Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(899,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.899");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bp (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1349.9 | ||
Character | \(\chi\) | \(=\) | 3150.1349 |
Dual form | 3150.2.bp.g.899.9 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.16005 | − | 1.52781i | 0.816421 | − | 0.577458i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.29783 | − | 2.48135i | 1.29584 | − | 0.748156i | 0.316160 | − | 0.948706i | \(-0.397606\pi\) |
0.979683 | + | 0.200550i | \(0.0642729\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.49388 | 1.52373 | 0.761864 | − | 0.647737i | \(-0.224285\pi\) | ||||
0.761864 | + | 0.647737i | \(0.224285\pi\) | |||||||
\(14\) | 0.243099 | + | 2.63456i | 0.0649709 | + | 0.704116i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.66237 | + | 1.53712i | −0.645719 | + | 0.372806i | −0.786814 | − | 0.617190i | \(-0.788271\pi\) |
0.141095 | + | 0.989996i | \(0.454938\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.68622 | + | 1.55089i | 0.616261 | + | 0.355798i | 0.775412 | − | 0.631456i | \(-0.217542\pi\) |
−0.159151 | + | 0.987254i | \(0.550876\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.96270i | 1.05805i | ||||||||
\(23\) | 3.08810 | − | 5.34875i | 0.643914 | − | 1.11529i | −0.340638 | − | 0.940195i | \(-0.610643\pi\) |
0.984551 | − | 0.175097i | \(-0.0560238\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.74694 | + | 4.75784i | −0.538719 | + | 0.933089i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.40314 | − | 1.10675i | −0.454152 | − | 0.209156i | ||||
\(29\) | 6.67885i | 1.24023i | 0.784510 | + | 0.620116i | \(0.212914\pi\) | ||||
−0.784510 | + | 0.620116i | \(0.787086\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.01653 | + | 0.586893i | −0.182574 | + | 0.105409i | −0.588501 | − | 0.808496i | \(-0.700282\pi\) |
0.405928 | + | 0.913905i | \(0.366949\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 3.07424i | − | 0.527228i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.27339 | + | 5.35400i | 1.52454 | + | 0.880192i | 0.999578 | + | 0.0290640i | \(0.00925266\pi\) |
0.524959 | + | 0.851128i | \(0.324081\pi\) | |||||||
\(38\) | −2.68622 | + | 1.55089i | −0.435762 | + | 0.251587i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.39427 | −1.31096 | −0.655482 | − | 0.755211i | \(-0.727534\pi\) | ||||
−0.655482 | + | 0.755211i | \(0.727534\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.81025i | − | 1.34355i | −0.740755 | − | 0.671776i | \(-0.765532\pi\) | ||
0.740755 | − | 0.671776i | \(-0.234468\pi\) | |||||||
\(44\) | −4.29783 | − | 2.48135i | −0.647922 | − | 0.374078i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.08810 | + | 5.34875i | 0.455316 | + | 0.788630i | ||||
\(47\) | −3.59075 | − | 2.07312i | −0.523765 | − | 0.302396i | 0.214709 | − | 0.976678i | \(-0.431120\pi\) |
−0.738474 | + | 0.674282i | \(0.764453\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.33160 | − | 6.60028i | 0.333085 | − | 0.942897i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.74694 | − | 4.75784i | −0.380932 | − | 0.659793i | ||||
\(53\) | 2.22536 | + | 3.85443i | 0.305676 | + | 0.529446i | 0.977412 | − | 0.211345i | \(-0.0677842\pi\) |
−0.671736 | + | 0.740791i | \(0.734451\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.16005 | − | 1.52781i | 0.288648 | − | 0.204162i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.78405 | − | 3.33943i | −0.759484 | − | 0.438488i | ||||
\(59\) | −3.00381 | − | 5.20275i | −0.391062 | − | 0.677340i | 0.601528 | − | 0.798852i | \(-0.294559\pi\) |
−0.992590 | + | 0.121512i | \(0.961226\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.05018 | + | 5.22512i | 1.15876 | + | 0.669008i | 0.951006 | − | 0.309173i | \(-0.100052\pi\) |
0.207751 | + | 0.978182i | \(0.433386\pi\) | |||||||
\(62\) | − | 1.17379i | − | 0.149071i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.3529 | + | 5.97727i | −1.26481 | + | 0.730240i | −0.974002 | − | 0.226540i | \(-0.927259\pi\) |
−0.290811 | + | 0.956780i | \(0.593925\pi\) | |||||||
\(68\) | 2.66237 | + | 1.53712i | 0.322860 | + | 0.186403i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.973522i | − | 0.115536i | −0.998330 | − | 0.0577679i | \(-0.981602\pi\) | ||
0.998330 | − | 0.0577679i | \(-0.0183983\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.34916 | − | 14.4612i | −0.977196 | − | 1.69255i | −0.672490 | − | 0.740106i | \(-0.734775\pi\) |
−0.304706 | − | 0.952446i | \(-0.598558\pi\) | |||||||
\(74\) | −9.27339 | + | 5.35400i | −1.07801 | + | 0.622389i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.10178i | − | 0.355798i | ||||||
\(77\) | 5.49247 | − | 11.9261i | 0.625925 | − | 1.35910i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.12328 | + | 3.67763i | −0.238887 | + | 0.413765i | −0.960395 | − | 0.278641i | \(-0.910116\pi\) |
0.721508 | + | 0.692406i | \(0.243449\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.19713 | − | 7.26965i | 0.463496 | − | 0.802798i | ||||
\(83\) | − | 14.2841i | − | 1.56789i | −0.620831 | − | 0.783944i | \(-0.713205\pi\) | ||
0.620831 | − | 0.783944i | \(-0.286795\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.62990 | + | 4.40513i | 0.822754 | + | 0.475017i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.29783 | − | 2.48135i | 0.458150 | − | 0.264513i | ||||
\(89\) | −7.38517 | + | 12.7915i | −0.782826 | + | 1.35590i | 0.147463 | + | 0.989068i | \(0.452889\pi\) |
−0.930289 | + | 0.366827i | \(0.880444\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.8670 | − | 8.39360i | 1.24400 | − | 0.879888i | ||||
\(92\) | −6.17620 | −0.643914 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.59075 | − | 2.07312i | 0.370358 | − | 0.213826i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.41643 | 0.448420 | 0.224210 | − | 0.974541i | \(-0.428020\pi\) | ||||
0.224210 | + | 0.974541i | \(0.428020\pi\) | |||||||
\(98\) | 4.55021 | + | 5.31936i | 0.459641 | + | 0.537336i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.19825 | + | 9.00364i | 0.517245 | + | 0.895895i | 0.999799 | + | 0.0200290i | \(0.00637586\pi\) |
−0.482554 | + | 0.875866i | \(0.660291\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.11942 | − | 8.86709i | 0.504431 | − | 0.873701i | −0.495556 | − | 0.868576i | \(-0.665035\pi\) |
0.999987 | − | 0.00512447i | \(-0.00163118\pi\) | |||||||
\(104\) | 5.49388 | 0.538719 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.45071 | −0.432291 | ||||||||
\(107\) | −3.28972 | + | 5.69797i | −0.318030 | + | 0.550844i | −0.980077 | − | 0.198619i | \(-0.936355\pi\) |
0.662047 | + | 0.749462i | \(0.269688\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.34219 | + | 2.32474i | 0.128558 | + | 0.222669i | 0.923118 | − | 0.384516i | \(-0.125632\pi\) |
−0.794560 | + | 0.607186i | \(0.792298\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.243099 | + | 2.63456i | 0.0229707 | + | 0.248942i | ||||
\(113\) | 3.55031 | 0.333985 | 0.166992 | − | 0.985958i | \(-0.446594\pi\) | ||||
0.166992 | + | 0.985958i | \(0.446594\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.78405 | − | 3.33943i | 0.537036 | − | 0.310058i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00761 | 0.553046 | ||||||||
\(119\) | −3.40241 | + | 7.38784i | −0.311899 | + | 0.677242i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.81421 | − | 11.8026i | 0.619474 | − | 1.07296i | ||||
\(122\) | −9.05018 | + | 5.22512i | −0.819365 | + | 0.473060i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.01653 | + | 0.586893i | 0.0912869 | + | 0.0527045i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.51567i | − | 0.489437i | −0.969594 | − | 0.244719i | \(-0.921304\pi\) | ||
0.969594 | − | 0.244719i | \(-0.0786955\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3068 | + | 17.8519i | −0.900510 | + | 1.55973i | −0.0736773 | + | 0.997282i | \(0.523473\pi\) |
−0.826833 | + | 0.562447i | \(0.809860\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.17182 | − | 0.754039i | 0.708586 | − | 0.0653835i | ||||
\(134\) | − | 11.9545i | − | 1.03272i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.66237 | + | 1.53712i | −0.228296 | + | 0.131807i | ||||
\(137\) | −5.72807 | − | 9.92131i | −0.489382 | − | 0.847635i | 0.510543 | − | 0.859852i | \(-0.329444\pi\) |
−0.999925 | + | 0.0122175i | \(0.996111\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.16700i | − | 0.0989840i | −0.998775 | − | 0.0494920i | \(-0.984240\pi\) | ||
0.998775 | − | 0.0494920i | \(-0.0157602\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.843095 | + | 0.486761i | 0.0707509 | + | 0.0408481i | ||||
\(143\) | 23.6117 | − | 13.6322i | 1.97451 | − | 1.13999i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.6983 | 1.38196 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 10.7080i | − | 0.880192i | ||||||
\(149\) | 13.3404 | + | 7.70205i | 1.09288 | + | 0.630977i | 0.934343 | − | 0.356375i | \(-0.115988\pi\) |
0.158541 | + | 0.987352i | \(0.449321\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.511281 | − | 0.885565i | −0.0416075 | − | 0.0720663i | 0.844472 | − | 0.535600i | \(-0.179915\pi\) |
−0.886079 | + | 0.463534i | \(0.846581\pi\) | |||||||
\(152\) | 2.68622 | + | 1.55089i | 0.217881 | + | 0.125794i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.58207 | + | 10.7197i | 0.610980 | + | 0.863815i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.68294 | + | 4.64699i | 0.214122 | + | 0.370871i | 0.953001 | − | 0.302968i | \(-0.0979776\pi\) |
−0.738878 | + | 0.673839i | \(0.764644\pi\) | |||||||
\(158\) | −2.12328 | − | 3.67763i | −0.168919 | − | 0.292576i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.50143 | − | 16.2716i | −0.118329 | − | 1.28238i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.69677 | + | 5.02108i | 0.681184 | + | 0.393282i | 0.800301 | − | 0.599599i | \(-0.204673\pi\) |
−0.119117 | + | 0.992880i | \(0.538006\pi\) | |||||||
\(164\) | 4.19713 | + | 7.26965i | 0.327741 | + | 0.567664i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.3704 | + | 7.14207i | 0.960131 | + | 0.554332i | ||||
\(167\) | − | 2.46005i | − | 0.190364i | −0.995460 | − | 0.0951822i | \(-0.969657\pi\) | ||
0.995460 | − | 0.0951822i | \(-0.0303434\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.1827 | 1.32175 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.62990 | + | 4.40513i | −0.581775 | + | 0.335888i | ||||
\(173\) | 2.59880 | + | 1.50042i | 0.197583 | + | 0.114075i | 0.595528 | − | 0.803335i | \(-0.296943\pi\) |
−0.397944 | + | 0.917410i | \(0.630276\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.96270i | 0.374078i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.38517 | − | 12.7915i | −0.553542 | − | 0.958763i | ||||
\(179\) | −3.18036 | + | 1.83618i | −0.237711 | + | 0.137243i | −0.614124 | − | 0.789209i | \(-0.710491\pi\) |
0.376413 | + | 0.926452i | \(0.377157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.13560i | 0.456056i | 0.973655 | + | 0.228028i | \(0.0732278\pi\) | ||||
−0.973655 | + | 0.228028i | \(0.926772\pi\) | |||||||
\(182\) | 1.33556 | + | 14.4739i | 0.0989980 | + | 1.07288i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.08810 | − | 5.34875i | 0.227658 | − | 0.394315i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.62827 | + | 13.2125i | −0.557834 | + | 0.966197i | ||||
\(188\) | 4.14624i | 0.302396i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.95227 | − | 2.85920i | −0.358334 | − | 0.206884i | 0.310016 | − | 0.950731i | \(-0.399666\pi\) |
−0.668350 | + | 0.743847i | \(0.732999\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.39819 | + | 3.11665i | −0.388570 | + | 0.224341i | −0.681541 | − | 0.731780i | \(-0.738690\pi\) |
0.292970 | + | 0.956122i | \(0.405356\pi\) | |||||||
\(194\) | −2.20821 | + | 3.82474i | −0.158540 | + | 0.274600i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.88181 | + | 1.28092i | −0.491558 | + | 0.0914941i | ||||
\(197\) | 1.32234 | 0.0942128 | 0.0471064 | − | 0.998890i | \(-0.485000\pi\) | ||||
0.0471064 | + | 0.998890i | \(0.485000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.27163 | − | 4.77563i | 0.586360 | − | 0.338535i | −0.177297 | − | 0.984157i | \(-0.556735\pi\) |
0.763657 | + | 0.645622i | \(0.223402\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.3965 | −0.731495 | ||||||||
\(203\) | 10.2040 | + | 14.4266i | 0.716181 | + | 1.01255i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.11942 | + | 8.86709i | 0.356687 | + | 0.617800i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.74694 | + | 4.75784i | −0.190466 | + | 0.329897i | ||||
\(209\) | 15.3932 | 1.06477 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.0219 | 1.79142 | 0.895711 | − | 0.444636i | \(-0.146667\pi\) | ||||
0.895711 | + | 0.444636i | \(0.146667\pi\) | |||||||
\(212\) | 2.22536 | − | 3.85443i | 0.152838 | − | 0.264723i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.28972 | − | 5.69797i | −0.224881 | − | 0.389505i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.29909 | + | 2.82078i | −0.0881878 | + | 0.191487i | ||||
\(218\) | −2.68437 | −0.181809 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.6267 | + | 8.44475i | −0.983900 | + | 0.568055i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.25222 | −0.485644 | −0.242822 | − | 0.970071i | \(-0.578073\pi\) | ||||
−0.242822 | + | 0.970071i | \(0.578073\pi\) | |||||||
\(224\) | −2.40314 | − | 1.10675i | −0.160567 | − | 0.0739478i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.77515 | + | 3.07466i | −0.118081 | + | 0.204523i | ||||
\(227\) | 23.1409 | − | 13.3604i | 1.53592 | − | 0.886762i | 0.536846 | − | 0.843680i | \(-0.319616\pi\) |
0.999072 | − | 0.0430820i | \(-0.0137177\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.0473 | − | 12.1517i | −1.39085 | − | 0.803006i | −0.397439 | − | 0.917629i | \(-0.630101\pi\) |
−0.993409 | + | 0.114622i | \(0.963434\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.67885i | 0.438488i | ||||||||
\(233\) | −4.62788 | + | 8.01573i | −0.303183 | + | 0.525128i | −0.976855 | − | 0.213902i | \(-0.931383\pi\) |
0.673672 | + | 0.739030i | \(0.264716\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.00381 | + | 5.20275i | −0.195531 | + | 0.338670i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.69685 | − | 6.64050i | −0.304452 | − | 0.430439i | ||||
\(239\) | − | 0.253367i | − | 0.0163889i | −0.999966 | − | 0.00819446i | \(-0.997392\pi\) | ||
0.999966 | − | 0.00819446i | \(-0.00260841\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.57538 | − | 1.48689i | 0.165895 | − | 0.0957792i | −0.414754 | − | 0.909934i | \(-0.636132\pi\) |
0.580649 | + | 0.814154i | \(0.302799\pi\) | |||||||
\(242\) | 6.81421 | + | 11.8026i | 0.438034 | + | 0.758698i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 10.4502i | − | 0.669008i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.7578 | + | 8.52039i | 0.939013 | + | 0.542140i | ||||
\(248\) | −1.01653 | + | 0.586893i | −0.0645496 | + | 0.0372677i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.0800 | −0.825599 | −0.412800 | − | 0.910822i | \(-0.635449\pi\) | ||||
−0.412800 | + | 0.910822i | \(0.635449\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 30.6507i | − | 1.92699i | ||||||
\(254\) | 4.77671 | + | 2.75784i | 0.299718 | + | 0.173042i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −10.9084 | − | 6.29797i | −0.680447 | − | 0.392856i | 0.119576 | − | 0.992825i | \(-0.461846\pi\) |
−0.800023 | + | 0.599969i | \(0.795180\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.2108 | − | 2.60310i | 1.75294 | − | 0.161749i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.3068 | − | 17.8519i | −0.636757 | − | 1.10290i | ||||
\(263\) | 8.33594 | + | 14.4383i | 0.514016 | + | 0.890302i | 0.999868 | + | 0.0162609i | \(0.00517625\pi\) |
−0.485852 | + | 0.874041i | \(0.661490\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.43289 | + | 7.45402i | −0.210484 | + | 0.457035i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.3529 | + | 5.97727i | 0.632407 | + | 0.365120i | ||||
\(269\) | 10.0035 | + | 17.3265i | 0.609923 | + | 1.05642i | 0.991253 | + | 0.131978i | \(0.0421328\pi\) |
−0.381330 | + | 0.924439i | \(0.624534\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.4684 | − | 8.93068i | −0.939638 | − | 0.542500i | −0.0497914 | − | 0.998760i | \(-0.515856\pi\) |
−0.889847 | + | 0.456259i | \(0.849189\pi\) | |||||||
\(272\) | − | 3.07424i | − | 0.186403i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.4561 | 0.692091 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.7167 | − | 9.07406i | 0.944327 | − | 0.545207i | 0.0530128 | − | 0.998594i | \(-0.483118\pi\) |
0.891314 | + | 0.453386i | \(0.149784\pi\) | |||||||
\(278\) | 1.01066 | + | 0.583502i | 0.0606151 | + | 0.0349961i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 15.5129i | − | 0.925425i | −0.886508 | − | 0.462713i | \(-0.846876\pi\) | ||
0.886508 | − | 0.462713i | \(-0.153124\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.82268 | + | 15.2813i | 0.524454 | + | 0.908381i | 0.999595 | + | 0.0284708i | \(0.00906377\pi\) |
−0.475141 | + | 0.879910i | \(0.657603\pi\) | |||||||
\(284\) | −0.843095 | + | 0.486761i | −0.0500285 | + | 0.0288840i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 27.2645i | 1.61218i | ||||||||
\(287\) | −18.1320 | + | 12.8248i | −1.07030 | + | 0.757026i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.77453 | + | 6.53767i | −0.222031 | + | 0.384569i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.34916 | + | 14.4612i | −0.488598 | + | 0.846276i | ||||
\(293\) | − | 10.4489i | − | 0.610432i | −0.952283 | − | 0.305216i | \(-0.901271\pi\) | ||
0.952283 | − | 0.305216i | \(-0.0987287\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.27339 | + | 5.35400i | 0.539005 | + | 0.311195i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.3404 | + | 7.70205i | −0.772786 | + | 0.446168i | ||||
\(299\) | 16.9657 | − | 29.3854i | 0.981149 | − | 1.69940i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.4604 | − | 19.0306i | −0.775844 | − | 1.09690i | ||||
\(302\) | 1.02256 | 0.0588419 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.68622 | + | 1.55089i | −0.154065 | + | 0.0889496i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.724648 | −0.0413579 | −0.0206789 | − | 0.999786i | \(-0.506583\pi\) | ||||
−0.0206789 | + | 0.999786i | \(0.506583\pi\) | |||||||
\(308\) | −13.0745 | + | 1.20643i | −0.744991 | + | 0.0687426i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.1225 | − | 24.4609i | −0.800813 | − | 1.38705i | −0.919081 | − | 0.394068i | \(-0.871068\pi\) |
0.118268 | − | 0.992982i | \(-0.462266\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.2651 | + | 17.7797i | −0.580218 | + | 1.00497i | 0.415235 | + | 0.909714i | \(0.363699\pi\) |
−0.995453 | + | 0.0952528i | \(0.969634\pi\) | |||||||
\(314\) | −5.36589 | −0.302815 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.24656 | 0.238887 | ||||||||
\(317\) | −1.13674 | + | 1.96890i | −0.0638459 | + | 0.110584i | −0.896181 | − | 0.443688i | \(-0.853670\pi\) |
0.832336 | + | 0.554272i | \(0.187003\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.5726 | + | 28.7045i | 0.927886 | + | 1.60715i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 14.8423 | + | 6.83551i | 0.827130 | + | 0.380928i | ||||
\(323\) | −9.53560 | −0.530575 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.69677 | + | 5.02108i | −0.481670 | + | 0.278092i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.39427 | −0.463496 | ||||||||
\(329\) | −10.9235 | + | 1.00795i | −0.602233 | + | 0.0555699i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.0646 | − | 31.2889i | 0.992922 | − | 1.71979i | 0.393605 | − | 0.919280i | \(-0.371228\pi\) |
0.599317 | − | 0.800512i | \(-0.295439\pi\) | |||||||
\(332\) | −12.3704 | + | 7.14207i | −0.678915 | + | 0.391972i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.13047 | + | 1.23003i | 0.116574 | + | 0.0673040i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.76361i | − | 0.205017i | −0.994732 | − | 0.102508i | \(-0.967313\pi\) | ||
0.994732 | − | 0.102508i | \(-0.0326869\pi\) | |||||||
\(338\) | −8.59134 | + | 14.8806i | −0.467308 | + | 0.809400i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.91258 | + | 5.04473i | −0.157725 | + | 0.273187i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.04761 | − | 17.8191i | −0.272546 | − | 0.962143i | ||||
\(344\) | − | 8.81025i | − | 0.475017i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.59880 | + | 1.50042i | −0.139713 | + | 0.0806631i | ||||
\(347\) | −2.02389 | − | 3.50549i | −0.108648 | − | 0.188184i | 0.806575 | − | 0.591132i | \(-0.201319\pi\) |
−0.915223 | + | 0.402948i | \(0.867986\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.9364i | 1.28129i | 0.767838 | + | 0.640644i | \(0.221333\pi\) | ||||
−0.767838 | + | 0.640644i | \(0.778667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.29783 | − | 2.48135i | −0.229075 | − | 0.132256i | ||||
\(353\) | 22.0679 | − | 12.7409i | 1.17455 | − | 0.678129i | 0.219805 | − | 0.975544i | \(-0.429458\pi\) |
0.954748 | + | 0.297415i | \(0.0961244\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.7703 | 0.782826 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 3.67236i | − | 0.194091i | ||||||
\(359\) | −15.4893 | − | 8.94277i | −0.817496 | − | 0.471981i | 0.0320565 | − | 0.999486i | \(-0.489794\pi\) |
−0.849552 | + | 0.527505i | \(0.823128\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.68949 | − | 8.12243i | −0.246815 | − | 0.427496i | ||||
\(362\) | −5.31359 | − | 3.06780i | −0.279276 | − | 0.161240i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.2026 | − | 6.08035i | −0.692003 | − | 0.318697i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.63851 | − | 4.57004i | −0.137729 | − | 0.238554i | 0.788907 | − | 0.614512i | \(-0.210647\pi\) |
−0.926637 | + | 0.375958i | \(0.877314\pi\) | |||||||
\(368\) | 3.08810 | + | 5.34875i | 0.160978 | + | 0.278823i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.6957 | + | 4.92582i | 0.555293 | + | 0.255736i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5988 | + | 7.27390i | 0.652339 | + | 0.376628i | 0.789352 | − | 0.613941i | \(-0.210417\pi\) |
−0.137013 | + | 0.990569i | \(0.543750\pi\) | |||||||
\(374\) | −7.62827 | − | 13.2125i | −0.394448 | − | 0.683205i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.59075 | − | 2.07312i | −0.185179 | − | 0.106913i | ||||
\(377\) | 36.6928i | 1.88977i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.66669 | −0.188345 | −0.0941726 | − | 0.995556i | \(-0.530021\pi\) | ||||
−0.0941726 | + | 0.995556i | \(0.530021\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.95227 | − | 2.85920i | 0.253380 | − | 0.146289i | ||||
\(383\) | 16.9091 | + | 9.76247i | 0.864015 | + | 0.498839i | 0.865355 | − | 0.501160i | \(-0.167093\pi\) |
−0.00134002 | + | 0.999999i | \(0.500427\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 6.23330i | − | 0.317266i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.20821 | − | 3.82474i | −0.112105 | − | 0.194172i | ||||
\(389\) | 14.9711 | − | 8.64356i | 0.759064 | − | 0.438246i | −0.0698956 | − | 0.997554i | \(-0.522267\pi\) |
0.828960 | + | 0.559309i | \(0.188933\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.9871i | 0.960220i | ||||||||
\(392\) | 2.33160 | − | 6.60028i | 0.117763 | − | 0.333364i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.661170 | + | 1.14518i | −0.0333092 | + | 0.0576933i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.8423 | + | 23.9755i | −0.694724 | + | 1.20330i | 0.275549 | + | 0.961287i | \(0.411140\pi\) |
−0.970274 | + | 0.242011i | \(0.922193\pi\) | |||||||
\(398\) | 9.55125i | 0.478761i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.7521 | + | 18.9095i | 1.63556 | + | 0.944293i | 0.982335 | + | 0.187132i | \(0.0599194\pi\) |
0.653229 | + | 0.757161i | \(0.273414\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.58468 | + | 3.22432i | −0.278193 | + | 0.160615i | ||||
\(404\) | 5.19825 | − | 9.00364i | 0.258623 | − | 0.447948i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.5958 | + | 1.62362i | −0.873266 | + | 0.0805790i | ||||
\(407\) | 53.1406 | 2.63408 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.6028 | + | 18.2459i | −1.56266 | + | 0.902202i | −0.565673 | + | 0.824630i | \(0.691383\pi\) |
−0.996987 | + | 0.0775719i | \(0.975283\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.2388 | −0.504431 | ||||||||
\(413\) | −14.4372 | − | 6.64893i | −0.710407 | − | 0.327172i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.74694 | − | 4.75784i | −0.134680 | − | 0.233272i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.69660 | + | 13.3309i | −0.376453 | + | 0.652036i | ||||
\(419\) | 21.6669 | 1.05850 | 0.529249 | − | 0.848466i | \(-0.322474\pi\) | ||||
0.529249 | + | 0.848466i | \(0.322474\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.84193 | −0.430929 | −0.215465 | − | 0.976512i | \(-0.569127\pi\) | ||||
−0.215465 | + | 0.976512i | \(0.569127\pi\) | |||||||
\(422\) | −13.0110 | + | 22.5356i | −0.633363 | + | 1.09702i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.22536 | + | 3.85443i | 0.108073 | + | 0.187188i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.5318 | − | 2.54044i | 1.33236 | − | 0.122941i | ||||
\(428\) | 6.57945 | 0.318030 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.7481 | + | 14.8656i | −1.24024 | + | 0.716053i | −0.969143 | − | 0.246499i | \(-0.920720\pi\) |
−0.271097 | + | 0.962552i | \(0.587386\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.5666 | 1.27671 | 0.638356 | − | 0.769741i | \(-0.279615\pi\) | ||||
0.638356 | + | 0.769741i | \(0.279615\pi\) | |||||||
\(434\) | −1.79332 | − | 2.53543i | −0.0860822 | − | 0.121705i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.34219 | − | 2.32474i | 0.0642791 | − | 0.111335i | ||||
\(437\) | 16.5906 | − | 9.57860i | 0.793637 | − | 0.458207i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.4067 | − | 8.31774i | −0.687597 | − | 0.396984i | 0.115114 | − | 0.993352i | \(-0.463277\pi\) |
−0.802711 | + | 0.596368i | \(0.796610\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 16.8895i | − | 0.803351i | ||||||
\(443\) | 1.63637 | − | 2.83428i | 0.0777464 | − | 0.134661i | −0.824531 | − | 0.565817i | \(-0.808561\pi\) |
0.902277 | + | 0.431156i | \(0.141894\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.62611 | − | 6.28060i | 0.171701 | − | 0.297395i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.16005 | − | 1.52781i | 0.102053 | − | 0.0721822i | ||||
\(449\) | − | 10.4322i | − | 0.492324i | −0.969229 | − | 0.246162i | \(-0.920831\pi\) | ||
0.969229 | − | 0.246162i | \(-0.0791695\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.0771 | + | 20.8291i | −1.69880 | + | 0.980805i | ||||
\(452\) | −1.77515 | − | 3.07466i | −0.0834962 | − | 0.144620i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 26.7208i | 1.25407i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.6471 | − | 16.5394i | −1.34005 | − | 0.773680i | −0.353238 | − | 0.935533i | \(-0.614920\pi\) |
−0.986815 | + | 0.161853i | \(0.948253\pi\) | |||||||
\(458\) | 21.0473 | − | 12.1517i | 0.983478 | − | 0.567811i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.5639 | −0.538585 | −0.269293 | − | 0.963058i | \(-0.586790\pi\) | ||||
−0.269293 | + | 0.963058i | \(0.586790\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.6061i | 1.79418i | 0.441848 | + | 0.897090i | \(0.354323\pi\) | ||||
−0.441848 | + | 0.897090i | \(0.645677\pi\) | |||||||
\(464\) | −5.78405 | − | 3.33943i | −0.268518 | − | 0.155029i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.62788 | − | 8.01573i | −0.214383 | − | 0.371322i | ||||
\(467\) | −4.08230 | − | 2.35692i | −0.188906 | − | 0.109065i | 0.402564 | − | 0.915392i | \(-0.368119\pi\) |
−0.591471 | + | 0.806327i | \(0.701452\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.2307 | + | 28.7285i | −0.610937 | + | 1.32656i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.00381 | − | 5.20275i | −0.138261 | − | 0.239476i | ||||
\(473\) | −21.8613 | − | 37.8649i | −1.00519 | − | 1.74103i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 8.09926 | − | 0.747344i | 0.371229 | − | 0.0342545i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.219422 | + | 0.126683i | 0.0100361 | + | 0.00579436i | ||||
\(479\) | 10.0096 | + | 17.3371i | 0.457349 | + | 0.792152i | 0.998820 | − | 0.0485678i | \(-0.0154657\pi\) |
−0.541471 | + | 0.840720i | \(0.682132\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.9469 | + | 29.4142i | 2.32298 | + | 1.34117i | ||||
\(482\) | 2.97379i | 0.135452i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.6284 | −0.619474 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.09706 | − | 2.36544i | 0.185656 | − | 0.107188i | −0.404292 | − | 0.914630i | \(-0.632482\pi\) |
0.589947 | + | 0.807442i | \(0.299149\pi\) | |||||||
\(488\) | 9.05018 | + | 5.22512i | 0.409682 | + | 0.236530i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 16.0027i | − | 0.722190i | −0.932529 | − | 0.361095i | \(-0.882403\pi\) | ||
0.932529 | − | 0.361095i | \(-0.117597\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2662 | − | 17.7816i | −0.462366 | − | 0.800841i | ||||
\(494\) | −14.7578 | + | 8.52039i | −0.663983 | + | 0.383351i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 1.17379i | − | 0.0527045i | ||||||
\(497\) | −1.48736 | − | 2.10285i | −0.0667170 | − | 0.0943258i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.18097 | − | 5.50961i | 0.142400 | − | 0.246644i | −0.786000 | − | 0.618227i | \(-0.787851\pi\) |
0.928400 | + | 0.371583i | \(0.121185\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.53998 | − | 11.3276i | 0.291893 | − | 0.505574i | ||||
\(503\) | − | 36.3826i | − | 1.62222i | −0.584895 | − | 0.811109i | \(-0.698864\pi\) | ||
0.584895 | − | 0.811109i | \(-0.301136\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 26.5443 | + | 15.3253i | 1.18004 | + | 0.681294i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.77671 | + | 2.75784i | −0.211932 | + | 0.122359i | ||||
\(509\) | −8.55353 | + | 14.8151i | −0.379128 | + | 0.656670i | −0.990936 | − | 0.134337i | \(-0.957109\pi\) |
0.611807 | + | 0.791007i | \(0.290443\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −40.1285 | − | 18.4809i | −1.77518 | − | 0.817546i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.9084 | − | 6.29797i | 0.481149 | − | 0.277791i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.5766 | −0.904956 | ||||||||
\(518\) | −11.8511 | + | 25.7329i | −0.520706 | + | 1.13064i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.2375 | − | 35.0524i | −0.886622 | − | 1.53567i | −0.843843 | − | 0.536590i | \(-0.819712\pi\) |
−0.0427789 | − | 0.999085i | \(-0.513621\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.8420 | + | 37.8314i | −0.955083 | + | 1.65425i | −0.220905 | + | 0.975295i | \(0.570901\pi\) |
−0.734178 | + | 0.678957i | \(0.762432\pi\) | |||||||
\(524\) | 20.6136 | 0.900510 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.6719 | −0.726929 | ||||||||
\(527\) | 1.80425 | − | 3.12505i | 0.0785943 | − | 0.136129i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.57274 | − | 13.1164i | −0.329250 | − | 0.570277i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.73893 | − | 6.69998i | −0.205458 | − | 0.290481i | ||||
\(533\) | −46.1171 | −1.99755 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.3529 | + | 5.97727i | −0.447179 | + | 0.258179i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20.0069 | −0.862561 | ||||||||
\(539\) | −6.35681 | − | 34.1524i | −0.273807 | − | 1.47105i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.85601 | − | 10.1429i | 0.251770 | − | 0.436078i | −0.712243 | − | 0.701933i | \(-0.752321\pi\) |
0.964013 | + | 0.265855i | \(0.0856541\pi\) | |||||||
\(542\) | 15.4684 | − | 8.93068i | 0.664425 | − | 0.383606i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.66237 | + | 1.53712i | 0.114148 | + | 0.0659035i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.6501i | 1.48153i | 0.671764 | + | 0.740765i | \(0.265537\pi\) | ||||
−0.671764 | + | 0.740765i | \(0.734463\pi\) | |||||||
\(548\) | −5.72807 | + | 9.92131i | −0.244691 | + | 0.423817i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.3582 | + | 17.9409i | −0.441272 | + | 0.764306i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.03233 | + | 11.1878i | 0.0438993 | + | 0.475754i | ||||
\(554\) | 18.1481i | 0.771040i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.01066 | + | 0.583502i | −0.0428613 | + | 0.0247460i | ||||
\(557\) | −17.6567 | − | 30.5822i | −0.748137 | − | 1.29581i | −0.948715 | − | 0.316134i | \(-0.897615\pi\) |
0.200578 | − | 0.979678i | \(-0.435718\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 48.4025i | − | 2.04721i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.4346 | + | 7.75647i | 0.566705 | + | 0.327187i | ||||
\(563\) | −33.5143 | + | 19.3495i | −1.41246 | + | 0.815483i | −0.995620 | − | 0.0934975i | \(-0.970195\pi\) |
−0.416839 | + | 0.908981i | \(0.636862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −17.6454 | −0.741690 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 0.973522i | − | 0.0408481i | ||||||
\(569\) | −6.20799 | − | 3.58419i | −0.260253 | − | 0.150257i | 0.364197 | − | 0.931322i | \(-0.381343\pi\) |
−0.624450 | + | 0.781065i | \(0.714677\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.7717 | + | 18.6571i | 0.450781 | + | 0.780776i | 0.998435 | − | 0.0559290i | \(-0.0178121\pi\) |
−0.547653 | + | 0.836705i | \(0.684479\pi\) | |||||||
\(572\) | −23.6117 | − | 13.6322i | −0.987256 | − | 0.569993i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.04064 | − | 22.1152i | −0.0851746 | − | 0.923070i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.86230 | − | 13.6179i | −0.327312 | − | 0.566921i | 0.654666 | − | 0.755919i | \(-0.272809\pi\) |
−0.981978 | + | 0.188998i | \(0.939476\pi\) | |||||||
\(578\) | −3.77453 | − | 6.53767i | −0.157000 | − | 0.271931i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.8234 | − | 30.8544i | −0.905389 | − | 1.28006i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.1284 | + | 11.0438i | 0.792217 | + | 0.457387i | ||||
\(584\) | −8.34916 | − | 14.4612i | −0.345491 | − | 0.598408i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.04902 | + | 5.22446i | 0.373812 | + | 0.215820i | ||||
\(587\) | 4.59252i | 0.189554i | 0.995499 | + | 0.0947769i | \(0.0302138\pi\) | ||||
−0.995499 | + | 0.0947769i | \(0.969786\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.64082 | −0.150017 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.27339 | + | 5.35400i | −0.381134 | + | 0.220048i | ||||
\(593\) | 3.31317 | + | 1.91286i | 0.136055 | + | 0.0785516i | 0.566483 | − | 0.824074i | \(-0.308304\pi\) |
−0.430427 | + | 0.902625i | \(0.641637\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 15.4041i | − | 0.630977i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.9657 | + | 29.3854i | 0.693777 | + | 1.20166i | ||||
\(599\) | 13.6589 | − | 7.88600i | 0.558089 | − | 0.322213i | −0.194289 | − | 0.980944i | \(-0.562240\pi\) |
0.752378 | + | 0.658731i | \(0.228907\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.39673i | 0.0569740i | 0.999594 | + | 0.0284870i | \(0.00906892\pi\) | ||||
−0.999594 | + | 0.0284870i | \(0.990931\pi\) | |||||||
\(602\) | 23.2111 | − | 2.14176i | 0.946015 | − | 0.0872918i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.511281 | + | 0.885565i | −0.0208037 | + | 0.0360331i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.16682 | − | 8.94920i | 0.209715 | − | 0.363237i | −0.741910 | − | 0.670500i | \(-0.766080\pi\) |
0.951625 | + | 0.307263i | \(0.0994131\pi\) | |||||||
\(608\) | − | 3.10178i | − | 0.125794i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.7271 | − | 11.3895i | −0.798075 | − | 0.460769i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.6482 | + | 6.14772i | −0.430075 | + | 0.248304i | −0.699379 | − | 0.714751i | \(-0.746540\pi\) |
0.269303 | + | 0.963055i | \(0.413207\pi\) | |||||||
\(614\) | 0.362324 | − | 0.627564i | 0.0146222 | − | 0.0253264i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.49247 | − | 11.9261i | 0.221298 | − | 0.480516i | ||||
\(617\) | −8.10935 | −0.326470 | −0.163235 | − | 0.986587i | \(-0.552193\pi\) | ||||
−0.163235 | + | 0.986587i | \(0.552193\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.03506 | + | 4.06170i | −0.282763 | + | 0.163253i | −0.634674 | − | 0.772780i | \(-0.718865\pi\) |
0.351911 | + | 0.936034i | \(0.385532\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 28.2450 | 1.13252 | ||||||||
\(623\) | 3.59065 | + | 38.9133i | 0.143857 | + | 1.55903i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.2651 | − | 17.7797i | −0.410276 | − | 0.710619i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.68294 | − | 4.64699i | 0.107061 | − | 0.185435i | ||||
\(629\) | −32.9189 | −1.31256 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.6011 | −1.61630 | −0.808151 | − | 0.588975i | \(-0.799532\pi\) | ||||
−0.808151 | + | 0.588975i | \(0.799532\pi\) | |||||||
\(632\) | −2.12328 | + | 3.67763i | −0.0844595 | + | 0.146288i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.13674 | − | 1.96890i | −0.0451459 | − | 0.0781950i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.8095 | − | 36.2611i | 0.507531 | − | 1.43672i | ||||
\(638\) | −33.1452 | −1.31223 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.0260 | − | 18.4902i | 1.26495 | − | 0.730319i | 0.290922 | − | 0.956747i | \(-0.406038\pi\) |
0.974028 | + | 0.226427i | \(0.0727046\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.86696 | 0.191934 | 0.0959671 | − | 0.995385i | \(-0.469406\pi\) | ||||
0.0959671 | + | 0.995385i | \(0.469406\pi\) | |||||||
\(644\) | −13.3409 | + | 9.43606i | −0.525704 | + | 0.371833i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.76780 | − | 8.25808i | 0.187587 | − | 0.324910i | ||||
\(647\) | 21.6217 | − | 12.4833i | 0.850037 | − | 0.490769i | −0.0106266 | − | 0.999944i | \(-0.503383\pi\) |
0.860663 | + | 0.509175i | \(0.170049\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.8197 | − | 14.9070i | −1.01351 | − | 0.585151i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 10.0422i | − | 0.393282i | ||||||
\(653\) | −7.29496 | + | 12.6352i | −0.285474 | + | 0.494455i | −0.972724 | − | 0.231966i | \(-0.925484\pi\) |
0.687250 | + | 0.726421i | \(0.258818\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.19713 | − | 7.26965i | 0.163870 | − | 0.283832i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.58885 | − | 9.96402i | 0.178892 | − | 0.388438i | ||||
\(659\) | − | 33.8468i | − | 1.31848i | −0.751931 | − | 0.659242i | \(-0.770877\pi\) | ||
0.751931 | − | 0.659242i | \(-0.229123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9053 | + | 8.60557i | −0.579749 | + | 0.334718i | −0.761034 | − | 0.648713i | \(-0.775308\pi\) |
0.181285 | + | 0.983431i | \(0.441974\pi\) | |||||||
\(662\) | 18.0646 | + | 31.2889i | 0.702102 | + | 1.21608i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 14.2841i | − | 0.554332i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.7235 | + | 20.6250i | 1.38322 | + | 0.798602i | ||||
\(668\) | −2.13047 | + | 1.23003i | −0.0824302 | + | 0.0475911i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 51.8615 | 2.00209 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.47971i | 0.0570387i | 0.999593 | + | 0.0285193i | \(0.00907922\pi\) | ||||
−0.999593 | + | 0.0285193i | \(0.990921\pi\) | |||||||
\(674\) | 3.25938 | + | 1.88181i | 0.125547 | + | 0.0724844i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.59134 | − | 14.8806i | −0.330436 | − | 0.572333i | ||||
\(677\) | −10.2632 | − | 5.92549i | −0.394448 | − | 0.227735i | 0.289637 | − | 0.957136i | \(-0.406465\pi\) |
−0.684086 | + | 0.729402i | \(0.739799\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.53968 | − | 6.74746i | 0.366099 | − | 0.258944i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.91258 | − | 5.04473i | −0.111528 | − | 0.193173i | ||||
\(683\) | 5.26389 | + | 9.11732i | 0.201417 | + | 0.348865i | 0.948985 | − | 0.315320i | \(-0.102112\pi\) |
−0.747568 | + | 0.664185i | \(0.768779\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.9556 | + | 4.53821i | 0.685549 | + | 0.173270i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.62990 | + | 4.40513i | 0.290887 | + | 0.167944i | ||||
\(689\) | 12.2258 | + | 21.1758i | 0.465767 | + | 0.806732i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.61628 | + | 3.81991i | 0.251695 | + | 0.145316i | 0.620540 | − | 0.784175i | \(-0.286913\pi\) |
−0.368845 | + | 0.929491i | \(0.620247\pi\) | |||||||
\(692\) | − | 3.00084i | − | 0.114075i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.04779 | 0.153652 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.3486 | − | 12.9030i | 0.846515 | − | 0.488736i | ||||
\(698\) | −20.7296 | − | 11.9682i | −0.784626 | − | 0.453004i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 35.2007i | − | 1.32951i | −0.747060 | − | 0.664757i | \(-0.768535\pi\) | ||
0.747060 | − | 0.664757i | \(-0.231465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.6069 | + | 28.7640i | 0.626341 | + | 1.08485i | ||||
\(704\) | 4.29783 | − | 2.48135i | 0.161980 | − | 0.0935195i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 25.4818i | 0.959019i | ||||||||
\(707\) | 24.9843 | + | 11.5063i | 0.939631 | + | 0.432740i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.1846 | + | 31.4966i | −0.682936 | + | 1.18288i | 0.291145 | + | 0.956679i | \(0.405964\pi\) |
−0.974081 | + | 0.226201i | \(0.927369\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.38517 | + | 12.7915i | −0.276771 | + | 0.479381i | ||||
\(713\) | 7.24954i | 0.271497i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.18036 | + | 1.83618i | 0.118856 | + | 0.0686214i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.4893 | − | 8.94277i | 0.578057 | − | 0.333741i | ||||
\(719\) | −0.772550 | + | 1.33810i | −0.0288113 | + | 0.0499026i | −0.880072 | − | 0.474841i | \(-0.842506\pi\) |
0.851260 | + | 0.524744i | \(0.175839\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.48905 | − | 26.9748i | −0.0926971 | − | 1.00460i | ||||
\(722\) | 9.37898 | 0.349049 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.31359 | − | 3.06780i | 0.197478 | − | 0.114014i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.1857 | −1.26788 | −0.633939 | − | 0.773383i | \(-0.718563\pi\) | ||||
−0.633939 | + | 0.773383i | \(0.718563\pi\) | |||||||
\(728\) | 11.8670 | − | 8.39360i | 0.439821 | − | 0.311087i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.5424 | + | 23.4561i | 0.500884 | + | 0.867557i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.9095 | + | 37.9485i | −0.809248 | + | 1.40166i | 0.104138 | + | 0.994563i | \(0.466792\pi\) |
−0.913386 | + | 0.407095i | \(0.866542\pi\) | |||||||
\(734\) | 5.27703 | 0.194779 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.17620 | −0.227658 | ||||||||
\(737\) | −29.6634 | + | 51.3786i | −1.09267 | + | 1.89255i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.86403 | − | 11.8888i | −0.252497 | − | 0.437338i | 0.711715 | − | 0.702468i | \(-0.247919\pi\) |
−0.964213 | + | 0.265130i | \(0.914585\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.61374 | + | 6.79984i | −0.352931 | + | 0.249630i | ||||
\(743\) | 20.8393 | 0.764520 | 0.382260 | − | 0.924055i | \(-0.375146\pi\) | ||||
0.382260 | + | 0.924055i | \(0.375146\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12.5988 | + | 7.27390i | −0.461274 | + | 0.266316i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15.2565 | 0.557834 | ||||||||
\(749\) | 1.59946 | + | 17.3339i | 0.0584429 | + | 0.633369i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.8346 | − | 37.8186i | 0.796755 | − | 1.38002i | −0.124964 | − | 0.992161i | \(-0.539881\pi\) |
0.921719 | − | 0.387859i | \(-0.126785\pi\) | |||||||
\(752\) | 3.59075 | − | 2.07312i | 0.130941 | − | 0.0755989i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −31.7769 | − | 18.3464i | −1.15725 | − | 0.668136i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 40.4115i | − | 1.46878i | −0.678727 | − | 0.734391i | \(-0.737468\pi\) | ||
0.678727 | − | 0.734391i | \(-0.262532\pi\) | |||||||
\(758\) | 1.83335 | − | 3.17545i | 0.0665901 | − | 0.115337i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.3292 | + | 31.7471i | −0.664432 | + | 1.15083i | 0.315007 | + | 0.949089i | \(0.397993\pi\) |
−0.979439 | + | 0.201741i | \(0.935340\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.45094 | + | 2.97093i | 0.233540 | + | 0.107555i | ||||
\(764\) | 5.71839i | 0.206884i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.9091 | + | 9.76247i | −0.610951 | + | 0.352732i | ||||
\(767\) | −16.5025 | − | 28.5833i | −0.595872 | − | 1.03208i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 20.4304i | − | 0.736738i | −0.929680 | − | 0.368369i | \(-0.879916\pi\) | ||
0.929680 | − | 0.368369i | \(-0.120084\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.39819 | + | 3.11665i | 0.194285 | + | 0.112171i | ||||
\(773\) | −11.8586 | + | 6.84657i | −0.426525 | + | 0.246254i | −0.697865 | − | 0.716229i | \(-0.745866\pi\) |
0.271340 | + | 0.962483i | \(0.412533\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.41643 | 0.158540 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.2871i | 0.619773i | ||||||||
\(779\) | −22.5488 | − | 13.0186i | −0.807896 | − | 0.466439i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.41565 | − | 4.18403i | −0.0864388 | − | 0.149716i | ||||
\(782\) | −16.4433 | − | 9.49356i | −0.588012 | − | 0.339489i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.55021 | + | 5.31936i | 0.162507 | + | 0.189977i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.70701 | − | 11.6169i | −0.239079 | − | 0.414097i | 0.721371 | − | 0.692549i | \(-0.243512\pi\) |
−0.960450 | + | 0.278451i | \(0.910179\pi\) | |||||||
\(788\) | −0.661170 | − | 1.14518i | −0.0235532 | − | 0.0407953i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.66883 | − | 5.42419i | 0.272672 | − | 0.192862i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.7206 | + | 28.7062i | 1.76563 | + | 1.01939i | ||||
\(794\) | −13.8423 | − | 23.9755i | −0.491244 | − | 0.850860i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.27163 | − | 4.77563i | −0.293180 | − | 0.169268i | ||||
\(797\) | − | 53.8858i | − | 1.90873i | −0.298636 | − | 0.954367i | \(-0.596532\pi\) | ||
0.298636 | − | 0.954367i | \(-0.403468\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.7465 | 0.450940 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −32.7521 | + | 18.9095i | −1.15652 | + | 0.667716i | ||||
\(803\) | −71.7665 | − | 41.4344i | −2.53259 | − | 1.46219i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 6.44864i | − | 0.227144i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.19825 | + | 9.00364i | 0.182874 | + | 0.316747i | ||||
\(809\) | −10.1762 | + | 5.87522i | −0.357775 | + | 0.206562i | −0.668104 | − | 0.744068i | \(-0.732894\pi\) |
0.310329 | + | 0.950629i | \(0.399561\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.8579i | 0.802649i | 0.915936 | + | 0.401325i | \(0.131450\pi\) | ||||
−0.915936 | + | 0.401325i | \(0.868550\pi\) | |||||||
\(812\) | 7.39182 | − | 16.0502i | 0.259402 | − | 0.563253i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −26.5703 | + | 46.0211i | −0.931288 | + | 1.61304i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.6637 | − | 23.6663i | 0.478033 | − | 0.827978i | ||||
\(818\) | − | 36.4918i | − | 1.27591i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.58876 | + | 5.53607i | 0.334650 | + | 0.193210i | 0.657904 | − | 0.753102i | \(-0.271443\pi\) |
−0.323254 | + | 0.946312i | \(0.604777\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.612108 | − | 0.353401i | 0.0213368 | − | 0.0123188i | −0.489294 | − | 0.872119i | \(-0.662745\pi\) |
0.510630 | + | 0.859800i | \(0.329412\pi\) | |||||||
\(824\) | 5.11942 | − | 8.86709i | 0.178343 | − | 0.308900i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.9767 | − | 9.17849i | 0.451518 | − | 0.319361i | ||||
\(827\) | −18.8230 | −0.654540 | −0.327270 | − | 0.944931i | \(-0.606129\pi\) | ||||
−0.327270 | + | 0.944931i | \(0.606129\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.7423 | − | 15.4397i | 0.928800 | − | 0.536243i | 0.0423683 | − | 0.999102i | \(-0.486510\pi\) |
0.886432 | + | 0.462859i | \(0.153176\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.49388 | 0.190466 | ||||||||
\(833\) | 3.93785 | + | 21.1563i | 0.136438 | + | 0.733023i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.69660 | − | 13.3309i | −0.266193 | − | 0.461059i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.8335 | + | 18.7641i | −0.374236 | + | 0.648195i | ||||
\(839\) | 20.9932 | 0.724766 | 0.362383 | − | 0.932029i | \(-0.381963\pi\) | ||||
0.362383 | + | 0.932029i | \(0.381963\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6071 | −0.538174 | ||||||||
\(842\) | 4.42096 | − | 7.65733i | 0.152356 | − | 0.263889i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.0110 | − | 22.5356i | −0.447856 | − | 0.775709i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.31306 | − | 35.9049i | −0.113838 | − | 1.23371i | ||||
\(848\) | −4.45071 | −0.152838 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 57.2744 | − | 33.0674i | 1.96334 | − | 1.13353i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.2167 | 0.623729 | 0.311864 | − | 0.950127i | \(-0.399047\pi\) | ||||
0.311864 | + | 0.950127i | \(0.399047\pi\) | |||||||
\(854\) | −11.5658 | + | 25.1135i | −0.395774 | + | 0.859365i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.28972 | + | 5.69797i | −0.112440 | + | 0.194753i | ||||
\(857\) | 10.7382 | − | 6.19973i | 0.366812 | − | 0.211779i | −0.305253 | − | 0.952271i | \(-0.598741\pi\) |
0.672065 | + | 0.740493i | \(0.265408\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.67438 | − | 3.85345i | −0.227727 | − | 0.131478i | 0.381796 | − | 0.924247i | \(-0.375306\pi\) |
−0.609523 | + | 0.792768i | \(0.708639\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 29.7313i | − | 1.01265i | ||||||
\(863\) | 3.77821 | − | 6.54406i | 0.128612 | − | 0.222762i | −0.794527 | − | 0.607229i | \(-0.792281\pi\) |
0.923139 | + | 0.384466i | \(0.125615\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −13.2833 | + | 23.0074i | −0.451386 | + | 0.781823i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.09241 | − | 0.285346i | 0.104963 | − | 0.00968528i | ||||
\(869\) | 21.0744i | 0.714900i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −56.8778 | + | 32.8384i | −1.92723 | + | 1.11269i | ||||
\(872\) | 1.34219 | + | 2.32474i | 0.0454522 | + | 0.0787255i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19.1572i | 0.648002i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.0843 | + | 15.0598i | 0.880803 | + | 0.508532i | 0.870923 | − | 0.491420i | \(-0.163522\pi\) |
0.00987971 | + | 0.999951i | \(0.496855\pi\) | |||||||
\(878\) | 14.4067 | − | 8.31774i | 0.486204 | − | 0.280710i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.6642 | −0.999411 | −0.499706 | − | 0.866195i | \(-0.666558\pi\) | ||||
−0.499706 | + | 0.866195i | \(0.666558\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 38.9643i | − | 1.31125i | −0.755086 | − | 0.655626i | \(-0.772405\pi\) | ||
0.755086 | − | 0.655626i | \(-0.227595\pi\) | |||||||
\(884\) | 14.6267 | + | 8.44475i | 0.491950 | + | 0.284028i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.63637 | + | 2.83428i | 0.0549750 | + | 0.0952195i | ||||
\(887\) | 17.9134 | + | 10.3423i | 0.601472 | + | 0.347260i | 0.769620 | − | 0.638502i | \(-0.220446\pi\) |
−0.168149 | + | 0.985762i | \(0.553779\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.42690 | − | 11.9141i | −0.282629 | − | 0.399586i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.62611 | + | 6.28060i | 0.121411 | + | 0.210290i | ||||
\(893\) | −6.43036 | − | 11.1377i | −0.215184 | − | 0.372709i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.243099 | + | 2.63456i | 0.00812137 | + | 0.0880144i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.03451 | + | 5.21608i | 0.301485 | + | 0.174063i | ||||
\(899\) | −3.91977 | − | 6.78924i | −0.130732 | − | 0.226434i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.8494 | − | 6.84127i | −0.394762 | − | 0.227916i | ||||
\(902\) | − | 41.6583i | − | 1.38707i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.55031 | 0.118081 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.5076 | + | 6.06658i | −0.348900 | + | 0.201437i | −0.664201 | − | 0.747554i | \(-0.731228\pi\) |
0.315301 | + | 0.948992i | \(0.397895\pi\) | |||||||
\(908\) | −23.1409 | − | 13.3604i | −0.767959 | − | 0.443381i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.5869i | 0.814600i | 0.913294 | + | 0.407300i | \(0.133530\pi\) | ||||
−0.913294 | + | 0.407300i | \(0.866470\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.4440 | − | 61.3908i | −1.17302 | − | 2.03174i | ||||
\(914\) | 28.6471 | − | 16.5394i | 0.947561 | − | 0.547074i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.3034i | 0.803006i | ||||||||
\(917\) | 5.01115 | + | 54.3078i | 0.165483 | + | 1.79340i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.5230 | + | 19.9585i | −0.380110 | + | 0.658369i | −0.991078 | − | 0.133286i | \(-0.957447\pi\) |
0.610968 | + | 0.791655i | \(0.290780\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.78196 | − | 10.0146i | 0.190419 | − | 0.329815i | ||||
\(923\) | − | 5.34841i | − | 0.176045i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −33.4339 | − | 19.3031i | −1.09871 | − | 0.634338i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.78405 | − | 3.33943i | 0.189871 | − | 0.109622i | ||||
\(929\) | −20.1685 | + | 34.9328i | −0.661706 | + | 1.14611i | 0.318461 | + | 0.947936i | \(0.396834\pi\) |
−0.980167 | + | 0.198173i | \(0.936499\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.4995 | − | 14.1137i | 0.540748 | − | 0.462559i | ||||
\(932\) | 9.25577 | 0.303183 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.08230 | − | 2.35692i | 0.133577 | − | 0.0771207i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.4861 | −1.35529 | −0.677646 | − | 0.735389i | \(-0.737000\pi\) | ||||
−0.677646 | + | 0.735389i | \(0.737000\pi\) | |||||||
\(938\) | −18.2643 | − | 25.8224i | −0.596350 | − | 0.843130i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.37786 | + | 16.2429i | 0.305710 | + | 0.529505i | 0.977419 | − | 0.211310i | \(-0.0677730\pi\) |
−0.671709 | + | 0.740815i | \(0.734440\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.9223 | + | 44.8988i | −0.844148 | + | 1.46211i | ||||
\(944\) | 6.00761 | 0.195531 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 43.7227 | 1.42155 | ||||||||
\(947\) | 21.6910 | − | 37.5699i | 0.704862 | − | 1.22086i | −0.261879 | − | 0.965101i | \(-0.584342\pi\) |
0.966741 | − | 0.255756i | \(-0.0823244\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.8693 | − | 79.4479i | −1.48898 | − | 2.57899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.40241 | + | 7.38784i | −0.110273 | + | 0.239441i | ||||
\(953\) | −18.1672 | −0.588492 | −0.294246 | − | 0.955730i | \(-0.595069\pi\) | ||||
−0.294246 | + | 0.955730i | \(0.595069\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.219422 | + | 0.126683i | −0.00709661 | + | 0.00409723i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20.0191 | −0.646789 | ||||||||
\(959\) | −27.5308 | − | 12.6791i | −0.889015 | − | 0.409429i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.8111 | + | 25.6536i | −0.477778 | + | 0.827536i | ||||
\(962\) | −50.9469 | + | 29.4142i | −1.64259 | + | 0.948352i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.57538 | − | 1.48689i | −0.0829473 | − | 0.0478896i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.7712i | 0.957378i | 0.877985 | + | 0.478689i | \(0.158888\pi\) | ||||
−0.877985 | + | 0.478689i | \(0.841112\pi\) | |||||||
\(968\) | 6.81421 | − | 11.8026i | 0.219017 | − | 0.379349i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.5472 | + | 32.1247i | −0.595209 | + | 1.03093i | 0.398309 | + | 0.917251i | \(0.369597\pi\) |
−0.993517 | + | 0.113680i | \(0.963736\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.78296 | − | 2.52078i | −0.0571591 | − | 0.0808126i | ||||
\(974\) | 4.73088i | 0.151587i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.05018 | + | 5.22512i | −0.289689 | + | 0.167252i | ||||
\(977\) | 0.505165 | + | 0.874971i | 0.0161617 | + | 0.0279928i | 0.873993 | − | 0.485938i | \(-0.161522\pi\) |
−0.857831 | + | 0.513931i | \(0.828189\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 73.3008i | 2.34270i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.8587 | + | 8.00133i | 0.442249 | + | 0.255333i | ||||
\(983\) | 21.9623 | − | 12.6799i | 0.700487 | − | 0.404427i | −0.107042 | − | 0.994255i | \(-0.534138\pi\) |
0.807529 | + | 0.589828i | \(0.200804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 20.5324 | 0.653884 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 17.0408i | − | 0.542140i | ||||||
\(989\) | −47.1238 | − | 27.2070i | −1.49845 | − | 0.865131i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.3875 | + | 37.0442i | 0.679396 | + | 1.17675i | 0.975163 | + | 0.221488i | \(0.0710914\pi\) |
−0.295767 | + | 0.955260i | \(0.595575\pi\) | |||||||
\(992\) | 1.01653 | + | 0.586893i | 0.0322748 | + | 0.0186339i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.56480 | − | 0.236662i | 0.0813506 | − | 0.00750647i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.6906 | − | 21.9808i | −0.401916 | − | 0.696139i | 0.592041 | − | 0.805908i | \(-0.298322\pi\) |
−0.993957 | + | 0.109769i | \(0.964989\pi\) | |||||||
\(998\) | 3.18097 | + | 5.50961i | 0.100692 | + | 0.174404i | ||||
\(999\) | 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 | 3150.2.bp.g.1349.9 | 24 | ||
3.2 | odd | 2 | 3150.2.bp.h.1349.9 | 24 | |||
5.2 | odd | 4 | 3150.2.bf.e.1601.1 | yes | 24 | ||
5.3 | odd | 4 | 3150.2.bf.d.1601.12 | yes | 24 | ||
5.4 | even | 2 | 3150.2.bp.h.1349.4 | 24 | |||
7.3 | odd | 6 | inner | 3150.2.bp.g.899.4 | 24 | ||
15.2 | even | 4 | 3150.2.bf.e.1601.12 | yes | 24 | ||
15.8 | even | 4 | 3150.2.bf.d.1601.1 | yes | 24 | ||
15.14 | odd | 2 | inner | 3150.2.bp.g.1349.4 | 24 | ||
21.17 | even | 6 | 3150.2.bp.h.899.4 | 24 | |||
35.3 | even | 12 | 3150.2.bf.d.1151.1 | ✓ | 24 | ||
35.17 | even | 12 | 3150.2.bf.e.1151.12 | yes | 24 | ||
35.24 | odd | 6 | 3150.2.bp.h.899.9 | 24 | |||
105.17 | odd | 12 | 3150.2.bf.e.1151.1 | yes | 24 | ||
105.38 | odd | 12 | 3150.2.bf.d.1151.12 | yes | 24 | ||
105.59 | even | 6 | inner | 3150.2.bp.g.899.9 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.bf.d.1151.1 | ✓ | 24 | 35.3 | even | 12 | ||
3150.2.bf.d.1151.12 | yes | 24 | 105.38 | odd | 12 | ||
3150.2.bf.d.1601.1 | yes | 24 | 15.8 | even | 4 | ||
3150.2.bf.d.1601.12 | yes | 24 | 5.3 | odd | 4 | ||
3150.2.bf.e.1151.1 | yes | 24 | 105.17 | odd | 12 | ||
3150.2.bf.e.1151.12 | yes | 24 | 35.17 | even | 12 | ||
3150.2.bf.e.1601.1 | yes | 24 | 5.2 | odd | 4 | ||
3150.2.bf.e.1601.12 | yes | 24 | 15.2 | even | 4 | ||
3150.2.bp.g.899.4 | 24 | 7.3 | odd | 6 | inner | ||
3150.2.bp.g.899.9 | 24 | 105.59 | even | 6 | inner | ||
3150.2.bp.g.1349.4 | 24 | 15.14 | odd | 2 | inner | ||
3150.2.bp.g.1349.9 | 24 | 1.1 | even | 1 | trivial | ||
3150.2.bp.h.899.4 | 24 | 21.17 | even | 6 | |||
3150.2.bp.h.899.9 | 24 | 35.24 | odd | 6 | |||
3150.2.bp.h.1349.4 | 24 | 5.4 | even | 2 | |||
3150.2.bp.h.1349.9 | 24 | 3.2 | odd | 2 |