Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(101,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.bh (of order \(6\), degree \(2\), 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: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 10.0.29471584693248.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 13x^{6} - 36x^{5} + 39x^{4} - 36x^{3} + 54x^{2} - 162x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.2 | ||
Root | \(0.527154 - 1.64988i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 420.101 |
Dual form | 420.2.bh.b.341.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.16526 | − | 1.28147i | −0.672765 | − | 0.739857i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.80025 | + | 1.93884i | −0.680432 | + | 0.732812i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.284326 | + | 2.98650i | −0.0947754 | + | 0.995499i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.05595 | − | 2.34170i | −1.22292 | − | 0.706050i | −0.257377 | − | 0.966311i | \(-0.582858\pi\) |
−0.965538 | + | 0.260261i | \(0.916192\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.18938i | − | 0.607225i | −0.952796 | − | 0.303612i | \(-0.901807\pi\) | ||
0.952796 | − | 0.303612i | \(-0.0981928\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.527154 | − | 1.64988i | 0.136110 | − | 0.425998i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.74984 | + | 6.49492i | −0.909470 | + | 1.57525i | −0.0946686 | + | 0.995509i | \(0.530179\pi\) |
−0.814802 | + | 0.579740i | \(0.803154\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.638109 | + | 0.368412i | −0.146392 | + | 0.0845196i | −0.571407 | − | 0.820667i | \(-0.693602\pi\) |
0.425015 | + | 0.905186i | \(0.360269\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.58233 | + | 0.0477143i | 0.999946 | + | 0.0104121i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.99627 | + | 4.03930i | −1.45882 | + | 0.842252i | −0.998954 | − | 0.0457338i | \(-0.985437\pi\) |
−0.459870 | + | 0.887986i | \(0.652104\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.15842 | − | 3.11570i | 0.800288 | − | 0.599616i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.15414i | 0.214318i | 0.994242 | + | 0.107159i | \(0.0341754\pi\) | ||||
−0.994242 | + | 0.107159i | \(0.965825\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.95201 | + | 5.16845i | 1.60783 | + | 0.928280i | 0.989855 | + | 0.142081i | \(0.0453794\pi\) |
0.617974 | + | 0.786199i | \(0.287954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.72543 | + | 7.92628i | 0.300358 | + | 1.37979i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.57921 | − | 0.589646i | −0.435966 | − | 0.0996684i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.30923 | + | 3.99970i | 0.379635 | + | 0.657547i | 0.991009 | − | 0.133795i | \(-0.0427163\pi\) |
−0.611374 | + | 0.791342i | \(0.709383\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.80562 | + | 2.55120i | −0.449259 | + | 0.408519i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.43758 | 0.224513 | 0.112256 | − | 0.993679i | \(-0.464192\pi\) | ||||
0.112256 | + | 0.993679i | \(0.464192\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.24142 | −1.40930 | −0.704651 | − | 0.709554i | \(-0.748897\pi\) | ||||
−0.704651 | + | 0.709554i | \(0.748897\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.72854 | + | 1.24701i | −0.406747 | + | 0.185894i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.34224 | − | 7.52098i | −0.633380 | − | 1.09705i | −0.986856 | − | 0.161603i | \(-0.948333\pi\) |
0.353475 | − | 0.935444i | \(-0.385000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.518179 | − | 6.98079i | −0.0740255 | − | 0.997256i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.6926 | − | 2.76298i | 1.77732 | − | 0.386894i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.03514 | − | 4.06174i | −0.966351 | − | 0.557923i | −0.0682291 | − | 0.997670i | \(-0.521735\pi\) |
−0.898122 | + | 0.439747i | \(0.855068\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.68341i | − | 0.631511i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.21567 | + | 0.388420i | 0.161020 | + | 0.0514475i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.48730 | + | 6.04018i | −0.454008 | + | 0.786364i | −0.998631 | − | 0.0523168i | \(-0.983339\pi\) |
0.544623 | + | 0.838681i | \(0.316673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.13811 | − | 2.96649i | 0.657867 | − | 0.379820i | −0.133596 | − | 0.991036i | \(-0.542653\pi\) |
0.791464 | + | 0.611216i | \(0.209319\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.27847 | − | 5.92771i | −0.665025 | − | 0.746821i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.89606 | − | 1.09469i | 0.235177 | − | 0.135780i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.691639 | − | 1.19795i | 0.0844971 | − | 0.146353i | −0.820680 | − | 0.571389i | \(-0.806405\pi\) |
0.905177 | + | 0.425035i | \(0.139738\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.3287 | + | 4.25866i | 1.60459 | + | 0.512683i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.26258i | − | 0.861909i | −0.902374 | − | 0.430955i | \(-0.858177\pi\) | ||
0.902374 | − | 0.430955i | \(-0.141823\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.211355 | − | 0.122026i | −0.0247372 | − | 0.0142820i | 0.487580 | − | 0.873078i | \(-0.337880\pi\) |
−0.512318 | + | 0.858796i | \(0.671213\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.69242 | − | 0.368412i | 0.195423 | − | 0.0425406i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.8419 | − | 3.64817i | 1.34951 | − | 0.415747i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.79653 | − | 10.0399i | −0.652160 | − | 1.12957i | −0.982598 | − | 0.185747i | \(-0.940530\pi\) |
0.330438 | − | 0.943828i | \(-0.392804\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.83832 | − | 1.69828i | −0.982035 | − | 0.188698i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.4610 | 1.80683 | 0.903413 | − | 0.428772i | \(-0.141054\pi\) | ||||
0.903413 | + | 0.428772i | \(0.141054\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.49968 | −0.813455 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.47899 | − | 1.34488i | 0.158565 | − | 0.144186i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.658248 | − | 1.14012i | −0.0697741 | − | 0.120852i | 0.829028 | − | 0.559208i | \(-0.188895\pi\) |
−0.898802 | + | 0.438355i | \(0.855561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.24485 | + | 3.94144i | 0.444981 | + | 0.413175i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.80824 | − | 17.4943i | −0.394896 | − | 1.81408i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.638109 | − | 0.368412i | −0.0654686 | − | 0.0377983i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.84232i | 0.491663i | 0.969313 | + | 0.245832i | \(0.0790611\pi\) | ||||
−0.969313 | + | 0.245832i | \(0.920939\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.14670 | − | 11.4473i | 0.818775 | − | 1.15049i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.38435 | + | 2.39776i | −0.137748 | + | 0.238586i | −0.926644 | − | 0.375941i | \(-0.877320\pi\) |
0.788896 | + | 0.614527i | \(0.210653\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.07000 | + | 4.08187i | −0.696628 | + | 0.402199i | −0.806090 | − | 0.591792i | \(-0.798421\pi\) |
0.109462 | + | 0.993991i | \(0.465087\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.24984 | + | 3.99227i | 0.219562 | + | 0.389606i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.186331 | − | 0.107578i | 0.0180133 | − | 0.0104000i | −0.490966 | − | 0.871179i | \(-0.663356\pi\) |
0.508980 | + | 0.860779i | \(0.330023\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.08683 | + | 1.88245i | −0.104100 | + | 0.180306i | −0.913370 | − | 0.407131i | \(-0.866529\pi\) |
0.809270 | + | 0.587436i | \(0.199863\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.43464 | − | 7.61990i | 0.231085 | − | 0.723249i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2195i | 1.05544i | 0.849419 | + | 0.527719i | \(0.176952\pi\) | ||||
−0.849419 | + | 0.527719i | \(0.823048\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.99627 | − | 4.03930i | −0.652406 | − | 0.376667i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.53858 | + | 0.622499i | 0.604492 | + | 0.0575500i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.84192 | − | 18.9628i | −0.535528 | − | 1.73832i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.46716 | + | 9.46940i | 0.497015 | + | 0.860854i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.67516 | − | 1.84222i | −0.151044 | − | 0.166107i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.2228 | 1.52828 | 0.764140 | − | 0.645051i | \(-0.223164\pi\) | ||||
0.764140 | + | 0.645051i | \(0.223164\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.7687 | + | 11.8426i | 0.948129 | + | 1.04268i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.65810 | + | 14.9963i | 0.756462 | + | 1.31023i | 0.944644 | + | 0.328096i | \(0.106407\pi\) |
−0.188183 | + | 0.982134i | \(0.560260\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.434466 | − | 1.90042i | 0.0376730 | − | 0.164788i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.77748 | + | 2.04345i | 0.411180 | + | 0.175872i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.68866 | − | 5.59375i | −0.827758 | − | 0.477907i | 0.0253261 | − | 0.999679i | \(-0.491938\pi\) |
−0.853085 | + | 0.521773i | \(0.825271\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.16017i | 0.183223i | 0.995795 | + | 0.0916116i | \(0.0292018\pi\) | ||||
−0.995795 | + | 0.0916116i | \(0.970798\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.57805 | + | 14.3284i | −0.385542 | + | 1.20667i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.12688 | + | 8.88002i | −0.428731 | + | 0.742585i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.999514 | + | 0.577070i | −0.0830051 | + | 0.0479230i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.34186 | + | 8.79849i | −0.688025 | + | 0.725687i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.37427 | + | 0.793438i | −0.112585 | + | 0.0650010i | −0.555235 | − | 0.831693i | \(-0.687372\pi\) |
0.442650 | + | 0.896694i | \(0.354038\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.12229 | + | 8.87206i | −0.416846 | + | 0.721998i | −0.995620 | − | 0.0934894i | \(-0.970198\pi\) |
0.578774 | + | 0.815488i | \(0.303531\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.3309 | − | 13.0456i | −1.48196 | − | 1.05467i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.3369i | 0.830279i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.62174 | − | 3.24572i | −0.448664 | − | 0.259036i | 0.258602 | − | 0.965984i | \(-0.416738\pi\) |
−0.707266 | + | 0.706948i | \(0.750072\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.99279 | + | 13.7483i | 0.237344 | + | 1.09031i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.76352 | − | 20.8364i | 0.375418 | − | 1.64214i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.68350 | − | 4.64797i | −0.210188 | − | 0.364057i | 0.741585 | − | 0.670859i | \(-0.234074\pi\) |
−0.951773 | + | 0.306802i | \(0.900741\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.00164 | + | 5.45740i | −0.467227 | + | 0.424858i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.84082 | 0.529359 | 0.264679 | − | 0.964336i | \(-0.414734\pi\) | ||||
0.264679 | + | 0.964336i | \(0.414734\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.20661 | 0.631278 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.918831 | − | 2.01046i | −0.0702648 | − | 0.153744i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.81618 | − | 10.0739i | −0.442196 | − | 0.765906i | 0.555656 | − | 0.831412i | \(-0.312467\pi\) |
−0.997852 | + | 0.0655063i | \(0.979134\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.778956 | − | 2.52848i | −0.0588835 | − | 0.191135i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.8039 | − | 2.56953i | 0.887237 | − | 0.193138i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.95741 | + | 4.01686i | 0.520021 | + | 0.300234i | 0.736943 | − | 0.675955i | \(-0.236268\pi\) |
−0.216922 | + | 0.976189i | \(0.569602\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.81789i | − | 0.729758i | −0.931055 | − | 0.364879i | \(-0.881110\pi\) | ||
0.931055 | − | 0.364879i | \(-0.118890\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.78871 | − | 3.12759i | −0.723602 | − | 0.231198i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.30923 | + | 3.99970i | −0.169778 | + | 0.294064i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30.4184 | − | 17.5620i | 2.22441 | − | 1.28426i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.44537 | + | 13.6715i | −0.105136 | + | 0.994458i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.9054 | + | 8.02830i | −1.00616 | + | 0.580907i | −0.910065 | − | 0.414465i | \(-0.863969\pi\) |
−0.0960953 | + | 0.995372i | \(0.530635\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.19143 | + | 5.52771i | −0.229724 | + | 0.397894i | −0.957726 | − | 0.287681i | \(-0.907116\pi\) |
0.728002 | + | 0.685575i | \(0.240449\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.61222 | − | 1.15414i | −0.258676 | − | 0.0826497i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.54995i | 0.181677i | 0.995866 | + | 0.0908384i | \(0.0289547\pi\) | ||||
−0.995866 | + | 0.0908384i | \(0.971045\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.27973 | − | 3.62561i | −0.445159 | − | 0.257012i | 0.260625 | − | 0.965440i | \(-0.416071\pi\) |
−0.705783 | + | 0.708428i | \(0.749405\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.34108 | + | 0.509617i | −0.165127 | + | 0.0359456i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.23769 | − | 2.07774i | −0.157055 | − | 0.145829i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.718792 | + | 1.24498i | 0.0502026 | + | 0.0869535i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.0741 | − | 22.0428i | −0.700200 | − | 1.53208i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.45085 | 0.238700 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.2654 | −0.913230 | −0.456615 | − | 0.889664i | \(-0.650938\pi\) | ||||
−0.456615 | + | 0.889664i | \(0.650938\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.30677 | + | 8.46281i | −0.637689 | + | 0.579862i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.62071 | − | 8.00330i | −0.315130 | − | 0.545821i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −26.1367 | + | 8.05198i | −1.77427 | + | 0.546604i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.0899116 | + | 0.413037i | 0.00607567 | + | 0.0279104i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.2198 | + | 8.20983i | 0.956530 | + | 0.552253i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.1032i | 1.88193i | 0.338506 | + | 0.940964i | \(0.390078\pi\) | ||||
−0.338506 | + | 0.940964i | \(0.609922\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.44422 | − | 1.73948i | −0.162948 | − | 0.115965i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.71504 | + | 11.6308i | −0.445693 | + | 0.771963i | −0.998100 | − | 0.0616117i | \(-0.980376\pi\) |
0.552407 | + | 0.833574i | \(0.313709\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.24605 | + | 4.18351i | −0.478833 | + | 0.276454i | −0.719930 | − | 0.694047i | \(-0.755826\pi\) |
0.241097 | + | 0.970501i | \(0.422493\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.4740 | − | 10.9240i | −1.21550 | − | 0.718745i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.07871 | − | 4.08689i | 0.463742 | − | 0.267741i | −0.249875 | − | 0.968278i | \(-0.580389\pi\) |
0.713616 | + | 0.700537i | \(0.247056\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.34224 | − | 7.52098i | 0.283256 | − | 0.490614i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.11132 | + | 19.1272i | −0.396973 | + | 1.24244i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.5553i | 0.812134i | 0.913843 | + | 0.406067i | \(0.133100\pi\) | ||||
−0.913843 | + | 0.406067i | \(0.866900\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.1154 | + | 11.0363i | 1.23133 | + | 0.710910i | 0.967308 | − | 0.253606i | \(-0.0816166\pi\) |
0.264025 | + | 0.964516i | \(0.414950\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.12267 | + | 13.3050i | 0.521069 | + | 0.853514i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.78646 | − | 3.93915i | 0.369683 | − | 0.251663i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.806595 | + | 1.39706i | 0.0513224 | + | 0.0888930i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.1813 | − | 21.0942i | −1.21557 | − | 1.33679i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.66808 | −0.105288 | −0.0526441 | − | 0.998613i | \(-0.516765\pi\) | ||||
−0.0526441 | + | 0.998613i | \(0.516765\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.8354 | 2.37869 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.73910 | + | 9.61061i | 0.547264 | + | 0.601840i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.602166 | − | 1.04298i | −0.0375621 | − | 0.0650594i | 0.846633 | − | 0.532177i | \(-0.178626\pi\) |
−0.884195 | + | 0.467117i | \(0.845293\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.9120 | − | 2.72326i | −0.740173 | − | 0.169215i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.44683 | − | 0.328152i | −0.213354 | − | 0.0203121i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.34275 | + | 2.50729i | 0.267785 | + | 0.154606i | 0.627881 | − | 0.778310i | \(-0.283923\pi\) |
−0.360095 | + | 0.932915i | \(0.617256\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8.12348i | − | 0.499021i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.693995 | + | 2.17206i | −0.0424718 | + | 0.132928i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.94487 | − | 13.7609i | 0.484407 | − | 0.839018i | −0.515432 | − | 0.856930i | \(-0.672369\pi\) |
0.999840 | + | 0.0179121i | \(0.00570189\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.4197 | + | 10.0573i | −1.05817 | + | 0.610937i | −0.924927 | − | 0.380146i | \(-0.875874\pi\) |
−0.133248 | + | 0.991083i | \(0.542541\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.104465 | − | 10.0325i | 0.00632250 | − | 0.607192i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.05595 | − | 2.34170i | 0.244583 | − | 0.141210i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.20512 | + | 3.81938i | −0.132493 | + | 0.229484i | −0.924637 | − | 0.380850i | \(-0.875631\pi\) |
0.792144 | + | 0.610334i | \(0.208965\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.9808 | + | 25.2656i | −1.07648 | + | 1.51261i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.9173i | 1.06886i | 0.845213 | + | 0.534429i | \(0.179473\pi\) | ||||
−0.845213 | + | 0.534429i | \(0.820527\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.0054 | + | 5.77663i | 0.594760 | + | 0.343385i | 0.766978 | − | 0.641674i | \(-0.221760\pi\) |
−0.172217 | + | 0.985059i | \(0.555093\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.271455 | + | 1.24701i | 0.0160796 | + | 0.0738667i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.58802 | + | 2.78724i | −0.152766 | + | 0.164526i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −19.6226 | − | 33.9874i | −1.15427 | − | 1.99926i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.20529 | − | 5.64258i | 0.363760 | − | 0.330774i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.17953 | 0.419433 | 0.209716 | − | 0.977762i | \(-0.432746\pi\) | ||||
0.209716 | + | 0.977762i | \(0.432746\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.97460 | −0.406077 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −24.1624 | + | 2.89933i | −1.40204 | + | 0.168236i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.84357 | + | 15.3175i | 0.511437 | + | 0.885834i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.6369 | − | 17.9176i | 0.958934 | − | 1.03275i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.68578 | − | 1.02002i | 0.269191 | − | 0.0585987i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.13811 | + | 2.96649i | 0.294207 | + | 0.169861i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.44348i | 0.139457i | 0.997566 | + | 0.0697284i | \(0.0222133\pi\) | ||||
−0.997566 | + | 0.0697284i | \(0.977787\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.4692 | + | 4.30354i | 0.766236 | + | 0.244820i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.56348 | + | 4.44007i | −0.145361 | + | 0.251773i | −0.929508 | − | 0.368803i | \(-0.879768\pi\) |
0.784146 | + | 0.620576i | \(0.213101\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.41881 | + | 0.819152i | −0.0801961 | + | 0.0463012i | −0.539562 | − | 0.841946i | \(-0.681410\pi\) |
0.459366 | + | 0.888247i | \(0.348077\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.49431 | − | 7.53514i | 0.140539 | − | 0.424557i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.3446 | − | 8.28184i | 0.805672 | − | 0.465155i | −0.0397789 | − | 0.999209i | \(-0.512665\pi\) |
0.845451 | + | 0.534054i | \(0.179332\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.70265 | − | 4.68113i | 0.151320 | − | 0.262093i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.354983 | − | 0.113421i | −0.0198132 | − | 0.00633052i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.52595i | − | 0.307472i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.89606 | + | 1.09469i | 0.105174 | + | 0.0607225i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.67874 | − | 0.800804i | 0.203435 | − | 0.0442846i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.3991 | + | 5.12077i | 1.23490 | + | 0.282317i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.9722 | + | 20.7364i | 0.658049 | + | 1.13977i | 0.981120 | + | 0.193400i | \(0.0619513\pi\) |
−0.323071 | + | 0.946375i | \(0.604715\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.6017 | + | 5.75928i | −0.690567 | + | 0.315607i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.38328 | 0.0755765 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.25410 | −0.504103 | −0.252051 | − | 0.967714i | \(-0.581105\pi\) | ||||
−0.252051 | + | 0.967714i | \(0.581105\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.3774 | − | 13.0736i | 0.780872 | − | 0.710061i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.2059 | − | 41.9259i | −1.31083 | − | 2.27042i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.4675 | + | 11.5625i | 0.781170 | + | 0.624318i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.97626 | + | 13.6724i | 0.160236 | + | 0.736095i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.0038 | + | 13.2812i | 1.23491 | + | 0.712973i | 0.968049 | − | 0.250763i | \(-0.0806814\pi\) |
0.266857 | + | 0.963736i | \(0.414015\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 14.8893i | − | 0.797004i | −0.917167 | − | 0.398502i | \(-0.869530\pi\) | ||
0.917167 | − | 0.398502i | \(-0.130470\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.82145 | − | 9.10436i | −0.364102 | − | 0.485955i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.41481 | − | 14.5749i | 0.447875 | − | 0.775743i | −0.550372 | − | 0.834919i | \(-0.685514\pi\) |
0.998248 | + | 0.0591766i | \(0.0188475\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.28957 | − | 3.63129i | 0.333816 | − | 0.192729i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −17.4929 | + | 29.5829i | −0.925823 | + | 1.56569i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.3673 | + | 14.0685i | −1.28606 | + | 0.742506i | −0.977949 | − | 0.208846i | \(-0.933029\pi\) |
−0.308109 | + | 0.951351i | \(0.599696\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.22854 | + | 15.9843i | −0.485713 | + | 0.841279i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.76407 | − | 18.0403i | 0.302535 | − | 0.946872i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 0.244052i | − | 0.0127742i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7963 | − | 7.38797i | −0.667963 | − | 0.385649i | 0.127341 | − | 0.991859i | \(-0.459356\pi\) |
−0.795304 | + | 0.606210i | \(0.792689\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.408743 | + | 4.29334i | −0.0212783 | + | 0.223502i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.5401 | − | 6.32783i | 1.06639 | − | 0.328525i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.9537 | + | 18.9723i | 0.567159 | + | 0.982348i | 0.996845 | + | 0.0793696i | \(0.0252907\pi\) |
−0.429687 | + | 0.902978i | \(0.641376\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.16526 | + | 1.28147i | 0.0601739 | + | 0.0661748i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.52685 | 0.130139 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.15057 | −0.418667 | −0.209333 | − | 0.977844i | \(-0.567129\pi\) | ||||
−0.209333 | + | 0.977844i | \(0.567129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.0691 | − | 22.0705i | −1.02817 | − | 1.13071i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.164775 | − | 0.285399i | −0.00841962 | − | 0.0145832i | 0.861785 | − | 0.507274i | \(-0.169347\pi\) |
−0.870205 | + | 0.492691i | \(0.836013\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.08037 | + | 8.43132i | 0.462778 | + | 0.429700i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.62758 | − | 27.5995i | 0.133567 | − | 1.40296i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.5387 | − | 6.66185i | −0.585033 | − | 0.337769i | 0.178098 | − | 0.984013i | \(-0.443006\pi\) |
−0.763131 | + | 0.646244i | \(0.776339\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 60.5869i | − | 3.06401i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.12830 | − | 28.5697i | 0.460462 | − | 1.44115i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.79653 | − | 10.0399i | 0.291655 | − | 0.505161i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.7694 | + | 14.3006i | −1.24314 | + | 0.717728i | −0.969733 | − | 0.244169i | \(-0.921485\pi\) |
−0.273409 | + | 0.961898i | \(0.588151\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.94160 | + | 1.65774i | −0.147264 | + | 0.0829908i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.2076 | − | 13.9763i | 1.20887 | − | 0.697941i | 0.246357 | − | 0.969179i | \(-0.420766\pi\) |
0.962512 | + | 0.271238i | \(0.0874330\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.3157 | − | 19.5994i | 0.563675 | − | 0.976314i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.94841 | − | 8.50335i | −0.146507 | − | 0.422535i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 21.6301i | − | 1.07217i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.852979 | + | 0.492468i | 0.0421771 | + | 0.0243510i | 0.520940 | − | 0.853593i | \(-0.325581\pi\) |
−0.478763 | + | 0.877944i | \(0.658915\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.12162 | + | 18.9339i | 0.203304 | + | 0.933941i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.43290 | − | 17.6352i | −0.267336 | − | 0.867769i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.23048 | + | 14.2556i | 0.404018 | + | 0.699780i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.76819 | − | 2.51716i | 0.135559 | − | 0.123266i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.2166 | 1.52503 | 0.762515 | − | 0.646970i | \(-0.223964\pi\) | ||||
0.762515 | + | 0.646970i | \(0.223964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.7393 | −1.69309 | −0.846544 | − | 0.532319i | \(-0.821321\pi\) | ||||
−0.846544 | + | 0.532319i | \(0.821321\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 23.6960 | − | 10.8297i | 1.15214 | − | 0.526556i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.74984 | − | 6.49492i | −0.181894 | − | 0.315050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.49836 | + | 15.3024i | −0.169297 | + | 0.740534i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 17.3536 | − | 3.77761i | 0.837841 | − | 0.182385i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.9115 | + | 9.18649i | 0.766429 | + | 0.442498i | 0.831599 | − | 0.555376i | \(-0.187426\pi\) |
−0.0651704 | + | 0.997874i | \(0.520759\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.6833i | 1.18621i | 0.805127 | + | 0.593103i | \(0.202097\pi\) | ||||
−0.805127 | + | 0.593103i | \(0.797903\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.90419 | + | 0.608409i | 0.0912991 | + | 0.0291710i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.97626 | − | 5.15503i | 0.142374 | − | 0.246598i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.1758 | + | 7.60702i | −0.628844 | + | 0.363063i | −0.780304 | − | 0.625400i | \(-0.784936\pi\) |
0.151460 | + | 0.988463i | \(0.451602\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.9954 | + | 0.437285i | 0.999783 | + | 0.0208231i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.1325 | + | 15.0876i | −1.24159 | + | 0.716834i | −0.969418 | − | 0.245414i | \(-0.921076\pi\) |
−0.272174 | + | 0.962248i | \(0.587743\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.658248 | − | 1.14012i | 0.0312039 | − | 0.0540468i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.61816 | + | 0.836527i | 0.123835 | + | 0.0395664i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 27.7596i | − | 1.31006i | −0.755603 | − | 0.655029i | \(-0.772656\pi\) | ||
0.755603 | − | 0.655029i | \(-0.227344\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.83077 | − | 3.36640i | −0.274560 | − | 0.158518i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.3381 | − | 3.77423i | 0.814614 | − | 0.177329i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.29096 | + | 5.64687i | −0.0605211 | + | 0.264729i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.9273 | − | 29.3189i | −0.791825 | − | 1.37148i | −0.924836 | − | 0.380366i | \(-0.875798\pi\) |
0.133011 | − | 0.991115i | \(-0.457535\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.64278 | + | 38.6919i | 0.216707 | + | 1.80599i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.7084 | −1.10421 | −0.552104 | − | 0.833775i | \(-0.686175\pi\) | ||||
−0.552104 | + | 0.833775i | \(0.686175\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.60640 | 0.0746559 | 0.0373280 | − | 0.999303i | \(-0.488115\pi\) | ||||
0.0373280 | + | 0.999303i | \(0.488115\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.2464 | − | 12.0452i | 0.614287 | − | 0.558582i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.18589 | − | 5.51812i | −0.147425 | − | 0.255348i | 0.782850 | − | 0.622211i | \(-0.213765\pi\) |
−0.930275 | + | 0.366863i | \(0.880432\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.07751 | + | 3.49759i | 0.0497549 | + | 0.161504i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.39152 | + | 10.9862i | 0.110196 | + | 0.506217i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 37.4827 | + | 21.6407i | 1.72346 | + | 0.995039i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.736825i | − | 0.0338078i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.1306 | − | 19.8556i | 0.646998 | − | 0.909124i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.66105 | − | 2.87702i | 0.0758953 | − | 0.131455i | −0.825580 | − | 0.564285i | \(-0.809152\pi\) |
0.901475 | + | 0.432831i | \(0.142485\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.75687 | − | 5.05578i | 0.399279 | − | 0.230524i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −32.2519 | + | 18.1756i | −1.46751 | + | 0.827017i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.19357 | + | 2.42116i | −0.190420 | + | 0.109939i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.3313 | − | 17.8943i | 0.468155 | − | 0.810868i | −0.531183 | − | 0.847257i | \(-0.678252\pi\) |
0.999338 | + | 0.0363892i | \(0.0115856\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.82924 | + | 8.85493i | −0.127943 | + | 0.400434i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.1679i | 0.684518i | 0.939606 | + | 0.342259i | \(0.111192\pi\) | ||||
−0.939606 | + | 0.342259i | \(0.888808\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.49604 | − | 4.32784i | −0.337605 | − | 0.194916i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.9870 | + | 1.33162i | 0.628668 | + | 0.0598517i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.0810 | + | 13.0745i | 0.631617 | + | 0.586470i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.10558 | − | 5.37903i | −0.139025 | − | 0.240798i | 0.788103 | − | 0.615544i | \(-0.211064\pi\) |
−0.927128 | + | 0.374745i | \(0.877730\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.97136 | − | 8.76631i | −0.356134 | − | 0.391650i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.52940 | 0.246544 | 0.123272 | − | 0.992373i | \(-0.460661\pi\) | ||||
0.123272 | + | 0.992373i | \(0.460661\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.76869 | −0.123205 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.56286 | − | 10.5165i | −0.424701 | − | 0.467055i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.8857 | − | 25.7827i | −0.659796 | − | 1.14280i | −0.980668 | − | 0.195678i | \(-0.937309\pi\) |
0.320872 | − | 0.947122i | \(-0.396024\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.617080 | − | 0.190105i | 0.0272980 | − | 0.00840977i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.50566 | + | 3.52017i | −0.0664766 | + | 0.155419i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.07000 | − | 4.08187i | −0.311542 | − | 0.179869i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.6729i | 1.78879i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.13204 | + | 19.1920i | −0.269167 | + | 0.842436i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.2112 | + | 19.4183i | −0.491170 | + | 0.850732i | −0.999948 | − | 0.0101659i | \(-0.996764\pi\) |
0.508778 | + | 0.860898i | \(0.330097\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.3535 | − | 11.7511i | 0.889996 | − | 0.513839i | 0.0160547 | − | 0.999871i | \(-0.494889\pi\) |
0.873941 | + | 0.486032i | \(0.161556\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.33249 | + | 3.94455i | −0.101798 | + | 0.172154i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −67.1372 | + | 38.7617i | −2.92454 | + | 1.68849i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.1319 | − | 36.6015i | 0.918778 | − | 1.59137i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.0474 | − | 12.1322i | −0.739796 | − | 0.526492i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3.14742i | − | 0.136330i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.186331 | + | 0.107578i | 0.00805579 | + | 0.00465101i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.95972 | − | 13.5964i | −0.127721 | − | 0.586728i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.2453 | + | 29.5272i | −0.613586 | + | 1.27183i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.0653647 | − | 0.113215i | −0.00281025 | − | 0.00486749i | 0.864617 | − | 0.502432i | \(-0.167561\pi\) |
−0.867427 | + | 0.497564i | \(0.834228\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.5813 | + | 11.4404i | −0.539916 | + | 0.490956i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.17366 | −0.0931095 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.2183 | 1.76237 | 0.881184 | − | 0.472774i | \(-0.156747\pi\) | ||||
0.881184 | + | 0.472774i | \(0.156747\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.39851 | + | 16.1884i | 0.315761 | + | 0.690904i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.425199 | − | 0.736467i | −0.0181141 | − | 0.0313745i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 29.9009 | + | 6.83580i | 1.27152 | + | 0.290688i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.81635 | − | 1.70150i | 0.331786 | − | 0.0722245i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.03375 | − | 2.90624i | −0.213287 | − | 0.123141i | 0.389551 | − | 0.921005i | \(-0.372630\pi\) |
−0.602838 | + | 0.797864i | \(0.705963\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.2330i | 0.855764i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −57.9506 | − | 18.5158i | −2.44668 | − | 0.781737i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.5187 | − | 18.2190i | 0.443312 | − | 0.767838i | −0.554621 | − | 0.832103i | \(-0.687137\pi\) |
0.997933 | + | 0.0642647i | \(0.0204702\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.71633 | + | 5.60973i | −0.408769 | + | 0.236003i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.2039 | − | 14.0787i | 0.806488 | − | 0.591251i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.2091 | + | 17.4412i | −1.26643 | + | 0.731173i | −0.974311 | − | 0.225209i | \(-0.927694\pi\) |
−0.292119 | + | 0.956382i | \(0.594360\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.9889 | + | 32.8897i | −0.794661 | + | 1.37639i | 0.128394 | + | 0.991723i | \(0.459018\pi\) |
−0.923054 | + | 0.384670i | \(0.874315\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.4915 | + | 8.46429i | 1.10670 | + | 0.353601i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 8.07860i | − | 0.336901i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.69855 | − | 2.71271i | −0.195603 | − | 0.112932i | 0.399000 | − | 0.916951i | \(-0.369357\pi\) |
−0.594603 | + | 0.804019i | \(0.702691\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.8024 | − | 2.35152i | 0.448934 | − | 0.0977260i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.6339 | + | 31.9151i | −1.22942 | + | 1.32406i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.0228 | + | 32.9484i | 0.787844 | + | 1.36459i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.73019 | + | 5.97382i | 0.112879 | + | 0.246987i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.71317 | −0.359631 | −0.179816 | − | 0.983700i | \(-0.557550\pi\) | ||||
−0.179816 | + | 0.983700i | \(0.557550\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.61648 | −0.313832 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.26769 | − | 2.97137i | 0.134415 | − | 0.122226i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.79341 | − | 16.9627i | −0.402167 | − | 0.696574i | 0.591820 | − | 0.806070i | \(-0.298410\pi\) |
−0.993987 | + | 0.109496i | \(0.965076\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.5013 | − | 14.5407i | 0.553500 | − | 0.596109i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.67144 | + | 12.2721i | 0.109335 | + | 0.502262i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.2397 | + | 8.22129i | 0.581818 | + | 0.335913i | 0.761855 | − | 0.647747i | \(-0.224289\pi\) |
−0.180038 | + | 0.983660i | \(0.557622\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 11.0177i | − | 0.449420i | −0.974426 | − | 0.224710i | \(-0.927857\pi\) | ||
0.974426 | − | 0.224710i | \(-0.0721435\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.38103 | + | 2.40619i | 0.137686 | + | 0.0979875i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.46716 | + | 9.46940i | −0.222272 | + | 0.384986i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.5191 | − | 6.07323i | 0.426959 | − | 0.246505i | −0.271091 | − | 0.962554i | \(-0.587385\pi\) |
0.698050 | + | 0.716049i | \(0.254051\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.0550690 | + | 5.28865i | −0.00223151 | + | 0.214307i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.4663 | + | 9.50681i | −0.666154 | + | 0.384604i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.26802 | − | 14.3206i | 0.333942 | − | 0.578405i | −0.649339 | − | 0.760499i | \(-0.724954\pi\) |
0.983281 | + | 0.182094i | \(0.0582877\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.757828 | − | 2.37184i | 0.0305586 | − | 0.0956420i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.8433i | 1.40274i | 0.712799 | + | 0.701368i | \(0.247427\pi\) | ||||
−0.712799 | + | 0.701368i | \(0.752573\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.3120 | − | 12.3045i | −0.856603 | − | 0.494560i | 0.00627057 | − | 0.999980i | \(-0.498004\pi\) |
−0.862873 | + | 0.505421i | \(0.831337\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.5082 | + | 38.5954i | −0.662451 | + | 1.54878i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.39552 | + | 0.776267i | 0.136039 | + | 0.0311005i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.02115 | − | 4.42216i | −0.160589 | − | 0.176604i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.6370 | −1.38107 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.4776 | −1.49196 | −0.745979 | − | 0.665969i | \(-0.768018\pi\) | ||||
−0.745979 | + | 0.665969i | \(0.768018\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.4577 | + | 16.9992i | 0.614389 | + | 0.675659i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.61142 | + | 14.9154i | 0.341734 | + | 0.591900i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.2836 | + | 1.13449i | −0.605559 | + | 0.0449501i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.6897 | + | 2.06494i | 0.858029 | + | 0.0816878i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.6348 | + | 7.87204i | 0.538541 | + | 0.310927i | 0.744488 | − | 0.667636i | \(-0.232694\pi\) |
−0.205946 | + | 0.978563i | \(0.566027\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.7173i | 0.462086i | 0.972943 | + | 0.231043i | \(0.0742139\pi\) | ||||
−0.972943 | + | 0.231043i | \(0.925786\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.87164 | + | 15.2472i | −0.191821 | + | 0.600360i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.2263 | − | 22.9086i | 0.519980 | − | 0.900632i | −0.479750 | − | 0.877405i | \(-0.659273\pi\) |
0.999730 | − | 0.0232268i | \(-0.00739398\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.2886 | − | 16.3324i | 1.11043 | − | 0.641105i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 40.7744 | + | 24.1106i | 1.59808 | + | 0.944971i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.13762 | − | 1.81151i | 0.122785 | − | 0.0708898i | −0.437350 | − | 0.899292i | \(-0.644083\pi\) |
0.560134 | + | 0.828402i | \(0.310749\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.65810 | + | 14.9963i | −0.338300 | + | 0.585953i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.424523 | − | 0.596515i | 0.0165622 | − | 0.0232723i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 24.1855i | − | 0.942132i | −0.882098 | − | 0.471066i | \(-0.843869\pi\) | ||
0.882098 | − | 0.471066i | \(-0.156131\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.7414 | + | 7.93363i | 0.534480 | + | 0.308582i | 0.742839 | − | 0.669470i | \(-0.233479\pi\) |
−0.208359 | + | 0.978053i | \(0.566812\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.04921 | − | 27.7889i | −0.234932 | − | 1.07923i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.86305 | − | 0.573954i | 0.0722460 | − | 0.0222570i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.66192 | − | 8.07468i | −0.180510 | − | 0.312653i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 36.0134 | − | 32.7476i | 1.39236 | − | 1.26609i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27.7866 | −1.07269 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.48623 | −0.134384 | −0.0671922 | − | 0.997740i | \(-0.521404\pi\) | ||||
−0.0671922 | + | 0.997740i | \(0.521404\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.619064 | + | 5.15914i | 0.0238278 | + | 0.198576i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.4486 | − | 33.6859i | −0.747469 | − | 1.29465i | −0.949032 | − | 0.315179i | \(-0.897936\pi\) |
0.201564 | − | 0.979475i | \(-0.435398\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.38847 | − | 8.71741i | −0.360297 | − | 0.334543i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.7293 | − | 4.94781i | 0.870988 | − | 0.189600i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.4809 | − | 6.05116i | −0.401041 | − | 0.231541i | 0.285892 | − | 0.958262i | \(-0.407710\pi\) |
−0.686933 | + | 0.726721i | \(0.741044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 11.1875i | − | 0.427453i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.8046 | + | 4.41070i | 0.526678 | + | 0.168279i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.89270 | + | 15.4026i | −0.338785 | + | 0.586792i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.7139 | + | 10.8044i | −0.711908 | + | 0.411021i | −0.811767 | − | 0.583981i | \(-0.801494\pi\) |
0.0998588 | + | 0.995002i | \(0.468161\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.52827 | + | 36.4031i | 0.285975 | + | 1.38284i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.87076 | + | 1.08008i | −0.0709620 | + | 0.0409699i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.39071 | + | 9.33699i | −0.204188 | + | 0.353664i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.4858 | − | 4.30884i | −0.510079 | − | 0.162975i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.2893i | 0.955163i | 0.878587 | + | 0.477582i | \(0.158487\pi\) | ||||
−0.878587 | + | 0.477582i | \(0.841513\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.94708 | − | 1.70150i | −0.111151 | − | 0.0641732i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.6977 | + | 3.19947i | −0.553549 | + | 0.120499i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.15669 | − | 7.00059i | −0.0811106 | − | 0.263284i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.13129 | + | 8.88765i | 0.192710 | + | 0.333783i | 0.946147 | − | 0.323737i | \(-0.104939\pi\) |
−0.753438 | + | 0.657519i | \(0.771606\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.6322 | − | 14.4567i | 1.18630 | − | 0.542169i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −83.5076 | −3.12738 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.2538 | −0.383469 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.0892 | − | 14.6302i | 0.600862 | − | 0.546375i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.3969 | − | 42.2566i | −0.909850 | − | 1.57591i | −0.814271 | − | 0.580485i | \(-0.802863\pi\) |
−0.0955793 | − | 0.995422i | \(-0.530470\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.81372 | − | 21.0560i | 0.179272 | − | 0.784166i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.13181 | − | 37.3560i | −0.302425 | − | 1.38928i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.999514 | − | 0.577070i | −0.0371210 | − | 0.0214318i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.98665i | − | 0.370384i | −0.982702 | − | 0.185192i | \(-0.940709\pi\) | ||
0.982702 | − | 0.185192i | \(-0.0592907\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.58487 | − | 25.9127i | 0.280921 | − | 0.959731i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 34.6538 | − | 60.0222i | 1.28172 | − | 2.22000i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.9630 | + | 18.4538i | −1.18058 | + | 0.681608i | −0.956149 | − | 0.292881i | \(-0.905386\pi\) |
−0.224432 | + | 0.974490i | \(0.572053\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.7906 | − | 2.82502i | −0.434904 | − | 0.104202i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.61051 | + | 3.23923i | −0.206666 | + | 0.119318i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.7107 | + | 34.1399i | −0.725070 | + | 1.25586i | 0.233875 | + | 0.972267i | \(0.424859\pi\) |
−0.958945 | + | 0.283591i | \(0.908474\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.850399 | − | 2.66157i | 0.0312402 | − | 0.0977753i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.7786i | 0.468800i | 0.972140 | + | 0.234400i | \(0.0753125\pi\) | ||||
−0.972140 | + | 0.234400i | \(0.924688\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.37427 | − | 0.793438i | −0.0503495 | − | 0.0290693i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.68028 | + | 49.1606i | −0.171243 | + | 1.79869i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.126866 | + | 0.554934i | −0.00463559 | + | 0.0202768i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.32518 | − | 7.49143i | −0.157828 | − | 0.273366i | 0.776257 | − | 0.630416i | \(-0.217116\pi\) |
−0.934085 | + | 0.357050i | \(0.883782\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.94375 | + | 2.13759i | 0.0708342 | + | 0.0778982i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.2446 | −0.372838 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.6532 | 0.968727 | 0.484364 | − | 0.874867i | \(-0.339051\pi\) | ||||
0.484364 | + | 0.874867i | \(0.339051\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −44.0882 | − | 48.4849i | −1.60030 | − | 1.75989i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.2462 | + | 31.6034i | 0.661425 | + | 1.14562i | 0.980241 | + | 0.197805i | \(0.0633814\pi\) |
−0.318816 | + | 0.947817i | \(0.603285\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.69319 | − | 5.49607i | −0.0612975 | − | 0.198971i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.13236 | − | 22.3978i | 0.0770955 | − | 0.809793i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.2242 | + | 7.63502i | 0.477500 | + | 0.275685i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.0781i | 0.940400i | 0.882560 | + | 0.470200i | \(0.155818\pi\) | ||||
−0.882560 | + | 0.470200i | \(0.844182\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.634868 | + | 1.98700i | −0.0228642 | + | 0.0715602i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.9307 | + | 34.5210i | −0.716858 | + | 1.24163i | 0.245381 | + | 0.969427i | \(0.421087\pi\) |
−0.962239 | + | 0.272208i | \(0.912246\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.95201 | + | 5.16845i | −0.321566 | + | 0.185656i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.3908 | + | 18.4381i | 0.372768 | + | 0.661464i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.917336 | + | 0.529624i | −0.0328670 | + | 0.0189757i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.0068 | + | 29.4566i | −0.608551 | + | 1.05404i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.59595 | + | 4.79939i | 0.128509 | + | 0.171516i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 6.49143i | − | 0.231689i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.2458 | + | 12.2663i | 0.757331 | + | 0.437245i | 0.828337 | − | 0.560231i | \(-0.189288\pi\) |
−0.0710057 | + | 0.997476i | \(0.522621\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.84743 | − | 8.48675i | −0.0657703 | − | 0.302136i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.7527 | − | 20.1978i | −0.773436 | − | 0.718153i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.49477 | − | 11.2493i | −0.230636 | − | 0.399473i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.4100 | + | 9.46599i | −0.369204 | + | 0.335724i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.4163 | 1.18367 | 0.591834 | − | 0.806060i | \(-0.298404\pi\) | ||||
0.591834 | + | 0.806060i | \(0.298404\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 65.1308 | 2.30416 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.59212 | − | 1.64169i | 0.126921 | − | 0.0580062i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.571497 | + | 0.989861i | 0.0201677 | + | 0.0349315i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.4266 | − | 6.29287i | 0.719943 | − | 0.221795i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.8921 | + | 5.85398i | −0.946645 | + | 0.206070i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.1974 | + | 24.9400i | 1.51874 | + | 0.876845i | 0.999757 | + | 0.0220612i | \(0.00702286\pi\) |
0.518984 | + | 0.854784i | \(0.326310\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 16.9220i | − | 0.594210i | −0.954845 | − | 0.297105i | \(-0.903979\pi\) | ||
0.954845 | − | 0.297105i | \(-0.0960212\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 33.1867 | + | 10.6035i | 1.16391 | + | 0.371880i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.68350 | − | 4.64797i | 0.0939990 | − | 0.162811i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.89703 | − | 3.40465i | 0.206311 | − | 0.119114i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.9780 | + | 11.5566i | −0.453489 | + | 0.403820i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.856494 | − | 0.494497i | 0.0298918 | − | 0.0172581i | −0.484980 | − | 0.874525i | \(-0.661173\pi\) |
0.514871 | + | 0.857267i | \(0.327840\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.8141 | − | 30.8549i | 0.620960 | − | 1.07553i | −0.368347 | − | 0.929688i | \(-0.620076\pi\) |
0.989307 | − | 0.145846i | \(-0.0465906\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.72707 | − | 2.46888i | −0.269022 | − | 0.0859552i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 48.8191i | − | 1.69761i | −0.528709 | − | 0.848803i | \(-0.677324\pi\) | ||
0.528709 | − | 0.848803i | \(-0.322676\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.5060 | + | 6.64300i | 0.399621 | + | 0.230721i | 0.686320 | − | 0.727299i | \(-0.259225\pi\) |
−0.286700 | + | 0.958021i | \(0.592558\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.46395 | − | 1.62479i | 0.258922 | − | 0.0563632i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 47.2828 | + | 22.8113i | 1.63825 | + | 0.790366i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.42041 | + | 5.92433i | 0.118368 | + | 0.205020i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 53.3295 | − | 6.39919i | 1.84334 | − | 0.221189i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.5549 | 1.46916 | 0.734579 | − | 0.678523i | \(-0.237380\pi\) | ||||
0.734579 | + | 0.678523i | \(0.237380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.6680 | 0.954068 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.9605 | − | 20.8784i | 0.790802 | − | 0.719090i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.10331 | + | 7.10714i | 0.141158 | + | 0.244493i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.2019 | − | 6.44738i | −0.969028 | − | 0.221535i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.25637 | − | 19.5529i | −0.146078 | − | 0.671055i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.3120 | − | 18.6553i | −1.10764 | − | 0.639496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 27.4196i | − | 0.938830i | −0.882978 | − | 0.469415i | \(-0.844465\pi\) | ||
0.882978 | − | 0.469415i | \(-0.155535\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.28169 | − | 1.80096i | 0.0438330 | − | 0.0615916i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.27514 | + | 7.40476i | −0.146036 | + | 0.252942i | −0.929759 | − | 0.368169i | \(-0.879985\pi\) |
0.783723 | + | 0.621111i | \(0.213318\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.23617 | + | 1.29105i | −0.0762970 | + | 0.0440501i | −0.537663 | − | 0.843160i | \(-0.680693\pi\) |
0.461366 | + | 0.887210i | \(0.347359\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.58748 | + | 0.0685934i | 0.224501 | + | 0.00233766i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.5478 | − | 10.7086i | 0.631373 | − | 0.364523i | −0.149911 | − | 0.988700i | \(-0.547899\pi\) |
0.781284 | + | 0.624176i | \(0.214565\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.81618 | − | 10.0739i | 0.197756 | − | 0.342524i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.6883 | + | 64.7500i | −0.702611 | + | 2.19903i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 54.2950i | 1.84183i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.62278 | − | 1.51426i | −0.0888694 | − | 0.0513088i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.4616 | − | 1.37680i | −0.489450 | − | 0.0465976i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.80025 | − | 1.93884i | 0.0608597 | − | 0.0655447i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.9665 | − | 41.5112i | −0.809291 | − | 1.40173i | −0.913355 | − | 0.407163i | \(-0.866518\pi\) |
0.104064 | − | 0.994571i | \(-0.466815\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.36604 | − | 9.20035i | −0.282179 | − | 0.310320i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.0526 | 0.540827 | 0.270413 | − | 0.962744i | \(-0.412840\pi\) | ||||
0.270413 | + | 0.962744i | \(0.412840\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −57.8898 | −1.94815 | −0.974073 | − | 0.226236i | \(-0.927358\pi\) | ||||
−0.974073 | + | 0.226236i | \(0.927358\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.12724 | + | 8.93773i | 0.273194 | + | 0.300439i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.415272 | + | 0.719272i | 0.0139435 | + | 0.0241508i | 0.872913 | − | 0.487876i | \(-0.162228\pi\) |
−0.858969 | + | 0.512027i | \(0.828895\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.0055 | + | 33.3923i | −1.03989 | + | 1.11994i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.8709 | + | 27.5849i | 1.06772 | + | 0.924128i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.54164 | + | 3.19947i | 0.185444 | + | 0.107066i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.03372i | 0.268538i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.32383 | − | 29.1817i | 0.311314 | − | 0.974348i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.96511 | + | 10.3319i | −0.198947 | + | 0.344587i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 52.7613 | − | 30.4618i | 1.75773 | − | 1.01483i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −42.3472 | − | 0.440948i | −1.40923 | − | 0.0146738i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.50255 | − | 4.90895i | 0.282634 | − | 0.163179i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.9547 | − | 38.0267i | 0.728995 | − | 1.26266i | −0.228313 | − | 0.973588i | \(-0.573321\pi\) |
0.957308 | − | 0.289069i | \(-0.0933456\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.76729 | − | 4.81609i | −0.224457 | − | 0.159740i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.64586i | 0.0545299i | 0.999628 | + | 0.0272649i | \(0.00867978\pi\) | ||||
−0.999628 | + | 0.0272649i | \(0.991320\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −66.7649 | − | 38.5467i | −2.20959 | − | 1.27571i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.18578 | − | 10.0411i | −0.0722597 | − | 0.331947i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −44.6621 | − | 10.2104i | −1.47487 | − | 0.337178i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.9387 | + | 39.7309i | 0.756677 | + | 1.31060i | 0.944537 | + | 0.328406i | \(0.106512\pi\) |
−0.187860 | + | 0.982196i | \(0.560155\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.13124 | − | 2.84730i | 0.103178 | − | 0.0938216i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.9005 | −0.523373 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.61846 | −0.151854 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.1803 | − | 22.2751i | −0.334365 | − | 0.731611i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.79774 | + | 10.0420i | 0.190218 | + | 0.329467i | 0.945322 | − | 0.326137i | \(-0.105747\pi\) |
−0.755105 | + | 0.655604i | \(0.772414\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.90247 | + | 4.26360i | 0.0951245 | + | 0.139734i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.67694 | − | 1.88883i | 0.284070 | − | 0.0618376i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.4184 | + | 17.5620i | 0.994786 | + | 0.574340i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.7618i | 1.29896i | 0.760378 | + | 0.649481i | \(0.225014\pi\) | ||||
−0.760378 | + | 0.649481i | \(0.774986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.70301 | + | 0.863638i | 0.0882094 | + | 0.0281838i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.7590 | − | 35.9557i | 0.676724 | − | 1.17212i | −0.299237 | − | 0.954179i | \(-0.596732\pi\) |
0.975962 | − | 0.217942i | \(-0.0699345\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.0577 | + | 5.80684i | −0.327525 | + | 0.189097i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.5626 | + | 5.58404i | −0.408661 | + | 0.181649i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.5502 | − | 15.3288i | 0.862767 | − | 0.498119i | −0.00217116 | − | 0.999998i | \(-0.500691\pi\) |
0.864938 | + | 0.501879i | \(0.167358\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.267161 | + | 0.462736i | −0.00867241 | + | 0.0150211i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.3281 | − | 8.73161i | −0.886175 | − | 0.283142i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 22.7409i | − | 0.736650i | −0.929697 | − | 0.368325i | \(-0.879931\pi\) | ||
0.929697 | − | 0.368325i | \(-0.120069\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.9054 | − | 8.02830i | −0.449969 | − | 0.259790i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.14803 | + | 1.99138i | −0.295714 | + | 0.0643723i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28.2874 | − | 8.71457i | 0.913449 | − | 0.281408i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.9257 | + | 65.6892i | 1.22341 | + | 2.11901i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.268303 | + | 0.587064i | 0.00864595 | + | 0.0189179i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.38285 | −0.205471 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.4381 | 0.592928 | 0.296464 | − | 0.955044i | \(-0.404193\pi\) | ||||
0.296464 | + | 0.955044i | \(0.404193\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.08134 | + | 6.43919i | −0.227485 | + | 0.206856i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.784910 | − | 1.35950i | −0.0251889 | − | 0.0436285i | 0.853156 | − | 0.521656i | \(-0.174685\pi\) |
−0.878345 | + | 0.478027i | \(0.841352\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.18822 | − | 3.88885i | −0.134268 | − | 0.124671i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.806595 | − | 3.70534i | −0.0258317 | − | 0.118666i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.3718 | + | 10.6070i | 0.587766 | + | 0.339347i | 0.764214 | − | 0.644963i | \(-0.223127\pi\) |
−0.176448 | + | 0.984310i | \(0.556461\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.16569i | 0.197056i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.31291 | − | 3.78105i | −0.169628 | − | 0.120720i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.2639 | − | 31.6340i | 0.582528 | − | 1.00897i | −0.412651 | − | 0.910889i | \(-0.635397\pi\) |
0.995179 | − | 0.0980782i | \(-0.0312695\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.20833 | + | 1.27498i | −0.0703631 | + | 0.0406242i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.5387 | − | 34.6708i | −0.621924 | − | 1.10358i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 64.6555 | − | 37.3289i | 2.05592 | − | 1.18699i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.43293 | − | 16.3383i | 0.299647 | − | 0.519004i | −0.676408 | − | 0.736527i | \(-0.736464\pi\) |
0.976055 | + | 0.217523i | \(0.0697978\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.6223 | − | 39.5053i | 0.400557 | − | 1.25366i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 7.25121i | − | 0.229879i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.2658 | + | 14.0098i | 0.768504 | + | 0.443696i | 0.832341 | − | 0.554264i | \(-0.187000\pi\) |
−0.0638366 | + | 0.997960i | \(0.520334\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.0646 | + | 9.43757i | 0.698093 | + | 0.298591i |
(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 | 420.2.bh.b.101.2 | yes | 10 | |
3.2 | odd | 2 | 420.2.bh.a.101.1 | ✓ | 10 | ||
5.2 | odd | 4 | 2100.2.bo.g.1949.3 | 20 | |||
5.3 | odd | 4 | 2100.2.bo.g.1949.8 | 20 | |||
5.4 | even | 2 | 2100.2.bi.j.101.4 | 10 | |||
7.3 | odd | 6 | 2940.2.d.b.881.5 | 10 | |||
7.4 | even | 3 | 2940.2.d.a.881.6 | 10 | |||
7.5 | odd | 6 | 420.2.bh.a.341.1 | yes | 10 | ||
15.2 | even | 4 | 2100.2.bo.h.1949.4 | 20 | |||
15.8 | even | 4 | 2100.2.bo.h.1949.7 | 20 | |||
15.14 | odd | 2 | 2100.2.bi.k.101.5 | 10 | |||
21.5 | even | 6 | inner | 420.2.bh.b.341.2 | yes | 10 | |
21.11 | odd | 6 | 2940.2.d.b.881.6 | 10 | |||
21.17 | even | 6 | 2940.2.d.a.881.5 | 10 | |||
35.12 | even | 12 | 2100.2.bo.h.1349.7 | 20 | |||
35.19 | odd | 6 | 2100.2.bi.k.1601.5 | 10 | |||
35.33 | even | 12 | 2100.2.bo.h.1349.4 | 20 | |||
105.47 | odd | 12 | 2100.2.bo.g.1349.8 | 20 | |||
105.68 | odd | 12 | 2100.2.bo.g.1349.3 | 20 | |||
105.89 | even | 6 | 2100.2.bi.j.1601.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bh.a.101.1 | ✓ | 10 | 3.2 | odd | 2 | ||
420.2.bh.a.341.1 | yes | 10 | 7.5 | odd | 6 | ||
420.2.bh.b.101.2 | yes | 10 | 1.1 | even | 1 | trivial | |
420.2.bh.b.341.2 | yes | 10 | 21.5 | even | 6 | inner | |
2100.2.bi.j.101.4 | 10 | 5.4 | even | 2 | |||
2100.2.bi.j.1601.4 | 10 | 105.89 | even | 6 | |||
2100.2.bi.k.101.5 | 10 | 15.14 | odd | 2 | |||
2100.2.bi.k.1601.5 | 10 | 35.19 | odd | 6 | |||
2100.2.bo.g.1349.3 | 20 | 105.68 | odd | 12 | |||
2100.2.bo.g.1349.8 | 20 | 105.47 | odd | 12 | |||
2100.2.bo.g.1949.3 | 20 | 5.2 | odd | 4 | |||
2100.2.bo.g.1949.8 | 20 | 5.3 | odd | 4 | |||
2100.2.bo.h.1349.4 | 20 | 35.33 | even | 12 | |||
2100.2.bo.h.1349.7 | 20 | 35.12 | even | 12 | |||
2100.2.bo.h.1949.4 | 20 | 15.2 | even | 4 | |||
2100.2.bo.h.1949.7 | 20 | 15.8 | even | 4 | |||
2940.2.d.a.881.5 | 10 | 21.17 | even | 6 | |||
2940.2.d.a.881.6 | 10 | 7.4 | even | 3 | |||
2940.2.d.b.881.5 | 10 | 7.3 | odd | 6 | |||
2940.2.d.b.881.6 | 10 | 21.11 | odd | 6 |