Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(323,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.j (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.42 | ||
Character | \(\chi\) | \(=\) | 1512.323 |
Dual form | 1512.2.j.d.323.41 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.25654 | + | 0.648937i | 0.888505 | + | 0.458867i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.15776 | + | 1.63082i | 0.578881 | + | 0.815412i | ||||
\(5\) | 1.27600 | 0.570644 | 0.285322 | − | 0.958432i | \(-0.407899\pi\) | ||||
0.285322 | + | 0.958432i | \(0.407899\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0.396469 | + | 2.80050i | 0.140173 | + | 0.990127i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.60334 | + | 0.828043i | 0.507020 | + | 0.261850i | ||||
\(11\) | 6.57401i | 1.98214i | 0.133353 | + | 0.991069i | \(0.457426\pi\) | ||||
−0.133353 | + | 0.991069i | \(0.542574\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.05196i | 1.12381i | 0.827201 | + | 0.561906i | \(0.189932\pi\) | ||||
−0.827201 | + | 0.561906i | \(0.810068\pi\) | |||||||
\(14\) | 0.648937 | − | 1.25654i | 0.173436 | − | 0.335823i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.31917 | + | 3.77621i | −0.329793 | + | 0.944053i | ||||
\(17\) | − | 6.09788i | − | 1.47895i | −0.673182 | − | 0.739477i | \(-0.735073\pi\) | ||
0.673182 | − | 0.739477i | \(-0.264927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.08352 | −0.477993 | −0.238997 | − | 0.971020i | \(-0.576819\pi\) | ||||
−0.238997 | + | 0.971020i | \(0.576819\pi\) | |||||||
\(20\) | 1.47730 | + | 2.08093i | 0.330335 | + | 0.465310i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.26611 | + | 8.26047i | −0.909538 | + | 1.76114i | ||||
\(23\) | 6.85760 | 1.42991 | 0.714954 | − | 0.699171i | \(-0.246448\pi\) | ||||
0.714954 | + | 0.699171i | \(0.246448\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.37182 | −0.674365 | ||||||||
\(26\) | −2.62946 | + | 5.09143i | −0.515680 | + | 0.998511i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.63082 | − | 1.15776i | 0.308197 | − | 0.218797i | ||||
\(29\) | −6.53304 | −1.21316 | −0.606578 | − | 0.795024i | \(-0.707458\pi\) | ||||
−0.606578 | + | 0.795024i | \(0.707458\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.26844i | − | 0.587028i | −0.955955 | − | 0.293514i | \(-0.905175\pi\) | ||
0.955955 | − | 0.293514i | \(-0.0948248\pi\) | |||||||
\(32\) | −4.10811 | + | 3.88889i | −0.726218 | + | 0.687465i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.95714 | − | 7.66220i | 0.678643 | − | 1.31406i | ||||
\(35\) | − | 1.27600i | − | 0.215683i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.95562i | 0.485901i | 0.970039 | + | 0.242950i | \(0.0781152\pi\) | ||||
−0.970039 | + | 0.242950i | \(0.921885\pi\) | |||||||
\(38\) | −2.61802 | − | 1.35208i | −0.424699 | − | 0.219336i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.505894 | + | 3.57344i | 0.0799889 | + | 0.565010i | ||||
\(41\) | 3.35381i | 0.523777i | 0.965098 | + | 0.261888i | \(0.0843452\pi\) | ||||
−0.965098 | + | 0.261888i | \(0.915655\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.9901 | 1.67598 | 0.837991 | − | 0.545685i | \(-0.183730\pi\) | ||||
0.837991 | + | 0.545685i | \(0.183730\pi\) | |||||||
\(44\) | −10.7210 | + | 7.61114i | −1.61626 | + | 1.14742i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.61682 | + | 4.45015i | 1.27048 | + | 0.656138i | ||||
\(47\) | 7.12041 | 1.03862 | 0.519310 | − | 0.854586i | \(-0.326189\pi\) | ||||
0.519310 | + | 0.854586i | \(0.326189\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −4.23682 | − | 2.18810i | −0.599176 | − | 0.309444i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.60803 | + | 4.69121i | −0.916369 | + | 0.650553i | ||||
\(53\) | 2.87278 | 0.394607 | 0.197304 | − | 0.980342i | \(-0.436782\pi\) | ||||
0.197304 | + | 0.980342i | \(0.436782\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.38843i | 1.13110i | ||||||||
\(56\) | 2.80050 | − | 0.396469i | 0.374233 | − | 0.0529804i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.20900 | − | 4.23953i | −1.07789 | − | 0.556677i | ||||
\(59\) | − | 7.75213i | − | 1.00924i | −0.863341 | − | 0.504621i | \(-0.831632\pi\) | ||
0.863341 | − | 0.504621i | \(-0.168368\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0251i | 1.53966i | 0.638249 | + | 0.769830i | \(0.279659\pi\) | ||||
−0.638249 | + | 0.769830i | \(0.720341\pi\) | |||||||
\(62\) | 2.12101 | − | 4.10691i | 0.269368 | − | 0.521578i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.68562 | + | 2.22063i | −0.960703 | + | 0.277578i | ||||
\(65\) | 5.17030i | 0.641296i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.01966 | −0.368910 | −0.184455 | − | 0.982841i | \(-0.559052\pi\) | ||||
−0.184455 | + | 0.982841i | \(0.559052\pi\) | |||||||
\(68\) | 9.94457 | − | 7.05990i | 1.20596 | − | 0.856138i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.828043 | − | 1.60334i | 0.0989700 | − | 0.191636i | ||||
\(71\) | 3.48158 | 0.413188 | 0.206594 | − | 0.978427i | \(-0.433762\pi\) | ||||
0.206594 | + | 0.978427i | \(0.433762\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.76889 | 0.324075 | 0.162037 | − | 0.986785i | \(-0.448194\pi\) | ||||
0.162037 | + | 0.986785i | \(0.448194\pi\) | |||||||
\(74\) | −1.91801 | + | 3.71384i | −0.222964 | + | 0.431725i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.41223 | − | 3.39786i | −0.276701 | − | 0.389761i | ||||
\(77\) | 6.57401 | 0.749177 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.849261i | 0.0955494i | 0.998858 | + | 0.0477747i | \(0.0152129\pi\) | ||||
−0.998858 | + | 0.0477747i | \(0.984787\pi\) | |||||||
\(80\) | −1.68326 | + | 4.81845i | −0.188194 | + | 0.538719i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.17641 | + | 4.21418i | −0.240344 | + | 0.465378i | ||||
\(83\) | − | 15.8068i | − | 1.73503i | −0.497414 | − | 0.867513i | \(-0.665717\pi\) | ||
0.497414 | − | 0.867513i | \(-0.334283\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 7.78089i | − | 0.843956i | ||||||
\(86\) | 13.8095 | + | 7.13191i | 1.48912 | + | 0.769053i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −18.4105 | + | 2.60639i | −1.96257 | + | 0.277842i | ||||
\(89\) | − | 4.06349i | − | 0.430729i | −0.976534 | − | 0.215365i | \(-0.930906\pi\) | ||
0.976534 | − | 0.215365i | \(-0.0690940\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.05196 | 0.424761 | ||||||||
\(92\) | 7.93947 | + | 11.1835i | 0.827747 | + | 1.16596i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.94705 | + | 4.62070i | 0.922818 | + | 0.476589i | ||||
\(95\) | −2.65858 | −0.272764 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.90438 | −0.497964 | −0.248982 | − | 0.968508i | \(-0.580096\pi\) | ||||
−0.248982 | + | 0.968508i | \(0.580096\pi\) | |||||||
\(98\) | −1.25654 | − | 0.648937i | −0.126929 | − | 0.0655525i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.90377 | − | 5.49885i | −0.390377 | − | 0.549885i | ||||
\(101\) | 16.5134 | 1.64314 | 0.821572 | − | 0.570105i | \(-0.193098\pi\) | ||||
0.821572 | + | 0.570105i | \(0.193098\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7097i | 1.05526i | 0.849475 | + | 0.527629i | \(0.176919\pi\) | ||||
−0.849475 | + | 0.527629i | \(0.823081\pi\) | |||||||
\(104\) | −11.3475 | + | 1.60648i | −1.11272 | + | 0.157528i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.60975 | + | 1.86425i | 0.350610 | + | 0.181072i | ||||
\(107\) | − | 9.41994i | − | 0.910660i | −0.890323 | − | 0.455330i | \(-0.849521\pi\) | ||
0.890323 | − | 0.455330i | \(-0.150479\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.95370i | 0.761826i | 0.924611 | + | 0.380913i | \(0.124390\pi\) | ||||
−0.924611 | + | 0.380913i | \(0.875610\pi\) | |||||||
\(110\) | −5.44356 | + | 10.5404i | −0.519023 | + | 1.00498i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.77621 | + | 1.31917i | 0.356819 | + | 0.124650i | ||||
\(113\) | 1.56398i | 0.147127i | 0.997291 | + | 0.0735636i | \(0.0234372\pi\) | ||||
−0.997291 | + | 0.0735636i | \(0.976563\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.75029 | 0.815969 | ||||||||
\(116\) | −7.56371 | − | 10.6542i | −0.702273 | − | 0.989221i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.03064 | − | 9.74083i | 0.463108 | − | 0.896716i | ||||
\(119\) | −6.09788 | −0.558992 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −32.2175 | −2.92887 | ||||||||
\(122\) | −7.80354 | + | 15.1100i | −0.706499 | + | 1.36799i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.33024 | − | 3.78407i | 0.478670 | − | 0.339820i | ||||
\(125\) | −10.6824 | −0.955467 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 19.7895i | − | 1.75603i | −0.478629 | − | 0.878017i | \(-0.658866\pi\) | ||
0.478629 | − | 0.878017i | \(-0.341134\pi\) | |||||||
\(128\) | −11.0983 | − | 2.19719i | −0.980961 | − | 0.194206i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.35519 | + | 6.49666i | −0.294270 | + | 0.569795i | ||||
\(131\) | − | 13.6907i | − | 1.19616i | −0.801436 | − | 0.598080i | \(-0.795931\pi\) | ||
0.801436 | − | 0.598080i | \(-0.204069\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.08352i | 0.180664i | ||||||||
\(134\) | −3.79431 | − | 1.95957i | −0.327778 | − | 0.169281i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.0771 | − | 2.41762i | 1.46435 | − | 0.207309i | ||||
\(137\) | − | 20.0099i | − | 1.70956i | −0.518990 | − | 0.854780i | \(-0.673692\pi\) | ||
0.518990 | − | 0.854780i | \(-0.326308\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.0306 | −0.935607 | −0.467804 | − | 0.883832i | \(-0.654955\pi\) | ||||
−0.467804 | + | 0.883832i | \(0.654955\pi\) | |||||||
\(140\) | 2.08093 | − | 1.47730i | 0.175871 | − | 0.124855i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.37473 | + | 2.25932i | 0.367119 | + | 0.189598i | ||||
\(143\) | −26.6376 | −2.22755 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.33616 | −0.692280 | ||||||||
\(146\) | 3.47921 | + | 1.79684i | 0.287942 | + | 0.148707i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.82009 | + | 3.42190i | −0.396209 | + | 0.281279i | ||||
\(149\) | −0.391867 | −0.0321030 | −0.0160515 | − | 0.999871i | \(-0.505110\pi\) | ||||
−0.0160515 | + | 0.999871i | \(0.505110\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.3302i | 0.840662i | 0.907371 | + | 0.420331i | \(0.138086\pi\) | ||||
−0.907371 | + | 0.420331i | \(0.861914\pi\) | |||||||
\(152\) | −0.826053 | − | 5.83492i | −0.0670018 | − | 0.473274i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.26047 | + | 4.26611i | 0.665648 | + | 0.343773i | ||||
\(155\) | − | 4.17052i | − | 0.334984i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.78139i | 0.780640i | 0.920679 | + | 0.390320i | \(0.127636\pi\) | ||||
−0.920679 | + | 0.390320i | \(0.872364\pi\) | |||||||
\(158\) | −0.551117 | + | 1.06713i | −0.0438445 | + | 0.0848961i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.24194 | + | 4.96222i | −0.414412 | + | 0.392298i | ||||
\(161\) | − | 6.85760i | − | 0.540455i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.11525 | 0.0873533 | 0.0436766 | − | 0.999046i | \(-0.486093\pi\) | ||||
0.0436766 | + | 0.999046i | \(0.486093\pi\) | |||||||
\(164\) | −5.46947 | + | 3.88291i | −0.427094 | + | 0.303205i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.2576 | − | 19.8619i | 0.796147 | − | 1.54158i | ||||
\(167\) | 16.7973 | 1.29982 | 0.649908 | − | 0.760013i | \(-0.274807\pi\) | ||||
0.649908 | + | 0.760013i | \(0.274807\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.41837 | −0.262951 | ||||||||
\(170\) | 5.04931 | − | 9.77697i | 0.387264 | − | 0.749859i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.7240 | + | 17.9230i | 0.970194 | + | 1.36661i | ||||
\(173\) | 18.2063 | 1.38420 | 0.692100 | − | 0.721802i | \(-0.256686\pi\) | ||||
0.692100 | + | 0.721802i | \(0.256686\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.37182i | 0.254886i | ||||||||
\(176\) | −24.8248 | − | 8.67223i | −1.87124 | − | 0.653694i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.63695 | − | 5.10592i | 0.197648 | − | 0.382705i | ||||
\(179\) | 8.03488i | 0.600555i | 0.953852 | + | 0.300278i | \(0.0970793\pi\) | ||||
−0.953852 | + | 0.300278i | \(0.902921\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.5478i | − | 1.37865i | −0.724454 | − | 0.689323i | \(-0.757908\pi\) | ||
0.724454 | − | 0.689323i | \(-0.242092\pi\) | |||||||
\(182\) | 5.09143 | + | 2.62946i | 0.377402 | + | 0.194909i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.71883 | + | 19.2047i | 0.200435 | + | 1.41579i | ||||
\(185\) | 3.77137i | 0.277276i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 40.0875 | 2.93149 | ||||||||
\(188\) | 8.24375 | + | 11.6121i | 0.601237 | + | 0.846902i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.34060 | − | 1.72525i | −0.242352 | − | 0.125163i | ||||
\(191\) | 22.8458 | 1.65306 | 0.826532 | − | 0.562890i | \(-0.190311\pi\) | ||||
0.826532 | + | 0.562890i | \(0.190311\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.49311 | 0.251439 | 0.125720 | − | 0.992066i | \(-0.459876\pi\) | ||||
0.125720 | + | 0.992066i | \(0.459876\pi\) | |||||||
\(194\) | −6.16252 | − | 3.18263i | −0.442443 | − | 0.228499i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.15776 | − | 1.63082i | −0.0826973 | − | 0.116487i | ||||
\(197\) | −21.9432 | −1.56339 | −0.781693 | − | 0.623663i | \(-0.785644\pi\) | ||||
−0.781693 | + | 0.623663i | \(0.785644\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 23.0870i | − | 1.63660i | −0.574793 | − | 0.818299i | \(-0.694918\pi\) | ||
0.574793 | − | 0.818299i | \(-0.305082\pi\) | |||||||
\(200\) | −1.33682 | − | 9.44280i | −0.0945278 | − | 0.667707i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.7497 | + | 10.7161i | 1.45994 | + | 0.753985i | ||||
\(203\) | 6.53304i | 0.458529i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.27946i | 0.298890i | ||||||||
\(206\) | −6.94992 | + | 13.4571i | −0.484224 | + | 0.937602i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −15.3011 | − | 5.34522i | −1.06094 | − | 0.370625i | ||||
\(209\) | − | 13.6971i | − | 0.947448i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.71426 | −0.118014 | −0.0590072 | − | 0.998258i | \(-0.518793\pi\) | ||||
−0.0590072 | + | 0.998258i | \(0.518793\pi\) | |||||||
\(212\) | 3.32600 | + | 4.68500i | 0.228431 | + | 0.321767i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.11294 | − | 11.8365i | 0.417872 | − | 0.809126i | ||||
\(215\) | 14.0234 | 0.956389 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.26844 | −0.221876 | ||||||||
\(218\) | −5.16145 | + | 9.99411i | −0.349577 | + | 0.676886i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −13.6800 | + | 9.71181i | −0.922309 | + | 0.654770i | ||||
\(221\) | 24.7084 | 1.66206 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 0.545891i | − | 0.0365556i | −0.999833 | − | 0.0182778i | \(-0.994182\pi\) | ||
0.999833 | − | 0.0182778i | \(-0.00581832\pi\) | |||||||
\(224\) | 3.88889 | + | 4.10811i | 0.259837 | + | 0.274484i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.01493 | + | 1.96520i | −0.0675119 | + | 0.130723i | ||||
\(227\) | 1.60514i | 0.106537i | 0.998580 | + | 0.0532685i | \(0.0169639\pi\) | ||||
−0.998580 | + | 0.0532685i | \(0.983036\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.39412i | − | 0.0921257i | −0.998939 | − | 0.0460629i | \(-0.985333\pi\) | ||
0.998939 | − | 0.0460629i | \(-0.0146675\pi\) | |||||||
\(230\) | 10.9951 | + | 5.67839i | 0.724993 | + | 0.374422i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.59015 | − | 18.2958i | −0.170052 | − | 1.20118i | ||||
\(233\) | − | 10.0130i | − | 0.655971i | −0.944683 | − | 0.327985i | \(-0.893630\pi\) | ||
0.944683 | − | 0.327985i | \(-0.106370\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.08565 | 0.592682 | ||||||||
\(236\) | 12.6424 | − | 8.97513i | 0.822948 | − | 0.584231i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.66220 | − | 3.95714i | −0.496667 | − | 0.256503i | ||||
\(239\) | −9.62073 | −0.622313 | −0.311157 | − | 0.950359i | \(-0.600716\pi\) | ||||
−0.311157 | + | 0.950359i | \(0.600716\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.9788 | 0.900456 | 0.450228 | − | 0.892914i | \(-0.351343\pi\) | ||||
0.450228 | + | 0.892914i | \(0.351343\pi\) | |||||||
\(242\) | −40.4825 | − | 20.9071i | −2.60231 | − | 1.34396i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −19.6109 | + | 13.9222i | −1.25546 | + | 0.891280i | ||||
\(245\) | −1.27600 | −0.0815206 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.44235i | − | 0.537174i | ||||||
\(248\) | 9.15326 | − | 1.29583i | 0.581233 | − | 0.0822855i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13.4229 | − | 6.93223i | −0.848937 | − | 0.438433i | ||||
\(251\) | 6.99814i | 0.441719i | 0.975306 | + | 0.220859i | \(0.0708862\pi\) | ||||
−0.975306 | + | 0.220859i | \(0.929114\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 45.0819i | 2.83427i | ||||||||
\(254\) | 12.8421 | − | 24.8662i | 0.805787 | − | 1.56024i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.5196 | − | 9.96294i | −0.782474 | − | 0.622684i | ||||
\(257\) | − | 4.39346i | − | 0.274057i | −0.990567 | − | 0.137028i | \(-0.956245\pi\) | ||
0.990567 | − | 0.137028i | \(-0.0437551\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.95562 | 0.183653 | ||||||||
\(260\) | −8.43184 | + | 5.98598i | −0.522921 | + | 0.371235i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.88438 | − | 17.2028i | 0.548879 | − | 1.06279i | ||||
\(263\) | 8.54094 | 0.526657 | 0.263328 | − | 0.964706i | \(-0.415180\pi\) | ||||
0.263328 | + | 0.964706i | \(0.415180\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.66567 | 0.225180 | ||||||||
\(266\) | −1.35208 | + | 2.61802i | −0.0829010 | + | 0.160521i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.49605 | − | 4.92453i | −0.213555 | − | 0.300814i | ||||
\(269\) | −14.7389 | −0.898647 | −0.449324 | − | 0.893369i | \(-0.648335\pi\) | ||||
−0.449324 | + | 0.893369i | \(0.648335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.21696i | − | 0.256162i | −0.991764 | − | 0.128081i | \(-0.959118\pi\) | ||
0.991764 | − | 0.128081i | \(-0.0408817\pi\) | |||||||
\(272\) | 23.0269 | + | 8.04414i | 1.39621 | + | 0.487748i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.9852 | − | 25.1431i | 0.784462 | − | 1.51895i | ||||
\(275\) | − | 22.1664i | − | 1.33668i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.73096i | − | 0.164088i | −0.996629 | − | 0.0820438i | \(-0.973855\pi\) | ||
0.996629 | − | 0.0820438i | \(-0.0261447\pi\) | |||||||
\(278\) | −13.8604 | − | 7.15819i | −0.831291 | − | 0.429320i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.57344 | − | 0.505894i | 0.213554 | − | 0.0302330i | ||||
\(281\) | − | 9.32789i | − | 0.556455i | −0.960515 | − | 0.278228i | \(-0.910253\pi\) | ||
0.960515 | − | 0.278228i | \(-0.0897469\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.2355 | 1.20288 | 0.601438 | − | 0.798919i | \(-0.294595\pi\) | ||||
0.601438 | + | 0.798919i | \(0.294595\pi\) | |||||||
\(284\) | 4.03084 | + | 5.67784i | 0.239187 | + | 0.336918i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −33.4711 | − | 17.2861i | −1.97919 | − | 1.02215i | ||||
\(287\) | 3.35381 | 0.197969 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.1841 | −1.18730 | ||||||||
\(290\) | −10.4747 | − | 5.40964i | −0.615094 | − | 0.317665i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.20572 | + | 4.51558i | 0.187601 | + | 0.264254i | ||||
\(293\) | −0.259973 | −0.0151878 | −0.00759391 | − | 0.999971i | \(-0.502417\pi\) | ||||
−0.00759391 | + | 0.999971i | \(0.502417\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.89172i | − | 0.575918i | ||||||
\(296\) | −8.27722 | + | 1.17181i | −0.481103 | + | 0.0681101i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.492395 | − | 0.254297i | −0.0285237 | − | 0.0147310i | ||||
\(299\) | 27.7867i | 1.60695i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 10.9901i | − | 0.633461i | ||||||
\(302\) | −6.70367 | + | 12.9803i | −0.385753 | + | 0.746933i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.74852 | − | 7.86783i | 0.157639 | − | 0.451251i | ||||
\(305\) | 15.3441i | 0.878598i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.8255 | 1.47394 | 0.736969 | − | 0.675927i | \(-0.236257\pi\) | ||||
0.736969 | + | 0.675927i | \(0.236257\pi\) | |||||||
\(308\) | 7.61114 | + | 10.7210i | 0.433685 | + | 0.610888i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.70640 | − | 5.24041i | 0.153713 | − | 0.297635i | ||||
\(311\) | −19.8253 | −1.12419 | −0.562094 | − | 0.827074i | \(-0.690004\pi\) | ||||
−0.562094 | + | 0.827074i | \(0.690004\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.2201 | 0.577673 | 0.288837 | − | 0.957378i | \(-0.406732\pi\) | ||||
0.288837 | + | 0.957378i | \(0.406732\pi\) | |||||||
\(314\) | −6.34750 | + | 12.2907i | −0.358210 | + | 0.693602i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.38500 | + | 0.983243i | −0.0779121 | + | 0.0553117i | ||||
\(317\) | −3.21191 | −0.180399 | −0.0901995 | − | 0.995924i | \(-0.528750\pi\) | ||||
−0.0901995 | + | 0.995924i | \(0.528750\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 42.9482i | − | 2.40464i | ||||||
\(320\) | −9.80685 | + | 2.83352i | −0.548220 | + | 0.158398i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.45015 | − | 8.61682i | 0.247997 | − | 0.480196i | ||||
\(323\) | 12.7051i | 0.706930i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 13.6625i | − | 0.757859i | ||||||
\(326\) | 1.40135 | + | 0.723728i | 0.0776138 | + | 0.0400836i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.39234 | + | 1.32968i | −0.518605 | + | 0.0734193i | ||||
\(329\) | − | 7.12041i | − | 0.392561i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.8260 | −1.63939 | −0.819694 | − | 0.572802i | \(-0.805856\pi\) | ||||
−0.819694 | + | 0.572802i | \(0.805856\pi\) | |||||||
\(332\) | 25.7782 | − | 18.3006i | 1.41476 | − | 1.00437i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 21.1064 | + | 10.9004i | 1.15489 | + | 0.596443i | ||||
\(335\) | −3.85308 | −0.210516 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.9588 | −1.46854 | −0.734271 | − | 0.678857i | \(-0.762476\pi\) | ||||
−0.734271 | + | 0.678857i | \(0.762476\pi\) | |||||||
\(338\) | −4.29530 | − | 2.21830i | −0.233633 | − | 0.120660i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.6893 | − | 9.00843i | 0.688172 | − | 0.488551i | ||||
\(341\) | 21.4867 | 1.16357 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 4.35725 | + | 30.7779i | 0.234927 | + | 1.65943i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.8769 | + | 11.8147i | 1.22987 | + | 0.635164i | ||||
\(347\) | 1.73769i | 0.0932843i | 0.998912 | + | 0.0466421i | \(0.0148520\pi\) | ||||
−0.998912 | + | 0.0466421i | \(0.985148\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 16.8981i | − | 0.904536i | −0.891882 | − | 0.452268i | \(-0.850615\pi\) | ||
0.891882 | − | 0.452268i | \(-0.149385\pi\) | |||||||
\(350\) | −2.18810 | + | 4.23682i | −0.116959 | + | 0.226467i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −25.5656 | − | 27.0067i | −1.36265 | − | 1.43946i | ||||
\(353\) | 12.2774i | 0.653459i | 0.945118 | + | 0.326730i | \(0.105947\pi\) | ||||
−0.945118 | + | 0.326730i | \(0.894053\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.44249 | 0.235783 | ||||||||
\(356\) | 6.62684 | − | 4.70456i | 0.351222 | − | 0.249341i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.21413 | + | 10.0961i | −0.275575 | + | 0.533596i | ||||
\(359\) | 3.77380 | 0.199173 | 0.0995867 | − | 0.995029i | \(-0.468248\pi\) | ||||
0.0995867 | + | 0.995029i | \(0.468248\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.6589 | −0.771522 | ||||||||
\(362\) | 12.0363 | − | 23.3060i | 0.632616 | − | 1.22493i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.69121 | + | 6.60803i | 0.245886 | + | 0.346355i | ||||
\(365\) | 3.53311 | 0.184931 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.6703i | 1.49658i | 0.663372 | + | 0.748289i | \(0.269125\pi\) | ||||
−0.663372 | + | 0.748289i | \(0.730875\pi\) | |||||||
\(368\) | −9.04634 | + | 25.8958i | −0.471573 | + | 1.34991i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.44738 | + | 4.73886i | −0.127233 | + | 0.246361i | ||||
\(371\) | − | 2.87278i | − | 0.149147i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 27.3540i | − | 1.41634i | −0.706043 | − | 0.708169i | \(-0.749522\pi\) | ||
0.706043 | − | 0.708169i | \(-0.250478\pi\) | |||||||
\(374\) | 50.3714 | + | 26.0142i | 2.60464 | + | 1.34516i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.82302 | + | 19.9407i | 0.145586 | + | 1.02836i | ||||
\(377\) | − | 26.4716i | − | 1.36336i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.6336 | −0.957146 | −0.478573 | − | 0.878048i | \(-0.658846\pi\) | ||||
−0.478573 | + | 0.878048i | \(0.658846\pi\) | |||||||
\(380\) | −3.07800 | − | 4.33567i | −0.157898 | − | 0.222415i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 28.7065 | + | 14.8255i | 1.46875 | + | 0.758537i | ||||
\(383\) | −27.8368 | −1.42240 | −0.711198 | − | 0.702992i | \(-0.751847\pi\) | ||||
−0.711198 | + | 0.702992i | \(0.751847\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.38843 | 0.427514 | ||||||||
\(386\) | 4.38921 | + | 2.26680i | 0.223405 | + | 0.115377i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.67810 | − | 7.99817i | −0.288262 | − | 0.406046i | ||||
\(389\) | 7.10860 | 0.360420 | 0.180210 | − | 0.983628i | \(-0.442322\pi\) | ||||
0.180210 | + | 0.983628i | \(0.442322\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 41.8168i | − | 2.11477i | ||||||
\(392\) | −0.396469 | − | 2.80050i | −0.0200247 | − | 0.141447i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −27.5724 | − | 14.2397i | −1.38908 | − | 0.717387i | ||||
\(395\) | 1.08366i | 0.0545247i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 32.8312i | − | 1.64775i | −0.566771 | − | 0.823875i | \(-0.691808\pi\) | ||
0.566771 | − | 0.823875i | \(-0.308192\pi\) | |||||||
\(398\) | 14.9820 | − | 29.0097i | 0.750981 | − | 1.45412i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.44801 | − | 12.7327i | 0.222401 | − | 0.636637i | ||||
\(401\) | 29.0585i | 1.45111i | 0.688164 | + | 0.725555i | \(0.258417\pi\) | ||||
−0.688164 | + | 0.725555i | \(0.741583\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.2436 | 0.659709 | ||||||||
\(404\) | 19.1186 | + | 26.9304i | 0.951185 | + | 1.33984i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.23953 | + | 8.20900i | −0.210404 | + | 0.407406i | ||||
\(407\) | −19.4303 | −0.963122 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.68368 | −0.281040 | −0.140520 | − | 0.990078i | \(-0.544877\pi\) | ||||
−0.140520 | + | 0.990078i | \(0.544877\pi\) | |||||||
\(410\) | −2.77710 | + | 5.37729i | −0.137151 | + | 0.265565i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.4656 | + | 12.3993i | −0.860470 | + | 0.610869i | ||||
\(413\) | −7.75213 | −0.381458 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 20.1695i | − | 0.990083i | ||||||
\(416\) | −15.7576 | − | 16.6459i | −0.772581 | − | 0.816131i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.88855 | − | 17.2109i | 0.434753 | − | 0.841812i | ||||
\(419\) | 2.00749i | 0.0980722i | 0.998797 | + | 0.0490361i | \(0.0156149\pi\) | ||||
−0.998797 | + | 0.0490361i | \(0.984385\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.4735i | 0.802871i | 0.915887 | + | 0.401435i | \(0.131489\pi\) | ||||
−0.915887 | + | 0.401435i | \(0.868511\pi\) | |||||||
\(422\) | −2.15403 | − | 1.11244i | −0.104856 | − | 0.0541530i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.13897 | + | 8.04524i | 0.0553133 | + | 0.390711i | ||||
\(425\) | 20.5610i | 0.997354i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0251 | 0.581936 | ||||||||
\(428\) | 15.3623 | − | 10.9061i | 0.742563 | − | 0.527164i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 17.6209 | + | 9.10031i | 0.849757 | + | 0.438856i | ||||
\(431\) | 17.2399 | 0.830417 | 0.415209 | − | 0.909726i | \(-0.363709\pi\) | ||||
0.415209 | + | 0.909726i | \(0.363709\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.1465 | −1.83321 | −0.916603 | − | 0.399799i | \(-0.869080\pi\) | ||||
−0.916603 | + | 0.399799i | \(0.869080\pi\) | |||||||
\(434\) | −4.10691 | − | 2.12101i | −0.197138 | − | 0.101812i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.9711 | + | 9.20850i | −0.621202 | + | 0.441007i | ||||
\(437\) | −14.2880 | −0.683487 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 7.30831i | − | 0.348806i | −0.984674 | − | 0.174403i | \(-0.944200\pi\) | ||
0.984674 | − | 0.174403i | \(-0.0557996\pi\) | |||||||
\(440\) | −23.4918 | + | 3.32575i | −1.11993 | + | 0.158549i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 31.0469 | + | 16.0342i | 1.47675 | + | 0.762667i | ||||
\(443\) | 21.7787i | 1.03474i | 0.855763 | + | 0.517368i | \(0.173088\pi\) | ||||
−0.855763 | + | 0.517368i | \(0.826912\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 5.18501i | − | 0.245793i | ||||||
\(446\) | 0.354249 | − | 0.685931i | 0.0167742 | − | 0.0324798i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.22063 | + | 7.68562i | 0.104915 | + | 0.363112i | ||||
\(449\) | − | 1.30200i | − | 0.0614451i | −0.999528 | − | 0.0307225i | \(-0.990219\pi\) | ||
0.999528 | − | 0.0307225i | \(-0.00978083\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.0479 | −1.03820 | ||||||||
\(452\) | −2.55058 | + | 1.81072i | −0.119969 | + | 0.0851692i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.04163 | + | 2.01692i | −0.0488863 | + | 0.0946585i | ||||
\(455\) | 5.17030 | 0.242387 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.17657 | 0.148594 | 0.0742968 | − | 0.997236i | \(-0.476329\pi\) | ||||
0.0742968 | + | 0.997236i | \(0.476329\pi\) | |||||||
\(458\) | 0.904692 | − | 1.75176i | 0.0422735 | − | 0.0818542i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.1308 | + | 14.2702i | 0.472349 | + | 0.665351i | ||||
\(461\) | −8.56764 | −0.399035 | −0.199517 | − | 0.979894i | \(-0.563937\pi\) | ||||
−0.199517 | + | 0.979894i | \(0.563937\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.9440i | 0.926877i | 0.886129 | + | 0.463438i | \(0.153385\pi\) | ||||
−0.886129 | + | 0.463438i | \(0.846615\pi\) | |||||||
\(464\) | 8.61819 | − | 24.6702i | 0.400090 | − | 1.14528i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.49777 | − | 12.5816i | 0.301004 | − | 0.582833i | ||||
\(467\) | 11.5091i | 0.532579i | 0.963893 | + | 0.266290i | \(0.0857978\pi\) | ||||
−0.963893 | + | 0.266290i | \(0.914202\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.01966i | 0.139435i | ||||||||
\(470\) | 11.4164 | + | 5.89601i | 0.526601 | + | 0.271963i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 21.7099 | − | 3.07348i | 0.999278 | − | 0.141468i | ||||
\(473\) | 72.2493i | 3.32203i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.02528 | 0.322342 | ||||||||
\(476\) | −7.05990 | − | 9.94457i | −0.323590 | − | 0.455808i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.0888 | − | 6.24324i | −0.552928 | − | 0.285559i | ||||
\(479\) | 5.91391 | 0.270213 | 0.135107 | − | 0.990831i | \(-0.456862\pi\) | ||||
0.135107 | + | 0.990831i | \(0.456862\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.9760 | −0.546061 | ||||||||
\(482\) | 17.5649 | + | 9.07138i | 0.800059 | + | 0.413190i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −37.3003 | − | 52.5411i | −1.69547 | − | 2.38823i | ||||
\(485\) | −6.25798 | −0.284160 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.4470i | 0.926541i | 0.886217 | + | 0.463271i | \(0.153324\pi\) | ||||
−0.886217 | + | 0.463271i | \(0.846676\pi\) | |||||||
\(488\) | −33.6764 | + | 4.76759i | −1.52446 | + | 0.215819i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.60334 | − | 0.828043i | −0.0724315 | − | 0.0374072i | ||||
\(491\) | − | 24.0391i | − | 1.08487i | −0.840098 | − | 0.542434i | \(-0.817503\pi\) | ||
0.840098 | − | 0.542434i | \(-0.182497\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.8377i | 1.79420i | ||||||||
\(494\) | 5.47855 | − | 10.6081i | 0.246492 | − | 0.477282i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.3423 | + | 4.31162i | 0.554186 | + | 0.193598i | ||||
\(497\) | − | 3.48158i | − | 0.156170i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.1375 | 1.30438 | 0.652188 | − | 0.758057i | \(-0.273851\pi\) | ||||
0.652188 | + | 0.758057i | \(0.273851\pi\) | |||||||
\(500\) | −12.3677 | − | 17.4212i | −0.553102 | − | 0.779099i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.54135 | + | 8.79342i | −0.202690 | + | 0.392469i | ||||
\(503\) | 9.70604 | 0.432771 | 0.216386 | − | 0.976308i | \(-0.430573\pi\) | ||||
0.216386 | + | 0.976308i | \(0.430573\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.0711 | 0.937651 | ||||||||
\(506\) | −29.2553 | + | 56.6470i | −1.30056 | + | 2.51827i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 32.2732 | − | 22.9115i | 1.43189 | − | 1.01654i | ||||
\(509\) | 15.5042 | 0.687213 | 0.343606 | − | 0.939114i | \(-0.388351\pi\) | ||||
0.343606 | + | 0.939114i | \(0.388351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 2.76889i | − | 0.122489i | ||||||
\(512\) | −9.26598 | − | 20.6432i | −0.409502 | − | 0.912309i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.85108 | − | 5.52054i | 0.125756 | − | 0.243501i | ||||
\(515\) | 13.6656i | 0.602177i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 46.8096i | 2.05869i | ||||||||
\(518\) | 3.71384 | + | 1.91801i | 0.163177 | + | 0.0842725i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −14.4794 | + | 2.04986i | −0.634965 | + | 0.0898924i | ||||
\(521\) | − | 6.22420i | − | 0.272687i | −0.990662 | − | 0.136344i | \(-0.956465\pi\) | ||
0.990662 | − | 0.136344i | \(-0.0435351\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.3752 | 1.45939 | 0.729697 | − | 0.683770i | \(-0.239661\pi\) | ||||
0.729697 | + | 0.683770i | \(0.239661\pi\) | |||||||
\(524\) | 22.3271 | − | 15.8506i | 0.975363 | − | 0.692435i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.7320 | + | 5.54253i | 0.467937 | + | 0.241666i | ||||
\(527\) | −19.9305 | −0.868188 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.0267 | 1.04464 | ||||||||
\(530\) | 4.60605 | + | 2.37879i | 0.200074 | + | 0.103328i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.39786 | + | 2.41223i | −0.147316 | + | 0.104583i | ||||
\(533\) | −13.5895 | −0.588626 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 12.0198i | − | 0.519663i | ||||||
\(536\) | −1.19720 | − | 8.45656i | −0.0517112 | − | 0.365268i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18.5200 | − | 9.56462i | −0.798452 | − | 0.412360i | ||||
\(539\) | − | 6.57401i | − | 0.283162i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 4.04207i | − | 0.173782i | −0.996218 | − | 0.0868911i | \(-0.972307\pi\) | ||
0.996218 | − | 0.0868911i | \(-0.0276932\pi\) | |||||||
\(542\) | 2.73654 | − | 5.29876i | 0.117544 | − | 0.227601i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 23.7140 | + | 25.0507i | 1.01673 | + | 1.07404i | ||||
\(545\) | 10.1489i | 0.434732i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.7497 | −0.844436 | −0.422218 | − | 0.906494i | \(-0.638748\pi\) | ||||
−0.422218 | + | 0.906494i | \(0.638748\pi\) | |||||||
\(548\) | 32.6326 | − | 23.1667i | 1.39400 | − | 0.989633i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 14.3846 | − | 27.8529i | 0.613361 | − | 1.18765i | ||||
\(551\) | 13.6117 | 0.579880 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.849261 | 0.0361143 | ||||||||
\(554\) | 1.77222 | − | 3.43155i | 0.0752944 | − | 0.145793i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.7709 | − | 17.9890i | −0.541605 | − | 0.762905i | ||||
\(557\) | −11.2192 | −0.475373 | −0.237687 | − | 0.971342i | \(-0.576389\pi\) | ||||
−0.237687 | + | 0.971342i | \(0.576389\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44.5316i | 1.88349i | ||||||||
\(560\) | 4.81845 | + | 1.68326i | 0.203617 | + | 0.0711308i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.05321 | − | 11.7208i | 0.255339 | − | 0.494413i | ||||
\(563\) | − | 8.66666i | − | 0.365256i | −0.983182 | − | 0.182628i | \(-0.941540\pi\) | ||
0.983182 | − | 0.182628i | \(-0.0584604\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.99564i | 0.0839573i | ||||||||
\(566\) | 25.4266 | + | 13.1316i | 1.06876 | + | 0.551961i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.38034 | + | 9.75017i | 0.0579177 | + | 0.409108i | ||||
\(569\) | 27.0778i | 1.13516i | 0.823317 | + | 0.567581i | \(0.192121\pi\) | ||||
−0.823317 | + | 0.567581i | \(0.807879\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.5104 | 0.816485 | 0.408243 | − | 0.912873i | \(-0.366142\pi\) | ||||
0.408243 | + | 0.912873i | \(0.366142\pi\) | |||||||
\(572\) | −30.8400 | − | 43.4412i | −1.28949 | − | 1.81637i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.21418 | + | 2.17641i | 0.175896 | + | 0.0908415i | ||||
\(575\) | −23.1226 | −0.964280 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.4544 | −0.976421 | −0.488211 | − | 0.872726i | \(-0.662350\pi\) | ||||
−0.488211 | + | 0.872726i | \(0.662350\pi\) | |||||||
\(578\) | −25.3621 | − | 13.0982i | −1.05492 | − | 0.544814i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.65129 | − | 13.5948i | −0.400748 | − | 0.564493i | ||||
\(581\) | −15.8068 | −0.655778 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.8857i | 0.782165i | ||||||||
\(584\) | 1.09778 | + | 7.75430i | 0.0454265 | + | 0.320875i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.326666 | − | 0.168706i | −0.0134944 | − | 0.00696919i | ||||
\(587\) | − | 8.29331i | − | 0.342302i | −0.985245 | − | 0.171151i | \(-0.945251\pi\) | ||
0.985245 | − | 0.171151i | \(-0.0547485\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.80987i | 0.280596i | ||||||||
\(590\) | 6.41910 | − | 12.4293i | 0.264270 | − | 0.511706i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.1610 | − | 3.89897i | −0.458716 | − | 0.160246i | ||||
\(593\) | 5.99359i | 0.246127i | 0.992399 | + | 0.123064i | \(0.0392719\pi\) | ||||
−0.992399 | + | 0.123064i | \(0.960728\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.78089 | −0.318986 | ||||||||
\(596\) | −0.453689 | − | 0.639066i | −0.0185838 | − | 0.0261772i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18.0318 | + | 34.9150i | −0.737376 | + | 1.42778i | ||||
\(599\) | 41.0912 | 1.67894 | 0.839470 | − | 0.543405i | \(-0.182865\pi\) | ||||
0.839470 | + | 0.543405i | \(0.182865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.9084 | −0.608128 | −0.304064 | − | 0.952652i | \(-0.598344\pi\) | ||||
−0.304064 | + | 0.952652i | \(0.598344\pi\) | |||||||
\(602\) | 7.13191 | − | 13.8095i | 0.290675 | − | 0.562833i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16.8468 | + | 11.9600i | −0.685486 | + | 0.486644i | ||||
\(605\) | −41.1096 | −1.67134 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.1672i | 0.859152i | 0.903031 | + | 0.429576i | \(0.141337\pi\) | ||||
−0.903031 | + | 0.429576i | \(0.858663\pi\) | |||||||
\(608\) | 8.55934 | − | 8.10259i | 0.347127 | − | 0.328604i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.95732 | + | 19.2803i | −0.403160 | + | 0.780638i | ||||
\(611\) | 28.8516i | 1.16721i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.0293i | 0.849367i | 0.905342 | + | 0.424683i | \(0.139615\pi\) | ||||
−0.905342 | + | 0.424683i | \(0.860385\pi\) | |||||||
\(614\) | 32.4506 | + | 16.7591i | 1.30960 | + | 0.676342i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.60639 | + | 18.4105i | 0.105014 | + | 0.741781i | ||||
\(617\) | − | 29.2848i | − | 1.17896i | −0.807783 | − | 0.589480i | \(-0.799333\pi\) | ||
0.807783 | − | 0.589480i | \(-0.200667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.6407 | 1.75407 | 0.877034 | − | 0.480428i | \(-0.159519\pi\) | ||||
0.877034 | + | 0.480428i | \(0.159519\pi\) | |||||||
\(620\) | 6.80139 | − | 4.82848i | 0.273150 | − | 0.193916i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.9111 | − | 12.8653i | −0.998846 | − | 0.515853i | ||||
\(623\) | −4.06349 | −0.162800 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.22833 | 0.129133 | ||||||||
\(626\) | 12.8419 | + | 6.63219i | 0.513266 | + | 0.265075i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.9517 | + | 11.3245i | −0.636543 | + | 0.451898i | ||||
\(629\) | 18.0230 | 0.718624 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 33.7501i | − | 1.34357i | −0.740747 | − | 0.671784i | \(-0.765528\pi\) | ||
0.740747 | − | 0.671784i | \(-0.234472\pi\) | |||||||
\(632\) | −2.37836 | + | 0.336706i | −0.0946060 | + | 0.0133934i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.03588 | − | 2.08433i | −0.160285 | − | 0.0827792i | ||||
\(635\) | − | 25.2514i | − | 1.00207i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.05196i | − | 0.160544i | ||||||
\(638\) | 27.8707 | − | 53.9660i | 1.10341 | − | 2.13653i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −14.1614 | − | 2.80361i | −0.559780 | − | 0.110822i | ||||
\(641\) | − | 13.1478i | − | 0.519306i | −0.965702 | − | 0.259653i | \(-0.916392\pi\) | ||
0.965702 | − | 0.259653i | \(-0.0836083\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.7796 | −1.05608 | −0.528042 | − | 0.849218i | \(-0.677074\pi\) | ||||
−0.528042 | + | 0.849218i | \(0.677074\pi\) | |||||||
\(644\) | 11.1835 | − | 7.93947i | 0.440693 | − | 0.312859i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.24479 | + | 15.9644i | −0.324387 | + | 0.628110i | ||||
\(647\) | 13.7850 | 0.541944 | 0.270972 | − | 0.962587i | \(-0.412655\pi\) | ||||
0.270972 | + | 0.962587i | \(0.412655\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 50.9626 | 2.00046 | ||||||||
\(650\) | 8.86609 | − | 17.1674i | 0.347757 | − | 0.673361i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.29120 | + | 1.81878i | 0.0505672 | + | 0.0712289i | ||||
\(653\) | 34.5245 | 1.35105 | 0.675524 | − | 0.737338i | \(-0.263917\pi\) | ||||
0.675524 | + | 0.737338i | \(0.263917\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 17.4693i | − | 0.682582i | ||||||
\(656\) | −12.6647 | − | 4.42424i | −0.494473 | − | 0.172738i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.62070 | − | 8.94705i | 0.180134 | − | 0.348792i | ||||
\(659\) | 31.8035i | 1.23889i | 0.785040 | + | 0.619445i | \(0.212642\pi\) | ||||
−0.785040 | + | 0.619445i | \(0.787358\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.7156i | 0.572370i | 0.958174 | + | 0.286185i | \(0.0923873\pi\) | ||||
−0.958174 | + | 0.286185i | \(0.907613\pi\) | |||||||
\(662\) | −37.4775 | − | 19.3552i | −1.45660 | − | 0.752261i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 44.2671 | − | 6.26692i | 1.71790 | − | 0.243204i | ||||
\(665\) | 2.65858i | 0.103095i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −44.8010 | −1.73470 | ||||||||
\(668\) | 19.4473 | + | 27.3935i | 0.752439 | + | 1.05989i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.84154 | − | 2.50041i | −0.187045 | − | 0.0965991i | ||||
\(671\) | −79.0532 | −3.05182 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.1705 | 0.546233 | 0.273116 | − | 0.961981i | \(-0.411946\pi\) | ||||
0.273116 | + | 0.961981i | \(0.411946\pi\) | |||||||
\(674\) | −33.8747 | − | 17.4946i | −1.30481 | − | 0.673866i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.95766 | − | 5.57475i | −0.152218 | − | 0.214414i | ||||
\(677\) | −33.9994 | −1.30670 | −0.653351 | − | 0.757055i | \(-0.726638\pi\) | ||||
−0.653351 | + | 0.757055i | \(0.726638\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.90438i | 0.188213i | ||||||||
\(680\) | 21.7904 | − | 3.08488i | 0.835624 | − | 0.118300i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 26.9988 | + | 13.9435i | 1.03384 | + | 0.533925i | ||||
\(683\) | 24.7265i | 0.946132i | 0.881027 | + | 0.473066i | \(0.156853\pi\) | ||||
−0.881027 | + | 0.473066i | \(0.843147\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 25.5326i | − | 0.975551i | ||||||
\(686\) | −0.648937 | + | 1.25654i | −0.0247765 | + | 0.0479747i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14.4979 | + | 41.5011i | −0.552726 | + | 1.58222i | ||||
\(689\) | 11.6404i | 0.443464i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.2490 | −0.732267 | −0.366134 | − | 0.930562i | \(-0.619319\pi\) | ||||
−0.366134 | + | 0.930562i | \(0.619319\pi\) | |||||||
\(692\) | 21.0786 | + | 29.6913i | 0.801288 | + | 1.12869i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.12765 | + | 2.18347i | −0.0428051 | + | 0.0828835i | ||||
\(695\) | −14.0751 | −0.533899 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.4511 | 0.774641 | ||||||||
\(698\) | 10.9658 | − | 21.2331i | 0.415062 | − | 0.803685i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.49885 | + | 3.90377i | −0.207837 | + | 0.147549i | ||||
\(701\) | −13.4914 | −0.509563 | −0.254781 | − | 0.966999i | \(-0.582004\pi\) | ||||
−0.254781 | + | 0.966999i | \(0.582004\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6.15810i | − | 0.232257i | ||||||
\(704\) | −14.5984 | − | 50.5253i | −0.550198 | − | 1.90425i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.96724 | + | 15.4270i | −0.299851 | + | 0.580601i | ||||
\(707\) | − | 16.5134i | − | 0.621050i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.1839i | 0.457575i | 0.973476 | + | 0.228788i | \(0.0734761\pi\) | ||||
−0.973476 | + | 0.228788i | \(0.926524\pi\) | |||||||
\(710\) | 5.58215 | + | 2.88290i | 0.209494 | + | 0.108193i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.3798 | − | 1.61105i | 0.426477 | − | 0.0603766i | ||||
\(713\) | − | 22.4136i | − | 0.839397i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −33.9896 | −1.27114 | ||||||||
\(716\) | −13.1035 | + | 9.30248i | −0.489700 | + | 0.347650i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.74191 | + | 2.44896i | 0.176967 | + | 0.0913942i | ||||
\(719\) | 2.14139 | 0.0798603 | 0.0399301 | − | 0.999202i | \(-0.487286\pi\) | ||||
0.0399301 | + | 0.999202i | \(0.487286\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.7097 | 0.398850 | ||||||||
\(722\) | −18.4195 | − | 9.51271i | −0.685501 | − | 0.354026i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 30.2482 | − | 21.4739i | 1.12416 | − | 0.798073i | ||||
\(725\) | 22.0283 | 0.818109 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.8865i | 1.36804i | 0.729462 | + | 0.684022i | \(0.239771\pi\) | ||||
−0.729462 | + | 0.684022i | \(0.760229\pi\) | |||||||
\(728\) | 1.60648 | + | 11.3475i | 0.0595400 | + | 0.420567i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.43948 | + | 2.29276i | 0.164312 | + | 0.0848590i | ||||
\(731\) | − | 67.0166i | − | 2.47870i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 28.2007i | − | 1.04162i | −0.853674 | − | 0.520808i | \(-0.825631\pi\) | ||
0.853674 | − | 0.520808i | \(-0.174369\pi\) | |||||||
\(734\) | −18.6052 | + | 36.0253i | −0.686731 | + | 1.32972i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −28.1718 | + | 26.6684i | −1.03842 | + | 0.983012i | ||||
\(737\) | − | 19.8513i | − | 0.731230i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.9006 | −0.511341 | −0.255670 | − | 0.966764i | \(-0.582296\pi\) | ||||
−0.255670 | + | 0.966764i | \(0.582296\pi\) | |||||||
\(740\) | −6.15044 | + | 4.36635i | −0.226095 | + | 0.160510i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.86425 | − | 3.60975i | 0.0684389 | − | 0.132518i | ||||
\(743\) | 5.81892 | 0.213476 | 0.106738 | − | 0.994287i | \(-0.465959\pi\) | ||||
0.106738 | + | 0.994287i | \(0.465959\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.500022 | −0.0183194 | ||||||||
\(746\) | 17.7510 | − | 34.3713i | 0.649911 | − | 1.25842i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 46.4118 | + | 65.3756i | 1.69698 | + | 2.39037i | ||||
\(749\) | −9.41994 | −0.344197 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.7860i | 1.34234i | 0.741304 | + | 0.671170i | \(0.234208\pi\) | ||||
−0.741304 | + | 0.671170i | \(0.765792\pi\) | |||||||
\(752\) | −9.39304 | + | 26.8882i | −0.342529 | + | 0.980512i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 17.1784 | − | 33.2625i | 0.625600 | − | 1.21135i | ||||
\(755\) | 13.1814i | 0.479719i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.6555i | 0.605356i | 0.953093 | + | 0.302678i | \(0.0978806\pi\) | ||||
−0.953093 | + | 0.302678i | \(0.902119\pi\) | |||||||
\(758\) | −23.4138 | − | 12.0921i | −0.850429 | − | 0.439203i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.05404 | − | 7.44535i | −0.0382342 | − | 0.270071i | ||||
\(761\) | 38.2510i | 1.38660i | 0.720651 | + | 0.693298i | \(0.243843\pi\) | ||||
−0.720651 | + | 0.693298i | \(0.756157\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.95370 | 0.287943 | ||||||||
\(764\) | 26.4500 | + | 37.2575i | 0.956928 | + | 1.34793i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −34.9780 | − | 18.0643i | −1.26380 | − | 0.652691i | ||||
\(767\) | 31.4113 | 1.13420 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.1021 | −1.44612 | −0.723059 | − | 0.690787i | \(-0.757264\pi\) | ||||
−0.723059 | + | 0.690787i | \(0.757264\pi\) | |||||||
\(770\) | 10.5404 | + | 5.44356i | 0.379848 | + | 0.196172i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.04419 | + | 5.69664i | 0.145554 | + | 0.205027i | ||||
\(773\) | −1.84516 | −0.0663659 | −0.0331830 | − | 0.999449i | \(-0.510564\pi\) | ||||
−0.0331830 | + | 0.999449i | \(0.510564\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.0206i | 0.395871i | ||||||||
\(776\) | −1.94443 | − | 13.7347i | −0.0698011 | − | 0.493047i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.93221 | + | 4.61303i | 0.320235 | + | 0.165385i | ||||
\(779\) | − | 6.98774i | − | 0.250362i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.8879i | 0.818994i | ||||||||
\(782\) | 27.1365 | − | 52.5443i | 0.970398 | − | 1.87898i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.31917 | − | 3.77621i | 0.0471132 | − | 0.134865i | ||||
\(785\) | 12.4810i | 0.445468i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.4160 | −1.44068 | −0.720338 | − | 0.693623i | \(-0.756013\pi\) | ||||
−0.720338 | + | 0.693623i | \(0.756013\pi\) | |||||||
\(788\) | −25.4050 | − | 35.7855i | −0.905015 | − | 1.27480i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.703225 | + | 1.36165i | −0.0250196 | + | 0.0484455i | ||||
\(791\) | 1.56398 | 0.0556088 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48.7253 | −1.73029 | ||||||||
\(794\) | 21.3054 | − | 41.2536i | 0.756099 | − | 1.46403i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 37.6509 | − | 26.7293i | 1.33450 | − | 0.947396i | ||||
\(797\) | −47.9867 | −1.69978 | −0.849889 | − | 0.526962i | \(-0.823331\pi\) | ||||
−0.849889 | + | 0.526962i | \(0.823331\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 43.4194i | − | 1.53607i | ||||||
\(800\) | 13.8518 | − | 13.1127i | 0.489736 | − | 0.463602i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.8571 | + | 36.5130i | −0.665867 | + | 1.28932i | ||||
\(803\) | 18.2027i | 0.642360i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 8.75029i | − | 0.308407i | ||||||
\(806\) | 16.6410 | + | 8.59423i | 0.586155 | + | 0.302719i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.54705 | + | 46.2458i | 0.230324 | + | 1.62692i | ||||
\(809\) | − | 14.1754i | − | 0.498379i | −0.968455 | − | 0.249190i | \(-0.919836\pi\) | ||
0.968455 | − | 0.249190i | \(-0.0801643\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.80289 | −0.203767 | −0.101884 | − | 0.994796i | \(-0.532487\pi\) | ||||
−0.101884 | + | 0.994796i | \(0.532487\pi\) | |||||||
\(812\) | −10.6542 | + | 7.56371i | −0.373890 | + | 0.265434i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −24.4148 | − | 12.6090i | −0.855738 | − | 0.441945i | ||||
\(815\) | 1.42306 | 0.0498477 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.8982 | −0.801108 | ||||||||
\(818\) | −7.14174 | − | 3.68834i | −0.249705 | − | 0.128960i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.97904 | + | 4.95460i | −0.243719 | + | 0.173022i | ||||
\(821\) | −8.67601 | −0.302795 | −0.151397 | − | 0.988473i | \(-0.548377\pi\) | ||||
−0.151397 | + | 0.988473i | \(0.548377\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 0.199240i | − | 0.00694506i | −0.999994 | − | 0.00347253i | \(-0.998895\pi\) | ||
0.999994 | − | 0.00347253i | \(-0.00110534\pi\) | |||||||
\(824\) | −29.9925 | + | 4.24607i | −1.04484 | + | 0.147919i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.74083 | − | 5.03064i | −0.338927 | − | 0.175038i | ||||
\(827\) | 42.2411i | 1.46887i | 0.678681 | + | 0.734433i | \(0.262552\pi\) | ||||
−0.678681 | + | 0.734433i | \(0.737448\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.9282i | 0.379554i | 0.981827 | + | 0.189777i | \(0.0607765\pi\) | ||||
−0.981827 | + | 0.189777i | \(0.939224\pi\) | |||||||
\(830\) | 13.0887 | − | 25.3437i | 0.454317 | − | 0.879694i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.99788 | − | 31.1418i | −0.311945 | − | 1.07965i | ||||
\(833\) | 6.09788i | 0.211279i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.4334 | 0.741733 | ||||||||
\(836\) | 22.3376 | − | 15.8580i | 0.772561 | − | 0.548460i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.30273 | + | 2.52248i | −0.0450021 | + | 0.0871376i | ||||
\(839\) | −41.6038 | −1.43632 | −0.718161 | − | 0.695877i | \(-0.755016\pi\) | ||||
−0.718161 | + | 0.695877i | \(0.755016\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.6806 | 0.471745 | ||||||||
\(842\) | −10.6903 | + | 20.6996i | −0.368411 | + | 0.713354i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.98470 | − | 2.79565i | −0.0683163 | − | 0.0962303i | ||||
\(845\) | −4.36184 | −0.150052 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.2175i | 1.10701i | ||||||||
\(848\) | −3.78969 | + | 10.8482i | −0.130139 | + | 0.372530i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.3428 | + | 25.8356i | −0.457653 | + | 0.886154i | ||||
\(851\) | 20.2684i | 0.694793i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 10.8964i | − | 0.373084i | −0.982447 | − | 0.186542i | \(-0.940272\pi\) | ||
0.982447 | − | 0.186542i | \(-0.0597281\pi\) | |||||||
\(854\) | 15.1100 | + | 7.80354i | 0.517053 | + | 0.267032i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 26.3806 | − | 3.73471i | 0.901669 | − | 0.127650i | ||||
\(857\) | − | 11.9467i | − | 0.408093i | −0.978961 | − | 0.204046i | \(-0.934591\pi\) | ||
0.978961 | − | 0.204046i | \(-0.0654093\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.8684 | −0.541423 | −0.270711 | − | 0.962661i | \(-0.587259\pi\) | ||||
−0.270711 | + | 0.962661i | \(0.587259\pi\) | |||||||
\(860\) | 16.2358 | + | 22.8697i | 0.553636 | + | 0.779851i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.6626 | + | 11.1876i | 0.737830 | + | 0.381051i | ||||
\(863\) | −36.7712 | −1.25171 | −0.625853 | − | 0.779941i | \(-0.715249\pi\) | ||||
−0.625853 | + | 0.779941i | \(0.715249\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.2312 | 0.789886 | ||||||||
\(866\) | −47.9325 | − | 24.7547i | −1.62881 | − | 0.841198i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.78407 | − | 5.33024i | −0.128440 | − | 0.180920i | ||||
\(869\) | −5.58305 | −0.189392 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 12.2355i | − | 0.414585i | ||||||
\(872\) | −22.2744 | + | 3.15340i | −0.754305 | + | 0.106787i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17.9534 | − | 9.27199i | −0.607281 | − | 0.313630i | ||||
\(875\) | 10.6824i | 0.361133i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 48.2439i | − | 1.62908i | −0.580106 | − | 0.814541i | \(-0.696989\pi\) | ||
0.580106 | − | 0.814541i | \(-0.303011\pi\) | |||||||
\(878\) | 4.74263 | − | 9.18315i | 0.160056 | − | 0.309916i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −31.6765 | − | 11.0658i | −1.06781 | − | 0.373027i | ||||
\(881\) | 21.4780i | 0.723611i | 0.932254 | + | 0.361805i | \(0.117840\pi\) | ||||
−0.932254 | + | 0.361805i | \(0.882160\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.78771 | −0.0938139 | −0.0469070 | − | 0.998899i | \(-0.514936\pi\) | ||||
−0.0469070 | + | 0.998899i | \(0.514936\pi\) | |||||||
\(884\) | 28.6064 | + | 40.2950i | 0.962138 | + | 1.35527i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.1330 | + | 27.3657i | −0.474807 | + | 0.919368i | ||||
\(887\) | 37.3399 | 1.25375 | 0.626875 | − | 0.779120i | \(-0.284334\pi\) | ||||
0.626875 | + | 0.779120i | \(0.284334\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.7895 | −0.663719 | ||||||||
\(890\) | 3.36474 | − | 6.51515i | 0.112786 | − | 0.218388i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.890252 | − | 0.632012i | 0.0298078 | − | 0.0211613i | ||||
\(893\) | −14.8356 | −0.496453 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.2525i | 0.342703i | ||||||||
\(896\) | −2.19719 | + | 11.0983i | −0.0734029 | + | 0.370768i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.844914 | − | 1.63601i | 0.0281951 | − | 0.0545943i | ||||
\(899\) | 21.3528i | 0.712156i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 17.5179i | − | 0.583605i | ||||||
\(902\) | −27.7040 | − | 14.3077i | −0.922443 | − | 0.476395i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.37994 | + | 0.620071i | −0.145675 | + | 0.0206233i | ||||
\(905\) | − | 23.6670i | − | 0.786717i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.2433 | 1.26985 | 0.634924 | − | 0.772574i | \(-0.281031\pi\) | ||||
0.634924 | + | 0.772574i | \(0.281031\pi\) | |||||||
\(908\) | −2.61770 | + | 1.85837i | −0.0868714 | + | 0.0616722i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.49666 | + | 3.35519i | 0.215362 | + | 0.111224i | ||||
\(911\) | −2.40878 | −0.0798063 | −0.0399032 | − | 0.999204i | \(-0.512705\pi\) | ||||
−0.0399032 | + | 0.999204i | \(0.512705\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 103.914 | 3.43906 | ||||||||
\(914\) | 3.99147 | + | 2.06139i | 0.132026 | + | 0.0681848i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.27356 | − | 1.61406i | 0.0751204 | − | 0.0533299i | ||||
\(917\) | −13.6907 | −0.452106 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.5153i | 0.709723i | 0.934919 | + | 0.354862i | \(0.115472\pi\) | ||||
−0.934919 | + | 0.354862i | \(0.884528\pi\) | |||||||
\(920\) | 3.46922 | + | 24.5052i | 0.114377 | + | 0.807913i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.7655 | − | 5.55985i | −0.354544 | − | 0.183104i | ||||
\(923\) | 14.1072i | 0.464345i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 9.96583i | − | 0.327674i | ||||||
\(926\) | −12.9424 | + | 25.0604i | −0.425314 | + | 0.823535i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 26.8384 | − | 25.4063i | 0.881015 | − | 0.834001i | ||||
\(929\) | − | 21.9659i | − | 0.720677i | −0.932822 | − | 0.360339i | \(-0.882661\pi\) | ||
0.932822 | − | 0.360339i | \(-0.117339\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.08352 | 0.0682848 | ||||||||
\(932\) | 16.3294 | − | 11.5926i | 0.534886 | − | 0.379729i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.46870 | + | 14.4616i | −0.244383 | + | 0.473199i | ||||
\(935\) | 51.1516 | 1.67284 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.9371 | −0.781991 | −0.390995 | − | 0.920393i | \(-0.627869\pi\) | ||||
−0.390995 | + | 0.920393i | \(0.627869\pi\) | |||||||
\(938\) | −1.95957 | + | 3.79431i | −0.0639821 | + | 0.123889i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.5190 | + | 14.8171i | 0.343093 | + | 0.483280i | ||||
\(941\) | 9.56414 | 0.311782 | 0.155891 | − | 0.987774i | \(-0.450175\pi\) | ||||
0.155891 | + | 0.987774i | \(0.450175\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.9991i | 0.748953i | ||||||||
\(944\) | 29.2737 | + | 10.2264i | 0.952778 | + | 0.332841i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −46.8852 | + | 90.7838i | −1.52437 | + | 2.95164i | ||||
\(947\) | 35.0824i | 1.14003i | 0.821636 | + | 0.570013i | \(0.193062\pi\) | ||||
−0.821636 | + | 0.570013i | \(0.806938\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.2194i | 0.364199i | ||||||||
\(950\) | 8.82751 | + | 4.55896i | 0.286402 | + | 0.147912i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.41762 | − | 17.0771i | −0.0783555 | − | 0.553473i | ||||
\(953\) | − | 14.3190i | − | 0.463837i | −0.972735 | − | 0.231919i | \(-0.925500\pi\) | ||
0.972735 | − | 0.231919i | \(-0.0745003\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.1512 | 0.943311 | ||||||||
\(956\) | −11.1385 | − | 15.6897i | −0.360246 | − | 0.507442i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.43103 | + | 3.83775i | 0.240086 | + | 0.123992i | ||||
\(959\) | −20.0099 | −0.646153 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.3173 | 0.655398 | ||||||||
\(962\) | −15.0483 | − | 7.77169i | −0.485177 | − | 0.250569i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.1842 | + | 22.7970i | 0.521257 | + | 0.734242i | ||||
\(965\) | 4.45720 | 0.143482 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 48.7056i | − | 1.56627i | −0.621855 | − | 0.783133i | \(-0.713621\pi\) | ||
0.621855 | − | 0.783133i | \(-0.286379\pi\) | |||||||
\(968\) | −12.7733 | − | 90.2253i | −0.410548 | − | 2.89995i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.86338 | − | 4.06103i | −0.252478 | − | 0.130392i | ||||
\(971\) | − | 2.39723i | − | 0.0769308i | −0.999260 | − | 0.0384654i | \(-0.987753\pi\) | ||
0.999260 | − | 0.0384654i | \(-0.0122469\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.0306i | 0.353626i | ||||||||
\(974\) | −13.2688 | + | 25.6924i | −0.425160 | + | 0.823236i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −45.4094 | − | 15.8632i | −1.45352 | − | 0.507768i | ||||
\(977\) | 6.33844i | 0.202785i | 0.994847 | + | 0.101392i | \(0.0323297\pi\) | ||||
−0.994847 | + | 0.101392i | \(0.967670\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.7134 | 0.853764 | ||||||||
\(980\) | −1.47730 | − | 2.08093i | −0.0471908 | − | 0.0664729i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.5998 | − | 30.2060i | 0.497811 | − | 0.963911i | ||||
\(983\) | 13.6385 | 0.434999 | 0.217500 | − | 0.976060i | \(-0.430210\pi\) | ||||
0.217500 | + | 0.976060i | \(0.430210\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.9995 | −0.892138 | ||||||||
\(986\) | −25.8521 | + | 50.0575i | −0.823300 | + | 1.59415i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.7680 | − | 9.77424i | 0.438018 | − | 0.310960i | ||||
\(989\) | 75.3660 | 2.39650 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.8997i | 0.790964i | 0.918474 | + | 0.395482i | \(0.129422\pi\) | ||||
−0.918474 | + | 0.395482i | \(0.870578\pi\) | |||||||
\(992\) | 12.7106 | + | 13.4271i | 0.403561 | + | 0.426310i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.25932 | − | 4.37473i | 0.0716614 | − | 0.138758i | ||||
\(995\) | − | 29.4591i | − | 0.933915i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.3869i | 0.804011i | 0.915637 | + | 0.402005i | \(0.131687\pi\) | ||||
−0.915637 | + | 0.402005i | \(0.868313\pi\) | |||||||
\(998\) | 36.6124 | + | 18.9084i | 1.15894 | + | 0.598535i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.j.d.323.42 | yes | 48 | |
3.2 | odd | 2 | inner | 1512.2.j.d.323.7 | ✓ | 48 | |
4.3 | odd | 2 | 6048.2.j.d.5615.32 | 48 | |||
8.3 | odd | 2 | inner | 1512.2.j.d.323.8 | yes | 48 | |
8.5 | even | 2 | 6048.2.j.d.5615.18 | 48 | |||
12.11 | even | 2 | 6048.2.j.d.5615.17 | 48 | |||
24.5 | odd | 2 | 6048.2.j.d.5615.31 | 48 | |||
24.11 | even | 2 | inner | 1512.2.j.d.323.41 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.d.323.7 | ✓ | 48 | 3.2 | odd | 2 | inner | |
1512.2.j.d.323.8 | yes | 48 | 8.3 | odd | 2 | inner | |
1512.2.j.d.323.41 | yes | 48 | 24.11 | even | 2 | inner | |
1512.2.j.d.323.42 | yes | 48 | 1.1 | even | 1 | trivial | |
6048.2.j.d.5615.17 | 48 | 12.11 | even | 2 | |||
6048.2.j.d.5615.18 | 48 | 8.5 | even | 2 | |||
6048.2.j.d.5615.31 | 48 | 24.5 | odd | 2 | |||
6048.2.j.d.5615.32 | 48 | 4.3 | odd | 2 |