Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(767,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.767");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.n (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: | \(10.2208514587\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 27x^{8} + 107x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 640) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1023.2 | ||
Root | \(-1.53448 + 1.53448i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.1023 |
Dual form | 1280.2.n.r.767.2 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.20864 | + | 1.20864i | −0.697809 | + | 0.697809i | −0.963937 | − | 0.266129i | \(-0.914255\pi\) |
0.266129 | + | 0.963937i | \(0.414255\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.17009 | + | 0.539189i | −0.970492 | + | 0.241133i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.446112 | + | 0.446112i | 0.168614 | + | 0.168614i | 0.786370 | − | 0.617756i | \(-0.211958\pi\) |
−0.617756 | + | 0.786370i | \(0.711958\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.0783777i | 0.0261259i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.72065i | − | 1.12182i | −0.827877 | − | 0.560909i | \(-0.810452\pi\) | ||
0.827877 | − | 0.560909i | \(-0.189548\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.709275 | − | 0.709275i | −0.196718 | − | 0.196718i | 0.601874 | − | 0.798591i | \(-0.294421\pi\) |
−0.798591 | + | 0.601874i | \(0.794421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.97117 | − | 3.27454i | 0.508953 | − | 0.845482i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.34017 | − | 3.34017i | 0.810111 | − | 0.810111i | −0.174539 | − | 0.984650i | \(-0.555844\pi\) |
0.984650 | + | 0.174539i | \(0.0558436\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.35348 | −0.998758 | −0.499379 | − | 0.866384i | \(-0.666438\pi\) | ||||
−0.499379 | + | 0.866384i | \(0.666438\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.07838 | −0.235321 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.69182 | + | 5.69182i | −1.18683 | + | 1.18683i | −0.208887 | + | 0.977940i | \(0.566984\pi\) |
−0.977940 | + | 0.208887i | \(0.933016\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.41855 | − | 2.34017i | 0.883710 | − | 0.468035i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.72065 | − | 3.72065i | −0.716040 | − | 0.716040i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.41855i | 0.263418i | 0.991288 | + | 0.131709i | \(0.0420465\pi\) | ||||
−0.991288 | + | 0.131709i | \(0.957954\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.72678i | − | 1.02856i | −0.857622 | − | 0.514280i | \(-0.828059\pi\) | ||
0.857622 | − | 0.514280i | \(-0.171941\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.49693 | + | 4.49693i | 0.782815 | + | 0.782815i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.20864 | − | 0.727563i | −0.204297 | − | 0.122981i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.78765 | − | 3.78765i | 0.622686 | − | 0.622686i | −0.323531 | − | 0.946218i | \(-0.604870\pi\) |
0.946218 | + | 0.323531i | \(0.104870\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.71452 | 0.274543 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.75872 | 1.52406 | 0.762028 | − | 0.647544i | \(-0.224204\pi\) | ||||
0.762028 | + | 0.647544i | \(0.224204\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.20864 | − | 1.20864i | 0.184316 | − | 0.184316i | −0.608918 | − | 0.793233i | \(-0.708396\pi\) |
0.793233 | + | 0.608918i | \(0.208396\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.0422604 | − | 0.170086i | −0.00629981 | − | 0.0253550i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.79960 | + | 4.79960i | 0.700093 | + | 0.700093i | 0.964430 | − | 0.264337i | \(-0.0851532\pi\) |
−0.264337 | + | 0.964430i | \(0.585153\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 6.60197i | − | 0.943138i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.07413i | 1.13060i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.04945 | + | 9.04945i | 1.24304 | + | 1.24304i | 0.958735 | + | 0.284303i | \(0.0917621\pi\) |
0.284303 | + | 0.958735i | \(0.408238\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00613 | + | 8.07413i | 0.270507 | + | 1.08872i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.26180 | − | 5.26180i | 0.696942 | − | 0.696942i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.7948 | 1.53555 | 0.767775 | − | 0.640719i | \(-0.221364\pi\) | ||||
0.767775 | + | 0.640719i | \(0.221364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.340173 | 0.0435547 | 0.0217773 | − | 0.999763i | \(-0.493068\pi\) | ||||
0.0217773 | + | 0.999763i | \(0.493068\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0349653 | + | 0.0349653i | −0.00440521 | + | 0.00440521i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.92162 | + | 1.15676i | 0.238348 | + | 0.143478i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.44821 | + | 4.44821i | 0.543436 | + | 0.543436i | 0.924534 | − | 0.381099i | \(-0.124454\pi\) |
−0.381099 | + | 0.924534i | \(0.624454\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 13.7587i | − | 1.65636i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.4338i | − | 1.71297i | −0.516171 | − | 0.856486i | \(-0.672643\pi\) | ||
0.516171 | − | 0.856486i | \(-0.327357\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.261795 | − | 0.261795i | −0.0306408 | − | 0.0306408i | 0.691620 | − | 0.722261i | \(-0.256897\pi\) |
−0.722261 | + | 0.691620i | \(0.756897\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.51201 | + | 8.16887i | −0.290062 | + | 0.943259i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.65983 | − | 1.65983i | 0.189155 | − | 0.189155i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.1483 | −1.81682 | −0.908411 | − | 0.418078i | \(-0.862704\pi\) | ||||
−0.908411 | + | 0.418078i | \(0.862704\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.75872 | 0.973192 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.56212 | − | 5.56212i | 0.610522 | − | 0.610522i | −0.332560 | − | 0.943082i | \(-0.607912\pi\) |
0.943082 | + | 0.332560i | \(0.107912\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.44748 | + | 9.04945i | −0.590862 | + | 0.981550i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.71452 | − | 1.71452i | −0.183816 | − | 0.183816i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.15676i | 0.228616i | 0.993445 | + | 0.114308i | \(0.0364650\pi\) | ||||
−0.993445 | + | 0.114308i | \(0.963535\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.632832i | − | 0.0663389i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.92162 | + | 6.92162i | 0.717739 | + | 0.717739i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.44744 | − | 2.34735i | 0.969286 | − | 0.240833i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.41855 | − | 6.41855i | 0.651705 | − | 0.651705i | −0.301698 | − | 0.953403i | \(-0.597554\pi\) |
0.953403 | + | 0.301698i | \(0.0975535\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.291616 | 0.0293085 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.5236 | −1.04714 | −0.523568 | − | 0.851984i | \(-0.675399\pi\) | ||||
−0.523568 | + | 0.851984i | \(0.675399\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.74948 | − | 1.74948i | 0.172382 | − | 0.172382i | −0.615643 | − | 0.788025i | \(-0.711104\pi\) |
0.788025 | + | 0.615643i | \(0.211104\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.34017 | − | 0.581449i | 0.228377 | − | 0.0567436i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.99309 | + | 2.99309i | 0.289353 | + | 0.289353i | 0.836824 | − | 0.547472i | \(-0.184410\pi\) |
−0.547472 | + | 0.836824i | \(0.684410\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.7587i | − | 1.31785i | −0.752210 | − | 0.658923i | \(-0.771012\pi\) | ||
0.752210 | − | 0.658923i | \(-0.228988\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.15582i | 0.869032i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.92162 | + | 1.92162i | 0.180771 | + | 0.180771i | 0.791692 | − | 0.610921i | \(-0.209201\pi\) |
−0.610921 | + | 0.791692i | \(0.709201\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.28277 | − | 15.4207i | 0.865623 | − | 1.43799i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0555914 | − | 0.0555914i | 0.00513943 | − | 0.00513943i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.98018 | 0.273193 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.84324 | −0.258477 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.7948 | + | 11.7948i | −1.06350 | + | 1.06350i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.32684 | + | 7.46081i | −0.744775 | + | 0.667315i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.99519 | + | 6.99519i | 0.620723 | + | 0.620723i | 0.945716 | − | 0.324993i | \(-0.105362\pi\) |
−0.324993 | + | 0.945716i | \(0.605362\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.92162i | 0.257234i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 7.73292i | − | 0.675628i | −0.941213 | − | 0.337814i | \(-0.890312\pi\) | ||
0.941213 | − | 0.337814i | \(-0.109688\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.94214 | − | 1.94214i | −0.168405 | − | 0.168405i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.0803 | + | 6.06800i | 0.867571 | + | 0.522250i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.00000 | + | 5.00000i | −0.427179 | + | 0.427179i | −0.887666 | − | 0.460487i | \(-0.847675\pi\) |
0.460487 | + | 0.887666i | \(0.347675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.341216 | 0.0289416 | 0.0144708 | − | 0.999895i | \(-0.495394\pi\) | ||||
0.0144708 | + | 0.999895i | \(0.495394\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.6020 | −0.977062 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.63897 | + | 2.63897i | −0.220681 | + | 0.220681i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.764867 | − | 3.07838i | −0.0635187 | − | 0.255645i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.97940 | + | 7.97940i | 0.658130 | + | 0.658130i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.4391i | 0.855202i | 0.903968 | + | 0.427601i | \(0.140641\pi\) | ||||
−0.903968 | + | 0.427601i | \(0.859359\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 13.1681i | − | 1.07160i | −0.844344 | − | 0.535802i | \(-0.820009\pi\) | ||
0.844344 | − | 0.535802i | \(-0.179991\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.261795 | + | 0.261795i | 0.0211649 | + | 0.0211649i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.08782 | + | 12.4276i | 0.248020 | + | 0.998210i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.55252 | − | 4.55252i | 0.363331 | − | 0.363331i | −0.501707 | − | 0.865038i | \(-0.667294\pi\) |
0.865038 | + | 0.501707i | \(0.167294\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21.8751 | −1.73480 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.07838 | −0.400232 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.23266 | − | 6.23266i | 0.488180 | − | 0.488180i | −0.419552 | − | 0.907731i | \(-0.637813\pi\) |
0.907731 | + | 0.419552i | \(0.137813\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.1834 | − | 7.33403i | −0.948478 | − | 0.570953i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.2409 | − | 12.2409i | −0.947229 | − | 0.947229i | 0.0514466 | − | 0.998676i | \(-0.483617\pi\) |
−0.998676 | + | 0.0514466i | \(0.983617\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.9939i | − | 0.922604i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 0.341216i | − | 0.0260935i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.94441 | + | 9.94441i | 0.756059 | + | 0.756059i | 0.975603 | − | 0.219543i | \(-0.0704567\pi\) |
−0.219543 | + | 0.975603i | \(0.570457\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.01515 | + | 0.927189i | 0.227924 | + | 0.0700889i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.2557 | + | 14.2557i | −1.07152 | + | 1.07152i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.2484 | −1.73766 | −0.868832 | − | 0.495107i | \(-0.835129\pi\) | ||||
−0.868832 | + | 0.495107i | \(0.835129\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.20394 | 0.535464 | 0.267732 | − | 0.963493i | \(-0.413726\pi\) | ||||
0.267732 | + | 0.963493i | \(0.413726\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.411147 | + | 0.411147i | −0.0303928 | + | 0.0303928i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.17727 | + | 10.2618i | −0.454162 | + | 0.754462i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.4276 | − | 12.4276i | −0.908797 | − | 0.908797i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 3.31965i | − | 0.241469i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.4215i | 0.754072i | 0.926199 | + | 0.377036i | \(0.123057\pi\) | ||||
−0.926199 | + | 0.377036i | \(0.876943\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.1773 | − | 16.1773i | −1.16447 | − | 1.16447i | −0.983487 | − | 0.180979i | \(-0.942074\pi\) |
−0.180979 | − | 0.983487i | \(-0.557926\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.72065 | + | 0.924449i | −0.266441 | + | 0.0662011i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.7877 | − | 13.7877i | 0.982330 | − | 0.982330i | −0.0175170 | − | 0.999847i | \(-0.505576\pi\) |
0.999847 | + | 0.0175170i | \(0.00557611\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.1483 | 1.14472 | 0.572360 | − | 0.820002i | \(-0.306028\pi\) | ||||
0.572360 | + | 0.820002i | \(0.306028\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.7526 | −0.758429 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.632832 | + | 0.632832i | −0.0444161 | + | 0.0444161i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.1773 | + | 5.26180i | −1.47909 | + | 0.367500i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.446112 | − | 0.446112i | −0.0310069 | − | 0.0310069i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.1978i | 1.12042i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.73292i | 0.532356i | 0.963924 | + | 0.266178i | \(0.0857609\pi\) | ||||
−0.963924 | + | 0.266178i | \(0.914239\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.4452 | + | 17.4452i | 1.19533 | + | 1.19533i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.97117 | + | 3.27454i | −0.134433 | + | 0.223322i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.55479 | − | 2.55479i | 0.173430 | − | 0.173430i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.632832 | 0.0427629 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.73820 | −0.318726 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.33834 | + | 1.33834i | −0.0896216 | + | 0.0896216i | −0.750496 | − | 0.660875i | \(-0.770185\pi\) |
0.660875 | + | 0.750496i | \(0.270185\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.183417 | + | 0.346316i | 0.0122278 | + | 0.0230877i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.8140 | − | 12.8140i | −0.850493 | − | 0.850493i | 0.139701 | − | 0.990194i | \(-0.455386\pi\) |
−0.990194 | + | 0.139701i | \(0.955386\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 21.4186i | − | 1.41538i | −0.706524 | − | 0.707689i | \(-0.749738\pi\) | ||
0.706524 | − | 0.707689i | \(-0.250262\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.01227i | 0.263988i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0205 | + | 10.0205i | 0.656466 | + | 0.656466i | 0.954542 | − | 0.298076i | \(-0.0963449\pi\) |
−0.298076 | + | 0.954542i | \(0.596345\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.0034 | − | 7.82765i | −0.848250 | − | 0.510620i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.5174 | − | 19.5174i | 1.26779 | − | 1.26779i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.8949 | 1.22221 | 0.611104 | − | 0.791550i | \(-0.290726\pi\) | ||||
0.611104 | + | 0.791550i | \(0.290726\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.9627 | −1.09266 | −0.546330 | − | 0.837570i | \(-0.683976\pi\) | ||||
−0.546330 | + | 0.837570i | \(0.683976\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.575808 | − | 0.575808i | 0.0369381 | − | 0.0369381i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.55971 | + | 14.3268i | 0.227421 | + | 0.915308i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.08782 | + | 3.08782i | 0.196473 | + | 0.196473i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.4452i | 0.852056i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 11.1620i | − | 0.704536i | −0.935899 | − | 0.352268i | \(-0.885411\pi\) | ||
0.935899 | − | 0.352268i | \(-0.114589\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.1773 | + | 21.1773i | 1.33140 | + | 1.33140i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.35348 | − | 17.5216i | −0.272626 | − | 1.09724i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.60197 | + | 8.60197i | −0.536576 | + | 0.536576i | −0.922522 | − | 0.385946i | \(-0.873875\pi\) |
0.385946 | + | 0.922522i | \(0.373875\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.37943 | 0.209988 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.111183 | −0.00688204 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.5443 | + | 13.5443i | −0.835175 | + | 0.835175i | −0.988219 | − | 0.153044i | \(-0.951092\pi\) |
0.153044 | + | 0.988219i | \(0.451092\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.5174 | − | 14.7587i | −1.50609 | − | 0.906621i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.60674 | − | 2.60674i | −0.159530 | − | 0.159530i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 18.0722i | − | 1.10188i | −0.834544 | − | 0.550942i | \(-0.814269\pi\) | ||
0.834544 | − | 0.550942i | \(-0.185731\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 17.8628i | − | 1.08509i | −0.840028 | − | 0.542544i | \(-0.817461\pi\) | ||
0.840028 | − | 0.542544i | \(-0.182539\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.764867 | + | 0.764867i | 0.0462918 | + | 0.0462918i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.70697 | − | 16.4399i | −0.525050 | − | 0.991362i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.38962 | + | 7.38962i | −0.443999 | + | 0.443999i | −0.893354 | − | 0.449354i | \(-0.851654\pi\) |
0.449354 | + | 0.893354i | \(0.351654\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.448852 | 0.0268721 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.0722 | −1.31672 | −0.658360 | − | 0.752704i | \(-0.728749\pi\) | ||||
−0.658360 | + | 0.752704i | \(0.728749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.5861 | − | 10.5861i | 0.629281 | − | 0.629281i | −0.318606 | − | 0.947887i | \(-0.603215\pi\) |
0.947887 | + | 0.318606i | \(0.103215\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.58145 | + | 14.2557i | −0.508321 | + | 0.844432i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.35348 | + | 4.35348i | 0.256978 | + | 0.256978i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 5.31351i | − | 0.312559i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.5154i | 0.909531i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.80817 | − | 8.80817i | −0.514579 | − | 0.514579i | 0.401347 | − | 0.915926i | \(-0.368542\pi\) |
−0.915926 | + | 0.401347i | \(0.868542\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −25.5957 | + | 6.35962i | −1.49024 | + | 0.370271i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.8432 | + | 13.8432i | −0.803267 | + | 0.803267i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.07413 | 0.466939 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.07838 | 0.0621567 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.7192 | − | 12.7192i | 0.730701 | − | 0.730701i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.738205 | + | 0.183417i | −0.0422695 | + | 0.0105025i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.9018 | + | 15.9018i | 0.907563 | + | 0.907563i | 0.996075 | − | 0.0885124i | \(-0.0282113\pi\) |
−0.0885124 | + | 0.996075i | \(0.528211\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.22899i | 0.240579i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.46112i | 0.252967i | 0.991969 | + | 0.126483i | \(0.0403691\pi\) | ||||
−0.991969 | + | 0.126483i | \(0.959631\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.6020 | − | 18.6020i | −1.05145 | − | 1.05145i | −0.998603 | − | 0.0528426i | \(-0.983172\pi\) |
−0.0528426 | − | 0.998603i | \(-0.516828\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0570247 | − | 0.0947305i | 0.00321298 | − | 0.00533746i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.02893 | − | 4.02893i | 0.226287 | − | 0.226287i | −0.584852 | − | 0.811140i | \(-0.698848\pi\) |
0.811140 | + | 0.584852i | \(0.198848\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.27793 | 0.295507 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.23513 | −0.403826 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.5414 | + | 14.5414i | −0.809104 | + | 0.809104i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.79380 | − | 1.47414i | −0.265912 | − | 0.0817707i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.6293 | + | 16.6293i | 0.919605 | + | 0.919605i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.28231i | 0.236092i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 0.291616i | − | 0.0160287i | −0.999968 | − | 0.00801434i | \(-0.997449\pi\) | ||
0.999968 | − | 0.00801434i | \(-0.00255107\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.296868 | + | 0.296868i | 0.0162683 | + | 0.0162683i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.0514 | − | 7.25458i | −0.658440 | − | 0.396360i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.68649 | + | 2.68649i | −0.146342 | + | 0.146342i | −0.776482 | − | 0.630140i | \(-0.782998\pi\) |
0.630140 | + | 0.776482i | \(0.282998\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.64510 | −0.252287 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.3074 | −1.15386 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.06800 | − | 6.06800i | 0.327641 | − | 0.327641i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.41855 | + | 29.8576i | 0.399401 | + | 1.60748i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.80170 | + | 8.80170i | 0.472500 | + | 0.472500i | 0.902723 | − | 0.430223i | \(-0.141565\pi\) |
−0.430223 | + | 0.902723i | \(0.641565\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 11.9421i | − | 0.639248i | −0.947544 | − | 0.319624i | \(-0.896443\pi\) | ||
0.947544 | − | 0.319624i | \(-0.103557\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.27793i | 0.281715i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.15676 | − | 1.15676i | −0.0615679 | − | 0.0615679i | 0.675652 | − | 0.737220i | \(-0.263862\pi\) |
−0.737220 | + | 0.675652i | \(0.763862\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.78252 | + | 31.3225i | 0.413053 | + | 1.66243i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.60197 | + | 3.60197i | −0.190636 | + | 0.190636i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.1360 | −0.640514 | −0.320257 | − | 0.947331i | \(-0.603769\pi\) | ||||
−0.320257 | + | 0.947331i | \(0.603769\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.0471809 | −0.00248321 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.43646 | − | 3.43646i | 0.180367 | − | 0.180367i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.709275 | + | 0.426961i | 0.0371252 | + | 0.0223482i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.45838 | − | 4.45838i | −0.232726 | − | 0.232726i | 0.581104 | − | 0.813829i | \(-0.302621\pi\) |
−0.813829 | + | 0.581104i | \(0.802621\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.764867i | 0.0398174i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.07413i | 0.419188i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.0494 | + | 19.0494i | 0.986343 | + | 0.986343i | 0.999908 | − | 0.0135649i | \(-0.00431799\pi\) |
−0.0135649 | + | 0.999908i | \(0.504318\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.04672 | − | 19.0816i | 0.0540524 | − | 0.985369i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.00614 | − | 1.00614i | 0.0518190 | − | 0.0518190i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.8071 | 0.811954 | 0.405977 | − | 0.913883i | \(-0.366931\pi\) | ||||
0.405977 | + | 0.913883i | \(0.366931\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.9093 | −0.866292 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.1152 | − | 10.1152i | 0.516864 | − | 0.516864i | −0.399757 | − | 0.916621i | \(-0.630905\pi\) |
0.916621 | + | 0.399757i | \(0.130905\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.70701 | + | 4.49693i | −0.137962 | + | 0.229185i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.0947305 | + | 0.0947305i | 0.00481542 | + | 0.00481542i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 25.2762i | − | 1.28155i | −0.767728 | − | 0.640776i | \(-0.778613\pi\) | ||
0.767728 | − | 0.640776i | \(-0.221387\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 38.0233i | 1.92292i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.34632 | + | 9.34632i | 0.471459 | + | 0.471459i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 35.0431 | − | 8.70697i | 1.76321 | − | 0.438095i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.8348 | + | 14.8348i | −0.744539 | + | 0.744539i | −0.973448 | − | 0.228909i | \(-0.926484\pi\) |
0.228909 | + | 0.973448i | \(0.426484\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.69470 | 0.235029 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.36683 | 0.317945 | 0.158972 | − | 0.987283i | \(-0.449182\pi\) | ||||
0.158972 | + | 0.987283i | \(0.449182\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.06187 | + | 4.06187i | −0.202336 | + | 0.202336i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.0072 | + | 4.72261i | −0.944475 | + | 0.234668i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.0925 | − | 14.0925i | −0.698541 | − | 0.698541i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 19.2762i | − | 0.953145i | −0.879135 | − | 0.476573i | \(-0.841879\pi\) | ||
0.879135 | − | 0.476573i | \(-0.158121\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 12.0864i | − | 0.596178i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.26180 | + | 5.26180i | 0.258916 | + | 0.258916i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.07125 | + | 15.0693i | −0.445290 | + | 0.739724i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.412408 | + | 0.412408i | −0.0201957 | + | 0.0201957i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.5140 | 1.19759 | 0.598794 | − | 0.800903i | \(-0.295647\pi\) | ||||
0.598794 | + | 0.800903i | \(0.295647\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.6947 | −0.911125 | −0.455562 | − | 0.890204i | \(-0.650562\pi\) | ||||
−0.455562 | + | 0.890204i | \(0.650562\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.376181 | + | 0.376181i | −0.0182906 | + | 0.0182906i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.94214 | − | 22.5753i | 0.336743 | − | 1.09506i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.151755 | + | 0.151755i | 0.00734395 | + | 0.00734395i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 6.37912i | − | 0.307987i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.4338i | 0.695249i | 0.937634 | + | 0.347625i | \(0.113012\pi\) | ||||
−0.937634 | + | 0.347625i | \(0.886988\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.10504 | − | 4.10504i | −0.197276 | − | 0.197276i | 0.601555 | − | 0.798831i | \(-0.294548\pi\) |
−0.798831 | + | 0.601555i | \(0.794548\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.64510 | + | 2.79620i | 0.222715 | + | 0.134068i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.7792 | − | 24.7792i | 1.18535 | − | 1.18535i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.1605 | 0.962210 | 0.481105 | − | 0.876663i | \(-0.340236\pi\) | ||||
0.481105 | + | 0.876663i | \(0.340236\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.517447 | 0.0246404 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.14484 | − | 3.14484i | 0.149416 | − | 0.149416i | −0.628441 | − | 0.777857i | \(-0.716307\pi\) |
0.777857 | + | 0.628441i | \(0.216307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.16290 | − | 4.68035i | −0.0551267 | − | 0.221870i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.6171 | − | 12.6171i | −0.596767 | − | 0.596767i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.3919i | 0.726388i | 0.931714 | + | 0.363194i | \(0.118314\pi\) | ||||
−0.931714 | + | 0.363194i | \(0.881686\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 36.3088i | − | 1.70971i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.9155 | + | 15.9155i | 0.747774 | + | 0.747774i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.341216 | + | 1.37330i | 0.0159965 | + | 0.0643814i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.07838 | + | 8.07838i | −0.377891 | + | 0.377891i | −0.870341 | − | 0.492450i | \(-0.836101\pi\) |
0.492450 | + | 0.870341i | \(0.336101\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −24.8552 | −1.16014 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.1629 | −0.799356 | −0.399678 | − | 0.916656i | \(-0.630878\pi\) | ||||
−0.399678 | + | 0.916656i | \(0.630878\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.01515 | + | 3.01515i | −0.140126 | + | 0.140126i | −0.773690 | − | 0.633564i | \(-0.781591\pi\) |
0.633564 | + | 0.773690i | \(0.281591\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.7526 | − | 11.2885i | −0.869630 | − | 0.523490i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.0947305 | − | 0.0947305i | −0.00438360 | − | 0.00438360i | 0.704912 | − | 0.709295i | \(-0.250987\pi\) |
−0.709295 | + | 0.704912i | \(0.750987\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.96880i | 0.183262i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.0047i | 0.507071i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.49693 | − | 4.49693i | −0.206769 | − | 0.206769i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.2361 | + | 10.1879i | −0.882612 | + | 0.467453i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.709275 | + | 0.709275i | −0.0324755 | + | 0.0324755i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.0431 | 1.60116 | 0.800581 | − | 0.599225i | \(-0.204524\pi\) | ||||
0.800581 | + | 0.599225i | \(0.204524\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.37298 | −0.244987 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.13793 | − | 6.13793i | 0.279286 | − | 0.279286i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.4680 | + | 17.3896i | −0.475327 | + | 0.789622i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.99519 | − | 6.99519i | −0.316982 | − | 0.316982i | 0.530625 | − | 0.847607i | \(-0.321957\pi\) |
−0.847607 | + | 0.530625i | \(0.821957\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.0661i | 0.681312i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.1469i | 1.13486i | 0.823421 | + | 0.567431i | \(0.192063\pi\) | ||||
−0.823421 | + | 0.567431i | \(0.807937\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.73820 | + | 4.73820i | 0.213398 | + | 0.213398i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.632832 | + | 0.157236i | −0.0284437 | + | 0.00706724i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.43907 | − | 6.43907i | 0.288832 | − | 0.288832i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.924449 | −0.0413840 | −0.0206920 | − | 0.999786i | \(-0.506587\pi\) | ||||
−0.0206920 | + | 0.999786i | \(0.506587\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 29.5897 | 1.32197 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.9100 | − | 21.9100i | 0.976919 | − | 0.976919i | −0.0228201 | − | 0.999740i | \(-0.507264\pi\) |
0.999740 | + | 0.0228201i | \(0.00726450\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.8371 | − | 5.67420i | 1.01624 | − | 0.252499i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.4963 | + | 14.4963i | 0.643801 | + | 0.643801i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.10504i | 0.403574i | 0.979429 | + | 0.201787i | \(0.0646748\pi\) | ||||
−0.979429 | + | 0.201787i | \(0.935325\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 0.233580i | − | 0.0103330i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.1978 | + | 16.1978i | 0.715150 | + | 0.715150i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.85323 | + | 4.73983i | −0.125728 | + | 0.208862i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.8576 | − | 17.8576i | 0.785377 | − | 0.785377i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.0384 | −1.05517 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 43.1917 | 1.89226 | 0.946130 | − | 0.323786i | \(-0.104956\pi\) | ||||
0.946130 | + | 0.323786i | \(0.104956\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.30873 | + | 8.30873i | −0.363315 | + | 0.363315i | −0.865032 | − | 0.501717i | \(-0.832702\pi\) |
0.501717 | + | 0.865032i | \(0.332702\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.76487 | + | 2.52359i | −0.207956 | + | 0.110139i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.1285 | − | 19.1285i | −0.833248 | − | 0.833248i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 41.7936i | − | 1.81711i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.924449i | 0.0401177i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.92162 | − | 6.92162i | −0.299809 | − | 0.299809i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.10910 | − | 4.88142i | −0.350587 | − | 0.211042i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 28.0989 | − | 28.0989i | 1.21256 | − | 1.21256i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.5636 | −1.05803 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.5113 | 1.22580 | 0.612898 | − | 0.790162i | \(-0.290004\pi\) | ||||
0.612898 | + | 0.790162i | \(0.290004\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.70697 | + | 8.70697i | −0.373652 | + | 0.373652i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.41855 | + | 29.8576i | 0.317776 | + | 1.27896i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.4309 | − | 26.4309i | −1.13010 | − | 1.13010i | −0.990159 | − | 0.139945i | \(-0.955308\pi\) |
−0.139945 | − | 0.990159i | \(-0.544692\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.0266620i | 0.00113791i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6.17564i | − | 0.263091i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.20394 | − | 7.20394i | −0.306343 | − | 0.306343i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.93672 | − | 19.8689i | −0.209552 | − | 0.843389i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.4163 | − | 23.4163i | 0.992180 | − | 0.992180i | −0.00778989 | − | 0.999970i | \(-0.502480\pi\) |
0.999970 | + | 0.00778989i | \(0.00247962\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.71452 | −0.0725164 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.0410 | 1.26833 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.9396 | − | 14.9396i | 0.629630 | − | 0.629630i | −0.318345 | − | 0.947975i | \(-0.603127\pi\) |
0.947975 | + | 0.318345i | \(0.103127\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.20620 | − | 3.13397i | −0.219027 | − | 0.131847i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.90737 | + | 3.90737i | 0.164094 | + | 0.164094i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.9155i | 1.08643i | 0.839593 | + | 0.543217i | \(0.182794\pi\) | ||||
−0.839593 | + | 0.543217i | \(0.817206\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.5759i | 1.19586i | 0.801547 | + | 0.597932i | \(0.204011\pi\) | ||||
−0.801547 | + | 0.597932i | \(0.795989\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.5958 | − | 12.5958i | −0.526198 | − | 0.526198i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.8298 | + | 38.4694i | −0.493335 | + | 1.60429i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.4329 | − | 30.4329i | 1.26694 | − | 1.26694i | 0.319278 | − | 0.947661i | \(-0.396560\pi\) |
0.947661 | − | 0.319278i | \(-0.103440\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 39.1050 | 1.62515 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.96266 | 0.205886 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.6698 | − | 33.6698i | 1.39446 | − | 1.39446i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0906639 | + | 0.150612i | −0.00374849 | + | 0.00622706i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.10700 | + | 4.10700i | 0.169514 | + | 0.169514i | 0.786766 | − | 0.617252i | \(-0.211754\pi\) |
−0.617252 | + | 0.786766i | \(0.711754\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.9315i | 1.02728i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 33.3286i | 1.37096i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.1506 | + | 20.1506i | 0.827486 | + | 0.827486i | 0.987169 | − | 0.159682i | \(-0.0510469\pi\) |
−0.159682 | + | 0.987169i | \(0.551047\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.46725 | + | 1.60688i | −0.265132 | + | 0.0658757i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.5174 | + | 19.5174i | −0.798796 | + | 0.798796i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.12373 | −0.331927 | −0.165963 | − | 0.986132i | \(-0.553073\pi\) | ||||
−0.165963 | + | 0.986132i | \(0.553073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.08452 | −0.166611 | −0.0833055 | − | 0.996524i | \(-0.526548\pi\) | ||||
−0.0833055 | + | 0.996524i | \(0.526548\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.348641 | + | 0.348641i | −0.0141978 | + | 0.0141978i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.17009 | − | 1.53305i | 0.250850 | − | 0.0623272i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.3609 | − | 15.3609i | −0.623481 | − | 0.623481i | 0.322939 | − | 0.946420i | \(-0.395329\pi\) |
−0.946420 | + | 0.322939i | \(0.895329\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 1.52973i | − | 0.0619879i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 6.80847i | − | 0.275441i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0700 | + | 14.0700i | 0.568281 | + | 0.568281i | 0.931647 | − | 0.363366i | \(-0.118373\pi\) |
−0.363366 | + | 0.931647i | \(0.618373\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.2361 | − | 31.9553i | 0.775674 | − | 1.28856i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.8104 | + | 21.8104i | −0.878055 | + | 0.878055i | −0.993333 | − | 0.115278i | \(-0.963224\pi\) |
0.115278 | + | 0.993333i | \(0.463224\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.61915 | −0.225853 | −0.112926 | − | 0.993603i | \(-0.536022\pi\) | ||||
−0.112926 | + | 0.993603i | \(0.536022\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 42.3545 | 1.69963 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.962154 | + | 0.962154i | −0.0385479 | + | 0.0385479i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.0472 | − | 20.6803i | 0.561887 | − | 0.827214i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19.5773 | − | 19.5773i | −0.781842 | − | 0.781842i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 25.3028i | − | 1.00889i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.8505i | 0.551380i | 0.961247 | + | 0.275690i | \(0.0889064\pi\) | ||||
−0.961247 | + | 0.275690i | \(0.911094\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.34632 | − | 9.34632i | −0.371483 | − | 0.371483i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.9519 | − | 11.4084i | −0.752083 | − | 0.452730i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.68261 | + | 4.68261i | −0.185532 | + | 0.185532i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.13128 | 0.0447529 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.08452 | 0.161329 | 0.0806644 | − | 0.996741i | \(-0.474296\pi\) | ||||
0.0806644 | + | 0.996741i | \(0.474296\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.0001 | + | 28.0001i | −1.10422 | + | 1.10422i | −0.110319 | + | 0.993896i | \(0.535187\pi\) |
−0.993896 | + | 0.110319i | \(0.964813\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.57531 | − | 6.34017i | −0.0620276 | − | 0.249644i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.14081 | + | 5.14081i | 0.202106 | + | 0.202106i | 0.800902 | − | 0.598796i | \(-0.204354\pi\) |
−0.598796 | + | 0.800902i | \(0.704354\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 43.8843i | − | 1.72261i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.17564i | 0.242042i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.2062 | − | 15.2062i | −0.595065 | − | 0.595065i | 0.343930 | − | 0.938995i | \(-0.388242\pi\) |
−0.938995 | + | 0.343930i | \(0.888242\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.16950 | + | 16.7811i | 0.162916 | + | 0.655692i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.0205189 | − | 0.0205189i | 0.000800519 | − | 0.000800519i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.60688 | 0.0625952 | 0.0312976 | − | 0.999510i | \(-0.490036\pi\) | ||||
0.0312976 | + | 0.999510i | \(0.490036\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.7480 | −1.35154 | −0.675771 | − | 0.737111i | \(-0.736189\pi\) | ||||
−0.675771 | + | 0.737111i | \(0.736189\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.72678 | − | 5.72678i | 0.222410 | − | 0.222410i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.26180 | + | 3.16743i | 0.204044 | + | 0.122828i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.07413 | − | 8.07413i | −0.312632 | − | 0.312632i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 3.23513i | − | 0.125077i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.26566i | − | 0.0488605i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.785386 | − | 0.785386i | −0.0302744 | − | 0.0302744i | 0.691808 | − | 0.722082i | \(-0.256815\pi\) |
−0.722082 | + | 0.691808i | \(0.756815\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.1469 | − | 7.73292i | −0.967903 | − | 0.297640i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.72979 | + | 5.72979i | −0.220214 | + | 0.220214i | −0.808588 | − | 0.588375i | \(-0.799768\pi\) |
0.588375 | + | 0.808588i | \(0.299768\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.72678 | 0.219774 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30.9749 | 1.18696 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.23266 | + | 6.23266i | −0.238486 | + | 0.238486i | −0.816223 | − | 0.577737i | \(-0.803936\pi\) |
0.577737 | + | 0.816223i | \(0.303936\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.15449 | − | 13.5464i | 0.311567 | − | 0.517580i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.8873 | + | 25.8873i | 0.987663 | + | 0.987663i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 12.8371i | − | 0.489055i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 39.4462i | − | 1.50061i | −0.661095 | − | 0.750303i | \(-0.729908\pi\) | ||
0.661095 | − | 0.750303i | \(-0.270092\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.130094 | + | 0.130094i | 0.00494184 | + | 0.00494184i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.740469 | + | 0.183980i | −0.0280876 | + | 0.00697876i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.5958 | − | 32.5958i | 1.23465 | − | 1.23465i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.2224 | −0.916175 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.3874 | −0.807789 | −0.403895 | − | 0.914806i | \(-0.632344\pi\) | ||||
−0.403895 | + | 0.914806i | \(0.632344\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.4895 | + | 16.4895i | −0.621913 | + | 0.621913i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 25.1773 | − | 6.25565i | 0.948231 | − | 0.235601i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.69470 | − | 4.69470i | −0.176562 | − | 0.176562i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.8827i | 1.08471i | 0.840149 | + | 0.542356i | \(0.182468\pi\) | ||||
−0.840149 | + | 0.542356i | \(0.817532\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1.26566i | − | 0.0474661i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 32.5958 | + | 32.5958i | 1.22072 | + | 1.22072i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.30388 | − | 7.14969i | 0.160956 | − | 0.267383i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.8371 | + | 22.8371i | −0.852867 | + | 0.852867i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.48094 | −0.0552296 | −0.0276148 | − | 0.999619i | \(-0.508791\pi\) | ||||
−0.0276148 | + | 0.999619i | \(0.508791\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.56093 | 0.0581321 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.5018 | − | 20.5018i | 0.762468 | − | 0.762468i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.31965 | + | 6.26794i | 0.123289 | + | 0.232785i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.4187 | + | 10.4187i | 0.386410 | + | 0.386410i | 0.873405 | − | 0.486995i | \(-0.161907\pi\) |
−0.486995 | + | 0.873405i | \(0.661907\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.6681i | 1.02474i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 8.07413i | − | 0.298633i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.579182 | − | 0.579182i | −0.0213926 | − | 0.0213926i | 0.696330 | − | 0.717722i | \(-0.254815\pi\) |
−0.717722 | + | 0.696330i | \(0.754815\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −21.6184 | − | 13.0136i | −0.797407 | − | 0.480014i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.5503 | − | 16.5503i | 0.609636 | − | 0.609636i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.19011 | 0.0805646 | 0.0402823 | − | 0.999188i | \(-0.487174\pi\) | ||||
0.0402823 | + | 0.999188i | \(0.487174\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.46412 | −0.274201 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.42053 | + | 5.42053i | −0.198860 | + | 0.198860i | −0.799511 | − | 0.600651i | \(-0.794908\pi\) |
0.600651 | + | 0.799511i | \(0.294908\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.62863 | − | 22.6537i | −0.206217 | − | 0.829967i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.435947 | + | 0.435947i | 0.0159505 | + | 0.0159505i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.67050i | 0.0975781i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 51.6403i | − | 1.88438i | −0.335079 | − | 0.942190i | \(-0.608763\pi\) | ||
0.335079 | − | 0.942190i | \(-0.391237\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.4908 | + | 13.4908i | 0.491632 | + | 0.491632i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.10009 | + | 28.5759i | 0.258399 | + | 1.03998i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.80817 | − | 8.80817i | 0.320138 | − | 0.320138i | −0.528682 | − | 0.848820i | \(-0.677313\pi\) |
0.848820 | + | 0.528682i | \(0.177313\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −51.1914 | −1.85813 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.6803 | −0.532162 | −0.266081 | − | 0.963951i | \(-0.585729\pi\) | ||||
−0.266081 | + | 0.963951i | \(0.585729\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.13793 | − | 6.13793i | 0.222208 | − | 0.222208i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.709275 | − | 0.426961i | −0.0256439 | − | 0.0154368i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.36575 | − | 8.36575i | −0.302070 | − | 0.302070i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.1506i | 0.402101i | 0.979581 | + | 0.201051i | \(0.0644356\pi\) | ||||
−0.979581 | + | 0.201051i | \(0.935564\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 20.7934i | − | 0.748855i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.44748 | − | 5.44748i | −0.195932 | − | 0.195932i | 0.602321 | − | 0.798254i | \(-0.294243\pi\) |
−0.798254 | + | 0.602321i | \(0.794243\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.4017 | − | 25.3041i | −0.481402 | − | 0.908950i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.08452 | + | 4.08452i | −0.146531 | + | 0.146531i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −42.4844 | −1.52216 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −53.7030 | −1.92164 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.27793 | − | 5.27793i | 0.188618 | − | 0.188618i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.42469 | + | 12.3340i | −0.264999 | + | 0.440220i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.6239 | + | 10.6239i | 0.378699 | + | 0.378699i | 0.870633 | − | 0.491933i | \(-0.163710\pi\) |
−0.491933 | + | 0.870633i | \(0.663710\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 32.7403i | − | 1.16559i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.71452i | 0.0609612i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.241276 | − | 0.241276i | −0.00856797 | − | 0.00856797i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 47.4708 | − | 11.7948i | 1.68361 | − | 0.418318i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.02893 | − | 4.02893i | 0.142712 | − | 0.142712i | −0.632141 | − | 0.774853i | \(-0.717824\pi\) |
0.774853 | + | 0.632141i | \(0.217824\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.0630 | 1.13431 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.169042 | −0.00597279 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.974049 | + | 0.974049i | −0.0343734 | + | 0.0343734i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.0205 | − | 2.73820i | 0.388422 | − | 0.0965090i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.8428 | + | 21.8428i | 0.768904 | + | 0.768904i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 23.0349i | − | 0.809864i | −0.914347 | − | 0.404932i | \(-0.867295\pi\) | ||
0.914347 | − | 0.404932i | \(-0.132705\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.0172i | 1.26473i | 0.774669 | + | 0.632367i | \(0.217917\pi\) | ||||
−0.774669 | + | 0.632367i | \(0.782083\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.5897 | + | 21.5897i | 0.757183 | + | 0.757183i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.1648 | + | 16.8860i | −0.356059 | + | 0.591491i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.26180 | + | 5.26180i | −0.184087 | + | 0.184087i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.0496000 | 0.00173316 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.9733 | 0.417872 | 0.208936 | − | 0.977929i | \(-0.433000\pi\) | ||||
0.208936 | + | 0.977929i | \(0.433000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.2937 | + | 33.2937i | −1.16054 | + | 1.16054i | −0.176187 | + | 0.984357i | \(0.556376\pi\) |
−0.984357 | + | 0.176187i | \(0.943624\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 30.3935 | + | 9.34632i | 1.05817 | + | 0.325397i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.9500 | + | 24.9500i | 0.867595 | + | 0.867595i | 0.992206 | − | 0.124610i | \(-0.0397681\pi\) |
−0.124610 | + | 0.992206i | \(0.539768\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 21.1317i | − | 0.733934i | −0.930234 | − | 0.366967i | \(-0.880396\pi\) | ||
0.930234 | − | 0.366967i | \(-0.119604\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 17.8628i | − | 0.619653i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.0517 | − | 22.0517i | −0.764047 | − | 0.764047i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.1640 | + | 19.9637i | 1.14769 | + | 0.690871i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.3074 | + | 21.3074i | −0.736490 | + | 0.736490i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.3513 | 0.426413 | 0.213207 | − | 0.977007i | \(-0.431609\pi\) | ||||
0.213207 | + | 0.977007i | \(0.431609\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.9877 | 0.930611 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26.6774 | − | 26.6774i | 0.918818 | − | 0.918818i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.46695 | + | 26.0277i | 0.222470 | + | 0.895380i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.26841 | − | 1.26841i | −0.0435829 | − | 0.0435829i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.5897i | 0.878236i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43.1173i | 1.47804i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.9588 | − | 33.9588i | −1.16273 | − | 1.16273i | −0.983876 | − | 0.178850i | \(-0.942762\pi\) |
−0.178850 | − | 0.983876i | \(-0.557238\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.183980 | + | 0.740469i | 0.00629198 | + | 0.0253235i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.1568 | − | 21.1568i | 0.722701 | − | 0.722701i | −0.246454 | − | 0.969155i | \(-0.579265\pi\) |
0.969155 | + | 0.246454i | \(0.0792653\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.3261 | 0.488801 | 0.244400 | − | 0.969674i | \(-0.421409\pi\) | ||||
0.244400 | + | 0.969674i | \(0.421409\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.5236 | −0.358643 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.3865 | − | 10.3865i | 0.353561 | − | 0.353561i | −0.507872 | − | 0.861433i | \(-0.669568\pi\) |
0.861433 | + | 0.507872i | \(0.169568\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.9421 | − | 16.2183i | −0.916060 | − | 0.551439i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.42212 | + | 6.42212i | 0.218107 | + | 0.218107i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 60.0821i | 2.03814i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 6.31002i | − | 0.213807i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.503072 | + | 0.503072i | 0.0170264 | + | 0.0170264i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.04306 | − | 0.386347i | −0.238099 | − | 0.0130609i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.29072 | + | 9.29072i | −0.313725 | + | 0.313725i | −0.846351 | − | 0.532626i | \(-0.821205\pi\) |
0.532626 | + | 0.846351i | \(0.321205\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.2918 | 0.718155 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.2762 | 0.986339 | 0.493170 | − | 0.869933i | \(-0.335838\pi\) | ||||
0.493170 | + | 0.869933i | \(0.335838\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.6808 | + | 39.6808i | −1.33537 | + | 1.33537i | −0.434875 | + | 0.900491i | \(0.643207\pi\) |
−0.900491 | + | 0.434875i | \(0.856793\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23.2495 | − | 38.6225i | 0.781524 | − | 1.29828i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.7946 | + | 30.7946i | 1.03398 | + | 1.03398i | 0.999402 | + | 0.0345779i | \(0.0110087\pi\) |
0.0345779 | + | 0.999402i | \(0.488991\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.24128i | 0.209326i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 32.5882i | − | 1.09174i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.8950 | − | 20.8950i | −0.699223 | − | 0.699223i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50.4509 | − | 12.5353i | 1.68639 | − | 0.419007i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.75872 | + | 9.75872i | −0.325834 | + | 0.325834i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.12373 | 0.270942 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 60.4534 | 2.01400 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.30337 | + | 1.30337i | −0.0433735 | + | 0.0433735i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.6332 | + | 3.88428i | −0.519664 | + | 0.129118i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.1536 | + | 23.1536i | 0.768803 | + | 0.768803i | 0.977896 | − | 0.209092i | \(-0.0670509\pi\) |
−0.209092 | + | 0.977896i | \(0.567051\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 0.824815i | − | 0.0273574i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 28.6339i | − | 0.948684i | −0.880341 | − | 0.474342i | \(-0.842686\pi\) | ||
0.880341 | − | 0.474342i | \(-0.157314\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.6947 | − | 20.6947i | −0.684895 | − | 0.684895i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.670538 | − | 1.11391i | 0.0221673 | − | 0.0368247i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.44975 | − | 3.44975i | 0.113921 | − | 0.113921i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.26566 | −0.0417504 | −0.0208752 | − | 0.999782i | \(-0.506645\pi\) | ||||
−0.0208752 | + | 0.999782i | \(0.506645\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −38.4391 | −1.26661 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.2375 | + | 10.2375i | −0.336972 | + | 0.336972i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.87217 | − | 25.5997i | 0.258835 | − | 0.841713i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.137121 | + | 0.137121i | 0.00450363 | + | 0.00450363i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 8.75258i | − | 0.287163i | −0.989639 | − | 0.143581i | \(-0.954138\pi\) | ||
0.989639 | − | 0.143581i | \(-0.0458619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.7416i | 0.941967i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.39189 | − | 5.39189i | −0.176523 | − | 0.176523i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 33.6698 | + | 20.2682i | 1.10112 | + | 0.662840i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.6598 | + | 26.6598i | −0.870939 | + | 0.870939i | −0.992575 | − | 0.121636i | \(-0.961186\pi\) |
0.121636 | + | 0.992575i | \(0.461186\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 44.9662 | 1.46742 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.2388 | 1.50734 | 0.753671 | − | 0.657251i | \(-0.228281\pi\) | ||||
0.753671 | + | 0.657251i | \(0.228281\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −55.5449 | + | 55.5449i | −1.80879 | + | 1.80879i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.78992 | + | 7.20394i | 0.0582261 | + | 0.234344i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.46048 | + | 8.46048i | 0.274929 | + | 0.274929i | 0.831081 | − | 0.556152i | \(-0.187723\pi\) |
−0.556152 | + | 0.831081i | \(0.687723\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.371370i | 0.0120552i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.73905i | 0.315810i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.40417 | − | 2.40417i | −0.0778789 | − | 0.0778789i | 0.667094 | − | 0.744973i | \(-0.267538\pi\) |
−0.744973 | + | 0.667094i | \(0.767538\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.61915 | − | 22.6155i | −0.181831 | − | 0.731821i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.37912 | + | 6.37912i | −0.206208 | + | 0.206208i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.46112 | −0.144057 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.79606 | −0.0579375 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.234591 | + | 0.234591i | −0.00755961 | + | 0.00755961i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 43.8287 | + | 26.3835i | 1.41090 | + | 0.849314i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.3741 | − | 42.3741i | −1.36266 | − | 1.36266i | −0.870513 | − | 0.492145i | \(-0.836213\pi\) |
−0.492145 | − | 0.870513i | \(-0.663787\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 35.1506i | − | 1.12920i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 48.0540i | − | 1.54213i | −0.636759 | − | 0.771063i | \(-0.719725\pi\) | ||
0.636759 | − | 0.771063i | \(-0.280275\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.152221 | + | 0.152221i | 0.00487997 | + | 0.00487997i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.57568 | − | 4.01227i | 0.242616 | − | 0.128495i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.2967 | + | 29.2967i | −0.937284 | + | 0.937284i | −0.998146 | − | 0.0608620i | \(-0.980615\pi\) |
0.0608620 | + | 0.998146i | \(0.480615\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.02453 | 0.256465 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.07838 | 0.0344300 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.2512 | + | 22.2512i | −0.709704 | + | 0.709704i | −0.966473 | − | 0.256769i | \(-0.917342\pi\) |
0.256769 | + | 0.966473i | \(0.417342\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.4863 | + | 37.3545i | −0.716472 | + | 1.19021i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.17578 | − | 5.17578i | −0.164747 | − | 0.164747i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.7587i | 0.437502i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 27.1530i | − | 0.862543i | −0.902222 | − | 0.431272i | \(-0.858065\pi\) | ||
0.902222 | − | 0.431272i | \(-0.141935\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.352459 | + | 0.352459i | 0.0111850 | + | 0.0111850i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35.0431 | + | 8.70697i | −1.11094 | + | 0.276029i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.0228 | + | 33.0228i | −1.04584 | + | 1.04584i | −0.0469446 | + | 0.998897i | \(0.514948\pi\) |
−0.998897 | + | 0.0469446i | \(0.985052\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28.1851 | −0.891736 |
(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 | 1280.2.n.r.1023.2 | 12 | ||
4.3 | odd | 2 | inner | 1280.2.n.r.1023.5 | 12 | ||
5.2 | odd | 4 | inner | 1280.2.n.r.767.5 | 12 | ||
8.3 | odd | 2 | 1280.2.n.s.1023.2 | 12 | |||
8.5 | even | 2 | 1280.2.n.s.1023.5 | 12 | |||
16.3 | odd | 4 | 640.2.o.j.63.5 | yes | 12 | ||
16.5 | even | 4 | 640.2.o.k.63.5 | yes | 12 | ||
16.11 | odd | 4 | 640.2.o.k.63.2 | yes | 12 | ||
16.13 | even | 4 | 640.2.o.j.63.2 | ✓ | 12 | ||
20.7 | even | 4 | inner | 1280.2.n.r.767.2 | 12 | ||
40.27 | even | 4 | 1280.2.n.s.767.5 | 12 | |||
40.37 | odd | 4 | 1280.2.n.s.767.2 | 12 | |||
80.27 | even | 4 | 640.2.o.j.447.2 | yes | 12 | ||
80.37 | odd | 4 | 640.2.o.j.447.5 | yes | 12 | ||
80.67 | even | 4 | 640.2.o.k.447.5 | yes | 12 | ||
80.77 | odd | 4 | 640.2.o.k.447.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.2.o.j.63.2 | ✓ | 12 | 16.13 | even | 4 | ||
640.2.o.j.63.5 | yes | 12 | 16.3 | odd | 4 | ||
640.2.o.j.447.2 | yes | 12 | 80.27 | even | 4 | ||
640.2.o.j.447.5 | yes | 12 | 80.37 | odd | 4 | ||
640.2.o.k.63.2 | yes | 12 | 16.11 | odd | 4 | ||
640.2.o.k.63.5 | yes | 12 | 16.5 | even | 4 | ||
640.2.o.k.447.2 | yes | 12 | 80.77 | odd | 4 | ||
640.2.o.k.447.5 | yes | 12 | 80.67 | even | 4 | ||
1280.2.n.r.767.2 | 12 | 20.7 | even | 4 | inner | ||
1280.2.n.r.767.5 | 12 | 5.2 | odd | 4 | inner | ||
1280.2.n.r.1023.2 | 12 | 1.1 | even | 1 | trivial | ||
1280.2.n.r.1023.5 | 12 | 4.3 | odd | 2 | inner | ||
1280.2.n.s.767.2 | 12 | 40.37 | odd | 4 | |||
1280.2.n.s.767.5 | 12 | 40.27 | even | 4 | |||
1280.2.n.s.1023.2 | 12 | 8.3 | odd | 2 | |||
1280.2.n.s.1023.5 | 12 | 8.5 | even | 2 |