253.014i | −1.07662 | + | 1.18786i | ||||
\(214\) | −233.240 | −1.08991 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −61.3386 | − | 45.4926i | −0.283975 | − | 0.210614i | ||||
\(217\) | −113.534 | −0.523200 | ||||||||
\(218\) | − | 136.741i | − | 0.627253i | ||||||
\(219\) | −233.560 | − | 211.688i | −1.06649 | − | 0.966611i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 44.4872i | 0.201300i | ||||||||
\(222\) | 51.6404 | − | 56.9761i | 0.232615 | − | 0.256649i | ||||
\(223\) | −442.370 | −1.98372 | −0.991860 | − | 0.127331i | \(-0.959359\pi\) | ||||
−0.991860 | + | 0.127331i | \(0.959359\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −158.793 | −0.702624 | ||||||||
\(227\) | 105.606i | 0.465225i | 0.972569 | + | 0.232613i | \(0.0747274\pi\) | ||||
−0.972569 | + | 0.232613i | \(0.925273\pi\) | |||||||
\(228\) | 141.154 | + | 127.935i | 0.619095 | + | 0.561118i | ||||
\(229\) | 300.234 | 1.31107 | 0.655534 | − | 0.755166i | \(-0.272444\pi\) | ||||
0.655534 | + | 0.755166i | \(0.272444\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −32.5332 | + | 35.8946i | −0.140836 | + | 0.155388i | ||||
\(232\) | 116.000 | 0.500000 | ||||||||
\(233\) | 224.338i | 0.962823i | 0.876495 | + | 0.481411i | \(0.159876\pi\) | ||||
−0.876495 | + | 0.481411i | \(0.840124\pi\) | |||||||
\(234\) | −77.1734 | + | 7.60048i | −0.329801 | + | 0.0324807i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 8.45449i | − | 0.0358241i | ||||||
\(237\) | 166.298 | + | 150.725i | 0.701681 | + | 0.635970i | ||||
\(238\) | 27.3208 | 0.114793 | ||||||||
\(239\) | − | 298.399i | − | 1.24853i | −0.781212 | − | 0.624266i | \(-0.785398\pi\) | ||
0.781212 | − | 0.624266i | \(-0.214602\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 37.2693 | 0.154645 | 0.0773223 | − | 0.997006i | \(-0.475363\pi\) | ||||
0.0773223 | + | 0.997006i | \(0.475363\pi\) | |||||||
\(242\) | − | 118.438i | − | 0.489415i | ||||||
\(243\) | −208.426 | − | 124.930i | −0.857721 | − | 0.514115i | ||||
\(244\) | −33.7872 | −0.138472 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −114.530 | − | 103.805i | −0.465571 | − | 0.421971i | ||||
\(247\) | 193.446 | 0.783181 | ||||||||
\(248\) | 121.373i | 0.489409i | ||||||||
\(249\) | 154.315 | − | 170.259i | 0.619738 | − | 0.683771i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 247.604i | 0.986471i | 0.869896 | + | 0.493235i | \(0.164186\pi\) | ||||
−0.869896 | + | 0.493235i | \(0.835814\pi\) | |||||||
\(252\) | 4.66765 | + | 47.3942i | 0.0185224 | + | 0.188072i | ||||
\(253\) | −206.817 | −0.817459 | ||||||||
\(254\) | 279.494i | 1.10037i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 75.6252i | 0.294262i | 0.989117 | + | 0.147131i | \(0.0470038\pi\) | ||||
−0.989117 | + | 0.147131i | \(0.952996\pi\) | |||||||
\(258\) | −50.4375 | + | 55.6489i | −0.195494 | + | 0.215694i | ||||
\(259\) | −47.9532 | −0.185147 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 367.333 | − | 36.1770i | 1.40741 | − | 0.138609i | ||||
\(262\) | 53.7993 | 0.205341 | ||||||||
\(263\) | − | 56.5685i | − | 0.215089i | −0.994200 | − | 0.107545i | \(-0.965701\pi\) | ||
0.994200 | − | 0.107545i | \(-0.0342989\pi\) | |||||||
\(264\) | 38.3730 | + | 34.7795i | 0.145352 | + | 0.131740i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 118.800i | − | 0.446617i | ||||||
\(267\) | −54.1079 | + | 59.6985i | −0.202651 | + | 0.223590i | ||||
\(268\) | 34.2785 | 0.127905 | ||||||||
\(269\) | − | 253.707i | − | 0.943149i | −0.881826 | − | 0.471574i | \(-0.843686\pi\) | ||
0.881826 | − | 0.471574i | \(-0.156314\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 256.392 | 0.946096 | 0.473048 | − | 0.881037i | \(-0.343154\pi\) | ||||
0.473048 | + | 0.881037i | \(0.343154\pi\) | |||||||
\(272\) | − | 29.2071i | − | 0.107379i | ||||||
\(273\) | 35.8315 | + | 32.4760i | 0.131251 | + | 0.118960i | ||||
\(274\) | −61.9317 | −0.226028 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −136.538 | + | 150.645i | −0.494702 | + | 0.545816i | ||||
\(277\) | 185.677 | 0.670312 | 0.335156 | − | 0.942163i | \(-0.391211\pi\) | ||||
0.335156 | + | 0.942163i | \(0.391211\pi\) | |||||||
\(278\) | − | 248.800i | − | 0.894966i | ||||||
\(279\) | 37.8528 | + | 384.349i | 0.135673 | + | 1.37759i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 260.250i | 0.926157i | 0.886317 | + | 0.463078i | \(0.153255\pi\) | ||||
−0.886317 | + | 0.463078i | \(0.846745\pi\) | |||||||
\(282\) | −142.451 | − | 129.111i | −0.505147 | − | 0.457841i | ||||
\(283\) | 445.523 | 1.57429 | 0.787143 | − | 0.616770i | \(-0.211559\pi\) | ||||
0.787143 | + | 0.616770i | \(0.211559\pi\) | |||||||
\(284\) | − | 227.648i | − | 0.801578i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 52.5887 | 0.183877 | ||||||||
\(287\) | 96.3929i | 0.335864i | ||||||||
\(288\) | 50.6666 | − | 4.98993i | 0.175926 | − | 0.0173261i | ||||
\(289\) | 235.684 | 0.815515 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −266.935 | − | 241.937i | −0.917302 | − | 0.831399i | ||||
\(292\) | 210.145 | 0.719675 | ||||||||
\(293\) | − | 173.565i | − | 0.592371i | −0.955130 | − | 0.296186i | \(-0.904285\pi\) | ||
0.955130 | − | 0.296186i | \(-0.0957147\pi\) | |||||||
\(294\) | 19.9443 | − | 22.0051i | 0.0678379 | − | 0.0748472i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 51.2641i | 0.173189i | ||||||||
\(297\) | 132.361 | + | 98.1673i | 0.445660 | + | 0.330530i | ||||
\(298\) | 212.971 | 0.714666 | ||||||||
\(299\) | 206.453i | 0.690480i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 46.8361 | 0.155602 | ||||||||
\(302\) | 7.96241i | 0.0263656i | ||||||||
\(303\) | 328.358 | − | 362.285i | 1.08369 | − | 1.19566i | ||||
\(304\) | −127.003 | −0.417772 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.10885 | − | 92.4891i | −0.0297675 | − | 0.302252i | ||||
\(307\) | 243.521 | 0.793227 | 0.396613 | − | 0.917986i | \(-0.370185\pi\) | ||||
0.396613 | + | 0.917986i | \(0.370185\pi\) | |||||||
\(308\) | − | 32.2961i | − | 0.104857i | ||||||
\(309\) | −414.292 | − | 375.495i | −1.34075 | − | 1.21519i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 257.759i | 0.828809i | 0.910093 | + | 0.414404i | \(0.136010\pi\) | ||||
−0.910093 | + | 0.414404i | \(0.863990\pi\) | |||||||
\(312\) | 34.7183 | − | 38.3055i | 0.111277 | − | 0.122774i | ||||
\(313\) | −156.412 | −0.499718 | −0.249859 | − | 0.968282i | \(-0.580384\pi\) | ||||
−0.249859 | + | 0.968282i | \(0.580384\pi\) | |||||||
\(314\) | 168.376i | 0.536228i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −149.626 | −0.473501 | ||||||||
\(317\) | 269.689i | 0.850754i | 0.905016 | + | 0.425377i | \(0.139858\pi\) | ||||
−0.905016 | + | 0.425377i | \(0.860142\pi\) | |||||||
\(318\) | −57.0209 | − | 51.6811i | −0.179311 | − | 0.162519i | ||||
\(319\) | −250.314 | −0.784682 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 332.273 | − | 366.605i | 1.03512 | − | 1.14207i | ||||
\(322\) | 126.788 | 0.393753 | ||||||||
\(323\) | 231.836i | 0.717760i | ||||||||
\(324\) | 158.888 | − | 31.6028i | 0.490394 | − | 0.0975396i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 105.476i | − | 0.323547i | ||||||
\(327\) | 214.928 | + | 194.801i | 0.657273 | + | 0.595721i | ||||
\(328\) | 103.048 | 0.314172 | ||||||||
\(329\) | 119.892i | 0.364414i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 100.748 | 0.304374 | 0.152187 | − | 0.988352i | \(-0.451368\pi\) | ||||
0.152187 | + | 0.988352i | \(0.451368\pi\) | |||||||
\(332\) | 153.190i | 0.461416i | ||||||||
\(333\) | 15.9878 | + | 162.336i | 0.0480113 | + | 0.487495i | ||||
\(334\) | 161.813 | 0.484470 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −23.5244 | − | 21.3214i | −0.0700131 | − | 0.0634566i | ||||
\(337\) | 172.052 | 0.510541 | 0.255270 | − | 0.966870i | \(-0.417835\pi\) | ||||
0.255270 | + | 0.966870i | \(0.417835\pi\) | |||||||
\(338\) | 186.506i | 0.551793i | ||||||||
\(339\) | 226.216 | − | 249.589i | 0.667303 | − | 0.736252i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 261.909i | − | 0.768060i | ||||||
\(342\) | −402.174 | + | 39.6084i | −1.17595 | + | 0.115814i | ||||
\(343\) | −18.5203 | −0.0539949 | ||||||||
\(344\) | − | 50.0699i | − | 0.145552i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 245.818 | 0.710458 | ||||||||
\(347\) | − | 376.866i | − | 1.08607i | −0.839711 | − | 0.543034i | \(-0.817275\pi\) | ||
0.839711 | − | 0.543034i | \(-0.182725\pi\) | |||||||
\(348\) | −165.253 | + | 182.328i | −0.474866 | + | 0.523931i | ||||
\(349\) | 334.570 | 0.958652 | 0.479326 | − | 0.877637i | \(-0.340881\pi\) | ||||
0.479326 | + | 0.877637i | \(0.340881\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 97.9946 | − | 132.128i | 0.279187 | − | 0.376433i | ||||
\(352\) | −34.5260 | −0.0980852 | ||||||||
\(353\) | − | 291.223i | − | 0.824995i | −0.910959 | − | 0.412497i | \(-0.864657\pi\) | ||
0.910959 | − | 0.412497i | \(-0.135343\pi\) | |||||||
\(354\) | 13.2887 | + | 12.0442i | 0.0375387 | + | 0.0340233i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 53.7136i | − | 0.150881i | ||||||
\(357\) | −38.9211 | + | 42.9426i | −0.109023 | + | 0.120287i | ||||
\(358\) | −189.776 | −0.530102 | ||||||||
\(359\) | − | 204.579i | − | 0.569858i | −0.958549 | − | 0.284929i | \(-0.908030\pi\) | ||
0.958549 | − | 0.284929i | \(-0.0919701\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 647.104 | 1.79253 | ||||||||
\(362\) | 281.589i | 0.777869i | ||||||||
\(363\) | 186.161 | + | 168.727i | 0.512839 | + | 0.464813i | ||||
\(364\) | −32.2393 | −0.0885695 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 48.1331 | − | 53.1063i | 0.131511 | − | 0.145099i | ||||
\(367\) | −242.592 | −0.661015 | −0.330507 | − | 0.943803i | \(-0.607220\pi\) | ||||
−0.330507 | + | 0.943803i | \(0.607220\pi\) | |||||||
\(368\) | − | 135.543i | − | 0.368322i | ||||||
\(369\) | 326.319 | − | 32.1378i | 0.884334 | − | 0.0870942i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 47.9909i | 0.129355i | ||||||||
\(372\) | −190.774 | − | 172.908i | −0.512832 | − | 0.464807i | ||||
\(373\) | 101.784 | 0.272880 | 0.136440 | − | 0.990648i | \(-0.456434\pi\) | ||||
0.136440 | + | 0.990648i | \(0.456434\pi\) | |||||||
\(374\) | 63.0253i | 0.168517i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 128.170 | 0.340878 | ||||||||
\(377\) | 249.873i | 0.662794i | ||||||||
\(378\) | −81.1433 | − | 60.1811i | −0.214665 | − | 0.159209i | ||||
\(379\) | −247.028 | −0.651789 | −0.325894 | − | 0.945406i | \(-0.605665\pi\) | ||||
−0.325894 | + | 0.945406i | \(0.605665\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −439.306 | − | 398.166i | −1.15303 | − | 1.04505i | ||||
\(382\) | 317.075 | 0.830040 | ||||||||
\(383\) | − | 18.9699i | − | 0.0495297i | −0.999693 | − | 0.0247649i | \(-0.992116\pi\) | ||
0.999693 | − | 0.0247649i | \(-0.00788371\pi\) | |||||||
\(384\) | −22.7935 | + | 25.1487i | −0.0593582 | + | 0.0654913i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 481.008i | − | 1.24613i | ||||||
\(387\) | −15.6153 | − | 158.554i | −0.0403497 | − | 0.409702i | ||||
\(388\) | 240.174 | 0.619005 | ||||||||
\(389\) | 623.289i | 1.60229i | 0.598473 | + | 0.801143i | \(0.295774\pi\) | ||||
−0.598473 | + | 0.801143i | \(0.704226\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −247.426 | −0.632802 | ||||||||
\(392\) | 19.7990i | 0.0505076i | ||||||||
\(393\) | −76.6422 | + | 84.5612i | −0.195018 | + | 0.215168i | ||||
\(394\) | 163.205 | 0.414227 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −109.332 | + | 10.7676i | −0.276091 | + | 0.0271910i | ||||
\(397\) | −368.913 | −0.929253 | −0.464626 | − | 0.885507i | \(-0.653811\pi\) | ||||
−0.464626 | + | 0.885507i | \(0.653811\pi\) | |||||||
\(398\) | 263.849i | 0.662937i | ||||||||
\(399\) | 186.729 | + | 169.242i | 0.467992 | + | 0.424166i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 291.137i | − | 0.726027i | −0.931784 | − | 0.363014i | \(-0.881748\pi\) | ||
0.931784 | − | 0.363014i | \(-0.118252\pi\) | |||||||
\(402\) | −48.8330 | + | 53.8786i | −0.121475 | + | 0.134026i | ||||
\(403\) | −261.448 | −0.648754 | ||||||||
\(404\) | 325.965i | 0.806844i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 153.454 | 0.377965 | ||||||||
\(407\) | − | 110.621i | − | 0.271797i | ||||||
\(408\) | 45.9075 | + | 41.6084i | 0.112518 | + | 0.101981i | ||||
\(409\) | 131.054 | 0.320425 | 0.160212 | − | 0.987083i | \(-0.448782\pi\) | ||||
0.160212 | + | 0.987083i | \(0.448782\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 88.2277 | − | 97.3437i | 0.214666 | − | 0.236846i | ||||
\(412\) | 372.758 | 0.904753 | ||||||||
\(413\) | − | 11.1842i | − | 0.0270805i | ||||||
\(414\) | −42.2718 | − | 429.217i | −0.102106 | − | 1.03676i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 34.4652i | 0.0828492i | ||||||||
\(417\) | 391.062 | + | 354.440i | 0.937799 | + | 0.849976i | ||||
\(418\) | 274.056 | 0.655635 | ||||||||
\(419\) | 639.030i | 1.52513i | 0.646911 | + | 0.762566i | \(0.276061\pi\) | ||||
−0.646911 | + | 0.762566i | \(0.723939\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 496.330 | 1.17893 | 0.589466 | − | 0.807793i | \(-0.299338\pi\) | ||||
0.589466 | + | 0.807793i | \(0.299338\pi\) | |||||||
\(422\) | 493.408i | 1.16921i | ||||||||
\(423\) | 405.871 | − | 39.9725i | 0.959506 | − | 0.0944976i | ||||
\(424\) | 51.3044 | 0.121001 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 357.815 | + | 324.307i | 0.839942 | + | 0.761284i | ||||
\(427\) | −44.6962 | −0.104675 | ||||||||
\(428\) | 329.851i | 0.770681i | ||||||||
\(429\) | −74.9177 | + | 82.6584i | −0.174633 | + | 0.192677i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 242.169i | 0.561877i | 0.959726 | + | 0.280939i | \(0.0906457\pi\) | ||||
−0.959726 | + | 0.280939i | \(0.909354\pi\) | |||||||
\(432\) | −64.3363 | + | 86.7459i | −0.148927 | + | 0.200801i | ||||
\(433\) | 123.653 | 0.285574 | 0.142787 | − | 0.989753i | \(-0.454394\pi\) | ||||
0.142787 | + | 0.989753i | \(0.454394\pi\) | |||||||
\(434\) | 160.562i | 0.369959i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −193.381 | −0.443535 | ||||||||
\(437\) | 1075.89i | 2.46199i | ||||||||
\(438\) | −299.372 | + | 330.304i | −0.683497 | + | 0.754119i | ||||
\(439\) | −419.828 | −0.956328 | −0.478164 | − | 0.878271i | \(-0.658698\pi\) | ||||
−0.478164 | + | 0.878271i | \(0.658698\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.17472 | + | 62.6967i | 0.0140016 | + | 0.142169i | ||||
\(442\) | 62.9145 | 0.142340 | ||||||||
\(443\) | 95.9458i | 0.216582i | 0.994119 | + | 0.108291i | \(0.0345378\pi\) | ||||
−0.994119 | + | 0.108291i | \(0.965462\pi\) | |||||||
\(444\) | −80.5764 | − | 73.0306i | −0.181478 | − | 0.164483i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 625.605i | 1.40270i | ||||||||
\(447\) | −303.397 | + | 334.745i | −0.678741 | + | 0.748871i | ||||
\(448\) | 21.1660 | 0.0472456 | ||||||||
\(449\) | − | 780.855i | − | 1.73910i | −0.493847 | − | 0.869549i | \(-0.664410\pi\) | ||
0.493847 | − | 0.869549i | \(-0.335590\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −222.365 | −0.493050 | ||||||||
\(452\) | 224.567i | 0.496830i | ||||||||
\(453\) | −12.5152 | − | 11.3432i | −0.0276275 | − | 0.0250402i | ||||
\(454\) | 149.350 | 0.328964 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 180.927 | − | 199.621i | 0.396771 | − | 0.437766i | ||||
\(457\) | 615.383 | 1.34657 | 0.673286 | − | 0.739383i | \(-0.264882\pi\) | ||||
0.673286 | + | 0.739383i | \(0.264882\pi\) | |||||||
\(458\) | − | 424.596i | − | 0.927064i | ||||||
\(459\) | 158.350 | + | 117.442i | 0.344989 | + | 0.255866i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 463.592i | 1.00562i | 0.864396 | + | 0.502811i | \(0.167701\pi\) | ||||
−0.864396 | + | 0.502811i | \(0.832299\pi\) | |||||||
\(462\) | 50.7627 | + | 46.0089i | 0.109876 | + | 0.0995863i | ||||
\(463\) | 249.784 | 0.539491 | 0.269746 | − | 0.962932i | \(-0.413060\pi\) | ||||
0.269746 | + | 0.962932i | \(0.413060\pi\) | |||||||
\(464\) | − | 164.049i | − | 0.353554i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 317.261 | 0.680819 | ||||||||
\(467\) | − | 629.113i | − | 1.34714i | −0.739124 | − | 0.673569i | \(-0.764760\pi\) | ||
0.739124 | − | 0.673569i | \(-0.235240\pi\) | |||||||
\(468\) | 10.7487 | + | 109.140i | 0.0229673 | + | 0.233205i | ||||
\(469\) | 45.3462 | 0.0966869 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −264.651 | − | 239.867i | −0.561892 | − | 0.509272i | ||||
\(472\) | −11.9565 | −0.0253315 | ||||||||
\(473\) | 108.045i | 0.228424i | ||||||||
\(474\) | 213.157 | − | 235.181i | 0.449699 | − | 0.496163i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 38.6374i | − | 0.0811711i | ||||||
\(477\) | 162.464 | − | 16.0003i | 0.340595 | − | 0.0335437i | ||||
\(478\) | −422.000 | −0.882845 | ||||||||
\(479\) | − | 554.807i | − | 1.15826i | −0.815235 | − | 0.579131i | \(-0.803392\pi\) | ||
0.815235 | − | 0.579131i | \(-0.196608\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −110.427 | −0.229578 | ||||||||
\(482\) | − | 52.7068i | − | 0.109350i | ||||||
\(483\) | −180.622 | + | 199.285i | −0.373959 | + | 0.412598i | ||||
\(484\) | −167.497 | −0.346069 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −176.678 | + | 294.759i | −0.363534 | + | 0.606501i | ||||
\(487\) | 244.109 | 0.501251 | 0.250626 | − | 0.968084i | \(-0.419364\pi\) | ||||
0.250626 | + | 0.968084i | \(0.419364\pi\) | |||||||
\(488\) | 47.7823i | 0.0979145i | ||||||||
\(489\) | 165.786 | + | 150.261i | 0.339032 | + | 0.307282i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 170.600i | − | 0.347454i | −0.984794 | − | 0.173727i | \(-0.944419\pi\) | ||
0.984794 | − | 0.173727i | \(-0.0555810\pi\) | |||||||
\(492\) | −146.802 | + | 161.970i | −0.298379 | + | 0.329208i | ||||
\(493\) | −299.463 | −0.607429 | ||||||||
\(494\) | − | 273.573i | − | 0.553793i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 171.648 | 0.346065 | ||||||||
\(497\) | − | 301.150i | − | 0.605936i | ||||||
\(498\) | −240.783 | − | 218.234i | −0.483499 | − | 0.438221i | ||||
\(499\) | 965.312 | 1.93449 | 0.967247 | − | 0.253837i | \(-0.0816927\pi\) | ||||
0.967247 | + | 0.253837i | \(0.0816927\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −230.518 | + | 254.336i | −0.460116 | + | 0.507657i | ||||
\(502\) | 350.165 | 0.697540 | ||||||||
\(503\) | − | 86.1692i | − | 0.171311i | −0.996325 | − | 0.0856553i | \(-0.972702\pi\) | ||
0.996325 | − | 0.0856553i | \(-0.0272984\pi\) | |||||||
\(504\) | 67.0256 | − | 6.60106i | 0.132987 | − | 0.0130973i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 292.484i | 0.578031i | ||||||||
\(507\) | −293.148 | − | 265.696i | −0.578202 | − | 0.524054i | ||||
\(508\) | 395.264 | 0.778078 | ||||||||
\(509\) | − | 115.697i | − | 0.227303i | −0.993521 | − | 0.113651i | \(-0.963745\pi\) | ||
0.993521 | − | 0.113651i | \(-0.0362547\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 277.996 | 0.544023 | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 510.680 | − | 688.559i | 0.995477 | − | 1.34222i | ||||
\(514\) | 106.950 | 0.208074 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 78.6995 | + | 71.3294i | 0.152518 | + | 0.138235i | ||||
\(517\) | −276.575 | −0.534961 | ||||||||
\(518\) | 67.8160i | 0.130919i | ||||||||
\(519\) | −350.192 | + | 386.375i | −0.674744 | + | 0.744461i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 527.925i | − | 1.01329i | −0.862154 | − | 0.506646i | \(-0.830885\pi\) | ||
0.862154 | − | 0.506646i | \(-0.169115\pi\) | |||||||
\(522\) | −51.1620 | − | 519.487i | −0.0980116 | − | 0.995186i | ||||
\(523\) | 637.700 | 1.21931 | 0.609656 | − | 0.792666i | \(-0.291307\pi\) | ||||
0.609656 | + | 0.792666i | \(0.291307\pi\) | |||||||
\(524\) | − | 76.0837i | − | 0.145198i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −79.9999 | −0.152091 | ||||||||
\(527\) | − | 313.334i | − | 0.594562i | ||||||
\(528\) | 49.1856 | − | 54.2676i | 0.0931545 | − | 0.102780i | ||||
\(529\) | −619.237 | −1.17058 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −37.8620 | + | 3.72887i | −0.0713033 | + | 0.00702235i | ||||
\(532\) | −168.009 | −0.315806 | ||||||||
\(533\) | 221.974i | 0.416462i | ||||||||
\(534\) | 84.4265 | + | 76.5202i | 0.158102 | + | 0.143296i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 48.4771i | − | 0.0904423i | ||||||
\(537\) | 270.355 | − | 298.289i | 0.503454 | − | 0.555472i | ||||
\(538\) | −358.796 | −0.666907 | ||||||||
\(539\) | − | 42.7237i | − | 0.0792648i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −749.392 | −1.38520 | −0.692599 | − | 0.721323i | \(-0.743534\pi\) | ||||
−0.692599 | + | 0.721323i | \(0.743534\pi\) | |||||||
\(542\) | − | 362.593i | − | 0.668991i | ||||||
\(543\) | −442.598 | − | 401.150i | −0.815098 | − | 0.738766i | ||||
\(544\) | −41.3051 | −0.0759286 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 45.9280 | − | 50.6734i | 0.0841172 | − | 0.0928084i | ||||
\(547\) | 129.416 | 0.236592 | 0.118296 | − | 0.992978i | \(-0.462257\pi\) | ||||
0.118296 | + | 0.992978i | \(0.462257\pi\) | |||||||
\(548\) | 87.5847i | 0.159826i | ||||||||
\(549\) | 14.9019 | + | 151.310i | 0.0271437 | + | 0.275610i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1302.16i | 2.36328i | ||||||||
\(552\) | 213.045 | + | 193.093i | 0.385950 | + | 0.349807i | ||||
\(553\) | −197.937 | −0.357933 | ||||||||
\(554\) | − | 262.586i | − | 0.473982i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −351.857 | −0.632836 | ||||||||
\(557\) | − | 926.902i | − | 1.66410i | −0.554703 | − | 0.832049i | \(-0.687168\pi\) | ||
0.554703 | − | 0.832049i | \(-0.312832\pi\) | |||||||
\(558\) | 543.551 | − | 53.5320i | 0.974106 | − | 0.0959354i | ||||
\(559\) | 107.855 | 0.192942 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −99.0626 | − | 89.7856i | −0.176582 | − | 0.160046i | ||||
\(562\) | 368.049 | 0.654892 | ||||||||
\(563\) | 690.211i | 1.22595i | 0.790101 | + | 0.612976i | \(0.210028\pi\) | ||||
−0.790101 | + | 0.612976i | \(0.789972\pi\) | |||||||
\(564\) | −182.591 | + | 201.457i | −0.323742 | + | 0.357193i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 630.065i | − | 1.11319i | ||||||
\(567\) | 210.189 | − | 41.8066i | 0.370703 | − | 0.0737330i | ||||
\(568\) | −321.943 | −0.566801 | ||||||||
\(569\) | 155.630i | 0.273515i | 0.990605 | + | 0.136757i | \(0.0436680\pi\) | ||||
−0.990605 | + | 0.136757i | \(0.956332\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −961.721 | −1.68427 | −0.842137 | − | 0.539263i | \(-0.818703\pi\) | ||||
−0.842137 | + | 0.539263i | \(0.818703\pi\) | |||||||
\(572\) | − | 74.3716i | − | 0.130020i | ||||||
\(573\) | −451.704 | + | 498.376i | −0.788315 | + | 0.869766i | ||||
\(574\) | 136.320 | 0.237492 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.05683 | − | 71.6533i | −0.0122514 | − | 0.124398i | ||||
\(577\) | −670.111 | −1.16137 | −0.580685 | − | 0.814128i | \(-0.697215\pi\) | ||||
−0.580685 | + | 0.814128i | \(0.697215\pi\) | |||||||
\(578\) | − | 333.307i | − | 0.576656i | ||||||
\(579\) | 756.043 | + | 685.241i | 1.30577 | + | 1.18349i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 202.651i | 0.348797i | ||||||||
\(582\) | −342.151 | + | 377.503i | −0.587888 | + | 0.648631i | ||||
\(583\) | −110.708 | −0.189894 | ||||||||
\(584\) | − | 297.190i | − | 0.508887i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −245.458 | −0.418870 | ||||||||
\(587\) | − | 671.384i | − | 1.14376i | −0.820339 | − | 0.571878i | \(-0.806215\pi\) | ||
0.820339 | − | 0.571878i | \(-0.193785\pi\) | |||||||
\(588\) | −31.1199 | − | 28.2056i | −0.0529249 | − | 0.0479686i | ||||
\(589\) | −1362.48 | −2.31322 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −232.502 | + | 256.525i | −0.393404 | + | 0.434052i | ||||
\(592\) | 72.4984 | 0.122463 | ||||||||
\(593\) | 173.594i | 0.292738i | 0.989230 | + | 0.146369i | \(0.0467587\pi\) | ||||
−0.989230 | + | 0.146369i | \(0.953241\pi\) | |||||||
\(594\) | 138.830 | − | 187.187i | 0.233720 | − | 0.315129i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 301.186i | − | 0.505345i | ||||||
\(597\) | −414.715 | − | 375.878i | −0.694665 | − | 0.629612i | ||||
\(598\) | 291.969 | 0.488243 | ||||||||
\(599\) | 561.565i | 0.937504i | 0.883330 | + | 0.468752i | \(0.155296\pi\) | ||||
−0.883330 | + | 0.468752i | \(0.844704\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 382.578 | 0.636568 | 0.318284 | − | 0.947995i | \(-0.396893\pi\) | ||||
0.318284 | + | 0.947995i | \(0.396893\pi\) | |||||||
\(602\) | − | 66.2363i | − | 0.110027i | ||||||
\(603\) | −15.1186 | − | 153.510i | −0.0250723 | − | 0.254578i | ||||
\(604\) | 11.2606 | 0.0186433 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −512.349 | − | 464.369i | −0.845460 | − | 0.766285i | ||||
\(607\) | −489.748 | −0.806833 | −0.403417 | − | 0.915016i | \(-0.632177\pi\) | ||||
−0.403417 | + | 0.915016i | \(0.632177\pi\) | |||||||
\(608\) | 179.609i | 0.295409i | ||||||||
\(609\) | −218.610 | + | 241.197i | −0.358965 | + | 0.396054i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 276.088i | 0.451863i | ||||||||
\(612\) | −130.799 | + | 12.8819i | −0.213724 | + | 0.0210488i | ||||
\(613\) | −103.287 | −0.168494 | −0.0842472 | − | 0.996445i | \(-0.526849\pi\) | ||||
−0.0842472 | + | 0.996445i | \(0.526849\pi\) | |||||||
\(614\) | − | 344.390i | − | 0.560896i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −45.6736 | −0.0741454 | ||||||||
\(617\) | − | 103.427i | − | 0.167629i | −0.996481 | − | 0.0838144i | \(-0.973290\pi\) | ||
0.996481 | − | 0.0838144i | \(-0.0267103\pi\) | |||||||
\(618\) | −531.030 | + | 585.898i | −0.859271 | + | 0.948054i | ||||
\(619\) | −1040.92 | −1.68162 | −0.840809 | − | 0.541332i | \(-0.817920\pi\) | ||||
−0.840809 | + | 0.541332i | \(0.817920\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 734.860 | + | 545.019i | 1.18335 | + | 0.877647i | ||||
\(622\) | 364.527 | 0.586056 | ||||||||
\(623\) | − | 71.0564i | − | 0.114055i | ||||||
\(624\) | −54.1722 | − | 49.0991i | −0.0868144 | − | 0.0786844i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 221.199i | 0.353354i | ||||||||
\(627\) | −390.418 | + | 430.758i | −0.622677 | + | 0.687014i | ||||
\(628\) | 238.119 | 0.379170 | ||||||||
\(629\) | − | 132.342i | − | 0.210400i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1243.34 | −1.97043 | −0.985216 | − | 0.171315i | \(-0.945198\pi\) | ||||
−0.985216 | + | 0.171315i | \(0.945198\pi\) | |||||||
\(632\) | 211.604i | 0.334816i | ||||||||
\(633\) | −775.534 | − | 702.907i | −1.22517 | − | 1.11044i | ||||
\(634\) | 381.398 | 0.601574 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −73.0881 | + | 80.6398i | −0.114918 | + | 0.126792i | ||||
\(637\) | −42.6486 | −0.0669522 | ||||||||
\(638\) | 353.997i | 0.554854i | ||||||||
\(639\) | −1019.48 | + | 100.405i | −1.59544 | + | 0.157128i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 168.859i | − | 0.263431i | −0.991288 | − | 0.131715i | \(-0.957951\pi\) | ||
0.991288 | − | 0.131715i | \(-0.0420485\pi\) | |||||||
\(642\) | −518.457 | − | 469.905i | −0.807566 | − | 0.731939i | ||||
\(643\) | 290.872 | 0.452366 | 0.226183 | − | 0.974085i | \(-0.427375\pi\) | ||||
0.226183 | + | 0.974085i | \(0.427375\pi\) | |||||||
\(644\) | − | 179.306i | − | 0.278425i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 327.866 | 0.507533 | ||||||||
\(647\) | 725.855i | 1.12188i | 0.827857 | + | 0.560939i | \(0.189560\pi\) | ||||
−0.827857 | + | 0.560939i | \(0.810440\pi\) | |||||||
\(648\) | −44.6931 | − | 224.701i | −0.0689709 | − | 0.346761i | ||||
\(649\) | 25.8005 | 0.0397543 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −252.370 | − | 228.736i | −0.387665 | − | 0.351361i | ||||
\(652\) | −149.166 | −0.228782 | ||||||||
\(653\) | − | 977.062i | − | 1.49627i | −0.663548 | − | 0.748133i | \(-0.730950\pi\) | ||
0.663548 | − | 0.748133i | \(-0.269050\pi\) | |||||||
\(654\) | 275.490 | − | 303.955i | 0.421238 | − | 0.464762i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 145.732i | − | 0.222153i | ||||||
\(657\) | −92.6848 | − | 941.100i | −0.141073 | − | 1.43242i | ||||
\(658\) | 169.553 | 0.257680 | ||||||||
\(659\) | − | 157.771i | − | 0.239409i | −0.992810 | − | 0.119705i | \(-0.961805\pi\) | ||
0.992810 | − | 0.119705i | \(-0.0381948\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1072.89 | 1.62314 | 0.811568 | − | 0.584258i | \(-0.198614\pi\) | ||||
0.811568 | + | 0.584258i | \(0.198614\pi\) | |||||||
\(662\) | − | 142.479i | − | 0.215225i | ||||||
\(663\) | −89.6277 | + | 98.8884i | −0.135185 | + | 0.149153i | ||||
\(664\) | 216.643 | 0.326270 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 229.578 | − | 22.6101i | 0.344711 | − | 0.0339491i | ||||
\(667\) | −1389.73 | −2.08355 | ||||||||
\(668\) | − | 228.838i | − | 0.342572i | ||||||
\(669\) | −983.320 | − | 891.235i | −1.46984 | − | 1.33219i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 103.108i | − | 0.153663i | ||||||
\(672\) | −30.1530 | + | 33.2685i | −0.0448706 | + | 0.0495068i | ||||
\(673\) | 293.836 | 0.436606 | 0.218303 | − | 0.975881i | \(-0.429948\pi\) | ||||
0.218303 | + | 0.975881i | \(0.429948\pi\) | |||||||
\(674\) | − | 243.319i | − | 0.361007i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 263.759 | 0.390176 | ||||||||
\(677\) | 569.262i | 0.840859i | 0.907325 | + | 0.420429i | \(0.138121\pi\) | ||||
−0.907325 | + | 0.420429i | \(0.861879\pi\) | |||||||
\(678\) | −352.973 | − | 319.918i | −0.520609 | − | 0.471855i | ||||
\(679\) | 317.720 | 0.467924 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −212.763 | + | 234.746i | −0.312427 | + | 0.344708i | ||||
\(682\) | −370.395 | −0.543101 | ||||||||
\(683\) | − | 21.2129i | − | 0.0310585i | −0.999879 | − | 0.0155292i | \(-0.995057\pi\) | ||
0.999879 | − | 0.0155292i | \(-0.00494331\pi\) | |||||||
\(684\) | 56.0147 | + | 568.760i | 0.0818928 | + | 0.831520i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916i | 0.0381802i | ||||||||
\(687\) | 667.375 | + | 604.877i | 0.971434 | + | 0.880462i | ||||
\(688\) | −70.8096 | −0.102921 | ||||||||
\(689\) | 110.514i | 0.160397i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −698.350 | −1.01064 | −0.505318 | − | 0.862933i | \(-0.668625\pi\) | ||||
−0.505318 | + | 0.862933i | \(0.668625\pi\) | |||||||
\(692\) | − | 347.640i | − | 0.502370i | ||||||
\(693\) | −144.633 | + | 14.2442i | −0.208705 | + | 0.0205545i | ||||
\(694\) | −532.969 | −0.767966 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 257.851 | + | 233.703i | 0.370475 | + | 0.335781i | ||||
\(697\) | −266.027 | −0.381674 | ||||||||
\(698\) | − | 473.153i | − | 0.677869i | ||||||
\(699\) | −451.969 | + | 498.669i | −0.646594 | + | 0.713403i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1019.57i | − | 1.45445i | −0.686399 | − | 0.727225i | \(-0.740810\pi\) | ||
0.686399 | − | 0.727225i | \(-0.259190\pi\) | |||||||
\(702\) | −186.857 | − | 138.585i | −0.266179 | − | 0.197415i | ||||
\(703\) | −575.468 | −0.818588 | ||||||||
\(704\) | 48.8271i | 0.0693567i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −411.852 | −0.583359 | ||||||||
\(707\) | 431.211i | 0.609917i | ||||||||
\(708\) | 17.0331 | − | 18.7930i | 0.0240581 | − | 0.0265438i | ||||
\(709\) | 482.736 | 0.680869 | 0.340435 | − | 0.940268i | \(-0.389426\pi\) | ||||
0.340435 | + | 0.940268i | \(0.389426\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 65.9930 | + | 670.077i | 0.0928171 | + | 0.942443i | ||||
\(712\) | −75.9625 | −0.106689 | ||||||||
\(713\) | − | 1454.10i | − | 2.03941i | ||||||
\(714\) | 60.7299 | + | 55.0427i | 0.0850559 | + | 0.0770906i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 268.384i | 0.374838i | ||||||||
\(717\) | 601.180 | − | 663.296i | 0.838466 | − | 0.925099i | ||||
\(718\) | −289.319 | −0.402951 | ||||||||
\(719\) | 1275.40i | 1.77385i | 0.461915 | + | 0.886924i | \(0.347162\pi\) | ||||
−0.461915 | + | 0.886924i | \(0.652838\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 493.113 | 0.683929 | ||||||||
\(722\) | − | 915.143i | − | 1.26751i | ||||||
\(723\) | 82.8441 | + | 75.0859i | 0.114584 | + | 0.103853i | ||||
\(724\) | 398.226 | 0.550036 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 238.616 | − | 263.271i | 0.328672 | − | 0.362632i | ||||
\(727\) | −90.3245 | −0.124243 | −0.0621214 | − | 0.998069i | \(-0.519787\pi\) | ||||
−0.0621214 | + | 0.998069i | \(0.519787\pi\) | |||||||
\(728\) | 45.5932i | 0.0626281i | ||||||||
\(729\) | −211.606 | − | 697.613i | −0.290268 | − | 0.956945i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 129.259i | 0.176825i | ||||||||
\(732\) | −75.1037 | − | 68.0704i | −0.102601 | − | 0.0929924i | ||||
\(733\) | 515.475 | 0.703240 | 0.351620 | − | 0.936143i | \(-0.385631\pi\) | ||||
0.351620 | + | 0.936143i | \(0.385631\pi\) | |||||||
\(734\) | 343.077i | 0.467408i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −191.686 | −0.260443 | ||||||||
\(737\) | 104.607i | 0.141937i | ||||||||
\(738\) | −45.4497 | − | 461.485i | −0.0615849 | − | 0.625318i | ||||
\(739\) | 91.7703 | 0.124182 | 0.0620909 | − | 0.998071i | \(-0.480223\pi\) | ||||
0.0620909 | + | 0.998071i | \(0.480223\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 430.000 | + | 389.732i | 0.580297 | + | 0.525954i | ||||
\(742\) | 67.8694 | 0.0914681 | ||||||||
\(743\) | − | 680.829i | − | 0.916324i | −0.888869 | − | 0.458162i | \(-0.848508\pi\) | ||
0.888869 | − | 0.458162i | \(-0.151492\pi\) | |||||||
\(744\) | −244.529 | + | 269.795i | −0.328668 | + | 0.362627i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 143.944i | − | 0.192955i | ||||||
\(747\) | 686.036 | − | 67.5647i | 0.918388 | − | 0.0904481i | ||||
\(748\) | 89.1313 | 0.119159 | ||||||||
\(749\) | 436.352i | 0.582580i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 275.733 | 0.367155 | 0.183577 | − | 0.983005i | \(-0.441232\pi\) | ||||
0.183577 | + | 0.983005i | \(0.441232\pi\) | |||||||
\(752\) | − | 181.260i | − | 0.241037i | ||||||
\(753\) | −498.844 | + | 550.386i | −0.662475 | + | 0.730925i | ||||
\(754\) | 353.374 | 0.468666 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −85.1089 | + | 114.754i | −0.112578 | + | 0.151791i | ||||
\(757\) | −622.898 | −0.822851 | −0.411425 | − | 0.911443i | \(-0.634969\pi\) | ||||
−0.411425 | + | 0.911443i | \(0.634969\pi\) | |||||||
\(758\) | 349.350i | 0.460884i | ||||||||
\(759\) | −459.723 | − | 416.671i | −0.605696 | − | 0.548974i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1122.56i | − | 1.47511i | −0.675288 | − | 0.737554i | \(-0.735981\pi\) | ||
0.675288 | − | 0.737554i | \(-0.264019\pi\) | |||||||
\(762\) | −563.091 | + | 621.272i | −0.738965 | + | 0.815317i | ||||
\(763\) | −255.819 | −0.335281 | ||||||||
\(764\) | − | 448.412i | − | 0.586927i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.8275 | −0.0350228 | ||||||||
\(767\) | − | 25.7551i | − | 0.0335791i | ||||||
\(768\) | 35.5656 | + | 32.2349i | 0.0463093 | + | 0.0419726i | ||||
\(769\) | −344.788 | −0.448359 | −0.224179 | − | 0.974548i | \(-0.571970\pi\) | ||||
−0.224179 | + | 0.974548i | \(0.571970\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −152.361 | + | 168.103i | −0.197615 | + | 0.218033i | ||||
\(772\) | −680.247 | −0.881149 | ||||||||
\(773\) | 235.375i | 0.304495i | 0.988342 | + | 0.152248i | \(0.0486511\pi\) | ||||
−0.988342 | + | 0.152248i | \(0.951349\pi\) | |||||||
\(774\) | −224.230 | + | 22.0834i | −0.289703 | + | 0.0285316i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 339.657i | − | 0.437702i | ||||||
\(777\) | −106.593 | − | 96.6104i | −0.137185 | − | 0.124338i | ||||
\(778\) | 881.464 | 1.13299 | ||||||||
\(779\) | 1156.77i | 1.48495i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 694.713 | 0.889517 | ||||||||
\(782\) | 349.913i | 0.447459i | ||||||||
\(783\) | 889.410 | + | 659.643i | 1.13590 | + | 0.842456i | ||||
\(784\) | 28.0000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 119.588 | + | 108.388i | 0.152147 | + | 0.137899i | ||||
\(787\) | −579.779 | −0.736695 | −0.368348 | − | 0.929688i | \(-0.620076\pi\) | ||||
−0.368348 | + | 0.929688i | \(0.620076\pi\) | |||||||
\(788\) | − | 230.807i | − | 0.292903i | ||||||
\(789\) | 113.968 | − | 125.743i | 0.144446 | − | 0.159370i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 297.074i | 0.375568i | ||||||||
\(792\) | 15.2277 | + | 154.619i | 0.0192269 | + | 0.195226i | ||||
\(793\) | −102.927 | −0.129794 | ||||||||
\(794\) | 521.722i | 0.657081i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 373.139 | 0.468767 | ||||||||
\(797\) | − | 391.482i | − | 0.491195i | −0.969372 | − | 0.245597i | \(-0.921016\pi\) | ||
0.969372 | − | 0.245597i | \(-0.0789841\pi\) | |||||||
\(798\) | 239.344 | − | 264.074i | 0.299930 | − | 0.330920i | ||||
\(799\) | −330.880 | −0.414118 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −240.547 | + | 23.6905i | −0.300309 | + | 0.0295761i | ||||
\(802\) | −411.730 | −0.513379 | ||||||||
\(803\) | 641.299i | 0.798628i | ||||||||
\(804\) | 76.1958 | + | 69.0603i | 0.0947710 | + | 0.0858959i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 369.743i | 0.458738i | ||||||||
\(807\) | 511.139 | − | 563.952i | 0.633382 | − | 0.698826i | ||||
\(808\) | 460.984 | 0.570525 | ||||||||
\(809\) | − | 1062.72i | − | 1.31362i | −0.754054 | − | 0.656812i | \(-0.771904\pi\) | ||
0.754054 | − | 0.656812i | \(-0.228096\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −243.505 | −0.300253 | −0.150126 | − | 0.988667i | \(-0.547968\pi\) | ||||
−0.150126 | + | 0.988667i | \(0.547968\pi\) | |||||||
\(812\) | − | 217.016i | − | 0.267261i | ||||||
\(813\) | 569.921 | + | 516.549i | 0.701009 | + | 0.635361i | ||||
\(814\) | −156.442 | −0.192190 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 58.8431 | − | 64.9230i | 0.0721117 | − | 0.0795625i | ||||
\(817\) | 562.063 | 0.687959 | ||||||||
\(818\) | − | 185.338i | − | 0.226574i | ||||||
\(819\) | 14.2192 | + | 144.378i | 0.0173617 | + | 0.176286i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 570.152i | − | 0.694460i | −0.937780 | − | 0.347230i | \(-0.887122\pi\) | ||
0.937780 | − | 0.347230i | \(-0.112878\pi\) | |||||||
\(822\) | −137.665 | − | 124.773i | −0.167475 | − | 0.151792i | ||||
\(823\) | −1588.27 | −1.92985 | −0.964925 | − | 0.262527i | \(-0.915444\pi\) | ||||
−0.964925 | + | 0.262527i | \(0.915444\pi\) | |||||||
\(824\) | − | 527.160i | − | 0.639757i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.8169 | −0.0191488 | ||||||||
\(827\) | − | 1084.80i | − | 1.31173i | −0.754878 | − | 0.655865i | \(-0.772304\pi\) | ||
0.754878 | − | 0.655865i | \(-0.227696\pi\) | |||||||
\(828\) | −607.005 | + | 59.7813i | −0.733098 | + | 0.0721996i | ||||
\(829\) | 330.609 | 0.398805 | 0.199402 | − | 0.979918i | \(-0.436100\pi\) | ||||
0.199402 | + | 0.979918i | \(0.436100\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 412.731 | + | 374.079i | 0.496667 | + | 0.450156i | ||||
\(832\) | 48.7412 | 0.0585832 | ||||||||
\(833\) | − | 51.1125i | − | 0.0613595i | ||||||
\(834\) | 501.254 | − | 553.046i | 0.601024 | − | 0.663124i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 387.573i | − | 0.463604i | ||||||
\(837\) | −690.199 | + | 930.610i | −0.824611 | + | 1.11184i | ||||
\(838\) | 903.725 | 1.07843 | ||||||||
\(839\) | − | 150.651i | − | 0.179560i | −0.995962 | − | 0.0897802i | \(-0.971384\pi\) | ||
0.995962 | − | 0.0897802i | \(-0.0286165\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −841.003 | −1.00000 | ||||||||
\(842\) | − | 701.917i | − | 0.833631i | ||||||
\(843\) | −524.321 | + | 578.496i | −0.621971 | + | 0.686235i | ||||
\(844\) | 697.785 | 0.826759 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −56.5296 | − | 573.989i | −0.0668199 | − | 0.678474i | ||||
\(847\) | −221.578 | −0.261603 | ||||||||
\(848\) | − | 72.5554i | − | 0.0855606i | ||||||
\(849\) | 990.330 | + | 897.588i | 1.16647 | + | 1.05723i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 614.164i | − | 0.721696i | ||||||
\(852\) | 458.639 | − | 506.027i | 0.538309 | − | 0.593929i | ||||
\(853\) | 1239.94 | 1.45362 | 0.726812 | − | 0.686836i | \(-0.241001\pi\) | ||||
0.726812 | + | 0.686836i | \(0.241001\pi\) | |||||||
\(854\) | 63.2100i | 0.0740164i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 466.480 | 0.544954 | ||||||||
\(857\) | − | 1016.43i | − | 1.18604i | −0.805189 | − | 0.593018i | \(-0.797936\pi\) | ||
0.805189 | − | 0.593018i | \(-0.202064\pi\) | |||||||
\(858\) | 116.897 | + | 105.950i | 0.136243 | + | 0.123484i | ||||
\(859\) | 810.174 | 0.943160 | 0.471580 | − | 0.881823i | \(-0.343684\pi\) | ||||
0.471580 | + | 0.881823i | \(0.343684\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −194.201 | + | 214.267i | −0.225553 | + | 0.248858i | ||||
\(862\) | 342.479 | 0.397307 | ||||||||
\(863\) | 23.4880i | 0.0272167i | 0.999907 | + | 0.0136083i | \(0.00433180\pi\) | ||||
−0.999907 | + | 0.0136083i | \(0.995668\pi\) | |||||||
\(864\) | 122.677 | + | 90.9852i | 0.141987 | + | 0.105307i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 174.872i | − | 0.201931i | ||||||
\(867\) | 523.889 | + | 474.828i | 0.604255 | + | 0.547668i | ||||
\(868\) | 227.069 | 0.261600 | ||||||||
\(869\) | − | 456.614i | − | 0.525448i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 104.423 | 0.119889 | ||||||||
\(872\) | 273.482i | 0.313626i | ||||||||
\(873\) | −105.929 | − | 1075.58i | −0.121339 | − | 1.23205i | ||||
\(874\) | 1521.54 | 1.74089 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 467.121 | + | 423.376i | 0.533243 | + | 0.483306i | ||||
\(877\) | 580.082 | 0.661439 | 0.330719 | − | 0.943729i | \(-0.392709\pi\) | ||||
0.330719 | + | 0.943729i | \(0.392709\pi\) | |||||||
\(878\) | 593.727i | 0.676226i | ||||||||
\(879\) | 349.678 | − | 385.808i | 0.397813 | − | 0.438917i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 444.274i | 0.504284i | 0.967690 | + | 0.252142i | \(0.0811350\pi\) | ||||
−0.967690 | + | 0.252142i | \(0.918865\pi\) | |||||||
\(882\) | 88.6665 | − | 8.73238i | 0.100529 | − | 0.00990065i | ||||
\(883\) | −192.468 | −0.217970 | −0.108985 | − | 0.994043i | \(-0.534760\pi\) | ||||
−0.108985 | + | 0.994043i | \(0.534760\pi\) | |||||||
\(884\) | − | 88.9745i | − | 0.100650i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 135.688 | 0.153147 | ||||||||
\(887\) | 1294.72i | 1.45966i | 0.683630 | + | 0.729829i | \(0.260400\pi\) | ||||
−0.683630 | + | 0.729829i | \(0.739600\pi\) | |||||||
\(888\) | −103.281 | + | 113.952i | −0.116307 | + | 0.128325i | ||||
\(889\) | 522.885 | 0.588172 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 96.4422 | + | 484.876i | 0.108240 | + | 0.544193i | ||||
\(892\) | 884.739 | 0.991860 | ||||||||
\(893\) | 1438.78i | 1.61118i | ||||||||
\(894\) | 473.401 | + | 429.068i | 0.529532 | + | 0.479942i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 29.9333i | − | 0.0334077i | ||||||
\(897\) | −415.938 | + | 458.915i | −0.463699 | + | 0.511611i | ||||
\(898\) | −1104.30 | −1.22973 | ||||||||
\(899\) | − | 1759.92i | − | 1.95764i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −132.446 | −0.146999 | ||||||||
\(902\) | 314.472i | 0.348639i | ||||||||
\(903\) | 104.110 | + | 94.3600i | 0.115293 | + | 0.104496i | ||||
\(904\) | 317.586 | 0.351312 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −16.0417 | + | 17.6992i | −0.0177061 | + | 0.0195356i | ||||
\(907\) | −1622.83 | −1.78922 | −0.894612 | − | 0.446844i | \(-0.852548\pi\) | ||||
−0.894612 | + | 0.446844i | \(0.852548\pi\) | |||||||
\(908\) | − | 211.212i | − | 0.232613i | ||||||
\(909\) | 1459.78 | − | 143.767i | 1.60592 | − | 0.158160i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 181.811i | 0.199573i | 0.995009 | + | 0.0997865i | \(0.0318160\pi\) | ||||
−0.995009 | + | 0.0997865i | \(0.968184\pi\) | |||||||
\(912\) | −282.307 | − | 255.870i | −0.309548 | − | 0.280559i | ||||
\(913\) | −467.489 | −0.512036 | ||||||||
\(914\) | − | 870.283i | − | 0.952170i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −600.469 | −0.655534 | ||||||||
\(917\) | − | 100.649i | − | 0.109759i | ||||||
\(918\) | 166.089 | − | 223.941i | 0.180924 | − | 0.243944i | ||||
\(919\) | −690.193 | −0.751026 | −0.375513 | − | 0.926817i | \(-0.622533\pi\) | ||||
−0.375513 | + | 0.926817i | \(0.622533\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 541.309 | + | 490.617i | 0.587741 | + | 0.532700i | ||||
\(922\) | 655.618 | 0.711082 | ||||||||
\(923\) | − | 693.491i | − | 0.751344i | ||||||
\(924\) | 65.0664 | − | 71.7893i | 0.0704182 | − | 0.0776940i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 353.248i | − | 0.381478i | ||||||
\(927\) | −164.406 | − | 1669.34i | −0.177352 | − | 1.80079i | ||||
\(928\) | −232.000 | −0.250000 | ||||||||
\(929\) | 1269.52i | 1.36654i | 0.730165 | + | 0.683271i | \(0.239443\pi\) | ||||
−0.730165 | + | 0.683271i | \(0.760557\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −222.255 | −0.238727 | ||||||||
\(932\) | − | 448.675i | − | 0.481411i | ||||||
\(933\) | −519.304 | + | 572.960i | −0.556596 | + | 0.614105i | ||||
\(934\) | −889.701 | −0.952570 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 154.347 | − | 15.2010i | 0.164901 | − | 0.0162403i | ||||
\(937\) | 65.8708 | 0.0702997 | 0.0351499 | − | 0.999382i | \(-0.488809\pi\) | ||||
0.0351499 | + | 0.999382i | \(0.488809\pi\) | |||||||
\(938\) | − | 64.1292i | − | 0.0683680i | ||||||
\(939\) | −347.679 | − | 315.120i | −0.370265 | − | 0.335591i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1456.21i | − | 1.54751i | −0.633485 | − | 0.773755i | \(-0.718376\pi\) | ||
0.633485 | − | 0.773755i | \(-0.281624\pi\) | |||||||
\(942\) | −339.223 | + | 374.273i | −0.360110 | + | 0.397318i | ||||
\(943\) | −1234.56 | −1.30918 | ||||||||
\(944\) | 16.9090i | 0.0179121i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 152.798 | 0.161520 | ||||||||
\(947\) | 1143.90i | 1.20792i | 0.797015 | + | 0.603959i | \(0.206411\pi\) | ||||
−0.797015 | + | 0.603959i | \(0.793589\pi\) | |||||||
\(948\) | −332.597 | − | 301.450i | −0.350840 | − | 0.317985i | ||||
\(949\) | 640.171 | 0.674574 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −543.338 | + | 599.477i | −0.571333 | + | 0.630365i | ||||
\(952\) | −54.6416 | −0.0573966 | ||||||||
\(953\) | − | 675.499i | − | 0.708814i | −0.935091 | − | 0.354407i | \(-0.884683\pi\) | ||
0.935091 | − | 0.354407i | \(-0.115317\pi\) | |||||||
\(954\) | −22.6279 | − | 229.758i | −0.0237190 | − | 0.240837i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 596.798i | 0.624266i | ||||||||
\(957\) | −556.409 | − | 504.302i | −0.581409 | − | 0.526962i | ||||
\(958\) | −784.616 | −0.819014 | ||||||||
\(959\) | 115.864i | 0.120817i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 880.440 | 0.916171 | ||||||||
\(962\) | 156.167i | 0.162336i | ||||||||
\(963\) | 1477.18 | − | 145.482i | 1.53394 | − | 0.151071i | ||||
\(964\) | −74.5387 | −0.0773223 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 281.831 | + | 255.439i | 0.291751 | + | 0.264429i | ||||
\(967\) | 451.801 | 0.467220 | 0.233610 | − | 0.972330i | \(-0.424946\pi\) | ||||
0.233610 | + | 0.972330i | \(0.424946\pi\) | |||||||
\(968\) | 236.877i | 0.244708i | ||||||||
\(969\) | −467.077 | + | 515.337i | −0.482020 | + | 0.531824i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 587.257i | − | 0.604796i | −0.953182 | − | 0.302398i | \(-0.902213\pi\) | ||
0.953182 | − | 0.302398i | \(-0.0977872\pi\) | |||||||
\(972\) | 416.853 | + | 249.860i | 0.428861 | + | 0.257057i | ||||
\(973\) | −465.463 | −0.478379 | ||||||||
\(974\) | − | 345.223i | − | 0.354438i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 67.5743 | 0.0692360 | ||||||||
\(977\) | − | 1077.86i | − | 1.10324i | −0.834096 | − | 0.551620i | \(-0.814010\pi\) | ||
0.834096 | − | 0.551620i | \(-0.185990\pi\) | |||||||
\(978\) | 212.501 | − | 234.457i | 0.217281 | − | 0.239732i | ||||
\(979\) | 163.917 | 0.167434 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 85.2910 | + | 866.025i | 0.0869430 | + | 0.882798i | ||||
\(982\) | −241.265 | −0.245687 | ||||||||
\(983\) | 1663.72i | 1.69249i | 0.532794 | + | 0.846245i | \(0.321142\pi\) | ||||
−0.532794 | + | 0.846245i | \(0.678858\pi\) | |||||||
\(984\) | 229.061 | + | 207.610i | 0.232785 | + | 0.210986i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 423.504i | 0.429517i | ||||||||
\(987\) | −241.545 | + | 266.502i | −0.244726 | + | 0.270012i | ||||
\(988\) | −386.891 | −0.391590 | ||||||||
\(989\) | 599.857i | 0.606529i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 873.134 | 0.881064 | 0.440532 | − | 0.897737i | \(-0.354790\pi\) | ||||
0.440532 | + | 0.897737i | \(0.354790\pi\) | |||||||
\(992\) | − | 242.747i | − | 0.244705i | ||||||
\(993\) | 223.947 | + | 202.975i | 0.225525 | + | 0.204405i | ||||
\(994\) | −425.891 | −0.428462 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −308.629 | + | 340.518i | −0.309869 | + | 0.341886i | ||||
\(997\) | 1548.17 | 1.55283 | 0.776413 | − | 0.630224i | \(-0.217037\pi\) | ||||
0.776413 | + | 0.630224i | \(0.217037\pi\) | |||||||
\(998\) | − | 1365.16i | − | 1.36789i | ||||||
\(999\) | −291.517 | + | 393.058i | −0.291809 | + | 0.393452i |
(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 | 1050.3.e.e.701.6 | 24 | ||
3.2 | odd | 2 | inner | 1050.3.e.e.701.8 | 24 | ||
5.2 | odd | 4 | 210.3.c.a.29.21 | yes | 24 | ||
5.3 | odd | 4 | 210.3.c.a.29.4 | yes | 24 | ||
5.4 | even | 2 | inner | 1050.3.e.e.701.7 | 24 | ||
15.2 | even | 4 | 210.3.c.a.29.3 | ✓ | 24 | ||
15.8 | even | 4 | 210.3.c.a.29.22 | yes | 24 | ||
15.14 | odd | 2 | inner | 1050.3.e.e.701.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.c.a.29.3 | ✓ | 24 | 15.2 | even | 4 | ||
210.3.c.a.29.4 | yes | 24 | 5.3 | odd | 4 | ||
210.3.c.a.29.21 | yes | 24 | 5.2 | odd | 4 | ||
210.3.c.a.29.22 | yes | 24 | 15.8 | even | 4 | ||
1050.3.e.e.701.5 | 24 | 15.14 | odd | 2 | inner | ||
1050.3.e.e.701.6 | 24 | 1.1 | even | 1 | trivial | ||
1050.3.e.e.701.7 | 24 | 5.4 | even | 2 | inner | ||
1050.3.e.e.701.8 | 24 | 3.2 | odd | 2 | inner |