Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(739,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.739");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.e (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 2 x^{14} + 8 x^{13} + 138 x^{12} - 220 x^{11} + 196 x^{10} + 744 x^{9} + 4241 x^{8} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 739.16 | ||
Root | \(2.23405 + 2.23405i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.739 |
Dual form | 1110.2.e.d.739.8 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.23405 | − | 0.0950871i | 0.999095 | − | 0.0425243i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 3.20752i | 1.21233i | 0.795339 | + | 0.606165i | \(0.207293\pi\) | ||||
−0.795339 | + | 0.606165i | \(0.792707\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.23405 | − | 0.0950871i | 0.706467 | − | 0.0300692i | ||||
\(11\) | −3.73314 | −1.12558 | −0.562792 | − | 0.826599i | \(-0.690273\pi\) | ||||
−0.562792 | + | 0.826599i | \(0.690273\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | −0.424858 | −0.117834 | −0.0589172 | − | 0.998263i | \(-0.518765\pi\) | ||||
−0.0589172 | + | 0.998263i | \(0.518765\pi\) | |||||||
\(14\) | 3.20752i | 0.857247i | ||||||||
\(15\) | 0.0950871 | + | 2.23405i | 0.0245514 | + | 0.576828i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.90738 | 1.67529 | 0.837643 | − | 0.546218i | \(-0.183933\pi\) | ||||
0.837643 | + | 0.546218i | \(0.183933\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 8.02549i | 1.84117i | 0.390539 | + | 0.920586i | \(0.372289\pi\) | ||||
−0.390539 | + | 0.920586i | \(0.627711\pi\) | |||||||
\(20\) | 2.23405 | − | 0.0950871i | 0.499548 | − | 0.0212621i | ||||
\(21\) | −3.20752 | −0.699939 | ||||||||
\(22\) | −3.73314 | −0.795907 | ||||||||
\(23\) | −6.34959 | −1.32398 | −0.661990 | − | 0.749512i | \(-0.730288\pi\) | ||||
−0.661990 | + | 0.749512i | \(0.730288\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | 4.98192 | − | 0.424858i | 0.996383 | − | 0.0849716i | ||||
\(26\) | −0.424858 | −0.0833215 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 3.20752i | 0.606165i | ||||||||
\(29\) | − | 3.39355i | − | 0.630167i | −0.949064 | − | 0.315084i | \(-0.897967\pi\) | ||
0.949064 | − | 0.315084i | \(-0.102033\pi\) | |||||||
\(30\) | 0.0950871 | + | 2.23405i | 0.0173605 | + | 0.407879i | ||||
\(31\) | − | 1.20338i | − | 0.216134i | −0.994144 | − | 0.108067i | \(-0.965534\pi\) | ||
0.994144 | − | 0.108067i | \(-0.0344660\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | − | 3.73314i | − | 0.649856i | ||||||
\(34\) | 6.90738 | 1.18461 | ||||||||
\(35\) | 0.304994 | + | 7.16575i | 0.0515534 | + | 1.21123i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −5.90637 | − | 1.45421i | −0.971002 | − | 0.239071i | ||||
\(38\) | 8.02549i | 1.30191i | ||||||||
\(39\) | − | 0.424858i | − | 0.0680317i | ||||||
\(40\) | 2.23405 | − | 0.0950871i | 0.353234 | − | 0.0150346i | ||||
\(41\) | 5.74899 | 0.897841 | 0.448921 | − | 0.893572i | \(-0.351809\pi\) | ||||
0.448921 | + | 0.893572i | \(0.351809\pi\) | |||||||
\(42\) | −3.20752 | −0.494932 | ||||||||
\(43\) | 9.31001 | 1.41976 | 0.709882 | − | 0.704321i | \(-0.248748\pi\) | ||||
0.709882 | + | 0.704321i | \(0.248748\pi\) | |||||||
\(44\) | −3.73314 | −0.562792 | ||||||||
\(45\) | −2.23405 | + | 0.0950871i | −0.333032 | + | 0.0141748i | ||||
\(46\) | −6.34959 | −0.936196 | ||||||||
\(47\) | 2.04357i | 0.298085i | 0.988831 | + | 0.149043i | \(0.0476191\pi\) | ||||
−0.988831 | + | 0.149043i | \(0.952381\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −3.28821 | −0.469744 | ||||||||
\(50\) | 4.98192 | − | 0.424858i | 0.704549 | − | 0.0600840i | ||||
\(51\) | 6.90738i | 0.967227i | ||||||||
\(52\) | −0.424858 | −0.0589172 | ||||||||
\(53\) | − | 11.8045i | − | 1.62147i | −0.585414 | − | 0.810734i | \(-0.699068\pi\) | ||
0.585414 | − | 0.810734i | \(-0.300932\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | −8.34000 | + | 0.354973i | −1.12456 | + | 0.0478646i | ||||
\(56\) | 3.20752i | 0.428623i | ||||||||
\(57\) | −8.02549 | −1.06300 | ||||||||
\(58\) | − | 3.39355i | − | 0.445596i | ||||||
\(59\) | 2.16131i | 0.281379i | 0.990054 | + | 0.140689i | \(0.0449318\pi\) | ||||
−0.990054 | + | 0.140689i | \(0.955068\pi\) | |||||||
\(60\) | 0.0950871 | + | 2.23405i | 0.0122757 | + | 0.288414i | ||||
\(61\) | 1.45108i | 0.185791i | 0.995676 | + | 0.0928957i | \(0.0296123\pi\) | ||||
−0.995676 | + | 0.0928957i | \(0.970388\pi\) | |||||||
\(62\) | − | 1.20338i | − | 0.152829i | ||||||
\(63\) | − | 3.20752i | − | 0.404110i | ||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.949152 | + | 0.0403985i | −0.117728 | + | 0.00501082i | ||||
\(66\) | − | 3.73314i | − | 0.459517i | ||||||
\(67\) | − | 11.4940i | − | 1.40422i | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||
0.712069 | − | 0.702109i | \(-0.247758\pi\) | |||||||
\(68\) | 6.90738 | 0.837643 | ||||||||
\(69\) | − | 6.34959i | − | 0.764401i | ||||||
\(70\) | 0.304994 | + | 7.16575i | 0.0364538 | + | 0.856471i | ||||
\(71\) | −5.59683 | −0.664222 | −0.332111 | − | 0.943240i | \(-0.607761\pi\) | ||||
−0.332111 | + | 0.943240i | \(0.607761\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 12.5062i | 1.46374i | 0.681444 | + | 0.731870i | \(0.261352\pi\) | ||||
−0.681444 | + | 0.731870i | \(0.738648\pi\) | |||||||
\(74\) | −5.90637 | − | 1.45421i | −0.686602 | − | 0.169049i | ||||
\(75\) | 0.424858 | + | 4.98192i | 0.0490584 | + | 0.575262i | ||||
\(76\) | 8.02549i | 0.920586i | ||||||||
\(77\) | − | 11.9741i | − | 1.36458i | ||||||
\(78\) | − | 0.424858i | − | 0.0481057i | ||||||
\(79\) | − | 4.50480i | − | 0.506830i | −0.967358 | − | 0.253415i | \(-0.918446\pi\) | ||
0.967358 | − | 0.253415i | \(-0.0815538\pi\) | |||||||
\(80\) | 2.23405 | − | 0.0950871i | 0.249774 | − | 0.0106311i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.74899 | 0.634870 | ||||||||
\(83\) | − | 7.00128i | − | 0.768491i | −0.923231 | − | 0.384245i | \(-0.874462\pi\) | ||
0.923231 | − | 0.384245i | \(-0.125538\pi\) | |||||||
\(84\) | −3.20752 | −0.349969 | ||||||||
\(85\) | 15.4314 | − | 0.656803i | 1.67377 | − | 0.0712403i | ||||
\(86\) | 9.31001 | 1.00392 | ||||||||
\(87\) | 3.39355 | 0.363827 | ||||||||
\(88\) | −3.73314 | −0.397954 | ||||||||
\(89\) | 15.9242i | 1.68796i | 0.536373 | + | 0.843981i | \(0.319794\pi\) | ||||
−0.536373 | + | 0.843981i | \(0.680206\pi\) | |||||||
\(90\) | −2.23405 | + | 0.0950871i | −0.235489 | + | 0.0100231i | ||||
\(91\) | − | 1.36274i | − | 0.142854i | ||||||
\(92\) | −6.34959 | −0.661990 | ||||||||
\(93\) | 1.20338 | 0.124785 | ||||||||
\(94\) | 2.04357i | 0.210778i | ||||||||
\(95\) | 0.763120 | + | 17.9293i | 0.0782945 | + | 1.83951i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −4.43763 | −0.450573 | −0.225286 | − | 0.974293i | \(-0.572332\pi\) | ||||
−0.225286 | + | 0.974293i | \(0.572332\pi\) | |||||||
\(98\) | −3.28821 | −0.332159 | ||||||||
\(99\) | 3.73314 | 0.375194 | ||||||||
\(100\) | 4.98192 | − | 0.424858i | 0.498192 | − | 0.0424858i | ||||
\(101\) | 13.0171 | 1.29525 | 0.647623 | − | 0.761961i | \(-0.275763\pi\) | ||||
0.647623 | + | 0.761961i | \(0.275763\pi\) | |||||||
\(102\) | 6.90738i | 0.683933i | ||||||||
\(103\) | 7.17254 | 0.706732 | 0.353366 | − | 0.935485i | \(-0.385037\pi\) | ||||
0.353366 | + | 0.935485i | \(0.385037\pi\) | |||||||
\(104\) | −0.424858 | −0.0416608 | ||||||||
\(105\) | −7.16575 | + | 0.304994i | −0.699306 | + | 0.0297644i | ||||
\(106\) | − | 11.8045i | − | 1.14655i | ||||||
\(107\) | − | 3.80308i | − | 0.367658i | −0.982958 | − | 0.183829i | \(-0.941151\pi\) | ||
0.982958 | − | 0.183829i | \(-0.0588492\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | 4.93476i | 0.472664i | 0.971672 | + | 0.236332i | \(0.0759454\pi\) | ||||
−0.971672 | + | 0.236332i | \(0.924055\pi\) | |||||||
\(110\) | −8.34000 | + | 0.354973i | −0.795187 | + | 0.0338454i | ||||
\(111\) | 1.45421 | − | 5.90637i | 0.138028 | − | 0.560608i | ||||
\(112\) | 3.20752i | 0.303082i | ||||||||
\(113\) | 9.29880 | 0.874758 | 0.437379 | − | 0.899277i | \(-0.355907\pi\) | ||||
0.437379 | + | 0.899277i | \(0.355907\pi\) | |||||||
\(114\) | −8.02549 | −0.751656 | ||||||||
\(115\) | −14.1853 | + | 0.603764i | −1.32278 | + | 0.0563013i | ||||
\(116\) | − | 3.39355i | − | 0.315084i | ||||||
\(117\) | 0.424858 | 0.0392781 | ||||||||
\(118\) | 2.16131i | 0.198965i | ||||||||
\(119\) | 22.1556i | 2.03100i | ||||||||
\(120\) | 0.0950871 | + | 2.23405i | 0.00868023 | + | 0.203940i | ||||
\(121\) | 2.93631 | 0.266937 | ||||||||
\(122\) | 1.45108i | 0.131374i | ||||||||
\(123\) | 5.74899i | 0.518369i | ||||||||
\(124\) | − | 1.20338i | − | 0.108067i | ||||||
\(125\) | 11.0894 | − | 1.42287i | 0.991869 | − | 0.127265i | ||||
\(126\) | − | 3.20752i | − | 0.285749i | ||||||
\(127\) | − | 14.3747i | − | 1.27555i | −0.770222 | − | 0.637776i | \(-0.779855\pi\) | ||
0.770222 | − | 0.637776i | \(-0.220145\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 9.31001i | 0.819701i | ||||||||
\(130\) | −0.949152 | + | 0.0403985i | −0.0832461 | + | 0.00354319i | ||||
\(131\) | − | 12.3237i | − | 1.07672i | −0.842714 | − | 0.538362i | \(-0.819043\pi\) | ||
0.842714 | − | 0.538362i | \(-0.180957\pi\) | |||||||
\(132\) | − | 3.73314i | − | 0.324928i | ||||||
\(133\) | −25.7419 | −2.23211 | ||||||||
\(134\) | − | 11.4940i | − | 0.992933i | ||||||
\(135\) | −0.0950871 | − | 2.23405i | −0.00818380 | − | 0.192276i | ||||
\(136\) | 6.90738 | 0.592303 | ||||||||
\(137\) | − | 17.4773i | − | 1.49319i | −0.665280 | − | 0.746594i | \(-0.731688\pi\) | ||
0.665280 | − | 0.746594i | \(-0.268312\pi\) | |||||||
\(138\) | − | 6.34959i | − | 0.540513i | ||||||
\(139\) | −0.125741 | −0.0106652 | −0.00533261 | − | 0.999986i | \(-0.501697\pi\) | ||||
−0.00533261 | + | 0.999986i | \(0.501697\pi\) | |||||||
\(140\) | 0.304994 | + | 7.16575i | 0.0257767 | + | 0.605617i | ||||
\(141\) | −2.04357 | −0.172100 | ||||||||
\(142\) | −5.59683 | −0.469676 | ||||||||
\(143\) | 1.58605 | 0.132632 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −0.322683 | − | 7.58136i | −0.0267974 | − | 0.629597i | ||||
\(146\) | 12.5062i | 1.03502i | ||||||||
\(147\) | − | 3.28821i | − | 0.271207i | ||||||
\(148\) | −5.90637 | − | 1.45421i | −0.485501 | − | 0.119536i | ||||
\(149\) | 2.43147 | 0.199194 | 0.0995968 | − | 0.995028i | \(-0.468245\pi\) | ||||
0.0995968 | + | 0.995028i | \(0.468245\pi\) | |||||||
\(150\) | 0.424858 | + | 4.98192i | 0.0346895 | + | 0.406772i | ||||
\(151\) | −15.1683 | −1.23438 | −0.617188 | − | 0.786816i | \(-0.711728\pi\) | ||||
−0.617188 | + | 0.786816i | \(0.711728\pi\) | |||||||
\(152\) | 8.02549i | 0.650953i | ||||||||
\(153\) | −6.90738 | −0.558429 | ||||||||
\(154\) | − | 11.9741i | − | 0.964902i | ||||||
\(155\) | −0.114426 | − | 2.68841i | −0.00919092 | − | 0.215938i | ||||
\(156\) | − | 0.424858i | − | 0.0340159i | ||||||
\(157\) | − | 19.1941i | − | 1.53185i | −0.642928 | − | 0.765927i | \(-0.722281\pi\) | ||
0.642928 | − | 0.765927i | \(-0.277719\pi\) | |||||||
\(158\) | − | 4.50480i | − | 0.358383i | ||||||
\(159\) | 11.8045 | 0.936156 | ||||||||
\(160\) | 2.23405 | − | 0.0950871i | 0.176617 | − | 0.00751730i | ||||
\(161\) | − | 20.3665i | − | 1.60510i | ||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −7.14619 | −0.559733 | −0.279867 | − | 0.960039i | \(-0.590290\pi\) | ||||
−0.279867 | + | 0.960039i | \(0.590290\pi\) | |||||||
\(164\) | 5.74899 | 0.448921 | ||||||||
\(165\) | −0.354973 | − | 8.34000i | −0.0276346 | − | 0.649268i | ||||
\(166\) | − | 7.00128i | − | 0.543405i | ||||||
\(167\) | 12.6692 | 0.980373 | 0.490187 | − | 0.871618i | \(-0.336929\pi\) | ||||
0.490187 | + | 0.871618i | \(0.336929\pi\) | |||||||
\(168\) | −3.20752 | −0.247466 | ||||||||
\(169\) | −12.8195 | −0.986115 | ||||||||
\(170\) | 15.4314 | − | 0.656803i | 1.18353 | − | 0.0503745i | ||||
\(171\) | − | 8.02549i | − | 0.613724i | ||||||
\(172\) | 9.31001 | 0.709882 | ||||||||
\(173\) | 19.7245i | 1.49963i | 0.661649 | + | 0.749814i | \(0.269857\pi\) | ||||
−0.661649 | + | 0.749814i | \(0.730143\pi\) | |||||||
\(174\) | 3.39355 | 0.257265 | ||||||||
\(175\) | 1.36274 | + | 15.9796i | 0.103014 | + | 1.20795i | ||||
\(176\) | −3.73314 | −0.281396 | ||||||||
\(177\) | −2.16131 | −0.162454 | ||||||||
\(178\) | 15.9242i | 1.19357i | ||||||||
\(179\) | 3.19619i | 0.238895i | 0.992841 | + | 0.119447i | \(0.0381123\pi\) | ||||
−0.992841 | + | 0.119447i | \(0.961888\pi\) | |||||||
\(180\) | −2.23405 | + | 0.0950871i | −0.166516 | + | 0.00708738i | ||||
\(181\) | −11.3735 | −0.845387 | −0.422694 | − | 0.906273i | \(-0.638915\pi\) | ||||
−0.422694 | + | 0.906273i | \(0.638915\pi\) | |||||||
\(182\) | − | 1.36274i | − | 0.101013i | ||||||
\(183\) | −1.45108 | −0.107267 | ||||||||
\(184\) | −6.34959 | −0.468098 | ||||||||
\(185\) | −13.3334 | − | 2.68716i | −0.980290 | − | 0.197564i | ||||
\(186\) | 1.20338 | 0.0882361 | ||||||||
\(187\) | −25.7862 | −1.88567 | ||||||||
\(188\) | 2.04357i | 0.149043i | ||||||||
\(189\) | 3.20752 | 0.233313 | ||||||||
\(190\) | 0.763120 | + | 17.9293i | 0.0553626 | + | 1.30073i | ||||
\(191\) | − | 12.4830i | − | 0.903235i | −0.892212 | − | 0.451617i | \(-0.850847\pi\) | ||
0.892212 | − | 0.451617i | \(-0.149153\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 12.1559 | 0.874999 | 0.437499 | − | 0.899219i | \(-0.355864\pi\) | ||||
0.437499 | + | 0.899219i | \(0.355864\pi\) | |||||||
\(194\) | −4.43763 | −0.318603 | ||||||||
\(195\) | −0.0403985 | − | 0.949152i | −0.00289300 | − | 0.0679702i | ||||
\(196\) | −3.28821 | −0.234872 | ||||||||
\(197\) | − | 8.89921i | − | 0.634042i | −0.948418 | − | 0.317021i | \(-0.897317\pi\) | ||
0.948418 | − | 0.317021i | \(-0.102683\pi\) | |||||||
\(198\) | 3.73314 | 0.265302 | ||||||||
\(199\) | 10.3470i | 0.733481i | 0.930323 | + | 0.366740i | \(0.119526\pi\) | ||||
−0.930323 | + | 0.366740i | \(0.880474\pi\) | |||||||
\(200\) | 4.98192 | − | 0.424858i | 0.352275 | − | 0.0300420i | ||||
\(201\) | 11.4940 | 0.810726 | ||||||||
\(202\) | 13.0171 | 0.915878 | ||||||||
\(203\) | 10.8849 | 0.763971 | ||||||||
\(204\) | 6.90738i | 0.483613i | ||||||||
\(205\) | 12.8435 | − | 0.546655i | 0.897029 | − | 0.0381800i | ||||
\(206\) | 7.17254 | 0.499735 | ||||||||
\(207\) | 6.34959 | 0.441327 | ||||||||
\(208\) | −0.424858 | −0.0294586 | ||||||||
\(209\) | − | 29.9602i | − | 2.07239i | ||||||
\(210\) | −7.16575 | + | 0.304994i | −0.494484 | + | 0.0210466i | ||||
\(211\) | 5.52374 | 0.380270 | 0.190135 | − | 0.981758i | \(-0.439107\pi\) | ||||
0.190135 | + | 0.981758i | \(0.439107\pi\) | |||||||
\(212\) | − | 11.8045i | − | 0.810734i | ||||||
\(213\) | − | 5.59683i | − | 0.383489i | ||||||
\(214\) | − | 3.80308i | − | 0.259973i | ||||||
\(215\) | 20.7990 | − | 0.885263i | 1.41848 | − | 0.0603744i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 3.85987 | 0.262025 | ||||||||
\(218\) | 4.93476i | 0.334224i | ||||||||
\(219\) | −12.5062 | −0.845091 | ||||||||
\(220\) | −8.34000 | + | 0.354973i | −0.562282 | + | 0.0239323i | ||||
\(221\) | −2.93466 | −0.197406 | ||||||||
\(222\) | 1.45421 | − | 5.90637i | 0.0976005 | − | 0.396410i | ||||
\(223\) | − | 3.24704i | − | 0.217438i | −0.994073 | − | 0.108719i | \(-0.965325\pi\) | ||
0.994073 | − | 0.108719i | \(-0.0346748\pi\) | |||||||
\(224\) | 3.20752i | 0.214312i | ||||||||
\(225\) | −4.98192 | + | 0.424858i | −0.332128 | + | 0.0283239i | ||||
\(226\) | 9.29880 | 0.618547 | ||||||||
\(227\) | 3.24282 | 0.215234 | 0.107617 | − | 0.994192i | \(-0.465678\pi\) | ||||
0.107617 | + | 0.994192i | \(0.465678\pi\) | |||||||
\(228\) | −8.02549 | −0.531501 | ||||||||
\(229\) | −23.2392 | −1.53569 | −0.767845 | − | 0.640636i | \(-0.778671\pi\) | ||||
−0.767845 | + | 0.640636i | \(0.778671\pi\) | |||||||
\(230\) | −14.1853 | + | 0.603764i | −0.935349 | + | 0.0398110i | ||||
\(231\) | 11.9741 | 0.787839 | ||||||||
\(232\) | − | 3.39355i | − | 0.222798i | ||||||
\(233\) | − | 23.5036i | − | 1.53977i | −0.638181 | − | 0.769886i | \(-0.720313\pi\) | ||
0.638181 | − | 0.769886i | \(-0.279687\pi\) | |||||||
\(234\) | 0.424858 | 0.0277738 | ||||||||
\(235\) | 0.194317 | + | 4.56543i | 0.0126759 | + | 0.297815i | ||||
\(236\) | 2.16131i | 0.140689i | ||||||||
\(237\) | 4.50480 | 0.292618 | ||||||||
\(238\) | 22.1556i | 1.43613i | ||||||||
\(239\) | − | 6.75627i | − | 0.437027i | −0.975834 | − | 0.218514i | \(-0.929879\pi\) | ||
0.975834 | − | 0.218514i | \(-0.0701208\pi\) | |||||||
\(240\) | 0.0950871 | + | 2.23405i | 0.00613785 | + | 0.144207i | ||||
\(241\) | − | 27.0533i | − | 1.74266i | −0.490699 | − | 0.871329i | \(-0.663259\pi\) | ||
0.490699 | − | 0.871329i | \(-0.336741\pi\) | |||||||
\(242\) | 2.93631 | 0.188753 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 1.45108i | 0.0928957i | ||||||||
\(245\) | −7.34600 | + | 0.312666i | −0.469319 | + | 0.0199755i | ||||
\(246\) | 5.74899i | 0.366542i | ||||||||
\(247\) | − | 3.40969i | − | 0.216953i | ||||||
\(248\) | − | 1.20338i | − | 0.0764147i | ||||||
\(249\) | 7.00128 | 0.443688 | ||||||||
\(250\) | 11.0894 | − | 1.42287i | 0.701357 | − | 0.0899901i | ||||
\(251\) | − | 12.9375i | − | 0.816609i | −0.912846 | − | 0.408305i | \(-0.866120\pi\) | ||
0.912846 | − | 0.408305i | \(-0.133880\pi\) | |||||||
\(252\) | − | 3.20752i | − | 0.202055i | ||||||
\(253\) | 23.7039 | 1.49025 | ||||||||
\(254\) | − | 14.3747i | − | 0.901951i | ||||||
\(255\) | 0.656803 | + | 15.4314i | 0.0411306 | + | 0.966352i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.5960 | 0.910473 | 0.455237 | − | 0.890370i | \(-0.349555\pi\) | ||||
0.455237 | + | 0.890370i | \(0.349555\pi\) | |||||||
\(258\) | 9.31001i | 0.579616i | ||||||||
\(259\) | 4.66443 | − | 18.9448i | 0.289833 | − | 1.17717i | ||||
\(260\) | −0.949152 | + | 0.0403985i | −0.0588639 | + | 0.00250541i | ||||
\(261\) | 3.39355i | 0.210056i | ||||||||
\(262\) | − | 12.3237i | − | 0.761358i | ||||||
\(263\) | − | 12.2500i | − | 0.755370i | −0.925934 | − | 0.377685i | \(-0.876720\pi\) | ||
0.925934 | − | 0.377685i | \(-0.123280\pi\) | |||||||
\(264\) | − | 3.73314i | − | 0.229759i | ||||||
\(265\) | −1.12245 | − | 26.3717i | −0.0689518 | − | 1.62000i | ||||
\(266\) | −25.7419 | −1.57834 | ||||||||
\(267\) | −15.9242 | −0.974545 | ||||||||
\(268\) | − | 11.4940i | − | 0.702109i | ||||||
\(269\) | 14.1886 | 0.865094 | 0.432547 | − | 0.901611i | \(-0.357615\pi\) | ||||
0.432547 | + | 0.901611i | \(0.357615\pi\) | |||||||
\(270\) | −0.0950871 | − | 2.23405i | −0.00578682 | − | 0.135960i | ||||
\(271\) | −8.82413 | −0.536028 | −0.268014 | − | 0.963415i | \(-0.586367\pi\) | ||||
−0.268014 | + | 0.963415i | \(0.586367\pi\) | |||||||
\(272\) | 6.90738 | 0.418821 | ||||||||
\(273\) | 1.36274 | 0.0824769 | ||||||||
\(274\) | − | 17.4773i | − | 1.05584i | ||||||
\(275\) | −18.5982 | + | 1.58605i | −1.12151 | + | 0.0956426i | ||||
\(276\) | − | 6.34959i | − | 0.382200i | ||||||
\(277\) | −12.6061 | −0.757426 | −0.378713 | − | 0.925514i | \(-0.623633\pi\) | ||||
−0.378713 | + | 0.925514i | \(0.623633\pi\) | |||||||
\(278\) | −0.125741 | −0.00754145 | ||||||||
\(279\) | 1.20338i | 0.0720445i | ||||||||
\(280\) | 0.304994 | + | 7.16575i | 0.0182269 | + | 0.428236i | ||||
\(281\) | 15.8731i | 0.946908i | 0.880819 | + | 0.473454i | \(0.156993\pi\) | ||||
−0.880819 | + | 0.473454i | \(0.843007\pi\) | |||||||
\(282\) | −2.04357 | −0.121693 | ||||||||
\(283\) | 29.1588 | 1.73331 | 0.866656 | − | 0.498906i | \(-0.166265\pi\) | ||||
0.866656 | + | 0.498906i | \(0.166265\pi\) | |||||||
\(284\) | −5.59683 | −0.332111 | ||||||||
\(285\) | −17.9293 | + | 0.763120i | −1.06204 | + | 0.0452034i | ||||
\(286\) | 1.58605 | 0.0937853 | ||||||||
\(287\) | 18.4400i | 1.08848i | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 30.7119 | 1.80658 | ||||||||
\(290\) | −0.322683 | − | 7.58136i | −0.0189486 | − | 0.445193i | ||||
\(291\) | − | 4.43763i | − | 0.260138i | ||||||
\(292\) | 12.5062i | 0.731870i | ||||||||
\(293\) | 28.4275i | 1.66075i | 0.557204 | + | 0.830376i | \(0.311874\pi\) | ||||
−0.557204 | + | 0.830376i | \(0.688126\pi\) | |||||||
\(294\) | − | 3.28821i | − | 0.191772i | ||||||
\(295\) | 0.205513 | + | 4.82846i | 0.0119654 | + | 0.281124i | ||||
\(296\) | −5.90637 | − | 1.45421i | −0.343301 | − | 0.0845245i | ||||
\(297\) | 3.73314i | 0.216619i | ||||||||
\(298\) | 2.43147 | 0.140851 | ||||||||
\(299\) | 2.69767 | 0.156010 | ||||||||
\(300\) | 0.424858 | + | 4.98192i | 0.0245292 | + | 0.287631i | ||||
\(301\) | 29.8621i | 1.72122i | ||||||||
\(302\) | −15.1683 | −0.872835 | ||||||||
\(303\) | 13.0171i | 0.747811i | ||||||||
\(304\) | 8.02549i | 0.460293i | ||||||||
\(305\) | 0.137979 | + | 3.24177i | 0.00790064 | + | 0.185623i | ||||
\(306\) | −6.90738 | −0.394869 | ||||||||
\(307\) | 20.6139i | 1.17650i | 0.808680 | + | 0.588249i | \(0.200182\pi\) | ||||
−0.808680 | + | 0.588249i | \(0.799818\pi\) | |||||||
\(308\) | − | 11.9741i | − | 0.682289i | ||||||
\(309\) | 7.17254i | 0.408032i | ||||||||
\(310\) | −0.114426 | − | 2.68841i | −0.00649896 | − | 0.152691i | ||||
\(311\) | − | 15.0056i | − | 0.850887i | −0.904985 | − | 0.425443i | \(-0.860118\pi\) | ||
0.904985 | − | 0.425443i | \(-0.139882\pi\) | |||||||
\(312\) | − | 0.424858i | − | 0.0240528i | ||||||
\(313\) | −28.8720 | −1.63194 | −0.815972 | − | 0.578092i | \(-0.803798\pi\) | ||||
−0.815972 | + | 0.578092i | \(0.803798\pi\) | |||||||
\(314\) | − | 19.1941i | − | 1.08318i | ||||||
\(315\) | −0.304994 | − | 7.16575i | −0.0171845 | − | 0.403744i | ||||
\(316\) | − | 4.50480i | − | 0.253415i | ||||||
\(317\) | − | 14.7214i | − | 0.826837i | −0.910541 | − | 0.413419i | \(-0.864335\pi\) | ||
0.910541 | − | 0.413419i | \(-0.135665\pi\) | |||||||
\(318\) | 11.8045 | 0.661962 | ||||||||
\(319\) | 12.6686i | 0.709306i | ||||||||
\(320\) | 2.23405 | − | 0.0950871i | 0.124887 | − | 0.00531553i | ||||
\(321\) | 3.80308 | 0.212267 | ||||||||
\(322\) | − | 20.3665i | − | 1.13498i | ||||||
\(323\) | 55.4351i | 3.08449i | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.11661 | + | 0.180504i | −0.117408 | + | 0.0100126i | ||||
\(326\) | −7.14619 | −0.395791 | ||||||||
\(327\) | −4.93476 | −0.272893 | ||||||||
\(328\) | 5.74899 | 0.317435 | ||||||||
\(329\) | −6.55479 | −0.361378 | ||||||||
\(330\) | −0.354973 | − | 8.34000i | −0.0195406 | − | 0.459102i | ||||
\(331\) | − | 8.15238i | − | 0.448095i | −0.974578 | − | 0.224048i | \(-0.928073\pi\) | ||
0.974578 | − | 0.224048i | \(-0.0719271\pi\) | |||||||
\(332\) | − | 7.00128i | − | 0.384245i | ||||||
\(333\) | 5.90637 | + | 1.45421i | 0.323667 | + | 0.0796904i | ||||
\(334\) | 12.6692 | 0.693228 | ||||||||
\(335\) | −1.09293 | − | 25.6782i | −0.0597134 | − | 1.40295i | ||||
\(336\) | −3.20752 | −0.174985 | ||||||||
\(337\) | 28.0034i | 1.52544i | 0.646726 | + | 0.762722i | \(0.276138\pi\) | ||||
−0.646726 | + | 0.762722i | \(0.723862\pi\) | |||||||
\(338\) | −12.8195 | −0.697289 | ||||||||
\(339\) | 9.29880i | 0.505042i | ||||||||
\(340\) | 15.4314 | − | 0.656803i | 0.836885 | − | 0.0356201i | ||||
\(341\) | 4.49238i | 0.243276i | ||||||||
\(342\) | − | 8.02549i | − | 0.433969i | ||||||
\(343\) | 11.9057i | 0.642846i | ||||||||
\(344\) | 9.31001 | 0.501962 | ||||||||
\(345\) | −0.603764 | − | 14.1853i | −0.0325056 | − | 0.763709i | ||||
\(346\) | 19.7245i | 1.06040i | ||||||||
\(347\) | −6.82853 | −0.366575 | −0.183287 | − | 0.983059i | \(-0.558674\pi\) | ||||
−0.183287 | + | 0.983059i | \(0.558674\pi\) | |||||||
\(348\) | 3.39355 | 0.181914 | ||||||||
\(349\) | −5.65418 | −0.302662 | −0.151331 | − | 0.988483i | \(-0.548356\pi\) | ||||
−0.151331 | + | 0.988483i | \(0.548356\pi\) | |||||||
\(350\) | 1.36274 | + | 15.9796i | 0.0728416 | + | 0.854146i | ||||
\(351\) | 0.424858i | 0.0226772i | ||||||||
\(352\) | −3.73314 | −0.198977 | ||||||||
\(353\) | −12.7850 | −0.680476 | −0.340238 | − | 0.940339i | \(-0.610508\pi\) | ||||
−0.340238 | + | 0.940339i | \(0.610508\pi\) | |||||||
\(354\) | −2.16131 | −0.114872 | ||||||||
\(355\) | −12.5036 | + | 0.532187i | −0.663621 | + | 0.0282456i | ||||
\(356\) | 15.9242i | 0.843981i | ||||||||
\(357\) | −22.1556 | −1.17260 | ||||||||
\(358\) | 3.19619i | 0.168924i | ||||||||
\(359\) | 11.3292 | 0.597933 | 0.298966 | − | 0.954264i | \(-0.403358\pi\) | ||||
0.298966 | + | 0.954264i | \(0.403358\pi\) | |||||||
\(360\) | −2.23405 | + | 0.0950871i | −0.117745 | + | 0.00501153i | ||||
\(361\) | −45.4084 | −2.38992 | ||||||||
\(362\) | −11.3735 | −0.597779 | ||||||||
\(363\) | 2.93631i | 0.154116i | ||||||||
\(364\) | − | 1.36274i | − | 0.0714271i | ||||||
\(365\) | 1.18918 | + | 27.9394i | 0.0622445 | + | 1.46242i | ||||
\(366\) | −1.45108 | −0.0758490 | ||||||||
\(367\) | 10.0590i | 0.525075i | 0.964922 | + | 0.262538i | \(0.0845594\pi\) | ||||
−0.964922 | + | 0.262538i | \(0.915441\pi\) | |||||||
\(368\) | −6.34959 | −0.330995 | ||||||||
\(369\) | −5.74899 | −0.299280 | ||||||||
\(370\) | −13.3334 | − | 2.68716i | −0.693170 | − | 0.139699i | ||||
\(371\) | 37.8631 | 1.96576 | ||||||||
\(372\) | 1.20338 | 0.0623924 | ||||||||
\(373\) | − | 9.39169i | − | 0.486283i | −0.969991 | − | 0.243142i | \(-0.921822\pi\) | ||
0.969991 | − | 0.243142i | \(-0.0781780\pi\) | |||||||
\(374\) | −25.7862 | −1.33337 | ||||||||
\(375\) | 1.42287 | + | 11.0894i | 0.0734766 | + | 0.572656i | ||||
\(376\) | 2.04357i | 0.105389i | ||||||||
\(377\) | 1.44178i | 0.0742554i | ||||||||
\(378\) | 3.20752 | 0.164977 | ||||||||
\(379\) | −10.7371 | −0.551526 | −0.275763 | − | 0.961226i | \(-0.588930\pi\) | ||||
−0.275763 | + | 0.961226i | \(0.588930\pi\) | |||||||
\(380\) | 0.763120 | + | 17.9293i | 0.0391473 | + | 0.919754i | ||||
\(381\) | 14.3747 | 0.736440 | ||||||||
\(382\) | − | 12.4830i | − | 0.638683i | ||||||
\(383\) | 11.2412 | 0.574399 | 0.287199 | − | 0.957871i | \(-0.407276\pi\) | ||||
0.287199 | + | 0.957871i | \(0.407276\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | −1.13859 | − | 26.7507i | −0.0580277 | − | 1.36334i | ||||
\(386\) | 12.1559 | 0.618717 | ||||||||
\(387\) | −9.31001 | −0.473255 | ||||||||
\(388\) | −4.43763 | −0.225286 | ||||||||
\(389\) | − | 7.80757i | − | 0.395860i | −0.980216 | − | 0.197930i | \(-0.936578\pi\) | ||
0.980216 | − | 0.197930i | \(-0.0634218\pi\) | |||||||
\(390\) | −0.0403985 | − | 0.949152i | −0.00204566 | − | 0.0480622i | ||||
\(391\) | −43.8590 | −2.21805 | ||||||||
\(392\) | −3.28821 | −0.166079 | ||||||||
\(393\) | 12.3237 | 0.621646 | ||||||||
\(394\) | − | 8.89921i | − | 0.448336i | ||||||
\(395\) | −0.428349 | − | 10.0639i | −0.0215526 | − | 0.506371i | ||||
\(396\) | 3.73314 | 0.187597 | ||||||||
\(397\) | − | 33.1348i | − | 1.66299i | −0.555534 | − | 0.831494i | \(-0.687486\pi\) | ||
0.555534 | − | 0.831494i | \(-0.312514\pi\) | |||||||
\(398\) | 10.3470i | 0.518649i | ||||||||
\(399\) | − | 25.7419i | − | 1.28871i | ||||||
\(400\) | 4.98192 | − | 0.424858i | 0.249096 | − | 0.0212429i | ||||
\(401\) | 33.2206i | 1.65896i | 0.558540 | + | 0.829478i | \(0.311362\pi\) | ||||
−0.558540 | + | 0.829478i | \(0.688638\pi\) | |||||||
\(402\) | 11.4940 | 0.573270 | ||||||||
\(403\) | 0.511266i | 0.0254680i | ||||||||
\(404\) | 13.0171 | 0.647623 | ||||||||
\(405\) | 2.23405 | − | 0.0950871i | 0.111011 | − | 0.00472492i | ||||
\(406\) | 10.8849 | 0.540209 | ||||||||
\(407\) | 22.0493 | + | 5.42878i | 1.09294 | + | 0.269095i | ||||
\(408\) | 6.90738i | 0.341966i | ||||||||
\(409\) | 18.4622i | 0.912899i | 0.889749 | + | 0.456449i | \(0.150879\pi\) | ||||
−0.889749 | + | 0.456449i | \(0.849121\pi\) | |||||||
\(410\) | 12.8435 | − | 0.546655i | 0.634295 | − | 0.0269974i | ||||
\(411\) | 17.4773 | 0.862092 | ||||||||
\(412\) | 7.17254 | 0.353366 | ||||||||
\(413\) | −6.93245 | −0.341124 | ||||||||
\(414\) | 6.34959 | 0.312065 | ||||||||
\(415\) | −0.665732 | − | 15.6412i | −0.0326795 | − | 0.767796i | ||||
\(416\) | −0.424858 | −0.0208304 | ||||||||
\(417\) | − | 0.125741i | − | 0.00615757i | ||||||
\(418\) | − | 29.9602i | − | 1.46540i | ||||||
\(419\) | 0.759460 | 0.0371021 | 0.0185510 | − | 0.999828i | \(-0.494095\pi\) | ||||
0.0185510 | + | 0.999828i | \(0.494095\pi\) | |||||||
\(420\) | −7.16575 | + | 0.304994i | −0.349653 | + | 0.0148822i | ||||
\(421\) | 27.6679i | 1.34845i | 0.738525 | + | 0.674227i | \(0.235523\pi\) | ||||
−0.738525 | + | 0.674227i | \(0.764477\pi\) | |||||||
\(422\) | 5.52374 | 0.268891 | ||||||||
\(423\) | − | 2.04357i | − | 0.0993617i | ||||||
\(424\) | − | 11.8045i | − | 0.573276i | ||||||
\(425\) | 34.4120 | − | 2.93466i | 1.66923 | − | 0.142352i | ||||
\(426\) | − | 5.59683i | − | 0.271168i | ||||||
\(427\) | −4.65437 | −0.225241 | ||||||||
\(428\) | − | 3.80308i | − | 0.183829i | ||||||
\(429\) | 1.58605i | 0.0765754i | ||||||||
\(430\) | 20.7990 | − | 0.885263i | 1.00302 | − | 0.0426911i | ||||
\(431\) | − | 4.94514i | − | 0.238199i | −0.992882 | − | 0.119100i | \(-0.961999\pi\) | ||
0.992882 | − | 0.119100i | \(-0.0380008\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | 3.83656i | 0.184373i | 0.995742 | + | 0.0921867i | \(0.0293857\pi\) | ||||
−0.995742 | + | 0.0921867i | \(0.970614\pi\) | |||||||
\(434\) | 3.85987 | 0.185280 | ||||||||
\(435\) | 7.58136 | − | 0.322683i | 0.363498 | − | 0.0154715i | ||||
\(436\) | 4.93476i | 0.236332i | ||||||||
\(437\) | − | 50.9585i | − | 2.43768i | ||||||
\(438\) | −12.5062 | −0.597569 | ||||||||
\(439\) | 27.6321i | 1.31881i | 0.751789 | + | 0.659404i | \(0.229191\pi\) | ||||
−0.751789 | + | 0.659404i | \(0.770809\pi\) | |||||||
\(440\) | −8.34000 | + | 0.354973i | −0.397594 | + | 0.0169227i | ||||
\(441\) | 3.28821 | 0.156581 | ||||||||
\(442\) | −2.93466 | −0.139587 | ||||||||
\(443\) | 17.7327i | 0.842504i | 0.906944 | + | 0.421252i | \(0.138409\pi\) | ||||
−0.906944 | + | 0.421252i | \(0.861591\pi\) | |||||||
\(444\) | 1.45421 | − | 5.90637i | 0.0690139 | − | 0.280304i | ||||
\(445\) | 1.51419 | + | 35.5754i | 0.0717793 | + | 1.68643i | ||||
\(446\) | − | 3.24704i | − | 0.153752i | ||||||
\(447\) | 2.43147i | 0.115004i | ||||||||
\(448\) | 3.20752i | 0.151541i | ||||||||
\(449\) | 25.3794i | 1.19773i | 0.800850 | + | 0.598864i | \(0.204381\pi\) | ||||
−0.800850 | + | 0.598864i | \(0.795619\pi\) | |||||||
\(450\) | −4.98192 | + | 0.424858i | −0.234850 | + | 0.0200280i | ||||
\(451\) | −21.4618 | −1.01059 | ||||||||
\(452\) | 9.29880 | 0.437379 | ||||||||
\(453\) | − | 15.1683i | − | 0.712667i | ||||||
\(454\) | 3.24282 | 0.152193 | ||||||||
\(455\) | −0.129579 | − | 3.04443i | −0.00607477 | − | 0.142725i | ||||
\(456\) | −8.02549 | −0.375828 | ||||||||
\(457\) | −41.8627 | −1.95826 | −0.979128 | − | 0.203243i | \(-0.934852\pi\) | ||||
−0.979128 | + | 0.203243i | \(0.934852\pi\) | |||||||
\(458\) | −23.2392 | −1.08590 | ||||||||
\(459\) | − | 6.90738i | − | 0.322409i | ||||||
\(460\) | −14.1853 | + | 0.603764i | −0.661392 | + | 0.0281506i | ||||
\(461\) | 9.86731i | 0.459567i | 0.973242 | + | 0.229783i | \(0.0738017\pi\) | ||||
−0.973242 | + | 0.229783i | \(0.926198\pi\) | |||||||
\(462\) | 11.9741 | 0.557087 | ||||||||
\(463\) | 2.13573 | 0.0992558 | 0.0496279 | − | 0.998768i | \(-0.484196\pi\) | ||||
0.0496279 | + | 0.998768i | \(0.484196\pi\) | |||||||
\(464\) | − | 3.39355i | − | 0.157542i | ||||||
\(465\) | 2.68841 | − | 0.114426i | 0.124672 | − | 0.00530638i | ||||
\(466\) | − | 23.5036i | − | 1.08878i | ||||||
\(467\) | 23.1295 | 1.07031 | 0.535154 | − | 0.844755i | \(-0.320254\pi\) | ||||
0.535154 | + | 0.844755i | \(0.320254\pi\) | |||||||
\(468\) | 0.424858 | 0.0196391 | ||||||||
\(469\) | 36.8674 | 1.70238 | ||||||||
\(470\) | 0.194317 | + | 4.56543i | 0.00896318 | + | 0.210587i | ||||
\(471\) | 19.1941 | 0.884416 | ||||||||
\(472\) | 2.16131i | 0.0994823i | ||||||||
\(473\) | −34.7556 | −1.59806 | ||||||||
\(474\) | 4.50480 | 0.206912 | ||||||||
\(475\) | 3.40969 | + | 39.9823i | 0.156447 | + | 1.83451i | ||||
\(476\) | 22.1556i | 1.01550i | ||||||||
\(477\) | 11.8045i | 0.540490i | ||||||||
\(478\) | − | 6.75627i | − | 0.309025i | ||||||
\(479\) | 42.3018i | 1.93282i | 0.257006 | + | 0.966410i | \(0.417264\pi\) | ||||
−0.257006 | + | 0.966410i | \(0.582736\pi\) | |||||||
\(480\) | 0.0950871 | + | 2.23405i | 0.00434011 | + | 0.101970i | ||||
\(481\) | 2.50937 | + | 0.617834i | 0.114417 | + | 0.0281708i | ||||
\(482\) | − | 27.0533i | − | 1.23225i | ||||||
\(483\) | 20.3665 | 0.926706 | ||||||||
\(484\) | 2.93631 | 0.133469 | ||||||||
\(485\) | −9.91386 | + | 0.421961i | −0.450165 | + | 0.0191603i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 10.2364 | 0.463858 | 0.231929 | − | 0.972733i | \(-0.425496\pi\) | ||||
0.231929 | + | 0.972733i | \(0.425496\pi\) | |||||||
\(488\) | 1.45108i | 0.0656872i | ||||||||
\(489\) | − | 7.14619i | − | 0.323162i | ||||||
\(490\) | −7.34600 | + | 0.312666i | −0.331859 | + | 0.0141248i | ||||
\(491\) | −30.2449 | −1.36494 | −0.682468 | − | 0.730916i | \(-0.739093\pi\) | ||||
−0.682468 | + | 0.730916i | \(0.739093\pi\) | |||||||
\(492\) | 5.74899i | 0.259184i | ||||||||
\(493\) | − | 23.4406i | − | 1.05571i | ||||||
\(494\) | − | 3.40969i | − | 0.153409i | ||||||
\(495\) | 8.34000 | − | 0.354973i | 0.374855 | − | 0.0159549i | ||||
\(496\) | − | 1.20338i | − | 0.0540334i | ||||||
\(497\) | − | 17.9520i | − | 0.805256i | ||||||
\(498\) | 7.00128 | 0.313735 | ||||||||
\(499\) | − | 5.43439i | − | 0.243277i | −0.992574 | − | 0.121638i | \(-0.961185\pi\) | ||
0.992574 | − | 0.121638i | \(-0.0388148\pi\) | |||||||
\(500\) | 11.0894 | − | 1.42287i | 0.495934 | − | 0.0636326i | ||||
\(501\) | 12.6692i | 0.566019i | ||||||||
\(502\) | − | 12.9375i | − | 0.577430i | ||||||
\(503\) | 1.52679 | 0.0680760 | 0.0340380 | − | 0.999421i | \(-0.489163\pi\) | ||||
0.0340380 | + | 0.999421i | \(0.489163\pi\) | |||||||
\(504\) | − | 3.20752i | − | 0.142874i | ||||||
\(505\) | 29.0807 | − | 1.23776i | 1.29407 | − | 0.0550794i | ||||
\(506\) | 23.7039 | 1.05377 | ||||||||
\(507\) | − | 12.8195i | − | 0.569334i | ||||||
\(508\) | − | 14.3747i | − | 0.637776i | ||||||
\(509\) | 10.8171 | 0.479459 | 0.239729 | − | 0.970840i | \(-0.422941\pi\) | ||||
0.239729 | + | 0.970840i | \(0.422941\pi\) | |||||||
\(510\) | 0.656803 | + | 15.4314i | 0.0290837 | + | 0.683314i | ||||
\(511\) | −40.1139 | −1.77454 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 8.02549 | 0.354334 | ||||||||
\(514\) | 14.5960 | 0.643802 | ||||||||
\(515\) | 16.0238 | − | 0.682016i | 0.706092 | − | 0.0300532i | ||||
\(516\) | 9.31001i | 0.409850i | ||||||||
\(517\) | − | 7.62892i | − | 0.335520i | ||||||
\(518\) | 4.66443 | − | 18.9448i | 0.204943 | − | 0.832388i | ||||
\(519\) | −19.7245 | −0.865811 | ||||||||
\(520\) | −0.949152 | + | 0.0403985i | −0.0416231 | + | 0.00177159i | ||||
\(521\) | −39.8552 | −1.74609 | −0.873044 | − | 0.487642i | \(-0.837857\pi\) | ||||
−0.873044 | + | 0.487642i | \(0.837857\pi\) | |||||||
\(522\) | 3.39355i | 0.148532i | ||||||||
\(523\) | 17.5477 | 0.767309 | 0.383654 | − | 0.923477i | \(-0.374665\pi\) | ||||
0.383654 | + | 0.923477i | \(0.374665\pi\) | |||||||
\(524\) | − | 12.3237i | − | 0.538362i | ||||||
\(525\) | −15.9796 | + | 1.36274i | −0.697408 | + | 0.0594749i | ||||
\(526\) | − | 12.2500i | − | 0.534127i | ||||||
\(527\) | − | 8.31221i | − | 0.362085i | ||||||
\(528\) | − | 3.73314i | − | 0.162464i | ||||||
\(529\) | 17.3173 | 0.752925 | ||||||||
\(530\) | −1.12245 | − | 26.3717i | −0.0487563 | − | 1.14551i | ||||
\(531\) | − | 2.16131i | − | 0.0937928i | ||||||
\(532\) | −25.7419 | −1.11605 | ||||||||
\(533\) | −2.44250 | −0.105797 | ||||||||
\(534\) | −15.9242 | −0.689107 | ||||||||
\(535\) | −0.361624 | − | 8.49625i | −0.0156344 | − | 0.367325i | ||||
\(536\) | − | 11.4940i | − | 0.496466i | ||||||
\(537\) | −3.19619 | −0.137926 | ||||||||
\(538\) | 14.1886 | 0.611714 | ||||||||
\(539\) | 12.2753 | 0.528736 | ||||||||
\(540\) | −0.0950871 | − | 2.23405i | −0.00409190 | − | 0.0961380i | ||||
\(541\) | 23.3560i | 1.00415i | 0.864824 | + | 0.502076i | \(0.167430\pi\) | ||||
−0.864824 | + | 0.502076i | \(0.832570\pi\) | |||||||
\(542\) | −8.82413 | −0.379029 | ||||||||
\(543\) | − | 11.3735i | − | 0.488085i | ||||||
\(544\) | 6.90738 | 0.296152 | ||||||||
\(545\) | 0.469232 | + | 11.0245i | 0.0200997 | + | 0.472237i | ||||
\(546\) | 1.36274 | 0.0583200 | ||||||||
\(547\) | 15.6858 | 0.670675 | 0.335337 | − | 0.942098i | \(-0.391150\pi\) | ||||
0.335337 | + | 0.942098i | \(0.391150\pi\) | |||||||
\(548\) | − | 17.4773i | − | 0.746594i | ||||||
\(549\) | − | 1.45108i | − | 0.0619305i | ||||||
\(550\) | −18.5982 | + | 1.58605i | −0.793029 | + | 0.0676295i | ||||
\(551\) | 27.2349 | 1.16025 | ||||||||
\(552\) | − | 6.34959i | − | 0.270256i | ||||||
\(553\) | 14.4493 | 0.614445 | ||||||||
\(554\) | −12.6061 | −0.535581 | ||||||||
\(555\) | 2.68716 | − | 13.3334i | 0.114064 | − | 0.565971i | ||||
\(556\) | −0.125741 | −0.00533261 | ||||||||
\(557\) | −39.5638 | −1.67637 | −0.838186 | − | 0.545384i | \(-0.816384\pi\) | ||||
−0.838186 | + | 0.545384i | \(0.816384\pi\) | |||||||
\(558\) | 1.20338i | 0.0509432i | ||||||||
\(559\) | −3.95543 | −0.167297 | ||||||||
\(560\) | 0.304994 | + | 7.16575i | 0.0128884 | + | 0.302808i | ||||
\(561\) | − | 25.7862i | − | 1.08869i | ||||||
\(562\) | 15.8731i | 0.669565i | ||||||||
\(563\) | −32.4565 | −1.36788 | −0.683939 | − | 0.729540i | \(-0.739734\pi\) | ||||
−0.683939 | + | 0.729540i | \(0.739734\pi\) | |||||||
\(564\) | −2.04357 | −0.0860498 | ||||||||
\(565\) | 20.7739 | − | 0.884197i | 0.873967 | − | 0.0371984i | ||||
\(566\) | 29.1588 | 1.22564 | ||||||||
\(567\) | 3.20752i | 0.134703i | ||||||||
\(568\) | −5.59683 | −0.234838 | ||||||||
\(569\) | − | 3.24636i | − | 0.136094i | −0.997682 | − | 0.0680472i | \(-0.978323\pi\) | ||
0.997682 | − | 0.0680472i | \(-0.0216769\pi\) | |||||||
\(570\) | −17.9293 | + | 0.763120i | −0.750976 | + | 0.0319636i | ||||
\(571\) | 28.9822 | 1.21287 | 0.606433 | − | 0.795134i | \(-0.292600\pi\) | ||||
0.606433 | + | 0.795134i | \(0.292600\pi\) | |||||||
\(572\) | 1.58605 | 0.0663162 | ||||||||
\(573\) | 12.4830 | 0.521483 | ||||||||
\(574\) | 18.4400i | 0.769671i | ||||||||
\(575\) | −31.6331 | + | 2.69767i | −1.31919 | + | 0.112501i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 14.3774 | 0.598538 | 0.299269 | − | 0.954169i | \(-0.403257\pi\) | ||||
0.299269 | + | 0.954169i | \(0.403257\pi\) | |||||||
\(578\) | 30.7119 | 1.27745 | ||||||||
\(579\) | 12.1559i | 0.505181i | ||||||||
\(580\) | −0.322683 | − | 7.58136i | −0.0133987 | − | 0.314799i | ||||
\(581\) | 22.4568 | 0.931664 | ||||||||
\(582\) | − | 4.43763i | − | 0.183946i | ||||||
\(583\) | 44.0677i | 1.82510i | ||||||||
\(584\) | 12.5062i | 0.517510i | ||||||||
\(585\) | 0.949152 | − | 0.0403985i | 0.0392426 | − | 0.00167027i | ||||
\(586\) | 28.4275i | 1.17433i | ||||||||
\(587\) | −11.8386 | −0.488632 | −0.244316 | − | 0.969696i | \(-0.578563\pi\) | ||||
−0.244316 | + | 0.969696i | \(0.578563\pi\) | |||||||
\(588\) | − | 3.28821i | − | 0.135603i | ||||||
\(589\) | 9.65771 | 0.397939 | ||||||||
\(590\) | 0.205513 | + | 4.82846i | 0.00846082 | + | 0.198785i | ||||
\(591\) | 8.89921 | 0.366064 | ||||||||
\(592\) | −5.90637 | − | 1.45421i | −0.242751 | − | 0.0597678i | ||||
\(593\) | 1.69514i | 0.0696112i | 0.999394 | + | 0.0348056i | \(0.0110812\pi\) | ||||
−0.999394 | + | 0.0348056i | \(0.988919\pi\) | |||||||
\(594\) | 3.73314i | 0.153172i | ||||||||
\(595\) | 2.10671 | + | 49.4966i | 0.0863667 | + | 2.02916i | ||||
\(596\) | 2.43147 | 0.0995968 | ||||||||
\(597\) | −10.3470 | −0.423475 | ||||||||
\(598\) | 2.69767 | 0.110316 | ||||||||
\(599\) | 44.7372 | 1.82791 | 0.913956 | − | 0.405813i | \(-0.133012\pi\) | ||||
0.913956 | + | 0.405813i | \(0.133012\pi\) | |||||||
\(600\) | 0.424858 | + | 4.98192i | 0.0173448 | + | 0.203386i | ||||
\(601\) | 6.63433 | 0.270620 | 0.135310 | − | 0.990803i | \(-0.456797\pi\) | ||||
0.135310 | + | 0.990803i | \(0.456797\pi\) | |||||||
\(602\) | 29.8621i | 1.21709i | ||||||||
\(603\) | 11.4940i | 0.468073i | ||||||||
\(604\) | −15.1683 | −0.617188 | ||||||||
\(605\) | 6.55985 | − | 0.279205i | 0.266696 | − | 0.0113513i | ||||
\(606\) | 13.0171i | 0.528782i | ||||||||
\(607\) | 29.4488 | 1.19529 | 0.597645 | − | 0.801760i | \(-0.296103\pi\) | ||||
0.597645 | + | 0.801760i | \(0.296103\pi\) | |||||||
\(608\) | 8.02549i | 0.325476i | ||||||||
\(609\) | 10.8849i | 0.441079i | ||||||||
\(610\) | 0.137979 | + | 3.24177i | 0.00558660 | + | 0.131256i | ||||
\(611\) | − | 0.868226i | − | 0.0351247i | ||||||
\(612\) | −6.90738 | −0.279214 | ||||||||
\(613\) | − | 47.2277i | − | 1.90751i | −0.300590 | − | 0.953754i | \(-0.597183\pi\) | ||
0.300590 | − | 0.953754i | \(-0.402817\pi\) | |||||||
\(614\) | 20.6139i | 0.831910i | ||||||||
\(615\) | 0.546655 | + | 12.8435i | 0.0220433 | + | 0.517900i | ||||
\(616\) | − | 11.9741i | − | 0.482451i | ||||||
\(617\) | 39.6156i | 1.59487i | 0.603408 | + | 0.797433i | \(0.293809\pi\) | ||||
−0.603408 | + | 0.797433i | \(0.706191\pi\) | |||||||
\(618\) | 7.17254i | 0.288522i | ||||||||
\(619\) | −21.3347 | −0.857512 | −0.428756 | − | 0.903420i | \(-0.641048\pi\) | ||||
−0.428756 | + | 0.903420i | \(0.641048\pi\) | |||||||
\(620\) | −0.114426 | − | 2.68841i | −0.00459546 | − | 0.107969i | ||||
\(621\) | 6.34959i | 0.254800i | ||||||||
\(622\) | − | 15.0056i | − | 0.601668i | ||||||
\(623\) | −51.0772 | −2.04637 | ||||||||
\(624\) | − | 0.424858i | − | 0.0170079i | ||||||
\(625\) | 24.6390 | − | 4.23321i | 0.985560 | − | 0.169329i | ||||
\(626\) | −28.8720 | −1.15396 | ||||||||
\(627\) | 29.9602 | 1.19650 | ||||||||
\(628\) | − | 19.1941i | − | 0.765927i | ||||||
\(629\) | −40.7976 | − | 10.0448i | −1.62671 | − | 0.400513i | ||||
\(630\) | −0.304994 | − | 7.16575i | −0.0121513 | − | 0.285490i | ||||
\(631\) | 13.9231i | 0.554269i | 0.960831 | + | 0.277134i | \(0.0893847\pi\) | ||||
−0.960831 | + | 0.277134i | \(0.910615\pi\) | |||||||
\(632\) | − | 4.50480i | − | 0.179191i | ||||||
\(633\) | 5.52374i | 0.219549i | ||||||||
\(634\) | − | 14.7214i | − | 0.584662i | ||||||
\(635\) | −1.36685 | − | 32.1138i | −0.0542419 | − | 1.27440i | ||||
\(636\) | 11.8045 | 0.468078 | ||||||||
\(637\) | 1.39702 | 0.0553520 | ||||||||
\(638\) | 12.6686i | 0.501555i | ||||||||
\(639\) | 5.59683 | 0.221407 | ||||||||
\(640\) | 2.23405 | − | 0.0950871i | 0.0883084 | − | 0.00375865i | ||||
\(641\) | 25.1770 | 0.994431 | 0.497216 | − | 0.867627i | \(-0.334356\pi\) | ||||
0.497216 | + | 0.867627i | \(0.334356\pi\) | |||||||
\(642\) | 3.80308 | 0.150096 | ||||||||
\(643\) | 6.70070 | 0.264250 | 0.132125 | − | 0.991233i | \(-0.457820\pi\) | ||||
0.132125 | + | 0.991233i | \(0.457820\pi\) | |||||||
\(644\) | − | 20.3665i | − | 0.802551i | ||||||
\(645\) | 0.885263 | + | 20.7990i | 0.0348572 | + | 0.818959i | ||||
\(646\) | 55.4351i | 2.18106i | ||||||||
\(647\) | −2.02361 | −0.0795562 | −0.0397781 | − | 0.999209i | \(-0.512665\pi\) | ||||
−0.0397781 | + | 0.999209i | \(0.512665\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | − | 8.06846i | − | 0.316715i | ||||||
\(650\) | −2.11661 | + | 0.180504i | −0.0830202 | + | 0.00707996i | ||||
\(651\) | 3.85987i | 0.151280i | ||||||||
\(652\) | −7.14619 | −0.279867 | ||||||||
\(653\) | −17.8433 | −0.698262 | −0.349131 | − | 0.937074i | \(-0.613523\pi\) | ||||
−0.349131 | + | 0.937074i | \(0.613523\pi\) | |||||||
\(654\) | −4.93476 | −0.192964 | ||||||||
\(655\) | −1.17182 | − | 27.5316i | −0.0457869 | − | 1.07575i | ||||
\(656\) | 5.74899 | 0.224460 | ||||||||
\(657\) | − | 12.5062i | − | 0.487913i | ||||||
\(658\) | −6.55479 | −0.255532 | ||||||||
\(659\) | −28.2166 | −1.09916 | −0.549582 | − | 0.835440i | \(-0.685213\pi\) | ||||
−0.549582 | + | 0.835440i | \(0.685213\pi\) | |||||||
\(660\) | −0.354973 | − | 8.34000i | −0.0138173 | − | 0.324634i | ||||
\(661\) | 14.9551i | 0.581687i | 0.956771 | + | 0.290843i | \(0.0939358\pi\) | ||||
−0.956771 | + | 0.290843i | \(0.906064\pi\) | |||||||
\(662\) | − | 8.15238i | − | 0.316851i | ||||||
\(663\) | − | 2.93466i | − | 0.113973i | ||||||
\(664\) | − | 7.00128i | − | 0.271703i | ||||||
\(665\) | −57.5086 | + | 2.44773i | −2.23009 | + | 0.0949188i | ||||
\(666\) | 5.90637 | + | 1.45421i | 0.228867 | + | 0.0563496i | ||||
\(667\) | 21.5477i | 0.834329i | ||||||||
\(668\) | 12.6692 | 0.490187 | ||||||||
\(669\) | 3.24704 | 0.125538 | ||||||||
\(670\) | −1.09293 | − | 25.6782i | −0.0422237 | − | 0.992035i | ||||
\(671\) | − | 5.41707i | − | 0.209124i | ||||||
\(672\) | −3.20752 | −0.123733 | ||||||||
\(673\) | 26.7443i | 1.03092i | 0.856915 | + | 0.515458i | \(0.172378\pi\) | ||||
−0.856915 | + | 0.515458i | \(0.827622\pi\) | |||||||
\(674\) | 28.0034i | 1.07865i | ||||||||
\(675\) | −0.424858 | − | 4.98192i | −0.0163528 | − | 0.191754i | ||||
\(676\) | −12.8195 | −0.493058 | ||||||||
\(677\) | 23.3020i | 0.895569i | 0.894141 | + | 0.447785i | \(0.147787\pi\) | ||||
−0.894141 | + | 0.447785i | \(0.852213\pi\) | |||||||
\(678\) | 9.29880i | 0.357118i | ||||||||
\(679\) | − | 14.2338i | − | 0.546243i | ||||||
\(680\) | 15.4314 | − | 0.656803i | 0.591767 | − | 0.0251872i | ||||
\(681\) | 3.24282i | 0.124265i | ||||||||
\(682\) | 4.49238i | 0.172022i | ||||||||
\(683\) | 0.507613 | 0.0194233 | 0.00971163 | − | 0.999953i | \(-0.496909\pi\) | ||||
0.00971163 | + | 0.999953i | \(0.496909\pi\) | |||||||
\(684\) | − | 8.02549i | − | 0.306862i | ||||||
\(685\) | −1.66187 | − | 39.0451i | −0.0634967 | − | 1.49184i | ||||
\(686\) | 11.9057i | 0.454560i | ||||||||
\(687\) | − | 23.2392i | − | 0.886631i | ||||||
\(688\) | 9.31001 | 0.354941 | ||||||||
\(689\) | 5.01522i | 0.191065i | ||||||||
\(690\) | −0.603764 | − | 14.1853i | −0.0229849 | − | 0.540024i | ||||
\(691\) | −25.1513 | −0.956801 | −0.478401 | − | 0.878142i | \(-0.658783\pi\) | ||||
−0.478401 | + | 0.878142i | \(0.658783\pi\) | |||||||
\(692\) | 19.7245i | 0.749814i | ||||||||
\(693\) | 11.9741i | 0.454859i | ||||||||
\(694\) | −6.82853 | −0.259208 | ||||||||
\(695\) | −0.280911 | + | 0.0119564i | −0.0106556 | + | 0.000453531i | ||||
\(696\) | 3.39355 | 0.128632 | ||||||||
\(697\) | 39.7105 | 1.50414 | ||||||||
\(698\) | −5.65418 | −0.214014 | ||||||||
\(699\) | 23.5036 | 0.888988 | ||||||||
\(700\) | 1.36274 | + | 15.9796i | 0.0515068 | + | 0.603973i | ||||
\(701\) | − | 13.4801i | − | 0.509136i | −0.967055 | − | 0.254568i | \(-0.918067\pi\) | ||
0.967055 | − | 0.254568i | \(-0.0819332\pi\) | |||||||
\(702\) | 0.424858i | 0.0160352i | ||||||||
\(703\) | 11.6708 | − | 47.4015i | 0.440172 | − | 1.78778i | ||||
\(704\) | −3.73314 | −0.140698 | ||||||||
\(705\) | −4.56543 | + | 0.194317i | −0.171944 | + | 0.00731841i | ||||
\(706\) | −12.7850 | −0.481169 | ||||||||
\(707\) | 41.7525i | 1.57027i | ||||||||
\(708\) | −2.16131 | −0.0812270 | ||||||||
\(709\) | 16.0914i | 0.604326i | 0.953256 | + | 0.302163i | \(0.0977086\pi\) | ||||
−0.953256 | + | 0.302163i | \(0.902291\pi\) | |||||||
\(710\) | −12.5036 | + | 0.532187i | −0.469251 | + | 0.0199726i | ||||
\(711\) | 4.50480i | 0.168943i | ||||||||
\(712\) | 15.9242i | 0.596785i | ||||||||
\(713\) | 7.64097i | 0.286157i | ||||||||
\(714\) | −22.1556 | −0.829152 | ||||||||
\(715\) | 3.54331 | − | 0.150813i | 0.132512 | − | 0.00564010i | ||||
\(716\) | 3.19619i | 0.119447i | ||||||||
\(717\) | 6.75627 | 0.252318 | ||||||||
\(718\) | 11.3292 | 0.422802 | ||||||||
\(719\) | −32.6719 | −1.21845 | −0.609227 | − | 0.792996i | \(-0.708520\pi\) | ||||
−0.609227 | + | 0.792996i | \(0.708520\pi\) | |||||||
\(720\) | −2.23405 | + | 0.0950871i | −0.0832580 | + | 0.00354369i | ||||
\(721\) | 23.0061i | 0.856792i | ||||||||
\(722\) | −45.4084 | −1.68993 | ||||||||
\(723\) | 27.0533 | 1.00612 | ||||||||
\(724\) | −11.3735 | −0.422694 | ||||||||
\(725\) | −1.44178 | − | 16.9064i | −0.0535463 | − | 0.627888i | ||||
\(726\) | 2.93631i | 0.108977i | ||||||||
\(727\) | −31.3272 | −1.16186 | −0.580931 | − | 0.813953i | \(-0.697311\pi\) | ||||
−0.580931 | + | 0.813953i | \(0.697311\pi\) | |||||||
\(728\) | − | 1.36274i | − | 0.0505066i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 1.18918 | + | 27.9394i | 0.0440135 | + | 1.03408i | ||||
\(731\) | 64.3078 | 2.37851 | ||||||||
\(732\) | −1.45108 | −0.0536334 | ||||||||
\(733\) | − | 28.4514i | − | 1.05088i | −0.850831 | − | 0.525439i | \(-0.823901\pi\) | ||
0.850831 | − | 0.525439i | \(-0.176099\pi\) | |||||||
\(734\) | 10.0590i | 0.371284i | ||||||||
\(735\) | −0.312666 | − | 7.34600i | −0.0115329 | − | 0.270961i | ||||
\(736\) | −6.34959 | −0.234049 | ||||||||
\(737\) | 42.9088i | 1.58057i | ||||||||
\(738\) | −5.74899 | −0.211623 | ||||||||
\(739\) | 15.5668 | 0.572635 | 0.286318 | − | 0.958135i | \(-0.407569\pi\) | ||||
0.286318 | + | 0.958135i | \(0.407569\pi\) | |||||||
\(740\) | −13.3334 | − | 2.68716i | −0.490145 | − | 0.0987820i | ||||
\(741\) | 3.40969 | 0.125258 | ||||||||
\(742\) | 37.8631 | 1.39000 | ||||||||
\(743\) | 50.7985i | 1.86362i | 0.362950 | + | 0.931809i | \(0.381770\pi\) | ||||
−0.362950 | + | 0.931809i | \(0.618230\pi\) | |||||||
\(744\) | 1.20338 | 0.0441181 | ||||||||
\(745\) | 5.43201 | − | 0.231201i | 0.199013 | − | 0.00847056i | ||||
\(746\) | − | 9.39169i | − | 0.343854i | ||||||
\(747\) | 7.00128i | 0.256164i | ||||||||
\(748\) | −25.7862 | −0.942837 | ||||||||
\(749\) | 12.1985 | 0.445722 | ||||||||
\(750\) | 1.42287 | + | 11.0894i | 0.0519558 | + | 0.404929i | ||||
\(751\) | −33.5086 | −1.22275 | −0.611373 | − | 0.791342i | \(-0.709383\pi\) | ||||
−0.611373 | + | 0.791342i | \(0.709383\pi\) | |||||||
\(752\) | 2.04357i | 0.0745213i | ||||||||
\(753\) | 12.9375 | 0.471470 | ||||||||
\(754\) | 1.44178i | 0.0525065i | ||||||||
\(755\) | −33.8866 | + | 1.44231i | −1.23326 | + | 0.0524909i | ||||
\(756\) | 3.20752 | 0.116656 | ||||||||
\(757\) | 26.5221 | 0.963964 | 0.481982 | − | 0.876181i | \(-0.339917\pi\) | ||||
0.481982 | + | 0.876181i | \(0.339917\pi\) | |||||||
\(758\) | −10.7371 | −0.389988 | ||||||||
\(759\) | 23.7039i | 0.860396i | ||||||||
\(760\) | 0.763120 | + | 17.9293i | 0.0276813 | + | 0.650364i | ||||
\(761\) | 31.0909 | 1.12704 | 0.563521 | − | 0.826102i | \(-0.309446\pi\) | ||||
0.563521 | + | 0.826102i | \(0.309446\pi\) | |||||||
\(762\) | 14.3747 | 0.520742 | ||||||||
\(763\) | −15.8284 | −0.573025 | ||||||||
\(764\) | − | 12.4830i | − | 0.451617i | ||||||
\(765\) | −15.4314 | + | 0.656803i | −0.557924 | + | 0.0237468i | ||||
\(766\) | 11.2412 | 0.406161 | ||||||||
\(767\) | − | 0.918249i | − | 0.0331561i | ||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | − | 6.61015i | − | 0.238368i | −0.992872 | − | 0.119184i | \(-0.961972\pi\) | ||
0.992872 | − | 0.119184i | \(-0.0380278\pi\) | |||||||
\(770\) | −1.13859 | − | 26.7507i | −0.0410318 | − | 0.964030i | ||||
\(771\) | 14.5960i | 0.525662i | ||||||||
\(772\) | 12.1559 | 0.437499 | ||||||||
\(773\) | − | 35.7529i | − | 1.28594i | −0.765890 | − | 0.642971i | \(-0.777702\pi\) | ||
0.765890 | − | 0.642971i | \(-0.222298\pi\) | |||||||
\(774\) | −9.31001 | −0.334642 | ||||||||
\(775\) | −0.511266 | − | 5.99514i | −0.0183652 | − | 0.215352i | ||||
\(776\) | −4.43763 | −0.159302 | ||||||||
\(777\) | 18.9448 | + | 4.66443i | 0.679642 | + | 0.167335i | ||||
\(778\) | − | 7.80757i | − | 0.279915i | ||||||
\(779\) | 46.1384i | 1.65308i | ||||||||
\(780\) | −0.0403985 | − | 0.949152i | −0.00144650 | − | 0.0339851i | ||||
\(781\) | 20.8937 | 0.747637 | ||||||||
\(782\) | −43.8590 | −1.56840 | ||||||||
\(783\) | −3.39355 | −0.121276 | ||||||||
\(784\) | −3.28821 | −0.117436 | ||||||||
\(785\) | −1.82511 | − | 42.8804i | −0.0651409 | − | 1.53047i | ||||
\(786\) | 12.3237 | 0.439570 | ||||||||
\(787\) | − | 21.9895i | − | 0.783840i | −0.919999 | − | 0.391920i | \(-0.871811\pi\) | ||
0.919999 | − | 0.391920i | \(-0.128189\pi\) | |||||||
\(788\) | − | 8.89921i | − | 0.317021i | ||||||
\(789\) | 12.2500 | 0.436113 | ||||||||
\(790\) | −0.428349 | − | 10.0639i | −0.0152400 | − | 0.358059i | ||||
\(791\) | 29.8261i | 1.06050i | ||||||||
\(792\) | 3.73314 | 0.132651 | ||||||||
\(793\) | − | 0.616502i | − | 0.0218926i | ||||||
\(794\) | − | 33.1348i | − | 1.17591i | ||||||
\(795\) | 26.3717 | − | 1.12245i | 0.935309 | − | 0.0398093i | ||||
\(796\) | 10.3470i | 0.366740i | ||||||||
\(797\) | 16.6230 | 0.588817 | 0.294409 | − | 0.955680i | \(-0.404877\pi\) | ||||
0.294409 | + | 0.955680i | \(0.404877\pi\) | |||||||
\(798\) | − | 25.7419i | − | 0.911255i | ||||||
\(799\) | 14.1157i | 0.499378i | ||||||||
\(800\) | 4.98192 | − | 0.424858i | 0.176137 | − | 0.0150210i | ||||
\(801\) | − | 15.9242i | − | 0.562654i | ||||||
\(802\) | 33.2206i | 1.17306i | ||||||||
\(803\) | − | 46.6874i | − | 1.64756i | ||||||
\(804\) | 11.4940 | 0.405363 | ||||||||
\(805\) | −1.93659 | − | 45.4996i | −0.0682557 | − | 1.60365i | ||||
\(806\) | 0.511266i | 0.0180086i | ||||||||
\(807\) | 14.1886i | 0.499462i | ||||||||
\(808\) | 13.0171 | 0.457939 | ||||||||
\(809\) | − | 37.6802i | − | 1.32476i | −0.749166 | − | 0.662382i | \(-0.769546\pi\) | ||
0.749166 | − | 0.662382i | \(-0.230454\pi\) | |||||||
\(810\) | 2.23405 | − | 0.0950871i | 0.0784964 | − | 0.00334102i | ||||
\(811\) | 9.23902 | 0.324426 | 0.162213 | − | 0.986756i | \(-0.448137\pi\) | ||||
0.162213 | + | 0.986756i | \(0.448137\pi\) | |||||||
\(812\) | 10.8849 | 0.381985 | ||||||||
\(813\) | − | 8.82413i | − | 0.309476i | ||||||
\(814\) | 22.0493 | + | 5.42878i | 0.772828 | + | 0.190279i | ||||
\(815\) | −15.9649 | + | 0.679511i | −0.559227 | + | 0.0238022i | ||||
\(816\) | 6.90738i | 0.241807i | ||||||||
\(817\) | 74.7174i | 2.61403i | ||||||||
\(818\) | 18.4622i | 0.645517i | ||||||||
\(819\) | 1.36274i | 0.0476181i | ||||||||
\(820\) | 12.8435 | − | 0.546655i | 0.448514 | − | 0.0190900i | ||||
\(821\) | −2.02441 | −0.0706525 | −0.0353262 | − | 0.999376i | \(-0.511247\pi\) | ||||
−0.0353262 | + | 0.999376i | \(0.511247\pi\) | |||||||
\(822\) | 17.4773 | 0.609591 | ||||||||
\(823\) | 21.4801i | 0.748748i | 0.927278 | + | 0.374374i | \(0.122142\pi\) | ||||
−0.927278 | + | 0.374374i | \(0.877858\pi\) | |||||||
\(824\) | 7.17254 | 0.249867 | ||||||||
\(825\) | −1.58605 | − | 18.5982i | −0.0552193 | − | 0.647505i | ||||
\(826\) | −6.93245 | −0.241211 | ||||||||
\(827\) | −46.1615 | −1.60519 | −0.802597 | − | 0.596522i | \(-0.796549\pi\) | ||||
−0.802597 | + | 0.596522i | \(0.796549\pi\) | |||||||
\(828\) | 6.34959 | 0.220663 | ||||||||
\(829\) | − | 7.43600i | − | 0.258263i | −0.991627 | − | 0.129131i | \(-0.958781\pi\) | ||
0.991627 | − | 0.129131i | \(-0.0412189\pi\) | |||||||
\(830\) | −0.665732 | − | 15.6412i | −0.0231079 | − | 0.542913i | ||||
\(831\) | − | 12.6061i | − | 0.437300i | ||||||
\(832\) | −0.424858 | −0.0147293 | ||||||||
\(833\) | −22.7129 | −0.786955 | ||||||||
\(834\) | − | 0.125741i | − | 0.00435406i | ||||||
\(835\) | 28.3036 | − | 1.20468i | 0.979486 | − | 0.0416896i | ||||
\(836\) | − | 29.9602i | − | 1.03620i | ||||||
\(837\) | −1.20338 | −0.0415949 | ||||||||
\(838\) | 0.759460 | 0.0262351 | ||||||||
\(839\) | −31.3881 | −1.08364 | −0.541819 | − | 0.840495i | \(-0.682264\pi\) | ||||
−0.541819 | + | 0.840495i | \(0.682264\pi\) | |||||||
\(840\) | −7.16575 | + | 0.304994i | −0.247242 | + | 0.0105233i | ||||
\(841\) | 17.4838 | 0.602889 | ||||||||
\(842\) | 27.6679i | 0.953500i | ||||||||
\(843\) | −15.8731 | −0.546698 | ||||||||
\(844\) | 5.52374 | 0.190135 | ||||||||
\(845\) | −28.6393 | + | 1.21897i | −0.985223 | + | 0.0419338i | ||||
\(846\) | − | 2.04357i | − | 0.0702593i | ||||||
\(847\) | 9.41828i | 0.323616i | ||||||||
\(848\) | − | 11.8045i | − | 0.405367i | ||||||
\(849\) | 29.1588i | 1.00073i | ||||||||
\(850\) | 34.4120 | − | 2.93466i | 1.18032 | − | 0.100658i | ||||
\(851\) | 37.5030 | + | 9.23366i | 1.28559 | + | 0.316526i | ||||
\(852\) | − | 5.59683i | − | 0.191744i | ||||||
\(853\) | −29.1070 | −0.996605 | −0.498302 | − | 0.867003i | \(-0.666043\pi\) | ||||
−0.498302 | + | 0.867003i | \(0.666043\pi\) | |||||||
\(854\) | −4.65437 | −0.159269 | ||||||||
\(855\) | −0.763120 | − | 17.9293i | −0.0260982 | − | 0.613169i | ||||
\(856\) | − | 3.80308i | − | 0.129987i | ||||||
\(857\) | 26.4364 | 0.903050 | 0.451525 | − | 0.892259i | \(-0.350880\pi\) | ||||
0.451525 | + | 0.892259i | \(0.350880\pi\) | |||||||
\(858\) | 1.58605i | 0.0541470i | ||||||||
\(859\) | − | 3.12912i | − | 0.106764i | −0.998574 | − | 0.0533821i | \(-0.983000\pi\) | ||
0.998574 | − | 0.0533821i | \(-0.0170001\pi\) | |||||||
\(860\) | 20.7990 | − | 0.885263i | 0.709240 | − | 0.0301872i | ||||
\(861\) | −18.4400 | −0.628434 | ||||||||
\(862\) | − | 4.94514i | − | 0.168432i | ||||||
\(863\) | − | 40.9780i | − | 1.39491i | −0.716631 | − | 0.697453i | \(-0.754317\pi\) | ||
0.716631 | − | 0.697453i | \(-0.245683\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | 1.87555 | + | 44.0655i | 0.0637706 | + | 1.49827i | ||||
\(866\) | 3.83656i | 0.130372i | ||||||||
\(867\) | 30.7119i | 1.04303i | ||||||||
\(868\) | 3.85987 | 0.131013 | ||||||||
\(869\) | 16.8170i | 0.570479i | ||||||||
\(870\) | 7.58136 | − | 0.322683i | 0.257032 | − | 0.0109400i | ||||
\(871\) | 4.88333i | 0.165465i | ||||||||
\(872\) | 4.93476i | 0.167112i | ||||||||
\(873\) | 4.43763 | 0.150191 | ||||||||
\(874\) | − | 50.9585i | − | 1.72370i | ||||||
\(875\) | 4.56388 | + | 35.5696i | 0.154287 | + | 1.20247i | ||||
\(876\) | −12.5062 | −0.422545 | ||||||||
\(877\) | − | 52.0228i | − | 1.75669i | −0.478030 | − | 0.878343i | \(-0.658649\pi\) | ||
0.478030 | − | 0.878343i | \(-0.341351\pi\) | |||||||
\(878\) | 27.6321i | 0.932538i | ||||||||
\(879\) | −28.4275 | −0.958836 | ||||||||
\(880\) | −8.34000 | + | 0.354973i | −0.281141 | + | 0.0119661i | ||||
\(881\) | −12.4748 | −0.420288 | −0.210144 | − | 0.977670i | \(-0.567393\pi\) | ||||
−0.210144 | + | 0.977670i | \(0.567393\pi\) | |||||||
\(882\) | 3.28821 | 0.110720 | ||||||||
\(883\) | −5.68269 | −0.191238 | −0.0956189 | − | 0.995418i | \(-0.530483\pi\) | ||||
−0.0956189 | + | 0.995418i | \(0.530483\pi\) | |||||||
\(884\) | −2.93466 | −0.0987032 | ||||||||
\(885\) | −4.82846 | + | 0.205513i | −0.162307 | + | 0.00690823i | ||||
\(886\) | 17.7327i | 0.595740i | ||||||||
\(887\) | − | 45.8573i | − | 1.53974i | −0.638203 | − | 0.769868i | \(-0.720322\pi\) | ||
0.638203 | − | 0.769868i | \(-0.279678\pi\) | |||||||
\(888\) | 1.45421 | − | 5.90637i | 0.0488002 | − | 0.198205i | ||||
\(889\) | 46.1073 | 1.54639 | ||||||||
\(890\) | 1.51419 | + | 35.5754i | 0.0507556 | + | 1.19249i | ||||
\(891\) | −3.73314 | −0.125065 | ||||||||
\(892\) | − | 3.24704i | − | 0.108719i | ||||||
\(893\) | −16.4006 | −0.548826 | ||||||||
\(894\) | 2.43147i | 0.0813204i | ||||||||
\(895\) | 0.303917 | + | 7.14044i | 0.0101588 | + | 0.238678i | ||||
\(896\) | 3.20752i | 0.107156i | ||||||||
\(897\) | 2.69767i | 0.0900727i | ||||||||
\(898\) | 25.3794i | 0.846922i | ||||||||
\(899\) | −4.08374 | −0.136200 | ||||||||
\(900\) | −4.98192 | + | 0.424858i | −0.166064 | + | 0.0141619i | ||||
\(901\) | − | 81.5380i | − | 2.71642i | ||||||
\(902\) | −21.4618 | −0.714598 | ||||||||
\(903\) | −29.8621 | −0.993748 | ||||||||
\(904\) | 9.29880 | 0.309274 | ||||||||
\(905\) | −25.4090 | + | 1.08148i | −0.844623 | + | 0.0359495i | ||||
\(906\) | − | 15.1683i | − | 0.503932i | ||||||
\(907\) | 56.7099 | 1.88302 | 0.941510 | − | 0.336985i | \(-0.109407\pi\) | ||||
0.941510 | + | 0.336985i | \(0.109407\pi\) | |||||||
\(908\) | 3.24282 | 0.107617 | ||||||||
\(909\) | −13.0171 | −0.431749 | ||||||||
\(910\) | −0.129579 | − | 3.04443i | −0.00429551 | − | 0.100922i | ||||
\(911\) | − | 36.6773i | − | 1.21517i | −0.794254 | − | 0.607586i | \(-0.792138\pi\) | ||
0.794254 | − | 0.607586i | \(-0.207862\pi\) | |||||||
\(912\) | −8.02549 | −0.265750 | ||||||||
\(913\) | 26.1367i | 0.865000i | ||||||||
\(914\) | −41.8627 | −1.38470 | ||||||||
\(915\) | −3.24177 | + | 0.137979i | −0.107170 | + | 0.00456144i | ||||
\(916\) | −23.2392 | −0.767845 | ||||||||
\(917\) | 39.5284 | 1.30534 | ||||||||
\(918\) | − | 6.90738i | − | 0.227978i | ||||||
\(919\) | 9.37210i | 0.309157i | 0.987981 | + | 0.154578i | \(0.0494019\pi\) | ||||
−0.987981 | + | 0.154578i | \(0.950598\pi\) | |||||||
\(920\) | −14.1853 | + | 0.603764i | −0.467674 | + | 0.0199055i | ||||
\(921\) | −20.6139 | −0.679251 | ||||||||
\(922\) | 9.86731i | 0.324963i | ||||||||
\(923\) | 2.37786 | 0.0782682 | ||||||||
\(924\) | 11.9741 | 0.393920 | ||||||||
\(925\) | −30.0429 | − | 4.73540i | −0.987805 | − | 0.155699i | ||||
\(926\) | 2.13573 | 0.0701844 | ||||||||
\(927\) | −7.17254 | −0.235577 | ||||||||
\(928\) | − | 3.39355i | − | 0.111399i | ||||||
\(929\) | −50.0310 | −1.64146 | −0.820732 | − | 0.571314i | \(-0.806434\pi\) | ||||
−0.820732 | + | 0.571314i | \(0.806434\pi\) | |||||||
\(930\) | 2.68841 | − | 0.114426i | 0.0881563 | − | 0.00375218i | ||||
\(931\) | − | 26.3894i | − | 0.864879i | ||||||
\(932\) | − | 23.5036i | − | 0.769886i | ||||||
\(933\) | 15.0056 | 0.491260 | ||||||||
\(934\) | 23.1295 | 0.756822 | ||||||||
\(935\) | −57.6075 | + | 2.45194i | −1.88397 | + | 0.0801869i | ||||
\(936\) | 0.424858 | 0.0138869 | ||||||||
\(937\) | 32.5441i | 1.06317i | 0.847005 | + | 0.531585i | \(0.178403\pi\) | ||||
−0.847005 | + | 0.531585i | \(0.821597\pi\) | |||||||
\(938\) | 36.8674 | 1.20376 | ||||||||
\(939\) | − | 28.8720i | − | 0.942203i | ||||||
\(940\) | 0.194317 | + | 4.56543i | 0.00633793 | + | 0.148908i | ||||
\(941\) | −23.1571 | −0.754900 | −0.377450 | − | 0.926030i | \(-0.623199\pi\) | ||||
−0.377450 | + | 0.926030i | \(0.623199\pi\) | |||||||
\(942\) | 19.1941 | 0.625376 | ||||||||
\(943\) | −36.5037 | −1.18872 | ||||||||
\(944\) | 2.16131i | 0.0703446i | ||||||||
\(945\) | 7.16575 | − | 0.304994i | 0.233102 | − | 0.00992146i | ||||
\(946\) | −34.7556 | −1.13000 | ||||||||
\(947\) | −18.7484 | −0.609242 | −0.304621 | − | 0.952474i | \(-0.598530\pi\) | ||||
−0.304621 | + | 0.952474i | \(0.598530\pi\) | |||||||
\(948\) | 4.50480 | 0.146309 | ||||||||
\(949\) | − | 5.31336i | − | 0.172479i | ||||||
\(950\) | 3.40969 | + | 39.9823i | 0.110625 | + | 1.29720i | ||||
\(951\) | 14.7214 | 0.477375 | ||||||||
\(952\) | 22.1556i | 0.718067i | ||||||||
\(953\) | − | 17.1259i | − | 0.554763i | −0.960760 | − | 0.277382i | \(-0.910533\pi\) | ||
0.960760 | − | 0.277382i | \(-0.0894666\pi\) | |||||||
\(954\) | 11.8045i | 0.382184i | ||||||||
\(955\) | −1.18697 | − | 27.8875i | −0.0384094 | − | 0.902418i | ||||
\(956\) | − | 6.75627i | − | 0.218514i | ||||||
\(957\) | −12.6686 | −0.409518 | ||||||||
\(958\) | 42.3018i | 1.36671i | ||||||||
\(959\) | 56.0589 | 1.81024 | ||||||||
\(960\) | 0.0950871 | + | 2.23405i | 0.00306892 | + | 0.0721035i | ||||
\(961\) | 29.5519 | 0.953286 | ||||||||
\(962\) | 2.50937 | + | 0.617834i | 0.0809053 | + | 0.0199198i | ||||
\(963\) | 3.80308i | 0.122553i | ||||||||
\(964\) | − | 27.0533i | − | 0.871329i | ||||||
\(965\) | 27.1568 | − | 1.15587i | 0.874207 | − | 0.0372087i | ||||
\(966\) | 20.3665 | 0.655280 | ||||||||
\(967\) | 22.1462 | 0.712175 | 0.356087 | − | 0.934453i | \(-0.384111\pi\) | ||||
0.356087 | + | 0.934453i | \(0.384111\pi\) | |||||||
\(968\) | 2.93631 | 0.0943766 | ||||||||
\(969\) | −55.4351 | −1.78083 | ||||||||
\(970\) | −9.91386 | + | 0.421961i | −0.318315 | + | 0.0135484i | ||||
\(971\) | −7.32119 | −0.234948 | −0.117474 | − | 0.993076i | \(-0.537480\pi\) | ||||
−0.117474 | + | 0.993076i | \(0.537480\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | − | 0.403318i | − | 0.0129298i | ||||||
\(974\) | 10.2364 | 0.327997 | ||||||||
\(975\) | −0.180504 | − | 2.11661i | −0.00578076 | − | 0.0677857i | ||||
\(976\) | 1.45108i | 0.0464479i | ||||||||
\(977\) | −51.6787 | −1.65335 | −0.826675 | − | 0.562680i | \(-0.809770\pi\) | ||||
−0.826675 | + | 0.562680i | \(0.809770\pi\) | |||||||
\(978\) | − | 7.14619i | − | 0.228510i | ||||||
\(979\) | − | 59.4472i | − | 1.89994i | ||||||
\(980\) | −7.34600 | + | 0.312666i | −0.234659 | + | 0.00998775i | ||||
\(981\) | − | 4.93476i | − | 0.157555i | ||||||
\(982\) | −30.2449 | −0.965155 | ||||||||
\(983\) | 37.3050i | 1.18985i | 0.803783 | + | 0.594923i | \(0.202817\pi\) | ||||
−0.803783 | + | 0.594923i | \(0.797183\pi\) | |||||||
\(984\) | 5.74899i | 0.183271i | ||||||||
\(985\) | −0.846200 | − | 19.8812i | −0.0269622 | − | 0.633469i | ||||
\(986\) | − | 23.4406i | − | 0.746500i | ||||||
\(987\) | − | 6.55479i | − | 0.208641i | ||||||
\(988\) | − | 3.40969i | − | 0.108477i | ||||||
\(989\) | −59.1147 | −1.87974 | ||||||||
\(990\) | 8.34000 | − | 0.354973i | 0.265062 | − | 0.0112818i | ||||
\(991\) | − | 25.2376i | − | 0.801699i | −0.916144 | − | 0.400850i | \(-0.868715\pi\) | ||
0.916144 | − | 0.400850i | \(-0.131285\pi\) | |||||||
\(992\) | − | 1.20338i | − | 0.0382074i | ||||||
\(993\) | 8.15238 | 0.258708 | ||||||||
\(994\) | − | 17.9520i | − | 0.569402i | ||||||
\(995\) | 0.983869 | + | 23.1157i | 0.0311907 | + | 0.732817i | ||||
\(996\) | 7.00128 | 0.221844 | ||||||||
\(997\) | −45.6991 | −1.44731 | −0.723653 | − | 0.690164i | \(-0.757538\pi\) | ||||
−0.723653 | + | 0.690164i | \(0.757538\pi\) | |||||||
\(998\) | − | 5.43439i | − | 0.172023i | ||||||
\(999\) | −1.45421 | + | 5.90637i | −0.0460093 | + | 0.186869i |
(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 | 1110.2.e.d.739.16 | yes | 16 | |
3.2 | odd | 2 | 3330.2.e.e.739.2 | 16 | |||
5.4 | even | 2 | 1110.2.e.c.739.1 | ✓ | 16 | ||
15.14 | odd | 2 | 3330.2.e.f.739.16 | 16 | |||
37.36 | even | 2 | 1110.2.e.c.739.9 | yes | 16 | ||
111.110 | odd | 2 | 3330.2.e.f.739.15 | 16 | |||
185.184 | even | 2 | inner | 1110.2.e.d.739.8 | yes | 16 | |
555.554 | odd | 2 | 3330.2.e.e.739.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.e.c.739.1 | ✓ | 16 | 5.4 | even | 2 | ||
1110.2.e.c.739.9 | yes | 16 | 37.36 | even | 2 | ||
1110.2.e.d.739.8 | yes | 16 | 185.184 | even | 2 | inner | |
1110.2.e.d.739.16 | yes | 16 | 1.1 | even | 1 | trivial | |
3330.2.e.e.739.1 | 16 | 555.554 | odd | 2 | |||
3330.2.e.e.739.2 | 16 | 3.2 | odd | 2 | |||
3330.2.e.f.739.15 | 16 | 111.110 | odd | 2 | |||
3330.2.e.f.739.16 | 16 | 15.14 | odd | 2 |