Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1583,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1583");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.v (of order \(4\), degree \(2\), not 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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 1008) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1583.16 | ||
Character | \(\chi\) | \(=\) | 4032.1583 |
Dual form | 4032.2.v.e.3599.16 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.65702 | + | 1.65702i | 0.741043 | + | 0.741043i | 0.972779 | − | 0.231736i | \(-0.0744405\pi\) |
−0.231736 | + | 0.972779i | \(0.574441\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.993222 | + | 0.993222i | −0.299468 | + | 0.299468i | −0.840805 | − | 0.541338i | \(-0.817918\pi\) |
0.541338 | + | 0.840805i | \(0.317918\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.62686 | + | 2.62686i | 0.728560 | + | 0.728560i | 0.970333 | − | 0.241773i | \(-0.0777290\pi\) |
−0.241773 | + | 0.970333i | \(0.577729\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.77728i | 0.673589i | 0.941578 | + | 0.336795i | \(0.109343\pi\) | ||||
−0.941578 | + | 0.336795i | \(0.890657\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.56309 | + | 1.56309i | −0.358598 | + | 0.358598i | −0.863296 | − | 0.504698i | \(-0.831604\pi\) |
0.504698 | + | 0.863296i | \(0.331604\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.05272i | − | 0.219507i | −0.993959 | − | 0.109754i | \(-0.964994\pi\) | ||
0.993959 | − | 0.109754i | \(-0.0350062\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.491445i | 0.0982890i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.47823 | + | 3.47823i | −0.645891 | + | 0.645891i | −0.951997 | − | 0.306106i | \(-0.900974\pi\) |
0.306106 | + | 0.951997i | \(0.400974\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.06124i | 0.190605i | 0.995448 | + | 0.0953026i | \(0.0303819\pi\) | ||||
−0.995448 | + | 0.0953026i | \(0.969618\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.65702 | − | 1.65702i | −0.280088 | − | 0.280088i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0657126 | + | 0.0657126i | −0.0108031 | + | 0.0108031i | −0.712488 | − | 0.701685i | \(-0.752432\pi\) |
0.701685 | + | 0.712488i | \(0.252432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.31313 | −0.985945 | −0.492972 | − | 0.870045i | \(-0.664090\pi\) | ||||
−0.492972 | + | 0.870045i | \(0.664090\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.38841 | + | 2.38841i | 0.364229 | + | 0.364229i | 0.865367 | − | 0.501138i | \(-0.167085\pi\) |
−0.501138 | + | 0.865367i | \(0.667085\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.47190 | −0.214699 | −0.107349 | − | 0.994221i | \(-0.534236\pi\) | ||||
−0.107349 | + | 0.994221i | \(0.534236\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.63807 | + | 7.63807i | 1.04917 | + | 1.04917i | 0.998727 | + | 0.0504431i | \(0.0160634\pi\) |
0.0504431 | + | 0.998727i | \(0.483937\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.29158 | −0.443837 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.15490 | + | 4.15490i | −0.540921 | + | 0.540921i | −0.923799 | − | 0.382878i | \(-0.874933\pi\) |
0.382878 | + | 0.923799i | \(0.374933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.78123 | − | 7.78123i | −0.996285 | − | 0.996285i | 0.00370838 | − | 0.999993i | \(-0.498820\pi\) |
−0.999993 | + | 0.00370838i | \(0.998820\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.70553i | 1.07979i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.98557 | + | 1.98557i | −0.242576 | + | 0.242576i | −0.817915 | − | 0.575339i | \(-0.804870\pi\) |
0.575339 | + | 0.817915i | \(0.304870\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.0855i | − | 1.55297i | −0.630137 | − | 0.776484i | \(-0.717001\pi\) | ||
0.630137 | − | 0.776484i | \(-0.282999\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.50329i | − | 1.11228i | −0.831090 | − | 0.556138i | \(-0.812283\pi\) | ||
0.831090 | − | 0.556138i | \(-0.187717\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.993222 | − | 0.993222i | 0.113188 | − | 0.113188i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.85051i | 1.10827i | 0.832427 | + | 0.554134i | \(0.186951\pi\) | ||||
−0.832427 | + | 0.554134i | \(0.813049\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.13002 | + | 1.13002i | 0.124036 | + | 0.124036i | 0.766400 | − | 0.642364i | \(-0.222046\pi\) |
−0.642364 | + | 0.766400i | \(0.722046\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.60202 | + | 4.60202i | −0.499159 | + | 0.499159i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.04453 | −0.746718 | −0.373359 | − | 0.927687i | \(-0.621794\pi\) | ||||
−0.373359 | + | 0.927687i | \(0.621794\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.62686 | − | 2.62686i | −0.275370 | − | 0.275370i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.18016 | −0.531473 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.35352 | 0.543568 | 0.271784 | − | 0.962358i | \(-0.412386\pi\) | ||||
0.271784 | + | 0.962358i | \(0.412386\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.34591 | + | 5.34591i | 0.531938 | + | 0.531938i | 0.921149 | − | 0.389211i | \(-0.127252\pi\) |
−0.389211 | + | 0.921149i | \(0.627252\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.41355 | −0.336347 | −0.168173 | − | 0.985757i | \(-0.553787\pi\) | ||||
−0.168173 | + | 0.985757i | \(0.553787\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.7004 | + | 10.7004i | −1.03445 | + | 1.03445i | −0.0350640 | + | 0.999385i | \(0.511164\pi\) |
−0.999385 | + | 0.0350640i | \(0.988836\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.36354 | − | 5.36354i | −0.513734 | − | 0.513734i | 0.401934 | − | 0.915668i | \(-0.368338\pi\) |
−0.915668 | + | 0.401934i | \(0.868338\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.2463i | 1.71647i | 0.513256 | + | 0.858236i | \(0.328439\pi\) | ||||
−0.513256 | + | 0.858236i | \(0.671561\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.74438 | − | 1.74438i | 0.162664 | − | 0.162664i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.77728i | − | 0.254593i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.02702i | 0.820638i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.47078 | − | 7.47078i | 0.668206 | − | 0.668206i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.0998053i | 0.00885629i | 0.999990 | + | 0.00442814i | \(0.00140953\pi\) | ||||
−0.999990 | + | 0.00442814i | \(0.998590\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.8436 | + | 12.8436i | 1.12215 | + | 1.12215i | 0.991417 | + | 0.130734i | \(0.0417335\pi\) |
0.130734 | + | 0.991417i | \(0.458266\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.56309 | − | 1.56309i | 0.135537 | − | 0.135537i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.10918 | 0.265635 | 0.132817 | − | 0.991141i | \(-0.457598\pi\) | ||||
0.132817 | + | 0.991141i | \(0.457598\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.5794 | − | 10.5794i | −0.897330 | − | 0.897330i | 0.0978696 | − | 0.995199i | \(-0.468797\pi\) |
−0.995199 | + | 0.0978696i | \(0.968797\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.21811 | −0.436360 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.5270 | −0.957266 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.32230 | + | 6.32230i | 0.517943 | + | 0.517943i | 0.916948 | − | 0.399006i | \(-0.130645\pi\) |
−0.399006 | + | 0.916948i | \(0.630645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.9393 | −1.86677 | −0.933385 | − | 0.358877i | \(-0.883160\pi\) | ||||
−0.933385 | + | 0.358877i | \(0.883160\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.75851 | + | 1.75851i | −0.141247 | + | 0.141247i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.7269 | − | 12.7269i | −1.01571 | − | 1.01571i | −0.999875 | − | 0.0158402i | \(-0.994958\pi\) |
−0.0158402 | − | 0.999875i | \(-0.505042\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.05272i | 0.0829660i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.66445 | + | 5.66445i | −0.443674 | + | 0.443674i | −0.893245 | − | 0.449571i | \(-0.851577\pi\) |
0.449571 | + | 0.893245i | \(0.351577\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.3445i | 1.57431i | 0.616756 | + | 0.787154i | \(0.288446\pi\) | ||||
−0.616756 | + | 0.787154i | \(0.711554\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.800782i | 0.0615986i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.94764 | − | 3.94764i | 0.300133 | − | 0.300133i | −0.540933 | − | 0.841066i | \(-0.681929\pi\) |
0.841066 | + | 0.540933i | \(0.181929\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.491445i | − | 0.0371497i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.5761 | + | 12.5761i | 0.939982 | + | 0.939982i | 0.998298 | − | 0.0583166i | \(-0.0185733\pi\) |
−0.0583166 | + | 0.998298i | \(0.518573\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0136 | − | 16.0136i | 1.19028 | − | 1.19028i | 0.213295 | − | 0.976988i | \(-0.431580\pi\) |
0.976988 | − | 0.213295i | \(-0.0684196\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.217775 | −0.0160111 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.75846 | − | 2.75846i | −0.201718 | − | 0.201718i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.8336 | −0.856251 | −0.428126 | − | 0.903719i | \(-0.640826\pi\) | ||||
−0.428126 | + | 0.903719i | \(0.640826\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.1021 | 1.51896 | 0.759481 | − | 0.650529i | \(-0.225453\pi\) | ||||
0.759481 | + | 0.650529i | \(0.225453\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.83308 | − | 5.83308i | −0.415590 | − | 0.415590i | 0.468091 | − | 0.883680i | \(-0.344942\pi\) |
−0.883680 | + | 0.468091i | \(0.844942\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.2865 | −1.65074 | −0.825369 | − | 0.564594i | \(-0.809033\pi\) | ||||
−0.825369 | + | 0.564594i | \(0.809033\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.47823 | − | 3.47823i | 0.244124 | − | 0.244124i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.4610 | − | 10.4610i | −0.730627 | − | 0.730627i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3.10500i | − | 0.214777i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.2720 | − | 16.2720i | 1.12021 | − | 1.12021i | 0.128501 | − | 0.991709i | \(-0.458983\pi\) |
0.991709 | − | 0.128501i | \(-0.0410165\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.91529i | 0.539818i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.06124i | − | 0.0720420i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.29553 | + | 7.29553i | −0.490750 | + | 0.490750i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.8221i | 1.52828i | 0.645051 | + | 0.764139i | \(0.276836\pi\) | ||||
−0.645051 | + | 0.764139i | \(0.723164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.09419 | + | 6.09419i | 0.404486 | + | 0.404486i | 0.879810 | − | 0.475325i | \(-0.157669\pi\) |
−0.475325 | + | 0.879810i | \(0.657669\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.57148 | + | 8.57148i | −0.566420 | + | 0.566420i | −0.931124 | − | 0.364704i | \(-0.881170\pi\) |
0.364704 | + | 0.931124i | \(0.381170\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.90649 | −0.321435 | −0.160717 | − | 0.987000i | \(-0.551381\pi\) | ||||
−0.160717 | + | 0.987000i | \(0.551381\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.43897 | − | 2.43897i | −0.159101 | − | 0.159101i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.1659 | 0.722260 | 0.361130 | − | 0.932515i | \(-0.382391\pi\) | ||||
0.361130 | + | 0.932515i | \(0.382391\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.8083 | −1.14713 | −0.573566 | − | 0.819159i | \(-0.694440\pi\) | ||||
−0.573566 | + | 0.819159i | \(0.694440\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.65702 | + | 1.65702i | 0.105863 | + | 0.105863i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.21206 | −0.522521 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.7431 | + | 10.7431i | −0.678099 | + | 0.678099i | −0.959570 | − | 0.281471i | \(-0.909178\pi\) |
0.281471 | + | 0.959570i | \(0.409178\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.04559 | + | 1.04559i | 0.0657354 | + | 0.0657354i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.20282i | 0.0750300i | 0.999296 | + | 0.0375150i | \(0.0119442\pi\) | ||||
−0.999296 | + | 0.0375150i | \(0.988056\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0657126 | − | 0.0657126i | 0.00408318 | − | 0.00408318i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 14.9654i | − | 0.922803i | −0.887191 | − | 0.461402i | \(-0.847347\pi\) | ||
0.887191 | − | 0.461402i | \(-0.152653\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.3129i | 1.55496i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.58780 | − | 6.58780i | 0.401665 | − | 0.401665i | −0.477154 | − | 0.878819i | \(-0.658332\pi\) |
0.878819 | + | 0.477154i | \(0.158332\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 27.1436i | − | 1.64886i | −0.565965 | − | 0.824429i | \(-0.691496\pi\) | ||
0.565965 | − | 0.824429i | \(-0.308504\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.488114 | − | 0.488114i | −0.0294344 | − | 0.0294344i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0118 | − | 12.0118i | 0.721720 | − | 0.721720i | −0.247235 | − | 0.968955i | \(-0.579522\pi\) |
0.968955 | + | 0.247235i | \(0.0795221\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.46830 | −0.505176 | −0.252588 | − | 0.967574i | \(-0.581282\pi\) | ||||
−0.252588 | + | 0.967574i | \(0.581282\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.77919 | − | 8.77919i | −0.521868 | − | 0.521868i | 0.396267 | − | 0.918135i | \(-0.370305\pi\) |
−0.918135 | + | 0.396267i | \(0.870305\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.31313 | 0.372652 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.28671 | 0.546277 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.25965 | − | 9.25965i | −0.540955 | − | 0.540955i | 0.382854 | − | 0.923809i | \(-0.374941\pi\) |
−0.923809 | + | 0.382854i | \(0.874941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.7695 | −0.801692 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.76535 | − | 2.76535i | 0.159924 | − | 0.159924i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.38841 | − | 2.38841i | −0.137665 | − | 0.137665i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 25.7873i | − | 1.47658i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.60065 | − | 9.60065i | 0.547938 | − | 0.547938i | −0.377906 | − | 0.925844i | \(-0.623356\pi\) |
0.925844 | + | 0.377906i | \(0.123356\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.1840i | 1.31464i | 0.753611 | + | 0.657321i | \(0.228310\pi\) | ||||
−0.753611 | + | 0.657321i | \(0.771690\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.9361i | 1.57904i | 0.613723 | + | 0.789522i | \(0.289671\pi\) | ||||
−0.613723 | + | 0.789522i | \(0.710329\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.5910 | + | 21.5910i | −1.21267 | + | 1.21267i | −0.242529 | + | 0.970144i | \(0.577977\pi\) |
−0.970144 | + | 0.242529i | \(0.922023\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.90931i | − | 0.386847i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.34115 | − | 4.34115i | −0.241548 | − | 0.241548i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.29096 | + | 1.29096i | −0.0716094 | + | 0.0716094i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.47190 | 0.0811485 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.4892 | + | 18.4892i | 1.01626 | + | 1.01626i | 0.999866 | + | 0.0163917i | \(0.00521788\pi\) |
0.0163917 | + | 0.999866i | \(0.494782\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.58027 | −0.359519 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.58189 | −0.467486 | −0.233743 | − | 0.972298i | \(-0.575097\pi\) | ||||
−0.233743 | + | 0.972298i | \(0.575097\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.05405 | − | 1.05405i | −0.0570801 | − | 0.0570801i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.6238 | − | 19.6238i | 1.05346 | − | 1.05346i | 0.0549718 | − | 0.998488i | \(-0.482493\pi\) |
0.998488 | − | 0.0549718i | \(-0.0175069\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.67820 | + | 7.67820i | 0.411004 | + | 0.411004i | 0.882088 | − | 0.471084i | \(-0.156137\pi\) |
−0.471084 | + | 0.882088i | \(0.656137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.9405i | 1.38067i | 0.723489 | + | 0.690336i | \(0.242537\pi\) | ||||
−0.723489 | + | 0.690336i | \(0.757463\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.6830 | − | 21.6830i | 1.15082 | − | 1.15082i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.08367i | 0.162750i | 0.996684 | + | 0.0813750i | \(0.0259312\pi\) | ||||
−0.996684 | + | 0.0813750i | \(0.974069\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.1135i | 0.742814i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.7472 | − | 15.7472i | 0.824244 | − | 0.824244i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.1386i | 0.946825i | 0.880841 | + | 0.473412i | \(0.156978\pi\) | ||||
−0.880841 | + | 0.473412i | \(0.843022\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.63807 | − | 7.63807i | −0.396549 | − | 0.396549i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.70711 | + | 1.70711i | −0.0883908 | + | 0.0883908i | −0.749920 | − | 0.661529i | \(-0.769908\pi\) |
0.661529 | + | 0.749920i | \(0.269908\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.2736 | −0.941140 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.2888 | + | 24.2888i | 1.24763 | + | 1.24763i | 0.956762 | + | 0.290870i | \(0.0939448\pi\) |
0.290870 | + | 0.956762i | \(0.406055\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.2655 | −0.524544 | −0.262272 | − | 0.964994i | \(-0.584472\pi\) | ||||
−0.262272 | + | 0.964994i | \(0.584472\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.29158 | 0.167755 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.924351 | − | 0.924351i | −0.0468664 | − | 0.0468664i | 0.683285 | − | 0.730152i | \(-0.260551\pi\) |
−0.730152 | + | 0.683285i | \(0.760551\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.92370 | 0.147858 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.3225 | + | 16.3225i | −0.821275 | + | 0.821275i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.2727 | − | 18.2727i | −0.917080 | − | 0.917080i | 0.0797361 | − | 0.996816i | \(-0.474592\pi\) |
−0.996816 | + | 0.0797361i | \(0.974592\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.9686i | 1.84612i | 0.384651 | + | 0.923062i | \(0.374322\pi\) | ||||
−0.384651 | + | 0.923062i | \(0.625678\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.78774 | + | 2.78774i | −0.138867 | + | 0.138867i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.130534i | − | 0.00647035i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.66305i | 0.230573i | 0.993332 | + | 0.115286i | \(0.0367786\pi\) | ||||
−0.993332 | + | 0.115286i | \(0.963221\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.15490 | − | 4.15490i | 0.204449 | − | 0.204449i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.74494i | 0.183832i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.9392 | + | 20.9392i | 1.02294 | + | 1.02294i | 0.999731 | + | 0.0232142i | \(0.00738996\pi\) |
0.0232142 | + | 0.999731i | \(0.492610\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.0980 | + | 18.0980i | −0.882042 | + | 0.882042i | −0.993742 | − | 0.111700i | \(-0.964370\pi\) |
0.111700 | + | 0.993742i | \(0.464370\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.36488 | −0.0662064 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.78123 | + | 7.78123i | 0.376560 | + | 0.376560i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.3329 | −1.46108 | −0.730541 | − | 0.682868i | \(-0.760732\pi\) | ||||
−0.730541 | + | 0.682868i | \(0.760732\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.8726 | −1.24336 | −0.621679 | − | 0.783272i | \(-0.713549\pi\) | ||||
−0.621679 | + | 0.783272i | \(0.713549\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.64550 | + | 1.64550i | 0.0787150 | + | 0.0787150i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.1840 | 0.867874 | 0.433937 | − | 0.900943i | \(-0.357124\pi\) | ||||
0.433937 | + | 0.900943i | \(0.357124\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.0172574 | − | 0.0172574i | 0.000819922 | − | 0.000819922i | −0.706697 | − | 0.707517i | \(-0.749815\pi\) |
0.707517 | + | 0.706697i | \(0.249815\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.6729 | − | 11.6729i | −0.553350 | − | 0.553350i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 8.83335i | − | 0.416872i | −0.978036 | − | 0.208436i | \(-0.933163\pi\) | ||
0.978036 | − | 0.208436i | \(-0.0668372\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.27034 | − | 6.27034i | 0.295259 | − | 0.295259i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 8.70553i | − | 0.408121i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.53330i | 0.165281i | 0.996579 | + | 0.0826404i | \(0.0263353\pi\) | ||||
−0.996579 | + | 0.0826404i | \(0.973665\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.9587 | − | 13.9587i | 0.650123 | − | 0.650123i | −0.302900 | − | 0.953022i | \(-0.597955\pi\) |
0.953022 | + | 0.302900i | \(0.0979547\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.6448i | − | 0.494705i | −0.968926 | − | 0.247353i | \(-0.920439\pi\) | ||
0.968926 | − | 0.247353i | \(-0.0795606\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.4545 | + | 12.4545i | 0.576325 | + | 0.576325i | 0.933889 | − | 0.357564i | \(-0.116393\pi\) |
−0.357564 | + | 0.933889i | \(0.616393\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.98557 | − | 1.98557i | 0.0916852 | − | 0.0916852i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.74444 | −0.218149 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.768175 | − | 0.768175i | −0.0352463 | − | 0.0352463i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.0204 | 1.00614 | 0.503068 | − | 0.864247i | \(-0.332205\pi\) | ||||
0.503068 | + | 0.864247i | \(0.332205\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.345236 | −0.0157414 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.87091 | + | 8.87091i | 0.402807 | + | 0.402807i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.2822 | 1.05502 | 0.527509 | − | 0.849549i | \(-0.323126\pi\) | ||||
0.527509 | + | 0.849549i | \(0.323126\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.129520 | + | 0.129520i | −0.00584515 | + | 0.00584515i | −0.710023 | − | 0.704178i | \(-0.751316\pi\) |
0.704178 | + | 0.710023i | \(0.251316\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.66002 | − | 9.66002i | −0.435065 | − | 0.435065i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.0855i | 0.586967i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.7818 | − | 10.7818i | 0.482661 | − | 0.482661i | −0.423319 | − | 0.905980i | \(-0.639135\pi\) |
0.905980 | + | 0.423319i | \(0.139135\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 6.04034i | − | 0.269326i | −0.990891 | − | 0.134663i | \(-0.957005\pi\) | ||
0.990891 | − | 0.134663i | \(-0.0429951\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.7166i | 0.788378i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.74993 | + | 9.74993i | −0.432158 | + | 0.432158i | −0.889362 | − | 0.457204i | \(-0.848851\pi\) |
0.457204 | + | 0.889362i | \(0.348851\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.50329i | 0.420401i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.65632 | − | 5.65632i | −0.249247 | − | 0.249247i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.46192 | − | 1.46192i | 0.0642954 | − | 0.0642954i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.68047 | −0.0736225 | −0.0368113 | − | 0.999322i | \(-0.511720\pi\) | ||||
−0.0368113 | + | 0.999322i | \(0.511720\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.9606 | + | 16.9606i | 0.741635 | + | 0.741635i | 0.972892 | − | 0.231258i | \(-0.0742841\pi\) |
−0.231258 | + | 0.972892i | \(0.574284\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.94737 | −0.128390 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.8918 | 0.951816 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.5837 | − | 16.5837i | −0.718320 | − | 0.718320i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −35.4617 | −1.53314 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.993222 | + | 0.993222i | −0.0427811 | + | 0.0427811i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.82266 | − | 5.82266i | −0.250336 | − | 0.250336i | 0.570773 | − | 0.821108i | \(-0.306644\pi\) |
−0.821108 | + | 0.570773i | \(0.806644\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 17.7750i | − | 0.761398i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.9661 | − | 15.9661i | 0.682662 | − | 0.682662i | −0.277937 | − | 0.960599i | \(-0.589651\pi\) |
0.960599 | + | 0.277937i | \(0.0896507\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.8736i | − | 0.463231i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 9.85051i | − | 0.418886i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.1695 | − | 14.1695i | 0.600381 | − | 0.600381i | −0.340033 | − | 0.940414i | \(-0.610438\pi\) |
0.940414 | + | 0.340033i | \(0.110438\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.5480i | 0.530725i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.96715 | + | 5.96715i | 0.251485 | + | 0.251485i | 0.821579 | − | 0.570094i | \(-0.193093\pi\) |
−0.570094 | + | 0.821579i | \(0.693093\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.2346 | + | 30.2346i | −1.27198 | + | 1.27198i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.5770 | −0.611099 | −0.305550 | − | 0.952176i | \(-0.598840\pi\) | ||||
−0.305550 | + | 0.952176i | \(0.598840\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.94424 | + | 1.94424i | 0.0813641 | + | 0.0813641i | 0.746618 | − | 0.665253i | \(-0.231677\pi\) |
−0.665253 | + | 0.746618i | \(0.731677\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.517354 | 0.0215752 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.60353 | −0.233278 | −0.116639 | − | 0.993174i | \(-0.537212\pi\) | ||||
−0.116639 | + | 0.993174i | \(0.537212\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.13002 | − | 1.13002i | −0.0468812 | − | 0.0468812i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.1726 | −0.628385 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.8040 | − | 15.8040i | 0.652300 | − | 0.652300i | −0.301246 | − | 0.953546i | \(-0.597403\pi\) |
0.953546 | + | 0.301246i | \(0.0974026\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.65883 | − | 1.65883i | −0.0683507 | − | 0.0683507i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 8.08911i | − | 0.332180i | −0.986111 | − | 0.166090i | \(-0.946886\pi\) | ||
0.986111 | − | 0.166090i | \(-0.0531142\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.60202 | − | 4.60202i | 0.188664 | − | 0.188664i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 25.5885i | − | 1.04552i | −0.852480 | − | 0.522759i | \(-0.824903\pi\) | ||
0.852480 | − | 0.522759i | \(-0.175097\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.8368i | 1.09470i | 0.836905 | + | 0.547348i | \(0.184363\pi\) | ||||
−0.836905 | + | 0.547348i | \(0.815637\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.9580 | + | 14.9580i | −0.608128 | + | 0.608128i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 17.9052i | − | 0.726750i | −0.931643 | − | 0.363375i | \(-0.881624\pi\) | ||
0.931643 | − | 0.363375i | \(-0.118376\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.86648 | − | 3.86648i | −0.156421 | − | 0.156421i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.9653 | − | 13.9653i | 0.564053 | − | 0.564053i | −0.366403 | − | 0.930456i | \(-0.619411\pi\) |
0.930456 | + | 0.366403i | \(0.119411\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.19844 | 0.249540 | 0.124770 | − | 0.992186i | \(-0.460181\pi\) | ||||
0.124770 | + | 0.992186i | \(0.460181\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.7837 | − | 26.7837i | −1.07653 | − | 1.07653i | −0.996818 | − | 0.0797087i | \(-0.974601\pi\) |
−0.0797087 | − | 0.996818i | \(-0.525399\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.04453 | 0.282233 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 27.2157 | 1.08863 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.182502 | − | 0.182502i | −0.00727685 | − | 0.00727685i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.5763 | 1.21723 | 0.608613 | − | 0.793468i | \(-0.291726\pi\) | ||||
0.608613 | + | 0.793468i | \(0.291726\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.165380 | + | 0.165380i | −0.00656289 | + | 0.00656289i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.62686 | + | 2.62686i | 0.104080 | + | 0.104080i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 43.7713i | − | 1.72886i | −0.502752 | − | 0.864431i | \(-0.667679\pi\) | ||
0.502752 | − | 0.864431i | \(-0.332321\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.5474 | − | 24.5474i | 0.968053 | − | 0.968053i | −0.0314518 | − | 0.999505i | \(-0.510013\pi\) |
0.999505 | + | 0.0314518i | \(0.0100131\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.216780i | 0.00852248i | 0.999991 | + | 0.00426124i | \(0.00135640\pi\) | ||||
−0.999991 | + | 0.00426124i | \(0.998644\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 8.25347i | − | 0.323977i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.1867 | − | 12.1867i | 0.476904 | − | 0.476904i | −0.427236 | − | 0.904140i | \(-0.640513\pi\) |
0.904140 | + | 0.427236i | \(0.140513\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 42.5643i | 1.66313i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.3745 | + | 14.3745i | 0.559951 | + | 0.559951i | 0.929293 | − | 0.369343i | \(-0.120417\pi\) |
−0.369343 | + | 0.929293i | \(0.620417\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.7815 | − | 28.7815i | 1.11947 | − | 1.11947i | 0.127651 | − | 0.991819i | \(-0.459256\pi\) |
0.991819 | − | 0.127651i | \(-0.0407436\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.18016 | 0.200878 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.66160 | + | 3.66160i | 0.141778 | + | 0.141778i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.4570 | 0.596710 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.5913 | 1.52613 | 0.763066 | − | 0.646320i | \(-0.223693\pi\) | ||||
0.763066 | + | 0.646320i | \(0.223693\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.7471 | − | 13.7471i | −0.528342 | − | 0.528342i | 0.391735 | − | 0.920078i | \(-0.371875\pi\) |
−0.920078 | + | 0.391735i | \(0.871875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.35352 | −0.205449 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.00325507 | − | 0.00325507i | 0.000124552 | − | 0.000124552i | −0.707045 | − | 0.707169i | \(-0.749972\pi\) |
0.707169 | + | 0.707045i | \(0.249972\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.15197 | + | 5.15197i | 0.196847 | + | 0.196847i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.1283i | 1.52877i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.5751 | − | 17.5751i | 0.668590 | − | 0.668590i | −0.288800 | − | 0.957390i | \(-0.593256\pi\) |
0.957390 | + | 0.288800i | \(0.0932562\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 35.0605i | − | 1.32992i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 17.5333i | − | 0.664122i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.3683 | − | 29.3683i | 1.10923 | − | 1.10923i | 0.115975 | − | 0.993252i | \(-0.463001\pi\) |
0.993252 | − | 0.115975i | \(-0.0369991\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.205430i | − | 0.00774794i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.34591 | − | 5.34591i | −0.201054 | − | 0.201054i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.5493 | + | 21.5493i | −0.809300 | + | 0.809300i | −0.984528 | − | 0.175228i | \(-0.943934\pi\) |
0.175228 | + | 0.984528i | \(0.443934\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.11719 | 0.0418393 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.64652 | − | 8.64652i | −0.323362 | − | 0.323362i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.1027 | 0.861585 | 0.430793 | − | 0.902451i | \(-0.358234\pi\) | ||||
0.430793 | + | 0.902451i | \(0.358234\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.41355 | 0.127127 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.70936 | − | 1.70936i | −0.0634840 | − | 0.0634840i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.8397 | 0.402024 | 0.201012 | − | 0.979589i | \(-0.435577\pi\) | ||||
0.201012 | + | 0.979589i | \(0.435577\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.63328 | + | 6.63328i | −0.245341 | + | 0.245341i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.15354 | − | 5.15354i | −0.190350 | − | 0.190350i | 0.605497 | − | 0.795848i | \(-0.292974\pi\) |
−0.795848 | + | 0.605497i | \(0.792974\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.94423i | − | 0.145287i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.6864 | + | 12.6864i | −0.466678 | + | 0.466678i | −0.900837 | − | 0.434158i | \(-0.857046\pi\) |
0.434158 | + | 0.900837i | \(0.357046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 24.3109i | − | 0.891879i | −0.895063 | − | 0.445940i | \(-0.852870\pi\) | ||
0.895063 | − | 0.445940i | \(-0.147130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.9524i | 0.767635i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.7004 | − | 10.7004i | 0.390985 | − | 0.390985i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 47.8161i | − | 1.74483i | −0.488762 | − | 0.872417i | \(-0.662551\pi\) | ||
0.488762 | − | 0.872417i | \(-0.337449\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38.0109 | − | 38.0109i | −1.38336 | − | 1.38336i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.6181 | − | 20.6181i | 0.749377 | − | 0.749377i | −0.224986 | − | 0.974362i | \(-0.572234\pi\) |
0.974362 | + | 0.224986i | \(0.0722335\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.6635 | −0.676553 | −0.338276 | − | 0.941047i | \(-0.609844\pi\) | ||||
−0.338276 | + | 0.941047i | \(0.609844\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.36354 | + | 5.36354i | 0.194173 | + | 0.194173i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.8287 | −0.788187 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.7015 | −0.494090 | −0.247045 | − | 0.969004i | \(-0.579459\pi\) | ||||
−0.247045 | + | 0.969004i | \(0.579459\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.1383 | + | 21.1383i | 0.760294 | + | 0.760294i | 0.976375 | − | 0.216082i | \(-0.0693278\pi\) |
−0.216082 | + | 0.976375i | \(0.569328\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.521543 | −0.0187344 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.86801 | − | 9.86801i | 0.353558 | − | 0.353558i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.9969 | + | 12.9969i | 0.465064 | + | 0.465064i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 42.1774i | − | 1.50538i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.7503 | + | 25.7503i | −0.917899 | + | 0.917899i | −0.996876 | − | 0.0789778i | \(-0.974834\pi\) |
0.0789778 | + | 0.996876i | \(0.474834\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 18.2463i | − | 0.648765i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 40.8804i | − | 1.45171i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.2613 | − | 13.2613i | 0.469739 | − | 0.469739i | −0.432091 | − | 0.901830i | \(-0.642224\pi\) |
0.901830 | + | 0.432091i | \(0.142224\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4.08788i | − | 0.144619i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.43887 | + | 9.43887i | 0.333091 | + | 0.333091i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.74438 | + | 1.74438i | −0.0614814 | + | 0.0614814i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.0568 | 1.37316 | 0.686582 | − | 0.727053i | \(-0.259110\pi\) | ||||
0.686582 | + | 0.727053i | \(0.259110\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.8627 | − | 11.8627i | −0.416554 | − | 0.416554i | 0.467460 | − | 0.884014i | \(-0.345169\pi\) |
−0.884014 | + | 0.467460i | \(0.845169\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.7722 | −0.657563 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.46661 | −0.261224 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.89485 | + | 7.89485i | 0.275532 | + | 0.275532i | 0.831323 | − | 0.555790i | \(-0.187584\pi\) |
−0.555790 | + | 0.831323i | \(0.687584\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.6159 | 0.823199 | 0.411600 | − | 0.911365i | \(-0.364970\pi\) | ||||
0.411600 | + | 0.911365i | \(0.364970\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.44372 | − | 2.44372i | 0.0849766 | − | 0.0849766i | −0.663341 | − | 0.748317i | \(-0.730862\pi\) |
0.748317 | + | 0.663341i | \(0.230862\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.3029 | + | 29.3029i | 1.01773 | + | 1.01773i | 0.999840 | + | 0.0178910i | \(0.00569520\pi\) |
0.0178910 | + | 0.999840i | \(0.494305\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.77728i | 0.0962271i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33.7114 | + | 33.7114i | −1.16663 | + | 1.16663i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 25.2593i | − | 0.872047i | −0.899935 | − | 0.436024i | \(-0.856386\pi\) | ||
0.899935 | − | 0.436024i | \(-0.143614\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.80385i | 0.165650i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.32691 | + | 1.32691i | −0.0456472 | + | 0.0456472i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 9.02702i | − | 0.310172i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.0691771 | + | 0.0691771i | 0.00237136 | + | 0.00237136i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.7213 | − | 25.7213i | 0.880680 | − | 0.880680i | −0.112924 | − | 0.993604i | \(-0.536022\pi\) |
0.993604 | + | 0.112924i | \(0.0360215\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −46.7116 | −1.59564 | −0.797819 | − | 0.602897i | \(-0.794013\pi\) | ||||
−0.797819 | + | 0.602897i | \(0.794013\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.01594 | + | 2.01594i | 0.0687829 | + | 0.0687829i | 0.740661 | − | 0.671878i | \(-0.234512\pi\) |
−0.671878 | + | 0.740661i | \(0.734512\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.21180 | 0.245493 | 0.122746 | − | 0.992438i | \(-0.460830\pi\) | ||||
0.122746 | + | 0.992438i | \(0.460830\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.0826 | 0.444823 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.78374 | − | 9.78374i | −0.331891 | − | 0.331891i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.4316 | −0.353462 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.47078 | + | 7.47078i | −0.252558 | + | 0.252558i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.12742 | − | 8.12742i | −0.274443 | − | 0.274443i | 0.556443 | − | 0.830886i | \(-0.312166\pi\) |
−0.830886 | + | 0.556443i | \(0.812166\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 41.1175i | − | 1.38529i | −0.721281 | − | 0.692643i | \(-0.756446\pi\) | ||
0.721281 | − | 0.692643i | \(-0.243554\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.38694 | + | 9.38694i | −0.315896 | + | 0.315896i | −0.847188 | − | 0.531293i | \(-0.821706\pi\) |
0.531293 | + | 0.847188i | \(0.321706\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 17.8506i | − | 0.599366i | −0.954039 | − | 0.299683i | \(-0.903119\pi\) | ||
0.954039 | − | 0.299683i | \(-0.0968809\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 0.0998053i | − | 0.00334736i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.30072 | − | 2.30072i | 0.0769906 | − | 0.0769906i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 41.6777i | 1.39313i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.69125 | − | 3.69125i | −0.123110 | − | 0.123110i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.2131 | + | 21.2131i | −0.706710 | + | 0.706710i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 53.0698 | 1.76410 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.6866 | + | 16.6866i | 0.554070 | + | 0.554070i | 0.927613 | − | 0.373543i | \(-0.121857\pi\) |
−0.373543 | + | 0.927613i | \(0.621857\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.1236 | 1.62754 | 0.813769 | − | 0.581189i | \(-0.197412\pi\) | ||||
0.813769 | + | 0.581189i | \(0.197412\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.24472 | −0.0742895 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.8436 | − | 12.8436i | −0.424134 | − | 0.424134i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.5272 | −1.53479 | −0.767395 | − | 0.641174i | \(-0.778448\pi\) | ||||
−0.767395 | + | 0.641174i | \(0.778448\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.3739 | − | 34.3739i | 1.13143 | − | 1.13143i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.0322941 | − | 0.0322941i | −0.00106182 | − | 0.00106182i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.44879i | 0.145960i | 0.997333 | + | 0.0729800i | \(0.0232509\pi\) | ||||
−0.997333 | + | 0.0729800i | \(0.976749\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.56309 | + | 1.56309i | −0.0512283 | + | 0.0512283i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 9.14165i | − | 0.298964i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 45.1282i | − | 1.47428i | −0.675742 | − | 0.737138i | \(-0.736177\pi\) | ||
0.675742 | − | 0.737138i | \(-0.263823\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.54964 | + | 7.54964i | −0.246111 | + | 0.246111i | −0.819373 | − | 0.573261i | \(-0.805678\pi\) |
0.573261 | + | 0.819373i | \(0.305678\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.64596i | 0.216422i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.1642 | + | 16.1642i | 0.525265 | + | 0.525265i | 0.919157 | − | 0.393892i | \(-0.128872\pi\) |
−0.393892 | + | 0.919157i | \(0.628872\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.9638 | − | 24.9638i | 0.810359 | − | 0.810359i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.4691 | −0.630667 | −0.315334 | − | 0.948981i | \(-0.602116\pi\) | ||||
−0.315334 | + | 0.948981i | \(0.602116\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.6086 | − | 19.6086i | −0.634519 | − | 0.634519i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.10918 | −0.100401 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.8738 | 0.963670 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 34.9667 | + | 34.9667i | 1.12562 | + | 1.12562i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.4224 | 1.52500 | 0.762501 | − | 0.646987i | \(-0.223971\pi\) | ||||
0.762501 | + | 0.646987i | \(0.223971\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.3134 | + | 26.3134i | −0.844437 | + | 0.844437i | −0.989432 | − | 0.144995i | \(-0.953683\pi\) |
0.144995 | + | 0.989432i | \(0.453683\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.5794 | + | 10.5794i | 0.339159 | + | 0.339159i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 15.9988i | − | 0.511848i | −0.966697 | − | 0.255924i | \(-0.917620\pi\) | ||
0.966697 | − | 0.255924i | \(-0.0823797\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.99678 | − | 6.99678i | 0.223618 | − | 0.223618i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.1634i | 0.834483i | 0.908796 | + | 0.417242i | \(0.137003\pi\) | ||||
−0.908796 | + | 0.417242i | \(0.862997\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 19.3311i | − | 0.615939i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.51433 | − | 2.51433i | 0.0799509 | − | 0.0799509i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 18.2140i | − | 0.578587i | −0.957240 | − | 0.289294i | \(-0.906580\pi\) | ||
0.957240 | − | 0.289294i | \(-0.0934204\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38.5863 | − | 38.5863i | −1.22327 | − | 1.22327i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.0322 | + | 10.0322i | −0.317722 | + | 0.317722i | −0.847892 | − | 0.530170i | \(-0.822128\pi\) |
0.530170 | + | 0.847892i | \(0.322128\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 4032.2.v.e.1583.16 | 40 | ||
3.2 | odd | 2 | inner | 4032.2.v.e.1583.5 | 40 | ||
4.3 | odd | 2 | 1008.2.v.e.323.15 | yes | 40 | ||
12.11 | even | 2 | 1008.2.v.e.323.6 | ✓ | 40 | ||
16.5 | even | 4 | 1008.2.v.e.827.6 | yes | 40 | ||
16.11 | odd | 4 | inner | 4032.2.v.e.3599.5 | 40 | ||
48.5 | odd | 4 | 1008.2.v.e.827.15 | yes | 40 | ||
48.11 | even | 4 | inner | 4032.2.v.e.3599.16 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.v.e.323.6 | ✓ | 40 | 12.11 | even | 2 | ||
1008.2.v.e.323.15 | yes | 40 | 4.3 | odd | 2 | ||
1008.2.v.e.827.6 | yes | 40 | 16.5 | even | 4 | ||
1008.2.v.e.827.15 | yes | 40 | 48.5 | odd | 4 | ||
4032.2.v.e.1583.5 | 40 | 3.2 | odd | 2 | inner | ||
4032.2.v.e.1583.16 | 40 | 1.1 | even | 1 | trivial | ||
4032.2.v.e.3599.5 | 40 | 16.11 | odd | 4 | inner | ||
4032.2.v.e.3599.16 | 40 | 48.11 | even | 4 | inner |