Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(449,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.m (of order \(4\), 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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 449.4 | ||
Root | \(0.500000 + 2.10607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.449 |
Dual form | 1792.2.m.b.1345.4 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 0.898966 | − | 0.898966i | 0.519018 | − | 0.519018i | −0.398256 | − | 0.917274i | \(-0.630384\pi\) |
0.917274 | + | 0.398256i | \(0.130384\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.786578 | − | 0.786578i | −0.351768 | − | 0.351768i | 0.508999 | − | 0.860767i | \(-0.330016\pi\) |
−0.860767 | + | 0.508999i | \(0.830016\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.38372i | 0.461240i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.15894 | + | 2.15894i | 0.650945 | + | 0.650945i | 0.953221 | − | 0.302275i | \(-0.0977462\pi\) |
−0.302275 | + | 0.953221i | \(0.597746\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.31318 | − | 1.31318i | 0.364211 | − | 0.364211i | −0.501150 | − | 0.865360i | \(-0.667089\pi\) |
0.865360 | + | 0.501150i | \(0.167089\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.79793 | −0.436063 | −0.218031 | − | 0.975942i | \(-0.569964\pi\) | ||||
−0.218031 | + | 0.975942i | \(0.569964\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.531306 | − | 0.531306i | 0.121890 | − | 0.121890i | −0.643531 | − | 0.765420i | \(-0.722531\pi\) |
0.765420 | + | 0.643531i | \(0.222531\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.898966 | − | 0.898966i | −0.196171 | − | 0.196171i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.95687i | − | 1.24209i | −0.783773 | − | 0.621047i | \(-0.786708\pi\) | ||
0.783773 | − | 0.621047i | \(-0.213292\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 3.76259i | − | 0.752518i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.94082 | + | 3.94082i | 0.758410 | + | 0.758410i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.62636 | − | 5.62636i | 1.04479 | − | 1.04479i | 0.0458400 | − | 0.998949i | \(-0.485404\pi\) |
0.998949 | − | 0.0458400i | \(-0.0145964\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.34059 | 0.779594 | 0.389797 | − | 0.920901i | \(-0.372545\pi\) | ||||
0.389797 | + | 0.920901i | \(0.372545\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.88163 | 0.675705 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.786578 | + | 0.786578i | −0.132956 | + | 0.132956i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.12845 | + | 2.12845i | 0.349915 | + | 0.349915i | 0.860078 | − | 0.510163i | \(-0.170415\pi\) |
−0.510163 | + | 0.860078i | \(0.670415\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.36101i | − | 0.378064i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.712611i | − | 0.111291i | −0.998451 | − | 0.0556456i | \(-0.982278\pi\) | ||
0.998451 | − | 0.0556456i | \(-0.0177217\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.96951 | + | 2.96951i | 0.452845 | + | 0.452845i | 0.896298 | − | 0.443453i | \(-0.146247\pi\) |
−0.443453 | + | 0.896298i | \(0.646247\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.08840 | − | 1.08840i | 0.162249 | − | 0.162249i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.20207 | −0.321205 | −0.160602 | − | 0.987019i | \(-0.551344\pi\) | ||||
−0.160602 | + | 0.987019i | \(0.551344\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.61628 | + | 1.61628i | −0.226325 | + | 0.226325i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.38372 | − | 3.38372i | −0.464790 | − | 0.464790i | 0.435432 | − | 0.900222i | \(-0.356596\pi\) |
−0.900222 | + | 0.435432i | \(0.856596\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.39635i | − | 0.457964i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.955252i | − | 0.126526i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.41549 | + | 2.41549i | 0.314470 | + | 0.314470i | 0.846638 | − | 0.532168i | \(-0.178623\pi\) |
−0.532168 | + | 0.846638i | \(0.678623\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.09505 | − | 7.09505i | 0.908429 | − | 0.908429i | −0.0877169 | − | 0.996145i | \(-0.527957\pi\) |
0.996145 | + | 0.0877169i | \(0.0279571\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.38372 | 0.174332 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.06584 | −0.256235 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.76744 | + | 6.76744i | −0.826774 | + | 0.826774i | −0.987069 | − | 0.160295i | \(-0.948755\pi\) |
0.160295 | + | 0.987069i | \(0.448755\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.35503 | − | 5.35503i | −0.644670 | − | 0.644670i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.96788i | − | 0.233545i | −0.993159 | − | 0.116772i | \(-0.962745\pi\) | ||
0.993159 | − | 0.116772i | \(-0.0372548\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.3633i | − | 1.21293i | −0.795109 | − | 0.606466i | \(-0.792586\pi\) | ||
0.795109 | − | 0.606466i | \(-0.207414\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.38244 | − | 3.38244i | −0.390571 | − | 0.390571i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.15894 | − | 2.15894i | 0.246034 | − | 0.246034i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.2449 | −1.60268 | −0.801340 | − | 0.598209i | \(-0.795879\pi\) | ||||
−0.801340 | + | 0.598209i | \(0.795879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.93416 | 0.326018 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.95217 | − | 5.95217i | 0.653336 | − | 0.653336i | −0.300459 | − | 0.953795i | \(-0.597140\pi\) |
0.953795 | + | 0.300459i | \(0.0971399\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.41421 | + | 1.41421i | 0.153393 | + | 0.153393i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 10.1158i | − | 1.08453i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 16.9417i | − | 1.79582i | −0.440184 | − | 0.897908i | \(-0.645087\pi\) | ||
0.440184 | − | 0.897908i | \(-0.354913\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.31318 | − | 1.31318i | −0.137659 | − | 0.137659i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.90205 | − | 3.90205i | 0.404623 | − | 0.404623i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.835826 | −0.0857540 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.6796 | 1.79509 | 0.897544 | − | 0.440925i | \(-0.145350\pi\) | ||||
0.897544 | + | 0.440925i | \(0.145350\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.98737 | + | 2.98737i | −0.300242 | + | 0.300242i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.66156 | − | 6.66156i | −0.662850 | − | 0.662850i | 0.293201 | − | 0.956051i | \(-0.405279\pi\) |
−0.956051 | + | 0.293201i | \(0.905279\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.88418i | − | 0.185654i | −0.995682 | − | 0.0928271i | \(-0.970410\pi\) | ||
0.995682 | − | 0.0928271i | \(-0.0295904\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.41421i | 0.138013i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.94909 | + | 8.94909i | 0.865141 | + | 0.865141i | 0.991930 | − | 0.126789i | \(-0.0404670\pi\) |
−0.126789 | + | 0.991930i | \(0.540467\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.73210 | + | 4.73210i | −0.453253 | + | 0.453253i | −0.896433 | − | 0.443180i | \(-0.853850\pi\) |
0.443180 | + | 0.896433i | \(0.353850\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.82680 | 0.363224 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.93416 | −0.746383 | −0.373192 | − | 0.927754i | \(-0.621737\pi\) | ||||
−0.373192 | + | 0.927754i | \(0.621737\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.68554 | + | 4.68554i | −0.436929 | + | 0.436929i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.81707 | + | 1.81707i | 0.167988 | + | 0.167988i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.79793i | 0.164816i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 1.67794i | − | 0.152540i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.640613 | − | 0.640613i | −0.0577622 | − | 0.0577622i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.89246 | + | 6.89246i | −0.616480 | + | 0.616480i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.93161 | −0.703817 | −0.351908 | − | 0.936034i | \(-0.614467\pi\) | ||||
−0.351908 | + | 0.936034i | \(0.614467\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.33897 | 0.470070 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.98429 | + | 5.98429i | −0.522850 | + | 0.522850i | −0.918431 | − | 0.395581i | \(-0.870543\pi\) |
0.395581 | + | 0.918431i | \(0.370543\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.531306 | − | 0.531306i | −0.0460700 | − | 0.0460700i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 6.19951i | − | 0.533569i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 12.3380i | − | 1.05411i | −0.849831 | − | 0.527055i | \(-0.823296\pi\) | ||
0.849831 | − | 0.527055i | \(-0.176704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.0393 | + | 13.0393i | 1.10598 | + | 1.10598i | 0.993674 | + | 0.112305i | \(0.0358234\pi\) |
0.112305 | + | 0.993674i | \(0.464177\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.97958 | + | 1.97958i | −0.166711 | + | 0.166711i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.67016 | 0.474162 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.85114 | −0.735047 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.898966 | + | 0.898966i | −0.0741455 | + | 0.0741455i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.62798 | + | 8.62798i | 0.706832 | + | 0.706832i | 0.965868 | − | 0.259036i | \(-0.0834048\pi\) |
−0.259036 | + | 0.965868i | \(0.583405\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.55274i | 0.777391i | 0.921366 | + | 0.388695i | \(0.127074\pi\) | ||||
−0.921366 | + | 0.388695i | \(0.872926\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.48783i | − | 0.201129i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.41421 | − | 3.41421i | −0.274236 | − | 0.274236i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.25742 | − | 8.25742i | 0.659014 | − | 0.659014i | −0.296133 | − | 0.955147i | \(-0.595697\pi\) |
0.955147 | + | 0.296133i | \(0.0956971\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.08370 | −0.482469 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.95687 | −0.469467 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.01263 | + | 1.01263i | −0.0793154 | + | 0.0793154i | −0.745652 | − | 0.666336i | \(-0.767862\pi\) |
0.666336 | + | 0.745652i | \(0.267862\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.05320 | − | 3.05320i | −0.237692 | − | 0.237692i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.79793i | 0.448657i | 0.974514 | + | 0.224329i | \(0.0720189\pi\) | ||||
−0.974514 | + | 0.224329i | \(0.927981\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.55112i | 0.734701i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.735178 | + | 0.735178i | 0.0562205 | + | 0.0562205i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.65215 | + | 2.65215i | −0.201639 | + | 0.201639i | −0.800702 | − | 0.599063i | \(-0.795540\pi\) |
0.599063 | + | 0.800702i | \(0.295540\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.76259 | −0.284425 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.34289 | 0.326431 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.55045 | − | 1.55045i | 0.115886 | − | 0.115886i | −0.646786 | − | 0.762672i | \(-0.723887\pi\) |
0.762672 | + | 0.646786i | \(0.223887\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0315 | + | 11.0315i | 0.819966 | + | 0.819966i | 0.986103 | − | 0.166137i | \(-0.0531293\pi\) |
−0.166137 | + | 0.986103i | \(0.553129\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 12.7564i | − | 0.942982i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.34838i | − | 0.246178i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.88163 | − | 3.88163i | −0.283853 | − | 0.283853i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.94082 | − | 3.94082i | 0.286652 | − | 0.286652i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.5664 | −1.19870 | −0.599352 | − | 0.800485i | \(-0.704575\pi\) | ||||
−0.599352 | + | 0.800485i | \(0.704575\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.3795 | 1.25101 | 0.625503 | − | 0.780221i | \(-0.284894\pi\) | ||||
0.625503 | + | 0.780221i | \(0.284894\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.85712 | + | 1.85712i | −0.132991 | + | 0.132991i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.44110 | + | 1.44110i | 0.102674 | + | 0.102674i | 0.756578 | − | 0.653904i | \(-0.226870\pi\) |
−0.653904 | + | 0.756578i | \(0.726870\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.1438i | 0.931736i | 0.884854 | + | 0.465868i | \(0.154258\pi\) | ||||
−0.884854 | + | 0.465868i | \(0.845742\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.1674i | 0.858222i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.62636 | − | 5.62636i | −0.394893 | − | 0.394893i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.560524 | + | 0.560524i | −0.0391487 | + | 0.0391487i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.24264 | 0.572903 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.29412 | 0.158687 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.59587 | − | 3.59587i | 0.247550 | − | 0.247550i | −0.572415 | − | 0.819964i | \(-0.693993\pi\) |
0.819964 | + | 0.572415i | \(0.193993\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.76906 | − | 1.76906i | −0.121214 | − | 0.121214i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 4.67149i | − | 0.318593i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 4.34059i | − | 0.294659i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.31626 | − | 9.31626i | −0.629535 | − | 0.629535i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.36101 | + | 2.36101i | −0.158819 | + | 0.158819i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.5132 | 1.84242 | 0.921211 | − | 0.389064i | \(-0.127201\pi\) | ||||
0.921211 | + | 0.389064i | \(0.127201\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.20637 | 0.347091 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.0418 | − | 11.0418i | 0.732873 | − | 0.732873i | −0.238315 | − | 0.971188i | \(-0.576595\pi\) |
0.971188 | + | 0.238315i | \(0.0765950\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.9717 | − | 11.9717i | −0.791109 | − | 0.791109i | 0.190565 | − | 0.981675i | \(-0.438968\pi\) |
−0.981675 | + | 0.190565i | \(0.938968\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 3.88163i | − | 0.255393i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.7013i | 1.88029i | 0.340778 | + | 0.940144i | \(0.389310\pi\) | ||||
−0.340778 | + | 0.940144i | \(0.610690\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.73210 | + | 1.73210i | 0.112990 | + | 0.112990i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.8057 | + | 12.8057i | −0.831821 | + | 0.831821i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.6348 | −1.07602 | −0.538008 | − | 0.842939i | \(-0.680823\pi\) | ||||
−0.538008 | + | 0.842939i | \(0.680823\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.77267 | −0.243019 | −0.121510 | − | 0.992590i | \(-0.538773\pi\) | ||||
−0.121510 | + | 0.992590i | \(0.538773\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.18473 | + | 9.18473i | −0.589201 | + | 0.589201i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.786578 | + | 0.786578i | 0.0502526 | + | 0.0502526i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.39540i | − | 0.0887872i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 10.7016i | − | 0.678186i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.1264 | + | 20.1264i | 1.27037 | + | 1.27037i | 0.945895 | + | 0.324474i | \(0.105187\pi\) |
0.324474 | + | 0.945895i | \(0.394813\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.8605 | − | 12.8605i | 0.808535 | − | 0.808535i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.54266 | 0.159228 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.8408 | −1.61190 | −0.805952 | − | 0.591980i | \(-0.798346\pi\) | ||||
−0.805952 | + | 0.591980i | \(0.798346\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.12845 | − | 2.12845i | 0.132255 | − | 0.132255i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.78530 | + | 7.78530i | 0.481898 | + | 0.481898i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.24035i | 0.138146i | 0.997612 | + | 0.0690728i | \(0.0220041\pi\) | ||||
−0.997612 | + | 0.0690728i | \(0.977996\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.32312i | 0.326996i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.2300 | − | 15.2300i | −0.932061 | − | 0.932061i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.3489 | + | 13.3489i | −0.813897 | + | 0.813897i | −0.985216 | − | 0.171319i | \(-0.945197\pi\) |
0.171319 | + | 0.985216i | \(0.445197\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.5670 | 0.824136 | 0.412068 | − | 0.911153i | \(-0.364807\pi\) | ||||
0.412068 | + | 0.911153i | \(0.364807\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.36101 | −0.142895 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.12322 | − | 8.12322i | 0.489848 | − | 0.489848i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.22060 | + | 8.22060i | 0.493928 | + | 0.493928i | 0.909541 | − | 0.415613i | \(-0.136433\pi\) |
−0.415613 | + | 0.909541i | \(0.636433\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.00616i | 0.359580i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.95365i | 0.295510i | 0.989024 | + | 0.147755i | \(0.0472047\pi\) | ||||
−0.989024 | + | 0.147755i | \(0.952795\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.6184 | − | 15.6184i | −0.928419 | − | 0.928419i | 0.0691845 | − | 0.997604i | \(-0.477960\pi\) |
−0.997604 | + | 0.0691845i | \(0.977960\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.751380 | + | 0.751380i | −0.0445079 | + | 0.0445079i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.712611 | −0.0420641 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.7674 | −0.809849 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.8933 | − | 15.8933i | 0.931684 | − | 0.931684i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.6749 | − | 14.6749i | −0.857315 | − | 0.857315i | 0.133706 | − | 0.991021i | \(-0.457312\pi\) |
−0.991021 | + | 0.133706i | \(0.957312\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3.79994i | − | 0.221241i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.0160i | 0.987367i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.82245 | − | 7.82245i | −0.452384 | − | 0.452384i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.96951 | − | 2.96951i | 0.171159 | − | 0.171159i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.9770 | −0.688063 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.1616 | −0.639113 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.72484 | − | 9.72484i | 0.555026 | − | 0.555026i | −0.372861 | − | 0.927887i | \(-0.621623\pi\) |
0.927887 | + | 0.372861i | \(0.121623\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.69382 | − | 1.69382i | −0.0963579 | − | 0.0963579i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.1376i | 1.53883i | 0.638748 | + | 0.769416i | \(0.279453\pi\) | ||||
−0.638748 | + | 0.769416i | \(0.720547\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.1116i | 0.741114i | 0.928810 | + | 0.370557i | \(0.120833\pi\) | ||||
−0.928810 | + | 0.370557i | \(0.879167\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.08840 | − | 1.08840i | −0.0613245 | − | 0.0613245i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.4901 | − | 11.4901i | 0.645350 | − | 0.645350i | −0.306516 | − | 0.951866i | \(-0.599163\pi\) |
0.951866 | + | 0.306516i | \(0.0991632\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.2940 | 1.36020 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.0899 | 0.898048 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.955252 | + | 0.955252i | −0.0531516 | + | 0.0531516i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.94096 | − | 4.94096i | −0.274075 | − | 0.274075i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.50799i | 0.470493i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.20207i | 0.121404i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.4094 | − | 11.4094i | −0.627116 | − | 0.627116i | 0.320226 | − | 0.947341i | \(-0.396241\pi\) |
−0.947341 | + | 0.320226i | \(0.896241\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.94517 | + | 2.94517i | −0.161394 | + | 0.161394i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.6462 | 0.581666 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.6355 | −1.66882 | −0.834411 | − | 0.551142i | \(-0.814192\pi\) | ||||
−0.834411 | + | 0.551142i | \(0.814192\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.13255 | + | 7.13255i | −0.387387 | + | 0.387387i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.37109 | + | 9.37109i | 0.507473 | + | 0.507473i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.42429i | 0.453549i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.28321 | + | 4.28321i | 0.229935 | + | 0.229935i | 0.812665 | − | 0.582730i | \(-0.198016\pi\) |
−0.582730 | + | 0.812665i | \(0.698016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.9861 | + | 22.9861i | −1.23042 | + | 1.23042i | −0.266614 | + | 0.963803i | \(0.585905\pi\) |
−0.963803 | + | 0.266614i | \(0.914095\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.3500 | 0.552442 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.0523 | 0.854376 | 0.427188 | − | 0.904163i | \(-0.359504\pi\) | ||||
0.427188 | + | 0.904163i | \(0.359504\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.54789 | + | 1.54789i | −0.0821536 | + | 0.0821536i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.61628 | + | 1.61628i | 0.0855427 | + | 0.0855427i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.8317i | 0.835563i | 0.908548 | + | 0.417781i | \(0.137192\pi\) | ||||
−0.908548 | + | 0.417781i | \(0.862808\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.4354i | 0.970286i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.50841 | − | 1.50841i | −0.0791712 | − | 0.0791712i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.15154 | + | 8.15154i | −0.426671 | + | 0.426671i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 37.3527 | 1.94979 | 0.974897 | − | 0.222656i | \(-0.0714728\pi\) | ||||
0.974897 | + | 0.222656i | \(0.0714728\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.986054 | 0.0513319 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.38372 | + | 3.38372i | −0.175674 | + | 0.175674i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.4321 | + | 12.4321i | 0.643709 | + | 0.643709i | 0.951465 | − | 0.307757i | \(-0.0995782\pi\) |
−0.307757 | + | 0.951465i | \(0.599578\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.3922i | 0.639929i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 14.7768i | − | 0.761046i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.68374 | + | 2.68374i | 0.137854 | + | 0.137854i | 0.772667 | − | 0.634812i | \(-0.218923\pi\) |
−0.634812 | + | 0.772667i | \(0.718923\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.13025 | + | 7.13025i | −0.365294 | + | 0.365294i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.7195 | −0.547739 | −0.273870 | − | 0.961767i | \(-0.588304\pi\) | ||||
−0.273870 | + | 0.961767i | \(0.588304\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.39635 | −0.173094 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.10896 | + | 4.10896i | −0.208870 | + | 0.208870i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.4499 | − | 18.4499i | −0.935449 | − | 0.935449i | 0.0625902 | − | 0.998039i | \(-0.480064\pi\) |
−0.998039 | + | 0.0625902i | \(0.980064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.7101i | 0.541631i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.7593i | 0.542737i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.2047 | + | 11.2047i | 0.563772 | + | 0.563772i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.43982 | − | 8.43982i | 0.423583 | − | 0.423583i | −0.462853 | − | 0.886435i | \(-0.653174\pi\) |
0.886435 | + | 0.462853i | \(0.153174\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.955252 | −0.0478224 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.3744 | −1.66664 | −0.833320 | − | 0.552791i | \(-0.813563\pi\) | ||||
−0.833320 | + | 0.552791i | \(0.813563\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.69998 | − | 5.69998i | 0.283936 | − | 0.283936i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.30795 | − | 2.30795i | −0.114683 | − | 0.114683i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.19039i | 0.455551i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 8.19011i | − | 0.404975i | −0.979285 | − | 0.202487i | \(-0.935097\pi\) | ||
0.979285 | − | 0.202487i | \(-0.0649025\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.0915 | − | 11.0915i | −0.547103 | − | 0.547103i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.41549 | − | 2.41549i | 0.118858 | − | 0.118858i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.36369 | −0.459645 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 23.4438 | 1.14805 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.7021 | − | 21.7021i | 1.06022 | − | 1.06022i | 0.0621518 | − | 0.998067i | \(-0.480204\pi\) |
0.998067 | − | 0.0621518i | \(-0.0197963\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.4513 | + | 27.4513i | 1.33789 | + | 1.33789i | 0.898097 | + | 0.439798i | \(0.144950\pi\) |
0.439798 | + | 0.898097i | \(0.355050\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 3.04704i | − | 0.148152i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.76489i | 0.328145i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.09505 | − | 7.09505i | −0.343354 | − | 0.343354i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.09728 | − | 5.09728i | 0.246099 | − | 0.246099i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.85598 | 0.330241 | 0.165121 | − | 0.986273i | \(-0.447199\pi\) | ||||
0.165121 | + | 0.986273i | \(0.447199\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.3144 | 1.88933 | 0.944665 | − | 0.328037i | \(-0.106387\pi\) | ||||
0.944665 | + | 0.328037i | \(0.106387\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.95687 | + | 7.95687i | −0.381503 | + | 0.381503i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.16492 | − | 3.16492i | −0.151399 | − | 0.151399i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.76192i | 0.0840918i | 0.999116 | + | 0.0420459i | \(0.0133876\pi\) | ||||
−0.999116 | + | 0.0420459i | \(0.986612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 1.38372i | − | 0.0658914i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.1344 | − | 13.1344i | −0.624032 | − | 0.624032i | 0.322528 | − | 0.946560i | \(-0.395467\pi\) |
−0.946560 | + | 0.322528i | \(0.895467\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.3260 | + | 13.3260i | −0.631711 | + | 0.631711i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.5125 | 0.733718 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.8852 | −0.938443 | −0.469221 | − | 0.883081i | \(-0.655465\pi\) | ||||
−0.469221 | + | 0.883081i | \(0.655465\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.53849 | − | 1.53849i | 0.0724445 | − | 0.0724445i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.58759 | + | 8.58759i | 0.403480 | + | 0.403480i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.06584i | 0.0968479i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.7983i | 0.785792i | 0.919583 | + | 0.392896i | \(0.128527\pi\) | ||||
−0.919583 | + | 0.392896i | \(0.871473\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.08532 | − | 7.08532i | −0.330714 | − | 0.330714i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.5576 | + | 23.5576i | −1.09719 | + | 1.09719i | −0.102450 | + | 0.994738i | \(0.532668\pi\) |
−0.994738 | + | 0.102450i | \(0.967332\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.6063 | −0.632340 | −0.316170 | − | 0.948703i | \(-0.602397\pi\) | ||||
−0.316170 | + | 0.948703i | \(0.602397\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.13853 | −0.284667 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.8703 | − | 17.8703i | 0.826938 | − | 0.826938i | −0.160154 | − | 0.987092i | \(-0.551199\pi\) |
0.987092 | + | 0.160154i | \(0.0511992\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.76744 | + | 6.76744i | 0.312491 | + | 0.312491i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 14.8463i | − | 0.684081i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.8220i | 0.589555i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.99909 | − | 1.99909i | −0.0917244 | − | 0.0917244i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.68212 | − | 4.68212i | 0.214379 | − | 0.214379i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −37.3075 | −1.70463 | −0.852313 | − | 0.523033i | \(-0.824801\pi\) | ||||
−0.852313 | + | 0.523033i | \(0.824801\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.59007 | 0.254885 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.35503 | + | 5.35503i | −0.243662 | + | 0.243662i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.9063 | − | 13.9063i | −0.631455 | − | 0.631455i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.61373i | − | 0.345011i | −0.985009 | − | 0.172505i | \(-0.944814\pi\) | ||
0.985009 | − | 0.172505i | \(-0.0551863\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.82064i | 0.0823323i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.1091 | − | 25.1091i | −1.13316 | − | 1.13316i | −0.989649 | − | 0.143508i | \(-0.954162\pi\) |
−0.143508 | − | 0.989649i | \(-0.545838\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.1158 | + | 10.1158i | −0.455593 | + | 0.455593i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.69959 | 0.211231 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.96788 | −0.0882716 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.5674 | + | 16.5674i | −0.741658 | + | 0.741658i | −0.972897 | − | 0.231239i | \(-0.925722\pi\) |
0.231239 | + | 0.972897i | \(0.425722\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.21215 | + | 5.21215i | 0.232862 | + | 0.232862i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.9297i | 1.46826i | 0.679007 | + | 0.734132i | \(0.262411\pi\) | ||||
−0.679007 | + | 0.734132i | \(0.737589\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.4797i | 0.466339i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.58613 | + | 8.58613i | 0.381324 | + | 0.381324i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.330168 | − | 0.330168i | 0.0146345 | − | 0.0146345i | −0.699752 | − | 0.714386i | \(-0.746706\pi\) |
0.714386 | + | 0.699752i | \(0.246706\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.3633 | −0.458446 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.18756 | 0.184885 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.48206 | + | 1.48206i | −0.0653072 | + | 0.0653072i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.75413 | − | 4.75413i | −0.209087 | − | 0.209087i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.76839i | 0.209309i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.94331i | − | 0.260381i | −0.991489 | − | 0.130191i | \(-0.958441\pi\) | ||
0.991489 | − | 0.130191i | \(-0.0415589\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.4703 | − | 14.4703i | −0.632743 | − | 0.632743i | 0.316012 | − | 0.948755i | \(-0.397656\pi\) |
−0.948755 | + | 0.316012i | \(0.897656\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.38244 | + | 3.38244i | −0.147622 | + | 0.147622i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.80409 | −0.339952 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.4844 | −0.542798 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.34236 | + | 3.34236i | −0.145046 | + | 0.145046i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.935787 | − | 0.935787i | −0.0405334 | − | 0.0405334i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 14.0783i | − | 0.608658i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 2.78760i | − | 0.120294i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.15894 | − | 2.15894i | −0.0929922 | − | 0.0929922i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.23256 | − | 8.23256i | 0.353945 | − | 0.353945i | −0.507630 | − | 0.861575i | \(-0.669478\pi\) |
0.861575 | + | 0.507630i | \(0.169478\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.8339 | 0.851155 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.44432 | 0.318880 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.9144 | + | 16.9144i | −0.723208 | + | 0.723208i | −0.969257 | − | 0.246049i | \(-0.920868\pi\) |
0.246049 | + | 0.969257i | \(0.420868\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.81756 | + | 9.81756i | 0.419003 | + | 0.419003i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 5.97863i | − | 0.254698i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.2449i | 0.605756i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.01008 | − | 3.01008i | −0.127771 | − | 0.127771i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.0529 | + | 28.0529i | −1.18864 | + | 1.18864i | −0.211198 | + | 0.977443i | \(0.567737\pi\) |
−0.977443 | + | 0.211198i | \(0.932263\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.79899 | 0.329862 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.97891 | −0.294650 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.7240 | + | 10.7240i | −0.451961 | + | 0.451961i | −0.896005 | − | 0.444044i | \(-0.853543\pi\) |
0.444044 | + | 0.896005i | \(0.353543\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.24084 | + | 6.24084i | 0.262554 | + | 0.262554i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.93416i | − | 0.123223i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 7.70067i | − | 0.322829i | −0.986887 | − | 0.161414i | \(-0.948394\pi\) | ||
0.986887 | − | 0.161414i | \(-0.0516056\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.1892 | + | 33.1892i | 1.38892 | + | 1.38892i | 0.827588 | + | 0.561336i | \(0.189712\pi\) |
0.561336 | + | 0.827588i | \(0.310288\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.8927 | + | 14.8927i | −0.622150 | + | 0.622150i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.4133 | −0.934699 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.15827 | 0.298003 | 0.149001 | − | 0.988837i | \(-0.452394\pi\) | ||||
0.149001 | + | 0.988837i | \(0.452394\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.6236 | − | 15.6236i | 0.649296 | − | 0.649296i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.95217 | − | 5.95217i | −0.246938 | − | 0.246938i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 14.6105i | − | 0.605105i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 2.85854i | − | 0.118186i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.8145 | + | 18.8145i | 0.776558 | + | 0.776558i | 0.979244 | − | 0.202686i | \(-0.0649669\pi\) |
−0.202686 | + | 0.979244i | \(0.564967\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.30618 | − | 2.30618i | 0.0950246 | − | 0.0950246i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.59100 | 0.106579 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.45182 | −0.182814 | −0.0914072 | − | 0.995814i | \(-0.529136\pi\) | ||||
−0.0914072 | + | 0.995814i | \(0.529136\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.41421 | − | 1.41421i | 0.0579771 | − | 0.0579771i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.8158 | + | 11.8158i | 0.483588 | + | 0.483588i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.5201i | 1.20616i | 0.797682 | + | 0.603079i | \(0.206060\pi\) | ||||
−0.797682 | + | 0.603079i | \(0.793940\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 24.5564i | − | 1.00168i | −0.865541 | − | 0.500838i | \(-0.833025\pi\) | ||
0.865541 | − | 0.500838i | \(-0.166975\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.36423 | − | 9.36423i | −0.381341 | − | 0.381341i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.31983 | + | 1.31983i | −0.0536588 | + | 0.0536588i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.1536 | −1.46743 | −0.733714 | − | 0.679458i | \(-0.762215\pi\) | ||||
−0.733714 | + | 0.679458i | \(0.762215\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.1158 | −0.409914 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.89171 | + | 2.89171i | −0.116986 | + | 0.116986i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.35616 | + | 3.35616i | 0.135554 | + | 0.135554i | 0.771628 | − | 0.636074i | \(-0.219443\pi\) |
−0.636074 | + | 0.771628i | \(0.719443\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.00778i | 0.0406378i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 25.5502i | − | 1.02861i | −0.857607 | − | 0.514306i | \(-0.828050\pi\) | ||
0.857607 | − | 0.514306i | \(-0.171950\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.1501 | + | 11.1501i | 0.448159 | + | 0.448159i | 0.894742 | − | 0.446583i | \(-0.147359\pi\) |
−0.446583 | + | 0.894742i | \(0.647359\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.4749 | − | 23.4749i | 0.942017 | − | 0.942017i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.9417 | −0.678755 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.97005 | −0.318802 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.06233 | − | 2.06233i | 0.0823616 | − | 0.0823616i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.82680 | − | 3.82680i | −0.152585 | − | 0.152585i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.7069i | 1.02337i | 0.859172 | + | 0.511687i | \(0.170979\pi\) | ||||
−0.859172 | + | 0.511687i | \(0.829021\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6.46512i | − | 0.256966i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.23883 | + | 6.23883i | 0.247580 | + | 0.247580i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.31318 | + | 1.31318i | −0.0520301 | + | 0.0520301i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.72300 | 0.107720 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.39970 | −0.292271 | −0.146135 | − | 0.989265i | \(-0.546683\pi\) | ||||
−0.146135 | + | 0.989265i | \(0.546683\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.2666 | + | 17.2666i | −0.680929 | + | 0.680929i | −0.960210 | − | 0.279280i | \(-0.909904\pi\) |
0.279280 | + | 0.960210i | \(0.409904\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.19951 | − | 4.19951i | −0.165356 | − | 0.165356i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.71205i | 0.303192i | 0.988443 | + | 0.151596i | \(0.0484412\pi\) | ||||
−0.988443 | + | 0.151596i | \(0.951559\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.4298i | 0.409406i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.90205 | − | 3.90205i | −0.152933 | − | 0.152933i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.78463 | − | 4.78463i | 0.187237 | − | 0.187237i | −0.607263 | − | 0.794501i | \(-0.707733\pi\) |
0.794501 | + | 0.607263i | \(0.207733\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.41421 | 0.367844 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.3399 | 0.559453 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.1016 | − | 28.1016i | 1.09468 | − | 1.09468i | 0.0996599 | − | 0.995022i | \(-0.468225\pi\) |
0.995022 | − | 0.0996599i | \(-0.0317755\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.0875 | + | 10.0875i | 0.392357 | + | 0.392357i | 0.875527 | − | 0.483170i | \(-0.160515\pi\) |
−0.483170 | + | 0.875527i | \(0.660515\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.24494i | 0.164860i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.835826i | 0.0324120i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −33.5155 | − | 33.5155i | −1.29773 | − | 1.29773i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.7335 | − | 24.7335i | 0.956251 | − | 0.956251i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.6356 | 1.18267 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.2930 | 1.20626 | 0.603129 | − | 0.797644i | \(-0.293920\pi\) | ||||
0.603129 | + | 0.797644i | \(0.293920\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.8277 | − | 14.8277i | 0.570718 | − | 0.570718i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.75969 | − | 3.75969i | −0.144497 | − | 0.144497i | 0.631158 | − | 0.775654i | \(-0.282580\pi\) |
−0.775654 | + | 0.631158i | \(0.782580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 17.6796i | − | 0.678479i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 19.8525i | − | 0.760750i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.31693 | + | 8.31693i | 0.318239 | + | 0.318239i | 0.848090 | − | 0.529852i | \(-0.177752\pi\) |
−0.529852 | + | 0.848090i | \(0.677752\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.70483 | + | 9.70483i | −0.370802 | + | 0.370802i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.5242 | −0.821201 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.88686 | −0.338563 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.6065 | + | 33.6065i | −1.27845 | + | 1.27845i | −0.336916 | + | 0.941535i | \(0.609384\pi\) |
−0.941535 | + | 0.336916i | \(0.890616\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.98737 | + | 2.98737i | 0.113481 | + | 0.113481i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 20.5128i | − | 0.778096i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.28123i | 0.0485299i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.8015 | + | 25.8015i | 0.975904 | + | 0.975904i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.3319 | − | 33.3319i | 1.25893 | − | 1.25893i | 0.307322 | − | 0.951606i | \(-0.400567\pi\) |
0.951606 | − | 0.307322i | \(-0.0994329\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.26171 | 0.0853021 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.11419 | 0.117287 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.66156 | + | 6.66156i | −0.250534 | + | 0.250534i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.4665 | − | 16.4665i | −0.618412 | − | 0.618412i | 0.326712 | − | 0.945124i | \(-0.394059\pi\) |
−0.945124 | + | 0.326712i | \(0.894059\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 19.7110i | − | 0.739220i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 25.8564i | − | 0.968329i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.46002 | − | 4.46002i | −0.166795 | − | 0.166795i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.9541 | + | 14.9541i | −0.558473 | + | 0.558473i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.5122 | −0.951443 | −0.475722 | − | 0.879596i | \(-0.657813\pi\) | ||||
−0.475722 | + | 0.879596i | \(0.657813\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.88418 | −0.0701707 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.39150 | + | 3.39150i | −0.126131 | + | 0.126131i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.1697 | − | 21.1697i | −0.786223 | − | 0.786223i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.8327i | 0.401764i | 0.979615 | + | 0.200882i | \(0.0643807\pi\) | ||||
−0.979615 | + | 0.200882i | \(0.935619\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.3160i | 0.937630i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.33897 | − | 5.33897i | −0.197469 | − | 0.197469i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.64351 | + | 3.64351i | −0.134576 | + | 0.134576i | −0.771186 | − | 0.636610i | \(-0.780336\pi\) |
0.636610 | + | 0.771186i | \(0.280336\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.41421 | 0.0521641 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.2210 | −1.07637 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.72954 | + | 1.72954i | −0.0636223 | + | 0.0636223i | −0.738202 | − | 0.674580i | \(-0.764325\pi\) |
0.674580 | + | 0.738202i | \(0.264325\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.25442 | − | 1.25442i | −0.0460822 | − | 0.0460822i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 38.1023i | − | 1.39784i | −0.715202 | − | 0.698918i | \(-0.753665\pi\) | ||
0.715202 | − | 0.698918i | \(-0.246335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 13.5732i | − | 0.497282i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.23613 | + | 8.23613i | 0.301344 | + | 0.301344i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.94909 | − | 8.94909i | 0.326993 | − | 0.326993i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.6119 | 1.22651 | 0.613257 | − | 0.789883i | \(-0.289859\pi\) | ||||
0.613257 | + | 0.789883i | \(0.289859\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.1860 | 1.31869 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.51397 | − | 7.51397i | 0.273461 | − | 0.273461i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.39019 | − | 2.39019i | −0.0868729 | − | 0.0868729i | 0.662335 | − | 0.749208i | \(-0.269566\pi\) |
−0.749208 | + | 0.662335i | \(0.769566\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 23.1224i | − | 0.839290i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3.87733i | − | 0.140553i | −0.997528 | − | 0.0702765i | \(-0.977612\pi\) | ||
0.997528 | − | 0.0702765i | \(-0.0223882\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.73210 | + | 4.73210i | 0.171313 | + | 0.171313i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.95687 | + | 1.95687i | −0.0707509 | + | 0.0707509i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.34395 | 0.229067 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.8126 | 0.894764 | 0.447382 | − | 0.894343i | \(-0.352356\pi\) | ||||
0.447382 | + | 0.894343i | \(0.352356\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.2300 | + | 23.2300i | −0.836608 | + | 0.836608i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.49465 | + | 8.49465i | 0.305531 | + | 0.305531i | 0.843173 | − | 0.537642i | \(-0.180685\pi\) |
−0.537642 | + | 0.843173i | \(0.680685\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 16.3319i | − | 0.586658i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 3.82680i | − | 0.137286i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.378614 | − | 0.378614i | −0.0135653 | − | 0.0135653i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.24854 | − | 4.24854i | 0.152025 | − | 0.152025i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 44.3449 | 1.58476 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.9902 | −0.463640 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.92149 | − | 1.92149i | 0.0684939 | − | 0.0684939i | −0.672030 | − | 0.740524i | \(-0.734577\pi\) |
0.740524 | + | 0.672030i | \(0.234577\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.01400 | + | 2.01400i | 0.0717001 | + | 0.0717001i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.93416i | 0.282106i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 18.6342i | − | 0.661719i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.78530 | + | 4.78530i | 0.169717 | + | 0.169717i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.95191 | − | 8.95191i | 0.317093 | − | 0.317093i | −0.530557 | − | 0.847650i | \(-0.678017\pi\) |
0.847650 | + | 0.530557i | \(0.178017\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.95917 | 0.140065 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23.4425 | 0.828301 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.3738 | − | 22.3738i | 0.789553 | − | 0.789553i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.68554 | + | 4.68554i | 0.165144 | + | 0.165144i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.0004i | 0.844855i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 3.51709i | − | 0.123654i | −0.998087 | − | 0.0618272i | \(-0.980307\pi\) | ||
0.998087 | − | 0.0618272i | \(-0.0196928\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.7994 | + | 16.7994i | 0.589907 | + | 0.589907i | 0.937606 | − | 0.347699i | \(-0.113037\pi\) |
−0.347699 | + | 0.937606i | \(0.613037\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.1963 | − | 12.1963i | 0.427742 | − | 0.427742i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.59303 | 0.0558013 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.15543 | 0.110395 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.81707 | − | 1.81707i | 0.0634936 | − | 0.0634936i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.2771 | − | 27.2771i | −0.951976 | − | 0.951976i | 0.0469228 | − | 0.998899i | \(-0.485059\pi\) |
−0.998899 | + | 0.0469228i | \(0.985059\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 48.5252i | − | 1.69148i | −0.533593 | − | 0.845742i | \(-0.679158\pi\) | ||
0.533593 | − | 0.845742i | \(-0.320842\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 14.6050i | − | 0.508481i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.1041 | + | 12.1041i | 0.420901 | + | 0.420901i | 0.885514 | − | 0.464613i | \(-0.153806\pi\) |
−0.464613 | + | 0.885514i | \(0.653806\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.264075 | − | 0.264075i | 0.00917169 | − | 0.00917169i | −0.702506 | − | 0.711678i | \(-0.747936\pi\) |
0.711678 | + | 0.702506i | \(0.247936\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.7801 | 0.512716 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.79793 | 0.0622947 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.56052 | − | 4.56052i | 0.157823 | − | 0.157823i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.1055 | + | 17.1055i | 0.591252 | + | 0.591252i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 2.31074i | − | 0.0797757i | −0.999204 | − | 0.0398878i | \(-0.987300\pi\) | ||
0.999204 | − | 0.0398878i | \(-0.0127001\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 34.3118i | − | 1.18317i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.45316 | + | 4.45316i | 0.153375 | + | 0.153375i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.51269 | − | 7.51269i | 0.258445 | − | 0.258445i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.67794 | −0.0576548 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.0809 | −0.963734 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.6789 | − | 12.6789i | 0.434627 | − | 0.434627i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.5400 | − | 35.5400i | −1.21687 | − | 1.21687i | −0.968723 | − | 0.248143i | \(-0.920180\pi\) |
−0.248143 | − | 0.968723i | \(-0.579820\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.15655i | − | 0.0395531i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.9222i | 0.851327i | 0.904882 | + | 0.425664i | \(0.139959\pi\) | ||||
−0.904882 | + | 0.425664i | \(0.860041\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.931083 | + | 0.931083i | 0.0317682 | + | 0.0317682i | 0.722812 | − | 0.691044i | \(-0.242849\pi\) |
−0.691044 | + | 0.722812i | \(0.742849\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.640613 | + | 0.640613i | −0.0218320 | + | 0.0218320i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.9398 | −0.951081 | −0.475541 | − | 0.879694i | \(-0.657748\pi\) | ||||
−0.475541 | + | 0.879694i | \(0.657748\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.17224 | 0.141861 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.3765 | + | 12.3765i | −0.420327 | + | 0.420327i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.7540 | − | 30.7540i | −1.04326 | − | 1.04326i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.7737i | 0.602240i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.4636i | 0.827966i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.89246 | + | 6.89246i | 0.233008 | + | 0.233008i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.7935 | − | 37.7935i | 1.27620 | − | 1.27620i | 0.333416 | − | 0.942780i | \(-0.391799\pi\) |
0.942780 | − | 0.333416i | \(-0.108201\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.3844 | −0.889924 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.6692 | 1.23542 | 0.617709 | − | 0.786407i | \(-0.288061\pi\) | ||||
0.617709 | + | 0.786407i | \(0.288061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.2105 | + | 20.2105i | −0.680138 | + | 0.680138i | −0.960031 | − | 0.279893i | \(-0.909701\pi\) |
0.279893 | + | 0.960031i | \(0.409701\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.41602 | − | 3.41602i | −0.114828 | − | 0.114828i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 30.7180i | − | 1.03141i | −0.856767 | − | 0.515704i | \(-0.827530\pi\) | ||
0.856767 | − | 0.515704i | \(-0.172470\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.93161i | 0.266018i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.33469 | + | 6.33469i | 0.212220 | + | 0.212220i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.16997 | + | 1.16997i | −0.0391516 | + | 0.0391516i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.43909 | −0.0815298 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.0642 | −0.469591 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.4217 | − | 24.4217i | 0.814511 | − | 0.814511i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.08370 | + | 6.08370i | 0.202677 | + | 0.202677i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 5.33897i | − | 0.177670i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 17.3543i | − | 0.576876i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.77429 | + | 4.77429i | 0.158528 | + | 0.158528i | 0.781914 | − | 0.623386i | \(-0.214244\pi\) |
−0.623386 | + | 0.781914i | \(0.714244\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.21772 | − | 9.21772i | 0.305733 | − | 0.305733i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.31693 | −0.275552 | −0.137776 | − | 0.990463i | \(-0.543995\pi\) | ||||
−0.137776 | + | 0.990463i | \(0.543995\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.7008 | 0.850572 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.0339 | + | 10.0339i | −0.331711 | + | 0.331711i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.98429 | + | 5.98429i | 0.197619 | + | 0.197619i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 21.2142i | − | 0.699790i | −0.936789 | − | 0.349895i | \(-0.886217\pi\) | ||
0.936789 | − | 0.349895i | \(-0.113783\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 17.4846i | − | 0.576137i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.58418 | − | 2.58418i | −0.0850595 | − | 0.0850595i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00848 | − | 8.00848i | 0.263317 | − | 0.263317i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.60718 | 0.0856311 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.9785 | −1.60693 | −0.803466 | − | 0.595351i | \(-0.797013\pi\) | ||||
−0.803466 | + | 0.595351i | \(0.797013\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.531306 | + | 0.531306i | −0.0174128 | + | 0.0174128i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.3958 | + | 24.3958i | 0.798682 | + | 0.798682i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.10641i | 0.199701i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.92705i | 0.0629540i | 0.999504 | + | 0.0314770i | \(0.0100211\pi\) | ||||
−0.999504 | + | 0.0314770i | \(0.989979\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.7869 | + | 11.7869i | 0.384652 | + | 0.384652i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.2347 | − | 12.2347i | 0.398840 | − | 0.398840i | −0.478984 | − | 0.877824i | \(-0.658995\pi\) |
0.877824 | + | 0.478984i | \(0.158995\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.24494 | −0.138234 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.19951 | −0.201670 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.2543 | + | 17.2543i | −0.560690 | + | 0.560690i | −0.929503 | − | 0.368813i | \(-0.879764\pi\) |
0.368813 | + | 0.929503i | \(0.379764\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.6089 | − | 13.6089i | −0.441763 | − | 0.441763i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 20.6585i | − | 0.669897i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.34866i | 0.0436875i | 0.999761 | + | 0.0218438i | \(0.00695364\pi\) | ||||
−0.999761 | + | 0.0218438i | \(0.993046\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.0308 | + | 13.0308i | 0.421666 | + | 0.421666i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.8395 | − | 21.8395i | 0.705969 | − | 0.705969i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.3380 | −0.398416 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.1592 | −0.392234 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.3830 | + | 12.3830i | −0.399037 | + | 0.399037i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.6704 | − | 13.6704i | −0.440064 | − | 0.440064i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 36.7348i | − | 1.18131i | −0.806924 | − | 0.590655i | \(-0.798869\pi\) | ||
0.806924 | − | 0.590655i | \(-0.201131\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.71748i | 0.0551734i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.6384 | + | 22.6384i | 0.726501 | + | 0.726501i | 0.969921 | − | 0.243420i | \(-0.0782693\pi\) |
−0.243420 | + | 0.969921i | \(0.578269\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.0393 | − | 13.0393i | 0.418021 | − | 0.418021i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.88351 | −0.284500 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.4361 | 1.35765 | 0.678826 | − | 0.734300i | \(-0.262489\pi\) | ||||
0.678826 | + | 0.734300i | \(0.262489\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.5761 | − | 36.5761i | 1.16898 | − | 1.16898i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.54789 | − | 6.54789i | −0.209058 | − | 0.209058i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 61.1841i | − | 1.95147i | −0.218957 | − | 0.975734i | \(-0.570266\pi\) | ||
0.218957 | − | 0.975734i | \(-0.429734\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2.26707i | − | 0.0722349i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.97958 | + | 1.97958i | 0.0630109 | + | 0.0630109i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.6890 | − | 17.6890i | 0.562477 | − | 0.562477i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.09769 | −0.130168 | −0.0650838 | − | 0.997880i | \(-0.520731\pi\) | ||||
−0.0650838 | + | 0.997880i | \(0.520731\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.5133 | −0.650969 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.3386 | − | 10.3386i | 0.327755 | − | 0.327755i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.08175 | + | 7.08175i | 0.224281 | + | 0.224281i | 0.810299 | − | 0.586017i | \(-0.199305\pi\) |
−0.586017 | + | 0.810299i | \(0.699305\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.7756i | 0.530758i |
(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 | 1792.2.m.b.449.4 | yes | 8 | |
4.3 | odd | 2 | 1792.2.m.d.449.1 | yes | 8 | ||
8.3 | odd | 2 | 1792.2.m.a.449.4 | ✓ | 8 | ||
8.5 | even | 2 | 1792.2.m.c.449.1 | yes | 8 | ||
16.3 | odd | 4 | 1792.2.m.d.1345.1 | yes | 8 | ||
16.5 | even | 4 | 1792.2.m.c.1345.1 | yes | 8 | ||
16.11 | odd | 4 | 1792.2.m.a.1345.4 | yes | 8 | ||
16.13 | even | 4 | inner | 1792.2.m.b.1345.4 | yes | 8 | |
32.3 | odd | 8 | 7168.2.a.x.1.2 | 4 | |||
32.13 | even | 8 | 7168.2.a.s.1.2 | 4 | |||
32.19 | odd | 8 | 7168.2.a.t.1.3 | 4 | |||
32.29 | even | 8 | 7168.2.a.w.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1792.2.m.a.449.4 | ✓ | 8 | 8.3 | odd | 2 | ||
1792.2.m.a.1345.4 | yes | 8 | 16.11 | odd | 4 | ||
1792.2.m.b.449.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1792.2.m.b.1345.4 | yes | 8 | 16.13 | even | 4 | inner | |
1792.2.m.c.449.1 | yes | 8 | 8.5 | even | 2 | ||
1792.2.m.c.1345.1 | yes | 8 | 16.5 | even | 4 | ||
1792.2.m.d.449.1 | yes | 8 | 4.3 | odd | 2 | ||
1792.2.m.d.1345.1 | yes | 8 | 16.3 | odd | 4 | ||
7168.2.a.s.1.2 | 4 | 32.13 | even | 8 | |||
7168.2.a.t.1.3 | 4 | 32.19 | odd | 8 | |||
7168.2.a.w.1.3 | 4 | 32.29 | even | 8 | |||
7168.2.a.x.1.2 | 4 | 32.3 | odd | 8 |