Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [471,2,Mod(313,471)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(471, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("471.313");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 471 = 3 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 471.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.76095393520\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 24x^{12} + 224x^{10} + 1027x^{8} + 2399x^{6} + 2652x^{4} + 1094x^{2} + 147 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 313.11 | ||
Root | \(1.66261i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 471.313 |
Dual form | 471.2.b.b.313.4 |
$q$-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 \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).
\(n\) | \(158\) | \(319\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.66261i | 1.17564i | 0.808991 | + | 0.587821i | \(0.200014\pi\) | ||||
−0.808991 | + | 0.587821i | \(0.799986\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.764270 | −0.382135 | ||||||||
\(5\) | 1.85555i | 0.829826i | 0.909861 | + | 0.414913i | \(0.136188\pi\) | ||||
−0.909861 | + | 0.414913i | \(0.863812\pi\) | |||||||
\(6\) | 1.66261i | 0.678757i | ||||||||
\(7\) | − | 0.948177i | − | 0.358377i | −0.983815 | − | 0.179189i | \(-0.942653\pi\) | ||
0.983815 | − | 0.179189i | \(-0.0573472\pi\) | |||||||
\(8\) | 2.05454i | 0.726388i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.08505 | −0.975578 | ||||||||
\(11\) | 5.18060 | 1.56201 | 0.781005 | − | 0.624525i | \(-0.214707\pi\) | ||||
0.781005 | + | 0.624525i | \(0.214707\pi\) | |||||||
\(12\) | −0.764270 | −0.220626 | ||||||||
\(13\) | 2.15208 | 0.596881 | 0.298440 | − | 0.954428i | \(-0.403534\pi\) | ||||
0.298440 | + | 0.954428i | \(0.403534\pi\) | |||||||
\(14\) | 1.57645 | 0.421323 | ||||||||
\(15\) | 1.85555i | 0.479100i | ||||||||
\(16\) | −4.94443 | −1.23611 | ||||||||
\(17\) | −1.84477 | −0.447421 | −0.223711 | − | 0.974656i | \(-0.571817\pi\) | ||||
−0.223711 | + | 0.974656i | \(0.571817\pi\) | |||||||
\(18\) | 1.66261i | 0.391881i | ||||||||
\(19\) | −8.04487 | −1.84562 | −0.922809 | − | 0.385257i | \(-0.874113\pi\) | ||||
−0.922809 | + | 0.385257i | \(0.874113\pi\) | |||||||
\(20\) | − | 1.41814i | − | 0.317105i | ||||||
\(21\) | − | 0.948177i | − | 0.206909i | ||||||
\(22\) | 8.61331i | 1.83636i | ||||||||
\(23\) | − | 4.20591i | − | 0.876992i | −0.898733 | − | 0.438496i | \(-0.855511\pi\) | ||
0.898733 | − | 0.438496i | \(-0.144489\pi\) | |||||||
\(24\) | 2.05454i | 0.419380i | ||||||||
\(25\) | 1.55695 | 0.311389 | ||||||||
\(26\) | 3.57808i | 0.701718i | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.724663i | 0.136949i | ||||||||
\(29\) | 5.35559i | 0.994507i | 0.867605 | + | 0.497254i | \(0.165658\pi\) | ||||
−0.867605 | + | 0.497254i | \(0.834342\pi\) | |||||||
\(30\) | −3.08505 | −0.563250 | ||||||||
\(31\) | −2.86427 | −0.514437 | −0.257219 | − | 0.966353i | \(-0.582806\pi\) | ||||
−0.257219 | + | 0.966353i | \(0.582806\pi\) | |||||||
\(32\) | − | 4.11159i | − | 0.726833i | ||||||
\(33\) | 5.18060 | 0.901827 | ||||||||
\(34\) | − | 3.06712i | − | 0.526007i | ||||||
\(35\) | 1.75939 | 0.297391 | ||||||||
\(36\) | −0.764270 | −0.127378 | ||||||||
\(37\) | −1.28782 | −0.211716 | −0.105858 | − | 0.994381i | \(-0.533759\pi\) | ||||
−0.105858 | + | 0.994381i | \(0.533759\pi\) | |||||||
\(38\) | − | 13.3755i | − | 2.16979i | ||||||
\(39\) | 2.15208 | 0.344609 | ||||||||
\(40\) | −3.81229 | −0.602776 | ||||||||
\(41\) | − | 0.936712i | − | 0.146290i | −0.997321 | − | 0.0731449i | \(-0.976696\pi\) | ||
0.997321 | − | 0.0731449i | \(-0.0233036\pi\) | |||||||
\(42\) | 1.57645 | 0.243251 | ||||||||
\(43\) | 0.0513523i | 0.00783115i | 0.999992 | + | 0.00391557i | \(0.00124637\pi\) | ||||
−0.999992 | + | 0.00391557i | \(0.998754\pi\) | |||||||
\(44\) | −3.95938 | −0.596899 | ||||||||
\(45\) | 1.85555i | 0.276609i | ||||||||
\(46\) | 6.99278 | 1.03103 | ||||||||
\(47\) | 1.22122 | 0.178134 | 0.0890668 | − | 0.996026i | \(-0.471612\pi\) | ||||
0.0890668 | + | 0.996026i | \(0.471612\pi\) | |||||||
\(48\) | −4.94443 | −0.713667 | ||||||||
\(49\) | 6.10096 | 0.871566 | ||||||||
\(50\) | 2.58860i | 0.366083i | ||||||||
\(51\) | −1.84477 | −0.258319 | ||||||||
\(52\) | −1.64477 | −0.228089 | ||||||||
\(53\) | 0.958722i | 0.131691i | 0.997830 | + | 0.0658453i | \(0.0209744\pi\) | ||||
−0.997830 | + | 0.0658453i | \(0.979026\pi\) | |||||||
\(54\) | 1.66261i | 0.226252i | ||||||||
\(55\) | 9.61284i | 1.29620i | ||||||||
\(56\) | 1.94806 | 0.260321 | ||||||||
\(57\) | −8.04487 | −1.06557 | ||||||||
\(58\) | −8.90425 | −1.16919 | ||||||||
\(59\) | − | 3.20638i | − | 0.417435i | −0.977976 | − | 0.208717i | \(-0.933071\pi\) | ||
0.977976 | − | 0.208717i | \(-0.0669289\pi\) | |||||||
\(60\) | − | 1.41814i | − | 0.183081i | ||||||
\(61\) | − | 13.5254i | − | 1.73176i | −0.500256 | − | 0.865878i | \(-0.666761\pi\) | ||
0.500256 | − | 0.865878i | \(-0.333239\pi\) | |||||||
\(62\) | − | 4.76216i | − | 0.604794i | ||||||
\(63\) | − | 0.948177i | − | 0.119459i | ||||||
\(64\) | −3.05290 | −0.381613 | ||||||||
\(65\) | 3.99329i | 0.495307i | ||||||||
\(66\) | 8.61331i | 1.06023i | ||||||||
\(67\) | −3.65206 | −0.446170 | −0.223085 | − | 0.974799i | \(-0.571613\pi\) | ||||
−0.223085 | + | 0.974799i | \(0.571613\pi\) | |||||||
\(68\) | 1.40990 | 0.170975 | ||||||||
\(69\) | − | 4.20591i | − | 0.506332i | ||||||
\(70\) | 2.92517i | 0.349625i | ||||||||
\(71\) | 2.98061 | 0.353733 | 0.176867 | − | 0.984235i | \(-0.443404\pi\) | ||||
0.176867 | + | 0.984235i | \(0.443404\pi\) | |||||||
\(72\) | 2.05454i | 0.242129i | ||||||||
\(73\) | − | 12.3024i | − | 1.43989i | −0.694033 | − | 0.719943i | \(-0.744168\pi\) | ||
0.694033 | − | 0.719943i | \(-0.255832\pi\) | |||||||
\(74\) | − | 2.14114i | − | 0.248902i | ||||||
\(75\) | 1.55695 | 0.179781 | ||||||||
\(76\) | 6.14845 | 0.705276 | ||||||||
\(77\) | − | 4.91213i | − | 0.559789i | ||||||
\(78\) | 3.57808i | 0.405137i | ||||||||
\(79\) | − | 3.34723i | − | 0.376593i | −0.982112 | − | 0.188296i | \(-0.939703\pi\) | ||
0.982112 | − | 0.188296i | \(-0.0602965\pi\) | |||||||
\(80\) | − | 9.17462i | − | 1.02575i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.55739 | 0.171985 | ||||||||
\(83\) | − | 15.2183i | − | 1.67042i | −0.549929 | − | 0.835211i | \(-0.685345\pi\) | ||
0.549929 | − | 0.835211i | \(-0.314655\pi\) | |||||||
\(84\) | 0.724663i | 0.0790673i | ||||||||
\(85\) | − | 3.42305i | − | 0.371282i | ||||||
\(86\) | −0.0853788 | −0.00920663 | ||||||||
\(87\) | 5.35559i | 0.574179i | ||||||||
\(88\) | 10.6437i | 1.13463i | ||||||||
\(89\) | 15.1938 | 1.61054 | 0.805272 | − | 0.592905i | \(-0.202019\pi\) | ||||
0.805272 | + | 0.592905i | \(0.202019\pi\) | |||||||
\(90\) | −3.08505 | −0.325193 | ||||||||
\(91\) | − | 2.04056i | − | 0.213908i | ||||||
\(92\) | 3.21445i | 0.335129i | ||||||||
\(93\) | −2.86427 | −0.297011 | ||||||||
\(94\) | 2.03041i | 0.209421i | ||||||||
\(95\) | − | 14.9276i | − | 1.53154i | ||||||
\(96\) | − | 4.11159i | − | 0.419637i | ||||||
\(97\) | 18.3611i | 1.86429i | 0.362084 | + | 0.932146i | \(0.382066\pi\) | ||||
−0.362084 | + | 0.932146i | \(0.617934\pi\) | |||||||
\(98\) | 10.1435i | 1.02465i | ||||||||
\(99\) | 5.18060 | 0.520670 | ||||||||
\(100\) | −1.18993 | −0.118993 | ||||||||
\(101\) | −4.58292 | −0.456018 | −0.228009 | − | 0.973659i | \(-0.573222\pi\) | ||||
−0.228009 | + | 0.973659i | \(0.573222\pi\) | |||||||
\(102\) | − | 3.06712i | − | 0.303691i | ||||||
\(103\) | − | 4.02054i | − | 0.396156i | −0.980186 | − | 0.198078i | \(-0.936530\pi\) | ||
0.980186 | − | 0.198078i | \(-0.0634699\pi\) | |||||||
\(104\) | 4.42153i | 0.433567i | ||||||||
\(105\) | 1.75939 | 0.171699 | ||||||||
\(106\) | −1.59398 | −0.154821 | ||||||||
\(107\) | 8.75884i | 0.846749i | 0.905955 | + | 0.423375i | \(0.139155\pi\) | ||||
−0.905955 | + | 0.423375i | \(0.860845\pi\) | |||||||
\(108\) | −0.764270 | −0.0735419 | ||||||||
\(109\) | 10.2946 | 0.986044 | 0.493022 | − | 0.870017i | \(-0.335892\pi\) | ||||
0.493022 | + | 0.870017i | \(0.335892\pi\) | |||||||
\(110\) | −15.9824 | −1.52386 | ||||||||
\(111\) | −1.28782 | −0.122234 | ||||||||
\(112\) | 4.68820i | 0.442993i | ||||||||
\(113\) | 6.05386 | 0.569500 | 0.284750 | − | 0.958602i | \(-0.408089\pi\) | ||||
0.284750 | + | 0.958602i | \(0.408089\pi\) | |||||||
\(114\) | − | 13.3755i | − | 1.25273i | ||||||
\(115\) | 7.80425 | 0.727750 | ||||||||
\(116\) | − | 4.09312i | − | 0.380036i | ||||||
\(117\) | 2.15208 | 0.198960 | ||||||||
\(118\) | 5.33095 | 0.490754 | ||||||||
\(119\) | 1.74916i | 0.160346i | ||||||||
\(120\) | −3.81229 | −0.348013 | ||||||||
\(121\) | 15.8386 | 1.43987 | ||||||||
\(122\) | 22.4875 | 2.03592 | ||||||||
\(123\) | − | 0.936712i | − | 0.0844605i | ||||||
\(124\) | 2.18907 | 0.196585 | ||||||||
\(125\) | 12.1667i | 1.08822i | ||||||||
\(126\) | 1.57645 | 0.140441 | ||||||||
\(127\) | −3.56745 | −0.316560 | −0.158280 | − | 0.987394i | \(-0.550595\pi\) | ||||
−0.158280 | + | 0.987394i | \(0.550595\pi\) | |||||||
\(128\) | − | 13.2990i | − | 1.17547i | ||||||
\(129\) | 0.0513523i | 0.00452131i | ||||||||
\(130\) | −6.63928 | −0.582304 | ||||||||
\(131\) | − | 1.78218i | − | 0.155710i | −0.996965 | − | 0.0778551i | \(-0.975193\pi\) | ||
0.996965 | − | 0.0778551i | \(-0.0248072\pi\) | |||||||
\(132\) | −3.95938 | −0.344620 | ||||||||
\(133\) | 7.62796i | 0.661428i | ||||||||
\(134\) | − | 6.07195i | − | 0.524536i | ||||||
\(135\) | 1.85555i | 0.159700i | ||||||||
\(136\) | − | 3.79014i | − | 0.325002i | ||||||
\(137\) | − | 0.187329i | − | 0.0160046i | −0.999968 | − | 0.00800230i | \(-0.997453\pi\) | ||
0.999968 | − | 0.00800230i | \(-0.00254724\pi\) | |||||||
\(138\) | 6.99278 | 0.595265 | ||||||||
\(139\) | − | 16.8727i | − | 1.43112i | −0.698551 | − | 0.715561i | \(-0.746171\pi\) | ||
0.698551 | − | 0.715561i | \(-0.253829\pi\) | |||||||
\(140\) | −1.34465 | −0.113643 | ||||||||
\(141\) | 1.22122 | 0.102845 | ||||||||
\(142\) | 4.95559i | 0.415864i | ||||||||
\(143\) | 11.1491 | 0.932333 | ||||||||
\(144\) | −4.94443 | −0.412036 | ||||||||
\(145\) | −9.93754 | −0.825268 | ||||||||
\(146\) | 20.4541 | 1.69279 | ||||||||
\(147\) | 6.10096 | 0.503199 | ||||||||
\(148\) | 0.984241 | 0.0809041 | ||||||||
\(149\) | 13.2732i | 1.08738i | 0.839285 | + | 0.543692i | \(0.182974\pi\) | ||||
−0.839285 | + | 0.543692i | \(0.817026\pi\) | |||||||
\(150\) | 2.58860i | 0.211358i | ||||||||
\(151\) | 21.6037i | 1.75808i | 0.476744 | + | 0.879042i | \(0.341817\pi\) | ||||
−0.476744 | + | 0.879042i | \(0.658183\pi\) | |||||||
\(152\) | − | 16.5285i | − | 1.34064i | ||||||
\(153\) | −1.84477 | −0.149140 | ||||||||
\(154\) | 8.16695 | 0.658111 | ||||||||
\(155\) | − | 5.31478i | − | 0.426893i | ||||||
\(156\) | −1.64477 | −0.131687 | ||||||||
\(157\) | −6.45803 | − | 10.7375i | −0.515407 | − | 0.856946i | ||||
\(158\) | 5.56513 | 0.442738 | ||||||||
\(159\) | 0.958722i | 0.0760316i | ||||||||
\(160\) | 7.62924 | 0.603144 | ||||||||
\(161\) | −3.98794 | −0.314294 | ||||||||
\(162\) | 1.66261i | 0.130627i | ||||||||
\(163\) | − | 16.3116i | − | 1.27762i | −0.769363 | − | 0.638812i | \(-0.779426\pi\) | ||
0.769363 | − | 0.638812i | \(-0.220574\pi\) | |||||||
\(164\) | 0.715901i | 0.0559025i | ||||||||
\(165\) | 9.61284i | 0.748359i | ||||||||
\(166\) | 25.3020 | 1.96382 | ||||||||
\(167\) | −12.8059 | −0.990952 | −0.495476 | − | 0.868622i | \(-0.665006\pi\) | ||||
−0.495476 | + | 0.868622i | \(0.665006\pi\) | |||||||
\(168\) | 1.94806 | 0.150296 | ||||||||
\(169\) | −8.36853 | −0.643733 | ||||||||
\(170\) | 5.69119 | 0.436494 | ||||||||
\(171\) | −8.04487 | −0.615206 | ||||||||
\(172\) | − | 0.0392470i | − | 0.00299256i | ||||||
\(173\) | −15.4077 | −1.17143 | −0.585714 | − | 0.810518i | \(-0.699186\pi\) | ||||
−0.585714 | + | 0.810518i | \(0.699186\pi\) | |||||||
\(174\) | −8.90425 | −0.675029 | ||||||||
\(175\) | − | 1.47626i | − | 0.111595i | ||||||
\(176\) | −25.6151 | −1.93081 | ||||||||
\(177\) | − | 3.20638i | − | 0.241006i | ||||||
\(178\) | 25.2614i | 1.89342i | ||||||||
\(179\) | − | 3.92776i | − | 0.293575i | −0.989168 | − | 0.146787i | \(-0.953107\pi\) | ||
0.989168 | − | 0.146787i | \(-0.0468933\pi\) | |||||||
\(180\) | − | 1.41814i | − | 0.105702i | ||||||
\(181\) | − | 4.44053i | − | 0.330062i | −0.986288 | − | 0.165031i | \(-0.947228\pi\) | ||
0.986288 | − | 0.165031i | \(-0.0527724\pi\) | |||||||
\(182\) | 3.39265 | 0.251480 | ||||||||
\(183\) | − | 13.5254i | − | 0.999829i | ||||||
\(184\) | 8.64118 | 0.637037 | ||||||||
\(185\) | − | 2.38961i | − | 0.175687i | ||||||
\(186\) | − | 4.76216i | − | 0.349178i | ||||||
\(187\) | −9.55699 | −0.698876 | ||||||||
\(188\) | −0.933343 | −0.0680711 | ||||||||
\(189\) | − | 0.948177i | − | 0.0689697i | ||||||
\(190\) | 24.8188 | 1.80055 | ||||||||
\(191\) | 18.7649i | 1.35778i | 0.734240 | + | 0.678890i | \(0.237539\pi\) | ||||
−0.734240 | + | 0.678890i | \(0.762461\pi\) | |||||||
\(192\) | −3.05290 | −0.220324 | ||||||||
\(193\) | −9.21645 | −0.663415 | −0.331707 | − | 0.943382i | \(-0.607625\pi\) | ||||
−0.331707 | + | 0.943382i | \(0.607625\pi\) | |||||||
\(194\) | −30.5274 | −2.19174 | ||||||||
\(195\) | 3.99329i | 0.285966i | ||||||||
\(196\) | −4.66278 | −0.333056 | ||||||||
\(197\) | −15.2713 | −1.08803 | −0.544017 | − | 0.839074i | \(-0.683097\pi\) | ||||
−0.544017 | + | 0.839074i | \(0.683097\pi\) | |||||||
\(198\) | 8.61331i | 0.612122i | ||||||||
\(199\) | 11.1866 | 0.792994 | 0.396497 | − | 0.918036i | \(-0.370226\pi\) | ||||
0.396497 | + | 0.918036i | \(0.370226\pi\) | |||||||
\(200\) | 3.19880i | 0.226190i | ||||||||
\(201\) | −3.65206 | −0.257596 | ||||||||
\(202\) | − | 7.61961i | − | 0.536114i | ||||||
\(203\) | 5.07804 | 0.356409 | ||||||||
\(204\) | 1.40990 | 0.0987127 | ||||||||
\(205\) | 1.73811 | 0.121395 | ||||||||
\(206\) | 6.68459 | 0.465737 | ||||||||
\(207\) | − | 4.20591i | − | 0.292331i | ||||||
\(208\) | −10.6408 | −0.737809 | ||||||||
\(209\) | −41.6772 | −2.88287 | ||||||||
\(210\) | 2.92517i | 0.201856i | ||||||||
\(211\) | − | 9.40401i | − | 0.647399i | −0.946160 | − | 0.323699i | \(-0.895073\pi\) | ||
0.946160 | − | 0.323699i | \(-0.104927\pi\) | |||||||
\(212\) | − | 0.732722i | − | 0.0503236i | ||||||
\(213\) | 2.98061 | 0.204228 | ||||||||
\(214\) | −14.5625 | −0.995474 | ||||||||
\(215\) | −0.0952865 | −0.00649849 | ||||||||
\(216\) | 2.05454i | 0.139793i | ||||||||
\(217\) | 2.71583i | 0.184363i | ||||||||
\(218\) | 17.1159i | 1.15924i | ||||||||
\(219\) | − | 12.3024i | − | 0.831319i | ||||||
\(220\) | − | 7.34681i | − | 0.495322i | ||||||
\(221\) | −3.97009 | −0.267057 | ||||||||
\(222\) | − | 2.14114i | − | 0.143704i | ||||||
\(223\) | − | 20.5618i | − | 1.37692i | −0.725276 | − | 0.688458i | \(-0.758288\pi\) | ||
0.725276 | − | 0.688458i | \(-0.241712\pi\) | |||||||
\(224\) | −3.89851 | −0.260480 | ||||||||
\(225\) | 1.55695 | 0.103796 | ||||||||
\(226\) | 10.0652i | 0.669528i | ||||||||
\(227\) | 14.3241i | 0.950724i | 0.879790 | + | 0.475362i | \(0.157683\pi\) | ||||
−0.879790 | + | 0.475362i | \(0.842317\pi\) | |||||||
\(228\) | 6.14845 | 0.407191 | ||||||||
\(229\) | 7.72860i | 0.510720i | 0.966846 | + | 0.255360i | \(0.0821940\pi\) | ||||
−0.966846 | + | 0.255360i | \(0.917806\pi\) | |||||||
\(230\) | 12.9754i | 0.855574i | ||||||||
\(231\) | − | 4.91213i | − | 0.323194i | ||||||
\(232\) | −11.0032 | −0.722398 | ||||||||
\(233\) | 20.1052 | 1.31713 | 0.658566 | − | 0.752523i | \(-0.271163\pi\) | ||||
0.658566 | + | 0.752523i | \(0.271163\pi\) | |||||||
\(234\) | 3.57808i | 0.233906i | ||||||||
\(235\) | 2.26603i | 0.147820i | ||||||||
\(236\) | 2.45054i | 0.159516i | ||||||||
\(237\) | − | 3.34723i | − | 0.217426i | ||||||
\(238\) | −2.90818 | −0.188509 | ||||||||
\(239\) | −0.953647 | −0.0616863 | −0.0308432 | − | 0.999524i | \(-0.509819\pi\) | ||||
−0.0308432 | + | 0.999524i | \(0.509819\pi\) | |||||||
\(240\) | − | 9.17462i | − | 0.592219i | ||||||
\(241\) | 19.8937i | 1.28146i | 0.767764 | + | 0.640732i | \(0.221369\pi\) | ||||
−0.767764 | + | 0.640732i | \(0.778631\pi\) | |||||||
\(242\) | 26.3334i | 1.69278i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 10.3371i | 0.661764i | ||||||||
\(245\) | 11.3206i | 0.723248i | ||||||||
\(246\) | 1.55739 | 0.0992953 | ||||||||
\(247\) | −17.3132 | −1.10161 | ||||||||
\(248\) | − | 5.88474i | − | 0.373681i | ||||||
\(249\) | − | 15.2183i | − | 0.964419i | ||||||
\(250\) | −20.2285 | −1.27936 | ||||||||
\(251\) | 13.8606i | 0.874872i | 0.899250 | + | 0.437436i | \(0.144113\pi\) | ||||
−0.899250 | + | 0.437436i | \(0.855887\pi\) | |||||||
\(252\) | 0.724663i | 0.0456495i | ||||||||
\(253\) | − | 21.7891i | − | 1.36987i | ||||||
\(254\) | − | 5.93128i | − | 0.372161i | ||||||
\(255\) | − | 3.42305i | − | 0.214360i | ||||||
\(256\) | 16.0052 | 1.00032 | ||||||||
\(257\) | −18.2210 | −1.13660 | −0.568299 | − | 0.822822i | \(-0.692398\pi\) | ||||
−0.568299 | + | 0.822822i | \(0.692398\pi\) | |||||||
\(258\) | −0.0853788 | −0.00531545 | ||||||||
\(259\) | 1.22108i | 0.0758742i | ||||||||
\(260\) | − | 3.05195i | − | 0.189274i | ||||||
\(261\) | 5.35559i | 0.331502i | ||||||||
\(262\) | 2.96308 | 0.183059 | ||||||||
\(263\) | −20.0832 | −1.23838 | −0.619192 | − | 0.785240i | \(-0.712540\pi\) | ||||
−0.619192 | + | 0.785240i | \(0.712540\pi\) | |||||||
\(264\) | 10.6437i | 0.655076i | ||||||||
\(265\) | −1.77895 | −0.109280 | ||||||||
\(266\) | −12.6823 | −0.777603 | ||||||||
\(267\) | 15.1938 | 0.929848 | ||||||||
\(268\) | 2.79116 | 0.170497 | ||||||||
\(269\) | 12.2622i | 0.747637i | 0.927502 | + | 0.373818i | \(0.121952\pi\) | ||||
−0.927502 | + | 0.373818i | \(0.878048\pi\) | |||||||
\(270\) | −3.08505 | −0.187750 | ||||||||
\(271\) | 7.77995i | 0.472598i | 0.971680 | + | 0.236299i | \(0.0759345\pi\) | ||||
−0.971680 | + | 0.236299i | \(0.924065\pi\) | |||||||
\(272\) | 9.12132 | 0.553061 | ||||||||
\(273\) | − | 2.04056i | − | 0.123500i | ||||||
\(274\) | 0.311455 | 0.0188157 | ||||||||
\(275\) | 8.06592 | 0.486393 | ||||||||
\(276\) | 3.21445i | 0.193487i | ||||||||
\(277\) | −20.0599 | −1.20529 | −0.602643 | − | 0.798011i | \(-0.705886\pi\) | ||||
−0.602643 | + | 0.798011i | \(0.705886\pi\) | |||||||
\(278\) | 28.0527 | 1.68249 | ||||||||
\(279\) | −2.86427 | −0.171479 | ||||||||
\(280\) | 3.61472i | 0.216021i | ||||||||
\(281\) | 19.2987 | 1.15126 | 0.575631 | − | 0.817709i | \(-0.304756\pi\) | ||||
0.575631 | + | 0.817709i | \(0.304756\pi\) | |||||||
\(282\) | 2.03041i | 0.120909i | ||||||||
\(283\) | 24.7780 | 1.47290 | 0.736449 | − | 0.676493i | \(-0.236501\pi\) | ||||
0.736449 | + | 0.676493i | \(0.236501\pi\) | |||||||
\(284\) | −2.27799 | −0.135174 | ||||||||
\(285\) | − | 14.9276i | − | 0.884236i | ||||||
\(286\) | 18.5366i | 1.09609i | ||||||||
\(287\) | −0.888169 | −0.0524269 | ||||||||
\(288\) | − | 4.11159i | − | 0.242278i | ||||||
\(289\) | −13.5968 | −0.799814 | ||||||||
\(290\) | − | 16.5222i | − | 0.970220i | ||||||
\(291\) | 18.3611i | 1.07635i | ||||||||
\(292\) | 9.40236i | 0.550231i | ||||||||
\(293\) | 22.7709i | 1.33029i | 0.746714 | + | 0.665145i | \(0.231630\pi\) | ||||
−0.746714 | + | 0.665145i | \(0.768370\pi\) | |||||||
\(294\) | 10.1435i | 0.591582i | ||||||||
\(295\) | 5.94958 | 0.346398 | ||||||||
\(296\) | − | 2.64587i | − | 0.153788i | ||||||
\(297\) | 5.18060 | 0.300609 | ||||||||
\(298\) | −22.0682 | −1.27838 | ||||||||
\(299\) | − | 9.05146i | − | 0.523460i | ||||||
\(300\) | −1.18993 | −0.0687006 | ||||||||
\(301\) | 0.0486910 | 0.00280650 | ||||||||
\(302\) | −35.9185 | −2.06688 | ||||||||
\(303\) | −4.58292 | −0.263282 | ||||||||
\(304\) | 39.7773 | 2.28138 | ||||||||
\(305\) | 25.0971 | 1.43705 | ||||||||
\(306\) | − | 3.06712i | − | 0.175336i | ||||||
\(307\) | − | 15.0199i | − | 0.857230i | −0.903487 | − | 0.428615i | \(-0.859002\pi\) | ||
0.903487 | − | 0.428615i | \(-0.140998\pi\) | |||||||
\(308\) | 3.75419i | 0.213915i | ||||||||
\(309\) | − | 4.02054i | − | 0.228721i | ||||||
\(310\) | 8.83640 | 0.501874 | ||||||||
\(311\) | 11.6671 | 0.661582 | 0.330791 | − | 0.943704i | \(-0.392684\pi\) | ||||
0.330791 | + | 0.943704i | \(0.392684\pi\) | |||||||
\(312\) | 4.42153i | 0.250320i | ||||||||
\(313\) | −27.4233 | −1.55005 | −0.775027 | − | 0.631928i | \(-0.782264\pi\) | ||||
−0.775027 | + | 0.631928i | \(0.782264\pi\) | |||||||
\(314\) | 17.8523 | − | 10.7372i | 1.00746 | − | 0.605934i | ||||
\(315\) | 1.75939 | 0.0991302 | ||||||||
\(316\) | 2.55819i | 0.143909i | ||||||||
\(317\) | −28.3482 | −1.59220 | −0.796098 | − | 0.605168i | \(-0.793106\pi\) | ||||
−0.796098 | + | 0.605168i | \(0.793106\pi\) | |||||||
\(318\) | −1.59398 | −0.0893859 | ||||||||
\(319\) | 27.7452i | 1.55343i | ||||||||
\(320\) | − | 5.66480i | − | 0.316672i | ||||||
\(321\) | 8.75884i | 0.488871i | ||||||||
\(322\) | − | 6.63039i | − | 0.369497i | ||||||
\(323\) | 14.8409 | 0.825769 | ||||||||
\(324\) | −0.764270 | −0.0424595 | ||||||||
\(325\) | 3.35068 | 0.185862 | ||||||||
\(326\) | 27.1199 | 1.50203 | ||||||||
\(327\) | 10.2946 | 0.569293 | ||||||||
\(328\) | 1.92451 | 0.106263 | ||||||||
\(329\) | − | 1.15793i | − | 0.0638390i | ||||||
\(330\) | −15.9824 | −0.879802 | ||||||||
\(331\) | −2.43583 | −0.133886 | −0.0669428 | − | 0.997757i | \(-0.521324\pi\) | ||||
−0.0669428 | + | 0.997757i | \(0.521324\pi\) | |||||||
\(332\) | 11.6309i | 0.638327i | ||||||||
\(333\) | −1.28782 | −0.0705720 | ||||||||
\(334\) | − | 21.2912i | − | 1.16500i | ||||||
\(335\) | − | 6.77657i | − | 0.370243i | ||||||
\(336\) | 4.68820i | 0.255762i | ||||||||
\(337\) | − | 9.24995i | − | 0.503877i | −0.967743 | − | 0.251938i | \(-0.918932\pi\) | ||
0.967743 | − | 0.251938i | \(-0.0810681\pi\) | |||||||
\(338\) | − | 13.9136i | − | 0.756800i | ||||||
\(339\) | 6.05386 | 0.328801 | ||||||||
\(340\) | 2.61613i | 0.141880i | ||||||||
\(341\) | −14.8386 | −0.803556 | ||||||||
\(342\) | − | 13.3755i | − | 0.723263i | ||||||
\(343\) | − | 12.4220i | − | 0.670727i | ||||||
\(344\) | −0.105505 | −0.00568845 | ||||||||
\(345\) | 7.80425 | 0.420167 | ||||||||
\(346\) | − | 25.6170i | − | 1.37718i | ||||||
\(347\) | −19.7509 | −1.06028 | −0.530142 | − | 0.847909i | \(-0.677861\pi\) | ||||
−0.530142 | + | 0.847909i | \(0.677861\pi\) | |||||||
\(348\) | − | 4.09312i | − | 0.219414i | ||||||
\(349\) | −21.9046 | −1.17253 | −0.586263 | − | 0.810121i | \(-0.699402\pi\) | ||||
−0.586263 | + | 0.810121i | \(0.699402\pi\) | |||||||
\(350\) | 2.45445 | 0.131196 | ||||||||
\(351\) | 2.15208 | 0.114870 | ||||||||
\(352\) | − | 21.3005i | − | 1.13532i | ||||||
\(353\) | 4.50263 | 0.239651 | 0.119825 | − | 0.992795i | \(-0.461767\pi\) | ||||
0.119825 | + | 0.992795i | \(0.461767\pi\) | |||||||
\(354\) | 5.33095 | 0.283337 | ||||||||
\(355\) | 5.53066i | 0.293537i | ||||||||
\(356\) | −11.6122 | −0.615445 | ||||||||
\(357\) | 1.74916i | 0.0925756i | ||||||||
\(358\) | 6.53034 | 0.345139 | ||||||||
\(359\) | 13.0296i | 0.687675i | 0.939029 | + | 0.343837i | \(0.111727\pi\) | ||||
−0.939029 | + | 0.343837i | \(0.888273\pi\) | |||||||
\(360\) | −3.81229 | −0.200925 | ||||||||
\(361\) | 45.7199 | 2.40631 | ||||||||
\(362\) | 7.38286 | 0.388035 | ||||||||
\(363\) | 15.8386 | 0.831312 | ||||||||
\(364\) | 1.55954i | 0.0817419i | ||||||||
\(365\) | 22.8277 | 1.19485 | ||||||||
\(366\) | 22.4875 | 1.17544 | ||||||||
\(367\) | − | 7.88279i | − | 0.411478i | −0.978607 | − | 0.205739i | \(-0.934040\pi\) | ||
0.978607 | − | 0.205739i | \(-0.0659598\pi\) | |||||||
\(368\) | 20.7958i | 1.08406i | ||||||||
\(369\) | − | 0.936712i | − | 0.0487633i | ||||||
\(370\) | 3.97298 | 0.206545 | ||||||||
\(371\) | 0.909038 | 0.0471949 | ||||||||
\(372\) | 2.18907 | 0.113498 | ||||||||
\(373\) | − | 5.72028i | − | 0.296185i | −0.988974 | − | 0.148093i | \(-0.952687\pi\) | ||
0.988974 | − | 0.148093i | \(-0.0473134\pi\) | |||||||
\(374\) | − | 15.8895i | − | 0.821629i | ||||||
\(375\) | 12.1667i | 0.628287i | ||||||||
\(376\) | 2.50904i | 0.129394i | ||||||||
\(377\) | 11.5257i | 0.593602i | ||||||||
\(378\) | 1.57645 | 0.0810837 | ||||||||
\(379\) | − | 32.1508i | − | 1.65148i | −0.564053 | − | 0.825739i | \(-0.690759\pi\) | ||
0.564053 | − | 0.825739i | \(-0.309241\pi\) | |||||||
\(380\) | 11.4087i | 0.585256i | ||||||||
\(381\) | −3.56745 | −0.182766 | ||||||||
\(382\) | −31.1987 | −1.59626 | ||||||||
\(383\) | 31.7510i | 1.62240i | 0.584770 | + | 0.811199i | \(0.301185\pi\) | ||||
−0.584770 | + | 0.811199i | \(0.698815\pi\) | |||||||
\(384\) | − | 13.2990i | − | 0.678659i | ||||||
\(385\) | 9.11468 | 0.464527 | ||||||||
\(386\) | − | 15.3234i | − | 0.779938i | ||||||
\(387\) | 0.0513523i | 0.00261038i | ||||||||
\(388\) | − | 14.0329i | − | 0.712411i | ||||||
\(389\) | 14.8408 | 0.752460 | 0.376230 | − | 0.926526i | \(-0.377220\pi\) | ||||
0.376230 | + | 0.926526i | \(0.377220\pi\) | |||||||
\(390\) | −6.63928 | −0.336193 | ||||||||
\(391\) | 7.75891i | 0.392385i | ||||||||
\(392\) | 12.5346i | 0.633095i | ||||||||
\(393\) | − | 1.78218i | − | 0.0898993i | ||||||
\(394\) | − | 25.3902i | − | 1.27914i | ||||||
\(395\) | 6.21094 | 0.312506 | ||||||||
\(396\) | −3.95938 | −0.198966 | ||||||||
\(397\) | 14.0638i | 0.705840i | 0.935653 | + | 0.352920i | \(0.114811\pi\) | ||||
−0.935653 | + | 0.352920i | \(0.885189\pi\) | |||||||
\(398\) | 18.5989i | 0.932277i | ||||||||
\(399\) | 7.62796i | 0.381876i | ||||||||
\(400\) | −7.69822 | −0.384911 | ||||||||
\(401\) | − | 26.3420i | − | 1.31545i | −0.753256 | − | 0.657727i | \(-0.771518\pi\) | ||
0.753256 | − | 0.657727i | \(-0.228482\pi\) | |||||||
\(402\) | − | 6.07195i | − | 0.302841i | ||||||
\(403\) | −6.16414 | −0.307058 | ||||||||
\(404\) | 3.50259 | 0.174260 | ||||||||
\(405\) | 1.85555i | 0.0922028i | ||||||||
\(406\) | 8.44280i | 0.419009i | ||||||||
\(407\) | −6.67167 | −0.330702 | ||||||||
\(408\) | − | 3.79014i | − | 0.187640i | ||||||
\(409\) | 31.2012i | 1.54280i | 0.636352 | + | 0.771399i | \(0.280443\pi\) | ||||
−0.636352 | + | 0.771399i | \(0.719557\pi\) | |||||||
\(410\) | 2.88980i | 0.142717i | ||||||||
\(411\) | − | 0.187329i | − | 0.00924026i | ||||||
\(412\) | 3.07278i | 0.151385i | ||||||||
\(413\) | −3.04021 | −0.149599 | ||||||||
\(414\) | 6.99278 | 0.343676 | ||||||||
\(415\) | 28.2382 | 1.38616 | ||||||||
\(416\) | − | 8.84848i | − | 0.433832i | ||||||
\(417\) | − | 16.8727i | − | 0.826258i | ||||||
\(418\) | − | 69.2930i | − | 3.38923i | ||||||
\(419\) | 9.65000 | 0.471434 | 0.235717 | − | 0.971822i | \(-0.424256\pi\) | ||||
0.235717 | + | 0.971822i | \(0.424256\pi\) | |||||||
\(420\) | −1.34465 | −0.0656120 | ||||||||
\(421\) | 20.1709i | 0.983070i | 0.870858 | + | 0.491535i | \(0.163564\pi\) | ||||
−0.870858 | + | 0.491535i | \(0.836436\pi\) | |||||||
\(422\) | 15.6352 | 0.761109 | ||||||||
\(423\) | 1.22122 | 0.0593778 | ||||||||
\(424\) | −1.96973 | −0.0956585 | ||||||||
\(425\) | −2.87220 | −0.139322 | ||||||||
\(426\) | 4.95559i | 0.240099i | ||||||||
\(427\) | −12.8245 | −0.620622 | ||||||||
\(428\) | − | 6.69412i | − | 0.323573i | ||||||
\(429\) | 11.1491 | 0.538283 | ||||||||
\(430\) | − | 0.158424i | − | 0.00763990i | ||||||
\(431\) | 15.5239 | 0.747762 | 0.373881 | − | 0.927477i | \(-0.378027\pi\) | ||||
0.373881 | + | 0.927477i | \(0.378027\pi\) | |||||||
\(432\) | −4.94443 | −0.237889 | ||||||||
\(433\) | − | 7.22083i | − | 0.347011i | −0.984833 | − | 0.173506i | \(-0.944491\pi\) | ||
0.984833 | − | 0.173506i | \(-0.0555095\pi\) | |||||||
\(434\) | −4.51537 | −0.216745 | ||||||||
\(435\) | −9.93754 | −0.476469 | ||||||||
\(436\) | −7.86786 | −0.376802 | ||||||||
\(437\) | 33.8359i | 1.61859i | ||||||||
\(438\) | 20.4541 | 0.977334 | ||||||||
\(439\) | − | 25.2189i | − | 1.20363i | −0.798635 | − | 0.601816i | \(-0.794444\pi\) | ||
0.798635 | − | 0.601816i | \(-0.205556\pi\) | |||||||
\(440\) | −19.7499 | −0.941541 | ||||||||
\(441\) | 6.10096 | 0.290522 | ||||||||
\(442\) | − | 6.60071i | − | 0.313964i | ||||||
\(443\) | − | 15.8470i | − | 0.752914i | −0.926434 | − | 0.376457i | \(-0.877142\pi\) | ||
0.926434 | − | 0.376457i | \(-0.122858\pi\) | |||||||
\(444\) | 0.984241 | 0.0467100 | ||||||||
\(445\) | 28.1929i | 1.33647i | ||||||||
\(446\) | 34.1862 | 1.61876 | ||||||||
\(447\) | 13.2732i | 0.627802i | ||||||||
\(448\) | 2.89469i | 0.136761i | ||||||||
\(449\) | 32.4060i | 1.52933i | 0.644426 | + | 0.764666i | \(0.277096\pi\) | ||||
−0.644426 | + | 0.764666i | \(0.722904\pi\) | |||||||
\(450\) | 2.58860i | 0.122028i | ||||||||
\(451\) | − | 4.85273i | − | 0.228506i | ||||||
\(452\) | −4.62679 | −0.217626 | ||||||||
\(453\) | 21.6037i | 1.01503i | ||||||||
\(454\) | −23.8154 | −1.11771 | ||||||||
\(455\) | 3.78635 | 0.177507 | ||||||||
\(456\) | − | 16.5285i | − | 0.774016i | ||||||
\(457\) | 25.8272 | 1.20814 | 0.604072 | − | 0.796930i | \(-0.293544\pi\) | ||||
0.604072 | + | 0.796930i | \(0.293544\pi\) | |||||||
\(458\) | −12.8496 | −0.600424 | ||||||||
\(459\) | −1.84477 | −0.0861063 | ||||||||
\(460\) | −5.96456 | −0.278099 | ||||||||
\(461\) | −42.1335 | −1.96235 | −0.981176 | − | 0.193116i | \(-0.938141\pi\) | ||||
−0.981176 | + | 0.193116i | \(0.938141\pi\) | |||||||
\(462\) | 8.16695 | 0.379961 | ||||||||
\(463\) | − | 0.0617504i | − | 0.00286978i | −0.999999 | − | 0.00143489i | \(-0.999543\pi\) | ||
0.999999 | − | 0.00143489i | \(-0.000456740\pi\) | |||||||
\(464\) | − | 26.4803i | − | 1.22932i | ||||||
\(465\) | − | 5.31478i | − | 0.246467i | ||||||
\(466\) | 33.4270i | 1.54848i | ||||||||
\(467\) | −8.97496 | −0.415312 | −0.207656 | − | 0.978202i | \(-0.566583\pi\) | ||||
−0.207656 | + | 0.978202i | \(0.566583\pi\) | |||||||
\(468\) | −1.64477 | −0.0760297 | ||||||||
\(469\) | 3.46280i | 0.159897i | ||||||||
\(470\) | −3.76753 | −0.173783 | ||||||||
\(471\) | −6.45803 | − | 10.7375i | −0.297570 | − | 0.494758i | ||||
\(472\) | 6.58762 | 0.303220 | ||||||||
\(473\) | 0.266036i | 0.0122323i | ||||||||
\(474\) | 5.56513 | 0.255615 | ||||||||
\(475\) | −12.5254 | −0.574706 | ||||||||
\(476\) | − | 1.33683i | − | 0.0612737i | ||||||
\(477\) | 0.958722i | 0.0438968i | ||||||||
\(478\) | − | 1.58554i | − | 0.0725211i | ||||||
\(479\) | − | 26.8788i | − | 1.22812i | −0.789258 | − | 0.614062i | \(-0.789534\pi\) | ||
0.789258 | − | 0.614062i | \(-0.210466\pi\) | |||||||
\(480\) | 7.62924 | 0.348226 | ||||||||
\(481\) | −2.77149 | −0.126369 | ||||||||
\(482\) | −33.0754 | −1.50654 | ||||||||
\(483\) | −3.98794 | −0.181458 | ||||||||
\(484\) | −12.1050 | −0.550226 | ||||||||
\(485\) | −34.0699 | −1.54704 | ||||||||
\(486\) | 1.66261i | 0.0754175i | ||||||||
\(487\) | 29.7779 | 1.34936 | 0.674682 | − | 0.738109i | \(-0.264281\pi\) | ||||
0.674682 | + | 0.738109i | \(0.264281\pi\) | |||||||
\(488\) | 27.7885 | 1.25793 | ||||||||
\(489\) | − | 16.3116i | − | 0.737637i | ||||||
\(490\) | −18.8218 | −0.850281 | ||||||||
\(491\) | − | 21.8336i | − | 0.985334i | −0.870218 | − | 0.492667i | \(-0.836022\pi\) | ||
0.870218 | − | 0.492667i | \(-0.163978\pi\) | |||||||
\(492\) | 0.715901i | 0.0322753i | ||||||||
\(493\) | − | 9.87980i | − | 0.444964i | ||||||
\(494\) | − | 28.7851i | − | 1.29510i | ||||||
\(495\) | 9.61284i | 0.432065i | ||||||||
\(496\) | 14.1622 | 0.635900 | ||||||||
\(497\) | − | 2.82614i | − | 0.126770i | ||||||
\(498\) | 25.3020 | 1.13381 | ||||||||
\(499\) | 15.4479i | 0.691544i | 0.938319 | + | 0.345772i | \(0.112383\pi\) | ||||
−0.938319 | + | 0.345772i | \(0.887617\pi\) | |||||||
\(500\) | − | 9.29866i | − | 0.415849i | ||||||
\(501\) | −12.8059 | −0.572126 | ||||||||
\(502\) | −23.0447 | −1.02854 | ||||||||
\(503\) | 20.6611i | 0.921235i | 0.887599 | + | 0.460617i | \(0.152372\pi\) | ||||
−0.887599 | + | 0.460617i | \(0.847628\pi\) | |||||||
\(504\) | 1.94806 | 0.0867737 | ||||||||
\(505\) | − | 8.50382i | − | 0.378415i | ||||||
\(506\) | 36.2268 | 1.61048 | ||||||||
\(507\) | −8.36853 | −0.371660 | ||||||||
\(508\) | 2.72650 | 0.120969 | ||||||||
\(509\) | 10.8204i | 0.479604i | 0.970822 | + | 0.239802i | \(0.0770826\pi\) | ||||
−0.970822 | + | 0.239802i | \(0.922917\pi\) | |||||||
\(510\) | 5.69119 | 0.252010 | ||||||||
\(511\) | −11.6649 | −0.516023 | ||||||||
\(512\) | 0.0124320i | 0.000549420i | ||||||||
\(513\) | −8.04487 | −0.355190 | ||||||||
\(514\) | − | 30.2945i | − | 1.33623i | ||||||
\(515\) | 7.46030 | 0.328740 | ||||||||
\(516\) | − | 0.0392470i | − | 0.00172775i | ||||||
\(517\) | 6.32666 | 0.278246 | ||||||||
\(518\) | −2.03018 | −0.0892009 | ||||||||
\(519\) | −15.4077 | −0.676324 | ||||||||
\(520\) | −8.20436 | −0.359785 | ||||||||
\(521\) | − | 41.7159i | − | 1.82761i | −0.406157 | − | 0.913803i | \(-0.633132\pi\) | ||
0.406157 | − | 0.913803i | \(-0.366868\pi\) | |||||||
\(522\) | −8.90425 | −0.389728 | ||||||||
\(523\) | −19.7750 | −0.864701 | −0.432351 | − | 0.901706i | \(-0.642316\pi\) | ||||
−0.432351 | + | 0.901706i | \(0.642316\pi\) | |||||||
\(524\) | 1.36207i | 0.0595023i | ||||||||
\(525\) | − | 1.47626i | − | 0.0644293i | ||||||
\(526\) | − | 33.3905i | − | 1.45590i | ||||||
\(527\) | 5.28390 | 0.230170 | ||||||||
\(528\) | −25.6151 | −1.11476 | ||||||||
\(529\) | 5.31036 | 0.230885 | ||||||||
\(530\) | − | 2.95770i | − | 0.128474i | ||||||
\(531\) | − | 3.20638i | − | 0.139145i | ||||||
\(532\) | − | 5.82982i | − | 0.252755i | ||||||
\(533\) | − | 2.01588i | − | 0.0873176i | ||||||
\(534\) | 25.2614i | 1.09317i | ||||||||
\(535\) | −16.2524 | −0.702654 | ||||||||
\(536\) | − | 7.50329i | − | 0.324093i | ||||||
\(537\) | − | 3.92776i | − | 0.169496i | ||||||
\(538\) | −20.3872 | −0.878954 | ||||||||
\(539\) | 31.6066 | 1.36139 | ||||||||
\(540\) | − | 1.41814i | − | 0.0610270i | ||||||
\(541\) | − | 12.3635i | − | 0.531548i | −0.964035 | − | 0.265774i | \(-0.914372\pi\) | ||
0.964035 | − | 0.265774i | \(-0.0856276\pi\) | |||||||
\(542\) | −12.9350 | −0.555606 | ||||||||
\(543\) | − | 4.44053i | − | 0.190561i | ||||||
\(544\) | 7.58491i | 0.325200i | ||||||||
\(545\) | 19.1021i | 0.818245i | ||||||||
\(546\) | 3.39265 | 0.145192 | ||||||||
\(547\) | 22.8415 | 0.976630 | 0.488315 | − | 0.872667i | \(-0.337612\pi\) | ||||
0.488315 | + | 0.872667i | \(0.337612\pi\) | |||||||
\(548\) | 0.143170i | 0.00611592i | ||||||||
\(549\) | − | 13.5254i | − | 0.577252i | ||||||
\(550\) | 13.4105i | 0.571825i | ||||||||
\(551\) | − | 43.0850i | − | 1.83548i | ||||||
\(552\) | 8.64118 | 0.367793 | ||||||||
\(553\) | −3.17377 | −0.134962 | ||||||||
\(554\) | − | 33.3519i | − | 1.41698i | ||||||
\(555\) | − | 2.38961i | − | 0.101433i | ||||||
\(556\) | 12.8953i | 0.546882i | ||||||||
\(557\) | −17.9096 | −0.758853 | −0.379427 | − | 0.925222i | \(-0.623879\pi\) | ||||
−0.379427 | + | 0.925222i | \(0.623879\pi\) | |||||||
\(558\) | − | 4.76216i | − | 0.201598i | ||||||
\(559\) | 0.110514i | 0.00467426i | ||||||||
\(560\) | −8.69917 | −0.367607 | ||||||||
\(561\) | −9.55699 | −0.403496 | ||||||||
\(562\) | 32.0862i | 1.35347i | ||||||||
\(563\) | − | 36.0327i | − | 1.51860i | −0.650741 | − | 0.759299i | \(-0.725542\pi\) | ||
0.650741 | − | 0.759299i | \(-0.274458\pi\) | |||||||
\(564\) | −0.933343 | −0.0393008 | ||||||||
\(565\) | 11.2332i | 0.472585i | ||||||||
\(566\) | 41.1961i | 1.73160i | ||||||||
\(567\) | − | 0.948177i | − | 0.0398197i | ||||||
\(568\) | 6.12377i | 0.256948i | ||||||||
\(569\) | 37.7979i | 1.58457i | 0.610151 | + | 0.792285i | \(0.291109\pi\) | ||||
−0.610151 | + | 0.792285i | \(0.708891\pi\) | |||||||
\(570\) | 24.8188 | 1.03955 | ||||||||
\(571\) | 11.1738 | 0.467608 | 0.233804 | − | 0.972284i | \(-0.424883\pi\) | ||||
0.233804 | + | 0.972284i | \(0.424883\pi\) | |||||||
\(572\) | −8.52091 | −0.356277 | ||||||||
\(573\) | 18.7649i | 0.783915i | ||||||||
\(574\) | − | 1.47668i | − | 0.0616353i | ||||||
\(575\) | − | 6.54837i | − | 0.273086i | ||||||
\(576\) | −3.05290 | −0.127204 | ||||||||
\(577\) | 11.1762 | 0.465273 | 0.232637 | − | 0.972564i | \(-0.425265\pi\) | ||||
0.232637 | + | 0.972564i | \(0.425265\pi\) | |||||||
\(578\) | − | 22.6062i | − | 0.940295i | ||||||
\(579\) | −9.21645 | −0.383023 | ||||||||
\(580\) | 7.59497 | 0.315364 | ||||||||
\(581\) | −14.4296 | −0.598641 | ||||||||
\(582\) | −30.5274 | −1.26540 | ||||||||
\(583\) | 4.96675i | 0.205702i | ||||||||
\(584\) | 25.2757 | 1.04592 | ||||||||
\(585\) | 3.99329i | 0.165102i | ||||||||
\(586\) | −37.8591 | −1.56395 | ||||||||
\(587\) | 21.6444i | 0.893362i | 0.894693 | + | 0.446681i | \(0.147394\pi\) | ||||
−0.894693 | + | 0.446681i | \(0.852606\pi\) | |||||||
\(588\) | −4.66278 | −0.192290 | ||||||||
\(589\) | 23.0426 | 0.949455 | ||||||||
\(590\) | 9.89183i | 0.407240i | ||||||||
\(591\) | −15.2713 | −0.628176 | ||||||||
\(592\) | 6.36753 | 0.261704 | ||||||||
\(593\) | 27.8072 | 1.14190 | 0.570952 | − | 0.820984i | \(-0.306574\pi\) | ||||
0.570952 | + | 0.820984i | \(0.306574\pi\) | |||||||
\(594\) | 8.61331i | 0.353409i | ||||||||
\(595\) | −3.24566 | −0.133059 | ||||||||
\(596\) | − | 10.1443i | − | 0.415528i | ||||||
\(597\) | 11.1866 | 0.457835 | ||||||||
\(598\) | 15.0490 | 0.615401 | ||||||||
\(599\) | 5.41734i | 0.221346i | 0.993857 | + | 0.110673i | \(0.0353007\pi\) | ||||
−0.993857 | + | 0.110673i | \(0.964699\pi\) | |||||||
\(600\) | 3.19880i | 0.130591i | ||||||||
\(601\) | −2.43791 | −0.0994443 | −0.0497222 | − | 0.998763i | \(-0.515834\pi\) | ||||
−0.0497222 | + | 0.998763i | \(0.515834\pi\) | |||||||
\(602\) | 0.0809542i | 0.00329945i | ||||||||
\(603\) | −3.65206 | −0.148723 | ||||||||
\(604\) | − | 16.5111i | − | 0.671826i | ||||||
\(605\) | 29.3893i | 1.19484i | ||||||||
\(606\) | − | 7.61961i | − | 0.309525i | ||||||
\(607\) | 4.04993i | 0.164382i | 0.996617 | + | 0.0821908i | \(0.0261917\pi\) | ||||
−0.996617 | + | 0.0821908i | \(0.973808\pi\) | |||||||
\(608\) | 33.0772i | 1.34146i | ||||||||
\(609\) | 5.07804 | 0.205773 | ||||||||
\(610\) | 41.7266i | 1.68946i | ||||||||
\(611\) | 2.62817 | 0.106324 | ||||||||
\(612\) | 1.40990 | 0.0569918 | ||||||||
\(613\) | 41.9205i | 1.69315i | 0.532268 | + | 0.846576i | \(0.321340\pi\) | ||||
−0.532268 | + | 0.846576i | \(0.678660\pi\) | |||||||
\(614\) | 24.9722 | 1.00780 | ||||||||
\(615\) | 1.73811 | 0.0700875 | ||||||||
\(616\) | 10.0921 | 0.406624 | ||||||||
\(617\) | −9.88482 | −0.397948 | −0.198974 | − | 0.980005i | \(-0.563761\pi\) | ||||
−0.198974 | + | 0.980005i | \(0.563761\pi\) | |||||||
\(618\) | 6.68459 | 0.268894 | ||||||||
\(619\) | 30.2104 | 1.21426 | 0.607129 | − | 0.794603i | \(-0.292321\pi\) | ||||
0.607129 | + | 0.794603i | \(0.292321\pi\) | |||||||
\(620\) | 4.06193i | 0.163131i | ||||||||
\(621\) | − | 4.20591i | − | 0.168777i | ||||||
\(622\) | 19.3979i | 0.777784i | ||||||||
\(623\) | − | 14.4065i | − | 0.577182i | ||||||
\(624\) | −10.6408 | −0.425974 | ||||||||
\(625\) | −14.7912 | −0.591647 | ||||||||
\(626\) | − | 45.5942i | − | 1.82231i | ||||||
\(627\) | −41.6772 | −1.66443 | ||||||||
\(628\) | 4.93568 | + | 8.20635i | 0.196955 | + | 0.327469i | ||||
\(629\) | 2.37572 | 0.0947262 | ||||||||
\(630\) | 2.92517i | 0.116542i | ||||||||
\(631\) | 17.8454 | 0.710416 | 0.355208 | − | 0.934787i | \(-0.384410\pi\) | ||||
0.355208 | + | 0.934787i | \(0.384410\pi\) | |||||||
\(632\) | 6.87700 | 0.273552 | ||||||||
\(633\) | − | 9.40401i | − | 0.373776i | ||||||
\(634\) | − | 47.1320i | − | 1.87185i | ||||||
\(635\) | − | 6.61957i | − | 0.262690i | ||||||
\(636\) | − | 0.732722i | − | 0.0290543i | ||||||
\(637\) | 13.1298 | 0.520221 | ||||||||
\(638\) | −46.1294 | −1.82628 | ||||||||
\(639\) | 2.98061 | 0.117911 | ||||||||
\(640\) | 24.6768 | 0.975437 | ||||||||
\(641\) | 3.98574 | 0.157427 | 0.0787136 | − | 0.996897i | \(-0.474919\pi\) | ||||
0.0787136 | + | 0.996897i | \(0.474919\pi\) | |||||||
\(642\) | −14.5625 | −0.574737 | ||||||||
\(643\) | − | 0.471620i | − | 0.0185989i | −0.999957 | − | 0.00929944i | \(-0.997040\pi\) | ||
0.999957 | − | 0.00929944i | \(-0.00296015\pi\) | |||||||
\(644\) | 3.04787 | 0.120103 | ||||||||
\(645\) | −0.0952865 | −0.00375190 | ||||||||
\(646\) | 24.6746i | 0.970809i | ||||||||
\(647\) | 8.01922 | 0.315268 | 0.157634 | − | 0.987498i | \(-0.449613\pi\) | ||||
0.157634 | + | 0.987498i | \(0.449613\pi\) | |||||||
\(648\) | 2.05454i | 0.0807098i | ||||||||
\(649\) | − | 16.6110i | − | 0.652037i | ||||||
\(650\) | 5.57087i | 0.218508i | ||||||||
\(651\) | 2.71583i | 0.106442i | ||||||||
\(652\) | 12.4665i | 0.488225i | ||||||||
\(653\) | −44.8929 | −1.75680 | −0.878398 | − | 0.477930i | \(-0.841387\pi\) | ||||
−0.878398 | + | 0.477930i | \(0.841387\pi\) | |||||||
\(654\) | 17.1159i | 0.669285i | ||||||||
\(655\) | 3.30693 | 0.129212 | ||||||||
\(656\) | 4.63151i | 0.180830i | ||||||||
\(657\) | − | 12.3024i | − | 0.479962i | ||||||
\(658\) | 1.92519 | 0.0750518 | ||||||||
\(659\) | −25.8025 | −1.00512 | −0.502562 | − | 0.864541i | \(-0.667609\pi\) | ||||
−0.502562 | + | 0.864541i | \(0.667609\pi\) | |||||||
\(660\) | − | 7.34681i | − | 0.285974i | ||||||
\(661\) | 1.16190 | 0.0451925 | 0.0225962 | − | 0.999745i | \(-0.492807\pi\) | ||||
0.0225962 | + | 0.999745i | \(0.492807\pi\) | |||||||
\(662\) | − | 4.04984i | − | 0.157402i | ||||||
\(663\) | −3.97009 | −0.154186 | ||||||||
\(664\) | 31.2665 | 1.21338 | ||||||||
\(665\) | −14.1540 | −0.548870 | ||||||||
\(666\) | − | 2.14114i | − | 0.0829674i | ||||||
\(667\) | 22.5251 | 0.872175 | ||||||||
\(668\) | 9.78718 | 0.378677 | ||||||||
\(669\) | − | 20.5618i | − | 0.794963i | ||||||
\(670\) | 11.2668 | 0.435274 | ||||||||
\(671\) | − | 70.0699i | − | 2.70502i | ||||||
\(672\) | −3.89851 | −0.150388 | ||||||||
\(673\) | 46.0707i | 1.77589i | 0.459945 | + | 0.887947i | \(0.347869\pi\) | ||||
−0.459945 | + | 0.887947i | \(0.652131\pi\) | |||||||
\(674\) | 15.3791 | 0.592379 | ||||||||
\(675\) | 1.55695 | 0.0599269 | ||||||||
\(676\) | 6.39582 | 0.245993 | ||||||||
\(677\) | −22.3341 | −0.858370 | −0.429185 | − | 0.903217i | \(-0.641199\pi\) | ||||
−0.429185 | + | 0.903217i | \(0.641199\pi\) | |||||||
\(678\) | 10.0652i | 0.386552i | ||||||||
\(679\) | 17.4096 | 0.668120 | ||||||||
\(680\) | 7.03277 | 0.269695 | ||||||||
\(681\) | 14.3241i | 0.548901i | ||||||||
\(682\) | − | 24.6708i | − | 0.944695i | ||||||
\(683\) | 13.3210i | 0.509713i | 0.966979 | + | 0.254856i | \(0.0820282\pi\) | ||||
−0.966979 | + | 0.254856i | \(0.917972\pi\) | |||||||
\(684\) | 6.14845 | 0.235092 | ||||||||
\(685\) | 0.347598 | 0.0132810 | ||||||||
\(686\) | 20.6530 | 0.788535 | ||||||||
\(687\) | 7.72860i | 0.294864i | ||||||||
\(688\) | − | 0.253908i | − | 0.00968014i | ||||||
\(689\) | 2.06325i | 0.0786035i | ||||||||
\(690\) | 12.9754i | 0.493966i | ||||||||
\(691\) | 49.3055i | 1.87567i | 0.347081 | + | 0.937835i | \(0.387173\pi\) | ||||
−0.347081 | + | 0.937835i | \(0.612827\pi\) | |||||||
\(692\) | 11.7757 | 0.447644 | ||||||||
\(693\) | − | 4.91213i | − | 0.186596i | ||||||
\(694\) | − | 32.8380i | − | 1.24651i | ||||||
\(695\) | 31.3080 | 1.18758 | ||||||||
\(696\) | −11.0032 | −0.417077 | ||||||||
\(697\) | 1.72801i | 0.0654532i | ||||||||
\(698\) | − | 36.4188i | − | 1.37847i | ||||||
\(699\) | 20.1052 | 0.760447 | ||||||||
\(700\) | 1.12826i | 0.0426443i | ||||||||
\(701\) | 16.3168i | 0.616276i | 0.951342 | + | 0.308138i | \(0.0997058\pi\) | ||||
−0.951342 | + | 0.308138i | \(0.900294\pi\) | |||||||
\(702\) | 3.57808i | 0.135046i | ||||||||
\(703\) | 10.3603 | 0.390747 | ||||||||
\(704\) | −15.8159 | −0.596083 | ||||||||
\(705\) | 2.26603i | 0.0853438i | ||||||||
\(706\) | 7.48611i | 0.281743i | ||||||||
\(707\) | 4.34542i | 0.163426i | ||||||||
\(708\) | 2.45054i | 0.0920968i | ||||||||
\(709\) | 28.6314 | 1.07527 | 0.537637 | − | 0.843177i | \(-0.319317\pi\) | ||||
0.537637 | + | 0.843177i | \(0.319317\pi\) | |||||||
\(710\) | −9.19532 | −0.345094 | ||||||||
\(711\) | − | 3.34723i | − | 0.125531i | ||||||
\(712\) | 31.2163i | 1.16988i | ||||||||
\(713\) | 12.0468i | 0.451157i | ||||||||
\(714\) | −2.90818 | −0.108836 | ||||||||
\(715\) | 20.6876i | 0.773674i | ||||||||
\(716\) | 3.00187i | 0.112185i | ||||||||
\(717\) | −0.953647 | −0.0356146 | ||||||||
\(718\) | −21.6631 | −0.808460 | ||||||||
\(719\) | 3.46375i | 0.129176i | 0.997912 | + | 0.0645881i | \(0.0205733\pi\) | ||||
−0.997912 | + | 0.0645881i | \(0.979427\pi\) | |||||||
\(720\) | − | 9.17462i | − | 0.341918i | ||||||
\(721\) | −3.81218 | −0.141973 | ||||||||
\(722\) | 76.0143i | 2.82896i | ||||||||
\(723\) | 19.8937i | 0.739854i | ||||||||
\(724\) | 3.39376i | 0.126128i | ||||||||
\(725\) | 8.33837i | 0.309679i | ||||||||
\(726\) | 26.3334i | 0.977325i | ||||||||
\(727\) | −26.3139 | −0.975930 | −0.487965 | − | 0.872863i | \(-0.662261\pi\) | ||||
−0.487965 | + | 0.872863i | \(0.662261\pi\) | |||||||
\(728\) | 4.19240 | 0.155381 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 37.9535i | 1.40472i | ||||||||
\(731\) | − | 0.0947329i | − | 0.00350382i | ||||||
\(732\) | 10.3371i | 0.382070i | ||||||||
\(733\) | −21.9385 | −0.810317 | −0.405158 | − | 0.914246i | \(-0.632784\pi\) | ||||
−0.405158 | + | 0.914246i | \(0.632784\pi\) | |||||||
\(734\) | 13.1060 | 0.483751 | ||||||||
\(735\) | 11.3206i | 0.417567i | ||||||||
\(736\) | −17.2929 | −0.637426 | ||||||||
\(737\) | −18.9199 | −0.696922 | ||||||||
\(738\) | 1.55739 | 0.0573282 | ||||||||
\(739\) | −22.3359 | −0.821638 | −0.410819 | − | 0.911717i | \(-0.634757\pi\) | ||||
−0.410819 | + | 0.911717i | \(0.634757\pi\) | |||||||
\(740\) | 1.82630i | 0.0671363i | ||||||||
\(741\) | −17.3132 | −0.636017 | ||||||||
\(742\) | 1.51137i | 0.0554843i | ||||||||
\(743\) | −13.9806 | −0.512897 | −0.256449 | − | 0.966558i | \(-0.582552\pi\) | ||||
−0.256449 | + | 0.966558i | \(0.582552\pi\) | |||||||
\(744\) | − | 5.88474i | − | 0.215745i | ||||||
\(745\) | −24.6291 | −0.902340 | ||||||||
\(746\) | 9.51060 | 0.348208 | ||||||||
\(747\) | − | 15.2183i | − | 0.556807i | ||||||
\(748\) | 7.30412 | 0.267065 | ||||||||
\(749\) | 8.30493 | 0.303456 | ||||||||
\(750\) | −20.2285 | −0.738641 | ||||||||
\(751\) | 32.5497i | 1.18775i | 0.804556 | + | 0.593877i | \(0.202403\pi\) | ||||
−0.804556 | + | 0.593877i | \(0.797597\pi\) | |||||||
\(752\) | −6.03825 | −0.220192 | ||||||||
\(753\) | 13.8606i | 0.505107i | ||||||||
\(754\) | −19.1627 | −0.697864 | ||||||||
\(755\) | −40.0867 | −1.45890 | ||||||||
\(756\) | 0.724663i | 0.0263558i | ||||||||
\(757\) | 29.6680i | 1.07830i | 0.842209 | + | 0.539151i | \(0.181255\pi\) | ||||
−0.842209 | + | 0.539151i | \(0.818745\pi\) | |||||||
\(758\) | 53.4543 | 1.94155 | ||||||||
\(759\) | − | 21.7891i | − | 0.790895i | ||||||
\(760\) | 30.6693 | 1.11249 | ||||||||
\(761\) | 34.1236i | 1.23698i | 0.785793 | + | 0.618489i | \(0.212255\pi\) | ||||
−0.785793 | + | 0.618489i | \(0.787745\pi\) | |||||||
\(762\) | − | 5.93128i | − | 0.214867i | ||||||
\(763\) | − | 9.76111i | − | 0.353376i | ||||||
\(764\) | − | 14.3414i | − | 0.518855i | ||||||
\(765\) | − | 3.42305i | − | 0.123761i | ||||||
\(766\) | −52.7894 | −1.90736 | ||||||||
\(767\) | − | 6.90039i | − | 0.249159i | ||||||
\(768\) | 16.0052 | 0.577537 | ||||||||
\(769\) | −9.19160 | −0.331458 | −0.165729 | − | 0.986171i | \(-0.552998\pi\) | ||||
−0.165729 | + | 0.986171i | \(0.552998\pi\) | |||||||
\(770\) | 15.1542i | 0.546118i | ||||||||
\(771\) | −18.2210 | −0.656215 | ||||||||
\(772\) | 7.04386 | 0.253514 | ||||||||
\(773\) | 40.2062 | 1.44612 | 0.723059 | − | 0.690786i | \(-0.242735\pi\) | ||||
0.723059 | + | 0.690786i | \(0.242735\pi\) | |||||||
\(774\) | −0.0853788 | −0.00306888 | ||||||||
\(775\) | −4.45951 | −0.160190 | ||||||||
\(776\) | −37.7236 | −1.35420 | ||||||||
\(777\) | 1.22108i | 0.0438060i | ||||||||
\(778\) | 24.6745i | 0.884623i | ||||||||
\(779\) | 7.53572i | 0.269995i | ||||||||
\(780\) | − | 3.05195i | − | 0.109277i | ||||||
\(781\) | 15.4413 | 0.552535 | ||||||||
\(782\) | −12.9000 | −0.461304 | ||||||||
\(783\) | 5.35559i | 0.191393i | ||||||||
\(784\) | −30.1658 | −1.07735 | ||||||||
\(785\) | 19.9239 | − | 11.9832i | 0.711116 | − | 0.427698i | ||||
\(786\) | 2.96308 | 0.105689 | ||||||||
\(787\) | 24.2272i | 0.863607i | 0.901968 | + | 0.431804i | \(0.142123\pi\) | ||||
−0.901968 | + | 0.431804i | \(0.857877\pi\) | |||||||
\(788\) | 11.6714 | 0.415776 | ||||||||
\(789\) | −20.0832 | −0.714981 | ||||||||
\(790\) | 10.3264i | 0.367396i | ||||||||
\(791\) | − | 5.74014i | − | 0.204096i | ||||||
\(792\) | 10.6437i | 0.378208i | ||||||||
\(793\) | − | 29.1079i | − | 1.03365i | ||||||
\(794\) | −23.3826 | −0.829816 | ||||||||
\(795\) | −1.77895 | −0.0630929 | ||||||||
\(796\) | −8.54955 | −0.303031 | ||||||||
\(797\) | 39.7328 | 1.40741 | 0.703704 | − | 0.710494i | \(-0.251528\pi\) | ||||
0.703704 | + | 0.710494i | \(0.251528\pi\) | |||||||
\(798\) | −12.6823 | −0.448949 | ||||||||
\(799\) | −2.25287 | −0.0797007 | ||||||||
\(800\) | − | 6.40152i | − | 0.226328i | ||||||
\(801\) | 15.1938 | 0.536848 | ||||||||
\(802\) | 43.7964 | 1.54650 | ||||||||
\(803\) | − | 63.7338i | − | 2.24912i | ||||||
\(804\) | 2.79116 | 0.0984366 | ||||||||
\(805\) | − | 7.39981i | − | 0.260809i | ||||||
\(806\) | − | 10.2486i | − | 0.360990i | ||||||
\(807\) | 12.2622i | 0.431648i | ||||||||
\(808\) | − | 9.41578i | − | 0.331246i | ||||||
\(809\) | − | 38.8549i | − | 1.36607i | −0.730387 | − | 0.683033i | \(-0.760660\pi\) | ||
0.730387 | − | 0.683033i | \(-0.239340\pi\) | |||||||
\(810\) | −3.08505 | −0.108398 | ||||||||
\(811\) | 5.45752i | 0.191640i | 0.995399 | + | 0.0958198i | \(0.0305473\pi\) | ||||
−0.995399 | + | 0.0958198i | \(0.969453\pi\) | |||||||
\(812\) | −3.88100 | −0.136196 | ||||||||
\(813\) | 7.77995i | 0.272855i | ||||||||
\(814\) | − | 11.0924i | − | 0.388788i | ||||||
\(815\) | 30.2670 | 1.06021 | ||||||||
\(816\) | 9.12132 | 0.319310 | ||||||||
\(817\) | − | 0.413122i | − | 0.0144533i | ||||||
\(818\) | −51.8754 | −1.81378 | ||||||||
\(819\) | − | 2.04056i | − | 0.0713028i | ||||||
\(820\) | −1.32839 | −0.0463893 | ||||||||
\(821\) | 42.6751 | 1.48937 | 0.744686 | − | 0.667415i | \(-0.232599\pi\) | ||||
0.744686 | + | 0.667415i | \(0.232599\pi\) | |||||||
\(822\) | 0.311455 | 0.0108632 | ||||||||
\(823\) | 15.3052i | 0.533506i | 0.963765 | + | 0.266753i | \(0.0859507\pi\) | ||||
−0.963765 | + | 0.266753i | \(0.914049\pi\) | |||||||
\(824\) | 8.26034 | 0.287763 | ||||||||
\(825\) | 8.06592 | 0.280819 | ||||||||
\(826\) | − | 5.05469i | − | 0.175875i | ||||||
\(827\) | 16.4588 | 0.572329 | 0.286165 | − | 0.958180i | \(-0.407620\pi\) | ||||
0.286165 | + | 0.958180i | \(0.407620\pi\) | |||||||
\(828\) | 3.21445i | 0.111710i | ||||||||
\(829\) | 45.9078 | 1.59444 | 0.797221 | − | 0.603687i | \(-0.206302\pi\) | ||||
0.797221 | + | 0.603687i | \(0.206302\pi\) | |||||||
\(830\) | 46.9491i | 1.62963i | ||||||||
\(831\) | −20.0599 | −0.695872 | ||||||||
\(832\) | −6.57010 | −0.227777 | ||||||||
\(833\) | −11.2548 | −0.389957 | ||||||||
\(834\) | 28.0527 | 0.971384 | ||||||||
\(835\) | − | 23.7620i | − | 0.822317i | ||||||
\(836\) | 31.8527 | 1.10165 | ||||||||
\(837\) | −2.86427 | −0.0990035 | ||||||||
\(838\) | 16.0442i | 0.554237i | ||||||||
\(839\) | − | 51.1787i | − | 1.76689i | −0.468539 | − | 0.883443i | \(-0.655220\pi\) | ||
0.468539 | − | 0.883443i | \(-0.344780\pi\) | |||||||
\(840\) | 3.61472i | 0.124720i | ||||||||
\(841\) | 0.317695 | 0.0109550 | ||||||||
\(842\) | −33.5363 | −1.15574 | ||||||||
\(843\) | 19.2987 | 0.664682 | ||||||||
\(844\) | 7.18720i | 0.247394i | ||||||||
\(845\) | − | 15.5282i | − | 0.534186i | ||||||
\(846\) | 2.03041i | 0.0698071i | ||||||||
\(847\) | − | 15.0178i | − | 0.516018i | ||||||
\(848\) | − | 4.74033i | − | 0.162784i | ||||||
\(849\) | 24.7780 | 0.850379 | ||||||||
\(850\) | − | 4.77535i | − | 0.163793i | ||||||
\(851\) | 5.41644i | 0.185673i | ||||||||
\(852\) | −2.27799 | −0.0780427 | ||||||||
\(853\) | −47.5724 | −1.62885 | −0.814425 | − | 0.580269i | \(-0.802947\pi\) | ||||
−0.814425 | + | 0.580269i | \(0.802947\pi\) | |||||||
\(854\) | − | 21.3222i | − | 0.729629i | ||||||
\(855\) | − | 14.9276i | − | 0.510514i | ||||||
\(856\) | −17.9954 | −0.615069 | ||||||||
\(857\) | − | 27.0365i | − | 0.923548i | −0.886998 | − | 0.461774i | \(-0.847213\pi\) | ||
0.886998 | − | 0.461774i | \(-0.152787\pi\) | |||||||
\(858\) | 18.5366i | 0.632828i | ||||||||
\(859\) | 37.5771i | 1.28211i | 0.767493 | + | 0.641057i | \(0.221504\pi\) | ||||
−0.767493 | + | 0.641057i | \(0.778496\pi\) | |||||||
\(860\) | 0.0728246 | 0.00248330 | ||||||||
\(861\) | −0.888169 | −0.0302687 | ||||||||
\(862\) | 25.8103i | 0.879101i | ||||||||
\(863\) | − | 22.9205i | − | 0.780222i | −0.920768 | − | 0.390111i | \(-0.872437\pi\) | ||
0.920768 | − | 0.390111i | \(-0.127563\pi\) | |||||||
\(864\) | − | 4.11159i | − | 0.139879i | ||||||
\(865\) | − | 28.5898i | − | 0.972081i | ||||||
\(866\) | 12.0054 | 0.407961 | ||||||||
\(867\) | −13.5968 | −0.461773 | ||||||||
\(868\) | − | 2.07563i | − | 0.0704514i | ||||||
\(869\) | − | 17.3407i | − | 0.588241i | ||||||
\(870\) | − | 16.5222i | − | 0.560157i | ||||||
\(871\) | −7.85954 | −0.266310 | ||||||||
\(872\) | 21.1506i | 0.716251i | ||||||||
\(873\) | 18.3611i | 0.621430i | ||||||||
\(874\) | −56.2560 | −1.90289 | ||||||||
\(875\) | 11.5362 | 0.389995 | ||||||||
\(876\) | 9.40236i | 0.317676i | ||||||||
\(877\) | − | 12.4486i | − | 0.420358i | −0.977663 | − | 0.210179i | \(-0.932595\pi\) | ||
0.977663 | − | 0.210179i | \(-0.0674047\pi\) | |||||||
\(878\) | 41.9292 | 1.41504 | ||||||||
\(879\) | 22.7709i | 0.768044i | ||||||||
\(880\) | − | 47.5300i | − | 1.60224i | ||||||
\(881\) | − | 24.3022i | − | 0.818761i | −0.912364 | − | 0.409381i | \(-0.865745\pi\) | ||
0.912364 | − | 0.409381i | \(-0.134255\pi\) | |||||||
\(882\) | 10.1435i | 0.341550i | ||||||||
\(883\) | − | 17.2499i | − | 0.580507i | −0.956950 | − | 0.290253i | \(-0.906260\pi\) | ||
0.956950 | − | 0.290253i | \(-0.0937396\pi\) | |||||||
\(884\) | 3.03422 | 0.102052 | ||||||||
\(885\) | 5.94958 | 0.199993 | ||||||||
\(886\) | 26.3474 | 0.885157 | ||||||||
\(887\) | − | 18.8361i | − | 0.632455i | −0.948683 | − | 0.316227i | \(-0.897584\pi\) | ||
0.948683 | − | 0.316227i | \(-0.102416\pi\) | |||||||
\(888\) | − | 2.64587i | − | 0.0887895i | ||||||
\(889\) | 3.38257i | 0.113448i | ||||||||
\(890\) | −46.8738 | −1.57121 | ||||||||
\(891\) | 5.18060 | 0.173557 | ||||||||
\(892\) | 15.7147i | 0.526168i | ||||||||
\(893\) | −9.82457 | −0.328767 | ||||||||
\(894\) | −22.0682 | −0.738071 | ||||||||
\(895\) | 7.28815 | 0.243616 | ||||||||
\(896\) | −12.6098 | −0.421263 | ||||||||
\(897\) | − | 9.05146i | − | 0.302219i | ||||||
\(898\) | −53.8785 | −1.79795 | ||||||||
\(899\) | − | 15.3398i | − | 0.511612i | ||||||
\(900\) | −1.18993 | −0.0396643 | ||||||||
\(901\) | − | 1.76862i | − | 0.0589212i | ||||||
\(902\) | 8.06820 | 0.268642 | ||||||||
\(903\) | 0.0486910 | 0.00162034 | ||||||||
\(904\) | 12.4379i | 0.413678i | ||||||||
\(905\) | 8.23961 | 0.273894 | ||||||||
\(906\) | −35.9185 | −1.19331 | ||||||||
\(907\) | −47.5393 | −1.57852 | −0.789258 | − | 0.614061i | \(-0.789535\pi\) | ||||
−0.789258 | + | 0.614061i | \(0.789535\pi\) | |||||||
\(908\) | − | 10.9475i | − | 0.363305i | ||||||
\(909\) | −4.58292 | −0.152006 | ||||||||
\(910\) | 6.29522i | 0.208684i | ||||||||
\(911\) | −0.316553 | −0.0104879 | −0.00524393 | − | 0.999986i | \(-0.501669\pi\) | ||||
−0.00524393 | + | 0.999986i | \(0.501669\pi\) | |||||||
\(912\) | 39.7773 | 1.31716 | ||||||||
\(913\) | − | 78.8398i | − | 2.60922i | ||||||
\(914\) | 42.9405i | 1.42035i | ||||||||
\(915\) | 25.0971 | 0.829684 | ||||||||
\(916\) | − | 5.90673i | − | 0.195164i | ||||||
\(917\) | −1.68983 | −0.0558030 | ||||||||
\(918\) | − | 3.06712i | − | 0.101230i | ||||||
\(919\) | 23.0906i | 0.761689i | 0.924639 | + | 0.380844i | \(0.124367\pi\) | ||||
−0.924639 | + | 0.380844i | \(0.875633\pi\) | |||||||
\(920\) | 16.0341i | 0.528629i | ||||||||
\(921\) | − | 15.0199i | − | 0.494922i | ||||||
\(922\) | − | 70.0515i | − | 2.30702i | ||||||
\(923\) | 6.41452 | 0.211136 | ||||||||
\(924\) | 3.75419i | 0.123504i | ||||||||
\(925\) | −2.00506 | −0.0659261 | ||||||||
\(926\) | 0.102667 | 0.00337384 | ||||||||
\(927\) | − | 4.02054i | − | 0.132052i | ||||||
\(928\) | 22.0200 | 0.722840 | ||||||||
\(929\) | −20.3673 | −0.668230 | −0.334115 | − | 0.942532i | \(-0.608437\pi\) | ||||
−0.334115 | + | 0.942532i | \(0.608437\pi\) | |||||||
\(930\) | 8.83640 | 0.289757 | ||||||||
\(931\) | −49.0814 | −1.60858 | ||||||||
\(932\) | −15.3658 | −0.503323 | ||||||||
\(933\) | 11.6671 | 0.381965 | ||||||||
\(934\) | − | 14.9219i | − | 0.488258i | ||||||
\(935\) | − | 17.7334i | − | 0.579946i | ||||||
\(936\) | 4.42153i | 0.144522i | ||||||||
\(937\) | − | 42.5596i | − | 1.39036i | −0.718835 | − | 0.695181i | \(-0.755324\pi\) | ||
0.718835 | − | 0.695181i | \(-0.244676\pi\) | |||||||
\(938\) | −5.75728 | −0.187982 | ||||||||
\(939\) | −27.4233 | −0.894924 | ||||||||
\(940\) | − | 1.73186i | − | 0.0564871i | ||||||
\(941\) | 23.9270 | 0.779996 | 0.389998 | − | 0.920816i | \(-0.372476\pi\) | ||||
0.389998 | + | 0.920816i | \(0.372476\pi\) | |||||||
\(942\) | 17.8523 | − | 10.7372i | 0.581658 | − | 0.349836i | ||||
\(943\) | −3.93972 | −0.128295 | ||||||||
\(944\) | 15.8537i | 0.515994i | ||||||||
\(945\) | 1.75939 | 0.0572328 | ||||||||
\(946\) | −0.442313 | −0.0143808 | ||||||||
\(947\) | 10.2660i | 0.333601i | 0.985991 | + | 0.166800i | \(0.0533436\pi\) | ||||
−0.985991 | + | 0.166800i | \(0.946656\pi\) | |||||||
\(948\) | 2.55819i | 0.0830861i | ||||||||
\(949\) | − | 26.4758i | − | 0.859441i | ||||||
\(950\) | − | 20.8249i | − | 0.675649i | ||||||
\(951\) | −28.3482 | −0.919254 | ||||||||
\(952\) | −3.59372 | −0.116473 | ||||||||
\(953\) | −50.6371 | −1.64030 | −0.820148 | − | 0.572151i | \(-0.806109\pi\) | ||||
−0.820148 | + | 0.572151i | \(0.806109\pi\) | |||||||
\(954\) | −1.59398 | −0.0516070 | ||||||||
\(955\) | −34.8191 | −1.12672 | ||||||||
\(956\) | 0.728844 | 0.0235725 | ||||||||
\(957\) | 27.7452i | 0.896873i | ||||||||
\(958\) | 44.6890 | 1.44384 | ||||||||
\(959\) | −0.177621 | −0.00573569 | ||||||||
\(960\) | − | 5.66480i | − | 0.182831i | ||||||
\(961\) | −22.7960 | −0.735354 | ||||||||
\(962\) | − | 4.60791i | − | 0.148565i | ||||||
\(963\) | 8.75884i | 0.282250i | ||||||||
\(964\) | − | 15.2041i | − | 0.489693i | ||||||
\(965\) | − | 17.1016i | − | 0.550518i | ||||||
\(966\) | − | 6.63039i | − | 0.213329i | ||||||
\(967\) | −7.19667 | −0.231429 | −0.115715 | − | 0.993282i | \(-0.536916\pi\) | ||||
−0.115715 | + | 0.993282i | \(0.536916\pi\) | |||||||
\(968\) | 32.5410i | 1.04591i | ||||||||
\(969\) | 14.8409 | 0.476758 | ||||||||
\(970\) | − | 56.6450i | − | 1.81876i | ||||||
\(971\) | − | 1.23786i | − | 0.0397247i | −0.999803 | − | 0.0198624i | \(-0.993677\pi\) | ||
0.999803 | − | 0.0198624i | \(-0.00632280\pi\) | |||||||
\(972\) | −0.764270 | −0.0245140 | ||||||||
\(973\) | −15.9983 | −0.512881 | ||||||||
\(974\) | 49.5090i | 1.58637i | ||||||||
\(975\) | 3.35068 | 0.107308 | ||||||||
\(976\) | 66.8756i | 2.14064i | ||||||||
\(977\) | 37.4266 | 1.19738 | 0.598692 | − | 0.800979i | \(-0.295687\pi\) | ||||
0.598692 | + | 0.800979i | \(0.295687\pi\) | |||||||
\(978\) | 27.1199 | 0.867197 | ||||||||
\(979\) | 78.7132 | 2.51569 | ||||||||
\(980\) | − | 8.65201i | − | 0.276378i | ||||||
\(981\) | 10.2946 | 0.328681 | ||||||||
\(982\) | 36.3007 | 1.15840 | ||||||||
\(983\) | 15.8593i | 0.505834i | 0.967488 | + | 0.252917i | \(0.0813900\pi\) | ||||
−0.967488 | + | 0.252917i | \(0.918610\pi\) | |||||||
\(984\) | 1.92451 | 0.0613511 | ||||||||
\(985\) | − | 28.3366i | − | 0.902878i | ||||||
\(986\) | 16.4262 | 0.523118 | ||||||||
\(987\) | − | 1.15793i | − | 0.0368575i | ||||||
\(988\) | 13.2320 | 0.420965 | ||||||||
\(989\) | 0.215983 | 0.00686785 | ||||||||
\(990\) | −15.9824 | −0.507954 | ||||||||
\(991\) | 26.8582 | 0.853178 | 0.426589 | − | 0.904446i | \(-0.359715\pi\) | ||||
0.426589 | + | 0.904446i | \(0.359715\pi\) | |||||||
\(992\) | 11.7767i | 0.373910i | ||||||||
\(993\) | −2.43583 | −0.0772989 | ||||||||
\(994\) | 4.69877 | 0.149036 | ||||||||
\(995\) | 20.7572i | 0.658047i | ||||||||
\(996\) | 11.6309i | 0.368538i | ||||||||
\(997\) | 8.02275i | 0.254083i | 0.991897 | + | 0.127042i | \(0.0405481\pi\) | ||||
−0.991897 | + | 0.127042i | \(0.959452\pi\) | |||||||
\(998\) | −25.6838 | −0.813008 | ||||||||
\(999\) | −1.28782 | −0.0407448 |
(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 | 471.2.b.b.313.11 | yes | 14 | |
3.2 | odd | 2 | 1413.2.b.e.784.4 | 14 | |||
157.156 | even | 2 | inner | 471.2.b.b.313.4 | ✓ | 14 | |
471.470 | odd | 2 | 1413.2.b.e.784.11 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
471.2.b.b.313.4 | ✓ | 14 | 157.156 | even | 2 | inner | |
471.2.b.b.313.11 | yes | 14 | 1.1 | even | 1 | trivial | |
1413.2.b.e.784.4 | 14 | 3.2 | odd | 2 | |||
1413.2.b.e.784.11 | 14 | 471.470 | odd | 2 |