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: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.23 | ||
Character | \(\chi\) | \(=\) | 1512.323 |
Dual form | 1512.2.j.c.323.24 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.985454 | − | 1.01434i | 0.696821 | − | 0.717245i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.0577616 | − | 1.99917i | −0.0288808 | − | 0.999583i | ||||
\(5\) | −0.206991 | −0.0925694 | −0.0462847 | − | 0.998928i | \(-0.514738\pi\) | ||||
−0.0462847 | + | 0.998928i | \(0.514738\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −2.08475 | − | 1.91150i | −0.737071 | − | 0.675816i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.203980 | + | 0.209959i | −0.0645043 | + | 0.0663949i | ||||
\(11\) | 6.42190i | 1.93628i | 0.250418 | + | 0.968138i | \(0.419432\pi\) | ||||
−0.250418 | + | 0.968138i | \(0.580568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.52336i | 0.977204i | 0.872507 | + | 0.488602i | \(0.162493\pi\) | ||||
−0.872507 | + | 0.488602i | \(0.837507\pi\) | |||||||
\(14\) | 1.01434 | + | 0.985454i | 0.271093 | + | 0.263374i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.99333 | + | 0.230950i | −0.998332 | + | 0.0577375i | ||||
\(17\) | 3.90616i | 0.947383i | 0.880691 | + | 0.473692i | \(0.157079\pi\) | ||||
−0.880691 | + | 0.473692i | \(0.842921\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.48691 | −1.25878 | −0.629392 | − | 0.777088i | \(-0.716696\pi\) | ||||
−0.629392 | + | 0.777088i | \(0.716696\pi\) | |||||||
\(20\) | 0.0119562 | + | 0.413810i | 0.00267348 | + | 0.0925307i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.51397 | + | 6.32848i | 1.38878 | + | 1.34924i | ||||
\(23\) | 0.880512 | 0.183599 | 0.0917997 | − | 0.995777i | \(-0.470738\pi\) | ||||
0.0917997 | + | 0.995777i | \(0.470738\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.95715 | −0.991431 | ||||||||
\(26\) | 3.57387 | + | 3.47211i | 0.700894 | + | 0.680936i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.99917 | − | 0.0577616i | 0.377807 | − | 0.0109159i | ||||
\(29\) | 3.20814 | 0.595737 | 0.297868 | − | 0.954607i | \(-0.403724\pi\) | ||||
0.297868 | + | 0.954607i | \(0.403724\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0631261i | 0.0113378i | 0.999984 | + | 0.00566890i | \(0.00180448\pi\) | ||||
−0.999984 | + | 0.00566890i | \(0.998196\pi\) | |||||||
\(32\) | −3.70098 | + | 4.27817i | −0.654247 | + | 0.756281i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.96217 | + | 3.84934i | 0.679506 | + | 0.660157i | ||||
\(35\) | − | 0.206991i | − | 0.0349879i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.91837i | 1.63057i | 0.579060 | + | 0.815285i | \(0.303420\pi\) | ||||
−0.579060 | + | 0.815285i | \(0.696580\pi\) | |||||||
\(38\) | −5.40710 | + | 5.56558i | −0.877147 | + | 0.902856i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.431525 | + | 0.395663i | 0.0682302 | + | 0.0625598i | ||||
\(41\) | − | 5.94221i | − | 0.928017i | −0.885831 | − | 0.464009i | \(-0.846411\pi\) | ||
0.885831 | − | 0.464009i | \(-0.153589\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.13960 | −0.173788 | −0.0868938 | − | 0.996218i | \(-0.527694\pi\) | ||||
−0.0868938 | + | 0.996218i | \(0.527694\pi\) | |||||||
\(44\) | 12.8384 | − | 0.370939i | 1.93547 | − | 0.0559212i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.867704 | − | 0.893136i | 0.127936 | − | 0.131686i | ||||
\(47\) | −6.81266 | −0.993729 | −0.496864 | − | 0.867828i | \(-0.665515\pi\) | ||||
−0.496864 | + | 0.867828i | \(0.665515\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −4.88505 | + | 5.02823i | −0.690850 | + | 0.711099i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.04378 | − | 0.203515i | 0.976796 | − | 0.0282224i | ||||
\(53\) | 12.6324 | 1.73520 | 0.867598 | − | 0.497265i | \(-0.165662\pi\) | ||||
0.867598 | + | 0.497265i | \(0.165662\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.32928i | − | 0.179240i | ||||||
\(56\) | 1.91150 | − | 2.08475i | 0.255434 | − | 0.278586i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.16147 | − | 3.25414i | 0.415122 | − | 0.427289i | ||||
\(59\) | − | 4.23338i | − | 0.551139i | −0.961281 | − | 0.275570i | \(-0.911134\pi\) | ||
0.961281 | − | 0.275570i | \(-0.0888664\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 12.3006i | − | 1.57493i | −0.616359 | − | 0.787465i | \(-0.711393\pi\) | ||
0.616359 | − | 0.787465i | \(-0.288607\pi\) | |||||||
\(62\) | 0.0640312 | + | 0.0622079i | 0.00813197 | + | 0.00790041i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.692368 | + | 7.96998i | 0.0865460 | + | 0.996248i | ||||
\(65\) | − | 0.729305i | − | 0.0904591i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.74666 | −0.702067 | −0.351033 | − | 0.936363i | \(-0.614170\pi\) | ||||
−0.351033 | + | 0.936363i | \(0.614170\pi\) | |||||||
\(68\) | 7.80906 | − | 0.225626i | 0.946988 | − | 0.0273612i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.209959 | − | 0.203980i | −0.0250949 | − | 0.0243803i | ||||
\(71\) | 10.1795 | 1.20809 | 0.604043 | − | 0.796952i | \(-0.293556\pi\) | ||||
0.604043 | + | 0.796952i | \(0.293556\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.27618 | 0.968653 | 0.484327 | − | 0.874887i | \(-0.339065\pi\) | ||||
0.484327 | + | 0.874887i | \(0.339065\pi\) | |||||||
\(74\) | 10.0606 | + | 9.77409i | 1.16952 | + | 1.13622i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.316933 | + | 10.9692i | 0.0363547 | + | 1.25826i | ||||
\(77\) | −6.42190 | −0.731843 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.86426i | − | 0.547272i | −0.961833 | − | 0.273636i | \(-0.911774\pi\) | ||
0.961833 | − | 0.273636i | \(-0.0882264\pi\) | |||||||
\(80\) | 0.826584 | − | 0.0478047i | 0.0924149 | − | 0.00534472i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.02741 | − | 5.85577i | −0.665616 | − | 0.646662i | ||||
\(83\) | 7.51539i | 0.824921i | 0.910976 | + | 0.412460i | \(0.135331\pi\) | ||||
−0.910976 | + | 0.412460i | \(0.864669\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 0.808542i | − | 0.0876987i | ||||||
\(86\) | −1.12302 | + | 1.15594i | −0.121099 | + | 0.124648i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.2754 | − | 13.3881i | 1.30857 | − | 1.42717i | ||||
\(89\) | 4.44682i | 0.471362i | 0.971830 | + | 0.235681i | \(0.0757320\pi\) | ||||
−0.971830 | + | 0.235681i | \(0.924268\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.52336 | −0.369348 | ||||||||
\(92\) | −0.0508598 | − | 1.76029i | −0.00530250 | − | 0.183523i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.71356 | + | 6.91034i | −0.692451 | + | 0.712747i | ||||
\(95\) | 1.13574 | 0.116525 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.3929 | −1.76599 | −0.882993 | − | 0.469387i | \(-0.844475\pi\) | ||||
−0.882993 | + | 0.469387i | \(0.844475\pi\) | |||||||
\(98\) | −0.985454 | + | 1.01434i | −0.0995459 | + | 0.102464i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.286333 | + | 9.91017i | 0.0286333 | + | 0.991017i | ||||
\(101\) | 19.0273 | 1.89329 | 0.946643 | − | 0.322284i | \(-0.104450\pi\) | ||||
0.946643 | + | 0.322284i | \(0.104450\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7903i | 1.06320i | 0.846995 | + | 0.531601i | \(0.178409\pi\) | ||||
−0.846995 | + | 0.531601i | \(0.821591\pi\) | |||||||
\(104\) | 6.73488 | − | 7.34532i | 0.660410 | − | 0.720268i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.4487 | − | 12.8135i | 1.20912 | − | 1.24456i | ||||
\(107\) | 4.97087i | 0.480553i | 0.970705 | + | 0.240276i | \(0.0772380\pi\) | ||||
−0.970705 | + | 0.240276i | \(0.922762\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.84810i | 0.272798i | 0.990654 | + | 0.136399i | \(0.0435530\pi\) | ||||
−0.990654 | + | 0.136399i | \(0.956447\pi\) | |||||||
\(110\) | −1.34834 | − | 1.30994i | −0.128559 | − | 0.124898i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.230950 | − | 3.99333i | −0.0218227 | − | 0.377334i | ||||
\(113\) | − | 2.88561i | − | 0.271455i | −0.990746 | − | 0.135728i | \(-0.956663\pi\) | ||
0.990746 | − | 0.135728i | \(-0.0433372\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.182258 | −0.0169957 | ||||||||
\(116\) | −0.185307 | − | 6.41360i | −0.0172054 | − | 0.595488i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.29408 | − | 4.17180i | −0.395302 | − | 0.384045i | ||||
\(119\) | −3.90616 | −0.358077 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −30.2408 | −2.74916 | ||||||||
\(122\) | −12.4770 | − | 12.1217i | −1.12961 | − | 1.09744i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.126200 | − | 0.00364627i | 0.0113331 | − | 0.000327444i | ||||
\(125\) | 2.06105 | 0.184345 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.23082i | − | 0.641631i | −0.947142 | − | 0.320816i | \(-0.896043\pi\) | ||
0.947142 | − | 0.320816i | \(-0.103957\pi\) | |||||||
\(128\) | 8.76655 | + | 7.15175i | 0.774861 | + | 0.632132i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.739761 | − | 0.718696i | −0.0648813 | − | 0.0630338i | ||||
\(131\) | 12.8026i | 1.11857i | 0.828975 | + | 0.559286i | \(0.188924\pi\) | ||||
−0.828975 | + | 0.559286i | \(0.811076\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.48691i | − | 0.475776i | ||||||
\(134\) | −5.66307 | + | 5.82906i | −0.489215 | + | 0.503554i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.46661 | − | 8.14337i | 0.640257 | − | 0.698288i | ||||
\(137\) | 0.363873i | 0.0310878i | 0.999879 | + | 0.0155439i | \(0.00494798\pi\) | ||||
−0.999879 | + | 0.0155439i | \(0.995052\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.32338 | −0.790799 | −0.395399 | − | 0.918509i | \(-0.629394\pi\) | ||||
−0.395399 | + | 0.918509i | \(0.629394\pi\) | |||||||
\(140\) | −0.413810 | + | 0.0119562i | −0.0349733 | + | 0.00101048i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.0314 | − | 10.3255i | 0.841819 | − | 0.866493i | ||||
\(143\) | −22.6266 | −1.89214 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.664057 | −0.0551470 | ||||||||
\(146\) | 8.15579 | − | 8.39484i | 0.674978 | − | 0.694762i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 19.8285 | − | 0.572901i | 1.62989 | − | 0.0470922i | ||||
\(149\) | 4.82519 | 0.395295 | 0.197648 | − | 0.980273i | \(-0.436670\pi\) | ||||
0.197648 | + | 0.980273i | \(0.436670\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.7969i | 1.04140i | 0.853740 | + | 0.520700i | \(0.174329\pi\) | ||||
−0.853740 | + | 0.520700i | \(0.825671\pi\) | |||||||
\(152\) | 11.4388 | + | 10.4882i | 0.927813 | + | 0.850706i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.32848 | + | 6.51397i | −0.509964 | + | 0.524911i | ||||
\(155\) | − | 0.0130666i | − | 0.00104953i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 15.5455i | − | 1.24067i | −0.784337 | − | 0.620335i | \(-0.786997\pi\) | ||
0.784337 | − | 0.620335i | \(-0.213003\pi\) | |||||||
\(158\) | −4.93400 | − | 4.79351i | −0.392528 | − | 0.381351i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.766071 | − | 0.885545i | 0.0605632 | − | 0.0700085i | ||||
\(161\) | 0.880512i | 0.0693940i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.4630 | 1.44613 | 0.723067 | − | 0.690778i | \(-0.242732\pi\) | ||||
0.723067 | + | 0.690778i | \(0.242732\pi\) | |||||||
\(164\) | −11.8795 | + | 0.343232i | −0.927630 | + | 0.0268019i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.62314 | + | 7.40607i | 0.591670 | + | 0.574822i | ||||
\(167\) | −12.5320 | −0.969754 | −0.484877 | − | 0.874582i | \(-0.661136\pi\) | ||||
−0.484877 | + | 0.874582i | \(0.661136\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.585951 | 0.0450731 | ||||||||
\(170\) | −0.820134 | − | 0.796781i | −0.0629014 | − | 0.0611103i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.0658252 | + | 2.27825i | 0.00501912 | + | 0.173715i | ||||
\(173\) | −5.49171 | −0.417527 | −0.208763 | − | 0.977966i | \(-0.566944\pi\) | ||||
−0.208763 | + | 0.977966i | \(0.566944\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.95715i | − | 0.374726i | ||||||
\(176\) | −1.48314 | − | 25.6447i | −0.111796 | − | 1.93305i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.51058 | + | 4.38214i | 0.338082 | + | 0.328455i | ||||
\(179\) | 14.5830i | 1.08998i | 0.838441 | + | 0.544992i | \(0.183467\pi\) | ||||
−0.838441 | + | 0.544992i | \(0.816533\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 17.2753i | − | 1.28407i | −0.766677 | − | 0.642033i | \(-0.778091\pi\) | ||
0.766677 | − | 0.642033i | \(-0.221909\pi\) | |||||||
\(182\) | −3.47211 | + | 3.57387i | −0.257370 | + | 0.264913i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.83565 | − | 1.68309i | −0.135326 | − | 0.124079i | ||||
\(185\) | − | 2.05302i | − | 0.150941i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.0850 | −1.83440 | ||||||||
\(188\) | 0.393510 | + | 13.6196i | 0.0286997 | + | 0.993314i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.11922 | − | 1.15203i | 0.0811969 | − | 0.0835768i | ||||
\(191\) | 7.29828 | 0.528085 | 0.264042 | − | 0.964511i | \(-0.414944\pi\) | ||||
0.264042 | + | 0.964511i | \(0.414944\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.1106 | 0.871742 | 0.435871 | − | 0.900009i | \(-0.356440\pi\) | ||||
0.435871 | + | 0.900009i | \(0.356440\pi\) | |||||||
\(194\) | −17.1399 | + | 17.6423i | −1.23058 | + | 1.26664i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.0577616 | + | 1.99917i | 0.00412583 | + | 0.142798i | ||||
\(197\) | 17.3925 | 1.23917 | 0.619584 | − | 0.784931i | \(-0.287301\pi\) | ||||
0.619584 | + | 0.784931i | \(0.287301\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.07583i | 0.218040i | 0.994040 | + | 0.109020i | \(0.0347712\pi\) | ||||
−0.994040 | + | 0.109020i | \(0.965229\pi\) | |||||||
\(200\) | 10.3344 | + | 9.47558i | 0.730755 | + | 0.670025i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18.7505 | − | 19.3001i | 1.31928 | − | 1.35795i | ||||
\(203\) | 3.20814i | 0.225167i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.22999i | 0.0859060i | ||||||||
\(206\) | 10.9450 | + | 10.6334i | 0.762576 | + | 0.740862i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.813720 | − | 14.0699i | −0.0564213 | − | 0.975573i | ||||
\(209\) | − | 35.2364i | − | 2.43735i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.57154 | 0.658932 | 0.329466 | − | 0.944167i | \(-0.393131\pi\) | ||||
0.329466 | + | 0.944167i | \(0.393131\pi\) | |||||||
\(212\) | −0.729669 | − | 25.2543i | −0.0501139 | − | 1.73447i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.04214 | + | 4.89857i | 0.344674 | + | 0.334859i | ||||
\(215\) | 0.235888 | 0.0160874 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.0631261 | −0.00428528 | ||||||||
\(218\) | 2.88893 | + | 2.80667i | 0.195663 | + | 0.190092i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.65745 | + | 0.0767812i | −0.179165 | + | 0.00517659i | ||||
\(221\) | −13.7628 | −0.925786 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 26.5694i | − | 1.77922i | −0.456722 | − | 0.889610i | \(-0.650976\pi\) | ||
0.456722 | − | 0.889610i | \(-0.349024\pi\) | |||||||
\(224\) | −4.27817 | − | 3.70098i | −0.285847 | − | 0.247282i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.92698 | − | 2.84363i | −0.194700 | − | 0.189156i | ||||
\(227\) | 20.7345i | 1.37620i | 0.725616 | + | 0.688100i | \(0.241555\pi\) | ||||
−0.725616 | + | 0.688100i | \(0.758445\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.2625i | 1.27290i | 0.771316 | + | 0.636452i | \(0.219599\pi\) | ||||
−0.771316 | + | 0.636452i | \(0.780401\pi\) | |||||||
\(230\) | −0.179607 | + | 0.184871i | −0.0118429 | + | 0.0121901i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.68817 | − | 6.13235i | −0.439100 | − | 0.402608i | ||||
\(233\) | − | 25.0038i | − | 1.63805i | −0.573756 | − | 0.819027i | \(-0.694514\pi\) | ||
0.573756 | − | 0.819027i | \(-0.305486\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.41016 | 0.0919889 | ||||||||
\(236\) | −8.46323 | + | 0.244527i | −0.550909 | + | 0.0159173i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.84934 | + | 3.96217i | −0.249516 | + | 0.256829i | ||||
\(239\) | −15.0439 | −0.973107 | −0.486553 | − | 0.873651i | \(-0.661746\pi\) | ||||
−0.486553 | + | 0.873651i | \(0.661746\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.23274 | −0.208239 | −0.104120 | − | 0.994565i | \(-0.533203\pi\) | ||||
−0.104120 | + | 0.994565i | \(0.533203\pi\) | |||||||
\(242\) | −29.8009 | + | 30.6744i | −1.91567 | + | 1.97182i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −24.5909 | + | 0.710502i | −1.57427 | + | 0.0454853i | ||||
\(245\) | 0.206991 | 0.0132242 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 19.3324i | − | 1.23009i | ||||||
\(248\) | 0.120665 | − | 0.131602i | 0.00766226 | − | 0.00835675i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.03106 | − | 2.09060i | 0.128456 | − | 0.132221i | ||||
\(251\) | 10.4258i | 0.658071i | 0.944318 | + | 0.329036i | \(0.106724\pi\) | ||||
−0.944318 | + | 0.329036i | \(0.893276\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.65456i | 0.355499i | ||||||||
\(254\) | −7.33449 | − | 7.12564i | −0.460207 | − | 0.447102i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.8933 | − | 1.84452i | 0.993333 | − | 0.115282i | ||||
\(257\) | − | 8.12452i | − | 0.506794i | −0.967362 | − | 0.253397i | \(-0.918452\pi\) | ||
0.967362 | − | 0.253397i | \(-0.0815479\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.91837 | −0.616297 | ||||||||
\(260\) | −1.45800 | + | 0.0421258i | −0.0904214 | + | 0.00261253i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.9862 | + | 12.6164i | 0.802290 | + | 0.779444i | ||||
\(263\) | −14.7639 | −0.910382 | −0.455191 | − | 0.890394i | \(-0.650429\pi\) | ||||
−0.455191 | + | 0.890394i | \(0.650429\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.61480 | −0.160626 | ||||||||
\(266\) | −5.56558 | − | 5.40710i | −0.341248 | − | 0.331530i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.331937 | + | 11.4885i | 0.0202762 | + | 0.701774i | ||||
\(269\) | −26.8961 | −1.63989 | −0.819943 | − | 0.572445i | \(-0.805995\pi\) | ||||
−0.819943 | + | 0.572445i | \(0.805995\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.5914i | 1.06860i | 0.845295 | + | 0.534301i | \(0.179425\pi\) | ||||
−0.845295 | + | 0.534301i | \(0.820575\pi\) | |||||||
\(272\) | −0.902128 | − | 15.5986i | −0.0546996 | − | 0.945803i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.369090 | + | 0.358580i | 0.0222976 | + | 0.0216626i | ||||
\(275\) | − | 31.8343i | − | 1.91968i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.8383i | 1.49239i | 0.665729 | + | 0.746194i | \(0.268121\pi\) | ||||
−0.665729 | + | 0.746194i | \(0.731879\pi\) | |||||||
\(278\) | −9.18776 | + | 9.45706i | −0.551045 | + | 0.567197i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.395663 | + | 0.431525i | −0.0236454 | + | 0.0257886i | ||||
\(281\) | − | 4.13370i | − | 0.246596i | −0.992370 | − | 0.123298i | \(-0.960653\pi\) | ||
0.992370 | − | 0.123298i | \(-0.0393471\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.9297 | −1.42247 | −0.711236 | − | 0.702954i | \(-0.751864\pi\) | ||||
−0.711236 | + | 0.702954i | \(0.751864\pi\) | |||||||
\(284\) | −0.587985 | − | 20.3505i | −0.0348905 | − | 1.20758i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −22.2975 | + | 22.9511i | −1.31848 | + | 1.35712i | ||||
\(287\) | 5.94221 | 0.350758 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.74190 | 0.102465 | ||||||||
\(290\) | −0.654398 | + | 0.673578i | −0.0384276 | + | 0.0395539i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.478045 | − | 16.5454i | −0.0279755 | − | 0.968249i | ||||
\(293\) | 12.0225 | 0.702360 | 0.351180 | − | 0.936308i | \(-0.385781\pi\) | ||||
0.351180 | + | 0.936308i | \(0.385781\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.876273i | 0.0510186i | ||||||||
\(296\) | 18.9589 | − | 20.6773i | 1.10196 | − | 1.20184i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.75501 | − | 4.89438i | 0.275450 | − | 0.283524i | ||||
\(299\) | 3.10236i | 0.179414i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.13960i | − | 0.0656855i | ||||||
\(302\) | 12.9804 | + | 12.6108i | 0.746939 | + | 0.725670i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 21.9110 | − | 1.26720i | 1.25668 | − | 0.0726790i | ||||
\(305\) | 2.54612i | 0.145790i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.82060 | −0.332199 | −0.166100 | − | 0.986109i | \(-0.553117\pi\) | ||||
−0.166100 | + | 0.986109i | \(0.553117\pi\) | |||||||
\(308\) | 0.370939 | + | 12.8384i | 0.0211362 | + | 0.731538i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.0132539 | − | 0.0128765i | −0.000752772 | − | 0.000731336i | ||||
\(311\) | −12.7884 | −0.725161 | −0.362580 | − | 0.931952i | \(-0.618104\pi\) | ||||
−0.362580 | + | 0.931952i | \(0.618104\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.74881 | 0.0988483 | 0.0494242 | − | 0.998778i | \(-0.484261\pi\) | ||||
0.0494242 | + | 0.998778i | \(0.484261\pi\) | |||||||
\(314\) | −15.7684 | − | 15.3194i | −0.889864 | − | 0.864525i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.72447 | + | 0.280968i | −0.547044 | + | 0.0158057i | ||||
\(317\) | 30.5938 | 1.71832 | 0.859159 | − | 0.511709i | \(-0.170987\pi\) | ||||
0.859159 | + | 0.511709i | \(0.170987\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.6024i | 1.15351i | ||||||||
\(320\) | −0.143314 | − | 1.64972i | −0.00801151 | − | 0.0922220i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.893136 | + | 0.867704i | 0.0497725 | + | 0.0483552i | ||||
\(323\) | − | 21.4328i | − | 1.19255i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 17.4658i | − | 0.968830i | ||||||
\(326\) | 18.1944 | − | 18.7277i | 1.00770 | − | 1.03723i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.3585 | + | 12.3880i | −0.627169 | + | 0.684014i | ||||
\(329\) | − | 6.81266i | − | 0.375594i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.7269 | −1.13925 | −0.569627 | − | 0.821904i | \(-0.692912\pi\) | ||||
−0.569627 | + | 0.821904i | \(0.692912\pi\) | |||||||
\(332\) | 15.0245 | − | 0.434101i | 0.824577 | − | 0.0238244i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.3497 | + | 12.7117i | −0.675745 | + | 0.695551i | ||||
\(335\) | 1.18951 | 0.0649899 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.9716 | 1.08792 | 0.543961 | − | 0.839110i | \(-0.316924\pi\) | ||||
0.543961 | + | 0.839110i | \(0.316924\pi\) | |||||||
\(338\) | 0.577427 | − | 0.594352i | 0.0314079 | − | 0.0323285i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.61641 | + | 0.0467027i | −0.0876621 | + | 0.00253281i | ||||
\(341\) | −0.405390 | −0.0219531 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 2.37578 | + | 2.17834i | 0.128094 | + | 0.117448i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.41182 | + | 5.57045i | −0.290942 | + | 0.299469i | ||||
\(347\) | − | 10.6443i | − | 0.571414i | −0.958317 | − | 0.285707i | \(-0.907772\pi\) | ||
0.958317 | − | 0.285707i | \(-0.0922284\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.1575i | 1.13254i | 0.824221 | + | 0.566268i | \(0.191613\pi\) | ||||
−0.824221 | + | 0.566268i | \(0.808387\pi\) | |||||||
\(350\) | −5.02823 | − | 4.88505i | −0.268770 | − | 0.261117i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −27.4740 | − | 23.7673i | −1.46437 | − | 1.26680i | ||||
\(353\) | − | 7.85498i | − | 0.418079i | −0.977907 | − | 0.209039i | \(-0.932966\pi\) | ||
0.977907 | − | 0.209039i | \(-0.0670337\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.10707 | −0.111832 | ||||||||
\(356\) | 8.88993 | − | 0.256855i | 0.471165 | − | 0.0136133i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.7921 | + | 14.3709i | 0.781785 | + | 0.759523i | ||||
\(359\) | 22.0102 | 1.16165 | 0.580826 | − | 0.814028i | \(-0.302730\pi\) | ||||
0.580826 | + | 0.814028i | \(0.302730\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.1062 | 0.584537 | ||||||||
\(362\) | −17.5230 | − | 17.0240i | −0.920990 | − | 0.894764i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.203515 | + | 7.04378i | 0.0106671 | + | 0.369194i | ||||
\(365\) | −1.71310 | −0.0896676 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 5.61196i | − | 0.292942i | −0.989215 | − | 0.146471i | \(-0.953209\pi\) | ||
0.989215 | − | 0.146471i | \(-0.0467915\pi\) | |||||||
\(368\) | −3.51617 | + | 0.203354i | −0.183293 | + | 0.0106006i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.08245 | − | 2.02315i | −0.108262 | − | 0.105179i | ||||
\(371\) | 12.6324i | 0.655843i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.5334i | 1.11496i | 0.830192 | + | 0.557478i | \(0.188231\pi\) | ||||
−0.830192 | + | 0.557478i | \(0.811769\pi\) | |||||||
\(374\) | −24.7201 | + | 25.4446i | −1.27825 | + | 1.31571i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 14.2027 | + | 13.0224i | 0.732448 | + | 0.671578i | ||||
\(377\) | 11.3034i | 0.582156i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.2973 | 1.86447 | 0.932233 | − | 0.361858i | \(-0.117857\pi\) | ||||
0.932233 | + | 0.361858i | \(0.117857\pi\) | |||||||
\(380\) | −0.0656024 | − | 2.27054i | −0.00336533 | − | 0.116476i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.19211 | − | 7.40292i | 0.367981 | − | 0.378766i | ||||
\(383\) | 12.4362 | 0.635462 | 0.317731 | − | 0.948181i | \(-0.397079\pi\) | ||||
0.317731 | + | 0.948181i | \(0.397079\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.32928 | 0.0677463 | ||||||||
\(386\) | 11.9345 | − | 12.2843i | 0.607448 | − | 0.625253i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.00464 | + | 34.7714i | 0.0510031 | + | 1.76525i | ||||
\(389\) | 5.47648 | 0.277669 | 0.138834 | − | 0.990316i | \(-0.455664\pi\) | ||||
0.138834 | + | 0.990316i | \(0.455664\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.43942i | 0.173939i | ||||||||
\(392\) | 2.08475 | + | 1.91150i | 0.105296 | + | 0.0965451i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 17.1396 | − | 17.6419i | 0.863478 | − | 0.888787i | ||||
\(395\) | 1.00686i | 0.0506606i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.58947i | 0.481282i | 0.970614 | + | 0.240641i | \(0.0773576\pi\) | ||||
−0.970614 | + | 0.240641i | \(0.922642\pi\) | |||||||
\(398\) | 3.11993 | + | 3.03108i | 0.156388 | + | 0.151935i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.7955 | − | 1.14486i | 0.989777 | − | 0.0572428i | ||||
\(401\) | − | 1.76702i | − | 0.0882408i | −0.999026 | − | 0.0441204i | \(-0.985951\pi\) | ||
0.999026 | − | 0.0441204i | \(-0.0140485\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.222416 | −0.0110793 | ||||||||
\(404\) | −1.09905 | − | 38.0387i | −0.0546796 | − | 1.89250i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.25414 | + | 3.16147i | 0.161500 | + | 0.156901i | ||||
\(407\) | −63.6948 | −3.15723 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.87490 | −0.290495 | −0.145248 | − | 0.989395i | \(-0.546398\pi\) | ||||
−0.145248 | + | 0.989395i | \(0.546398\pi\) | |||||||
\(410\) | 1.24762 | + | 1.21209i | 0.0616156 | + | 0.0598611i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 21.5716 | − | 0.623266i | 1.06276 | − | 0.0307061i | ||||
\(413\) | 4.23338 | 0.208311 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.55562i | − | 0.0763624i | ||||||
\(416\) | −15.0735 | − | 13.0399i | −0.739041 | − | 0.639332i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −35.7416 | − | 34.7238i | −1.74818 | − | 1.69840i | ||||
\(419\) | − | 18.9459i | − | 0.925567i | −0.886471 | − | 0.462783i | \(-0.846851\pi\) | ||
0.886471 | − | 0.462783i | \(-0.153149\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 25.2598i | − | 1.23109i | −0.788103 | − | 0.615544i | \(-0.788936\pi\) | ||
0.788103 | − | 0.615544i | \(-0.211064\pi\) | |||||||
\(422\) | 9.43231 | − | 9.70878i | 0.459158 | − | 0.472616i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −26.3355 | − | 24.1468i | −1.27896 | − | 1.17267i | ||||
\(425\) | − | 19.3634i | − | 0.939265i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.3006 | 0.595268 | ||||||||
\(428\) | 9.93760 | − | 0.287126i | 0.480352 | − | 0.0138787i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.232456 | − | 0.239270i | 0.0112100 | − | 0.0115386i | ||||
\(431\) | −37.5774 | −1.81004 | −0.905020 | − | 0.425369i | \(-0.860144\pi\) | ||||
−0.905020 | + | 0.425369i | \(0.860144\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.1040 | 1.01419 | 0.507097 | − | 0.861889i | \(-0.330719\pi\) | ||||
0.507097 | + | 0.861889i | \(0.330719\pi\) | |||||||
\(434\) | −0.0622079 | + | 0.0640312i | −0.00298607 | + | 0.00307360i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.69382 | − | 0.164511i | 0.272684 | − | 0.00787863i | ||||
\(437\) | −4.83129 | −0.231112 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.88405i | 0.137648i | 0.997629 | + | 0.0688240i | \(0.0219247\pi\) | ||||
−0.997629 | + | 0.0688240i | \(0.978075\pi\) | |||||||
\(440\) | −2.54091 | + | 2.77121i | −0.121133 | + | 0.132112i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.5626 | + | 13.9601i | −0.645107 | + | 0.664016i | ||||
\(443\) | 34.5978i | 1.64379i | 0.569640 | + | 0.821895i | \(0.307083\pi\) | ||||
−0.569640 | + | 0.821895i | \(0.692917\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 0.920453i | − | 0.0436337i | ||||||
\(446\) | −26.9504 | − | 26.1829i | −1.27614 | − | 1.23980i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.96998 | + | 0.692368i | −0.376546 | + | 0.0327113i | ||||
\(449\) | 14.8661i | 0.701575i | 0.936455 | + | 0.350787i | \(0.114086\pi\) | ||||
−0.936455 | + | 0.350787i | \(0.885914\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.1603 | 1.79690 | ||||||||
\(452\) | −5.76881 | + | 0.166677i | −0.271342 | + | 0.00783985i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.0318 | + | 20.4329i | 0.987072 | + | 0.958965i | ||||
\(455\) | 0.729305 | 0.0341903 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.0037 | 0.514730 | 0.257365 | − | 0.966314i | \(-0.417146\pi\) | ||||
0.257365 | + | 0.966314i | \(0.417146\pi\) | |||||||
\(458\) | 19.5387 | + | 18.9823i | 0.912984 | + | 0.886987i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.0105275 | + | 0.364365i | 0.000490849 | + | 0.0169886i | ||||
\(461\) | 32.9687 | 1.53551 | 0.767753 | − | 0.640746i | \(-0.221375\pi\) | ||||
0.767753 | + | 0.640746i | \(0.221375\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 12.3348i | − | 0.573245i | −0.958044 | − | 0.286622i | \(-0.907468\pi\) | ||
0.958044 | − | 0.286622i | \(-0.0925325\pi\) | |||||||
\(464\) | −12.8112 | + | 0.740920i | −0.594743 | + | 0.0343964i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25.3623 | − | 24.6401i | −1.17489 | − | 1.14143i | ||||
\(467\) | 33.5264i | 1.55142i | 0.631091 | + | 0.775709i | \(0.282607\pi\) | ||||
−0.631091 | + | 0.775709i | \(0.717393\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.74666i | − | 0.265356i | ||||||
\(470\) | 1.38965 | − | 1.43038i | 0.0640998 | − | 0.0659785i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.09209 | + | 8.82554i | −0.372468 | + | 0.406228i | ||||
\(473\) | − | 7.31840i | − | 0.336501i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27.1995 | 1.24800 | ||||||||
\(476\) | 0.225626 | + | 7.80906i | 0.0103416 | + | 0.357928i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.8250 | + | 15.2596i | −0.678081 | + | 0.697956i | ||||
\(479\) | −9.65791 | −0.441281 | −0.220641 | − | 0.975355i | \(-0.570815\pi\) | ||||
−0.220641 | + | 0.975355i | \(0.570815\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.9460 | −1.59340 | ||||||||
\(482\) | −3.18572 | + | 3.27909i | −0.145106 | + | 0.149359i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.74676 | + | 60.4563i | 0.0793980 | + | 2.74802i | ||||
\(485\) | 3.60019 | 0.163476 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.1008i | 1.13742i | 0.822537 | + | 0.568712i | \(0.192558\pi\) | ||||
−0.822537 | + | 0.568712i | \(0.807442\pi\) | |||||||
\(488\) | −23.5125 | + | 25.6437i | −1.06436 | + | 1.16083i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.203980 | − | 0.209959i | 0.00921490 | − | 0.00948499i | ||||
\(491\) | − | 10.5524i | − | 0.476224i | −0.971238 | − | 0.238112i | \(-0.923471\pi\) | ||
0.971238 | − | 0.238112i | \(-0.0765285\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.5315i | 0.564391i | ||||||||
\(494\) | −19.6095 | − | 19.0511i | −0.882275 | − | 0.857151i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.0145790 | − | 0.252083i | −0.000654616 | − | 0.0113189i | ||||
\(497\) | 10.1795i | 0.456613i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.6619 | −0.522059 | −0.261029 | − | 0.965331i | \(-0.584062\pi\) | ||||
−0.261029 | + | 0.965331i | \(0.584062\pi\) | |||||||
\(500\) | −0.119049 | − | 4.12037i | −0.00532405 | − | 0.184269i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.5753 | + | 10.2742i | 0.471998 | + | 0.458558i | ||||
\(503\) | 29.0202 | 1.29394 | 0.646972 | − | 0.762513i | \(-0.276035\pi\) | ||||
0.646972 | + | 0.762513i | \(0.276035\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.93849 | −0.175260 | ||||||||
\(506\) | 5.73563 | + | 5.57230i | 0.254980 | + | 0.247719i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.4556 | + | 0.417664i | −0.641364 | + | 0.0185308i | ||||
\(509\) | −22.0894 | −0.979096 | −0.489548 | − | 0.871976i | \(-0.662838\pi\) | ||||
−0.489548 | + | 0.871976i | \(0.662838\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.27618i | 0.366116i | ||||||||
\(512\) | 13.7912 | − | 17.9389i | 0.609489 | − | 0.792794i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.24101 | − | 8.00634i | −0.363495 | − | 0.353145i | ||||
\(515\) | − | 2.23350i | − | 0.0984199i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 43.7502i | − | 1.92413i | ||||||
\(518\) | −9.77409 | + | 10.0606i | −0.429449 | + | 0.442036i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.39406 | + | 1.52042i | −0.0611337 | + | 0.0666747i | ||||
\(521\) | 14.5460i | 0.637273i | 0.947877 | + | 0.318636i | \(0.103225\pi\) | ||||
−0.947877 | + | 0.318636i | \(0.896775\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.6350 | 1.38330 | 0.691651 | − | 0.722232i | \(-0.256884\pi\) | ||||
0.691651 | + | 0.722232i | \(0.256884\pi\) | |||||||
\(524\) | 25.5946 | − | 0.739501i | 1.11810 | − | 0.0323052i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.5491 | + | 14.9756i | −0.634373 | + | 0.652967i | ||||
\(527\) | −0.246581 | −0.0107412 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2247 | −0.966291 | ||||||||
\(530\) | −2.57677 | + | 2.65229i | −0.111928 | + | 0.115208i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −10.9692 | + | 0.316933i | −0.475577 | + | 0.0137408i | ||||
\(533\) | 20.9365 | 0.906862 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.02893i | − | 0.0444844i | ||||||
\(536\) | 11.9804 | + | 10.9847i | 0.517473 | + | 0.474468i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −26.5049 | + | 27.2818i | −1.14271 | + | 1.17620i | ||||
\(539\) | − | 6.42190i | − | 0.276611i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 22.7160i | − | 0.976639i | −0.872665 | − | 0.488319i | \(-0.837610\pi\) | ||
0.872665 | − | 0.488319i | \(-0.162390\pi\) | |||||||
\(542\) | 17.8436 | + | 17.3355i | 0.766449 | + | 0.744624i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −16.7112 | − | 14.4566i | −0.716488 | − | 0.619822i | ||||
\(545\) | − | 0.589532i | − | 0.0252528i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.2601 | −0.951774 | −0.475887 | − | 0.879506i | \(-0.657873\pi\) | ||||
−0.475887 | + | 0.879506i | \(0.657873\pi\) | |||||||
\(548\) | 0.727443 | − | 0.0210179i | 0.0310748 | − | 0.000897840i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −32.2908 | − | 31.3713i | −1.37688 | − | 1.33768i | ||||
\(551\) | −17.6028 | −0.749904 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.86426 | 0.206849 | ||||||||
\(554\) | 25.1944 | + | 24.4770i | 1.07041 | + | 1.03993i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.538533 | + | 18.6390i | 0.0228389 | + | 0.790469i | ||||
\(557\) | 2.99670 | 0.126974 | 0.0634872 | − | 0.997983i | \(-0.479778\pi\) | ||||
0.0634872 | + | 0.997983i | \(0.479778\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.01522i | − | 0.169826i | ||||||
\(560\) | 0.0478047 | + | 0.826584i | 0.00202012 | + | 0.0349296i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.19297 | − | 4.07357i | −0.176870 | − | 0.171833i | ||||
\(563\) | 13.4913i | 0.568589i | 0.958737 | + | 0.284295i | \(0.0917594\pi\) | ||||
−0.958737 | + | 0.284295i | \(0.908241\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.597296i | 0.0251284i | ||||||||
\(566\) | −23.5816 | + | 24.2728i | −0.991208 | + | 1.02026i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21.2217 | − | 19.4581i | −0.890444 | − | 0.816443i | ||||
\(569\) | − | 40.7445i | − | 1.70810i | −0.520191 | − | 0.854050i | \(-0.674139\pi\) | ||
0.520191 | − | 0.854050i | \(-0.325861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.0110 | 0.753739 | 0.376869 | − | 0.926266i | \(-0.377001\pi\) | ||||
0.376869 | + | 0.926266i | \(0.377001\pi\) | |||||||
\(572\) | 1.30695 | + | 45.2344i | 0.0546464 | + | 1.89135i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.85577 | − | 6.02741i | 0.244415 | − | 0.251579i | ||||
\(575\) | −4.36483 | −0.182026 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.3495 | 1.22184 | 0.610919 | − | 0.791693i | \(-0.290800\pi\) | ||||
0.610919 | + | 0.791693i | \(0.290800\pi\) | |||||||
\(578\) | 1.71656 | − | 1.76688i | 0.0713997 | − | 0.0734924i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.0383570 | + | 1.32756i | 0.00159269 | + | 0.0551240i | ||||
\(581\) | −7.51539 | −0.311791 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 81.1242i | 3.35982i | ||||||||
\(584\) | −17.2538 | − | 15.8199i | −0.713966 | − | 0.654631i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.8476 | − | 12.1948i | 0.489419 | − | 0.503764i | ||||
\(587\) | 11.1732i | 0.461168i | 0.973052 | + | 0.230584i | \(0.0740637\pi\) | ||||
−0.973052 | + | 0.230584i | \(0.925936\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.346368i | − | 0.0142718i | ||||||
\(590\) | 0.888837 | + | 0.863527i | 0.0365928 | + | 0.0355508i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.29065 | − | 39.6073i | −0.0941450 | − | 1.62785i | ||||
\(593\) | − | 29.9792i | − | 1.23110i | −0.788099 | − | 0.615549i | \(-0.788934\pi\) | ||
0.788099 | − | 0.615549i | \(-0.211066\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.808542 | 0.0331470 | ||||||||
\(596\) | −0.278711 | − | 9.64636i | −0.0114164 | − | 0.395130i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.14684 | + | 3.05723i | 0.128684 | + | 0.125019i | ||||
\(599\) | −6.38388 | −0.260838 | −0.130419 | − | 0.991459i | \(-0.541632\pi\) | ||||
−0.130419 | + | 0.991459i | \(0.541632\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.5445 | −0.960402 | −0.480201 | − | 0.877159i | \(-0.659436\pi\) | ||||
−0.480201 | + | 0.877159i | \(0.659436\pi\) | |||||||
\(602\) | −1.15594 | − | 1.12302i | −0.0471126 | − | 0.0457710i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 25.5832 | − | 0.739172i | 1.04097 | − | 0.0300765i | ||||
\(605\) | 6.25958 | 0.254488 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 33.9599i | − | 1.37839i | −0.724577 | − | 0.689194i | \(-0.757965\pi\) | ||
0.724577 | − | 0.689194i | \(-0.242035\pi\) | |||||||
\(608\) | 20.3069 | − | 23.4740i | 0.823555 | − | 0.951995i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.58262 | + | 2.50908i | 0.104567 | + | 0.101590i | ||||
\(611\) | − | 24.0034i | − | 0.971076i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.6042i | 0.832197i | 0.909320 | + | 0.416098i | \(0.136603\pi\) | ||||
−0.909320 | + | 0.416098i | \(0.863397\pi\) | |||||||
\(614\) | −5.73593 | + | 5.90405i | −0.231483 | + | 0.238268i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.3881 | + | 12.2754i | 0.539420 | + | 0.494591i | ||||
\(617\) | 37.4489i | 1.50764i | 0.657083 | + | 0.753818i | \(0.271790\pi\) | ||||
−0.657083 | + | 0.753818i | \(0.728210\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.2766 | 0.573825 | 0.286913 | − | 0.957957i | \(-0.407371\pi\) | ||||
0.286913 | + | 0.957957i | \(0.407371\pi\) | |||||||
\(620\) | −0.0261222 | 0.000754746i | −0.00104909 | 3.03113e-5i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.6023 | + | 12.9717i | −0.505307 | + | 0.520118i | ||||
\(623\) | −4.44682 | −0.178158 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.3592 | 0.974366 | ||||||||
\(626\) | 1.72337 | − | 1.77388i | 0.0688796 | − | 0.0708985i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −31.0781 | + | 0.897936i | −1.24015 | + | 0.0358315i | ||||
\(629\) | −38.7427 | −1.54477 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 7.00448i | − | 0.278844i | −0.990233 | − | 0.139422i | \(-0.955476\pi\) | ||
0.990233 | − | 0.139422i | \(-0.0445244\pi\) | |||||||
\(632\) | −9.29802 | + | 10.1408i | −0.369855 | + | 0.403378i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.1488 | − | 31.0324i | 1.19736 | − | 1.23245i | ||||
\(635\) | 1.49672i | 0.0593954i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 3.52336i | − | 0.139601i | ||||||
\(638\) | 20.8977 | + | 20.3027i | 0.827350 | + | 0.803790i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.81460 | − | 1.48035i | −0.0717284 | − | 0.0585160i | ||||
\(641\) | 9.23092i | 0.364599i | 0.983243 | + | 0.182300i | \(0.0583541\pi\) | ||||
−0.983243 | + | 0.182300i | \(0.941646\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.48603 | 0.0586031 | 0.0293016 | − | 0.999571i | \(-0.490672\pi\) | ||||
0.0293016 | + | 0.999571i | \(0.490672\pi\) | |||||||
\(644\) | 1.76029 | − | 0.0508598i | 0.0693651 | − | 0.00200416i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.7401 | − | 21.1210i | −0.855351 | − | 0.830995i | ||||
\(647\) | 16.2654 | 0.639457 | 0.319729 | − | 0.947509i | \(-0.396408\pi\) | ||||
0.319729 | + | 0.947509i | \(0.396408\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.1863 | 1.06716 | ||||||||
\(650\) | −17.7162 | − | 17.2118i | −0.694888 | − | 0.675101i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.06645 | − | 36.9106i | −0.0417655 | − | 1.44553i | ||||
\(653\) | 6.92310 | 0.270922 | 0.135461 | − | 0.990783i | \(-0.456748\pi\) | ||||
0.135461 | + | 0.990783i | \(0.456748\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2.65003i | − | 0.103545i | ||||||
\(656\) | 1.37235 | + | 23.7292i | 0.0535814 | + | 0.926469i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.91034 | − | 6.71356i | −0.269393 | − | 0.261722i | ||||
\(659\) | − | 11.3057i | − | 0.440407i | −0.975454 | − | 0.220203i | \(-0.929328\pi\) | ||
0.975454 | − | 0.220203i | \(-0.0706721\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 18.9877i | − | 0.738536i | −0.929323 | − | 0.369268i | \(-0.879608\pi\) | ||
0.929323 | − | 0.369268i | \(-0.120392\pi\) | |||||||
\(662\) | −20.4254 | + | 21.0241i | −0.793856 | + | 0.817124i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.3656 | − | 15.6677i | 0.557495 | − | 0.608025i | ||||
\(665\) | 1.13574i | 0.0440422i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.82481 | 0.109377 | ||||||||
\(668\) | 0.723867 | + | 25.0535i | 0.0280073 | + | 0.969349i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.17221 | − | 1.20656i | 0.0452863 | − | 0.0466137i | ||||
\(671\) | 78.9932 | 3.04950 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.6164 | 0.679061 | 0.339531 | − | 0.940595i | \(-0.389732\pi\) | ||||
0.339531 | + | 0.940595i | \(0.389732\pi\) | |||||||
\(674\) | 19.6811 | − | 20.2580i | 0.758088 | − | 0.780307i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.0338455 | − | 1.17141i | −0.00130175 | − | 0.0450543i | ||||
\(677\) | −7.42579 | −0.285396 | −0.142698 | − | 0.989766i | \(-0.545578\pi\) | ||||
−0.142698 | + | 0.989766i | \(0.545578\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 17.3929i | − | 0.667480i | ||||||
\(680\) | −1.54552 | + | 1.68561i | −0.0592681 | + | 0.0646401i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.399493 | + | 0.411202i | −0.0152974 | + | 0.0157457i | ||||
\(683\) | − | 22.8832i | − | 0.875600i | −0.899072 | − | 0.437800i | \(-0.855758\pi\) | ||
0.899072 | − | 0.437800i | \(-0.144242\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 0.0753186i | − | 0.00287778i | ||||||
\(686\) | −1.01434 | − | 0.985454i | −0.0387276 | − | 0.0376248i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.55080 | − | 0.263191i | 0.173498 | − | 0.0100341i | ||||
\(689\) | 44.5086i | 1.69564i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.6439 | 1.27987 | 0.639936 | − | 0.768428i | \(-0.278961\pi\) | ||||
0.639936 | + | 0.768428i | \(0.278961\pi\) | |||||||
\(692\) | 0.317210 | + | 10.9788i | 0.0120585 | + | 0.417353i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.7969 | − | 10.4894i | −0.409844 | − | 0.398173i | ||||
\(695\) | 1.92986 | 0.0732038 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.2112 | 0.879188 | ||||||||
\(698\) | 21.4609 | + | 20.8498i | 0.812306 | + | 0.789175i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.91017 | + | 0.286333i | −0.374569 | + | 0.0108224i | ||||
\(701\) | 35.4474 | 1.33883 | 0.669414 | − | 0.742890i | \(-0.266545\pi\) | ||||
0.669414 | + | 0.742890i | \(0.266545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 54.4212i | − | 2.05253i | ||||||
\(704\) | −51.1824 | + | 4.44632i | −1.92901 | + | 0.167577i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.96760 | − | 7.74072i | −0.299865 | − | 0.291326i | ||||
\(707\) | 19.0273i | 0.715595i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 8.71118i | − | 0.327155i | −0.986530 | − | 0.163578i | \(-0.947697\pi\) | ||
0.986530 | − | 0.163578i | \(-0.0523034\pi\) | |||||||
\(710\) | −2.07642 | + | 2.13728i | −0.0779267 | + | 0.0802107i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.50008 | − | 9.27051i | 0.318554 | − | 0.347427i | ||||
\(713\) | 0.0555833i | 0.00208161i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.68352 | 0.175154 | ||||||||
\(716\) | 29.1538 | − | 0.842337i | 1.08953 | − | 0.0314796i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 21.6900 | − | 22.3257i | 0.809463 | − | 0.833189i | ||||
\(719\) | −0.821108 | −0.0306222 | −0.0153111 | − | 0.999883i | \(-0.504874\pi\) | ||||
−0.0153111 | + | 0.999883i | \(0.504874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7903 | −0.401853 | ||||||||
\(722\) | 10.9446 | − | 11.2654i | 0.407318 | − | 0.419256i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −34.5363 | + | 0.997851i | −1.28353 | + | 0.0370848i | ||||
\(725\) | −15.9032 | −0.590632 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 28.0509i | − | 1.04035i | −0.854059 | − | 0.520176i | \(-0.825866\pi\) | ||
0.854059 | − | 0.520176i | \(-0.174134\pi\) | |||||||
\(728\) | 7.34532 | + | 6.73488i | 0.272236 | + | 0.249611i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.68818 | + | 1.73766i | −0.0624823 | + | 0.0643136i | ||||
\(731\) | − | 4.45147i | − | 0.164643i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.9677i | 0.811395i | 0.914007 | + | 0.405697i | \(0.132971\pi\) | ||||
−0.914007 | + | 0.405697i | \(0.867029\pi\) | |||||||
\(734\) | −5.69242 | − | 5.53032i | −0.210111 | − | 0.204128i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.25875 | + | 3.76698i | −0.120119 | + | 0.138853i | ||||
\(737\) | − | 36.9045i | − | 1.35939i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.6044 | −0.684374 | −0.342187 | − | 0.939632i | \(-0.611168\pi\) | ||||
−0.342187 | + | 0.939632i | \(0.611168\pi\) | |||||||
\(740\) | −4.10432 | + | 0.118586i | −0.150878 | + | 0.00435929i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.8135 | + | 12.4487i | 0.470400 | + | 0.457005i | ||||
\(743\) | 29.0849 | 1.06702 | 0.533512 | − | 0.845793i | \(-0.320872\pi\) | ||||
0.533512 | + | 0.845793i | \(0.320872\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.998774 | −0.0365922 | ||||||||
\(746\) | 21.8421 | + | 21.2201i | 0.799696 | + | 0.776925i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.44895 | + | 50.1490i | 0.0529788 | + | 1.83363i | ||||
\(749\) | −4.97087 | −0.181632 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.4693i | 0.527991i | 0.964524 | + | 0.263995i | \(0.0850403\pi\) | ||||
−0.964524 | + | 0.263995i | \(0.914960\pi\) | |||||||
\(752\) | 27.2052 | − | 1.57338i | 0.992071 | − | 0.0573754i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.4655 | + | 11.1390i | 0.417549 | + | 0.405659i | ||||
\(755\) | − | 2.64886i | − | 0.0964018i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.6988i | 0.497891i | 0.968517 | + | 0.248946i | \(0.0800840\pi\) | ||||
−0.968517 | + | 0.248946i | \(0.919916\pi\) | |||||||
\(758\) | 35.7693 | − | 36.8177i | 1.29920 | − | 1.33728i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.36774 | − | 2.17097i | −0.0858870 | − | 0.0787493i | ||||
\(761\) | 46.5579i | 1.68772i | 0.536562 | + | 0.843861i | \(0.319723\pi\) | ||||
−0.536562 | + | 0.843861i | \(0.680277\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.84810 | −0.103108 | ||||||||
\(764\) | −0.421560 | − | 14.5905i | −0.0152515 | − | 0.527864i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.2553 | − | 12.6145i | 0.442804 | − | 0.455782i | ||||
\(767\) | 14.9157 | 0.538575 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.6427 | 1.82622 | 0.913111 | − | 0.407711i | \(-0.133673\pi\) | ||||
0.913111 | + | 0.407711i | \(0.133673\pi\) | |||||||
\(770\) | 1.30994 | − | 1.34834i | 0.0472070 | − | 0.0485907i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.699530 | − | 24.2112i | −0.0251766 | − | 0.871379i | ||||
\(773\) | −6.66928 | −0.239877 | −0.119939 | − | 0.992781i | \(-0.538270\pi\) | ||||
−0.119939 | + | 0.992781i | \(0.538270\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 0.312926i | − | 0.0112406i | ||||||
\(776\) | 36.2599 | + | 33.2465i | 1.30166 | + | 1.19348i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.39682 | − | 5.55500i | 0.193485 | − | 0.199156i | ||||
\(779\) | 32.6044i | 1.16817i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 65.3718i | 2.33919i | ||||||||
\(782\) | 3.48873 | + | 3.38939i | 0.124757 | + | 0.121204i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.99333 | − | 0.230950i | 0.142619 | − | 0.00824822i | ||||
\(785\) | 3.21779i | 0.114848i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.759732 | −0.0270815 | −0.0135408 | − | 0.999908i | \(-0.504310\pi\) | ||||
−0.0135408 | + | 0.999908i | \(0.504310\pi\) | |||||||
\(788\) | −1.00462 | − | 34.7706i | −0.0357882 | − | 1.23865i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.02130 | + | 0.992214i | 0.0363361 | + | 0.0353014i | ||||
\(791\) | 2.88561 | 0.102600 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.3394 | 1.53903 | ||||||||
\(794\) | 9.72696 | + | 9.44998i | 0.345197 | + | 0.335367i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.14909 | − | 0.177665i | 0.217949 | − | 0.00629716i | ||||
\(797\) | −26.1758 | −0.927194 | −0.463597 | − | 0.886046i | \(-0.653441\pi\) | ||||
−0.463597 | + | 0.886046i | \(0.653441\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 26.6114i | − | 0.941442i | ||||||
\(800\) | 18.3463 | − | 21.2076i | 0.648640 | − | 0.749801i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.79236 | − | 1.74132i | −0.0632903 | − | 0.0614880i | ||||
\(803\) | 53.1488i | 1.87558i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 0.182258i | − | 0.00642376i | ||||||
\(806\) | −0.219181 | + | 0.225605i | −0.00772031 | + | 0.00794659i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −39.6672 | − | 36.3706i | −1.39549 | − | 1.27951i | ||||
\(809\) | 14.6876i | 0.516388i | 0.966093 | + | 0.258194i | \(0.0831273\pi\) | ||||
−0.966093 | + | 0.258194i | \(0.916873\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.13912 | −0.145344 | −0.0726721 | − | 0.997356i | \(-0.523153\pi\) | ||||
−0.0726721 | + | 0.997356i | \(0.523153\pi\) | |||||||
\(812\) | 6.41360 | − | 0.185307i | 0.225073 | − | 0.00650301i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −62.7682 | + | 64.6080i | −2.20003 | + | 2.26451i | ||||
\(815\) | −3.82168 | −0.133868 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.25289 | 0.218761 | ||||||||
\(818\) | −5.78944 | + | 5.95913i | −0.202423 | + | 0.208356i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.45895 | − | 0.0710460i | 0.0858701 | − | 0.00248103i | ||||
\(821\) | −30.7760 | −1.07409 | −0.537045 | − | 0.843554i | \(-0.680460\pi\) | ||||
−0.537045 | + | 0.843554i | \(0.680460\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.3750i | 0.989090i | 0.869152 | + | 0.494545i | \(0.164665\pi\) | ||||
−0.869152 | + | 0.494545i | \(0.835335\pi\) | |||||||
\(824\) | 20.6257 | − | 22.4951i | 0.718529 | − | 0.783655i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.17180 | − | 4.29408i | 0.145155 | − | 0.149410i | ||||
\(827\) | − | 26.2522i | − | 0.912880i | −0.889754 | − | 0.456440i | \(-0.849124\pi\) | ||
0.889754 | − | 0.456440i | \(-0.150876\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.40833i | 0.292033i | 0.989282 | + | 0.146017i | \(0.0466453\pi\) | ||||
−0.989282 | + | 0.146017i | \(0.953355\pi\) | |||||||
\(830\) | −1.57792 | − | 1.53299i | −0.0547706 | − | 0.0532109i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −28.0811 | + | 2.43946i | −0.973537 | + | 0.0845731i | ||||
\(833\) | − | 3.90616i | − | 0.135340i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.59401 | 0.0897695 | ||||||||
\(836\) | −70.4434 | + | 2.03531i | −2.43634 | + | 0.0703927i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −19.2175 | − | 18.6703i | −0.663858 | − | 0.644954i | ||||
\(839\) | 10.3099 | 0.355936 | 0.177968 | − | 0.984036i | \(-0.443048\pi\) | ||||
0.177968 | + | 0.984036i | \(0.443048\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.7078 | −0.645098 | ||||||||
\(842\) | −25.6220 | − | 24.8924i | −0.882991 | − | 0.857848i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.552868 | − | 19.1351i | −0.0190305 | − | 0.658657i | ||||
\(845\) | −0.121287 | −0.00417239 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 30.2408i | − | 1.03909i | ||||||
\(848\) | −50.4454 | + | 2.91746i | −1.73230 | + | 0.100186i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −19.6411 | − | 19.0818i | −0.673683 | − | 0.654500i | ||||
\(851\) | 8.73324i | 0.299372i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 42.6992i | − | 1.46199i | −0.682382 | − | 0.730996i | \(-0.739056\pi\) | ||
0.682382 | − | 0.730996i | \(-0.260944\pi\) | |||||||
\(854\) | 12.1217 | − | 12.4770i | 0.414795 | − | 0.426953i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.50180 | − | 10.3630i | 0.324765 | − | 0.354201i | ||||
\(857\) | 5.06990i | 0.173185i | 0.996244 | + | 0.0865923i | \(0.0275977\pi\) | ||||
−0.996244 | + | 0.0865923i | \(0.972402\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.9220 | 0.372654 | 0.186327 | − | 0.982488i | \(-0.440342\pi\) | ||||
0.186327 | + | 0.982488i | \(0.440342\pi\) | |||||||
\(860\) | −0.0136252 | − | 0.471578i | −0.000464617 | − | 0.0160807i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37.0308 | + | 38.1162i | −1.26127 | + | 1.29824i | ||||
\(863\) | 38.1030 | 1.29704 | 0.648520 | − | 0.761197i | \(-0.275388\pi\) | ||||
0.648520 | + | 0.761197i | \(0.275388\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.13674 | 0.0386502 | ||||||||
\(866\) | 20.7970 | − | 21.4066i | 0.706711 | − | 0.727425i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.00364627 | + | 0.126200i | 0.000123762 | + | 0.00428349i | ||||
\(869\) | 31.2378 | 1.05967 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 20.2476i | − | 0.686062i | ||||||
\(872\) | 5.44413 | − | 5.93757i | 0.184361 | − | 0.201072i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.76101 | + | 4.90056i | −0.161044 | + | 0.165764i | ||||
\(875\) | 2.06105i | 0.0696760i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 26.1674i | − | 0.883610i | −0.897111 | − | 0.441805i | \(-0.854338\pi\) | ||
0.897111 | − | 0.441805i | \(-0.145662\pi\) | |||||||
\(878\) | 2.92540 | + | 2.84209i | 0.0987273 | + | 0.0959160i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.306997 | + | 5.30824i | 0.0103489 | + | 0.178941i | ||||
\(881\) | 29.2903i | 0.986817i | 0.869798 | + | 0.493408i | \(0.164249\pi\) | ||||
−0.869798 | + | 0.493408i | \(0.835751\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.0887 | −1.65197 | −0.825983 | − | 0.563696i | \(-0.809379\pi\) | ||||
−0.825983 | + | 0.563696i | \(0.809379\pi\) | |||||||
\(884\) | 0.794962 | + | 27.5141i | 0.0267375 | + | 0.925400i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35.0938 | + | 34.0945i | 1.17900 | + | 1.14543i | ||||
\(887\) | 20.0617 | 0.673606 | 0.336803 | − | 0.941575i | \(-0.390654\pi\) | ||||
0.336803 | + | 0.941575i | \(0.390654\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.23082 | 0.242514 | ||||||||
\(890\) | −0.933651 | − | 0.907064i | −0.0312960 | − | 0.0304049i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −53.1167 | + | 1.53469i | −1.77848 | + | 0.0513853i | ||||
\(893\) | 37.3805 | 1.25089 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.01855i | − | 0.100899i | ||||||
\(896\) | −7.15175 | + | 8.76655i | −0.238923 | + | 0.292870i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.0792 | + | 14.6499i | 0.503201 | + | 0.488872i | ||||
\(899\) | 0.202518i | 0.00675434i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 49.3443i | 1.64390i | ||||||||
\(902\) | 37.6052 | − | 38.7074i | 1.25212 | − | 1.28882i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.51583 | + | 6.01577i | −0.183454 | + | 0.200082i | ||||
\(905\) | 3.57585i | 0.118865i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.0142 | 0.564948 | 0.282474 | − | 0.959275i | \(-0.408845\pi\) | ||||
0.282474 | + | 0.959275i | \(0.408845\pi\) | |||||||
\(908\) | 41.4518 | − | 1.19766i | 1.37563 | − | 0.0397457i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.718696 | − | 0.739761i | 0.0238245 | − | 0.0245228i | ||||
\(911\) | 8.54462 | 0.283096 | 0.141548 | − | 0.989931i | \(-0.454792\pi\) | ||||
0.141548 | + | 0.989931i | \(0.454792\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48.2631 | −1.59727 | ||||||||
\(914\) | 10.8436 | − | 11.1614i | 0.358675 | − | 0.369187i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 38.5090 | − | 1.11264i | 1.27237 | − | 0.0367625i | ||||
\(917\) | −12.8026 | −0.422780 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.49841i | 0.214363i | 0.994239 | + | 0.107181i | \(0.0341826\pi\) | ||||
−0.994239 | + | 0.107181i | \(0.965817\pi\) | |||||||
\(920\) | 0.379963 | + | 0.348386i | 0.0125270 | + | 0.0114859i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 32.4891 | − | 33.4414i | 1.06997 | − | 1.10133i | ||||
\(923\) | 35.8660i | 1.18055i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 49.1669i | − | 1.61660i | ||||||
\(926\) | −12.5116 | − | 12.1553i | −0.411157 | − | 0.399449i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −11.8733 | + | 13.7250i | −0.389759 | + | 0.450544i | ||||
\(929\) | − | 16.9216i | − | 0.555181i | −0.960699 | − | 0.277591i | \(-0.910464\pi\) | ||
0.960699 | − | 0.277591i | \(-0.0895358\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.48691 | 0.179826 | ||||||||
\(932\) | −49.9867 | + | 1.44426i | −1.63737 | + | 0.0473083i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 34.0071 | + | 33.0387i | 1.11275 | + | 1.08106i | ||||
\(935\) | 5.19237 | 0.169809 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.4249 | 0.471240 | 0.235620 | − | 0.971845i | \(-0.424288\pi\) | ||||
0.235620 | + | 0.971845i | \(0.424288\pi\) | |||||||
\(938\) | −5.82906 | − | 5.66307i | −0.190325 | − | 0.184906i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.0814532 | − | 2.81915i | −0.00265671 | − | 0.0919505i | ||||
\(941\) | 58.5364 | 1.90823 | 0.954116 | − | 0.299436i | \(-0.0967986\pi\) | ||||
0.954116 | + | 0.299436i | \(0.0967986\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.23218i | − | 0.170383i | ||||||
\(944\) | 0.977699 | + | 16.9053i | 0.0318214 | + | 0.550220i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.42333 | − | 7.21195i | −0.241353 | − | 0.234481i | ||||
\(947\) | − | 15.3006i | − | 0.497201i | −0.968606 | − | 0.248601i | \(-0.920029\pi\) | ||
0.968606 | − | 0.248601i | \(-0.0799707\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.1599i | 0.946571i | ||||||||
\(950\) | 26.8038 | − | 27.5894i | 0.869631 | − | 0.895120i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.14337 | + | 7.46661i | 0.263928 | + | 0.241994i | ||||
\(953\) | 14.9133i | 0.483089i | 0.970390 | + | 0.241544i | \(0.0776539\pi\) | ||||
−0.970390 | + | 0.241544i | \(0.922346\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.51068 | −0.0488845 | ||||||||
\(956\) | 0.868958 | + | 30.0752i | 0.0281041 | + | 0.972701i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.51743 | + | 9.79638i | −0.307494 | + | 0.316507i | ||||
\(959\) | −0.363873 | −0.0117501 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9960 | 0.999871 | ||||||||
\(962\) | −34.4376 | + | 35.4470i | −1.11031 | + | 1.14286i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.186729 | + | 6.46279i | 0.00601412 | + | 0.208153i | ||||
\(965\) | −2.50680 | −0.0806966 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.1896i | 0.874358i | 0.899375 | + | 0.437179i | \(0.144022\pi\) | ||||
−0.899375 | + | 0.437179i | \(0.855978\pi\) | |||||||
\(968\) | 63.0445 | + | 57.8051i | 2.02633 | + | 1.85793i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.54782 | − | 3.65181i | 0.113914 | − | 0.117252i | ||||
\(971\) | − | 35.0892i | − | 1.12607i | −0.826434 | − | 0.563034i | \(-0.809634\pi\) | ||
0.826434 | − | 0.563034i | \(-0.190366\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 9.32338i | − | 0.298894i | ||||||
\(974\) | 25.4606 | + | 24.7356i | 0.815811 | + | 0.792581i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.84082 | + | 49.1203i | 0.0909326 | + | 1.57230i | ||||
\(977\) | 32.0438i | 1.02517i | 0.858636 | + | 0.512586i | \(0.171312\pi\) | ||||
−0.858636 | + | 0.512586i | \(0.828688\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.5570 | −0.912687 | ||||||||
\(980\) | −0.0119562 | − | 0.413810i | −0.000381925 | − | 0.0132187i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.7037 | − | 10.3989i | −0.341569 | − | 0.331843i | ||||
\(983\) | −43.5719 | −1.38973 | −0.694864 | − | 0.719142i | \(-0.744535\pi\) | ||||
−0.694864 | + | 0.719142i | \(0.744535\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.60011 | −0.114709 | ||||||||
\(986\) | 12.7112 | + | 12.3492i | 0.404807 | + | 0.393280i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −38.6486 | + | 1.11667i | −1.22958 | + | 0.0355259i | ||||
\(989\) | −1.00343 | −0.0319073 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.2929i | 0.485794i | 0.970052 | + | 0.242897i | \(0.0780978\pi\) | ||||
−0.970052 | + | 0.242897i | \(0.921902\pi\) | |||||||
\(992\) | −0.270065 | − | 0.233628i | −0.00857456 | − | 0.00741771i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.3255 | + | 10.0314i | 0.327504 | + | 0.318178i | ||||
\(995\) | − | 0.636670i | − | 0.0201838i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 29.8050i | − | 0.943933i | −0.881616 | − | 0.471967i | \(-0.843544\pi\) | ||
0.881616 | − | 0.471967i | \(-0.156456\pi\) | |||||||
\(998\) | −11.4923 | + | 11.8291i | −0.363782 | + | 0.374444i | ||||
\(999\) | 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.c.323.23 | yes | 32 | |
3.2 | odd | 2 | inner | 1512.2.j.c.323.10 | yes | 32 | |
4.3 | odd | 2 | 6048.2.j.c.5615.14 | 32 | |||
8.3 | odd | 2 | inner | 1512.2.j.c.323.9 | ✓ | 32 | |
8.5 | even | 2 | 6048.2.j.c.5615.20 | 32 | |||
12.11 | even | 2 | 6048.2.j.c.5615.19 | 32 | |||
24.5 | odd | 2 | 6048.2.j.c.5615.13 | 32 | |||
24.11 | even | 2 | inner | 1512.2.j.c.323.24 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.c.323.9 | ✓ | 32 | 8.3 | odd | 2 | inner | |
1512.2.j.c.323.10 | yes | 32 | 3.2 | odd | 2 | inner | |
1512.2.j.c.323.23 | yes | 32 | 1.1 | even | 1 | trivial | |
1512.2.j.c.323.24 | yes | 32 | 24.11 | even | 2 | inner | |
6048.2.j.c.5615.13 | 32 | 24.5 | odd | 2 | |||
6048.2.j.c.5615.14 | 32 | 4.3 | odd | 2 | |||
6048.2.j.c.5615.19 | 32 | 12.11 | even | 2 | |||
6048.2.j.c.5615.20 | 32 | 8.5 | even | 2 |