Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1151,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bf (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.9 | ||
Character | \(\chi\) | \(=\) | 3150.1151 |
Dual form | 3150.2.bf.e.1601.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.397202 | + | 2.61577i | 0.150128 | + | 0.988667i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.429853 | + | 0.248176i | 0.129606 | + | 0.0748278i | 0.563401 | − | 0.826184i | \(-0.309493\pi\) |
−0.433795 | + | 0.901011i | \(0.642826\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.74440i | 0.761160i | 0.924748 | + | 0.380580i | \(0.124276\pi\) | ||||
−0.924748 | + | 0.380580i | \(0.875724\pi\) | |||||||
\(14\) | 1.65187 | + | 2.06672i | 0.441481 | + | 0.552354i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.82992 | + | 3.16952i | −0.443821 | + | 0.768721i | −0.997969 | − | 0.0636974i | \(-0.979711\pi\) |
0.554148 | + | 0.832418i | \(0.313044\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.12125 | − | 1.80205i | 0.716064 | − | 0.413420i | −0.0972384 | − | 0.995261i | \(-0.531001\pi\) |
0.813302 | + | 0.581841i | \(0.197668\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.496352 | 0.105823 | ||||||||
\(23\) | −5.56351 | + | 3.21210i | −1.16007 | + | 0.669768i | −0.951321 | − | 0.308200i | \(-0.900273\pi\) |
−0.208751 | + | 0.977969i | \(0.566940\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.37220 | + | 2.37672i | 0.269111 | + | 0.466114i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.46392 | + | 0.963896i | 0.465637 | + | 0.182159i | ||||
\(29\) | 8.87959i | 1.64890i | 0.565937 | + | 0.824449i | \(0.308515\pi\) | ||||
−0.565937 | + | 0.824449i | \(0.691485\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.90736 | − | 3.98797i | −1.24060 | − | 0.716260i | −0.271383 | − | 0.962472i | \(-0.587481\pi\) |
−0.969216 | + | 0.246211i | \(0.920814\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.65984i | 0.627658i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.14545 | − | 1.98397i | −0.188311 | − | 0.326163i | 0.756377 | − | 0.654136i | \(-0.226968\pi\) |
−0.944687 | + | 0.327973i | \(0.893634\pi\) | |||||||
\(38\) | 1.80205 | − | 3.12125i | 0.292332 | − | 0.506334i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.22816 | −0.347980 | −0.173990 | − | 0.984747i | \(-0.555666\pi\) | ||||
−0.173990 | + | 0.984747i | \(0.555666\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.22575 | 0.339424 | 0.169712 | − | 0.985494i | \(-0.445716\pi\) | ||||
0.169712 | + | 0.985494i | \(0.445716\pi\) | |||||||
\(44\) | 0.429853 | − | 0.248176i | 0.0648028 | − | 0.0374139i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.21210 | + | 5.56351i | −0.473598 | + | 0.820295i | ||||
\(47\) | 3.27213 | + | 5.66749i | 0.477289 | + | 0.826688i | 0.999661 | − | 0.0260292i | \(-0.00828628\pi\) |
−0.522373 | + | 0.852717i | \(0.674953\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.68446 | + | 2.07798i | −0.954923 | + | 0.296854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.37672 | + | 1.37220i | 0.329592 | + | 0.190290i | ||||
\(53\) | −6.72594 | − | 3.88322i | −0.923879 | − | 0.533402i | −0.0390085 | − | 0.999239i | \(-0.512420\pi\) |
−0.884870 | + | 0.465837i | \(0.845753\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.61577 | − | 0.397202i | 0.349546 | − | 0.0530784i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.43979 | + | 7.68995i | 0.582973 | + | 1.00974i | ||||
\(59\) | −3.05194 | + | 5.28611i | −0.397328 | + | 0.688193i | −0.993395 | − | 0.114742i | \(-0.963396\pi\) |
0.596067 | + | 0.802935i | \(0.296729\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.24271 | − | 1.87218i | 0.415187 | − | 0.239708i | −0.277829 | − | 0.960630i | \(-0.589615\pi\) |
0.693016 | + | 0.720922i | \(0.256282\pi\) | |||||||
\(62\) | −7.97593 | −1.01294 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.08889 | + | 7.08216i | −0.499537 | + | 0.865224i | −1.00000 | 0.000534152i | \(-0.999830\pi\) | |
0.500463 | + | 0.865758i | \(0.333163\pi\) | |||||||
\(68\) | 1.82992 | + | 3.16952i | 0.221911 | + | 0.384360i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.3761i | − | 1.23141i | −0.787975 | − | 0.615707i | \(-0.788871\pi\) | ||
0.787975 | − | 0.615707i | \(-0.211129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3165 | + | 6.53361i | 1.32450 | + | 0.764701i | 0.984443 | − | 0.175704i | \(-0.0562201\pi\) |
0.340058 | + | 0.940405i | \(0.389553\pi\) | |||||||
\(74\) | −1.98397 | − | 1.14545i | −0.230632 | − | 0.133156i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.60411i | − | 0.413420i | ||||||
\(77\) | −0.478431 | + | 1.22297i | −0.0545223 | + | 0.139370i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.44344 | + | 7.69627i | 0.499926 | + | 0.865898i | 1.00000 | 8.52501e-5i | \(-2.71360e-5\pi\) | |
−0.500074 | + | 0.865983i | \(0.666694\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.92964 | + | 1.11408i | −0.213093 | + | 0.123030i | ||||
\(83\) | −4.79091 | −0.525871 | −0.262935 | − | 0.964813i | \(-0.584691\pi\) | ||||
−0.262935 | + | 0.964813i | \(0.584691\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.92756 | − | 1.11288i | 0.207854 | − | 0.120005i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.248176 | − | 0.429853i | 0.0264556 | − | 0.0458225i | ||||
\(89\) | 0.743586 | + | 1.28793i | 0.0788199 | + | 0.136520i | 0.902741 | − | 0.430184i | \(-0.141551\pi\) |
−0.823921 | + | 0.566704i | \(0.808218\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.17871 | + | 1.09008i | −0.752534 | + | 0.114272i | ||||
\(92\) | 6.42419i | 0.669768i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.66749 | + | 3.27213i | 0.584557 | + | 0.337494i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.05174i | 0.919064i | 0.888161 | + | 0.459532i | \(0.151983\pi\) | ||||
−0.888161 | + | 0.459532i | \(0.848017\pi\) | |||||||
\(98\) | −4.74992 | + | 5.14181i | −0.479815 | + | 0.519401i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.50180 | − | 2.60119i | 0.149434 | − | 0.258828i | −0.781584 | − | 0.623800i | \(-0.785588\pi\) |
0.931019 | + | 0.364972i | \(0.118921\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4491 | − | 7.18752i | 1.22665 | − | 0.708207i | 0.260323 | − | 0.965522i | \(-0.416171\pi\) |
0.966328 | + | 0.257314i | \(0.0828376\pi\) | |||||||
\(104\) | 2.74440 | 0.269111 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.76645 | −0.754344 | ||||||||
\(107\) | −1.84141 | + | 1.06314i | −0.178016 | + | 0.102778i | −0.586360 | − | 0.810050i | \(-0.699440\pi\) |
0.408344 | + | 0.912828i | \(0.366106\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.95181 | + | 6.84474i | −0.378515 | + | 0.655607i | −0.990846 | − | 0.134994i | \(-0.956899\pi\) |
0.612331 | + | 0.790601i | \(0.290232\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.06672 | − | 1.65187i | 0.195287 | − | 0.156087i | ||||
\(113\) | 12.2968i | 1.15678i | 0.815760 | + | 0.578391i | \(0.196319\pi\) | ||||
−0.815760 | + | 0.578391i | \(0.803681\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.68995 | + | 4.43979i | 0.713994 | + | 0.412224i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.10388i | 0.561907i | ||||||||
\(119\) | −9.01756 | − | 3.52771i | −0.826638 | − | 0.323384i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.37682 | − | 9.31292i | −0.488802 | − | 0.846629i | ||||
\(122\) | 1.87218 | − | 3.24271i | 0.169499 | − | 0.293581i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.90736 | + | 3.98797i | −0.620299 | + | 0.358130i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.753445 | 0.0668574 | 0.0334287 | − | 0.999441i | \(-0.489357\pi\) | ||||
0.0334287 | + | 0.999441i | \(0.489357\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.35624 | + | 11.0093i | 0.555347 | + | 0.961890i | 0.997876 | + | 0.0651355i | \(0.0207479\pi\) |
−0.442529 | + | 0.896754i | \(0.645919\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.95352 | + | 7.44868i | 0.516236 | + | 0.645882i | ||||
\(134\) | 8.17778i | 0.706452i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.16952 | + | 1.82992i | 0.271784 | + | 0.156914i | ||||
\(137\) | −3.73673 | − | 2.15740i | −0.319250 | − | 0.184319i | 0.331808 | − | 0.943347i | \(-0.392341\pi\) |
−0.651058 | + | 0.759028i | \(0.725675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0681276i | 0.00577851i | 0.999996 | + | 0.00288926i | \(0.000919680\pi\) | ||||
−0.999996 | + | 0.00288926i | \(0.999080\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.18804 | − | 8.98595i | −0.435371 | − | 0.754084i | ||||
\(143\) | −0.681094 | + | 1.17969i | −0.0569560 | + | 0.0986507i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.0672 | 1.08145 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.29090 | −0.188311 | ||||||||
\(149\) | −14.4611 | + | 8.34911i | −1.18470 | + | 0.683986i | −0.957097 | − | 0.289768i | \(-0.906422\pi\) |
−0.227602 | + | 0.973754i | \(0.573088\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.51016 | − | 11.2759i | 0.529789 | − | 0.917622i | −0.469607 | − | 0.882876i | \(-0.655604\pi\) |
0.999396 | − | 0.0347463i | \(-0.0110623\pi\) | |||||||
\(152\) | −1.80205 | − | 3.12125i | −0.146166 | − | 0.253167i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.197152 | + | 1.29834i | 0.0158870 | + | 0.104623i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.8242 | + | 7.40408i | 1.02349 | + | 0.590910i | 0.915112 | − | 0.403200i | \(-0.132102\pi\) |
0.108374 | + | 0.994110i | \(0.465436\pi\) | |||||||
\(158\) | 7.69627 | + | 4.44344i | 0.612282 | + | 0.353501i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.6119 | − | 13.2770i | −0.836337 | − | 1.04637i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.68966 | + | 13.3189i | 0.602301 | + | 1.04322i | 0.992472 | + | 0.122473i | \(0.0390825\pi\) |
−0.390171 | + | 0.920742i | \(0.627584\pi\) | |||||||
\(164\) | −1.11408 | + | 1.92964i | −0.0869950 | + | 0.150680i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.14905 | + | 2.39546i | −0.322029 | + | 0.185923i | ||||
\(167\) | 24.5161 | 1.89712 | 0.948558 | − | 0.316603i | \(-0.102542\pi\) | ||||
0.948558 | + | 0.316603i | \(0.102542\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.46825 | 0.420635 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.11288 | − | 1.92756i | 0.0848561 | − | 0.146975i | ||||
\(173\) | −6.26213 | − | 10.8463i | −0.476101 | − | 0.824631i | 0.523524 | − | 0.852011i | \(-0.324617\pi\) |
−0.999625 | + | 0.0273795i | \(0.991284\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.496352i | − | 0.0374139i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.28793 | + | 0.743586i | 0.0965343 | + | 0.0557341i | ||||
\(179\) | 1.58961 | + | 0.917762i | 0.118813 | + | 0.0685968i | 0.558229 | − | 0.829687i | \(-0.311481\pi\) |
−0.439416 | + | 0.898284i | \(0.644814\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 23.6564i | − | 1.75837i | −0.476481 | − | 0.879185i | \(-0.658088\pi\) | ||
0.476481 | − | 0.879185i | \(-0.341912\pi\) | |||||||
\(182\) | −5.67191 | + | 4.53340i | −0.420430 | + | 0.336038i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.21210 | + | 5.56351i | 0.236799 | + | 0.410148i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.57319 | + | 0.908284i | −0.115043 | + | 0.0664203i | ||||
\(188\) | 6.54425 | 0.477289 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.02253 | + | 4.05446i | −0.508133 | + | 0.293371i | −0.732066 | − | 0.681234i | \(-0.761444\pi\) |
0.223933 | + | 0.974605i | \(0.428110\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.02502 | − | 10.4356i | 0.433691 | − | 0.751174i | −0.563497 | − | 0.826118i | \(-0.690544\pi\) |
0.997188 | + | 0.0749438i | \(0.0238777\pi\) | |||||||
\(194\) | 4.52587 | + | 7.83903i | 0.324938 | + | 0.562810i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.54265 | + | 6.82790i | −0.110189 | + | 0.487707i | ||||
\(197\) | 12.7463i | 0.908137i | 0.890967 | + | 0.454068i | \(0.150028\pi\) | ||||
−0.890967 | + | 0.454068i | \(0.849972\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.4954 | + | 9.52361i | 1.16933 | + | 0.675111i | 0.953521 | − | 0.301325i | \(-0.0974290\pi\) |
0.215805 | + | 0.976436i | \(0.430762\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 3.00359i | − | 0.211332i | ||||||
\(203\) | −23.2269 | + | 3.52699i | −1.63021 | + | 0.247546i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.18752 | − | 12.4491i | 0.500778 | − | 0.867373i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.37672 | − | 1.37220i | 0.164796 | − | 0.0951450i | ||||
\(209\) | 1.78891 | 0.123741 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.92057 | −0.614117 | −0.307059 | − | 0.951691i | \(-0.599345\pi\) | ||||
−0.307059 | + | 0.951691i | \(0.599345\pi\) | |||||||
\(212\) | −6.72594 | + | 3.88322i | −0.461939 | + | 0.266701i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.06314 | + | 1.84141i | −0.0726748 | + | 0.125876i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.68797 | − | 19.6521i | 0.521893 | − | 1.33407i | ||||
\(218\) | 7.90363i | 0.535301i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.69843 | − | 5.02204i | −0.585120 | − | 0.337819i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.5443i | 1.57664i | 0.615265 | + | 0.788320i | \(0.289049\pi\) | ||||
−0.615265 | + | 0.788320i | \(0.710951\pi\) | |||||||
\(224\) | 0.963896 | − | 2.46392i | 0.0644030 | − | 0.164628i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.14838 | + | 10.6493i | 0.408984 | + | 0.708382i | ||||
\(227\) | −4.66223 | + | 8.07522i | −0.309443 | + | 0.535971i | −0.978241 | − | 0.207473i | \(-0.933476\pi\) |
0.668797 | + | 0.743445i | \(0.266809\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.1545 | − | 11.6362i | 1.33185 | − | 0.768944i | 0.346266 | − | 0.938136i | \(-0.387449\pi\) |
0.985583 | + | 0.169193i | \(0.0541160\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.87959 | 0.582973 | ||||||||
\(233\) | −10.9295 | + | 6.31017i | −0.716018 | + | 0.413393i | −0.813285 | − | 0.581865i | \(-0.802323\pi\) |
0.0972676 | + | 0.995258i | \(0.468990\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.05194 | + | 5.28611i | 0.198664 | + | 0.344097i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.57329 | + | 1.45370i | −0.620544 | + | 0.0942292i | ||||
\(239\) | − | 16.1198i | − | 1.04270i | −0.853342 | − | 0.521351i | \(-0.825428\pi\) | ||
0.853342 | − | 0.521351i | \(-0.174572\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.3222 | − | 10.5783i | −1.18024 | − | 0.681411i | −0.224168 | − | 0.974550i | \(-0.571966\pi\) |
−0.956070 | + | 0.293140i | \(0.905300\pi\) | |||||||
\(242\) | −9.31292 | − | 5.37682i | −0.598657 | − | 0.345635i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 3.74436i | − | 0.239708i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.94556 | + | 8.56597i | 0.314679 | + | 0.545039i | ||||
\(248\) | −3.98797 | + | 6.90736i | −0.253236 | + | 0.438618i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.06317 | −0.382704 | −0.191352 | − | 0.981522i | \(-0.561287\pi\) | ||||
−0.191352 | + | 0.981522i | \(0.561287\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.18866 | −0.200469 | ||||||||
\(254\) | 0.652503 | − | 0.376723i | 0.0409416 | − | 0.0236377i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −5.49266 | − | 9.51357i | −0.342623 | − | 0.593440i | 0.642296 | − | 0.766457i | \(-0.277982\pi\) |
−0.984919 | + | 0.173016i | \(0.944649\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.73464 | − | 3.78426i | 0.294196 | − | 0.235143i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.0093 | + | 6.35624i | 0.680159 | + | 0.392690i | ||||
\(263\) | 1.15937 | + | 0.669365i | 0.0714901 | + | 0.0412748i | 0.535319 | − | 0.844650i | \(-0.320191\pi\) |
−0.463829 | + | 0.885925i | \(0.653525\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.88024 | + | 3.47399i | 0.544482 | + | 0.213004i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.08889 | + | 7.08216i | 0.249769 | + | 0.432612i | ||||
\(269\) | −0.311161 | + | 0.538946i | −0.0189718 | + | 0.0328601i | −0.875355 | − | 0.483480i | \(-0.839373\pi\) |
0.856384 | + | 0.516340i | \(0.172706\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.4634 | − | 10.6598i | 1.12157 | − | 0.647539i | 0.179769 | − | 0.983709i | \(-0.442465\pi\) |
0.941801 | + | 0.336170i | \(0.109132\pi\) | |||||||
\(272\) | 3.65984 | 0.221911 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.31480 | −0.260667 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.593544 | + | 1.02805i | −0.0356626 | + | 0.0617694i | −0.883306 | − | 0.468797i | \(-0.844688\pi\) |
0.847643 | + | 0.530567i | \(0.178021\pi\) | |||||||
\(278\) | 0.0340638 | + | 0.0590003i | 0.00204301 | + | 0.00353860i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.97593i | − | 0.117874i | −0.998262 | − | 0.0589370i | \(-0.981229\pi\) | ||
0.998262 | − | 0.0589370i | \(-0.0187711\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.4960 | − | 13.5654i | −1.39669 | − | 0.806382i | −0.402650 | − | 0.915354i | \(-0.631911\pi\) |
−0.994045 | + | 0.108972i | \(0.965244\pi\) | |||||||
\(284\) | −8.98595 | − | 5.18804i | −0.533218 | − | 0.307853i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.36219i | 0.0805479i | ||||||||
\(287\) | −0.885030 | − | 5.82835i | −0.0522417 | − | 0.344036i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.80278 | + | 3.12250i | 0.106046 | + | 0.183677i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.3165 | − | 6.53361i | 0.662250 | − | 0.382350i | ||||
\(293\) | 10.3808 | 0.606456 | 0.303228 | − | 0.952918i | \(-0.401936\pi\) | ||||
0.303228 | + | 0.952918i | \(0.401936\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.98397 | + | 1.14545i | −0.115316 | + | 0.0665778i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.34911 | + | 14.4611i | −0.483651 | + | 0.837708i | ||||
\(299\) | −8.81529 | − | 15.2685i | −0.509801 | − | 0.883002i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.884074 | + | 5.82205i | 0.0509572 | + | 0.335577i | ||||
\(302\) | − | 13.0203i | − | 0.749235i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.12125 | − | 1.80205i | −0.179016 | − | 0.103355i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.1364i | 0.806808i | 0.915022 | + | 0.403404i | \(0.132173\pi\) | ||||
−0.915022 | + | 0.403404i | \(0.867827\pi\) | |||||||
\(308\) | 0.819908 | + | 1.02582i | 0.0467186 | + | 0.0584515i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.32643 | − | 5.76155i | 0.188625 | − | 0.326708i | −0.756167 | − | 0.654378i | \(-0.772930\pi\) |
0.944792 | + | 0.327671i | \(0.106264\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.5184 | − | 6.07282i | 0.594537 | − | 0.343256i | −0.172352 | − | 0.985035i | \(-0.555137\pi\) |
0.766890 | + | 0.641779i | \(0.221803\pi\) | |||||||
\(314\) | 14.8082 | 0.835673 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.88688 | 0.499926 | ||||||||
\(317\) | 26.6051 | − | 15.3605i | 1.49429 | − | 0.862730i | 0.494314 | − | 0.869283i | \(-0.335419\pi\) |
0.999979 | + | 0.00655283i | \(0.00208584\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.20370 | + | 3.81692i | −0.123383 | + | 0.213706i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15.8287 | − | 6.19225i | −0.882099 | − | 0.345081i | ||||
\(323\) | 13.1905i | 0.733937i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.3189 | + | 7.68966i | 0.737665 | + | 0.425891i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.22816i | 0.123030i | ||||||||
\(329\) | −13.5251 | + | 10.8103i | −0.745664 | + | 0.595989i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.5140 | + | 26.8710i | 0.852724 | + | 1.47696i | 0.878741 | + | 0.477300i | \(0.158384\pi\) |
−0.0260166 | + | 0.999662i | \(0.508282\pi\) | |||||||
\(332\) | −2.39546 | + | 4.14905i | −0.131468 | + | 0.227709i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 21.2316 | − | 12.2581i | 1.16174 | − | 0.670732i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.91470 | −0.376668 | −0.188334 | − | 0.982105i | \(-0.560309\pi\) | ||||
−0.188334 | + | 0.982105i | \(0.560309\pi\) | |||||||
\(338\) | 4.73565 | − | 2.73413i | 0.257585 | − | 0.148717i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.97943 | − | 3.42848i | −0.107192 | − | 0.185663i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.09058 | − | 16.6596i | −0.436850 | − | 0.899534i | ||||
\(344\) | − | 2.22575i | − | 0.120005i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.8463 | − | 6.26213i | −0.583103 | − | 0.336654i | ||||
\(347\) | 6.49006 | + | 3.74704i | 0.348405 | + | 0.201152i | 0.663982 | − | 0.747748i | \(-0.268865\pi\) |
−0.315578 | + | 0.948900i | \(0.602198\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.4552i | − | 0.666714i | −0.942801 | − | 0.333357i | \(-0.891819\pi\) | ||
0.942801 | − | 0.333357i | \(-0.108181\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.248176 | − | 0.429853i | −0.0132278 | − | 0.0229113i | ||||
\(353\) | 9.47011 | − | 16.4027i | 0.504043 | − | 0.873028i | −0.495946 | − | 0.868353i | \(-0.665179\pi\) |
0.999989 | − | 0.00467471i | \(-0.00148801\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.48717 | 0.0788199 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.83552 | 0.0970105 | ||||||||
\(359\) | 23.0590 | − | 13.3131i | 1.21701 | − | 0.702639i | 0.252730 | − | 0.967537i | \(-0.418671\pi\) |
0.964277 | + | 0.264898i | \(0.0853381\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00520 | + | 5.20516i | −0.158168 | + | 0.273956i | ||||
\(362\) | −11.8282 | − | 20.4871i | −0.621677 | − | 1.07678i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.64532 | + | 6.76199i | −0.138652 | + | 0.354425i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.45017 | + | 5.45606i | 0.493295 | + | 0.284804i | 0.725940 | − | 0.687758i | \(-0.241405\pi\) |
−0.232646 | + | 0.972562i | \(0.574738\pi\) | |||||||
\(368\) | 5.56351 | + | 3.21210i | 0.290018 | + | 0.167442i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.48604 | − | 19.1359i | 0.388656 | − | 0.993487i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.2539 | + | 19.4924i | 0.582707 | + | 1.00928i | 0.995157 | + | 0.0982976i | \(0.0313397\pi\) |
−0.412450 | + | 0.910980i | \(0.635327\pi\) | |||||||
\(374\) | −0.908284 | + | 1.57319i | −0.0469663 | + | 0.0813480i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.66749 | − | 3.27213i | 0.292278 | − | 0.168747i | ||||
\(377\) | −24.3692 | −1.25508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.25909 | −0.167408 | −0.0837040 | − | 0.996491i | \(-0.526675\pi\) | ||||
−0.0837040 | + | 0.996491i | \(0.526675\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.05446 | + | 7.02253i | −0.207444 | + | 0.359304i | ||||
\(383\) | 8.66098 | + | 15.0013i | 0.442555 | + | 0.766528i | 0.997878 | − | 0.0651064i | \(-0.0207387\pi\) |
−0.555323 | + | 0.831635i | \(0.687405\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 12.0500i | − | 0.613331i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.83903 | + | 4.52587i | 0.397967 | + | 0.229766i | ||||
\(389\) | −27.4515 | − | 15.8491i | −1.39185 | − | 0.803582i | −0.398326 | − | 0.917244i | \(-0.630409\pi\) |
−0.993520 | + | 0.113662i | \(0.963742\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 23.5115i | − | 1.18903i | ||||||
\(392\) | 2.07798 | + | 6.68446i | 0.104954 | + | 0.337616i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.37315 | + | 11.0386i | 0.321075 | + | 0.556118i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.0224 | + | 16.7561i | −1.45659 | + | 0.840964i | −0.998842 | − | 0.0481170i | \(-0.984678\pi\) |
−0.457750 | + | 0.889081i | \(0.651345\pi\) | |||||||
\(398\) | 19.0472 | 0.954751 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.0404 | + | 17.9212i | −1.55008 | + | 0.894940i | −0.551947 | + | 0.833879i | \(0.686115\pi\) |
−0.998134 | + | 0.0610611i | \(0.980552\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.9446 | − | 18.9566i | 0.545189 | − | 0.944295i | ||||
\(404\) | −1.50180 | − | 2.60119i | −0.0747171 | − | 0.129414i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.3516 | + | 14.6679i | −0.910775 | + | 0.727957i | ||||
\(407\) | − | 1.13709i | − | 0.0563635i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.3474 | − | 12.3249i | −1.05556 | − | 0.609429i | −0.131361 | − | 0.991335i | \(-0.541935\pi\) |
−0.924201 | + | 0.381905i | \(0.875268\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 14.3750i | − | 0.708207i | ||||||
\(413\) | −15.0395 | − | 5.88350i | −0.740044 | − | 0.289508i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.37220 | − | 2.37672i | 0.0672777 | − | 0.116528i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.54924 | − | 0.894453i | 0.0757757 | − | 0.0437491i | ||||
\(419\) | 10.6574 | 0.520646 | 0.260323 | − | 0.965522i | \(-0.416171\pi\) | ||||
0.260323 | + | 0.965522i | \(0.416171\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.6815 | 1.10543 | 0.552714 | − | 0.833371i | \(-0.313592\pi\) | ||||
0.552714 | + | 0.833371i | \(0.313592\pi\) | |||||||
\(422\) | −7.72544 | + | 4.46028i | −0.376068 | + | 0.217123i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.88322 | + | 6.72594i | −0.188586 | + | 0.326641i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.18520 | + | 7.73854i | 0.299323 | + | 0.374494i | ||||
\(428\) | 2.12628i | 0.102778i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.0439 | − | 15.0364i | −1.25449 | − | 0.724279i | −0.282491 | − | 0.959270i | \(-0.591161\pi\) |
−0.971998 | + | 0.234991i | \(0.924494\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 14.9203i | − | 0.717025i | −0.933525 | − | 0.358512i | \(-0.883284\pi\) | ||
0.933525 | − | 0.358512i | \(-0.116716\pi\) | |||||||
\(434\) | −3.16806 | − | 20.8632i | −0.152072 | − | 1.00146i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.95181 | + | 6.84474i | 0.189258 | + | 0.327804i | ||||
\(437\) | −11.5767 | + | 20.0515i | −0.553791 | + | 0.959194i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.1126 | − | 6.41586i | 0.530375 | − | 0.306212i | −0.210794 | − | 0.977530i | \(-0.567605\pi\) |
0.741169 | + | 0.671318i | \(0.234272\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.0441 | −0.477748 | ||||||||
\(443\) | −17.6792 | + | 10.2071i | −0.839963 | + | 0.484953i | −0.857252 | − | 0.514898i | \(-0.827830\pi\) |
0.0172887 | + | 0.999851i | \(0.494497\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.7721 | + | 20.3899i | 0.557426 | + | 0.965491i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.397202 | − | 2.61577i | −0.0187660 | − | 0.123583i | ||||
\(449\) | 20.8404i | 0.983519i | 0.870731 | + | 0.491760i | \(0.163646\pi\) | ||||
−0.870731 | + | 0.491760i | \(0.836354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.957782 | − | 0.552976i | −0.0451002 | − | 0.0260386i | ||||
\(452\) | 10.6493 | + | 6.14838i | 0.500901 | + | 0.289196i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.32446i | 0.437619i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.01424 | − | 13.8811i | −0.374890 | − | 0.649329i | 0.615420 | − | 0.788199i | \(-0.288986\pi\) |
−0.990311 | + | 0.138870i | \(0.955653\pi\) | |||||||
\(458\) | 11.6362 | − | 20.1545i | 0.543725 | − | 0.941760i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.98400 | −0.0924039 | −0.0462020 | − | 0.998932i | \(-0.514712\pi\) | ||||
−0.0462020 | + | 0.998932i | \(0.514712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.3987 | −1.69159 | −0.845796 | − | 0.533506i | \(-0.820874\pi\) | ||||
−0.845796 | + | 0.533506i | \(0.820874\pi\) | |||||||
\(464\) | 7.68995 | − | 4.43979i | 0.356997 | − | 0.206112i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.31017 | + | 10.9295i | −0.292313 | + | 0.506301i | ||||
\(467\) | −15.5372 | − | 26.9113i | −0.718977 | − | 1.24530i | −0.961405 | − | 0.275136i | \(-0.911277\pi\) |
0.242428 | − | 0.970169i | \(-0.422056\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.1494 | − | 7.88253i | −0.930413 | − | 0.363981i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.28611 | + | 3.05194i | 0.243313 | + | 0.140477i | ||||
\(473\) | 0.956747 | + | 0.552378i | 0.0439913 | + | 0.0253984i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.56386 | + | 6.04558i | −0.346689 | + | 0.277099i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.05990 | − | 13.9601i | −0.368651 | − | 0.638522i | ||||
\(479\) | 18.2404 | − | 31.5933i | 0.833426 | − | 1.44354i | −0.0618788 | − | 0.998084i | \(-0.519709\pi\) |
0.895305 | − | 0.445453i | \(-0.146957\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.44483 | − | 3.14357i | 0.248263 | − | 0.143335i | ||||
\(482\) | −21.1567 | −0.963660 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.7536 | −0.488802 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.06672 | − | 12.2399i | 0.320224 | − | 0.554644i | −0.660310 | − | 0.750993i | \(-0.729575\pi\) |
0.980534 | + | 0.196349i | \(0.0629086\pi\) | |||||||
\(488\) | −1.87218 | − | 3.24271i | −0.0847496 | − | 0.146791i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 32.5466i | − | 1.46881i | −0.678714 | − | 0.734403i | \(-0.737462\pi\) | ||
0.678714 | − | 0.734403i | \(-0.262538\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.1440 | − | 16.2489i | −1.26754 | − | 0.731815i | ||||
\(494\) | 8.56597 | + | 4.94556i | 0.385401 | + | 0.222511i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.97593i | 0.358130i | ||||||||
\(497\) | 27.1414 | − | 4.12140i | 1.21746 | − | 0.184870i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.87396 | − | 10.1740i | −0.262955 | − | 0.455451i | 0.704071 | − | 0.710130i | \(-0.251364\pi\) |
−0.967026 | + | 0.254679i | \(0.918030\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.25086 | + | 3.03158i | −0.234357 | + | 0.135306i | ||||
\(503\) | 24.5250 | 1.09352 | 0.546758 | − | 0.837291i | \(-0.315862\pi\) | ||||
0.546758 | + | 0.837291i | \(0.315862\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.76146 | + | 1.59433i | −0.122762 | + | 0.0708766i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.376723 | − | 0.652503i | 0.0167144 | − | 0.0289501i | ||||
\(509\) | −5.84634 | − | 10.1262i | −0.259135 | − | 0.448834i | 0.706876 | − | 0.707338i | \(-0.250104\pi\) |
−0.966010 | + | 0.258503i | \(0.916771\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.5954 | + | 32.1966i | −0.557189 | + | 1.42429i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.51357 | − | 5.49266i | −0.419626 | − | 0.242271i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.24825i | 0.142858i | ||||||||
\(518\) | 2.20819 | − | 5.64459i | 0.0970221 | − | 0.248009i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.8674 | + | 25.7511i | −0.651354 | + | 1.12818i | 0.331441 | + | 0.943476i | \(0.392465\pi\) |
−0.982795 | + | 0.184702i | \(0.940868\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.90024 | − | 2.82915i | 0.214272 | − | 0.123710i | −0.389023 | − | 0.921228i | \(-0.627187\pi\) |
0.603295 | + | 0.797518i | \(0.293854\pi\) | |||||||
\(524\) | 12.7125 | 0.555347 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.33873 | 0.0583714 | ||||||||
\(527\) | 25.2799 | − | 14.5953i | 1.10121 | − | 0.635783i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.13513 | − | 15.8225i | 0.397179 | − | 0.687935i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9.42751 | − | 1.43156i | 0.408734 | − | 0.0620660i | ||||
\(533\) | − | 6.11497i | − | 0.264869i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.08216 | + | 4.08889i | 0.305903 | + | 0.176613i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.622322i | 0.0268302i | ||||||||
\(539\) | −3.38904 | − | 0.765697i | −0.145976 | − | 0.0329809i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.6742 | + | 30.6126i | 0.759874 | + | 1.31614i | 0.942915 | + | 0.333035i | \(0.108073\pi\) |
−0.183041 | + | 0.983105i | \(0.558594\pi\) | |||||||
\(542\) | 10.6598 | − | 18.4634i | 0.457879 | − | 0.793070i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.16952 | − | 1.82992i | 0.135892 | − | 0.0784572i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.4806 | 0.918445 | 0.459223 | − | 0.888321i | \(-0.348128\pi\) | ||||
0.459223 | + | 0.888321i | \(0.348128\pi\) | |||||||
\(548\) | −3.73673 | + | 2.15740i | −0.159625 | + | 0.0921595i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.0015 | + | 27.7154i | 0.681687 | + | 1.18072i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.3667 | + | 14.6800i | −0.781031 | + | 0.624256i | ||||
\(554\) | 1.18709i | 0.0504345i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.0590003 | + | 0.0340638i | 0.00250217 | + | 0.00144463i | ||||
\(557\) | −34.4939 | − | 19.9150i | −1.46155 | − | 0.843828i | −0.462469 | − | 0.886635i | \(-0.653036\pi\) |
−0.999083 | + | 0.0428076i | \(0.986370\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.10836i | 0.258356i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.987964 | − | 1.71120i | −0.0416747 | − | 0.0721828i | ||||
\(563\) | 5.17056 | − | 8.95567i | 0.217913 | − | 0.377437i | −0.736257 | − | 0.676702i | \(-0.763408\pi\) |
0.954170 | + | 0.299266i | \(0.0967417\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −27.1309 | −1.14040 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.3761 | −0.435371 | ||||||||
\(569\) | −24.3464 | + | 14.0564i | −1.02065 | + | 0.589275i | −0.914293 | − | 0.405053i | \(-0.867253\pi\) |
−0.106361 | + | 0.994328i | \(0.533920\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.7146 | − | 23.7544i | 0.573938 | − | 0.994090i | −0.422218 | − | 0.906494i | \(-0.638748\pi\) |
0.996156 | − | 0.0875958i | \(-0.0279184\pi\) | |||||||
\(572\) | 0.681094 | + | 1.17969i | 0.0284780 | + | 0.0493253i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.68063 | − | 4.60498i | −0.153627 | − | 0.192208i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.2914 | − | 6.51910i | −0.470068 | − | 0.271394i | 0.246200 | − | 0.969219i | \(-0.420818\pi\) |
−0.716268 | + | 0.697825i | \(0.754151\pi\) | |||||||
\(578\) | 3.12250 | + | 1.80278i | 0.129879 | + | 0.0749857i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.90296 | − | 12.5319i | −0.0789481 | − | 0.519911i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.92744 | − | 3.33843i | −0.0798266 | − | 0.138264i | ||||
\(584\) | 6.53361 | − | 11.3165i | 0.270363 | − | 0.468282i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.99008 | − | 5.19042i | 0.371377 | − | 0.214414i | ||||
\(587\) | 35.0223 | 1.44553 | 0.722763 | − | 0.691096i | \(-0.242872\pi\) | ||||
0.722763 | + | 0.691096i | \(0.242872\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.7461 | −1.18446 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.14545 | + | 1.98397i | −0.0470776 | + | 0.0815409i | ||||
\(593\) | −8.19370 | − | 14.1919i | −0.336475 | − | 0.582792i | 0.647292 | − | 0.762242i | \(-0.275901\pi\) |
−0.983767 | + | 0.179450i | \(0.942568\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.6982i | 0.683986i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15.2685 | − | 8.81529i | −0.624376 | − | 0.360484i | ||||
\(599\) | 26.0718 | + | 15.0526i | 1.06527 | + | 0.615032i | 0.926884 | − | 0.375347i | \(-0.122476\pi\) |
0.138382 | + | 0.990379i | \(0.455810\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.75569i | − | 0.0716162i | −0.999359 | − | 0.0358081i | \(-0.988599\pi\) | ||
0.999359 | − | 0.0358081i | \(-0.0114005\pi\) | |||||||
\(602\) | 3.67666 | + | 4.60001i | 0.149849 | + | 0.187482i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.51016 | − | 11.2759i | −0.264895 | − | 0.458811i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.6511 | + | 9.03616i | −0.635258 | + | 0.366766i | −0.782785 | − | 0.622292i | \(-0.786202\pi\) |
0.147528 | + | 0.989058i | \(0.452868\pi\) | |||||||
\(608\) | −3.60411 | −0.146166 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.5539 | + | 8.98003i | −0.629242 | + | 0.363293i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.42507 | − | 11.1285i | 0.259506 | − | 0.449478i | −0.706604 | − | 0.707610i | \(-0.749774\pi\) |
0.966110 | + | 0.258132i | \(0.0831069\pi\) | |||||||
\(614\) | 7.06821 | + | 12.2425i | 0.285250 | + | 0.494067i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.22297 | + | 0.478431i | 0.0492749 | + | 0.0192765i | ||||
\(617\) | 37.3633i | 1.50419i | 0.659055 | + | 0.752094i | \(0.270956\pi\) | ||||
−0.659055 | + | 0.752094i | \(0.729044\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.7213 | + | 13.6955i | 0.953439 | + | 0.550468i | 0.894147 | − | 0.447773i | \(-0.147783\pi\) |
0.0592911 | + | 0.998241i | \(0.481116\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 6.65287i | − | 0.266756i | ||||||
\(623\) | −3.07356 | + | 2.45661i | −0.123140 | + | 0.0984222i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.07282 | − | 10.5184i | 0.242719 | − | 0.420401i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.8242 | − | 7.40408i | 0.511743 | − | 0.295455i | ||||
\(629\) | 8.38432 | 0.334305 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.09420 | −0.162987 | −0.0814937 | − | 0.996674i | \(-0.525969\pi\) | ||||
−0.0814937 | + | 0.996674i | \(0.525969\pi\) | |||||||
\(632\) | 7.69627 | − | 4.44344i | 0.306141 | − | 0.176751i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 15.3605 | − | 26.6051i | 0.610043 | − | 1.05662i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.70280 | − | 18.3449i | −0.225953 | − | 0.726850i | ||||
\(638\) | 4.40740i | 0.174491i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.4700 | + | 16.4371i | 1.12450 | + | 0.649228i | 0.942545 | − | 0.334080i | \(-0.108426\pi\) |
0.181951 | + | 0.983308i | \(0.441759\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 48.1790i | − | 1.89999i | −0.312261 | − | 0.949996i | \(-0.601086\pi\) | ||
0.312261 | − | 0.949996i | \(-0.398914\pi\) | |||||||
\(644\) | −16.8042 | + | 2.55170i | −0.662178 | + | 0.100551i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.59524 | + | 11.4233i | 0.259486 | + | 0.449443i | ||||
\(647\) | 2.64703 | − | 4.58478i | 0.104065 | − | 0.180246i | −0.809291 | − | 0.587408i | \(-0.800148\pi\) |
0.913356 | + | 0.407162i | \(0.133482\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.62377 | + | 1.51483i | −0.102992 | + | 0.0594625i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.3793 | 0.602301 | ||||||||
\(653\) | 43.4057 | − | 25.0603i | 1.69860 | − | 0.980686i | 0.751503 | − | 0.659729i | \(-0.229329\pi\) |
0.947094 | − | 0.320956i | \(-0.104004\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.11408 | + | 1.92964i | 0.0434975 | + | 0.0753399i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.30798 | + | 16.1245i | −0.245911 | + | 0.628599i | ||||
\(659\) | 2.20149i | 0.0857579i | 0.999080 | + | 0.0428790i | \(0.0136530\pi\) | ||||
−0.999080 | + | 0.0428790i | \(0.986347\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.7612 | − | 19.4921i | −1.31316 | − | 0.758153i | −0.330542 | − | 0.943791i | \(-0.607231\pi\) |
−0.982618 | + | 0.185638i | \(0.940565\pi\) | |||||||
\(662\) | 26.8710 | + | 15.5140i | 1.04437 | + | 0.602967i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.79091i | 0.185923i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.5221 | − | 49.4017i | −1.10438 | − | 1.91284i | ||||
\(668\) | 12.2581 | − | 21.2316i | 0.474279 | − | 0.821475i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.85852 | 0.0717473 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.4830 | −1.67615 | −0.838074 | − | 0.545556i | \(-0.816318\pi\) | ||||
−0.838074 | + | 0.545556i | \(0.816318\pi\) | |||||||
\(674\) | −5.98830 | + | 3.45735i | −0.230661 | + | 0.133172i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.73413 | − | 4.73565i | 0.105159 | − | 0.182140i | ||||
\(677\) | 20.8309 | + | 36.0802i | 0.800597 | + | 1.38668i | 0.919223 | + | 0.393736i | \(0.128818\pi\) |
−0.118626 | + | 0.992939i | \(0.537849\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.6772 | + | 3.59537i | −0.908648 | + | 0.137978i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.42848 | − | 1.97943i | −0.131283 | − | 0.0757965i | ||||
\(683\) | −41.3332 | − | 23.8637i | −1.58157 | − | 0.913120i | −0.994631 | − | 0.103490i | \(-0.966999\pi\) |
−0.586940 | − | 0.809630i | \(-0.699668\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.3365 | − | 10.3824i | −0.585548 | − | 0.396400i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.11288 | − | 1.92756i | −0.0424280 | − | 0.0734875i | ||||
\(689\) | 10.6571 | − | 18.4587i | 0.406004 | − | 0.703220i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.6953 | − | 19.4540i | 1.28183 | − | 0.740066i | 0.304648 | − | 0.952465i | \(-0.401461\pi\) |
0.977183 | + | 0.212399i | \(0.0681277\pi\) | |||||||
\(692\) | −12.5243 | −0.476101 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.49408 | 0.284471 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.07736 | − | 7.06219i | 0.154441 | − | 0.267500i | ||||
\(698\) | −6.22762 | − | 10.7866i | −0.235719 | − | 0.408277i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.73610i | 0.329958i | 0.986297 | + | 0.164979i | \(0.0527556\pi\) | ||||
−0.986297 | + | 0.164979i | \(0.947244\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.15046 | − | 4.12832i | −0.269685 | − | 0.155703i | ||||
\(704\) | −0.429853 | − | 0.248176i | −0.0162007 | − | 0.00935348i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 18.9402i | − | 0.712824i | ||||||
\(707\) | 7.40061 | + | 2.89515i | 0.278329 | + | 0.108883i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.25544 | − | 14.2988i | −0.310039 | − | 0.537004i | 0.668331 | − | 0.743864i | \(-0.267009\pi\) |
−0.978371 | + | 0.206860i | \(0.933676\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.28793 | − | 0.743586i | 0.0482671 | − | 0.0278671i | ||||
\(713\) | 51.2389 | 1.91891 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.58961 | − | 0.917762i | 0.0594066 | − | 0.0342984i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.3131 | − | 23.0590i | 0.496841 | − | 0.860554i | ||||
\(719\) | 22.5570 | + | 39.0699i | 0.841234 | + | 1.45706i | 0.888852 | + | 0.458195i | \(0.151504\pi\) |
−0.0476171 | + | 0.998866i | \(0.515163\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.7457 | + | 29.7092i | 0.884336 | + | 1.10643i | ||||
\(722\) | 6.01040i | 0.223684i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.4871 | − | 11.8282i | −0.761396 | − | 0.439592i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.9760i | 1.18593i | 0.805230 | + | 0.592963i | \(0.202042\pi\) | ||||
−0.805230 | + | 0.592963i | \(0.797958\pi\) | |||||||
\(728\) | 1.09008 | + | 7.17871i | 0.0404012 | + | 0.266061i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.07295 | + | 7.05456i | −0.150644 | + | 0.260922i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.4618 | − | 23.3606i | 1.49449 | − | 0.862844i | 0.494509 | − | 0.869172i | \(-0.335348\pi\) |
0.999980 | + | 0.00632839i | \(0.00201440\pi\) | |||||||
\(734\) | 10.9121 | 0.402773 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.42419 | 0.236799 | ||||||||
\(737\) | −3.51524 | + | 2.02953i | −0.129486 | + | 0.0747586i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.59353 | − | 7.95623i | 0.168976 | − | 0.292675i | −0.769084 | − | 0.639147i | \(-0.779287\pi\) |
0.938060 | + | 0.346473i | \(0.112621\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.08485 | − | 20.3152i | −0.113248 | − | 0.745795i | ||||
\(743\) | − | 28.5353i | − | 1.04686i | −0.852069 | − | 0.523430i | \(-0.824652\pi\) | ||
0.852069 | − | 0.523430i | \(-0.175348\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 19.4924 | + | 11.2539i | 0.713667 | + | 0.412036i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.81657i | 0.0664203i | ||||||||
\(749\) | −3.51234 | − | 4.39442i | −0.128338 | − | 0.160569i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.4749 | + | 37.1956i | 0.783629 | + | 1.35729i | 0.929814 | + | 0.368029i | \(0.119967\pi\) |
−0.146185 | + | 0.989257i | \(0.546700\pi\) | |||||||
\(752\) | 3.27213 | − | 5.66749i | 0.119322 | − | 0.206672i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −21.1043 | + | 12.1846i | −0.768574 | + | 0.443736i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.4415 | −0.706612 | −0.353306 | − | 0.935508i | \(-0.614943\pi\) | ||||
−0.353306 | + | 0.935508i | \(0.614943\pi\) | |||||||
\(758\) | −2.82245 | + | 1.62954i | −0.102516 | + | 0.0591877i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.9154 | + | 43.1547i | 0.903182 | + | 1.56436i | 0.823339 | + | 0.567550i | \(0.192109\pi\) |
0.0798434 | + | 0.996807i | \(0.474558\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.4739 | − | 7.61827i | −0.705003 | − | 0.275800i | ||||
\(764\) | 8.10892i | 0.293371i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.0013 | + | 8.66098i | 0.542017 | + | 0.312934i | ||||
\(767\) | −14.5072 | − | 8.37575i | −0.523825 | − | 0.302431i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 29.5025i | − | 1.06389i | −0.846779 | − | 0.531944i | \(-0.821462\pi\) | ||
0.846779 | − | 0.531944i | \(-0.178538\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.02502 | − | 10.4356i | −0.216845 | − | 0.375587i | ||||
\(773\) | 12.6641 | − | 21.9349i | 0.455498 | − | 0.788945i | −0.543219 | − | 0.839591i | \(-0.682795\pi\) |
0.998717 | + | 0.0506458i | \(0.0161280\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.05174 | 0.324938 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.6982 | −1.13644 | ||||||||
\(779\) | −6.95465 | + | 4.01527i | −0.249176 | + | 0.143862i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.57509 | − | 4.46019i | 0.0921440 | − | 0.159598i | ||||
\(782\) | −11.7558 | − | 20.3616i | −0.420385 | − | 0.728129i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.14181 | + | 4.74992i | 0.183636 | + | 0.169640i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.89278 | + | 3.40220i | 0.210055 | + | 0.121275i | 0.601337 | − | 0.798996i | \(-0.294635\pi\) |
−0.391282 | + | 0.920271i | \(0.627968\pi\) | |||||||
\(788\) | 11.0386 | + | 6.37315i | 0.393235 | + | 0.227034i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.1655 | + | 4.88430i | −1.14367 | + | 0.173666i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.13802 | + | 8.89931i | 0.182456 | + | 0.316024i | ||||
\(794\) | −16.7561 | + | 29.0224i | −0.594651 | + | 1.02997i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.4954 | − | 9.52361i | 0.584663 | − | 0.337556i | ||||
\(797\) | 31.6373 | 1.12065 | 0.560326 | − | 0.828272i | \(-0.310676\pi\) | ||||
0.560326 | + | 0.828272i | \(0.310676\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.9509 | −0.847323 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17.9212 | + | 31.0404i | −0.632818 | + | 1.09607i | ||||
\(803\) | 3.24297 | + | 5.61698i | 0.114442 | + | 0.198219i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 21.8892i | − | 0.771013i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.60119 | − | 1.50180i | −0.0915094 | − | 0.0528330i | ||||
\(809\) | 22.9302 | + | 13.2388i | 0.806183 | + | 0.465450i | 0.845629 | − | 0.533772i | \(-0.179226\pi\) |
−0.0394457 | + | 0.999222i | \(0.512559\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.4799i | 0.894720i | 0.894354 | + | 0.447360i | \(0.147636\pi\) | ||||
−0.894354 | + | 0.447360i | \(0.852364\pi\) | |||||||
\(812\) | −8.55899 | + | 21.8786i | −0.300362 | + | 0.767788i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.568545 | − | 0.984749i | −0.0199275 | − | 0.0345154i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.94713 | − | 4.01093i | 0.243049 | − | 0.140325i | ||||
\(818\) | −24.6499 | −0.861863 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.9335 | + | 19.0141i | −1.14939 | + | 0.663598i | −0.948738 | − | 0.316065i | \(-0.897638\pi\) |
−0.200649 | + | 0.979663i | \(0.564305\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.78791 | − | 3.09676i | 0.0623228 | − | 0.107946i | −0.833181 | − | 0.553001i | \(-0.813483\pi\) |
0.895503 | + | 0.445055i | \(0.146816\pi\) | |||||||
\(824\) | −7.18752 | − | 12.4491i | −0.250389 | − | 0.433687i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.9663 | + | 2.42447i | −0.555539 | + | 0.0843582i | ||||
\(827\) | − | 15.0648i | − | 0.523855i | −0.965088 | − | 0.261927i | \(-0.915642\pi\) | ||
0.965088 | − | 0.261927i | \(-0.0843581\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.5046 | − | 15.8798i | −0.955273 | − | 0.551527i | −0.0605582 | − | 0.998165i | \(-0.519288\pi\) |
−0.894715 | + | 0.446637i | \(0.852621\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 2.74440i | − | 0.0951450i | ||||||
\(833\) | 5.64586 | − | 24.9890i | 0.195617 | − | 0.865819i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.894453 | − | 1.54924i | 0.0309353 | − | 0.0535815i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.22954 | − | 5.32868i | 0.318829 | − | 0.184076i | ||||
\(839\) | 15.1305 | 0.522362 | 0.261181 | − | 0.965290i | \(-0.415888\pi\) | ||||
0.261181 | + | 0.965290i | \(0.415888\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −49.8470 | −1.71886 | ||||||||
\(842\) | 19.6427 | − | 11.3407i | 0.676933 | − | 0.390828i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.46028 | + | 7.72544i | −0.153529 | + | 0.265920i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.2247 | − | 17.7636i | 0.763651 | − | 0.610365i | ||||
\(848\) | 7.76645i | 0.266701i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.7454 | + | 7.35858i | 0.436908 | + | 0.252249i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.1586i | 0.416302i | 0.978097 | + | 0.208151i | \(0.0667445\pi\) | ||||
−0.978097 | + | 0.208151i | \(0.933255\pi\) | |||||||
\(854\) | 9.22581 | + | 3.60917i | 0.315701 | + | 0.123503i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.06314 | + | 1.84141i | 0.0363374 | + | 0.0629382i | ||||
\(857\) | −15.6668 | + | 27.1356i | −0.535167 | + | 0.926936i | 0.463989 | + | 0.885841i | \(0.346418\pi\) |
−0.999155 | + | 0.0410947i | \(0.986915\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.7872 | + | 7.38268i | −0.436293 | + | 0.251894i | −0.702024 | − | 0.712153i | \(-0.747720\pi\) |
0.265731 | + | 0.964047i | \(0.414387\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −30.0728 | −1.02429 | ||||||||
\(863\) | −12.4950 | + | 7.21398i | −0.425334 | + | 0.245567i | −0.697357 | − | 0.716724i | \(-0.745641\pi\) |
0.272023 | + | 0.962291i | \(0.412307\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.46016 | − | 12.9214i | −0.253507 | − | 0.439086i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13.1752 | − | 16.4840i | −0.447196 | − | 0.559504i | ||||
\(869\) | 4.41102i | 0.149634i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.4363 | − | 11.2216i | −0.658574 | − | 0.380228i | ||||
\(872\) | 6.84474 | + | 3.95181i | 0.231792 | + | 0.133825i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 23.1535i | 0.783179i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.28153 | − | 9.14788i | −0.178345 | − | 0.308902i | 0.762969 | − | 0.646435i | \(-0.223741\pi\) |
−0.941314 | + | 0.337533i | \(0.890408\pi\) | |||||||
\(878\) | 6.41586 | − | 11.1126i | 0.216525 | − | 0.375032i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.4300 | 0.452469 | 0.226234 | − | 0.974073i | \(-0.427358\pi\) | ||||
0.226234 | + | 0.974073i | \(0.427358\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.06019 | 0.136636 | 0.0683181 | − | 0.997664i | \(-0.478237\pi\) | ||||
0.0683181 | + | 0.997664i | \(0.478237\pi\) | |||||||
\(884\) | −8.69843 | + | 5.02204i | −0.292560 | + | 0.168909i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.2071 | + | 17.6792i | −0.342913 | + | 0.593943i | ||||
\(887\) | −16.5177 | − | 28.6095i | −0.554611 | − | 0.960614i | −0.997934 | − | 0.0642519i | \(-0.979534\pi\) |
0.443323 | − | 0.896362i | \(-0.353799\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.299270 | + | 1.97084i | 0.0100372 | + | 0.0660997i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.3899 | + | 11.7721i | 0.682705 | + | 0.394160i | ||||
\(893\) | 20.4262 | + | 11.7931i | 0.683538 | + | 0.394641i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.65187 | − | 2.06672i | −0.0551851 | − | 0.0690442i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.4202 | + | 18.0483i | 0.347727 | + | 0.602280i | ||||
\(899\) | 35.4115 | − | 61.3345i | 1.18104 | − | 2.04562i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.6159 | − | 14.2120i | 0.820074 | − | 0.473470i | ||||
\(902\) | −1.10595 | −0.0368241 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.2968 | 0.408984 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.6659 | − | 23.6700i | 0.453768 | − | 0.785949i | −0.544848 | − | 0.838535i | \(-0.683413\pi\) |
0.998616 | + | 0.0525853i | \(0.0167461\pi\) | |||||||
\(908\) | 4.66223 | + | 8.07522i | 0.154722 | + | 0.267986i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.06838i | 0.0353972i | 0.999843 | + | 0.0176986i | \(0.00563393\pi\) | ||||
−0.999843 | + | 0.0176986i | \(0.994366\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.05939 | − | 1.18899i | −0.0681558 | − | 0.0393498i | ||||
\(914\) | −13.8811 | − | 8.01424i | −0.459145 | − | 0.265087i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 23.2725i | − | 0.768944i | ||||||
\(917\) | −26.2731 | + | 20.9994i | −0.867615 | + | 0.693460i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.8653 | + | 46.5320i | 0.886203 | + | 1.53495i | 0.844329 | + | 0.535826i | \(0.180000\pi\) |
0.0418743 | + | 0.999123i | \(0.486667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.71819 | + | 0.991998i | −0.0565856 | + | 0.0326697i | ||||
\(923\) | 28.4761 | 0.937303 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −31.5222 | + | 18.1994i | −1.03588 | + | 0.598068i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.43979 | − | 7.68995i | 0.145743 | − | 0.252435i | ||||
\(929\) | 4.80716 | + | 8.32625i | 0.157718 | + | 0.273175i | 0.934045 | − | 0.357154i | \(-0.116253\pi\) |
−0.776327 | + | 0.630330i | \(0.782920\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.1192 | + | 18.5316i | −0.561061 | + | 0.607350i | ||||
\(932\) | 12.6203i | 0.413393i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −26.9113 | − | 15.5372i | −0.880563 | − | 0.508394i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.8030i | 0.418256i | 0.977888 | + | 0.209128i | \(0.0670626\pi\) | ||||
−0.977888 | + | 0.209128i | \(0.932937\pi\) | |||||||
\(938\) | −21.3912 | + | 3.24823i | −0.698446 | + | 0.106059i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.2221 | − | 41.9538i | 0.789616 | − | 1.36766i | −0.136586 | − | 0.990628i | \(-0.543613\pi\) |
0.926202 | − | 0.377028i | \(-0.123054\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.3964 | − | 7.15707i | 0.403682 | − | 0.233066i | ||||
\(944\) | 6.10388 | 0.198664 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.10476 | 0.0359187 | ||||||||
\(947\) | 32.9055 | − | 18.9980i | 1.06929 | − | 0.617353i | 0.141300 | − | 0.989967i | \(-0.454872\pi\) |
0.927986 | + | 0.372614i | \(0.121539\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.9308 | + | 31.0571i | −0.582060 | + | 1.00816i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.52771 | + | 9.01756i | −0.114334 | + | 0.292261i | ||||
\(953\) | 15.2394i | 0.493652i | 0.969060 | + | 0.246826i | \(0.0793877\pi\) | ||||
−0.969060 | + | 0.246826i | \(0.920612\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.9601 | − | 8.05990i | −0.451503 | − | 0.260676i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 36.4809i | − | 1.17864i | ||||||
\(959\) | 4.15902 | − | 10.6313i | 0.134302 | − | 0.343303i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.3078 | + | 28.2459i | 0.526057 | + | 0.911157i | ||||
\(962\) | 3.14357 | − | 5.44483i | 0.101353 | − | 0.175548i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.3222 | + | 10.5783i | −0.590119 | + | 0.340705i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.7458 | −0.892244 | −0.446122 | − | 0.894972i | \(-0.647195\pi\) | ||||
−0.446122 | + | 0.894972i | \(0.647195\pi\) | |||||||
\(968\) | −9.31292 | + | 5.37682i | −0.299329 | + | 0.172817i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.2730 | + | 17.7934i | 0.329677 | + | 0.571018i | 0.982448 | − | 0.186538i | \(-0.0597268\pi\) |
−0.652771 | + | 0.757556i | \(0.726393\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.178206 | + | 0.0270604i | −0.00571302 | + | 0.000867518i | ||||
\(974\) | − | 14.1334i | − | 0.452865i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.24271 | − | 1.87218i | −0.103797 | − | 0.0599270i | ||||
\(977\) | −6.60604 | − | 3.81400i | −0.211346 | − | 0.122021i | 0.390591 | − | 0.920564i | \(-0.372271\pi\) |
−0.601937 | + | 0.798544i | \(0.705604\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.738160i | 0.0235917i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16.2733 | − | 28.1861i | −0.519301 | − | 0.899456i | ||||
\(983\) | 11.8347 | − | 20.4984i | 0.377470 | − | 0.653797i | −0.613224 | − | 0.789909i | \(-0.710128\pi\) |
0.990693 | + | 0.136113i | \(0.0434609\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −32.4979 | −1.03494 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.89113 | 0.314679 | ||||||||
\(989\) | −12.3830 | + | 7.14933i | −0.393757 | + | 0.227336i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.3947 | + | 23.2003i | −0.425497 | + | 0.736982i | −0.996467 | − | 0.0839887i | \(-0.973234\pi\) |
0.570970 | + | 0.820971i | \(0.306567\pi\) | |||||||
\(992\) | 3.98797 | + | 6.90736i | 0.126618 | + | 0.219309i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 21.4444 | − | 17.1399i | 0.680176 | − | 0.543646i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.5656 | − | 21.1111i | −1.15804 | − | 0.668596i | −0.207209 | − | 0.978297i | \(-0.566438\pi\) |
−0.950834 | + | 0.309700i | \(0.899771\pi\) | |||||||
\(998\) | −10.1740 | − | 5.87396i | −0.322053 | − | 0.185937i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3150.2.bf.e.1151.9 | yes | 24 | |
3.2 | odd | 2 | inner | 3150.2.bf.e.1151.4 | yes | 24 | |
5.2 | odd | 4 | 3150.2.bp.h.899.2 | 24 | |||
5.3 | odd | 4 | 3150.2.bp.g.899.11 | 24 | |||
5.4 | even | 2 | 3150.2.bf.d.1151.4 | ✓ | 24 | ||
7.5 | odd | 6 | inner | 3150.2.bf.e.1601.4 | yes | 24 | |
15.2 | even | 4 | 3150.2.bp.g.899.2 | 24 | |||
15.8 | even | 4 | 3150.2.bp.h.899.11 | 24 | |||
15.14 | odd | 2 | 3150.2.bf.d.1151.9 | yes | 24 | ||
21.5 | even | 6 | inner | 3150.2.bf.e.1601.9 | yes | 24 | |
35.12 | even | 12 | 3150.2.bp.h.1349.11 | 24 | |||
35.19 | odd | 6 | 3150.2.bf.d.1601.9 | yes | 24 | ||
35.33 | even | 12 | 3150.2.bp.g.1349.2 | 24 | |||
105.47 | odd | 12 | 3150.2.bp.g.1349.11 | 24 | |||
105.68 | odd | 12 | 3150.2.bp.h.1349.2 | 24 | |||
105.89 | even | 6 | 3150.2.bf.d.1601.4 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.bf.d.1151.4 | ✓ | 24 | 5.4 | even | 2 | ||
3150.2.bf.d.1151.9 | yes | 24 | 15.14 | odd | 2 | ||
3150.2.bf.d.1601.4 | yes | 24 | 105.89 | even | 6 | ||
3150.2.bf.d.1601.9 | yes | 24 | 35.19 | odd | 6 | ||
3150.2.bf.e.1151.4 | yes | 24 | 3.2 | odd | 2 | inner | |
3150.2.bf.e.1151.9 | yes | 24 | 1.1 | even | 1 | trivial | |
3150.2.bf.e.1601.4 | yes | 24 | 7.5 | odd | 6 | inner | |
3150.2.bf.e.1601.9 | yes | 24 | 21.5 | even | 6 | inner | |
3150.2.bp.g.899.2 | 24 | 15.2 | even | 4 | |||
3150.2.bp.g.899.11 | 24 | 5.3 | odd | 4 | |||
3150.2.bp.g.1349.2 | 24 | 35.33 | even | 12 | |||
3150.2.bp.g.1349.11 | 24 | 105.47 | odd | 12 | |||
3150.2.bp.h.899.2 | 24 | 5.2 | odd | 4 | |||
3150.2.bp.h.899.11 | 24 | 15.8 | even | 4 | |||
3150.2.bp.h.1349.2 | 24 | 105.68 | odd | 12 | |||
3150.2.bp.h.1349.11 | 24 | 35.12 | even | 12 |