Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,5,Mod(163,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.163");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.d (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: | \(33.4918680392\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 163.1 | ||
Character | \(\chi\) | \(=\) | 324.163 |
Dual form | 324.5.d.e.163.2 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.99662 | − | 0.164298i | −0.999156 | − | 0.0410745i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 15.9460 | + | 1.31328i | 0.996626 | + | 0.0820797i | ||||
\(5\) | −29.7694 | −1.19078 | −0.595388 | − | 0.803438i | \(-0.703002\pi\) | ||||
−0.595388 | + | 0.803438i | \(0.703002\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 59.8988i | − | 1.22242i | −0.791467 | − | 0.611212i | \(-0.790682\pi\) | ||
0.791467 | − | 0.611212i | \(-0.209318\pi\) | |||||||
\(8\) | −63.5145 | − | 7.86857i | −0.992413 | − | 0.122946i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 118.977 | + | 4.89106i | 1.18977 | + | 0.0489106i | ||||
\(11\) | − | 225.488i | − | 1.86353i | −0.363057 | − | 0.931767i | \(-0.618267\pi\) | ||
0.363057 | − | 0.931767i | \(-0.381733\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 171.765 | 1.01636 | 0.508180 | − | 0.861251i | \(-0.330318\pi\) | ||||
0.508180 | + | 0.861251i | \(0.330318\pi\) | |||||||
\(14\) | −9.84126 | + | 239.393i | −0.0502105 | + | 1.22139i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 252.551 | + | 41.8830i | 0.986526 | + | 0.163606i | ||||
\(17\) | 99.0725 | 0.342812 | 0.171406 | − | 0.985201i | \(-0.445169\pi\) | ||||
0.171406 | + | 0.985201i | \(0.445169\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 169.267i | − | 0.468884i | −0.972130 | − | 0.234442i | \(-0.924674\pi\) | ||
0.972130 | − | 0.234442i | \(-0.0753262\pi\) | |||||||
\(20\) | −474.703 | − | 39.0954i | −1.18676 | − | 0.0977386i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −37.0472 | + | 901.189i | −0.0765438 | + | 1.86196i | ||||
\(23\) | 358.855i | 0.678364i | 0.940721 | + | 0.339182i | \(0.110150\pi\) | ||||
−0.940721 | + | 0.339182i | \(0.889850\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 261.217 | 0.417948 | ||||||||
\(26\) | −686.480 | − | 28.2206i | −1.01550 | − | 0.0417465i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 78.6636 | − | 955.147i | 0.100336 | − | 1.21830i | ||||
\(29\) | 18.0327 | 0.0214420 | 0.0107210 | − | 0.999943i | \(-0.496587\pi\) | ||||
0.0107210 | + | 0.999943i | \(0.496587\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 775.841i | − | 0.807326i | −0.914908 | − | 0.403663i | \(-0.867737\pi\) | ||
0.914908 | − | 0.403663i | \(-0.132263\pi\) | |||||||
\(32\) | −1002.47 | − | 208.884i | −0.978973 | − | 0.203989i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −395.956 | − | 16.2774i | −0.342522 | − | 0.0140808i | ||||
\(35\) | 1783.15i | 1.45563i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 609.762 | 0.445407 | 0.222703 | − | 0.974886i | \(-0.428512\pi\) | ||||
0.222703 | + | 0.974886i | \(0.428512\pi\) | |||||||
\(38\) | −27.8102 | + | 676.496i | −0.0192592 | + | 0.468488i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1890.79 | + | 234.243i | 1.18174 | + | 0.146402i | ||||
\(41\) | 413.091 | 0.245741 | 0.122871 | − | 0.992423i | \(-0.460790\pi\) | ||||
0.122871 | + | 0.992423i | \(0.460790\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 306.571i | 0.165804i | 0.996558 | + | 0.0829019i | \(0.0264188\pi\) | ||||
−0.996558 | + | 0.0829019i | \(0.973581\pi\) | |||||||
\(44\) | 296.127 | − | 3595.63i | 0.152958 | − | 1.85725i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 58.9591 | − | 1434.21i | 0.0278635 | − | 0.677791i | ||||
\(47\) | − | 2621.85i | − | 1.18689i | −0.804873 | − | 0.593447i | \(-0.797767\pi\) | ||
0.804873 | − | 0.593447i | \(-0.202233\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1186.86 | −0.494321 | ||||||||
\(50\) | −1043.99 | − | 42.9175i | −0.417595 | − | 0.0171670i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2738.96 | + | 225.575i | 1.01293 | + | 0.0834226i | ||||
\(53\) | −2034.30 | −0.724209 | −0.362104 | − | 0.932138i | \(-0.617942\pi\) | ||||
−0.362104 | + | 0.932138i | \(0.617942\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6712.63i | 2.21905i | ||||||||
\(56\) | −471.318 | + | 3804.44i | −0.150293 | + | 1.21315i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −72.0699 | − | 2.96274i | −0.0214239 | − | 0.000880719i | ||||
\(59\) | − | 2598.63i | − | 0.746520i | −0.927727 | − | 0.373260i | \(-0.878240\pi\) | ||
0.927727 | − | 0.373260i | \(-0.121760\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1417.36 | −0.380909 | −0.190455 | − | 0.981696i | \(-0.560996\pi\) | ||||
−0.190455 | + | 0.981696i | \(0.560996\pi\) | |||||||
\(62\) | −127.469 | + | 3100.74i | −0.0331606 | + | 0.806645i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3972.17 | + | 999.536i | 0.969768 | + | 0.244027i | ||||
\(65\) | −5113.34 | −1.21026 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5995.13i | − | 1.33552i | −0.744379 | − | 0.667758i | \(-0.767254\pi\) | ||
0.744379 | − | 0.667758i | \(-0.232746\pi\) | |||||||
\(68\) | 1579.81 | + | 130.110i | 0.341655 | + | 0.0281379i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 292.968 | − | 7126.58i | 0.0597895 | − | 1.45441i | ||||
\(71\) | 1239.44i | 0.245872i | 0.992415 | + | 0.122936i | \(0.0392310\pi\) | ||||
−0.992415 | + | 0.122936i | \(0.960769\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5060.60 | −0.949633 | −0.474817 | − | 0.880085i | \(-0.657486\pi\) | ||||
−0.474817 | + | 0.880085i | \(0.657486\pi\) | |||||||
\(74\) | −2436.99 | − | 100.183i | −0.445031 | − | 0.0182949i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 222.294 | − | 2699.13i | 0.0384858 | − | 0.467301i | ||||
\(77\) | −13506.4 | −2.27803 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1889.08i | 0.302688i | 0.988481 | + | 0.151344i | \(0.0483601\pi\) | ||||
−0.988481 | + | 0.151344i | \(0.951640\pi\) | |||||||
\(80\) | −7518.28 | − | 1246.83i | −1.17473 | − | 0.194818i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1650.97 | − | 67.8700i | −0.245534 | − | 0.0100937i | ||||
\(83\) | 6733.68i | 0.977455i | 0.872437 | + | 0.488727i | \(0.162539\pi\) | ||||
−0.872437 | + | 0.488727i | \(0.837461\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2949.33 | −0.408212 | ||||||||
\(86\) | 50.3691 | − | 1225.25i | 0.00681031 | − | 0.165664i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1774.27 | + | 14321.7i | −0.229115 | + | 1.84940i | ||||
\(89\) | −9436.67 | −1.19135 | −0.595674 | − | 0.803226i | \(-0.703115\pi\) | ||||
−0.595674 | + | 0.803226i | \(0.703115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 10288.5i | − | 1.24242i | ||||||
\(92\) | −471.275 | + | 5722.30i | −0.0556799 | + | 0.676075i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −430.765 | + | 10478.6i | −0.0487511 | + | 1.18589i | ||||
\(95\) | 5038.98i | 0.558335i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14595.8 | −1.55126 | −0.775631 | − | 0.631186i | \(-0.782568\pi\) | ||||
−0.775631 | + | 0.631186i | \(0.782568\pi\) | |||||||
\(98\) | 4743.45 | + | 195.000i | 0.493904 | + | 0.0203040i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4165.37 | + | 343.050i | 0.416537 | + | 0.0343050i | ||||
\(101\) | −6461.42 | −0.633411 | −0.316705 | − | 0.948524i | \(-0.602577\pi\) | ||||
−0.316705 | + | 0.948524i | \(0.602577\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16156.1i | 1.52286i | 0.648244 | + | 0.761432i | \(0.275504\pi\) | ||||
−0.648244 | + | 0.761432i | \(0.724496\pi\) | |||||||
\(104\) | −10909.6 | − | 1351.54i | −1.00865 | − | 0.124958i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8130.34 | + | 334.232i | 0.723597 | + | 0.0297465i | ||||
\(107\) | − | 3065.27i | − | 0.267732i | −0.990999 | − | 0.133866i | \(-0.957261\pi\) | ||
0.990999 | − | 0.133866i | \(-0.0427392\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17728.8 | −1.49220 | −0.746098 | − | 0.665836i | \(-0.768075\pi\) | ||||
−0.746098 | + | 0.665836i | \(0.768075\pi\) | |||||||
\(110\) | 1102.87 | − | 26827.9i | 0.0911465 | − | 2.21718i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2508.74 | − | 15127.5i | 0.199995 | − | 1.20595i | ||||
\(113\) | 14793.1 | 1.15852 | 0.579259 | − | 0.815143i | \(-0.303342\pi\) | ||||
0.579259 | + | 0.815143i | \(0.303342\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 10682.9i | − | 0.807780i | ||||||
\(116\) | 287.550 | + | 23.6819i | 0.0213696 | + | 0.00175995i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −426.951 | + | 10385.8i | −0.0306629 | + | 0.745890i | ||||
\(119\) | − | 5934.32i | − | 0.419061i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −36203.7 | −2.47276 | ||||||||
\(122\) | 5664.67 | + | 232.870i | 0.380588 | + | 0.0156457i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1018.89 | − | 12371.6i | 0.0662651 | − | 0.804602i | ||||
\(125\) | 10829.6 | 0.693094 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 18478.7i | − | 1.14568i | −0.819667 | − | 0.572841i | \(-0.805841\pi\) | ||
0.819667 | − | 0.572841i | \(-0.194159\pi\) | |||||||
\(128\) | −15711.1 | − | 4647.39i | −0.958927 | − | 0.283654i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 20436.1 | + | 840.112i | 1.20924 | + | 0.0497108i | ||||
\(131\) | 8320.71i | 0.484862i | 0.970169 | + | 0.242431i | \(0.0779447\pi\) | ||||
−0.970169 | + | 0.242431i | \(0.922055\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10138.9 | −0.573175 | ||||||||
\(134\) | −984.989 | + | 23960.3i | −0.0548557 | + | 1.33439i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6292.54 | − | 779.559i | −0.340211 | − | 0.0421474i | ||||
\(137\) | 21406.7 | 1.14054 | 0.570268 | − | 0.821459i | \(-0.306840\pi\) | ||||
0.570268 | + | 0.821459i | \(0.306840\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18225.3i | 0.943292i | 0.881788 | + | 0.471646i | \(0.156340\pi\) | ||||
−0.881788 | + | 0.471646i | \(0.843660\pi\) | |||||||
\(140\) | −2341.77 | + | 28434.1i | −0.119478 | + | 1.45072i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 203.638 | − | 4953.59i | 0.0100991 | − | 0.245665i | ||||
\(143\) | − | 38730.8i | − | 1.89402i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −536.823 | −0.0255326 | ||||||||
\(146\) | 20225.3 | + | 831.446i | 0.948832 | + | 0.0390057i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9723.27 | + | 800.785i | 0.443904 | + | 0.0365589i | ||||
\(149\) | 16239.4 | 0.731473 | 0.365736 | − | 0.930718i | \(-0.380817\pi\) | ||||
0.365736 | + | 0.930718i | \(0.380817\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24526.3i | 1.07567i | 0.843050 | + | 0.537835i | \(0.180758\pi\) | ||||
−0.843050 | + | 0.537835i | \(0.819242\pi\) | |||||||
\(152\) | −1331.89 | + | 10750.9i | −0.0576476 | + | 0.465326i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 53980.1 | + | 2219.08i | 2.27611 | + | 0.0935690i | ||||
\(155\) | 23096.3i | 0.961345i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 39654.1 | 1.60875 | 0.804375 | − | 0.594122i | \(-0.202500\pi\) | ||||
0.804375 | + | 0.594122i | \(0.202500\pi\) | |||||||
\(158\) | 310.372 | − | 7549.92i | 0.0124328 | − | 0.302432i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 29842.9 | + | 6218.36i | 1.16574 | + | 0.242905i | ||||
\(161\) | 21494.9 | 0.829248 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 25324.6i | 0.953162i | 0.879130 | + | 0.476581i | \(0.158124\pi\) | ||||
−0.879130 | + | 0.476581i | \(0.841876\pi\) | |||||||
\(164\) | 6587.15 | + | 542.502i | 0.244912 | + | 0.0201704i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1106.33 | − | 26912.0i | 0.0401485 | − | 0.976630i | ||||
\(167\) | − | 27839.5i | − | 0.998226i | −0.866537 | − | 0.499113i | \(-0.833659\pi\) | ||
0.866537 | − | 0.499113i | \(-0.166341\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 942.163 | 0.0329877 | ||||||||
\(170\) | 11787.4 | + | 484.569i | 0.407867 | + | 0.0167671i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −402.612 | + | 4888.59i | −0.0136091 | + | 0.165244i | ||||
\(173\) | 22054.5 | 0.736895 | 0.368448 | − | 0.929648i | \(-0.379889\pi\) | ||||
0.368448 | + | 0.929648i | \(0.379889\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 15646.6i | − | 0.510909i | ||||||
\(176\) | 9444.10 | − | 56947.0i | 0.304885 | − | 1.83842i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 37714.8 | + | 1550.43i | 1.19034 | + | 0.0489341i | ||||
\(179\) | 52513.4i | 1.63895i | 0.573118 | + | 0.819473i | \(0.305734\pi\) | ||||
−0.573118 | + | 0.819473i | \(0.694266\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7223.25 | −0.220483 | −0.110242 | − | 0.993905i | \(-0.535162\pi\) | ||||
−0.110242 | + | 0.993905i | \(0.535162\pi\) | |||||||
\(182\) | −1690.38 | + | 41119.3i | −0.0510319 | + | 1.24137i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2823.67 | − | 22792.4i | 0.0834024 | − | 0.673217i | ||||
\(185\) | −18152.2 | −0.530380 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 22339.6i | − | 0.638841i | ||||||
\(188\) | 3443.21 | − | 41808.1i | 0.0974200 | − | 1.18289i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 827.894 | − | 20138.9i | 0.0229334 | − | 0.557864i | ||||
\(191\) | 10582.8i | 0.290090i | 0.989425 | + | 0.145045i | \(0.0463326\pi\) | ||||
−0.989425 | + | 0.145045i | \(0.953667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −39086.5 | −1.04933 | −0.524665 | − | 0.851309i | \(-0.675809\pi\) | ||||
−0.524665 | + | 0.851309i | \(0.675809\pi\) | |||||||
\(194\) | 58334.0 | + | 2398.07i | 1.54995 | + | 0.0637174i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −18925.7 | − | 1558.68i | −0.492653 | − | 0.0405737i | ||||
\(197\) | 10820.0 | 0.278802 | 0.139401 | − | 0.990236i | \(-0.455482\pi\) | ||||
0.139401 | + | 0.990236i | \(0.455482\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 807.389i | − | 0.0203881i | −0.999948 | − | 0.0101940i | \(-0.996755\pi\) | ||
0.999948 | − | 0.0101940i | \(-0.00324492\pi\) | |||||||
\(200\) | −16591.1 | − | 2055.41i | −0.414777 | − | 0.0513852i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 25823.9 | + | 1061.60i | 0.632876 | + | 0.0260171i | ||||
\(203\) | − | 1080.14i | − | 0.0262112i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12297.5 | −0.292623 | ||||||||
\(206\) | 2654.41 | − | 64569.8i | 0.0625510 | − | 1.52158i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 43379.3 | + | 7194.03i | 1.00267 | + | 0.166282i | ||||
\(209\) | −38167.6 | −0.873780 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 60834.1i | − | 1.36641i | −0.730225 | − | 0.683207i | \(-0.760585\pi\) | ||
0.730225 | − | 0.683207i | \(-0.239415\pi\) | |||||||
\(212\) | −32439.0 | − | 2671.60i | −0.721765 | − | 0.0594429i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −503.618 | + | 12250.7i | −0.0109970 | + | 0.267506i | ||||
\(215\) | − | 9126.44i | − | 0.197435i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −46471.9 | −0.986895 | ||||||||
\(218\) | 70855.3 | + | 2912.81i | 1.49094 | + | 0.0612913i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8815.54 | + | 107040.i | −0.182139 | + | 2.21156i | ||||
\(221\) | 17017.2 | 0.348420 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10729.6i | 0.215762i | 0.994164 | + | 0.107881i | \(0.0344065\pi\) | ||||
−0.994164 | + | 0.107881i | \(0.965594\pi\) | |||||||
\(224\) | −12511.9 | + | 60046.6i | −0.249361 | + | 1.19672i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −59122.5 | − | 2430.48i | −1.15754 | − | 0.0475856i | ||||
\(227\) | − | 75731.3i | − | 1.46968i | −0.678239 | − | 0.734842i | \(-0.737256\pi\) | ||
0.678239 | − | 0.734842i | \(-0.262744\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −53366.6 | −1.01765 | −0.508825 | − | 0.860870i | \(-0.669920\pi\) | ||||
−0.508825 | + | 0.860870i | \(0.669920\pi\) | |||||||
\(230\) | −1755.18 | + | 42695.5i | −0.0331792 | + | 0.807098i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1145.34 | − | 141.892i | −0.0212793 | − | 0.00263621i | ||||
\(233\) | −56485.5 | −1.04046 | −0.520230 | − | 0.854026i | \(-0.674154\pi\) | ||||
−0.520230 | + | 0.854026i | \(0.674154\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 78050.9i | 1.41333i | ||||||||
\(236\) | 3412.72 | − | 41437.9i | 0.0612741 | − | 0.744001i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −974.998 | + | 23717.3i | −0.0172127 | + | 0.418707i | ||||
\(239\) | 47991.4i | 0.840171i | 0.907484 | + | 0.420086i | \(0.138000\pi\) | ||||
−0.907484 | + | 0.420086i | \(0.862000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −64150.1 | −1.10449 | −0.552247 | − | 0.833681i | \(-0.686229\pi\) | ||||
−0.552247 | + | 0.833681i | \(0.686229\pi\) | |||||||
\(242\) | 144692. | + | 5948.19i | 2.47067 | + | 0.101567i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −22601.3 | − | 1861.39i | −0.379624 | − | 0.0312649i | ||||
\(245\) | 35332.2 | 0.588625 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 29074.1i | − | 0.476555i | ||||||
\(248\) | −6104.76 | + | 49277.1i | −0.0992579 | + | 0.801201i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −43281.8 | − | 1779.28i | −0.692509 | − | 0.0284685i | ||||
\(251\) | 65230.8i | 1.03539i | 0.855564 | + | 0.517696i | \(0.173210\pi\) | ||||
−0.855564 | + | 0.517696i | \(0.826790\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 80917.3 | 1.26415 | ||||||||
\(254\) | −3036.02 | + | 73852.4i | −0.0470583 | + | 1.14471i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 62027.6 | + | 21155.2i | 0.946466 | + | 0.322802i | ||||
\(257\) | 43315.8 | 0.655813 | 0.327907 | − | 0.944710i | \(-0.393657\pi\) | ||||
0.327907 | + | 0.944710i | \(0.393657\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 36524.0i | − | 0.544476i | ||||||
\(260\) | −81537.3 | − | 6715.22i | −1.20617 | − | 0.0993376i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1367.08 | − | 33254.7i | 0.0199155 | − | 0.484452i | ||||
\(263\) | − | 84805.2i | − | 1.22606i | −0.790061 | − | 0.613029i | \(-0.789951\pi\) | ||
0.790061 | − | 0.613029i | \(-0.210049\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 60560.0 | 0.862370 | ||||||||
\(266\) | 40521.3 | + | 1665.80i | 0.572691 | + | 0.0235429i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7873.26 | − | 95598.4i | 0.109619 | − | 1.33101i | ||||
\(269\) | 66685.5 | 0.921567 | 0.460784 | − | 0.887513i | \(-0.347568\pi\) | ||||
0.460784 | + | 0.887513i | \(0.347568\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 122426.i | − | 1.66700i | −0.552516 | − | 0.833502i | \(-0.686332\pi\) | ||
0.552516 | − | 0.833502i | \(-0.313668\pi\) | |||||||
\(272\) | 25020.8 | + | 4149.46i | 0.338192 | + | 0.0560859i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −85554.5 | − | 3517.08i | −1.13957 | − | 0.0468469i | ||||
\(275\) | − | 58901.3i | − | 0.778860i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 137452. | 1.79140 | 0.895699 | − | 0.444661i | \(-0.146676\pi\) | ||||
0.895699 | + | 0.444661i | \(0.146676\pi\) | |||||||
\(278\) | 2994.39 | − | 72839.8i | 0.0387453 | − | 0.942496i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 14030.8 | − | 113256.i | 0.178965 | − | 1.44459i | ||||
\(281\) | −14003.2 | −0.177344 | −0.0886718 | − | 0.996061i | \(-0.528262\pi\) | ||||
−0.0886718 | + | 0.996061i | \(0.528262\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 115048.i | 1.43650i | 0.695786 | + | 0.718249i | \(0.255056\pi\) | ||||
−0.695786 | + | 0.718249i | \(0.744944\pi\) | |||||||
\(284\) | −1627.73 | + | 19764.2i | −0.0201811 | + | 0.245043i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6363.41 | + | 154793.i | −0.0777961 | + | 1.89242i | ||||
\(287\) | − | 24743.6i | − | 0.300400i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −73705.6 | −0.882480 | ||||||||
\(290\) | 2145.48 | + | 88.1990i | 0.0255110 | + | 0.00104874i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −80696.3 | − | 6645.96i | −0.946429 | − | 0.0779457i | ||||
\(293\) | −28518.6 | −0.332195 | −0.166097 | − | 0.986109i | \(-0.553117\pi\) | ||||
−0.166097 | + | 0.986109i | \(0.553117\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 77359.8i | 0.888938i | ||||||||
\(296\) | −38728.7 | − | 4797.95i | −0.442027 | − | 0.0547611i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −64902.9 | − | 2668.11i | −0.730856 | − | 0.0300449i | ||||
\(299\) | 61638.6i | 0.689462i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18363.2 | 0.202682 | ||||||||
\(302\) | 4029.63 | − | 98022.5i | 0.0441826 | − | 1.07476i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7089.41 | − | 42748.5i | 0.0767120 | − | 0.462566i | ||||
\(305\) | 42194.0 | 0.453577 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 115338.i | 1.22376i | 0.790952 | + | 0.611879i | \(0.209586\pi\) | ||||
−0.790952 | + | 0.611879i | \(0.790414\pi\) | |||||||
\(308\) | −215374. | − | 17737.7i | −2.27034 | − | 0.186980i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3794.68 | − | 92307.3i | 0.0394868 | − | 0.960534i | ||||
\(311\) | 98803.8i | 1.02153i | 0.859719 | + | 0.510767i | \(0.170639\pi\) | ||||
−0.859719 | + | 0.510767i | \(0.829361\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −74132.1 | −0.756690 | −0.378345 | − | 0.925665i | \(-0.623507\pi\) | ||||
−0.378345 | + | 0.925665i | \(0.623507\pi\) | |||||||
\(314\) | −158482. | − | 6515.09i | −1.60739 | − | 0.0660786i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2480.88 | + | 30123.2i | −0.0248445 | + | 0.301667i | ||||
\(317\) | 2114.59 | 0.0210430 | 0.0105215 | − | 0.999945i | \(-0.496651\pi\) | ||||
0.0105215 | + | 0.999945i | \(0.496651\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4066.15i | − | 0.0399579i | ||||||
\(320\) | −118249. | − | 29755.6i | −1.15478 | − | 0.290582i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −85907.2 | − | 3531.58i | −0.828549 | − | 0.0340610i | ||||
\(323\) | − | 16769.7i | − | 0.160739i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 44868.0 | 0.424785 | ||||||||
\(326\) | 4160.78 | − | 101213.i | 0.0391507 | − | 0.952358i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −26237.2 | − | 3250.43i | −0.243877 | − | 0.0302130i | ||||
\(329\) | −157046. | −1.45089 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14242.0i | 0.129992i | 0.997886 | + | 0.0649960i | \(0.0207034\pi\) | ||||
−0.997886 | + | 0.0649960i | \(0.979297\pi\) | |||||||
\(332\) | −8843.19 | + | 107375.i | −0.0802292 | + | 0.974156i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4573.98 | + | 111264.i | −0.0410017 | + | 0.997384i | ||||
\(335\) | 178471.i | 1.59030i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 75423.6 | 0.664121 | 0.332061 | − | 0.943258i | \(-0.392256\pi\) | ||||
0.332061 | + | 0.943258i | \(0.392256\pi\) | |||||||
\(338\) | −3765.47 | − | 154.796i | −0.0329599 | − | 0.00135496i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −47030.1 | − | 3873.28i | −0.406834 | − | 0.0335059i | ||||
\(341\) | −174942. | −1.50448 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 72725.3i | − | 0.618155i | ||||||
\(344\) | 2412.28 | − | 19471.7i | 0.0203850 | − | 0.164546i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −88143.7 | − | 3623.52i | −0.736274 | − | 0.0302676i | ||||
\(347\) | − | 148440.i | − | 1.23280i | −0.787432 | − | 0.616401i | \(-0.788590\pi\) | ||
0.787432 | − | 0.616401i | \(-0.211410\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23330.9 | −0.191549 | −0.0957745 | − | 0.995403i | \(-0.530533\pi\) | ||||
−0.0957745 | + | 0.995403i | \(0.530533\pi\) | |||||||
\(350\) | −2570.71 | + | 62533.6i | −0.0209854 | + | 0.510478i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −47100.8 | + | 226044.i | −0.380140 | + | 1.82435i | ||||
\(353\) | −19374.4 | −0.155482 | −0.0777409 | − | 0.996974i | \(-0.524771\pi\) | ||||
−0.0777409 | + | 0.996974i | \(0.524771\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 36897.5i | − | 0.292779i | ||||||
\(356\) | −150477. | − | 12393.0i | −1.18733 | − | 0.0977856i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8627.86 | − | 209877.i | 0.0673189 | − | 1.63756i | ||||
\(359\) | − | 139927.i | − | 1.08571i | −0.839827 | − | 0.542854i | \(-0.817344\pi\) | ||
0.839827 | − | 0.542854i | \(-0.182656\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 101670. | 0.780148 | ||||||||
\(362\) | 28868.6 | + | 1186.77i | 0.220297 | + | 0.00905625i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13511.6 | − | 164061.i | 0.101978 | − | 1.23823i | ||||
\(365\) | 150651. | 1.13080 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 91572.9i | − | 0.679884i | −0.940446 | − | 0.339942i | \(-0.889593\pi\) | ||
0.940446 | − | 0.339942i | \(-0.110407\pi\) | |||||||
\(368\) | −15029.9 | + | 90628.9i | −0.110984 | + | 0.669224i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 72547.7 | + | 2982.38i | 0.529932 | + | 0.0217851i | ||||
\(371\) | 121852.i | 0.885290i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 85580.8 | 0.615118 | 0.307559 | − | 0.951529i | \(-0.400488\pi\) | ||||
0.307559 | + | 0.951529i | \(0.400488\pi\) | |||||||
\(374\) | −3670.36 | + | 89283.1i | −0.0262401 | + | 0.638302i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −20630.2 | + | 166525.i | −0.145924 | + | 1.17789i | ||||
\(377\) | 3097.38 | 0.0217928 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 39838.1i | − | 0.277345i | −0.990338 | − | 0.138672i | \(-0.955716\pi\) | ||
0.990338 | − | 0.138672i | \(-0.0442835\pi\) | |||||||
\(380\) | −6617.57 | + | 80351.6i | −0.0458280 | + | 0.556451i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1738.73 | − | 42295.3i | 0.0119153 | − | 0.289845i | ||||
\(383\) | 170684.i | 1.16357i | 0.813341 | + | 0.581787i | \(0.197646\pi\) | ||||
−0.813341 | + | 0.581787i | \(0.802354\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 402078. | 2.71262 | ||||||||
\(386\) | 156214. | + | 6421.84i | 1.04844 | + | 0.0431007i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −232745. | − | 19168.3i | −1.54603 | − | 0.127327i | ||||
\(389\) | −215815. | −1.42621 | −0.713103 | − | 0.701059i | \(-0.752711\pi\) | ||||
−0.713103 | + | 0.701059i | \(0.752711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 35552.6i | 0.232551i | ||||||||
\(392\) | 75383.0 | + | 9338.92i | 0.490570 | + | 0.0607750i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −43243.6 | − | 1777.71i | −0.278567 | − | 0.0114517i | ||||
\(395\) | − | 56236.6i | − | 0.360434i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 292553. | 1.85620 | 0.928098 | − | 0.372336i | \(-0.121443\pi\) | ||||
0.928098 | + | 0.372336i | \(0.121443\pi\) | |||||||
\(398\) | −132.652 | + | 3226.83i | −0.000837431 | + | 0.0203709i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 65970.6 | + | 10940.6i | 0.412316 | + | 0.0683786i | ||||
\(401\) | −204314. | −1.27060 | −0.635300 | − | 0.772266i | \(-0.719123\pi\) | ||||
−0.635300 | + | 0.772266i | \(0.719123\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 133262.i | − | 0.820534i | ||||||
\(404\) | −103034. | − | 8485.63i | −0.631274 | − | 0.0519902i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −177.464 | + | 4316.90i | −0.00107661 | + | 0.0261891i | ||||
\(407\) | − | 137494.i | − | 0.830030i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34728.8 | 0.207607 | 0.103804 | − | 0.994598i | \(-0.466899\pi\) | ||||
0.103804 | + | 0.994598i | \(0.466899\pi\) | |||||||
\(410\) | 49148.3 | + | 2020.45i | 0.292376 | + | 0.0120193i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −21217.4 | + | 257625.i | −0.124996 | + | 1.51773i | ||||
\(413\) | −155655. | −0.912564 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 200458.i | − | 1.16393i | ||||||
\(416\) | −172189. | − | 35879.0i | −0.994989 | − | 0.207326i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 152542. | + | 6270.87i | 0.873043 | + | 0.0358901i | ||||
\(419\) | − | 320640.i | − | 1.82637i | −0.407541 | − | 0.913187i | \(-0.633614\pi\) | ||
0.407541 | − | 0.913187i | \(-0.366386\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 135771. | 0.766028 | 0.383014 | − | 0.923743i | \(-0.374886\pi\) | ||||
0.383014 | + | 0.923743i | \(0.374886\pi\) | |||||||
\(422\) | −9994.93 | + | 243131.i | −0.0561248 | + | 1.36526i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 129208. | + | 16007.0i | 0.718714 | + | 0.0890388i | ||||
\(425\) | 25879.5 | 0.143277 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 84898.3i | 0.465632i | ||||||||
\(428\) | 4025.54 | − | 48878.8i | 0.0219754 | − | 0.266829i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1499.46 | + | 36474.9i | −0.00810955 | + | 0.197268i | ||||
\(431\) | − | 31343.0i | − | 0.168728i | −0.996435 | − | 0.0843638i | \(-0.973114\pi\) | ||
0.996435 | − | 0.0843638i | \(-0.0268858\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 101022. | 0.538815 | 0.269407 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269407 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(434\) | 185731. | + | 7635.25i | 0.986062 | + | 0.0405363i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −282704. | − | 23282.8i | −1.48716 | − | 0.122479i | ||||
\(437\) | 60742.2 | 0.318074 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 181972.i | 0.944227i | 0.881538 | + | 0.472113i | \(0.156509\pi\) | ||||
−0.881538 | + | 0.472113i | \(0.843491\pi\) | |||||||
\(440\) | 52818.8 | − | 426349.i | 0.272824 | − | 2.20222i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −68011.3 | − | 2795.89i | −0.348126 | − | 0.0143112i | ||||
\(443\) | − | 37188.8i | − | 0.189498i | −0.995501 | − | 0.0947490i | \(-0.969795\pi\) | ||
0.995501 | − | 0.0947490i | \(-0.0302049\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 280924. | 1.41863 | ||||||||
\(446\) | 1762.85 | − | 42882.2i | 0.00886231 | − | 0.215580i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 59871.0 | − | 237928.i | 0.298305 | − | 1.18547i | ||||
\(449\) | 20385.0 | 0.101115 | 0.0505577 | − | 0.998721i | \(-0.483900\pi\) | ||||
0.0505577 | + | 0.998721i | \(0.483900\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 93146.9i | − | 0.457947i | ||||||
\(452\) | 235891. | + | 19427.4i | 1.15461 | + | 0.0950909i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12442.5 | + | 302670.i | −0.0603666 | + | 1.46844i | ||||
\(455\) | 306283.i | 1.47945i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −279658. | −1.33904 | −0.669521 | − | 0.742793i | \(-0.733501\pi\) | ||||
−0.669521 | + | 0.742793i | \(0.733501\pi\) | |||||||
\(458\) | 213286. | + | 8768.03i | 1.01679 | + | 0.0417995i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14029.6 | − | 170349.i | 0.0663023 | − | 0.805054i | ||||
\(461\) | 160597. | 0.755675 | 0.377838 | − | 0.925872i | \(-0.376668\pi\) | ||||
0.377838 | + | 0.925872i | \(0.376668\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 99153.6i | 0.462537i | 0.972890 | + | 0.231268i | \(0.0742876\pi\) | ||||
−0.972890 | + | 0.231268i | \(0.925712\pi\) | |||||||
\(464\) | 4554.17 | + | 755.264i | 0.0211531 | + | 0.00350803i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 225752. | + | 9280.47i | 1.03958 | + | 0.0427364i | ||||
\(467\) | 278790.i | 1.27833i | 0.769068 | + | 0.639167i | \(0.220721\pi\) | ||||
−0.769068 | + | 0.639167i | \(0.779279\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −359101. | −1.63257 | ||||||||
\(470\) | 12823.6 | − | 311940.i | 0.0580517 | − | 1.41213i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −20447.5 | + | 165051.i | −0.0917819 | + | 0.740856i | ||||
\(473\) | 69128.0 | 0.308981 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 44215.5i | − | 0.195969i | ||||||
\(476\) | 7793.40 | − | 94628.8i | 0.0343964 | − | 0.417647i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7884.90 | − | 191804.i | 0.0345096 | − | 0.839462i | ||||
\(479\) | 31991.6i | 0.139433i | 0.997567 | + | 0.0697163i | \(0.0222094\pi\) | ||||
−0.997567 | + | 0.0697163i | \(0.977791\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 104736. | 0.452693 | ||||||||
\(482\) | 256384. | + | 10539.7i | 1.10356 | + | 0.0453666i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −577304. | − | 47545.4i | −2.46442 | − | 0.202963i | ||||
\(485\) | 434509. | 1.84721 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 346823.i | 1.46235i | 0.682192 | + | 0.731173i | \(0.261027\pi\) | ||||
−0.682192 | + | 0.731173i | \(0.738973\pi\) | |||||||
\(488\) | 90023.0 | + | 11152.6i | 0.378019 | + | 0.0468314i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −141210. | − | 5805.02i | −0.588129 | − | 0.0241775i | ||||
\(491\) | 239982.i | 0.995440i | 0.867338 | + | 0.497720i | \(0.165829\pi\) | ||||
−0.867338 | + | 0.497720i | \(0.834171\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1786.55 | 0.00735056 | ||||||||
\(494\) | −4776.82 | + | 116198.i | −0.0195743 | + | 0.476152i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32494.6 | − | 195939.i | 0.132083 | − | 0.796448i | ||||
\(497\) | 74241.1 | 0.300560 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 341046.i | − | 1.36966i | −0.728705 | − | 0.684828i | \(-0.759877\pi\) | ||
0.728705 | − | 0.684828i | \(-0.240123\pi\) | |||||||
\(500\) | 172689. | + | 14222.2i | 0.690755 | + | 0.0568890i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10717.3 | − | 260703.i | 0.0425283 | − | 1.03452i | ||||
\(503\) | − | 3886.22i | − | 0.0153600i | −0.999971 | − | 0.00768001i | \(-0.997555\pi\) | ||
0.999971 | − | 0.00768001i | \(-0.00244465\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 192353. | 0.754250 | ||||||||
\(506\) | −323396. | − | 13294.6i | −1.26309 | − | 0.0519245i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 24267.6 | − | 294662.i | 0.0940373 | − | 1.14182i | ||||
\(509\) | −197346. | −0.761717 | −0.380858 | − | 0.924633i | \(-0.624371\pi\) | ||||
−0.380858 | + | 0.924633i | \(0.624371\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 303124.i | 1.16085i | ||||||||
\(512\) | −244425. | − | 94740.3i | −0.932409 | − | 0.361405i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −173117. | − | 7116.71i | −0.655260 | − | 0.0269372i | ||||
\(515\) | − | 480957.i | − | 1.81339i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −591195. | −2.21182 | ||||||||
\(518\) | −6000.82 | + | 145973.i | −0.0223641 | + | 0.544016i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 324771. | + | 40234.7i | 1.20108 | + | 0.148797i | ||||
\(521\) | −229165. | −0.844255 | −0.422127 | − | 0.906536i | \(-0.638717\pi\) | ||||
−0.422127 | + | 0.906536i | \(0.638717\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 346673.i | 1.26741i | 0.773575 | + | 0.633705i | \(0.218467\pi\) | ||||
−0.773575 | + | 0.633705i | \(0.781533\pi\) | |||||||
\(524\) | −10927.4 | + | 132682.i | −0.0397973 | + | 0.483226i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13933.3 | + | 338934.i | −0.0503597 | + | 1.22502i | ||||
\(527\) | − | 76864.5i | − | 0.276761i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 151064. | 0.539822 | ||||||||
\(530\) | −242035. | − | 9949.89i | −0.861642 | − | 0.0354215i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −161675. | − | 13315.2i | −0.571241 | − | 0.0470460i | ||||
\(533\) | 70954.5 | 0.249761 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 91251.2i | 0.318809i | ||||||||
\(536\) | −47173.1 | + | 380777.i | −0.164197 | + | 1.32538i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −266517. | − | 10956.3i | −0.920789 | − | 0.0378529i | ||||
\(539\) | 267623.i | 0.921184i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −287354. | −0.981799 | −0.490900 | − | 0.871216i | \(-0.663332\pi\) | ||||
−0.490900 | + | 0.871216i | \(0.663332\pi\) | |||||||
\(542\) | −20114.4 | + | 489293.i | −0.0684714 | + | 1.66560i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −99317.1 | − | 20694.7i | −0.335603 | − | 0.0699296i | ||||
\(545\) | 527776. | 1.77687 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 561865.i | − | 1.87783i | −0.344144 | − | 0.938917i | \(-0.611831\pi\) | ||
0.344144 | − | 0.938917i | \(-0.388169\pi\) | |||||||
\(548\) | 341352. | + | 28112.9i | 1.13669 | + | 0.0936148i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9677.37 | + | 235406.i | −0.0319913 | + | 0.778203i | ||||
\(551\) | − | 3052.34i | − | 0.0100538i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 113153. | 0.370013 | ||||||||
\(554\) | −549345. | − | 22583.1i | −1.78989 | − | 0.0735808i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −23934.9 | + | 290621.i | −0.0774251 | + | 0.940109i | ||||
\(557\) | 393303. | 1.26770 | 0.633850 | − | 0.773456i | \(-0.281474\pi\) | ||||
0.633850 | + | 0.773456i | \(0.281474\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 52658.1i | 0.168516i | ||||||||
\(560\) | −74683.8 | + | 450336.i | −0.238150 | + | 1.43602i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 55965.6 | + | 2300.70i | 0.177194 | + | 0.00728431i | ||||
\(563\) | − | 556412.i | − | 1.75541i | −0.479198 | − | 0.877707i | \(-0.659072\pi\) | ||
0.479198 | − | 0.877707i | \(-0.340928\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −440382. | −1.37954 | ||||||||
\(566\) | 18902.1 | − | 459802.i | 0.0590035 | − | 1.43529i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9752.64 | − | 78722.5i | 0.0302291 | − | 0.244007i | ||||
\(569\) | −182062. | −0.562333 | −0.281167 | − | 0.959659i | \(-0.590721\pi\) | ||||
−0.281167 | + | 0.959659i | \(0.590721\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 219715.i | − | 0.673888i | −0.941525 | − | 0.336944i | \(-0.890607\pi\) | ||
0.941525 | − | 0.336944i | \(-0.109393\pi\) | |||||||
\(572\) | 50864.3 | − | 617603.i | 0.155461 | − | 1.88763i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4065.33 | + | 98891.0i | −0.0123388 | + | 0.300146i | ||||
\(575\) | 93739.0i | 0.283521i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9527.81 | 0.0286181 | 0.0143091 | − | 0.999898i | \(-0.495445\pi\) | ||||
0.0143091 | + | 0.999898i | \(0.495445\pi\) | |||||||
\(578\) | 294574. | + | 12109.7i | 0.881736 | + | 0.0362475i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8560.18 | − | 704.996i | −0.0254464 | − | 0.00209571i | ||||
\(581\) | 403339. | 1.19486 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 458710.i | 1.34959i | ||||||||
\(584\) | 321421. | + | 39819.7i | 0.942429 | + | 0.116754i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 113978. | + | 4685.55i | 0.331914 | + | 0.0136447i | ||||
\(587\) | − | 10333.0i | − | 0.0299882i | −0.999888 | − | 0.0149941i | \(-0.995227\pi\) | ||
0.999888 | − | 0.0149941i | \(-0.00477294\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −131324. | −0.378542 | ||||||||
\(590\) | 12710.1 | − | 309178.i | 0.0365127 | − | 0.888188i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 153996. | + | 25538.7i | 0.439405 | + | 0.0728710i | ||||
\(593\) | −143639. | −0.408473 | −0.204236 | − | 0.978922i | \(-0.565471\pi\) | ||||
−0.204236 | + | 0.978922i | \(0.565471\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 176661.i | 0.499008i | ||||||||
\(596\) | 258954. | + | 21326.9i | 0.729005 | + | 0.0600391i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10127.1 | − | 246346.i | 0.0283193 | − | 0.688880i | ||||
\(599\) | − | 352934.i | − | 0.983649i | −0.870694 | − | 0.491824i | \(-0.836330\pi\) | ||
0.870694 | − | 0.491824i | \(-0.163670\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35467.7 | 0.0981937 | 0.0490969 | − | 0.998794i | \(-0.484366\pi\) | ||||
0.0490969 | + | 0.998794i | \(0.484366\pi\) | |||||||
\(602\) | −73390.9 | − | 3017.04i | −0.202511 | − | 0.00832509i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −32209.8 | + | 391097.i | −0.0882907 | + | 1.07204i | ||||
\(605\) | 1.07776e6 | 2.94450 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 489950.i | − | 1.32976i | −0.746949 | − | 0.664881i | \(-0.768482\pi\) | ||
0.746949 | − | 0.664881i | \(-0.231518\pi\) | |||||||
\(608\) | −35357.2 | + | 169685.i | −0.0956469 | + | 0.459024i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −168634. | − | 6932.40i | −0.453195 | − | 0.0186305i | ||||
\(611\) | − | 450342.i | − | 1.20631i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 284390. | 0.756821 | 0.378410 | − | 0.925638i | \(-0.376471\pi\) | ||||
0.378410 | + | 0.925638i | \(0.376471\pi\) | |||||||
\(614\) | 18949.8 | − | 460962.i | 0.0502653 | − | 1.22272i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 857854. | + | 106276.i | 2.26075 | + | 0.280075i | ||||
\(617\) | −196475. | −0.516103 | −0.258052 | − | 0.966131i | \(-0.583080\pi\) | ||||
−0.258052 | + | 0.966131i | \(0.583080\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 67817.0i | − | 0.176993i | −0.996076 | − | 0.0884967i | \(-0.971794\pi\) | ||
0.996076 | − | 0.0884967i | \(-0.0282063\pi\) | |||||||
\(620\) | −30331.8 | + | 368294.i | −0.0789069 | + | 0.958101i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16233.3 | − | 394882.i | 0.0419590 | − | 1.02067i | ||||
\(623\) | 565245.i | 1.45633i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −485651. | −1.24327 | ||||||||
\(626\) | 296278. | + | 12179.8i | 0.756051 | + | 0.0310807i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 632324. | + | 52076.7i | 1.60332 | + | 0.132046i | ||||
\(629\) | 60410.6 | 0.152691 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 716972.i | − | 1.80071i | −0.435158 | − | 0.900354i | \(-0.643308\pi\) | ||
0.435158 | − | 0.900354i | \(-0.356692\pi\) | |||||||
\(632\) | 14864.3 | − | 119984.i | 0.0372144 | − | 0.300392i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8451.23 | − | 347.423i | −0.0210253 | − | 0.000864332i | ||||
\(635\) | 550100.i | 1.36425i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −203862. | −0.502408 | ||||||||
\(638\) | −668.061 | + | 16250.9i | −0.00164125 | + | 0.0399241i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 467709. | + | 138350.i | 1.14187 | + | 0.337769i | ||||
\(641\) | −642891. | −1.56466 | −0.782332 | − | 0.622861i | \(-0.785970\pi\) | ||||
−0.782332 | + | 0.622861i | \(0.785970\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1531.82i | − | 0.00370498i | −0.999998 | − | 0.00185249i | \(-0.999410\pi\) | ||
0.999998 | − | 0.00185249i | \(-0.000589666\pi\) | |||||||
\(644\) | 342759. | + | 28228.8i | 0.826450 | + | 0.0680645i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2755.23 | + | 67022.2i | −0.00660227 | + | 0.160603i | ||||
\(647\) | − | 106720.i | − | 0.254938i | −0.991843 | − | 0.127469i | \(-0.959315\pi\) | ||
0.991843 | − | 0.127469i | \(-0.0406854\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −585960. | −1.39116 | ||||||||
\(650\) | −179320. | − | 7371.72i | −0.424427 | − | 0.0174479i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −33258.1 | + | 403826.i | −0.0782353 | + | 0.949946i | ||||
\(653\) | −229665. | −0.538603 | −0.269301 | − | 0.963056i | \(-0.586793\pi\) | ||||
−0.269301 | + | 0.963056i | \(0.586793\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 247703.i | − | 0.577362i | ||||||
\(656\) | 104326. | + | 17301.5i | 0.242430 | + | 0.0402046i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 627652. | + | 25802.3i | 1.44966 | + | 0.0595946i | ||||
\(659\) | 390184.i | 0.898460i | 0.893416 | + | 0.449230i | \(0.148302\pi\) | ||||
−0.893416 | + | 0.449230i | \(0.851698\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 446886. | 1.02281 | 0.511403 | − | 0.859341i | \(-0.329126\pi\) | ||||
0.511403 | + | 0.859341i | \(0.329126\pi\) | |||||||
\(662\) | 2339.94 | − | 56920.1i | 0.00533936 | − | 0.129882i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 52984.5 | − | 427686.i | 0.120175 | − | 0.970039i | ||||
\(665\) | 301829. | 0.682523 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6471.12i | 0.0145455i | ||||||||
\(668\) | 36561.0 | − | 443930.i | 0.0819342 | − | 0.994858i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 29322.5 | − | 713283.i | 0.0653208 | − | 1.58896i | ||||
\(671\) | 319598.i | 0.709837i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 339492. | 0.749548 | 0.374774 | − | 0.927116i | \(-0.377720\pi\) | ||||
0.374774 | + | 0.927116i | \(0.377720\pi\) | |||||||
\(674\) | −301440. | − | 12392.0i | −0.663561 | − | 0.0272785i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15023.7 | + | 1237.32i | 0.0328764 | + | 0.00270762i | ||||
\(677\) | −533403. | −1.16380 | −0.581900 | − | 0.813260i | \(-0.697690\pi\) | ||||
−0.581900 | + | 0.813260i | \(0.697690\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 874272.i | 1.89630i | ||||||||
\(680\) | 187325. | + | 23207.0i | 0.405115 | + | 0.0501882i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 699179. | + | 28742.7i | 1.50321 | + | 0.0617958i | ||||
\(683\) | 175866.i | 0.376999i | 0.982073 | + | 0.188500i | \(0.0603624\pi\) | ||||
−0.982073 | + | 0.188500i | \(0.939638\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −637265. | −1.35812 | ||||||||
\(686\) | −11948.6 | + | 290656.i | −0.0253904 | + | 0.617633i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12840.1 | + | 77424.7i | −0.0271264 | + | 0.163570i | ||||
\(689\) | −349422. | −0.736057 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 234536.i | 0.491194i | 0.969372 | + | 0.245597i | \(0.0789840\pi\) | ||||
−0.969372 | + | 0.245597i | \(0.921016\pi\) | |||||||
\(692\) | 351682. | + | 28963.7i | 0.734409 | + | 0.0604842i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24388.5 | + | 593261.i | −0.0506368 | + | 1.23176i | ||||
\(695\) | − | 542557.i | − | 1.12325i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40925.9 | 0.0842429 | ||||||||
\(698\) | 93244.6 | + | 3833.22i | 0.191387 | + | 0.00786778i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 20548.3 | − | 249501.i | 0.0419353 | − | 0.509185i | ||||
\(701\) | −192485. | −0.391707 | −0.195853 | − | 0.980633i | \(-0.562748\pi\) | ||||
−0.195853 | + | 0.980633i | \(0.562748\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 103213.i | − | 0.208844i | ||||||
\(704\) | 225383. | − | 895675.i | 0.454753 | − | 1.80720i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 77432.3 | + | 3183.18i | 0.155351 | + | 0.00638634i | ||||
\(707\) | 387031.i | 0.774297i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −600879. | −1.19535 | −0.597674 | − | 0.801739i | \(-0.703908\pi\) | ||||
−0.597674 | + | 0.801739i | \(0.703908\pi\) | |||||||
\(710\) | −6062.18 | + | 147465.i | −0.0120258 | + | 0.292532i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 599365. | + | 74253.1i | 1.18231 | + | 0.146472i | ||||
\(713\) | 278414. | 0.547661 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.15299e6i | 2.25536i | ||||||||
\(716\) | −68964.6 | + | 837380.i | −0.134524 | + | 1.63342i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22989.8 | + | 559236.i | −0.0445950 | + | 1.08479i | ||||
\(719\) | − | 37302.4i | − | 0.0721571i | −0.999349 | − | 0.0360786i | \(-0.988513\pi\) | ||
0.999349 | − | 0.0360786i | \(-0.0114867\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 967729. | 1.86159 | ||||||||
\(722\) | −406336. | − | 16704.1i | −0.779490 | − | 0.0320442i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −115182. | − | 9486.12i | −0.219739 | − | 0.0180972i | ||||
\(725\) | 4710.45 | 0.00896163 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 748065.i | − | 1.41537i | −0.706527 | − | 0.707686i | \(-0.749739\pi\) | ||
0.706527 | − | 0.707686i | \(-0.250261\pi\) | |||||||
\(728\) | −80955.8 | + | 653469.i | −0.152751 | + | 1.23300i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −602095. | − | 24751.7i | −1.12985 | − | 0.0464471i | ||||
\(731\) | 30372.8i | 0.0568394i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −263418. | −0.490272 | −0.245136 | − | 0.969489i | \(-0.578833\pi\) | ||||
−0.245136 | + | 0.969489i | \(0.578833\pi\) | |||||||
\(734\) | −15045.3 | + | 365983.i | −0.0279259 | + | 0.679310i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 74959.1 | − | 359740.i | 0.138379 | − | 0.664100i | ||||
\(737\) | −1.35183e6 | −2.48878 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 288908.i | − | 0.529018i | −0.964383 | − | 0.264509i | \(-0.914790\pi\) | ||
0.964383 | − | 0.264509i | \(-0.0852099\pi\) | |||||||
\(740\) | −289456. | − | 23838.9i | −0.528590 | − | 0.0435334i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20020.1 | − | 486997.i | 0.0363629 | − | 0.884543i | ||||
\(743\) | − | 313404.i | − | 0.567710i | −0.958867 | − | 0.283855i | \(-0.908387\pi\) | ||
0.958867 | − | 0.283855i | \(-0.0916134\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −483438. | −0.871020 | ||||||||
\(746\) | −342034. | − | 14060.8i | −0.614599 | − | 0.0252657i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 29338.1 | − | 356228.i | 0.0524359 | − | 0.636685i | ||||
\(749\) | −183606. | −0.327282 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 236182.i | − | 0.418761i | −0.977834 | − | 0.209381i | \(-0.932855\pi\) | ||
0.977834 | − | 0.209381i | \(-0.0671447\pi\) | |||||||
\(752\) | 109811. | − | 662150.i | 0.194183 | − | 1.17090i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12379.1 | − | 508.894i | −0.0217744 | − | 0.000895128i | ||||
\(755\) | − | 730134.i | − | 1.28088i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.00219e6 | −1.74888 | −0.874438 | − | 0.485137i | \(-0.838770\pi\) | ||||
−0.874438 | + | 0.485137i | \(0.838770\pi\) | |||||||
\(758\) | −6545.33 | + | 159218.i | −0.0113918 | + | 0.277111i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 39649.5 | − | 320048.i | 0.0686453 | − | 0.554099i | ||||
\(761\) | −912825. | −1.57622 | −0.788112 | − | 0.615532i | \(-0.788941\pi\) | ||||
−0.788112 | + | 0.615532i | \(0.788941\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.06193e6i | 1.82410i | ||||||||
\(764\) | −13898.1 | + | 168753.i | −0.0238105 | + | 0.289111i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28043.0 | − | 682158.i | 0.0477933 | − | 1.16259i | ||||
\(767\) | − | 446354.i | − | 0.758733i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −208651. | −0.352831 | −0.176416 | − | 0.984316i | \(-0.556450\pi\) | ||||
−0.176416 | + | 0.984316i | \(0.556450\pi\) | |||||||
\(770\) | −1.60696e6 | − | 66060.7i | −2.71033 | − | 0.111420i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −623274. | − | 51331.3i | −1.04579 | − | 0.0861287i | ||||
\(773\) | 661279. | 1.10669 | 0.553345 | − | 0.832952i | \(-0.313351\pi\) | ||||
0.553345 | + | 0.832952i | \(0.313351\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 202663.i | − | 0.337420i | ||||||
\(776\) | 927046. | + | 114848.i | 1.53949 | + | 0.190722i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 862531. | + | 35458.0i | 1.42500 | + | 0.0585808i | ||||
\(779\) | − | 69922.6i | − | 0.115224i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 279479. | 0.458191 | ||||||||
\(782\) | 5841.23 | − | 142090.i | 0.00955192 | − | 0.232355i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −299743. | − | 49709.5i | −0.487660 | − | 0.0808736i | ||||
\(785\) | −1.18048e6 | −1.91566 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38862.8i | 0.0627459i | 0.999508 | + | 0.0313729i | \(0.00998795\pi\) | ||||
−0.999508 | + | 0.0313729i | \(0.990012\pi\) | |||||||
\(788\) | 172536. | + | 14209.7i | 0.277861 | + | 0.0228840i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9239.58 | + | 224757.i | −0.0148046 | + | 0.360129i | ||||
\(791\) | − | 886090.i | − | 1.41620i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −243453. | −0.387141 | ||||||||
\(794\) | −1.16923e6 | − | 48065.9i | −1.85463 | − | 0.0762424i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1060.32 | − | 12874.6i | 0.00167345 | − | 0.0203193i | ||||
\(797\) | 642602. | 1.01164 | 0.505820 | − | 0.862639i | \(-0.331190\pi\) | ||||
0.505820 | + | 0.862639i | \(0.331190\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 259753.i | − | 0.406881i | ||||||
\(800\) | −261862. | − | 54564.2i | −0.409160 | − | 0.0852566i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 816565. | + | 33568.3i | 1.26953 | + | 0.0521893i | ||||
\(803\) | 1.14110e6i | 1.76967i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −639892. | −0.987449 | ||||||||
\(806\) | −21894.7 | + | 532599.i | −0.0337031 | + | 0.819842i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 410394. | + | 50842.2i | 0.628605 | + | 0.0778756i | ||||
\(809\) | −737297. | −1.12654 | −0.563269 | − | 0.826274i | \(-0.690456\pi\) | ||||
−0.563269 | + | 0.826274i | \(0.690456\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 823394.i | − | 1.25189i | −0.779867 | − | 0.625945i | \(-0.784714\pi\) | ||
0.779867 | − | 0.625945i | \(-0.215286\pi\) | |||||||
\(812\) | 1418.52 | − | 17223.9i | 0.00215141 | − | 0.0261227i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −22590.0 | + | 549511.i | −0.0340931 | + | 0.829330i | ||||
\(815\) | − | 753897.i | − | 1.13500i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51892.4 | 0.0777426 | ||||||||
\(818\) | −138798. | − | 5705.87i | −0.207432 | − | 0.00852738i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −196096. | − | 16150.0i | −0.291635 | − | 0.0240184i | ||||
\(821\) | 580247. | 0.860848 | 0.430424 | − | 0.902627i | \(-0.358364\pi\) | ||||
0.430424 | + | 0.902627i | \(0.358364\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 461966.i | − | 0.682040i | −0.940056 | − | 0.341020i | \(-0.889228\pi\) | ||
0.940056 | − | 0.341020i | \(-0.110772\pi\) | |||||||
\(824\) | 127125. | − | 1.02614e6i | 0.187231 | − | 1.51131i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 622095. | + | 25573.8i | 0.911793 | + | 0.0374831i | ||||
\(827\) | 1.11437e6i | 1.62936i | 0.579912 | + | 0.814679i | \(0.303087\pi\) | ||||
−0.579912 | + | 0.814679i | \(0.696913\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 915553. | 1.33222 | 0.666108 | − | 0.745856i | \(-0.267959\pi\) | ||||
0.666108 | + | 0.745856i | \(0.267959\pi\) | |||||||
\(830\) | −32934.8 | + | 801154.i | −0.0478079 | + | 1.16295i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 682279. | + | 171685.i | 0.985634 | + | 0.248020i | ||||
\(833\) | −117586. | −0.169459 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 828766.i | 1.18866i | ||||||||
\(836\) | −608621. | − | 50124.6i | −0.870832 | − | 0.0717197i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −52680.6 | + | 1.28148e6i | −0.0750175 | + | 1.82483i | ||||
\(839\) | 565403.i | 0.803219i | 0.915811 | + | 0.401610i | \(0.131549\pi\) | ||||
−0.915811 | + | 0.401610i | \(0.868451\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −706956. | −0.999540 | ||||||||
\(842\) | −542628. | − | 22307.0i | −0.765381 | − | 0.0314642i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 79891.9 | − | 970061.i | 0.112155 | − | 1.36180i | ||||
\(845\) | −28047.6 | −0.0392810 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.16856e6i | 3.02276i | ||||||||
\(848\) | −513764. | − | 85202.7i | −0.714450 | − | 0.118485i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −103430. | − | 4251.95i | −0.143156 | − | 0.00588505i | ||||
\(851\) | 218816.i | 0.302148i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 201979. | 0.277593 | 0.138796 | − | 0.990321i | \(-0.455677\pi\) | ||||
0.138796 | + | 0.990321i | \(0.455677\pi\) | |||||||
\(854\) | 13948.6 | − | 339307.i | 0.0191256 | − | 0.465240i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −24119.3 | + | 194689.i | −0.0329167 | + | 0.265701i | ||||
\(857\) | 504329. | 0.686676 | 0.343338 | − | 0.939212i | \(-0.388442\pi\) | ||||
0.343338 | + | 0.939212i | \(0.388442\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 764695.i | − | 1.03634i | −0.855278 | − | 0.518170i | \(-0.826614\pi\) | ||
0.855278 | − | 0.518170i | \(-0.173386\pi\) | |||||||
\(860\) | 11985.5 | − | 145530.i | 0.0162054 | − | 0.196769i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5149.60 | + | 125266.i | −0.00693041 | + | 0.168585i | ||||
\(863\) | 1.21817e6i | 1.63564i | 0.575477 | + | 0.817818i | \(0.304817\pi\) | ||||
−0.575477 | + | 0.817818i | \(0.695183\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −656551. | −0.877477 | ||||||||
\(866\) | −403746. | − | 16597.7i | −0.538360 | − | 0.0221316i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −741042. | − | 61030.4i | −0.983565 | − | 0.0810041i | ||||
\(869\) | 425963. | 0.564069 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.02975e6i | − | 1.35736i | ||||||
\(872\) | 1.12603e6 | + | 139500.i | 1.48088 | + | 0.183460i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −242764. | − | 9979.83i | −0.317805 | − | 0.0130647i | ||||
\(875\) | − | 648679.i | − | 0.847255i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 450910. | 0.586260 | 0.293130 | − | 0.956073i | \(-0.405303\pi\) | ||||
0.293130 | + | 0.956073i | \(0.405303\pi\) | |||||||
\(878\) | 29897.7 | − | 727275.i | 0.0387837 | − | 0.943430i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −281145. | + | 1.69528e6i | −0.363049 | + | 2.18915i | ||||
\(881\) | 1.04312e6 | 1.34395 | 0.671974 | − | 0.740575i | \(-0.265447\pi\) | ||||
0.671974 | + | 0.740575i | \(0.265447\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 303710.i | 0.389527i | 0.980850 | + | 0.194763i | \(0.0623939\pi\) | ||||
−0.980850 | + | 0.194763i | \(0.937606\pi\) | |||||||
\(884\) | 271356. | + | 22348.2i | 0.347244 | + | 0.0285982i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6110.05 | + | 148630.i | −0.00778354 | + | 0.189338i | ||||
\(887\) | 678530.i | 0.862426i | 0.902250 | + | 0.431213i | \(0.141914\pi\) | ||||
−0.902250 | + | 0.431213i | \(0.858086\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.10685e6 | −1.40051 | ||||||||
\(890\) | −1.12275e6 | − | 46155.3i | −1.41743 | − | 0.0582696i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14090.9 | + | 171094.i | −0.0177097 | + | 0.215034i | ||||
\(893\) | −443793. | −0.556515 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.56329e6i | − | 1.95162i | ||||||
\(896\) | −278373. | + | 941073.i | −0.346746 | + | 1.17222i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −81471.0 | − | 3349.21i | −0.101030 | − | 0.00415327i | ||||
\(899\) | − | 13990.5i | − | 0.0173107i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −201543. | −0.248267 | ||||||||
\(902\) | −15303.9 | + | 372273.i | −0.0188100 | + | 0.457560i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −939577. | − | 116401.i | −1.14973 | − | 0.142436i | ||||
\(905\) | 215032. | 0.262546 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.18664e6i | − | 1.44247i | −0.692692 | − | 0.721233i | \(-0.743576\pi\) | ||
0.692692 | − | 0.721233i | \(-0.256424\pi\) | |||||||
\(908\) | 99456.1 | − | 1.20761e6i | 0.120631 | − | 1.46472i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 50321.7 | − | 1.22410e6i | 0.0607676 | − | 1.47820i | ||||
\(911\) | − | 870726.i | − | 1.04917i | −0.851359 | − | 0.524584i | \(-0.824221\pi\) | ||
0.851359 | − | 0.524584i | \(-0.175779\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.51836e6 | 1.82152 | ||||||||
\(914\) | 1.11769e6 | + | 45947.2i | 1.33791 | + | 0.0550005i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −850984. | − | 70085.0i | −1.01422 | − | 0.0835284i | ||||
\(917\) | 498400. | 0.592706 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 60879.9i | − | 0.0720847i | −0.999350 | − | 0.0360423i | \(-0.988525\pi\) | ||
0.999350 | − | 0.0360423i | \(-0.0114751\pi\) | |||||||
\(920\) | −84059.0 | + | 678518.i | −0.0993136 | + | 0.801651i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −641845. | − | 26385.8i | −0.755038 | − | 0.0310390i | ||||
\(923\) | 212893.i | 0.249895i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 159280. | 0.186157 | ||||||||
\(926\) | 16290.7 | − | 396280.i | 0.0189985 | − | 0.462147i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −18077.2 | − | 3766.75i | −0.0209911 | − | 0.00437392i | ||||
\(929\) | 940810. | 1.09011 | 0.545055 | − | 0.838400i | \(-0.316509\pi\) | ||||
0.545055 | + | 0.838400i | \(0.316509\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 200897.i | 0.231779i | ||||||||
\(932\) | −900719. | − | 74181.1i | −1.03695 | − | 0.0854007i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 45804.7 | − | 1.11422e6i | 0.0525069 | − | 1.27725i | ||||
\(935\) | 665037.i | 0.760717i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −634530. | −0.722725 | −0.361362 | − | 0.932425i | \(-0.617688\pi\) | ||||
−0.361362 | + | 0.932425i | \(0.617688\pi\) | |||||||
\(938\) | 1.43519e6 | + | 58999.6i | 1.63119 | + | 0.0670569i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −102502. | + | 1.24460e6i | −0.116005 | + | 1.40856i | ||||
\(941\) | −68097.9 | −0.0769050 | −0.0384525 | − | 0.999260i | \(-0.512243\pi\) | ||||
−0.0384525 | + | 0.999260i | \(0.512243\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 148239.i | 0.166702i | ||||||||
\(944\) | 108839. | − | 656287.i | 0.122135 | − | 0.736461i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −276279. | − | 11357.6i | −0.308720 | − | 0.0126912i | ||||
\(947\) | − | 532720.i | − | 0.594017i | −0.954875 | − | 0.297009i | \(-0.904011\pi\) | ||
0.954875 | − | 0.297009i | \(-0.0959890\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −869232. | −0.965169 | ||||||||
\(950\) | −7264.52 | + | 176713.i | −0.00804933 | + | 0.195803i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −46694.6 | + | 376915.i | −0.0515221 | + | 0.415882i | ||||
\(953\) | −72542.5 | −0.0798742 | −0.0399371 | − | 0.999202i | \(-0.512716\pi\) | ||||
−0.0399371 | + | 0.999202i | \(0.512716\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 315042.i | − | 0.345432i | ||||||
\(956\) | −63026.0 | + | 765272.i | −0.0689610 | + | 0.837336i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5256.15 | − | 127858.i | 0.00572713 | − | 0.139315i | ||||
\(959\) | − | 1.28224e6i | − | 1.39422i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 321592. | 0.348224 | ||||||||
\(962\) | −418589. | − | 17207.9i | −0.452311 | − | 0.0185942i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.02294e6 | − | 84246.8i | −1.10077 | − | 0.0906566i | ||||
\(965\) | 1.16358e6 | 1.24952 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 814951.i | 0.871522i | 0.900062 | + | 0.435761i | \(0.143521\pi\) | ||||
−0.900062 | + | 0.435761i | \(0.856479\pi\) | |||||||
\(968\) | 2.29946e6 | + | 284871.i | 2.45400 | + | 0.304017i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.73657e6 | − | 71389.0i | −1.84565 | − | 0.0758731i | ||||
\(971\) | − | 939538.i | − | 0.996496i | −0.867034 | − | 0.498248i | \(-0.833977\pi\) | ||
0.867034 | − | 0.498248i | \(-0.166023\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.09168e6 | 1.15310 | ||||||||
\(974\) | 56982.4 | − | 1.38612e6i | 0.0600652 | − | 1.46111i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −357956. | − | 59363.4i | −0.375777 | − | 0.0623189i | ||||
\(977\) | −1.74116e6 | −1.82410 | −0.912051 | − | 0.410077i | \(-0.865502\pi\) | ||||
−0.912051 | + | 0.410077i | \(0.865502\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.12785e6i | 2.22012i | ||||||||
\(980\) | 563408. | + | 46401.0i | 0.586639 | + | 0.0483142i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 39428.5 | − | 959116.i | 0.0408872 | − | 0.994599i | ||||
\(983\) | − | 1.24396e6i | − | 1.28735i | −0.765298 | − | 0.643677i | \(-0.777408\pi\) | ||
0.765298 | − | 0.643677i | \(-0.222592\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −322106. | −0.331991 | ||||||||
\(986\) | −7140.15 | − | 293.526i | −0.00734435 | − | 0.000301921i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 38182.3 | − | 463616.i | 0.0391155 | − | 0.474946i | ||||
\(989\) | −110014. | −0.112475 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 766088.i | 0.780066i | 0.920801 | + | 0.390033i | \(0.127536\pi\) | ||||
−0.920801 | + | 0.390033i | \(0.872464\pi\) | |||||||
\(992\) | −162061. | + | 777756.i | −0.164685 | + | 0.790351i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −296714. | − | 12197.7i | −0.300307 | − | 0.0123454i | ||||
\(995\) | 24035.5i | 0.0242777i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 385359. | 0.387682 | 0.193841 | − | 0.981033i | \(-0.437905\pi\) | ||||
0.193841 | + | 0.981033i | \(0.437905\pi\) | |||||||
\(998\) | −56033.2 | + | 1.36303e6i | −0.0562580 | + | 1.36850i | ||||
\(999\) | 0 | 0 |
(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 | 324.5.d.e.163.1 | 22 | ||
3.2 | odd | 2 | 324.5.d.f.163.22 | 22 | |||
4.3 | odd | 2 | inner | 324.5.d.e.163.2 | 22 | ||
9.2 | odd | 6 | 36.5.f.a.31.9 | yes | 44 | ||
9.4 | even | 3 | 108.5.f.a.19.15 | 44 | |||
9.5 | odd | 6 | 36.5.f.a.7.8 | ✓ | 44 | ||
9.7 | even | 3 | 108.5.f.a.91.14 | 44 | |||
12.11 | even | 2 | 324.5.d.f.163.21 | 22 | |||
36.7 | odd | 6 | 108.5.f.a.91.15 | 44 | |||
36.11 | even | 6 | 36.5.f.a.31.8 | yes | 44 | ||
36.23 | even | 6 | 36.5.f.a.7.9 | yes | 44 | ||
36.31 | odd | 6 | 108.5.f.a.19.14 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.8 | ✓ | 44 | 9.5 | odd | 6 | ||
36.5.f.a.7.9 | yes | 44 | 36.23 | even | 6 | ||
36.5.f.a.31.8 | yes | 44 | 36.11 | even | 6 | ||
36.5.f.a.31.9 | yes | 44 | 9.2 | odd | 6 | ||
108.5.f.a.19.14 | 44 | 36.31 | odd | 6 | |||
108.5.f.a.19.15 | 44 | 9.4 | even | 3 | |||
108.5.f.a.91.14 | 44 | 9.7 | even | 3 | |||
108.5.f.a.91.15 | 44 | 36.7 | odd | 6 | |||
324.5.d.e.163.1 | 22 | 1.1 | even | 1 | trivial | ||
324.5.d.e.163.2 | 22 | 4.3 | odd | 2 | inner | ||
324.5.d.f.163.21 | 22 | 12.11 | even | 2 | |||
324.5.d.f.163.22 | 22 | 3.2 | odd | 2 |