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 | \(1.68614 + 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.59 |
Dual form | 210.2.t.c.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 | ||||
\(3\) | 1.68614 | − | 0.396143i | 0.973494 | − | 0.228714i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.50000 | − | 1.65831i | 0.670820 | − | 0.741620i | ||||
\(6\) | 1.18614 | + | 1.26217i | 0.484240 | + | 0.515278i | ||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.68614 | − | 1.33591i | 0.895380 | − | 0.445302i | ||||
\(10\) | 2.18614 | + | 0.469882i | 0.691318 | + | 0.148590i | ||||
\(11\) | 3.68614 | + | 2.12819i | 1.11141 | + | 0.641675i | 0.939195 | − | 0.343384i | \(-0.111573\pi\) |
0.172218 | + | 0.985059i | \(0.444907\pi\) | |||||||
\(12\) | −0.500000 | + | 1.65831i | −0.144338 | + | 0.478714i | ||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | −2.00000 | − | 1.73205i | −0.534522 | − | 0.462910i | ||||
\(15\) | 1.87228 | − | 3.39036i | 0.483421 | − | 0.875388i | ||||
\(16\) | −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 | \(0.463407\pi\) | |||||||
\(20\) | 0.686141 | + | 2.12819i | 0.153426 | + | 0.475879i | ||||
\(21\) | −3.87228 | + | 2.45060i | −0.845001 | + | 0.534765i | ||||
\(22\) | 4.25639i | 0.907465i | ||||||||
\(23\) | 2.18614 | + | 3.78651i | 0.455842 | + | 0.789541i | 0.998736 | − | 0.0502598i | \(-0.0160049\pi\) |
−0.542894 | + | 0.839801i | \(0.682672\pi\) | |||||||
\(24\) | −1.68614 | + | 0.396143i | −0.344182 | + | 0.0808625i | ||||
\(25\) | −0.500000 | − | 4.97494i | −0.100000 | − | 0.994987i | ||||
\(26\) | −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 | \(0.0996399\pi\) | ||||
−0.951405 | + | 0.307941i | \(0.900360\pi\) | |||||||
\(30\) | 3.87228 | − | 0.0737384i | 0.706979 | − | 0.0134627i | ||||
\(31\) | −2.05842 | − | 1.18843i | −0.369704 | − | 0.213448i | 0.303625 | − | 0.952791i | \(-0.401803\pi\) |
−0.673329 | + | 0.739343i | \(0.735136\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 7.05842 | + | 2.12819i | 1.22871 | + | 0.370471i | ||||
\(34\) | − | 6.63325i | − | 1.13759i | ||||||
\(35\) | −2.31386 | + | 5.44482i | −0.391114 | + | 0.920342i | ||||
\(36\) | −0.186141 | + | 2.99422i | −0.0310234 | + | 0.499037i | ||||
\(37\) | −10.1168 | + | 5.84096i | −1.66320 | + | 0.960248i | −0.692026 | + | 0.721873i | \(0.743282\pi\) |
−0.971173 | + | 0.238376i | \(0.923385\pi\) | |||||||
\(38\) | −3.00000 | − | 1.73205i | −0.486664 | − | 0.280976i | ||||
\(39\) | −3.37228 | + | 0.792287i | −0.539997 | + | 0.126867i | ||||
\(40\) | −1.50000 | + | 1.65831i | −0.237171 | + | 0.262202i | ||||
\(41\) | 1.62772 | 0.254207 | 0.127103 | − | 0.991889i | \(-0.459432\pi\) | ||||
0.127103 | + | 0.991889i | \(0.459432\pi\) | |||||||
\(42\) | −4.05842 | − | 2.12819i | −0.626228 | − | 0.328388i | ||||
\(43\) | − | 11.0371i | − | 1.68314i | −0.540145 | − | 0.841572i | \(-0.681631\pi\) | ||
0.540145 | − | 0.841572i | \(-0.318369\pi\) | |||||||
\(44\) | −3.68614 | + | 2.12819i | −0.555707 | + | 0.320837i | ||||
\(45\) | 1.81386 | − | 6.45832i | 0.270394 | − | 0.962750i | ||||
\(46\) | −2.18614 | + | 3.78651i | −0.322329 | + | 0.558290i | ||||
\(47\) | 1.62772 | − | 0.939764i | 0.237427 | − | 0.137079i | −0.376566 | − | 0.926390i | \(-0.622895\pi\) |
0.613994 | + | 0.789311i | \(0.289562\pi\) | |||||||
\(48\) | −1.18614 | − | 1.26217i | −0.171205 | − | 0.182178i | ||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 4.05842 | − | 2.92048i | 0.573948 | − | 0.413018i | ||||
\(51\) | −11.0000 | − | 3.31662i | −1.54031 | − | 0.464420i | ||||
\(52\) | 1.00000 | − | 1.73205i | 0.138675 | − | 0.240192i | ||||
\(53\) | 0.686141 | − | 1.18843i | 0.0942487 | − | 0.163243i | −0.815046 | − | 0.579396i | \(-0.803288\pi\) |
0.909295 | + | 0.416153i | \(0.136622\pi\) | |||||||
\(54\) | 4.87228 | + | 1.80579i | 0.663034 | + | 0.245737i | ||||
\(55\) | 9.05842 | − | 2.92048i | 1.22144 | − | 0.393798i | ||||
\(56\) | 2.50000 | − | 0.866025i | 0.334077 | − | 0.115728i | ||||
\(57\) | −4.37228 | + | 4.10891i | −0.579123 | + | 0.544239i | ||||
\(58\) | −2.87228 | + | 1.65831i | −0.377149 | + | 0.217747i | ||||
\(59\) | 2.05842 | − | 3.56529i | 0.267984 | − | 0.464161i | −0.700357 | − | 0.713792i | \(-0.746976\pi\) |
0.968341 | + | 0.249631i | \(0.0803093\pi\) | |||||||
\(60\) | 2.00000 | + | 3.31662i | 0.258199 | + | 0.428174i | ||||
\(61\) | −2.44158 | + | 1.40965i | −0.312612 | + | 0.180487i | −0.648095 | − | 0.761560i | \(-0.724434\pi\) |
0.335483 | + | 0.942046i | \(0.391101\pi\) | |||||||
\(62\) | − | 2.37686i | − | 0.301862i | ||||||
\(63\) | −5.55842 | + | 5.66603i | −0.700295 | + | 0.713853i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.00000 | + | 3.31662i | −0.372104 | + | 0.411377i | ||||
\(66\) | 1.68614 | + | 7.17687i | 0.207550 | + | 0.883412i | ||||
\(67\) | 6.55842 | + | 3.78651i | 0.801239 | + | 0.462595i | 0.843904 | − | 0.536494i | \(-0.180252\pi\) |
−0.0426654 | + | 0.999089i | \(0.513585\pi\) | |||||||
\(68\) | 5.74456 | − | 3.31662i | 0.696631 | − | 0.402200i | ||||
\(69\) | 5.18614 | + | 5.51856i | 0.624338 | + | 0.664356i | ||||
\(70\) | −5.87228 | + | 0.718549i | −0.701872 | + | 0.0858830i | ||||
\(71\) | − | 1.87953i | − | 0.223059i | −0.993761 | − | 0.111529i | \(-0.964425\pi\) | ||
0.993761 | − | 0.111529i | \(-0.0355749\pi\) | |||||||
\(72\) | −2.68614 | + | 1.33591i | −0.316565 | + | 0.157438i | ||||
\(73\) | 1.00000 | − | 1.73205i | 0.117041 | − | 0.202721i | −0.801553 | − | 0.597924i | \(-0.795992\pi\) |
0.918594 | + | 0.395203i | \(0.129326\pi\) | |||||||
\(74\) | −10.1168 | − | 5.84096i | −1.17606 | − | 0.678998i | ||||
\(75\) | −2.81386 | − | 8.19037i | −0.324916 | − | 0.945743i | ||||
\(76\) | − | 3.46410i | − | 0.397360i | ||||||
\(77\) | −11.0584 | − | 2.12819i | −1.26022 | − | 0.242530i | ||||
\(78\) | −2.37228 | − | 2.52434i | −0.268608 | − | 0.285825i | ||||
\(79\) | 4.05842 | + | 7.02939i | 0.456608 | + | 0.790869i | 0.998779 | − | 0.0493997i | \(-0.0157308\pi\) |
−0.542171 | + | 0.840268i | \(0.682397\pi\) | |||||||
\(80\) | −2.18614 | − | 0.469882i | −0.244418 | − | 0.0525344i | ||||
\(81\) | 5.43070 | − | 7.17687i | 0.603411 | − | 0.797430i | ||||
\(82\) | 0.813859 | + | 1.40965i | 0.0898757 | + | 0.155669i | ||||
\(83\) | 1.43710i | 0.157742i | 0.996885 | + | 0.0788710i | \(0.0251315\pi\) | ||||
−0.996885 | + | 0.0788710i | \(0.974868\pi\) | |||||||
\(84\) | −0.186141 | − | 4.57879i | −0.0203096 | − | 0.499587i | ||||
\(85\) | −14.1168 | + | 4.55134i | −1.53119 | + | 0.493662i | ||||
\(86\) | 9.55842 | − | 5.51856i | 1.03071 | − | 0.595081i | ||||
\(87\) | 1.31386 | + | 5.59230i | 0.140861 | + | 0.599557i | ||||
\(88\) | −3.68614 | − | 2.12819i | −0.392944 | − | 0.226866i | ||||
\(89\) | 2.18614 | + | 3.78651i | 0.231730 | + | 0.401369i | 0.958317 | − | 0.285706i | \(-0.0922279\pi\) |
−0.726587 | + | 0.687074i | \(0.758895\pi\) | |||||||
\(90\) | 6.50000 | − | 1.65831i | 0.685160 | − | 0.174801i | ||||
\(91\) | 5.00000 | − | 1.73205i | 0.524142 | − | 0.181568i | ||||
\(92\) | −4.37228 | −0.455842 | ||||||||
\(93\) | −3.94158 | − | 1.18843i | −0.408723 | − | 0.123235i | ||||
\(94\) | 1.62772 | + | 0.939764i | 0.167886 | + | 0.0969292i | ||||
\(95\) | −1.62772 | + | 7.57301i | −0.167000 | + | 0.776975i | ||||
\(96\) | 0.500000 | − | 1.65831i | 0.0510310 | − | 0.169251i | ||||
\(97\) | 2.11684 | 0.214933 | 0.107466 | − | 0.994209i | \(-0.465726\pi\) | ||||
0.107466 | + | 0.994209i | \(0.465726\pi\) | |||||||
\(98\) | 6.50000 | + | 2.59808i | 0.656599 | + | 0.262445i | ||||
\(99\) | 12.7446 | + | 0.792287i | 1.28088 | + | 0.0796278i | ||||
\(100\) | 4.55842 | + | 2.05446i | 0.455842 | + | 0.205446i | ||||
\(101\) | 8.18614 | − | 14.1788i | 0.814551 | − | 1.41084i | −0.0950981 | − | 0.995468i | \(-0.530316\pi\) |
0.909650 | − | 0.415377i | \(-0.136350\pi\) | |||||||
\(102\) | −2.62772 | − | 11.1846i | −0.260183 | − | 1.10744i | ||||
\(103\) | 7.55842 | + | 13.0916i | 0.744753 | + | 1.28995i | 0.950310 | + | 0.311306i | \(0.100766\pi\) |
−0.205556 | + | 0.978645i | \(0.565900\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | −1.74456 | + | 10.0974i | −0.170252 | + | 0.985401i | ||||
\(106\) | 1.37228 | 0.133288 | ||||||||
\(107\) | 8.87228 | + | 15.3672i | 0.857716 | + | 1.48561i | 0.874102 | + | 0.485742i | \(0.161450\pi\) |
−0.0163866 | + | 0.999866i | \(0.505216\pi\) | |||||||
\(108\) | 0.872281 | + | 5.12241i | 0.0839353 | + | 0.492905i | ||||
\(109\) | −4.55842 | + | 7.89542i | −0.436618 | + | 0.756244i | −0.997426 | − | 0.0717016i | \(-0.977157\pi\) |
0.560808 | + | 0.827946i | \(0.310490\pi\) | |||||||
\(110\) | 7.05842 | + | 6.38458i | 0.672994 | + | 0.608746i | ||||
\(111\) | −14.7446 | + | 13.8564i | −1.39949 | + | 1.31519i | ||||
\(112\) | 2.00000 | + | 1.73205i | 0.188982 | + | 0.163663i | ||||
\(113\) | 3.25544 | 0.306246 | 0.153123 | − | 0.988207i | \(-0.451067\pi\) | ||||
0.153123 | + | 0.988207i | \(0.451067\pi\) | |||||||
\(114\) | −5.74456 | − | 1.73205i | −0.538028 | − | 0.162221i | ||||
\(115\) | 9.55842 | + | 2.05446i | 0.891327 | + | 0.191579i | ||||
\(116\) | −2.87228 | − | 1.65831i | −0.266685 | − | 0.153970i | ||||
\(117\) | −5.37228 | + | 2.67181i | −0.496668 | + | 0.247009i | ||||
\(118\) | 4.11684 | 0.378986 | ||||||||
\(119\) | 17.2337 | + | 3.31662i | 1.57981 | + | 0.304034i | ||||
\(120\) | −1.87228 | + | 3.39036i | −0.170915 | + | 0.309496i | ||||
\(121\) | 3.55842 | + | 6.16337i | 0.323493 | + | 0.560306i | ||||
\(122\) | −2.44158 | − | 1.40965i | −0.221050 | − | 0.127623i | ||||
\(123\) | 2.74456 | − | 0.644810i | 0.247469 | − | 0.0581406i | ||||
\(124\) | 2.05842 | − | 1.18843i | 0.184852 | − | 0.106724i | ||||
\(125\) | −9.00000 | − | 6.63325i | −0.804984 | − | 0.593296i | ||||
\(126\) | −7.68614 | − | 1.98072i | −0.684736 | − | 0.176456i | ||||
\(127\) | − | 2.37686i | − | 0.210912i | −0.994424 | − | 0.105456i | \(-0.966370\pi\) | ||
0.994424 | − | 0.105456i | \(-0.0336303\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −4.37228 | − | 18.6101i | −0.384958 | − | 1.63853i | ||||
\(130\) | −4.37228 | − | 0.939764i | −0.383474 | − | 0.0824227i | ||||
\(131\) | 2.31386 | + | 4.00772i | 0.202163 | + | 0.350156i | 0.949225 | − | 0.314598i | \(-0.101870\pi\) |
−0.747062 | + | 0.664754i | \(0.768536\pi\) | |||||||
\(132\) | −5.37228 | + | 5.04868i | −0.467597 | + | 0.439431i | ||||
\(133\) | 6.00000 | − | 6.92820i | 0.520266 | − | 0.600751i | ||||
\(134\) | 7.57301i | 0.654209i | ||||||||
\(135\) | 0.500000 | − | 11.6082i | 0.0430331 | − | 0.999074i | ||||
\(136\) | 5.74456 | + | 3.31662i | 0.492592 | + | 0.284398i | ||||
\(137\) | 1.37228 | − | 2.37686i | 0.117242 | − | 0.203069i | −0.801432 | − | 0.598086i | \(-0.795928\pi\) |
0.918674 | + | 0.395017i | \(0.129261\pi\) | |||||||
\(138\) | −2.18614 | + | 7.25061i | −0.186097 | + | 0.617213i | ||||
\(139\) | 11.6819i | 0.990848i | 0.868651 | + | 0.495424i | \(0.164987\pi\) | ||||
−0.868651 | + | 0.495424i | \(0.835013\pi\) | |||||||
\(140\) | −3.55842 | − | 4.72627i | −0.300742 | − | 0.399443i | ||||
\(141\) | 2.37228 | − | 2.22938i | 0.199782 | − | 0.187748i | ||||
\(142\) | 1.62772 | − | 0.939764i | 0.136595 | − | 0.0788632i | ||||
\(143\) | −7.37228 | − | 4.25639i | −0.616501 | − | 0.355937i | ||||
\(144\) | −2.50000 | − | 1.65831i | −0.208333 | − | 0.138193i | ||||
\(145\) | 5.50000 | + | 4.97494i | 0.456750 | + | 0.413146i | ||||
\(146\) | 2.00000 | 0.165521 | ||||||||
\(147\) | 7.55842 | − | 9.47999i | 0.623408 | − | 0.781897i | ||||
\(148\) | − | 11.6819i | − | 0.960248i | ||||||
\(149\) | −12.3030 | + | 7.10313i | −1.00790 | + | 0.581911i | −0.910576 | − | 0.413342i | \(-0.864362\pi\) |
−0.0973237 | + | 0.995253i | \(0.531028\pi\) | |||||||
\(150\) | 5.68614 | − | 6.53206i | 0.464271 | − | 0.533340i | ||||
\(151\) | 4.05842 | − | 7.02939i | 0.330270 | − | 0.572044i | −0.652295 | − | 0.757965i | \(-0.726194\pi\) |
0.982565 | + | 0.185921i | \(0.0595270\pi\) | |||||||
\(152\) | 3.00000 | − | 1.73205i | 0.243332 | − | 0.140488i | ||||
\(153\) | −19.8614 | − | 1.23472i | −1.60570 | − | 0.0998210i | ||||
\(154\) | −3.68614 | − | 10.6410i | −0.297038 | − | 0.857474i | ||||
\(155\) | −5.05842 | + | 1.63086i | −0.406302 | + | 0.130994i | ||||
\(156\) | 1.00000 | − | 3.31662i | 0.0800641 | − | 0.265543i | ||||
\(157\) | 4.00000 | − | 6.92820i | 0.319235 | − | 0.552931i | −0.661094 | − | 0.750303i | \(-0.729907\pi\) |
0.980329 | + | 0.197372i | \(0.0632408\pi\) | |||||||
\(158\) | −4.05842 | + | 7.02939i | −0.322871 | + | 0.559228i | ||||
\(159\) | 0.686141 | − | 2.27567i | 0.0544145 | − | 0.180472i | ||||
\(160\) | −0.686141 | − | 2.12819i | −0.0542442 | − | 0.168249i | ||||
\(161\) | −8.74456 | − | 7.57301i | −0.689168 | − | 0.596837i | ||||
\(162\) | 8.93070 | + | 1.11469i | 0.701662 | + | 0.0875785i | ||||
\(163\) | 3.00000 | − | 1.73205i | 0.234978 | − | 0.135665i | −0.377888 | − | 0.925851i | \(-0.623350\pi\) |
0.612866 | + | 0.790186i | \(0.290016\pi\) | |||||||
\(164\) | −0.813859 | + | 1.40965i | −0.0635517 | + | 0.110075i | ||||
\(165\) | 14.1168 | − | 8.51278i | 1.09899 | − | 0.662719i | ||||
\(166\) | −1.24456 | + | 0.718549i | −0.0965968 | + | 0.0557702i | ||||
\(167\) | − | 11.3321i | − | 0.876902i | −0.898755 | − | 0.438451i | \(-0.855527\pi\) | ||
0.898755 | − | 0.438451i | \(-0.144473\pi\) | |||||||
\(168\) | 3.87228 | − | 2.45060i | 0.298753 | − | 0.189068i | ||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −11.0000 | − | 9.94987i | −0.843661 | − | 0.763121i | ||||
\(171\) | −5.74456 | + | 8.66025i | −0.439298 | + | 0.662266i | ||||
\(172\) | 9.55842 | + | 5.51856i | 0.728823 | + | 0.420786i | ||||
\(173\) | −3.25544 | + | 1.87953i | −0.247506 | + | 0.142898i | −0.618622 | − | 0.785689i | \(-0.712309\pi\) |
0.371116 | + | 0.928587i | \(0.378975\pi\) | |||||||
\(174\) | −4.18614 | + | 3.93398i | −0.317351 | + | 0.298235i | ||||
\(175\) | 5.55842 | + | 12.0043i | 0.420177 | + | 0.907442i | ||||
\(176\) | − | 4.25639i | − | 0.320837i | ||||||
\(177\) | 2.05842 | − | 6.82701i | 0.154720 | − | 0.513150i | ||||
\(178\) | −2.18614 | + | 3.78651i | −0.163858 | + | 0.283811i | ||||
\(179\) | −2.48913 | − | 1.43710i | −0.186046 | − | 0.107414i | 0.404084 | − | 0.914722i | \(-0.367590\pi\) |
−0.590130 | + | 0.807308i | \(0.700924\pi\) | |||||||
\(180\) | 4.68614 | + | 4.80001i | 0.349284 | + | 0.357772i | ||||
\(181\) | − | 17.9653i | − | 1.33535i | −0.744452 | − | 0.667676i | \(-0.767289\pi\) | ||
0.744452 | − | 0.667676i | \(-0.232711\pi\) | |||||||
\(182\) | 4.00000 | + | 3.46410i | 0.296500 | + | 0.256776i | ||||
\(183\) | −3.55842 | + | 3.34408i | −0.263046 | + | 0.247201i | ||||
\(184\) | −2.18614 | − | 3.78651i | −0.161164 | − | 0.279145i | ||||
\(185\) | −5.48913 | + | 25.5383i | −0.403569 | + | 1.87762i | ||||
\(186\) | −0.941578 | − | 4.00772i | −0.0690398 | − | 0.293860i | ||||
\(187\) | −14.1168 | − | 24.4511i | −1.03233 | − | 1.78804i | ||||
\(188\) | 1.87953i | 0.137079i | ||||||||
\(189\) | −7.12772 | + | 11.7557i | −0.518465 | + | 0.855099i | ||||
\(190\) | −7.37228 | + | 2.37686i | −0.534842 | + | 0.172436i | ||||
\(191\) | 3.25544 | − | 1.87953i | 0.235555 | − | 0.135998i | −0.377577 | − | 0.925978i | \(-0.623243\pi\) |
0.613132 | + | 0.789980i | \(0.289909\pi\) | |||||||
\(192\) | 1.68614 | − | 0.396143i | 0.121687 | − | 0.0285892i | ||||
\(193\) | 6.94158 | + | 4.00772i | 0.499666 | + | 0.288482i | 0.728575 | − | 0.684966i | \(-0.240183\pi\) |
−0.228910 | + | 0.973448i | \(0.573516\pi\) | |||||||
\(194\) | 1.05842 | + | 1.83324i | 0.0759903 | + | 0.131619i | ||||
\(195\) | −3.74456 | + | 6.78073i | −0.268154 | + | 0.485578i | ||||
\(196\) | 1.00000 | + | 6.92820i | 0.0714286 | + | 0.494872i | ||||
\(197\) | 20.2337 | 1.44159 | 0.720795 | − | 0.693148i | \(-0.243777\pi\) | ||||
0.720795 | + | 0.693148i | \(0.243777\pi\) | |||||||
\(198\) | 5.68614 | + | 11.4333i | 0.404096 | + | 0.812526i | ||||
\(199\) | −16.1168 | − | 9.30506i | −1.14249 | − | 0.659619i | −0.195446 | − | 0.980714i | \(-0.562615\pi\) |
−0.947047 | + | 0.321096i | \(0.895949\pi\) | |||||||
\(200\) | 0.500000 | + | 4.97494i | 0.0353553 | + | 0.351781i | ||||
\(201\) | 12.5584 | + | 3.78651i | 0.885803 | + | 0.267080i | ||||
\(202\) | 16.3723 | 1.15195 | ||||||||
\(203\) | −2.87228 | − | 8.29156i | −0.201595 | − | 0.581954i | ||||
\(204\) | 8.37228 | − | 7.86797i | 0.586177 | − | 0.550868i | ||||
\(205\) | 2.44158 | − | 2.69927i | 0.170527 | − | 0.188525i | ||||
\(206\) | −7.55842 | + | 13.0916i | −0.526620 | + | 0.912133i | ||||
\(207\) | 10.9307 | + | 7.25061i | 0.759736 | + | 0.503952i | ||||
\(208\) | 1.00000 | + | 1.73205i | 0.0693375 | + | 0.120096i | ||||
\(209\) | −14.7446 | −1.01990 | ||||||||
\(210\) | −9.61684 | + | 3.53784i | −0.663625 | + | 0.244134i | ||||
\(211\) | −18.2337 | −1.25526 | −0.627629 | − | 0.778512i | \(-0.715975\pi\) | ||||
−0.627629 | + | 0.778512i | \(0.715975\pi\) | |||||||
\(212\) | 0.686141 | + | 1.18843i | 0.0471243 | + | 0.0816217i | ||||
\(213\) | −0.744563 | − | 3.16915i | −0.0510166 | − | 0.217146i | ||||
\(214\) | −8.87228 | + | 15.3672i | −0.606497 | + | 1.05048i | ||||
\(215\) | −18.3030 | − | 16.5557i | −1.24825 | − | 1.12909i | ||||
\(216\) | −4.00000 | + | 3.31662i | −0.272166 | + | 0.225668i | ||||
\(217\) | 6.17527 | + | 1.18843i | 0.419204 | + | 0.0806759i | ||||
\(218\) | −9.11684 | −0.617471 | ||||||||
\(219\) | 1.00000 | − | 3.31662i | 0.0675737 | − | 0.224117i | ||||
\(220\) | −2.00000 | + | 9.30506i | −0.134840 | + | 0.627347i | ||||
\(221\) | 11.4891 | + | 6.63325i | 0.772842 | + | 0.446201i | ||||
\(222\) | −19.3723 | − | 5.84096i | −1.30018 | − | 0.392020i | ||||
\(223\) | −18.1168 | −1.21319 | −0.606597 | − | 0.795010i | \(-0.707466\pi\) | ||||
−0.606597 | + | 0.795010i | \(0.707466\pi\) | |||||||
\(224\) | −0.500000 | + | 2.59808i | −0.0334077 | + | 0.173591i | ||||
\(225\) | −7.98913 | − | 12.6954i | −0.532608 | − | 0.846362i | ||||
\(226\) | 1.62772 | + | 2.81929i | 0.108274 | + | 0.187536i | ||||
\(227\) | 13.5475 | + | 7.82168i | 0.899182 | + | 0.519143i | 0.876935 | − | 0.480609i | \(-0.159584\pi\) |
0.0222475 | + | 0.999752i | \(0.492918\pi\) | |||||||
\(228\) | −1.37228 | − | 5.84096i | −0.0908816 | − | 0.386827i | ||||
\(229\) | 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 | + | 9.30506i | 0.197814 | + | 0.613558i | ||||
\(231\) | −19.4891 | + | 0.792287i | −1.28229 | + | 0.0521287i | ||||
\(232\) | − | 3.31662i | − | 0.217747i | ||||||
\(233\) | −11.7446 | − | 20.3422i | −0.769412 | − | 1.33266i | −0.937882 | − | 0.346954i | \(-0.887216\pi\) |
0.168470 | − | 0.985707i | \(-0.446117\pi\) | |||||||
\(234\) | −5.00000 | − | 3.31662i | −0.326860 | − | 0.216815i | ||||
\(235\) | 0.883156 | − | 4.10891i | 0.0576107 | − | 0.268036i | ||||
\(236\) | 2.05842 | + | 3.56529i | 0.133992 | + | 0.232081i | ||||
\(237\) | 9.62772 | + | 10.2448i | 0.625388 | + | 0.665473i | ||||
\(238\) | 5.74456 | + | 16.5831i | 0.372365 | + | 1.07492i | ||||
\(239\) | 2.87419i | 0.185916i | 0.995670 | + | 0.0929581i | \(0.0296323\pi\) | ||||
−0.995670 | + | 0.0929581i | \(0.970368\pi\) | |||||||
\(240\) | −3.87228 | + | 0.0737384i | −0.249955 | + | 0.00475979i | ||||
\(241\) | 9.17527 | + | 5.29734i | 0.591031 | + | 0.341232i | 0.765505 | − | 0.643430i | \(-0.222489\pi\) |
−0.174474 | + | 0.984662i | \(0.555823\pi\) | |||||||
\(242\) | −3.55842 | + | 6.16337i | −0.228744 | + | 0.396196i | ||||
\(243\) | 6.31386 | − | 14.2525i | 0.405034 | − | 0.914302i | ||||
\(244\) | − | 2.81929i | − | 0.180487i | ||||||
\(245\) | 1.06930 | − | 15.6159i | 0.0683149 | − | 0.997664i | ||||
\(246\) | 1.93070 | + | 2.05446i | 0.123097 | + | 0.130987i | ||||
\(247\) | 6.00000 | − | 3.46410i | 0.381771 | − | 0.220416i | ||||
\(248\) | 2.05842 | + | 1.18843i | 0.130710 | + | 0.0754654i | ||||
\(249\) | 0.569297 | + | 2.42315i | 0.0360777 | + | 0.153561i | ||||
\(250\) | 1.24456 | − | 11.1109i | 0.0787131 | − | 0.702712i | ||||
\(251\) | 16.1168 | 1.01729 | 0.508643 | − | 0.860977i | \(-0.330147\pi\) | ||||
0.508643 | + | 0.860977i | \(0.330147\pi\) | |||||||
\(252\) | −2.12772 | − | 7.64675i | −0.134034 | − | 0.481700i | ||||
\(253\) | 18.6101i | 1.17001i | ||||||||
\(254\) | 2.05842 | − | 1.18843i | 0.129157 | − | 0.0745688i | ||||
\(255\) | −22.0000 | + | 13.2665i | −1.37769 | + | 0.830780i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −7.37228 | + | 4.25639i | −0.459870 | + | 0.265506i | −0.711990 | − | 0.702190i | \(-0.752206\pi\) |
0.252119 | + | 0.967696i | \(0.418872\pi\) | |||||||
\(258\) | 13.9307 | − | 13.0916i | 0.867288 | − | 0.815046i | ||||
\(259\) | 20.2337 | − | 23.3639i | 1.25726 | − | 1.45176i | ||||
\(260\) | −1.37228 | − | 4.25639i | −0.0851053 | − | 0.263970i | ||||
\(261\) | 4.43070 | + | 8.90892i | 0.274254 | + | 0.551448i | ||||
\(262\) | −2.31386 | + | 4.00772i | −0.142951 | + | 0.247598i | ||||
\(263\) | 0.813859 | − | 1.40965i | 0.0501847 | − | 0.0869225i | −0.839842 | − | 0.542831i | \(-0.817352\pi\) |
0.890027 | + | 0.455909i | \(0.150686\pi\) | |||||||
\(264\) | −7.05842 | − | 2.12819i | −0.434416 | − | 0.130981i | ||||
\(265\) | −0.941578 | − | 2.92048i | −0.0578407 | − | 0.179404i | ||||
\(266\) | 9.00000 | + | 1.73205i | 0.551825 | + | 0.106199i | ||||
\(267\) | 5.18614 | + | 5.51856i | 0.317387 | + | 0.337730i | ||||
\(268\) | −6.55842 | + | 3.78651i | −0.400619 | + | 0.231298i | ||||
\(269\) | 9.98913 | − | 17.3017i | 0.609048 | − | 1.05490i | −0.382350 | − | 0.924018i | \(-0.624885\pi\) |
0.991398 | − | 0.130884i | \(-0.0417815\pi\) | |||||||
\(270\) | 10.3030 | − | 5.37108i | 0.627020 | − | 0.326874i | ||||
\(271\) | −18.1753 | + | 10.4935i | −1.10407 | + | 0.637434i | −0.937287 | − | 0.348559i | \(-0.886671\pi\) |
−0.166782 | + | 0.985994i | \(0.553338\pi\) | |||||||
\(272\) | 6.63325i | 0.402200i | ||||||||
\(273\) | 7.74456 | − | 4.90120i | 0.468722 | − | 0.296634i | ||||
\(274\) | 2.74456 | 0.165805 | ||||||||
\(275\) | 8.74456 | − | 19.4024i | 0.527317 | − | 1.17001i | ||||
\(276\) | −7.37228 | + | 1.73205i | −0.443759 | + | 0.104257i | ||||
\(277\) | −25.1168 | − | 14.5012i | −1.50912 | − | 0.871294i | −0.999943 | − | 0.0106345i | \(-0.996615\pi\) |
−0.509181 | − | 0.860659i | \(-0.670052\pi\) | |||||||
\(278\) | −10.1168 | + | 5.84096i | −0.606768 | + | 0.350318i | ||||
\(279\) | −7.11684 | − | 0.442430i | −0.426074 | − | 0.0264876i | ||||
\(280\) | 2.31386 | − | 5.44482i | 0.138280 | − | 0.325390i | ||||
\(281\) | − | 21.7793i | − | 1.29924i | −0.760258 | − | 0.649621i | \(-0.774927\pi\) | ||
0.760258 | − | 0.649621i | \(-0.225073\pi\) | |||||||
\(282\) | 3.11684 | + | 0.939764i | 0.185605 | + | 0.0559621i | ||||
\(283\) | −8.00000 | + | 13.8564i | −0.475551 | + | 0.823678i | −0.999608 | − | 0.0280052i | \(-0.991084\pi\) |
0.524057 | + | 0.851683i | \(0.324418\pi\) | |||||||
\(284\) | 1.62772 | + | 0.939764i | 0.0965873 | + | 0.0557647i | ||||
\(285\) | 0.255437 | + | 13.4140i | 0.0151308 | + | 0.794575i | ||||
\(286\) | − | 8.51278i | − | 0.503371i | ||||||
\(287\) | −4.06930 | + | 1.40965i | −0.240203 | + | 0.0832088i | ||||
\(288\) | 0.186141 | − | 2.99422i | 0.0109684 | − | 0.176436i | ||||
\(289\) | 13.5000 | + | 23.3827i | 0.794118 | + | 1.37545i | ||||
\(290\) | −1.55842 | + | 7.25061i | −0.0915137 | + | 0.425770i | ||||
\(291\) | 3.56930 | − | 0.838574i | 0.209236 | − | 0.0491581i | ||||
\(292\) | 1.00000 | + | 1.73205i | 0.0585206 | + | 0.101361i | ||||
\(293\) | 25.0410i | 1.46291i | 0.681889 | + | 0.731455i | \(0.261159\pi\) | ||||
−0.681889 | + | 0.731455i | \(0.738841\pi\) | |||||||
\(294\) | 11.9891 | + | 1.80579i | 0.699220 | + | 0.105316i | ||||
\(295\) | −2.82473 | − | 8.76144i | −0.164462 | − | 0.510111i | ||||
\(296\) | 10.1168 | − | 5.84096i | 0.588030 | − | 0.339499i | ||||
\(297\) | 21.8030 | − | 3.71277i | 1.26514 | − | 0.215437i | ||||
\(298\) | −12.3030 | − | 7.10313i | −0.712693 | − | 0.411473i | ||||
\(299\) | −4.37228 | − | 7.57301i | −0.252856 | − | 0.437959i | ||||
\(300\) | 8.50000 | + | 1.65831i | 0.490748 | + | 0.0957427i | ||||
\(301\) | 9.55842 | + | 27.5928i | 0.550938 | + | 1.59042i | ||||
\(302\) | 8.11684 | 0.467072 | ||||||||
\(303\) | 8.18614 | − | 27.1504i | 0.470281 | − | 1.55975i | ||||
\(304\) | 3.00000 | + | 1.73205i | 0.172062 | + | 0.0993399i | ||||
\(305\) | −1.32473 | + | 6.16337i | −0.0758541 | + | 0.352913i | ||||
\(306\) | −8.86141 | − | 17.8178i | −0.506573 | − | 1.01858i | ||||
\(307\) | −6.88316 | −0.392842 | −0.196421 | − | 0.980520i | \(-0.562932\pi\) | ||||
−0.196421 | + | 0.980520i | \(0.562932\pi\) | |||||||
\(308\) | 7.37228 | − | 8.51278i | 0.420075 | − | 0.485060i | ||||
\(309\) | 17.9307 | + | 19.0800i | 1.02004 | + | 1.08542i | ||||
\(310\) | −3.94158 | − | 3.56529i | −0.223867 | − | 0.202495i | ||||
\(311\) | −7.11684 | + | 12.3267i | −0.403559 | + | 0.698985i | −0.994153 | − | 0.107984i | \(-0.965560\pi\) |
0.590593 | + | 0.806969i | \(0.298894\pi\) | |||||||
\(312\) | 3.37228 | − | 0.792287i | 0.190918 | − | 0.0448544i | ||||
\(313\) | −7.05842 | − | 12.2255i | −0.398966 | − | 0.691029i | 0.594633 | − | 0.803997i | \(-0.297297\pi\) |
−0.993599 | + | 0.112969i | \(0.963964\pi\) | |||||||
\(314\) | 8.00000 | 0.451466 | ||||||||
\(315\) | 1.05842 | + | 17.7167i | 0.0596353 | + | 0.998220i | ||||
\(316\) | −8.11684 | −0.456608 | ||||||||
\(317\) | 8.05842 | + | 13.9576i | 0.452606 | + | 0.783937i | 0.998547 | − | 0.0538869i | \(-0.0171611\pi\) |
−0.545941 | + | 0.837824i | \(0.683828\pi\) | |||||||
\(318\) | 2.31386 | − | 0.543620i | 0.129755 | − | 0.0304847i | ||||
\(319\) | −7.05842 | + | 12.2255i | −0.395196 | + | 0.684499i | ||||
\(320\) | 1.50000 | − | 1.65831i | 0.0838525 | − | 0.0927025i | ||||
\(321\) | 21.0475 | + | 22.3966i | 1.17476 | + | 1.25006i | ||||
\(322\) | 2.18614 | − | 11.3595i | 0.121829 | − | 0.633041i | ||||
\(323\) | 22.9783 | 1.27854 | ||||||||
\(324\) | 3.50000 | + | 8.29156i | 0.194444 | + | 0.460642i | ||||
\(325\) | 1.00000 | + | 9.94987i | 0.0554700 | + | 0.551920i | ||||
\(326\) | 3.00000 | + | 1.73205i | 0.166155 | + | 0.0959294i | ||||
\(327\) | −4.55842 | + | 15.1186i | −0.252081 | + | 0.836059i | ||||
\(328\) | −1.62772 | −0.0898757 | ||||||||
\(329\) | −3.25544 | + | 3.75906i | −0.179478 | + | 0.207243i | ||||
\(330\) | 14.4307 | + | 7.96916i | 0.794384 | + | 0.438688i | ||||
\(331\) | −5.11684 | − | 8.86263i | −0.281247 | − | 0.487134i | 0.690445 | − | 0.723385i | \(-0.257415\pi\) |
−0.971692 | + | 0.236250i | \(0.924081\pi\) | |||||||
\(332\) | −1.24456 | − | 0.718549i | −0.0683042 | − | 0.0394355i | ||||
\(333\) | −19.3723 | + | 29.2048i | −1.06159 | + | 1.60041i | ||||
\(334\) | 9.81386 | − | 5.66603i | 0.536990 | − | 0.310032i | ||||
\(335\) | 16.1168 | − | 5.19615i | 0.880557 | − | 0.283896i | ||||
\(336\) | 4.05842 | + | 2.12819i | 0.221405 | + | 0.116103i | ||||
\(337\) | − | 9.30506i | − | 0.506879i | −0.967351 | − | 0.253440i | \(-0.918438\pi\) | ||
0.967351 | − | 0.253440i | \(-0.0815619\pi\) | |||||||
\(338\) | −4.50000 | − | 7.79423i | −0.244768 | − | 0.423950i | ||||
\(339\) | 5.48913 | − | 1.28962i | 0.298128 | − | 0.0700426i | ||||
\(340\) | 3.11684 | − | 14.5012i | 0.169035 | − | 0.786439i | ||||
\(341\) | −5.05842 | − | 8.76144i | −0.273929 | − | 0.474459i | ||||
\(342\) | −10.3723 | − | 0.644810i | −0.560869 | − | 0.0348673i | ||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 11.0371i | 0.595081i | ||||||||
\(345\) | 16.9307 | − | 0.322405i | 0.911518 | − | 0.0173577i | ||||
\(346\) | −3.25544 | − | 1.87953i | −0.175013 | − | 0.101044i | ||||
\(347\) | 9.55842 | − | 16.5557i | 0.513123 | − | 0.888755i | −0.486761 | − | 0.873535i | \(-0.661822\pi\) |
0.999884 | − | 0.0152200i | \(-0.00484486\pi\) | |||||||
\(348\) | −5.50000 | − | 1.65831i | −0.294831 | − | 0.0888949i | ||||
\(349\) | − | 24.0087i | − | 1.28515i | −0.766221 | − | 0.642577i | \(-0.777865\pi\) | ||
0.766221 | − | 0.642577i | \(-0.222135\pi\) | |||||||
\(350\) | −7.61684 | + | 10.8159i | −0.407137 | + | 0.578134i | ||||
\(351\) | −8.00000 | + | 6.63325i | −0.427008 | + | 0.354057i | ||||
\(352\) | 3.68614 | − | 2.12819i | 0.196472 | − | 0.113433i | ||||
\(353\) | 16.3723 | + | 9.45254i | 0.871409 | + | 0.503108i | 0.867816 | − | 0.496886i | \(-0.165523\pi\) |
0.00359253 | + | 0.999994i | \(0.498856\pi\) | |||||||
\(354\) | 6.94158 | − | 1.63086i | 0.368941 | − | 0.0866793i | ||||
\(355\) | −3.11684 | − | 2.81929i | −0.165425 | − | 0.149632i | ||||
\(356\) | −4.37228 | −0.231730 | ||||||||
\(357\) | 30.3723 | − | 1.23472i | 1.60747 | − | 0.0653482i | ||||
\(358\) | − | 2.87419i | − | 0.151906i | ||||||
\(359\) | 12.2554 | − | 7.07568i | 0.646817 | − | 0.373440i | −0.140419 | − | 0.990092i | \(-0.544845\pi\) |
0.787236 | + | 0.616652i | \(0.211511\pi\) | |||||||
\(360\) | −1.81386 | + | 6.45832i | −0.0955988 | + | 0.340383i | ||||
\(361\) | −3.50000 | + | 6.06218i | −0.184211 | + | 0.319062i | ||||
\(362\) | 15.5584 | − | 8.98266i | 0.817733 | − | 0.472118i | ||||
\(363\) | 8.44158 | + | 8.98266i | 0.443068 | + | 0.471467i | ||||
\(364\) | −1.00000 | + | 5.19615i | −0.0524142 | + | 0.272352i | ||||
\(365\) | −1.37228 | − | 4.25639i | −0.0718285 | − | 0.222790i | ||||
\(366\) | −4.67527 | − | 1.40965i | −0.244380 | − | 0.0736834i | ||||
\(367\) | −10.6168 | + | 18.3889i | −0.554195 | + | 0.959893i | 0.443771 | + | 0.896140i | \(0.353640\pi\) |
−0.997966 | + | 0.0637532i | \(0.979693\pi\) | |||||||
\(368\) | 2.18614 | − | 3.78651i | 0.113960 | − | 0.197385i | ||||
\(369\) | 4.37228 | − | 2.17448i | 0.227612 | − | 0.113199i | ||||
\(370\) | −24.8614 | + | 8.01544i | −1.29248 | + | 0.416703i | ||||
\(371\) | −0.686141 | + | 3.56529i | −0.0356226 | + | 0.185101i | ||||
\(372\) | 3.00000 | − | 2.81929i | 0.155543 | − | 0.146173i | ||||
\(373\) | 14.2337 | − | 8.21782i | 0.736992 | − | 0.425503i | −0.0839823 | − | 0.996467i | \(-0.526764\pi\) |
0.820975 | + | 0.570964i | \(0.193431\pi\) | |||||||
\(374\) | 14.1168 | − | 24.4511i | 0.729965 | − | 1.26434i | ||||
\(375\) | −17.8030 | − | 7.61930i | −0.919342 | − | 0.393459i | ||||
\(376\) | −1.62772 | + | 0.939764i | −0.0839432 | + | 0.0484646i | ||||
\(377\) | − | 6.63325i | − | 0.341630i | ||||||
\(378\) | −13.7446 | − | 0.294954i | −0.706944 | − | 0.0151708i | ||||
\(379\) | 22.2337 | 1.14207 | 0.571034 | − | 0.820926i | \(-0.306542\pi\) | ||||
0.571034 | + | 0.820926i | \(0.306542\pi\) | |||||||
\(380\) | −5.74456 | − | 5.19615i | −0.294690 | − | 0.266557i | ||||
\(381\) | −0.941578 | − | 4.00772i | −0.0482385 | − | 0.205322i | ||||
\(382\) | 3.25544 | + | 1.87953i | 0.166563 | + | 0.0961650i | ||||
\(383\) | −18.0475 | + | 10.4198i | −0.922187 | + | 0.532425i | −0.884332 | − | 0.466859i | \(-0.845386\pi\) |
−0.0378546 | + | 0.999283i | \(0.512052\pi\) | |||||||
\(384\) | 1.18614 | + | 1.26217i | 0.0605300 | + | 0.0644098i | ||||
\(385\) | −20.1168 | + | 15.1460i | −1.02525 | + | 0.771913i | ||||
\(386\) | 8.01544i | 0.407975i | ||||||||
\(387\) | −14.7446 | − | 29.6472i | −0.749508 | − | 1.50705i | ||||
\(388\) | −1.05842 | + | 1.83324i | −0.0537332 | + | 0.0930687i | ||||
\(389\) | −29.4891 | − | 17.0256i | −1.49516 | − | 0.863230i | −0.495173 | − | 0.868794i | \(-0.664896\pi\) |
−0.999985 | + | 0.00556424i | \(0.998229\pi\) | |||||||
\(390\) | −7.74456 | + | 0.147477i | −0.392161 | + | 0.00746778i | ||||
\(391\) | − | 29.0024i | − | 1.46672i | ||||||
\(392\) | −5.50000 | + | 4.33013i | −0.277792 | + | 0.218704i | ||||
\(393\) | 5.48913 | + | 5.84096i | 0.276890 | + | 0.294638i | ||||
\(394\) | 10.1168 | + | 17.5229i | 0.509679 | + | 0.882790i | ||||
\(395\) | 17.7446 | + | 3.81396i | 0.892826 | + | 0.191901i | ||||
\(396\) | −7.05842 | + | 10.6410i | −0.354699 | + | 0.534729i | ||||
\(397\) | 4.00000 | + | 6.92820i | 0.200754 | + | 0.347717i | 0.948772 | − | 0.315963i | \(-0.102327\pi\) |
−0.748017 | + | 0.663679i | \(0.768994\pi\) | |||||||
\(398\) | − | 18.6101i | − | 0.932841i | ||||||
\(399\) | 7.37228 | − | 14.0588i | 0.369076 | − | 0.703820i | ||||
\(400\) | −4.05842 | + | 2.92048i | −0.202921 | + | 0.146024i | ||||
\(401\) | −17.1861 | + | 9.92242i | −0.858235 | + | 0.495502i | −0.863421 | − | 0.504484i | \(-0.831683\pi\) |
0.00518590 | + | 0.999987i | \(0.498349\pi\) | |||||||
\(402\) | 3.00000 | + | 12.7692i | 0.149626 | + | 0.636868i | ||||
\(403\) | 4.11684 | + | 2.37686i | 0.205075 | + | 0.118400i | ||||
\(404\) | 8.18614 | + | 14.1788i | 0.407276 | + | 0.705422i | ||||
\(405\) | −3.75544 | − | 19.7711i | −0.186609 | − | 0.982434i | ||||
\(406\) | 5.74456 | − | 6.63325i | 0.285098 | − | 0.329203i | ||||
\(407\) | −49.7228 | −2.46467 | ||||||||
\(408\) | 11.0000 | + | 3.31662i | 0.544581 | + | 0.164197i | ||||
\(409\) | −30.7337 | − | 17.7441i | −1.51968 | − | 0.877389i | −0.999731 | − | 0.0231940i | \(-0.992616\pi\) |
−0.519952 | − | 0.854195i | \(-0.674050\pi\) | |||||||
\(410\) | 3.55842 | + | 0.764836i | 0.175738 | + | 0.0377725i | ||||
\(411\) | 1.37228 | − | 4.55134i | 0.0676896 | − | 0.224501i | ||||
\(412\) | −15.1168 | −0.744753 | ||||||||
\(413\) | −2.05842 | + | 10.6959i | −0.101288 | + | 0.526310i | ||||
\(414\) | −0.813859 | + | 13.0916i | −0.0399990 | + | 0.643416i | ||||
\(415\) | 2.38316 | + | 2.15565i | 0.116985 | + | 0.105816i | ||||
\(416\) | −1.00000 | + | 1.73205i | −0.0490290 | + | 0.0849208i | ||||
\(417\) | 4.62772 | + | 19.6974i | 0.226620 | + | 0.964584i | ||||
\(418\) | −7.37228 | − | 12.7692i | −0.360590 | − | 0.624560i | ||||
\(419\) | −29.4891 | −1.44064 | −0.720319 | − | 0.693643i | \(-0.756005\pi\) | ||||
−0.720319 | + | 0.693643i | \(0.756005\pi\) | |||||||
\(420\) | −7.87228 | − | 6.55951i | −0.384128 | − | 0.320071i | ||||
\(421\) | 15.1168 | 0.736750 | 0.368375 | − | 0.929677i | \(-0.379914\pi\) | ||||
0.368375 | + | 0.929677i | \(0.379914\pi\) | |||||||
\(422\) | −9.11684 | − | 15.7908i | −0.443801 | − | 0.768686i | ||||
\(423\) | 3.11684 | − | 4.69882i | 0.151546 | − | 0.228464i | ||||
\(424\) | −0.686141 | + | 1.18843i | −0.0333219 | + | 0.0577153i | ||||
\(425\) | −13.6277 | + | 30.2372i | −0.661041 | + | 1.46672i | ||||
\(426\) | 2.37228 | − | 2.22938i | 0.114937 | − | 0.108014i | ||||
\(427\) | 4.88316 | − | 5.63858i | 0.236312 | − | 0.272870i | ||||
\(428\) | −17.7446 | −0.857716 | ||||||||
\(429\) | −14.1168 | − | 4.25639i | −0.681568 | − | 0.205500i | ||||
\(430\) | 5.18614 | − | 24.1287i | 0.250098 | − | 1.16359i | ||||
\(431\) | −3.25544 | − | 1.87953i | −0.156809 | − | 0.0905337i | 0.419542 | − | 0.907736i | \(-0.362191\pi\) |
−0.576351 | + | 0.817202i | \(0.695524\pi\) | |||||||
\(432\) | −4.87228 | − | 1.80579i | −0.234418 | − | 0.0868811i | ||||
\(433\) | 34.0000 | 1.63394 | 0.816968 | − | 0.576683i | \(-0.195653\pi\) | ||||
0.816968 | + | 0.576683i | \(0.195653\pi\) | |||||||
\(434\) | 2.05842 | + | 5.94215i | 0.0988074 | + | 0.285232i | ||||
\(435\) | 11.2446 | + | 6.20965i | 0.539136 | + | 0.297730i | ||||
\(436\) | −4.55842 | − | 7.89542i | −0.218309 | − | 0.378122i | ||||
\(437\) | −13.1168 | − | 7.57301i | −0.627464 | − | 0.362266i | ||||
\(438\) | 3.37228 | − | 0.792287i | 0.161134 | − | 0.0378569i | ||||
\(439\) | −11.0584 | + | 6.38458i | −0.527790 | + | 0.304720i | −0.740116 | − | 0.672479i | \(-0.765229\pi\) |
0.212326 | + | 0.977199i | \(0.431896\pi\) | |||||||
\(440\) | −9.05842 | + | 2.92048i | −0.431843 | + | 0.139228i | ||||
\(441\) | 8.98913 | − | 18.9788i | 0.428054 | − | 0.903753i | ||||
\(442\) | 13.2665i | 0.631023i | ||||||||
\(443\) | 4.50000 | + | 7.79423i | 0.213801 | + | 0.370315i | 0.952901 | − | 0.303281i | \(-0.0980821\pi\) |
−0.739100 | + | 0.673596i | \(0.764749\pi\) | |||||||
\(444\) | −4.62772 | − | 19.6974i | −0.219622 | − | 0.934796i | ||||
\(445\) | 9.55842 | + | 2.05446i | 0.453113 | + | 0.0973905i | ||||
\(446\) | −9.05842 | − | 15.6896i | −0.428929 | − | 0.742926i | ||||
\(447\) | −17.9307 | + | 16.8506i | −0.848093 | + | 0.797007i | ||||
\(448\) | −2.50000 | + | 0.866025i | −0.118114 | + | 0.0409159i | ||||
\(449\) | 35.9855i | 1.69826i | 0.528182 | + | 0.849131i | \(0.322874\pi\) | ||||
−0.528182 | + | 0.849131i | \(0.677126\pi\) | |||||||
\(450\) | 7.00000 | − | 13.2665i | 0.329983 | − | 0.625389i | ||||
\(451\) | 6.00000 | + | 3.46410i | 0.282529 | + | 0.163118i | ||||
\(452\) | −1.62772 | + | 2.81929i | −0.0765614 | + | 0.132608i | ||||
\(453\) | 4.05842 | − | 13.4603i | 0.190681 | − | 0.632418i | ||||
\(454\) | 15.6434i | 0.734179i | ||||||||
\(455\) | 4.62772 | − | 10.8896i | 0.216951 | − | 0.510514i | ||||
\(456\) | 4.37228 | − | 4.10891i | 0.204751 | − | 0.192417i | ||||
\(457\) | −11.0584 | + | 6.38458i | −0.517291 | + | 0.298658i | −0.735826 | − | 0.677171i | \(-0.763206\pi\) |
0.218534 | + | 0.975829i | \(0.429872\pi\) | |||||||
\(458\) | 12.0000 | + | 6.92820i | 0.560723 | + | 0.323734i | ||||
\(459\) | −33.9783 | + | 5.78606i | −1.58597 | + | 0.270070i | ||||
\(460\) | −6.55842 | + | 7.25061i | −0.305788 | + | 0.338061i | ||||
\(461\) | −0.510875 | −0.0237938 | −0.0118969 | − | 0.999929i | \(-0.503787\pi\) | ||||
−0.0118969 | + | 0.999929i | \(0.503787\pi\) | |||||||
\(462\) | −10.4307 | − | 16.4819i | −0.485280 | − | 0.766809i | ||||
\(463\) | 36.5754i | 1.69981i | 0.526940 | + | 0.849903i | \(0.323339\pi\) | ||||
−0.526940 | + | 0.849903i | \(0.676661\pi\) | |||||||
\(464\) | 2.87228 | − | 1.65831i | 0.133342 | − | 0.0769852i | ||||
\(465\) | −7.88316 | + | 4.75372i | −0.365573 | + | 0.220449i | ||||
\(466\) | 11.7446 | − | 20.3422i | 0.544056 | − | 0.942333i | ||||
\(467\) | −0.0475473 | + | 0.0274514i | −0.00220023 | + | 0.00127030i | −0.501100 | − | 0.865390i | \(-0.667071\pi\) |
0.498899 | + | 0.866660i | \(0.333738\pi\) | |||||||
\(468\) | 0.372281 | − | 5.98844i | 0.0172087 | − | 0.276816i | ||||
\(469\) | −19.6753 | − | 3.78651i | −0.908519 | − | 0.174845i | ||||
\(470\) | 4.00000 | − | 1.28962i | 0.184506 | − | 0.0594858i | ||||
\(471\) | 4.00000 | − | 13.2665i | 0.184310 | − | 0.611288i | ||||
\(472\) | −2.05842 | + | 3.56529i | −0.0947466 | + | 0.164106i | ||||
\(473\) | 23.4891 | − | 40.6844i | 1.08003 | − | 1.87067i | ||||
\(474\) | −4.05842 | + | 13.4603i | −0.186409 | + | 0.618250i | ||||
\(475\) | 10.1168 | + | 14.0588i | 0.464193 | + | 0.645061i | ||||
\(476\) | −11.4891 | + | 13.2665i | −0.526603 | + | 0.608069i | ||||
\(477\) | 0.255437 | − | 4.10891i | 0.0116957 | − | 0.188134i | ||||
\(478\) | −2.48913 | + | 1.43710i | −0.113850 | + | 0.0657313i | ||||
\(479\) | −4.37228 | + | 7.57301i | −0.199775 | + | 0.346020i | −0.948455 | − | 0.316911i | \(-0.897354\pi\) |
0.748681 | + | 0.662931i | \(0.230688\pi\) | |||||||
\(480\) | −2.00000 | − | 3.31662i | −0.0912871 | − | 0.151383i | ||||
\(481\) | 20.2337 | − | 11.6819i | 0.922577 | − | 0.532650i | ||||
\(482\) | 10.5947i | 0.482575i | ||||||||
\(483\) | −17.7446 | − | 9.30506i | −0.807406 | − | 0.423395i | ||||
\(484\) | −7.11684 | −0.323493 | ||||||||
\(485\) | 3.17527 | − | 3.51039i | 0.144181 | − | 0.159399i | ||||
\(486\) | 15.5000 | − | 1.65831i | 0.703094 | − | 0.0752226i | ||||
\(487\) | −3.94158 | − | 2.27567i | −0.178610 | − | 0.103121i | 0.408029 | − | 0.912969i | \(-0.366216\pi\) |
−0.586639 | + | 0.809848i | \(0.699549\pi\) | |||||||
\(488\) | 2.44158 | − | 1.40965i | 0.110525 | − | 0.0638117i | ||||
\(489\) | 4.37228 | − | 4.10891i | 0.197721 | − | 0.185811i | ||||
\(490\) | 14.0584 | − | 6.88192i | 0.635095 | − | 0.310893i | ||||
\(491\) | 26.9205i | 1.21491i | 0.794355 | + | 0.607453i | \(0.207809\pi\) | ||||
−0.794355 | + | 0.607453i | \(0.792191\pi\) | |||||||
\(492\) | −0.813859 | + | 2.69927i | −0.0366916 | + | 0.121692i | ||||
\(493\) | 11.0000 | − | 19.0526i | 0.495415 | − | 0.858084i | ||||
\(494\) | 6.00000 | + | 3.46410i | 0.269953 | + | 0.155857i | ||||
\(495\) | 20.4307 | − | 19.9460i | 0.918292 | − | 0.896508i | ||||
\(496\) | 2.37686i | 0.106724i | ||||||||
\(497\) | 1.62772 | + | 4.69882i | 0.0730132 | + | 0.210771i | ||||
\(498\) | −1.81386 | + | 1.70460i | −0.0812810 | + | 0.0763849i | ||||
\(499\) | −14.1168 | − | 24.4511i | −0.631957 | − | 1.09458i | −0.987151 | − | 0.159789i | \(-0.948919\pi\) |
0.355195 | − | 0.934792i | \(-0.384415\pi\) | |||||||
\(500\) | 10.2446 | − | 4.47760i | 0.458151 | − | 0.200245i | ||||
\(501\) | −4.48913 | − | 19.1075i | −0.200559 | − | 0.853658i | ||||
\(502\) | 8.05842 | + | 13.9576i | 0.359665 | + | 0.622958i | ||||
\(503\) | 9.45254i | 0.421468i | 0.977543 | + | 0.210734i | \(0.0675854\pi\) | ||||
−0.977543 | + | 0.210734i | \(0.932415\pi\) | |||||||
\(504\) | 5.55842 | − | 5.66603i | 0.247592 | − | 0.252385i | ||||
\(505\) | −11.2337 | − | 34.8434i | −0.499893 | − | 1.55051i | ||||
\(506\) | −16.1168 | + | 9.30506i | −0.716481 | + | 0.413661i | ||||
\(507\) | −15.1753 | + | 3.56529i | −0.673957 | + | 0.158340i | ||||
\(508\) | 2.05842 | + | 1.18843i | 0.0913277 | + | 0.0527281i | ||||
\(509\) | −0.127719 | − | 0.221215i | −0.00566103 | − | 0.00980519i | 0.863181 | − | 0.504895i | \(-0.168469\pi\) |
−0.868842 | + | 0.495089i | \(0.835135\pi\) | |||||||
\(510\) | −22.4891 | − | 12.4193i | −0.995835 | − | 0.549936i | ||||
\(511\) | −1.00000 | + | 5.19615i | −0.0442374 | + | 0.229864i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.25544 | + | 16.8781i | −0.276184 | + | 0.745185i | ||||
\(514\) | −7.37228 | − | 4.25639i | −0.325177 | − | 0.187741i | ||||
\(515\) | 33.0475 | + | 7.10313i | 1.45625 | + | 0.313001i | ||||
\(516\) | 18.3030 | + | 5.51856i | 0.805744 | + | 0.242941i | ||||
\(517\) | 8.00000 | 0.351840 | ||||||||
\(518\) | 30.3505 | + | 5.84096i | 1.33353 | + | 0.256637i | ||||
\(519\) | −4.74456 | + | 4.45877i | −0.208263 | + | 0.195718i | ||||
\(520\) | 3.00000 | − | 3.31662i | 0.131559 | − | 0.145444i | ||||
\(521\) | −1.62772 | + | 2.81929i | −0.0713116 | + | 0.123515i | −0.899476 | − | 0.436969i | \(-0.856052\pi\) |
0.828165 | + | 0.560485i | \(0.189385\pi\) | |||||||
\(522\) | −5.50000 | + | 8.29156i | −0.240728 | + | 0.362912i | ||||
\(523\) | −12.1168 | − | 20.9870i | −0.529833 | − | 0.917697i | −0.999394 | − | 0.0347974i | \(-0.988921\pi\) |
0.469562 | − | 0.882900i | \(-0.344412\pi\) | |||||||
\(524\) | −4.62772 | −0.202163 | ||||||||
\(525\) | 14.1277 | + | 18.0391i | 0.616584 | + | 0.787289i | ||||
\(526\) | 1.62772 | 0.0709719 | ||||||||
\(527\) | 7.88316 | + | 13.6540i | 0.343396 | + | 0.594779i | ||||
\(528\) | −1.68614 | − | 7.17687i | −0.0733799 | − | 0.312333i | ||||
\(529\) | 1.94158 | − | 3.36291i | 0.0844164 | − | 0.146214i | ||||
\(530\) | 2.05842 | − | 2.27567i | 0.0894121 | − | 0.0988488i | ||||
\(531\) | 0.766312 | − | 12.3267i | 0.0332551 | − | 0.534935i | ||||
\(532\) | 3.00000 | + | 8.66025i | 0.130066 | + | 0.375470i | ||||
\(533\) | −3.25544 | −0.141009 | ||||||||
\(534\) | −2.18614 | + | 7.25061i | −0.0946036 | + | 0.313765i | ||||
\(535\) | 38.7921 | + | 8.33785i | 1.67713 | + | 0.360477i | ||||
\(536\) | −6.55842 | − | 3.78651i | −0.283281 | − | 0.163552i | ||||
\(537\) | −4.76631 | − | 1.43710i | −0.205682 | − | 0.0620153i | ||||
\(538\) | 19.9783 | 0.861324 | ||||||||
\(539\) | 29.4891 | − | 4.25639i | 1.27019 | − | 0.183336i | ||||
\(540\) | 9.80298 | + | 6.23711i | 0.421853 | + | 0.268402i | ||||
\(541\) | 6.67527 | + | 11.5619i | 0.286992 | + | 0.497085i | 0.973090 | − | 0.230424i | \(-0.0740113\pi\) |
−0.686098 | + | 0.727509i | \(0.740678\pi\) | |||||||
\(542\) | −18.1753 | − | 10.4935i | −0.780695 | − | 0.450734i | ||||
\(543\) | −7.11684 | − | 30.2921i | −0.305413 | − | 1.29996i | ||||
\(544\) | −5.74456 | + | 3.31662i | −0.246296 | + | 0.142199i | ||||
\(545\) | 6.25544 | + | 19.4024i | 0.267953 | + | 0.831108i | ||||
\(546\) | 8.11684 | + | 4.25639i | 0.347369 | + | 0.182157i | ||||
\(547\) | − | 0.644810i | − | 0.0275701i | −0.999905 | − | 0.0137850i | \(-0.995612\pi\) | ||
0.999905 | − | 0.0137850i | \(-0.00438806\pi\) | |||||||
\(548\) | 1.37228 | + | 2.37686i | 0.0586210 | + | 0.101534i | ||||
\(549\) | −4.67527 | + | 7.04823i | −0.199535 | + | 0.300811i | ||||
\(550\) | 21.1753 | − | 2.12819i | 0.902916 | − | 0.0907465i | ||||
\(551\) | −5.74456 | − | 9.94987i | −0.244727 | − | 0.423879i | ||||
\(552\) | −5.18614 | − | 5.51856i | −0.220737 | − | 0.234885i | ||||
\(553\) | −16.2337 | − | 14.0588i | −0.690327 | − | 0.597840i | ||||
\(554\) | − | 29.0024i | − | 1.23220i | ||||||
\(555\) | 0.861407 | + | 45.2357i | 0.0365647 | + | 1.92015i | ||||
\(556\) | −10.1168 | − | 5.84096i | −0.429050 | − | 0.247712i | ||||
\(557\) | −0.430703 | + | 0.746000i | −0.0182495 | + | 0.0316090i | −0.875006 | − | 0.484112i | \(-0.839143\pi\) |
0.856756 | + | 0.515721i | \(0.172476\pi\) | |||||||
\(558\) | −3.17527 | − | 6.38458i | −0.134420 | − | 0.270281i | ||||
\(559\) | 22.0742i | 0.933640i | ||||||||
\(560\) | 5.87228 | − | 0.718549i | 0.248149 | − | 0.0303642i | ||||
\(561\) | −33.4891 | − | 35.6357i | −1.41391 | − | 1.50454i | ||||
\(562\) | 18.8614 | − | 10.8896i | 0.795620 | − | 0.459352i | ||||
\(563\) | −10.2446 | − | 5.91470i | −0.431757 | − | 0.249275i | 0.268338 | − | 0.963325i | \(-0.413526\pi\) |
−0.700095 | + | 0.714050i | \(0.746859\pi\) | |||||||
\(564\) | 0.744563 | + | 3.16915i | 0.0313517 | + | 0.133445i | ||||
\(565\) | 4.88316 | − | 5.39853i | 0.205436 | − | 0.227118i | ||||
\(566\) | −16.0000 | −0.672530 | ||||||||
\(567\) | −7.36141 | + | 22.6453i | −0.309150 | + | 0.951013i | ||||
\(568\) | 1.87953i | 0.0788632i | ||||||||
\(569\) | −18.8614 | + | 10.8896i | −0.790711 | + | 0.456517i | −0.840213 | − | 0.542257i | \(-0.817570\pi\) |
0.0495016 | + | 0.998774i | \(0.484237\pi\) | |||||||
\(570\) | −11.4891 | + | 6.92820i | −0.481227 | + | 0.290191i | ||||
\(571\) | −17.1168 | + | 29.6472i | −0.716318 | + | 1.24070i | 0.246132 | + | 0.969236i | \(0.420840\pi\) |
−0.962449 | + | 0.271462i | \(0.912493\pi\) | |||||||
\(572\) | 7.37228 | − | 4.25639i | 0.308251 | − | 0.177969i | ||||
\(573\) | 4.74456 | − | 4.45877i | 0.198207 | − | 0.186268i | ||||
\(574\) | −3.25544 | − | 2.81929i | −0.135879 | − | 0.117675i | ||||
\(575\) | 17.7446 | − | 12.7692i | 0.739999 | − | 0.532511i | ||||
\(576\) | 2.68614 | − | 1.33591i | 0.111923 | − | 0.0556628i | ||||
\(577\) | −8.94158 | + | 15.4873i | −0.372243 | + | 0.644743i | −0.989910 | − | 0.141696i | \(-0.954744\pi\) |
0.617667 | + | 0.786439i | \(0.288078\pi\) | |||||||
\(578\) | −13.5000 | + | 23.3827i | −0.561526 | + | 0.972592i | ||||
\(579\) | 13.2921 | + | 4.00772i | 0.552401 | + | 0.166555i | ||||
\(580\) | −7.05842 | + | 2.27567i | −0.293085 | + | 0.0944921i | ||||
\(581\) | −1.24456 | − | 3.59274i | −0.0516332 | − | 0.149052i | ||||
\(582\) | 2.51087 | + | 2.67181i | 0.104079 | + | 0.110750i | ||||
\(583\) | 5.05842 | − | 2.92048i | 0.209498 | − | 0.120954i | ||||
\(584\) | −1.00000 | + | 1.73205i | −0.0413803 | + | 0.0716728i | ||||
\(585\) | −3.62772 | + | 12.9166i | −0.149988 | + | 0.534037i | ||||
\(586\) | −21.6861 | + | 12.5205i | −0.895846 | + | 0.517217i | ||||
\(587\) | − | 36.4280i | − | 1.50354i | −0.659424 | − | 0.751772i | \(-0.729200\pi\) | ||
0.659424 | − | 0.751772i | \(-0.270800\pi\) | |||||||
\(588\) | 4.43070 | + | 11.2858i | 0.182719 | + | 0.465418i | ||||
\(589\) | 8.23369 | 0.339263 | ||||||||
\(590\) | 6.17527 | − | 6.82701i | 0.254232 | − | 0.281064i | ||||
\(591\) | 34.1168 | − | 8.01544i | 1.40338 | − | 0.329711i | ||||
\(592\) | 10.1168 | + | 5.84096i | 0.415800 | + | 0.240062i | ||||
\(593\) | −12.2554 | + | 7.07568i | −0.503270 | + | 0.290563i | −0.730063 | − | 0.683380i | \(-0.760509\pi\) |
0.226793 | + | 0.973943i | \(0.427176\pi\) | |||||||
\(594\) | 14.1168 | + | 17.0256i | 0.579221 | + | 0.698567i | ||||
\(595\) | 31.3505 | − | 23.6039i | 1.28525 | − | 0.967666i | ||||
\(596\) | − | 14.2063i | − | 0.581911i | ||||||
\(597\) | −30.8614 | − | 9.30506i | −1.26307 | − | 0.380831i | ||||
\(598\) | 4.37228 | − | 7.57301i | 0.178796 | − | 0.309684i | ||||
\(599\) | −7.37228 | − | 4.25639i | −0.301223 | − | 0.173911i | 0.341769 | − | 0.939784i | \(-0.388974\pi\) |
−0.642992 | + | 0.765873i | \(0.722307\pi\) | |||||||
\(600\) | 2.81386 | + | 8.19037i | 0.114875 | + | 0.334371i | ||||
\(601\) | 10.5947i | 0.432166i | 0.976375 | + | 0.216083i | \(0.0693282\pi\) | ||||
−0.976375 | + | 0.216083i | \(0.930672\pi\) | |||||||
\(602\) | −19.1168 | + | 22.0742i | −0.779144 | + | 0.899678i | ||||
\(603\) | 22.6753 | + | 1.40965i | 0.923408 | + | 0.0574052i | ||||
\(604\) | 4.05842 | + | 7.02939i | 0.165135 | + | 0.286022i | ||||
\(605\) | 15.5584 | + | 3.34408i | 0.632540 | + | 0.135956i | ||||
\(606\) | 27.6060 | − | 6.48577i | 1.12142 | − | 0.263467i | ||||
\(607\) | 13.7337 | + | 23.7874i | 0.557433 | + | 0.965503i | 0.997710 | + | 0.0676404i | \(0.0215471\pi\) |
−0.440277 | + | 0.897862i | \(0.645120\pi\) | |||||||
\(608\) | 3.46410i | 0.140488i | ||||||||
\(609\) | −8.12772 | − | 12.8429i | −0.329352 | − | 0.520421i | ||||
\(610\) | −6.00000 | + | 1.93443i | −0.242933 | + | 0.0783228i | ||||
\(611\) | −3.25544 | + | 1.87953i | −0.131701 | + | 0.0760375i | ||||
\(612\) | 11.0000 | − | 16.5831i | 0.444649 | − | 0.670333i | ||||
\(613\) | 11.2337 | + | 6.48577i | 0.453724 | + | 0.261958i | 0.709402 | − | 0.704804i | \(-0.248965\pi\) |
−0.255677 | + | 0.966762i | \(0.582299\pi\) | |||||||
\(614\) | −3.44158 | − | 5.96099i | −0.138891 | − | 0.240566i | ||||
\(615\) | 3.04755 | − | 5.51856i | 0.122889 | − | 0.222530i | ||||
\(616\) | 11.0584 | + | 2.12819i | 0.445557 | + | 0.0857474i | ||||
\(617\) | 1.02175 | 0.0411341 | 0.0205670 | − | 0.999788i | \(-0.493453\pi\) | ||||
0.0205670 | + | 0.999788i | \(0.493453\pi\) | |||||||
\(618\) | −7.55842 | + | 25.0684i | −0.304044 | + | 1.00840i | ||||
\(619\) | 20.2337 | + | 11.6819i | 0.813261 | + | 0.469536i | 0.848087 | − | 0.529857i | \(-0.177754\pi\) |
−0.0348263 | + | 0.999393i | \(0.511088\pi\) | |||||||
\(620\) | 1.11684 | − | 5.19615i | 0.0448535 | − | 0.208683i | ||||
\(621\) | 21.3030 | + | 7.89542i | 0.854859 | + | 0.316832i | ||||
\(622\) | −14.2337 | −0.570719 | ||||||||
\(623\) | −8.74456 | − | 7.57301i | −0.350344 | − | 0.303406i | ||||
\(624\) | 2.37228 | + | 2.52434i | 0.0949673 | + | 0.101054i | ||||
\(625\) | −24.5000 | + | 4.97494i | −0.980000 | + | 0.198997i | ||||
\(626\) | 7.05842 | − | 12.2255i | 0.282111 | − | 0.488631i | ||||
\(627\) | −24.8614 | + | 5.84096i | −0.992869 | + | 0.233266i | ||||
\(628\) | 4.00000 | + | 6.92820i | 0.159617 | + | 0.276465i | ||||
\(629\) | 77.4891 | 3.08969 | ||||||||
\(630\) | −14.8139 | + | 9.77495i | −0.590198 | + | 0.389443i | ||||
\(631\) | 30.1168 | 1.19893 | 0.599466 | − | 0.800400i | \(-0.295380\pi\) | ||||
0.599466 | + | 0.800400i | \(0.295380\pi\) | |||||||
\(632\) | −4.05842 | − | 7.02939i | −0.161435 | − | 0.279614i | ||||
\(633\) | −30.7446 | + | 7.22316i | −1.22199 | + | 0.287095i | ||||
\(634\) | −8.05842 | + | 13.9576i | −0.320041 | + | 0.554327i | ||||
\(635\) | −3.94158 | − | 3.56529i | −0.156417 | − | 0.141484i | ||||
\(636\) | 1.62772 | + | 1.73205i | 0.0645432 | + | 0.0686803i | ||||
\(637\) | −11.0000 | + | 8.66025i | −0.435836 | + | 0.343132i | ||||
\(638\) | −14.1168 | −0.558891 | ||||||||
\(639\) | −2.51087 | − | 5.04868i | −0.0993287 | − | 0.199723i | ||||
\(640\) | 2.18614 | + | 0.469882i | 0.0864148 | + | 0.0185737i | ||||
\(641\) | 12.3030 | + | 7.10313i | 0.485939 | + | 0.280557i | 0.722888 | − | 0.690965i | \(-0.242814\pi\) |
−0.236949 | + | 0.971522i | \(0.576148\pi\) | |||||||
\(642\) | −8.87228 | + | 29.4260i | −0.350161 | + | 1.16135i | ||||
\(643\) | −16.2337 | −0.640194 | −0.320097 | − | 0.947385i | \(-0.603716\pi\) | ||||
−0.320097 | + | 0.947385i | \(0.603716\pi\) | |||||||
\(644\) | 10.9307 | − | 3.78651i | 0.430730 | − | 0.149209i | ||||
\(645\) | −37.4198 | − | 20.6646i | −1.47340 | − | 0.813667i | ||||
\(646\) | 11.4891 | + | 19.8997i | 0.452034 | + | 0.782945i | ||||
\(647\) | −22.0693 | − | 12.7417i | −0.867634 | − | 0.500928i | −0.00107245 | − | 0.999999i | \(-0.500341\pi\) |
−0.866561 | + | 0.499071i | \(0.833675\pi\) | |||||||
\(648\) | −5.43070 | + | 7.17687i | −0.213338 | + | 0.281934i | ||||
\(649\) | 15.1753 | − | 8.76144i | 0.595681 | − | 0.343917i | ||||
\(650\) | −8.11684 | + | 5.84096i | −0.318369 | + | 0.229101i | ||||
\(651\) | 10.8832 | − | 0.442430i | 0.426545 | − | 0.0173402i | ||||
\(652\) | 3.46410i | 0.135665i | ||||||||
\(653\) | −5.31386 | − | 9.20387i | −0.207947 | − | 0.360175i | 0.743120 | − | 0.669158i | \(-0.233345\pi\) |
−0.951068 | + | 0.308982i | \(0.900012\pi\) | |||||||
\(654\) | −15.3723 | + | 3.61158i | −0.601104 | + | 0.141224i | ||||
\(655\) | 10.1168 | + | 2.17448i | 0.395298 | + | 0.0849640i | ||||
\(656\) | −0.813859 | − | 1.40965i | −0.0317759 | − | 0.0550374i | ||||
\(657\) | 0.372281 | − | 5.98844i | 0.0145241 | − | 0.233631i | ||||
\(658\) | −4.88316 | − | 0.939764i | −0.190365 | − | 0.0366358i | ||||
\(659\) | − | 36.9253i | − | 1.43841i | −0.694800 | − | 0.719203i | \(-0.744507\pi\) | ||
0.694800 | − | 0.719203i | \(-0.255493\pi\) | |||||||
\(660\) | 0.313859 | + | 16.4819i | 0.0122170 | + | 0.641558i | ||||
\(661\) | 2.44158 | + | 1.40965i | 0.0949664 | + | 0.0548289i | 0.546731 | − | 0.837308i | \(-0.315872\pi\) |
−0.451765 | + | 0.892137i | \(0.649205\pi\) | |||||||
\(662\) | 5.11684 | − | 8.86263i | 0.198872 | − | 0.344456i | ||||
\(663\) | 22.0000 | + | 6.63325i | 0.854409 | + | 0.257614i | ||||
\(664\) | − | 1.43710i | − | 0.0557702i | ||||||
\(665\) | −2.48913 | − | 20.3422i | −0.0965241 | − | 0.788836i | ||||
\(666\) | −34.9783 | − | 2.17448i | −1.35538 | − | 0.0842594i | ||||
\(667\) | −12.5584 | + | 7.25061i | −0.486264 | + | 0.280745i | ||||
\(668\) | 9.81386 | + | 5.66603i | 0.379710 | + | 0.219225i | ||||
\(669\) | −30.5475 | + | 7.17687i | −1.18104 | + | 0.277474i | ||||
\(670\) | 12.5584 | + | 11.3595i | 0.485174 | + | 0.438857i | ||||
\(671\) | −12.0000 | −0.463255 | ||||||||
\(672\) | 0.186141 | + | 4.57879i | 0.00718053 | + | 0.176631i | ||||
\(673\) | − | 17.1181i | − | 0.659855i | −0.944006 | − | 0.329928i | \(-0.892976\pi\) | ||
0.944006 | − | 0.329928i | \(-0.107024\pi\) | |||||||
\(674\) | 8.05842 | − | 4.65253i | 0.310399 | − | 0.179209i | ||||
\(675\) | −18.5000 | − | 18.2414i | −0.712065 | − | 0.702113i | ||||
\(676\) | 4.50000 | − | 7.79423i | 0.173077 | − | 0.299778i | ||||
\(677\) | 38.9198 | − | 22.4704i | 1.49581 | − | 0.863607i | 0.495822 | − | 0.868424i | \(-0.334867\pi\) |
0.999988 | + | 0.00481749i | \(0.00153346\pi\) | |||||||
\(678\) | 3.86141 | + | 4.10891i | 0.148296 | + | 0.157802i | ||||
\(679\) | −5.29211 | + | 1.83324i | −0.203093 | + | 0.0703533i | ||||
\(680\) | 14.1168 | − | 4.55134i | 0.541356 | − | 0.174536i | ||||
\(681\) | 25.9416 | + | 7.82168i | 0.994083 | + | 0.299727i | ||||
\(682\) | 5.05842 | − | 8.76144i | 0.193697 | − | 0.335493i | ||||
\(683\) | −6.98913 | + | 12.1055i | −0.267431 | + | 0.463205i | −0.968198 | − | 0.250186i | \(-0.919508\pi\) |
0.700766 | + | 0.713391i | \(0.252842\pi\) | |||||||
\(684\) | −4.62772 | − | 9.30506i | −0.176945 | − | 0.355788i | ||||
\(685\) | −1.88316 | − | 5.84096i | −0.0719517 | − | 0.223172i | ||||
\(686\) | −18.5000 | − | 0.866025i | −0.706333 | − | 0.0330650i | ||||
\(687\) | 17.4891 | − | 16.4356i | 0.667252 | − | 0.627059i | ||||
\(688\) | −9.55842 | + | 5.51856i | −0.364411 | + | 0.210393i | ||||
\(689\) | −1.37228 | + | 2.37686i | −0.0522798 | + | 0.0905512i | ||||
\(690\) | 8.74456 | + | 14.5012i | 0.332900 | + | 0.552052i | ||||
\(691\) | −26.2337 | + | 15.1460i | −0.997977 | + | 0.576182i | −0.907649 | − | 0.419730i | \(-0.862125\pi\) |
−0.0903276 | + | 0.995912i | \(0.528791\pi\) | |||||||
\(692\) | − | 3.75906i | − | 0.142898i | ||||||
\(693\) | −32.5475 | + | 9.05640i | −1.23638 | + | 0.344024i | ||||
\(694\) | 19.1168 | 0.725665 | ||||||||
\(695\) | 19.3723 | + | 17.5229i | 0.734833 | + | 0.664681i | ||||
\(696\) | −1.31386 | − | 5.59230i | −0.0498017 | − | 0.211975i | ||||
\(697\) | −9.35053 | − | 5.39853i | −0.354177 | − | 0.204484i | ||||
\(698\) | 20.7921 | − | 12.0043i | 0.786993 | − | 0.454371i | ||||
\(699\) | −27.8614 | − | 29.6472i | −1.05382 | − | 1.12136i | ||||
\(700\) | −13.1753 | − | 1.18843i | −0.497978 | − | 0.0449185i | ||||
\(701\) | − | 12.7143i | − | 0.480211i | −0.970747 | − | 0.240106i | \(-0.922818\pi\) | ||
0.970747 | − | 0.240106i | \(-0.0771821\pi\) | |||||||
\(702\) | −9.74456 | − | 3.61158i | −0.367785 | − | 0.136310i | ||||
\(703\) | 20.2337 | − | 35.0458i | 0.763128 | − | 1.32178i | ||||
\(704\) | 3.68614 | + | 2.12819i | 0.138927 | + | 0.0802093i | ||||
\(705\) | −0.138593 | − | 7.27806i | −0.00521973 | − | 0.274108i | ||||
\(706\) | 18.9051i | 0.711502i | ||||||||
\(707\) | −8.18614 | + | 42.5364i | −0.307872 | + | 1.59975i | ||||
\(708\) | 4.88316 | + | 5.19615i | 0.183520 | + | 0.195283i | ||||
\(709\) | 2.55842 | + | 4.43132i | 0.0960836 | + | 0.166422i | 0.910060 | − | 0.414476i | \(-0.136035\pi\) |
−0.813977 | + | 0.580897i | \(0.802702\pi\) | |||||||
\(710\) | 0.883156 | − | 4.10891i | 0.0331443 | − | 0.154205i | ||||
\(711\) | 20.2921 | + | 13.4603i | 0.761014 | + | 0.504799i | ||||
\(712\) | −2.18614 | − | 3.78651i | −0.0819291 | − | 0.141905i | ||||
\(713\) | − | 10.3923i | − | 0.389195i | ||||||
\(714\) | 16.2554 | + | 25.6858i | 0.608344 | + | 0.961267i | ||||
\(715\) | −18.1168 | + | 5.84096i | −0.677532 | + | 0.218440i | ||||
\(716\) | 2.48913 | − | 1.43710i | 0.0930230 | − | 0.0537068i | ||||
\(717\) | 1.13859 | + | 4.84630i | 0.0425215 | + | 0.180988i | ||||
\(718\) | 12.2554 | + | 7.07568i | 0.457369 | + | 0.264062i | ||||
\(719\) | 16.6277 | + | 28.8001i | 0.620109 | + | 1.07406i | 0.989465 | + | 0.144773i | \(0.0462451\pi\) |
−0.369356 | + | 0.929288i | \(0.620422\pi\) | |||||||
\(720\) | −6.50000 | + | 1.65831i | −0.242241 | + | 0.0618017i | ||||
\(721\) | −30.2337 | − | 26.1831i | −1.12596 | − | 0.975111i | ||||
\(722\) | −7.00000 | −0.260513 | ||||||||
\(723\) | 17.5693 | + | 5.29734i | 0.653409 | + | 0.197010i | ||||
\(724\) | 15.5584 | + | 8.98266i | 0.578224 | + | 0.333838i | ||||
\(725\) | 16.5000 | − | 1.65831i | 0.612795 | − | 0.0615882i | ||||
\(726\) | −3.55842 | + | 11.8020i | −0.132065 | + | 0.438011i | ||||
\(727\) | 19.0000 | 0.704671 | 0.352335 | − | 0.935874i | \(-0.385388\pi\) | ||||
0.352335 | + | 0.935874i | \(0.385388\pi\) | |||||||
\(728\) | −5.00000 | + | 1.73205i | −0.185312 | + | 0.0641941i | ||||
\(729\) | 5.00000 | − | 26.5330i | 0.185185 | − | 0.982704i | ||||
\(730\) | 3.00000 | − | 3.31662i | 0.111035 | − | 0.122754i | ||||
\(731\) | −36.6060 | + | 63.4034i | −1.35392 | + | 2.34506i | ||||
\(732\) | −1.11684 | − | 4.75372i | −0.0412797 | − | 0.175703i | ||||
\(733\) | 18.2337 | + | 31.5817i | 0.673477 | + | 1.16650i | 0.976912 | + | 0.213644i | \(0.0685331\pi\) |
−0.303435 | + | 0.952852i | \(0.598134\pi\) | |||||||
\(734\) | −21.2337 | −0.783750 | ||||||||
\(735\) | −4.38316 | − | 26.7542i | −0.161675 | − | 0.986844i | ||||
\(736\) | 4.37228 | 0.161164 | ||||||||
\(737\) | 16.1168 | + | 27.9152i | 0.593672 | + | 1.02827i | ||||
\(738\) | 4.06930 | + | 2.69927i | 0.149793 | + | 0.0993614i | ||||
\(739\) | 18.1168 | − | 31.3793i | 0.666439 | − | 1.15431i | −0.312454 | − | 0.949933i | \(-0.601151\pi\) |
0.978893 | − | 0.204373i | \(-0.0655156\pi\) | |||||||
\(740\) | −19.3723 | − | 17.5229i | −0.712139 | − | 0.644154i | ||||
\(741\) | 8.74456 | − | 8.21782i | 0.321240 | − | 0.301889i | ||||
\(742\) | −3.43070 | + | 1.18843i | −0.125945 | + | 0.0436287i | ||||
\(743\) | 18.6060 | 0.682587 | 0.341293 | − | 0.939957i | \(-0.389135\pi\) | ||||
0.341293 | + | 0.939957i | \(0.389135\pi\) | |||||||
\(744\) | 3.94158 | + | 1.18843i | 0.144505 | + | 0.0435700i | ||||
\(745\) | −6.67527 | + | 31.0569i | −0.244563 | + | 1.13784i | ||||
\(746\) | 14.2337 | + | 8.21782i | 0.521132 | + | 0.300876i | ||||
\(747\) | 1.91983 | + | 3.86025i | 0.0702429 | + | 0.141239i | ||||
\(748\) | 28.2337 | 1.03233 | ||||||||
\(749\) | −35.4891 | − | 30.7345i | −1.29674 | − | 1.12301i | ||||
\(750\) | −2.30298 | − | 19.2275i | −0.0840931 | − | 0.702089i | ||||
\(751\) | −21.0584 | − | 36.4743i | −0.768433 | − | 1.33096i | −0.938412 | − | 0.345517i | \(-0.887704\pi\) |
0.169980 | − | 0.985448i | \(-0.445630\pi\) | |||||||
\(752\) | −1.62772 | − | 0.939764i | −0.0593568 | − | 0.0342697i | ||||
\(753\) | 27.1753 | − | 6.38458i | 0.990322 | − | 0.232667i | ||||
\(754\) | 5.74456 | − | 3.31662i | 0.209205 | − | 0.120784i | ||||
\(755\) | −5.56930 | − | 17.2742i | −0.202687 | − | 0.628673i | ||||
\(756\) | −6.61684 | − | 12.0506i | −0.240652 | − | 0.438277i | ||||
\(757\) | − | 5.63858i | − | 0.204938i | −0.994736 | − | 0.102469i | \(-0.967326\pi\) | ||
0.994736 | − | 0.102469i | \(-0.0326742\pi\) | |||||||
\(758\) | 11.1168 | + | 19.2549i | 0.403782 | + | 0.699371i | ||||
\(759\) | 7.37228 | + | 31.3793i | 0.267597 | + | 1.13900i | ||||
\(760\) | 1.62772 | − | 7.57301i | 0.0590436 | − | 0.274702i | ||||
\(761\) | 26.4891 | + | 45.8805i | 0.960230 | + | 1.66317i | 0.721918 | + | 0.691979i | \(0.243261\pi\) |
0.238312 | + | 0.971189i | \(0.423406\pi\) | |||||||
\(762\) | 3.00000 | − | 2.81929i | 0.108679 | − | 0.102132i | ||||
\(763\) | 4.55842 | − | 23.6863i | 0.165026 | − | 0.857500i | ||||
\(764\) | 3.75906i | 0.135998i | ||||||||
\(765\) | −31.8397 | + | 31.0843i | −1.15117 | + | 1.12386i | ||||
\(766\) | −18.0475 | − | 10.4198i | −0.652084 | − | 0.376481i | ||||
\(767\) | −4.11684 | + | 7.13058i | −0.148651 | + | 0.257470i | ||||
\(768\) | −0.500000 | + | 1.65831i | −0.0180422 | + | 0.0598392i | ||||
\(769\) | 40.4820i | 1.45982i | 0.683545 | + | 0.729909i | \(0.260437\pi\) | ||||
−0.683545 | + | 0.729909i | \(0.739563\pi\) | |||||||
\(770\) | −23.1753 | − | 9.84868i | −0.835179 | − | 0.354922i | ||||
\(771\) | −10.7446 | + | 10.0974i | −0.386956 | + | 0.363647i | ||||
\(772\) | −6.94158 | + | 4.00772i | −0.249833 | + | 0.144241i | ||||
\(773\) | −1.62772 | − | 0.939764i | −0.0585450 | − | 0.0338010i | 0.470442 | − | 0.882431i | \(-0.344095\pi\) |
−0.528987 | + | 0.848630i | \(0.677428\pi\) | |||||||
\(774\) | 18.3030 | − | 27.5928i | 0.657887 | − | 0.991802i | ||||
\(775\) | −4.88316 | + | 10.8347i | −0.175408 | + | 0.389195i | ||||
\(776\) | −2.11684 | −0.0759903 | ||||||||
\(777\) | 24.8614 | − | 47.4102i | 0.891898 | − | 1.70083i | ||||
\(778\) | − | 34.0511i | − | 1.22079i | ||||||
\(779\) | −4.88316 | + | 2.81929i | −0.174957 | + | 0.101012i | ||||
\(780\) | −4.00000 | − | 6.63325i | −0.143223 | − | 0.237508i | ||||
\(781\) | 4.00000 | − | 6.92820i | 0.143131 | − | 0.247911i | ||||
\(782\) | 25.1168 | − | 14.5012i | 0.898177 | − | 0.518562i | ||||
\(783\) | 11.0000 | + | 13.2665i | 0.393108 | + | 0.474106i | ||||
\(784\) | −6.50000 | − | 2.59808i | −0.232143 | − | 0.0927884i | ||||
\(785\) | −5.48913 | − | 17.0256i | −0.195915 | − | 0.607668i | ||||
\(786\) | −2.31386 | + | 7.67420i | −0.0825326 | + | 0.273730i | ||||
\(787\) | 13.5584 | − | 23.4839i | 0.483306 | − | 0.837110i | −0.516511 | − | 0.856281i | \(-0.672769\pi\) |
0.999816 | + | 0.0191710i | \(0.00610269\pi\) | |||||||
\(788\) | −10.1168 | + | 17.5229i | −0.360398 | + | 0.624227i | ||||
\(789\) | 0.813859 | − | 2.69927i | 0.0289742 | − | 0.0960964i | ||||
\(790\) | 5.56930 | + | 17.2742i | 0.198147 | + | 0.614589i | ||||
\(791\) | −8.13859 | + | 2.81929i | −0.289375 | + | 0.100242i | ||||
\(792\) | −12.7446 | − | 0.792287i | −0.452858 | − | 0.0281527i | ||||
\(793\) | 4.88316 | − | 2.81929i | 0.173406 | − | 0.100116i | ||||
\(794\) | −4.00000 | + | 6.92820i | −0.141955 | + | 0.245873i | ||||
\(795\) | −2.74456 | − | 4.55134i | −0.0973396 | − | 0.161419i | ||||
\(796\) | 16.1168 | − | 9.30506i | 0.571246 | − | 0.329809i | ||||
\(797\) | 4.25639i | 0.150769i | 0.997155 | + | 0.0753845i | \(0.0240184\pi\) | ||||
−0.997155 | + | 0.0753845i | \(0.975982\pi\) | |||||||
\(798\) | 15.8614 | − | 0.644810i | 0.561488 | − | 0.0228260i | ||||
\(799\) | −12.4674 | −0.441064 | ||||||||
\(800\) | −4.55842 | − | 2.05446i | −0.161165 | − | 0.0726360i | ||||
\(801\) | 10.9307 | + | 7.25061i | 0.386217 | + | 0.256188i | ||||
\(802\) | −17.1861 | − | 9.92242i | −0.606864 | − | 0.350373i | ||||
\(803\) | 7.37228 | − | 4.25639i | 0.260162 | − | 0.150205i | ||||
\(804\) | −9.55842 | + | 8.98266i | −0.337100 | + | 0.316794i | ||||
\(805\) | −25.6753 | + | 3.14170i | −0.904934 | + | 0.110730i | ||||
\(806\) | 4.75372i | 0.167443i | ||||||||
\(807\) | 9.98913 | − | 33.1302i | 0.351634 | − | 1.16624i | ||||
\(808\) | −8.18614 | + | 14.1788i | −0.287987 | + | 0.498809i | ||||
\(809\) | 22.0693 | + | 12.7417i | 0.775915 | + | 0.447975i | 0.834981 | − | 0.550279i | \(-0.185479\pi\) |
−0.0590655 | + | 0.998254i | \(0.518812\pi\) | |||||||
\(810\) | 15.2446 | − | 13.1379i | 0.535639 | − | 0.461617i | ||||
\(811\) | 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 | ||||
\(813\) | −26.4891 | + | 24.8935i | −0.929014 | + | 0.873054i | ||||
\(814\) | −24.8614 | − | 43.0612i | −0.871392 | − | 1.50929i | ||||
\(815\) | 1.62772 | − | 7.57301i | 0.0570165 | − | 0.265271i | ||||
\(816\) | 2.62772 | + | 11.1846i | 0.0919886 | + | 0.391539i | ||||
\(817\) | 19.1168 | + | 33.1113i | 0.668814 | + | 1.15842i | ||||
\(818\) | − | 35.4882i | − | 1.24082i | ||||||
\(819\) | 11.1168 | − | 11.3321i | 0.388454 | − | 0.395975i | ||||
\(820\) | 1.11684 | + | 3.46410i | 0.0390019 | + | 0.120972i | ||||
\(821\) | 18.4307 | − | 10.6410i | 0.643236 | − | 0.371372i | −0.142624 | − | 0.989777i | \(-0.545554\pi\) |
0.785860 | + | 0.618404i | \(0.212221\pi\) | |||||||
\(822\) | 4.62772 | − | 1.08724i | 0.161410 | − | 0.0379219i | ||||
\(823\) | −37.6753 | − | 21.7518i | −1.31328 | − | 0.758221i | −0.330640 | − | 0.943757i | \(-0.607265\pi\) |
−0.982637 | + | 0.185536i | \(0.940598\pi\) | |||||||
\(824\) | −7.55842 | − | 13.0916i | −0.263310 | − | 0.456066i | ||||
\(825\) | 7.05842 | − | 36.1793i | 0.245743 | − | 1.25960i | ||||
\(826\) | −10.2921 | + | 3.56529i | −0.358108 | + | 0.124052i | ||||
\(827\) | −33.0000 | −1.14752 | −0.573761 | − | 0.819023i | \(-0.694516\pi\) | ||||
−0.573761 | + | 0.819023i | \(0.694516\pi\) | |||||||
\(828\) | −11.7446 | + | 5.84096i | −0.408152 | + | 0.202987i | ||||
\(829\) | −16.1168 | − | 9.30506i | −0.559761 | − | 0.323178i | 0.193288 | − | 0.981142i | \(-0.438085\pi\) |
−0.753050 | + | 0.657964i | \(0.771418\pi\) | |||||||
\(830\) | −0.675266 | + | 3.14170i | −0.0234388 | + | 0.109050i | ||||
\(831\) | −48.0951 | − | 14.5012i | −1.66840 | − | 0.503042i | ||||
\(832\) | −2.00000 | −0.0693375 | ||||||||
\(833\) | −45.9565 | + | 6.63325i | −1.59230 | + | 0.229828i | ||||
\(834\) | −14.7446 | + | 13.8564i | −0.510562 | + | 0.479808i | ||||
\(835\) | −18.7921 | − | 16.9981i | −0.650328 | − | 0.588244i | ||||
\(836\) | 7.37228 | − | 12.7692i | 0.254976 | − | 0.441631i | ||||
\(837\) | −12.1753 | + | 2.07329i | −0.420839 | + | 0.0716634i | ||||
\(838\) | −14.7446 | − | 25.5383i | −0.509342 | − | 0.882207i | ||||
\(839\) | 1.72281 | 0.0594781 | 0.0297391 | − | 0.999558i | \(-0.490532\pi\) | ||||
0.0297391 | + | 0.999558i | \(0.490532\pi\) | |||||||
\(840\) | 1.74456 | − | 10.0974i | 0.0601931 | − | 0.348392i | ||||
\(841\) | 18.0000 | 0.620690 | ||||||||
\(842\) | 7.55842 | + | 13.0916i | 0.260480 | + | 0.451165i | ||||
\(843\) | −8.62772 | − | 36.7229i | −0.297154 | − | 1.26480i | ||||
\(844\) | 9.11684 | − | 15.7908i | 0.313815 | − | 0.543543i | ||||
\(845\) | −13.5000 | + | 14.9248i | −0.464414 | + | 0.513429i | ||||
\(846\) | 5.62772 | + | 0.349857i | 0.193485 | + | 0.0120283i | ||||
\(847\) | −14.2337 | − | 12.3267i | −0.489075 | − | 0.423552i | ||||
\(848\) | −1.37228 | −0.0471243 | ||||||||
\(849\) | −8.00000 | + | 26.5330i | −0.274559 | + | 0.910610i | ||||
\(850\) | −33.0000 | + | 3.31662i | −1.13189 | + | 0.113759i | ||||
\(851\) | −44.2337 | − | 25.5383i | −1.51631 | − | 0.875443i | ||||
\(852\) | 3.11684 | + | 0.939764i | 0.106781 | + | 0.0321958i | ||||
\(853\) | −30.4674 | −1.04318 | −0.521592 | − | 0.853195i | \(-0.674661\pi\) | ||||
−0.521592 | + | 0.853195i | \(0.674661\pi\) | |||||||
\(854\) | 7.32473 | + | 1.40965i | 0.250647 | + | 0.0482371i | ||||
\(855\) | 5.74456 | + | 22.5167i | 0.196460 | + | 0.770054i | ||||
\(856\) | −8.87228 | − | 15.3672i | −0.303248 | − | 0.525242i | ||||
\(857\) | −32.7446 | − | 18.9051i | −1.11853 | − | 0.645785i | −0.177507 | − | 0.984120i | \(-0.556803\pi\) |
−0.941026 | + | 0.338334i | \(0.890137\pi\) | |||||||
\(858\) | −3.37228 | − | 14.3537i | −0.115128 | − | 0.490029i | ||||
\(859\) | 28.4674 | − | 16.4356i | 0.971294 | − | 0.560777i | 0.0716637 | − | 0.997429i | \(-0.477169\pi\) |
0.899631 | + | 0.436652i | \(0.143836\pi\) | |||||||
\(860\) | 23.4891 | − | 7.57301i | 0.800973 | − | 0.258238i | ||||
\(861\) | −6.30298 | + | 3.98889i | −0.214805 | + | 0.135941i | ||||
\(862\) | − | 3.75906i | − | 0.128034i | ||||||
\(863\) | 3.81386 | + | 6.60580i | 0.129825 | + | 0.224864i | 0.923609 | − | 0.383336i | \(-0.125225\pi\) |
−0.793783 | + | 0.608200i | \(0.791892\pi\) | |||||||
\(864\) | −0.872281 | − | 5.12241i | −0.0296756 | − | 0.174268i | ||||
\(865\) | −1.76631 | + | 8.21782i | −0.0600564 | + | 0.279414i | ||||
\(866\) | 17.0000 | + | 29.4449i | 0.577684 | + | 1.00058i | ||||
\(867\) | 32.0258 | + | 34.0786i | 1.08765 | + | 1.15737i | ||||
\(868\) | −4.11684 | + | 4.75372i | −0.139735 | + | 0.161352i | ||||
\(869\) | 34.5484i | 1.17198i | ||||||||
\(870\) | 0.244563 | + | 12.8429i | 0.00829145 | + | 0.435415i | ||||
\(871\) | −13.1168 | − | 7.57301i | −0.444447 | − | 0.256602i | ||||
\(872\) | 4.55842 | − | 7.89542i | 0.154368 | − | 0.267373i | ||||
\(873\) | 5.68614 | − | 2.82791i | 0.192447 | − | 0.0957102i | ||||
\(874\) | − | 15.1460i | − | 0.512322i | ||||||
\(875\) | 28.2446 | + | 8.78890i | 0.954840 | + | 0.297119i | ||||
\(876\) | 2.37228 | + | 2.52434i | 0.0801520 | + | 0.0852895i | ||||
\(877\) | 27.3505 | − | 15.7908i | 0.923562 | − | 0.533219i | 0.0387922 | − | 0.999247i | \(-0.487649\pi\) |
0.884770 | + | 0.466029i | \(0.154316\pi\) | |||||||
\(878\) | −11.0584 | − | 6.38458i | −0.373204 | − | 0.215469i | ||||
\(879\) | 9.91983 | + | 42.2226i | 0.334588 | + | 1.42413i | ||||
\(880\) | −7.05842 | − | 6.38458i | −0.237939 | − | 0.215224i | ||||
\(881\) | −51.3505 | −1.73004 | −0.865022 | − | 0.501734i | \(-0.832695\pi\) | ||||
−0.865022 | + | 0.501734i | \(0.832695\pi\) | |||||||
\(882\) | 20.9307 | − | 1.70460i | 0.704773 | − | 0.0573968i | ||||
\(883\) | 54.9455i | 1.84906i | 0.381104 | + | 0.924532i | \(0.375544\pi\) | ||||
−0.381104 | + | 0.924532i | \(0.624456\pi\) | |||||||
\(884\) | −11.4891 | + | 6.63325i | −0.386421 | + | 0.223100i | ||||
\(885\) | −8.23369 | − | 13.6540i | −0.276772 | − | 0.458975i | ||||
\(886\) | −4.50000 | + | 7.79423i | −0.151180 | + | 0.261852i | ||||
\(887\) | 47.5367 | − | 27.4453i | 1.59613 | − | 0.921523i | 0.603901 | − | 0.797059i | \(-0.293612\pi\) |
0.992224 | − | 0.124464i | \(-0.0397212\pi\) | |||||||
\(888\) | 14.7446 | − | 13.8564i | 0.494795 | − | 0.464991i | ||||
\(889\) | 2.05842 | + | 5.94215i | 0.0690373 | + | 0.199293i | ||||
\(890\) | 3.00000 | + | 9.30506i | 0.100560 | + | 0.311906i | ||||
\(891\) | 35.2921 | − | 14.8974i | 1.18233 | − | 0.499080i | ||||
\(892\) | 9.05842 | − | 15.6896i | 0.303298 | − | 0.525328i | ||||
\(893\) | −3.25544 | + | 5.63858i | −0.108939 | + | 0.188688i | ||||
\(894\) | −23.5584 | − | 7.10313i | −0.787911 | − | 0.237564i | ||||
\(895\) | −6.11684 | + | 1.97210i | −0.204464 | + | 0.0659201i | ||||
\(896\) | −2.00000 | − | 1.73205i | −0.0668153 | − | 0.0578638i | ||||
\(897\) | −10.3723 | − | 11.0371i | −0.346320 | − | 0.368519i | ||||
\(898\) | −31.1644 | + | 17.9928i | −1.03997 | + | 0.600427i | ||||
\(899\) | 3.94158 | − | 6.82701i | 0.131459 | − | 0.227694i | ||||
\(900\) | 14.9891 | − | 0.571072i | 0.499638 | − | 0.0190357i | ||||
\(901\) | −7.88316 | + | 4.55134i | −0.262626 | + | 0.151627i | ||||
\(902\) | 6.92820i | 0.230684i | ||||||||
\(903\) | 27.0475 | + | 42.7388i | 0.900086 | + | 1.42226i | ||||
\(904\) | −3.25544 | −0.108274 | ||||||||
\(905\) | −29.7921 | − | 26.9480i | −0.990323 | − | 0.895781i | ||||
\(906\) | 13.6861 | − | 3.21543i | 0.454692 | − | 0.106826i | ||||
\(907\) | 38.7921 | + | 22.3966i | 1.28807 | + | 0.743668i | 0.978310 | − | 0.207146i | \(-0.0664177\pi\) |
0.309761 | + | 0.950814i | \(0.399751\pi\) | |||||||
\(908\) | −13.5475 | + | 7.82168i | −0.449591 | + | 0.259572i | ||||
\(909\) | 3.04755 | − | 49.0222i | 0.101081 | − | 1.62596i | ||||
\(910\) | 11.7446 | − | 1.43710i | 0.389328 | − | 0.0476393i | ||||
\(911\) | 24.5437i | 0.813168i | 0.913613 | + | 0.406584i | \(0.133280\pi\) | ||||
−0.913613 | + | 0.406584i | \(0.866720\pi\) | |||||||
\(912\) | 5.74456 | + | 1.73205i | 0.190221 | + | 0.0573539i | ||||
\(913\) | −3.05842 | + | 5.29734i | −0.101219 | + | 0.175316i | ||||
\(914\) | −11.0584 | − | 6.38458i | −0.365780 | − | 0.211183i | ||||
\(915\) | 0.207890 | + | 10.9171i | 0.00687263 | + | 0.360908i | ||||
\(916\) | 13.8564i | 0.457829i | ||||||||
\(917\) | −9.25544 | − | 8.01544i | −0.305641 | − | 0.264693i | ||||
\(918\) | −22.0000 | − | 26.5330i | −0.726108 | − | 0.875719i | ||||
\(919\) | 9.11684 | + | 15.7908i | 0.300737 | + | 0.520892i | 0.976303 | − | 0.216408i | \(-0.0694341\pi\) |
−0.675566 | + | 0.737299i | \(0.736101\pi\) | |||||||
\(920\) | −9.55842 | − | 2.05446i | −0.315132 | − | 0.0677334i | ||||
\(921\) | −11.6060 | + | 2.72672i | −0.382430 | + | 0.0898484i | ||||
\(922\) | −0.255437 | − | 0.442430i | −0.00841238 | − | 0.0145707i | ||||
\(923\) | 3.75906i | 0.123731i | ||||||||
\(924\) | 9.05842 | − | 17.2742i | 0.298000 | − | 0.568280i | ||||
\(925\) | 34.1168 | + | 47.4102i | 1.12175 | + | 1.55884i | ||||
\(926\) | −31.6753 | + | 18.2877i | −1.04091 | + | 0.600972i | ||||
\(927\) | 37.7921 | + | 25.0684i | 1.24126 | + | 0.823356i | ||||
\(928\) | 2.87228 | + | 1.65831i | 0.0942873 | + | 0.0544368i | ||||
\(929\) | −8.44158 | − | 14.6212i | −0.276959 | − | 0.479707i | 0.693668 | − | 0.720295i | \(-0.255993\pi\) |
−0.970628 | + | 0.240587i | \(0.922660\pi\) | |||||||
\(930\) | −8.05842 | − | 4.45015i | −0.264246 | − | 0.145926i | ||||
\(931\) | −9.00000 | + | 22.5167i | −0.294963 | + | 0.737954i | ||||
\(932\) | 23.4891 | 0.769412 | ||||||||
\(933\) | −7.11684 | + | 23.6039i | −0.232995 | + | 0.772757i | ||||
\(934\) | −0.0475473 | − | 0.0274514i | −0.00155579 | − | 0.000898238i | ||||
\(935\) | −61.7228 | − | 13.2665i | −2.01855 | − | 0.433861i | ||||
\(936\) | 5.37228 | − | 2.67181i | 0.175599 | − | 0.0873310i | ||||
\(937\) | −50.3505 | −1.64488 | −0.822440 | − | 0.568852i | \(-0.807388\pi\) | ||||
−0.822440 | + | 0.568852i | \(0.807388\pi\) | |||||||
\(938\) | −6.55842 | − | 18.9325i | −0.214140 | − | 0.618169i | ||||
\(939\) | −16.7446 | − | 17.8178i | −0.546438 | − | 0.581463i | ||||
\(940\) | 3.11684 | + | 2.81929i | 0.101660 | + | 0.0919551i | ||||
\(941\) | 12.1753 | − | 21.0882i | 0.396902 | − | 0.687455i | −0.596440 | − | 0.802658i | \(-0.703418\pi\) |
0.993342 | + | 0.115203i | \(0.0367518\pi\) | |||||||
\(942\) | 13.4891 | − | 3.16915i | 0.439499 | − | 0.103256i | ||||
\(943\) | 3.55842 | + | 6.16337i | 0.115878 | + | 0.200707i | ||||
\(944\) | −4.11684 | −0.133992 | ||||||||
\(945\) | 8.80298 | + | 29.4535i | 0.286361 | + | 0.958122i | ||||
\(946\) | 46.9783 | 1.52739 | ||||||||
\(947\) | 21.5584 | + | 37.3403i | 0.700555 | + | 1.21340i | 0.968272 | + | 0.249899i | \(0.0803973\pi\) |
−0.267717 | + | 0.963497i | \(0.586269\pi\) | |||||||
\(948\) | −13.6861 | + | 3.21543i | −0.444505 | + | 0.104432i | ||||
\(949\) | −2.00000 | + | 3.46410i | −0.0649227 | + | 0.112449i | ||||
\(950\) | −7.11684 | + | 15.7908i | −0.230901 | + | 0.512322i | ||||
\(951\) | 19.1168 | + | 20.3422i | 0.619906 | + | 0.659640i | ||||
\(952\) | −17.2337 | − | 3.31662i | −0.558547 | − | 0.107492i | ||||
\(953\) | 48.0000 | 1.55487 | 0.777436 | − | 0.628962i | \(-0.216520\pi\) | ||||
0.777436 | + | 0.628962i | \(0.216520\pi\) | |||||||
\(954\) | 3.68614 | − | 1.83324i | 0.119343 | − | 0.0593534i | ||||
\(955\) | 1.76631 | − | 8.21782i | 0.0571565 | − | 0.265923i | ||||
\(956\) | −2.48913 | − | 1.43710i | −0.0805041 | − | 0.0464790i | ||||
\(957\) | −7.05842 | + | 23.4101i | −0.228166 | + | 0.756742i | ||||
\(958\) | −8.74456 | −0.282524 | ||||||||
\(959\) | −1.37228 | + | 7.13058i | −0.0443133 | + | 0.230259i | ||||
\(960\) | 1.87228 | − | 3.39036i | 0.0604276 | − | 0.109424i | ||||
\(961\) | −12.6753 | − | 21.9542i | −0.408880 | − | 0.708200i | ||||
\(962\) | 20.2337 | + | 11.6819i | 0.652360 | + | 0.376640i | ||||
\(963\) | 44.3614 | + | 29.4260i | 1.42953 | + | 0.948241i | ||||
\(964\) | −9.17527 | + | 5.29734i | −0.295515 | + | 0.170616i | ||||
\(965\) | 17.0584 | − | 5.49972i | 0.549130 | − | 0.177042i | ||||
\(966\) | −0.813859 | − | 20.0198i | −0.0261855 | − | 0.644126i | ||||
\(967\) | − | 51.9239i | − | 1.66976i | −0.550433 | − | 0.834879i | \(-0.685537\pi\) | ||
0.550433 | − | 0.834879i | \(-0.314463\pi\) | |||||||
\(968\) | −3.55842 | − | 6.16337i | −0.114372 | − | 0.198098i | ||||
\(969\) | 38.7446 | − | 9.10268i | 1.24465 | − | 0.292420i | ||||
\(970\) | 4.62772 | + | 0.994667i | 0.148587 | + | 0.0319368i | ||||
\(971\) | −14.3139 | − | 24.7923i | −0.459354 | − | 0.795624i | 0.539573 | − | 0.841939i | \(-0.318586\pi\) |
−0.998927 | + | 0.0463149i | \(0.985252\pi\) | |||||||
\(972\) | 9.18614 | + | 12.5942i | 0.294646 | + | 0.403960i | ||||
\(973\) | −10.1168 | − | 29.2048i | −0.324331 | − | 0.936263i | ||||
\(974\) | − | 4.55134i | − | 0.145834i | ||||||
\(975\) | 5.62772 | + | 16.3807i | 0.180231 | + | 0.524604i | ||||
\(976\) | 2.44158 | + | 1.40965i | 0.0781530 | + | 0.0451217i | ||||
\(977\) | −20.2337 | + | 35.0458i | −0.647333 | + | 1.12121i | 0.336424 | + | 0.941710i | \(0.390782\pi\) |
−0.983757 | + | 0.179503i | \(0.942551\pi\) | |||||||
\(978\) | 5.74456 | + | 1.73205i | 0.183691 | + | 0.0553849i | ||||
\(979\) | 18.6101i | 0.594782i | ||||||||
\(980\) | 12.9891 | + | 8.73399i | 0.414922 | + | 0.278997i | ||||
\(981\) | −1.69702 | + | 27.2978i | −0.0541815 | + | 0.871553i | ||||
\(982\) | −23.3139 | + | 13.4603i | −0.743975 | + | 0.429534i | ||||
\(983\) | 18.8139 | + | 10.8622i | 0.600069 | + | 0.346450i | 0.769069 | − | 0.639166i | \(-0.220720\pi\) |
−0.169000 | + | 0.985616i | \(0.554054\pi\) | |||||||
\(984\) | −2.74456 | + | 0.644810i | −0.0874935 | + | 0.0205558i | ||||
\(985\) | 30.3505 | − | 33.5538i | 0.967048 | − | 1.06911i | ||||
\(986\) | 22.0000 | 0.700623 | ||||||||
\(987\) | −4.00000 | + | 7.62792i | −0.127321 | + | 0.242799i | ||||
\(988\) | 6.92820i | 0.220416i | ||||||||
\(989\) | 41.7921 | − | 24.1287i | 1.32891 | − | 0.767248i | ||||
\(990\) | 27.4891 | + | 7.72049i | 0.873662 | + | 0.245373i | ||||
\(991\) | 14.1753 | − | 24.5523i | 0.450292 | − | 0.779929i | −0.548112 | − | 0.836405i | \(-0.684653\pi\) |
0.998404 | + | 0.0564762i | \(0.0179865\pi\) | |||||||
\(992\) | −2.05842 | + | 1.18843i | −0.0653550 | + | 0.0377327i | ||||
\(993\) | −12.1386 | − | 12.9166i | −0.385207 | − | 0.409897i | ||||
\(994\) | −3.25544 | + | 3.75906i | −0.103256 | + | 0.119230i | ||||
\(995\) | −39.6060 | + | 12.7692i | −1.25559 | + | 0.404810i | ||||
\(996\) | −2.38316 | − | 0.718549i | −0.0755132 | − | 0.0227681i | ||||
\(997\) | 15.2337 | − | 26.3855i | 0.482456 | − | 0.835638i | −0.517341 | − | 0.855779i | \(-0.673078\pi\) |
0.999797 | + | 0.0201413i | \(0.00641159\pi\) | |||||||
\(998\) | 14.1168 | − | 24.4511i | 0.446861 | − | 0.773986i | ||||
\(999\) | −21.0951 | + | 56.9176i | −0.667419 | + | 1.80079i |
(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.c.59.2 | yes | 4 | |
3.2 | odd | 2 | 210.2.t.a.59.1 | ✓ | 4 | ||
5.2 | odd | 4 | 1050.2.s.d.101.1 | 8 | |||
5.3 | odd | 4 | 1050.2.s.d.101.4 | 8 | |||
5.4 | even | 2 | 210.2.t.b.59.1 | yes | 4 | ||
7.3 | odd | 6 | 1470.2.d.a.1469.4 | 4 | |||
7.4 | even | 3 | 1470.2.d.b.1469.1 | 4 | |||
7.5 | odd | 6 | 210.2.t.d.89.1 | yes | 4 | ||
15.2 | even | 4 | 1050.2.s.e.101.3 | 8 | |||
15.8 | even | 4 | 1050.2.s.e.101.2 | 8 | |||
15.14 | odd | 2 | 210.2.t.d.59.2 | yes | 4 | ||
21.5 | even | 6 | 210.2.t.b.89.1 | yes | 4 | ||
21.11 | odd | 6 | 1470.2.d.d.1469.2 | 4 | |||
21.17 | even | 6 | 1470.2.d.c.1469.3 | 4 | |||
35.4 | even | 6 | 1470.2.d.c.1469.4 | 4 | |||
35.12 | even | 12 | 1050.2.s.e.551.3 | 8 | |||
35.19 | odd | 6 | 210.2.t.a.89.2 | yes | 4 | ||
35.24 | odd | 6 | 1470.2.d.d.1469.1 | 4 | |||
35.33 | even | 12 | 1050.2.s.e.551.2 | 8 | |||
105.47 | odd | 12 | 1050.2.s.d.551.1 | 8 | |||
105.59 | even | 6 | 1470.2.d.b.1469.2 | 4 | |||
105.68 | odd | 12 | 1050.2.s.d.551.4 | 8 | |||
105.74 | odd | 6 | 1470.2.d.a.1469.3 | 4 | |||
105.89 | even | 6 | inner | 210.2.t.c.89.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.t.a.59.1 | ✓ | 4 | 3.2 | odd | 2 | ||
210.2.t.a.89.2 | yes | 4 | 35.19 | odd | 6 | ||
210.2.t.b.59.1 | yes | 4 | 5.4 | even | 2 | ||
210.2.t.b.89.1 | yes | 4 | 21.5 | even | 6 | ||
210.2.t.c.59.2 | yes | 4 | 1.1 | even | 1 | trivial | |
210.2.t.c.89.2 | yes | 4 | 105.89 | even | 6 | inner | |
210.2.t.d.59.2 | yes | 4 | 15.14 | odd | 2 | ||
210.2.t.d.89.1 | yes | 4 | 7.5 | odd | 6 | ||
1050.2.s.d.101.1 | 8 | 5.2 | odd | 4 | |||
1050.2.s.d.101.4 | 8 | 5.3 | odd | 4 | |||
1050.2.s.d.551.1 | 8 | 105.47 | odd | 12 | |||
1050.2.s.d.551.4 | 8 | 105.68 | odd | 12 | |||
1050.2.s.e.101.2 | 8 | 15.8 | even | 4 | |||
1050.2.s.e.101.3 | 8 | 15.2 | even | 4 | |||
1050.2.s.e.551.2 | 8 | 35.33 | even | 12 | |||
1050.2.s.e.551.3 | 8 | 35.12 | even | 12 | |||
1470.2.d.a.1469.3 | 4 | 105.74 | odd | 6 | |||
1470.2.d.a.1469.4 | 4 | 7.3 | odd | 6 | |||
1470.2.d.b.1469.1 | 4 | 7.4 | even | 3 | |||
1470.2.d.b.1469.2 | 4 | 105.59 | even | 6 | |||
1470.2.d.c.1469.3 | 4 | 21.17 | even | 6 | |||
1470.2.d.c.1469.4 | 4 | 35.4 | even | 6 | |||
1470.2.d.d.1469.1 | 4 | 35.24 | odd | 6 | |||
1470.2.d.d.1469.2 | 4 | 21.11 | odd | 6 |