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: | \( x^{16} - 2 x^{15} + 2 x^{14} + 8 x^{13} + 138 x^{12} - 220 x^{11} + 196 x^{10} + 744 x^{9} + 4241 x^{8} - 3018 x^{7} + 658 x^{6} - 1584 x^{5} + 16372 x^{4} - 18840 x^{3} + 10952 x^{2} + \cdots + 64 \) |
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 | 739.9 | ||
Root | \(2.23405 + 2.23405i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1110.739 |
Dual form | 1110.2.e.c.739.1 |
$q$-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 | \(-0.481235\pi\) | ||||
0.0589172 | + | 0.998263i | \(0.481235\pi\) | |||||||
\(14\) | − | 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 | \(-0.816067\pi\) | ||||
−0.837643 | + | 0.546218i | \(0.816067\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | − | 8.02549i | − | 1.84117i | −0.390539 | − | 0.920586i | \(-0.627711\pi\) | ||
0.390539 | − | 0.920586i | \(-0.372289\pi\) | |||||||
\(20\) | −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 | \(-0.269712\pi\) | ||||
0.661990 | + | 0.749512i | \(0.269712\pi\) | |||||||
\(24\) | − | 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 | \(0.102033\pi\) | ||||
−0.949064 | + | 0.315084i | \(0.897967\pi\) | |||||||
\(30\) | 0.0950871 | + | 2.23405i | 0.0173605 | + | 0.407879i | ||||
\(31\) | 1.20338i | 0.216134i | 0.994144 | + | 0.108067i | \(0.0344660\pi\) | ||||
−0.994144 | + | 0.108067i | \(0.965534\pi\) | |||||||
\(32\) | −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 | \(-0.751252\pi\) | ||||
−0.709882 | + | 0.704321i | \(0.751252\pi\) | |||||||
\(44\) | −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 | \(-0.955068\pi\) | ||
0.990054 | − | 0.140689i | \(-0.0449318\pi\) | |||||||
\(60\) | −0.0950871 | − | 2.23405i | −0.0122757 | − | 0.288414i | ||||
\(61\) | − | 1.45108i | − | 0.185791i | −0.995676 | − | 0.0928957i | \(-0.970388\pi\) | ||
0.995676 | − | 0.0928957i | \(-0.0296123\pi\) | |||||||
\(62\) | − | 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 | \(0.0815538\pi\) | ||||
−0.967358 | + | 0.253415i | \(0.918446\pi\) | |||||||
\(80\) | −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 | \(-0.680206\pi\) | ||
0.536373 | − | 0.843981i | \(-0.319794\pi\) | |||||||
\(90\) | −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 | \(-0.427668\pi\) | ||||
0.225286 | + | 0.974293i | \(0.427668\pi\) | |||||||
\(98\) | 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 | \(-0.614963\pi\) | ||||
−0.353366 | + | 0.935485i | \(0.614963\pi\) | |||||||
\(104\) | −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 | \(-0.924055\pi\) | ||
0.971672 | − | 0.236332i | \(-0.0759454\pi\) | |||||||
\(110\) | −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 | \(-0.644093\pi\) | ||||
−0.437379 | + | 0.899277i | \(0.644093\pi\) | |||||||
\(114\) | −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 | \(0.180957\pi\) | ||||
−0.842714 | + | 0.538362i | \(0.819043\pi\) | |||||||
\(132\) | − | 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 | \(-0.409710\pi\) | ||||
0.279867 | + | 0.960039i | \(0.409710\pi\) | |||||||
\(164\) | 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 | \(-0.663071\pi\) | ||||
−0.490187 | + | 0.871618i | \(0.663071\pi\) | |||||||
\(168\) | 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 | \(-0.961888\pi\) | ||
0.992841 | − | 0.119447i | \(-0.0381123\pi\) | |||||||
\(180\) | 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 | ||||||||
\(185\) | −13.0568 | + | 3.81040i | −0.959957 | + | 0.280146i | ||||
\(186\) | 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 | \(0.149153\pi\) | ||||
−0.892212 | + | 0.451617i | \(0.850847\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | −12.1559 | −0.874999 | −0.437499 | − | 0.899219i | \(-0.644136\pi\) | ||||
−0.437499 | + | 0.899219i | \(0.644136\pi\) | |||||||
\(194\) | −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 | \(-0.880474\pi\) | ||
0.930323 | − | 0.366740i | \(-0.119526\pi\) | |||||||
\(200\) | −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 | \(-0.534322\pi\) | ||||
−0.107617 | + | 0.994192i | \(0.534322\pi\) | |||||||
\(228\) | 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 | \(0.0701208\pi\) | ||||
−0.975834 | + | 0.218514i | \(0.929879\pi\) | |||||||
\(240\) | −0.0950871 | − | 2.23405i | −0.00613785 | − | 0.144207i | ||||
\(241\) | 27.0533i | 1.74266i | 0.490699 | + | 0.871329i | \(0.336741\pi\) | ||||
−0.490699 | + | 0.871329i | \(0.663259\pi\) | |||||||
\(242\) | −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 | \(0.133880\pi\) | ||||
−0.912846 | + | 0.408305i | \(0.866120\pi\) | |||||||
\(252\) | − | 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 | \(-0.650445\pi\) | ||||
−0.455237 | + | 0.890370i | \(0.650445\pi\) | |||||||
\(258\) | 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 | \(-0.376367\pi\) | ||||
0.378713 | + | 0.925514i | \(0.376367\pi\) | |||||||
\(278\) | 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 | \(-0.843007\pi\) | ||
0.880819 | − | 0.473454i | \(-0.156993\pi\) | |||||||
\(282\) | 2.04357 | 0.121693 | ||||||||
\(283\) | −29.1588 | −1.73331 | −0.866656 | − | 0.498906i | \(-0.833735\pi\) | ||||
−0.866656 | + | 0.498906i | \(0.833735\pi\) | |||||||
\(284\) | −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 | \(0.139882\pi\) | ||||
−0.904985 | + | 0.425443i | \(0.860118\pi\) | |||||||
\(312\) | − | 0.424858i | − | 0.0240528i | ||||||
\(313\) | 28.8720 | 1.63194 | 0.815972 | − | 0.578092i | \(-0.196202\pi\) | ||||
0.815972 | + | 0.578092i | \(0.196202\pi\) | |||||||
\(314\) | 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 | \(0.0719271\pi\) | ||||
−0.974578 | + | 0.224048i | \(0.928073\pi\) | |||||||
\(332\) | − | 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 | \(-0.441326\pi\) | ||||
0.183287 | + | 0.983059i | \(0.441326\pi\) | |||||||
\(348\) | −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 | \(-0.389492\pi\) | ||||
0.340238 | + | 0.940339i | \(0.389492\pi\) | |||||||
\(354\) | −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 | ||||||||
\(370\) | 13.0568 | − | 3.81040i | 0.678792 | − | 0.198093i | ||||
\(371\) | 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 | \(-0.592724\pi\) | ||||
−0.287199 | + | 0.957871i | \(0.592724\pi\) | |||||||
\(384\) | − | 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 | \(0.0634218\pi\) | ||||
−0.980216 | + | 0.197930i | \(0.936578\pi\) | |||||||
\(390\) | 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 | \(-0.688638\pi\) | ||
0.558540 | − | 0.829478i | \(-0.311362\pi\) | |||||||
\(402\) | −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 | \(-0.849121\pi\) | ||
0.889749 | − | 0.456449i | \(-0.150879\pi\) | |||||||
\(410\) | 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 | \(-0.764477\pi\) | ||
0.738525 | − | 0.674227i | \(-0.235523\pi\) | |||||||
\(422\) | −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 | \(0.0380008\pi\) | ||||
−0.992882 | + | 0.119100i | \(0.961999\pi\) | |||||||
\(432\) | − | 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 | \(-0.770809\pi\) | ||
0.751789 | − | 0.659404i | \(-0.229191\pi\) | |||||||
\(440\) | −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 | \(-0.795619\pi\) | ||
0.800850 | − | 0.598864i | \(-0.204381\pi\) | |||||||
\(450\) | 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 | \(-0.0651480\pi\) | ||||
0.979128 | + | 0.203243i | \(0.0651480\pi\) | |||||||
\(458\) | 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 | \(-0.926198\pi\) | ||
0.973242 | − | 0.229783i | \(-0.0738017\pi\) | |||||||
\(462\) | −11.9741 | −0.557087 | ||||||||
\(463\) | −2.13573 | −0.0992558 | −0.0496279 | − | 0.998768i | \(-0.515804\pi\) | ||||
−0.0496279 | + | 0.998768i | \(0.515804\pi\) | |||||||
\(464\) | 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 | \(-0.679746\pi\) | ||||
−0.535154 | + | 0.844755i | \(0.679746\pi\) | |||||||
\(468\) | −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 | \(-0.582736\pi\) | ||
0.257006 | − | 0.966410i | \(-0.417264\pi\) | |||||||
\(480\) | 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 | \(-0.574504\pi\) | ||||
−0.231929 | + | 0.972733i | \(0.574504\pi\) | |||||||
\(488\) | 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 | \(0.0388148\pi\) | ||||
−0.992574 | + | 0.121638i | \(0.961185\pi\) | |||||||
\(500\) | −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 | \(-0.510837\pi\) | ||||
−0.0340380 | + | 0.999421i | \(0.510837\pi\) | |||||||
\(504\) | 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 | \(-0.625335\pi\) | ||||
−0.383654 | + | 0.923477i | \(0.625335\pi\) | |||||||
\(524\) | 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 | \(-0.832570\pi\) | ||
0.864824 | − | 0.502076i | \(-0.167430\pi\) | |||||||
\(542\) | 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 | \(-0.608850\pi\) | ||||
−0.335337 | + | 0.942098i | \(0.608850\pi\) | |||||||
\(548\) | − | 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 | ||||||||
\(555\) | −3.81040 | − | 13.0568i | −0.161742 | − | 0.554232i | ||||
\(556\) | −0.125741 | −0.00533261 | ||||||||
\(557\) | 39.5638 | 1.67637 | 0.838186 | − | 0.545384i | \(-0.183616\pi\) | ||||
0.838186 | + | 0.545384i | \(0.183616\pi\) | |||||||
\(558\) | 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 | \(-0.260266\pi\) | ||||
0.683939 | + | 0.729540i | \(0.260266\pi\) | |||||||
\(564\) | −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 | \(0.0216769\pi\) | ||||
−0.997682 | + | 0.0680472i | \(0.978323\pi\) | |||||||
\(570\) | 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 | \(-0.596743\pi\) | ||||
−0.299269 | + | 0.954169i | \(0.596743\pi\) | |||||||
\(578\) | −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 | \(-0.421437\pi\) | ||||
0.244316 | + | 0.969696i | \(0.421437\pi\) | |||||||
\(588\) | − | 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 | \(-0.703897\pi\) | ||||
−0.597645 | + | 0.801760i | \(0.703897\pi\) | |||||||
\(608\) | 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 | \(-0.910615\pi\) | ||
0.960831 | − | 0.277134i | \(-0.0893847\pi\) | |||||||
\(632\) | − | 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 | \(-0.542180\pi\) | ||||
−0.132125 | + | 0.991233i | \(0.542180\pi\) | |||||||
\(644\) | 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 | \(-0.487335\pi\) | ||||
0.0397781 | + | 0.999209i | \(0.487335\pi\) | |||||||
\(648\) | −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 | \(-0.386477\pi\) | ||||
0.349131 | + | 0.937074i | \(0.386477\pi\) | |||||||
\(654\) | −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 | \(-0.906064\pi\) | ||
0.956771 | − | 0.290843i | \(-0.0939358\pi\) | |||||||
\(662\) | − | 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 | \(-0.503091\pi\) | ||||
−0.00971163 | + | 0.999953i | \(0.503091\pi\) | |||||||
\(684\) | 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 | \(0.0819332\pi\) | ||||
−0.967055 | + | 0.254568i | \(0.918067\pi\) | |||||||
\(702\) | 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 | \(-0.902291\pi\) | ||
0.953256 | − | 0.302163i | \(-0.0977086\pi\) | |||||||
\(710\) | −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 | \(-0.302689\pi\) | ||||
0.580931 | + | 0.813953i | \(0.302689\pi\) | |||||||
\(728\) | − | 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 | \(0.407569\pi\) | |||||||
\(740\) | −13.0568 | + | 3.81040i | −0.479979 | + | 0.140073i | ||||
\(741\) | 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 | \(-0.660083\pi\) | ||||
−0.481982 | + | 0.876181i | \(0.660083\pi\) | |||||||
\(758\) | 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 | \(0.0380278\pi\) | ||||
−0.992872 | + | 0.119184i | \(0.961972\pi\) | |||||||
\(770\) | −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 | \(-0.595123\pi\) | ||||
−0.294409 | + | 0.955680i | \(0.595123\pi\) | |||||||
\(798\) | − | 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 | \(0.230454\pi\) | ||||
−0.749166 | + | 0.662382i | \(0.769546\pi\) | |||||||
\(810\) | 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 | \(-0.203451\pi\) | ||||
0.802597 | + | 0.596522i | \(0.203451\pi\) | |||||||
\(828\) | −6.34959 | −0.220663 | ||||||||
\(829\) | 7.43600i | 0.258263i | 0.991627 | + | 0.129131i | \(0.0412189\pi\) | ||||
−0.991627 | + | 0.129131i | \(0.958781\pi\) | |||||||
\(830\) | −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 | \(-0.333957\pi\) | ||||
0.498302 | + | 0.867003i | \(0.333957\pi\) | |||||||
\(854\) | −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 | \(-0.649120\pi\) | ||||
−0.451525 | + | 0.892259i | \(0.649120\pi\) | |||||||
\(858\) | 1.58605i | 0.0541470i | ||||||||
\(859\) | 3.12912i | 0.106764i | 0.998574 | + | 0.0533821i | \(0.0170001\pi\) | ||||
−0.998574 | + | 0.0533821i | \(0.983000\pi\) | |||||||
\(860\) | 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 | \(-0.469517\pi\) | ||||
0.0956189 | + | 0.995418i | \(0.469517\pi\) | |||||||
\(884\) | −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 | \(-0.890593\pi\) | ||||
−0.941510 | + | 0.336985i | \(0.890593\pi\) | |||||||
\(908\) | −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 | \(0.207862\pi\) | ||||
−0.794254 | + | 0.607586i | \(0.792138\pi\) | |||||||
\(912\) | 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 | \(-0.950598\pi\) | ||
0.987981 | − | 0.154578i | \(-0.0494019\pi\) | |||||||
\(920\) | 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 | ||||||||
\(925\) | 28.8072 | − | 9.75414i | 0.947176 | − | 0.320714i | ||||
\(926\) | 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 | \(-0.401470\pi\) | ||||
0.304621 | + | 0.952474i | \(0.401470\pi\) | |||||||
\(948\) | −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 | \(-0.615889\pi\) | ||||
−0.356087 | + | 0.934453i | \(0.615889\pi\) | |||||||
\(968\) | −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 | \(-0.190230\pi\) | ||||
0.826675 | + | 0.562680i | \(0.190230\pi\) | |||||||
\(978\) | − | 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 | \(0.131285\pi\) | ||||
−0.916144 | + | 0.400850i | \(0.868715\pi\) | |||||||
\(992\) | − | 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 | \(-0.242462\pi\) | ||||
0.723653 | + | 0.690164i | \(0.242462\pi\) | |||||||
\(998\) | − | 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.c.739.9 | yes | 16 | |
3.2 | odd | 2 | 3330.2.e.f.739.15 | 16 | |||
5.4 | even | 2 | 1110.2.e.d.739.8 | yes | 16 | ||
15.14 | odd | 2 | 3330.2.e.e.739.1 | 16 | |||
37.36 | even | 2 | 1110.2.e.d.739.16 | yes | 16 | ||
111.110 | odd | 2 | 3330.2.e.e.739.2 | 16 | |||
185.184 | even | 2 | inner | 1110.2.e.c.739.1 | ✓ | 16 | |
555.554 | odd | 2 | 3330.2.e.f.739.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.e.c.739.1 | ✓ | 16 | 185.184 | even | 2 | inner | |
1110.2.e.c.739.9 | yes | 16 | 1.1 | even | 1 | trivial | |
1110.2.e.d.739.8 | yes | 16 | 5.4 | even | 2 | ||
1110.2.e.d.739.16 | yes | 16 | 37.36 | even | 2 | ||
3330.2.e.e.739.1 | 16 | 15.14 | odd | 2 | |||
3330.2.e.e.739.2 | 16 | 111.110 | odd | 2 | |||
3330.2.e.f.739.15 | 16 | 3.2 | odd | 2 | |||
3330.2.e.f.739.16 | 16 | 555.554 | odd | 2 |