Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(59,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.59");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.t (of order \(6\), degree \(2\), 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: | \(1.67685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 59.2 | ||
Root | \(-1.18614 + 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.59 |
Dual form | 210.2.t.b.89.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 1.18614 | − | 1.26217i | 0.684819 | − | 0.728714i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.686141 | + | 2.12819i | 0.306851 | + | 0.951757i | ||||
\(6\) | −1.68614 | − | 0.396143i | −0.688364 | − | 0.161725i | ||||
\(7\) | 2.50000 | − | 0.866025i | 0.944911 | − | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.186141 | − | 2.99422i | −0.0620469 | − | 0.998073i | ||||
\(10\) | 1.50000 | − | 1.65831i | 0.474342 | − | 0.524404i | ||||
\(11\) | 0.813859 | + | 0.469882i | 0.245388 | + | 0.141675i | 0.617651 | − | 0.786453i | \(-0.288085\pi\) |
−0.372263 | + | 0.928127i | \(0.621418\pi\) | |||||||
\(12\) | 0.500000 | + | 1.65831i | 0.144338 | + | 0.478714i | ||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | −2.00000 | − | 1.73205i | −0.534522 | − | 0.462910i | ||||
\(15\) | 3.50000 | + | 1.65831i | 0.903696 | + | 0.428174i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −5.74456 | − | 3.31662i | −1.39326 | − | 0.804400i | −0.399586 | − | 0.916696i | \(-0.630846\pi\) |
−0.993675 | + | 0.112296i | \(0.964180\pi\) | |||||||
\(18\) | −2.50000 | + | 1.65831i | −0.589256 | + | 0.390868i | ||||
\(19\) | −3.00000 | + | 1.73205i | −0.688247 | + | 0.397360i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | −2.18614 | − | 0.469882i | −0.488836 | − | 0.105069i | ||||
\(21\) | 1.87228 | − | 4.18265i | 0.408565 | − | 0.912729i | ||||
\(22\) | − | 0.939764i | − | 0.200358i | ||||||
\(23\) | 0.686141 | + | 1.18843i | 0.143070 | + | 0.247805i | 0.928651 | − | 0.370954i | \(-0.120969\pi\) |
−0.785581 | + | 0.618759i | \(0.787636\pi\) | |||||||
\(24\) | 1.18614 | − | 1.26217i | 0.242120 | − | 0.257639i | ||||
\(25\) | −4.05842 | + | 2.92048i | −0.811684 | + | 0.584096i | ||||
\(26\) | −1.00000 | − | 1.73205i | −0.196116 | − | 0.339683i | ||||
\(27\) | −4.00000 | − | 3.31662i | −0.769800 | − | 0.638285i | ||||
\(28\) | −0.500000 | + | 2.59808i | −0.0944911 | + | 0.490990i | ||||
\(29\) | − | 3.31662i | − | 0.615882i | −0.951405 | − | 0.307941i | \(-0.900360\pi\) | ||
0.951405 | − | 0.307941i | \(-0.0996399\pi\) | |||||||
\(30\) | −0.313859 | − | 3.86025i | −0.0573026 | − | 0.704781i | ||||
\(31\) | 6.55842 | + | 3.78651i | 1.17793 | + | 0.680077i | 0.955534 | − | 0.294880i | \(-0.0952798\pi\) |
0.222393 | + | 0.974957i | \(0.428613\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 1.55842 | − | 0.469882i | 0.271286 | − | 0.0817959i | ||||
\(34\) | 6.63325i | 1.13759i | ||||||||
\(35\) | 3.55842 | + | 4.72627i | 0.601483 | + | 0.798886i | ||||
\(36\) | 2.68614 | + | 1.33591i | 0.447690 | + | 0.222651i | ||||
\(37\) | −7.11684 | + | 4.10891i | −1.17000 | + | 0.675501i | −0.953681 | − | 0.300821i | \(-0.902739\pi\) |
−0.216321 | + | 0.976322i | \(0.569406\pi\) | |||||||
\(38\) | 3.00000 | + | 1.73205i | 0.486664 | + | 0.280976i | ||||
\(39\) | 2.37228 | − | 2.52434i | 0.379869 | − | 0.404218i | ||||
\(40\) | 0.686141 | + | 2.12819i | 0.108488 | + | 0.336497i | ||||
\(41\) | 7.37228 | 1.15136 | 0.575678 | − | 0.817676i | \(-0.304738\pi\) | ||||
0.575678 | + | 0.817676i | \(0.304738\pi\) | |||||||
\(42\) | −4.55842 | + | 0.469882i | −0.703380 | + | 0.0725044i | ||||
\(43\) | 1.08724i | 0.165803i | 0.996558 | + | 0.0829013i | \(0.0264186\pi\) | ||||
−0.996558 | + | 0.0829013i | \(0.973581\pi\) | |||||||
\(44\) | −0.813859 | + | 0.469882i | −0.122694 | + | 0.0708374i | ||||
\(45\) | 6.24456 | − | 2.45060i | 0.930884 | − | 0.365314i | ||||
\(46\) | 0.686141 | − | 1.18843i | 0.101166 | − | 0.175225i | ||||
\(47\) | −7.37228 | + | 4.25639i | −1.07536 | + | 0.620858i | −0.929640 | − | 0.368468i | \(-0.879882\pi\) |
−0.145717 | + | 0.989326i | \(0.546549\pi\) | |||||||
\(48\) | −1.68614 | − | 0.396143i | −0.243373 | − | 0.0571784i | ||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 4.55842 | + | 2.05446i | 0.644658 | + | 0.290544i | ||||
\(51\) | −11.0000 | + | 3.31662i | −1.54031 | + | 0.464420i | ||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | 2.18614 | − | 3.78651i | 0.300290 | − | 0.520117i | −0.675912 | − | 0.736982i | \(-0.736250\pi\) |
0.976201 | + | 0.216866i | \(0.0695834\pi\) | |||||||
\(54\) | −0.872281 | + | 5.12241i | −0.118702 | + | 0.697072i | ||||
\(55\) | −0.441578 | + | 2.05446i | −0.0595424 | + | 0.277023i | ||||
\(56\) | 2.50000 | − | 0.866025i | 0.334077 | − | 0.115728i | ||||
\(57\) | −1.37228 | + | 5.84096i | −0.181763 | + | 0.773654i | ||||
\(58\) | −2.87228 | + | 1.65831i | −0.377149 | + | 0.217747i | ||||
\(59\) | −6.55842 | + | 11.3595i | −0.853834 | + | 1.47888i | 0.0238889 | + | 0.999715i | \(0.492395\pi\) |
−0.877723 | + | 0.479169i | \(0.840938\pi\) | |||||||
\(60\) | −3.18614 | + | 2.20193i | −0.411329 | + | 0.284268i | ||||
\(61\) | −11.0584 | + | 6.38458i | −1.41589 | + | 0.817462i | −0.995934 | − | 0.0900844i | \(-0.971286\pi\) |
−0.419952 | + | 0.907546i | \(0.637953\pi\) | |||||||
\(62\) | − | 7.57301i | − | 0.961774i | ||||||
\(63\) | −3.05842 | − | 7.32435i | −0.385325 | − | 0.922781i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.37228 | + | 4.25639i | 0.170211 | + | 0.527940i | ||||
\(66\) | −1.18614 | − | 1.11469i | −0.146004 | − | 0.137209i | ||||
\(67\) | 2.05842 | + | 1.18843i | 0.251476 | + | 0.145190i | 0.620440 | − | 0.784254i | \(-0.286954\pi\) |
−0.368964 | + | 0.929444i | \(0.620287\pi\) | |||||||
\(68\) | 5.74456 | − | 3.31662i | 0.696631 | − | 0.402200i | ||||
\(69\) | 2.31386 | + | 0.543620i | 0.278556 | + | 0.0654442i | ||||
\(70\) | 2.31386 | − | 5.44482i | 0.276559 | − | 0.650780i | ||||
\(71\) | − | 8.51278i | − | 1.01028i | −0.863037 | − | 0.505140i | \(-0.831441\pi\) | ||
0.863037 | − | 0.505140i | \(-0.168559\pi\) | |||||||
\(72\) | −0.186141 | − | 2.99422i | −0.0219369 | − | 0.352872i | ||||
\(73\) | −1.00000 | + | 1.73205i | −0.117041 | + | 0.202721i | −0.918594 | − | 0.395203i | \(-0.870674\pi\) |
0.801553 | + | 0.597924i | \(0.204008\pi\) | |||||||
\(74\) | 7.11684 | + | 4.10891i | 0.827316 | + | 0.477651i | ||||
\(75\) | −1.12772 | + | 8.58652i | −0.130218 | + | 0.991485i | ||||
\(76\) | − | 3.46410i | − | 0.397360i | ||||||
\(77\) | 2.44158 | + | 0.469882i | 0.278244 | + | 0.0535480i | ||||
\(78\) | −3.37228 | − | 0.792287i | −0.381836 | − | 0.0897088i | ||||
\(79\) | −4.55842 | − | 7.89542i | −0.512863 | − | 0.888304i | −0.999889 | − | 0.0149166i | \(-0.995252\pi\) |
0.487026 | − | 0.873387i | \(-0.338082\pi\) | |||||||
\(80\) | 1.50000 | − | 1.65831i | 0.167705 | − | 0.185405i | ||||
\(81\) | −8.93070 | + | 1.11469i | −0.992300 | + | 0.123855i | ||||
\(82\) | −3.68614 | − | 6.38458i | −0.407066 | − | 0.705059i | ||||
\(83\) | 11.8294i | 1.29845i | 0.760598 | + | 0.649223i | \(0.224906\pi\) | ||||
−0.760598 | + | 0.649223i | \(0.775094\pi\) | |||||||
\(84\) | 2.68614 | + | 3.71277i | 0.293082 | + | 0.405096i | ||||
\(85\) | 3.11684 | − | 14.5012i | 0.338069 | − | 1.57288i | ||||
\(86\) | 0.941578 | − | 0.543620i | 0.101533 | − | 0.0586201i | ||||
\(87\) | −4.18614 | − | 3.93398i | −0.448801 | − | 0.421767i | ||||
\(88\) | 0.813859 | + | 0.469882i | 0.0867577 | + | 0.0500896i | ||||
\(89\) | −0.686141 | − | 1.18843i | −0.0727308 | − | 0.125973i | 0.827366 | − | 0.561662i | \(-0.189838\pi\) |
−0.900097 | + | 0.435689i | \(0.856505\pi\) | |||||||
\(90\) | −5.24456 | − | 4.18265i | −0.552825 | − | 0.440890i | ||||
\(91\) | 5.00000 | − | 1.73205i | 0.524142 | − | 0.181568i | ||||
\(92\) | −1.37228 | −0.143070 | ||||||||
\(93\) | 12.5584 | − | 3.78651i | 1.30225 | − | 0.392642i | ||||
\(94\) | 7.37228 | + | 4.25639i | 0.760393 | + | 0.439013i | ||||
\(95\) | −5.74456 | − | 5.19615i | −0.589380 | − | 0.533114i | ||||
\(96\) | 0.500000 | + | 1.65831i | 0.0510310 | + | 0.169251i | ||||
\(97\) | 15.1168 | 1.53488 | 0.767441 | − | 0.641119i | \(-0.221530\pi\) | ||||
0.767441 | + | 0.641119i | \(0.221530\pi\) | |||||||
\(98\) | −6.50000 | − | 2.59808i | −0.656599 | − | 0.262445i | ||||
\(99\) | 1.25544 | − | 2.52434i | 0.126176 | − | 0.253705i | ||||
\(100\) | −0.500000 | − | 4.97494i | −0.0500000 | − | 0.497494i | ||||
\(101\) | 5.31386 | − | 9.20387i | 0.528749 | − | 0.915820i | −0.470689 | − | 0.882299i | \(-0.655995\pi\) |
0.999438 | − | 0.0335207i | \(-0.0106720\pi\) | |||||||
\(102\) | 8.37228 | + | 7.86797i | 0.828979 | + | 0.779045i | ||||
\(103\) | 1.05842 | + | 1.83324i | 0.104289 | + | 0.180635i | 0.913448 | − | 0.406956i | \(-0.133410\pi\) |
−0.809158 | + | 0.587591i | \(0.800077\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 10.1861 | + | 1.11469i | 0.994066 | + | 0.108783i | ||||
\(106\) | −4.37228 | −0.424674 | ||||||||
\(107\) | −3.12772 | − | 5.41737i | −0.302368 | − | 0.523717i | 0.674304 | − | 0.738454i | \(-0.264444\pi\) |
−0.976672 | + | 0.214737i | \(0.931110\pi\) | |||||||
\(108\) | 4.87228 | − | 1.80579i | 0.468835 | − | 0.173762i | ||||
\(109\) | 4.05842 | − | 7.02939i | 0.388726 | − | 0.673294i | −0.603552 | − | 0.797324i | \(-0.706248\pi\) |
0.992278 | + | 0.124030i | \(0.0395818\pi\) | |||||||
\(110\) | 2.00000 | − | 0.644810i | 0.190693 | − | 0.0614802i | ||||
\(111\) | −3.25544 | + | 13.8564i | −0.308992 | + | 1.31519i | ||||
\(112\) | −2.00000 | − | 1.73205i | −0.188982 | − | 0.163663i | ||||
\(113\) | −14.7446 | −1.38705 | −0.693526 | − | 0.720432i | \(-0.743944\pi\) | ||||
−0.693526 | + | 0.720432i | \(0.743944\pi\) | |||||||
\(114\) | 5.74456 | − | 1.73205i | 0.538028 | − | 0.162221i | ||||
\(115\) | −2.05842 | + | 2.27567i | −0.191949 | + | 0.212207i | ||||
\(116\) | 2.87228 | + | 1.65831i | 0.266685 | + | 0.153970i | ||||
\(117\) | −0.372281 | − | 5.98844i | −0.0344174 | − | 0.553631i | ||||
\(118\) | 13.1168 | 1.20750 | ||||||||
\(119\) | −17.2337 | − | 3.31662i | −1.57981 | − | 0.304034i | ||||
\(120\) | 3.50000 | + | 1.65831i | 0.319505 | + | 0.151383i | ||||
\(121\) | −5.05842 | − | 8.76144i | −0.459857 | − | 0.796495i | ||||
\(122\) | 11.0584 | + | 6.38458i | 1.00118 | + | 0.578033i | ||||
\(123\) | 8.74456 | − | 9.30506i | 0.788471 | − | 0.839009i | ||||
\(124\) | −6.55842 | + | 3.78651i | −0.588964 | + | 0.340038i | ||||
\(125\) | −9.00000 | − | 6.63325i | −0.804984 | − | 0.593296i | ||||
\(126\) | −4.81386 | + | 6.31084i | −0.428853 | + | 0.562215i | ||||
\(127\) | − | 7.57301i | − | 0.671996i | −0.941863 | − | 0.335998i | \(-0.890926\pi\) | ||
0.941863 | − | 0.335998i | \(-0.109074\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.37228 | + | 1.28962i | 0.120823 | + | 0.113545i | ||||
\(130\) | 3.00000 | − | 3.31662i | 0.263117 | − | 0.290887i | ||||
\(131\) | 5.18614 | + | 8.98266i | 0.453115 | + | 0.784819i | 0.998578 | − | 0.0533167i | \(-0.0169793\pi\) |
−0.545462 | + | 0.838135i | \(0.683646\pi\) | |||||||
\(132\) | −0.372281 | + | 1.58457i | −0.0324029 | + | 0.137919i | ||||
\(133\) | −6.00000 | + | 6.92820i | −0.520266 | + | 0.600751i | ||||
\(134\) | − | 2.37686i | − | 0.205330i | ||||||
\(135\) | 4.31386 | − | 10.7884i | 0.371278 | − | 0.928522i | ||||
\(136\) | −5.74456 | − | 3.31662i | −0.492592 | − | 0.284398i | ||||
\(137\) | 4.37228 | − | 7.57301i | 0.373549 | − | 0.647006i | −0.616560 | − | 0.787308i | \(-0.711474\pi\) |
0.990109 | + | 0.140302i | \(0.0448074\pi\) | |||||||
\(138\) | −0.686141 | − | 2.27567i | −0.0584082 | − | 0.193718i | ||||
\(139\) | − | 8.21782i | − | 0.697027i | −0.937304 | − | 0.348513i | \(-0.886687\pi\) | ||
0.937304 | − | 0.348513i | \(-0.113313\pi\) | |||||||
\(140\) | −5.87228 | + | 0.718549i | −0.496298 | + | 0.0607284i | ||||
\(141\) | −3.37228 | + | 14.3537i | −0.283997 | + | 1.20880i | ||||
\(142\) | −7.37228 | + | 4.25639i | −0.618668 | + | 0.357188i | ||||
\(143\) | 1.62772 | + | 0.939764i | 0.136117 | + | 0.0785870i | ||||
\(144\) | −2.50000 | + | 1.65831i | −0.208333 | + | 0.138193i | ||||
\(145\) | 7.05842 | − | 2.27567i | 0.586170 | − | 0.188984i | ||||
\(146\) | 2.00000 | 0.165521 | ||||||||
\(147\) | 1.05842 | − | 12.0781i | 0.0872972 | − | 0.996182i | ||||
\(148\) | − | 8.21782i | − | 0.675501i | ||||||
\(149\) | 7.80298 | − | 4.50506i | 0.639245 | − | 0.369069i | −0.145078 | − | 0.989420i | \(-0.546343\pi\) |
0.784324 | + | 0.620352i | \(0.213010\pi\) | |||||||
\(150\) | 8.00000 | − | 3.31662i | 0.653197 | − | 0.270801i | ||||
\(151\) | −4.55842 | + | 7.89542i | −0.370959 | + | 0.642520i | −0.989713 | − | 0.143065i | \(-0.954304\pi\) |
0.618754 | + | 0.785585i | \(0.287638\pi\) | |||||||
\(152\) | −3.00000 | + | 1.73205i | −0.243332 | + | 0.140488i | ||||
\(153\) | −8.86141 | + | 17.8178i | −0.716402 | + | 1.44049i | ||||
\(154\) | −0.813859 | − | 2.34941i | −0.0655827 | − | 0.189321i | ||||
\(155\) | −3.55842 | + | 16.5557i | −0.285819 | + | 1.32978i | ||||
\(156\) | 1.00000 | + | 3.31662i | 0.0800641 | + | 0.265543i | ||||
\(157\) | −4.00000 | + | 6.92820i | −0.319235 | + | 0.552931i | −0.980329 | − | 0.197372i | \(-0.936759\pi\) |
0.661094 | + | 0.750303i | \(0.270093\pi\) | |||||||
\(158\) | −4.55842 | + | 7.89542i | −0.362649 | + | 0.628126i | ||||
\(159\) | −2.18614 | − | 7.25061i | −0.173372 | − | 0.575011i | ||||
\(160\) | −2.18614 | − | 0.469882i | −0.172830 | − | 0.0371474i | ||||
\(161\) | 2.74456 | + | 2.37686i | 0.216302 | + | 0.187323i | ||||
\(162\) | 5.43070 | + | 7.17687i | 0.426676 | + | 0.563868i | ||||
\(163\) | −3.00000 | + | 1.73205i | −0.234978 | + | 0.135665i | −0.612866 | − | 0.790186i | \(-0.709984\pi\) |
0.377888 | + | 0.925851i | \(0.376650\pi\) | |||||||
\(164\) | −3.68614 | + | 6.38458i | −0.287839 | + | 0.498552i | ||||
\(165\) | 2.06930 | + | 2.99422i | 0.161095 | + | 0.233100i | ||||
\(166\) | 10.2446 | − | 5.91470i | 0.795132 | − | 0.459070i | ||||
\(167\) | 14.6487i | 1.13355i | 0.823873 | + | 0.566775i | \(0.191809\pi\) | ||||
−0.823873 | + | 0.566775i | \(0.808191\pi\) | |||||||
\(168\) | 1.87228 | − | 4.18265i | 0.144450 | − | 0.322698i | ||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −14.1168 | + | 4.55134i | −1.08271 | + | 0.349072i | ||||
\(171\) | 5.74456 | + | 8.66025i | 0.439298 | + | 0.662266i | ||||
\(172\) | −0.941578 | − | 0.543620i | −0.0717947 | − | 0.0414507i | ||||
\(173\) | 14.7446 | − | 8.51278i | 1.12101 | − | 0.647214i | 0.179350 | − | 0.983785i | \(-0.442600\pi\) |
0.941658 | + | 0.336571i | \(0.109267\pi\) | |||||||
\(174\) | −1.31386 | + | 5.59230i | −0.0996034 | + | 0.423951i | ||||
\(175\) | −7.61684 | + | 10.8159i | −0.575779 | + | 0.817605i | ||||
\(176\) | − | 0.939764i | − | 0.0708374i | ||||||
\(177\) | 6.55842 | + | 21.7518i | 0.492961 | + | 1.63497i | ||||
\(178\) | −0.686141 | + | 1.18843i | −0.0514284 | + | 0.0890766i | ||||
\(179\) | 20.4891 | + | 11.8294i | 1.53143 | + | 0.884171i | 0.999296 | + | 0.0375102i | \(0.0119427\pi\) |
0.532133 | + | 0.846661i | \(0.321391\pi\) | |||||||
\(180\) | −1.00000 | + | 6.63325i | −0.0745356 | + | 0.494413i | ||||
\(181\) | − | 8.01544i | − | 0.595783i | −0.954600 | − | 0.297892i | \(-0.903717\pi\) | ||
0.954600 | − | 0.297892i | \(-0.0962834\pi\) | |||||||
\(182\) | −4.00000 | − | 3.46410i | −0.296500 | − | 0.256776i | ||||
\(183\) | −5.05842 | + | 21.5306i | −0.373929 | + | 1.59159i | ||||
\(184\) | 0.686141 | + | 1.18843i | 0.0505830 | + | 0.0876123i | ||||
\(185\) | −13.6277 | − | 12.3267i | −1.00193 | − | 0.906280i | ||||
\(186\) | −9.55842 | − | 8.98266i | −0.700858 | − | 0.658641i | ||||
\(187\) | −3.11684 | − | 5.39853i | −0.227926 | − | 0.394780i | ||||
\(188\) | − | 8.51278i | − | 0.620858i | ||||||
\(189\) | −12.8723 | − | 4.82746i | −0.936321 | − | 0.351146i | ||||
\(190\) | −1.62772 | + | 7.57301i | −0.118087 | + | 0.549404i | ||||
\(191\) | 14.7446 | − | 8.51278i | 1.06688 | − | 0.615963i | 0.139552 | − | 0.990215i | \(-0.455434\pi\) |
0.927327 | + | 0.374252i | \(0.122100\pi\) | |||||||
\(192\) | 1.18614 | − | 1.26217i | 0.0856023 | − | 0.0910892i | ||||
\(193\) | −15.5584 | − | 8.98266i | −1.11992 | − | 0.646586i | −0.178539 | − | 0.983933i | \(-0.557137\pi\) |
−0.941380 | + | 0.337347i | \(0.890470\pi\) | |||||||
\(194\) | −7.55842 | − | 13.0916i | −0.542663 | − | 0.939920i | ||||
\(195\) | 7.00000 | + | 3.31662i | 0.501280 | + | 0.237508i | ||||
\(196\) | 1.00000 | + | 6.92820i | 0.0714286 | + | 0.494872i | ||||
\(197\) | 14.2337 | 1.01411 | 0.507054 | − | 0.861914i | \(-0.330734\pi\) | ||||
0.507054 | + | 0.861914i | \(0.330734\pi\) | |||||||
\(198\) | −2.81386 | + | 0.174928i | −0.199972 | + | 0.0124316i | ||||
\(199\) | 1.11684 | + | 0.644810i | 0.0791710 | + | 0.0457094i | 0.539063 | − | 0.842266i | \(-0.318779\pi\) |
−0.459892 | + | 0.887975i | \(0.652112\pi\) | |||||||
\(200\) | −4.05842 | + | 2.92048i | −0.286974 | + | 0.206509i | ||||
\(201\) | 3.94158 | − | 1.18843i | 0.278017 | − | 0.0838254i | ||||
\(202\) | −10.6277 | −0.747764 | ||||||||
\(203\) | −2.87228 | − | 8.29156i | −0.201595 | − | 0.581954i | ||||
\(204\) | 2.62772 | − | 11.1846i | 0.183977 | − | 0.783078i | ||||
\(205\) | 5.05842 | + | 15.6896i | 0.353296 | + | 1.09581i | ||||
\(206\) | 1.05842 | − | 1.83324i | 0.0737438 | − | 0.127728i | ||||
\(207\) | 3.43070 | − | 2.27567i | 0.238450 | − | 0.158170i | ||||
\(208\) | −1.00000 | − | 1.73205i | −0.0693375 | − | 0.120096i | ||||
\(209\) | −3.25544 | −0.225183 | ||||||||
\(210\) | −4.12772 | − | 9.37880i | −0.284840 | − | 0.647199i | ||||
\(211\) | 16.2337 | 1.11757 | 0.558787 | − | 0.829311i | \(-0.311267\pi\) | ||||
0.558787 | + | 0.829311i | \(0.311267\pi\) | |||||||
\(212\) | 2.18614 | + | 3.78651i | 0.150145 | + | 0.260058i | ||||
\(213\) | −10.7446 | − | 10.0974i | −0.736205 | − | 0.691859i | ||||
\(214\) | −3.12772 | + | 5.41737i | −0.213806 | + | 0.370324i | ||||
\(215\) | −2.31386 | + | 0.746000i | −0.157804 | + | 0.0508768i | ||||
\(216\) | −4.00000 | − | 3.31662i | −0.272166 | − | 0.225668i | ||||
\(217\) | 19.6753 | + | 3.78651i | 1.33564 | + | 0.257045i | ||||
\(218\) | −8.11684 | −0.549742 | ||||||||
\(219\) | 1.00000 | + | 3.31662i | 0.0675737 | + | 0.224117i | ||||
\(220\) | −1.55842 | − | 1.40965i | −0.105069 | − | 0.0950383i | ||||
\(221\) | −11.4891 | − | 6.63325i | −0.772842 | − | 0.446201i | ||||
\(222\) | 13.6277 | − | 4.10891i | 0.914633 | − | 0.275772i | ||||
\(223\) | 0.883156 | 0.0591405 | 0.0295703 | − | 0.999563i | \(-0.490586\pi\) | ||||
0.0295703 | + | 0.999563i | \(0.490586\pi\) | |||||||
\(224\) | −0.500000 | + | 2.59808i | −0.0334077 | + | 0.173591i | ||||
\(225\) | 9.50000 | + | 11.6082i | 0.633333 | + | 0.773879i | ||||
\(226\) | 7.37228 | + | 12.7692i | 0.490397 | + | 0.849392i | ||||
\(227\) | 18.0475 | + | 10.4198i | 1.19786 | + | 0.691584i | 0.960077 | − | 0.279735i | \(-0.0902467\pi\) |
0.237781 | + | 0.971319i | \(0.423580\pi\) | |||||||
\(228\) | −4.37228 | − | 4.10891i | −0.289561 | − | 0.272119i | ||||
\(229\) | 12.0000 | − | 6.92820i | 0.792982 | − | 0.457829i | −0.0480291 | − | 0.998846i | \(-0.515294\pi\) |
0.841011 | + | 0.541017i | \(0.181961\pi\) | |||||||
\(230\) | 3.00000 | + | 0.644810i | 0.197814 | + | 0.0425175i | ||||
\(231\) | 3.48913 | − | 2.52434i | 0.229568 | − | 0.166089i | ||||
\(232\) | − | 3.31662i | − | 0.217747i | ||||||
\(233\) | 0.255437 | + | 0.442430i | 0.0167343 | + | 0.0289846i | 0.874271 | − | 0.485438i | \(-0.161340\pi\) |
−0.857537 | + | 0.514422i | \(0.828006\pi\) | |||||||
\(234\) | −5.00000 | + | 3.31662i | −0.326860 | + | 0.216815i | ||||
\(235\) | −14.1168 | − | 12.7692i | −0.920881 | − | 0.832969i | ||||
\(236\) | −6.55842 | − | 11.3595i | −0.426917 | − | 0.739442i | ||||
\(237\) | −15.3723 | − | 3.61158i | −0.998537 | − | 0.234597i | ||||
\(238\) | 5.74456 | + | 16.5831i | 0.372365 | + | 1.07492i | ||||
\(239\) | − | 23.6588i | − | 1.53036i | −0.643816 | − | 0.765180i | \(-0.722650\pi\) | ||
0.643816 | − | 0.765180i | \(-0.277350\pi\) | |||||||
\(240\) | −0.313859 | − | 3.86025i | −0.0202595 | − | 0.249178i | ||||
\(241\) | −16.6753 | − | 9.62747i | −1.07415 | − | 0.620160i | −0.144836 | − | 0.989456i | \(-0.546266\pi\) |
−0.929312 | + | 0.369296i | \(0.879599\pi\) | |||||||
\(242\) | −5.05842 | + | 8.76144i | −0.325168 | + | 0.563207i | ||||
\(243\) | −9.18614 | + | 12.5942i | −0.589291 | + | 0.807921i | ||||
\(244\) | − | 12.7692i | − | 0.817462i | ||||||
\(245\) | 12.9891 | + | 8.73399i | 0.829845 | + | 0.557994i | ||||
\(246\) | −12.4307 | − | 2.92048i | −0.792553 | − | 0.186203i | ||||
\(247\) | −6.00000 | + | 3.46410i | −0.381771 | + | 0.220416i | ||||
\(248\) | 6.55842 | + | 3.78651i | 0.416460 | + | 0.240443i | ||||
\(249\) | 14.9307 | + | 14.0313i | 0.946195 | + | 0.889200i | ||||
\(250\) | −1.24456 | + | 11.1109i | −0.0787131 | + | 0.702712i | ||||
\(251\) | −1.11684 | −0.0704946 | −0.0352473 | − | 0.999379i | \(-0.511222\pi\) | ||||
−0.0352473 | + | 0.999379i | \(0.511222\pi\) | |||||||
\(252\) | 7.87228 | + | 1.01350i | 0.495907 | + | 0.0638446i | ||||
\(253\) | 1.28962i | 0.0810777i | ||||||||
\(254\) | −6.55842 | + | 3.78651i | −0.411512 | + | 0.237587i | ||||
\(255\) | −14.6060 | − | 21.1345i | −0.914661 | − | 1.32349i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1.62772 | − | 0.939764i | 0.101534 | − | 0.0586209i | −0.448373 | − | 0.893847i | \(-0.647996\pi\) |
0.549907 | + | 0.835226i | \(0.314663\pi\) | |||||||
\(258\) | 0.430703 | − | 1.83324i | 0.0268144 | − | 0.114133i | ||||
\(259\) | −14.2337 | + | 16.4356i | −0.884438 | + | 1.02126i | ||||
\(260\) | −4.37228 | − | 0.939764i | −0.271157 | − | 0.0582817i | ||||
\(261\) | −9.93070 | + | 0.617359i | −0.614695 | + | 0.0382135i | ||||
\(262\) | 5.18614 | − | 8.98266i | 0.320401 | − | 0.554951i | ||||
\(263\) | −3.68614 | + | 6.38458i | −0.227297 | + | 0.393690i | −0.957006 | − | 0.290068i | \(-0.906322\pi\) |
0.729709 | + | 0.683758i | \(0.239656\pi\) | |||||||
\(264\) | 1.55842 | − | 0.469882i | 0.0959142 | − | 0.0289192i | ||||
\(265\) | 9.55842 | + | 2.05446i | 0.587169 | + | 0.126204i | ||||
\(266\) | 9.00000 | + | 1.73205i | 0.551825 | + | 0.106199i | ||||
\(267\) | −2.31386 | − | 0.543620i | −0.141606 | − | 0.0332690i | ||||
\(268\) | −2.05842 | + | 1.18843i | −0.125738 | + | 0.0725949i | ||||
\(269\) | −12.9891 | + | 22.4978i | −0.791961 | + | 1.37172i | 0.132790 | + | 0.991144i | \(0.457606\pi\) |
−0.924751 | + | 0.380572i | \(0.875727\pi\) | |||||||
\(270\) | −11.5000 | + | 1.65831i | −0.699868 | + | 0.100922i | ||||
\(271\) | 7.67527 | − | 4.43132i | 0.466239 | − | 0.269183i | −0.248425 | − | 0.968651i | \(-0.579913\pi\) |
0.714664 | + | 0.699468i | \(0.246580\pi\) | |||||||
\(272\) | 6.63325i | 0.402200i | ||||||||
\(273\) | 3.74456 | − | 8.36530i | 0.226631 | − | 0.506291i | ||||
\(274\) | −8.74456 | −0.528278 | ||||||||
\(275\) | −4.67527 | + | 0.469882i | −0.281929 | + | 0.0283349i | ||||
\(276\) | −1.62772 | + | 1.73205i | −0.0979772 | + | 0.104257i | ||||
\(277\) | 7.88316 | + | 4.55134i | 0.473653 | + | 0.273464i | 0.717768 | − | 0.696283i | \(-0.245164\pi\) |
−0.244115 | + | 0.969746i | \(0.578497\pi\) | |||||||
\(278\) | −7.11684 | + | 4.10891i | −0.426840 | + | 0.246436i | ||||
\(279\) | 10.1168 | − | 20.3422i | 0.605680 | − | 1.21785i | ||||
\(280\) | 3.55842 | + | 4.72627i | 0.212656 | + | 0.282449i | ||||
\(281\) | 11.3870i | 0.679290i | 0.940554 | + | 0.339645i | \(0.110307\pi\) | ||||
−0.940554 | + | 0.339645i | \(0.889693\pi\) | |||||||
\(282\) | 14.1168 | − | 4.25639i | 0.840646 | − | 0.253464i | ||||
\(283\) | 8.00000 | − | 13.8564i | 0.475551 | − | 0.823678i | −0.524057 | − | 0.851683i | \(-0.675582\pi\) |
0.999608 | + | 0.0280052i | \(0.00891551\pi\) | |||||||
\(284\) | 7.37228 | + | 4.25639i | 0.437464 | + | 0.252570i | ||||
\(285\) | −13.3723 | + | 1.08724i | −0.792106 | + | 0.0644026i | ||||
\(286\) | − | 1.87953i | − | 0.111139i | ||||||
\(287\) | 18.4307 | − | 6.38458i | 1.08793 | − | 0.376870i | ||||
\(288\) | 2.68614 | + | 1.33591i | 0.158282 | + | 0.0787191i | ||||
\(289\) | 13.5000 | + | 23.3827i | 0.794118 | + | 1.37545i | ||||
\(290\) | −5.50000 | − | 4.97494i | −0.322971 | − | 0.292138i | ||||
\(291\) | 17.9307 | − | 19.0800i | 1.05112 | − | 1.11849i | ||||
\(292\) | −1.00000 | − | 1.73205i | −0.0585206 | − | 0.101361i | ||||
\(293\) | − | 21.7244i | − | 1.26915i | −0.772861 | − | 0.634576i | \(-0.781175\pi\) | ||
0.772861 | − | 0.634576i | \(-0.218825\pi\) | |||||||
\(294\) | −10.9891 | + | 5.12241i | −0.640899 | + | 0.298745i | ||||
\(295\) | −28.6753 | − | 6.16337i | −1.66954 | − | 0.358845i | ||||
\(296\) | −7.11684 | + | 4.10891i | −0.413658 | + | 0.238826i | ||||
\(297\) | −1.69702 | − | 4.57879i | −0.0984708 | − | 0.265689i | ||||
\(298\) | −7.80298 | − | 4.50506i | −0.452015 | − | 0.260971i | ||||
\(299\) | 1.37228 | + | 2.37686i | 0.0793611 | + | 0.137457i | ||||
\(300\) | −6.87228 | − | 5.26989i | −0.396771 | − | 0.304257i | ||||
\(301\) | 0.941578 | + | 2.71810i | 0.0542717 | + | 0.156669i | ||||
\(302\) | 9.11684 | 0.524615 | ||||||||
\(303\) | −5.31386 | − | 17.6241i | −0.305273 | − | 1.01248i | ||||
\(304\) | 3.00000 | + | 1.73205i | 0.172062 | + | 0.0993399i | ||||
\(305\) | −21.1753 | − | 19.1537i | −1.21249 | − | 1.09674i | ||||
\(306\) | 19.8614 | − | 1.23472i | 1.13540 | − | 0.0705841i | ||||
\(307\) | 24.1168 | 1.37642 | 0.688210 | − | 0.725511i | \(-0.258397\pi\) | ||||
0.688210 | + | 0.725511i | \(0.258397\pi\) | |||||||
\(308\) | −1.62772 | + | 1.87953i | −0.0927479 | + | 0.107096i | ||||
\(309\) | 3.56930 | + | 0.838574i | 0.203050 | + | 0.0477048i | ||||
\(310\) | 16.1168 | − | 5.19615i | 0.915375 | − | 0.295122i | ||||
\(311\) | 10.1168 | − | 17.5229i | 0.573674 | − | 0.993632i | −0.422511 | − | 0.906358i | \(-0.638851\pi\) |
0.996184 | − | 0.0872739i | \(-0.0278155\pi\) | |||||||
\(312\) | 2.37228 | − | 2.52434i | 0.134304 | − | 0.142912i | ||||
\(313\) | −1.55842 | − | 2.69927i | −0.0880872 | − | 0.152572i | 0.818615 | − | 0.574342i | \(-0.194742\pi\) |
−0.906703 | + | 0.421771i | \(0.861409\pi\) | |||||||
\(314\) | 8.00000 | 0.451466 | ||||||||
\(315\) | 13.4891 | − | 11.5344i | 0.760026 | − | 0.649893i | ||||
\(316\) | 9.11684 | 0.512863 | ||||||||
\(317\) | 0.558422 | + | 0.967215i | 0.0313641 | + | 0.0543242i | 0.881281 | − | 0.472592i | \(-0.156682\pi\) |
−0.849917 | + | 0.526916i | \(0.823348\pi\) | |||||||
\(318\) | −5.18614 | + | 5.51856i | −0.290824 | + | 0.309465i | ||||
\(319\) | 1.55842 | − | 2.69927i | 0.0872549 | − | 0.151130i | ||||
\(320\) | 0.686141 | + | 2.12819i | 0.0383564 | + | 0.118970i | ||||
\(321\) | −10.5475 | − | 2.47805i | −0.588707 | − | 0.138311i | ||||
\(322\) | 0.686141 | − | 3.56529i | 0.0382371 | − | 0.198686i | ||||
\(323\) | 22.9783 | 1.27854 | ||||||||
\(324\) | 3.50000 | − | 8.29156i | 0.194444 | − | 0.460642i | ||||
\(325\) | −8.11684 | + | 5.84096i | −0.450241 | + | 0.323998i | ||||
\(326\) | 3.00000 | + | 1.73205i | 0.166155 | + | 0.0959294i | ||||
\(327\) | −4.05842 | − | 13.4603i | −0.224431 | − | 0.744354i | ||||
\(328\) | 7.37228 | 0.407066 | ||||||||
\(329\) | −14.7446 | + | 17.0256i | −0.812894 | + | 0.938649i | ||||
\(330\) | 1.55842 | − | 3.28917i | 0.0857883 | − | 0.181063i | ||||
\(331\) | 12.1168 | + | 20.9870i | 0.666002 | + | 1.15355i | 0.979013 | + | 0.203800i | \(0.0653291\pi\) |
−0.313011 | + | 0.949750i | \(0.601338\pi\) | |||||||
\(332\) | −10.2446 | − | 5.91470i | −0.562243 | − | 0.324611i | ||||
\(333\) | 13.6277 | + | 20.5446i | 0.746794 | + | 1.12583i | ||||
\(334\) | 12.6861 | − | 7.32435i | 0.694155 | − | 0.400770i | ||||
\(335\) | −1.11684 | + | 5.19615i | −0.0610197 | + | 0.283896i | ||||
\(336\) | −4.55842 | + | 0.469882i | −0.248682 | + | 0.0256342i | ||||
\(337\) | − | 0.644810i | − | 0.0351250i | −0.999846 | − | 0.0175625i | \(-0.994409\pi\) | ||
0.999846 | − | 0.0175625i | \(-0.00559061\pi\) | |||||||
\(338\) | 4.50000 | + | 7.79423i | 0.244768 | + | 0.423950i | ||||
\(339\) | −17.4891 | + | 18.6101i | −0.949879 | + | 1.01076i | ||||
\(340\) | 11.0000 | + | 9.94987i | 0.596559 | + | 0.539608i | ||||
\(341\) | 3.55842 | + | 6.16337i | 0.192699 | + | 0.333765i | ||||
\(342\) | 4.62772 | − | 9.30506i | 0.250238 | − | 0.503160i | ||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 1.08724i | 0.0586201i | ||||||||
\(345\) | 0.430703 | + | 5.29734i | 0.0231883 | + | 0.285199i | ||||
\(346\) | −14.7446 | − | 8.51278i | −0.792673 | − | 0.457650i | ||||
\(347\) | −0.941578 | + | 1.63086i | −0.0505466 | + | 0.0875492i | −0.890192 | − | 0.455586i | \(-0.849430\pi\) |
0.839645 | + | 0.543135i | \(0.182763\pi\) | |||||||
\(348\) | 5.50000 | − | 1.65831i | 0.294831 | − | 0.0888949i | ||||
\(349\) | 25.7407i | 1.37787i | 0.724824 | + | 0.688934i | \(0.241921\pi\) | ||||
−0.724824 | + | 0.688934i | \(0.758079\pi\) | |||||||
\(350\) | 13.1753 | + | 1.18843i | 0.704248 | + | 0.0635243i | ||||
\(351\) | −8.00000 | − | 6.63325i | −0.427008 | − | 0.354057i | ||||
\(352\) | −0.813859 | + | 0.469882i | −0.0433788 | + | 0.0250448i | ||||
\(353\) | −10.6277 | − | 6.13592i | −0.565656 | − | 0.326582i | 0.189756 | − | 0.981831i | \(-0.439230\pi\) |
−0.755413 | + | 0.655249i | \(0.772564\pi\) | |||||||
\(354\) | 15.5584 | − | 16.5557i | 0.826921 | − | 0.879924i | ||||
\(355\) | 18.1168 | − | 5.84096i | 0.961542 | − | 0.310006i | ||||
\(356\) | 1.37228 | 0.0727308 | ||||||||
\(357\) | −24.6277 | + | 17.8178i | −1.30344 | + | 0.943020i | ||||
\(358\) | − | 23.6588i | − | 1.25041i | ||||||
\(359\) | 23.7446 | − | 13.7089i | 1.25319 | − | 0.723530i | 0.281448 | − | 0.959576i | \(-0.409185\pi\) |
0.971742 | + | 0.236047i | \(0.0758518\pi\) | |||||||
\(360\) | 6.24456 | − | 2.45060i | 0.329117 | − | 0.129158i | ||||
\(361\) | −3.50000 | + | 6.06218i | −0.184211 | + | 0.319062i | ||||
\(362\) | −6.94158 | + | 4.00772i | −0.364841 | + | 0.210641i | ||||
\(363\) | −17.0584 | − | 4.00772i | −0.895335 | − | 0.210351i | ||||
\(364\) | −1.00000 | + | 5.19615i | −0.0524142 | + | 0.272352i | ||||
\(365\) | −4.37228 | − | 0.939764i | −0.228856 | − | 0.0491895i | ||||
\(366\) | 21.1753 | − | 6.38458i | 1.10685 | − | 0.333727i | ||||
\(367\) | −6.61684 | + | 11.4607i | −0.345396 | + | 0.598244i | −0.985426 | − | 0.170106i | \(-0.945589\pi\) |
0.640029 | + | 0.768351i | \(0.278922\pi\) | |||||||
\(368\) | 0.686141 | − | 1.18843i | 0.0357676 | − | 0.0619512i | ||||
\(369\) | −1.37228 | − | 22.0742i | −0.0714381 | − | 1.14914i | ||||
\(370\) | −3.86141 | + | 17.9653i | −0.200745 | + | 0.933972i | ||||
\(371\) | 2.18614 | − | 11.3595i | 0.113499 | − | 0.589757i | ||||
\(372\) | −3.00000 | + | 12.7692i | −0.155543 | + | 0.662050i | ||||
\(373\) | 20.2337 | − | 11.6819i | 1.04766 | − | 0.604867i | 0.125667 | − | 0.992072i | \(-0.459893\pi\) |
0.921994 | + | 0.387205i | \(0.126560\pi\) | |||||||
\(374\) | −3.11684 | + | 5.39853i | −0.161168 | + | 0.279151i | ||||
\(375\) | −19.0475 | + | 3.49155i | −0.983611 | + | 0.180303i | ||||
\(376\) | −7.37228 | + | 4.25639i | −0.380196 | + | 0.219506i | ||||
\(377\) | − | 6.63325i | − | 0.341630i | ||||||
\(378\) | 2.25544 | + | 13.5615i | 0.116007 | + | 0.697526i | ||||
\(379\) | −12.2337 | −0.628402 | −0.314201 | − | 0.949356i | \(-0.601737\pi\) | ||||
−0.314201 | + | 0.949356i | \(0.601737\pi\) | |||||||
\(380\) | 7.37228 | − | 2.37686i | 0.378190 | − | 0.121930i | ||||
\(381\) | −9.55842 | − | 8.98266i | −0.489693 | − | 0.460196i | ||||
\(382\) | −14.7446 | − | 8.51278i | −0.754397 | − | 0.435552i | ||||
\(383\) | −13.5475 | + | 7.82168i | −0.692247 | + | 0.399669i | −0.804453 | − | 0.594016i | \(-0.797542\pi\) |
0.112206 | + | 0.993685i | \(0.464208\pi\) | |||||||
\(384\) | −1.68614 | − | 0.396143i | −0.0860455 | − | 0.0202156i | ||||
\(385\) | 0.675266 | + | 5.51856i | 0.0344147 | + | 0.281252i | ||||
\(386\) | 17.9653i | 0.914411i | ||||||||
\(387\) | 3.25544 | − | 0.202380i | 0.165483 | − | 0.0102875i | ||||
\(388\) | −7.55842 | + | 13.0916i | −0.383721 | + | 0.664624i | ||||
\(389\) | −6.51087 | − | 3.75906i | −0.330114 | − | 0.190592i | 0.325777 | − | 0.945446i | \(-0.394374\pi\) |
−0.655892 | + | 0.754855i | \(0.727707\pi\) | |||||||
\(390\) | −0.627719 | − | 7.72049i | −0.0317858 | − | 0.390942i | ||||
\(391\) | − | 9.10268i | − | 0.460343i | ||||||
\(392\) | 5.50000 | − | 4.33013i | 0.277792 | − | 0.218704i | ||||
\(393\) | 17.4891 | + | 4.10891i | 0.882210 | + | 0.207267i | ||||
\(394\) | −7.11684 | − | 12.3267i | −0.358541 | − | 0.621012i | ||||
\(395\) | 13.6753 | − | 15.1186i | 0.688077 | − | 0.760698i | ||||
\(396\) | 1.55842 | + | 2.34941i | 0.0783137 | + | 0.118062i | ||||
\(397\) | −4.00000 | − | 6.92820i | −0.200754 | − | 0.347717i | 0.748017 | − | 0.663679i | \(-0.231006\pi\) |
−0.948772 | + | 0.315963i | \(0.897673\pi\) | |||||||
\(398\) | − | 1.28962i | − | 0.0646428i | ||||||
\(399\) | 1.62772 | + | 15.7908i | 0.0814879 | + | 0.790531i | ||||
\(400\) | 4.55842 | + | 2.05446i | 0.227921 | + | 0.102723i | ||||
\(401\) | −14.3139 | + | 8.26411i | −0.714800 | + | 0.412690i | −0.812836 | − | 0.582493i | \(-0.802077\pi\) |
0.0980358 | + | 0.995183i | \(0.468744\pi\) | |||||||
\(402\) | −3.00000 | − | 2.81929i | −0.149626 | − | 0.140613i | ||||
\(403\) | 13.1168 | + | 7.57301i | 0.653397 | + | 0.377239i | ||||
\(404\) | 5.31386 | + | 9.20387i | 0.264374 | + | 0.457910i | ||||
\(405\) | −8.50000 | − | 18.2414i | −0.422368 | − | 0.906424i | ||||
\(406\) | −5.74456 | + | 6.63325i | −0.285098 | + | 0.329203i | ||||
\(407\) | −7.72281 | −0.382806 | ||||||||
\(408\) | −11.0000 | + | 3.31662i | −0.544581 | + | 0.164197i | ||||
\(409\) | 3.73369 | + | 2.15565i | 0.184619 | + | 0.106590i | 0.589461 | − | 0.807797i | \(-0.299340\pi\) |
−0.404842 | + | 0.914387i | \(0.632673\pi\) | |||||||
\(410\) | 11.0584 | − | 12.2255i | 0.546137 | − | 0.603777i | ||||
\(411\) | −4.37228 | − | 14.5012i | −0.215669 | − | 0.715292i | ||||
\(412\) | −2.11684 | −0.104289 | ||||||||
\(413\) | −6.55842 | + | 34.0786i | −0.322719 | + | 1.67690i | ||||
\(414\) | −3.68614 | − | 1.83324i | −0.181164 | − | 0.0900989i | ||||
\(415\) | −25.1753 | + | 8.11663i | −1.23581 | + | 0.398430i | ||||
\(416\) | −1.00000 | + | 1.73205i | −0.0490290 | + | 0.0849208i | ||||
\(417\) | −10.3723 | − | 9.74749i | −0.507933 | − | 0.477337i | ||||
\(418\) | 1.62772 | + | 2.81929i | 0.0796143 | + | 0.137896i | ||||
\(419\) | −6.51087 | −0.318077 | −0.159039 | − | 0.987272i | \(-0.550839\pi\) | ||||
−0.159039 | + | 0.987272i | \(0.550839\pi\) | |||||||
\(420\) | −6.05842 | + | 8.26411i | −0.295621 | + | 0.403247i | ||||
\(421\) | −2.11684 | −0.103169 | −0.0515843 | − | 0.998669i | \(-0.516427\pi\) | ||||
−0.0515843 | + | 0.998669i | \(0.516427\pi\) | |||||||
\(422\) | −8.11684 | − | 14.0588i | −0.395122 | − | 0.684371i | ||||
\(423\) | 14.1168 | + | 21.2819i | 0.686384 | + | 1.03476i | ||||
\(424\) | 2.18614 | − | 3.78651i | 0.106168 | − | 0.183889i | ||||
\(425\) | 33.0000 | − | 3.31662i | 1.60074 | − | 0.160880i | ||||
\(426\) | −3.37228 | + | 14.3537i | −0.163388 | + | 0.695441i | ||||
\(427\) | −22.1168 | + | 25.5383i | −1.07031 | + | 1.23589i | ||||
\(428\) | 6.25544 | 0.302368 | ||||||||
\(429\) | 3.11684 | − | 0.939764i | 0.150483 | − | 0.0453722i | ||||
\(430\) | 1.80298 | + | 1.63086i | 0.0869476 | + | 0.0786471i | ||||
\(431\) | −14.7446 | − | 8.51278i | −0.710221 | − | 0.410046i | 0.100922 | − | 0.994894i | \(-0.467821\pi\) |
−0.811143 | + | 0.584848i | \(0.801154\pi\) | |||||||
\(432\) | −0.872281 | + | 5.12241i | −0.0419677 | + | 0.246452i | ||||
\(433\) | −34.0000 | −1.63394 | −0.816968 | − | 0.576683i | \(-0.804347\pi\) | ||||
−0.816968 | + | 0.576683i | \(0.804347\pi\) | |||||||
\(434\) | −6.55842 | − | 18.9325i | −0.314814 | − | 0.908791i | ||||
\(435\) | 5.50000 | − | 11.6082i | 0.263705 | − | 0.556570i | ||||
\(436\) | 4.05842 | + | 7.02939i | 0.194363 | + | 0.336647i | ||||
\(437\) | −4.11684 | − | 2.37686i | −0.196935 | − | 0.113701i | ||||
\(438\) | 2.37228 | − | 2.52434i | 0.113352 | − | 0.120618i | ||||
\(439\) | −2.44158 | + | 1.40965i | −0.116530 | + | 0.0672787i | −0.557132 | − | 0.830424i | \(-0.688098\pi\) |
0.440602 | + | 0.897703i | \(0.354765\pi\) | |||||||
\(440\) | −0.441578 | + | 2.05446i | −0.0210514 | + | 0.0979423i | ||||
\(441\) | −13.9891 | − | 15.6622i | −0.666149 | − | 0.745819i | ||||
\(442\) | 13.2665i | 0.631023i | ||||||||
\(443\) | −4.50000 | − | 7.79423i | −0.213801 | − | 0.370315i | 0.739100 | − | 0.673596i | \(-0.235251\pi\) |
−0.952901 | + | 0.303281i | \(0.901918\pi\) | |||||||
\(444\) | −10.3723 | − | 9.74749i | −0.492247 | − | 0.462596i | ||||
\(445\) | 2.05842 | − | 2.27567i | 0.0975786 | − | 0.107877i | ||||
\(446\) | −0.441578 | − | 0.764836i | −0.0209093 | − | 0.0362160i | ||||
\(447\) | 3.56930 | − | 15.1923i | 0.168822 | − | 0.718572i | ||||
\(448\) | 2.50000 | − | 0.866025i | 0.118114 | − | 0.0409159i | ||||
\(449\) | − | 20.3971i | − | 0.962598i | −0.876557 | − | 0.481299i | \(-0.840165\pi\) | ||
0.876557 | − | 0.481299i | \(-0.159835\pi\) | |||||||
\(450\) | 5.30298 | − | 14.0313i | 0.249985 | − | 0.661443i | ||||
\(451\) | 6.00000 | + | 3.46410i | 0.282529 | + | 0.163118i | ||||
\(452\) | 7.37228 | − | 12.7692i | 0.346763 | − | 0.600611i | ||||
\(453\) | 4.55842 | + | 15.1186i | 0.214173 | + | 0.710333i | ||||
\(454\) | − | 20.8395i | − | 0.978047i | ||||||
\(455\) | 7.11684 | + | 9.45254i | 0.333643 | + | 0.443142i | ||||
\(456\) | −1.37228 | + | 5.84096i | −0.0642630 | + | 0.273528i | ||||
\(457\) | 2.44158 | − | 1.40965i | 0.114212 | − | 0.0659404i | −0.441806 | − | 0.897111i | \(-0.645662\pi\) |
0.556018 | + | 0.831170i | \(0.312329\pi\) | |||||||
\(458\) | −12.0000 | − | 6.92820i | −0.560723 | − | 0.323734i | ||||
\(459\) | 11.9783 | + | 32.3191i | 0.559097 | + | 1.50852i | ||||
\(460\) | −0.941578 | − | 2.92048i | −0.0439013 | − | 0.136168i | ||||
\(461\) | −23.4891 | −1.09400 | −0.546999 | − | 0.837133i | \(-0.684230\pi\) | ||||
−0.546999 | + | 0.837133i | \(0.684230\pi\) | |||||||
\(462\) | −3.93070 | − | 1.75950i | −0.182873 | − | 0.0818595i | ||||
\(463\) | − | 6.72582i | − | 0.312576i | −0.987712 | − | 0.156288i | \(-0.950047\pi\) | ||
0.987712 | − | 0.156288i | \(-0.0499527\pi\) | |||||||
\(464\) | −2.87228 | + | 1.65831i | −0.133342 | + | 0.0769852i | ||||
\(465\) | 16.6753 | + | 24.1287i | 0.773297 | + | 1.11894i | ||||
\(466\) | 0.255437 | − | 0.442430i | 0.0118329 | − | 0.0204952i | ||||
\(467\) | −31.5475 | + | 18.2140i | −1.45985 | + | 0.842843i | −0.999003 | − | 0.0446389i | \(-0.985786\pi\) |
−0.460843 | + | 0.887482i | \(0.652453\pi\) | |||||||
\(468\) | 5.37228 | + | 2.67181i | 0.248334 | + | 0.123505i | ||||
\(469\) | 6.17527 | + | 1.18843i | 0.285147 | + | 0.0548766i | ||||
\(470\) | −4.00000 | + | 18.6101i | −0.184506 | + | 0.858421i | ||||
\(471\) | 4.00000 | + | 13.2665i | 0.184310 | + | 0.611288i | ||||
\(472\) | −6.55842 | + | 11.3595i | −0.301876 | + | 0.522864i | ||||
\(473\) | −0.510875 | + | 0.884861i | −0.0234900 | + | 0.0406859i | ||||
\(474\) | 4.55842 | + | 15.1186i | 0.209375 | + | 0.694419i | ||||
\(475\) | 7.11684 | − | 15.7908i | 0.326543 | − | 0.724533i | ||||
\(476\) | 11.4891 | − | 13.2665i | 0.526603 | − | 0.608069i | ||||
\(477\) | −11.7446 | − | 5.84096i | −0.537747 | − | 0.267439i | ||||
\(478\) | −20.4891 | + | 11.8294i | −0.937151 | + | 0.541064i | ||||
\(479\) | 1.37228 | − | 2.37686i | 0.0627011 | − | 0.108602i | −0.832971 | − | 0.553317i | \(-0.813362\pi\) |
0.895672 | + | 0.444715i | \(0.146695\pi\) | |||||||
\(480\) | −3.18614 | + | 2.20193i | −0.145427 | + | 0.100504i | ||||
\(481\) | −14.2337 | + | 8.21782i | −0.649000 | + | 0.374701i | ||||
\(482\) | 19.2549i | 0.877038i | ||||||||
\(483\) | 6.25544 | − | 0.644810i | 0.284632 | − | 0.0293399i | ||||
\(484\) | 10.1168 | 0.459857 | ||||||||
\(485\) | 10.3723 | + | 32.1716i | 0.470981 | + | 1.46084i | ||||
\(486\) | 15.5000 | + | 1.65831i | 0.703094 | + | 0.0752226i | ||||
\(487\) | 12.5584 | + | 7.25061i | 0.569076 | + | 0.328556i | 0.756780 | − | 0.653669i | \(-0.226771\pi\) |
−0.187704 | + | 0.982226i | \(0.560105\pi\) | |||||||
\(488\) | −11.0584 | + | 6.38458i | −0.500591 | + | 0.289016i | ||||
\(489\) | −1.37228 | + | 5.84096i | −0.0620567 | + | 0.264137i | ||||
\(490\) | 1.06930 | − | 15.6159i | 0.0483059 | − | 0.705455i | ||||
\(491\) | 30.2372i | 1.36458i | 0.731080 | + | 0.682292i | \(0.239017\pi\) | ||||
−0.731080 | + | 0.682292i | \(0.760983\pi\) | |||||||
\(492\) | 3.68614 | + | 12.2255i | 0.166184 | + | 0.551170i | ||||
\(493\) | −11.0000 | + | 19.0526i | −0.495415 | + | 0.858084i | ||||
\(494\) | 6.00000 | + | 3.46410i | 0.269953 | + | 0.155857i | ||||
\(495\) | 6.23369 | + | 0.939764i | 0.280183 | + | 0.0422392i | ||||
\(496\) | − | 7.57301i | − | 0.340038i | ||||||
\(497\) | −7.37228 | − | 21.2819i | −0.330692 | − | 0.954626i | ||||
\(498\) | 4.68614 | − | 19.9460i | 0.209991 | − | 0.893803i | ||||
\(499\) | 3.11684 | + | 5.39853i | 0.139529 | + | 0.241671i | 0.927318 | − | 0.374273i | \(-0.122108\pi\) |
−0.787789 | + | 0.615945i | \(0.788774\pi\) | |||||||
\(500\) | 10.2446 | − | 4.47760i | 0.458151 | − | 0.200245i | ||||
\(501\) | 18.4891 | + | 17.3754i | 0.826033 | + | 0.776276i | ||||
\(502\) | 0.558422 | + | 0.967215i | 0.0249236 | + | 0.0431689i | ||||
\(503\) | − | 6.13592i | − | 0.273587i | −0.990600 | − | 0.136793i | \(-0.956320\pi\) | ||
0.990600 | − | 0.136793i | \(-0.0436797\pi\) | |||||||
\(504\) | −3.05842 | − | 7.32435i | −0.136233 | − | 0.326252i | ||||
\(505\) | 23.2337 | + | 4.99377i | 1.03389 | + | 0.222220i | ||||
\(506\) | 1.11684 | − | 0.644810i | 0.0496498 | − | 0.0286653i | ||||
\(507\) | −10.6753 | + | 11.3595i | −0.474105 | + | 0.504494i | ||||
\(508\) | 6.55842 | + | 3.78651i | 0.290983 | + | 0.167999i | ||||
\(509\) | −5.87228 | − | 10.1711i | −0.260284 | − | 0.450826i | 0.706033 | − | 0.708179i | \(-0.250483\pi\) |
−0.966317 | + | 0.257353i | \(0.917150\pi\) | |||||||
\(510\) | −11.0000 | + | 23.2164i | −0.487088 | + | 1.02804i | ||||
\(511\) | −1.00000 | + | 5.19615i | −0.0442374 | + | 0.229864i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 17.7446 | + | 3.02167i | 0.783442 | + | 0.133410i | ||||
\(514\) | −1.62772 | − | 0.939764i | −0.0717956 | − | 0.0414512i | ||||
\(515\) | −3.17527 | + | 3.51039i | −0.139919 | + | 0.154686i | ||||
\(516\) | −1.80298 | + | 0.543620i | −0.0793720 | + | 0.0239316i | ||||
\(517\) | −8.00000 | −0.351840 | ||||||||
\(518\) | 21.3505 | + | 4.10891i | 0.938089 | + | 0.180535i | ||||
\(519\) | 6.74456 | − | 28.7075i | 0.296053 | − | 1.26012i | ||||
\(520\) | 1.37228 | + | 4.25639i | 0.0601785 | + | 0.186655i | ||||
\(521\) | −7.37228 | + | 12.7692i | −0.322986 | + | 0.559427i | −0.981103 | − | 0.193488i | \(-0.938020\pi\) |
0.658117 | + | 0.752916i | \(0.271353\pi\) | |||||||
\(522\) | 5.50000 | + | 8.29156i | 0.240728 | + | 0.362912i | ||||
\(523\) | −5.11684 | − | 8.86263i | −0.223744 | − | 0.387536i | 0.732198 | − | 0.681092i | \(-0.238495\pi\) |
−0.955942 | + | 0.293556i | \(0.905161\pi\) | |||||||
\(524\) | −10.3723 | −0.453115 | ||||||||
\(525\) | 4.61684 | + | 22.4429i | 0.201496 | + | 0.979489i | ||||
\(526\) | 7.37228 | 0.321447 | ||||||||
\(527\) | −25.1168 | − | 43.5036i | −1.09411 | − | 1.89505i | ||||
\(528\) | −1.18614 | − | 1.11469i | −0.0516201 | − | 0.0485107i | ||||
\(529\) | 10.5584 | − | 18.2877i | 0.459062 | − | 0.795118i | ||||
\(530\) | −3.00000 | − | 9.30506i | −0.130312 | − | 0.404186i | ||||
\(531\) | 35.2337 | + | 17.5229i | 1.52901 | + | 0.760429i | ||||
\(532\) | −3.00000 | − | 8.66025i | −0.130066 | − | 0.375470i | ||||
\(533\) | 14.7446 | 0.638658 | ||||||||
\(534\) | 0.686141 | + | 2.27567i | 0.0296922 | + | 0.0984779i | ||||
\(535\) | 9.38316 | − | 10.3735i | 0.405669 | − | 0.448484i | ||||
\(536\) | 2.05842 | + | 1.18843i | 0.0889103 | + | 0.0513324i | ||||
\(537\) | 39.2337 | − | 11.8294i | 1.69306 | − | 0.510476i | ||||
\(538\) | 25.9783 | 1.12000 | ||||||||
\(539\) | 6.51087 | − | 0.939764i | 0.280443 | − | 0.0404785i | ||||
\(540\) | 7.18614 | + | 9.13014i | 0.309242 | + | 0.392898i | ||||
\(541\) | −19.1753 | − | 33.2125i | −0.824409 | − | 1.42792i | −0.902370 | − | 0.430962i | \(-0.858174\pi\) |
0.0779610 | − | 0.996956i | \(-0.475159\pi\) | |||||||
\(542\) | −7.67527 | − | 4.43132i | −0.329681 | − | 0.190341i | ||||
\(543\) | −10.1168 | − | 9.50744i | −0.434155 | − | 0.408003i | ||||
\(544\) | 5.74456 | − | 3.31662i | 0.246296 | − | 0.142199i | ||||
\(545\) | 17.7446 | + | 3.81396i | 0.760094 | + | 0.163372i | ||||
\(546\) | −9.11684 | + | 0.939764i | −0.390165 | + | 0.0402182i | ||||
\(547\) | − | 9.30506i | − | 0.397856i | −0.980014 | − | 0.198928i | \(-0.936254\pi\) | ||
0.980014 | − | 0.198928i | \(-0.0637460\pi\) | |||||||
\(548\) | 4.37228 | + | 7.57301i | 0.186775 | + | 0.323503i | ||||
\(549\) | 21.1753 | + | 31.9229i | 0.903738 | + | 1.36244i | ||||
\(550\) | 2.74456 | + | 3.81396i | 0.117029 | + | 0.162628i | ||||
\(551\) | 5.74456 | + | 9.94987i | 0.244727 | + | 0.423879i | ||||
\(552\) | 2.31386 | + | 0.543620i | 0.0984844 | + | 0.0231380i | ||||
\(553\) | −18.2337 | − | 15.7908i | −0.775375 | − | 0.671495i | ||||
\(554\) | − | 9.10268i | − | 0.386736i | ||||||
\(555\) | −31.7228 | + | 2.57924i | −1.34656 | + | 0.109483i | ||||
\(556\) | 7.11684 | + | 4.10891i | 0.301821 | + | 0.174257i | ||||
\(557\) | −13.9307 | + | 24.1287i | −0.590263 | + | 1.02237i | 0.403934 | + | 0.914788i | \(0.367643\pi\) |
−0.994197 | + | 0.107577i | \(0.965691\pi\) | |||||||
\(558\) | −22.6753 | + | 1.40965i | −0.959921 | + | 0.0596751i | ||||
\(559\) | 2.17448i | 0.0919708i | ||||||||
\(560\) | 2.31386 | − | 5.44482i | 0.0977784 | − | 0.230086i | ||||
\(561\) | −10.5109 | − | 2.46943i | −0.443769 | − | 0.104260i | ||||
\(562\) | 9.86141 | − | 5.69349i | 0.415978 | − | 0.240165i | ||||
\(563\) | −1.24456 | − | 0.718549i | −0.0524521 | − | 0.0302832i | 0.473545 | − | 0.880770i | \(-0.342974\pi\) |
−0.525997 | + | 0.850487i | \(0.676308\pi\) | |||||||
\(564\) | −10.7446 | − | 10.0974i | −0.452428 | − | 0.425175i | ||||
\(565\) | −10.1168 | − | 31.3793i | −0.425619 | − | 1.32014i | ||||
\(566\) | −16.0000 | −0.672530 | ||||||||
\(567\) | −21.3614 | + | 10.5209i | −0.897095 | + | 0.441838i | ||||
\(568\) | − | 8.51278i | − | 0.357188i | ||||||
\(569\) | 9.86141 | − | 5.69349i | 0.413412 | − | 0.238683i | −0.278843 | − | 0.960337i | \(-0.589951\pi\) |
0.692255 | + | 0.721653i | \(0.256618\pi\) | |||||||
\(570\) | 7.62772 | + | 11.0371i | 0.319490 | + | 0.462294i | ||||
\(571\) | 0.116844 | − | 0.202380i | 0.00488977 | − | 0.00846933i | −0.863570 | − | 0.504229i | \(-0.831777\pi\) |
0.868460 | + | 0.495759i | \(0.165110\pi\) | |||||||
\(572\) | −1.62772 | + | 0.939764i | −0.0680583 | + | 0.0392935i | ||||
\(573\) | 6.74456 | − | 28.7075i | 0.281758 | − | 1.19927i | ||||
\(574\) | −14.7446 | − | 12.7692i | −0.615426 | − | 0.532975i | ||||
\(575\) | −6.25544 | − | 2.81929i | −0.260870 | − | 0.117573i | ||||
\(576\) | −0.186141 | − | 2.99422i | −0.00775586 | − | 0.124759i | ||||
\(577\) | 17.5584 | − | 30.4121i | 0.730967 | − | 1.26607i | −0.225504 | − | 0.974242i | \(-0.572403\pi\) |
0.956470 | − | 0.291829i | \(-0.0942639\pi\) | |||||||
\(578\) | 13.5000 | − | 23.3827i | 0.561526 | − | 0.972592i | ||||
\(579\) | −29.7921 | + | 8.98266i | −1.23812 | + | 0.373307i | ||||
\(580\) | −1.55842 | + | 7.25061i | −0.0647100 | + | 0.301065i | ||||
\(581\) | 10.2446 | + | 29.5735i | 0.425016 | + | 1.22692i | ||||
\(582\) | −25.4891 | − | 5.98844i | −1.05656 | − | 0.248229i | ||||
\(583\) | 3.55842 | − | 2.05446i | 0.147375 | − | 0.0850869i | ||||
\(584\) | −1.00000 | + | 1.73205i | −0.0413803 | + | 0.0716728i | ||||
\(585\) | 12.4891 | − | 4.90120i | 0.516362 | − | 0.202640i | ||||
\(586\) | −18.8139 | + | 10.8622i | −0.777193 | + | 0.448713i | ||||
\(587\) | − | 0.0549029i | − | 0.00226608i | −0.999999 | − | 0.00113304i | \(-0.999639\pi\) | ||
0.999999 | − | 0.00113304i | \(-0.000360659\pi\) | |||||||
\(588\) | 9.93070 | + | 6.95565i | 0.409535 | + | 0.286846i | ||||
\(589\) | −26.2337 | −1.08094 | ||||||||
\(590\) | 9.00000 | + | 27.9152i | 0.370524 | + | 1.14925i | ||||
\(591\) | 16.8832 | − | 17.9653i | 0.694480 | − | 0.738994i | ||||
\(592\) | 7.11684 | + | 4.10891i | 0.292500 | + | 0.168875i | ||||
\(593\) | 23.7446 | − | 13.7089i | 0.975072 | − | 0.562958i | 0.0742935 | − | 0.997236i | \(-0.476330\pi\) |
0.900779 | + | 0.434278i | \(0.142997\pi\) | |||||||
\(594\) | −3.11684 | + | 3.75906i | −0.127886 | + | 0.154236i | ||||
\(595\) | −4.76631 | − | 38.9523i | −0.195400 | − | 1.59689i | ||||
\(596\) | 9.01011i | 0.369069i | ||||||||
\(597\) | 2.13859 | − | 0.644810i | 0.0875268 | − | 0.0263903i | ||||
\(598\) | 1.37228 | − | 2.37686i | 0.0561168 | − | 0.0971971i | ||||
\(599\) | −1.62772 | − | 0.939764i | −0.0665068 | − | 0.0383977i | 0.466378 | − | 0.884586i | \(-0.345559\pi\) |
−0.532885 | + | 0.846188i | \(0.678892\pi\) | |||||||
\(600\) | −1.12772 | + | 8.58652i | −0.0460389 | + | 0.350543i | ||||
\(601\) | − | 19.2549i | − | 0.785425i | −0.919661 | − | 0.392713i | \(-0.871537\pi\) | ||
0.919661 | − | 0.392713i | \(-0.128463\pi\) | |||||||
\(602\) | 1.88316 | − | 2.17448i | 0.0767517 | − | 0.0886252i | ||||
\(603\) | 3.17527 | − | 6.38458i | 0.129307 | − | 0.260000i | ||||
\(604\) | −4.55842 | − | 7.89542i | −0.185480 | − | 0.321260i | ||||
\(605\) | 15.1753 | − | 16.7769i | 0.616962 | − | 0.682077i | ||||
\(606\) | −12.6060 | + | 13.4140i | −0.512082 | + | 0.544906i | ||||
\(607\) | 20.7337 | + | 35.9118i | 0.841554 | + | 1.45762i | 0.888580 | + | 0.458721i | \(0.151692\pi\) |
−0.0470257 | + | 0.998894i | \(0.514974\pi\) | |||||||
\(608\) | − | 3.46410i | − | 0.140488i | ||||||
\(609\) | −13.8723 | − | 6.20965i | −0.562133 | − | 0.251628i | ||||
\(610\) | −6.00000 | + | 27.9152i | −0.242933 | + | 1.13025i | ||||
\(611\) | −14.7446 | + | 8.51278i | −0.596501 | + | 0.344390i | ||||
\(612\) | −11.0000 | − | 16.5831i | −0.444649 | − | 0.670333i | ||||
\(613\) | 23.2337 | + | 13.4140i | 0.938400 | + | 0.541785i | 0.889458 | − | 0.457016i | \(-0.151082\pi\) |
0.0489415 | + | 0.998802i | \(0.484415\pi\) | |||||||
\(614\) | −12.0584 | − | 20.8858i | −0.486638 | − | 0.842882i | ||||
\(615\) | 25.8030 | + | 12.2255i | 1.04048 | + | 0.492982i | ||||
\(616\) | 2.44158 | + | 0.469882i | 0.0983740 | + | 0.0189321i | ||||
\(617\) | −46.9783 | −1.89127 | −0.945637 | − | 0.325225i | \(-0.894560\pi\) | ||||
−0.945637 | + | 0.325225i | \(0.894560\pi\) | |||||||
\(618\) | −1.05842 | − | 3.51039i | −0.0425760 | − | 0.141209i | ||||
\(619\) | −14.2337 | − | 8.21782i | −0.572100 | − | 0.330302i | 0.185888 | − | 0.982571i | \(-0.440484\pi\) |
−0.757988 | + | 0.652269i | \(0.773817\pi\) | |||||||
\(620\) | −12.5584 | − | 11.3595i | −0.504358 | − | 0.456209i | ||||
\(621\) | 1.19702 | − | 7.02939i | 0.0480346 | − | 0.282080i | ||||
\(622\) | −20.2337 | −0.811297 | ||||||||
\(623\) | −2.74456 | − | 2.37686i | −0.109959 | − | 0.0952269i | ||||
\(624\) | −3.37228 | − | 0.792287i | −0.134999 | − | 0.0317169i | ||||
\(625\) | 7.94158 | − | 23.7051i | 0.317663 | − | 0.948204i | ||||
\(626\) | −1.55842 | + | 2.69927i | −0.0622871 | + | 0.107884i | ||||
\(627\) | −3.86141 | + | 4.10891i | −0.154210 | + | 0.164094i | ||||
\(628\) | −4.00000 | − | 6.92820i | −0.159617 | − | 0.276465i | ||||
\(629\) | 54.5109 | 2.17349 | ||||||||
\(630\) | −16.7337 | − | 5.91470i | −0.666686 | − | 0.235647i | ||||
\(631\) | 12.8832 | 0.512870 | 0.256435 | − | 0.966561i | \(-0.417452\pi\) | ||||
0.256435 | + | 0.966561i | \(0.417452\pi\) | |||||||
\(632\) | −4.55842 | − | 7.89542i | −0.181324 | − | 0.314063i | ||||
\(633\) | 19.2554 | − | 20.4897i | 0.765335 | − | 0.814391i | ||||
\(634\) | 0.558422 | − | 0.967215i | 0.0221778 | − | 0.0384130i | ||||
\(635\) | 16.1168 | − | 5.19615i | 0.639577 | − | 0.206203i | ||||
\(636\) | 7.37228 | + | 1.73205i | 0.292330 | + | 0.0686803i | ||||
\(637\) | 11.0000 | − | 8.66025i | 0.435836 | − | 0.343132i | ||||
\(638\) | −3.11684 | −0.123397 | ||||||||
\(639\) | −25.4891 | + | 1.58457i | −1.00833 | + | 0.0626848i | ||||
\(640\) | 1.50000 | − | 1.65831i | 0.0592927 | − | 0.0655506i | ||||
\(641\) | −7.80298 | − | 4.50506i | −0.308199 | − | 0.177939i | 0.337921 | − | 0.941174i | \(-0.390276\pi\) |
−0.646120 | + | 0.763235i | \(0.723610\pi\) | |||||||
\(642\) | 3.12772 | + | 10.3735i | 0.123441 | + | 0.409408i | ||||
\(643\) | −18.2337 | −0.719066 | −0.359533 | − | 0.933132i | \(-0.617064\pi\) | ||||
−0.359533 | + | 0.933132i | \(0.617064\pi\) | |||||||
\(644\) | −3.43070 | + | 1.18843i | −0.135189 | + | 0.0468307i | ||||
\(645\) | −1.80298 | + | 3.80534i | −0.0709925 | + | 0.149835i | ||||
\(646\) | −11.4891 | − | 19.8997i | −0.452034 | − | 0.782945i | ||||
\(647\) | 36.4307 | + | 21.0333i | 1.43224 | + | 0.826903i | 0.997291 | − | 0.0735524i | \(-0.0234336\pi\) |
0.434947 | + | 0.900456i | \(0.356767\pi\) | |||||||
\(648\) | −8.93070 | + | 1.11469i | −0.350831 | + | 0.0437892i | ||||
\(649\) | −10.6753 | + | 6.16337i | −0.419041 | + | 0.241933i | ||||
\(650\) | 9.11684 | + | 4.10891i | 0.357592 | + | 0.161165i | ||||
\(651\) | 28.1168 | − | 20.3422i | 1.10199 | − | 0.797273i | ||||
\(652\) | − | 3.46410i | − | 0.135665i | ||||||
\(653\) | 8.18614 | + | 14.1788i | 0.320348 | + | 0.554860i | 0.980560 | − | 0.196220i | \(-0.0628667\pi\) |
−0.660211 | + | 0.751080i | \(0.729533\pi\) | |||||||
\(654\) | −9.62772 | + | 10.2448i | −0.376474 | + | 0.400604i | ||||
\(655\) | −15.5584 | + | 17.2005i | −0.607918 | + | 0.672078i | ||||
\(656\) | −3.68614 | − | 6.38458i | −0.143920 | − | 0.249276i | ||||
\(657\) | 5.37228 | + | 2.67181i | 0.209593 | + | 0.104237i | ||||
\(658\) | 22.1168 | + | 4.25639i | 0.862204 | + | 0.165931i | ||||
\(659\) | 16.1407i | 0.628752i | 0.949299 | + | 0.314376i | \(0.101795\pi\) | ||||
−0.949299 | + | 0.314376i | \(0.898205\pi\) | |||||||
\(660\) | −3.62772 | + | 0.294954i | −0.141209 | + | 0.0114811i | ||||
\(661\) | 11.0584 | + | 6.38458i | 0.430123 | + | 0.248331i | 0.699399 | − | 0.714732i | \(-0.253451\pi\) |
−0.269276 | + | 0.963063i | \(0.586784\pi\) | |||||||
\(662\) | 12.1168 | − | 20.9870i | 0.470935 | − | 0.815683i | ||||
\(663\) | −22.0000 | + | 6.63325i | −0.854409 | + | 0.257614i | ||||
\(664\) | 11.8294i | 0.459070i | ||||||||
\(665\) | −18.8614 | − | 8.01544i | −0.731414 | − | 0.310826i | ||||
\(666\) | 10.9783 | − | 22.0742i | 0.425399 | − | 0.855359i | ||||
\(667\) | 3.94158 | − | 2.27567i | 0.152619 | − | 0.0881143i | ||||
\(668\) | −12.6861 | − | 7.32435i | −0.490842 | − | 0.283387i | ||||
\(669\) | 1.04755 | − | 1.11469i | 0.0405005 | − | 0.0430965i | ||||
\(670\) | 5.05842 | − | 1.63086i | 0.195424 | − | 0.0630057i | ||||
\(671\) | −12.0000 | −0.463255 | ||||||||
\(672\) | 2.68614 | + | 3.71277i | 0.103620 | + | 0.143223i | ||||
\(673\) | 46.9678i | 1.81047i | 0.424907 | + | 0.905237i | \(0.360307\pi\) | ||||
−0.424907 | + | 0.905237i | \(0.639693\pi\) | |||||||
\(674\) | −0.558422 | + | 0.322405i | −0.0215096 | + | 0.0124186i | ||||
\(675\) | 25.9198 | + | 1.77834i | 0.997655 | + | 0.0684483i | ||||
\(676\) | 4.50000 | − | 7.79423i | 0.173077 | − | 0.299778i | ||||
\(677\) | −1.58017 | + | 0.912312i | −0.0607309 | + | 0.0350630i | −0.530058 | − | 0.847961i | \(-0.677830\pi\) |
0.469327 | + | 0.883024i | \(0.344497\pi\) | |||||||
\(678\) | 24.8614 | + | 5.84096i | 0.954797 | + | 0.224321i | ||||
\(679\) | 37.7921 | − | 13.0916i | 1.45033 | − | 0.502408i | ||||
\(680\) | 3.11684 | − | 14.5012i | 0.119526 | − | 0.556096i | ||||
\(681\) | 34.5584 | − | 10.4198i | 1.32428 | − | 0.399286i | ||||
\(682\) | 3.55842 | − | 6.16337i | 0.136259 | − | 0.236008i | ||||
\(683\) | −15.9891 | + | 27.6940i | −0.611807 | + | 1.05968i | 0.379129 | + | 0.925344i | \(0.376224\pi\) |
−0.990936 | + | 0.134337i | \(0.957110\pi\) | |||||||
\(684\) | −10.3723 | + | 0.644810i | −0.396594 | + | 0.0246549i | ||||
\(685\) | 19.1168 | + | 4.10891i | 0.730417 | + | 0.156993i | ||||
\(686\) | −18.5000 | − | 0.866025i | −0.706333 | − | 0.0330650i | ||||
\(687\) | 5.48913 | − | 23.3639i | 0.209423 | − | 0.891386i | ||||
\(688\) | 0.941578 | − | 0.543620i | 0.0358973 | − | 0.0207253i | ||||
\(689\) | 4.37228 | − | 7.57301i | 0.166571 | − | 0.288509i | ||||
\(690\) | 4.37228 | − | 3.02167i | 0.166450 | − | 0.115033i | ||||
\(691\) | 8.23369 | − | 4.75372i | 0.313224 | − | 0.180840i | −0.335144 | − | 0.942167i | \(-0.608785\pi\) |
0.648368 | + | 0.761327i | \(0.275452\pi\) | |||||||
\(692\) | 17.0256i | 0.647214i | ||||||||
\(693\) | 0.952453 | − | 7.39809i | 0.0361807 | − | 0.281030i | ||||
\(694\) | 1.88316 | 0.0714836 | ||||||||
\(695\) | 17.4891 | − | 5.63858i | 0.663400 | − | 0.213884i | ||||
\(696\) | −4.18614 | − | 3.93398i | −0.158675 | − | 0.149117i | ||||
\(697\) | −42.3505 | − | 24.4511i | −1.60414 | − | 0.926151i | ||||
\(698\) | 22.2921 | − | 12.8704i | 0.843769 | − | 0.487150i | ||||
\(699\) | 0.861407 | + | 0.202380i | 0.0325814 | + | 0.00765470i | ||||
\(700\) | −5.55842 | − | 12.0043i | −0.210089 | − | 0.453721i | ||||
\(701\) | − | 39.2473i | − | 1.48235i | −0.671313 | − | 0.741174i | \(-0.734269\pi\) | ||
0.671313 | − | 0.741174i | \(-0.265731\pi\) | |||||||
\(702\) | −1.74456 | + | 10.2448i | −0.0658443 | + | 0.386666i | ||||
\(703\) | 14.2337 | − | 24.6535i | 0.536834 | − | 0.929823i | ||||
\(704\) | 0.813859 | + | 0.469882i | 0.0306735 | + | 0.0177093i | ||||
\(705\) | −32.8614 | + | 2.67181i | −1.23763 | + | 0.100626i | ||||
\(706\) | 12.2718i | 0.461857i | ||||||||
\(707\) | 5.31386 | − | 27.6116i | 0.199848 | − | 1.03844i | ||||
\(708\) | −22.1168 | − | 5.19615i | −0.831202 | − | 0.195283i | ||||
\(709\) | −6.05842 | − | 10.4935i | −0.227529 | − | 0.394091i | 0.729546 | − | 0.683931i | \(-0.239731\pi\) |
−0.957075 | + | 0.289840i | \(0.906398\pi\) | |||||||
\(710\) | −14.1168 | − | 12.7692i | −0.529796 | − | 0.479218i | ||||
\(711\) | −22.7921 | + | 15.1186i | −0.854771 | + | 0.566991i | ||||
\(712\) | −0.686141 | − | 1.18843i | −0.0257142 | − | 0.0445383i | ||||
\(713\) | 10.3923i | 0.389195i | ||||||||
\(714\) | 27.7446 | + | 12.4193i | 1.03831 | + | 0.464781i | ||||
\(715\) | −0.883156 | + | 4.10891i | −0.0330282 | + | 0.153665i | ||||
\(716\) | −20.4891 | + | 11.8294i | −0.765715 | + | 0.442086i | ||||
\(717\) | −29.8614 | − | 28.0627i | −1.11519 | − | 1.04802i | ||||
\(718\) | −23.7446 | − | 13.7089i | −0.886139 | − | 0.511613i | ||||
\(719\) | 22.3723 | + | 38.7499i | 0.834345 | + | 1.44513i | 0.894562 | + | 0.446943i | \(0.147487\pi\) |
−0.0602171 | + | 0.998185i | \(0.519179\pi\) | |||||||
\(720\) | −5.24456 | − | 4.18265i | −0.195453 | − | 0.155878i | ||||
\(721\) | 4.23369 | + | 3.66648i | 0.157671 | + | 0.136547i | ||||
\(722\) | 7.00000 | 0.260513 | ||||||||
\(723\) | −31.9307 | + | 9.62747i | −1.18752 | + | 0.358049i | ||||
\(724\) | 6.94158 | + | 4.00772i | 0.257982 | + | 0.148946i | ||||
\(725\) | 9.68614 | + | 13.4603i | 0.359734 | + | 0.499902i | ||||
\(726\) | 5.05842 | + | 16.7769i | 0.187736 | + | 0.622649i | ||||
\(727\) | −19.0000 | −0.704671 | −0.352335 | − | 0.935874i | \(-0.614612\pi\) | ||||
−0.352335 | + | 0.935874i | \(0.614612\pi\) | |||||||
\(728\) | 5.00000 | − | 1.73205i | 0.185312 | − | 0.0641941i | ||||
\(729\) | 5.00000 | + | 26.5330i | 0.185185 | + | 0.982704i | ||||
\(730\) | 1.37228 | + | 4.25639i | 0.0507904 | + | 0.157536i | ||||
\(731\) | 3.60597 | − | 6.24572i | 0.133372 | − | 0.231006i | ||||
\(732\) | −16.1168 | − | 15.1460i | −0.595696 | − | 0.559813i | ||||
\(733\) | 16.2337 | + | 28.1176i | 0.599605 | + | 1.03855i | 0.992879 | + | 0.119125i | \(0.0380089\pi\) |
−0.393274 | + | 0.919421i | \(0.628658\pi\) | |||||||
\(734\) | 13.2337 | 0.488464 | ||||||||
\(735\) | 26.4307 | − | 6.03473i | 0.974911 | − | 0.222594i | ||||
\(736\) | −1.37228 | −0.0505830 | ||||||||
\(737\) | 1.11684 | + | 1.93443i | 0.0411395 | + | 0.0712557i | ||||
\(738\) | −18.4307 | + | 12.2255i | −0.678444 | + | 0.450029i | ||||
\(739\) | 0.883156 | − | 1.52967i | 0.0324874 | − | 0.0562699i | −0.849325 | − | 0.527871i | \(-0.822990\pi\) |
0.881812 | + | 0.471601i | \(0.156324\pi\) | |||||||
\(740\) | 17.4891 | − | 5.63858i | 0.642913 | − | 0.207278i | ||||
\(741\) | −2.74456 | + | 11.6819i | −0.100824 | + | 0.429146i | ||||
\(742\) | −10.9307 | + | 3.78651i | −0.401279 | + | 0.139007i | ||||
\(743\) | 21.6060 | 0.792646 | 0.396323 | − | 0.918111i | \(-0.370286\pi\) | ||||
0.396323 | + | 0.918111i | \(0.370286\pi\) | |||||||
\(744\) | 12.5584 | − | 3.78651i | 0.460414 | − | 0.138820i | ||||
\(745\) | 14.9416 | + | 13.5152i | 0.547417 | + | 0.495157i | ||||
\(746\) | −20.2337 | − | 11.6819i | −0.740808 | − | 0.427706i | ||||
\(747\) | 35.4198 | − | 2.20193i | 1.29594 | − | 0.0805645i | ||||
\(748\) | 6.23369 | 0.227926 | ||||||||
\(749\) | −12.5109 | − | 10.8347i | −0.457137 | − | 0.395893i | ||||
\(750\) | 12.5475 | + | 14.7499i | 0.458172 | + | 0.538590i | ||||
\(751\) | −12.4416 | − | 21.5494i | −0.454000 | − | 0.786350i | 0.544630 | − | 0.838676i | \(-0.316670\pi\) |
−0.998630 | + | 0.0523257i | \(0.983337\pi\) | |||||||
\(752\) | 7.37228 | + | 4.25639i | 0.268839 | + | 0.155215i | ||||
\(753\) | −1.32473 | + | 1.40965i | −0.0482760 | + | 0.0513703i | ||||
\(754\) | −5.74456 | + | 3.31662i | −0.209205 | + | 0.120784i | ||||
\(755\) | −19.9307 | − | 4.28384i | −0.725353 | − | 0.155905i | ||||
\(756\) | 10.6168 | − | 8.73399i | 0.386131 | − | 0.317652i | ||||
\(757\) | 25.5383i | 0.928206i | 0.885781 | + | 0.464103i | \(0.153623\pi\) | ||||
−0.885781 | + | 0.464103i | \(0.846377\pi\) | |||||||
\(758\) | 6.11684 | + | 10.5947i | 0.222174 | + | 0.384816i | ||||
\(759\) | 1.62772 | + | 1.52967i | 0.0590824 | + | 0.0555235i | ||||
\(760\) | −5.74456 | − | 5.19615i | −0.208377 | − | 0.188484i | ||||
\(761\) | 3.51087 | + | 6.08101i | 0.127269 | + | 0.220437i | 0.922618 | − | 0.385716i | \(-0.126045\pi\) |
−0.795349 | + | 0.606152i | \(0.792712\pi\) | |||||||
\(762\) | −3.00000 | + | 12.7692i | −0.108679 | + | 0.462578i | ||||
\(763\) | 4.05842 | − | 21.0882i | 0.146925 | − | 0.763443i | ||||
\(764\) | 17.0256i | 0.615963i | ||||||||
\(765\) | −44.0000 | − | 6.63325i | −1.59082 | − | 0.239826i | ||||
\(766\) | 13.5475 | + | 7.82168i | 0.489493 | + | 0.282609i | ||||
\(767\) | −13.1168 | + | 22.7190i | −0.473622 | + | 0.820337i | ||||
\(768\) | 0.500000 | + | 1.65831i | 0.0180422 | + | 0.0598392i | ||||
\(769\) | 30.5321i | 1.10102i | 0.834830 | + | 0.550508i | \(0.185566\pi\) | ||||
−0.834830 | + | 0.550508i | \(0.814434\pi\) | |||||||
\(770\) | 4.44158 | − | 3.34408i | 0.160063 | − | 0.120512i | ||||
\(771\) | 0.744563 | − | 3.16915i | 0.0268148 | − | 0.114134i | ||||
\(772\) | 15.5584 | − | 8.98266i | 0.559960 | − | 0.323293i | ||||
\(773\) | 7.37228 | + | 4.25639i | 0.265163 | + | 0.153092i | 0.626687 | − | 0.779271i | \(-0.284410\pi\) |
−0.361525 | + | 0.932363i | \(0.617744\pi\) | |||||||
\(774\) | −1.80298 | − | 2.71810i | −0.0648069 | − | 0.0977001i | ||||
\(775\) | −37.6753 | + | 3.78651i | −1.35334 | + | 0.136015i | ||||
\(776\) | 15.1168 | 0.542663 | ||||||||
\(777\) | 3.86141 | + | 37.4603i | 0.138527 | + | 1.34388i | ||||
\(778\) | 7.51811i | 0.269537i | ||||||||
\(779\) | −22.1168 | + | 12.7692i | −0.792418 | + | 0.457503i | ||||
\(780\) | −6.37228 | + | 4.40387i | −0.228164 | + | 0.157684i | ||||
\(781\) | 4.00000 | − | 6.92820i | 0.143131 | − | 0.247911i | ||||
\(782\) | −7.88316 | + | 4.55134i | −0.281901 | + | 0.162756i | ||||
\(783\) | −11.0000 | + | 13.2665i | −0.393108 | + | 0.474106i | ||||
\(784\) | −6.50000 | − | 2.59808i | −0.232143 | − | 0.0927884i | ||||
\(785\) | −17.4891 | − | 3.75906i | −0.624214 | − | 0.134166i | ||||
\(786\) | −5.18614 | − | 17.2005i | −0.184984 | − | 0.613521i | ||||
\(787\) | −4.94158 | + | 8.55906i | −0.176148 | + | 0.305098i | −0.940558 | − | 0.339633i | \(-0.889697\pi\) |
0.764410 | + | 0.644731i | \(0.223030\pi\) | |||||||
\(788\) | −7.11684 | + | 12.3267i | −0.253527 | + | 0.439122i | ||||
\(789\) | 3.68614 | + | 12.2255i | 0.131230 | + | 0.435241i | ||||
\(790\) | −19.9307 | − | 4.28384i | −0.709103 | − | 0.152412i | ||||
\(791\) | −36.8614 | + | 12.7692i | −1.31064 | + | 0.454019i | ||||
\(792\) | 1.25544 | − | 2.52434i | 0.0446100 | − | 0.0896984i | ||||
\(793\) | −22.1168 | + | 12.7692i | −0.785392 | + | 0.453446i | ||||
\(794\) | −4.00000 | + | 6.92820i | −0.141955 | + | 0.245873i | ||||
\(795\) | 13.9307 | − | 9.62747i | 0.494071 | − | 0.341451i | ||||
\(796\) | −1.11684 | + | 0.644810i | −0.0395855 | + | 0.0228547i | ||||
\(797\) | − | 0.939764i | − | 0.0332881i | −0.999861 | − | 0.0166441i | \(-0.994702\pi\) | ||
0.999861 | − | 0.0166441i | \(-0.00529822\pi\) | |||||||
\(798\) | 12.8614 | − | 9.30506i | 0.455289 | − | 0.329396i | ||||
\(799\) | 56.4674 | 1.99767 | ||||||||
\(800\) | −0.500000 | − | 4.97494i | −0.0176777 | − | 0.175891i | ||||
\(801\) | −3.43070 | + | 2.27567i | −0.121218 | + | 0.0804069i | ||||
\(802\) | 14.3139 | + | 8.26411i | 0.505440 | + | 0.291816i | ||||
\(803\) | −1.62772 | + | 0.939764i | −0.0574409 | + | 0.0331635i | ||||
\(804\) | −0.941578 | + | 4.00772i | −0.0332069 | + | 0.141341i | ||||
\(805\) | −3.17527 | + | 7.47182i | −0.111913 | + | 0.263347i | ||||
\(806\) | − | 15.1460i | − | 0.533496i | ||||||
\(807\) | 12.9891 | + | 43.0801i | 0.457239 | + | 1.51649i | ||||
\(808\) | 5.31386 | − | 9.20387i | 0.186941 | − | 0.323791i | ||||
\(809\) | 36.4307 | + | 21.0333i | 1.28084 | + | 0.739491i | 0.977001 | − | 0.213234i | \(-0.0683998\pi\) |
0.303834 | + | 0.952725i | \(0.401733\pi\) | |||||||
\(810\) | −11.5475 | + | 16.4819i | −0.405739 | + | 0.579116i | ||||
\(811\) | 10.3923i | 0.364923i | 0.983213 | + | 0.182462i | \(0.0584065\pi\) | ||||
−0.983213 | + | 0.182462i | \(0.941593\pi\) | |||||||
\(812\) | 8.61684 | + | 1.65831i | 0.302392 | + | 0.0581954i | ||||
\(813\) | 3.51087 | − | 14.9436i | 0.123132 | − | 0.524097i | ||||
\(814\) | 3.86141 | + | 6.68815i | 0.135342 | + | 0.234420i | ||||
\(815\) | −5.74456 | − | 5.19615i | −0.201223 | − | 0.182013i | ||||
\(816\) | 8.37228 | + | 7.86797i | 0.293088 | + | 0.275434i | ||||
\(817\) | −1.88316 | − | 3.26172i | −0.0658833 | − | 0.114113i | ||||
\(818\) | − | 4.31129i | − | 0.150741i | ||||||
\(819\) | −6.11684 | − | 14.6487i | −0.213740 | − | 0.511867i | ||||
\(820\) | −16.1168 | − | 3.46410i | −0.562825 | − | 0.120972i | ||||
\(821\) | 4.06930 | − | 2.34941i | 0.142019 | − | 0.0819950i | −0.427307 | − | 0.904107i | \(-0.640538\pi\) |
0.569326 | + | 0.822112i | \(0.307204\pi\) | |||||||
\(822\) | −10.3723 | + | 11.0371i | −0.361775 | + | 0.384964i | ||||
\(823\) | 11.8247 | + | 6.82701i | 0.412184 | + | 0.237975i | 0.691728 | − | 0.722158i | \(-0.256850\pi\) |
−0.279544 | + | 0.960133i | \(0.590183\pi\) | |||||||
\(824\) | 1.05842 | + | 1.83324i | 0.0368719 | + | 0.0638640i | ||||
\(825\) | −4.95245 | + | 6.45832i | −0.172422 | + | 0.224850i | ||||
\(826\) | 32.7921 | − | 11.3595i | 1.14098 | − | 0.395248i | ||||
\(827\) | 33.0000 | 1.14752 | 0.573761 | − | 0.819023i | \(-0.305484\pi\) | ||||
0.573761 | + | 0.819023i | \(0.305484\pi\) | |||||||
\(828\) | 0.255437 | + | 4.10891i | 0.00887706 | + | 0.142795i | ||||
\(829\) | 1.11684 | + | 0.644810i | 0.0387896 | + | 0.0223952i | 0.519269 | − | 0.854611i | \(-0.326204\pi\) |
−0.480480 | + | 0.877006i | \(0.659537\pi\) | |||||||
\(830\) | 19.6168 | + | 17.7441i | 0.680911 | + | 0.615907i | ||||
\(831\) | 15.0951 | − | 4.55134i | 0.523643 | − | 0.157884i | ||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | −45.9565 | + | 6.63325i | −1.59230 | + | 0.229828i | ||||
\(834\) | −3.25544 | + | 13.8564i | −0.112727 | + | 0.479808i | ||||
\(835\) | −31.1753 | + | 10.0511i | −1.07886 | + | 0.347831i | ||||
\(836\) | 1.62772 | − | 2.81929i | 0.0562958 | − | 0.0975072i | ||||
\(837\) | −13.6753 | − | 36.8979i | −0.472686 | − | 1.27538i | ||||
\(838\) | 3.25544 | + | 5.63858i | 0.112457 | + | 0.194782i | ||||
\(839\) | −55.7228 | −1.92377 | −0.961883 | − | 0.273463i | \(-0.911831\pi\) | ||||
−0.961883 | + | 0.273463i | \(0.911831\pi\) | |||||||
\(840\) | 10.1861 | + | 1.11469i | 0.351455 | + | 0.0384605i | ||||
\(841\) | 18.0000 | 0.620690 | ||||||||
\(842\) | 1.05842 | + | 1.83324i | 0.0364756 | + | 0.0631776i | ||||
\(843\) | 14.3723 | + | 13.5065i | 0.495008 | + | 0.465190i | ||||
\(844\) | −8.11684 | + | 14.0588i | −0.279393 | + | 0.483923i | ||||
\(845\) | −6.17527 | − | 19.1537i | −0.212436 | − | 0.658909i | ||||
\(846\) | 11.3723 | − | 22.8665i | 0.390987 | − | 0.786167i | ||||
\(847\) | −20.2337 | − | 17.5229i | −0.695238 | − | 0.602094i | ||||
\(848\) | −4.37228 | −0.150145 | ||||||||
\(849\) | −8.00000 | − | 26.5330i | −0.274559 | − | 0.910610i | ||||
\(850\) | −19.3723 | − | 26.9205i | −0.664464 | − | 0.923366i | ||||
\(851\) | −9.76631 | − | 5.63858i | −0.334785 | − | 0.193288i | ||||
\(852\) | 14.1168 | − | 4.25639i | 0.483635 | − | 0.145821i | ||||
\(853\) | −38.4674 | −1.31710 | −0.658549 | − | 0.752538i | \(-0.728829\pi\) | ||||
−0.658549 | + | 0.752538i | \(0.728829\pi\) | |||||||
\(854\) | 33.1753 | + | 6.38458i | 1.13523 | + | 0.218476i | ||||
\(855\) | −14.4891 | + | 18.1677i | −0.495518 | + | 0.621322i | ||||
\(856\) | −3.12772 | − | 5.41737i | −0.106903 | − | 0.185162i | ||||
\(857\) | 21.2554 | + | 12.2718i | 0.726072 | + | 0.419198i | 0.816983 | − | 0.576661i | \(-0.195645\pi\) |
−0.0909115 | + | 0.995859i | \(0.528978\pi\) | |||||||
\(858\) | −2.37228 | − | 2.22938i | −0.0809883 | − | 0.0761099i | ||||
\(859\) | −40.4674 | + | 23.3639i | −1.38073 | + | 0.797164i | −0.992246 | − | 0.124291i | \(-0.960334\pi\) |
−0.388483 | + | 0.921456i | \(0.627001\pi\) | |||||||
\(860\) | 0.510875 | − | 2.37686i | 0.0174207 | − | 0.0810503i | ||||
\(861\) | 13.8030 | − | 30.8357i | 0.470404 | − | 1.05088i | ||||
\(862\) | 17.0256i | 0.579893i | ||||||||
\(863\) | −6.68614 | − | 11.5807i | −0.227599 | − | 0.394213i | 0.729497 | − | 0.683984i | \(-0.239754\pi\) |
−0.957096 | + | 0.289771i | \(0.906421\pi\) | |||||||
\(864\) | 4.87228 | − | 1.80579i | 0.165758 | − | 0.0614342i | ||||
\(865\) | 28.2337 | + | 25.5383i | 0.959974 | + | 0.868329i | ||||
\(866\) | 17.0000 | + | 29.4449i | 0.577684 | + | 1.00058i | ||||
\(867\) | 45.5258 | + | 10.6959i | 1.54614 | + | 0.363251i | ||||
\(868\) | −13.1168 | + | 15.1460i | −0.445215 | + | 0.514090i | ||||
\(869\) | − | 8.56768i | − | 0.290639i | ||||||
\(870\) | −12.8030 | + | 1.04095i | −0.434062 | + | 0.0352916i | ||||
\(871\) | 4.11684 | + | 2.37686i | 0.139494 | + | 0.0805369i | ||||
\(872\) | 4.05842 | − | 7.02939i | 0.137436 | − | 0.238045i | ||||
\(873\) | −2.81386 | − | 45.2632i | −0.0952347 | − | 1.53193i | ||||
\(874\) | 4.75372i | 0.160797i | ||||||||
\(875\) | −28.2446 | − | 8.78890i | −0.954840 | − | 0.297119i | ||||
\(876\) | −3.37228 | − | 0.792287i | −0.113939 | − | 0.0267689i | ||||
\(877\) | 24.3505 | − | 14.0588i | 0.822259 | − | 0.474731i | −0.0289358 | − | 0.999581i | \(-0.509212\pi\) |
0.851195 | + | 0.524850i | \(0.175879\pi\) | |||||||
\(878\) | 2.44158 | + | 1.40965i | 0.0823993 | + | 0.0475732i | ||||
\(879\) | −27.4198 | − | 25.7682i | −0.924848 | − | 0.869139i | ||||
\(880\) | 2.00000 | − | 0.644810i | 0.0674200 | − | 0.0217365i | ||||
\(881\) | 0.350532 | 0.0118097 | 0.00590486 | − | 0.999983i | \(-0.498120\pi\) | ||||
0.00590486 | + | 0.999983i | \(0.498120\pi\) | |||||||
\(882\) | −6.56930 | + | 19.9460i | −0.221200 | + | 0.671618i | ||||
\(883\) | 44.5532i | 1.49934i | 0.661815 | + | 0.749668i | \(0.269787\pi\) | ||||
−0.661815 | + | 0.749668i | \(0.730213\pi\) | |||||||
\(884\) | 11.4891 | − | 6.63325i | 0.386421 | − | 0.223100i | ||||
\(885\) | −41.7921 | + | 28.8824i | −1.40483 | + | 0.970872i | ||||
\(886\) | −4.50000 | + | 7.79423i | −0.151180 | + | 0.261852i | ||||
\(887\) | 7.03667 | − | 4.06262i | 0.236268 | − | 0.136410i | −0.377192 | − | 0.926135i | \(-0.623110\pi\) |
0.613460 | + | 0.789725i | \(0.289777\pi\) | |||||||
\(888\) | −3.25544 | + | 13.8564i | −0.109245 | + | 0.464991i | ||||
\(889\) | −6.55842 | − | 18.9325i | −0.219962 | − | 0.634977i | ||||
\(890\) | −3.00000 | − | 0.644810i | −0.100560 | − | 0.0216141i | ||||
\(891\) | −7.79211 | − | 3.28917i | −0.261046 | − | 0.110191i | ||||
\(892\) | −0.441578 | + | 0.764836i | −0.0147851 | + | 0.0256086i | ||||
\(893\) | 14.7446 | − | 25.5383i | 0.493408 | − | 0.854608i | ||||
\(894\) | −14.9416 | + | 4.50506i | −0.499721 | + | 0.150672i | ||||
\(895\) | −11.1168 | + | 51.7215i | −0.371595 | + | 1.72886i | ||||
\(896\) | −2.00000 | − | 1.73205i | −0.0668153 | − | 0.0578638i | ||||
\(897\) | 4.62772 | + | 1.08724i | 0.154515 | + | 0.0363019i | ||||
\(898\) | −17.6644 | + | 10.1985i | −0.589468 | + | 0.340330i | ||||
\(899\) | 12.5584 | − | 21.7518i | 0.418847 | − | 0.725464i | ||||
\(900\) | −14.8030 | + | 2.42315i | −0.493433 | + | 0.0807716i | ||||
\(901\) | −25.1168 | + | 14.5012i | −0.836763 | + | 0.483106i | ||||
\(902\) | − | 6.92820i | − | 0.230684i | ||||||
\(903\) | 4.54755 | + | 2.03562i | 0.151333 | + | 0.0677412i | ||||
\(904\) | −14.7446 | −0.490397 | ||||||||
\(905\) | 17.0584 | − | 5.49972i | 0.567041 | − | 0.182817i | ||||
\(906\) | 10.8139 | − | 11.5070i | 0.359266 | − | 0.382294i | ||||
\(907\) | 4.29211 | + | 2.47805i | 0.142517 | + | 0.0822823i | 0.569563 | − | 0.821948i | \(-0.307112\pi\) |
−0.427046 | + | 0.904230i | \(0.640446\pi\) | |||||||
\(908\) | −18.0475 | + | 10.4198i | −0.598929 | + | 0.345792i | ||||
\(909\) | −28.5475 | − | 14.1976i | −0.946862 | − | 0.470906i | ||||
\(910\) | 4.62772 | − | 10.8896i | 0.153407 | − | 0.360988i | ||||
\(911\) | 37.8102i | 1.25271i | 0.779539 | + | 0.626353i | \(0.215453\pi\) | ||||
−0.779539 | + | 0.626353i | \(0.784547\pi\) | |||||||
\(912\) | 5.74456 | − | 1.73205i | 0.190221 | − | 0.0573539i | ||||
\(913\) | −5.55842 | + | 9.62747i | −0.183957 | + | 0.318623i | ||||
\(914\) | −2.44158 | − | 1.40965i | −0.0807602 | − | 0.0466269i | ||||
\(915\) | −49.2921 | + | 4.00772i | −1.62955 | + | 0.132491i | ||||
\(916\) | 13.8564i | 0.457829i | ||||||||
\(917\) | 20.7446 | + | 17.9653i | 0.685046 | + | 0.593267i | ||||
\(918\) | 22.0000 | − | 26.5330i | 0.726108 | − | 0.875719i | ||||
\(919\) | −8.11684 | − | 14.0588i | −0.267750 | − | 0.463757i | 0.700530 | − | 0.713622i | \(-0.252947\pi\) |
−0.968280 | + | 0.249866i | \(0.919613\pi\) | |||||||
\(920\) | −2.05842 | + | 2.27567i | −0.0678642 | + | 0.0750267i | ||||
\(921\) | 28.6060 | − | 30.4395i | 0.942599 | − | 1.00302i | ||||
\(922\) | 11.7446 | + | 20.3422i | 0.386787 | + | 0.669934i | ||||
\(923\) | − | 17.0256i | − | 0.560403i | ||||||
\(924\) | 0.441578 | + | 4.28384i | 0.0145269 | + | 0.140928i | ||||
\(925\) | 16.8832 | − | 37.4603i | 0.555115 | − | 1.23169i | ||||
\(926\) | −5.82473 | + | 3.36291i | −0.191413 | + | 0.110512i | ||||
\(927\) | 5.29211 | − | 3.51039i | 0.173816 | − | 0.115296i | ||||
\(928\) | 2.87228 | + | 1.65831i | 0.0942873 | + | 0.0544368i | ||||
\(929\) | −17.0584 | − | 29.5461i | −0.559669 | − | 0.969375i | −0.997524 | − | 0.0703291i | \(-0.977595\pi\) |
0.437855 | − | 0.899046i | \(-0.355738\pi\) | |||||||
\(930\) | 12.5584 | − | 26.5055i | 0.411807 | − | 0.869151i | ||||
\(931\) | −9.00000 | + | 22.5167i | −0.294963 | + | 0.737954i | ||||
\(932\) | −0.510875 | −0.0167343 | ||||||||
\(933\) | −10.1168 | − | 33.5538i | −0.331211 | − | 1.09850i | ||||
\(934\) | 31.5475 | + | 18.2140i | 1.03227 | + | 0.595980i | ||||
\(935\) | 9.35053 | − | 10.3374i | 0.305795 | − | 0.338069i | ||||
\(936\) | −0.372281 | − | 5.98844i | −0.0121684 | − | 0.195738i | ||||
\(937\) | −1.35053 | −0.0441200 | −0.0220600 | − | 0.999757i | \(-0.507022\pi\) | ||||
−0.0220600 | + | 0.999757i | \(0.507022\pi\) | |||||||
\(938\) | −2.05842 | − | 5.94215i | −0.0672099 | − | 0.194018i | ||||
\(939\) | −5.25544 | − | 1.23472i | −0.171505 | − | 0.0402935i | ||||
\(940\) | 18.1168 | − | 5.84096i | 0.590906 | − | 0.190511i | ||||
\(941\) | −13.6753 | + | 23.6863i | −0.445801 | + | 0.772150i | −0.998108 | − | 0.0614911i | \(-0.980414\pi\) |
0.552307 | + | 0.833641i | \(0.313748\pi\) | |||||||
\(942\) | 9.48913 | − | 10.0974i | 0.309172 | − | 0.328989i | ||||
\(943\) | 5.05842 | + | 8.76144i | 0.164725 | + | 0.285312i | ||||
\(944\) | 13.1168 | 0.426917 | ||||||||
\(945\) | 1.44158 | − | 30.7070i | 0.0468945 | − | 0.998900i | ||||
\(946\) | 1.02175 | 0.0332199 | ||||||||
\(947\) | −12.9416 | − | 22.4155i | −0.420545 | − | 0.728405i | 0.575448 | − | 0.817838i | \(-0.304828\pi\) |
−0.995993 | + | 0.0894334i | \(0.971494\pi\) | |||||||
\(948\) | 10.8139 | − | 11.5070i | 0.351218 | − | 0.373730i | ||||
\(949\) | −2.00000 | + | 3.46410i | −0.0649227 | + | 0.112449i | ||||
\(950\) | −17.2337 | + | 1.73205i | −0.559135 | + | 0.0561951i | ||||
\(951\) | 1.88316 | + | 0.442430i | 0.0610655 | + | 0.0143468i | ||||
\(952\) | −17.2337 | − | 3.31662i | −0.558547 | − | 0.107492i | ||||
\(953\) | −48.0000 | −1.55487 | −0.777436 | − | 0.628962i | \(-0.783480\pi\) | ||||
−0.777436 | + | 0.628962i | \(0.783480\pi\) | |||||||
\(954\) | 0.813859 | + | 13.0916i | 0.0263497 | + | 0.423855i | ||||
\(955\) | 28.2337 | + | 25.5383i | 0.913621 | + | 0.826401i | ||||
\(956\) | 20.4891 | + | 11.8294i | 0.662666 | + | 0.382590i | ||||
\(957\) | −1.55842 | − | 5.16870i | −0.0503766 | − | 0.167080i | ||||
\(958\) | −2.74456 | −0.0886728 | ||||||||
\(959\) | 4.37228 | − | 22.7190i | 0.141188 | − | 0.733636i | ||||
\(960\) | 3.50000 | + | 1.65831i | 0.112962 | + | 0.0535218i | ||||
\(961\) | 13.1753 | + | 22.8202i | 0.425009 | + | 0.736136i | ||||
\(962\) | 14.2337 | + | 8.21782i | 0.458913 | + | 0.264953i | ||||
\(963\) | −15.6386 | + | 10.3735i | −0.503947 | + | 0.334280i | ||||
\(964\) | 16.6753 | − | 9.62747i | 0.537074 | − | 0.310080i | ||||
\(965\) | 8.44158 | − | 39.2747i | 0.271744 | − | 1.26430i | ||||
\(966\) | −3.68614 | − | 5.09496i | −0.118600 | − | 0.163928i | ||||
\(967\) | − | 27.6751i | − | 0.889973i | −0.895537 | − | 0.444986i | \(-0.853209\pi\) | ||
0.895537 | − | 0.444986i | \(-0.146791\pi\) | |||||||
\(968\) | −5.05842 | − | 8.76144i | −0.162584 | − | 0.281603i | ||||
\(969\) | 27.2554 | − | 29.0024i | 0.875571 | − | 0.931692i | ||||
\(970\) | 22.6753 | − | 25.0684i | 0.728059 | − | 0.804899i | ||||
\(971\) | −17.1861 | − | 29.7673i | −0.551530 | − | 0.955277i | −0.998165 | − | 0.0605609i | \(-0.980711\pi\) |
0.446635 | − | 0.894716i | \(-0.352622\pi\) | |||||||
\(972\) | −6.31386 | − | 14.2525i | −0.202517 | − | 0.457151i | ||||
\(973\) | −7.11684 | − | 20.5446i | −0.228156 | − | 0.658628i | ||||
\(974\) | − | 14.5012i | − | 0.464649i | ||||||
\(975\) | −2.25544 | + | 17.1730i | −0.0722318 | + | 0.549977i | ||||
\(976\) | 11.0584 | + | 6.38458i | 0.353971 | + | 0.204366i | ||||
\(977\) | −14.2337 | + | 24.6535i | −0.455376 | + | 0.788734i | −0.998710 | − | 0.0507824i | \(-0.983829\pi\) |
0.543334 | + | 0.839517i | \(0.317162\pi\) | |||||||
\(978\) | 5.74456 | − | 1.73205i | 0.183691 | − | 0.0553849i | ||||
\(979\) | − | 1.28962i | − | 0.0412164i | ||||||
\(980\) | −14.0584 | + | 6.88192i | −0.449080 | + | 0.219835i | ||||
\(981\) | −21.8030 | − | 10.8434i | −0.696116 | − | 0.346202i | ||||
\(982\) | 26.1861 | − | 15.1186i | 0.835633 | − | 0.482453i | ||||
\(983\) | −21.6861 | − | 12.5205i | −0.691680 | − | 0.399342i | 0.112561 | − | 0.993645i | \(-0.464095\pi\) |
−0.804241 | + | 0.594303i | \(0.797428\pi\) | |||||||
\(984\) | 8.74456 | − | 9.30506i | 0.278766 | − | 0.296635i | ||||
\(985\) | 9.76631 | + | 30.2921i | 0.311181 | + | 0.965185i | ||||
\(986\) | 22.0000 | 0.700623 | ||||||||
\(987\) | 4.00000 | + | 38.8048i | 0.127321 | + | 1.23517i | ||||
\(988\) | − | 6.92820i | − | 0.220416i | ||||||
\(989\) | −1.29211 | + | 0.746000i | −0.0410867 | + | 0.0237214i | ||||
\(990\) | −2.30298 | − | 5.86841i | −0.0731937 | − | 0.186510i | ||||
\(991\) | −11.6753 | + | 20.2222i | −0.370877 | + | 0.642378i | −0.989701 | − | 0.143152i | \(-0.954276\pi\) |
0.618824 | + | 0.785530i | \(0.287610\pi\) | |||||||
\(992\) | −6.55842 | + | 3.78651i | −0.208230 | + | 0.120222i | ||||
\(993\) | 40.8614 | + | 9.60002i | 1.29670 | + | 0.304647i | ||||
\(994\) | −14.7446 | + | 17.0256i | −0.467669 | + | 0.540018i | ||||
\(995\) | −0.605969 | + | 2.81929i | −0.0192105 | + | 0.0893775i | ||||
\(996\) | −19.6168 | + | 5.91470i | −0.621583 | + | 0.187414i | ||||
\(997\) | 19.2337 | − | 33.3137i | 0.609137 | − | 1.05506i | −0.382246 | − | 0.924061i | \(-0.624849\pi\) |
0.991383 | − | 0.130996i | \(-0.0418174\pi\) | |||||||
\(998\) | 3.11684 | − | 5.39853i | 0.0986620 | − | 0.170888i | ||||
\(999\) | 42.0951 | + | 7.16825i | 1.33183 | + | 0.226794i |
(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 | 210.2.t.b.59.2 | yes | 4 | |
3.2 | odd | 2 | 210.2.t.d.59.1 | yes | 4 | ||
5.2 | odd | 4 | 1050.2.s.d.101.3 | 8 | |||
5.3 | odd | 4 | 1050.2.s.d.101.2 | 8 | |||
5.4 | even | 2 | 210.2.t.c.59.1 | yes | 4 | ||
7.3 | odd | 6 | 1470.2.d.d.1469.4 | 4 | |||
7.4 | even | 3 | 1470.2.d.c.1469.1 | 4 | |||
7.5 | odd | 6 | 210.2.t.a.89.1 | yes | 4 | ||
15.2 | even | 4 | 1050.2.s.e.101.1 | 8 | |||
15.8 | even | 4 | 1050.2.s.e.101.4 | 8 | |||
15.14 | odd | 2 | 210.2.t.a.59.2 | ✓ | 4 | ||
21.5 | even | 6 | 210.2.t.c.89.1 | yes | 4 | ||
21.11 | odd | 6 | 1470.2.d.a.1469.2 | 4 | |||
21.17 | even | 6 | 1470.2.d.b.1469.3 | 4 | |||
35.4 | even | 6 | 1470.2.d.b.1469.4 | 4 | |||
35.12 | even | 12 | 1050.2.s.e.551.1 | 8 | |||
35.19 | odd | 6 | 210.2.t.d.89.2 | yes | 4 | ||
35.24 | odd | 6 | 1470.2.d.a.1469.1 | 4 | |||
35.33 | even | 12 | 1050.2.s.e.551.4 | 8 | |||
105.47 | odd | 12 | 1050.2.s.d.551.3 | 8 | |||
105.59 | even | 6 | 1470.2.d.c.1469.2 | 4 | |||
105.68 | odd | 12 | 1050.2.s.d.551.2 | 8 | |||
105.74 | odd | 6 | 1470.2.d.d.1469.3 | 4 | |||
105.89 | even | 6 | inner | 210.2.t.b.89.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.t.a.59.2 | ✓ | 4 | 15.14 | odd | 2 | ||
210.2.t.a.89.1 | yes | 4 | 7.5 | odd | 6 | ||
210.2.t.b.59.2 | yes | 4 | 1.1 | even | 1 | trivial | |
210.2.t.b.89.2 | yes | 4 | 105.89 | even | 6 | inner | |
210.2.t.c.59.1 | yes | 4 | 5.4 | even | 2 | ||
210.2.t.c.89.1 | yes | 4 | 21.5 | even | 6 | ||
210.2.t.d.59.1 | yes | 4 | 3.2 | odd | 2 | ||
210.2.t.d.89.2 | yes | 4 | 35.19 | odd | 6 | ||
1050.2.s.d.101.2 | 8 | 5.3 | odd | 4 | |||
1050.2.s.d.101.3 | 8 | 5.2 | odd | 4 | |||
1050.2.s.d.551.2 | 8 | 105.68 | odd | 12 | |||
1050.2.s.d.551.3 | 8 | 105.47 | odd | 12 | |||
1050.2.s.e.101.1 | 8 | 15.2 | even | 4 | |||
1050.2.s.e.101.4 | 8 | 15.8 | even | 4 | |||
1050.2.s.e.551.1 | 8 | 35.12 | even | 12 | |||
1050.2.s.e.551.4 | 8 | 35.33 | even | 12 | |||
1470.2.d.a.1469.1 | 4 | 35.24 | odd | 6 | |||
1470.2.d.a.1469.2 | 4 | 21.11 | odd | 6 | |||
1470.2.d.b.1469.3 | 4 | 21.17 | even | 6 | |||
1470.2.d.b.1469.4 | 4 | 35.4 | even | 6 | |||
1470.2.d.c.1469.1 | 4 | 7.4 | even | 3 | |||
1470.2.d.c.1469.2 | 4 | 105.59 | even | 6 | |||
1470.2.d.d.1469.3 | 4 | 105.74 | odd | 6 | |||
1470.2.d.d.1469.4 | 4 | 7.3 | odd | 6 |