Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(91,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("1380.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.p (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: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.20 | ||
Character | \(\chi\) | \(=\) | 1380.91 |
Dual form | 1380.2.p.b.91.19 |
$q$-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 \(\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(691\) | \(1201\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.651202 | + | 1.25536i | −0.460469 | + | 0.887676i | ||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.15187 | − | 1.63499i | −0.575937 | − | 0.817494i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 1.25536 | + | 0.651202i | 0.512500 | + | 0.265852i | ||||
\(7\) | −2.14037 | −0.808986 | −0.404493 | − | 0.914541i | \(-0.632552\pi\) | ||||
−0.404493 | + | 0.914541i | \(0.632552\pi\) | |||||||
\(8\) | 2.80261 | − | 0.381312i | 0.990871 | − | 0.134814i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −1.25536 | − | 0.651202i | −0.396981 | − | 0.205928i | ||||
\(11\) | 3.55021 | 1.07043 | 0.535214 | − | 0.844716i | \(-0.320231\pi\) | ||||
0.535214 | + | 0.844716i | \(0.320231\pi\) | |||||||
\(12\) | −1.63499 | + | 1.15187i | −0.471981 | + | 0.332517i | ||||
\(13\) | −4.04464 | −1.12178 | −0.560891 | − | 0.827890i | \(-0.689541\pi\) | ||||
−0.560891 | + | 0.827890i | \(0.689541\pi\) | |||||||
\(14\) | 1.39382 | − | 2.68695i | 0.372513 | − | 0.718117i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −1.34638 | + | 3.76660i | −0.336594 | + | 0.941650i | ||||
\(17\) | 0.843658i | 0.204617i | 0.994753 | + | 0.102309i | \(0.0326229\pi\) | ||||
−0.994753 | + | 0.102309i | \(0.967377\pi\) | |||||||
\(18\) | 0.651202 | − | 1.25536i | 0.153490 | − | 0.295892i | ||||
\(19\) | 5.13553 | 1.17817 | 0.589085 | − | 0.808071i | \(-0.299488\pi\) | ||||
0.589085 | + | 0.808071i | \(0.299488\pi\) | |||||||
\(20\) | 1.63499 | − | 1.15187i | 0.365595 | − | 0.257567i | ||||
\(21\) | 2.14037i | 0.467068i | ||||||||
\(22\) | −2.31190 | + | 4.45680i | −0.492899 | + | 0.950193i | ||||
\(23\) | −2.71512 | − | 3.95324i | −0.566142 | − | 0.824308i | ||||
\(24\) | −0.381312 | − | 2.80261i | −0.0778349 | − | 0.572080i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 2.63388 | − | 5.07749i | 0.516546 | − | 0.995778i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 2.46544 | + | 3.49949i | 0.465924 | + | 0.661341i | ||||
\(29\) | 0.275665 | 0.0511898 | 0.0255949 | − | 0.999672i | \(-0.491852\pi\) | ||||
0.0255949 | + | 0.999672i | \(0.491852\pi\) | |||||||
\(30\) | −0.651202 | + | 1.25536i | −0.118893 | + | 0.229197i | ||||
\(31\) | 8.41233i | 1.51090i | 0.655207 | + | 0.755450i | \(0.272581\pi\) | ||||
−0.655207 | + | 0.755450i | \(0.727419\pi\) | |||||||
\(32\) | −3.85169 | − | 4.14301i | −0.680888 | − | 0.732387i | ||||
\(33\) | − | 3.55021i | − | 0.618012i | ||||||
\(34\) | −1.05910 | − | 0.549392i | −0.181634 | − | 0.0942199i | ||||
\(35\) | − | 2.14037i | − | 0.361789i | ||||||
\(36\) | 1.15187 | + | 1.63499i | 0.191979 | + | 0.272498i | ||||
\(37\) | − | 2.63854i | − | 0.433773i | −0.976197 | − | 0.216886i | \(-0.930410\pi\) | ||
0.976197 | − | 0.216886i | \(-0.0695901\pi\) | |||||||
\(38\) | −3.34426 | + | 6.44695i | −0.542511 | + | 1.04583i | ||||
\(39\) | 4.04464i | 0.647661i | ||||||||
\(40\) | 0.381312 | + | 2.80261i | 0.0602907 | + | 0.443131i | ||||
\(41\) | 7.36818 | 1.15072 | 0.575358 | − | 0.817901i | \(-0.304863\pi\) | ||||
0.575358 | + | 0.817901i | \(0.304863\pi\) | |||||||
\(42\) | −2.68695 | − | 1.39382i | −0.414605 | − | 0.215070i | ||||
\(43\) | 11.6118 | 1.77078 | 0.885389 | − | 0.464850i | \(-0.153892\pi\) | ||||
0.885389 | + | 0.464850i | \(0.153892\pi\) | |||||||
\(44\) | −4.08939 | − | 5.80455i | −0.616499 | − | 0.875069i | ||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 6.73084 | − | 0.834108i | 0.992409 | − | 0.122983i | ||||
\(47\) | 10.4234i | 1.52040i | 0.649686 | + | 0.760202i | \(0.274900\pi\) | ||||
−0.649686 | + | 0.760202i | \(0.725100\pi\) | |||||||
\(48\) | 3.76660 | + | 1.34638i | 0.543662 | + | 0.194333i | ||||
\(49\) | −2.41880 | −0.345542 | ||||||||
\(50\) | 0.651202 | − | 1.25536i | 0.0920938 | − | 0.177535i | ||||
\(51\) | 0.843658 | 0.118136 | ||||||||
\(52\) | 4.65891 | + | 6.61294i | 0.646075 | + | 0.917050i | ||||
\(53\) | − | 5.60182i | − | 0.769470i | −0.923027 | − | 0.384735i | \(-0.874293\pi\) | ||
0.923027 | − | 0.384735i | \(-0.125707\pi\) | |||||||
\(54\) | −1.25536 | − | 0.651202i | −0.170833 | − | 0.0886173i | ||||
\(55\) | 3.55021i | 0.478710i | ||||||||
\(56\) | −5.99863 | + | 0.816150i | −0.801600 | + | 0.109063i | ||||
\(57\) | − | 5.13553i | − | 0.680217i | ||||||
\(58\) | −0.179514 | + | 0.346060i | −0.0235713 | + | 0.0454399i | ||||
\(59\) | 2.95080i | 0.384162i | 0.981379 | + | 0.192081i | \(0.0615236\pi\) | ||||
−0.981379 | + | 0.192081i | \(0.938476\pi\) | |||||||
\(60\) | −1.15187 | − | 1.63499i | −0.148706 | − | 0.211076i | ||||
\(61\) | 7.05529i | 0.903338i | 0.892186 | + | 0.451669i | \(0.149171\pi\) | ||||
−0.892186 | + | 0.451669i | \(0.850829\pi\) | |||||||
\(62\) | −10.5605 | − | 5.47812i | −1.34119 | − | 0.695722i | ||||
\(63\) | 2.14037 | 0.269662 | ||||||||
\(64\) | 7.70920 | − | 2.13733i | 0.963650 | − | 0.267167i | ||||
\(65\) | − | 4.04464i | − | 0.501676i | ||||||
\(66\) | 4.45680 | + | 2.31190i | 0.548594 | + | 0.284575i | ||||
\(67\) | 2.62970 | 0.321269 | 0.160634 | − | 0.987014i | \(-0.448646\pi\) | ||||
0.160634 | + | 0.987014i | \(0.448646\pi\) | |||||||
\(68\) | 1.37937 | − | 0.971787i | 0.167273 | − | 0.117847i | ||||
\(69\) | −3.95324 | + | 2.71512i | −0.475914 | + | 0.326862i | ||||
\(70\) | 2.68695 | + | 1.39382i | 0.321152 | + | 0.166593i | ||||
\(71\) | 2.73387i | 0.324450i | 0.986754 | + | 0.162225i | \(0.0518671\pi\) | ||||
−0.986754 | + | 0.162225i | \(0.948133\pi\) | |||||||
\(72\) | −2.80261 | + | 0.381312i | −0.330290 | + | 0.0449380i | ||||
\(73\) | 4.84511 | 0.567077 | 0.283538 | − | 0.958961i | \(-0.408492\pi\) | ||||
0.283538 | + | 0.958961i | \(0.408492\pi\) | |||||||
\(74\) | 3.31232 | + | 1.71822i | 0.385050 | + | 0.199739i | ||||
\(75\) | 1.00000i | 0.115470i | ||||||||
\(76\) | −5.91548 | − | 8.39653i | −0.678552 | − | 0.963148i | ||||
\(77\) | −7.59878 | −0.865961 | ||||||||
\(78\) | −5.07749 | − | 2.63388i | −0.574913 | − | 0.298228i | ||||
\(79\) | 16.2338 | 1.82645 | 0.913223 | − | 0.407461i | \(-0.133586\pi\) | ||||
0.913223 | + | 0.407461i | \(0.133586\pi\) | |||||||
\(80\) | −3.76660 | − | 1.34638i | −0.421119 | − | 0.150530i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.79817 | + | 9.24974i | −0.529869 | + | 1.02146i | ||||
\(83\) | 9.45106 | 1.03739 | 0.518694 | − | 0.854960i | \(-0.326418\pi\) | ||||
0.518694 | + | 0.854960i | \(0.326418\pi\) | |||||||
\(84\) | 3.49949 | − | 2.46544i | 0.381826 | − | 0.269002i | ||||
\(85\) | −0.843658 | −0.0915076 | ||||||||
\(86\) | −7.56161 | + | 14.5770i | −0.815389 | + | 1.57188i | ||||
\(87\) | − | 0.275665i | − | 0.0295544i | ||||||
\(88\) | 9.94984 | − | 1.35374i | 1.06066 | − | 0.144309i | ||||
\(89\) | 16.0179i | 1.69789i | 0.528482 | + | 0.848945i | \(0.322762\pi\) | ||||
−0.528482 | + | 0.848945i | \(0.677238\pi\) | |||||||
\(90\) | 1.25536 | + | 0.651202i | 0.132327 | + | 0.0686427i | ||||
\(91\) | 8.65705 | 0.907505 | ||||||||
\(92\) | −3.33603 | + | 8.99283i | −0.347805 | + | 0.937567i | ||||
\(93\) | 8.41233 | 0.872318 | ||||||||
\(94\) | −13.0851 | − | 6.78772i | −1.34963 | − | 0.700099i | ||||
\(95\) | 5.13553i | 0.526894i | ||||||||
\(96\) | −4.14301 | + | 3.85169i | −0.422844 | + | 0.393111i | ||||
\(97\) | − | 0.845087i | − | 0.0858056i | −0.999079 | − | 0.0429028i | \(-0.986339\pi\) | ||
0.999079 | − | 0.0429028i | \(-0.0136606\pi\) | |||||||
\(98\) | 1.57512 | − | 3.03647i | 0.159112 | − | 0.306730i | ||||
\(99\) | −3.55021 | −0.356810 | ||||||||
\(100\) | 1.15187 | + | 1.63499i | 0.115187 | + | 0.163499i | ||||
\(101\) | 7.04680 | 0.701182 | 0.350591 | − | 0.936529i | \(-0.385981\pi\) | ||||
0.350591 | + | 0.936529i | \(0.385981\pi\) | |||||||
\(102\) | −0.549392 | + | 1.05910i | −0.0543979 | + | 0.104866i | ||||
\(103\) | 13.7768 | 1.35747 | 0.678736 | − | 0.734382i | \(-0.262528\pi\) | ||||
0.678736 | + | 0.734382i | \(0.262528\pi\) | |||||||
\(104\) | −11.3355 | + | 1.54227i | −1.11154 | + | 0.151232i | ||||
\(105\) | −2.14037 | −0.208879 | ||||||||
\(106\) | 7.03232 | + | 3.64792i | 0.683040 | + | 0.354317i | ||||
\(107\) | −1.44719 | −0.139905 | −0.0699526 | − | 0.997550i | \(-0.522285\pi\) | ||||
−0.0699526 | + | 0.997550i | \(0.522285\pi\) | |||||||
\(108\) | 1.63499 | − | 1.15187i | 0.157327 | − | 0.110839i | ||||
\(109\) | 1.02911i | 0.0985713i | 0.998785 | + | 0.0492856i | \(0.0156945\pi\) | ||||
−0.998785 | + | 0.0492856i | \(0.984306\pi\) | |||||||
\(110\) | −4.45680 | − | 2.31190i | −0.424939 | − | 0.220431i | ||||
\(111\) | −2.63854 | −0.250439 | ||||||||
\(112\) | 2.88175 | − | 8.06193i | 0.272300 | − | 0.761781i | ||||
\(113\) | 11.0913i | 1.04338i | 0.853135 | + | 0.521689i | \(0.174698\pi\) | ||||
−0.853135 | + | 0.521689i | \(0.825302\pi\) | |||||||
\(114\) | 6.44695 | + | 3.34426i | 0.603812 | + | 0.313219i | ||||
\(115\) | 3.95324 | − | 2.71512i | 0.368642 | − | 0.253186i | ||||
\(116\) | −0.317532 | − | 0.450710i | −0.0294821 | − | 0.0418474i | ||||
\(117\) | 4.04464 | 0.373927 | ||||||||
\(118\) | −3.70433 | − | 1.92157i | −0.341011 | − | 0.176894i | ||||
\(119\) | − | 1.80574i | − | 0.165532i | ||||||
\(120\) | 2.80261 | − | 0.381312i | 0.255842 | − | 0.0348088i | ||||
\(121\) | 1.60399 | 0.145817 | ||||||||
\(122\) | −8.85696 | − | 4.59442i | −0.801871 | − | 0.415959i | ||||
\(123\) | − | 7.36818i | − | 0.664367i | ||||||
\(124\) | 13.7541 | − | 9.68994i | 1.23515 | − | 0.870182i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −1.39382 | + | 2.68695i | −0.124171 | + | 0.239372i | ||||
\(127\) | 20.3834i | 1.80873i | 0.426758 | + | 0.904366i | \(0.359656\pi\) | ||||
−0.426758 | + | 0.904366i | \(0.640344\pi\) | |||||||
\(128\) | −2.33712 | + | 11.0697i | −0.206574 | + | 0.978431i | ||||
\(129\) | − | 11.6118i | − | 1.02236i | ||||||
\(130\) | 5.07749 | + | 2.63388i | 0.445326 | + | 0.231006i | ||||
\(131\) | − | 3.33061i | − | 0.290997i | −0.989358 | − | 0.145498i | \(-0.953521\pi\) | ||
0.989358 | − | 0.145498i | \(-0.0464786\pi\) | |||||||
\(132\) | −5.80455 | + | 4.08939i | −0.505222 | + | 0.355936i | ||||
\(133\) | −10.9920 | −0.953123 | ||||||||
\(134\) | −1.71246 | + | 3.30123i | −0.147934 | + | 0.285183i | ||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0.321697 | + | 2.36444i | 0.0275853 | + | 0.202749i | ||||
\(137\) | − | 21.9555i | − | 1.87579i | −0.346924 | − | 0.937893i | \(-0.612774\pi\) | ||
0.346924 | − | 0.937893i | \(-0.387226\pi\) | |||||||
\(138\) | −0.834108 | − | 6.73084i | −0.0710040 | − | 0.572968i | ||||
\(139\) | 15.4357i | 1.30924i | 0.755960 | + | 0.654618i | \(0.227170\pi\) | ||||
−0.755960 | + | 0.654618i | \(0.772830\pi\) | |||||||
\(140\) | −3.49949 | + | 2.46544i | −0.295761 | + | 0.208368i | ||||
\(141\) | 10.4234 | 0.877806 | ||||||||
\(142\) | −3.43200 | − | 1.78030i | −0.288007 | − | 0.149399i | ||||
\(143\) | −14.3593 | −1.20079 | ||||||||
\(144\) | 1.34638 | − | 3.76660i | 0.112198 | − | 0.313883i | ||||
\(145\) | 0.275665i | 0.0228928i | ||||||||
\(146\) | −3.15514 | + | 6.08237i | −0.261121 | + | 0.503380i | ||||
\(147\) | 2.41880i | 0.199499i | ||||||||
\(148\) | −4.31398 | + | 3.03926i | −0.354607 | + | 0.249826i | ||||
\(149\) | 1.22216i | 0.100123i | 0.998746 | + | 0.0500615i | \(0.0159417\pi\) | ||||
−0.998746 | + | 0.0500615i | \(0.984058\pi\) | |||||||
\(150\) | −1.25536 | − | 0.651202i | −0.102500 | − | 0.0531704i | ||||
\(151\) | − | 9.64939i | − | 0.785256i | −0.919697 | − | 0.392628i | \(-0.871566\pi\) | ||
0.919697 | − | 0.392628i | \(-0.128434\pi\) | |||||||
\(152\) | 14.3929 | − | 1.95824i | 1.16742 | − | 0.158834i | ||||
\(153\) | − | 0.843658i | − | 0.0682057i | ||||||
\(154\) | 4.94834 | − | 9.53923i | 0.398748 | − | 0.768693i | ||||
\(155\) | −8.41233 | −0.675695 | ||||||||
\(156\) | 6.61294 | − | 4.65891i | 0.529459 | − | 0.373012i | ||||
\(157\) | 15.1421i | 1.20847i | 0.796807 | + | 0.604234i | \(0.206521\pi\) | ||||
−0.796807 | + | 0.604234i | \(0.793479\pi\) | |||||||
\(158\) | −10.5715 | + | 20.3793i | −0.841021 | + | 1.62129i | ||||
\(159\) | −5.60182 | −0.444254 | ||||||||
\(160\) | 4.14301 | − | 3.85169i | 0.327533 | − | 0.304503i | ||||
\(161\) | 5.81138 | + | 8.46142i | 0.458001 | + | 0.666853i | ||||
\(162\) | −0.651202 | + | 1.25536i | −0.0511632 | + | 0.0986306i | ||||
\(163\) | 6.70557i | 0.525221i | 0.964902 | + | 0.262610i | \(0.0845833\pi\) | ||||
−0.964902 | + | 0.262610i | \(0.915417\pi\) | |||||||
\(164\) | −8.48721 | − | 12.0469i | −0.662740 | − | 0.940705i | ||||
\(165\) | 3.55021 | 0.276383 | ||||||||
\(166\) | −6.15454 | + | 11.8645i | −0.477685 | + | 0.920865i | ||||
\(167\) | − | 22.2534i | − | 1.72202i | −0.508589 | − | 0.861010i | \(-0.669833\pi\) | ||
0.508589 | − | 0.861010i | \(-0.330167\pi\) | |||||||
\(168\) | 0.816150 | + | 5.99863i | 0.0629673 | + | 0.462804i | ||||
\(169\) | 3.35912 | 0.258394 | ||||||||
\(170\) | 0.549392 | − | 1.05910i | 0.0421364 | − | 0.0812291i | ||||
\(171\) | −5.13553 | −0.392724 | ||||||||
\(172\) | −13.3753 | − | 18.9851i | −1.01986 | − | 1.44760i | ||||
\(173\) | −20.8806 | −1.58752 | −0.793762 | − | 0.608228i | \(-0.791881\pi\) | ||||
−0.793762 | + | 0.608228i | \(0.791881\pi\) | |||||||
\(174\) | 0.346060 | + | 0.179514i | 0.0262348 | + | 0.0136089i | ||||
\(175\) | 2.14037 | 0.161797 | ||||||||
\(176\) | −4.77992 | + | 13.3722i | −0.360300 | + | 1.00797i | ||||
\(177\) | 2.95080 | 0.221796 | ||||||||
\(178\) | −20.1082 | − | 10.4309i | −1.50718 | − | 0.781826i | ||||
\(179\) | − | 11.9933i | − | 0.896420i | −0.893928 | − | 0.448210i | \(-0.852062\pi\) | ||
0.893928 | − | 0.448210i | \(-0.147938\pi\) | |||||||
\(180\) | −1.63499 | + | 1.15187i | −0.121865 | + | 0.0858555i | ||||
\(181\) | − | 11.8382i | − | 0.879927i | −0.898016 | − | 0.439964i | \(-0.854991\pi\) | ||
0.898016 | − | 0.439964i | \(-0.145009\pi\) | |||||||
\(182\) | −5.63748 | + | 10.8677i | −0.417878 | + | 0.805570i | ||||
\(183\) | 7.05529 | 0.521542 | ||||||||
\(184\) | −9.11684 | − | 10.0441i | −0.672102 | − | 0.740459i | ||||
\(185\) | 2.63854 | 0.193989 | ||||||||
\(186\) | −5.47812 | + | 10.5605i | −0.401675 | + | 0.774336i | ||||
\(187\) | 2.99516i | 0.219028i | ||||||||
\(188\) | 17.0421 | − | 12.0064i | 1.24292 | − | 0.875657i | ||||
\(189\) | − | 2.14037i | − | 0.155689i | ||||||
\(190\) | −6.44695 | − | 3.34426i | −0.467711 | − | 0.242618i | ||||
\(191\) | −1.29520 | −0.0937173 | −0.0468587 | − | 0.998902i | \(-0.514921\pi\) | ||||
−0.0468587 | + | 0.998902i | \(0.514921\pi\) | |||||||
\(192\) | −2.13733 | − | 7.70920i | −0.154249 | − | 0.556364i | ||||
\(193\) | −1.48140 | −0.106634 | −0.0533169 | − | 0.998578i | \(-0.516979\pi\) | ||||
−0.0533169 | + | 0.998578i | \(0.516979\pi\) | |||||||
\(194\) | 1.06089 | + | 0.550322i | 0.0761675 | + | 0.0395108i | ||||
\(195\) | −4.04464 | −0.289643 | ||||||||
\(196\) | 2.78615 | + | 3.95471i | 0.199010 | + | 0.282479i | ||||
\(197\) | −13.9422 | −0.993338 | −0.496669 | − | 0.867940i | \(-0.665444\pi\) | ||||
−0.496669 | + | 0.867940i | \(0.665444\pi\) | |||||||
\(198\) | 2.31190 | − | 4.45680i | 0.164300 | − | 0.316731i | ||||
\(199\) | −5.33970 | −0.378521 | −0.189261 | − | 0.981927i | \(-0.560609\pi\) | ||||
−0.189261 | + | 0.981927i | \(0.560609\pi\) | |||||||
\(200\) | −2.80261 | + | 0.381312i | −0.198174 | + | 0.0269628i | ||||
\(201\) | − | 2.62970i | − | 0.185485i | ||||||
\(202\) | −4.58889 | + | 8.84629i | −0.322873 | + | 0.622423i | ||||
\(203\) | −0.590027 | −0.0414118 | ||||||||
\(204\) | −0.971787 | − | 1.37937i | −0.0680387 | − | 0.0965753i | ||||
\(205\) | 7.36818i | 0.514616i | ||||||||
\(206\) | −8.97150 | + | 17.2949i | −0.625074 | + | 1.20500i | ||||
\(207\) | 2.71512 | + | 3.95324i | 0.188714 | + | 0.274769i | ||||
\(208\) | 5.44561 | − | 15.2345i | 0.377585 | − | 1.05633i | ||||
\(209\) | 18.2322 | 1.26115 | ||||||||
\(210\) | 1.39382 | − | 2.68695i | 0.0961824 | − | 0.185417i | ||||
\(211\) | 2.76105i | 0.190078i | 0.995474 | + | 0.0950392i | \(0.0302976\pi\) | ||||
−0.995474 | + | 0.0950392i | \(0.969702\pi\) | |||||||
\(212\) | −9.15892 | + | 6.45259i | −0.629037 | + | 0.443166i | ||||
\(213\) | 2.73387 | 0.187321 | ||||||||
\(214\) | 0.942413 | − | 1.81675i | 0.0644220 | − | 0.124190i | ||||
\(215\) | 11.6118i | 0.791916i | ||||||||
\(216\) | 0.381312 | + | 2.80261i | 0.0259450 | + | 0.190693i | ||||
\(217\) | − | 18.0055i | − | 1.22230i | ||||||
\(218\) | −1.29191 | − | 0.670161i | −0.0874993 | − | 0.0453890i | ||||
\(219\) | − | 4.84511i | − | 0.327402i | ||||||
\(220\) | 5.80455 | − | 4.08939i | 0.391343 | − | 0.275707i | ||||
\(221\) | − | 3.41229i | − | 0.229536i | ||||||
\(222\) | 1.71822 | − | 3.31232i | 0.115319 | − | 0.222308i | ||||
\(223\) | 7.40876i | 0.496127i | 0.968744 | + | 0.248063i | \(0.0797942\pi\) | ||||
−0.968744 | + | 0.248063i | \(0.920206\pi\) | |||||||
\(224\) | 8.24405 | + | 8.86759i | 0.550829 | + | 0.592491i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −13.9236 | − | 7.22265i | −0.926182 | − | 0.480444i | ||||
\(227\) | 10.8648 | 0.721119 | 0.360560 | − | 0.932736i | \(-0.382586\pi\) | ||||
0.360560 | + | 0.932736i | \(0.382586\pi\) | |||||||
\(228\) | −8.39653 | + | 5.91548i | −0.556074 | + | 0.391762i | ||||
\(229\) | 12.6365i | 0.835044i | 0.908667 | + | 0.417522i | \(0.137101\pi\) | ||||
−0.908667 | + | 0.417522i | \(0.862899\pi\) | |||||||
\(230\) | 0.834108 | + | 6.73084i | 0.0549995 | + | 0.443819i | ||||
\(231\) | 7.59878i | 0.499963i | ||||||||
\(232\) | 0.772582 | − | 0.105114i | 0.0507225 | − | 0.00690110i | ||||
\(233\) | 2.14877 | 0.140771 | 0.0703854 | − | 0.997520i | \(-0.477577\pi\) | ||||
0.0703854 | + | 0.997520i | \(0.477577\pi\) | |||||||
\(234\) | −2.63388 | + | 5.07749i | −0.172182 | + | 0.331926i | ||||
\(235\) | −10.4234 | −0.679946 | ||||||||
\(236\) | 4.82453 | − | 3.39895i | 0.314050 | − | 0.221253i | ||||
\(237\) | − | 16.2338i | − | 1.05450i | ||||||
\(238\) | 2.26687 | + | 1.17590i | 0.146939 | + | 0.0762225i | ||||
\(239\) | − | 15.5046i | − | 1.00291i | −0.865183 | − | 0.501456i | \(-0.832798\pi\) | ||
0.865183 | − | 0.501456i | \(-0.167202\pi\) | |||||||
\(240\) | −1.34638 | + | 3.76660i | −0.0869083 | + | 0.243133i | ||||
\(241\) | 12.5601i | 0.809065i | 0.914524 | + | 0.404532i | \(0.132566\pi\) | ||||
−0.914524 | + | 0.404532i | \(0.867434\pi\) | |||||||
\(242\) | −1.04452 | + | 2.01359i | −0.0671443 | + | 0.129438i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 11.5353 | − | 8.12680i | 0.738474 | − | 0.520265i | ||||
\(245\) | − | 2.41880i | − | 0.154531i | ||||||
\(246\) | 9.24974 | + | 4.79817i | 0.589742 | + | 0.305920i | ||||
\(247\) | −20.7714 | −1.32165 | ||||||||
\(248\) | 3.20772 | + | 23.5764i | 0.203690 | + | 1.49711i | ||||
\(249\) | − | 9.45106i | − | 0.598937i | ||||||
\(250\) | 1.25536 | + | 0.651202i | 0.0793961 | + | 0.0411856i | ||||
\(251\) | 24.6936 | 1.55865 | 0.779323 | − | 0.626622i | \(-0.215563\pi\) | ||||
0.779323 | + | 0.626622i | \(0.215563\pi\) | |||||||
\(252\) | −2.46544 | − | 3.49949i | −0.155308 | − | 0.220447i | ||||
\(253\) | −9.63925 | − | 14.0348i | −0.606015 | − | 0.882362i | ||||
\(254\) | −25.5885 | − | 13.2737i | −1.60557 | − | 0.832865i | ||||
\(255\) | 0.843658i | 0.0528319i | ||||||||
\(256\) | −12.3745 | − | 10.1425i | −0.773409 | − | 0.633908i | ||||
\(257\) | −29.0352 | −1.81116 | −0.905582 | − | 0.424171i | \(-0.860566\pi\) | ||||
−0.905582 | + | 0.424171i | \(0.860566\pi\) | |||||||
\(258\) | 14.5770 | + | 7.56161i | 0.907524 | + | 0.470765i | ||||
\(259\) | 5.64746i | 0.350916i | ||||||||
\(260\) | −6.61294 | + | 4.65891i | −0.410117 | + | 0.288933i | ||||
\(261\) | −0.275665 | −0.0170633 | ||||||||
\(262\) | 4.18113 | + | 2.16890i | 0.258311 | + | 0.133995i | ||||
\(263\) | −25.0910 | −1.54718 | −0.773589 | − | 0.633688i | \(-0.781540\pi\) | ||||
−0.773589 | + | 0.633688i | \(0.781540\pi\) | |||||||
\(264\) | −1.35374 | − | 9.94984i | −0.0833167 | − | 0.612370i | ||||
\(265\) | 5.60182 | 0.344117 | ||||||||
\(266\) | 7.15798 | − | 13.7989i | 0.438884 | − | 0.846064i | ||||
\(267\) | 16.0179 | 0.980277 | ||||||||
\(268\) | −3.02908 | − | 4.29953i | −0.185030 | − | 0.262636i | ||||
\(269\) | 15.8583 | 0.966900 | 0.483450 | − | 0.875372i | \(-0.339384\pi\) | ||||
0.483450 | + | 0.875372i | \(0.339384\pi\) | |||||||
\(270\) | 0.651202 | − | 1.25536i | 0.0396309 | − | 0.0763990i | ||||
\(271\) | − | 19.2143i | − | 1.16719i | −0.812046 | − | 0.583594i | \(-0.801646\pi\) | ||
0.812046 | − | 0.583594i | \(-0.198354\pi\) | |||||||
\(272\) | −3.17772 | − | 1.13588i | −0.192678 | − | 0.0688730i | ||||
\(273\) | − | 8.65705i | − | 0.523948i | ||||||
\(274\) | 27.5621 | + | 14.2975i | 1.66509 | + | 0.863741i | ||||
\(275\) | −3.55021 | −0.214086 | ||||||||
\(276\) | 8.99283 | + | 3.33603i | 0.541305 | + | 0.200805i | ||||
\(277\) | 2.32664 | 0.139794 | 0.0698972 | − | 0.997554i | \(-0.477733\pi\) | ||||
0.0698972 | + | 0.997554i | \(0.477733\pi\) | |||||||
\(278\) | −19.3774 | − | 10.0517i | −1.16218 | − | 0.602862i | ||||
\(279\) | − | 8.41233i | − | 0.503633i | ||||||
\(280\) | −0.816150 | − | 5.99863i | −0.0487743 | − | 0.358487i | ||||
\(281\) | − | 2.44660i | − | 0.145952i | −0.997334 | − | 0.0729758i | \(-0.976750\pi\) | ||
0.997334 | − | 0.0729758i | \(-0.0232496\pi\) | |||||||
\(282\) | −6.78772 | + | 13.0851i | −0.404203 | + | 0.779207i | ||||
\(283\) | −9.49613 | −0.564486 | −0.282243 | − | 0.959343i | \(-0.591078\pi\) | ||||
−0.282243 | + | 0.959343i | \(0.591078\pi\) | |||||||
\(284\) | 4.46984 | − | 3.14907i | 0.265236 | − | 0.186863i | ||||
\(285\) | 5.13553 | 0.304202 | ||||||||
\(286\) | 9.35081 | − | 18.0262i | 0.552925 | − | 1.06591i | ||||
\(287\) | −15.7707 | −0.930913 | ||||||||
\(288\) | 3.85169 | + | 4.14301i | 0.226963 | + | 0.244129i | ||||
\(289\) | 16.2882 | 0.958132 | ||||||||
\(290\) | −0.346060 | − | 0.179514i | −0.0203214 | − | 0.0105414i | ||||
\(291\) | −0.845087 | −0.0495399 | ||||||||
\(292\) | −5.58095 | − | 7.92169i | −0.326600 | − | 0.463582i | ||||
\(293\) | − | 16.0874i | − | 0.939836i | −0.882710 | − | 0.469918i | \(-0.844283\pi\) | ||
0.882710 | − | 0.469918i | \(-0.155717\pi\) | |||||||
\(294\) | −3.03647 | − | 1.57512i | −0.177090 | − | 0.0918631i | ||||
\(295\) | −2.95080 | −0.171802 | ||||||||
\(296\) | −1.00610 | − | 7.39478i | −0.0584786 | − | 0.429813i | ||||
\(297\) | 3.55021i | 0.206004i | ||||||||
\(298\) | −1.53425 | − | 0.795871i | −0.0888768 | − | 0.0461036i | ||||
\(299\) | 10.9817 | + | 15.9894i | 0.635088 | + | 0.924693i | ||||
\(300\) | 1.63499 | − | 1.15187i | 0.0943961 | − | 0.0665034i | ||||
\(301\) | −24.8535 | −1.43253 | ||||||||
\(302\) | 12.1135 | + | 6.28370i | 0.697053 | + | 0.361586i | ||||
\(303\) | − | 7.04680i | − | 0.404828i | ||||||
\(304\) | −6.91436 | + | 19.3435i | −0.396566 | + | 1.10942i | ||||
\(305\) | −7.05529 | −0.403985 | ||||||||
\(306\) | 1.05910 | + | 0.549392i | 0.0605446 | + | 0.0314066i | ||||
\(307\) | − | 1.09550i | − | 0.0625235i | −0.999511 | − | 0.0312618i | \(-0.990047\pi\) | ||
0.999511 | − | 0.0312618i | \(-0.00995255\pi\) | |||||||
\(308\) | 8.75283 | + | 12.4239i | 0.498739 | + | 0.707918i | ||||
\(309\) | − | 13.7768i | − | 0.783737i | ||||||
\(310\) | 5.47812 | − | 10.5605i | 0.311136 | − | 0.599798i | ||||
\(311\) | − | 33.0428i | − | 1.87368i | −0.349754 | − | 0.936842i | \(-0.613735\pi\) | ||
0.349754 | − | 0.936842i | \(-0.386265\pi\) | |||||||
\(312\) | 1.54227 | + | 11.3355i | 0.0873137 | + | 0.641748i | ||||
\(313\) | − | 17.6117i | − | 0.995472i | −0.867329 | − | 0.497736i | \(-0.834165\pi\) | ||
0.867329 | − | 0.497736i | \(-0.165835\pi\) | |||||||
\(314\) | −19.0088 | − | 9.86053i | −1.07273 | − | 0.556462i | ||||
\(315\) | 2.14037i | 0.120596i | ||||||||
\(316\) | −18.6993 | − | 26.5421i | −1.05192 | − | 1.49311i | ||||
\(317\) | 11.9669 | 0.672130 | 0.336065 | − | 0.941839i | \(-0.390904\pi\) | ||||
0.336065 | + | 0.941839i | \(0.390904\pi\) | |||||||
\(318\) | 3.64792 | − | 7.03232i | 0.204565 | − | 0.394353i | ||||
\(319\) | 0.978670 | 0.0547950 | ||||||||
\(320\) | 2.13733 | + | 7.70920i | 0.119481 | + | 0.430958i | ||||
\(321\) | 1.44719i | 0.0807743i | ||||||||
\(322\) | −14.4065 | + | 1.78530i | −0.802844 | + | 0.0994911i | ||||
\(323\) | 4.33263i | 0.241074i | ||||||||
\(324\) | −1.15187 | − | 1.63499i | −0.0639929 | − | 0.0908327i | ||||
\(325\) | 4.04464 | 0.224356 | ||||||||
\(326\) | −8.41792 | − | 4.36668i | −0.466226 | − | 0.241848i | ||||
\(327\) | 1.02911 | 0.0569101 | ||||||||
\(328\) | 20.6501 | − | 2.80957i | 1.14021 | − | 0.155133i | ||||
\(329\) | − | 22.3099i | − | 1.22999i | ||||||
\(330\) | −2.31190 | + | 4.45680i | −0.127266 | + | 0.245339i | ||||
\(331\) | − | 5.36132i | − | 0.294685i | −0.989086 | − | 0.147343i | \(-0.952928\pi\) | ||
0.989086 | − | 0.147343i | \(-0.0470720\pi\) | |||||||
\(332\) | −10.8864 | − | 15.4524i | −0.597470 | − | 0.848059i | ||||
\(333\) | 2.63854i | 0.144591i | ||||||||
\(334\) | 27.9361 | + | 14.4914i | 1.52859 | + | 0.792937i | ||||
\(335\) | 2.62970i | 0.143676i | ||||||||
\(336\) | −8.06193 | − | 2.88175i | −0.439814 | − | 0.157212i | ||||
\(337\) | 18.1283i | 0.987513i | 0.869600 | + | 0.493756i | \(0.164377\pi\) | ||||
−0.869600 | + | 0.493756i | \(0.835623\pi\) | |||||||
\(338\) | −2.18746 | + | 4.21691i | −0.118982 | + | 0.229370i | ||||
\(339\) | 11.0913 | 0.602395 | ||||||||
\(340\) | 0.971787 | + | 1.37937i | 0.0527026 | + | 0.0748069i | ||||
\(341\) | 29.8655i | 1.61731i | ||||||||
\(342\) | 3.34426 | − | 6.44695i | 0.180837 | − | 0.348611i | ||||
\(343\) | 20.1598 | 1.08852 | ||||||||
\(344\) | 32.5432 | − | 4.42770i | 1.75461 | − | 0.238726i | ||||
\(345\) | −2.71512 | − | 3.95324i | −0.146177 | − | 0.212835i | ||||
\(346\) | 13.5975 | − | 26.2128i | 0.731006 | − | 1.40921i | ||||
\(347\) | 6.76150i | 0.362976i | 0.983393 | + | 0.181488i | \(0.0580914\pi\) | ||||
−0.983393 | + | 0.181488i | \(0.941909\pi\) | |||||||
\(348\) | −0.450710 | + | 0.317532i | −0.0241606 | + | 0.0170215i | ||||
\(349\) | 35.9054 | 1.92197 | 0.960987 | − | 0.276593i | \(-0.0892055\pi\) | ||||
0.960987 | + | 0.276593i | \(0.0892055\pi\) | |||||||
\(350\) | −1.39382 | + | 2.68695i | −0.0745026 | + | 0.143623i | ||||
\(351\) | − | 4.04464i | − | 0.215887i | ||||||
\(352\) | −13.6743 | − | 14.7085i | −0.728842 | − | 0.783968i | ||||
\(353\) | 19.5489 | 1.04048 | 0.520240 | − | 0.854020i | \(-0.325842\pi\) | ||||
0.520240 | + | 0.854020i | \(0.325842\pi\) | |||||||
\(354\) | −1.92157 | + | 3.70433i | −0.102130 | + | 0.196883i | ||||
\(355\) | −2.73387 | −0.145099 | ||||||||
\(356\) | 26.1890 | − | 18.4505i | 1.38802 | − | 0.977877i | ||||
\(357\) | −1.80574 | −0.0955701 | ||||||||
\(358\) | 15.0559 | + | 7.81004i | 0.795730 | + | 0.412774i | ||||
\(359\) | −28.3999 | −1.49889 | −0.749446 | − | 0.662065i | \(-0.769680\pi\) | ||||
−0.749446 | + | 0.662065i | \(0.769680\pi\) | |||||||
\(360\) | −0.381312 | − | 2.80261i | −0.0200969 | − | 0.147710i | ||||
\(361\) | 7.37365 | 0.388087 | ||||||||
\(362\) | 14.8613 | + | 7.70906i | 0.781090 | + | 0.405179i | ||||
\(363\) | − | 1.60399i | − | 0.0841876i | ||||||
\(364\) | −9.97182 | − | 14.1542i | −0.522665 | − | 0.741880i | ||||
\(365\) | 4.84511i | 0.253604i | ||||||||
\(366\) | −4.59442 | + | 8.85696i | −0.240154 | + | 0.462961i | ||||
\(367\) | 17.3687 | 0.906639 | 0.453319 | − | 0.891348i | \(-0.350240\pi\) | ||||
0.453319 | + | 0.891348i | \(0.350240\pi\) | |||||||
\(368\) | 18.5459 | − | 4.90422i | 0.966769 | − | 0.255650i | ||||
\(369\) | −7.36818 | −0.383572 | ||||||||
\(370\) | −1.71822 | + | 3.31232i | −0.0893260 | + | 0.172199i | ||||
\(371\) | 11.9900i | 0.622490i | ||||||||
\(372\) | −9.68994 | − | 13.7541i | −0.502400 | − | 0.713115i | ||||
\(373\) | 16.4101i | 0.849683i | 0.905268 | + | 0.424841i | \(0.139670\pi\) | ||||
−0.905268 | + | 0.424841i | \(0.860330\pi\) | |||||||
\(374\) | −3.76002 | − | 1.95046i | −0.194426 | − | 0.100856i | ||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 3.97455 | + | 29.2126i | 0.204972 | + | 1.50652i | ||||
\(377\) | −1.11497 | −0.0574237 | ||||||||
\(378\) | 2.68695 | + | 1.39382i | 0.138202 | + | 0.0716901i | ||||
\(379\) | −19.6429 | −1.00899 | −0.504493 | − | 0.863416i | \(-0.668321\pi\) | ||||
−0.504493 | + | 0.863416i | \(0.668321\pi\) | |||||||
\(380\) | 8.39653 | − | 5.91548i | 0.430733 | − | 0.303458i | ||||
\(381\) | 20.3834 | 1.04427 | ||||||||
\(382\) | 0.843436 | − | 1.62594i | 0.0431539 | − | 0.0831906i | ||||
\(383\) | 18.4931 | 0.944955 | 0.472477 | − | 0.881343i | \(-0.343360\pi\) | ||||
0.472477 | + | 0.881343i | \(0.343360\pi\) | |||||||
\(384\) | 11.0697 | + | 2.33712i | 0.564897 | + | 0.119266i | ||||
\(385\) | − | 7.59878i | − | 0.387270i | ||||||
\(386\) | 0.964692 | − | 1.85970i | 0.0491015 | − | 0.0946562i | ||||
\(387\) | −11.6118 | −0.590260 | ||||||||
\(388\) | −1.38171 | + | 0.973433i | −0.0701456 | + | 0.0494186i | ||||
\(389\) | 18.5928i | 0.942690i | 0.881949 | + | 0.471345i | \(0.156231\pi\) | ||||
−0.881949 | + | 0.471345i | \(0.843769\pi\) | |||||||
\(390\) | 2.63388 | − | 5.07749i | 0.133372 | − | 0.257109i | ||||
\(391\) | 3.33518 | − | 2.29064i | 0.168668 | − | 0.115842i | ||||
\(392\) | −6.77893 | + | 0.922315i | −0.342388 | + | 0.0465839i | ||||
\(393\) | −3.33061 | −0.168007 | ||||||||
\(394\) | 9.07916 | − | 17.5025i | 0.457401 | − | 0.881762i | ||||
\(395\) | 16.2338i | 0.816811i | ||||||||
\(396\) | 4.08939 | + | 5.80455i | 0.205500 | + | 0.291690i | ||||
\(397\) | −17.8628 | −0.896510 | −0.448255 | − | 0.893906i | \(-0.647954\pi\) | ||||
−0.448255 | + | 0.893906i | \(0.647954\pi\) | |||||||
\(398\) | 3.47722 | − | 6.70326i | 0.174297 | − | 0.336004i | ||||
\(399\) | 10.9920i | 0.550286i | ||||||||
\(400\) | 1.34638 | − | 3.76660i | 0.0673189 | − | 0.188330i | ||||
\(401\) | − | 10.8994i | − | 0.544288i | −0.962257 | − | 0.272144i | \(-0.912267\pi\) | ||
0.962257 | − | 0.272144i | \(-0.0877327\pi\) | |||||||
\(402\) | 3.30123 | + | 1.71246i | 0.164650 | + | 0.0854100i | ||||
\(403\) | − | 34.0249i | − | 1.69490i | ||||||
\(404\) | −8.11701 | − | 11.5214i | −0.403837 | − | 0.573213i | ||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0.384227 | − | 0.740698i | 0.0190688 | − | 0.0367602i | ||||
\(407\) | − | 9.36736i | − | 0.464323i | ||||||
\(408\) | 2.36444 | − | 0.321697i | 0.117057 | − | 0.0159264i | ||||
\(409\) | 9.59039 | 0.474214 | 0.237107 | − | 0.971483i | \(-0.423801\pi\) | ||||
0.237107 | + | 0.971483i | \(0.423801\pi\) | |||||||
\(410\) | −9.24974 | − | 4.79817i | −0.456812 | − | 0.236965i | ||||
\(411\) | −21.9555 | −1.08299 | ||||||||
\(412\) | −15.8692 | − | 22.5250i | −0.781818 | − | 1.10973i | ||||
\(413\) | − | 6.31582i | − | 0.310781i | ||||||
\(414\) | −6.73084 | + | 0.834108i | −0.330803 | + | 0.0409942i | ||||
\(415\) | 9.45106i | 0.463934i | ||||||||
\(416\) | 15.5787 | + | 16.7570i | 0.763808 | + | 0.821578i | ||||
\(417\) | 15.4357 | 0.755887 | ||||||||
\(418\) | −11.8728 | + | 22.8880i | −0.580719 | + | 1.11949i | ||||
\(419\) | −3.49424 | −0.170705 | −0.0853525 | − | 0.996351i | \(-0.527202\pi\) | ||||
−0.0853525 | + | 0.996351i | \(0.527202\pi\) | |||||||
\(420\) | 2.46544 | + | 3.49949i | 0.120301 | + | 0.170758i | ||||
\(421\) | − | 19.9196i | − | 0.970823i | −0.874286 | − | 0.485411i | \(-0.838670\pi\) | ||
0.874286 | − | 0.485411i | \(-0.161330\pi\) | |||||||
\(422\) | −3.46612 | − | 1.79800i | −0.168728 | − | 0.0875252i | ||||
\(423\) | − | 10.4234i | − | 0.506802i | ||||||
\(424\) | −2.13604 | − | 15.6997i | −0.103735 | − | 0.762445i | ||||
\(425\) | − | 0.843658i | − | 0.0409234i | ||||||
\(426\) | −1.78030 | + | 3.43200i | −0.0862557 | + | 0.166281i | ||||
\(427\) | − | 15.1010i | − | 0.730787i | ||||||
\(428\) | 1.66698 | + | 2.36614i | 0.0805765 | + | 0.114372i | ||||
\(429\) | 14.3593i | 0.693275i | ||||||||
\(430\) | −14.5770 | − | 7.56161i | −0.702965 | − | 0.364653i | ||||
\(431\) | 1.01045 | 0.0486715 | 0.0243358 | − | 0.999704i | \(-0.492253\pi\) | ||||
0.0243358 | + | 0.999704i | \(0.492253\pi\) | |||||||
\(432\) | −3.76660 | − | 1.34638i | −0.181221 | − | 0.0647776i | ||||
\(433\) | 24.4879i | 1.17682i | 0.808564 | + | 0.588408i | \(0.200245\pi\) | ||||
−0.808564 | + | 0.588408i | \(0.799755\pi\) | |||||||
\(434\) | 22.6035 | + | 11.7252i | 1.08500 | + | 0.562829i | ||||
\(435\) | 0.275665 | 0.0132171 | ||||||||
\(436\) | 1.68259 | − | 1.18541i | 0.0805815 | − | 0.0567708i | ||||
\(437\) | −13.9436 | − | 20.3020i | −0.667012 | − | 0.971175i | ||||
\(438\) | 6.08237 | + | 3.15514i | 0.290627 | + | 0.150758i | ||||
\(439\) | 3.96239i | 0.189115i | 0.995519 | + | 0.0945573i | \(0.0301436\pi\) | ||||
−0.995519 | + | 0.0945573i | \(0.969856\pi\) | |||||||
\(440\) | 1.35374 | + | 9.94984i | 0.0645368 | + | 0.474340i | ||||
\(441\) | 2.41880 | 0.115181 | ||||||||
\(442\) | 4.28367 | + | 2.22209i | 0.203753 | + | 0.105694i | ||||
\(443\) | − | 3.21788i | − | 0.152886i | −0.997074 | − | 0.0764431i | \(-0.975644\pi\) | ||
0.997074 | − | 0.0764431i | \(-0.0243563\pi\) | |||||||
\(444\) | 3.03926 | + | 4.31398i | 0.144237 | + | 0.204732i | ||||
\(445\) | −16.0179 | −0.759319 | ||||||||
\(446\) | −9.30068 | − | 4.82459i | −0.440400 | − | 0.228451i | ||||
\(447\) | 1.22216 | 0.0578061 | ||||||||
\(448\) | −16.5006 | + | 4.57469i | −0.779579 | + | 0.216134i | ||||
\(449\) | 3.13859 | 0.148119 | 0.0740596 | − | 0.997254i | \(-0.476404\pi\) | ||||
0.0740596 | + | 0.997254i | \(0.476404\pi\) | |||||||
\(450\) | −0.651202 | + | 1.25536i | −0.0306979 | + | 0.0591784i | ||||
\(451\) | 26.1586 | 1.23176 | ||||||||
\(452\) | 18.1341 | − | 12.7757i | 0.852956 | − | 0.600920i | ||||
\(453\) | −9.64939 | −0.453368 | ||||||||
\(454\) | −7.07515 | + | 13.6392i | −0.332053 | + | 0.640120i | ||||
\(455\) | 8.65705i | 0.405849i | ||||||||
\(456\) | −1.95824 | − | 14.3929i | −0.0917028 | − | 0.674008i | ||||
\(457\) | − | 4.45089i | − | 0.208204i | −0.994567 | − | 0.104102i | \(-0.966803\pi\) | ||
0.994567 | − | 0.104102i | \(-0.0331968\pi\) | |||||||
\(458\) | −15.8634 | − | 8.22892i | −0.741248 | − | 0.384512i | ||||
\(459\) | −0.843658 | −0.0393786 | ||||||||
\(460\) | −8.99283 | − | 3.33603i | −0.419293 | − | 0.155543i | ||||
\(461\) | 18.0299 | 0.839738 | 0.419869 | − | 0.907585i | \(-0.362076\pi\) | ||||
0.419869 | + | 0.907585i | \(0.362076\pi\) | |||||||
\(462\) | −9.53923 | − | 4.94834i | −0.443805 | − | 0.230217i | ||||
\(463\) | − | 34.3361i | − | 1.59573i | −0.602835 | − | 0.797866i | \(-0.705962\pi\) | ||
0.602835 | − | 0.797866i | \(-0.294038\pi\) | |||||||
\(464\) | −0.371150 | + | 1.03832i | −0.0172302 | + | 0.0482028i | ||||
\(465\) | 8.41233i | 0.390112i | ||||||||
\(466\) | −1.39929 | + | 2.69749i | −0.0648206 | + | 0.124959i | ||||
\(467\) | −36.9009 | −1.70757 | −0.853786 | − | 0.520624i | \(-0.825699\pi\) | ||||
−0.853786 | + | 0.520624i | \(0.825699\pi\) | |||||||
\(468\) | −4.65891 | − | 6.61294i | −0.215358 | − | 0.305683i | ||||
\(469\) | −5.62854 | −0.259902 | ||||||||
\(470\) | 6.78772 | − | 13.0851i | 0.313094 | − | 0.603571i | ||||
\(471\) | 15.1421 | 0.697709 | ||||||||
\(472\) | 1.12517 | + | 8.26993i | 0.0517903 | + | 0.380654i | ||||
\(473\) | 41.2242 | 1.89549 | ||||||||
\(474\) | 20.3793 | + | 10.5715i | 0.936053 | + | 0.485564i | ||||
\(475\) | −5.13553 | −0.235634 | ||||||||
\(476\) | −2.95237 | + | 2.07999i | −0.135322 | + | 0.0953361i | ||||
\(477\) | 5.60182i | 0.256490i | ||||||||
\(478\) | 19.4639 | + | 10.0966i | 0.890260 | + | 0.461810i | ||||
\(479\) | −36.3522 | −1.66098 | −0.830488 | − | 0.557037i | \(-0.811938\pi\) | ||||
−0.830488 | + | 0.557037i | \(0.811938\pi\) | |||||||
\(480\) | −3.85169 | − | 4.14301i | −0.175805 | − | 0.189102i | ||||
\(481\) | 10.6719i | 0.486598i | ||||||||
\(482\) | −15.7674 | − | 8.17913i | −0.718187 | − | 0.372549i | ||||
\(483\) | 8.46142 | − | 5.81138i | 0.385008 | − | 0.264427i | ||||
\(484\) | −1.84759 | − | 2.62250i | −0.0839814 | − | 0.119205i | ||||
\(485\) | 0.845087 | 0.0383734 | ||||||||
\(486\) | 1.25536 | + | 0.651202i | 0.0569444 | + | 0.0295391i | ||||
\(487\) | − | 4.53486i | − | 0.205494i | −0.994708 | − | 0.102747i | \(-0.967237\pi\) | ||
0.994708 | − | 0.102747i | \(-0.0327632\pi\) | |||||||
\(488\) | 2.69027 | + | 19.7732i | 0.121783 | + | 0.895091i | ||||
\(489\) | 6.70557 | 0.303236 | ||||||||
\(490\) | 3.03647 | + | 1.57512i | 0.137174 | + | 0.0711569i | ||||
\(491\) | − | 13.4429i | − | 0.606670i | −0.952884 | − | 0.303335i | \(-0.901900\pi\) | ||
0.952884 | − | 0.303335i | \(-0.0981001\pi\) | |||||||
\(492\) | −12.0469 | + | 8.48721i | −0.543116 | + | 0.382633i | ||||
\(493\) | 0.232567i | 0.0104743i | ||||||||
\(494\) | 13.5263 | − | 26.0756i | 0.608579 | − | 1.17320i | ||||
\(495\) | − | 3.55021i | − | 0.159570i | ||||||
\(496\) | −31.6859 | − | 11.3262i | −1.42274 | − | 0.508560i | ||||
\(497\) | − | 5.85150i | − | 0.262476i | ||||||
\(498\) | 11.8645 | + | 6.15454i | 0.531661 | + | 0.275792i | ||||
\(499\) | 25.2907i | 1.13217i | 0.824347 | + | 0.566084i | \(0.191542\pi\) | ||||
−0.824347 | + | 0.566084i | \(0.808458\pi\) | |||||||
\(500\) | −1.63499 | + | 1.15187i | −0.0731189 | + | 0.0515133i | ||||
\(501\) | −22.2534 | −0.994208 | ||||||||
\(502\) | −16.0805 | + | 30.9994i | −0.717708 | + | 1.38357i | ||||
\(503\) | 37.8035 | 1.68557 | 0.842787 | − | 0.538247i | \(-0.180913\pi\) | ||||
0.842787 | + | 0.538247i | \(0.180913\pi\) | |||||||
\(504\) | 5.99863 | − | 0.816150i | 0.267200 | − | 0.0363542i | ||||
\(505\) | 7.04680i | 0.313578i | ||||||||
\(506\) | 23.8959 | − | 2.96126i | 1.06230 | − | 0.131644i | ||||
\(507\) | − | 3.35912i | − | 0.149184i | ||||||
\(508\) | 33.3266 | − | 23.4791i | 1.47863 | − | 1.04171i | ||||
\(509\) | −10.9894 | −0.487096 | −0.243548 | − | 0.969889i | \(-0.578311\pi\) | ||||
−0.243548 | + | 0.969889i | \(0.578311\pi\) | |||||||
\(510\) | −1.05910 | − | 0.549392i | −0.0468976 | − | 0.0243275i | ||||
\(511\) | −10.3703 | −0.458757 | ||||||||
\(512\) | 20.7909 | − | 8.92971i | 0.918835 | − | 0.394641i | ||||
\(513\) | 5.13553i | 0.226739i | ||||||||
\(514\) | 18.9078 | − | 36.4497i | 0.833985 | − | 1.60773i | ||||
\(515\) | 13.7768i | 0.607080i | ||||||||
\(516\) | −18.9851 | + | 13.3753i | −0.835773 | + | 0.588814i | ||||
\(517\) | 37.0052i | 1.62748i | ||||||||
\(518\) | −7.08961 | − | 3.67763i | −0.311500 | − | 0.161586i | ||||
\(519\) | 20.8806i | 0.916558i | ||||||||
\(520\) | −1.54227 | − | 11.3355i | −0.0676329 | − | 0.497096i | ||||
\(521\) | − | 28.5407i | − | 1.25039i | −0.780469 | − | 0.625195i | \(-0.785019\pi\) | ||
0.780469 | − | 0.625195i | \(-0.214981\pi\) | |||||||
\(522\) | 0.179514 | − | 0.346060i | 0.00785710 | − | 0.0151466i | ||||
\(523\) | −14.6277 | −0.639625 | −0.319813 | − | 0.947481i | \(-0.603620\pi\) | ||||
−0.319813 | + | 0.947481i | \(0.603620\pi\) | |||||||
\(524\) | −5.44551 | + | 3.83644i | −0.237888 | + | 0.167596i | ||||
\(525\) | − | 2.14037i | − | 0.0934136i | ||||||
\(526\) | 16.3393 | − | 31.4983i | 0.712427 | − | 1.37339i | ||||
\(527\) | −7.09713 | −0.309156 | ||||||||
\(528\) | 13.3722 | + | 4.77992i | 0.581951 | + | 0.208019i | ||||
\(529\) | −8.25622 | + | 21.4671i | −0.358966 | + | 0.933351i | ||||
\(530\) | −3.64792 | + | 7.03232i | −0.158455 | + | 0.305465i | ||||
\(531\) | − | 2.95080i | − | 0.128054i | ||||||
\(532\) | 12.6613 | + | 17.9717i | 0.548938 | + | 0.779173i | ||||
\(533\) | −29.8017 | −1.29085 | ||||||||
\(534\) | −10.4309 | + | 20.1082i | −0.451387 | + | 0.870168i | ||||
\(535\) | − | 1.44719i | − | 0.0625675i | ||||||
\(536\) | 7.37001 | − | 1.00273i | 0.318336 | − | 0.0433115i | ||||
\(537\) | −11.9933 | −0.517548 | ||||||||
\(538\) | −10.3270 | + | 19.9080i | −0.445227 | + | 0.858294i | ||||
\(539\) | −8.58724 | −0.369878 | ||||||||
\(540\) | 1.15187 | + | 1.63499i | 0.0495687 | + | 0.0703587i | ||||
\(541\) | −41.9847 | −1.80506 | −0.902532 | − | 0.430623i | \(-0.858294\pi\) | ||||
−0.902532 | + | 0.430623i | \(0.858294\pi\) | |||||||
\(542\) | 24.1210 | + | 12.5124i | 1.03608 | + | 0.537453i | ||||
\(543\) | −11.8382 | −0.508026 | ||||||||
\(544\) | 3.49528 | − | 3.24951i | 0.149859 | − | 0.139321i | ||||
\(545\) | −1.02911 | −0.0440824 | ||||||||
\(546\) | 10.8677 | + | 5.63748i | 0.465096 | + | 0.241262i | ||||
\(547\) | 33.7583i | 1.44340i | 0.692206 | + | 0.721700i | \(0.256639\pi\) | ||||
−0.692206 | + | 0.721700i | \(0.743361\pi\) | |||||||
\(548\) | −35.8970 | + | 25.2900i | −1.53344 | + | 1.08033i | ||||
\(549\) | − | 7.05529i | − | 0.301113i | ||||||
\(550\) | 2.31190 | − | 4.45680i | 0.0985798 | − | 0.190039i | ||||
\(551\) | 1.41569 | 0.0603103 | ||||||||
\(552\) | −10.0441 | + | 9.11684i | −0.427504 | + | 0.388038i | ||||
\(553\) | −34.7464 | −1.47757 | ||||||||
\(554\) | −1.51511 | + | 2.92078i | −0.0643710 | + | 0.124092i | ||||
\(555\) | − | 2.63854i | − | 0.112000i | ||||||
\(556\) | 25.2371 | − | 17.7799i | 1.07029 | − | 0.754037i | ||||
\(557\) | 16.9360i | 0.717602i | 0.933414 | + | 0.358801i | \(0.116814\pi\) | ||||
−0.933414 | + | 0.358801i | \(0.883186\pi\) | |||||||
\(558\) | 10.5605 | + | 5.47812i | 0.447063 | + | 0.231907i | ||||
\(559\) | −46.9655 | −1.98643 | ||||||||
\(560\) | 8.06193 | + | 2.88175i | 0.340679 | + | 0.121776i | ||||
\(561\) | 2.99516 | 0.126456 | ||||||||
\(562\) | 3.07137 | + | 1.59323i | 0.129558 | + | 0.0672062i | ||||
\(563\) | −1.63299 | −0.0688224 | −0.0344112 | − | 0.999408i | \(-0.510956\pi\) | ||||
−0.0344112 | + | 0.999408i | \(0.510956\pi\) | |||||||
\(564\) | −12.0064 | − | 17.0421i | −0.505561 | − | 0.717602i | ||||
\(565\) | −11.0913 | −0.466613 | ||||||||
\(566\) | 6.18389 | − | 11.9211i | 0.259928 | − | 0.501081i | ||||
\(567\) | −2.14037 | −0.0898873 | ||||||||
\(568\) | 1.04246 | + | 7.66195i | 0.0437404 | + | 0.321488i | ||||
\(569\) | 13.7080i | 0.574669i | 0.957830 | + | 0.287334i | \(0.0927691\pi\) | ||||
−0.957830 | + | 0.287334i | \(0.907231\pi\) | |||||||
\(570\) | −3.34426 | + | 6.44695i | −0.140076 | + | 0.270033i | ||||
\(571\) | −47.0402 | −1.96857 | −0.984285 | − | 0.176585i | \(-0.943495\pi\) | ||||
−0.984285 | + | 0.176585i | \(0.943495\pi\) | |||||||
\(572\) | 16.5401 | + | 23.4773i | 0.691577 | + | 0.981637i | ||||
\(573\) | 1.29520i | 0.0541077i | ||||||||
\(574\) | 10.2699 | − | 19.7979i | 0.428657 | − | 0.826349i | ||||
\(575\) | 2.71512 | + | 3.95324i | 0.113228 | + | 0.164862i | ||||
\(576\) | −7.70920 | + | 2.13733i | −0.321217 | + | 0.0890555i | ||||
\(577\) | −3.09943 | −0.129031 | −0.0645154 | − | 0.997917i | \(-0.520550\pi\) | ||||
−0.0645154 | + | 0.997917i | \(0.520550\pi\) | |||||||
\(578\) | −10.6069 | + | 20.4477i | −0.441190 | + | 0.850510i | ||||
\(579\) | 1.48140i | 0.0615650i | ||||||||
\(580\) | 0.450710 | − | 0.317532i | 0.0187147 | − | 0.0131848i | ||||
\(581\) | −20.2288 | −0.839232 | ||||||||
\(582\) | 0.550322 | − | 1.06089i | 0.0228116 | − | 0.0439753i | ||||
\(583\) | − | 19.8877i | − | 0.823662i | ||||||
\(584\) | 13.5789 | − | 1.84749i | 0.561900 | − | 0.0764499i | ||||
\(585\) | 4.04464i | 0.167225i | ||||||||
\(586\) | 20.1955 | + | 10.4761i | 0.834270 | + | 0.432766i | ||||
\(587\) | 21.9788i | 0.907160i | 0.891215 | + | 0.453580i | \(0.149853\pi\) | ||||
−0.891215 | + | 0.453580i | \(0.850147\pi\) | |||||||
\(588\) | 3.95471 | − | 2.78615i | 0.163089 | − | 0.114899i | ||||
\(589\) | 43.2018i | 1.78010i | ||||||||
\(590\) | 1.92157 | − | 3.70433i | 0.0791096 | − | 0.152505i | ||||
\(591\) | 13.9422i | 0.573504i | ||||||||
\(592\) | 9.93831 | + | 3.55247i | 0.408462 | + | 0.146005i | ||||
\(593\) | −31.2493 | −1.28326 | −0.641628 | − | 0.767016i | \(-0.721741\pi\) | ||||
−0.641628 | + | 0.767016i | \(0.721741\pi\) | |||||||
\(594\) | −4.45680 | − | 2.31190i | −0.182865 | − | 0.0948585i | ||||
\(595\) | 1.80574 | 0.0740283 | ||||||||
\(596\) | 1.99821 | − | 1.40777i | 0.0818500 | − | 0.0576645i | ||||
\(597\) | 5.33970i | 0.218539i | ||||||||
\(598\) | −27.2238 | + | 3.37367i | −1.11327 | + | 0.137960i | ||||
\(599\) | − | 19.4722i | − | 0.795614i | −0.917469 | − | 0.397807i | \(-0.869771\pi\) | ||
0.917469 | − | 0.397807i | \(-0.130229\pi\) | |||||||
\(600\) | 0.381312 | + | 2.80261i | 0.0155670 | + | 0.114416i | ||||
\(601\) | −27.7862 | −1.13342 | −0.566711 | − | 0.823917i | \(-0.691784\pi\) | ||||
−0.566711 | + | 0.823917i | \(0.691784\pi\) | |||||||
\(602\) | 16.1847 | − | 31.2002i | 0.659638 | − | 1.27163i | ||||
\(603\) | −2.62970 | −0.107090 | ||||||||
\(604\) | −15.7766 | + | 11.1149i | −0.641943 | + | 0.452258i | ||||
\(605\) | 1.60399i | 0.0652114i | ||||||||
\(606\) | 8.84629 | + | 4.58889i | 0.359356 | + | 0.186411i | ||||
\(607\) | 28.1233i | 1.14149i | 0.821127 | + | 0.570745i | \(0.193346\pi\) | ||||
−0.821127 | + | 0.570745i | \(0.806654\pi\) | |||||||
\(608\) | −19.7804 | − | 21.2765i | −0.802203 | − | 0.862877i | ||||
\(609\) | 0.590027i | 0.0239091i | ||||||||
\(610\) | 4.59442 | − | 8.85696i | 0.186023 | − | 0.358608i | ||||
\(611\) | − | 42.1588i | − | 1.70556i | ||||||
\(612\) | −1.37937 | + | 0.971787i | −0.0557578 | + | 0.0392822i | ||||
\(613\) | 23.6788i | 0.956378i | 0.878257 | + | 0.478189i | \(0.158707\pi\) | ||||
−0.878257 | + | 0.478189i | \(0.841293\pi\) | |||||||
\(614\) | 1.37525 | + | 0.713391i | 0.0555006 | + | 0.0287901i | ||||
\(615\) | 7.36818 | 0.297114 | ||||||||
\(616\) | −21.2964 | + | 2.89750i | −0.858056 | + | 0.116744i | ||||
\(617\) | − | 0.878056i | − | 0.0353492i | −0.999844 | − | 0.0176746i | \(-0.994374\pi\) | ||
0.999844 | − | 0.0176746i | \(-0.00562629\pi\) | |||||||
\(618\) | 17.2949 | + | 8.97150i | 0.695705 | + | 0.360887i | ||||
\(619\) | 4.28788 | 0.172344 | 0.0861722 | − | 0.996280i | \(-0.472536\pi\) | ||||
0.0861722 | + | 0.996280i | \(0.472536\pi\) | |||||||
\(620\) | 9.68994 | + | 13.7541i | 0.389157 | + | 0.552377i | ||||
\(621\) | 3.95324 | − | 2.71512i | 0.158638 | − | 0.108954i | ||||
\(622\) | 41.4807 | + | 21.5175i | 1.66322 | + | 0.862773i | ||||
\(623\) | − | 34.2842i | − | 1.37357i | ||||||
\(624\) | −15.2345 | − | 5.44561i | −0.609870 | − | 0.217999i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 22.1091 | + | 11.4688i | 0.883656 | + | 0.458384i | ||||
\(627\) | − | 18.2322i | − | 0.728124i | ||||||
\(628\) | 24.7571 | − | 17.4417i | 0.987916 | − | 0.696001i | ||||
\(629\) | 2.22602 | 0.0887574 | ||||||||
\(630\) | −2.68695 | − | 1.39382i | −0.107051 | − | 0.0555309i | ||||
\(631\) | 39.9346 | 1.58977 | 0.794886 | − | 0.606759i | \(-0.207531\pi\) | ||||
0.794886 | + | 0.606759i | \(0.207531\pi\) | |||||||
\(632\) | 45.4969 | − | 6.19014i | 1.80977 | − | 0.246230i | ||||
\(633\) | 2.76105 | 0.109742 | ||||||||
\(634\) | −7.79289 | + | 15.0228i | −0.309495 | + | 0.596633i | ||||
\(635\) | −20.3834 | −0.808890 | ||||||||
\(636\) | 6.45259 | + | 9.15892i | 0.255862 | + | 0.363175i | ||||
\(637\) | 9.78316 | 0.387623 | ||||||||
\(638\) | −0.637311 | + | 1.22859i | −0.0252314 | + | 0.0486402i | ||||
\(639\) | − | 2.73387i | − | 0.108150i | ||||||
\(640\) | −11.0697 | − | 2.33712i | −0.437568 | − | 0.0923827i | ||||
\(641\) | − | 20.1012i | − | 0.793951i | −0.917829 | − | 0.396976i | \(-0.870060\pi\) | ||
0.917829 | − | 0.396976i | \(-0.129940\pi\) | |||||||
\(642\) | −1.81675 | − | 0.942413i | −0.0717014 | − | 0.0371941i | ||||
\(643\) | 16.2281 | 0.639976 | 0.319988 | − | 0.947422i | \(-0.396321\pi\) | ||||
0.319988 | + | 0.947422i | \(0.396321\pi\) | |||||||
\(644\) | 7.14035 | − | 19.2480i | 0.281369 | − | 0.758478i | ||||
\(645\) | 11.6118 | 0.457213 | ||||||||
\(646\) | −5.43902 | − | 2.82142i | −0.213996 | − | 0.111007i | ||||
\(647\) | 14.3994i | 0.566100i | 0.959105 | + | 0.283050i | \(0.0913462\pi\) | ||||
−0.959105 | + | 0.283050i | \(0.908654\pi\) | |||||||
\(648\) | 2.80261 | − | 0.381312i | 0.110097 | − | 0.0149793i | ||||
\(649\) | 10.4760i | 0.411217i | ||||||||
\(650\) | −2.63388 | + | 5.07749i | −0.103309 | + | 0.199156i | ||||
\(651\) | −18.0055 | −0.705693 | ||||||||
\(652\) | 10.9635 | − | 7.72396i | 0.429365 | − | 0.302494i | ||||
\(653\) | −8.13213 | −0.318235 | −0.159118 | − | 0.987260i | \(-0.550865\pi\) | ||||
−0.159118 | + | 0.987260i | \(0.550865\pi\) | |||||||
\(654\) | −0.670161 | + | 1.29191i | −0.0262054 | + | 0.0505178i | ||||
\(655\) | 3.33061 | 0.130138 | ||||||||
\(656\) | −9.92035 | + | 27.7530i | −0.387325 | + | 1.08357i | ||||
\(657\) | −4.84511 | −0.189026 | ||||||||
\(658\) | 28.0070 | + | 14.5283i | 1.09183 | + | 0.566370i | ||||
\(659\) | 50.0704 | 1.95046 | 0.975232 | − | 0.221183i | \(-0.0709919\pi\) | ||||
0.975232 | + | 0.221183i | \(0.0709919\pi\) | |||||||
\(660\) | −4.08939 | − | 5.80455i | −0.159179 | − | 0.225942i | ||||
\(661\) | − | 34.2686i | − | 1.33290i | −0.745552 | − | 0.666448i | \(-0.767814\pi\) | ||
0.745552 | − | 0.666448i | \(-0.232186\pi\) | |||||||
\(662\) | 6.73041 | + | 3.49130i | 0.261585 | + | 0.135693i | ||||
\(663\) | −3.41229 | −0.132523 | ||||||||
\(664\) | 26.4876 | − | 3.60380i | 1.02792 | − | 0.139854i | ||||
\(665\) | − | 10.9920i | − | 0.426250i | ||||||
\(666\) | −3.31232 | − | 1.71822i | −0.128350 | − | 0.0665796i | ||||
\(667\) | −0.748465 | − | 1.08977i | −0.0289807 | − | 0.0421961i | ||||
\(668\) | −36.3841 | + | 25.6331i | −1.40774 | + | 0.991774i | ||||
\(669\) | 7.40876 | 0.286439 | ||||||||
\(670\) | −3.30123 | − | 1.71246i | −0.127538 | − | 0.0661583i | ||||
\(671\) | 25.0478i | 0.966959i | ||||||||
\(672\) | 8.86759 | − | 8.24405i | 0.342075 | − | 0.318021i | ||||
\(673\) | −15.3372 | −0.591205 | −0.295602 | − | 0.955311i | \(-0.595520\pi\) | ||||
−0.295602 | + | 0.955311i | \(0.595520\pi\) | |||||||
\(674\) | −22.7576 | − | 11.8052i | −0.876591 | − | 0.454719i | ||||
\(675\) | − | 1.00000i | − | 0.0384900i | ||||||
\(676\) | −3.86928 | − | 5.49212i | −0.148818 | − | 0.211236i | ||||
\(677\) | 22.2137i | 0.853742i | 0.904312 | + | 0.426871i | \(0.140384\pi\) | ||||
−0.904312 | + | 0.426871i | \(0.859616\pi\) | |||||||
\(678\) | −7.22265 | + | 13.9236i | −0.277384 | + | 0.534731i | ||||
\(679\) | 1.80880i | 0.0694155i | ||||||||
\(680\) | −2.36444 | + | 0.321697i | −0.0906722 | + | 0.0123365i | ||||
\(681\) | − | 10.8648i | − | 0.416338i | ||||||
\(682\) | −37.4921 | − | 19.4485i | −1.43565 | − | 0.744721i | ||||
\(683\) | − | 5.94111i | − | 0.227330i | −0.993519 | − | 0.113665i | \(-0.963741\pi\) | ||
0.993519 | − | 0.113665i | \(-0.0362591\pi\) | |||||||
\(684\) | 5.91548 | + | 8.39653i | 0.226184 | + | 0.321049i | ||||
\(685\) | 21.9555 | 0.838877 | ||||||||
\(686\) | −13.1281 | + | 25.3078i | −0.501232 | + | 0.966257i | ||||
\(687\) | 12.6365 | 0.482113 | ||||||||
\(688\) | −15.6338 | + | 43.7369i | −0.596034 | + | 1.66745i | ||||
\(689\) | 22.6574i | 0.863177i | ||||||||
\(690\) | 6.73084 | − | 0.834108i | 0.256239 | − | 0.0317539i | ||||
\(691\) | 0.937628i | 0.0356690i | 0.999841 | + | 0.0178345i | \(0.00567721\pi\) | ||||
−0.999841 | + | 0.0178345i | \(0.994323\pi\) | |||||||
\(692\) | 24.0518 | + | 34.1396i | 0.914313 | + | 1.29779i | ||||
\(693\) | 7.59878 | 0.288654 | ||||||||
\(694\) | −8.48814 | − | 4.40310i | −0.322205 | − | 0.167139i | ||||
\(695\) | −15.4357 | −0.585508 | ||||||||
\(696\) | −0.105114 | − | 0.772582i | −0.00398435 | − | 0.0292846i | ||||
\(697\) | 6.21623i | 0.235456i | ||||||||
\(698\) | −23.3817 | + | 45.0744i | −0.885010 | + | 1.70609i | ||||
\(699\) | − | 2.14877i | − | 0.0812741i | ||||||
\(700\) | −2.46544 | − | 3.49949i | −0.0931849 | − | 0.132268i | ||||
\(701\) | 36.2643i | 1.36968i | 0.728692 | + | 0.684842i | \(0.240129\pi\) | ||||
−0.728692 | + | 0.684842i | \(0.759871\pi\) | |||||||
\(702\) | 5.07749 | + | 2.63388i | 0.191638 | + | 0.0994093i | ||||
\(703\) | − | 13.5503i | − | 0.511058i | ||||||
\(704\) | 27.3693 | − | 7.58798i | 1.03152 | − | 0.285983i | ||||
\(705\) | 10.4234i | 0.392567i | ||||||||
\(706\) | −12.7302 | + | 24.5409i | −0.479109 | + | 0.923610i | ||||
\(707\) | −15.0828 | −0.567246 | ||||||||
\(708\) | −3.39895 | − | 4.82453i | −0.127740 | − | 0.181317i | ||||
\(709\) | 45.9613i | 1.72611i | 0.505107 | + | 0.863057i | \(0.331453\pi\) | ||||
−0.505107 | + | 0.863057i | \(0.668547\pi\) | |||||||
\(710\) | 1.78030 | − | 3.43200i | 0.0668134 | − | 0.128801i | ||||
\(711\) | −16.2338 | −0.608815 | ||||||||
\(712\) | 6.10779 | + | 44.8917i | 0.228899 | + | 1.68239i | ||||
\(713\) | 33.2560 | − | 22.8405i | 1.24545 | − | 0.855384i | ||||
\(714\) | 1.17590 | − | 2.26687i | 0.0440071 | − | 0.0848353i | ||||
\(715\) | − | 14.3593i | − | 0.537008i | ||||||
\(716\) | −19.6089 | + | 13.8147i | −0.732818 | + | 0.516281i | ||||
\(717\) | −15.5046 | −0.579031 | ||||||||
\(718\) | 18.4941 | − | 35.6522i | 0.690193 | − | 1.33053i | ||||
\(719\) | 26.7657i | 0.998193i | 0.866546 | + | 0.499097i | \(0.166335\pi\) | ||||
−0.866546 | + | 0.499097i | \(0.833665\pi\) | |||||||
\(720\) | 3.76660 | + | 1.34638i | 0.140373 | + | 0.0501765i | ||||
\(721\) | −29.4876 | −1.09818 | ||||||||
\(722\) | −4.80173 | + | 9.25660i | −0.178702 | + | 0.344495i | ||||
\(723\) | 12.5601 | 0.467114 | ||||||||
\(724\) | −19.3553 | + | 13.6361i | −0.719336 | + | 0.506782i | ||||
\(725\) | −0.275665 | −0.0102380 | ||||||||
\(726\) | 2.01359 | + | 1.04452i | 0.0747313 | + | 0.0387658i | ||||
\(727\) | 11.7279 | 0.434963 | 0.217482 | − | 0.976064i | \(-0.430216\pi\) | ||||
0.217482 | + | 0.976064i | \(0.430216\pi\) | |||||||
\(728\) | 24.2623 | − | 3.30103i | 0.899220 | − | 0.122344i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −6.08237 | − | 3.15514i | −0.225118 | − | 0.116777i | ||||
\(731\) | 9.79637i | 0.362332i | ||||||||
\(732\) | −8.12680 | − | 11.5353i | −0.300375 | − | 0.426358i | ||||
\(733\) | − | 10.5869i | − | 0.391036i | −0.980700 | − | 0.195518i | \(-0.937361\pi\) | ||
0.980700 | − | 0.195518i | \(-0.0626389\pi\) | |||||||
\(734\) | −11.3105 | + | 21.8040i | −0.417479 | + | 0.804801i | ||||
\(735\) | −2.41880 | −0.0892187 | ||||||||
\(736\) | −5.92050 | + | 26.4754i | −0.218233 | + | 0.975897i | ||||
\(737\) | 9.33598 | 0.343895 | ||||||||
\(738\) | 4.79817 | − | 9.24974i | 0.176623 | − | 0.340488i | ||||
\(739\) | − | 0.174301i | − | 0.00641178i | −0.999995 | − | 0.00320589i | \(-0.998980\pi\) | ||
0.999995 | − | 0.00320589i | \(-0.00102047\pi\) | |||||||
\(740\) | −3.03926 | − | 4.31398i | −0.111725 | − | 0.158585i | ||||
\(741\) | 20.7714i | 0.763055i | ||||||||
\(742\) | −15.0518 | − | 7.80791i | −0.552569 | − | 0.286637i | ||||
\(743\) | −14.7068 | −0.539540 | −0.269770 | − | 0.962925i | \(-0.586948\pi\) | ||||
−0.269770 | + | 0.962925i | \(0.586948\pi\) | |||||||
\(744\) | 23.5764 | − | 3.20772i | 0.864355 | − | 0.117601i | ||||
\(745\) | −1.22216 | −0.0447764 | ||||||||
\(746\) | −20.6006 | − | 10.6863i | −0.754243 | − | 0.391253i | ||||
\(747\) | −9.45106 | −0.345796 | ||||||||
\(748\) | 4.89706 | − | 3.45005i | 0.179054 | − | 0.126146i | ||||
\(749\) | 3.09753 | 0.113181 | ||||||||
\(750\) | 0.651202 | − | 1.25536i | 0.0237785 | − | 0.0458394i | ||||
\(751\) | 26.8301 | 0.979043 | 0.489522 | − | 0.871991i | \(-0.337171\pi\) | ||||
0.489522 | + | 0.871991i | \(0.337171\pi\) | |||||||
\(752\) | −39.2607 | − | 14.0338i | −1.43169 | − | 0.511760i | ||||
\(753\) | − | 24.6936i | − | 0.899885i | ||||||
\(754\) | 0.726069 | − | 1.39969i | 0.0264419 | − | 0.0509737i | ||||
\(755\) | 9.64939 | 0.351177 | ||||||||
\(756\) | −3.49949 | + | 2.46544i | −0.127275 | + | 0.0896672i | ||||
\(757\) | 54.6358i | 1.98577i | 0.119070 | + | 0.992886i | \(0.462009\pi\) | ||||
−0.119070 | + | 0.992886i | \(0.537991\pi\) | |||||||
\(758\) | 12.7915 | − | 24.6589i | 0.464607 | − | 0.895653i | ||||
\(759\) | −14.0348 | + | 9.63925i | −0.509432 | + | 0.349883i | ||||
\(760\) | 1.95824 | + | 14.3929i | 0.0710327 | + | 0.522084i | ||||
\(761\) | 31.9653 | 1.15874 | 0.579370 | − | 0.815064i | \(-0.303299\pi\) | ||||
0.579370 | + | 0.815064i | \(0.303299\pi\) | |||||||
\(762\) | −13.2737 | + | 25.5885i | −0.480855 | + | 0.926975i | ||||
\(763\) | − | 2.20269i | − | 0.0797427i | ||||||
\(764\) | 1.49190 | + | 2.11764i | 0.0539752 | + | 0.0766134i | ||||
\(765\) | 0.843658 | 0.0305025 | ||||||||
\(766\) | −12.0428 | + | 23.2156i | −0.435122 | + | 0.838813i | ||||
\(767\) | − | 11.9349i | − | 0.430945i | ||||||
\(768\) | −10.1425 | + | 12.3745i | −0.365987 | + | 0.446528i | ||||
\(769\) | 4.34029i | 0.156515i | 0.996933 | + | 0.0782574i | \(0.0249356\pi\) | ||||
−0.996933 | + | 0.0782574i | \(0.975064\pi\) | |||||||
\(770\) | 9.53923 | + | 4.94834i | 0.343770 | + | 0.178326i | ||||
\(771\) | 29.0352i | 1.04568i | ||||||||
\(772\) | 1.70639 | + | 2.42208i | 0.0614142 | + | 0.0871725i | ||||
\(773\) | − | 0.809691i | − | 0.0291226i | −0.999894 | − | 0.0145613i | \(-0.995365\pi\) | ||
0.999894 | − | 0.0145613i | \(-0.00463516\pi\) | |||||||
\(774\) | 7.56161 | − | 14.5770i | 0.271796 | − | 0.523959i | ||||
\(775\) | − | 8.41233i | − | 0.302180i | ||||||
\(776\) | −0.322241 | − | 2.36845i | −0.0115678 | − | 0.0850222i | ||||
\(777\) | 5.64746 | 0.202601 | ||||||||
\(778\) | −23.3407 | − | 12.1076i | −0.836803 | − | 0.434080i | ||||
\(779\) | 37.8395 | 1.35574 | ||||||||
\(780\) | 4.65891 | + | 6.61294i | 0.166816 | + | 0.236781i | ||||
\(781\) | 9.70580i | 0.347301i | ||||||||
\(782\) | 0.703702 | + | 5.67853i | 0.0251643 | + | 0.203064i | ||||
\(783\) | 0.275665i | 0.00985148i | ||||||||
\(784\) | 3.25661 | − | 9.11064i | 0.116308 | − | 0.325380i | ||||
\(785\) | −15.1421 | −0.540443 | ||||||||
\(786\) | 2.16890 | − | 4.18113i | 0.0773621 | − | 0.149136i | ||||
\(787\) | −30.8746 | −1.10056 | −0.550280 | − | 0.834980i | \(-0.685479\pi\) | ||||
−0.550280 | + | 0.834980i | \(0.685479\pi\) | |||||||
\(788\) | 16.0596 | + | 22.7953i | 0.572100 | + | 0.812048i | ||||
\(789\) | 25.0910i | 0.893263i | ||||||||
\(790\) | −20.3793 | − | 10.5715i | −0.725063 | − | 0.376116i | ||||
\(791\) | − | 23.7395i | − | 0.844078i | ||||||
\(792\) | −9.94984 | + | 1.35374i | −0.353552 | + | 0.0481029i | ||||
\(793\) | − | 28.5361i | − | 1.01335i | ||||||
\(794\) | 11.6323 | − | 22.4243i | 0.412815 | − | 0.795810i | ||||
\(795\) | − | 5.60182i | − | 0.198676i | ||||||
\(796\) | 6.15065 | + | 8.73034i | 0.218004 | + | 0.309439i | ||||
\(797\) | − | 39.2460i | − | 1.39016i | −0.718931 | − | 0.695082i | \(-0.755368\pi\) | ||
0.718931 | − | 0.695082i | \(-0.244632\pi\) | |||||||
\(798\) | −13.7989 | − | 7.15798i | −0.488475 | − | 0.253390i | ||||
\(799\) | −8.79376 | −0.311101 | ||||||||
\(800\) | 3.85169 | + | 4.14301i | 0.136178 | + | 0.146477i | ||||
\(801\) | − | 16.0179i | − | 0.565963i | ||||||
\(802\) | 13.6826 | + | 7.09768i | 0.483151 | + | 0.250628i | ||||
\(803\) | 17.2011 | 0.607015 | ||||||||
\(804\) | −4.29953 | + | 3.02908i | −0.151633 | + | 0.106827i | ||||
\(805\) | −8.46142 | + | 5.81138i | −0.298226 | + | 0.204824i | ||||
\(806\) | 42.7135 | + | 22.1570i | 1.50452 | + | 0.780448i | ||||
\(807\) | − | 15.8583i | − | 0.558240i | ||||||
\(808\) | 19.7494 | − | 2.68702i | 0.694781 | − | 0.0945292i | ||||
\(809\) | 41.1210 | 1.44574 | 0.722869 | − | 0.690985i | \(-0.242823\pi\) | ||||
0.722869 | + | 0.690985i | \(0.242823\pi\) | |||||||
\(810\) | −1.25536 | − | 0.651202i | −0.0441090 | − | 0.0228809i | ||||
\(811\) | − | 25.9894i | − | 0.912610i | −0.889823 | − | 0.456305i | \(-0.849173\pi\) | ||
0.889823 | − | 0.456305i | \(-0.150827\pi\) | |||||||
\(812\) | 0.679636 | + | 0.964688i | 0.0238506 | + | 0.0338539i | ||||
\(813\) | −19.2143 | −0.673876 | ||||||||
\(814\) | 11.7594 | + | 6.10004i | 0.412168 | + | 0.213806i | ||||
\(815\) | −6.70557 | −0.234886 | ||||||||
\(816\) | −1.13588 | + | 3.17772i | −0.0397638 | + | 0.111243i | ||||
\(817\) | 59.6326 | 2.08628 | ||||||||
\(818\) | −6.24528 | + | 12.0394i | −0.218361 | + | 0.420949i | ||||
\(819\) | −8.65705 | −0.302502 | ||||||||
\(820\) | 12.0469 | − | 8.48721i | 0.420696 | − | 0.296386i | ||||
\(821\) | −27.7229 | −0.967537 | −0.483769 | − | 0.875196i | \(-0.660732\pi\) | ||||
−0.483769 | + | 0.875196i | \(0.660732\pi\) | |||||||
\(822\) | 14.2975 | − | 27.5621i | 0.498681 | − | 0.961340i | ||||
\(823\) | 1.31299i | 0.0457679i | 0.999738 | + | 0.0228840i | \(0.00728483\pi\) | ||||
−0.999738 | + | 0.0228840i | \(0.992715\pi\) | |||||||
\(824\) | 38.6111 | − | 5.25327i | 1.34508 | − | 0.183006i | ||||
\(825\) | 3.55021i | 0.123602i | ||||||||
\(826\) | 7.92865 | + | 4.11287i | 0.275873 | + | 0.143105i | ||||
\(827\) | 41.1400 | 1.43058 | 0.715288 | − | 0.698830i | \(-0.246295\pi\) | ||||
0.715288 | + | 0.698830i | \(0.246295\pi\) | |||||||
\(828\) | 3.33603 | − | 8.99283i | 0.115935 | − | 0.312522i | ||||
\(829\) | −43.5731 | −1.51336 | −0.756678 | − | 0.653788i | \(-0.773179\pi\) | ||||
−0.756678 | + | 0.653788i | \(0.773179\pi\) | |||||||
\(830\) | −11.8645 | − | 6.15454i | −0.411823 | − | 0.213627i | ||||
\(831\) | − | 2.32664i | − | 0.0807104i | ||||||
\(832\) | −31.1810 | + | 8.64474i | −1.08101 | + | 0.299702i | ||||
\(833\) | − | 2.04064i | − | 0.0707039i | ||||||
\(834\) | −10.0517 | + | 19.3774i | −0.348063 | + | 0.670983i | ||||
\(835\) | 22.2534 | 0.770110 | ||||||||
\(836\) | −21.0012 | − | 29.8094i | −0.726341 | − | 1.03098i | ||||
\(837\) | −8.41233 | −0.290773 | ||||||||
\(838\) | 2.27546 | − | 4.38654i | 0.0786043 | − | 0.151531i | ||||
\(839\) | 24.5721 | 0.848323 | 0.424162 | − | 0.905586i | \(-0.360569\pi\) | ||||
0.424162 | + | 0.905586i | \(0.360569\pi\) | |||||||
\(840\) | −5.99863 | + | 0.816150i | −0.206972 | + | 0.0281598i | ||||
\(841\) | −28.9240 | −0.997380 | ||||||||
\(842\) | 25.0064 | + | 12.9717i | 0.861776 | + | 0.447034i | ||||
\(843\) | −2.44660 | −0.0842652 | ||||||||
\(844\) | 4.51428 | − | 3.18038i | 0.155388 | − | 0.109473i | ||||
\(845\) | 3.35912i | 0.115557i | ||||||||
\(846\) | 13.0851 | + | 6.78772i | 0.449876 | + | 0.233366i | ||||
\(847\) | −3.43314 | −0.117964 | ||||||||
\(848\) | 21.0998 | + | 7.54217i | 0.724571 | + | 0.258999i | ||||
\(849\) | 9.49613i | 0.325906i | ||||||||
\(850\) | 1.05910 | + | 0.549392i | 0.0363267 | + | 0.0188440i | ||||
\(851\) | −10.4308 | + | 7.16395i | −0.357562 | + | 0.245577i | ||||
\(852\) | −3.14907 | − | 4.46984i | −0.107885 | − | 0.153134i | ||||
\(853\) | 18.2241 | 0.623982 | 0.311991 | − | 0.950085i | \(-0.399004\pi\) | ||||
0.311991 | + | 0.950085i | \(0.399004\pi\) | |||||||
\(854\) | 18.9572 | + | 9.83378i | 0.648702 | + | 0.336505i | ||||
\(855\) | − | 5.13553i | − | 0.175631i | ||||||
\(856\) | −4.05590 | + | 0.551830i | −0.138628 | + | 0.0188612i | ||||
\(857\) | −36.4555 | −1.24529 | −0.622647 | − | 0.782503i | \(-0.713943\pi\) | ||||
−0.622647 | + | 0.782503i | \(0.713943\pi\) | |||||||
\(858\) | −18.0262 | − | 9.35081i | −0.615403 | − | 0.319232i | ||||
\(859\) | − | 8.31770i | − | 0.283796i | −0.989881 | − | 0.141898i | \(-0.954679\pi\) | ||
0.989881 | − | 0.141898i | \(-0.0453205\pi\) | |||||||
\(860\) | 18.9851 | − | 13.3753i | 0.647387 | − | 0.456094i | ||||
\(861\) | 15.7707i | 0.537463i | ||||||||
\(862\) | −0.658005 | + | 1.26848i | −0.0224117 | + | 0.0432045i | ||||
\(863\) | − | 6.91833i | − | 0.235503i | −0.993043 | − | 0.117751i | \(-0.962431\pi\) | ||
0.993043 | − | 0.117751i | \(-0.0375686\pi\) | |||||||
\(864\) | 4.14301 | − | 3.85169i | 0.140948 | − | 0.131037i | ||||
\(865\) | − | 20.8806i | − | 0.709963i | ||||||
\(866\) | −30.7413 | − | 15.9466i | −1.04463 | − | 0.541887i | ||||
\(867\) | − | 16.2882i | − | 0.553178i | ||||||
\(868\) | −29.4389 | + | 20.7401i | −0.999220 | + | 0.703965i | ||||
\(869\) | 57.6334 | 1.95508 | ||||||||
\(870\) | −0.179514 | + | 0.346060i | −0.00608609 | + | 0.0117325i | ||||
\(871\) | −10.6362 | −0.360394 | ||||||||
\(872\) | 0.392413 | + | 2.88420i | 0.0132888 | + | 0.0976714i | ||||
\(873\) | 0.845087i | 0.0286019i | ||||||||
\(874\) | 34.5664 | − | 4.28358i | 1.16923 | − | 0.144894i | ||||
\(875\) | 2.14037i | 0.0723579i | ||||||||
\(876\) | −7.92169 | + | 5.58095i | −0.267649 | + | 0.188563i | ||||
\(877\) | 16.8420 | 0.568714 | 0.284357 | − | 0.958718i | \(-0.408220\pi\) | ||||
0.284357 | + | 0.958718i | \(0.408220\pi\) | |||||||
\(878\) | −4.97424 | − | 2.58032i | −0.167872 | − | 0.0870814i | ||||
\(879\) | −16.0874 | −0.542615 | ||||||||
\(880\) | −13.3722 | − | 4.77992i | −0.450777 | − | 0.161131i | ||||
\(881\) | − | 40.7543i | − | 1.37305i | −0.727107 | − | 0.686524i | \(-0.759136\pi\) | ||
0.727107 | − | 0.686524i | \(-0.240864\pi\) | |||||||
\(882\) | −1.57512 | + | 3.03647i | −0.0530372 | + | 0.102243i | ||||
\(883\) | 31.2055i | 1.05015i | 0.851056 | + | 0.525075i | \(0.175963\pi\) | ||||
−0.851056 | + | 0.525075i | \(0.824037\pi\) | |||||||
\(884\) | −5.57906 | + | 3.93053i | −0.187644 | + | 0.132198i | ||||
\(885\) | 2.95080i | 0.0991901i | ||||||||
\(886\) | 4.03961 | + | 2.09549i | 0.135713 | + | 0.0703993i | ||||
\(887\) | 1.74524i | 0.0585996i | 0.999571 | + | 0.0292998i | \(0.00932774\pi\) | ||||
−0.999571 | + | 0.0292998i | \(0.990672\pi\) | |||||||
\(888\) | −7.39478 | + | 1.00610i | −0.248153 | + | 0.0337627i | ||||
\(889\) | − | 43.6281i | − | 1.46324i | ||||||
\(890\) | 10.4309 | − | 20.1082i | 0.349643 | − | 0.674029i | ||||
\(891\) | 3.55021 | 0.118937 | ||||||||
\(892\) | 12.1132 | − | 8.53395i | 0.405581 | − | 0.285738i | ||||
\(893\) | 53.5295i | 1.79130i | ||||||||
\(894\) | −0.795871 | + | 1.53425i | −0.0266179 | + | 0.0513130i | ||||
\(895\) | 11.9933 | 0.400891 | ||||||||
\(896\) | 5.00231 | − | 23.6933i | 0.167115 | − | 0.791537i | ||||
\(897\) | 15.9894 | − | 10.9817i | 0.533872 | − | 0.366668i | ||||
\(898\) | −2.04385 | + | 3.94007i | −0.0682043 | + | 0.131482i | ||||
\(899\) | 2.31899i | 0.0773426i | ||||||||
\(900\) | −1.15187 | − | 1.63499i | −0.0383958 | − | 0.0544996i | ||||
\(901\) | 4.72603 | 0.157447 | ||||||||
\(902\) | −17.0345 | + | 32.8385i | −0.567187 | + | 1.09340i | ||||
\(903\) | 24.8535i | 0.827074i | ||||||||
\(904\) | 4.22923 | + | 31.0845i | 0.140662 | + | 1.03385i | ||||
\(905\) | 11.8382 | 0.393515 | ||||||||
\(906\) | 6.28370 | − | 12.1135i | 0.208762 | − | 0.402444i | ||||
\(907\) | 58.1153 | 1.92969 | 0.964844 | − | 0.262824i | \(-0.0846539\pi\) | ||||
0.964844 | + | 0.262824i | \(0.0846539\pi\) | |||||||
\(908\) | −12.5148 | − | 17.7638i | −0.415319 | − | 0.589511i | ||||
\(909\) | −7.04680 | −0.233727 | ||||||||
\(910\) | −10.8677 | − | 5.63748i | −0.360262 | − | 0.186881i | ||||
\(911\) | 34.1132 | 1.13022 | 0.565110 | − | 0.825015i | \(-0.308834\pi\) | ||||
0.565110 | + | 0.825015i | \(0.308834\pi\) | |||||||
\(912\) | 19.3435 | + | 6.91436i | 0.640526 | + | 0.228957i | ||||
\(913\) | 33.5532 | 1.11045 | ||||||||
\(914\) | 5.58748 | + | 2.89843i | 0.184818 | + | 0.0958715i | ||||
\(915\) | 7.05529i | 0.233241i | ||||||||
\(916\) | 20.6606 | − | 14.5557i | 0.682644 | − | 0.480932i | ||||
\(917\) | 7.12876i | 0.235412i | ||||||||
\(918\) | 0.549392 | − | 1.05910i | 0.0181326 | − | 0.0349554i | ||||
\(919\) | −24.4239 | −0.805669 | −0.402834 | − | 0.915273i | \(-0.631975\pi\) | ||||
−0.402834 | + | 0.915273i | \(0.631975\pi\) | |||||||
\(920\) | 10.0441 | − | 9.11684i | 0.331143 | − | 0.300573i | ||||
\(921\) | −1.09550 | −0.0360980 | ||||||||
\(922\) | −11.7411 | + | 22.6341i | −0.386673 | + | 0.745415i | ||||
\(923\) | − | 11.0575i | − | 0.363962i | ||||||
\(924\) | 12.4239 | − | 8.75283i | 0.408717 | − | 0.287947i | ||||
\(925\) | 2.63854i | 0.0867545i | ||||||||
\(926\) | 43.1042 | + | 22.3597i | 1.41649 | + | 0.734785i | ||||
\(927\) | −13.7768 | −0.452491 | ||||||||
\(928\) | −1.06178 | − | 1.14208i | −0.0348545 | − | 0.0374907i | ||||
\(929\) | 30.3665 | 0.996294 | 0.498147 | − | 0.867093i | \(-0.334014\pi\) | ||||
0.498147 | + | 0.867093i | \(0.334014\pi\) | |||||||
\(930\) | −10.5605 | − | 5.47812i | −0.346293 | − | 0.179635i | ||||
\(931\) | −12.4218 | −0.407108 | ||||||||
\(932\) | −2.47512 | − | 3.51322i | −0.0810751 | − | 0.115079i | ||||
\(933\) | −33.0428 | −1.08177 | ||||||||
\(934\) | 24.0300 | − | 46.3241i | 0.786284 | − | 1.51577i | ||||
\(935\) | −2.99516 | −0.0979523 | ||||||||
\(936\) | 11.3355 | − | 1.54227i | 0.370514 | − | 0.0504106i | ||||
\(937\) | − | 29.6010i | − | 0.967022i | −0.875338 | − | 0.483511i | \(-0.839361\pi\) | ||
0.875338 | − | 0.483511i | \(-0.160639\pi\) | |||||||
\(938\) | 3.66532 | − | 7.06586i | 0.119677 | − | 0.230709i | ||||
\(939\) | −17.6117 | −0.574736 | ||||||||
\(940\) | 12.0064 | + | 17.0421i | 0.391606 | + | 0.555852i | ||||
\(941\) | 15.9140i | 0.518783i | 0.965772 | + | 0.259391i | \(0.0835219\pi\) | ||||
−0.965772 | + | 0.259391i | \(0.916478\pi\) | |||||||
\(942\) | −9.86053 | + | 19.0088i | −0.321274 | + | 0.619340i | ||||
\(943\) | −20.0055 | − | 29.1282i | −0.651469 | − | 0.948545i | ||||
\(944\) | −11.1145 | − | 3.97289i | −0.361746 | − | 0.129307i | ||||
\(945\) | 2.14037 | 0.0696264 | ||||||||
\(946\) | −26.8453 | + | 51.7514i | −0.872816 | + | 1.68258i | ||||
\(947\) | 19.8116i | 0.643789i | 0.946776 | + | 0.321894i | \(0.104320\pi\) | ||||
−0.946776 | + | 0.321894i | \(0.895680\pi\) | |||||||
\(948\) | −26.5421 | + | 18.6993i | −0.862047 | + | 0.607324i | ||||
\(949\) | −19.5967 | −0.636136 | ||||||||
\(950\) | 3.34426 | − | 6.44695i | 0.108502 | − | 0.209167i | ||||
\(951\) | − | 11.9669i | − | 0.388054i | ||||||
\(952\) | −0.688551 | − | 5.06079i | −0.0223161 | − | 0.164021i | ||||
\(953\) | 27.1642i | 0.879934i | 0.898014 | + | 0.439967i | \(0.145010\pi\) | ||||
−0.898014 | + | 0.439967i | \(0.854990\pi\) | |||||||
\(954\) | −7.03232 | − | 3.64792i | −0.227680 | − | 0.118106i | ||||
\(955\) | − | 1.29520i | − | 0.0419117i | ||||||
\(956\) | −25.3499 | + | 17.8594i | −0.819875 | + | 0.577613i | ||||
\(957\) | − | 0.978670i | − | 0.0316359i | ||||||
\(958\) | 23.6726 | − | 45.6352i | 0.764828 | − | 1.47441i | ||||
\(959\) | 46.9930i | 1.51748i | ||||||||
\(960\) | 7.70920 | − | 2.13733i | 0.248813 | − | 0.0689821i | ||||
\(961\) | −39.7673 | −1.28282 | ||||||||
\(962\) | −13.3972 | − | 6.94958i | −0.431941 | − | 0.224063i | ||||
\(963\) | 1.44719 | 0.0466351 | ||||||||
\(964\) | 20.5356 | − | 14.4676i | 0.661406 | − | 0.465970i | ||||
\(965\) | − | 1.48140i | − | 0.0476880i | ||||||
\(966\) | 1.78530 | + | 14.4065i | 0.0574412 | + | 0.463522i | ||||
\(967\) | − | 40.9044i | − | 1.31540i | −0.753281 | − | 0.657698i | \(-0.771530\pi\) | ||
0.753281 | − | 0.657698i | \(-0.228470\pi\) | |||||||
\(968\) | 4.49535 | − | 0.611620i | 0.144486 | − | 0.0196582i | ||||
\(969\) | 4.33263 | 0.139184 | ||||||||
\(970\) | −0.550322 | + | 1.06089i | −0.0176698 | + | 0.0340632i | ||||
\(971\) | −31.1852 | −1.00078 | −0.500390 | − | 0.865800i | \(-0.666810\pi\) | ||||
−0.500390 | + | 0.865800i | \(0.666810\pi\) | |||||||
\(972\) | −1.63499 | + | 1.15187i | −0.0524423 | + | 0.0369463i | ||||
\(973\) | − | 33.0381i | − | 1.05915i | ||||||
\(974\) | 5.69290 | + | 2.95311i | 0.182412 | + | 0.0946237i | ||||
\(975\) | − | 4.04464i | − | 0.129532i | ||||||
\(976\) | −26.5745 | − | 9.49909i | −0.850628 | − | 0.304058i | ||||
\(977\) | − | 43.9246i | − | 1.40527i | −0.711549 | − | 0.702637i | \(-0.752006\pi\) | ||
0.711549 | − | 0.702637i | \(-0.247994\pi\) | |||||||
\(978\) | −4.36668 | + | 8.41792i | −0.139631 | + | 0.269175i | ||||
\(979\) | 56.8668i | 1.81747i | ||||||||
\(980\) | −3.95471 | + | 2.78615i | −0.126328 | + | 0.0890002i | ||||
\(981\) | − | 1.02911i | − | 0.0328571i | ||||||
\(982\) | 16.8757 | + | 8.75404i | 0.538526 | + | 0.279353i | ||||
\(983\) | 37.6723 | 1.20156 | 0.600780 | − | 0.799414i | \(-0.294857\pi\) | ||||
0.600780 | + | 0.799414i | \(0.294857\pi\) | |||||||
\(984\) | −2.80957 | − | 20.6501i | −0.0895659 | − | 0.658302i | ||||
\(985\) | − | 13.9422i | − | 0.444234i | ||||||
\(986\) | −0.291957 | − | 0.151448i | −0.00929779 | − | 0.00482309i | ||||
\(987\) | −22.3099 | −0.710132 | ||||||||
\(988\) | 23.9260 | + | 33.9610i | 0.761187 | + | 1.08044i | ||||
\(989\) | −31.5274 | − | 45.9041i | −1.00251 | − | 1.45967i | ||||
\(990\) | 4.45680 | + | 2.31190i | 0.141646 | + | 0.0734771i | ||||
\(991\) | − | 8.15713i | − | 0.259120i | −0.991572 | − | 0.129560i | \(-0.958644\pi\) | ||
0.991572 | − | 0.129560i | \(-0.0413565\pi\) | |||||||
\(992\) | 34.8523 | − | 32.4017i | 1.10656 | − | 1.02875i | ||||
\(993\) | −5.36132 | −0.170136 | ||||||||
\(994\) | 7.34576 | + | 3.81051i | 0.232993 | + | 0.120862i | ||||
\(995\) | − | 5.33970i | − | 0.169280i | ||||||
\(996\) | −15.4524 | + | 10.8864i | −0.489627 | + | 0.344949i | ||||
\(997\) | 53.7457 | 1.70214 | 0.851071 | − | 0.525051i | \(-0.175954\pi\) | ||||
0.851071 | + | 0.525051i | \(0.175954\pi\) | |||||||
\(998\) | −31.7490 | − | 16.4694i | −1.00500 | − | 0.521329i | ||||
\(999\) | 2.63854 | 0.0834796 |
(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 | 1380.2.p.b.91.20 | yes | 48 | |
4.3 | odd | 2 | 1380.2.p.a.91.19 | ✓ | 48 | ||
23.22 | odd | 2 | 1380.2.p.a.91.20 | yes | 48 | ||
92.91 | even | 2 | inner | 1380.2.p.b.91.19 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.p.a.91.19 | ✓ | 48 | 4.3 | odd | 2 | ||
1380.2.p.a.91.20 | yes | 48 | 23.22 | odd | 2 | ||
1380.2.p.b.91.19 | yes | 48 | 92.91 | even | 2 | inner | |
1380.2.p.b.91.20 | yes | 48 | 1.1 | even | 1 | trivial |