Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [124,2,Mod(33,124)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(124, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("124.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 124 = 2^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 124.f (of order \(5\), degree \(4\), 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: | \(0.990144985064\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 33.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 124.33 |
Dual form | 124.2.f.a.109.1 |
$q$-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 \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).
\(n\) | \(63\) | \(65\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.30902 | + | 0.951057i | −0.755761 | + | 0.549093i | −0.897607 | − | 0.440796i | \(-0.854696\pi\) |
0.141846 | + | 0.989889i | \(0.454696\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.809017 | + | 2.48990i | 0.305780 | + | 0.941093i | 0.979385 | + | 0.202002i | \(0.0647447\pi\) |
−0.673605 | + | 0.739091i | \(0.735255\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.118034 | + | 0.363271i | −0.0393447 | + | 0.121090i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.809017 | + | 2.48990i | 0.243928 | + | 0.750733i | 0.995811 | + | 0.0914362i | \(0.0291457\pi\) |
−0.751883 | + | 0.659296i | \(0.770854\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.30902 | − | 0.951057i | 0.363056 | − | 0.263776i | −0.391270 | − | 0.920276i | \(-0.627964\pi\) |
0.754326 | + | 0.656500i | \(0.227964\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.61803 | + | 1.90211i | −0.675973 | + | 0.491123i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.42705 | − | 4.39201i | 0.346111 | − | 1.06522i | −0.614876 | − | 0.788624i | \(-0.710794\pi\) |
0.960987 | − | 0.276595i | \(-0.0892061\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.92705 | − | 2.85317i | −0.900927 | − | 0.654562i | 0.0377767 | − | 0.999286i | \(-0.487972\pi\) |
−0.938704 | + | 0.344724i | \(0.887972\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.42705 | − | 2.48990i | −0.747844 | − | 0.543340i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.66312 | − | 5.11855i | 0.346784 | − | 1.06729i | −0.613837 | − | 0.789433i | \(-0.710375\pi\) |
0.960622 | − | 0.277860i | \(-0.0896251\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.69098 | − | 5.20431i | −0.325430 | − | 1.00157i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.690983 | − | 0.502029i | −0.128312 | − | 0.0932244i | 0.521778 | − | 0.853081i | \(-0.325269\pi\) |
−0.650090 | + | 0.759857i | \(0.725269\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.23607 | + | 4.53077i | 0.581215 | + | 0.813750i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.42705 | − | 2.48990i | −0.596573 | − | 0.433436i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.61803 | + | 4.97980i | 0.273498 | + | 0.841739i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.809017 | + | 2.48990i | −0.129546 | + | 0.398703i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.78115 | + | 7.10642i | 1.52756 | + | 1.10984i | 0.957576 | + | 0.288181i | \(0.0930504\pi\) |
0.569983 | + | 0.821656i | \(0.306950\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.16312 | − | 5.20431i | −1.09237 | − | 0.793650i | −0.112568 | − | 0.993644i | \(-0.535908\pi\) |
−0.979797 | + | 0.199994i | \(0.935908\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.236068 | + | 0.726543i | −0.0351909 | + | 0.108307i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.690983 | − | 0.502029i | 0.100790 | − | 0.0732284i | −0.536249 | − | 0.844060i | \(-0.680159\pi\) |
0.637039 | + | 0.770832i | \(0.280159\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.118034 | − | 0.0857567i | 0.0168620 | − | 0.0122510i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.30902 | + | 7.10642i | 0.323327 | + | 0.995098i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.66312 | − | 8.19624i | 0.365808 | − | 1.12584i | −0.583666 | − | 0.811994i | \(-0.698382\pi\) |
0.949474 | − | 0.313846i | \(-0.101618\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.61803 | + | 4.97980i | 0.218176 | + | 0.671476i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.85410 | 1.04030 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.16312 | − | 5.20431i | 0.932559 | − | 0.677544i | −0.0140593 | − | 0.999901i | \(-0.504475\pi\) |
0.946618 | + | 0.322358i | \(0.104475\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.4164 | −1.71780 | −0.858898 | − | 0.512148i | \(-0.828850\pi\) | ||||
−0.858898 | + | 0.512148i | \(0.828850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.61803 | − | 1.90211i | 0.324727 | − | 0.235928i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.52786 | 0.186658 | 0.0933292 | − | 0.995635i | \(-0.470249\pi\) | ||||
0.0933292 | + | 0.995635i | \(0.470249\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.69098 | + | 8.28199i | 0.323956 | + | 0.997035i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.28115 | + | 3.94298i | −0.152045 | + | 0.467946i | −0.997849 | − | 0.0655468i | \(-0.979121\pi\) |
0.845805 | + | 0.533493i | \(0.179121\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.89919 | + | 12.0005i | 0.456365 | + | 1.40455i | 0.869525 | + | 0.493889i | \(0.164425\pi\) |
−0.413159 | + | 0.910659i | \(0.635575\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.30902 | − | 0.951057i | 0.151152 | − | 0.109819i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.54508 | + | 4.02874i | −0.631921 | + | 0.459118i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.19098 | − | 3.66547i | 0.133996 | − | 0.412397i | −0.861436 | − | 0.507865i | \(-0.830435\pi\) |
0.995433 | + | 0.0954679i | \(0.0304347\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.23607 | + | 4.53077i | 0.692896 | + | 0.503419i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.54508 | + | 1.84911i | 0.279359 | + | 0.202966i | 0.718638 | − | 0.695384i | \(-0.244766\pi\) |
−0.439279 | + | 0.898351i | \(0.644766\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.85410 | − | 8.78402i | 0.309571 | − | 0.952761i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.38197 | 0.148162 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.57295 | − | 7.91872i | −0.272732 | − | 0.839383i | −0.989811 | − | 0.142391i | \(-0.954521\pi\) |
0.717079 | − | 0.696992i | \(-0.245479\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.42705 | + | 2.48990i | 0.359253 | + | 0.261012i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.54508 | − | 2.85317i | −0.886084 | − | 0.295860i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.85410 | − | 5.70634i | −0.805814 | − | 0.585458i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.13525 | + | 15.8047i | 0.521406 | + | 1.60472i | 0.771315 | + | 0.636454i | \(0.219599\pi\) |
−0.249909 | + | 0.968269i | \(0.580401\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.57295 | + | 7.91872i | −0.256018 | + | 0.787942i | 0.737609 | + | 0.675228i | \(0.235955\pi\) |
−0.993627 | + | 0.112715i | \(0.964045\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.3992 | − | 10.4616i | −1.41879 | − | 1.03081i | −0.991969 | − | 0.126480i | \(-0.959632\pi\) |
−0.426825 | − | 0.904334i | \(-0.640368\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.85410 | − | 4.97980i | −0.668892 | − | 0.485978i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.95492 | − | 12.1720i | 0.382336 | − | 1.17671i | −0.556058 | − | 0.831143i | \(-0.687687\pi\) |
0.938394 | − | 0.345566i | \(-0.112313\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.39919 | + | 4.64928i | −0.612931 | + | 0.445320i | −0.850445 | − | 0.526064i | \(-0.823667\pi\) |
0.237514 | + | 0.971384i | \(0.423667\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.85410 | − | 4.25325i | 0.555647 | − | 0.403701i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.33688 | − | 10.2699i | −0.313907 | − | 0.966108i | −0.976202 | − | 0.216864i | \(-0.930417\pi\) |
0.662294 | − | 0.749244i | \(-0.269583\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.32624 | − | 10.2371i | 0.310173 | − | 0.954615i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.190983 | + | 0.587785i | 0.0176564 | + | 0.0543408i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.0902 | 1.10830 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.35410 | − | 2.43690i | 0.304918 | − | 0.221536i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.5623 | −1.76387 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.69098 | − | 1.95511i | 0.238786 | − | 0.173488i | −0.461956 | − | 0.886903i | \(-0.652852\pi\) |
0.700742 | + | 0.713414i | \(0.252852\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.3262 | 1.26135 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.33688 | + | 13.3475i | 0.378915 | + | 1.16618i | 0.940799 | + | 0.338965i | \(0.110077\pi\) |
−0.561884 | + | 0.827216i | \(0.689923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.92705 | − | 12.0862i | 0.340519 | − | 1.04801i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.38197 | − | 10.4086i | −0.291073 | − | 0.895831i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.3992 | + | 7.55545i | −0.888462 | + | 0.645506i | −0.935477 | − | 0.353388i | \(-0.885029\pi\) |
0.0470142 | + | 0.998894i | \(0.485029\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.39919 | − | 4.64928i | 0.542772 | − | 0.394347i | −0.282342 | − | 0.959314i | \(-0.591111\pi\) |
0.825113 | + | 0.564967i | \(0.191111\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.427051 | + | 1.31433i | −0.0359642 | + | 0.110686i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.42705 | + | 2.48990i | 0.286584 | + | 0.208216i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.38197 | − | 1.00406i | −0.114766 | − | 0.0833824i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.0729490 | + | 0.224514i | −0.00601673 | + | 0.0185176i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.4164 | −1.75450 | −0.877250 | − | 0.480033i | \(-0.840625\pi\) | ||||
−0.877250 | + | 0.480033i | \(0.840625\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.66312 | − | 11.2739i | −0.298100 | − | 0.917459i | −0.982162 | − | 0.188035i | \(-0.939788\pi\) |
0.684062 | − | 0.729424i | \(-0.260212\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.42705 | + | 1.03681i | 0.115370 | + | 0.0838214i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.47214 | + | 9.06154i | 0.519854 | + | 0.727840i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.54508 | + | 6.20837i | 0.681972 | + | 0.495482i | 0.874011 | − | 0.485906i | \(-0.161510\pi\) |
−0.192039 | + | 0.981387i | \(0.561510\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.30902 | + | 13.2618i | 0.341727 | + | 1.05173i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.0902 | 1.11046 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.57295 | + | 17.1518i | −0.436507 | + | 1.34343i | 0.455027 | + | 0.890477i | \(0.349629\pi\) |
−0.891534 | + | 0.452953i | \(0.850371\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.85410 | − | 4.97980i | −0.533591 | − | 0.387677i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.07295 | + | 2.95917i | 0.315174 | + | 0.228988i | 0.734114 | − | 0.679027i | \(-0.237598\pi\) |
−0.418939 | + | 0.908014i | \(0.637598\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.20820 | + | 9.87384i | −0.246785 | + | 0.759526i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.50000 | − | 1.08981i | 0.114708 | − | 0.0833401i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.92705 | + | 2.85317i | −0.298568 | + | 0.216922i | −0.726976 | − | 0.686663i | \(-0.759075\pi\) |
0.428408 | + | 0.903586i | \(0.359075\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.809017 | − | 2.48990i | −0.0611559 | − | 0.188219i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.42705 | + | 13.6251i | −0.332758 | + | 1.02412i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.57295 | + | 17.1518i | 0.416542 | + | 1.28198i | 0.910865 | + | 0.412705i | \(0.135416\pi\) |
−0.494323 | + | 0.869278i | \(0.664584\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.4721 | 1.81900 | 0.909500 | − | 0.415704i | \(-0.136465\pi\) | ||||
0.909500 | + | 0.415704i | \(0.136465\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.5623 | − | 12.7598i | 1.29824 | − | 0.943229i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.94427 | −0.657596 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.0902 | 0.884121 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.5902 | − | 8.42075i | 0.843061 | − | 0.612520i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.41641 | −0.536632 | −0.268316 | − | 0.963331i | \(-0.586467\pi\) | ||||
−0.268316 | + | 0.963331i | \(0.586467\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.75329 | − | 14.6291i | −0.342149 | − | 1.05303i | −0.963092 | − | 0.269171i | \(-0.913250\pi\) |
0.620943 | − | 0.783856i | \(-0.286750\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.61803 | + | 4.97980i | −0.115870 | + | 0.356611i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.89919 | + | 5.84510i | 0.135311 | + | 0.416446i | 0.995638 | − | 0.0932969i | \(-0.0297406\pi\) |
−0.860327 | + | 0.509743i | \(0.829741\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.7812 | + | 8.55951i | −0.835144 | + | 0.606767i | −0.921010 | − | 0.389539i | \(-0.872634\pi\) |
0.0858661 | + | 0.996307i | \(0.472634\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.00000 | + | 1.45309i | −0.141069 | + | 0.102493i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.690983 | − | 2.12663i | 0.0484975 | − | 0.149260i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.5623 | + | 14.2128i | 1.36629 | + | 0.992668i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.66312 | + | 1.20833i | 0.115595 | + | 0.0839845i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.92705 | − | 12.0862i | 0.271640 | − | 0.836021i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.07295 | − | 6.37988i | −0.142036 | − | 0.437142i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.3262 | − | 10.4086i | −0.977041 | − | 0.709862i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.66312 | + | 11.7229i | −0.588091 | + | 0.795806i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.5172 | − | 12.0005i | −1.11613 | − | 0.810916i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.30902 | − | 7.10642i | −0.155321 | − | 0.478030i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.944272 | 0.0632331 | 0.0316166 | − | 0.999500i | \(-0.489934\pi\) | ||||
0.0316166 | + | 0.999500i | \(0.489934\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.118034 | − | 0.363271i | 0.00786893 | − | 0.0242181i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.16312 | − | 2.29814i | −0.209944 | − | 0.152533i | 0.477845 | − | 0.878444i | \(-0.341418\pi\) |
−0.687788 | + | 0.725911i | \(0.741418\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.0729490 | + | 0.0530006i | 0.00482061 | + | 0.00350238i | 0.590193 | − | 0.807262i | \(-0.299052\pi\) |
−0.585372 | + | 0.810765i | \(0.699052\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.42705 | − | 10.5474i | 0.225483 | − | 0.693967i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.5451 | − | 9.11454i | 0.821856 | − | 0.597113i | −0.0953876 | − | 0.995440i | \(-0.530409\pi\) |
0.917243 | + | 0.398327i | \(0.130409\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.38197 | − | 1.00406i | 0.0901495 | − | 0.0654975i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.92705 | + | 5.93085i | 0.125175 | + | 0.385250i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.33688 | + | 25.6583i | −0.539268 | + | 1.65970i | 0.194974 | + | 0.980808i | \(0.437538\pi\) |
−0.734242 | + | 0.678888i | \(0.762462\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.190983 | + | 0.587785i | 0.0123023 | + | 0.0378626i | 0.957019 | − | 0.290024i | \(-0.0936635\pi\) |
−0.944717 | + | 0.327887i | \(0.893663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.94427 | 0.253025 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.236068 | − | 0.171513i | 0.0150818 | − | 0.0109576i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.85410 | −0.499745 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.09017 | −0.322576 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.07295 | + | 1.50609i | −0.130843 | + | 0.0950633i | −0.651282 | − | 0.758836i | \(-0.725768\pi\) |
0.520439 | + | 0.853899i | \(0.325768\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.0902 | 0.885841 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.61803 | + | 14.2128i | 0.289193 | + | 0.890043i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.19098 | − | 25.2093i | 0.510939 | − | 1.57251i | −0.279611 | − | 0.960113i | \(-0.590206\pi\) |
0.790551 | − | 0.612397i | \(-0.209794\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.61803 | − | 11.1352i | −0.224814 | − | 0.691905i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.263932 | − | 0.191758i | 0.0163370 | − | 0.0118695i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.0172 | + | 12.3637i | −1.04933 | + | 0.762381i | −0.972084 | − | 0.234632i | \(-0.924612\pi\) |
−0.0772425 | + | 0.997012i | \(0.524612\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.32624 | − | 16.3925i | 0.327188 | − | 1.00698i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.8992 | + | 7.91872i | 0.667019 | + | 0.484618i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.3992 | − | 9.00854i | −0.755992 | − | 0.549260i | 0.141687 | − | 0.989912i | \(-0.454747\pi\) |
−0.897678 | + | 0.440651i | \(0.854747\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.10081 | + | 21.8541i | −0.431344 | + | 1.32754i | 0.465444 | + | 0.885078i | \(0.345895\pi\) |
−0.896787 | + | 0.442462i | \(0.854105\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.85410 | −0.414829 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.809017 | − | 2.48990i | −0.0487856 | − | 0.150147i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.3992 | − | 10.4616i | −0.865163 | − | 0.628578i | 0.0641214 | − | 0.997942i | \(-0.479576\pi\) |
−0.929285 | + | 0.369364i | \(0.879576\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.02786 | + | 0.640786i | −0.121405 | + | 0.0383628i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.6353 | − | 11.3597i | −0.932721 | − | 0.677662i | 0.0139364 | − | 0.999903i | \(-0.495564\pi\) |
−0.946658 | + | 0.322241i | \(0.895564\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.48278 | − | 16.8743i | −0.325917 | − | 1.00307i | −0.971025 | − | 0.238979i | \(-0.923187\pi\) |
0.645107 | − | 0.764092i | \(-0.276813\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.7082 | 0.930474 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.78115 | + | 30.1033i | −0.577363 | + | 1.77694i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.50000 | − | 2.54290i | −0.205882 | − | 0.149582i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.7533 | − | 15.8047i | −1.27520 | − | 0.926487i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.33688 | + | 4.11450i | −0.0781014 | + | 0.240371i | −0.982483 | − | 0.186354i | \(-0.940333\pi\) |
0.904381 | + | 0.426725i | \(0.140333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.3262 | − | 10.4086i | 0.834106 | − | 0.606013i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.5902 | − | 8.42075i | 0.672530 | − | 0.488622i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.69098 | − | 8.28199i | −0.155624 | − | 0.478960i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.16312 | − | 22.0458i | 0.412875 | − | 1.27070i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.16312 | − | 12.8128i | −0.239165 | − | 0.736074i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −26.8328 | −1.53644 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.69098 | − | 4.86128i | 0.381875 | − | 0.277448i | −0.380243 | − | 0.924887i | \(-0.624160\pi\) |
0.762118 | + | 0.647438i | \(0.224160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.7984 | 1.63828 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.8885 | 1.24119 | 0.620593 | − | 0.784133i | \(-0.286892\pi\) | ||||
0.620593 | + | 0.784133i | \(0.286892\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.92705 | + | 1.40008i | −0.108923 | + | 0.0791375i | −0.640914 | − | 0.767613i | \(-0.721444\pi\) |
0.531990 | + | 0.846751i | \(0.321444\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.00000 | −0.112687 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.572949 | − | 1.76336i | −0.0321800 | − | 0.0990399i | 0.933676 | − | 0.358118i | \(-0.116581\pi\) |
−0.965856 | + | 0.259078i | \(0.916581\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.690983 | − | 2.12663i | 0.0386876 | − | 0.119068i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.39919 | + | 19.6947i | 0.357168 | + | 1.09925i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.1353 | + | 13.1760i | −1.00907 | + | 0.733134i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.30902 | + | 0.951057i | −0.0726112 | + | 0.0527551i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.95492 | − | 12.1720i | 0.218707 | − | 0.673112i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.80902 | + | 1.31433i | 0.0997343 | + | 0.0724612i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.54508 | + | 6.20837i | 0.469680 | + | 0.341243i | 0.797317 | − | 0.603561i | \(-0.206252\pi\) |
−0.327636 | + | 0.944804i | \(0.606252\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.527864 | − | 1.62460i | 0.0289268 | − | 0.0890274i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.05573 | 0.166952 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.13525 | + | 9.64932i | 0.170788 | + | 0.525632i | 0.999416 | − | 0.0341677i | \(-0.0108780\pi\) |
−0.828628 | + | 0.559800i | \(0.810878\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.1353 | + | 10.2699i | 0.767722 | + | 0.557782i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.66312 | + | 11.7229i | −0.469134 | + | 0.634833i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.1353 | + | 10.9964i | 0.817227 | + | 0.593750i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.38197 | + | 16.5640i | 0.289755 | + | 0.891775i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.8328 | −1.22573 | −0.612865 | − | 0.790188i | \(-0.709983\pi\) | ||||
−0.612865 | + | 0.790188i | \(0.709983\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.28115 | + | 7.02067i | −0.122107 | + | 0.375808i | −0.993363 | − | 0.115022i | \(-0.963306\pi\) |
0.871256 | + | 0.490829i | \(0.163306\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.16312 | − | 5.20431i | −0.382339 | − | 0.277786i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.7812 | + | 10.0126i | 0.733497 | + | 0.532917i | 0.890668 | − | 0.454655i | \(-0.150237\pi\) |
−0.157171 | + | 0.987571i | \(0.550237\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.56231 | + | 7.88597i | −0.135993 | + | 0.418544i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.8262 | + | 11.4984i | −0.837613 | + | 0.608562i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.63525 | − | 7.00042i | 0.508529 | − | 0.369468i | −0.303736 | − | 0.952756i | \(-0.598234\pi\) |
0.812265 | + | 0.583288i | \(0.198234\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.40983 | + | 4.33901i | 0.0742016 | + | 0.228369i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.07295 | + | 6.37988i | −0.108802 | + | 0.334857i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.79837 | + | 24.0009i | 0.408186 | + | 1.25627i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.9443 | 1.09328 | 0.546641 | − | 0.837367i | \(-0.315906\pi\) | ||||
0.546641 | + | 0.837367i | \(0.315906\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.73607 | + | 2.71441i | −0.194492 | + | 0.141307i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.5623 | 1.17138 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.94427 | −0.152449 | −0.0762243 | − | 0.997091i | \(-0.524287\pi\) | ||||
−0.0762243 | + | 0.997091i | \(0.524287\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.7082 | − | 11.4127i | 0.811168 | − | 0.589348i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.38197 | −0.0711749 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.57295 | + | 17.1518i | 0.286263 | + | 0.881027i | 0.986017 | + | 0.166644i | \(0.0532929\pi\) |
−0.699754 | + | 0.714384i | \(0.746707\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.66312 | + | 5.11855i | −0.0852042 | + | 0.262231i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.86475 | + | 5.73910i | 0.0952840 | + | 0.293254i | 0.987328 | − | 0.158695i | \(-0.0507288\pi\) |
−0.892044 | + | 0.451949i | \(0.850729\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.0902 | + | 8.05748i | −0.565207 | + | 0.410647i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.73607 | − | 1.98787i | 0.139082 | − | 0.101049i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.37132 | − | 13.4535i | 0.221635 | − | 0.682122i | −0.776981 | − | 0.629524i | \(-0.783250\pi\) |
0.998616 | − | 0.0525978i | \(-0.0167501\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.1074 | − | 14.6089i | −1.01687 | − | 0.738803i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.3713 | − | 13.3475i | −0.926711 | − | 0.673295i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.38197 | − | 7.33094i | 0.119850 | − | 0.368860i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.41641 | 0.0710875 | 0.0355437 | − | 0.999368i | \(-0.488684\pi\) | ||||
0.0355437 | + | 0.999368i | \(0.488684\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.35410 | + | 19.5559i | 0.318103 | + | 0.979020i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.1631 | − | 9.56357i | −0.657335 | − | 0.477582i | 0.208427 | − | 0.978038i | \(-0.433166\pi\) |
−0.865762 | + | 0.500456i | \(0.833166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.54508 | + | 2.85317i | 0.425661 | + | 0.142126i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.4721 | + | 9.06154i | 0.619745 | + | 0.450271i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.61803 | − | 11.1352i | −0.179339 | − | 0.551950i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.4721 | −0.616707 | −0.308354 | − | 0.951272i | \(-0.599778\pi\) | ||||
−0.308354 | + | 0.951272i | \(0.599778\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.42705 | − | 19.7804i | 0.317023 | − | 0.975697i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.7533 | + | 13.6251i | 0.922789 | + | 0.670445i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.09017 | + | 3.69822i | 0.249867 | + | 0.181539i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.95492 | + | 12.1720i | −0.193673 | + | 0.596064i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.8713 | − | 12.2577i | 0.824218 | − | 0.598829i | −0.0936995 | − | 0.995601i | \(-0.529869\pi\) |
0.917918 | + | 0.396771i | \(0.129869\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0172 | − | 9.45756i | 0.634421 | − | 0.460933i | −0.223508 | − | 0.974702i | \(-0.571751\pi\) |
0.857929 | + | 0.513769i | \(0.171751\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.100813 | + | 0.310271i | 0.00490170 | + | 0.0150859i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.42705 | + | 4.39201i | −0.0692221 | + | 0.213044i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.8541 | − | 33.4055i | −0.525267 | − | 1.61661i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.85410 | −0.330919 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.01722 | + | 3.64522i | −0.241671 | + | 0.175584i | −0.702027 | − | 0.712150i | \(-0.747722\pi\) |
0.460356 | + | 0.887734i | \(0.347722\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.8885 | −1.14801 | −0.574005 | − | 0.818852i | \(-0.694611\pi\) | ||||
−0.574005 | + | 0.818852i | \(0.694611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.76393 | 0.132520 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.1353 | + | 15.3557i | −1.01104 | + | 0.734561i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.4164 | −1.49942 | −0.749712 | − | 0.661765i | \(-0.769808\pi\) | ||||
−0.749712 | + | 0.661765i | \(0.769808\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0172209 | + | 0.0530006i | 0.000820044 | + | 0.00252384i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.42705 | − | 7.46969i | 0.115313 | − | 0.354896i | −0.876699 | − | 0.481039i | \(-0.840260\pi\) |
0.992012 | + | 0.126143i | \(0.0402597\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.14590 | − | 15.8374i | −0.243939 | − | 0.750767i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28.0344 | − | 20.3682i | 1.32598 | − | 0.963383i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.0172 | − | 18.1761i | 1.18064 | − | 0.857782i | 0.188392 | − | 0.982094i | \(-0.439672\pi\) |
0.992243 | + | 0.124312i | \(0.0396723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.78115 | + | 30.1033i | −0.460577 | + | 1.41751i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.5172 | + | 11.2739i | 0.729063 | + | 0.529695i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.85410 | + | 4.97980i | 0.321325 | + | 0.233456i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.663119 | − | 2.04087i | 0.0310194 | − | 0.0954679i | −0.934348 | − | 0.356361i | \(-0.884017\pi\) |
0.965368 | + | 0.260894i | \(0.0840172\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.2705 | −1.17953 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.57295 | − | 26.3848i | −0.399282 | − | 1.22886i | −0.925576 | − | 0.378561i | \(-0.876419\pi\) |
0.526294 | − | 0.850303i | \(-0.323581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.30902 | + | 6.76340i | 0.432627 | + | 0.314322i | 0.782698 | − | 0.622401i | \(-0.213843\pi\) |
−0.350072 | + | 0.936723i | \(0.613843\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.0902 | − | 5.70634i | −0.792538 | − | 0.264625i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.45492 | − | 3.96323i | −0.252423 | − | 0.183396i | 0.454377 | − | 0.890810i | \(-0.349862\pi\) |
−0.706800 | + | 0.707413i | \(0.749862\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.23607 | + | 3.80423i | 0.0570763 | + | 0.175663i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.0902 | −0.787473 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.16312 | − | 22.0458i | 0.329361 | − | 1.01367i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.92705 | + | 2.85317i | 0.180185 | + | 0.130912i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.66312 | + | 1.93487i | 0.121936 | + | 0.0885916i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.84346 | − | 17.9843i | 0.266994 | − | 0.821724i | −0.724233 | − | 0.689556i | \(-0.757806\pi\) |
0.991227 | − | 0.132169i | \(-0.0421941\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.85410 | + | 4.25325i | −0.266924 | + | 0.193932i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.4443 | + | 13.4005i | −0.839243 | + | 0.609746i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.2705 | + | 31.6094i | 0.466360 | + | 1.43531i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.19098 | − | 22.1316i | 0.325855 | − | 1.00288i | −0.645199 | − | 0.764015i | \(-0.723225\pi\) |
0.971053 | − | 0.238862i | \(-0.0767745\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.01722 | − | 27.7522i | −0.407773 | − | 1.25500i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.36068 | 0.377312 | 0.188656 | − | 0.982043i | \(-0.439587\pi\) | ||||
0.188656 | + | 0.982043i | \(0.439587\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.19098 | + | 2.31838i | −0.143715 | + | 0.104415i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.00000 | −0.0898933 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.8541 | −0.486873 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.30902 | + | 0.951057i | −0.0585996 | + | 0.0425751i | −0.616699 | − | 0.787199i | \(-0.711531\pi\) |
0.558100 | + | 0.829774i | \(0.311531\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.14590 | −0.363932 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.19098 | − | 15.9762i | −0.231454 | − | 0.712344i | −0.997572 | − | 0.0696431i | \(-0.977814\pi\) |
0.766117 | − | 0.642701i | \(-0.222186\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.14590 | + | 15.8374i | −0.228989 | + | 0.704757i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.19098 | − | 15.9762i | −0.230540 | − | 0.709528i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.0172 | − | 12.3637i | 0.754275 | − | 0.548013i | −0.142874 | − | 0.989741i | \(-0.545634\pi\) |
0.897149 | + | 0.441728i | \(0.145634\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.7254 | + | 19.4172i | −1.18226 | + | 0.858964i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.20820 | + | 25.2623i | −0.362401 | + | 1.11536i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −28.7984 | − | 20.9232i | −1.26901 | − | 0.921988i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.80902 | + | 1.31433i | 0.0795605 | + | 0.0578041i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.42705 | − | 7.46969i | 0.106536 | − | 0.327883i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.3607 | 1.50537 | 0.752684 | − | 0.658382i | \(-0.228759\pi\) | ||||
0.752684 | + | 0.658382i | \(0.228759\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.86475 | + | 30.3606i | 0.431355 | + | 1.32757i | 0.896776 | + | 0.442485i | \(0.145903\pi\) |
−0.465421 | + | 0.885090i | \(0.654097\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.42705 | + | 2.48990i | 0.149569 | + | 0.108668i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.5172 | − | 7.74721i | 1.06799 | − | 0.337474i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.82624 | − | 3.50647i | −0.209836 | − | 0.152455i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.04508 | + | 3.21644i | 0.0453528 | + | 0.139582i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.5623 | 0.847338 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.90983 | − | 24.3440i | 0.341972 | − | 1.05248i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.6074 | − | 17.1518i | −1.01873 | − | 0.740154i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.309017 | + | 0.224514i | 0.0133103 | + | 0.00967050i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.0451 | + | 33.9933i | −0.474865 | + | 1.46149i | 0.371274 | + | 0.928523i | \(0.378921\pi\) |
−0.846139 | + | 0.532962i | \(0.821079\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −32.0344 | + | 23.2744i | −1.37473 | + | 0.998799i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.7984 | + | 9.29856i | −0.548222 | + | 0.398307i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.84346 | − | 17.9843i | −0.249848 | − | 0.768954i | −0.994801 | − | 0.101837i | \(-0.967528\pi\) |
0.744953 | − | 0.667117i | \(-0.232472\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.58359 | − | 4.87380i | 0.0675861 | − | 0.208009i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.28115 | + | 3.94298i | 0.0545790 | + | 0.167977i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0902 | 0.429078 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.7082 | − | 8.50651i | 0.496986 | − | 0.361081i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.3607 | 1.11694 | 0.558469 | − | 0.829525i | \(-0.311389\pi\) | ||||
0.558469 | + | 0.829525i | \(0.311389\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.3262 | −0.605935 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.8262 | + | 11.4984i | −0.668184 | + | 0.485464i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.9443 | 1.21986 | 0.609928 | − | 0.792457i | \(-0.291198\pi\) | ||||
0.609928 | + | 0.792457i | \(0.291198\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.67376 | − | 20.5397i | −0.280767 | − | 0.864113i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.23607 | + | 19.1926i | −0.261890 | + | 0.806015i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.01064 | + | 18.4989i | 0.251979 | + | 0.775512i | 0.994410 | + | 0.105589i | \(0.0336729\pi\) |
−0.742431 | + | 0.669923i | \(0.766327\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.1074 | − | 14.6089i | 0.841468 | − | 0.611362i | −0.0813123 | − | 0.996689i | \(-0.525911\pi\) |
0.922780 | + | 0.385326i | \(0.125911\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.70820 | − | 7.05342i | 0.405566 | − | 0.294661i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.66312 | + | 5.11855i | −0.0693569 | + | 0.213458i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.92705 | − | 7.21242i | −0.413269 | − | 0.300257i | 0.361655 | − | 0.932312i | \(-0.382212\pi\) |
−0.774924 | + | 0.632055i | \(0.782212\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.1353 | + | 14.6291i | 0.836793 | + | 0.607965i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.54508 | + | 7.83297i | −0.105588 | + | 0.324966i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.5623 | 0.934435 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.381966 | + | 1.17557i | 0.0157924 | + | 0.0486039i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.0172 | + | 12.3637i | 0.702376 | + | 0.510306i | 0.880705 | − | 0.473665i | \(-0.157069\pi\) |
−0.178329 | + | 0.983971i | \(0.557069\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.218847 | − | 27.0256i | 0.00901744 | − | 1.11357i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.04508 | − | 5.84510i | −0.330931 | − | 0.240435i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.69756 | − | 5.22455i | −0.0697105 | − | 0.214547i | 0.910132 | − | 0.414318i | \(-0.135980\pi\) |
−0.979842 | + | 0.199772i | \(0.935980\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.1803 | 0.991297 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.28115 | − | 22.4091i | 0.297998 | − | 0.917143i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.4894 | + | 15.6129i | 0.878031 | + | 0.637927i | 0.932730 | − | 0.360576i | \(-0.117420\pi\) |
−0.0546986 | + | 0.998503i | \(0.517420\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.54508 | + | 3.30220i | 0.185398 | + | 0.134699i | 0.676613 | − | 0.736339i | \(-0.263447\pi\) |
−0.491215 | + | 0.871038i | \(0.663447\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.180340 | + | 0.555029i | −0.00734401 | + | 0.0226025i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.70820 | − | 4.87380i | 0.272727 | − | 0.198148i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.30902 | + | 3.85723i | −0.215486 | + | 0.156560i | −0.690293 | − | 0.723530i | \(-0.742518\pi\) |
0.474806 | + | 0.880090i | \(0.342518\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.11803 | + | 3.44095i | 0.0453050 | + | 0.139435i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.427051 | − | 1.31433i | 0.0172766 | − | 0.0531720i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.9549 | + | 33.7158i | 0.442465 | + | 1.36177i | 0.885240 | + | 0.465134i | \(0.153994\pi\) |
−0.442775 | + | 0.896633i | \(0.646006\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −39.1246 | −1.57766 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.3435 | + | 27.1316i | −1.50339 | + | 1.09228i | −0.534385 | + | 0.845241i | \(0.679457\pi\) |
−0.969006 | + | 0.247036i | \(0.920543\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.0557 | −0.444367 | −0.222184 | − | 0.975005i | \(-0.571318\pi\) | ||||
−0.222184 | + | 0.975005i | \(0.571318\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −29.4508 | −1.18182 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.6353 | − | 12.8128i | 0.706542 | − | 0.513332i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.35410 | + | 19.5559i | 0.253758 | + | 0.780988i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.38197 | + | 19.6417i | −0.254466 | + | 0.783165i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.37132 | − | 10.3759i | −0.134210 | − | 0.413057i | 0.861256 | − | 0.508171i | \(-0.169678\pi\) |
−0.995466 | + | 0.0951145i | \(0.969678\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.23607 | − | 3.80423i | 0.208115 | − | 0.151204i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.38197 | − | 3.91023i | 0.213577 | − | 0.155173i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0729490 | − | 0.224514i | 0.00289035 | − | 0.00889557i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.28115 | − | 0.930812i | −0.0506816 | − | 0.0368224i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.83688 | + | 2.06111i | 0.112050 | + | 0.0814091i | 0.642399 | − | 0.766370i | \(-0.277939\pi\) |
−0.530349 | + | 0.847779i | \(0.677939\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.93363 | + | 24.4172i | −0.312872 | + | 0.962920i | 0.663750 | + | 0.747955i | \(0.268964\pi\) |
−0.976622 | + | 0.214966i | \(0.931036\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 28.6525 | 1.12819 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.10081 | + | 9.54332i | 0.121906 | + | 0.375187i | 0.993325 | − | 0.115353i | \(-0.0367998\pi\) |
−0.871419 | + | 0.490539i | \(0.836800\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.7533 | + | 13.6251i | 0.736131 | + | 0.534830i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.190983 | − | 23.5847i | 0.00748521 | − | 0.924356i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.9615 | + | 26.1276i | 1.40728 | + | 1.02245i | 0.993711 | + | 0.111978i | \(0.0357188\pi\) |
0.413571 | + | 0.910472i | \(0.364281\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.67376 | + | 26.6951i | 0.338912 | + | 1.04306i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.81966 | −0.188033 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.62868 | + | 14.2456i | −0.180308 | + | 0.554930i | −0.999836 | − | 0.0181087i | \(-0.994236\pi\) |
0.819528 | + | 0.573039i | \(0.194236\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.7254 | + | 17.9641i | 0.961708 | + | 0.698721i | 0.953547 | − | 0.301245i | \(-0.0974023\pi\) |
0.00816087 | + | 0.999967i | \(0.497402\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.78115 | + | 7.10642i | 0.379869 | + | 0.275991i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.85410 | − | 24.1724i | 0.304569 | − | 0.937367i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.71885 | + | 2.70190i | −0.143994 | + | 0.104618i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.23607 | + | 0.898056i | −0.0477891 | + | 0.0347208i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.8541 | − | 33.4055i | −0.419018 | − | 1.28960i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.30244 | − | 7.08618i | 0.0887525 | − | 0.273152i | −0.896823 | − | 0.442390i | \(-0.854131\pi\) |
0.985575 | + | 0.169238i | \(0.0541307\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.69098 | + | 5.20431i | 0.0650860 | + | 0.200314i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −47.3050 | −1.81808 | −0.909038 | − | 0.416712i | \(-0.863182\pi\) | ||||
−0.909038 | + | 0.416712i | \(0.863182\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.1976 | + | 25.5725i | −1.35076 | + | 0.981383i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.32624 | 0.242422 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 48.7214 | 1.86427 | 0.932136 | − | 0.362110i | \(-0.117943\pi\) | ||||
0.932136 | + | 0.362110i | \(0.117943\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.7984 | + | 15.1109i | −0.794665 | + | 0.577358i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.145898 | −0.00556636 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.30902 | − | 13.2618i | −0.164160 | − | 0.505234i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.39261 | + | 4.28601i | −0.0529773 | + | 0.163048i | −0.974045 | − | 0.226356i | \(-0.927319\pi\) |
0.921067 | + | 0.389403i | \(0.127319\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.809017 | − | 2.48990i | −0.0307320 | − | 0.0945834i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.7984 | − | 9.29856i | 0.485470 | − | 0.352715i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.1697 | − | 32.8177i | 1.71092 | − | 1.24306i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.75329 | + | 23.8622i | −0.293256 | + | 0.902550i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.1631 | − | 16.8290i | −0.874859 | − | 0.635622i | 0.0570274 | − | 0.998373i | \(-0.481838\pi\) |
−0.931886 | + | 0.362750i | \(0.881838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.5623 | + | 12.7598i | 0.662375 | + | 0.481244i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.854102 | + | 2.62866i | −0.0321673 | + | 0.0990009i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.7984 | −0.819812 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.4615 | − | 38.3525i | −0.468001 | − | 1.44036i | −0.855169 | − | 0.518350i | \(-0.826546\pi\) |
0.387167 | − | 0.922009i | \(-0.373454\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.19098 | + | 0.865300i | 0.0446654 | + | 0.0324513i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.5729 | − | 9.02878i | 1.07007 | − | 0.338131i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.85410 | + | 4.97980i | 0.256329 | + | 0.186234i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.4894 | − | 41.5160i | −0.503769 | − | 1.55044i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.9443 | −1.22861 | −0.614307 | − | 0.789067i | \(-0.710564\pi\) | ||||
−0.614307 | + | 0.789067i | \(0.710564\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3992 | − | 44.3161i | 0.536254 | − | 1.65042i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.809017 | − | 0.587785i | −0.0300877 | − | 0.0218600i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.690983 | + | 0.502029i | 0.0256625 | + | 0.0186449i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.3156 | − | 31.7481i | 0.382584 | − | 1.17747i | −0.555633 | − | 0.831427i | \(-0.687524\pi\) |
0.938218 | − | 0.346046i | \(-0.112476\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8713 | + | 17.3435i | −0.884123 | + | 0.642353i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −33.0795 | + | 24.0337i | −1.22349 | + | 0.888918i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.86475 | − | 8.81678i | −0.105812 | − | 0.325655i | 0.884108 | − | 0.467282i | \(-0.154767\pi\) |
−0.989920 | + | 0.141627i | \(0.954767\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.145898 | + | 0.449028i | −0.00538153 | + | 0.0165626i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.23607 | + | 3.80423i | 0.0455311 | + | 0.140130i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.5279 | −1.52763 | −0.763814 | − | 0.645437i | \(-0.776675\pi\) | ||||
−0.763814 | + | 0.645437i | \(0.776675\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.2812 | − | 7.46969i | 0.377688 | − | 0.274406i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.0557 | −0.845833 | −0.422916 | − | 0.906169i | \(-0.638994\pi\) | ||||
−0.422916 | + | 0.906169i | \(0.638994\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −42.8328 | −1.56927 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.972136 | + | 0.706298i | −0.0355686 | + | 0.0258421i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.5066 | 1.22430 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.0106 | − | 46.1980i | −0.547746 | − | 1.68579i | −0.714370 | − | 0.699769i | \(-0.753286\pi\) |
0.166623 | − | 0.986021i | \(-0.446714\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.28115 | − | 3.94298i | 0.0466878 | − | 0.143690i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.32624 | − | 22.5478i | −0.266629 | − | 0.820600i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.1074 | + | 10.2496i | −0.512742 | + | 0.372529i | −0.813863 | − | 0.581057i | \(-0.802639\pi\) |
0.301121 | + | 0.953586i | \(0.402639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.4443 | + | 13.4005i | −0.669485 | + | 0.486409i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.0795 | − | 43.3323i | 0.510382 | − | 1.57080i | −0.281147 | − | 0.959665i | \(-0.590715\pi\) |
0.791529 | − | 0.611131i | \(-0.209285\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.7533 | − | 12.1720i | −0.606510 | − | 0.440655i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.85410 | + | 2.07363i | 0.103190 | + | 0.0749721i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.42705 | − | 13.6251i | 0.159852 | − | 0.491972i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.8328 | 1.32823 | 0.664113 | − | 0.747633i | \(-0.268810\pi\) | ||||
0.664113 | + | 0.747633i | \(0.268810\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.2533 | + | 40.7894i | 0.477306 | + | 1.46900i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.39919 | − | 3.19620i | −0.158228 | − | 0.114959i | 0.505854 | − | 0.862619i | \(-0.331177\pi\) |
−0.664082 | + | 0.747660i | \(0.731177\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.23607 | − | 4.53077i | −0.116243 | − | 0.162750i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.3262 | + | 11.1352i | 0.549826 | + | 0.399472i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.1353 | − | 55.8146i | −0.649763 | − | 1.99976i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.8541 | −0.388390 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.44427 | + | 4.44501i | −0.0516141 | + | 0.158852i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.0902 | + | 12.4167i | 0.609974 | + | 0.443172i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.48936 | + | 6.89442i | 0.338259 | + | 0.245760i | 0.743927 | − | 0.668261i | \(-0.232961\pi\) |
−0.405668 | + | 0.914021i | \(0.632961\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.5172 | − | 32.3687i | 0.374423 | − | 1.15236i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.8713 | − | 16.6170i | 0.813211 | − | 0.590832i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.5623 | + | 12.7598i | −0.623656 | + | 0.453112i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.61803 | + | 26.5236i | 0.305650 | + | 0.940694i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.46149 | + | 26.0418i | −0.299721 | + | 0.922448i | 0.681873 | + | 0.731471i | \(0.261166\pi\) |
−0.981594 | + | 0.190977i | \(0.938834\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.21885 | − | 3.75123i | −0.0431197 | − | 0.132709i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.18034 | 0.112372 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.7254 | + | 19.4172i | −0.943120 | + | 0.685217i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.1803 | 0.993226 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.7984 | 0.872944 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.25329 | − | 4.54328i | 0.219854 | − | 0.159733i | −0.472407 | − | 0.881381i | \(-0.656615\pi\) |
0.692261 | + | 0.721647i | \(0.256615\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.4721 | −0.929562 | −0.464781 | − | 0.885426i | \(-0.653867\pi\) | ||||
−0.464781 | + | 0.885426i | \(0.653867\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.4894 | − | 35.3606i | −0.402949 | − | 1.24015i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.1459 | + | 34.3035i | −0.390424 | + | 1.20160i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.2812 | + | 40.8752i | 0.464649 | + | 1.43004i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.30902 | + | 0.951057i | −0.0457408 | + | 0.0332326i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.8156 | + | 18.7561i | −0.900970 | + | 0.654593i | −0.938715 | − | 0.344694i | \(-0.887983\pi\) |
0.0377446 | + | 0.999287i | \(0.487983\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.1697 | + | 46.6875i | −0.528782 | + | 1.62742i | 0.227930 | + | 0.973677i | \(0.426804\pi\) |
−0.756713 | + | 0.653747i | \(0.773196\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.42705 | + | 2.48990i | 0.119315 | + | 0.0866871i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.2877 | − | 23.4584i | −1.12275 | − | 0.815729i | −0.138130 | − | 0.990414i | \(-0.544109\pi\) |
−0.984624 | + | 0.174685i | \(0.944109\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.53851 | − | 10.8904i | 0.122897 | − | 0.378239i | −0.870615 | − | 0.491965i | \(-0.836279\pi\) |
0.993512 | + | 0.113726i | \(0.0362786\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.7984 | 0.999005 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.208204 | − | 0.640786i | −0.00721384 | − | 0.0222019i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.14590 | + | 5.91834i | 0.281900 | + | 0.204813i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.1074 | − | 24.5030i | 0.625883 | − | 0.846946i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.6697 | + | 23.0094i | 1.09336 | + | 0.794372i | 0.979963 | − | 0.199178i | \(-0.0638271\pi\) |
0.113396 | + | 0.993550i | \(0.463827\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.73607 | − | 26.8869i | −0.301244 | − | 0.927133i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.2705 | 1.07701 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.41641 | + | 19.7477i | −0.220731 | + | 0.679341i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.78115 | + | 6.37988i | 0.301724 | + | 0.219215i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.2254 | + | 16.8743i | 0.797095 | + | 0.579123i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.43769 | + | 22.8909i | −0.254961 | + | 0.784689i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.1074 | + | 20.4212i | −0.962379 | + | 0.699209i | −0.953702 | − | 0.300753i | \(-0.902762\pi\) |
−0.00867675 | + | 0.999962i | \(0.502762\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.00000 | − | 2.17963i | 0.102598 | − | 0.0745417i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.60739 | + | 17.2578i | 0.191545 | + | 0.589514i | 1.00000 | 0.000955970i | \(0.000304295\pi\) | |
−0.808455 | + | 0.588558i | \(0.799696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.75329 | + | 11.5514i | −0.128061 | + | 0.394130i | −0.994446 | − | 0.105246i | \(-0.966437\pi\) |
0.866386 | + | 0.499375i | \(0.166437\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.8262 | − | 48.7082i | −0.539357 | − | 1.65997i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.3607 | −0.965409 | −0.482704 | − | 0.875783i | \(-0.660345\pi\) | ||||
−0.482704 | + | 0.875783i | \(0.660345\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.85410 | + | 5.70634i | −0.267047 | + | 0.194021i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.00000 | 0.237732 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.0902 | 0.342286 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.00000 | − | 1.45309i | 0.0677674 | − | 0.0492359i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.34752 | −0.214831 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.70820 | − | 29.8788i | −0.328197 | − | 1.01009i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.42705 | − | 4.39201i | 0.0481881 | − | 0.148308i | −0.924067 | − | 0.382230i | \(-0.875156\pi\) |
0.972255 | + | 0.233922i | \(0.0751562\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.16312 | − | 6.65740i | −0.0729602 | − | 0.224548i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.25329 | − | 5.99637i | 0.278060 | − | 0.202023i | −0.440011 | − | 0.897993i | \(-0.645025\pi\) |
0.718071 | + | 0.695970i | \(0.245025\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.1074 | − | 26.2336i | 1.21511 | − | 0.882829i | 0.219426 | − | 0.975629i | \(-0.429582\pi\) |
0.995685 | + | 0.0927998i | \(0.0295817\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.85410 | + | 27.2501i | −0.297627 | + | 0.916003i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.3435 | − | 14.0538i | −0.649490 | − | 0.471882i | 0.213608 | − | 0.976920i | \(-0.431479\pi\) |
−0.863097 | + | 0.505038i | \(0.831479\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.04508 | + | 5.11855i | 0.236285 | + | 0.171671i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.23607 | + | 19.1926i | −0.208916 | + | 0.642978i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.14590 | −0.138737 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.1459 | + | 34.3035i | 0.372566 | + | 1.14664i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.3992 | + | 8.28199i | 0.380608 | + | 0.276528i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.0385072 | − | 4.75528i | 0.00128429 | − | 0.158598i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.1976 | − | 23.3929i | −1.07266 | − | 0.779330i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.5902 | + | 35.6709i | 0.385697 | + | 1.18705i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 48.9443 | 1.62696 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.66312 | − | 11.2739i | 0.121632 | − | 0.374344i | −0.871641 | − | 0.490146i | \(-0.836944\pi\) |
0.993272 | + | 0.115801i | \(0.0369436\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.57295 | − | 1.86936i | −0.0853393 | − | 0.0620027i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.1074 | − | 14.6089i | −0.666188 | − | 0.484014i | 0.202559 | − | 0.979270i | \(-0.435074\pi\) |
−0.868747 | + | 0.495256i | \(0.835074\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.54508 | + | 7.83297i | −0.0842300 | + | 0.259233i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 35.1246 | − | 25.5195i | 1.16118 | − | 0.843649i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29.7254 | + | 21.5968i | −0.981620 | + | 0.713189i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.628677 | + | 1.93487i | 0.0207381 | + | 0.0638254i | 0.960890 | − | 0.276930i | \(-0.0893171\pi\) |
−0.940152 | + | 0.340756i | \(0.889317\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.13525 | + | 12.7270i | −0.136261 | + | 0.419369i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.07295 | + | 6.37988i | 0.0682319 | + | 0.209996i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.47214 | 0.147043 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.50000 | − | 3.99598i | 0.180644 | − | 0.131245i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.3607 | 1.65228 | 0.826140 | − | 0.563465i | \(-0.190532\pi\) | ||||
0.826140 | + | 0.563465i | \(0.190532\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.708204 | −0.0232104 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.6525 | + | 20.8172i | −0.938040 | + | 0.681526i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.1803 | 0.790782 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.60739 | + | 29.5685i | 0.313860 | + | 0.965961i | 0.976221 | + | 0.216777i | \(0.0695543\pi\) |
−0.662361 | + | 0.749184i | \(0.730446\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.19098 | − | 3.66547i | 0.0388663 | − | 0.119618i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.46149 | − | 13.7311i | −0.145441 | − | 0.447620i | 0.851627 | − | 0.524149i | \(-0.175616\pi\) |
−0.997067 | + | 0.0765287i | \(0.975616\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.6418 | − | 38.2465i | 1.71425 | − | 1.24548i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 23.1803 | − | 16.8415i | 0.754057 | − | 0.547854i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.89919 | − | 21.2335i | 0.224193 | − | 0.689996i | −0.774179 | − | 0.632967i | \(-0.781837\pi\) |
0.998372 | − | 0.0570298i | \(-0.0181630\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.5172 | + | 12.0005i | 0.536172 | + | 0.389552i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.42705 | + | 1.76336i | 0.0787025 | + | 0.0571807i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.1697 | + | 49.7652i | −0.523788 | + | 1.61205i | 0.242913 | + | 0.970048i | \(0.421897\pi\) |
−0.766700 | + | 0.642005i | \(0.778103\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.8328 | −0.479979 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.11803 | + | 3.44095i | 0.0361409 | + | 0.111230i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27.2254 | − | 19.7804i | −0.879155 | − | 0.638743i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.0557 | + | 29.3238i | −0.324378 | + | 0.945927i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.95492 | + | 2.87341i | 0.127445 | + | 0.0925945i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.50658 | − | 29.2582i | −0.306028 | − | 0.941856i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.4164 | −0.753021 | −0.376510 | − | 0.926412i | \(-0.622876\pi\) | ||||
−0.376510 | + | 0.926412i | \(0.622876\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.2082 | − | 34.4953i | 0.360059 | − | 1.10815i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.4894 | + | 24.3314i | 1.07472 | + | 0.780833i | 0.976756 | − | 0.214356i | \(-0.0687654\pi\) |
0.0979691 | + | 0.995189i | \(0.468765\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.7533 | + | 12.1720i | 0.537086 | + | 0.390216i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.809017 | − | 2.48990i | 0.0259093 | − | 0.0797406i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.45492 | + | 5.41631i | −0.238504 | + | 0.173283i | −0.700616 | − | 0.713538i | \(-0.747092\pi\) |
0.462113 | + | 0.886821i | \(0.347092\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.6353 | − | 12.8128i | 0.563625 | − | 0.409498i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.933629 | − | 2.87341i | −0.0298085 | − | 0.0917410i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.8090 | + | 45.5775i | −0.472334 | + | 1.45370i | 0.377185 | + | 0.926138i | \(0.376892\pi\) |
−0.849519 | + | 0.527558i | \(0.823108\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.79837 | + | 11.6902i | 0.121026 | + | 0.372481i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.61803 | −0.115163 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −38.5517 | + | 28.0094i | −1.22587 | + | 0.890648i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.7771 | 1.77182 | 0.885909 | − | 0.463859i | \(-0.153536\pi\) | ||||
0.885909 | + | 0.463859i | \(0.153536\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.0902 | −0.542340 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.5623 | + | 17.1190i | −0.746975 | + | 0.542709i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.0000 | −0.823428 | −0.411714 | − | 0.911313i | \(-0.635070\pi\) | ||||
−0.411714 | + | 0.911313i | \(0.635070\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.56231 | + | 23.2744i | 0.239261 | + | 0.736369i |
(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 | 124.2.f.a.33.1 | ✓ | 4 | |
3.2 | odd | 2 | 1116.2.m.a.901.1 | 4 | |||
4.3 | odd | 2 | 496.2.n.c.33.1 | 4 | |||
31.4 | even | 5 | 3844.2.a.h.1.2 | 2 | |||
31.16 | even | 5 | inner | 124.2.f.a.109.1 | yes | 4 | |
31.27 | odd | 10 | 3844.2.a.e.1.1 | 2 | |||
93.47 | odd | 10 | 1116.2.m.a.109.1 | 4 | |||
124.47 | odd | 10 | 496.2.n.c.481.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.2.f.a.33.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
124.2.f.a.109.1 | yes | 4 | 31.16 | even | 5 | inner | |
496.2.n.c.33.1 | 4 | 4.3 | odd | 2 | |||
496.2.n.c.481.1 | 4 | 124.47 | odd | 10 | |||
1116.2.m.a.109.1 | 4 | 93.47 | odd | 10 | |||
1116.2.m.a.901.1 | 4 | 3.2 | odd | 2 | |||
3844.2.a.e.1.1 | 2 | 31.27 | odd | 10 | |||
3844.2.a.h.1.2 | 2 | 31.4 | even | 5 |